Nancy is studying constellations in science class. Two things are strongly supported by all random samples of the number of stars in a constellation. Most constellations have from three to seven stars in them, and very few constellations have more than nine stars in them. Which of the following could be random samples of the number of stars in a constellation?

The total number of signs require to sell is 21 to earn $882.

Let's start by using the information given to write an expression for Jim's weekly income, I, as a function of the price per sign, x.

The number of signs Jim sells per week is given by:

[tex]63 - x[/tex]

And since Jim charges x dollars for each sign, his weekly income is:

[tex]I(x) = x(63 - x)[/tex]

Now we can use this expression to solve the problem. We want to find the smallest number of signs Jim can sell to have an income of $882 in one week.

In other words, we want to find the value of x that makes I(x) equal to $882. So we can set up the equation:

[tex]x(63 - x) = 882[/tex]

Expanding the left-hand side:

[tex]63x - x^2 = 882[/tex]

Rearranging and putting in the standard quadratic form:

[tex]x^2 - 63x + 882 = 0[/tex]

Now we can use the quadratic formula to solve for x:

[tex]x = \frac{-b \pm \sqrt{(b^2 - 4ac})} { 2a}[/tex]

where a = 1, b = -63, and c = 882. Plugging in these values:

[tex]x = \frac{63 \pm \sqrt{(63^2 - 4*1*882})} { 2*1}[/tex]

[tex]x = \frac{63 \pm sqrt(441)} {2} \\x = \frac{63 \pm 21}2[/tex]

So the two possible values of x are:

[tex]x = 42 \\ x = 21[/tex]

Of these, the only value that makes sense for the problem is x = 42, since we can't sell a negative number of signs.

Therefore, the smallest number of signs Jim can sell to have an income of $882 in one week is:

63 - x = 63 - 42 = 21 signs.

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The y-coordinate of the solution of the equation will be 2.

Given that:

x - 2y = 4

x + 3y = 14

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If the slopes are different then the lines are intersecting.

And if the slopes are different then the system has one solution.

The lines are drawn on the graph and their intersection point will be (8, 2).

The y-coordinate of the solution of the equation will be 2.

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1) Where the above conditions are given, our derived t-value is -2.67 which is less than the critical t-value of -1.753. Hence we must reject the null hypothesis.

2) The results of the p-value analysis shows that we must conclude that the water from the area is not safe to drink as far as EPA stndards of less thatn 700 ppt of PFOA is concerned.

The null hypothesis is that the mean concentration of PFOA in drinking water is 700 ppt or higher.

The alternate hypothesisis that drinking water has less than 700 ppt of PFOA on average.

H0: μ ≥ 700
Ha: μ  ≤ 700

Using one tailed t-test because the alt-hypothesis is one-sided:

t = (x - μ) / (s / √n)
= (625 - 700) / (150 / √16)
= -2

where n is the sample size, n is the sample size's square root, n is the sample size, x is the sample mean, is the population mean, s is the sample standard deviation.

The crucial t-value using a t-distribution table with 15 degrees of freedom (n-1) and a 5% threshold of significance is -1.753. We reject the null hypothesis since our computed t-value of -2  is lower than the crucial t-value of -1.753.

The likelihood of attaining a t-value of -2 or less with 15 degrees of freedom may also be used to compute the p-value. We determine the p-value to be 0.008 using a t-distribution table or calculator. We reject the null hypothesis since the p-value is less than the significance level of 0.05.

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Check the picture below.

[tex]2x+3=\cfrac{(176-2x)-47}{2}\implies 4x+6=(176-2x)-47 \\\\\\ 4x+6=129-2x\implies 6x+6=129\implies 6x=123 \\\\\\ x=\cfrac{123}{6}\implies x=\cfrac{41}{2}\implies x=20\frac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ 2\left( \frac{41}{2} \right)+3\implies 41+3\implies 44^o\impliedby \measuredangle MNO[/tex]

A pound of sugar will cost $1.59 in 2022

From the question, we have the following parameters that can be used in our computation:

Initial, a = 0.43

Rate, r = 3.6%

The equation of the function is represeted as

f(x) = a * (1 + r)^x

So, we have

f(x) = 0.43 * (1 + 3.6%)^x

2022 is 37 years from 1985

So, we have

f(x) = 0.43 * (1 + 3.6%)^37

Evaluate

f(x) = 1.59

HEnce, the cost is $1.59

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Answer:

(3x + 2) (x + 2)

Step-by-step explanation:

general form = ax² + bx + c

3x² + 8x + 4

a = 3

b = 8

c = 4

6 × 2 = a . c = 4 × 3 = 12

6 + 2 = b = 8

3x² + 6x +2x + 4

3x (x + 2) + 2 (x + 2)

(3x + 2) (x + 2)

Answer:

Step-by-step explanation:

You want to know which of the relations shown is a function.

The rule is pretty simple. A relation is a function if each element of the domain maps to exactly one range value.

If an element of the domain maps to two or more range values, the relation is not a function.

In the attachment, we have identified what you would look for to determine that the relation is not a function. The map of a function has one arrow from each domain value. The ordered pairs of a function have no repeated first-values.

Answer:

The answer is A. 4 < x < 12.

Step-by-step explanation:

By isolating the absolute value expression:

9|x – 8| < 36

|x – 8| < 4

Break this down into two separate inequalities, one without the absolute value:

x - 8 < 4 or x - 8 > -4

Simplifying each one:

x < 12 or x > 4

Now we can combine these two inequalities with an "and" statement, since the value of x must satisfy both inequalities:

4 < x < 12

Therefore, the solution to the inequality 9|x – 8| < 36 is 4 < x < 12.

The correct answer is option 3 i.e. At the 0.05 level of significance, the data provides sufficient evidence to conclude that the difference between the averages is real.

What is a two-sample test?

A two-sample test, also known as a two-sample hypothesis test, is a statistical test used to compare the means of two different groups. The test determines whether there is a significant difference between the means of two populations or groups based on the samples drawn from each group. The test is typically used when the samples are independent and the data is continuous. The goal of the test is to determine whether the observed difference between the two sample means is statistically significant or whether it is simply due to chance variation.

To perform an independent two-sample test, we need to formulate our null and alternative hypotheses:

Null hypothesis: The mean hours of pay for freshman at public universities is equal to the mean hours of pay for freshman at private universities.

Alternative hypothesis: The mean hours of pay for freshman at public universities is not equal to the mean hours of pay for freshman at private universities.

We can use a two-sample t-test to compare the means of the two groups, assuming unequal variances since the sample sizes and standard deviations are different.

Using a statistical software or calculator, we can find the test statistic and p-value:

Test statistic: t = -9.767

p-value: < 0.001

Since the p-value is less than the level of significance (0.05), we reject the null hypothesis and conclude that the mean hours of pay for freshman at public universities is significantly different from the mean hours of pay for freshman at private universities.

Therefore, the answer is: At the 0.05 level of significance, the data provides sufficient evidence to conclude that the difference between the averages is real.

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The price elasticity of demand measures the responsiveness of the quantity demanded to changes in the price of a product. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Using the given information, we can calculate the price elasticity of demand as follows:

Percentage change in price = 50%

Percentage change in quantity demanded = -25% (since it decreased)

Price elasticity of demand = (-25%) / (50%) = -0.5

Since the price elasticity of demand is negative, this means that pizza is a normal good (as the increase in price led to a decrease in quantity demanded). The magnitude of the elasticity (-0.5) indicates that the demand for pizza is relatively inelastic, meaning that a 50% increase in price led to only a 25% decrease in quantity demanded.

An equation that shows the cost of a pack of test tubes, t, in terms of the cost of a set of beakers is 10t = b - 4.

An equation with t and b that describes this situation is 8t + 12b = 348.

An equation that shows this substitution is 8t + 12(10t + 4) = 348.

The value of b is equal to $27.4.

The amount of money which the school paid for a set of beakers is $27.4 and $2.34 for a pack of test tubes.

In order to write a linear equation to describe this situation, we would assign variables to the cost of a pack of test tubes and the cost of a set of beakers respectively, and then translate the word problem into a linear equation as follows:

Since a pack of 10 test tubes costs $4 less than a set of nested beakers, a linear equation which can be used to model the cost of a pack of test tubes with respect to the cost of a set of beakers is given by;

10t = b - 4    .....equation 1.

For t and b, a linear equation which can be used to model the total cost is given by;

8t + 12b = 348      .....equation 2.

By making b the subject of formula in equation 1, we have;

b = 10t + 4

By substituting the value of b, we have;

8t + 12(10t + 4) = 348

8t + 120t + 48 = 348

128t = 300

t = 2.34

b = 10(2.34) + 4

b = 27.4

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Step-by-step explanation:

To calculate your after-tax return on investment, we need to know your tax rate. Let's assume your tax rate is 20%.

Your total income from the salary and interest is:

$29,000 + $125 = $29,125

Your tax liability on this income is:

$29,125 * 20% = $5,825

So your after-tax income is:

$29,125 - $5,825 = $23,300

Your after-tax return on the investment is:

$125 / $23,300 = 0.0054 or 0.54%

Therefore, your after-tax return on the investment is 0.54%.

After considering the given data we conclude that the cubic feet of natural gas used by world  from 1990 to 2020 is 426,000 billion cubic feet.

It is known to us that the demand for natural gas was growing exponentially at the rate of 7% per year since 1990. Then, we can applu the formula for exponential growth:
[tex]A = P(1 + r)^t[/tex]

Here,
A = amount after time t,
P = initial amount (at time t=0),
r = annual growth rate expressed as a decimal,
t= time in years.
For the given case,
P = 70223 billion cubic feet,
r = 0.07 (7% growth rate),
t = 2020 - 1990 = 30 years.
Staging these values into the formula gives:
A = 70223(1 + 0.07)³⁰
A ≈ 426,000 billion cubic feet

Hence, if there is a higher requirement for natural gas and it  grows at a rate of 7% per year from 1990 to 2020, the world will have consumed approximately 426,000 billion cubic feet of natural gas by 2020.

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Answer:

a polygon has ten sides and it is known as decagon

Using geometric sequence, we can find that the recursive formula will be:

[tex]a_{n}[/tex] = (-2) ([tex]a_{n-1}[/tex])

[tex]a_{1}[/tex] = 5

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios. In other words, each phrase in a geometric series is multiplied by a constant to produce the following term.

Here in the question,

The given expression is in the form of the explicit formula of a geometric sequence.

f(n) = [tex]a(r)^{n-1}[/tex]

Where 'a' is the first term of the sequence.

Here, r is the common ratio.

Recursive formula of a geometric sequence is,

[tex]a_{n}[/tex] = [tex](a_{n-1})[/tex] × [tex]r^{n-1}[/tex]

[tex]a_{n}[/tex] = (-2) ([tex]a_{n-1}[/tex])

Where, [tex]a_{1}[/tex] = 5

So, the recursive formula will be = [tex]a_{n}[/tex] = (-2) ([tex]a_{n-1}[/tex]).

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The number line shows the solution to the inequality is number line going from negative 8 to positive 2. An open circle is at negative 3.

We are given the inequality as;

y - 2 > -5

Solving an inequality involves finding the set of values that satisfy the inequality. This means that any value of x that is greater than 3 will satisfy the inequality.

We can isolate x:

y - 2 > -5

y  > -5+ 2

y  > -3

So, the solution is the number less than 1 but not 1. In the number line this number line going from negative 8 to positive 2. An open circle is at negative 3.

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The value of x is given as follows:

x = 7.

Similar triangles are triangles that share these two features listed as follows:

Considering the similar triangles, the equivalent side lengths are given as follows:

Hence we apply the proportional relationship among the equivalent side lengths to obtain the value of x as follows:

8/14 = (2x - 2)/3x

14(2x - 2) = 8(3x)

28x - 28 = 24x

4x = 28

x = 7.

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Answer:

[tex]m = \frac{ - 2 - 3}{5 - 1} = - \frac{5}{4} [/tex]

The probability of randomly selecting the number 1 is P = 0

Here we randomly select a number from the set:

S = {4, 7, 10, 13, 16, 19}

And we want to find the probability that the number is 1.

To get this, we need to take the quotient between the number of ttimes that the number 1 appears on the set, and the total number of numbers in the set.

Here you can see that we have 6 numbers in our set, and the number 1 does not appear, then the probability is:

P = 0/6 = 0

It makes sense, if the 1 does not belong to the set, we never can randomly select it.

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Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

a. client review and client growth percentage metrics likely relate to a strategic objective to satisfy and increase clients. The market share and profit margin metrics likely relate to a strategic objective to increase profits.

b.

New clients during the month

7

Lost clients during the month

(4)

Increase in clients

3

Total clients at the beginning of last month

÷ 72

Client growth percentage last month

4.17%

target met

c.

Number of 5-star reviews

55 × 5 =

275

Number of 4-star reviews

10 × 4 =

40

Number of 3-star reviews

3 × 3 =

9

Number of 2-star reviews

1 × 2 =

2

Number of 1-star reviews

1 × 1 =

1

Sum total of stars

327

Total number of reviews

÷ 70

Average online client satisfaction rating

4.67

stars, target

not met

d.

Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

• Invite clients to provide additional feedback through a brief online survey

• Have the company owner send a personal apology to any clients providing a review of 2 stars or less, and offer them some kind of compensation; also ask for their feedback regarding what caused them dissatisfaction

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Multiplying radical expressions √6(√2 + √6) involves multiplying the coefficients and then multiplying the radicands. Therefore, the final answer is 2√12 + 6√6.

The multiplication of two radicals can be done by using the product rule which states that the product of two radicals is equal to the product of the coefficients and the product of the radicands.

Multiplying radical expressions involves multiplying the coefficients and then multiplying the radicands.

In this case, the coefficients are 1 and the radicands are √6 and (√2 + √6). The first step is to multiply the coefficients, which is 1*1 = 1.

The second step is to multiply the radicands, which is √6*(√2 + √6).

In this case, the product of the radicands is (√2 * √6) + (√6 * √6).

This can be simplified to 2√12 + 6√6.

Therefore, the final answer is 1*(2√12 + 6√6) = 2√12 + 6√6.

In summary, multiplying radical expressions √6(√2 + √6) involves multiplying the coefficients and then multiplying the radicands. Therefore, the final answer is 2√12 + 6√6.

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The value of sides of rectangle = 5

And, For triangle = 4

Given that;

To solve the shape equation puzzle.

And, Rewrite the puzzle as a system of equations using the variables s

and t.

Now, By figures we get;

1) Let a number represented by rectangle is, 5

And, A number represented by triangle is, 4

Hence, We get;

5 + 4 = 9

5 - 4 = 1

2) Let us assume that;

Number of sides for rectangle = s

And, For triangle = t

Hence, We can formulate;

s + t = 9

s - t = 1

Add both equations;

2s = 10

s = 5

And., s - t = 1

5 - t = 1

5 - 1 = t

t = 4

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The number that is 1.5 standard deviations below the mean is approximately 0.631.

Standard deviation is a measure of the amount of dispersion in a set of data. It measures how much the data values deviate from the mean of the data set. A smaller standard deviation indicates that the values tend to be close to the mean, while a larger standard deviation indicates that the values are more spread out from the mean. Standard deviation is commonly used in statistical analysis to measure the spread of a data set and to help identify outliers.

To find the number that is 1.5 standard deviations below the mean, we first need to calculate the mean and standard deviation of X.

The mean is:

μ = Σ(x * f) / n = (0*3 + 1*15 + 2*30 + 3*27 + 4*11 + 5*7 + 6*7) / 100 = 2.77

The variance is:

σ^2 = Σ[(x - μ)^2 * f] / (n-1)

=  [(0-2.77)^2*3 + (1-2.77)^2*15 + (2-2.77)^2*30 + (3-2.77)^2*27 + (4-2.77)^2*11 + (5-2.77)^2*7 + (6-2.77)^2*7] / (100-1)

= 2.0346

The standard deviation is:

σ = [tex]\sqrt{2.0346}[/tex] = 1.426

Now we can find the number that is 1.5 standard deviations below the mean:

2.77 - 1.5(1.426) = 0.631

Therefore, the number that is 1.5 standard deviations below the mean is approximately 0.631.

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The formula for the curved surface area of a cylinder is given by:

Curved Surface Area = 2 × pi × radius × height

where pi is the mathematical constant approximately equal to 3.14, radius is the distance from the center of the circular base to the edge of the cylinder, and height is the distance between the two circular bases of the cylinder.

Given, the radius of the cylinder is 7 cm and the height is 2 cm, we can substitute these values in the above formula to find the curved surface area:

Curved Surface Area = 2 × (22/7) × 7 cm × 2 cm

= 2 × 22 × 2 cm^2

= 88 cm^2

Therefore, the curved surface area of the cylinder is 88 square centimeters.

I'm sorry to disturb but can you please mark me BRAINLEIST if this ans is helpfull

Answer:

a. 2 (numbers less than 0 are negative)

b. 4  (numbers greater than and including 0 are 'not negative')                                                                                  

The expression of the inequality word problems for each question is: As expressed below

A) x is negative. This can be expressed as;

x < 0

B) y is non-negative. This can be expressed as;

y > 0

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The solution by completing the square for the equation x² + 3x = 24 is x ≈ 3.55 or x ≈ -6.55, which is (3.55, -6.55) when rounded to the nearest hundredth. The correct answer is A).

To solve by completing the square, we need to take half of the coefficient of x, square it, and add and subtract it to both sides of the equation. Then, we can factor the left side and solve for x.

Starting with the equation

x² + 3x = 24

First, we add and subtract (3/2)² = 2.25 to both sides

x² + 3x + 2.25 - 2.25 = 24

(x + 1.5)² = 26.25

Taking the square root of both sides

x + 1.5 = ±√26.25

x = -1.5 ± √26.25

Rounding to the nearest hundredth, we get

x ≈ 3.55 or x ≈ -6.55

So the answer is (3.55, -6.55). The correct option is A).

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Answer:

A

Step-by-step explanation:

So the domain of m(x) is: Domain: x ∈ (-∞,-8) ∪ (-8,-3) ∪ (-3,5) ∪ (5,∞). So, as x approaches -3, m(x) approaches 4/3. So, the x-intercepts of m(x) are x=5 and x=-8. So, the y-intercept of m(x) is y=-32/3.

A function is a mathematical relationship between two sets of numbers, where each element in the first set (called the domain) is paired with a unique element in the second set (called the range). In other words, it is a rule or mapping that assigns each input value in the domain to exactly one output value in the range. Functions are often written in the form f(x) = y, where f is the name of the function, x is the input value, and y is the output value.

Here,

1. The denominator of the rational function cannot be equal to zero. Thus, x cannot be equal to -3 and x cannot be equal to 5 or -8, as those are the roots of the denominator. So the domain of m(x) is:

Domain: x ∈ (-∞,-8) ∪ (-8,-3) ∪ (-3,5) ∪ (5,∞)

2. To find the limit of m(x) as x approaches -3, we can simply substitute -3 for x in the function:

m(x) = (4(x-5)(x+8))/(x²-2x-15)

m(-3) = (4(-3-5)(-3+8))/((-3)²-2(-3)-15)

m(-3) = 32/24

m(-3) = 4/3

3. To describe the end behavior of m(x), we can look at the degree of the numerator and denominator. The degree of the numerator is 2 and the degree of the denominator is also 2. Thus, the end behavior of m(x) is:

As x approaches positive or negative infinity, m(x) approaches the horizontal asymptote y=4/1 or y=4.

4. To find the x-intercept, we set m(x) equal to zero and solve for x:

(4(x-5)(x+8))/(x²-2x-15) = 0

4(x-5)(x+8) = 0

x = 5 or x = -8

So, the x-intercepts of m(x) are x=5 and x=-8.

To find the y-intercept, we set x equal to zero and simplify:

m(0) = (4(0-5)(0+8))/(0-2(0)-15)

m(0) = -160/15

m(0) = -32/3

So, the y-intercept of m(x) is y=-32/3.

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maximillian walks 0.6 mile each day. He would walk 60 miles in =60/0.6 = 100 days

Answer:

He will have 60 miles in 100 days

Step-by-step explanation:

You only have to divide 60 by 0.6

[tex]60 / 0.6=100[/tex]

Hope This Helps :)

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