The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?

Minimum Score:

Answer:

d = 8

Step-by-step explanation:

(d-5)/ -3 = -1

Multiply each side by -3

(d-5)/ -3 *-3 = -1*-3

d-5 = 3

Add 5 to each side

d-5+5 = 3+5

d = 8

Answer:

(-0.3, 2.3)

Step-by-step explanation:

(-1.8+1.2)/2 = -0.3

(1.9+2.7)/2 = 2.3

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 1.8 , 1.9 ) ⇒( x₁ , y₁ )

B ( 1.2 , 2.7 )⇒ ( x₂ , y₂ )

Now, let's find the midpoint:

[tex] \mathsf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} )}[/tex]

Plug the values

[tex] \mathsf{ = (\frac{ - 1.8 + 1.2}{2} \: , \frac{1.9 + 2.7}{2} )}[/tex]

Calculate

[tex] \mathsf{ = ( \frac{ - 0.6}{2} \: , \frac{4.6}{2} )}[/tex]

[tex] \mathsf{ = (- 0.3 \:, 2.3)}[/tex]

Hope I helped!

Best regards!

Answer:

14 mi

Step-by-step explanation:

Cedarburg is 22 13/16 miles from Allenville and 8 13/16 miles from Lakeside.  You have to solve for the distance from Lakeside to Allenville.

8 13/16  +  x  =  22 13/16

(8 13/16  +  x)  -  8 13/16  =  22 13/16  -  8 13/16

x  =  14

The distance from Lakeside to Allenville is 14 miles.

[tex]\begin{cases}\large\bf{\green{ \implies}} \tt \: - \frac{6}{5} \: k \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{6k}{5} \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: - 6k \: = \: 12 \: \times \: 5 \\ \\ \large\bf{\green{ \implies}} \tt \: - 6k \: = \: 60 \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: \cancel\frac{60}{ - 6} \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: - 10 \end{cases}[/tex]

Answer:

540

Step-by-step explanation:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

Answer:

540

Step-by-step explanation:

Hey there!

Well we need to first find all the palindromic numbers,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99

Add

= 540

Hope this helps :)

Answer:

4.5

Step-by-step explanation:

2/8=x/18

Answer:

4.5 cups

Step-by-step explanation:

first you set up the problem like servings/cups. This would look like 8/2. Then you add the 18 servings and make it a cross multiplication problem. The expression would look like 8/2=18/x. You cross multiply and get 8x=36. Divide by 8 and get x=4.5 cups.

Answer:

3/4 is the slope

Step-by-step explanation:

We want to put this in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

0 = -12 + 4y - 3x

Subtract 4y from each side

-4y = -3x-12

Divide each side by -4

-4y/-4 = -3x/-4 -12/-4

y = 3/4 x +3

Answer:

Slope=3/4

Step-by-step explanation:

0=-12+4y-3x (Add 12 on the other side)

12=4y-3x (Add 3x on the other side)

3x+12=4y (Divide by 4)

y=3/4+3

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Answer:

The answer is usted

Step-by-step explanation:

And if you want to learn more download duolingo

Step-by-step explanation:

Set up f(x).

[tex] \sqrt[3]{11x - 3} = f(x)[/tex]

Replace f(x) with y

[tex] \sqrt[3]{11x - 3} = y[/tex]

Swap x and y

[tex] \sqrt[3]{11y - 3} = x[/tex]

Solve for y

Cube both sides

[tex]11y - 3 = {x}^{3} [/tex]

Add 3 to both sides

[tex]11y = {x}^{3} + 3[/tex]

Divide both sides by 11

[tex]y = \frac{x {}^{3} + 3 }{11} [/tex]

so

[tex]f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11} [/tex]

Answer:

y=4/3x-3

Step-by-step explanation:

Answer:

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1)

Step-by-step explanation:

Let a be the first term.

Let a+d be the second term where d is the common difference.

Then a+2d is the third....

And a+(n-1)d is the nth term.

Adding these terms we get:

an+(n-1)(n)/2×d

For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.

Let's simplify:

an+(n-1)(n)/2×d

Distribute:

an+(n^2d/2)-(nd/2)

Find common denominator:

(2an/2)+(n^2d/2)-(nd/2)

Combine terms into one:

(2an+n^2d-nd)/2

Reorder terms:

(n^2d+2an-nd)/2

Regroup terms:

(n^2d+(2a-d)n)/2

We want the following sum though:

4n^2+3n

This means d/2=4 (so d=8) and (2a-d)/2=3.

So plug d=8 into second equation to solve for a.

(2a-8)/2=3

2a-8=6

2a=14

a=7

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1).

Answer:

81+27= candidates

candidates-37=81

Answer:

2.8

Step-by-step explanation:

Hey there!

Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.

46.2 / 16.5

= 2.8

2.58 minutes

Hope this helps :)

Answer:

V≈113.1

Step-by-step explanation:

V=πr2h

3=π·32·12

3≈113.09734

Answer:

0.204

Step-by-step explanation:

The formula to use to solve this is the combination formula.

Combination formula =

C(n, r) = nCr = n!/r! (n - r)!

Total number of kittens = 8 boy kittens + 9 girl kittens

= 17 kittens

Step 1

We find the probability of choosing 4 boy kittens out of 8 boy kittens

= 8C4 = 8!/4! × (8 - 4)!

= 8C4 = 8! / 4! × 4!

= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)

8C4 = 70

Step 2

We find the probability of choosing 7 girl kittens out of 9 girl kittens

9C7 = 9!/7! × (9 - 7)!

= 9C7 = 9! / 7! × 2!

= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)

9C7 = 36

Step 3

Find the probability of Picking 11 kittens out of 17 kittens

17C11 = 17!/11! × (17 - 11)!

= 17C11 = 17! / 11! × 6!

= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)

17C11 = 12,376

Step 4

The final step

The probability that the director chooses 4 boy kittens and 7 girl kittens

= 8C4 × 9C7/ 17C11

= 70 × 36/12376

= 2520/12376

= 0.2036199095

Approximately to 3 decimal places = 0.204

Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204

Answer:

That would be written as $16,800.00, or as $19,811.90 if you convert it at the current rate of exchange.

Step-by-step explanation:

Periods are used in European numbers to split up each third placed number while commas are used in the U.S.

Answer:

= 19824 us dollars

Step-by-step explanation:

Today august 09 2020:

1€ = 1.18 us dollars

then:

16800€ = 16800*1.18 = 19824 us dollars

Answer:- 10[tex]m^{2}[/tex] + 3m -9

Step-by-step explanation: Given ;  

  A= -3 -m

  B= 3m -5[tex]m^{2}[/tex]

 2B + 3A

        solution

     2B + 3A

substitute A and B in the formula

    2(3m - 5[tex]m^{2}[/tex]) + 3(-3 -m)

    6m - 10[tex]m^{2}[/tex] - 9 - 3m   group like terms

    - 10[tex]m^{2}[/tex] + (6m -3m) -9

     - 10[tex]m^{2}[/tex] + 3m -9

Answer:

Step-by-step explanation:

If I choose a number from the integers 1 to 25, the total number of integers I can pick is the total outcome which is 25. n(U) = 25

Let the probability that the number chosen at random is a multiple of  6 be P(A) and the probability that the number chosen at random is is larger than 18 be P(B)

P(A) = P(multiple of 6)

P(B) = P(number larger than 18)

A = {6, 12, 18, 24}

B = {19, 20, 21, 22, 23, 24, 25}

The conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is expressed as P(A|B).

P(A|B) = P(A∩B)/P(B)

Since probability = expected outcome/total outcome

A∩B = {24}

n(A∩B) = 1

P(A∩B) = n(A∩B)/n(U)

P(A∩B) = 1/25

Given B = {19, 20, 21, 22, 23, 24, 25}.

n(B) = 7

p(B) = n(B)/n(U)

p(B) = 7/25

Since P(A|B) = P(A∩B)/P(B)

P(A|B) = (1/25)/(7/24)

P(A|B) = 1/25*25/7

P(A|B) = 1/7

Hence the conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is 1/7

Answer:

48

Step-by-step explanation:

Pythagorean Theorem = h^2=p^2+b^2

We have,

(Hypotenuse)h=50

Let 14 be p, i.e (Perpendicular ,Known side)p=14

(Remaining side ,base)b=?(

Now,  

h^2=p^2+b^2

or, 50^2=14^2+b^2

or, 2500-196=b^2

or, √2304=b

b=48

9514 1404 393

Answer:

  750 cm³

Step-by-step explanation:

The volume is given by the formula ...

  V = LWH . . . . where L, W, H represent length, width, height

The volume is the product of the dimensions.

  V = (15 cm)(5 cm)(10 cm) = 750 cm³

Answer:

1. 2 -- x-axis represents time, each vertical line represents 2 hours. (8 lines, 16 hours total)

2. 10 --- y-axis represents number of customers. (5 lines, 52 customers total. points go just above 5th line)

hope this helps :)

Answer:

y=1/3x

Step-by-step explanation:

change in y/ change in x

2-0/6-0= 2/6=1/3

since its a positive slope, it’s 1/3

Answer:

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

Step-by-step explanation:

Take the two points shown:

[tex](0,0)(6,2)[/tex]

Use these to make an equation in slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept (where x is equal to 0).

Use the slope formula:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert coordinate points:

[tex](0_{x1},0_{y1})\\\\(6_{x2},2_{y2})\\\\\frac{2-0}{6-0}[/tex]

Simplify:

[tex]\frac{2-0}{6-0} =\frac{2}{6} =\frac{1}{3}[/tex]

The slope is [tex]\frac{1}{3}[/tex]. Insert this into the equation:

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

Now find the y-intercept. Take one of the coordinate points and insert:

[tex](6_{x},2_{y})\\\\2=\frac{1}{3}(6)+b[/tex]

Solve for b. Simplify multiplication:

[tex]\frac{1}{3}*\frac{6}{1}=\frac{6}{3}=2\\\\ 2=2+b[/tex]

Use reverse operations to isolate the variable:

[tex]2-2=2-2+b\\\\0=b[/tex]

The y-intercept is equal to 0. Insert this into the equation:

[tex]y=\frac{1}{3}x+0[/tex]

or

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

:Done

Answer

The total probability is one:

Total probability of being greater than 25 is 1 because the totals of all values less than 25 is 1.

[tex]A\cup B=\{q,s,u,w,y,z\}\\(A\cup B)'=\{r,t,v,x\}\\\boxed{(A\cup B)'\cap C=\{v,x\}}[/tex]

Answer:

1/3

Step-by-step explanation:

1[tex]\\1\frac{2}{5} =1.4\\\\[/tex]

[tex]1\frac{3}{5} =1.6[/tex]

[tex]1.6+1.4=3[/tex]

3 Liters of Fruit Punch.

3/9=1/3 Fruit Punch among the 9 glasses.

Answer: Hi!

We can simplify this by combining like terms:

-12w + 7w - 3 - 6

-12w + 7w = -5w

-3 - 6 = -9

Out equation now looks like this:

-5w - 9

There's nothing left to simplify, so we're done!

Hope this helps!

Answer:

C) 3/2x-1/8

Step-by-step explanation:

We can see that it has a generally positive slope, which rules out B and D.

Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10).  This rules out A.

While it doesn’t fit perfectly, C is by far the closest.

Answer:

2 seconds

Step-by-step explanation:

Given the equation:

[tex]f(x) = -x^2 + x + 2[/tex]

Where f(x) represents the height of each ball thrown by machine.

and x represents the time in seconds.

To find:

The number of seconds after which the machine throws the balls hits the ground = ?

Solution:

In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]

(Because when the ball hits the ground, the height becomes 0).

Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]

[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]

[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.

So, the answer is after 2 seconds, the ball hits the ground.

*a clearer picture containing the graph is shown in the attachment

Answer:

20% of the class earned a D

Step-by-step Explanation:

Step 1: Determine the total number of students represented on the graph:

9 students => D

5 students => C

14 students => B

17 students => A

Total number of students = 45

Step 2: Express each category of students who scored a particular grade as a fraction and as percentage.

9 students => D => [tex] \frac{9}{45} = \frac{1}{5} [/tex] => as percentage, we have [tex] \frac{1}{5} * 100 = 20 percent [/tex]

5 students => C => [tex] \frac{5}{45} = \frac{1}{9} [/tex] => as percentage, we have [tex] \frac{1}{9} * 100 = 11.1 percent [/tex]

14 students => B => [tex] \frac{14}{45} [/tex] => as percentage, we have [tex] \frac{14}{45} * 100 = 31.1 percent [/tex]

17 students => A => [tex] \frac{17}{45} [/tex] => as percentage, we have [tex] \frac{17}{45} * 100 = 37.8 percent [/tex]

Step 3: Check each statement to see if they are true or not based on the calculations above.

Statement 1: "⅕ of the students earned a C."

This is NOT TRUE From our calculation, ⅑ of the students earned a C.

Statement 2: "3% more students earned an A than a B." This is also NOT TRUE.

37.8% earned A, while 31.1% earned a B. Thus, about 6.7% more students earned an A than a B.

Statement 3: "20% of the class earned a D".  This is TRUE.

Check calculation in step 2.

Statement 4: "¼ of the class earned a B". This is NOT TRUE.

¼ is 25% of the class. Those who earned a B account for 31.1% not 25% (¼ of the class).

The correct statement is: "20% of the class earned a D"