Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 40, n = 50, s = \frac{40}{\sqrt{50}} = 5.66[/tex]
The probability that the sample average will exceed $75 is one subtracted by the p-value of Z when X = 75, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (75 - 70)/5.66
Z = 0.88
Z = 0.88 has a p-value of 0.8106.
1 - 0.8106 = 0.1894.
0.1894 = 18.94% probability that the sample average will exceed $75.
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i need help quick, everything is in the image
Answer:
x = 3
Step-by-step explanation:
see image. Instead of distributive property, let's multiply by 2 to get rid of the fraction and also the parenthesis on the left. See image.
Then subtract 5 and finally, divide by 3 to solve. See image.
Distribute to create an equivalent expression with the fewest symbols possible.
7(4p + 2q + 3r) =7(4p+2q+3r)
The equivalent expression for the given expression is 28p + 14q + 21r.
What is an equivalent expression?An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.
An equivalent expression is simplified to the original expression by using the distributive property.
What is distributive property?The distributive property is
a(b + c) = ab + ac
Calculation:The given expression is 7(4p + 2q + 3r)
Applying the distributive property,
7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)
⇒ 28p + 14q + 21r
Thus, the equivalent expression for the given expression is 28p + 14q + 21r.
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7(4p+2q+3r)=7(4p+2q+3r)
Apply distributive law
a(b+c)=ab+acSo
28p+14q+21r=28p+14q+21rThis is the required expression
Let g be a one-to-one function and suppose f is the inverse function of g
if g(5)=11 and g(3)=5, find f(5)
Answer:
So g(6) comes out to be 2.
Step-by-step explanation:
So f(6)=5 means when f acts on 6, the result is 5....so the inverse would take 5 back to 6...or g(5)=6
So f(2)=6 means that f reassigns 2 to 6....so the inverse would take 6 back to 2....or g(6)=2
hope this helps :)
Answer: 3
Step-by-step explanation:
If f(x) = y, then invf(y) = x
So, f(5) = invg(5) = 3
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x-30 > 30
Answer:
[tex]x > 60[/tex]
Step-by-step explanation:
[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)
a swimming pool charges £3.60 for entry. you can save 1/3 of entry fee with a membership card. on his first visit, ken spends £5 on a membership card plus the reduced entry fee. how many times does ken visit before he gets back his £5
Answer:
5
Step-by-step explanation:
You save ⅓ of entry fee, so you save 1.20 and you pay 2.40. We only really care about the 1.20 reduction. 5 / 1.2 = 4.16 so he must go 5 times to get the 5 back
laura spends 4 hours reading a book that is 76 pages long. what is the average number of pages she read per hour?
The average number of pages she reads per hour is 19 pages per hour
How to determine the average number of pages she read per hour?The given parameters are:
Number of pages = 76 pages
Number of hours = 4 hours
The average number of pages she reads per hour is calculated using the following formula
Average = Number of pages/Number of hours
Substitute the known values in the above equation
Average = 76 pages/4 hours
Evaluate the quotient
Average = 19 pages per hours
Hence, the average number of pages she reads per hour is 19 pages per hours
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Round 229.371to the nearest one tenth and hundredths
Answer:
229.37, 229.4
Step-by-step explanation:
1. Hundredths
2. Tenths
How do you compute this? 4(-2, 3) - 2(6, -7)
Step-by-step explanation:
Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))
lim
n->infinity 4n^3-5/9n^3+7
Answer:
[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}=\frac{4}{9}[/tex]
Step-by-step explanation:
[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}[/tex]
Pull out n³
[tex]=\lim_{n\rightarrow +\infty } \frac{n^{3}\times \left( 4-\frac{5}{n^3} \right) }{n^{3}\times \left( 9+\frac{7}{n^3} \right) }[/tex]
Simplify by n³
[tex]=\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }[/tex]
Remark : [tex]\lim_{n\rightarrow +\infty } \frac{5}{n^3} \right) } = 0 \ \. \text{and} \ \ \lim_{n\rightarrow +\infty } \frac{7}{n^3} \right) } = 0[/tex]
Then
[tex]\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }=\frac{4-0}{9+0}[/tex]
[tex]=\frac{4}{9}[/tex]
A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper? One ream of paper is 500 sheets.
Please provide deep explanation so i can learn and understand
The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.
What is the thickness of a sheet of paper?The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.
If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.
The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.
Data and Calculations:
Number of reams of paper in a box = 5 reams
1 ream = 500 sheets
500 sheets = 5.4 cm thick
The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}
Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.
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Question Completion:Assume that one ream of paper is 5.4 cm thick.
During a drought, the water level in a reservoir dropped 3 in. each week for 5 straight weeks. Express the overall change in water level as a signed number.
Answer:
v = -3w
Step-by-step explanation:
water level/volume = -3 x weeks
v = -3w
Glynn's car has a 18 gallon gas tank. He travels 450 miles. What is the least miles per gallon this trip? Write and solve an inequality to answer the question.
The least miles per gallon this trip is 25 miles per gallon
How to determine the least miles per gallon?The given parameters are:
Distance = 450 miles
Tank size = 18 gallons
The least miles per gallon this trip is calculated as:
Miles per gallon = Distance/Tank size
This gives
Miles per gallon = 450/18
Evaluate the quotient
Miles per gallon =25
Represent as an inequality
x >= 25
Hence, the least miles per gallon this trip is 25 miles per gallon
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If the measure of WZX is 262 what is the measure of XWY?
Answer:
49°
Step-by-step explanation:
The circumference of a circle measures 360 degrees, so arc XW is 98°.
So, angle XWY is 49°.
Ke'o went shopping and spent $114 on clothes
and bought 5 pocket squares for the same price and one pairs
of $14 shorts. Write an equation for this story
problem, then solve for the price of the shirts.
Select two answers.
A. equation: 5[x+(1)(14)] = 114
B. price of each pocket square: $28
C. price of each pocket square: $25
D.equation: [(1)(14) - 5] = 114
E. price of each pocket square: $20
F. price of each pocket square: $19
G. equation: [5+ (1)(14)] = 114
H. equation: 5x+(1)(14) = 114
Please help 50 points
Answer:
m∠RQS = 109°
Step-by-step explanation:
Angles on a straight line sum to 180°.
Therefore:
⇒ m∠RQS + m∠SQT = 180°
⇒ (15x + 4) + (10x + 1) = 180
⇒ 15x + 4 + 10x + 1 = 180
⇒ 15x + 10x + 4 + 1 = 180
⇒ 25x + 5 = 180
⇒ 25x + 5 - 5 = 180 - 5
⇒ 25x = 175
⇒ 25x ÷ 25 = 175 ÷ 25
⇒ x = 7
Now that we have found the value of x, substitute this into the expression for m∠RQS:
⇒ m∠RQS = 15(7) + 4
= 105 + 4
= 109°
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Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet
The rate of the slower jet is 672 miles per hour.
The rate of the slower jet is 752 miles per hour.
How to find the rate of the jets?Two jets leave an air base at the same time and travel in opposite directions.
One jet travels 80 mi/h faster than the other.
let
x = rate of the slower jet
faster jet = 80 + x
Therefore,
rate = distance / time
The two jets are 11392 miles apart.
(80 + x)8 + 8x = 11392
640 + 8x + 8x = 11392
640 + 16x = 11392
16x = 11392 - 640
16x = 10752
divide both sides by 16
x = 10752 / 16
x = 672 miles per hour
rate of the faster jet = 80 + 672 = 752 miles per hour
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PLEASE ASAP!! ALSO PLEASE INCLUDE AN EXPLANATION OF HOW YOU GOT THE ANSWER!!! THANK YOU! BTW THERE ARE TWO PICTURES! :)
2/3 is 400% of 1/6
0.2 is 12.5% of 1 3/5
Calculating PercentagesFrom the question, we are to determine what percent of 1/6 is 2/3
Let the value be x
Thus,
We can write that
2/3 is x% of 1/6
This means
2/3 = x/100 × 1/6
Now, solve for x
2/3 = x/100 × 1/6
2/3 = x/600
x = (2×600)/3
x = 400
Hence, 2/3 is 400% of 1/6
We are to determine what percent of 1 3/5 is 0.2
Let the value be y
That is,
0.2 is y% of 1 3/5
This can be written as
0.2 = y% × 1.6
0.2 = y/100 × 1.6
Now, solve for y
0.2 = y/100 × 1.6
0.2 = 1.6y/100
1.6y = 0.2 × 100
1.6y = 20
y = 20/1.6
y = 12.5
Hence, 0.2 is 12.5% of 1 3/5
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How many pairs of parallel faces does this shape have?
Answer: one
Step-by-step explanation:
parallel faces are the ones that are opposite to each other.
Answer:
one
Step-by-step explanation:
there is only one pair of parallel faces.
Time to use my tools
96 100 132
6 ... 4 ....6
5....7......3
21...32...?
1)32
2)20
3)25
4)30
find the missing one
Answer:
the correct answer is 25
The figure shows a cylinder of diameter 12cm and height = 15cm. A hole in the shape of cone is bored into one of its end. If the cone has diameter equal to half of the diameter of the cylinder. find the volume of the remaining solid.
Answer:
[tex]\bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]
Step-by-step explanation:
There was no figure but the question is clear
Volume of a cylinder is given by the formula [tex]\bold{\pi r^2h}\\[/tex]
where r is radius of base of cylinder, h is the height
Volume of a cone is given by [tex]\bold{\frac{1}{3} \pi r^2 h}[/tex]
where r is the radius of base of cone, h is the height
The radius of the cylinder = [tex]\frac{1}{2}[/tex](diameter) = [tex]\frac{1}{2}[/tex](12) = 6cm
Height of cylinder = 15cm
Volume of cylinder [tex]V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}[/tex]
Radius of cone = [tex]\frac{1}{2}[/tex] (radius of cylinder) = [tex]\frac{1}{2}[/tex](6) = 3 cm
Height of cone same as height of cylinder = 15cm
Volume of cone, [tex]V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\[/tex]
Difference is the volume of the remaining solid
[tex]V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]
A home gardener estimates that 18 apple trees will produce an average yield of 80 apples per tree. But because of the size of the garden, for each additional tree planted, the yield will decrease by four apples per tree. How many trees should be planted to maximize the total
19 trees should be planted to maximize the total
How many trees should be planted to maximize the totalFrom the question, we have the following parameters:
Number of apples, x = 18
Yield, f(x) = 80 per tree
When the number of apple trees is increased (say by x).
We have:
Trees = 18 + x
The yield decreases by four apples per tree.
So, we have
Yield = 80 - 4x
So, the profit function is
P(x) = Apples * Yield
This gives
P(x) = (18 + x) *(80 - 4x)
Expand the bracket
P(x) = 1440 - 72x + 80x - 4x^2
Differentiate the function
P'(x) = 0 - 72 + 80 - 8x
Evaluate the like terms
P'(x) = 8 - 8x
Set P'(x) to 0
8 - 8x = 0
Divide through by 8
1 - x = 0
Solve for x
x = 1
Recall that:
Trees = 18 + x
So, we have
Trees = 18 + 1
Evaluate
Trees = 19
Hence, 19 trees should be planted to maximize the total
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A television is identified by the diagonal measurement of the screen. A television has a length of 57-inches and a height of 33 inches. What is the length of the diagonal of the television screen?
Answer: 65.86 inches
Step-by-step explanation:
Length of the hypotenuse (length of diagonal) : a^2 + b^2 = c^2
The length (a)= 57
The height (b) =33
57^2= 3,249
33^3= 1,089
3,249 + 1,089 = c^2
4,338 = c^2
We next square root both sides to find c by itself (length of the diagonal)
[tex]\sqrt{4,338} = c[/tex]
c= 65.8634952...
You can then round to however many decimals are required.
To the hundreds place: 65.86 inches
5. Based on your data, what is the experimental probability that the family has two dogs or
two cats?
Answer:
2 dogs
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each given function with the description of its graph.
y-intercept at (0, 2)
graph initially decreases slowly and then decreases rapidly
y-intercept at (0, 1)
graph initially decreases rapidly and then decreases slowly
y-intercept at (0, 1)
graph initially increases rapidly and then increases slowly
y-intercept at (0, 2)
graph initially decreases rapidly and then decreases slowly
y-intercept at (0, 1)
graph initially increases slowly and then increases rapidly
Y =
(4)*
y = 3²
y = 2(1) ²
The statements that applies are;
y-intercept at (0, 2), graph initially decreases rapidly and then decreases slowly.y-intercept at (0, 1), graph initially increases slowly and then increases rapidlyy-intercept at (0, 1) - graph initially decreases rapidly and then decreases slowly.What is the function about?The property of power function is known to be peculiar to the field of math. A power function is known to be one that is made up of a variable base that tends to be raised to a fixed power.
Note that the function is one that is made up of a constant base that is often raised to a variable power.
Following the property of power function, we can be able to obtain the information above.
Therefore, The statements that applies are;
y-intercept at (0, 2), graph initially decreases rapidly and then decreases slowly.y-intercept at (0, 1), graph initially increases slowly and then increases rapidlyy-intercept at (0, 1) - graph initially decreases rapidly and then decreases slowly.Learn more about function from
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3. What is a variable?
numbers that represent letters
a combination of letters and numbers
Oletters that represent numbers
O a operation between different letters
Solve for y. Simplify your answer as much as possible. 9/12=y/8
Answer:
6
Step-by-step explanation:
Solve for y:
[tex]y/8=9/12[/tex]
Multiply both sides by 8:
[tex]y=72/12[/tex]
Solve fraction
[tex]y=6[/tex]
A baker has 4 3/4 pounds of cookie dough. He uses 1/16 pound of dough for each cookie. How many cookies can he make? Simplify the answer.
This shows that 76 cookies will be made with the total pounds of cookies
Ratio and proportionFractions are written as a ratio of two integers. Given the following parameters
Total pounds of cookies made = 4 3/4 pounds
Total pounds of cookies made = 19/4 pounds
If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;
Number of cookies = 19/4 ÷ 1/16
Number of cookies = 19/4 * 16/1
Number of cookies = 19 * 4
Number of cookies = 76
This shows that 76 cookies will be made with the total pounds of cookies
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A survey was conducted among the students at Elmwood High School. What are the individuals in this study?
the types of sports
the music groups
the clubs
the students
Based on the information provided, the individuals in this study are: D. the students.
What is a study?A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.
What is a variable?In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.
Based on the information provided, the individuals in this study are the students and these include the following subclasses:
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The students are the individuals in this study and is therefore denoted as option D.
What is a Sample?This refers to a group of people which are chosen or taken from a large population for measurement or surveys.
In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.
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PLS HELP plsssssssssssssss
Answer:
a. 33
Step-by-step explanation:
a straight line is 180° so
3x = 180 - 81
3x = 99
to find x divide by 3
x = 99/3
x = 33
Alice placed $1,900 in a savings account which earns 2.2% interest, compounded every year. How much will she have in the account after 5 years.
She will have $2118 in her account after five years
How to determine the amount in five years?The given parameters about the compound interest are
Principal Amount, P = $1,900
Interest Rate, R = 2.2%
Time, t = 5
Compound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R)^t - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
Substitute the known values in the above equation
A = 1900 * (1 + 2.2%)^5
Express 2.2% as decimal
A = 1900 * (1 + 0.022)^5
Evaluate the sum
A = 1900 * (1.022)^5
Evaluate the exponent
A = 1900 * 1.11495
Evaluate the product
A = 2118
Hence, she will have $2118 in her account after five years
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