Answer:
[tex]Adam = 60[/tex]
[tex]Brandon = 66[/tex]
[tex]Chen = 74[/tex]
[tex]Damion = 75[/tex]
[tex]Erica = 75[/tex]
Step-by-step explanation:
Given
Represent each friend with the first letter of their name
So:
[tex]A + B + C =200[/tex]
[tex]B + C + D = 215[/tex]
[tex]C + D +E= 224[/tex]
[tex]A + B + C + D + E = 350[/tex]
[tex]D , E > C[/tex]
Substitute: [tex]A + B + C =200[/tex] in [tex]A + B + C + D + E = 350[/tex]
[tex]200 + D + E = 350[/tex]
Collect like terms
[tex]D + E = 350-200[/tex]
[tex]D + E = 150[/tex]
Make D + E the subject in [tex]C + D +E= 224[/tex]
[tex]D + E = 224 - C[/tex]
Substitute [tex]D + E = 224 - C[/tex] in [tex]D + E = 150[/tex]
[tex]224 - C = 150[/tex]
Collect like terms
[tex]C = 224 - 150[/tex]
[tex]C = 74[/tex]
Substitute [tex]C = 74[/tex] in [tex]A + B + C =200[/tex] and [tex]B + C + D = 215[/tex]
[tex]A + B + 74 = 200[/tex]
[tex]A + B =- 74 + 200[/tex]
[tex]A + B =126[/tex]
[tex]B + 74 + D = 215[/tex]
[tex]B + D = -74 + 215[/tex]
[tex]B + D = 141[/tex]
So, we have:
[tex]A + B =126[/tex]
[tex]B + D = 141[/tex]
[tex]D + E = 150[/tex]
We have: [tex]D , E > C[/tex]
i.e.
[tex]D , E > 74[/tex] and [tex]D + E = 150[/tex]
For [tex]D , E > 74[/tex] and [tex]D + E = 150[/tex] to be true,
[tex]D = E = 75[/tex]
i.e.
[tex]75 + 75 = 150[/tex]
So, we have:
[tex]D = 75[/tex]
[tex]E = 75[/tex]
[tex]B + D = 141[/tex]
[tex]B + 75 = 141[/tex]
[tex]B = 141 - 75[/tex]
[tex]B = 66[/tex]
[tex]A + B =126[/tex]
[tex]A + 66 = 126[/tex]
[tex]A = 126 - 66[/tex]
[tex]A = 60[/tex]
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
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.
A square has an area of 196 square centimeters. What is the length of each side?
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.
What choice is the range of f(x)=√x-3-1
Answer:
its not loading
Step-by-step explanation:
Help please
(Worth 10 points)
Please respond with a actual answer
*No robots no bad links*
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student works, given that it's a
senior.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P( Work | Senior) = [?]
Round to the nearest hundredth.
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).
will give brainliest
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:
Work out cube root of 512 : reciprocal of 0.4. Give your answer in the form n : 1
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
What is a cube root?
It is a number y such that y to the power 3 is equal to x.
How to find ratio?
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
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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 son. Find the present ages of the father and his son.
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.
Help just help please. !!!
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,
a = -1b = 1c = -4We'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
Bert measured a swimming pool and made a scale drawing. The scale of the drawing was
1 centimeter = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Submit
Tammy has scored 82, 78, and 93 on her previous three tests. What score does she need on her next test so that her average (mean) is 81?
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.
Ms. Lin’s son likes to lift weights. He was lifting 125 pounds last year. This year he can lift 35 more pounds. How much weight can he lift this year?
Answer:
He can lift 160 pounds
Step-by-step explanation:
125 (from last year) + 35 (more pounds) = 160 (total pounds)
125 + 35 = 160
A consumer group claims that the average annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. You believe it is higher. You take a simple random sample of 35 people in the U.S. and find an average of 53.8 pounds with a standard deviation of 4.4 pounds. Test at 1% significance. Round to the fourth
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]
What is the volume of a regular cylinder whose base has a radius of 14cm and has a height of 6 cm
Answer:
3692.64 cm³
Step-by-step explanation:
what time is seven to eight
Five friends are sharing 4 fruit bars. Each friend gets the same amount.
How much fruit bar does each friend get?
Answer:
4/5 of a fruit bar
Step-by-step explanation:
The area of the outer rectangle above is 80 ft, and the area of the inner rectangle is 68 ft. What is the area of the shaded region?
Answer:
B
Step-by-step explanation:
is the right answer
The area of the shaded region is 12 feet². The correct option is A.
What is a rectangle?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:
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A section of a deck is shaped like a trapezoid. For this section, the length of one base is 41 feet, and the length of the other base is 36 feet. The height is 20 feet. What is the area of this section of the deck?
Answer:
Step-by-step explanation:
What is the speed if the distance is 234 MI and time is 3 hrs
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
Please help me solve this problem
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!
Ashley started washing at 10:28 AM and finished at 10:41 AM.
How long did it take her? Give your answer in minutes.
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
Trying to finish this test at 3:30 am plz help
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.
I need help, please !
Answer: the answer is 8 because
Step-by-step explanation:
Please help me solve this
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°.
A vector is used to express a car's change in position, or displacement, by tracking its motion over a large area defined by a coordinate grid. If the car begins at (−3,−5) and ends at (5,9), which of these expresses the car's displacement in vector form?
A
(14,8)
B
(10,12)
C
(8,14)
D
(2,4)
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!
Practice
what is sin(-30*) ? Sketch a graph to help determine the answer.
a. 0.5
b. -0.5
c. 1
d. 0
Please select the best answer from the choices provided
Answer:
B. -0.5
Step-by-step explanation:
I calculated it logically
Could you please explain in detail how to graph this. Thank you:)
James drove 29 hours at a rate of 65 mph. How many miles did he drive?
Chile I’m struggling
Answer:
the answer is c
Step-by-step explanation:
guys help me
can u give me the answer
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.