i will give brainliest

Five friends take a maths test
Adam, Brandon, Chen together together scored 200 marks
Brandon, Chen and Damion together scored 215
Chen, Damion, Erica together scored 224
Damion and Erica scored more than Chen
The five of them together scored 350 marks

What are their individual scores

Answer:

a) SAT score = 1075

b) ACT score = 19.2.

c) ACT score = 27.9.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score

SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]

51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So

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

[tex]0.025 = \frac{X - 1070}{204}[/tex]

[tex]X - 1070 = 0.025*204[/tex]

[tex]X = 1075[/tex]

SAT score = 1075.

(B) What would be the equivalent ACT score for this student?

ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So

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

[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 0.025*5.2[/tex]

[tex]X = 19.2[/tex]

ACT score = 19.2.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score.

Z-score for the SAT:

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

[tex]Z = \frac{1417 - 1070}{204}[/tex]

[tex]Z = 1.7[/tex]

Equivalent score on the ACT:

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

[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 1.7*5.2[/tex]

[tex]X = 27.9[/tex]

ACT score = 27.9.

9514 1404 393

Answer:

  103°

Step-by-step explanation:

The law of sines tells you ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin(c/a·sin(A)) = arcsin(37/19·sin(30°)) ≈ 180° -76.8° ≈ 103°

Obtuse angle C is about 103°.

Answer:

B

Step-by-step explanation:

is the right answer

The area of the shaded region is 12 feet². The correct option is A.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that the area of the outer rectangle above is 80feet². The area of the inner rectangle is 68feet². The area of the shaded region=area of the outer rectangle- the area of the inner rectangle.

The area of the shaded region=(80-68 )feet²

The area of the shaded region= 12feet²

Thus,  the area of the shaded region is 12feet².

Learn more about rectangles here:

https://brainly.com/question/23515075

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Answer:

B. -0.5

Step-by-step explanation:

I calculated it logically

Step-by-step explanation:

Thanks, so cube root of 512 is 8 and reciprocal of 0.4 is 2.5 then:

8 : 2.5 / divide both by 2.5 to get:

3.2 : 1 that's my answer right?

The correct form of the ratio of cube root of 512: reciprocal of 0.4 is 3.2:1

It is a number y such that y to the power 3 is equal to x.

We have to find the ratio of cube root of 512 and the reciprocal of 0.4  which will be as follows

cube root of 512:  reciprocal of 0.4

8: 1/0.4

8=2.5

dividing by 2.5

3.2 : 1

Hence the ratio will be 3.2 :1 of cube root of 512 and the reciprocal of 0.4

Learn more about cube root at https://brainly.com/question/310302

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Answer:

The father is 42 years old and the son is 12 years old.

Step-by-step explanation:

Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:

F + S = 48

F + 6 + S + 6 = 3S

34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)

38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)

40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)

39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)

39 + 3 = 42

9 + 3 = 12

Therefore, the father is 42 years old and the son is 12 years old.

Answer:

[tex]P(Work | Senior) = 0.14[/tex]

Step-by-step explanation:

Given

The attached table

Required

[tex]P(Work | Senior)[/tex]

This is calculated using:

[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]

This gives:

[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]

From the table:

[tex]n(Work \ n\ Senior) = 5[/tex]

[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]

So:

[tex]P(Work | Senior) = \frac{5}{35}[/tex]

[tex]P(Work | Senior) = 0.14[/tex]

Answer:

14%

Step-by-step explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer:

speed = 78 miles per hour

Step-by-step explanation:

Speed is distance divided by time

speed = 234 miles / 3 hours

speed = 78 miles per hour

Answer:

She needs a grade of 71 on her next text.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Tammy has scored 82, 78, and 93 on her previous three tests.

Thus, her grades are 82, 78, 93 and x, in which x is her grade in the fourth test.

There are 4 tests.

What score does she need on her next test so that her average (mean) is 81?

We have to find x when the mean is 81. So

[tex]\frac{82 + 78 + 93 + x}{4} = 81[/tex]

[tex]253 + x = 324[/tex]

[tex]x = 324 - 253[/tex]

[tex]x = 71[/tex]

She needs a grade of 71 on her next text.

Answer: the answer is 8 because

Step-by-step explanation:

Answer:

The correct answer is option C: (8, 14).

Step-by-step explanation:

The car's displacement in vector form can be found by subtracting the initial points from the final points.    

Initial: (x₁, y₁) = (-3, -5)

Final: (x₂, y₂) = (5, 9)          

For the x-coordinate, we have:  

[tex] d_{x} = x_{2} - x_{1} = 5 - (-3) = 8 [/tex]

And for the y-coordinate, we have:

[tex] d_{y} = y_{2} - y_{1} = 9 - (-5) = 14 [/tex]

The car's displacement in vector form is:

[tex] d = (d_{x}, d_{y}) = (8, 14) [/tex]  

Therefore, the correct answer is option C: (8, 14).

I hope it helps you!                        

Answer:

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

It's simple, the angle of a line is 180°

∠EFG=90°

Line GD-∠EFG=180°-90°=90°

Please mark brainliest!

Answer:

A factor, in mathematics, a number or algebraic expression that divides another number or expression evenly, with no remainder. A multiple of a number is any integer multiplied by the number. Try it yourself, now you know the how it works.

Answer:

4/5 of a fruit bar

Step-by-step explanation:

Answer:

He can lift 160 pounds

Step-by-step explanation:

125 (from last year) + 35 (more pounds) = 160 (total pounds)

125 + 35 = 160

Answer:

13 minutes

Step-by-step explanation:

The reason why it is 13 minutes is because you subtract 10:41 AM from 10:28 AM and you get 13 minutes.

Answer:

13

Step-by-step explanation:

41-28= 13

the hours don't change so you just need to subtract the minutes

Answer:

The answer is simply 49.

Step-by-step explanation:

196 ÷ 4 is why because their are 4 sides on a square if you divide it by 4 you get the answer 49. You're probably in like 3rd grade or smth this is so easy.

Given:

The given sum is:

[tex]\sum _{k=4}^9(5k+3)[/tex]

To find:

The expanded form and find the sum.

Solution:

We have,

[tex]\sum _{k=4}^9(5k+3)[/tex]

The expanded form of given sum is:

[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]

[tex]\sum _{k=4}^9(5k+3)=213[/tex]

Therefore, the correct option is C.

Answer:

[tex]6.7159[/tex]

Step-by-step explanation:

[tex]\mu=48.8\\n=35\\\bar{x}=53.8\\\sigma=4.4\\\alpha=1\%=0.01[/tex]

Null and alternative hypothesis :

[tex]H_0:\mu=48.8\\H_a:\mu>48.8[/tex]

Test statistic,

[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]\Rightarrow t=\frac{53.8-48.8}{\frac{4.4}{\sqrt{35}}}[/tex]

[tex]\Rightarrow t=\frac{5\times 5.91}{4.4}[/tex]

[tex]\Rightarrow t=6.715[/tex]

Test statistic [tex]t=6.715[/tex]

[tex]P-[/tex]value [tex]=P(t>6.715)[/tex]

[tex]P-[/tex] value [tex]=0.0001[/tex]  by the p- table

Significance level [tex]0.01[/tex]

         [tex]p-[/tex]value [tex]<0.01[/tex]

  We reject [tex]H_0[/tex]

Answer:

3692.64 cm³

Step-by-step explanation:

Answer: The  maximum   value is   -3.75  

Note: -3.75 = -15/4

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

Explanation:

The given quadratic is in the form y = ax^2 + bx + c, where,

We'll plug the values of 'a' and b into the formula below

h = -b/(2a)

h = -1/(2(-1))

h = 1/2

h = 0.5

This represents the x coordinate of the vertex. Recall the vertex is (h,k).

Plug this x value into the function to find its corresponding y coordinate

y = -x^2 + x - 4

y = -(0.5)^2 + 0.5 - 4

y = -3.75

The vertex is located at (0.5, -3.75)

Since a < 0, this means the parabola opens downward and that the vertex is the highest point on the parabola. Therefore, the largest y can get is y = -3.75 which we consider the maximum.

The graph visually helps confirm this (see image attachment).

Side note: -3.75 = -15/4

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

Here's another way we can find the vertex (h,k). We'll complete the square to get the function into vertex form

y = -x^2 + x - 4

y + 4 = -x^2 + x

y + 4 = -(x^2 - x)

y + 4 = -(x^2 - x + 0)

y + 4 = -(x^2 - x + 0.25 - 0.25) .... see note below

y + 4 = -(x^2 - x + 0.25) -(-0.25)

y + 4 = -(x^2 - x + 0.25) + 0.25

y + 4 = -(x - 0.5)^2 + 0.25

y = -(x - 0.5)^2 + 0.25 - 4

y = -(x - 0.5)^2 - 3.75

This is in the form y = a(x-h)^2 + k where (h,k) = (0.5, -3.75).

Note: The x coefficient is -1 which cuts in half to -0.5, then that squares to 0.25

Answer:

its not loading

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/48 + 5/6    

The LCD of 48 and 6 is 48 so we have:

1/48 + 40/48

= 41/38

Answer:

41/48

Step-by-step explanation: