The probability that X will be greater than 25 is 0.42
Given,
The sample size, n = 39
The mean of the population, μ = 23
The standard deviation of the population, σ = 10
We have to find the probability for X > 25.
Here,
Z score = (X - μ) / σ
Z score = (X - 23) / 10
Now,
We have to find P(X > 25)
Then,
P(X > 25) = P(z > (25 - 23) / 10)
P(X > 25) = P(z > 2/10)
That is,
P(X > 25) = P(z > 0.2)
Here,
0.5 - P(0 ≤ z ≤ 0.2)
= (0.5 - 0.0792)
= 0.42
Therefore,
The probability that X will be greater than 25 is 0.42
Learn more about probability here;
https://brainly.com/question/22437739
#SPJ1
Mara solved an exponential equation by using logarithms. This is her work.
Latex: 7 \cdot 3^x=189
7
⋅
3
x
=
189
7
⋅
3
x
=
189
Latex: 3^x=27
3
x
=
27
3
x
=
27
Latex: \log _3\!(3^x)= \log _3\!27
log
3
(
3
x
)
=
log
3
27
log
3
(
3
x
)
=
log
3
27
Latex: x \log _3\!3=9
x
log
3
3
=
9
x
log
3
3
=
9
Latex: x \cdot 1=9
x
⋅
1
=
9
x
⋅
1
=
9
Latex: x=9
x
=
9
x
=
9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3
b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3
c) The mistake she made throughout is not applying the basic rule of logarithm.
How to solve Exponential Equations using logarithm?
She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;
Step 1. 7 x 3^x = 189
Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.
Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3
Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;
x log 3 = 3log 3
Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3
Step 6. x = 9; This is wrong because x = 3
Read more about Exponential Equations at; https://brainly.com/question/2456547
#SPJ1
Complete question is;
Mara solved an exponential equation by using logarithms. This is her work.
1. 7 x 3^x = 189
2. 3^x = 27
3. log^3 (^3) = log^27
4. xlog^33=9
5. x * 1 = 9
6. x = 9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
The radioactive substance cesium-137 has a half-life of 30 years. The amount At (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.
=At26612t30
Find the initial amount in the sample and the amount remaining after 80 years.
Round your answers to the nearest gram as necessary.
1. A cone-shaped filter has a diameter of 10 inches and a height of 4 inches.
What is the volume of liquid the filter can hold? Round your answer to
the nearest hundredth.
The volume of liquid contained by cone is 105 inches cube.
What is volume?
It can be defined as the total content which can be held inside a container.
Main body:
the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] , where r = radius and h = height of cone
diameter = 10 , so radius = d/2 = 5 inches
V = [tex]\frac{1}{3}\pi 5*5*4[/tex]
V = 3.14 *5*5*4*1/3
v≈105 inches cube
Hence the volume is 105 inches cube.
to learn more about volume click on the link below
https://brainly.com/question/1082469
#SPJ13
Which equation is the inverse of y = 100-x²?
Oy=± √100-x
O y=10± √√x
Oy=100+√x
Oy=+√x-100
Answer:
y = ±√100-x
Step-by-step explanation:
To work out the inverse of this function :
We solve for x then swap x and y :
Solving for x :
y = 100 - x²
Add x² to both sides :
x² + y = 100
Subtract y from both sides :
x² = 100-y
Square root both sides :
x = ±√100-y
Now we have solved for x. Now swap x and y :
y = ±√100-x
This is our final answer and is the first option.
Hope this helped and have a good day
how to interpret data from a frequency distribution
Answer:
The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.
The number written on the right of each category is its frequency
Step-by-step explanation:
△MNP≅△QST.
What is m∠S?
Enter your answer in the box.
Answer:
78°
Step-by-step explanation:
∠M=∠Q
∠N=∠S
∠P=∠T
Answer:
m∠S =78°---------------------
Given
Two congruent triangles △MNP≅△QSTWe know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):
∠M ≅ ∠Q, ∠N ≅ ∠S, ∠P ≅ ∠TAngle S corresponds to angle N, hence their values are equal:
m∠S = m∠N = 78°I don't understand please help me...
The total fencing material required to fence the playground and both flower beds is
perimeter of a rectangle is 2( / + w)perimeter of a square is 8aHow to find the material required for the fencingInformation from the question
The boundary of a park is shaped like a circle
The length of the rectangular playground is / and its width is w
The length of each side of the square flower beds is a
The problem is asking for the perimeter of a rectangle and 2 squares
perimeter of a rectangle is 2( / + w)
perimeter of a square is 4a
If there was no over lap the expression will have no reduction and hence the quantity of material required for the fencing is equal to their respective perimeters
The flower beds are two so the perimeter will be multiplied by 2 to give 8a
Learn more about perimeter here:
https://brainly.com/question/29430107
#SPJ1
Emma wrote one hundred thousand as 1,000,000. Explain what she did wrong.Then write the number correctly
Answer:
she wrote 1 million. It's 100,000
Step-by-step explanation:
she wrote 1 million. It's 100,000
A hexagon has exterior angle measures of (7n + 3), (10n-17)°,
(8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
Find the value of n.
Using the sum of exterior angle, the value of n is 11.
In the given question,
A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
We have to find the value of n.
As we know that the sum of exterior angle of any polygon is equal to 360°.
As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
So we can find the value of n by adding the all measures.
So the expression should be
(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°
Simplifying the bracket.
7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°
Solving the expression by solving the same term
(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°
33n-3 = 360°
Add 3 on both side
33n-3+3 = 360°+3
33n = 357°
Divide by 33 on both side
33/33 n= 363°/33
n = 11
Hence, the value of n is 11.
To learn more about sum of exterior angle link is here
brainly.com/question/1983075
#SPJ1
if p is false,which row represents when p v(q^r) is true?
E
F
G
H
Answer:
f and g 231
Step-by-step explanation:
Help with this math problem
The value of the investment after 3.25 years is $434.93.
What is the interest rate?The amount a lender charges a borrower, expressed as a percentage of the principle, is known as the interest rate.
Given that, the initial investment is P₀ = $400, the interest rate is n = 2.6%, and the time is x = 3.25 years.
The formula for the future value in continuous compounding is:
P(x) = P₀eⁿˣ
Substitute P₀ = 400, n = 2.6%, and x = 3.25 into the equation:
[tex]P(3.25) = (400)e^{2.6\%(3.25)}\\[/tex]
= 434.93
Hence, the value of the investment after 3.25 years is $434.93.
Learn more about the interest rates:
https://brainly.com/question/13324776
#SPJ1
Please Help!!!!
Kim and Tracy are collecting data for their final project in their psychology
class, in which they are conducting a survey about people’s overall job
satisfaction. They decide to go to the local mall to collect their data. To get a
more varied sample, Kim surveys shoppers coming out of store A, a discount
clothing store, while Tracy surveys shoppers coming out of store B, a high-end
boutique.
A. Identify a possible problem with this type of sampling method. (6 points)
B. How might Kim and Tracy improve on their sample design so as to get more
accurate information from the shoppers at the mall?
Answer:
below
Step-by-step explanation:
A problem would be that they are not surveying people from multiple places. They are doing it at 2 opposite stores, at the same times. They should try multiple different stores at other days and times to get more objective data.
Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
Find out more on inflation at https://brainly.com/question/8149429
#SPJ1
Find the slope of the line using rise/run formula please help
Answer:
20/5 is the slope, or 4.
Step-by-step explanation:
It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.
-Hope this helped
Need help solving this problem 35)210.35
Answer: The answer is 0.16638935108
Step-by-step explanation:
Red- 5 skittles
Purple- 8 skittles
Yellow- 1 skittle
Orange- 2 skittles
Green- 4 skittles
Tomas reaches in a bowl and pulls out a green skittle. Without replacing the green skittle, what is the probability he picks a yellow skittle.
A. 1/100
B. 1/80
C. 1/95
D. 1/76
Answer:
I think its C. 1/95
Step-by-step explanation:
I am not sure this is the answer, i haven't done this math in ages so I'm a bit rusty so good luck on the test!
At the toaster company, the weekly cost to run the factory is $1400 and the cost of producing each toaster is an additional $4 per toaster. Find a function rule representing the weekly cost in dollars, f(x), of producing x toasters.
Answer:
I believe... f(x)=1400+4x
Help me with these 2
1) y = 3x+2, where slope is 3 and point is(3, -5).
2) y+6 = 4(x-5) is the equation for the given slope and point.
The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,y = mx + b
The slope of a line can be calculated using two points lying on the straight line. Given the coordinates of the two points, we can apply the slope of line formula.Slope = m = tan θ = (y2 - y1)/(x2 - x1)
1) y + 5 = 3(x-1)x-x
Compare this equation to y - y₁ = m(x - x₁)
y = 3x - 3 + 5
y = 3x + 2
2) Given:
Slope = 4; point (5, -6)
y - y₁ = m(x - x₁)
y + 6 = 4(x -5 )
Option A
Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.
To know more about slopes check the below link:
https://brainly.com/question/3493733
#SPJ1
The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.
Answer: $4x4x
Step-by-step explanation:
A model rocket is launched with an initial upward velocity of 235 feet the Rockets height H in feet after t seconds is given by the following
By assuming that the initial height of the rocket is the ground, we will get the height equation:
H(t) = -16*t^2 + 235*t
How to find the equation for the height?The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:
H(t) = -16*t^2 + v*t + h
Where:
t represents the time in seconds.
the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.
v is the initial velocity, which in this case is 235 ft/s
h is the initial height, in this case we assume is zero (the rocket is launched from the ground)
Replacing all that in the height equation, we will get:
H(t) = -16*t^2 + 235*t
Learn more about gravity:
https://brainly.com/question/2537310
#SPJ1
The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters
The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.
What is the length and width of the rectangle?The perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let x represent the width be represented by variable x.
Width w = xLength l = x + 6Perimeter = 64Plug the values into the equation above above.
P = 2( l + w )
64 = 2( (x + 6 ) + x )
64 = 2( 2x + 6 )
64 = 4x + 12
64 - 12 = 4x
52 = 4x
x = 52/4
x = 13
Hence, the dimensions of the rectangle are;
Width = x = 13m
Length = x + 6 = 13 + 6 = 19m
Therefore, the dimension of the rectangle are 13m by 19m.
Learn more about rectangles here: https://brainly.com/question/27612962
#SPJ1
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
Answer:
none of them
Step-by-step explanation:
Name the points. I give you brainiac or whatever.
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)
Given f(x)=3x^2+kx+4 and the remainder when f(x) is divided by x-4 is 68 then What is the value of k?
Answer:
k = 4-----------------------------
GivenFunction f(x) = 3x² + kx + 4,Remainder of f(x) / (x - 4) is 68.According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.
f(x) = 3x² + kx + 4 - 68 = 3x² + kx - 64 = 0When x = 43*4² + k*4 - 64 = 048 + 4k - 64 = 04k - 16 = 04k = 16k = 4
10. Seven more than the quotient of a number b
and 45 is greater than 5.
A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent
Step-by-step explanation:
there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.
so, the tax is $1.50 for every $100 of the assessed value of the house.
how many $100 units are in that value ?
180,000 / 100 = 1,800 units.
that means the tax for that house is
1800 × 1.5 = $2,700
in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be
2700 / 12 = $225.00
A school is arranging a field trip to the zoo. The school spends 654.84 dollars on passes for 32 students and 2 teachers. The school also spends 281.92 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The money was spent on a pass and lunch for each student is $28.07
How to calculate the amount?It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.
Therefore the amount spent on pass will be:
= Total amount / Number of people
= 654.84 / 34
= 19.26
The amount spent on each student will be:
= 281.92 / 32
= 8.81
The amount spent in pass and lunch will be:
= 19.26 + 8.81
= $28.07
Learn more about money on:
brainly.com/question/24373500
#SPJ1
A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The distribution that is needed for the problem that we have here is the t distribution.
What is the t distribution?With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.
When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.
We have tn-1
where n = 70
so that we would have
t70 - 1
= t69
Therefore we would have to use the t distribution here.
Read more on the t distribution https://brainly.com/question/17469144
#SPJ1
What is 10,483,190 in word form?
Answer:
Ten million, Four hundred eighty-three thousand, one hundred ninety
Step-by-step explanation:
Break it down! into the tens digit, hundreds digit, etc.
