A 2-column table with 6 rows. The first column is labeled hours spent studying with entries 1, 2, 3, 4, 5. The second column is labeled test score with entries 72, 80, 90, 82, 95. Claudia records the hours she spent studying and her test scores for 5 tests. What is the correlation coefficient? What is the strength of the model?.

The probability that the gambler has strictly more than $32 after playing the game five times is 68.75%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. In this problem, we are dealing with a gambler who is playing a game with equal probability of doubling or reducing their stake to half.

The gambler's initial stake is $32. Let us consider the possible outcomes after one play of the game. The stake can either double to $64 or reduce to $16, each with equal probability. If the stake doubles, the gambler has more than their initial stake. If the stake is reduced to half, the gambler has less than their initial stake.

Now, let us consider the possible outcomes after two plays of the game. There are four possible outcomes:

(1) the stake doubles twice and the gambler has

=> $64 * 2 = $128,

(2) the stake doubles then reduces to half and the gambler has

=> $32 * 2 * 0.5 = $32,

(3) the stake reduces to half then doubles and the gambler has

=> $32 * 0.5 * 2 = $32,

(4) the stake reduces to half twice and the gambler has

=> $32 * 0.5 * 0.5 = $8.

We can represent these outcomes using a tree diagram. Each branch represents a possible outcome, and the probability of that outcome is written next to the branch.

After five plays of the game, there are 32 possible outcomes.

We can calculate the probability of the gambler having more than their initial stake by adding up the probabilities of all the outcomes where the gambler has more than $32. This turns out to be 0.6875 or 68.75%.

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Answer:

22.7 miles

Step-by-step explanation:

The hikers start walking 15 miles due east and then they turn north and walk 17 miles to a large pond.

The shape of their journey can be represented as a right angled triangle, shown below.

To find the distance between the pond and the base camp, we need to find the hypotenuse of the triangle.

We can do this by using Pythagoras theorem:

\(hyp^2 = a^2 + b^2\)

where a and b are the other two sides of the triangle. Therefore:

\(hyp^2 = 15^2 + 17^2\\\\hyp^2 = 514\\\\hyp = \sqrt{5`4} \\\\hyp = 22.7 miles\)

The pond is 22.7 miles far from the base camp.

Answer:

W = 100/6 ft = 16.67 ft

L = 2W = 2(16.67 ft) = 33.34 ft

Step-by-step explanation:

\(tan = \frac{opp}{adj} = \frac{x}{24} \)

\( \tan(62) = \frac{x}{24} \)

\(x = 24 \tan(62) \)

\(x = 45.1374351683\)

\(x = 45.14\)

Answer:

y = 2x + 5 (answer d)

Step-by-step explanation:

Parallel lines have the same slope, and thus, if we're given y = 2x + 7, we know that the slope of the 'new' line is 2.  This 'new line' passes through (3, 11).  Begin with the point-slope formula y - k = m(x - h) and substitute 3 for h, 11 for k and 2 for m:

y - 11 = 2(x - 3)

Rewriting this in slope-intercept form, we get:

y = 2x - 6 + 11. or y = 2x + 5 (answer d)

Answer:

2s + 0.13s

2.13s

Step-by-step explanation:

One shirt costs s.

2 shirts cost 2s.

The tax rate is 6.5%, so the tax on 2s is 0.065 × 2s = 0.13s

The total cost with tax is 2s + 0.13s

You can also find the total cost by realizing that since the tax is 6.5%, the total price with tax is 1.065 times the cost, so you can write it as 1.065 × 2s = 2.13s

Answer:

2s + 0.13s

2.13s

Answer:

2.13s

and

2s+0.13s

Step-by-step explanation:

Because 2 shirts is s and 6.5 per cent would turn into 6.5 because of 2 times 1.065 is 0.13 which is the answer for part 2

The total number of ways/ permutation that A occupies first position is 24 ,  A occupies the first position, and B the second is 6 and a appears before b is 10 ways.

What is permutation ?

Permutation is a meeting of objects in an exceedingly definite order. The members or components of sets square measure organized here in an exceedingly sequence or linear order.

Main body:

A) a occupies the first position-

As A is first, and arrange the remaining letters.  letters (B,C,D,E,F) can be arranged as-

4*3*2*1 = 24 ways

B) a occupies the first position, and b the second

As A is first and b is just after it , there are 5 position out of which 2 are taken by A, B in order , so number of ways they can be arranged is

3*2*1 = 6 ways

C) a appears before b

in this part there is no  condition that a appears just before b , so b can be places anywhere after A.

after fixing A at first place , B can be placed at 4 places.

after fixing A at 2nd place , B can be placed at 3 places.

after fixing A at 3rd place , B can be placed at 2 places.

after fixing A at 4th  place , B can be placed at 1 places.

total ways = 4+3+2+1 = 10

Hence the answer to these parts are 24, 6,10

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Answer:

25(45) +200= 1125+200=1325

The consecutive page no. are 126 and 127.

An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.

Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.

The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).

let the consecutive page numbers be x and x+1

according to question ,

          x + x + 1 = 253

          2x = 252

            x = 126

so the consecutive page numbers are 126 and 127.

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Answer:

Step-by-step explanation:

\(\frac{6}{7}x - 8 - \frac{4}{7}x - 8 = \frac{6}{7}x -\frac{4}{7}x - 8 - 8\\\\=\frac{6-4}{7}x - 16\\\\=\frac{2}{7}x - 16\\\)

We have the following information:

they have 280 customers per day and they charge $12 per person. For every increase of the cost by $2.10, they loose 16 customers.

Let's calculate the earning for each price to see which one makes the most amount of money

At the original prince, 280 customers for $12 each, they will earn 280x12 which is $3,360:

For the first increase of $2.1, the cost will be:

$12+$2.1=$14.1

but they will loose 16 people, so they will have:

280-16=264 customers.

The earinings for this set up are shown in the following image:

We repeat this process adding increases of $2.1 to the cost, and decreasing the number of customers by 16:

As we can see, unitl the charge of 24.6 the earnings are still increasing, we continue the table as follows:

For the charge of $26.7, the earning now decrease. So the most profitable charge for the bus is: $24.6

'≅' means 'approximately equal to'

Answer:

7

Step-by-step explanation:

variable = 84/12

             = 7

84 ÷ 12 = 7

Verification

12 × 7 = 84

Complete the space by dividing, 12 x 7 = 84: *

Answer:

Hey there the answer is 4.35 dollars for the tip which means the total price will be $33.35  and yes they should tip

Step-by-step explanation:

Answer:

that will be A

Step-by-step explanation:

The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  \(\frac{2}{3}\) π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = \(\frac{2}{3}\) π × 2³

                                      = \(\frac{16}{3}\) π

There are two hemispheres.

Volume of two hemispheres = 2 × \(\frac{16}{3}\) π =  \(\frac{32}{3}\) π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = \(\frac{32}{3}\) π + 16 π

                                                    = \(\frac{80}{3}\) π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

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Answer: -1

Step-by-step explanation:

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Note that assuming that the instrument used was exogenous, one can conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different: "The explanatory variable is endogenous and therefore 2SLS should be considered." (Option C)

Two-stage least squares (2SLS) regression analysis is a statistical approach used in structural equation analysis. The OLS approach has been extended using this methodology. It is employed when the error terms of the dependent variable are associated with the independent variables.

The ordinary least squares (OLS) approach is a linear regression methodology used to estimate a model's unknown parameters. The strategy is based on reducing the sum of squared residuals between the expected and actual values.

2SLS is utilized as an alternate strategy when we encounter endogeneity Problems in OLS. Endogeneity arises when the explanatory variable correlates with the error word. Then we utilize 2SLS, which employs an instrumental variable. The outcome will be different because if there is endogeneity in the model, OLS will produce biased results.

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Full Question:
What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous. Select one:

a. The explanatory variable is not endogenous and therefore using 2SLS is ill-advised.

b. The explanatory variable is not endogenous and therefore OLS should not be used.

c. The explanatory variable is endogenous and therefore using 2SLS should be considered.

d. The explanatory variable is endogenous and therefore OLS should be used.

a) Before rounding, the exact depths are continuous data.

b) For the listed earthquake depths, the data are quantitative.

c) The level of measurement of the listed earthquake depths is ratio.

d) Given that the listed earthquake depths are part of a larger collection of depths, the data constitute a population.

a) Before rounding, the exact depths are continuous data.

This is because, continuous data are those data types that can take any value between two numbers, including the values with decimal points.

b) For the listed earthquake depths, the data are quantitative.

This is because they can be measured and expressed as a numerical value.

c) The level of measurement of the listed earthquake depths is ratio.

This is because the data have an absolute zero point, which is 0 km, indicating that the absence of depth. Ratio measurement scales are those measurement scales where the data have an absolute zero point.

d) Given that the listed earthquake depths are part of a larger collection of depths, the data constitute a population.

This is because a population refers to the total group of items or events that are of interest to a study. Therefore, the listed earthquake depths are a subset of the entire group of earthquake depths.

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A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.

To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.

The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.

Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.

Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.

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Answer:

D:y=5x-8

steps- by- step explanation

Answer:

If your talking about the containers, then you would need 80

containers, hope this helps.

Step-by-step explanation:

Answer:

27%

Step-by-step explanation:

3000 + 3500 + 4000 + 4200 = 14700

4000 / 14700 ≈ 0.27

0.27 = 27%

Step-by-step explanation:

the process is show in the above picture.