Simplify the number into simplest radical form.

Answer:

Step-by-step explanation:

Mean = (87 + 105 + 130 + 160 + 180 + 195 + 135 + 145 + 213 + 105 + 145 + 151 152 + 136 + 87 + 99 + 92 + 119 + 129)/19 = 129

Variance = (summation(x - mean)²/n

Standard deviation = √(summation(x - mean)²/n

n = 19

Variance = [(87 - 129)^2 + (105 - 129)^2 + (130 - 129)^2+ (160 - 129)^2 + (180 - 129)^2 + (195 - 129)^2 + (135 - 129)^2 + (145 - 129)^2 + (213 - 129)^2 + (105 - 129)^2 + (145 - 129)^2 + (151 - 129)^2 + (152 - 129)^2 + (136 - 129)^2 + (87 - 129)^2 + (99 - 129)^2 + (92 - 129)^2 + (119 - 129)^2 + (129 - 129)^2]/19 = 23634/19 1243.895 min

Standard deviation = √1243.895 = 35.269 min

60 minutes = 1 hour

Converting the variance to hours,

Each division would have been divided by 60². 60² can be factorized out

Variance = 23634/60² = 6.565 hours

Converting the standard deviation to hours, it becomes

√6.565 = 2.562 hours

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is                

Answer:

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the  chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Answer:

The minimum score required for an A grade is 77.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 67.7, \sigma = 7.8[/tex]

Find the minimum score required for an A grade.

Top 12% of scores get an A.

100-12 = 88th percentile.

The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]

[tex]X - 67.7 = 7.8*1.175[/tex]

[tex]X = 76.865[/tex]

Rounding to the nearest whole number:

The minimum score required for an A grade is 77.

Answer:

$976

Step-by-step explanation:

Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610

Overtime Rate = 15.25×2= $30.50

Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366

Total Pay= Basic wage + Overtime Wage = $976

Answer:

8.7 ft

Step-by-step explanation:

The diagram of the ramp is attached below.

Volume of a Triangular Prism = Base Area X Width

From the diagram:

Base of the triangle = 6 ft

Height of the Triangle = 12 ft

Therefore:

Base Area of the Prism [tex]=\frac{1}{2}X 12X6=36$ ft^2[/tex]

From the diagram, Width of the ramp =x

Given that the volume of the ramp is 313.2 cubic feet.

Therefore, substituting into the formula for Volume of a Triangular Prism

[tex]313.2=36 X x\\x= 313.2 \div 36\\$Width of the ramp, x=8.7 ft[/tex]

Answer:

8.7

Step-by-step explanation:

Answer:

51.5m

Step-by-step explanation:

half 8.1 to get the radius (4.05)

then times pi by 4.05 squared

your answer is 51.5 (rounded)

Answer:

3√2

Step-by-step explanation:

If you draw the diagonal, you have a 45°45°90° triangle.

The two legs are 3, so the hypotenuse is 3√2

Answer:

4/11

Step-by-step explanation:

There are 11 marbles in total, if 4 of them are white, then you have a 4/11 chance of getting a white marble.

Answer:

Hello!

I believe your answer is:

4a(b+2c)

Step-by-step explanation:

I hope this worked for you!  Good luck!

Answer:

113 feet

Step-by-step explanation:

Use the ratio 1:50 to calculate the height of the tower.

The scale model height is 2.25 feet, so multiply that by 50

2.25 x 50 = 112.5

Round to 113 feet

Answer:

D. 113 feet

Step-by-step explanation:

We know that Josephine made a smaller model that is one-fiftieth the size of the real model. That means the height of the real model is fifty times as big as this model. All we need to do to find the height of the real thing is to multiply 50 and 2.25. (50) 2.25 = 112.5. That will round to 113 feet, which is the height of the new water tower.

Hope this helps ^-^

Answer:

He is incorrect. Ray RO and ray RL are not opposite rays.

Step-by-step explanation:

Two angles are linear pair if they are supplementary and share a leg. 

∠ORP and ∠LRP are not supplementary, because ray RO and ray RL are not opposite rays.

Therefore, ∠ORP and ∠LRP are not linear pair.

correct me if this is wrong

Answer:

D

Step-by-step explanation:

12 is lowest.

A bar chart is one of the most commonly used representations or visually translate groups of data.

We have given that,

When representing a frequency distribution with a bar chart.

frequency distribution, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times.

It is drawn in such a way that the x-axis of the graph would represent the items and the y-axis will be for the frequency.

Out of the choices given, the shortest among the bars will be that would frequency is only 36.

Hence, the answer to this item is the letter C.

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Answer:

11

Step-by-step explanation:

[tex]answer = 17.85 {inches} \\ solution \\ radius = 5 \: inches \\ perimeter \: of \: quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 5}{4} + 2 \times 5\\ = \frac{31.4}{4} + 10 \\ = \frac{31.4 + 10 \times 4}{4} \\ = \frac{31.4 + 40}{4} \\ = \frac{71.4}{4} \\ = 17.85 \: {inches} \\ hope \: it \: helps[/tex]

Answer:

17.85 in

Step-by-step explanation:

2πr is formula for the circumference but [tex]\frac{1}{2}[/tex]×π×r is the circumference for the quarter circle.

0.5×π×5=

2.5π≈

7.85

7.85+5+5=17.85 in

Answer:

a) 8.13

b) 4.10

Step-by-step explanation:

Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1

In order to get the total reaction R(t) to the drugs at this times, we need to first integrate the given function to get R(t)

On integrating R'(t)

∫ (2/t+1 + 1/√t+1)dt

In integration, k∫f'(x)/f(x) dx = 1/k ln(fx)+C where k is any constant.

∫ (2/t+1 + 1/√t+1)dt

= ∫ (2/t+1)dt+ ∫ (1/√t+1)dt

= 2∫ 1/t+1 dt +∫1/+(t+1)^1/2 dt

= 2ln(t+1) + 2(t+1)^1/2 + C

= 2ln(t+1) + 2√(t+1) + C

a) For total reactions from t = 1 to t = 12

When t = 1

R(1) = 2ln2 + 2√2

≈ 4.21

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

R(12) - R(1) ≈ 12.34-4.21

≈ 8.13

Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.

b) For total reactions from t = 12 to t = 24

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

When t = 24

R(24) = 2ln25 + 2√25

≈ 16.44

R(12) - R(1) ≈ 16.44-12.34

≈ 4.10

Total reactions to the drugs over the period from t = 12 to t= 24 is approx 4.10

Answer:

Step-by-step explanation:

Let s, b, a represent the numbers of servings of steak, baked eggs, and acorn squash, respectively. Then the equations we want to solve are ...

  40s +20b +4a = 64 . . . . grams of protein

  10s +2b +20a = 29 . . . . grams of carbohydrate

  1s +20b +32a = 72.5 . . . milligrams of vitamin A

There are any number of calculators or web sites that will solve this system of equations for you. The solution is ...

  s = 0.5

  b = 2

  a = 1

The dietitian should provide 1/2 serving of steak, 2 servings of baked eggs, and 1 serving of acorn squash.

Answer:

1:0.4641

Step-by-step explanation:

We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.

They tell us that the real world volume is 100,000, that if we assume a cube, we have to:

V = l ^ 3

l = 100000 ^ (1/3)

l = 46.41

46.41 meters would be each side, now the volume of the model would be:

100,000 * 0.1 = 10,000

Which means that its sides would be:

V = l ^ 3

l = 100000 ^ (1/3)

l = 21.54

We calculate the scale of the sides:

21.54 / 46.41 = 0.4641

Which means that for every 1 meter in the real world the model represents 0.4641 meters.

Answer:

5x - 4y = 20

Step-by-step explanation:

First find slope

(5- -10)/(8- -4) = 15/12 = 5/4

(y - 5) = 5/4 (x - 8), multiply everything by 4 so you don't have fractions

4y - 20 = 5x - 40

5x - 4y = 20

Answer:

Discount = $45

Final = $255

Step-by-step explanation:

First you would multiply $300 by .85. (You do this because your only paying for 85% of the computer) to get the final price

$255

In order to get the discount amount you would subtract 300 by 255 to get

$45

Answer:

july 11

Step-by-step explanation:

Answer:

(A) P (n,k) = n!/(n-k)! divided by 2

(B) C (n,3) = n!/(12)(n-3)!

(C) C (n,k) = n!/(n-k)!(k!)

Step-by-step explanation:

Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.

We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.

For (B), n=10

C (n,3) = n!/(n-3)!(3!) divided by 2

3! = 3×2×1 = 6

The expression divided by 2 means it will be multiplied by 1/2

Hence 6×2 = 12

And we arrive at

C (n,3) =n!/(12)(n-3)!

Answer:

j=13, g=20.8, h=24

Step-by-step explanation:

The overall shape given and the shape within, are both right triangles. With right triangles, you are allowed to use the pythagorean theorem formula ([tex]a^{2} + b^{2} = c^{2}[/tex]) in order to solve for some sides. In this case, that would be j and h. The five in the smaller triangle is represented by b and the 12 is the hypotenuse so it is represented by c. When you plug in those numbers in the pythagorean theorem formula, you will find the value of j to be 13. When looking at this, we see that 12 is the second greatest value in the right triangle values that we just found, so we know the the opposing angle for that one will be 60 degrees. The 5's opposing side is therefore 30 degrees. When subtracting 90 and 30, we get 60, so therefore you can use the 30 60 90 formula to find the sides of the bigger triangle. The 60 degrees represents g. This formula will be [tex]a\sqrt{3}[/tex]. The a is 12 since it is the smallest value. So therefore, g is [tex]12\sqrt{3}[/tex], which is 20.8. Now that we have this side, we can just use the pythagorean theorem formula to find the remaining side. Therefore, h is going to be 24

Answer:

Its depending on the angle

Answer:

9

Equivalent Fractions with the LCD

4 7/9 = 43/9

2 2/3 = 24/9

For the denominators (9, 3) the least common multiple (LCM) is 9.

Therefore, the least common denominator (LCD) is 9.

4 7/9 = 43/9 × 1/1 = 43/9

2 2/3 = 8/3 × 3/3 = 24/9

Hope this helps :)

The least common denominator of 4 7/9 and 2 2/3 is 9.

Given data:

To find the least common denominator (LCD) of 4 7/9 and 2 2/3, we need to first convert both fractions to their equivalent forms with a common denominator.

The given fractions are:

4 7/9 = 4 + 7/9

2 2/3 = 2 + 2/3

To find a common denominator, we need to find the least common multiple (LCM) of the denominators 9 and 3, which is 9.

Now, let's convert the fractions to their equivalent forms with a denominator of 9:

4 7/9 = (4 * 9)/9 + (7/9) = 36/9 + 7/9 = 43/9

2 2/3 = (2 * 9)/9 + (2/3) = 18/9 + 2/3 = 20/9

The fractions 4 7/9 and 2 2/3 are now expressed with a common denominator of 9.

Hence, the least common denominator (LCD) of 4 7/9 and 2 2/3 is 9.

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Answer:

  (-2.60, -6.80)

Step-by-step explanation:

The new coordinates can be found by multiplying by the rotation matrix:

  [tex]\left[\begin{array}{c}x'&y'\end{array}\right]=\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right][/tex]

That is, ...

  x' = x·cos(175°) -y·sin(175°) = 2(-0.9962) -7(0.0872) = -2.60

  y' = x·sin(175°) +y·cos(175°) = 2(0.0872) +7(-0.9962) = -6.80

The new coordinates are ...

  (x', y') = (-2.60, -6.80)

Answer:

Step-by-step explanation:

This problem brothers is the probability of mutually exclusive events,

Given the sample space of 80 separate events, the probability of of one event happening is

Pr(each event)= [tex]\frac{1}{80}[/tex]

Answer:

  (-3, 4) is a solution

Step-by-step explanation:

The point (-3, 4) is inside the shaded area of the graph, so is a solution.

You can check in the inequality

  y > -2x -3

  4 > -2(-3) -3 . . . . substitute for x and y

  4 > 3 . . . . . . . true; the given point is a solution

Answer:

the Answers are : B and E

Step-by-step explanation:

From the given quadratic equation [tex]x^2 + 10x + 25 = 7[/tex] Thus, the solution is x = -1 and -9.

Suppose that the given quadratic equation is

[tex]ax^2 + bx + c = 0[/tex]

Then its roots are given as:

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

We have been given a quadratic equation

[tex]x^2 + 10x + 25 = 7[/tex]

[tex]x^2 + 10x + 25 - 7=0\\\\x^2 + 10x + 18[/tex]

The solution of the given equation;

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-10 \pm \sqrt{10^2 - 4\times 18}}{2}\\\\x = \dfrac{-10 \pm \sqrt{100- 36}}{2}\\\\x = \dfrac{-10 \pm \sqrt{64}}{2}\\\\x = \dfrac{-10 \pm 8}{2}\\[/tex]

Therefore, the solution are x = -1 and -9.

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answer will be 10cm² as i calculate it