Answer:
The probability is [tex]P(X \le 0.60) = 0.000 [/tex]
Step-by-step explanation:
From the question we are told that
The overall pass rate is [tex]R = 76\% = 0.76[/tex]
The sample size is n = 400
The percentage that passed is [tex]k = 60\% = 0.60[/tex]
Generally the standard error is mathematically represented as
[tex]\sigma _{\= x } = \sqrt{\frac{R (1 -R)}{n} }[/tex]
=> [tex]\sigma _{\= x } = \sqrt{\frac{0.76 (1 -0.76)}{400} }[/tex]
=> [tex]\sigma _{\= x } = 0.0214 [/tex]
Generally the probability of a simple random sample of 400 having a pass rate of 60% or less is mathematically represented as
[tex]P(X \le 0.60) = P(\frac{X - R}{ \sigma_{\= x}} \le \frac{0.60 - 0.76}{0.0214} )[/tex]
=> [tex]P(X \le 0.60) = P(Z \le -7.48 )[/tex]
Generally from the z-table
[tex]P(Z \le -7.48 ) = 0.000[/tex]
So
[tex]P(X \le 0.60) = 0.000 [/tex]
Find the value of X
WILL MARK BRAINLIEST IF CORRECT!
Answer:
x = 52
Step-by-step explanation:
This is a picture of a right angle, which is 90 degrees. We should first make an equation to represent this problem.
(x - 12) + 50 = 90
1. Subtract 50 from both sides of the equation.
(x - 12) = 40
2. Add 12 from both sides of the equation
x = 52
The value of x is 52.
Answer:
52°
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An airplane on autopilot took 5 hours to travel 3540 kilometers. What is the unit rate for kilometers per hour?
Answer:
708 km.
Step-by-step explanation:
3540/5=708
Answer:
708 km/h
Step-by-step explanation:
3540 / 5 = 708
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
Answer:
(b) 67
Step-by-step explanation:
A solution to the differential equation describing the temperature according to Newton's Law of Cooling could be written as ...
T = (final temp) + (initial difference)×(decay factor)^t
where the decay factor is the fraction of change during 1 unit of time period t.
__
Here, the initial difference of 100-25 = 75 degrees decays to 90-25 = 65 degrees in 1 minute. So, the units of t are minutes, the decay factor is 65/75, the initial difference is 75 degrees, and the final temperature is 25 degrees. That lets us write the equation as ...
T = 25 +75(65/75)^t
Then for t=4, the temperature is ...
T = 25 +75(13/15)^4 ≈ 67.3 . . . . degrees
After 4 minutes the temperature of the coffee is about 67 degrees.
Joyce purchased 84.92 in groceries and gives the clerk $100 bill how much change should the clerk give back to her
Answer:
$15.08
Step-by-step explanation:
When subtract 84.92 from 100 you get 12.08 which is how much he clerk should give back
Answer:
15.08
Step-by-step explanation:
plss help mee
Show your work plss not just the answer
If two people share one soda, how much of the soda should each person get?
Answer:
1/2 of the soda:) sure yan
Answer:
sorry i dont know
Step-by-step explanation:
The mass of the apples harvested from a particular orchard follows a nearly normal distribution with a mean of 94 grams and a standard deviation of 27 grams. What size sample is needed to get a standard error of 3
The sample size needed to get a standard error of 3 is 81
How to determine the sample size?The given parameters are:
Mean = 94Standard deviation = 27Standard error = 3The standard error is calculated using:
[tex]SE = \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]3= \frac{27}{\sqrt n}[/tex]
Divide both sides by 3
[tex]1= \frac{9}{\sqrt n}[/tex]
Square both sides
1 = 81/n
Multiply both sides by n
n = 81
Hence, the sample size needed to get a standard error of 3 is 81
Read more about standard errors at:
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Write an inequality for the statement provided :
The cargo of the truck weighs at most 3,000 pounds
Answer: [tex]w \le 3000[/tex]
w is the weight of the truck in pounds.
Since w cannot be negative, we can write [tex]0 \le w \le 3000[/tex] or we could tack on the statement "w must be positive"
The phrase "at most" means "that is the largest w can get". Think of it as the ceiling.
Solve. Use the discount equation
S = R − rR, where S is the sale price, R is the regular price, and r is the discount rate.
An exercise bike is on sale for $320, having been marked down 20% off the regular price. Find the regular price.
Answer:
[tex]\$ 400[/tex].
Step-by-step explanation:
In this question, [tex]S[/tex] (sales price) and [tex]r[/tex] (discount rate) are both given. The unknown is the regular price, [tex]R[/tex].
Rearrange the discount equation to solve for [tex]R[/tex] in terms of [tex]S[/tex] and [tex]r[/tex].
[tex]S = R - r\, R[/tex].
[tex]S = (1 - r)\, R[/tex].
Divide both sides by [tex](1 - r)[/tex]:
[tex]\displaystyle \frac{S}{1 - r} = \frac{(1 - r)\, R}{1 - r}[/tex].
[tex]\begin{aligned}R &= \frac{S}{1 - r}\end{aligned}[/tex].
It is given that [tex]S = 320[/tex]. A mark-down of [tex]20\%[/tex] is equivalent to a discount rate of [tex]r = 20 / 100 = 0.20[/tex]. Substitute in [tex]S[/tex] and [tex]r[/tex] to find the value of [tex]R[/tex]:
[tex]\begin{aligned}R &= \frac{S}{1 - r} \\ &= \frac{320}{1 - 0.2} \\ &= \frac{320}{0.8} \\ &= 400\end{aligned}[/tex].
Thus, the regular price would be [tex]\$ 400[/tex].
They need to park the Mystery Machine. They could
either park in the lot that charges $5 and then $2 an
hour, or they could park using the meter on the street
that charges $3.75 per hour.
Write an equation that describes when the cost is the
same at both locations (the parking lot and on the
street).
Answer:
12 hours in the street=20 hours in the lot
Step-by-step explanation:
Well basically if you're at the street for 12 hours it will add up to 45 dollars. subtract the 5 starting dollars and you get 40. Divide 40 by 2 and you get 20. What does this mean? This means that in 12 hours on the street you can match the same amount of money if you were in the lot for 20 hours.
You have been asked to develop a composite measure of the quality of life on your campus.
1. Outline the social indicators you would use to develop such a measure. Be specific. Explain why you selected these indicators?
2. Now suppose data on your social indicators have been collected over a ten-year period. What might you be able to do with these data?
The social indicators that can be used to know the quality of life in campus are the number of hours spent in school, extra curricular activities, etc.
What are social indicators?It should be noted that social indicators are used to monitor the social system.
The social indicators that can be used to know the quality of life in campus are the number of hours spent in school, extra curricular activities, etc. They're important to assess ones social life.
In conclusion, after necessary data has been collected m, a research can be made to know how the quality of life is affected by the data.
Learn more about indicators on:
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A triangular bandana has an area of 78 square inches. The height of the triangle is 9 3 4 inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base. An equation to find the length of the base of the triangle is 78= The length of the base of the triangle is inches.
Area of triangle = 1/2 x base x height:
78 = 1/2 x base x 9 3/4
Multiply both sides by 2:
156 = base x 9 3/4
Divide both sides by 9 3/4:
Base = 16 inches
a chess club has 20 girls and 15 boys. seven of the girls and 7 of the boys in the chess club are also in the math club.
what percent of the students in the chess club are also in math club?
Answer:
40% why? because 20+15=35 that is the total but they are saying 7 boys and 7 girls are in math and chees so is 14 14/35 is 40%
what is the midpoint of AB if A = (-2,2) and B=(3,-1)?
Answer:
Midpoint = [tex](\frac{1}{2},\frac{1}{2} )[/tex]
Step-by-step explanation:
Midpoint formula: [tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]Plug in value: [tex](\frac{-2+3}{2} , \frac{2+(-1)}{2} )[/tex]Do the math: [tex](\frac{1}{2} ,\frac{1}{2} )[/tex]Write an equation with a slope of -5 And a y-intercept Of 0
[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+\underset{\stackrel{\uparrow }{b}}{0}\implies y=-5x[/tex]
A circle with the center C (4, -2) contains the point D (8,1). What is the equation of the line perpendicular to the radius of the circle passing through point C?
Answer:
y = -4x/3 + 10/3
Step-by-step explanation:
We find the slope of CD and get (-2 - 1)/(4 - 8) = -3/-4 = 3/4
The slope of a perpendicular line is the opposite reciprocal of the slope of the line it's perpendicular to, so we get a slope of -4/3.
We can use point-slope form and get (using point C):
y - (-2) = (-4/3)(x - 4) -->
y + 2 = -4x/3 + 16/3 -->
y = -4x/3 + 10/3
**NOTE** I can't see the picture (because of a problem on my computer) so if there is any info given there that isn't given in the text, then my answer will be incorrect.
An article reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation:
28.2 49.2 30.9 28.8 28.0 25.9 34.0 29.0 23.8 30.1
Compute the following. (Round your answers to four decimal places.)
a. The sample range.
b. The sample variance s2 from the definition
c. The sample standard deviation
d. s2 using the shortcut method.
Answer:
a)Range= 25.9
b)Variance =49.344
c)Standard deviation=7.0245
Step-by-step explanation:
Data : 28.2 49.2 30.9 28.8 28.0 25.9 34.0 29.0 23.8 30.1
Maximum Value : 49.4
Minimum Value : 23.5
Range= Maximum - Minimum
Range= 49.4 -23.5 = 25.9
(b)
[tex]Mean=\bar{x}=\frac{\sum x}{n}=\frac{309.2}{10}=30.92\\\\Variance=s^{2}=\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}=49.344[/tex]
(c) Sample standard deviation:
[tex]s=\sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=7.0245[/tex]
d)s2 using the shortcut method.
X [tex]X^2[/tex]
28.6 817.96
49.4 2440.36
30.3 918.09
28.2 795.24
28.9 835.21
26.4 696.96
33.8 1142.44
29.9 894.01
23.5 552.25
30.2 912.04
Total 309.2 10004.56
[tex]s=\sqrt{\frac{\sum x^{2}_{i}-\frac{\left ( \sum x_{i} \right )^{2}}{n}}{n-1}}\\s=\frac{10004.56-\frac{309.2^{2}}{10}}{9}\\s=7.0245[/tex]
White 4x+y=8 in slope intercept form
Answer:
y=-4x+8
Step-by-step explanation:
Use the appropriate conversions listed to convert 80 cups into gallons. Round to the nearest hundredth
Answer:
5 gallons
Step-by-step explanation:
You divide the number of cups by 16 to find how many gallons are there in a certain amount of cups.
Please answer this correctly without making mistakes
Answer:
The answer is 10 months
Step-by-step explanation:
8. A tree on a 30° slope grows straight up. What are the measures of the
greatest and smallest angles the tree makes with the hill? Explain.
The measure of the smallest angle of a tree with a hill is 60°.
The measure of the greatest angle of a tree with a hill is 120°.
Given:
A tree on a 30° slope grows straight up.
To find:
The measures of the
greatest and smallest angles the tree makes with the hill.
Solution:
In figure drawn:
[tex]\angle PQR = 30^o[/tex]
AB= Straight three
Construction:
Draw a parallel line CA to QR through point A.
Now,
[tex]\angle PQR = \angle PAC = 30^o\\\\\angle PAC +\angle PAB = 90^o \text{(Complimentary angles)}\\\\\angle PAB = 90^o -\angle PAC\\\\angle PAB=90^o-30^o=60^o[/tex]
The measure of the smallest angle of a tree with a hill is 60°.
[tex]\angle PAB + \angle BAQ= 180^o\text{(Supplementary angles)}\\\\ \angle BAQ= 180^o-\angle PAB \\\\ \angle BAQ=180^o-60^o=120^oC[/tex]
The measure of the greatest angle of a tree with a hill is 120°.
Learn more about complementary and supplementary angles here:
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the area of a rectangle is 30 to the square root of 3750 square inches, and the length is 3 to the square root of 250 inches. what is the width of the rectangle?
We are given that:
Area of rectangle is 30√3570Length of the rectangle is 3√250Area of rectangle is given by:
[tex] \implies\quad{\pmb{ \sf{Area = length\times width}} }[/tex]
Hence, putting the values in the formula:
[tex] \implies\quad \sf{ A = l\times w}[/tex]
[tex] \implies\quad \sf{ 30\sqrt{3750}=3\sqrt{250}\times w}[/tex]
[tex] \implies\quad \sf{3\sqrt{250}\times w = 30\sqrt{3750} }[/tex]
[tex] \implies\quad \sf{ w =\dfrac{30\sqrt{3750}}{3\sqrt{250}}}[/tex]
[tex] \implies\quad \sf{ w =10\dfrac{\sqrt{3750}}{\sqrt{250}}}[/tex]
[tex] \implies\quad \sf{ w = 10\times\sqrt{\dfrac{3750}{250}}}[/tex]
[tex] \implies\quad \underline{\underline{\pmb{\sf{ w =10\sqrt{15}}}}}[/tex]
3/7 + 5/6 ii) -3/15 x 7
[tex]\frac{53}{42}[/tex]
Step-by-step explanation:Calculate
[tex]\frac{3}{7}+\frac{5}{6}[/tex]
Find common denominator and write the numerators above common denominator
[tex]\frac{3\times6}{7\times6}+\frac{5\times7}{6\times7}[/tex]
Calculate the product or quotient
[tex]\frac{18}{7\times6}+\frac{5\times7}{6\times7}[/tex]
[tex]\frac{18}{42}+\frac{5\times7}{6\times7}[/tex]
[tex]\frac{18}{42}+\frac{35}{6\times7}[/tex]
[tex]\frac{18}{42}+\frac{35}{42}[/tex]
Write the numerators over common denominator
[tex]\frac{18+35}{42}[/tex]
Calculate the sum or difference
[tex]\frac{53}{42}[/tex]
Question #2 Answer[tex]-\frac{7}{5}[/tex]
Step-by-step explanation:Calculate
[tex]-\frac{3\times7}{15}[/tex]
Cross out the common factor
[tex]-\frac{7}{5}[/tex]
I hope this helps you
:)
Convert to find the equivalent rate
840 magazines /week into magazines/hour
Answer:
5 magazines per hour are manufactured
Pls help with this it’s easy
If u click there will be pic
Answer:
15, the second one.
Step-by-step explanation:
We can use this proportion:
[tex]\frac{centimeters}{meters}[/tex]
So, in this case:
[tex]\frac{5 centimeters}{20 meters}[/tex]=[tex]\frac{x centimeters}{60 meters}[/tex]
We can cross multiply, resulting in:
[tex]20x = 300 centimeters[/tex]
Divide both sides by 20, resulting in:
[tex]x = 15 centimeters[/tex]
Mr & Mrs Brown bought a new kitchen table for $450 it was 75% of the original price determine the original price of the kitchen table
1. A certain small factory employs 98 workers. Of these, 10 receive a wage of $150 per day and the rest receive $85.50 per day. To the management, a week is equal to 6 working days. How much does the factory pay out for each week
Answer:hello I'm from Philippines
Step-by-step explanation:
Solve: x2 - 2x + 1 = 4
Please help me
Let's solve your equation step-by-step.
x2−2x+1=4
Step 1: Subtract 4 from both sides.
x2−2x+1−4=4−4
x2−2x−3=0
Step 2: Factor left side of equation.
(x+1)(x−3)=0
Step 3: Set factors equal to 0.
x+1=0 or x−3=0
x=−1 or x=3
Answer:
x=−1 or x=3
When a result from a simple is extended to the population
Answer:
You can opt to study the entire population when the population is well defined(Complete sampling frame) and small.
It can eliminate any potential bias occurring through sampling technique, but other than that it is really not justified to consume more resources and time.
Dana is making a seating chart for an awards banquet. There are 120 people coming to the banquet.If 8 guests can be seated at each table, how many tables will be needed for seating for the awards banquet?
A t-shirt that was originally priced at $14 is marked down to $10.
About what is the percent decrease?
A. 40%
B. 28.6%
C. 71.4%
D. 140%