The data below shows the numbers of hours Mrs. Diaz works at the library each month fir eight months. The mean of the data set is 22 hours. What is the mean absolute deviation of the data

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

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Answer:143

Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive

Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

Given that the current balance is $800.

There were two types of schemes.

First scheme offer compounded annually at an interest rate of 9%

Second scheme offer compounded quarterly at an interest rate of 9%.

The formula of compound interest annually is

A = P(1+r)^t

P = principal = 800

r = rate of interest = 9% = 0.09

t = time = 3 year

A = 800(1+0.09)³

A = 1036.02.

The formula of compound interest annually is

A = P(1+(r/n))^tn

P = principal = 800

r = rate of interest = 3% = 0.03

t = time = 3 year

n = 4

nt = 4×3 =12

A = 800(1+0.03/4)¹²

A = 875.04

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.

If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.

Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.

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Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

Answer:

4

Step-by-step explanation:

let n be the integer , then n tripled is 3n, so

[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )

3n + 36 = 12n ( subtract 3n from both sides )

36 = 9n ( divide both sides by 9 )

4 = n

the required integer is 4

Answer:

The slope is 2/9.

Step-by-step explanation:

(15, 10) and (60, 20)

m = 20-10/60-15

m = 10/45

m = 2/9

The multiplications, applying the associative property, are given as follows:

1. (5 x 2) x 3 = 10 x 3 = 30.

2. 4 x (3 x 3) = 4 x 9 = 36.

3. (6 x 1) x 4 = 6 x 4 = 24.

4. 5 x (2 x 4) = 5 x 8 = 40.

5. (2 x 2) x 8 = 4 x 8 = 32.

6. 3 x (2 x 2) = 3 x 4 = 12.

7. (4 x 2) x 4 = 8 x 4 = 32.

8. 6 x (3 x 3) = 6 x 9 = 54.

The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.

In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.

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Between x=-1 and x=1, the average rate of change is 1.

It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:

(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.

Given line in the figure passes through the points A(4, 0), B(-1, -5)

Let the  equation of the line be:

y=mx+ c

Slope m=(-5-0)/(-1-4)

m=1

Therefore, y=x+ c

It passes through (4, 0)

y+ c=0

c=-4

y=x-4=f(x)

f(-1)= -1-4=-5

f(1)= 1-4=-3

The average rate of change=(f(b)-f(a))/(b-a)

=(f(1)-f(-1))/1-(-1)

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

=2/2

=1

Therefore, Between x=-1 and x=1, the average rate of change is 1.

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Answer:

X=54

Step-by-step explanation:

equate both the equations since angles of opposite sides are equal

2x+2=3x-52

3x-2x= 52+2

x=54

answer:

x=54

Step-by-step explanation:

2x+2=3x-52

move the 2x to 3x because x can't be negative

and add 52 to 2 so x=54

Answer:

1st & 4th answers are correct.

Step-by-step explanation:

-6 ( 2x + 5 )

Solve the brackets.

- 12x - 30

We can also write the answer like this.

Take -2 out of the brackets.

- 12x - 30 → -2 ( 6x + 15 )

Therefore, 1st & 4th answers are correct.

As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, A crew of six workers completes a job in 15 hours.

We know more crew will finish the job in less no. of hours so they are inversely proportional.

So, C = k/t.

6 = k/15.

k = 90.

Now, C = 10 hence,

10 = 90/t.

t = 90/10.

t = 10 hours.

So, They can finish in 10 hours.

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The value of y from the equation y = 150x when x = 2(1/4) is 337.5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

y varies directly with x.

y ∝ x

y = kx

Now,

y = 75 when x = 1/2

75 = k(1/2)

k = 75 x 2

k = 150

Now,

y = kx

y = 150x

When x = 2(1/4) = 9/4

y = 150 x 9/4

y = 337.5

Thus,

The value of y is 337.5.

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The result of the hypothesis test is that we cannot say if the mean is lower than 56.

Hypothesis are ,

H0 : ц = ц 1

H1 : ц ≠ ц 1

It is to be tested whether the mean daily high temperature for October in a large Midwestern city is actually lower than

56 F or not.

Then the test statistic is equal to minus 2.64610 degrees of tritomas degree of to equal to 1 equal to 29 point,

The appropriate conditions to be sufficed before performing the one-sample z-test are:

(i) The measurement of the sample drawn for the observation must be extensive. The desired threshold is 30.

(ii) Each observation should have an equal opportunity of getting selected in the sample.

(iii) The data need to be normal.

On performing the analysis we conclude that  it can not be said with 99 % confidence that the true mean temp is less than 56 F.

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The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

Given the radius in the question = a

The integration of the total distance before dividing the volume will be =

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]

⇒ [tex]\pi A^{4}[/tex]

Let us divide the average distance by the ball's volume,

⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]

⇒ [tex]{\frac{3a}4}[/tex]

By the use of the Parcly Taxel's way,

Let the radius of the ball be = A

f(x) = probability density function

Distance = D from the given point to the center.

P( D < a )

[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A

Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

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The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .

Given :

the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .

Quadratic equation :

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Formula :

= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]

Discriminant = b^2 - 4ac

if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .

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Answer:

A and B

Step-by-step explanation:

actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.

Option c is most likely to get unbiased results.

The best option for collecting unbiased data in this case would be option c: asking customers who visit retailers within a 15 mile radius of the company headquarters. This method would involve sampling a diverse group of customers who are not affiliated with the company in any way, and therefore are likely to provide more objective feedback about the new brand of soup.

Option a, asking distributors who supply the products to local retailers about the popularity of different soup brands, could be biased because the distributors may have their own interests in promoting certain brands over others.

Option b, asking the employees in the company which soup is the best, could also be biased because the employees may have a vested interest in the success of the company and its products, and therefore may not provide completely objective feedback.

Option d, asking customers who visit the grocery store nearest to the manager's house which soup they like the best, could also be biased because it may not be representative of the overall customer base for the soup. It is important to sample a diverse group of customers in order to get a more accurate sense of how the new brand of soup is being received.

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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.

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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

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Answer:

  (d)  The other solution to function f is -3 + 5i

Step-by-step explanation:

Given a solution to quadratic function f is -3-5i, you want to know the other solution.

The complex solutions to quadratic equations come in conjugate pairs. That is, if one solution is -3-5i, the other solution will be the same thing with the sign of the imaginary part reversed:

  The other solution is -3+5i.

__

Additional comment

This is true only if the quadratic has real coefficients. (We typically don't study any other kind.)

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Answer:

11 feet every minute

Step-by-step explanation:

We first need to figure out how far you traveled up.

240 - 130 = 110

Now, we can solve for the average rate of elevation.

If you travel 110 feet in 10 minutes, we can do this equation:

110 ÷ 10 = 11

The average change of elevation, every minute, was 11.

The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

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The test hypothesis is

H₀: p=0.08 (null hypothesis) and

Hₐ: p<0.08 (alternative hypothesis )

Given that,

8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:

0% of people who received the vaccine contracted the flu.

8% or less of people who received the vaccine ended up getting the flu.

In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.

If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.

The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )

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True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).

The critical value for alpha is 0.05 and z is 1.96 .

The corresponding confidence interval is ( 6.235 , 7.165).

Therefore the above statement is true.

Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].

An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)

The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.

[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]

[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]

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The complete question is-

[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

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