(-1, 4) and (0,-1) writing out linear equations giving two points

Answer:

(a) A 95% confidence interval for the mean score of all New Jersey third graders is [56.41, 59.59] .

(b) A 90% confidence interval for the difference in mean scores between Iowa and New Jersey is [3.363, 4.637]  .

(c) Yes, we are 90% confident that the population means for Iowa and New Jersey students are different.

Step-by-step explanation:

We are given that a new standardized test is given to 100 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 58 points and the sample standard deviation sY is 8 points.

(a) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~  \(t_n_-_1\)

where, \(\bar X\) = sample average score = 58 points

             s = sample standard deviation = 8 points

            n = sample of third-grade students = 100

             \(\mu\) = population mean score of all New Jersey third graders

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, a 95% confidence interval for the population mean, \(\mu\) is;

P(-1.987 < \(t_9_9\) < 1.987) = 0.95  {As the critical value of t at 99 degrees of

                                                 freedom are -1.987 & 1.987 with P = 2.5%}    P(-1.987 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 1.987) = 0.95

P( \(-1.987 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.987 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-1.987 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.987 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-1.987 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+1.987 \times {\frac{s}{\sqrt{n} } }\) ]

                                       = [ \(58-1.987 \times {\frac{8}{\sqrt{100} } }\) , \(58+1.987 \times {\frac{8}{\sqrt{100} } }\) ]

                                       = [56.41, 59.59]

Therefore, a 95% confidence interval for the mean score of all New Jersey third graders is [56.41, 59.59] .

Now, the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and a sample standard deviation of 11 points.

(b) Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                               P.Q.  =  \(\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\)  ~  \(t__n_1_+_n_2_-_2\)

where, \(s_p = \sqrt{\frac{(n_1-1)\times s_1 + (n_2-1)\times s_2}{n_1+n_2-2} }\)

                = \(\sqrt{\frac{(200-1)\times 11 + (100-1)\times 8}{200+100-2} }\) = 3.163

Here for constructing a 90% confidence interval we have used a two-sample t-test statistics because we don't know about population standard deviations.

So, a 90% confidence interval for the difference in two population means, (\(\mu_1-\mu_2\)) is;

P(-1.645 < \(t_2_9_8\) < 1.645) = 0.90  {As the critical value of t at 298 degrees of

                                                    freedom are -1.645 & 1.645 with P = 5%}    P(-1.645 < \(\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) < 1.645) = 0.90

90% confidence interval for (\(\mu_1-\mu_2\)) = [ \({(\bar X_1-\bar X_2) -1.645\times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) , \({(\bar X_1-\bar X_2) +1.645\times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) ]

= [ \({(62-58) -1.645\times {3.163 \times \sqrt{\frac{1}{200}+\frac{1}{100} } }\) , \({(62-58) +1.645\times {3.163 \times \sqrt{\frac{1}{200}+\frac{1}{100} } }\) ]

= [3.363, 4.637]

Therefore, a 90% confidence interval for the difference in mean scores between Iowa and New Jersey is [3.363, 4.637]  .

(c) Yes, we are 90% confident that the population means for Iowa and New Jersey students are different because in the above interval 0 is not included.

Answer

Option C is correct.

(g o f)(4) = 196

Step-by-step Explanation

f(x) = 3x

g(x) = (x + 2)²

We are then told to find

(g o f)(4)

We need to first interprete what (g o f) means

(g o f) refers to writing g(x) with f(x) replacing x. That is, f(x) replaces all the x that the function given by g(x) has.

(g o f) = g[f(x)]

g(x) = (x + 2)²

g[f(x)] = [f(x) + 2]²

Recall that f(x) = 3x

g[f(x)] = [3x + 2]²

We can then go further now to obtain (g o f)(4)

(g o f)(x) = g[f(x)] = [3x + 2]²

(g o f)(4) = [3(4) + 2]²

= [12 + 2]²

= 14²

= 196

Hence, option C is correct.

(g o f)(4) = 196

Hope this Helps!!!

The required net price using the net price factor is given as  $1829.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A catering company buys some items with a list price of $5,000. The supplier extends trade discount rates of 45/30/5,

Net price is given as,
net price = 5000 × [1 - 0.45] × [1 - 0.30] × [1 - 0.05]
net price = $1829

Thus, the required net price using the net price factor is given as  $1829.

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Answer:

b

Step-by-step explanation:

can you help me with my question

Answer:

The answer is B

Step-by-step explanation: Hope I helped

Answer:

67 math, 142 history

Step-by-step explanation:

lets say the number of math textbooks was x and the number of history textbooks is y. we have x+y=209 and x=y-75. we can plug the second equation into the first to get y-75+y=209. simplfy to get 2y=284 so y=142. since x=y-75, x=67

Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

Answer:

There is no table, but here's a formula;

48 miles multiplied by x amount of gallons

Step-by-step explanation:

Answer: I dont have the full answer, but this is what i could figure out.

Step-by-step explanation:

3.01 gallon per minute

60 minutes in an hour

3.01 times 60= 180.6

180.6 times 1.85= 334.11

I do not know what to do after this, I wish I could help more, but I hope someone or yourself can figure out the rest. Good luck!

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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Answer:

expected value is the mean : 10.5

Standard error for the sampling distribution : 0.375

it has a bell-shaped curve  with 99.7%  of the values between  9.375  and 11.625

Step-by-step explanation:

Answer:

3. 9 3/5

6. 4 3/5

Step-by-step explanation:

The perimeter of the figure is 4(π + 9)ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Given is a 2 - D figure as shown in the figure attached.

We can write the perimeter as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P =  (4π) + (36)

P = 4(π + 9)

Therefore, the perimeter of the figure is 4(π + 9)ft.

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EXPLANATION:

-FIRST STEP:

We must convert the mixed fractions to improper

-SECOND STEP:

We must do exactly a subtraction of fractions to know how far the bus is.

-THIRD STEP:

To convert a mixed fraction to improper we must multiply the integer by the denominator and then the result is added to the numerator.

Now If we convert the result into a mixed fraction then the answer as a mixed fraction is:

Answer:

No association

Explanation:

If there is a positive linear association, the graph would show something close to a straight line with a positive slope.

In the same way, if there is a negative linear association, the graph would be a straight line with a negative slope

If there is a nonlinear association we would see a curve.

Since all the data is dispersed in the graph, we can say that the best description of this relationship is No association.

Answer:

\(k=35\)°

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.

\(130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95\)

The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;

\((unknown_1)+(unknown_2)+(k)=180\)

Substitute,

\(50+95+k=180\)

Simplify,

\(50+95+k=180\\\\145+k=180\\\\k=35\)

\(\sf \bf {\boxed {\mathbb {TO\:FIND :}}}\)

The measure of angle \(k\).

\(\sf \bf {\boxed {\mathbb {SOLUTION:}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}\)

\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}\)

➪ \(x\) + 85° = 180°

➪ \(x\) = 180° - 85°

➪ \(x\) = 95°

Also,

Exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ 130° = \(k\) + \(x\)

➪ \(k\) + 95° = 130°

➪ \(k\) = 130°- 95°

➪ \(k\) = 35°

Therefore, the value of \(k\) is 35°.

\(\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}\)

\(\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ 50° + 35° + 95° = 180°

( where 50° = 180° - 130°)

➪ 180° = 180°

➪ L. H. S. = R. H. S.

Hence verified.

(Note: Kindly refer to the attached file.)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}\)

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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Answer:

Step-by-step explanation:

Tricky i give that to the question that so i think f 4 maybe it doesn't show  the options

Answer:

a

Step-by-step explanation:

I think it's a I am not sure

Answer:

3/4

Step-by-step explanation:

any thing in the form of y=mx+x,

mx is the slope

Answer:

2x + 8y + 2z

Step-by-step explanation:

Answer:

Just use the 2 to multiply the numbers in the bracket.

which is

2x+8y+2z.

Answer:

25 cat owners!!!

Step-by-step explanation:

It's a ratio word problem...

5:6

Multiply both Numerator and Denominator by 5.

25:30

May I please have Brainliest??!??

- ElizabethKate

Answer: 19

Step-by-step explanation: So 6+5=11 then 30-11=19

The calculated value of k on the line is 9

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

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

substitute the known values in the above equation, so, we have the following representation

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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The value of the summation expression given in the task content is; 16.

It follows from the task content that the value of the summation expression given is to be determined.

Since the given expression is; 2x - 3,

On this note;

On this note, the sum of all of the results above is the correct Evaluation of the given expression; 1 + 3 + 5 + 7 = 16.

On this note, the result of the evaluation is; 16.

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The total hours for the week is 32 hrs 55 mins.

Mon total hours = ( 12:00 - 8:30) + ( 17:35 - 12: 35)hrs

= 3 hrs 30 mins + 5 hrs

= 8hrs 30mins

Tue total hours = ( 12:15 - 8:25) + ( 17:30 - 13: 00)hrs

= 3hrs 50mins + 4hrs 30mins

= 8hrs 20mins

Wed total hours = ( 12:45- 8:28) + ( 16:25 - 13: 15)hrs

= 4 hrs 17 mins + 3hrs 10 mins

= 7hrs 27mins

Thu total hours = ( 01:08- 8:15) + ( 17:42 - 13: 45)hrs

= 4hrs 53mins + 3hrs 57 mins

=8hrs 50mins

Fri total hours = ( 12:30- 8:50) + ( 17:08 - 13: 00)hrs

=3hrs 40mins + 4hrs 8 mins

=7 hrs 48 mins

Therefore total work hours = 32 hrs 55 mins

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Answer:

x-25

Step-by-step explanation:

the number is x and the subtraction is the difference

Answer:

k = 15

Step-by-step explanation:

k + 45 = 60

k = 60 - 45

k = 15

Answer:

the answer is b, c, d, a, respectively

Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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