SAT Scores Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of these high school seniors, those who are in the National Honor Society, is selected, would you expect the distribution of scores to have the same mean and standard deviation? Explain your answer.

Answer:

C. acute angle

Step-by-step explanation:

As you know ,right angle is equal to 90 degrees so half of 90 degrees is 45 degree which is an acute angle (acute angles are the angles which are less than 90 degrees)

Hope this helps and pls mark as brainliest :)

Answer: acute

Step-by-step explanation:

An angle that is less than 90 degrees

Answer:

A. 1 milliliter

Step-by-step explanation:

1000 milliliters = 1 liter

0.001 liters = 1 milliliter

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

Answer:

72°

Step-by-step explanation:

Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).

The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.

The angle between thus two vectors is expressed as tan (theta) = opp/adj

tantheta = 3/1

theta = tan^-1(3)

Theta = 71.57° ≈ 72° to nearest degree

Answer:

x is 2

Step-by-step explanation:

To solve this you have to use the Pythagoram theorem A^2+B^2=C^2. So 9+16=C^2.

25=C^2

c=5

Than since u know the radius of the circle is 3, its 5-3 so x is 2.

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

27

Step-by-step explanation:

First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.

Answer:

Step-by-step explanation:

Perimeter of rectangle is 2(l) + 2(w).

The perimeter is given 100 units.

2(4x-1) + 2(3x+2) = 100

Solve for x.

8x-2+6x+4=100

14x+2=100

14x=98

x=7

Plug x as 7 for the side WX.

4(7) - 1

28-1

= 27

Answer:

Step-by-step explanation:

Hope you can see it.

Answer: all of them have one solutions

Step-by-step explanation:

Answer:

51.339

Step-by-step explanation:

Hello,

At the beginning Holly has $500

After one year

   he will get 500*(1+6.75%)=500*1.0675

After n year (n being real)

   he will get

   [tex]500\cdot1.0675^n[/tex]

and we are looking for n so that

   [tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]

so we need 51.339 years

Hope this helps

Answer:

90°

Step-by-step explanation:

Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.

Therefore, m∠GEA = 90°

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

inital height is 2 meters

Step-by-step explanation:

Looks like the series is

[tex]\displaystyle\sum_{k=1}^\infty\left(\frac4{\sqrt{k+5}}-\frac4{\sqrt{k+6}}\right)[/tex]

This series has n-th partial sum

[tex]S_n=\displaystyle\sum_{k=1}^n\bullet[/tex]

(where [tex]\bullet[/tex] is used as a placeholder for the summand)

[tex]S_n=\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)+\cdots+\left(\frac4{\sqrt{n+4}}-\frac4{\sqrt{n+5}}\right)+\left(\frac4{\sqrt{n+5}}-\frac4{\sqrt{n+6}}\right)[/tex]

In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,

[tex]\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)=\frac4{\sqrt6}-\frac4{\sqrt8}[/tex]

Ultimately, all the middle terms will vanish and we're left with

[tex]S_n=\dfrac4{\sqrt6}-\dfrac4{\sqrt{n+6}}[/tex]

As [tex]n\to\infty[/tex], the last term converges to 0 and we're left with

[tex]\displaystyle\sum_{k=1}^\infty\bullet=\lim_{n\to\infty}S_n=\frac4{\sqrt6}=\boxed{2\sqrt{\dfrac23}}[/tex]

Answer:

Step-by-step explanation:

Let b represent the number of cups of butter needed.

Let s represent the number of cups of sugar needed.

Let o represent the number of cups of oat needed.

Let f represent the number of cups of flour needed.

The recipe calls for two times as many cups of sugar as butter. It means that

s = 2b

Two times as many cups of oats as sugar. It means that

o = 2s

Two times as many cups of flour as oats. It means that

f = 2o

If Duane puts in one cup of butter, it means that b = 1

Therefore,

s = 2 × 1 = 2 cups

o = 2s = 2 × 2 = 4 cups

f = 2o = 2 × 4 = 8 cups

Therefore, he needs to add 8 cups of flour

Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour

Step-by-step explanation:

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

94.25 kg I think

Step-by-step explanation:

58/4 =14.5 kg per bushel

6.5 x 14.5=94.25 kg

Answer:

94.25

Step-by-step explanation:

First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25

Answer: Yes

Step-by-step explanation:

See explanations in the attached document

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

[tex]\boxed{x = 2\frac{2}{3} }[/tex]

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Answer:

115 miles

Step-by-step explanation:

First find the distance at 50 mph

d = 50 mph * .5 hours

   = 25 miles

Then find the distance at 60 mph

d = 60 mph * 1.5 hours

   = 90 miles

Add the distances together

25+90

115 miles

Answer:

he drives a 115 miles

Step-by-step explanation:

if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90

90+25=115 so he drove 115 miles.

Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:

Miss Pepper Mills

Credit Card Statement for the month of April:

a. Average Daily Balance:

Average balance = $618.66/5 = $123.73

b. Calculation of Miss Pepper Mill's Finance Charge for the month of April:

Finance charge

= 18.5% of $20.55 x 1/12

= $0.32

Step-by-step explanation:

a) Data and Calculations:

Activity on the credit card statement for April

Beginning balance = $342.57

Date    Activity    Location       Amount     Daily Balance

04/01  Balance                                           $342.57

04/05 Payment  Payment     $200.00       $142.57

04/15  Charge    Gas               $26.37        $116.20

04/22 Charge    Macy's        $105.42          $10.78

04/25 Charge    Starbuck's     $4.24          $6.54

30 days   Total =                                       $618.66

Average balance = Total of the daily balances divided by 30 days

= $618.66/30 = $20.55

The value of the average daily balance and the finance charge for Miss pepper mills are $123.732 and $0.32 respectively.

The average daily balance :

Sum of balances = (342.57+ (342.57-200) +(342.57 - 200 - 26.37) +(342.57-200-26.37-105.42) + (342.57-200-26.37-105.42-4.24)) = $618.66

Average daily balance :

Finance charge for April :

Average balance × daily rate

Therefore, the average daily balance and finance charge are $123.732 and $0.32 respectively

Learn more : 149.9448066146972668163077278862934016

Answer:

The plane is 388 miles far from the airport.

Step-by-step explanation:

We know that, the angle between southeast and south directions is [tex]135^\circ[/tex].

The plane travels as per the triangle as shown in the attached image.

A is the location of airport.

First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.

[tex]\angle ABC = 135^\circ[/tex]

To find:

Side AC = ?

Solution:

As we can see, the [tex]\triangle ABC[/tex] is an isosceles triangle with sides AB = BC = 210 miles.

So, we can say that the angles opposite to the equal angles in a triangle are also equal. [tex]\angle A = \angle C[/tex]

And sum of all three angles of a triangle is equal to [tex]180^\circ[/tex].

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ[/tex]

Now, we can use Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB}[/tex]

a, b are the sides opposite to the angles [tex]\angle A and \angle B[/tex] respectively.

[tex]\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles[/tex]

So, the answer is:

The plane is 388 miles far from the airport.

Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5

Hi there! Hopefully this helps!

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

So, we know that 4 to the 4th power equals 256.

4 to the 4th power = 4 x 4 x 4 x 4.

So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.

4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or you could break the equation into parts.

For example, there are FOUR 4s in the equation.

4 x 4 = 16.

4 x 4 = 16.

16 x 16 = 256.

Now since we've added ANOTHER 4, it should look like this:

16 x 16 = 256.

256 x 4 = 1024.

Answer:

[tex]79591.8872 in^3/s[/tex]

Step-by-step explanation:

we know that the volume of a right circular cone is give as

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

Therefore differentiating partially  with respect to  r and h we have

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]

Option B

Because the average points scored in the night is more than that of the day

Answer:

Initial amount (a)= 620

Growth factor (b)= 7.8

Step-by-step explanation:

620 is the initial amount and is multiplied by 7.8 x which is the growth factor.

Answer:

P [ Z > 21 ] = 0,5   or   P [ Z > 21 ] = 50 %

Step-by-step explanation:

Normal Distribution N(21;4)

The question here is what is the area of the bell shape curve. As 21 is a mean for this distribution is in the middle of the bell, so values bigger than 21 will have a probability of 0,5, and values smaller than 21 will have the same probability 0,5. We must remember that the whole area under the curve has an area of 1 ( or 100% )

According to the given situation, the computation of two number in a given ratio is shown below:-

We assume the numbers is x and y

Given that

[tex]\frac{x}{y} = \frac{3}{1}[/tex]

x = 3y

and

[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]

With the help of above formula we will put the value and be able to find the values of x and y

x - y = 6

3y - y = 6

2y = 6

y = 3

x = 3y = 9

x = 9, y = 3

Therefore the correct answer is x = 9 where as y = 3