Last year at a certain high school, there were 96 boys on the honor roll and 85 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

Answer:

a)Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

b) The 90% confidence interval for the population proportion is (0.68, 0.70).

Step-by-step explanation:

a) Evaluating the necessary conditions:

Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]

b) We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.69.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]

The 90% confidence interval for the population proportion is (0.68, 0.70).

Answer:

Step-by-step explanation:

_______________________________

Hey!!

Solution,

X+61+42=180[ sum of angle in triangle]

or,X+103=180

or,X=180-103

X=77°

So the value of X is 77°

Hope it helps..

Good luck on your assignment

____________________________

Answer:

-1, 1

13, 15

Step-by-step explanation:

x and x+2 are the integers

Roots of the quadratic equation are: -1 and 13.

So the integers pairs are: -1, 1 and 13, 15

Answer:

8 yds

Step-by-step explanation:

The sides have to have the same length

14 yd = 6yd + ?

Subtract 6 from each side

14-6 = 8

8 yds

Answer:

Yes, [tex]\frac{3}{4}[/tex] is a solution of the inequality.

Step-by-step explanation:

Solution of an inequality is given by the values of the variable t ≥ [tex]\frac{2}{3}[/tex]

Or t ≥ 0.67

If a solution of this inequality is t = [tex]\frac{3}{4}[/tex]

Or t = 0.75

Since, on a number line 0.75 > 0.67

Therefore, [tex]\frac{3}{4}[/tex] will be a solution of the inequality.

Answer:

c>-13/10

Step-by-step explanation:

55c+13<75c+39

55c+13-75c<39

-20c+13<39

-20c<39-13

-20c<26

c>26/-20

c>-13/10

Answer:

A unit cube has one cubic unit of volume.

Another unit cube with the same length, width and height as the unit cube shown would have the same volume

Step-by-step explanation:

A cube is a shape formed from the combination of a square.

A cube has equal sides.

But a unit cube has equal sides and equal volume to be equal to one, i.e unity.

Answer:

1.2 km

Step-by-step explanation:

The first thing that we should go over is the formula for the area of a trapezoid.

Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]

From this image, we have the following information

[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]

Now, we can plug this information into our formula and then solve for h.

[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]

Another method that can be employed is to use the pythagorean theorem.

A trapezoid can be be broken into a rectangle and two triangles.

If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.

As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.

[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]

Answer:

h=1.2 km

Step-by-step explanation:

This is the formula of a Trapezium

A=[tex]\frac{h(a+b)}{2}[/tex]

[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]

Answer:

x=135

Step-by-step explanation:

We know that sin(270) = -1/2

So 2x = 270

x = 135

Answer:

Taste

Step-by-step explanation:

In the challenge, participants were asked to taste cola from both Coke and Pepsi. They were to give a report on which of the two drinks tasted better.

The taste reported by the participants is dependent on the type of cola taken (either Coke or Pepsi).

Therefore, the taste is the dependent variable while the types of cola are the independent variables.

Answer:

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

  Let x = number of large boxes

       y = number of small boxes

 "There are 115 boxes in all"    means    x + y = 115      [eq1]

Now, the pounds for each kind of box is:

    (pounds per box)*(number of boxes)

So,

  pounds for large boxes     +    pounds for small boxes      =    4125 pounds

                 "the truck is carrying a total of 4125 pounds in boxes"

        (50)*(x)                   +              (25)*(y)                  = 4125    [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2.  Let's solve for x:

   x = 115 - y          [from eq1]

    50(115-y) + 25y = 4125             [from eq2]

     5750 - 50y  + 25y = 4125           [distribute]

     5750 - 25y = 4125

      -25y = -1625

         y = 65             [divide both sides by (-25)]

 There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

  x = 115 - y

  x = 115 - 65

  x = 50

  There are 50 large boxes.

Check (very important):

Is   50+65 = 115   ?       [eq1]

         115 = 115   ?yes

Is  50(50) + 25(65) = 4125   ?

     2500 + 1625 = 4125   ?

       4125 = 4125   ? ye

Answer:

The length of the diameter of this circular area is of 30 miles.

Step-by-step explanation:

The area of a circular region can be represented by the following equation:

[tex]A = \pi r^{2}[/tex]

In which r is the radius. The diameter is twice the radius.

In this question:

[tex]A = 225\pi[/tex]

So

[tex]A = \pi r^{2}[/tex]

[tex]225\pi = \pi r^{2}[/tex]

[tex]r^{2} = 225[/tex]

[tex]r = \pm \sqrt{225}[/tex]

The radius is a positive measure, so

[tex]r = 15[/tex]

Area in squared miles, so the radius in miles.

What is the approximate length of the diameter of this circular area

D = 2r = 2*15 = 30 miles

The length of the diameter of this circular area is of 30 miles.

Answer:

k = -4 (0, -14) also lies on the graph

Step-by-step explanation:

6 = (7 - 2)2 + k

6 = 10 + k

-4 = k

y = (0 - 5)2 - 4, y = -14

Answer:

All the elements in the sample share a common characteristic. All of them read the magazine, so we may have a biased sample. And we also have the bias of the fact that only the volunteers will respond to this survey, so this is a biased sample.

This type of sample is usually called convenience sampling, where the elements in the sample are the most readily available (and what is most readily available for a magazine than its own readers?)

Then the type of sample is a convenience sample and a biased sample.

Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360

hope this helped

Answer:

The capital B refers to the base of the area

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The capital B means the area of the base

Answer:

  see below

Step-by-step explanation:

Considering the last two table entries, we can find the slope of the line to be ...

  Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For (h, k) = (-2, -6) and m = 5/2, this is ...

  y -(-6) = 5/2(x -(-2))

  y +6 = 5/2(x +2) . . . . . matches the last choice

Answer:

d is the right choice

Step-by-step explanation:

Answer:

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]

And the best option would be:

[tex] V = \frac{539}{3} \pi cm^3 [/tex]

Step-by-step explanation:

For this case we know that the volume of the cone is given by:

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]

And the best option would be:

[tex] V = \frac{539}{3} \pi cm^3 [/tex]

Answer:

GH¢. 18098.46

Step-by-step explanation:

Let the first investment giving 12% interest per annum be Bank A

Let the 2nd investment giving 10% per annum be bank B

Let the first amount invested be

GH¢. X and let the second amount invested be GH¢. X + 580

Thus; In bank A;

Principal amount in first = GH¢. x

rate = 12 %

time = 1 year

Formula for simple interest = PRT/100

Where P is principal, R is rate and T is time.

So, interest in his investment = 12X/100 = 0.12X

while in bank B;

principal amount = GH¢. X + 580

rate = 14%

time = 1 yr

So, interest in his investment = [(X + 580) × 14]/100

= 0.14(X + 580)

So, total accumulated interest is;

0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2

Now, we are given accumulated interest = GH¢. 2,358.60

Thus;

2358.60 = (0.26X + 81.2)

2358.6 - 81.2 = 0.26X

X = 2277.4/0.26

X = 8759.23

So,

first amount invested = GH¢. 8759.23

Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23

Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46

Answer:

90% probability that she has at least one marble of each color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability that she has at least one marble of each color?

Desired outcomes:

Two red(from a set of 2) and one yellow(from a set of 3)

Or

One red(from a set of 2) and two yellows(from a set of 3).

So

[tex]D = C_{2,2}*C_{3,1} + C_{2,1}*C_{3,2} = \frac{2!}{2!(2-2)!}*\frac{3!}{1!(3-1)!} + \frac{2!}{1!(2-1)!}*\frac{3!}{2!(3-2)!} = 3 + 6 = 9[/tex]

Total outcomes:

Three marbles, from a set of 3 + 2 = 5. So

[tex]T = C_{5,3} = \frac{5!}{3!(5-3)!} = 10[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{9}{10} = 0.9[/tex]

90% probability that she has at least one marble of each color

Answer:

x = 54°

h = 7.5cm

w= 6cm

Step-by-step explanation:

Find attached the diagrams as found at Maths made easy.

Similar shapes have same shapes but different sizes.

When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.

B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A

To determine the value of x, h and w, let's look at the relationship of A and B.

h = 1.5 × 5cm

h = 7.5cm

9cm = 1.5 × w

w = 9cm/1.5

w= 6cm

Since the angles do not change when a shape is enlarged, the value of x = 54°

x = 54°

Answer:

5

Step-by-step explanation:

There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.

Explanation:

One method is to count all of the values that are between 15 and 19. Those values are highlighted in the diagram below. There are 5 values marked.

An alternative method is to note there are 19 values total. The items in the given table add to 5+2+1+2+4 = 14, so there must be 19-14 = 5 items missing to completely fill out the table.

[tex]answer \\ = 5 \sqrt{3} \\ please \: see \: the \: attached \: picture \: for \: \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

[tex]5 \sqrt{3} [/tex]

First answer is correct

Step-by-step explanation:

[tex] \frac{5}{x} = \cos(60) \\ \frac{5}{x} = \frac{1}{2} \\ x = 10 \\ \frac{y}{x} = \sin(60 ) \\ \frac{y}{10} = \frac{ \sqrt{3} }{2} \\ 2y = 10 \sqrt{3} \\ y = \frac{10 \sqrt{3} }{2} \\ y = 5 \sqrt{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Answer: 4615.66667

Steps: 1 foot=0.33333

total feets=30.5×454=13847

13847 feets=46.1566667 yards

Answer: No

Step-by-step explanation:

Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.

Hope that helped,

-sirswagger21

Answer:

Step-by-step explanation:

Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n

so, n + an = 24

n + an + a^2 n = 26

solve for a, then solve for n

Answer:

Step-by-step explanation:

BRUH YOU STUPID

Answer:

0

[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]

Answer:

The critical values of F at 95% confidence are 0.359 and 2.788.

Step-by-step explanation:

We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:

Store A                     Store B    

nA = 21                      nB = 16

SA = 28.284              SB = 20

And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.

AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.

The test statistics for F-test is =  [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex]  ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]

where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.

Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;

2.788 for right-part and 0.359 for the left-part.

Answer: y= -15 - 3x/5 is the answer.

Step-by-step explanation:

Answer:

The second graph

Step-by-step explanation:

Answer:

The answer would be 1,853,614,297