To the nearest integer, about how many times larger is 20 x 10 exponent 2 compared with 4 x 10 exponent -1?

D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.

The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.

62% of women in the sample are the primary investor in their household.

Inference: Women in the United States are likely to be the primary investors in their households.

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The directions of the function where it equals 3 are given by the vectors u for which ∇f(1,1) · u = 0.

What is Function ?

function can be defined in which it relates an input to output.

To find the directions u and the values of f(1,1) for which the following is true, we need to use the gradient of the function f(x, y). The gradient is a vector that points in the direction of the maximum increase of the function.

The gradient of f(x, y) is given by:

∇f(x,y) = ( ∂f/∂x , ∂f/∂y )

a. To find the direction u for which f(1,1) is largest, we need to find the direction of the maximum increase of the function at the point (1,1). The direction of the maximum increase is given by the gradient vector ∇f(1,1). We need to find the unit vector u in the direction of ∇f(1,1).

So, first, we need to calculate the gradient at (1,1):

∇f(1,1) = ( ∂f/∂x , ∂f/∂y ) at (1,1)

b. To find the direction u for which f(1,1) is smallest, we need to find the direction of the maximum decrease of the function at the point (1,1). The direction of the maximum decrease is given by the negative of the gradient vector -∇f(1,1). We need to find the unit vector u in the direction of -∇f(1,1).

So, first, we need to calculate the gradient at (1,1):

-∇f(1,1) = - ( ∂f/∂x , ∂f/∂y ) at (1,1)

c. To find the directions u for which f(1,1) > 0, we need to find the directions of the function where it is positive at the point (1,1). The directions of the function where it is positive are given by the vectors u for which ∇f(1,1) · u > 0.

So, first, we need to calculate the gradient at (1,1):

∇f(1,1) = ( ∂f/∂x , ∂f/∂y ) at (1,1)

Then, we need to find the unit vectors u for which ∇f(1,1) · u > 0.

d. To find the directions u for which f(1,1) = 4, we need to find the directions of the function where it equals 4 at the point (1,1). The directions of the function where it equals 4 are given by the vectors u for which ∇f(1,1) · u = 0.

So, first, we need to calculate the gradient at (1,1):

∇f(1,1) = ( ∂f/∂x , ∂f/∂y ) at (1,1)

Then, we need to find the unit vectors u for which ∇f(1,1) · u = 0.

e. To find the directions u for which f(1,1) = 3, we need to find the directions of the function where it equals 3 at the point (1,1).

Therefore,  The directions of the function where it equals 3 are given by the vectors u for which ∇f(1,1) · u = 0

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The cost to bowl a game is $2.5.

Two or more expressions with an Equal sign is called as Equation.

Let g  represent the cost of bowling a game and s represent the cost of renting shoes.

Bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00

3g+s=9..(1)

Leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00.

5g+s=14..(2)

Subtract equation 2 from 1

3g+s-5g-s=9-14

-2g=-5

Divide both sides by 2

g=2.5

Hence, the cost to bowl a game is $2.5.

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Answer:

$560.30 & $60.30

Step-by-step explanation:

A = $560.30

A = P + I where

P (principal) = $500.00

I (interest) = $60.30

Answer:

Step-by-step explanation:

Given

she works $30 for 1 hour

in 40 hours she will earn 40*30= $1200

this means that a week she earns $1200

let the number of  weeks she needs to work be x

40x*(30)<=2000

1200x<=2000

x<=2000/1200

x<=1.66

the number of hours in a week is 40

40*1.66=66.66

67hours

hence she must work for at least 67hours

Proof:-

In ∆XYZ and ∆VWZ

\(\because\sf\begin{cases}\sf XZ\cong VZ(Given)\\ \sf YZ\cong WZ(Given)\\ \sf <XZY\cong <WZV(Opposite angles)\end{cases}\)

Hence

∆XYZ\(\cong\)(Side-Angle-Side)

Answer: No, it is not a direct proportion equation

Explanation:

Direct proportions are always in the form \(y = kx\) where k is any nonzero real number. So for example, we could have the equation \(y = 9x\). The y intercept of any direct proportion is always zero. Visually, such equations will go through the origin.

Something like \(y = \frac{2}{3}x-7\) has a y intercept of -7 and it doesn't fit the form \(y = kx\), so it's not a direct proportion equation.

Answer:

si, por qué ecuación da diferente resultado

Answer:

y = -3/5x - 2

Step-by-step explanation:

y2 - y1 / x2 - x1

-5 - 1 / 5 - (-5)

-6/ 10

= -3/5

y = -3/5x + b

1 = -3/5(-5) + b

1 = 3 + b

-2 = b

The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.

In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.

The given expression is 6/(y-z) - 2/(y-z).

Simplifying the expression by combining the like terms we have:

(6 - 2)/(y-z) = 4/(y-z)

Hence, the value of the given expression is option 3 4/(y-z).

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Answer:

A

Step-by-step explanation:

The triangles are the same. Congruent is when all three sides are equal to each other on both triangles

Therefore, when Savannah is 42 feet above the ferris wheel's horizontal diameter, her angle of rotation is approximately 68.6 degrees.

Given by the question.

Let's first draw a diagram to visualize the situation.

      *

    *    *

  *        * <-- Ferris wheel at 3 o'clock position

 *          *

*            * <-- Highest point

*______________*______

      62 ft

The Ferris wheel is a circle with radius 62 feet, and Savannah is sitting in a bucket that moves along the circle. When she is at the highest point, she is 62 feet away from the center of the circle, and when she is on the horizontal diameter, she is 62 feet - 42 feet = 20 feet away from the center of the circle.

To find Savannah's angle of rotation, we can use the cosine function.

cos(theta) = adjacent / hypotenuse

In this case, the adjacent side is 20 feet, and the hypotenuse is 62 feet.

cos(theta) = 20/62

To solve for theta, we need to take the inverse cosine of both sides.

theta = cos^-1(20/62)

Using a calculator, we get:

theta = 68.6 degrees

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Answer:

b = 3

Step-by-step explanation:

the 2 indicated angles form a right angle and sum to 90° , that is

8b + 7 + 59 = 90

8b + 66 = 90 ( subtract 66 from both sides )

8b = 24 ( divide both sides by 8 )

b = 3

If the boys and girls must alternate, the total number of ways they can sit in a row is (b+g)!/(b/2)! (g/2)!.

If the boys and girls must alternate, then the first seat can be occupied by a boy or a girl. Without loss of generality, let's assume that the first seat is occupied by a boy. Then, the second seat must be occupied by a girl, the third seat by a boy, the fourth seat by a girl, and so on.

Let's say there are b boys and g girls. Then, there are b+g people in total. We can arrange the boys in b! ways and the girls in g! ways. However, we must also take into account the fact that the first seat is occupied by a boy. Since there are b choices for the first seat, there are b!(g-1)! ways to arrange the boys and girls if the first seat is occupied by a boy.

Similarly, if the first seat is occupied by a girl, then there are g!(b-1)! ways to arrange the boys and girls.

Therefore, the total number of ways to arrange the boys and girls if they must alternate is:

b!(g-1)! + g!(b-1)!

which can be simplified to:

(b+g)!/(2!(b/2)!(g/2)!) * (b/2)!(g/2)! + (b+g)!/(2!(b/2)!(g/2)!) * (b/2)!(g/2)!

= (b+g)!/(2!(b/2)!(g/2)!) * 2 * (b/2)!(g/2)!

= (b+g)!/(b/2)!(g/2)!

Therefore, the number of ways the boys and girls can sit in a row if they must alternate is (b+g)!/(b/2)!(g/2)!.

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Using the multiplication and addition operations, if Fabian leaves a 15% tip, his meal plus the tip, before tax, is $40.25.

Multiplication and addition operations are two of the four basic mathematical operations.

Multiplication involves the use of multiplicand, multiplier, multiplication operand, equal symbol, and product.

The addition operation involves using the two addends, the equal sign, and the sum.

Dinner cost before tip and tax = $35

Tip = 15%

Total cost before tax = 115% (100 + 15)

Dinner cost after tip = $40.25 ($35 x 1.15)

Thus, mathematically, Fabian will spend $40.25 for the dinner before tax.

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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The equation given is,

5x − 2x − 3 = −2 + 17

Step 1: 5x − 2x − 3 = −2 + 17

Step 2: 5x − 2x − 3 = 15

Step 3: 3x − 3 = 15

Step 4: Add 3 to both sides

3x − 3+3 = 15+3

3x=18

Hence, the most likely the next step is 3x = 18.

The 90th percentile of x is 70.

What is standard deviation?

A set of values' variance or dispersion is measured by the standard deviation. While a high standard deviation implies that the values are dispersed over a wider range, a low standard deviation shows that the values tend to be close to the mean of the collection.

Given:  Mean = 80, s = 5.

Computing values to standard deviation from mean,

Lower limit = mean - 2s

                  = 80 - 2(5)

                  = 80 - 10

Lower limit = 70

Hence, if x has a normal distribution with mean 80 and standard deviation 5 then the 90th percentile of x is 70.

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On rationalizing the expression 7/(2-√5) 7/(2-√5), the value is obtained as -7 (2 + √5).

What is rationalization?

In order to get rid of the irrational number in the denominator, the procedure of rationalisation is performed in elementary algebra. There are numerous rationalisation strategies that are used on the denominator.

The given expression is - 7/(2-√5).

Multiply the denominator and numerator by the (2 + √5).

= 7 × (2 + √5)/(2-√5) × (2 + √5)

= (14 + 7√5)/(2)² - (√5)²

Simplify it further -

= (14 + 7√5)/4 - 5

= (14 + 7√5)/-1

= -(14 + 7√5)

= -7 (2 + √5)

Therefore, the simplified expression is -7 (2 + √5).

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Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

Fruit punch is served during the reception in 154-ounce cups using division.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

For instance, 4 2 Equals 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.

The division is represented mathematically by a symbol consisting of a tiny horizontal line with dots above and below the line. The division of two integers is represented by one of two fundamental division symbols.

Total fruit punch foe prepared = 3696 ounces

Number of punch balls = 4

Each serving has = 6 ounces of punch

So, 4 servings will have

4 × 6 = 24

The number of servings of fruit punch available at reception is given by

3696÷24

= 154

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Answer:

Step-by-step explanation:

12/18= 2/3, that’s the ratio of how many questions he gets right compared to total questions

So if there are 30 questions total, he will get 20 right (30 x 2/3)

If you’re taking into consideration that he already answered 18 questions, he will get 8 more correct

Answer: 6

Step-by-step explanation:

Maybe

Answer:

\(y - z \\ = 7 - 11 \\ = - 4\)

The correct asnwer is (5, infinity).

Let's remember the definition of being a increasing function: If we take (arbitrary) two numbers a and b in the interval, and

Then

Answer:

converting to minutes

Step-by-step explanation:

3*60+20+40+2.75*60=405 min = 6 hours 45 minutes

In mathematics, the point below which a specified percentage of the observations fall is commonly referred to as the percentile.

A percentile is a measure that indicates the relative position of a particular value within a dataset.

For example, if a value is at the 80th percentile, it means that 80% of the observations in the dataset are below that value, and only 20% of the observations are above it.

Percentiles are often used to analyze and understand the distribution of data, especially in fields such as statistics, probability, and data analysis. They provide insights into how individual data points compare to the overall dataset and help identify outliers or extreme values.

A percentile is a statistical measure that indicates the relative standing of a particular value within a dataset. It represents the point below which a specified percentage of the observations or data points fall. Percentiles are primarily used to understand the distribution of data and analyze how individual values compare to the overall dataset.

To calculate a percentile, the dataset is arranged in ascending order, from the smallest value to the largest value. The position of a specific percentile is then determined based on the percentage of data points below it. For example, the 75th percentile represents the value below which 75% of the data points fall.

Percentiles are commonly used in various fields, including statistics, probability, and data analysis. They provide valuable insights into the spread, variability, and distribution of data. Here are a few key points to consider:

1. Median: The median is the 50th percentile, representing the value that divides the dataset into two equal halves. It is a measure of central tendency and provides information about the middle point of the distribution.

2. Quartiles: Quartiles divide the dataset into four equal parts. The first quartile, or the 25th percentile (Q1), represents the value below which 25% of the data points fall. The third quartile, or the 75th percentile (Q3), represents the value below which 75% of the data points fall. The difference between Q3 and Q1 is known as the interquartile range (IQR) and provides insights into the spread of the middle 50% of the data.

3. Percentile Ranks: Percentile ranks indicate the percentage of data points that are below a specific value. For example, if a student scores in the 80th percentile on a standardized test, it means they performed better than 80% of the test-takers.

4. Outliers: Percentiles can be useful in identifying outliers, which are data points that significantly deviate from the rest of the dataset. Extremely high or low percentiles may indicate unusual or extreme values that warrant further investigation.

5. Normal Distribution: In a normal distribution, the 50th percentile (median) coincides with the mean and mode, and specific percentiles have known standard deviations from the mean (e.g., the 68-95-99.7 rule).

Percentiles are versatile tools for summarizing and analyzing data, providing valuable insights into the distribution and relative positions of individual values. They enable comparisons and help make informed decisions based on the characteristics of a dataset.

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