Answer:
c. Both Tami and Vu performed equally well.
Step-by-step explanation:
To solve this question, we use z score
The formula for calculating a z-score is is z = (x-μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation.
a) For Tami , who took MCAT
We are told:
Scores on the MCAT follow a Normal distribution with a mean of 505.6 points and a standard deviation of 9.3 points.. If Tami earns 524.2 points on the MCAT.
x = 524.2 points
μ = 505.6 points
σ = 9.3 points
z = 524.2 - 505.6/9.3
= 2
The z score for Tami is 2
For Vu, who took LSAT
We were told:
Scores on the LSAT follow a Normal distribution with a mean of 150.7 points and a standard deviation of 10.2 points. Vu earns 171.1 points on the LSAT.
x = 171.1 points
μ = 150.7 points
σ = 10.2 points
z = 171.1 - 150.7/10.2
z = 2
The z score for Vu is also equal to 2
Therefore, we can say the bout Tami and Vu performed equally well.
Option c is the correct answer.
The wind is blowing N 35.0 degrees W at 1.60 * 10^2 mph. A plane has an engine speed of 3.20 * 10^2 mph. Where should the pilot point the plane in order to fly straight W?
Answer: 24.2° SouthWest
Step-by-step explanation:
First step: DRAW A PICTURE of the vectors from head to tail (see image)
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
Perpendicular (x):
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
Angle (θ):
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope of -0.5. The y-intercept of the line is
0.5 mi = 2, 640 ft
O True
False
Answer:True
Step-by-step explanation:
If you multiply the length value, you would get 2640 ft, so the answer is true.
If martha is walking 9meters south and turns and walks 10meters west how far is she from her starting point?
Answer:
She is 13.45 meters from her starting point.
Step-by-step explanation:
Use Pythagorean Theorem (a^2+b^2=c^2) so 9^2+10^2=c^2. Solve it algebraically and you get c= 13.45 (rounded to nearest hundredth).
Find the slope of (2,-3) (-4,7)
Answer:
m = 139167 / 329 = 423 / 1 = 423
Step-by-step explanation:
\displaystyle\int_{-\infty}^\infty e^{-x^2}dx = \sqrt{\pi}
\displaystyle \sum_{n} \frac{1}{n^s} = \prod_{p} {\frac{1}{1 - \frac{1}{p^s}}}
\displaystyle n! = \int_{0}^{\infty} {x^n e^{-x} \,dx}
F(n) = \frac{(\varphi)^n - (-\frac{1}{\varphi})^n}{\sqrt{5}}
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Point A is at (-2, 4) and point M is at (2.5, 3.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
let [tex] A(-2, 4) = (x_2, y_2) [/tex]
[tex] B(?, ?) = (x_1, y_1) [/tex]
[tex] M(2.5, 3.5) = (\frac{x_1 +(-2)}{2}, \frac{y_1 +(4)}{2}) [/tex]
Rewrite the equation to find the coordinates of B
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex] and [tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
Solve for each:
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex]
[tex] 2.5*2 = \frac{x_1 - 2}{2}*2 [/tex]
[tex] 5 = x_1 - 2 [/tex]
[tex] 5 + 2 = x_1 - 2 + 2 [/tex]
[tex] 7 = x_1 [/tex]
[tex] x_1 = 7 [/tex]
[tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
[tex] 3.5*2 = \frac{y_1 + 4}{2}*2 [/tex]
[tex] 7 = y_1 + 4 [/tex]
[tex] 7 - 4 = y_1 + 4 - 4 [/tex]
[tex] 3 = y_1 [/tex]
[tex] y_1 = 3 [/tex]
Coordinates of point B: (7, 3)
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
Rewrite the equation to find the coordinates of B
Coordinates of point B: (7, 3)
40% of 250 is equal to 60% of what number
Answer:
24
Step-by-step explanation:
250% × ? = 60
? =
60 ÷ 250% =
60 ÷ (250 ÷ 100) =
(100 × 60) ÷ 250 =
6,000 ÷ 250 =
24
Which expression is another way to write 10,000,000? 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Answer:
Step-by-step explanation:
10^6
Answer:
10^6
Step-by-step explanation:
I NEED HELP
(-8, 6); slope = 1/4
6 = 1/4(-8) +b
6 = -2 +b
8 = b
y = 1/4x +8The equation of this line having slope 1/4 and points (-8,6) is y = (1/4)x + 8.
What is slope ?Slope is the rate of change.It can also be thought of as rise over run.
According to the given question slope(m) is 1/4 and point is (-8,6).
We know equation of a line in slope intercept form is y = mx + b, where b is the y intercept.
∴ 6 = (-8)1/4 + b.
6 = - 2 + b.
b = 8.
Now the equation of this line in slope intercept from can be written as
y = (1/4)x + 8.
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Naron is 3 times older than his sister. In 2 years, Naron will be twice as old as his sister. How old is each now?
Answer:
A possible answer is that Naron is 6 yrs old and his sister is 2 yrs old.
Step-by-step explanation:
6 is 3 times as much as 2
(6+2)/2=2+2
8/2=4
Answer:
Naron is 6 years old and his sister is 2 years old
Step-by-step explanation:
Question
Example
Step by Step
Jennifer is saving money to buy a bike. The bike costs
$213. She has $123 saved, and each week she adds $18
to her savings.
How long will it take her to save enough money to buy
the bike?
It will take her
weeks _____to save for the bike.
Answer:
5
Step-by-step explanation:
18x5=90+123=213.
Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
Q: Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
A: 20 soccer balls
Hope this helped!
Can anybody help and get this right I keep getting it wrong ..
Answer:its d
Step-by-step explanation:
translation is the point (2, −6). At what coordinates is the image of point (−3, −2) located under the same translation?
Answer:
hey
Step-by-step explanation:
Graph y=3/4+4 Please! I need help!
Algebra 1 unit 4 mid quiz
The inequality that represents this graph is y < 2x + 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The dotted line represents strictly less than or greater than.
From the graph, we can conclude that when x = 0, y = 2, and when x = 1 y = 4, and values of y are strictly less.
∴ The inequality that represents this graph is y < 2x + 2.
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Find the value of x:
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. There you go!
Select each transformation that carries a square onto itself.
a reflection over one of the square's sides
3 rotation of 180' clockwise about the square's center
a rotation of 90: clockwise about the squares center
a rotation of 180: clockwise about one of the squares vertices
: reflection over one of the souare s diagonals
Answer:
1. a reflection over one of the square's sides
2. a rotation of 90: clockwise about the squares center
3. a rotation of 180' clockwise about the square's center
Step-by-step explanation:
I did a test :)
45 degrees+2k+k=180
can you help me with this?
Answer:
k=45
Step-by-step explanation:
45+2k+k=180
Step 1: Simplify both sides of the equation.
45+2k+k=180
(2k+k)+(45)=180(Combine Like Terms)
3k+45=180
3k+45=180
Step 2: Subtract 45 from both sides.
3k+45−45=180−45
3k=135
Step 3: Divide both sides by 3.
3k/3=135/3
k=45
Find the unknown value in the proportion.
4/7=?/14. please help
Answer:
8
Step-by-step explanation:
4/7 = ?/14
Multiply the numerator and denominator of the left fraction by 2.
8/14 = ?/14
That means that ? = 8
Answer: 8
Answer:
8
Step-by-step explanation:
Step 1:
4/7 = x/14 Proportion
Step 2:
7x = 56 Multiply
Step 3:
x = 56 ÷ 7 Divide
Answer:
x = 8
Hope This Helps :)
Si tienes 5 manzanas para comer durante la semana y te comes el 20% el primer día cuántas manzanas quedan para el resto de la seman?
Answer: El o Ella tiene 4 manazanas izquierda comer para el semana
Step-by-step explanation: Si necesitas ayuda con algo más estoy disponible generalmente de 9 a.m. a 3:50 p.m.
The number of apples left to eat are equivalent to 4.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that you have 5 apples to eat during the week and you eat 20% on the first day.
Assume the number of apples left are {x}. So, we can write -
{x] = 5 - 20% of 5
{x} = 5 - (20/100) x 5
{x} = 5 - 1
{x} = 4
Therefore,
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{Question in english -
If you have 5 apples to eat during the week and you eat 20% on the first day, how many apples are left for the rest of the week?}
Which postulate or theorem proves that these two triangles are
congruent?
HL Congruence Theorem
SAS Congruence Postulate
ASA Congruence Postulate
AAS Congruence Theorem
Answer:
ASA
Step-by-step explanation:
Took the test.
whats the degree of the polynomial 5a-2b^2+1
Answer:
hope it helps..
Step-by-step explanation:
PLEASE THANK MY ANSWER
Help ASAP). Which relation is a function. Where the hand is at thats graph A across is graph B. The graph under graph a is ( graph C). Under graph B is (graph D). Need answer now please and thank you. [ I chose B but not 100% sure]
How my calories are in 48 oz if tea
Answer:
2 calories
Step-by-step explanation:
yes
Answer:
The answer you are looking for is 2 calories.
Step-by-step explanation:
1 serving 8 fl oz cup (238 g)
if x=-3 is the only x-incercept of the graph of a quadratic equation which statement best describes the discrinant of the equation
Answer:
The discriminant must be zero.
Step-by-step explanation:
Quadratic Equation
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
The zeros, roots, or x-intercepts can be found by solving the equation:
[tex]ax^2+bx+c=0[/tex]
We can use the quadratic formula to find the roots:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Note this formula gives us two different roots if the square root is non-zero.
The only way there can be only one x-intercept is because the square root is zero.
If the square root is zero, then
[tex]b^2-4ac =0[/tex]
The expression is called the discriminant.
Thus, if x=-3 is the only x-intercept of the graph of a quadratic function, then the discriminant must be zero.
Which of the following is not a rational number? (-12/35) (10) (2/0) (2 1/2)
Answer:
(- 12/35) THIS IS THE MAIN ANSWER YOU CAN SEE IN THE GOOGLE
y - 5 = 1/10 (x – 10)
How do you rewrite the equation in slope-intercept form?
Answer.
Y=|10x-100|+5
For babysitting, Zou Jing charges a flat fee of $10, plus $15 per hour. Write an equation for the cost, C, after h hours of babysitting. How much money will she make if she baby-sits 5 hours? How many hours does Zou Jing need to babysit to afford a PS5 ($500)?
Answer:
C=5h+3 when h=5
C=28
Step-by-step explanation:
An acre is a unit of measure for area. One acre ie equal to 43,560 square feet. Often, an acre is a rectangle that measures 660 feet by 66 feet. However, the length and width of the rectangle can vary. An acre can actually have any shape, as long as it measures exactly 43,560 square feet. Rachel purchased 1/5 acre of land in the shape of an isosceles triangle. What is the area of the land Rachel purchased?
Answer:
area of land purchased =247
The area of the land Rachel purchased is approximately 10,055.64 square feet.
How to calculate the area?We can start by finding the area of one acre in square feet, which is given as 43,560 square feet.
To find the area of 1/5 acre, we can divide 43,560 by 5, which gives us 8,712 square feet.
Since Rachel's land is in the shape of an isosceles triangle, we need to find the base and height of the triangle in order to calculate its area. Let's call the length of the base "b" and the height "h".
We know that the area of a triangle is given by the formula:
Area = (1/2) x base x height
So, we can rearrange this formula to solve for the height:
height = 2 x Area / base
Now we can substitute in the values we know:
Area = 8,712 square feet
base = unknown
height = unknown
We also know that the triangle is isosceles, which means that two of the sides are equal in length. Let's call the length of one of these sides "s". Then the length of the base can be expressed in terms of s as:
base = 2s
We can use the Pythagorean theorem to find the height in terms of s:
s² + (h)² = (2s)²
s² + h² = 4s²
h² = 3s²
h = s x √(3)
Now we can substitute this expression for the height in terms of s into the formula we derived for the area:
Area = (1/2) x base x height
Area = (1/2) x 2s x s x √(3)
Area = s² x √(3)
We know that the area of the triangle is 1/5 of an acre or 8,712 square feet, so we can set this equal to the expression we just derived for the area and solve for s:
s² x √(3) = 8,712
s² = 8,712 / √(3)
s = √(8,712 / √(3))
Now that we know the length of one of the equal sides of the isosceles triangle, we can find the length of the base by multiplying by 2:
base = 2s
base = 2 x √(8,712 / √(3))
Finally, we can substitute in the values we just found for the base and height into the formula for the area of the triangle:
Area = (1/2) x base x height
Area = (1/2) x 2 x √(8,712 / √(3)) x √(3) x √(8,712 / √(3))
Area = 2 x 8,712 / √(3)
Area = 17,424 / √(3)
Therefore, the area of the land Rachel purchased is approximately 10,055.64 square feet.
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