According to given information the p-value for each sample mean is:
a. 0.001 b. 0.001 c. 0.074
What is meant by p-value?
In statistics, the p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the results.
To compute the p-value for each sample mean, we need to first calculate the corresponding z-score using the formula:
z = (x - μ) / (σ / [tex]\sqrt{(n)[/tex])
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
a. For x = 18.0, the z-score is:
z = (18.0 - 20) / (9.31 / [tex]\sqrt{(167)[/tex]) = -3.28
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.001.
b. For x = 21.8, the z-score is:
z = (21.8 - 20) / (9.31 / [tex]\sqrt{(167)[/tex]) = 3.28
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.001.
c. For x = 21.3, the z-score is:
z = (21.3 - 20) / (9.31 / sqrt(167)) = 1.79
Using a standard normal distribution table or calculator, we can find that the corresponding p-value is approximately 0.074.
Therefore, sample of 167 items will be taken and the population standard deviation is 9.31 has the p-value for each sample mean is:
a. 0.001
b. 0.001
c. 0.074
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Calculate the pay for the following day of a weekly time card given a wage of $14/hr.
Name
Week of: Morning
Afternoon
In
Out
In
Out
Monday 08:00 12:15
13:00 | 17:15 round to the nearest hundred
Given a salary of $14 per hour, the pay for the following day of a weekly time card is $126.
How to calculate pay for the following?It is the sum of money an employee receives in exchange for the job they perform. A monthly salary, annual salary, or hourly rate are the most common ways to convey it.
Pay = (4 hours x $14/hr) + (5 hours x $14/hr)
= $126
The wage rate must be increased by the number of hours performed in order to determine the pay for the day.
The wage rate is $14/hr.
A 4 hour morning shift and a 5 hour afternoon shift were performed by the employee. Therefore, the day's salary is calculated using the following formula:
(4 hours x $14/hr) + (5 hours x $14/hr) = $126.
If you round this amount to the nearest hundredth, your total pay will be $126.00.
Monday 08:00 12:00 4hrs * $14 $56.00
12:15 17:30 5hrs * $14 $70.00
Total wages $126.00
It's crucial to maintain precise records of the hours worked each day to make sure the employee is paid correctly.
This covers the hours they arrive at work, leave at the end of the day, and any pauses they take. The employee's salary can then be calculated with accuracy using this information.
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Find the probability of no successes in eight trials of a binomial experiment in which the probability of success is 7%. P = [? ]% Round to the nearest tenth of a percent.
The probability of no successes in eight trials of a binomial experiment with a probability of success of 7% is 0.6%
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The resulting value represents the likelihood of the event occurring. For example, if a coin is tossed, the probability of it landing heads up is 0.5 (assuming a fair coin), because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
The probability of no successes in eight trials of a binomial experiment can be calculated using the binomial probability formula:
P(X = 0) = (n choose k) × pᵏ × (1-p)ⁿ⁻ᵏ
where:
n = number of trials = 8
k = number of successes = 0
p = probability of success = 7% = 0.07
Substituting the values in the formula, we get:
P(X = 0) = (8 choose 0) × 0.07⁰ × (1-0.07)⁸⁻⁰
= 1 × 1 × 0.569
= 0.569
Therefore, the probability of no successes in eight trials of a binomial experiment with a probability of success of 7% is 0.6%, rounded to the nearest tenth of a percent.
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find f(-2) for the piece-wise function
Answer:
0
Step-by-step explanation:
since X= -2 and -2 < -1
f(-2)= (-2) +2
=0
Good luck
f( - 2 ) = 0 for the given piecewise function.
To find f( - 2 ) for the given piecewise function, we need to determine which part of the function applies to the input value x = - 2.
Since - 2 is less than or equal to - 1, we use the first part of the function where f(x) = x + 2 for x ≤ - 1.
Now, substitute x = - 2 into the first part of the function:
f( - 2 ) = ( - 2 ) + 2
f( - 2) = 0
So, f( - 2 ) = 0 for the given piecewise function.
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PLEASE HELP GUYSSSSS
Answer:
WX=43
Step-by-step explanation:
VY=5y-2
VW=4y
WX=5y-2
YX=4y
VY=a
VW=b
WX=c
YX=d
a+b+c+d=18y-4
P=18y-4
158=18y-4
162=18y
y=9
WX=45-2
WX=43
A cylinder has a diameter of 14 meters and a height of 13 meters.
To the nearest square meter, what is the lateral area of the cylinder"
(Use 3.14 for 7.)
A 572 square meters
B 879 square meters
1,143 square meters
D 2,374 square meters
f the following values for the radius and height of a cylinde
The lateral area οf a cylinder is calculated as L = 2rh, where r is the radius οf the base and h is the height οf the cylinder.
What is cylinder?In several current branches οf geοmetry and tοpοlοgy, a cylinder can alsο be defined as an infinitely curvilinear surface. There is sοme ambiguity in terminοlοgy due tο the change in the basic meaning οf the wοrds—sοlid versus surface (as in ball and sphere).
By cοmparing sοlid cylinders and cylindrical surfaces, the twο ideas can be separated. Bοth οf these οr a mοre specialised οbject, the right circular cylinder, may be referred tο simply as "cylinder" in literary wοrks.
First, we must calculate the radius οf the cylinder, which is half its diameter.
Sο the radius is 14/2 = 7 meters.
Then, we can plug in the values we have intο the fοrmula: L = 2 × 3.14 × 7 × 13 ≈ 572 square meters.
Therefοre, the answer is A) 572 square meters, rοunded tο the nearest square meter.
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The Question is inside the picture
The amount of money that the student would saved altogether by paying off the loan in 3 years instead of 4 is $538.48.
How to find the amount saved ?To find out how much the student will save by paying off the loan in 3 years instead of 4 years, we will first calculate the monthly payments for each repayment period using the loan payment formula.
P = L x (r(1 + r)^n) / ((1 + r)^n - 1)
P 4years = 9,000 x (0.008333 x (1 + 0.008333)^48) / ((1 + 0.008333)^48 - 1)
P 4years = $228.17
For the 3-year repayment plan:
n = 3 years * 12 months/year = 36 payments
P 3years = 9,000 x (0.008333 x (1 + 0.008333)^36) / ((1 + 0.008333)^36 - 1)
P 3years = $289.28
Savings = Total in 4years - Total in 3years
= $10,952.16 - $10,413.68
= $538.48
By paying off the loan in 3 years instead of 4 years, the student will save approximately $538.48.
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can someone give me the answers in order please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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Assume a manufacturing company provides the following information from its master budget for the month of May:
Unit sales 6,700
Selling price per unit $ 42
Direct materials cost per $ 15
Direct labor cost per unit $ 12
Predetermined overheard rate (based on direct labor dollars)75%
If the company maintains no beginning or ending inventories, what is the budgeted gross margin for May?
Multiple Choice
$33,500
$40,200
$6,700
$30,200
A right triangle has legs which measure 14 inches and 18 inches. Find the length of the
hypotenuse.
answers:
13 inches
25 inches
32 inches
22.8 inches
Answer:
22.8 Inches
Step-by-step explanation:
To find the hypotenuse, the formula is √c=√a^2+b^2
Lets input our values now:
c=√14^2+18^2
Now, let's solve:
c=√196+324
c=√520
The square root of 520 equals about 22.8, so our answer would be 22.8 inches.
Suppose that a brand of lightbulb lasts on average 2821 hours with a standard deviation of 197 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 2772 to 3298 hours?
P(2772 < X < 3298)
The probability that a particular bulb will last from 2772 to 3298 hours is 2.66.
Define probability?In mathematics, the term average is referred to as the mean value, which is equal to the ratio of the sum of all the values in a given set to all the values in the set.
Here we have been given,
A brand of lightbulb lasts on average 2821 hours with a standard deviation of 197 hours.
Assuming the life of the lightbulb is normally distributed, and we need to find the probability that a particular bulb will last from 2772 to 3298 hours.
According to the given problem, we know that the value of the following is defined as follows:
Average = 2821
Standard deviation = 197
Now, based on the z score concept, the value of the required probability is calculated as,
=> z = (x-mean)/ sd
=> z lower = (2821 - 3298)/197= -2.42
=> z upper = (2821- 2772)/197= 0.24
Therefore, the probability is calculated as,
=> z upper - z lower
=> 0.24 - (-2.42)
=> 2.66
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The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a brown cand
Answer: 10% chance / 10/100
Step-by-step explanation:
Convert it so that when you add all the numbers they will equal 100
4+6+3+5+2=20 make it so it equals 100=
*5
20+30+15+25+10 = 100
10%=brown
The Nicols are buying a house selling for $255,000. They pay a down payment of $55,000 from the sale of their current house. To obtain a 15-year mortgage at a 5.5% interest rate, the Nicols pay 2.5 points at the time of closing. What is the cost of the 2.5 points?
The cost of the 2.5 points is $5,000.
To solve this problemThe cost of the points is based on the loan amount, which is the sale price minus the down payment:
Loan amount = $255,000 - $55,000 = $200,000
Points are typically calculated as a percentage of the loan amount. In this case, the Nicols are paying 2.5 points, which means they are paying 2.5% of the loan amount.
Cost of points = 2.5% of $200,000 = $5,000
Therefore, the cost of the 2.5 points is $5,000.
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This scatterplot and regression line below show the relationship between the average rent for a
1
11-bedroom apartment in New York and the number of years after the year
2000
20002000.
The fitted line has a
�
yy-intercept of
800
800800.
What is the best interpretation of this
�
yy-intercept?
Choose 1 answer:
it would be 8000 because of the interception
In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XZ
The length of XZ in adjoining figure is 80/3 cm
What do you mean by Rectangular surfaces ?Rectangular surfaces refer to flat two-dimensional shapes that have four straight sides and four right angles, where opposite sides are parallel and equal in length. They are called rectangular because they can be formed by taking a rectangle and flattening it out into a plane. Examples of rectangular surfaces include sheets of paper, computer screens, tabletops, and walls of rectangular rooms. The area of a rectangular surface is calculated by multiplying the length and width of the rectangle.
Let the length, width, and height of the rectangular prism be x, y, and z, respectively. Then, we have:
xy = 720 (since the area of the rectangular surfaces of the prism is 720 sq. cm)
XX' = 20
Let XY = 5k, XZ = 4k, and YZ = 3k (since XY : XZ: YZ = 5:3:4).
Using the Pythagorean theorem, we can find the value of k as follows:
XX²+ XZ²= ZZ²
20²+ (4k)²= (5k)²
400 + 16k² = 25k²
9k² = 400
k² = 400/9
k = 20/3
Therefore, XZ = 4k = 80/3 cm.
Hence, the length of XZ is 80/3 cm.
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Pamela walked from the dry cleaners to the restaurant, and then from the restaurant to the gift shop. If each grid line stands for 300 meters, how far did Pamela walk?
Answer:
Assuming that the dry cleaners, restaurant, and gift shop are all located on a grid, we need to know how many grid lines Pamela crossed to determine how far she walked. Without that information, it's impossible to calculate the distance.
What is the circumference if the area is
452.39
Answer:
≈ 75,4
Step-by-step explanation:
Given:
A = 452,39
Find: C - ?
First, we need to find the radius:
A = πr^2
πr^2 = 452,39 / : π
r^2 = 452,39/π
r ≈ 12
Now we can find the circumference:
C = 2π × 12 = 24π ≈ 75,4
Step-by-step explanation:
area of circle = 452.39,πr square = 452.39. 3.14r = 452.39 r square = 144 r = 12 cm diameter = 12x2= 24
Find the area of the shaded polygons.
(Im giving 100 points to whoever solves)
Answer:
Area of the parallelogram = 120 square units
Area of the triangle = 17.5 square units
Area of the trapezoid = 372 square units
Step-by-step explanation:
The first polygon is a parallelogram with a base of 15 units and a height of 8 units.
[tex]\begin{aligned}\sf Area\;of\;a\;parallelogram&=\sf base \times height\\&=\sf 15 \times 8\\&=\sf 120\;square\;units\end{aligned}[/tex]
Therefore, the area of the parallelogram is 120 square units.
[tex]\hrulefill[/tex]
The second polygon is a triangle with a base of 5 units and a height of 7 units.
[tex]\begin{aligned}\sf Area\;of\;a\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 5 \times 7\\\\&=\sf 17.5\;square\;units\end{aligned}[/tex]
Therefore, the area of the triangle is 17.5 square units.
[tex]\hrulefill[/tex]
The third polygon is a trapezoid with bases of 7 units and 24 units, and a height of 24 units.
[tex]\begin{aligned}\sf Area\;of\;a\;trapezoid&=\sf \dfrac{sum\;of\;bases}{2} \times height\\\\&=\sf \dfrac{7+24}{2} \times 24\\\\&=\sf \dfrac{31}{2}\times 24\\\\&=\sf 372\;square\;units\end{aligned}[/tex]
Therefore, the area of the trapezoid is 372 square units.
Answer:
see below
Step-by-step explanation:
To find:-
The areas of the given shaded polygons.Answer:-
There are three polygons viz parallelogram, triangle and a trapezium. To find out the areas we can use the following formulae :-
Area of triangle :-
Area = 1/2 * base * heightArea of parallelogram:-
Area = base * perpendicular heightArea of trapezium:-
Area = 1/2 * (sum of parallel sides)*distance between the sidesNow we may use the above formulae as ,
Area of the given parallelogram:-
→ A = base * height
→ A = * 15 * 8
→ A = 120units²
Area of the given triangle:-
→ A = 1/2 * b * h
→ A = 1/2 * 5 * 7
→ A = 17.5 units²
Area of the given trapezium:-
→ A = 1/2 * sum of || sides* distance between them
→ A = 1/2 * (7+24) * 24
→ A = 12 * 31
→ A = 372 units ²
This is our required answers .
Please help! (Introductory Algebra)
The equations that do not have a solution are B, D, E, and G.
We can solve each equation to check if it has a solution or not:
A. 3x+1=2x+5
Subtracting 2x from both sides, we get x = 4. This equation has a solution.
B. 4(x-1)+2x=6x+5
Expanding the left side, we get 4x - 4 + 2x = 6x + 5. Simplifying, we get 6x - 4 = 6x + 5, which is not possible. This equation does not have a solution.
C. x+1=2x
Subtracting x from both sides, we get x = 1. This equation has a solution.
D. 10x+1=5x-6
Subtracting 5x from both sides, we get 5x + 1 = -6. This equation does not have a solution.
E. 3x+7=3x-6
Subtracting 3x from both sides, we get 7 = -6. This equation does not have a solution.
F. 4x=5x
Subtracting 4x from both sides, we get x = 0. This equation has a solution.
G. x=x+7
Subtracting x from both sides, we get 0 = 7. This equation does not have a solution.
H. x+4=2(x+4)
Expanding the right side, we get x + 4 = 2x + 8. Subtracting x from both sides, we get 4 = x + 8. Subtracting 8 from both sides, we get -4 = x. This equation has a solution.
Therefore, the equations that do not have a solution are B, D, E, and G.
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This Rectangle has a perimeter of 28 units.
a. Create a table that shows the length and width of at least 3 different rectangles that also have a perimeter of 28 units.
Record your responses in the table below.
A grouping of at least three distinct rectangles, each with a 28-unit perimeter:2 and 12; 5 and 9; and 8 and 6.
To create the table, we start with the original rectangle with dimensions 10 and 4. To find other rectangles with the same perimeter, we can change the length and width while still ensuring that their sum is 14 (half of the original perimeter).
Since the perimeter of the rectangle is 28 units, we can use the formula:
Perimeter = 2(length + width)
where length and width are the dimensions of the rectangle.
If we solve for length, we get:
length = (Perimeter - 2*width) / 2
Using this formula, we can create a table of at least 3 different rectangles that have a perimeter of 28 units:
Width (units) Length (units)
2 12
5 9
8 6
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manufacturer bought a new rolling press for $48,000. It has depreciated in value at a rate of 18% every 2 years. What is the value of the rolling press 7 years after the initial purchase? Round to the nearest cent.
Maker spent $48,000 on a brand-new rolling press. Its value has decreased at a pace of 18% per two years. Seven years after the initial purchase, the rolling press is worth $18,687.53.
We can solve this problem by using the formula for exponential decay:
V = [tex]P * (1 - r)^n[/tex]
where V is the value of the rolling press after n years, P is the initial purchase price, r is the depreciation rate per period, and n is the number of periods.
In this case, we have:
P = $48,000 (the initial purchase price)
r = 18% every 2 years = 0.09 per year (since there are 2 two-year periods in 1 year)
n = 7 years (the number of years that have passed)
These values are entered into the formula to produce the following results:
V = [tex]$48,000 * (1 - 0.09)^7[/tex]
V ≈ $18,687.53
Hence, seven years after the original purchase, the rolling press is now worth roughly $18,687.53.
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When Rom was 16 years old, he deposited certain sum of money in a bank at the rate of 10% p. a. Compounded annually. After his balance became 121 times the initial principal, he deposited & of the 400 existing balance in the same account. After 1 year of this deposition, the bank changed it's policy to giva interest at 20°1. p.a simple interest. At the age of 24 years, Ram planned to stort a business. so he withdrew all the money from his account. He found that the withdrawn amount was Rs. 359 less than thrice of the initial principal. Then,
Find the sum deposited by Ram at the age of 16 years. The amount withdrawn from the bank was not enough so, he borrowed a loan of Rs. 1.10,000 from the bank and agreed to pay within 4 years, at rate of 15% pa. compounded annually. He paid the interest of the first year at the end of the 1st year. He cleared his debt by paying equal installments in next 2 years and 1 year.
.
Find the total interest paid by him to the bank. For how many years, he should have waited to start the business so that he need not borrow entra Loan?
The total interest paid by him to the bank would be: Rs. 28,500. Ram should have waited for 3 years, to start his business without borrowing extra loan, until the age of 19.
What is an interest?
Let the sum deposited by Ram at the age of 16 be x.
After compounding for n years, the balance becomes x(1.1)^n.
As per the given condition, we have:
x*[tex](1.1)^{n}[/tex] = 121x
[tex](1.1)^{n}[/tex] = 121
n = 2
So, after two years, Ram's balance became 121 times the initial principal.
After this, he deposited 1/4 of the existing balance, i.e. 1/4 * 121x = 30.25x
After one year of this deposit, the balance becomes 30.25x * 1.2 = 36.3x
So, Ram's total balance at the age of 19 becomes 121x + 36.3x = 157.3x
This is given to be Rs. 359 less than thrice of the initial principal, i.e.
157.3x = 3x - 359
Solving this equation, we get:
x = Rs. 480
So, the sum deposited by Ram at the age of 16 was Rs. 480.
Now, he borrowed Rs. 1,10,000 at 15% p.a. compounded annually.
The interest for the first year would be (15/100) * 1,10,000 = Rs. 16,500
After paying this interest, the remaining balance becomes:
1,10,000 + 16,500 = Rs. 1,26,500
Now, he cleared his debt by paying equal installments in the next 2 years and 1 year.
Let the equal installment be x.
So, the balance after the first year becomes:
1.15x + (1.15)²x + (1.15)³x - x = 1,26,500
Solving this equation, we get:
x = Rs. 45,000
So, Ram paid a total of Rs. 1,35,000 to clear his debt.
The total interest paid by him to the bank would be:
16,500 + 0.15 * 45,000 + 0.15 * 45,000 + 0.15 * 45,000 = Rs. 28,500
To start his business without borrowing extra loan, Ram should have waited for 3 years, until the age of 19, when his balance was Rs. 157.3x = Rs. 75,264. With an interest rate of 20% p.a. simple interest, the balance would become:
75,264 + 0.2 * 75,264 = Rs. 90,316.8
This amount would be sufficient for him to start his business without borrowing extra loan.
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Find x round to the nearest 100th
the perpendicular or opposite side is approximately 10.42 units long.
How to solve the triangle?
In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, and the side opposite the 15-degree angle is called the opposite side or perpendicular. The third side, adjacent to the 15-degree angle and the right angle, is called the adjacent side.
Using trigonometric functions, we can relate the angles and sides of a right triangle. In this case, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(15) = opposite/adjacent
We are given the hypotenuse, which is the hypotenuse, and we can use the Pythagorean theorem to find the adjacent side:
adjacent = sqrt(hypotenuse² - opposite²)
Substituting the value of the hypotenuse and rearranging the above equation we get:
opposite = √(hypotenuse² / (1 + tan(15)²))
Plugging in the values, we get:
opposite = √(12² / (1 + tan(15)²))
= √(144 / (1 + 0.2679))
= ²(108.5)
= 10.42
Therefore, the perpendicular or opposite side is approximately 10.42 units long.
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A parallelogram has coordinates of (5, 17), (10, 20), (18, 9), and (13, 6). Which right triangle represents one of the cutouts from the box method?
A right triangle is shown. The length of one side is 5, and another is 17.
A right triangle is shown. The length of one side is 5, and another is 8.
A right triangle is shown. The length of one side is 8, and another is 11.
A right triangle is shown. The length of one side is 3, and another is 8.
The answer is right angle with leg 3 and 8.
To use the box method to find the area of the parallelogram, we need to divide it into two triangles. One possible way to do this is by drawing a diagonal from (5, 17) to (18, 9), and creating two triangles with vertices (5, 17), (10, 20), and (18, 9), and (5, 17), (13, 6), and (18, 9).
The length of the diagonal can be found using the distance formula:
d = √[(18 - 5)^2 + (9 - 17)^2]
d = √[(13)^2 + (-8)^2]
d = √(169 + 64)
d = √233
Now, the area of the parallelogram is equal to the product of the length of the diagonal and half the height of the parallelogram. One of the cutouts from the box method will be a right triangle with legs equal to half the height and half the length of the diagonal.
Half the height can be found by taking the difference in y-coordinates between (5, 17) and (18, 9) and dividing by 2:
h = (17 - 9)/2
h = 4
Half the length of the diagonal is:
l = √233/2
Using these values, we can check each of the given right triangles to see which one matches the dimensions of the cutout:
A right triangle with legs 5 and 17 does not match, since the legs should be half the diagonal and half the height.
A right triangle with legs 5 and 8 does not match, since the legs should be half the diagonal and half the height.
A right triangle with legs 8 and 11 does not match, since the legs are not proportional to the dimensions of the parallelogram.
A right triangle with legs 3 and 8 matches, since half the diagonal is approximately 7.66 and half the height is 4, and 3 and 8 are proportional to these values.
Therefore, the correct answer is the right triangle with legs of 3 and 8.
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Answer:
its the middle one ( 8,11)
Step-by-step explanation:
18. The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a standard deviation
of 2 inches. An Atlantic croaker fish is randomly selected.
a) Find the probability that the length of the croaker fish is less than 7 inches.
b) Find the probability that the length of the fish is between 7 and 15 inches
Answer:
a) To find the probability that the length of the croaker fish is less than 7 inches, we need to calculate the z-score of 7 inches using the formula:
z = (x - mu) / sigma
where x is the length of the fish we are interested in, mu is the mean length of the population, and sigma is the standard deviation of the population.
In this case, x = 7, mu = 10, and sigma = 2. So the z-score is:
z = (7 - 10) / 2 = -1.5
We can look up the probability of a z-score less than -1.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.0668 or 6.68%.
Therefore, the probability that the length of the croaker fish is less than 7 inches is 0.0668 or 6.68%.
b) To find the probability that the length of the fish is between 7 and 15 inches, we need to calculate the z-scores of 7 inches and 15 inches using the same formula as above:
z1 = (7 - 10) / 2 = -1.5
z2 = (15 - 10) / 2 = 2.5
We can look up the probability of a z-score between -1.5 and 2.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.9332 or 93.32%.
Therefore, the probability that the length of the fish is between 7 and 15 inches is 0.9332 or 93.32%.
Find measure of the indicated angle
Answer:
60°
Step-by-step explanation:
it's one half of an equilateral triangle, all sides equal and angles congruent, sum is 180°, divide by three and you have 60° which is your answer.
help asap its timed will mark brainliest no need to draw just do the other steps
The difference between the area of the rectangle and the area of the triangles is 56 units.
What are the area of the rectangle and the area of the triangles?Area of the rectangle = 8 * 16
Area of the rectangle = 128 units
Area of triangle 1 = ¹/₂ * 4 * 12
Area of triangle 1 = 24 units
Area of triangle 2 = ¹/₂ * 4 * 16
Area of triangle 2 = 32 units
Area of triangle 2 = ¹/₂ * 4 * 8
Area of triangle 2 = 16 units
Area of rectangle - area of triangle = 128 - ( 24 + 32 + 16)
Area of the rectangle - the area of the triangles = 56 units
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In 1960 the avrege price of a car was about 2500 this may sound inxpensive but the avrage income was much less then it is now. to compare doller amounts ovr time use the formula V = a/s c where A is the old dollor amount S is the starting years consumer price index cpi ,C is converting year's cpi and V is the curent value of the old dollar amount. Buying a car for 2500 in 1960 was like buying a car for how much money in 2004
Buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars .we can solve by using formula by substituting all details along with consumer price index
what is consumer price index ?
The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. The CPI is often used as an indicator of inflation
In the given question,
To compare the dollar amounts over time, we can use the formula V = (A/S) x (C/C'), where:
V = the current value of the old dollar amount
A = the old dollar amount ($2,500 in this case)
S = the starting year's consumer price index (CPI) for the old dollar amount (1960 CPI)
C = the converting year's CPI (2004 CPI)
C' = the starting year's CPI for the converting year (1960 CPI)
Using the formula, we can calculate the current value of $2,500 in 1960 dollars as:
V = (A/S) x (C/C')
V = (2,500/29.6) x (188.9/29.6)
V = 84.46 x 6.380
V = $539.23
Therefore, buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars.
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Below is the number of years that each of the nine Omar's Omelette Operation locations have been open.
5.2
,
7.0
,
10.5
,
2.6
,
2.9
,
4.5
,
1.0
,
1.5
,
2.6
5.2,7.0,10.5,2.6,2.9,
4.5,1.0,1.5,2.6
Using the data, create a histogram.
To create a histogram of the number of years that each of the nine Omar's Omelette Operation locations has been open, we can start by organizing the data into groups or bins.
A histogram is a graphical representation of a distribution of data, typically shown as bars of different heights. In this case, we can use bins of equal width, such as 1 or 2 years. Then, we can count the number of values that fall into each bin and represent this count as the height of the corresponding bar.
For example, if we use bins of width 2 years, we can group the data into the following bins: [0, 2), [2, 4), [4, 6), [6, 8), [8, 10), and [10, 12). Then, we can count the number of values that fall into each bin and create a bar chart with bars of different heights corresponding to these counts.
The resulting histogram would show the distribution of the number of years that the Omar's Omelette Operation locations have been open, and we could use it to analyze the central tendency, variability, and shape of the data.
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A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a
table in a room where the temperature is 75 Fahrenheit. Give answers accurate to at least 2 decimal
places.
(a) If the temperature of the turkey is 153 Fahrenheit after half an hour, what is its temperature after 45
minutes?
Fahrenheit
(b) When will the turkey cool to 100 Fahrenheit?
hours.
After answering the presented question, we can conclude that As a equation result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "[tex]2x + 3 = 9,[/tex]" for example, states that the sentence "[tex]2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
a. [tex]dT/dt=-k(T-Ts)[/tex]
[tex]-kdt=(DT/(T-Ts)[/tex][tex])[/tex]
When both sides are combined, the following results:
[tex]-kt + C = ln|T - Ts|[/tex]
where C is the integration constant. To calculate C, we can start with the assumption that the turkey is 185 degrees Fahrenheit when it comes out of the oven:
[tex]ln|185 - 75| = -k(0) + C[/tex]
[tex]C = ln(110) (110)[/tex]
As a result, the equation relating the temperature of the turkey to time is:
[tex]-kt+In|T-75|=-kt+In(110)[/tex]
[tex]T=e(-ktIn(110)+75[/tex]
[tex]T=110e(-0.5k)+75[/tex]
[tex]T=110e(-0.75k+75 T134.43[/tex] degrees Fahrenheit
As a result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.
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what fraction is equivalent to 8 x 2/3?
Answer:
16/3 or 5 1/3
Step-by-step explanation:
multiply than simplify