The value of t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
To test the hypothesis that the highlighters last less than 14 hours, we will use a one-sample t-test. The null hypothesis for this test is that the mean continuous writing time for the highlighters is equal to or greater than 14 hours. The alternative hypothesis is that the mean continuous writing time for the highlighters is less than 14 hours.
In this problem, we are given that x = 13.6 hours and s = 1.3 hours. The sample size is n = 40. Substituting these values into the formula for the test statistic, we get:
t = (13.6 - 14) / (1.3 / √(40)) = -1.946
The p-value for the test can be found using a t-distribution table or a statistical software program. The p-value is the probability of observing a t-value as extreme as the one we calculated, assuming the null hypothesis is true. In this problem, the p-value is 0.029.
To make a decision about the null hypothesis, we compare the p-value to the significance level, which is typically set at 0.05. If the p-value is less than the significance level, we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
In this problem, the p-value is less than 0.05, so we reject the null hypothesis. This means there is strong evidence to suggest that the highlighters last less than 14 hours. We can conclude that the manufacturer's claim that their highlighters can write continuously for 14 hours is not supported by the sample data.
Hence the correct option is (c).
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Complete Question:
Solve the problem. Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics:
x =13.6 hours,
s =1.3 hours
Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.
a) z = 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
b) t = -1.946; p = 0.029; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours. o
c) t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
d) z = 1.946; p = 0.974; Fail to reject the null hypothesis; there is not “strong evidence to suggest that the highlighters last less than 14 hours.
1. What does the term inflation mean? If meat prices go up, does this auto-
matically mean that there is inflation? Explain your answer.
2. Give an example of who is hurt and who is helped by inflation. Briefly
explain how inflation affects each group you have named.
3. How is the Consumer Price Index used to measure the rate of inflation?
Inflation refers to the general increase in prices of goods and services in an economy over a period of time.
A rise in meat prices may be an indication of inflation, but it is not necessarily an automatic or definitive sign of inflation.
Inflation can hurt savers and fixed-income earners, such as retirees on a fixed pension, as the purchasing power of their savings and income decreases.
The Consumer Price Index (CPI) is used to measure the rate of inflation by tracking the average price change of a basket of goods and services commonly purchased by households, including food, housing, transportation, and medical care.
The CPI measures the percentage change in prices from a base period and is calculated by dividing the cost of the basket of goods and services in the current period by the cost of the same basket in the base period and multiplying the result by 100.
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Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
The answer is option A. That is, the time taken in hours if the train traveled 13 miles in 30 minutes is 4.5 hours.
What is the relation between distance travelled and time?The relation between distance traveled and time is given by the formula:
Distance = Speed x Time
where distance is the total distance traveled, speed is the rate at which the distance is covered, and time is the duration for which the distance is covered. This formula applies to any type of motion, whether it is linear or circular, and it is often used to calculate the distance covered by an object given its speed and the time it traveled. Alternatively, the formula can also be used to calculate the time required to travel a certain distance given the speed at which the object is traveling.
Given that the total distance = 117 miles. We need to find the time taken in hours if the train traveled 13 miles in 30 minutes.
For that we can use the equation, distance = rate x time
Now, rate = distance/time
Distance = 13 miles, time = 30 minutes = 30/60 hours = 0.5 hours
Therefore, rate = 13 miles / 0.5 hours = 26 miles per hour
Now to find the time it took to travel the entire 117 miles:
time = distance/rate
time = 117 miles/ 26 miles per hour
time = 4.5 hours
Therefore, the answer is (A) 4.5 hours.
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using cramer rao lower bound method, with a random sample of size n, find a minimum variance unbiased estimator of the parameter,λ of a poisson population
The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.
What is variance?Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.
According to given information:Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:
[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]
Taking the natural logarithm and differentiating with respect to λ:
ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)
d/dλ ln L(λ | x) = -n + Σxi/λ
Setting the derivative equal to zero and solving for λ, we get:
λ = Σxi/n
This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.
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A surveyor whose eye level is 5 feet above the ground determines the angle of elevation to the top of an office building to be 41.7°. If the surveyor is standing 40 feet from the base of the building, what is the height of the building to the nearest foot?
A.) 32ft.
B)50 ft
C)36ft
D.)41ft
The height of the building when the surveyor is standing that far is D.)41ft
How to find the height of the building ?The tangent function would be best to use to find the height because we would be able to use the adjacent and and opposite.
Assuming that 5 feet is the height and the angle of elevation is 41. 7 degrees, and the distance of 40 feet, we have :
tan ( A ) = (h - x) / D
tan ( 41. 7° ) = ( h - 5 ) / 40
h - 5 = 40 x tan ( 41. 7 ° )
h - 5 = 40 x 0.8895
h = 35.58 + 5
= 40.58
= 41 feet
The height of the building is 41 feet.
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Assume that when human resource managers are randomly selected, 49% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that exactly 2 of them say job applicants should follow up within two weeks.
The probability that exactly 2 of them say job applicants should follow up within two weeks is 33.02%.
How to find the probability ?We can use the binomial probability formula:
P(x) = C ( n, x ) × p ^ x × ( 1 - p ) ^ ( n - x )
Solving then gives:
P ( 2 ) = C ( 7, 2 ) x 0.49 ^ 2 x ( 1 - 0. 49 ) ^ ( 7 - 2)
P ( 2 ) = 21 x 0. 49 ^ 2 x ( 1 - 0. 49) ^5
= 21 x 0. 2401 x 0. 078109
= 0. 3302
In conclusion, the probability that 2 of the 7 human resource managers say job applicants should follow up within two weeks is approximately 0.3302 or 33.02%.
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The box plot represents the scores on quizzes in a science class.
A box plot uses a number line from 74 to 86 with tick marks every one-half unit. The box extends from 77.5 to 81.5 on the number line. A line in the box is at 80. The lines outside the box end at 75 and 85. The graph is titled Science Quizzes, and the line is labeled Scores On Quizzes.
What value does 25% of the data lie above? Find the value.
What is the value of x in both these questions
Answer:
x + 5 + 7x - 5 + x = 180
9x = 180
x = 20
So the measure of angle M is x + 5 = 20 + 5 = 25°
For a confidence level of 80%, find the critical value. Round to 3 decimal places.
Answer:
Step-by-step explanation:
80.000
Each marble bag sold by Eric’s Marble Company contains 3 red marbles for every 4 blue marbles. If a bag has 36 blue marbles, how many red marbles does it contain?
Dr. Rollins is both an anthropologist and archeologist. While excavating some ruins in South America, he discovered a scale drawing of a replica of a Mayan pyramid.
-The scale for the drawing to the replica was 1 inch : 2 feet.
- The scale for the replica to the actual pyramid was 1 foot : 14 feet.
If the height of the pyramid on the drawing was 3 1/2 inches, what was the height of the actual pyramid?
A. 98 feet
B. 49 feet
C. 91 feet
D. 196 feet
Correct answer is option A. If the height of the pyramid on the drawing was 3 1/2 inches, then the height of the actual pyramid is 98 feet
How do we compare inches to feet comparison on a replica?When a scale drawing or model is made, the actual object is typically much larger than the drawing or model. In order to represent the object in a smaller size, a ratio is used to scale down the dimensions. This ratio is can be in a fraction form or 'is to' form. We can use this ratio to easily calculate the dimensions of a replica from the actual object or vice versa.
To find the height of the actual pyramid, we need to use both scales given in the problem.
We can start by finding the height of the replica using the first scale:
1 inch on the drawing = 2 feet on the replica
So, 3.5 inches on the drawing = (3.5 * 2) feet on the replica = 7 feet on the replica
Now, using the second scale we can find the height of the actual pyramid:
1 foot on the replica = 14 feet on the actual pyramid
So, 7 feet on the replica = (7 * 14) feet on the actual pyramid = 98 feet
Therefore, the height of the actual pyramid is 98 feet.
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#9
Identify an example of a solid from which a triangular, hexagonal, and trapezoidal cross section can be formed.
O cone
O sphere
O cylinder
O triangular prism
hexagonal prism
Solve for x
x = 1+2+3+4..... Infinity
Answer:
x = -1/12
Step-by-step explanation:
It is actually a rather simple proof. Before we get to that, it’s important to understand a couple of other things. Let’s consider the following infinite summation:
X = 1 - 1 + 1 - 1 + 1 - 1 ...
Rearranging the above equation a little bit, we get:
X = 1 - (1 - 1 + 1 - 1 + 1 - 1 ...)
If you look at the term inside the brackets, it in fact equals X. So let’s substitute that:
X = 1 - X
2X = 1
X = 1/2
Now let’s consider another sum.
Y = 1 - 2 + 3 - 4 + 5 - ...
Writing it in another way, we get:
Y = 0 + 1 - 2 + 3 - 4 + 5 + ...
Adding the above two equations:
Y + Y = (1 - 2 + 3 - 4 + 5 ...) + (0 + 1 - 2 + 3 - 4 + 5 ...)
Grouping the corresponding terms within the brackets, we get:
2Y = 1 + 0 - 2 + 1 + 3 - 2 - 4 + 3 + 5 - 4 ...
2Y = 1 - (2-1) + (3-2) - (4-3) + ...
2Y = 1 - 1 + 1 - 1 + 1 - 1 ...
But the summation on the right hand side is X. Let’s substitute it:
2Y = X
2Y = 1/2
Y = 1/4
Finally, let’s consider our original question at hand i.e. the sum of all natural numbers:
S = 1 + 2 + 3 + 4 + ...
We defined Y earlier as:
Y = 1 - 2 + 3 - 4 + ...
Subtracting Y from S:
S - Y = 1 - 1 + 2 + 2 + 3 - 3 + 4 + 4 + ...
S - Y = 4 + 8 + 12 + 16 + ...
We just calculated the value of Y to be 1/4. So let’s substitute it:
S - 1/4 = 4 x (1 + 2 + 3 + 4 + ...)
S - 1/4 = 4S
3S = -1/4
S = -1/12
Sarah has a coupon for an oil change with synthetic oil for $49.95. She can buy 5 quarts of synthetic oil, which is what her car needs, for $37.54 and an oil filter for $9.47. How much can she save by doing the oil change herself?
Step-by-step explanation:
If Sarah buys the oil and oil filter separately, she would spend:
Cost of oil = $37.54
Cost of oil filter = $9.47
Total cost = $37.54 + $9.47 = $47.01
Therefore, Sarah can save:
Coupon price - Total cost = $49.95 - $47.01 = $2.94
So, Sarah can save $2.94 by doing the oil change herself instead of using the coupon.
someone please help with finding the greatest common factor, my teacher didn't explain it well
The greatest common factor is 2z^2
How you find it is first you find the greatest common factor of the two numbers, which is 2 (2 is the greatest number that can be multiplied into 2 and 10; 2 times 1 = 2 and also 2 times 5 = 10)
Then you find the greatest common factor of the variables, which is z^2.
(z^2 is the largest that can go into z^3 and z^2 because z^2 times z = z^3 and z^2 = z^2)
After that, you just multiply them together to get 2z^2
Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 664
Americans and found that 69.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.
The margin of error is given by E:
A 99% confidence interval is given by:
To find the margin of error, we can use the formula: E = z√((p(1-p))/n)
How is margin of error determined?where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.
From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.
Plugging in the values, we get:
E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385
So the margin of error is 0.0385.
To find the confidence interval, we can use the formula:
p ± E
where p is the sample proportion and E is the margin of error.
Plugging in the values, we get:
0.696 ± 0.0385
So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].
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Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 15 4 31
Female 9 8 16 33
Total 21 23 20 64
If one student is chosen at random, find the probability that the student was male GIVEN they got a 'C':
Answer:
To find the probability that a randomly selected student who received a "C" was male, we need to calculate the total number of male students who received a "C" and divide it by the total number of students who received a "C".
Total number of male students who received a "C": 12
Total number of students who received a "C": 20
Probability that the student was male:
12/20 = 0.6
Therefore, the probability that a randomly selected student who received a "C" was male is 0.6, or 60%.
What is the value of x?
Answer:
12
Step-by-step explanation:
10x - 20 + 6x + 8 = 180
Supplementary angles
Answer:
x = 12
Step-by-step explanation:
The two given angles create a straight line (Definition of Straight Line). This means that:
[tex](10x - 20) + (6x + 8) = 180[/tex]
First, combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 12 to both sides of the equation:
[tex]16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192[/tex]
Next, divide 16 from both sides of the equation:
[tex]\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12[/tex]
12 is your answer.
~
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9999999999999999999999999999999999999999956596859873 -57854909049287634246299583729875472656475965593947699= ____________________________________________________________________98899876788877656687989/988998-*995895966++5966656566666666655555555555958545156548448489+4964898748/798784484878554659757564250216407694722=
Answer:
-4.7854909e+52
Step-by-step explanation:
how do i know
cuz i used a calculator
what evevn is your equation
find the values of variables then find the lengths of the sides of each quadrilateral
4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral .
What do math quadrilaterals mean?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.
There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.
2X + 2 = 4
2X = 4 -2
2X = 2
X = 1
2x + 2 = 2 * 1 + 2 = 4
4x + 3 = 4 * 1 + 3 = 7
2x = 2 * 1 = 2
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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral .
What do math quadrilaterals mean?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.
There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.
2X + 2 = 4
2X = 4 -2
2X = 2
X = 1
2x + 2 = 2 * 1 + 2 = 4
4x + 3 = 4 * 1 + 3 = 7
2x = 2 * 1 = 2
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Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour. If the total distance was 12 miles and the trip took 5 hours in all, how far did they go by boat?
The distance for boat is,
= 43.2 miles
Given that;
Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour
Now, For Walk DATA:
Rate = 2 mph ; time = x hrs.
Then, distance = 2x miles
For Boat DATA:
Rate = 10 mph ; time = 5 - x hrs
Then, distance = 10 (5 - x) miles
Hence, We can formulate;
distance + distance = 12 miles
2x + 10 (5 - x) = 20
2x + 50 - 10x = 20
30 = 8x
x = 3.6
Hence, Boat time ,
5 - x = 5 - 3.6 = 1.4 hr (boat time)
And, The value of Boat distance = 12x = 12 x 3.6 = 43.2 miles
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what is the answer to this problem
help math will give brainlist
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Find the total amount owed, to the nearest cent, for the following simple interest loans.
The total amount owed, to the nearest cent A = $ 3,283.44
What is simple interest?Simple interest is interest that is only calculated on the initial sum (the "principal") borrowed or deposited. Generally, simple interest is set as a fixed percentage for the duration of a loan. No matter how often simple interest is calculated, it only applies to this original principal amount.
A = P + I where
P (principal) = $ 2,950.00
I (interest) = $ 333.44
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
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Correct question:
Find the total amount owed, to the nearest cent, for a simple interest loan with a principal of $2950, an interest rate of 7.4% and a time period of 1.5 years. Show
Evaluate the function as indicated
[tex]g(x) = {5.9}^{x} [/tex]
(a) x = -1 G(-1) =
(b) G(-2) = x = -2
(c) x = √5 G(√5) =
what is the answer for a, b, and c?
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #1
The end behavior of f(x) is described as follows:
As x -> -∞, f(x) -> ∞.As x -> ∞, f(x) -> 0.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:
Increases to the left of the graph -> As x -> -∞, f(x) -> ∞.Approaches the horizontal asymptote y = 0 at the right of the graph -> As x -> ∞, f(x) -> 0.More can be learned about the end behavior of a function at brainly.com/question/1365136
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A soccer goal is 8 yards wide. Suppose a goalie is standing on her line in
the center of her goal as a striker from the opposing team moves the ball
towards her. The near post angle, a, is formed by rays extending from the
ball to the near post and the goalie. Similarly, the far post angle, ß, is
formed by rays extending from the ball to the far post and the goalie. See
the figure.
a) Determine the near post angle and the far post angle when the striker is
24 yards from the near post and 28 yards from the far post.
b) How far is the goalie from the ball?
c) To cover the near post, the goalie moves toward the near post in order
to make the near post angle and the far post angle equal. How far
toward her near post does the goalie need to move?
Where the following triangle problem is given, note that:
A) α [tex]\approx[/tex] 11.0
β β [tex]\approx[/tex] 9.4
B) 25.59 yrds
C) 0.38 yrds
What is the explanation for the above?A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post
1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)
Cos α = (24² + 655 - 5²)/ (2 x 24 x √655)
= 0.98171498561
α = Cos ⁻¹ 0.98171498561
α = 10.973603643623608717848651724941
α [tex]\approx[/tex] 11.0° (Cosine Law)
For 28 yards from the far post.
Cos β = (28² + 655 - 5²)/ (2 x 28 x √655)
= 0.98659913977
β = Cos ⁻¹ 0.98659913977
β = 9.3905311636838307510867912796592
β [tex]\approx[/tex] 9.4°
B) Distance between the goalie from the ball is
√655 = 25.592967784139454896443137575823
Distance [tex]\approx[/tex] 25.59 yrds
C) 5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)
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The mean weight of an adult is 70 kilograms with a standard deviation of 8 kilograms.
If 87 adults are randomly selected, what is the probability that the sample mean would be greater than 70.8 kilograms? Round your answer to four decimal places.
The probability that the sample mean would be greater than 70.8 kilograms is given as follows:
0.1762 = 17.62%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 8, n = 87, s = \frac{8}{\sqrt{87}} = 0.8577[/tex]
The probability is one subtracted by the p-value of Z when X = 70.8, hence:
Z = (70.8 - 70)/0.8577
Z = 0.93
Z = 0.93 has a p-value of 0.8238
1 - 0.8238 = 0.1762.
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Which two values are located at the same point on a number line? 4/1 and 4 , 1/3 and 3 , 8/8 and 8 , 6/2 and 4
The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.
Which answer choice represents equivalent points on the number line?It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.
On this note, such two values must be equivalent.
Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.
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The sector of a circle with a diameter of 8 feet has a central angle measure of 45°. What is the area of the sector?
A. π/2 ft²
B. π ft²
C. 2 π ft²
D. 8 π ft²
so, we know the diameter is 8, so that means its radius is half that, or 4.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2[/tex]
the Ponde family's Powerjet pumps 420 gallons of water per hour. At this rate, how many gallons of water will it pump in 45 minutes?
the number of gallons of water it can pump inn 45 minutes is
How to determine the amount of water?The given parameters that will help us to determine the quantity are
Powejet pumps 420 gallons of water per hour
how many gallons of water will it pump in 45 minutes = ?
1 hour = 60 minutes
This means = 450/60 = 7 gallons
Therefore in 45 minutes it can pump 7*45 = 315 gollons
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