An 8th Grader is paid for the chores they do around the house. (Although they shouldn't be paid... They don't pay rent and eat for free. That is payment enough!)


The table shows the frequency and cumulative frequency of their undeserved income. Fill in the missing blanks.


Months Income Cumulative

1 to 3 $100 .............$-----

4 to 6 $------ ------$300

7 to 9 $ ------------ $400

10 to 12 $300 ............$-----

The time at which 90% of the population has heard the rumor, we can use an exponential growth model. The formula is given by t = (ln(0.9) / k), where t represents the time in hours after 8 a.m. and k is the growth constant.

We are given that at 8 a.m., 360 people have heard the rumor, which is equivalent to 360/4500 = 0.08 or 8% of the population. By noon, half the town has heard the rumor, which is 50% of the population.

We can use the exponential growth model N(t) = N(0) * e^(kt), where N(t) represents the proportion of the population that has heard the rumor at time t, N(0) is the initial proportion (0.08), k is the growth constant, and t is the time in hours after 8 a.m.

Using the information given, we can set up the equation 0.5 = 0.08 * e^(k * 4), where 4 represents the number of hours from 8 a.m. to noon. Solving this equation for k, we find k ≈ 0.2923.

To determine the time at which 90% of the population has heard the rumor (0.9), we can use the formula t = (ln(0.9) / k). Plugging in the value of k, we get t ≈ (ln(0.9) / 0.2923).

Calculating this expression will give us the time in hours after 8 a.m. at which 90% of the population is expected to have heard the rumor, rounded to one decimal place.

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Answer:

(a) False

(b) False

(c) True

Step-by-step explanation:

(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.

No, since changing the units of measurement does not change the correlation coefficient

(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.

Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation

(c) There is a positive association between the heights of men and women.

We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women

Answer:

1. T, W, E, G

2. C, B, D, A

Step-by-step explanation:

For question 1:

G passes through (2, 3) and (0, -1). So, the slope is \(\frac{-1-3}{0-2}\) = 2.

T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = \(\frac{1}{4}\).

E has a slope of \(\frac{5}{3}\) because the equation is y = mx+b where m is the slope.

W has a slope of  \(\frac{1}{3}\)  since slope is increase in y divided by increase in x.

The order of these from least to greatest is \(\frac{1}{4}\), \(\frac{1}{3}\), \(\frac{5}{3}\), and 2.

Therefore, the answer is T, W, E, G.

For question 2:

A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = \(\frac{3}{2}\).

B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = \(\frac{1}{2}\).

C has a slope of \(\frac{1}{4}\) since the equation is y=mx+b where m is the slope.

D has a slope of \(\frac{3}{4}\) since the slope is increase in y divided by increase in x.

The order of these from least to greatest is \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{3}{4}\), and \(\frac{3}{2}\).

Therefore, the answer is C, B, D, A.

I hope this helps! :)

Didn't understand something? Some important formulas/things to remember that I used:

The equation of a linear function can be written as y=mx+b. m represents the slope.

The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.

The formula for the slope is \(\frac{Y2 - Y1}{X2 - X1}\), where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.

Answer:

I believe the answer is 7

Answer:

12

Step-by-step explanation:

9 * 12 - 2 = 61

7 * 12 + 12 = 61

The answer is D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is normal.

In order to perform inference with a confidence interval for the difference in population means, certain conditions need to be met. One of the conditions is that the sample sizes should be sufficiently large.

For the distribution of the difference in sample means to be approximately normal, both sample sizes should ideally be large, typically with a guideline of at least 30 observations. In this case, the sample sizes are 35 for manager A and 40 for manager B, which are relatively small compared to the guideline.

Therefore, (D) the condition of having large enough sample sizes to assume a normal distribution for the difference in sample means is not met. As a result, the conditions for inference with a confidence interval for the difference in population means have not been met.

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5. 25

6. 144

7. 64

8. 6

9. 16

10. 100

Answer:

0

Step-by-step explanation:

If you plug two points into the equation y2-y1/x2-x1, you will find the slope or rate of change. In this case I used the points (0,3) and (2,3). Plug them in to get 3-3/2-0. 0/2=0. Therefore, the rate of change is 0.  

If this helps please mark as brainliest

Answer:

0

Step-by-step explanation:

there is no rate of change. rate of change means what is the slope or the distance the beginning and end of the line. since it is going in a straight line there is no rate of change.

hope this helped

We have the expression

The square root of 1215 is

The probability that the random variable in a uniform distribution is equal to 7.91, given that the distribution is defined over the interval from 6 to 10, is zero.

In a uniform distribution, the probability is evenly spread across the entire interval. The probability of any specific value within the interval is determined by the width of the interval. In this case, the interval is from 6 to 10.
Since the random variable is continuous and the probability is spread evenly, the probability of any specific value within the interval is infinitesimally small. Therefore, the probability of the random variable being equal to 7.91, which falls within the interval from 6 to 10, is zero.
In conclusion, in a uniform distribution defined over the interval from 6 to 10, the probability of the random variable being equal to any specific value, including 7.91, is zero.

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Answer: B.x = 52

we have;

2x + 76 = 180

⇔ 2x = 104

⇔ x = 52

Step-by-step explanation:

Answer:

I think C but im not 100% sure so don't take my word

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

A pentagonal prism is a prism with five rectangular sides and two top and bottom pentagonal bases. With 7 faces, 10 vertices, and 15 edges, it is a particular form of heptahedron. A pentagonal prism can have five sides due to its pentagonal bases. The pentagonal prism is also called Five-sided polygon prism in other name.

The pentagonal prism is a prism with five rectangular sides and two pentagonal base

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Answer:

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

Step-by-step explanation:

hope this helped!

A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Answer:

Dang that’s Hard

Step-by-step explanation:

Answer:

Domain = 0≤m≤20 for mEZ+

Range = $100≤A≤$700 for all values of m

Step-by-step explanation:

Initial amount in the account = $100

Amount saved by beth monthly = $30

Amount in the bank after X month = $100+$30X where X is the number of months beth intend to save up to.

The amount in her bank in her first month = $100+$30(1)

= $100+$30

= $130

Amount saved in the second month will be when X = 2

= $100+$30(2)

= $100+$60

= $160

The amount in the bank will keep increasing by $30 monthly until the 20month.

The amount he will have in her bank in the 20th month will be at when X = 20

= $100+30X

= $100+30(20)

= $100+$600

= $700

This means that her money will be $130 in the first month and will keep increasing until it reaches $700 in the 20th month.

The DOMAIN will be the interval of the time she used in saving. Since she saved for 20months, the domain will be expressed as 0≤m≤20 for mEZ+ where m is the number of month she uses to save.

The Range will represent the amount she saved within the specified time and will be expressed as $100≤A≤$700 for all values of m.

Where $100 is the amount in the account initially and $700 is the amount in the account after 20 months.

The dimensions of the garden that minimize the cost are approximately 8.67 feet by 21.68 feet.

Let's assume the length of the rectangular garden is L and the width is W. Then the area of the garden is:

A = L * W = 188

We want to minimize the cost of enclosing the garden, which is given by:

C = 20L + 10(2L + W) = 20L + 20L + 10W = 40L + 10W

We can use the equation for the area of the garden to express one of the dimensions in terms of the other. For example, we can solve for W:

W = A / L = 188 / L

Substituting this expression for W into the cost equation, we get:

C = 40L + 10(A / L)

Taking the derivative of this expression with respect to L and setting it equal to zero to find the critical point(s):

dC/dL = 40 - 10(A / L^2) = 0

Solving for L, we get:

L^2 = A * 4/10 = 75.2

L ≈ 8.67 feet

Substituting this value of L back into the expression for W, we get:

W ≈ 21.68 feet

Therefore, the dimensions of the garden that minimize the cost are approximately 8.67 feet by 21.68 feet.

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Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

a) The measure of angle S₁ is 120 degrees.

b) The measure of angle Ô₂ is 85 degrees.

c) The measure of angle R₂ is 85 degrees.

d) If APSW is equilateral, then the measure of angle R₁ is 60 degrees.

In the given diagram, we have a cyclic quadrilateral PWRS inscribed in a circle with center O. APSW is an equilateral triangle, and TW is a tangent to the circle at W. We are given that angle WO₁R is 25 degrees. Let's analyze the angles in the diagram:

a) Angle S₁: Since PWRS is a cyclic quadrilateral, the opposite angles in the quadrilateral are supplementary. Therefore, we have:

Angle S₁ + Angle P = 180 degrees.

Since angle P is equal to 60 degrees (as APSW is an equilateral triangle), we can solve for angle S₁:

Angle S₁ + 60 degrees = 180 degrees.

Angle S₁ = 180 degrees - 60 degrees = 120 degrees.

b) Angle Ô₂: Angle Ô₂ is an exterior angle of triangle PWO₁. In a triangle, an exterior angle is equal to the sum of the two interior opposite angles. Therefore, we have:

Angle Ô₂ = Angle P + Angle WO₁.

Since angle P is 60 degrees (as APSW is an equilateral triangle) and angle WO₁ is given as 25 degrees, we can substitute these values:

Angle Ô₂ = 60 degrees + 25 degrees = 85 degrees.

c) Angle R₂: Angle R₂ is an exterior angle of triangle PW₁R. Using the same concept as above, we have:

Angle R₂ = Angle PW₁ + Angle W₁R.

Angle PW₁ is equal to angle P, which is 60 degrees (as APSW is an equilateral triangle). Angle W₁R is given as 25 degrees. Substituting these values, we get:

Angle R₂ = 60 degrees + 25 degrees = 85 degrees.

d) If APSW is equilateral, then all its angles are equal to 60 degrees. Since angle P is 60 degrees, we can conclude that angle R₁ is also 60 degrees.

In summary, based on the given information and the properties of the diagram, we can determine the following angle measurements:

a) Angle S₁ = 120 degrees

b) Angle Ô₂ = 85 degrees

c) Angle R₂ = 85 degrees

d) Angle R₁ = 60 degrees if APSW is equilateral.

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Answer:

Simplifying

(n + 9) + -1(2 + -2n) = 0

Reorder the terms:

(9 + n) + -1(2 + -2n) = 0

Remove parenthesis around (9 + n)

9 + n + -1(2 + -2n) = 0

9 + n + (2 * -1 + -2n * -1) = 0

9 + n + (-2 + 2n) = 0

Reorder the terms:

9 + -2 + n + 2n = 0

Combine like terms: 9 + -2 = 7

7 + n + 2n = 0

Combine like terms: n + 2n = 3n

7 + 3n = 0

Solving

7 + 3n = 0

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-7' to each side of the equation.

7 + -7 + 3n = 0 + -7

Combine like terms: 7 + -7 = 0

0 + 3n = 0 + -7

3n = 0 + -7

Combine like terms: 0 + -7 = -7

3n = -7

Divide each side by '3'.

n = -2.333333333

Simplifying

n = -2.333333333

Step-by-step explanation:

A pound of apples and a pound of oranges each cost $2.50.

Pound is a unit of weight or mass commonly used in the imperial system of measurement. It is equal to 0.453 kilograms and 16 ounces. It is also known as the avoirdupois pound, which is the most commonly used today. In some contexts, the term "pound" may also refer to a unit of currency, the British Pound Sterling (GBP).

This can be determined by subtracting Gina's total cost from Tom's total cost.
Tom's cost was $8.00, and Gina's cost was $5.00, so 8.00 - 5.00 = 3.00. Since Tom bought 3 pounds of apples more than Gina and the same amount of oranges, the cost of the extra apples is $3.00.
Since each pound of apples and oranges costs the same amount,
then $3.00 divided by 3 pounds is $1.00,
so each pound of apples and oranges costs $2.50.

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To write the form of the partial fraction decomposition of the given rational expressions, we need to express them as a sum of simpler fractions. The general form of a partial fraction decomposition is:

f(x) = A/(x-a) + B/(x-b) + C/(x-c) + ...

where A, B, C, etc., are constants and a, b, c, etc., are distinct linear factors in the denominator.

For the rational expression x^2 - 7x:

The denominator has two distinct linear factors: x and (x - 7). Therefore, the partial fraction decomposition form is:

(x^2 - 7x)/(x(x - 7)) = A/x + B/(x - 7)

For the rational expression 6x + 5 / (x + 8):

The denominator has one linear factor: (x + 8). Therefore, the partial fraction decomposition form is:

(6x + 5)/(x + 8) = A/(x + 8)

For the rational expression 20 - 3 / (4x + 3):

The denominator has one linear factor: (4x + 3). Therefore, the partial fraction decomposition form is:

(20 - 3)/(4x + 3) = A/(4x + 3)

In each case, we write the partial fraction decomposition form by expressing the given rational expression as a sum of fractions with simpler denominators. Note that we have not solved for the constants A, B, C, etc., as requested.

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A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.

A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).

The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).

In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.

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Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

Answer:

x = 1/5 ,  and   x = - 1/5

Step-by-step explanation:

25x² – 1 = 0

5²x² - 1² = 0

(5x - 1)(5x + 1) = 0

5x -1 = 0,  5x + 1 = 0

x = 1/5 ,     x = - 1/5

The data described, the number of televisions in different households, is discrete.

discrete data consists of individual values that can be counted and are distinct from one another. In this case, the number of televisions is a discrete variable because it can only take on whole numbers, such as 0, 1, 2, 3, and so on. You cannot have a fractional or continuous number of televisions. Each household will have a specific count of televisions, and there is no intermediate value between each whole number. Additionally, the number of televisions is distinct for each household, meaning that it can differ from one household to another.

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Answer:

a = -3, b = 1

Step-by-step explanation:

1. Plug in the given values into the equations:

a(-1) - b(2) = 1
a(2) + b(-1) = -7

2. Isolate a in the first equation:

a(-1) - b(2) = 1   =   a · -1 - b · 2 = 1

-a - 2b = 1

-a -2b+2b = 1+2b

-a = 1 + 2b

\(\frac{-a}{-1} =\frac{1}{-1} +\frac{2b}{-1}\)

a = -1 - 2b

3. Substitute "a = -1 - 2b" in for a in the second equation:

(-1 - 2b)2 + b(-1) = -7

4. Simplify:

-2 - 4b + b(-1) = -7

-2 - 4b -b = -7

-2 -5b = -7

5. Isolate for b:

-2+2 - 5b = -7+2

-5b = -5

\(\frac{-5b}{-5} =\frac{-5}{-5}\)

b = 1

6. Substitute the b value into an equation to solve for a:

a = -1 -2 · 1

a = -3 · 1

a = -3

hope this helps!

Bonds that do not have any assets of the issuer pledged as collateral and are often referred to as junk bonds are known as unsecured bonds.

Unsecured bonds, also known as non-collateralized bonds or debentures, are debt securities issued by companies or governments that do not have any specific assets pledged as collateral. These bonds rely solely on the creditworthiness and reputation of the issuer for repayment. They are considered riskier investments compared to secured bonds because in the event of default, there are no specific assets backing the bondholders' claims.

The term "junk bonds" is often used to describe high-yield bonds that carry a higher risk of default. These bonds are typically issued by companies with below-price-grade credit ratings. The term "junk" refers to the perceived low quality or higher risk associated with these bonds.

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Answer:

greater

Step-by-step explanation:

way greater because if youre going to the negatives, youre subtracting farther into 0, which brings you into the negatives

Answer:

greater than

Step-by-step explanation:

any positive number will always be greater than any negative number

Answer:

8:9 = eight to nine

Step-by-step explanation:

16:18 - divide each by 2 in order to simplify

= 8:9