Is the following an isosceles trapezoid?
A. No, the bases are parallel, but the legs are not congruent.
B. No, the bases are not parallel and the legs are not congruent.
C. Yes, the bases are parallel and the legs are congruent.
D. Yes, all 4 sides are parallel.
Answers
The answer is C. Yes, the bases are parallel and the legs are congruent.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. There are different types of trapezoids, including isosceles trapezoids where the legs are congruent and right trapezoids where one of the angles between a leg and a base is a right angle. A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs. The legs can be either congruent or non-congruent.
There are several types of trapezoids, based on the relationships between their sides and angles:
Isosceles trapezoid: This is a trapezoid where the legs are congruent. The bases may or may not be congruent.
Right trapezoid: This is a trapezoid where one of the angles between a leg and a base is a right angle (90 degrees).
Scalene trapezoid: This is a trapezoid where none of the sides are congruent.
Trapezium: In British English, a trapezium is a quadrilateral with no parallel sides. In American English, this shape is called a general quadrilateral.
Trapezoids are used in many areas of mathematics, including geometry and calculus. In geometry, they can be used to calculate the area and perimeter of various shapes. In calculus, they can be used to calculate integrals over regions with curved boundaries.
Here,
In an isosceles trapezoid, the legs (non-parallel sides) are congruent, and the bases (parallel sides) are also congruent.
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Related Questions
1)A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean length of the shafts. She randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. The lengths are known to follow a normal distribution whose standard deviation is 2 mm. Calculate a 95% confidence interval for the true mean length of the shafts. Input your answers for the margin of error, lower bound, and upper bound.
a)Determine Margin of Error for this 95% confidence interval.
b)Input the lower bound. (Round to three decimal places)
c)Input the upper bound. (Round to three decimal places)
2)To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of ± 0.0001?
3)A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment.
In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.
In a future study, it is determined that the new treatment does not increase the mean survival time in the population of all patients with this particular type of cancer. The researcher has
Committed a type I error.
Incorrectly used a 0.05 significance test when she should have computed the P-value.
Incorrectly used a 0.05 significance level when she should have used a 0.01 significance level.
Committed a type II error.
4)If the level of significance, α{"version":"1.1","math":"\alpha"}, is made very small, thereby making the probability of committing a Type 1 error very small, what happens to the probability of committing a Type 2 error?
By reducing the probability of committing a Type 1 error, we increase the probability of committing a Type 2 error.
There is no specific relationship between the two probabilities.
By reducing the probability of committing a Type 1 error, we also reduce the probability of committing a Type 2 error.
The relationship between the two probabilities depends on how the study is set up.
Answers
Therefore, with a 95% confidence interval, we can estimate the true mean length of the drive shafts to be between 992.16 mm and 1007.84 mm.
The true mean length of the drive shafts can be estimated using a 95% confidence interval. The margin of error is calculated as 2*1.96*2 = 7.84 mm. The lower bound of the confidence interval is 1000 - 7.84 = 992.16 mm and the upper bound is 1000 + 7.84 = 1007.84 mm.
This confidence interval states that there is a 95% probability that the true mean length of the drive shafts falls within the range of 992.16 mm to 1007.84 mm. The relationship between the two probabilities is that the probability of the true mean length falling within the confidence interval is 95%. If the sample size was increased, the margin of error would decrease, resulting in a tighter range and higher probability that the true mean would fall within the confidence interval.
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William writes a function f(x) = 2x - 10. He uses an
input-output table to represent the function.
Input: 4
Output: -8
What is the output of William's function when the
input is 4?
Answers
Answer: -8
Step-by-step explanation:
When the input is 4, according to the input-output table, the output is -8.
Plugging 4 into the function f(x) = 2x - 10 directly also gives the same result:
f(4) = 2(4) - 10 = 8 - 10 = -2
So the output of William's function when the input is 4 is -8.
please help
this is all the information i have!
Answers
New points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)
Define the term Translation?In graph theory, the term "translation" refers to a type of operation that moves all the vertices and edges of a graph by a fixed distance in a given direction. Specifically, a translation of a graph involves shifting every vertex a certain distance horizontally and/or vertically, without changing the shape or connectivity of the graph.
Translation: 4 left and 2 down
Start with a point at its original location and then move it 4 units to the left and 2 units down. This can be done by subtracting 4 from the x-coordinate and subtracting 2 from the y-coordinate of the point or shape.
Given points in a graph ABCD are, A(2, 0), B(2, 2), C(0, 2), D(0, 1)
Subtract 4 from the x-coordinate and subtract 2 from the y-coordinate, resulting in a new points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)
The figure shown in below diagram.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify the expression 8 2 + 9 ( 12 ÷ 3 × 2 ) − 7. Explain each of your steps
Answers
the simplified expression is 129.
To simplify the expression 8² + 9(12 ÷ 3 × 2) - 7, we follow the order of operations, which is:
Parentheses (do the calculations inside parentheses first)
Exponents (do the calculations involving exponents)
Multiplication and Division (do these operations from left to right)
Addition and Subtraction (do these operations from left to right)
Using these rules, we can simplify the expression step by step as follows:
8² + 9(12 ÷ 3 × 2) - 7 (Apply parentheses first)
= 8² + 9(4 × 2) - 7 (Evaluate 12 ÷ 3 as 4 and then 4 × 2 as 8 inside the parentheses)
= 8² + 9(8) - 7 (Evaluate 9 times 8 as 72)
= 64 + 72 - 7 (Evaluate 8² as 64)
= 129 (Perform the final subtraction and add the remaining terms)
Therefore, the simplified expression is 129.
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Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3. Complete the following probability table. (Round your answers to 2 decimal places.)
Prior
Probabilities Conditional
Probabilities Joint
Probabilities Posterior
Probabilities
P(B1) = 0.11 P(A | B1) = 0.45 P(A ∩ B1) = P(B1 | A) = P(B2) = P(A | B2) = 0.62 P(A ∩ B2) = P(B2 | A) = P(B3) = 0.38 P(A | B3) = 0.85 P(A ∩ B3) = P(B3 | A) = Total = P(A) = Total =
Answers
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3.We have to complete the following probability table, prior probabilities, conditional probabilities, joint probabilities, and posterior probabilities, and also we have to round our answers to 2 decimal places.
Given information:Probability of B1, P(B1) = 0.11 Probability of A given B1, P(A | B1) = 0.45 Probability of A intersection B1, P(A ∩ B1) = ?
Probability of B1 given A, P(B1 | A) = ? Probability of B2, P(B2) = ? Probability of A given B2, P(A | B2) = 0.62, Probability of A intersection B2, P(A ∩ B2) = ? Probability of B2 given A, P(B2 | A) = ?
Probability of B3, P(B3) = 0.38. Probability of A given B3, P(A | B3) = 0.85. Probability of A intersection B3,
P(A ∩ B3) = ?
Probability of B3 given A, P(B3 | A) = ?
Total probability of A, P(A) = ?
Total probability of sample space = 1. Let's complete the probability table:Prior probabilities, Conditional probabilities, Joint probabilities, Posterior probabilities P(B1) = 0.11P(A | B1) = 0.45P(A ∩ B1) = P(A | B1) * P(B1) / P(A)P(B1 | A) = P(A | B1) * P(B1) / P(A)P(B2) = 1 - (P(B1) + P(B3)) = 1 - (0.11 + 0.38) = 0.51P(A | B2) = 0.62P(A ∩ B2) = P(A | B2) * P(B2) / P(A)P(B2 | A) = P(A | B2) * P(B2) / P(A)P(B3) = 0.38P(A | B3) = 0.85P(A ∩ B3) = P(A | B3) * P(B3) / P(A)P(B3 | A) = P(A | B3) * P(B3) / P(A)Total = 1P(A) = P(A ∩ B1) + P(A ∩ B2) + P(A ∩ B3) = 0.11 * 0.45 + 0.51 * 0.62 + 0.38 * 0.85 = 0.6579. So, the probability table is as follows:Prior probabilities,Conditional probabilities,Joint probabilities,Posterior probabilities
P(B1) = 0.11P(A | B1) = 0.45P(A ∩ B1) = 0.0495P(B1 | A) = 0.3419P(B2) = 0.51P(A | B2) = 0.62P(A ∩ B2) = 0.3162P(B2 | A) = 0.4857P(B3) = 0.38P(A | B3) = 0.85P(A ∩ B3) = 0.3217P(B3 | A) = 0.1724Total = 1P(A) = 0.6579
Hence, the completed probability table is as shown above.
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Based on the following sorted 20 values for age, what are the possible split points?
{20, 22, 24, 26, 28, 31, 32, 33, 35, 40, 42, 43, 45, 47, 49, 50, 52, 53, 55, 57}
Multiple Choice
a {20, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52, 54, 56}
b {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56, 57}
c {0, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56}
d {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52. 5, 54, 56}
Answers
Based on the following sorted 20 values for age, the possible split points are {20, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52, 54, 56} (option a).
Option A suggests that the split points are {20, 21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49.5, 51, 52, 54, 56}. Notice that every split point falls between two consecutive ages in the original list. For example, the first split point is 20 because it is between 20 and 22. The second split point is 21 because it is between 20 and 22 as well.
Option B suggests that the split points are {21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49, 51, 52.5, 54, 56, 57}. Notice that the only difference between this option and Option A is that the last split point is 57 instead of 49.5.
Option C suggests that the split points are {0, 21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49, 51, 52.5, 54, 56}. Notice that the first split point is 0, which is not a possible age in the original list.
Option D suggests that the split points are {21, 23, 25, 27, 29.5, 31.5, 32.5, 34, 37.5, 41, 42.5, 44, 46, 48, 49.5, 51, 52.5, 54, 56}. Notice that the only difference between this option and Option A is that the split point after 49 is 49.5 instead of 49.5.
In summary, the correct answer is Option A because it provides all the possible split points that fall between the ages in the original list. When working with split points, it's important to consider the specific context and criteria for dividing the data.
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Y= 1/3x-9
Write the equation of a line PERPENDICULAR to
point (-6, 10).
that passes through the
Answers
The equation of the line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10) is y = -3x - 8.
The given equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, we can see that the slope of the given line is 1/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/3 is -3.
Now, we have the slope of the perpendicular line and a point that it passes through. We can use point-slope form to find the equation of the line.
Point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values we have
y - 10 = -3(x - (-6))
y - 10 = -3(x + 6)
y - 10 = -3x - 18
y = -3x - 8
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The given question is incomplete, the complete question is:
Write the equation of a line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10)
Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 180 gallons of orange juice last year. This year, the hotel served 70% more orange juice than it did the previous year. How much was served this year?
Answers
The hotel served 306 gallons of orange juice this year.
To find the amount of orange juice served this year, we need to add 70% more of the amount served last year to the amount served last year. Let's denote the amount served last year as "x". Then we can set up the equation:
Amount served this year = x + 0.7xSimplifying this equation gives us:
Amount served this year = 1.7xWe know from the problem that the amount served last year was 180 gallons. Plugging this into our equation, we get:
Amount served this year = 1.7(180)Simplifying this equation gives us:
Amount served this year = 306Therefore, the hotel served 306 gallons of orange juice this year.
In summary, we used the information given in the problem to set up an equation and solve for the amount of orange juice served this year. We first found the amount served last year, and then added 70% more of that amount to get the total amount served this year.
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the classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter.
Answers
The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable. The correct option is A.
What is a random variable?A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.
The types of random variables are as follows:
i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.
ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.
iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.
Therefore, the correct option is A.
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The ____________ assumption requires that all variation around the regression line should be equal at all possible values (levels) of the ___________variable.
A. control variance, dependent
B. constant variance, independent
C. constant variance, dependent
D. control variance, independent
Answers
The B) constant variance assumption requires that all variation around the regression line should be equal at all possible values (levels) of the independent variable.
The constant variance assumption, also known as homoscedasticity, requires that the variance of the residuals (i.e., the differences between observed and predicted values) should be approximately the same across all levels of the independent variable.
This assumption is necessary for valid statistical inference in linear regression analysis because violations of constant variance can result in biased estimates of the regression coefficients and incorrect hypothesis tests.
The independent variable is the variable that is used to predict the dependent variable. The constant variance assumption applies to the residuals at all possible values of the independent variable. Therefore, the correct answer is B. constant variance, independent.
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HELP ASAP!!! WILL MARK BRAINLIEST!!!
What does k equal in the equation y = kx³, so that it represents the graph shown?
A. -8
B. 8
C. 1/8
D. -1/8
Answers
Answer:
D. -1/8
Step-by-step explanation:
Look at the coordinates on the graph
(-4,8)
(-2,1)
(0,0)
(2,-1)
(4,-8)
These will correspond to
y = kx^3
=> k = y/x^3
When you substitute the coordinates, you find k = -1/8
y = -1/8x^3
Charles is 10 years old what is the best estimate of the length of his shoe
Answers
Answer:
Size 3 ♀️
Step-by-step explanation:
In the US, the average shoe size for 10-Year-Old is USA Size 3.
-Jul 12, 2020
In a 7-sided figure, three of the angles are equal
and each of the other four angles is 150 greater
than each of the first three. Find the angles.
Answers
The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).
So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:
3x + 4(x+15) = 900
7x + 60 = 900
7x = 840
x = 120
The figure has three angles of 120 degrees, and four angles of 135 degrees.
11. Figure EFGH is a parallelogram. Find the length of Line FG.
Answers
The length οf line FG is 12 cm, If Figure EFGH is a parallelοgram.
What is parallelοgram?A parallelοgram is a type οf quadrilateral with twο pairs οf parallel sides. The οppοsite sides οf a parallelοgram are equal in length and parallel tο each οther.
Since EFGH is a parallelοgram, we knοw that the οppοsite sides are parallel and equal in length. Therefοre, the length οf line FG is equal tο the length οf line EH.
We can find the length οf EH by using the Pythagοrean theοrem οn right triangle EFG:
[tex]EF^2 + FG^2 = EG^2[/tex]
Since EF = 5 cm, EG = 13 cm, and angle FEG is a right angle (as οppοsite angles in a parallelοgram are equal), we can sοlve fοr FG:
[tex]FG^2 = EG^2 - EF^2[/tex]
[tex]FG^2 = 13^2 - 5^2[/tex]
[tex]FG^2 = 144[/tex]
[tex]FG = \sqrt{(144)[/tex]
[tex]FG = 12 cm[/tex]
Therefοre, the length οf line FG is 12 cm.
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Qual o resultado do problema 3528÷98?
Answers
Answer:
36
Step-by-step explanation:
Connor bought a box of mini peanut butter cookies to take on a trip. On the back of
The
box, he reads that 10 cookies weigh 30 grams.
) How much does each cookie weigh?
Answers
Please help, this is due in 10 minutes, im giving 35 points for it.
Answers
The scientific and standard notation and clue obtained from the clue sheet are;
1. Name starts with; J
2. Difference = 145 million miles = Weight = 145 lbs
3. Height: 5 ft, 6 in
4. I. 2.54 × 10⁸ miles corresponding to letter I
II. 0.0005825 corresponds to letter G
III. 5.0432 × 10⁶ corresponds to letter N
IV. 1.547 × 10³ corresponds to letter R
V. 4.977 × 10⁻² corresponds to letter W
VI. 1.3 × 10¹⁰ light years away; corresponds to letter D
VII. 5.04 × 10⁻⁵ corresponds to letter A
The suspects hubby is DRAWING
What is the scientific notation of presenting numbers?Scientific notation is a format used to express very large or very small numbers such that they are much easier to work with. The scientific notation format is; a × 10ⁿ, where; a is the coefficient, which is a number between 1 and 10 (10 excluded), and n is an integer.
1. G = (6.07 × 10⁷)/(7.035 × 10³) ≈ 8628.29
J = (6.03 × 10⁻³)/(5.05 × 10⁻⁷) ≈ 11940.59
Therefore; J > G
The suspects name starts with J
2. The distance the telescope in the laboratory allows the viewer to see = 1.5 × 10⁹ miles away
The distance the other telescope a few hours away allows the viewer to see = 1.355 × 10⁹ miles away
The difference between the distances = (1.5 - 1.355) × 10⁹ miles = 1.45 × 10⁸ miles
The difference in the distance is 1.45 × 10⁸ miles = 145 million miles
The suspect weight is 145 lbs
3. The numbers are;
Feet; 532.063 × 10³ = 5.32063 × 10⁵
Inches; 5,030,045 = 5.030045 × 10⁶
The height of the suspect is 5 feet 6 inches (5'6'') = 5.5 feet
Height; = 5 ft, 6 in
4. I. The difference in distances between Earth and Saturn can be found as follows;
The difference in the distances = (1000 - 746) million miles = 254 million miles apart
Scientific notation is the expression of numbers in the form consisting of a number between 1 and 10, multiplied by 10 raised to a power
254 million miles = 2.54 × 10⁸ miles
The corresponding letter from the code cracker is; I
II Standard notation is the expression of numbers in the standard form without the use of exponents or special symbols
The number 5.825 × 10⁻⁴ in standard notation is; 0.0005825
The corresponding letter from the code cracker is; G
III. The number 504.32 × 10⁴ in scientific notation can be obtained by moving the decimal point two places to the left followed by increasing the index of 10 by 2 as follows;
504.32 × 10⁴ = 5.0432 × 10⁶
The corresponding letter from the code cracker is; N
IV. The sum of the numbers 1.202 × 10³ and 3.45 × 10² can be obtained by expressing both numbers to the same power of 10 as follows;
1.202 × 10³ + 3.45 × 10² = 12.02 × 10² + 3.45 × 10² = 15.47 × 10²
15.47 × 10² = 1.547 × 10³
Therefore; 1.202 × 10³ + 3.45 × 10² = 1.547 × 10³
The corresponding letter from the code cracker is; R
V. The difference of the numbers can be obtained as follows;
5.023 × 10⁻² - 4.6 × 10⁻⁴ = 502.3 × 10⁻⁴ - 4.6 × 10⁻⁴ = 497.7 × 10⁻⁴
497.7 × 10⁻⁴ = 4.977 × 10⁻²
Therefore; 5.023 × 10⁻² - 4.6 × 10⁻⁴ = 4.977 × 10⁻²
The corresponding letter from the code cracker is; W
VI. 13 billion light years = 13 × 10⁹ light years = 1.3 × 10¹⁰ light years
The distance a standard telescope can allow to be seen is 1.3 × 10¹⁰ light years away
The corresponding letter from the code cracker is; D
VII. 0.0000504 in scientific notation is; 5.04 × 10⁻⁵
The corresponding letter from the code cracker is; A
IGNRWDA
The suspects favorite hubby is DRAWING
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how can we use models to estimate percent questions? Give examples to support your answer.
Answers
Answer:
Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars each.
Answer:
Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars eac
Step-by-step explanation:
A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded
annually.
swer:
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answers
Answer:
Step-by-step explanation:
(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:
A = P(1 + r)^t
In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:
A = 500(1 + 0.015)^t
Simplifying this gives:
A = 500(1.015)^t
Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.
(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:
500(1.015)^t = 800
Dividing both sides by 500:
(1.015)^t = 1.6
Taking the natural logarithm of both sides:
ln(1.015)^t = ln(1.6)
Using the power rule of logarithms:
t ln(1.015) = ln(1.6)
Dividing both sides by ln(1.015):
t = ln(1.6) / ln(1.015)
Using a calculator:
t ≈ 24.7
Therefore, it takes approximately 24.7 years for the account balance to reach $800.
the dog eats 8 ounces of dog food each day his owner bought 28 pound bag at the 8 ounces cost $3.50 so how much did the owner spend for 28 bag
Answers
Answer:
$196
Step-by-step explanation:
1 lb = 16oz
28 lbs x 16 = 448 ozs (in 28 lb bag)
448/8 = 56 (8 oz portions)
56 x $3.50= $196
A $2,000 investment was made 16 years ago into an account that earned quarterly
compounded interest. If the investment is currently worth $6,883.55, what is the
annual rate of interest?
Answers
Answer:
We can use the formula for compound interest to solve the problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we know that P = $2,000, A = $6,883.55, n = 4 (quarterly compounding), and t = 16. We can solve for r by rearranging the formula as follows:
r = n[(A/P)^(1/nt) - 1]
Substituting the values, we get:
r = 4[(6,883.55/2,000)^(1/(4*16)) - 1] = 0.0522 or 5.22%
Therefore, the annual interest rate is approximately 5.22%
The blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in. If the shorter sides of the actual patio are each 10.5 ft long, how long is the third side?
Answers
The length of the third side of the actual patio is 15.75 feet.
What is similarity of triangle?In order to solve issues requiring proportional connections between the sides of two triangles, it is crucial to understand the idea of triangle similarity. If the matching sides and angles of two triangles are identical, then two triangles are said to be similar. When referring to similarities, the symbol is used.
Let us suppose the length of third side = x.
Given that, blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in.
Thus, the blueprint and the actual patio form two similar triangles.
The sides of the similar triangles are equal in ratio thus,
3.5/5.25 = 10.5/x
3.5x = 5.25 * 10.5
x = (5.25 * 10.5) / 3.5
x = 15.75
Hence, the length of the third side of the actual patio is 15.75 feet.
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Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0
Answers
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
What does the expression mean?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).
For x =7,x+|x| =7+|7| =14
For x =10,x+|x|= 10+|10| =20
For x = 0,x+|x| =0+|0| =0
For x = -3, x + |x| = -3 + |-3| = 0
For x = -8, x + |x| = -8 + |-8| = 0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
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After heating up in a teapot, a cup of hot water is poured at a temperature of
201°F. The cup sits to cool in a room at a temperature of 73° F. Newton's Law
of Cooling explains that the temperature of the cup of water will decrease
proportionally to the difference between the temperature of the water and the
temperature of the room, as given by the formula below:
T = Ta + (To-Ta)e-kt
Ta
the temperature surrounding the object
To the initial temperature of the object
t = the time in minutes
=
T =
the temperature of the object after t minutes
k = decay constant
The cup of water reaches the temperature of 189°F after 3 minutes. Using
this information, find the value of k, to the nearest thousandth. Use the
resulting equation to determine the Fahrenheit temperature of the cup of
water, to the nearest degree, after 6 minutes.
Answers
The temperature of the cup of water is approximately 180°F after 6 minutes.
How to find temperature and time?Using the given formula, we can write:
T = Ta + (To - Ta) * e^(-kt)
where Ta = 73°F (the temperature of the room), To = 201°F (the initial temperature of the water), and T = 189°F (the temperature of the water after 3 minutes).
We can solve for the decay constant k as follows:
(T - Ta) / (To - Ta) = e^(-kt)
ln[(T - Ta) / (To - Ta)] = -kt
k = -ln[(T - Ta) / (To - Ta)] / t
Substituting the given values, we get:
k = -ln[(189°F - 73°F) / (201°F - 73°F)] / 3 minutes
k = -ln[116 / 128] / 3 minutes
k ≈ 0.0434 minutes^-1 (rounded to the nearest thousandth)
Now we can use this value of k to find the temperature of the water after 6 minutes:
T = Ta + (To - Ta) * e^(-kt)
T = 73°F + (201°F - 73°F) * e^(-0.0434 minutes^-1 * 6 minutes)
T ≈ 180°F (rounded to the nearest degree)
Therefore, the temperature of the cup of water is approximately 180°F after 6 minutes.
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ABCD is a quadrilateral in which BD = 15 cm., perpendiculars from A and Con BD are 6 cm and 8 cm respectively. Calculate the area of the quadrilaterals
Answers
The area of the quadrilateral is 161.24 cm².
How to deal with quadrilateral?We can see that we can divide the quadrilateral into two triangles: ABD and CBD. We know that the height of ABD is 6 cm and the height of CBD is 8 cm. We also know that BD is 15 cm. To find the area of each triangle, we need to find the base of each triangle. We can do this using the Pythagorean theorem.
For triangle ABD:
AB² = AD² + BD²
AB² = (6 cm)² + (15 cm)²
AB² = 261 cm²
AB = [tex]\sqrt(261) cm[/tex]
For triangle CBD:
BC² = CD² + BD²
BC² = (8 cm)² + (15 cm)²
BC² = 289 cm²
BC = 17 cm
Now we can find the areas of the triangles:
Area of ABD =[tex]\frac{1}{2}[/tex] * AB * 6 cm
Area of ABD = [tex]\frac{1}{2}[/tex] * [tex]\sqrt(261) cm[/tex] * 6 cm
Area of ABD = 93.24 cm^2
Area of CBD = [tex]\frac{1}{2}[/tex] * BC * 8 cm
Area of CBD = [tex]\frac{1}{2}[/tex] * 17 cm * 8 cm
Area of CBD = 68 cm²
Finally, we can find the area of the quadrilateral by adding the areas of the triangles:
Area of ABCD = Area of ABD + Area of CBD
Area of ABCD = 93.24 cm² + 68 cm²
Area of ABCD = 161.24 cm²
Therefore, the area of the quadrilateral is 161.24 cm².
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find the product. Write your answer in scientific notation (5 x 10^-7) x (3 x 10^6)
Answers
(5 x 10^-7) x (3 x 10^6) = (5 x 3) x (10^-7 x 10^6) = 15 x 10^-1
However, we usually write our answer in scientific notation with the coefficient between 1 and 10, so we can convert this to scientific notation by moving the decimal point one place to the left:
15 x 10^-1 = 1.5 x 10^1
Therefore, the product of (5 x 10^-7) and (3 x 10^6) is 1.5 x 10^1 in scientific notation.
PLEASE HELP ME
(Answer these four questions please)
Answers
3. The statement is true, the correlation coefficient is close to -1. 4. temperature for a city with a latitude of 48 is 43. 5. The statement is false. 6. cannot make a reasonable estimate
Describe Equation?Equations can be used to model real-world situations and solve problems in many fields, including science, engineering, finance, and more. They are an essential tool in mathematics and are used extensively in algebra, calculus, and other advanced branches of math.
Equations can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and others.
Question 3:
The statement is true. We can check this by calculating the correlation coefficient between the latitude and temperature data points, which should be close to -1. The calculated line of best fit is also consistent with the given data.
Question 4:
To estimate the temperature for a city with a latitude of 48, we can use the equation of the line of best fit:
y = -1.07x + 92.87
Substituting x = 48, we get:
y = -1.07(48) + 92.87
y = 42.79
Rounding to the nearest whole number, the estimated temperature for a city with a latitude of 48 is 43.
Question 5:
The statement is false. We can check this by calculating the correlation coefficient between the passengers and suitcases data points, which should be close to 1. The given line of best fit has a negative slope, which is inconsistent with the positive correlation between the variables.
Question 6:
To estimate the number of suitcases for a flight carrying 250 people, we can use the equation of the line of best fit:
y = -1.98x + 7.97
Substituting x = 250, we get:
y = -1.98(250) + 7.97
y = -485.03
However, it does not make sense for the number of suitcases to be negative. Therefore, we cannot make a reasonable estimate for the number of suitcases on a flight carrying 250 people using this line of best fit.
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Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
please help it’s due today(midnight right now), I will mark brainliest
Answers
There are 48 toy soldiers, which is 6 x 8 of them.
How did Like Toy Soldiers come to be?The anger Eminem expresses in "Like Toy Soldiers" is a result of his personal beefs with rappers Ja Rule and Benzino, who was the editor of The Source at the time. The song, "Toy Soldiers," by Martika, was sampled on the 2004 release Encore.
Let's name Leo's collection of toy soldiers "x" the amount.
As a result of the problem statement, we are aware of:
There are no more when he arranges them in groups of four, proving that x is divisible by four.
Six remain after he divides them into groups of seven, proving that (x - 6) is divisible by seven.
He organizes them into fives. If there are still 3 after multiplying by 5, (x - 3) can be divided by 5.
We may create a system of equations based on these three conditions:
x = 4a (from the first condition)
x - 6 = 7b (from the second condition)
x - 3 = 5c (from the third condition)
where a, b, and c are integers.
4a - 6 = 7b
4a - 3 = 5c
Now we need to solve for a, b, and c.
7b = 4a - 6
7b + 6 = 4a
Since 7 and 4 are relatively prime, we know that (7b + 6) must be divisible by 4. Therefore, we can write:
7b + 6 = 4k
where k is some integer. Solving for b, we get:
b = (4k - 6) / 7
Since b is an integer, k must be 2, which gives us:
b = (4(2) - 6) / 7 = -1
We can try the next possible value of k, which is 3:
b = (4(3) - 6) / 7 = 0
x - 3 = 5c
6 - 3 = 5c
c = 1
6 divided by 4 is 1 with no remainder.
(6 - 6) divided by 7 is 0 with a remainder of 0.
(6 - 3) divided by 5 is 1 with a remainder of 0.
Therefore, the answer is 48, which is 6 times 8.
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Joseph paints ornaments for a school play. Each ornament is made up of two identical cylinders, as shown. All surfaces of each cylinder must be painted. How many cans of paint does he need to paint 75 ornaments?
PLEASE HELP ME BIG GRADE!!!!!!!!!
Answers
Number of cylindrical cans of paint does he need to paint 75 ornaments is 20.
What is the Surface Area of a Cylinder?The total area that the cylinder's curved surface and round bases enclose is referred to as its surface area. The cylinder's total surface area consists of the curving surface as well as the areas of the two bases, each of which is shaped like a circle. A cylinder is a 3D solid object made up of two circular bases connected by a curving face.
Surface Area of Cylinder = 2πrh+2πr²
where , r is radius of cylinder=4.6cm
H is height of cylinder=2*6.5cm=13cm
A=2×π×4.6×13+2×π×4.6²≈508.68668cm²
Total Number of cans of paint needed to paint 75 ornaments=75×508.68668
/1900=20.
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Write an expression that can be a rule for the number sequence below.
5, 9, 13, 17, 21, …
Answers
The possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
What is expression?As an illustration, the expression x + y is one where x and y are words with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only comprise numbers, and algebraic expressions, which also include variables.
According to question:
One possible expression that can be a rule for the number sequence is:
[tex]$a_n = 4n + 1$[/tex], where n is the position of the term in the sequence.
Using this expression, we can find the values of the first few terms as follows:
[tex]$a_1 = 4(1) + 1 = 5$[/tex]
[tex]$a_2 = 4(2) + 1 = 9$[/tex]
[tex]$a_3 = 4(3) + 1 = 13$[/tex]
[tex]$a_4 = 4(4) + 1 = 17$[/tex]
[tex]$a_5 = 4(5) + 1 = 21$[/tex]
Thus, possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
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Answer:
5n, where n is equal to 0, 1, 2, 3, 4
Step-by-step explanation:
5, 9, 13, 17, 21,
