Simplify.
Remove all perfect squares from inside the square roots. Assume
�
xx and
�
zz are positive.
72
�
3
�
3
=
72x
3
z
3

​
=square root of, 72, x, cubed, z, cubed, end square root, equals

Answer:

Step-by-step explanation:

100000³ = 100000 × 100000 × 100000

100000 × 100000 × 100000 =

10000000000 × 100000 =

1e+15 or 1.000.000.000.000.000

Using composite figures, we can find that the area of the shape is 18unit² and the perimeter of the shape is 20 + √8 units.

A composite shape is a shape that is made by connecting a few polygons to form a different shape. These shapes or figures can be formed from a variety of shapes, including triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.

In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In this composite figure,

We have 2 rectangles and a triangle.

Dimension of rectangle:

Base = 2units

Height = 2 units.

Hypotenuse = √ (2² + 2²)

= √8

Area of the triangle = 1/2 × b × h

= 1/2 × 2 × 2

= 2unit².

Now, the rectangles are equal in shape and size.

Dimensions are:

Length = 4 units

Breadth = 2 units.

Area = l × b

= 4 × 2

= 8unit².

We have 2 rectangles so total area = 2 × 8

= 16unit².

Total area of the shape = area of triangle + area of 2 rectangles

= 2 + 16

= 18unit²

Now coming to the perimeter of the shape, we have to find the sum of the measure of the sides of the shape:

So, we have

2 + 4 + 2 + 6 + 6 + √8

= 20 + √8 units.

To know more about composite figures, visit:

https://brainly.com/question/27234680

#SPJ1

Answer:

DE = √21

x = 10

Step-by-step explanation:

4)

AC is bisected by BX

AC/2 = 8/2 = 4 = AB

BX² + AB² = AX²

3² + 4² = AX²

AX = 5 = radius of the circle

DE² = DX² - EX²

DE² = 5² - 2² = 25 - 4 = 21

DE = √21

6)

x² = (11-5)² + 8² = 36 + 64 = 100

x = √100 = 10

x = 10

Answer:

sin0= 9/15

cos0= 12/15

tan0 = 9/12

The solutions to the equation are x = 7/2 or x = 2. This is because if either of the factors (2x - 7) or (x - 2) equals zero, then the whole expression will equal zero.

To solve the quadratic equation 2x²-11x=-14 by factorization, we need to rearrange the equation to bring all terms to one side so that it is in the form ax² + bx + c = 0.

First, we add 14 to both sides of the equation, which gives us:

2x² - 11x + 14 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to give the constant term (14) and add to give the coefficient of the middle term (-11). In this case, the two numbers are -2 and -7, as (-2) x (-7) = 14 and (-2) + (-7) = -9.

Using these two numbers, we can rewrite the middle term as -2x - 7x, which gives us:

2x² - 2x - 7x + 14 = 0

We can then factorize the first two terms and the last two terms separately, which gives us:

2x(x - 1) - 7(x - 2) = 0

We can then use the distributive property to simplify the equation:

2x² - 2x - 7x + 14 = 0

2x(x - 1) - 7(x - 2) = 0

(2x - 7)(x - 2) = 0

To learn more about factors click on,

https://brainly.com/question/14549998

#SPJ4

Answer:

Box A: 2 × 4.5 × 6 = 54 cubic inches

Box B: 6 × 2.5 × 3 = 45 cubic inches

Box C: 5 × 4.5 × 2.25 =

50.625 cubic inches

Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches

From least to greatest, the order of the boxes' volumes is D, B, C, A.

Answer: Empirical Exercise 8.2(l) involves running a regression to estimate the relationship between two variables of interest. In evaluating the internal validity of the regression used to answer this exercise, we need to consider several potential sources of bias and other issues that could affect the accuracy of the estimated relationship.

Omitted variable bias: This occurs when a relevant variable is left out of the regression model. If this happens, the estimated coefficients may be biased and inconsistent. For example, if we are estimating the effect of education on earnings but fail to include information about work experience, the coefficient on education may be biased upwards.

Misspecification of the functional form of the regression: If the relationship between the dependent variable and the independent variable(s) is nonlinear, we may need to use a different functional form of the regression equation to obtain accurate estimates. If we fail to do so, the estimated coefficients may be biased and inconsistent.

Errors in variables: When measurement errors occur in the independent variable(s), this can cause the estimated coefficients to be biased and inconsistent.

Sample selection: If the sample used to estimate the regression equation is not representative of the population of interest, then the estimated coefficients may be biased and inconsistent.

Simultaneous causality: When there is a two-way causal relationship between the dependent variable and the independent variable(s), it may not be possible to determine the direction of causality from the regression coefficients.

Inconsistency of the OLS standard errors: If there is heteroskedasticity or autocorrelation in the data, then the ordinary least squares (OLS) standard errors may be inconsistent. This can lead to incorrect conclusions about the statistical significance of the estimated coefficients.

To address these issues, researchers should take care to select an appropriate sample, use a suitable functional form of the regression equation, and account for any relevant variables that could be omitted or measured with errors. It may also be necessary to use alternative statistical techniques to account for simultaneous causality or heteroskedasticity in the data. Finally, researchers should always test the robustness of their results to different model specifications and sensitivity to potential sources of bias.

Step-by-step explanation:

Step-by-step explanation:

We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.

We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:

Change in elevation = 4 miles x tan(9.5°)

Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:

Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:

Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.

a. The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.

b. The probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.

c. The probability of no flaws in a 25-yard piece of material is approximately 0.3679.

To find the probability of exactly two flaws in a 50-yard piece of material, we can use the Poisson distribution. Let λ be the average number of flaws per 50 yards of material, which is 2. Then, the probability of exactly k flaws occurring in a 50-yard piece of material is given by

P(k flaws) = (e^(-λ) × λ^k) / k!

So, for k=2, we have

P(2 flaws) = (e^(-2) × 2^2) / 2! ≈ 0.2707

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.

b. To find the probability of no more than two flaws in a 50-yard piece of material, we need to sum the probabilities of having 0, 1, or 2 flaws. So, we have

P(no more than 2 flaws) = P(0 flaws) + P(1 flaw) + P(2 flaws)

We already know P(2 flaws) from part (a). To find P(1 flaw), we can use the same formula as before with λ=2 and k=1

P(1 flaw) = (e^(-2) × 2^1) / 1! ≈ 0.2707

To find P(0 flaws), we use the same formula with λ=2 and k=0

P(0 flaws) = (e^(-2) × 2^0) / 0! ≈ 0.1353

Therefore, we have:

P(no more than 2 flaws) = 0.2707 + 0.2707 + 0.1353 ≈ 0.6767

So, the probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.

c. To find the probability of no flaws in a 25-yard piece of material, we can again use the Poisson distribution, but with a different value of λ. Since the average number of flaws per 50 yards is 2, the average number of flaws per 25 yards is 1. So, we have:

P(0 flaws) = (e^(-1) × 1^0) / 0! ≈ 0.3679

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The area of the right triangle is 173.25 square feet.

The formula for the area of a right triangle is:

A = (1/2)bh

where A is the area, b is the base, and h is the height.

We are given that the height of the right triangle is ten and one-half feet (10.5 ft) and the base is 33 feet.

Substituting the given values into the formula, we get:

A = (1/2)(33)(10.5)

Simplifying the expression on the right side, we get:

A = 173.25

Therefore, the area of the right triangle is 173.25 square feet.

Read more about right triangle at

https://brainly.com/question/2437195

#SPJ1

Does this table represent a function: C. No, because one x-value corresponds to two different y-values.

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).

Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 4

4 → 4

Read more on function here: https://brainly.com/question/27862183

#SPJ1

Answer:

D, A, B, C

Step-by-step explanation:

-12/3, or -4, is lowest

-11/3, or -3.6, is 0.3 more, therefore closer to 0.

-2/3, or -0.6, is much closer to 0, precisely 3 units closer.

1/3, or 0.3, is the only positive number, so it is the most amount.

The value of quadratic equation with the help of  hit and trial method is 39

A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable (usually x) in the equation is 2. It is in the form:

ax^2 + bx + c = 0

where a, b, and c are constants and a is not equal to zero.

the value of  given quadratic equation is

given

y=4x²+8x+7

using hit and trial method:

The value of the quadratic equation y = 4x² + 8x + 7 depends on the value of x.

To find the value of y for a specific value of x, simply substitute that value of x into the equation and solve for y.

For example, if x = 2, then:

y = 4(2)² + 8(2) + 7

y = 16 + 16 + 7

y = 39

So the value of the quadratic equation y = 4x^2 + 8x + 7 when x = 2 is 39.

To know more about Quadratic Equation Visit:

https://brainly.com/question/30098550

#SPJ1

If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The area of a rectangle is calculated by multiplying its length and width. If the dimensions of a rectangle are multiplied by a factor of k, then the new area of the rectangle is equal to k times the original area.

In this case, the dimensions of the original rectangle are multiplied by 1/2, which means that the new length and width of the rectangle are 1/2 times the original length and width. Therefore, the new area of the rectangle is equal to (1/2) times the original length multiplied by (1/2) times the original width. This can be simplified to 1/4 times the original area. Therefore, the area of the new rectangle is one-fourth of the area of the original rectangle.

Therefore, If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

To learn more about the area of the rectangle visit:

brainly.com/question/2607596

#SPJ1

a) His monthly salary is, 555.6

b) Total amount spent on his parent​ is, 111.1

Given that;

Mr. Ade plans to spend his monthly salary as follows

food-20%

children-25%

parents-20%

car-10%

entertainment-10%

saving-2½

miscellenceous-2½

And, the amount of saving kept for saving is Ghc 250.00.

Hence, We get;

Monthly salary is,

Since, We have;

Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%

                             = 45%

Hence, We get;

45% of salary = 250

45/100 x salary = 250

Monthly salary = 25000 / 45

Monthly salary = 555.6

And, Money spent on parents;

20% of 555.6

20/100 x 555.6

111.1

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Answer:

Sam balance was -10 and the ending balance was $70

=80+(-10)

=$70

in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:

State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).

Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).

Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:

t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5

where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.

Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:

df = n1 + n2 - 2

Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To learn more about variances visit:

brainly.com/question/14116780

#SPJ11

Answer:

Step-by-step explanation:

6213.712

Answer:

10,000 Kilometers = 6,213.7119 Miles

Step-by-step explanation:

The area of the figure is 197 square miles

To find the area of the figure, we need to first identify the shape of the figure. From the given dimensions, it appears to be an irregular quadrilateral with a triangle on top.

We can divide the figure into two parts: a rectangle with dimensions 17 mi by 10 mi, and a triangle with base 18 mi and height 3 mi.

The area of the rectangle is:

Area of rectangle = length x width = 17 mi x 10 mi = 170 mi^2

The area of the triangle is:

Area of triangle = (base x height) / 2 = (18 mi x 3 mi) / 2 = 27 mi^2

Therefore, the total area of the figure is the sum of the areas of the rectangle and triangle:

Total area = 170 mi^2 + 27 mi^2 = 197 mi^2

So the area of the figure is 197 square miles.

Learn more about area at https://brainly.com/question/25292087

#SPJ1

Answer:

FH = 26

Step-by-step explanatio

I only know the answer

Answer:

FH ≈ 11.62

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem , then

FH² = EH × GH = 9 × 15 = 135 ( take square root of both sides )

FH = [tex]\sqrt{135}[/tex] ≈ 11.62 ( to the nearest hundredth )

Answer:

  increasing: x > 0

Step-by-step explanation:

Given a table of function values, you want to know the interval on which the function is increasing.

A function is increasing if f(x)-values get larger when x-values get larger. As we go down the table, the x-values get larger.

In the first three lines of the table, the f(x)-values are getting smaller. The function is decreasing on that interval, x < 0.

In the last three lines of the table, the f(x) values are getting larger. The function is increasing on that interval, x > 0.

__

Additional comment

The point (0, 0) represents a minimum. The function is not increasing or decreasing at that point, so the interval of interest is x > 0, not x ≥ 0.

The variance of the number of green voters in the sample is 160.

What is variance?

In statistics, variance is a measure of the spread or variability of a set of data. It measures how much the values in a dataset differ from the mean or average value. Specifically, variance is the average of the squared differences from the mean.

We can use the binomial distribution to model the number of green voters in the sample, where the probability of success (voter being green) is p = 0.2 and the number of trials (voters in the sample) is n = 1000.

The expectation or mean of the number of green voters in the sample is given by the formula:

E(X) = np

where X is the random variable representing the number of green voters in the sample. Substituting the values, we get:

E(X) = 1000 * 0.2 = 200

So we expect to see about 200 green voters in the sample.

The variance of the number of green voters in the sample is given by the formula:

Var(X) = np(1 - p)

Substituting the values, we get:

Var(X) = 1000 * 0.2 * (1 - 0.2) = 160

So the variance of the number of green voters in the sample is 160.

To learn more about variance visit:

https://brainly.com/question/9304306

#SPJ1

Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.

To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get

(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶

This is the given polynomial, so option A is correct.

For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.

Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.

To know more about product of polynomials:

https://brainly.com/question/30595235

#SPJ4

--The given question is incomplete, the complete question is given

" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--

Answer:5000 meters

Step-by-step explanation:1km=1000m

1. The numeric values of the function are given as follows:

2. As x approaches negative infinity, y approaches zero.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric values for this problem are given as follows:

Increasing the negative exponent, the number gets closer to zero.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

The commission for $150 in sales is $15. This corresponds to option (c) in the given answer choices.

We are told that the salesman's commission varies directly with his sales. This means that if the sales increase by a certain percentage, then the commission will also increase by the same percentage. We can set up a proportion to solve for the commission:

Commission/Sales = Commission Rate

We are given that the commission rate is $10 for every $100 in sales. We can use this information to set up a proportion:

Commission/150 = 10/100

To solve for the commission, we can cross-multiply and simplify:

Commission = (150 x 10)/100 = $15

In general, if we let x represent the sales amount, and c represent the commission, then we can use the formula:

c = (x/100) * 10

where 10 represents the commission rate of $10 per $100 in sales. We can use this formula to calculate the commission for any given sales amount.

Therefore, Correct option is C.

To learn more about commission click on,

https://brainly.com/question/929522

#SPJ4

Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

Answer:

z > - [tex]\frac{11}{9}[/tex]

Step-by-step explanation:

7z + 7 > - 2z - 4

9z + 7 > - 4

9z > -11

z > - [tex]\frac{11}{9}[/tex]

Answer: Just turn it into an equation! Replace the > with a =.

Step-by-step explanation:

Subtract 7 from both sides (bc you’re doing the opposite of +7) So 7z +7-7 cancels out so you just have 7z. 7z = -2z -4 -7, so 7z = -2z -11

Add 2z to both sides (bc your doing the opposite again) to get 9z = -11

Divide both sides by the number of the of the term with both a number and variable, in this case 9z, the number is 9. So 9z/9= -11/9 so simplified, z= -11/9

Final answer = -11/9

Hope this helps :D