Evaluate g(x) = 3x when x= -2,0, and 5.

For a confidence interval, she would use her sample mean, hence the mean of 6.7 pounds.

In the context of this problem, we use the t-distribution instead of the z-distribution, as we have the standard deviation for her sample.

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the parameters are defined as follows:

From the first bullet point, we get that she should use her sample mean for the calculation of the confidence interval, that is, the mean of 6.7 pounds should be used.

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The linear equation in the form p = mn + b that gives the price p they can change charge for n- shirts is; p = (9/1000)n - 9.

As per the given question;

number of shirts = n

The charge per shirt = p.

The equation describing the relation is;

p = mn + b

The price of 6000 shirts = $81.

Put the value is equation;

81 = 6,000m + b  .....eq 1

The price of 10,000 shirts = $45.

45 = 10,000m + b .....eq 2

Solving eq 1 and eq 2 by elimination method.

m = 9/1000

Put the value of m in eq 2 and find b.

b = -9

Now, put the value of b and m in the equation.

p = (9/1000)n - 9

Thus, the equation in the form p = mn + b that gives the price p they can change charge for n shirts is; p = (9/1000)n - 9.

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With a 95% confidence interval, the average is between 13.4667 and 26.5333.

Confidence interval is the measure of the degree of uncertainty or certainty in a sampling method. It is equal to the sample mean, plus or minus the margin of error (z value multiplied by standard deviation divide by the square root of the sample size).

CI = x ± z(σ/√n)

where CI = confidence interval

x = mean

σ = standard deviation

n = sample mean

z = z value at the confidence interval

The corresponding z value at 95% confidence interval is 1.96.

Substitute the given into the formula and solve for CI.

CI = x ± z(σ/√n)

CI = 20 ± (1.96)(10/√9)

CI = 20 ± (1.96)(10/3)

CI = 20 ± 6.5333

CI = (13.4667, 26.5333)

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The trigonometric expression sin(30°) + cos(60°) is equal to 1.

What is trigonometry?

Trigonometry is the study of relationships between angles and side lengths of triangles. The use of geometry in astronomical studies gave rise to the field in the Hellenistic era in the third century BC. Greek mathematicians focused on chord calculation, whereas Indian mathematicians created the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine.

There are two trigonometric ratios in the given expression,

sin(30°) and cos(60°).

Here, sin(30°) is equal to the value 1/2

i.e. sin(30°) = 1/2

And, cos(60°) is equal to the value 1/2

i.e. cos(60°) = 1/2

Adding these equations, we get

sin(30°) + cos(60°) = 1/2 + 1/2 = 2/2 = 1

therefore, on solving the given trigonometric expression we get answer value 1.

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Answer:

42

Step-by-step explanation:

This triangle is right angled so we know it has a 90-degree angle at the corner with the box.

All angles add up to 180 in a triangle.

180 = 90 + 48 + x

180 - 90 = 48 + x

90 - 48 = x

x = 42

Hope that helps

Answer:

(x + 2)² - 11, so a = 2 and b = 11

Answer:

x = -21

Step-by-step explanation:

The first you have to do is distribut the -8 to the -14 and x. Once you do that, you get 280 = 112 - 8x. Next, you need to subtract 112 from each side, so you get 168 = -8x. Now, you divide -8 from each side and you get -21 = x. Hope this helps!

Answer:

D 5

Step-by-step explanation:

Solve the inequality

5-2x ≥-3

Subtract 5 from each side

5-2x-5 ≥-3-5

-2x ≥-8

Divide by -2, remembering to flip the inequality

-2x/-2 ≤-8/-2

x ≤4

The only number not less than or equal to 4 in the choices is 5.

5 is not a solution

Answer:

Answer D is correct

Step-by-step explanation:

First, let us solve for x.

[tex]5 - 2x \geqslant - 3[/tex]

First, subtract 5 by both sides.

[tex] - 2x \geqslant - 3 - 5 \\ - 2x \geqslant - 8[/tex]

Divide both sides by -2.

[tex]x \leqslant 4[/tex]

Now, let us identify the equality sign and write the solutions of it.

[tex] \sf \leqslant \: \: \rightarrow \: \: x \: is \: less \: than \: or \: equals \: to \: 4[/tex]

Solutions

x = { 4, 3, 2, 1, 0...}

Accordingly, as 5 is greater than 4, 5 is not a solution for this given inequality.

Answer:

3

Step-by-step explanation:

You have 3 lots of 2 1/4 to get as close to 7 7/8 without going over it. Meaning thats how many batches you can make.

The true statement is the range of Mrs Plum's class is 14 greater than the range of Mr Scarlet's class.

A box plot is a graph that is used to describe a dataset. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the whiskers is the range.

Range is used to measure the variation of a dataset. It is the difference between the maximum number and the minimum number.

Range = maximum number - minimum number

Range of Miss Scarlet's class = 98 - 65 = 33

Range of Miss Plum's class = 98 - 51 = 47

Difference in range = 47 - 33 = 14

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The correct option is A :the number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils.

Given cost of one pencil is $3

Thus when we have to find the cost of three pencils we will multiply it with 3 and would be able to get the required amount that is $ 9.

Thus we can say that the number of pencil and cost has direct relationship.

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The statement "The sum of the slopes of line b and c is 0" is not always true.

Given:

Lines a and b are parallel.

Line c is perpendicular to both line a and line b.

The reason is that a perpendicular line has a slope of -1 /m when one line has a slope of m. Alternatively put, the slopes are negative reciprocals of one another.

This is because two lines that are parallel have the same slope.

This is because even if the two lines are perpendicular on adding their slopes together the outcome would not be 0. For instance, if b has a slope of 2, then c will have a slope of -1/2, and their sum will be 3/2.

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Answer:

3 1/2

Step-by-step explanation:

each dozen needs 1/2 cup of chocolate chips so 1/2 times 7 = 3 1/2

Answer:

18.75

Step-by-step explanation:

I'm not exactly sure.

I divided 30 by 2 and 45 by 2 and took both answers and added them together and then took the sum of that and divided it by 2.

Answer: 5= 4x + 8

             -8           -8

-3= 4x

the answer is x = 0.75

i don't know if I'm right if I am not I am sorry

Answer:

a.25

b.26

c. Eva as her unit rate is faster than Sarah

ask me if u want me to explain

The inequality shows that the number of visits that Janelys needs at least 165 points for a free movie ticket is 12.

From the information, Janelys has a points card for a movie theater and she receives 20 rewards points just for signing up and earns 12.5 points for each visit to the movie theater.

The number of visits that are needed to earn at least 165 points will be illustrated as x. This will be:

20 + 12.5x >= 165

Collect like terms

12.5x >= 165 - 20

12.5x >= 145

Divide

x >= 145 / 12.5

x >= 11.6

Therefore, she needs at least 12 visits.

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Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket. How may visits are needed?

Answer:

Yes the other person is correct

Step-by-step explanation:

oop their answer got deleted

my bad

Football scores of Ali and Mohammad are 213 and 207 respectively.

Given,

Sum of Ali and Mohammad's football score is 420.

Difference between Ali's football score and Mohammad's football score is 6.

Then,

A - B = 6  ⇒Equation1

Where A = Ali's football score, and B= Mohammad's football score

Let's assume,

Ali's football score =

Mohammad's football score =

Sum of Ali's football score and Mohammad's football score:

A + B = 420 ⇒Equation2

After subtracting Equation2 from Equation 1

(A+B) - (A-B) = 420 - 6

A + B - A + B = 414

Since first A is positive and second A is negative, they will cancel out each other.

2B = 414

B = 207

After putting value of B in Equation2,

A + 207 = 420

A = 420- 207

A = 213

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Answer: 20.8

Step-by-step explanation:

(8*5.2)/2 so 8/2=4*5.2=20.8

Answer: 20.8 [tex]cm^{2}[/tex]

Step-by-step explanation:

Hello! So...

We are given the following to simplify:

[tex]7\sqrt{28x^6} -5\sqrt{63x^6}[/tex]

_________________________________________________

To solve this, we must simply simplify.

[tex]7\sqrt{28x^6} =14\sqrt{7} x^3[/tex]

[tex]5\sqrt{63x^6}=15\sqrt{7}x^3[/tex]

[tex]=14\sqrt{7}x^3-15\sqrt{7}x^3[/tex]

Now, add the similar elements:

[tex]14\sqrt{7}x^3 -15\sqrt{7} x^3=-\sqrt{7}x^3 \\[/tex]

Now, considering we are assuming all variables are positive in this situation, we need to convert the negative into a positive solution.

[tex]=-\sqrt{7}x^3[/tex]

[tex]= x^3\sqrt{7}[/tex]

^Hence, our solution.^

______________________________________________________

Hope this helps! If so, please lmk! Thanks and good luck!

Answer:

-3x+y = -3

Step-by-step explanation:

First, I would write this in the point slop form of a line and the translate it into the standard form of a line.

[tex]y_{1}[/tex] - y = m([tex]x_{1}[/tex] -x)  If the slope from of a line.  Put in the x, y and the slope.  You call the gradient, what I would call the slope.

y - 3 = 3(x -2)    Distribute the 3

y - 3 = 3x -6  Subtract 3 from both sides

-3x + y - 3 = -6  Add 3 to both sides

-3x + y = -6

Step-by-step explanation:

y = kx

3 = k × 12

.: k = 12/3 = 4

Inputting that to when y = 96 Ibs.

We have:

96 = 4 × x

96 = 4x

.: x = 96/4

x = 24 realms.

Answer:

72[tex]units^{2}[/tex]

Step-by-step explanation:

See pictures

Answer:

Step-by-step explanation:

A=25xB
B=18xC
A=3600cm

B=A/25
B=3600/25
B=144
C=B/18
C=144/18
C=8

Answer:

Step-by-step explanation:

4 1/7 = 29/7

6 = 42/7

What you need to add to 4 1/7 is:

6 - 4 1/7

42/7 - 29/7

13/7.

In mixed fractions, it's 1 6/7.

Using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.

So, the total cost of hair coloring:

Now, calculate as follows:

Therefore, using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.

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The complete question is given below:
Could Mrs.Davis and her two sisters get their hair colored for less than $100 if they include a $10 tip explain also the cost is $28.95 for the hair coloring.

The capacity of 9 cm cylinder is 435 mililiters.

The capacity of 3 cm cylinder is 145 mililiters.

For the given question;

The capacity of larger cylinder; 15 cm height is 725 millilitres.

Volume of 15 cm height cylinder = 725 cu. cm.

Thus,

πr²h = 725

Put h = 15 cm

πr²15 = 725

r² = 725/ 15π

r² = 145/3π

The volume of 9 cm cylinder =   πr²9

Put the value of r² = 145/3π

V(h = 9 cm) =  π×145×9/3π

V(h = 9 cm) = 435 cu. cm.

The volume of 3 cm cylinder =   πr²3

Put the value of r² = 145/3π

V(h = 3 cm) =  π×145×3/3π

V(h = 3 cm) =  145 cu. cm.

The capacity of 9 cm cylinder is 435 mililiters.

The capacity of 3 cm cylinder is 145 mililiters.

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Answer:

B) Observational

Explanation:

Observational studies are studies where the researchers only observe the variables and don't make changes. When the political pollster reports the percentage, it only observes the decision of the people but they can't change what makes a person select one candidate or the other.