Answer:
the chance of a blizzard tommorrow is 5%. write the complement of this event
Step-by-step explanation:
The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:
100% - 5% = 95%
Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.
in which of the following numbers is the value of the 5 digit 10 times it value in the number 4,597
According to the question the value of the 5 digit in 4,597 is 9.
What is digit?Digit is a numerical symbol used to represent numbers in the decimal system. It is a single symbol used to represent a number ranging from 0 to 9. Digits are used to represent numbers in all forms of mathematical calculations and equations. The most common digits used in calculations are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit has an associated numerical value, which can be used to create larger numbers or to perform complex mathematical operations.
The answer is D) 9. The value of the 5 digit in 4,597 is 5. To find the 10 times its value, you must multiply 5 by 10, which equals 50. Therefore, the value of the 5 digit in 4,597 is 9.
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in a group of 100 students 50 like online class and 70 loke physical class .represent in venn diagram and how many students like bith type pf classes
Answer:
Step-by-step explanation:
100 students all together.
50+70=120....so 20 must like both.
Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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Audrey and Harper are selling fruit for a band fundraiser. Customers can buy small crates of apples and large containers of peaches. Audrey sold 3 small crates of apples and 10 large containers of peaches for a total of $116. Harper sold 11 small crates of apples and 20 large containers of peaches for a total of $292. Find the cost each of one small crate of apples and one large container of peaches. A) Define your variables. Write a system of equations to represent the situation. Solve using any method. Show all of your work. Andrew decides he wants to help the band as well. He sells 7 small crates of apples and 5 larges containers of peaches. How much money does he raise for the band?
The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.
What is the cost of 7 small crates and 5 large containers?The system of equations that describe the question is:
3s + 10l = 116 equation 1
11s + 20l = 292 equation 2
Where:
s = cost of one small crate of apples
l = cost of one large crate of peaches
The elimination method would be used to determine the values of s and l.
Multiply equation 1 by 2
6s + 20l = 232 equation 3
Subtract equation 3 from equation 2:
5s = 60
Divide both sides of the equation by 5
s = 60 / 5
s = $12
Substitute for s in equation 1:
3(12) + 10l = 116
36 + 10l = 116
10l = 116 - 36
10l = 80
l = 80 / 10
l = 8
Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124
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a survey found that 10% of americans believe that they have seen a ufo. for a sample of 10 people, find each probability: a. that at least 2 people believe that they have seen a ufo b. that 2 or 3 people believe that they have seen a ufo c. that exactly 1 person believes that he or she has seen a ufo
The probability that at least 2 people believe that they have seen a ufo is 0.1937102445. The probability that exactly 1 person believes that he or she has seen a ufo is problem: P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890.
What is the probability?The probability that at least 2 people believe that they have seen a UFO would be 0.1937102445. For this we use the binomial distribution formula.
P(X ≥ 2) = 1 − P(X = 0) − P(X = 1)P(X = 0) = (9/10)¹⁰
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
P(X ≥ 2) = 1 − 0.3874204890 − 0.3486784401 = 0.1937102445 (rounded to 10 decimal places)
The probability that 2 or 3 people believe that they have seen a UFO would be 0.1937102445. Using the formula of binomial distribution again we can solve for the probability of this event.
P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3)P(X = 2) = 10C₂ (0.10)² (0.90)⁸= 0.1937102445 (rounded to 10 decimal places)
P(X = 3) = 10C₃ (0.10)³ (0.90)⁷= 0.0573956280 (rounded to 10 decimal places)
P(2 ≤ X ≤ 3) = 0.1937102445 + 0.0573956280 = 0.2511058725 (rounded to 10 decimal places)
The probability that exactly 1 person believes that he or she has seen a UFO would be 0.3874204890. Using the binomial distribution formula to solve this problem:
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
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A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.
Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).
0.5333
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly
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25. Students in a class took an algebra test if 15 students passed the test what percent pass the test
Answer:
15/x * 100 %
Step-by-step explanation:
Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)
Consider the validity of the statement "A Triangle with side lengths 20,21, and 28 is a right triangle"
the statement "A Triangle with side lengths 20,21, and 28 is a right triangle" is invalidated.
As, You may simply rule out the first three options if you are familiar with specific Pythagorean triples and other triangle relationships.
Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most important triplets are (3,4,5).
So,
20² +21² = 400 +441 = 841 = 29²
The appropriate choice is 20, 21, and 29
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(5x^2+2x-7)-(3x^2+6x-9)
Answer:
2x^2-4x+2
Step-by-step explanation:
depends what the question is telling you to do
if its askin you to simplify this is the answer
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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What’s a ,40,70,70 degree triangle look like?
Answer:
see attached
Step-by-step explanation:
You want a picture of an isosceles triangle with base angles of 70°.
TriangleSuch a triangle is shown in the attachment.
__
Additional comment
You can draw one of these yourself using a protractor to measure the angles.
The side lengths have the approximate ratio of 13:19:19.
(a) describe the relationship between distance and travel time. (select all that apply.) positive negative moderate weak linear nonlinear
The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.
positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•
Positive• Linear• Moderate
Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.
The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.
Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.
Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.
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4. (5pts each) Given f(x) = 6x² +1and g(x) = 11x +7 determine the following:
a (fog)(x)\
b. (fog)(-3)
=6XTI
Answer:
(fog)(x) = 726x^2 + 924x + 295, and (fog)(-3) = 6,817.
elise is a project manager in 2016 she earned a monthly salary of £2100
in 2017 she was awarded a 3% increase on her monthly salary
given that in 2017 elise worked 42 hours per week for 45 weeks
work out her average pay per hour for the year
Answer:
Elise's average pay per hour for the year 2017 was £11.88.
Step-by-step explanation:
First, we need to calculate Elise's monthly salary in 2017 after the 3% increase:
3% of £2100 = 0.03 x £2100 = £63
Elise's new monthly salary in 2017 = £2100 + £63 = £2163
Next, we need to calculate her total earnings in 2017:
Total earnings = monthly salary x number of months worked
Elise worked for 45 weeks in 2017, which is approximately 10.4 months:
Total earnings = £2163 x 10.4 = £22,477.20
Finally, we can calculate her average pay per hour for the year:
Total number of hours worked = 42 hours/week x 45 weeks = 1890 hours
Average pay per hour = total earnings / total number of hours worked
Average pay per hour = £22,477.20 / 1890 hours = £11.88 per hour
Answer:
I got $13.73 per hour
Step-by-step explanation:
If you multiply 2100 by 12 months you get $25200 for an annual salary before percent increase.
Then you include the 3% salary increase each month 25200 x .03 = 756 then add the two 25200 + 756 = 25956 OR you can calculate the longer way by doing each individual month, either way it will be the same answer. 2100 x .03 = 63 then 2100 + 63 = 2163 then 2163 x 12 = 25956
Then you divide 25956 by the number of weeks worked in the year. 25956/45 = 576.8
So, each week $576.8 was earned.
Then to get an hourly rate, you divide this by the number of hours worked in each week. 576.8/42 = 13.73
So, the hourly rate is $13.73.
I hope this helped :)
6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?
The coordinates of the point P is (-1,2) .
What is translation?
In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.
Finding the coordinates of the point P :
The coordinates of point P can be found by subtracting the vector from point Q.
To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).
Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:
3 - 4 = -1
Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:
-1 - (-3) = 2
Therefore, the coordinates of point P are (-1, 2).
So, the correct answer is (C) (-1, 2).
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Write the equation of the circle in standard form. Then identify the center and radius of the circle. X2 + y2 – 10x + 8y + 37 = 0
The equation of the circle in standard form is (x-5)² + (y+1)² = 9. The center of the circle is (5,-1) and the radius is 3.
To write the equation of the circle in standard form, we need to complete the square for both x and y terms:
x² - 10x + y² + 8y + 37 = 0
(x² - 10x + 25) + (y² + 8y + 16) + 37 = 25 + 16
(x - 5)² + (y + 4)² = 6²
So the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36.
The center of the circle is (5, -4), and the radius is 6.
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Answer:
center is 5,-4 radius is 2
Step-by-step explanation:
If u dissolve 50 grams of sugar in 30 grams of water what would the sugar concentration be?
The sugar concentration would be approximately 62.5%.
To find the concentration of sugar in the solution, we need to use the formula:
Concentration = Mass of solute ÷ Volume of solutionIn this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.
We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.
Now we can use the formula to find the concentration of sugar:
Concentration = 50 g ÷ 80 mL ≈ 0.625 g/mLSo the concentration of sugar in the solution is approximately 0.625 grams per milliliter.
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Can anyone please help with this math problem? Thanks!
Answer: Yes Sofia will have enough money
=======================================================
Explanation:
Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.
The area of the rectangle is 16*7 = 112 square meters.
The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be
sum of the exterior sides = perimeter
6+7+16+7+6+x = 54
42+x = 54
x = 54-42
x = 12
The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.
area of the trapezoid = 0.5*height*(base1+base2)
area = 0.5*5.66*(16+12)
area = 79.24 square meters
----------------
Recap so far
area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square metersThe total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.
Let's convert that to square decimeters.
Recall that 1 decimeter = 10 centimeters
Multiply both sides by 10
1 decimeter = 10 centimeters
10*(1 decimeter) = 10*(10 centimeters)
10 decimeters = 100 centimeters
10 decimeters = 1 meter
Then,
[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]
The entire lawn is 19124 square decimeters.
----------------
We have one final block of calculations to determine the total price.
x = number of rolls
1 roll covers 90 square decimeters
x rolls cover 90x square decimeters
90x = 19124
x = 19124/90
x = 212.489 approximately
Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).
In short, Sofia needs 213 rolls.
1 roll costs $4.50
213 rolls will cost 213*4.50 = 958.50 dollars.
This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).
Sofia will have enough money to pay for all of the grass.
Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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When solving the equation 3(x-2)=-12, what is a possible first step?
*
1)Distributing the 3 into each term of the parenthesis.
2)She could either divide by 3 or distribute 3 into the parenthesis
3)Adding 2 to each side of the equation
4) Subtracting 2 on each side of the equation
5) Dividing each side of the equation by 3
6)none of the answer choices tell what the first step could be.
Answer:
2)She could either divide by 3 or distribute 3 into the parenthesis
The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.
The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.
We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:
b + h = 22
We want to find the dimensions of the triangle that will give us the maximum area.
The formula for the area of a triangle is A = (1/2)bh.
We can use the equation b + h = 22 to solve for one of the variables in terms of the other.
we can solve for h:
h = 22 - b
Substituting this into the formula for the area, we get:
A = (1/2)b(22 - b)
The equation 0 = 11b - (1/2)b² can be rearranged to:
(1/2)b² - 11b = 0
We can then use the quadratic formula to solve for "b"
b = 11 ± 11
So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:
h = 22 - 11 = 11 cm
Triangle has a base of 11 cm and a height of 11 cm.
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in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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In triangle ABC, AB = (x + 2) cm, AC = (x + 1) cm and BC = x cm.
Given that cos BAC=3/4 , find the value of x.
Answer:
the value of x is approximately 0.382 cm.
Step-by-step explanation:
Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching
jim
rate, in
of the cupric chloride.
min
After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so
he used the data to calculate the following least squares regression equation for predicting the etching rate from
the room temperature:
= 2 + 5
1
-2
What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5
min
The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.
The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.
Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x
where, x = temperature in °C
y = etching rate in μm/min
Observed value of etching rate of cupric chloride = 5 μm/min for 25°C
To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x
=> y = 2 + (1/5)× 25
=> y = 7
So, Predicted Value = 7 μm/min
Observed Value = 5 μm/min.
Residual = Observed Value - Predicted
= 5 - 7 = -2
Hence, required value is -2 μm/min.
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Complete question:
Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator
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
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
you wish to compute the 90% confidence interval for the population proportion. how large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05? no prior estimate for the population proportion is available.
To compute the 90% confidence interval for the population proportion, large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05, 271 is the minimum sample
How do we find the minimum sample size?A confidence interval is a range of values where an unknown population parameter lies. The level of confidence is the likelihood of the interval containing the parameter.
The formula to calculate the sample size required to produce a specific margin of error with a known level of confidence for the estimation of a population proportion is given below: 95% confidence interval for population proportion using a sample size formula
[tex]\[n=\frac{z^{2}p(1-p)}{E^{2}}\][/tex]
Where
[tex]\[E\][/tex]is the margin of error[tex]\[p\][/tex] is the sample proportion.[tex]\[z\][/tex] is the z-score The formula is modified to calculate the sample size required to produce a specific margin of error with a known level of confidence as follows:
[tex]\[n=\frac{z^{2}}{4E^{2}}\][/tex]
Note: For this problem, the sample size needs to be large enough to ensure that the sample proportion does not deviate from the population proportion by more than 0.05.
Using a Z-score Table, the z-value that corresponds to 90% confidence interval is 1.645.
[tex]n=\frac{z^{2}}{4E^{2}}\ = \frac{1.645^{2}}{4(0.05)^{2}} = \frac{2.706225}{0.0100} = 270.6[/tex]
(rounded up to the next highest integer)Therefore, 271 is the minimum sample size required to compute a 90% confidence interval for the population proportion.
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Ñamandu es un genio dibujó un cuadrado de x cm cada lado en la parte superior del cuadrado partió en tres partes iguales quedando el corte expresado de esta manera x bajo 3 unió el primer punto de corte con el vértice del lado paralelo trazando un segmento a lo que llamó y Descubre que figuras se forman y entra el perímetro de cada figura formado
The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).
When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.
Using the Pythagorean theorem, we can solve for y:
y^2 = (x/3)^2 + x^2
y^2 = x^2/9 + x^2
y^2 = (10x^2)/9
y = x×sqrt(10)/3
Now we can find the perimeter of each figure that is created
Perimeter of the original square = 4x
Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3
Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)
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Complete the table. In the row with X as the input write the rule as an algebraic expression for the output then complete the last row of the table using the rule. Express the values in your answers as decimals
The last two rows of the table should be completed as follows:
Input Output
8 22.80
10 28.50
What is algebraic expression?An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.
The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.
To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.
Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.
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The Turners have purchased a house for $170,000. They made an initial down payment of $34,000 and secured a mortgage with interest charged at a rate of 3.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 15 years. (Round all answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$
(b) What will be their total interest payment?
$
(c) What will be their equity (disregard depreciation and inflation) after 10 years?
$
(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).
What monthly payment will the Turners be required to make?Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).
Applying the values provided, we obtain:
(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.
Amount paid: $1,054.63
Hence, the installment will be $1,054.63 per month.
What will be their total interest payment?(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:
Total interest equals PV minus (Payment x n)
Applying the values provided, we obtain:
$1,054.63 multiplied by 180 equals $136,000 in interest.
Interest totaled $88,833.40.
The total interest payment will therefore be $88,833.40.
What will be their equity (disregard depreciation and inflation) after 10 years?(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:
The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i
Where n denotes how many payments are still due (180 - 120 = 60).
Applying the values provided, we obtain:
The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917
Balance remaining: $71,587.90
As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.
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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!!!!!!!!!
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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