Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
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.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
SCALCET8 3.9.015. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 35 ft from the pole
Answer:
[tex]X=6.67ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Height of pole [tex]H_p=15[/tex]
Height of man [tex]h_m=6ft[/tex]
Speed of Man [tex]\triangle a =4ft/s[/tex]
Distance from pole [tex]d=35ft[/tex]
Let
Distance from pole to man=a
Distance from man to shadow =b
Therefore
[tex]\frac{a+b}{15}=\frac{b}{6}[/tex]
[tex]6a+6b=15y[/tex]
[tex]2a=3b[/tex]
Generally the equation for change in velocity is mathematically given by
[tex]2(\triangle a)=3(\triangle b )[/tex]
[tex]2*4=3(\triangle b)[/tex]
[tex]\triangle a=\frac{8}{3}[/tex]
Since
The speed of the shadow is given as
[tex]X=\triangle b+\triangle a[/tex]
[tex]X=4+8/3[/tex]
[tex]X=6.67ft/s[/tex]
find the exact value cos5pi/6
Answer:
[tex] - \frac{ \sqrt{3} }{2} [/tex]
Step-by-step explanation:
Unit circle
Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)
Answer:
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]P(1) = 2[/tex]
Required
The solution
We have:
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]
Split
[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]
Divide both sides by [tex]P^\frac{1}{2}[/tex]
[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]
Multiply both sides by dt
[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]
Integrate
[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Rewrite as:
[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the left hand side
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the right hand side
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)
To solve for c, we first make c the subject
[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]
[tex]P(1) = 2[/tex] means
[tex]t = 1; P =2[/tex]
So:
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]
[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]
So, we have:
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]
Divide through by 2
[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]
Square both sides
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?
What angles can you construct using just a pair of compasses and a ruler?
Answer:
By using a pair of compasses and a ruler you can draw all angles
write the equation of the line shown in the graph above in slope-intercept form
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score
Answer:
Mean scores.
Step-by-step explanation:
The golf player will score in the first round, according to these scores the golf player scores can be predicted. The golf player can perform high in first round but he may score lesser in the second round due to stress or mental pressure. The scores can be predicted taking mean of the scores and adding standard deviation to it.
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta.
A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.
In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
In the diagram, WZ=StartRoot 26 EndRoot.
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).
What is the perimeter of parallelogram WXYZ?
units
units
units
units
Answer:
[tex]P = 8 + 2\sqrt{26}[/tex]
Step-by-step explanation:
Given
[tex]W = (-2, 4)[/tex]
[tex]X = (2, 4)[/tex]
[tex]Y = (1, -1)[/tex]
[tex]Z = (-3,-1)[/tex]
Required
The perimeter
First, calculate the distance between each point using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]
So, we have:
[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]
[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]
[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]
[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]
So, the perimeter (P) is:
[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]
[tex]P = 8 + 2\sqrt{26}[/tex]
Answer:
its D.
Step-by-step explanation:
took test
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
if side of square is 4.05 find its area
Answer:
A
≈
16.4
please give brain listIf 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
Find the perimeter of a football field which measures 90m by 60m
Hello!
[tex]\large\boxed{P = 300m}[/tex]
Use the following formula for the perimeter:
P = 2l + 2w, where:
l = length
w = width
Therefore:
P = 2(90) + 2(60)
Simplify:
P = 180 + 120 = 300 m
Answer:
well how about you use common sense 100 yards long on each side 200 yards then add 5o yards since the the that is how wide it is then add another 50 and you get 300 yards then convert that to meters
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
i need help solving this .
Answer:b
Step-by-step explanation:
Answer:
just be smart trust me u dont need us to give u the answer ur super smart
Step-by-step explanation:
make me brainliest to help people be encourage
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
9. Mariah has 28 centimeters of reed
and 10 meters of reed for weaving
baskets. How many meters of reed
does she have? Write your answer as a
decimal and explain your answer.
PLEASE HELP!!! Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
Answer:
is it going to be 10.5
Step-by-step explanation:
I do not have any explanation
Answer: 0 (zero)
Step-by-step explanation:
Start Learning & start growing! edge2023
*DROPS THE MIC*
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
F(x) =-2x-4 find x if f(x)=14
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) c, c, c , where c > 0
Answer:
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Step-by-step explanation:
Given the data in the question;
vector is z = < c,c,c >
the direction cosines and direction angles of the vector = ?
Cosines are the angle made with the respect to the axes.
cos(∝) = z < 1,0,0 > / |z|
so
cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]
cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3
∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]
cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3
β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]
cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3
γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
Therefore;
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
At the Fidelity Credit Union, a mean of 5.8 customers arrive hourly at the drive-through window. What is the probability that, in any hour, more than 5 customers will arrive
Answer:
0.5217
Step-by-step explanation:
P(more than 5 customer arrive):
P(X>=6)=1-P(X<=5)= 1-∑x=0x e-λ*λx/x!= 0.5217
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
9514 1404 393
Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds.Swimmer Spandex Speedo Fastskin1 31.1 29.12 28.9 30.43 31.4 32.04 34.9 31.75 27.7 28.26 36.7 32.97 33.3 28.68 30.8 26.2Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance.t = _____df = _____Critical value of t = _____ (use alpha = 0.05)Would you reject the null hypothesis?
Answer:
T = 2.215
df = 7
Critical value = 2.364
Fail to reject the null
Step-by-step explanation:
Swimmer __Spandex __Speedo Fastskin__ d
1 __________31.1 _______29.1 __ 2
2_________ 28.9 ______30.4 __ -1.5
3_________ 31.4 ______ 32.0 __ - 0.6
4_________ 34.9 ______31.7 __ 3.2
5 _________27.7 ______28.2 __ - 0.5
6_________ 36.7 _____ 32.9 ___ 3.8
7 _________ 33.3 _____28.6 ___ 4.7
8_________ 30.8 _____26.2 ___ 4.6
The mean difference = Σd / n
2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6
μd = Σd / n = 15.7 / 8 = 1.9625
Sd = standard deviation of difference = 2.5065 (using calculator)
H0 : μd = 0
H1 : μd ≠ 0
The test statistic:
T = μd / (Sd/√n)
T = 1.9625 / (2.5065/√8)
T = 2.2145574
The degree of freedom, df = n - 1 = 8 - 1 = 7
Using a Pvalue calculator :
α = 0.05
Critical value, Tcritical = 2.364 (T distribution table)
Since Test statistic < Critical value
we fail to reject H0 ;
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
PLSHELPASAPDFFFFFFFFFFFFFFFFFFFFFFFFFF
im struggling with the same one
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
