A professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter are given below.Student No. Hours Spent Studying Total Points Earned1 25 182 10 133 70 534 40 435 85 686 45 287 70 688 60 589 35 2310 55 43Simple Regression - POINTS vs. HOURSDependent variable: POINTSIndependent variable: HOURSLinear model: Y=a +b*XCoefficientsLeast Squares Standard TParameter Estimate Error Statistics P-ValueIntercept 0.437798 5.9182 0.073948 o.9428Slope 0.829539 0.109474 7.57748 0.0001Analysis of VarianceSource Sum of Squares Df Mean Square F-Ratio P-ValueModel 3249.72 1 3249.72 57.42 0.0001Residual 452.779 8 56.5974 Total (Corr.) 3702.5 9The following questions are based on the information above.1) Write down the estimated regression equation that could be used to estimate the total points earned in the course given the hours spent studying.2) At the 0.05 level of significance, does hours spent studying have a significant effect on the total points earned in this course?3) Find the standard error of the estimate.4) Use the estimated regression to predict the points of a student who spent 50 hours studying for this course.5) If a student spent 120 hours studying for this course, would you feel comfortable to use your estimated regression equation to predict his points? Why?6) What's the R-squared?7) Do you believe your estimated regression equation would provide a good prediction of the points? Use R-squared from Question 8 to support your answer.

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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Answer:

(h + g)(10) = -6

Step-by-step explanation:

Step 1: Define

h(x) = 3x + 3

g(x) = -4x + 1

Step 2: Find (h + g)(x)

(h + g)(x) = 3x + 3 + -4x + 1

(h + g)(x) = -x + 4

Step 3: Substitute and Evaluate

(h + g)(10) = -10 + 4

(h + g)(10) = -6

Answer:

Step-by-step explanation:

First method information:

Sample size  n₁  = 549

x₁ ( people ignoring on-line harassment )  =  412

Proportion of people ignoring on-line harassment  p₁

p₁ =  412/549   p₁  =  0,75   q₁ =  1  -  p₁    q₁ = 0,25

Second method ( people chosen to respond)

Sample size   n₂  =  368

number of people responding   x₂  = 305

Proportion of people responding

p₂ =  305/ 368    p₂ =  0,83   then  q₂  =  0,17

a) Looking for differences in the approachs

Hypothesis test:

Null Hypothesis                     H₀         p₁  =  p₂

Alternative Hypothesis         Hₐ         p₁  ≠  p₂

Alternative Hypothesis indicates that the test is a two-tail test

Choosing a confidence interval  CI = 95 % then a significance level is       α = 5%     α  = 0,05  and from z-table we get  z(c) =  1.64

To calculate z(s)

z(s)  =  (  p₁  -  p₂ ) / EED

EED = √  p₁*q₁)/n₁  +  (p₂*q₂)n₂

EED = √  (0,75*0,25)/549   +  0,83*0,17)/368

EED = √ 3,41 *10⁻⁴   +  3,83*10⁻⁴

EED =   10⁻² *√ 3,41 + 3,83

EED =   10⁻² * 2,69

EED = 0,0269

z(s)  =  (  p₁  -  p₂ )/0,0269

z(s)  = -  0,08 / 0,0269

z(s)  =  - 2,97

p-value for z(s)  is  pvalue  = 0,0015

Comparing  z(s)  and  z(c)   modules

z(s) > z(c)  therefor z(s) is in the rejection region we have to reject H₀ and claim that there is a difference between the proportions

b) How large is the difference

Answer:

The square has a greater area having an area of 9 cm more than that of the rectangle.

Step-by-step explanation:

Length of square = x

Length of rectangle = 3+x

Width of rectangle = x-3

Area of square:

=> \(Length*Length\)

=> x × x

=> x²

Area of Rectangle:

=> \(Length*Width\)

=> (3+x)(x-3)

Using FOIL

=> 3x-9+x²-3x

=> x²-9

From the above calculations, we come to know that the square has a greater area having an area of 9 cm more than that of the rectangle.

Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

Answer:

Flipping three coins: Each coin has 2 equally likely outcomes, so the sample space is 2 • 2 • 2 or 8 equally likely outcomes. Rolling a six-sided die and flipping a coin: The sample space is 6 • 2 or 12 equally likely outcomes.

...

First coin Second coin outcome

H T HT

T H TH

T T TT

Step-by-step explanation:

sorry if its wrong mate

Answer:

12

Step-by-step explanation:

AD is 6. a bisector splits a line in half. X would equal 6 meaning AD would equal 12.

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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Answer:

here u go gurly

Step-by-step explanation:

To complete the table, plug each given x value into the equation. Then,

Therefore, you would get the table

The computed values f(-3)+f(1) is 64 and f(-3)-f(1) is 52

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=3x²-7x+10.

we need to find the values of f(-3)+f(1) and f(-3)-f(1)

First let us compute the values of f(-3) and f(1)

f(-3)=3(-3)²-7(-3)+10

=27+21+10

f(-3)=58

f(1)=3(1)-7(1)+10

=3-7+10

f(1)=6

f(-3)+f(1)=58+6

=64

f(-3)-f(1)=58-6

=52

Hence, the values of f(-3)+f(1) is 64 and f(-3)-f(1) is 52

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Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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\( \frac{2 }{5} \times 100 = \\ \)

\(40\)

Thus 40 percent of the starring players are taller than 6 feet.

Answer:

71 degrees.

Step-by-step explanation:

m < CED = 180 - 152 = 28 degrees ( adjacent angles).

m <BAC = 28 degrees( alternate angles).

m < ACD = 28 + 43 = 71 degrees (external angle theorem).

Answer:

128°

Explanation:

total sum of interior angle in triangle is 180°

Find the missing angle inside the triangle:

180° - 38° - 90°

52°

∵ a straight line always has 180°

Now find for missing exterior angle:

x° + 52° = 180°

x° = 180° - 52°

x° = 128°

Answer:

128 degrees

Step-by-step explanation:

180-52= 128

so your answer is 128 degrees.

The length of each rope if all the ropes had the same length is 3 ft

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

The dot plot

From the dot plot, we can see that the data are normally distributed

This means that the length of each rope is the mean, the median and the mode

Given that the data on the dot plot is normally distributed, we have the following values

So, we can conclude that the length is 3 ft

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Answer:

$1,024.56

Step-by-step explanation:

Simple math, So what you would do to find this answer would be taking the amount of money hes earning an hour and times that by how many hours he worked that week. so $28.46 x 36 = $1,024.56

Answer:

1024.56

Step-by-step explanation:

     28.46

x          36

___________

      17076

+     85380

____________

    1024.56

Answer:

B

Step-by-step explanation:

20,24,25,27,29,31,34

min = 20

Q1 = 24

median = 27

Q3 = 31

max = 34

============================================================

Explanation:

Original Data Set = {29, 31, 27, 20, 25, 34, 24}

Sorted Data Set = {20, 24, 25, 27, 29, 31, 34}

The middle-most value of the sorted set is 27, since there are 3 values above it and 3 values below. So the median is 27.

The median is represented by the vertical line inside the box. It does not have to be at the visual midpoint between the left and right edges. It simply needs to be anywhere inside the box.

So we can rule out choice B for instance because this answer choice shows a median of 25, when we want 27 instead.

Choices A, C and D all have the same median of 27.

-------------

Break up the sorted set into two smaller sets like this

L = {20, 24, 25}

U = {29, 31, 34}

L represents the set of lower values, which are smaller than the median. U is the upper set of values larger than the median. The median itself is not in L or U.

Find the median of L and U to get 24 and 31 respectively. These are the Q1 and Q3 values in that order.

Q1 = 24

Q3 = 31

These are the left and right edges of the box.

We can cross choice A off the list because the right edge of the box in that diagram is at 29 instead of 31.

The answer is between C and D.

-------------

The last things to consider are the min and max, which are the smallest and largest elements. These are the left and right tips of the whiskers, assuming that we don't have small or large outliers. In this case, we don't have to worry about outliers.

The min and max is 20 and 34 which must mean the answer is choice C

We can rule out choice D because the max shown here is 35.

-------------

In short, the data set has the following five number summary:

all of these five values correspond to a specific visual feature of the boxplot (see diagram below)

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer:

x = 52

Step-by-step explanation:

Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.

Answer:

66.6667%

Step-by-step explanation:

Answer: 62.83

Step-by-step explanation:

The formula for the circumference of a circle is C = 2 π r

So, let’s set up our equation.
2 •π •10 (your radius is 10!)

Now just multiply it together.

2 • π • 10 = 62.83 ft^squared

Hopefully this is what you were looking for. :)

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

Step-by-step explanation:

Given the following data:

31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 40.5 37.2 45.3 36.1 45.5 42.3 33.3 30.3 37.2 45.5 54.3 37.2 49.8 32.1 39.3 40.3 44.2 28.4 46.0 47.2 32.8 32.2 38.5 44.5 44.6 40.9 29.5 41.3 35.4

Value ___frequency____relative frequency %

28.4_______1 __________1. 96

28.6_______2__________3.92

29.5_______1___________1.96

30.3_______1___________1.96

31.5_______2___________3.92

32.1_______1____________1.96

32.2_______1___________1.96

32.8_______1___________1.96

32.9_______2___________3.92

33________2___________3.92

33.3_______1___________1.96

35.4_______1___________1.96

35.5_______2___________3.92

36.1________1___________1.96

36.2_______2___________3.92

37.2_______7___________13.73

38.5_______1____________1.96

39.3_______1____________1.96

40.3_______1____________1.96

40.5_______1____________ 1.96

40.9_______1____________1.96

41.3_______1 ____________1.96

42.3______1_____________1.96

43.3______2____________ 3.92

44.2______1 _____________1.96

44.5______1 _____________1.96

44.6_____ 1 ______________1.96

45.3_____1 _______1.96

45.5_____2 ______3.92

45.9_____2 ______3.92

46______1 _______1.96

47.2_____1 _______1.96

49.8_____1 _______1.96

54.3____1________1.96

68.8____2________3.92

Lower outlier = Q1 - (1.5 × IQR)

Upper outlier = Q3 + (1.5 × IQR)

IQR = Interquartile range ;

Q1 = 1/4(n+1)th term

Q3 = 3/4(n+1)th term

IQR = Q3 - Q1

n = number of observations = 51

Q1 = (51 + 1)/4= 52/4 = 13 th term = 33

Q3 = 3(51 + 1) /4 = 156/4 = 39th term = 44.5

IQR = 44.5 - 33 = 11.5

LOWER OUTLIER = 33 - (1.5*11.5) = 33 - 17.25 = entries < 15.75

UPPER OUTLIER = 44.5 + (1.5*11.5) = 44.5 + 17.25 = 61.75

Entries > 61.75

sorry i actually dont know :(

Answer:

You must know what a quotient is first.

Step-by-step explanation:

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Check the 1st picture below.  Let's see if that's true for the 1st one, by substituting the values

\(\begin{cases} x = 9\\ y = -3\end{cases} \\\\[-0.35em] ~\dotfill\\\\ y = -x + 6 \implies -3 = -(9)+6\implies -3=-3\qquad \textit{\large \checkmark} \\\\\\ y = \cfrac{2}{3}x-9 \implies -3 = \cfrac{2}{3}(9)-9\implies -3=6-9\implies -3=-3\qquad \textit{\large \checkmark}\)

now let's do the 4th one, Check the 2nd picture below.

\(\begin{cases} x = 12\\ y = 18\end{cases} \\\\[-0.35em] ~\dotfill\\\\ y = \cfrac{3}{2}x \implies 18 = \cfrac{3}{2}(12)\implies 18=6\cdot 3\implies 18=18\qquad \textit{\large \checkmark} \\\\\\ y = \cfrac{3}{4}x+9 \implies 18 = \cfrac{3}{4}(12)+9\implies 18 = (3\cdot 3)+9 \\\\\\ 18=9+9\implies 18=18\qquad \textit{\large \checkmark}\)