Using the normal distribituion, it is found that 2.28% of of scores were less than 40.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively:
[tex]\mu = 52, \sigma = 6[/tex].
The proportion of scores that were less than 40 is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 52}{6}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
2.28% of of scores were less than 40.
More can be learned about the normal distribituion at https://brainly.com/question/24663213
Convert the angle to radians: 85
Answer:
17pi/36 (PLATO answer)
Step-by-step explanation:
there were 63 fewer pears than apples in the supermarket. After 37 pears were sold, how many fewer pears than apples ?
Step-by-step explanation:
63/37 = 1.702 = 1.7
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What is the value of x? Enter your answer in the box.
Answer:
x = 8
y = 6
Step-by-step explanation:
First and foremost, it's an equilateral triangle, therefore all sides and angles are equal.
Knowing that the sum of angle in a triangle is 180°, therefore each angle is 60°.
Then equating (7x+4)° to 60, we have that,
7x+4=60
7x=60-4
7x=56
x=56÷7
x=8.
Simpifly x + x + y x y
x+x + y * y = 2x + y²
Answer:
[tex]2x + y^{2}[/tex]
Step-by-step explanation:
[tex]\text{If a number is being added to itself, it is basically a number being multiplied by 2. }[/tex]
[tex]\rightarrow x + x[/tex]
[tex]\rightarrow \boxed{\bold{2x}}[/tex]
[tex]\text{If a number is being multiplied by itself, it is basically the number squared.}[/tex]
[tex]\rightarrow y \times y[/tex]
[tex]\rightarrow \boxed{\bold{y^{2}}}[/tex]
Thus, the simplified expression is 2x + y².
CAN SOMEONE HELP PLS?? I rlly dont get this.
The little square on the angle means that the entire angle is 90 degrees
The larger angle is made up of two angles of measure 'x - 18' and 'x'
Let's put that into an equation form:
(x - 18) + (x) = 90
2x - 18 = 90
2x = 108
x = 54
So x = 54
Hope that helps!
. A particle moves on a line away from its initial position so that after t seconds its distance is s = 3t^2+tmeters from its initial position. (a) At what time does the particle have a velocity of 25 m/s? (b) Is the acceleration ever 0? Why or why/not? Explain your answer
pls solve and explain fast
Answer:
The velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].
Acceleration is constantly [tex]6\; {\rm m\cdot s^{-2}}[/tex] (and thus is never [tex]0[/tex].)
Step-by-step explanation:
The distance between the particle and the initial position is the displacement of this particle. Let [tex]x(t)[/tex] denote the displacement (in meters) of this particle at time [tex]t[/tex] (in seconds.) The question states that [tex]x(t) = 3\, t^{2} + t[/tex].
Differentiate displacement [tex]x(t)[/tex] with respect to time [tex]t[/tex] to find the velocity [tex]v(t)[/tex] (in [tex]{\rm m \cdot s^{-1}}[/tex]) of this particle:
[tex]\begin{aligned}v(t) &= \frac{d}{d t}\left[x(t)\right] \\ &= \frac{d}{d t}\left[3\, t^{2} + t\right] \\ &= 6\, t + 1 \end{aligned}[/tex].
Set velocity to [tex]25\; {\rm m\cdot s^{-1}}[/tex] and solve for time [tex]t[/tex] (in seconds):
[tex]v(t) = 25[/tex].
[tex]6\, t + 1 = 25[/tex].
[tex]t = 4[/tex].
Thus, the velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].
Differentiate velocity [tex]v(t)[/tex] with respect to time [tex]t[/tex] to find the acceleration (in [tex]{\rm m\cdot s^{-2}}[/tex]) of this particle:
[tex]\begin{aligned}a(t) &= \frac{d}{d t}\left[v(t)\right] \\ &= \frac{d}{d t}\left[6\, t + 1\right] \\ &= 6\end{aligned}[/tex].
In other words, the acceleration of this particle is constantly equal to [tex]6\; {\rm m\cdot s^{-2}}[/tex]. Hence, the acceleration of this particle is never [tex]0[/tex].
A rectangular room measures 18 ft by 37 ft. How many
square feet of tile are needed to cover the floor?
Step-by-step explanation:
the area of a rectangle is length × width.
in our case
37 × 18 = 666 ft²
so, we need 666 ft² of tiles.
Answer:
666 square feet
Step-by-step explanation:
To find the number of square feet of tile, we need to find the area:
A = L × W
A = 18 × 37
A = 666 ft²
Suppose that the volume of a right circular cylinder is 500 A cubic
centimeters and the radius of its base is 5 centimeters. What is the
height of the cylinder?
The height of the right circular cylinder with volume of 500π cubic centimetre and radius of 5 centimetre is 20 cm.
Volume of a cylindervolume = πr²h
where
r = radiush = heightTherefore,
volume = 500π cm³
r = 5 cm
Therefore,
volume of the cylinder = πr²h
500π = 5²πh
500π = 25πh
divide both sides by 25π
500π / 25π = 25πh / 25π
h = 20 cm
learn more on cylinder here: https://brainly.com/question/11083770
Answer:
A) 20 cm
Step-by-step explanation:
The area of a circle is 100π in². What is the circumference, in inches? Express your answer in terms of
π.
Answer:
20π
Step-by-step explanation:
Area = πr^2
100π = πr^2
solve for r and r = 10
circumference of a circle is 2πr
therefore 2π×10=20π in
Damon has $200 in a savings account that earns 4% annually. The interest is not compounded. How much will he have in total in 1 year?
If y varies inversely as x, and y=16 when x=4, find y when x=10
Answer:
40
Step-by-step explanation:
you have to multiply x by 4 to get y when x=4 and y=16. so if x=10, then you have to multiply what x is (10) by 4 because there is a common ratio.
hope this helps!! please give brainliest!!!!!!
Liz records the amount of rainfall in her backyard. It rained 3/8 inch for 4 days in a row.
Which shows the amount of rainfall after 4 days?
A : 1 4/8
B : 1 5/8
C : 1 6/8
D : 1 7/8
Which fraction equals 29 }}16 ?
Graph a quadratic function with a vertex at (2, -3) with a = 3.
Answer:
bottom one
Step-by-step explanation:
use (x , y)
the top one is -3,2
the bottom one is 2,-3
This graph represents function of y = 3(x−2)²-3.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
The vertex form of parabola :
y=a(x−h)²+k
(h,k)is the vertex of the parabola, and
Substitute vertex(2,-3), into equation
y = a(x−2)²-3
Substitute a = 3 into equation
y = 3(x−2)²-3
Here is a graph of the y = 3(x−2)²-3
Learn more about parabola here:
brainly.com/question/4074088
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1.
3 ft
2 ft
6 ft
what is the surface area of the rectangular prism?
Sasha is making custom designs using these small trapezoidal prisms. She wants To cover each of the eight prisms in her current design and strive cloth on all sizes she has 3500 cm² of striped cloth does Sasha have enough cloth to cover all prisons in her current design choose from the drop-down menu to correctly complete the statement
Answer:
the answer is 3040 and does
The train station clock runs too fast and gains 8 minutes every 5 days. How many minutes and seconds will it have gained at the end of 8 days?
MATHEMATICS
NEED
SOME
HELP
OF
YOURS
TY<3
Answer:
The answer is 157 mm.
Step-by-step explanation:
Given;Diameter (d) = 50 mmπ = 3.14To Find;The circumference of the circle.Formula;C = πdNow,
C = πd
C = 3.14 × 50 mm
C = 157 mm
Thus, The circumference of the circle is 157 mm.
Find the values of x for which the denominator is equal to zero for 2x^2+5/x^2-2x .
x = 0, x = 2
x = 1, x = 2
none
x = 2
Let's see
[tex]\\ \rm\rightarrowtail x^2-2x=0[/tex]
[tex]\\ \rm\rightarrowtail x(x-2)=0[/tex]
[tex]\\ \rm\rightarrowtail x=0\:or\:x-2=0[/tex]
[tex]\\ \rm\rightarrowtail x=0\:or\:x=2[/tex]
[tex] \green{••••••••••••••••••••••} \blue{••••••••••••••••••••••••••}[/tex]
[tex] \sf {x^2 - 2x = 0} [/tex]
[tex] \sf {x ( x - 2) = 0} [/tex]
[tex] \sf {x = 0 \: or \: x-2 = 0} [/tex]
[tex] \sf \green{ {x = 0 \: or \: x = 2}} [/tex]
#CarryOnLearning
#LibreAngMatuto
Kaya brought $30 to the mall. She spent $7.28 on food, and $18.94 on a necklace. How much does she have left?
Answer:
$3.78
Step-by-step explanation:
30 dollars minus 7 dollars and 28 cents is twenty-two and seventy-two cents, then minus another eighteen and ninety-four cents, would end up at three dollars and seventy-eight cents.
Answer:
[tex]\boxed{\$3.78}[/tex]
Step-by-step explanation:
To find out how much money does Kaya have left, we need to subtract the total money spent from the total money brought to the mall.
In this problem, we can tell that Kaya brought $30 to the mall as stated in the question. Furthermore, the problem states that she spent $7.28 on food, and $18.94 on a necklace. This means that the sum of 7.28 and 18.94 is the money spent by Kaya.
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[tex]\$30 - (\$7.28 + \$18.94) = \text{Money remained}[/tex]
➡ [tex]\$30 - (\$26.22) = \text{Money remained}[/tex]
➡ [tex]\$30 - \$26.22 = \text{Money remained}[/tex]
➡ [tex]\bold{\underline{\$3.78} = Money \ remained}}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability of selecting
two prime numbers?
Answer: 1/6
Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.
Mary’s trapezoid-shaped garden has a perimeter of 24 yd. She knows the length of three of the sides, 3 yd, 6 yd, and 9 yd.
What is the length of the fourth side?
Choose...
Answer:
6
Step-by-step explanation:
to find the perimeter of a trapezoid you add all the sides together
therefore we do it backwards
24-3-6-9=6
Solution :-
We know that perimeter is the sum of all sides, and here we have been provided with perimeter and the length of three sides. Now, we can assume the length of other side as any variable, say x. And develop a linear equation, and solve it. Thus,
A/Q,
→ 3yd + 6yd + 9yd + x = 24yd
→ 18yd + x = 24yd
→ x = 24yd - 18yd
→ x = 6yd
Thus, the length of the fourth side is 6yd.
Hope that helps :)
c) Brett buys 120 chocolate bars for £60 He sells them all, making a 50% profit to give to charity. He sells each bar for the same price. How much does he sell each bar for?
Answer:
I believe he sells each bar for .75 cents
J F F 570 K po 142° G H Find the value of x.
Answer:
I'm stuck on the same question
Step-by-step explanation:
100 students went on a field trip. Six busses were filled and 10 students traveled in
cars with their parents. How many students were on each bus?
Answer:
15 students in each bus.
Step-by-step explanation:
Subtract 10 from 100 and you get 90 then divide 90 by 6 and that gives you how many students in each bus
Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make lead balls that have a radius of 7.5in . If lead costs $0.36 per in3 , how much will the lead cost to make one ball?
Answer:
$636.17
Step-by-step explanation:
First, we need to find the volume of the ball. Then, we will solve for the cost of it.
Volume of a sphere and solving for the area:
V = [tex]\frac{4}{3}[/tex]πr³
V = [tex]\frac{4}{3}[/tex]π(7.5)³
V ≈ 1767.15 in³
Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.
1767.15 in³ * $0.36 = 636.174
Money rounds to the hundredth place,
636.174 -> $636.17
It will cost $636.17 to make one ball.
Answer:
Volume of a sphere = 4/3 Pi r³
if r = 7.5
= 4/3 pi 7.5³
= 4/3 pi 421.87
= 1687.5/3 pi
= 562.5 Pi
= 1767.15 in³
then
1767.15 x 0.36 = 636.17
if 1 in³ costs 0.36$
then 1767.15 in³ costs 636.17$
Please show steps and show restrictions
[tex]\dfrac{x^2+7x+12}{x^2-x-12}\\\\=\dfrac{x^2 +3x+4x +12}{x^2 -4x+3x-12}\\\\=\dfrac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}\\\\=\dfrac{(x+4)(x+3)}{(x-4)(x+3)}\\\\=\dfrac{x+4}{x-4}\\\\\text{Restrictions:}~ x\neq 4 ,~ x\neq -3[/tex]
A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, and the total money collected was $275. Which of the following options represents the number of children and the number of adults who purchased team shirts that day, and the pair of equations that can be solved to find the numbers?
Answer:
D.)25 children and 75 adults
Equation 1: a + c = 100
Equation 2: 3a + 2c = 275
Step-by-step explanation:
A team t-shirt costs $3 per adult and $2 per child.
Let the number of children be = c
Let the number of adults be = a
A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:
On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes:
Now to know the number of children and adult, we can check by plugging in the values from options provided.
25 children and 75 adults = 25(2)+75(3)=50+225 =275
The longest worm is blank times as long as the shortest worm
Use the order of operations to simplify the expression.
(5)^2 - (1/4)^2
[tex]5^2 - \left(\dfrac 14 \right)^2= 25 - \dfrac{1}{16} = \dfrac{400-1}{16} = \dfrac{399}{16}=24\dfrac{15}{16}[/tex]