the length of the steel beam is approximately 31.4 meters to the nearest meter.
The length of the steel beam is equal to the circumference of the semi-circle formed by bending the beam into the shape of an arch.
The formula for the circumference of a circle is:
C = πd
Where C is the circumference, π is the value of pi, and d is the diameter of the circle.
Since the arch is a semi-circle, the diameter is equal to the span of the arch, which is 20m. So we can calculate the circumference of the arch as follows:
C = πd/2
= 3.14 x 20m / 2
= 31.4m
Therefore, The steel beam measures, to the nearest meter, 31.4 meters in length.
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Complete Question
An arch of a bridge is made by bending a steel beam into the shape of a semi circle, if the span (diameter) of the arch in 20m, use the value 3.14 for pi to find the length of the steel beam to the nearest meter.
use a blank number line to solve. which of the following expressions have a value that is less than 0? select all that apply. Sorry is it says i am in high school i am in 7th grade
a)-5+3
b)6+(-8)
c)5+(-3)
d)-2+5
The expressions that have values less than 0 are a) and b)
According to the question
Here's how you can use a number line to solve this problem:
Draw a blank number line with a zero in the middle.For each expression, start at zero and move to the right or left depending on the sign of the first number.Then, add or subtract the second number to get the final position on the number line.If the final position is to the left of zero, the expression has a value that is less than 0.For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.
Similarly expression b) has a value that is less than zero.
Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.
In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.
What is a number line?
A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.
What is meant by expressions?
An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.
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18 ft
14 ft
Find the area.
10 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.
The area of the given shape is 109.25 ft² .
What is Area?
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is the size of the surface of the shape, and it is measured in square units, such as square meters, square centimeters, or square inches.The area of a shape can be found by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms
Given : height of triangle = diameter of semicircle = 10 ft
radius of semicircle = 5 ft
base of triangle = 14 ft
we know that, The area of given shape :
= area of given triangle + area of semi circle
= 1/2 × base × height + πr²/2
= 1/2 × 14 × 10 + (3.14 × 5²)/2
= 70 + 39.25
= 109.25 ft²
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Hey guys I need you to answer these questions for my flipgrid I’m about to make
1. How do you find the middle angle in a right triangle using trig?
2. What is the relationship the sine and cosine of the two non right angles in a right triangle define the ratios sine, cosine ,tangent
the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature.
How to find middle angle?
In a right triangle, the middle angle is the angle opposite the hypotenuse. To find this angle using trigonometry, you can use either the sine, cosine, or tangent ratio. Let's say that the two legs of the right triangle are a and b, and the hypotenuse is c. Then, you can use the following trig ratios to find the middle angle:
Sine ratio: sin(theta) = a/c
Cosine ratio: cos(theta) = b/c
Tangent ratio: tan(theta) = a/b
To find the middle angle, you would use the inverse sine, cosine, or tangent function, depending on which ratio you used. For example, if you used the sine ratio, you would take the inverse sine of a/c to find the angle: theta = sin²-1(a/c).
What is the relationship between the sine and cosine of the two non-right angles in a right triangle, and how do they define the ratios sine, cosine, and tangent?
In a right triangle, the two non-right angles are complementary, which means that their sum is 90 degrees. Let's call these angles alpha and beta. The sine and cosine of these angles are defined as follows:
Sine of alpha: sin(alpha) = opposite leg / hypotenuse
Cosine of alpha: cos(alpha) = adjacent leg / hypotenuse
Sine of beta: sin(beta) = adjacent leg / hypotenuse
Cosine of beta: cos(beta) = opposite leg / hypotenuse
Note that the opposite and adjacent legs are relative to the angle being considered. The ratios sine, cosine, and tangent are defined in terms of these ratios:
Sine ratio: sin(theta) = opposite leg / hypotenuse
Cosine ratio: cos(theta) = adjacent leg / hypotenuse
Tangent ratio: tan(theta) = opposite leg / adjacent leg
Therefore, the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature. If you know the value of one of these ratios, you can use it to find the value of the other using the fact that sin(alpha) = cos(beta) and cos(alpha) = sin(beta). This relationship is known as the complementary angle identities.
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A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
The claim of the production manager is not true because more than 4000 insulating washers are defective per day.
How to determine if the claim was true or not?The total amount of insulating washer for the electrical devices produced per day = 225,000.
The amount chosen at random for sampling = 200 washers.
The amount shown to be defective in the chosen sample = 4
If every 200 = 4 defective
225,000 = X
Make c the subject of formula;
X = 225000×4/200
X = 900000/200
X = 4,500.
This shows that the claim is wrong because more than 4000 insulating washers are defective per day.
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2.the data on arrival time is one of the available datasets in statkey, under test for a difference in means.) use statkey to create a randomization distribution for this test using at least 5,000 samples use the randomization distribution to indicate whether each of the following possible differences in means is very likely to occur just by random chance, relatively unlikely to occur but might occur occasionally, or very unlikely to ever occur just by random chance:
Difference in means -7 1 -4 -0.5 6
Likelihood ____________
Based on the randomization distribution, a difference in means of -7, -4, and 6 are very unlikely to ever occur just by random chance. A difference in means of 1 and -0.5 are relatively unlikely to occur but might occur occasionally.
What is difference in means?The difference in means refers to the numerical difference between the average values of two groups or samples. It is a measure of the distance between the means of two datasets, and is often used to compare the central tendencies of the groups or samples.
To create a randomization distribution for the test for a difference in means using StatKey, we can follow these steps:
"Randomization Tests" from the list of options select.
Select "Test for a Difference in Means" from the list of randomization tests.
"Two Independent Groups"as we are comparing two groups is to be delected.
Click on the "Upload" button and select the "arrival_time.csv" file provided in the dataset.
choose"Test Hypothesis" button to run the test.
Under the "Randomization Distribution" section, select "Create a Randomization Distribution" and choose a large number of samples, such as 5,000.
Select the "Create Distribution" button to generate the randomization distribution.
To determine the likelihood of each possible difference in means occurring just by random chance, we can compare the observed difference in means with the randomization distribution.
The table below summarizes the results possible difference in means:
Difference in Means Likelihood
-7 Very unlikely to ever occur just by random
chance
1 Relatively unlikely to occur but might occur
occasionally
-4 Very unlikely to ever occur just by random chance
-0.5 Relatively unlikely to occur but might occur
occasionally
6 Very unlikely to ever occur just by random chance
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Please help. Get more math
Step-by-step explanation:
since we can officially use only one point (the given point), we need to start with the point-slope form :
y - y1 = m(x - x1)
with m being the slope, (x1, y1) being the point.
sadly, to get the slope, we need a second point anyway, because the slope is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
I recommend to use (0, 50) for the "other" point, as there seems to be the smallest error in the coordinates.
so, when going from (0, 50) to the given point (6, -40) :
x changes by +6 (from 0 to 6).
y changes by -90 (from 50 to -40).
the slope m = -90/+6 = -15/1 = -15
y - -40 = -15(x - 6) = -15x + 90
y + 40 = -15x + 90
y = -15x + 50
that is the slope-intercept form.
m = -15
b = 50
y = -242
-242 = -15x + 50
-292 = -15x
x = -292/-15 = 292/15 = 19.46666666... ≈ 19
The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
The conclusion we can draw from the circle graph is (2) Jazz is the preferred music for 56 students.
Which of the conclusions can we draw from the circle graph?From the circle graph, we can draw the following conclusions:
Pop is the preferred music for 35% of the sample, which is equivalent to 0.35 x 400 = 140 students.
Therefore, conclusion (1) is incorrect.
Jazz is the preferred music for 14% of the sample, which is equivalent to 0.14 x 400 = 56 students.
Therefore, conclusion (2) is correct.
The combined percentage of Hip Hop, Rock, and Jazz is 13% + 25% + 14% = 52%, which is more than half of the sample.
Therefore, conclusion (3) is incorrect.
Hip Hop and Pop are the preferred music for 25% + 35% = 60% of the sample, which is equivalent to 0.6 x 400 = 240 students.
Therefore, conclusion (4) is incorrect.
Therefore, the only correct conclusion that can be drawn from the circle graph is that Jazz is the preferred music for 56 students.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
The probability of rolling one of these five numbers is 5/37.
Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:
35 | 25 | 33 | 9 | 19.
The total number of sides of a die is 37. As a result, there are 37 numbers in the die.
Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.
Therefore, the probability of rolling any of these numbers is:
1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37
So, the probability of rolling one of these five numbers is 5/37.
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find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.
The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.
Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:
Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.
Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.
Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.
The numbers of the form 35n in the interval [1000, 9999] are
1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.
To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.
Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is
9000 - 399 - 204 + 285 = 4680.
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Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Question 4(Multiple Choice Worth 2 points)
Answer: 24
Step-by-step explanation:
16/(8×2)=
16/8×2=
16-8/2=
Answer:
16/(8×2)=
16/8×2=
16-8/2=
8/2=
4
Step-by-step explanation:
first we subtract 8 from 16 and divide the result by 2.
how many square tiles are shaded and not shaded for the 8th figure?
Kate is x years old. Lethna is 3 times as old as Kate. Mike is 4 years older than Lethna. write down an expression, in terms of x for Mike's age
Answer: Mike is ( 3x + 4 ) years old
Step-by-step explanation:
K -> x y/o
L -> 3x y/o
M -> (3x + 4) y/o
A. x/4 +1= -3 B. x +4= -12 How can we get equation b from equation a? A. Add/subtract the same quantity to/from both sides B. Add/subtract a quantity to/from only one side C. Multiply/divide both sides by the same non-zero constant D. Multiply/divide both sides by the same variable expression
Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.
What are some integers non-constant?If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).
As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.
Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:
[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]
We obtain x = -16 by multiplying both of the equation's sides by 4.
Starting with the variable with one of the equation's equations, we can solve equation B for x:
[tex]x + 4 = -12[/tex]
Therefore, We obtain [tex]x = -16[/tex] by deducting [tex]4[/tex] from both of the equation's components.
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Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
Answer:
C. (0, –5) and (2, –1)
Solve for all possible values of x.
√3x 8-x-4
Type your answer...
The value of x -8.
What is an equation?An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressions is equal.
All formulas hav LHS = RHS (left side = right side).
You can solve equations to determine the values of unknown variables that represent unknown quantities.
If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.
Hence, the value of x -8.
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The measures of include mean and mode. The third of those measures is. Dividing the sum of all data values by the total frequency will give us the. Some data sets may have zero, one, or more than one. If there are 4999 values in a data set, then the will be located at the 2500th value, when those values are put into increasing order. If there are 4999 values in a data set, then the will be found by subtracting the first value from the 4999th value, when those values are put into increasing order. The measures of include variance and range. The third of those measures is. The is found by taking the square root of the. To approximate the variation of the data values from the mean, find the. In the excel function stdev. S, the last s stands for
The measures of central tendency include mean and mode, which include a third measure called median.
The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.
The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.
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Correct question is:
The measures of _________ include mean and mode. The third of those measures is ________.
Dividing the sum of all data values by the total frequency will give us the_____.
find the nth term of this quadratic sequence 4, 7, 12, 19, 28, . ..
Answer:
an = a1 + (n-1)d
Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:
an = 4 + (n-1)3
a5 = 4 + (5-1)3
a5 = 4 + 12
a5 = 16
Jadi, suku ke-5 dari barisan ini adalah 16.
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For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) = please help!
Answer: (5a + 3)(b + 1)
Step-by-step explanation:
We can factor out the common factor of (b + 1) from both terms:
5a(b + 1) + 3(b + 1) = (5a + 3)(b + 1)
Therefore, the expression in complete factored form is (5a + 3)(b + 1).
PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75 % of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. (a) Starting with the 75 % estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence? (Enter your answer as a whole number.) n = (b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.) n =
(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.
(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.
(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²
Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).
n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74
Since we need a whole number, we round up to the nearest whole number:
n = 51
(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):
n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65
Again, rounding up to the nearest whole number:
n = 68
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Solve the system of equations:
y = 2x + 1
y=x²+2x-8
OA. (-3,-5) and (3,7)
B. (-4, 0) and (2,0)
C. (0, 1) and (2, 5)
OD. (-3, 5) and (3, 2)
The solutions of the system of equations are option (A) (3, 7) and (-3, -5)
Solving system of equations:
To solve the system of equations, use the concept of substitution, which involves solving one equation for one variable and then substituting that expression into the other equation to eliminate one variable and solve for the other variable.
In this case, solve equation (1) for y in terms of x and substitute that expression into equation (2), which allowed us to solve for x. Then we used the values of x to find the corresponding values of y.
Here we have
y = 2x + 1 --- (1)
y = x²+ 2x -8 --- (2)
From (1) and (2)
=> x²+ 2x - 8 = 2x + 1
Subtract 2x + 1 from both sides
=> x²+ 2x - 8 - 2x - 1 = 2x + 1 - 2x - 1
=> x² - 9 = 0
Now add 9 on both sides
=> x² - 9 = 0 + 9
=> x² = 9
=> x = √9
=> x = ± 3
From (1)
At x = 3
=> y = 2(3) + 1 = 7
At x = - 3
=> y = 2(-3) + 1 = - 5
Therefore,
The solutions of the system of equations are option (A) (3, 7) and (-3, -5)
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Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
Find the rate of change of the area of a square with respect to the length z, the diagonal of the square. What is the rate when z = 3? a) dA/dz = z; rate = 6 b) dA/dz = zroot2; rate = 3 root2 c) dA/dz = 2z; rate = 3 d) dA/dz = z; rate = 3 e) dA/dz = 2z; rate = 6
The rate of change of the area of a square with respect to the length z, the diagonal of the square is dA/dz = 2z; rate = 6. The correct answer is C.
We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.
Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:
2s ds/dz = 2z/2
s ds/dz = z
Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:
dA/dz = d/dz (s²) = 2s ds/dz
Substituting the value of s ds/dz obtained earlier, we get:
dA/dz = 2s (z/s) = 2z
Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.
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What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the
function S=18.95 +0.60 M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I=4.90 +0.25 M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
C =
Hi. The terms of the standard charge and insurance charge equations are a little garbled, but it is possible to think that these are the right equations:
Standard charge, S = 18.95 + 0.60M, where 18.95 is the initial fee and 0.60 is the charge for each mile driven.
Insurance charge, I = 4.90 + 0.25M, where 4.90 also represents an initial fee and 0.25 a charge for each mile driven.
Then, the total cos, C = S + I =>
C = (18.95 + 0.60M) + (4.90 + 0.25M) which you can rearrange to show the like terms one next to each other =>
C = (18.95 + 4.90) + (0.60M + 0.25M), now add up the like terms=>
C = 23.85 + 0.85M which is the equation is the most simplified form
Answer: C = 23.85 + 0.85M
you roll two six-sided dice at the same time. what is the probability the second dice landed on an even number given the first one landed on an odd number?
The probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
Step-by-Step Explanation:Let A be the event that the first dice rolls an odd number, and let B be the event that the second dice rolls an even number. We want to find P(B|A), which is the probability of B given A. This can be found using the formula:P(B|A) = P(A and B) / P(A) We know that P(A) = 1/2, as half the numbers on a six-sided dice are odd.
To find P(A and B), we need to find the probability that both dice roll the desired numbers simultaneously. Since we know that the first dice rolled an odd number, only half of the numbers are possible for the second dice to be even. Therefore, P(A and B) = 1/2 x 1/2 = 1/4. So:P(B|A) = P(A and B) / P(A) = (1/4) / (1/2) = 1/2 or 0.5. Therefore, the probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
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a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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REALLY URGENT!!!
Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Thank you in advance!
The approximate circumference of spaceship Earth is 160m
How to determine the valuesThe formula for calculating the volume of a sphere is given as;
V = 4/3 πr³
Given that;
V is the volume.r is the radius.Now, substitute the values
65417 = 1. 3 ×3.14r³
Multiply the values
65417 = 4. 082r³
Make r the subject
r³ = 16025. 722
Find the cube root
r = 25. 2m
The circumference is expressed as;
Circumference = 2πr
Substitute the values, we have;
Circumference = 2× 3.14 × 25.2
Circumference = 160 m
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Solve
2n > 20
Pls help really quick
Answer:
n > 10
Step-by-step explanation:
2n > 20
2n/2 > 20/2
n > 10
