The circular rug with a diameter of 8 feet covers approximately 50.27 square feet of floor space. This was calculated by finding the area of the circle using the formula πr².
Explanation:The question refers to how much floor space a circular rug with a diameter of 8 feet will cover. To solve this, you need to calculate the area of the circle. The formula for the area of a circle is πr², where r is the radius of the circle. But we were given the diameter, which is twice the radius. So the radius of the rug is 8/2 = 4 feet.
Substitute r=4 into the formula: Area = π(4²) = 16π square feet. Therefore, the circular rug covers 16π, or approximately 50.27 square feet of floor space.
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Given:In quadrilateral WXYZ , WY and XZ bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram.
Given that the diagonals WY and XZ in a quadrilateral WXYZ bisect each other, we can confidently say that quadrilateral WXYZ is a parallelogram. This is based on the property of a parallelogram which states that its diagonals bisect each other.
Explanation:To prove that a quadrilateral is a parallelogram given that the diagonals bisect each other, we'll apply the properties of a parallelogram. According to the properties of a parallelogram, the diagonals bisect each other. That is to say, if WY and XZ bisect each other at point A (i.e., WA=AY and AZ=ZX), then WXYZ is a parallelogram. This satisfies the condition for the given quadrilateral and hence WXYZ is a parallelogram.
We use this information along with the parallelogram rule and the Pythagorean theorem to prove the quadrilateral is, in fact, a parallelogram. The rule states that if a quadrilateral has diagonals that bisect each other then it is a parallelogram.
In this case, since WY and XZ bisect each other at point A, we know that the lengths WA = AY and XA = AZ. Hence, quadrilateral WXYZ is indeed a parallelogram.
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please help me with this pre-calc question?
Debbie’s pizza shack cuts a large pizza into 10 equal slices. The diameter of the pizza is 16 inches. Bob eats two slices of pizza. How much pizza does he eat ?
Debbie’s pizza shack cuts a large pizza into 10 equal slices. The diameter of the pizza is 16 inches. Bob eats two slices of pizza. How much pizza does he eat ?
Solution:
There are 10 equal slices of pizza
Out of 10 slices bob eats 2 slices.
So, out of one pizza bob eats [tex] \frac{2}{10} [/tex] or [tex] \frac{1}{5} [/tex] th of the pizza
Calculating in terms of area,
Diameter of Pizza= 16 inches
So, Radius of Pizza= [tex] \frac{Diameter}{2} [/tex]
Radius of pizza=[tex] \frac{16}{2} [/tex]=8inches
Area of complete pizza= πr²=π8²=64π=200.96inches²
Area of the part had by Bob=[tex] \frac{1}{5} [/tex]*200.96 inches²
=40.192inches²
Bob had 40.192 inches² out of 200.96 inches² pizza
A gardener measured the heights of pepper plants in his garden. The results, rounded to the nearest inch, are shown on the line plot.Based on the graph, which statement about the heights of the pepper plants is true?
More than half of the plants are taller than 6 inches.
Fewer than one-quarter of the plants are taller than 4 inches and shorter than 7 inches.
More than half of the plants are less than 6 inches tall.
Fewer than one-quarter of the plants are taller than 7 inches and shorter than 10 inches.
Answer:
D) Fewer than one-quarter of the plants are taller than 7 inches and shorter than 10 inches.
Step-by-step explanation:
There are 17 total plants, 17/4=4.25
Plants taller than 7 inches and less than 10 are 8 or 9 inches tall
There are 3, 8 inch plants
There is 1, 9 inch plant
The total plants between 7 and 10 inches is 4
Answer:
D
Step-by-step explanation:
took the test
Marcus painted 1/3 of his bedroom in 4/5 of an hour. at this rate how long will it take him to paint his entire room
Answer:
So it took him 4/5 of an hour to paint 1/3
that means there is still 2/3 to go
so that means that he will have two times that time to paint the rest of the room
4/5 = ?
1/3 2/3
using cross multiplication
(4/5)(2/3) = (1/3) (?)
8/15 = 1/3 ?
divide both sides by 1/3
so that will be 8/5
that means it will take 8/5 of an hour to complete the rest
or 12/5 total to do entire room
Hope this helps ;)
Step-by-step explanation:
Proof: all radii of a circle are congruent, so , and since and , then are right triangles by the __________ congruency theorem. the corresponding sides of the triangles, and , are congruent, so zv = yx. thus, we know that 2zv = 2yx by the multiplication property of equality. by a congruency theorem that states, "if a diameter of a circle is perpendicular to a chord, then the __________," bisects and bisects , so vu = 2zv and xw = 2yx. therefore, we can conclude that vu = xw, or .
a. hl (hypotenuse-leg) . . . diameter bisects the chord and its other chord
b. sss (side-side-side) . . . diameter bisects the arc and its measurement
c. hl (hypotenuse-leg) . . . diameter bisects the chord and its arc
d. asa (angle-side-angle) . . . chord but not the diameter
The circumference of a circle is 18.84 millimeters. what is the circle's area
Joy and Cullen put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes after a certain amount of time (x), in weeks, is shown by the equations below:
Joy: y = 30x + 20
Cullen: y = 20x + 90
After how many weeks will Joy and Cullen have the same amount of money in their money boxes, and what is that amount?
6 weeks, $150
230 weeks, $7
7 weeks, $150
7 weeks, $230
John ,Rick , and Molli are painting a room together. It takes all of them 16 hours to paint the room to perfection. It takes John 8 hours to paint the room alone , and it takes Rick 2 hours to paint the room alone. What is the hourly rate it take’s of john to paint the room alone?
John's hourly rate of painting a room alone is 1/8 of the room per hour, which is calculated from the time he takes to complete the job on his own.
The question asks for the hourly rate at which John can paint a room alone. Knowing that John takes 8 hours to paint the room by himself, we can find his hourly rate by understanding the concept of work rates in combination tasks. Since painting can be considered a task that involves continuous work, the rate at which the room gets painted relates directly to a painter’s work rate, which is the fraction of the room they can paint per hour. For John, his work rate is the reciprocal of the time he takes to paint the room alone, which in this case is 1/8 of the room per hour.
. A circular window has a diameter of 40 centimeters. What is the circumference of the window? Use 3.14 for π π 251.2 cm
What is the point-slope form of a line with slope -3 that contains the point (10, -1)?
A.y + 1 = 3(x - 10)
B.x + 1 = -3(y - 10)
C.y + 1 = -3(x - 10)
D.y + 1 = 3(x + 10)
Please help me.......
If it’s the weekend, the chances of Allison going to the store is 4/5. If its a weekday, the chances are 2/5. Given that Allison will not go to the store, what is the probability that it’s the weekend?
Use the given information to find the amount aa in the account earning compound interest after 6 years when the principal is $3500. r=2.16%r=2.16%, compounded quarterly the amount after 6 years is $ .
Answer: $3,982.92
Step-by-step explanation:
$3,982.92
Equation for compound interest:
A = P (1+r/n)^nt
P = 3500
r = .0216
n = 4
t = 6
Tell whether the study is an experimental study or an observational study.
You want to study the effects of regular exercise on a person’s heart rate. You measure the heart rate of a person at rest and again after jogging in place for 5 minutes. The control group is every other student who enters the room. The experimental group is those students who are not in the control group.
Final answer:
The study described is an experimental study. The independent variable is regular exercise and the dependent variable is the person's heart rate. The control group is the group of students who do not exercise, while the experimental group is the group of students who engage in regular exercise.
Explanation:
The study described is an experimental study.
In an experimental study, the researcher directly manipulates the independent variable to determine its effect on the dependent variable. In this case, the independent variable is regular exercise and the dependent variable is the person's heart rate.
The control group is the group of students who do not exercise, while the experimental group is the group of students who engage in regular exercise. By comparing the heart rates of the two groups before and after exercise, the researcher can determine the effects of exercise on heart rate.
Determine the magnitude and the ordered pair that represents the vector from (18,3) to (-4,16)
Answer:
The answer is B.
Step-by-step explanation:
(-22,13); magnitude=25.6
I am taking the cumulative review.
If a section of a line graph falls to the right, what does that indicate?
an increase
a decrease
no change
a mistake in the graph
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find Lateral area of the pyramid
What rate of simple interest is needed for $700 to double, in 3 years?
The rate of simple interest required for $700 to double in 3 years is found using the formula I=PRT. In this scenario, the rate comes out to be approximately 33.3%.
Explanation:The subject of this question is finding the rate required for simple interest to cause an investment of $700 to double in a duration of 3 years.
Generally, we use the formula for simple interest: I=PRT where P is the principal amount (700 in this case), I is the interest earned, R is the rate we want to find and T is the time period in years.
However, since the aim is for the $700 to double, the interest earned will be an additional $700, thereby making the total $1400. Thus, substituting these values into the formula, we get 700 = 700 * R * 3. Simplifying this, we find that R = 700/(700*3) = 1/3 or approximately 33.3%.
Hence, the rate of simple interest required for $700 to double in 3 years is approximately 33.3%.
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R = 1/3 or 33.33%. So, the simple interest rate needed for $700 to double in 3 years is approximately 33.33%.
To find out the simple interest rate that is needed for $700 to double in 3 years, we can set up the equation based on the formula for simple interest, which is I = PRT (where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period in years).
Since the student wants the money to double, the interest gained should be equal to the principal, which means I = $700. The time given is T = 3 years. Plugging these values into our formula, we get:
$700 = $700 × R × 3
By dividing both sides by $2100 ($700 ×3), the equation simplifies to:
R = $700 / $2100
Therefore, R = 1/3 or 33.33%. So, the simple interest rate needed for $700 to double in 3 years is approximately 33.33%.
Harry was given an assignment. He had 32 days to get 256 tasks done at work.Which operation would he use to figure out how many tasks he needs to complete each day?
Answer:
d
Step-by-step explanation:
Write a report to the president of the company explaining the solutions.
Answer:
The negative part of the solution set is ignored, because you cannot produce a negative number of phones.
The company has at least an 80% success rate if the next 25 or more phones that are assembled work.
Because the company has already made 10 phones and 7 are not working, if the next 25 phones work, the 35th phone puts the company at its goal of 80% or more.
Step-by-step explanation:
The spheres radius is 1/3 the radius of the hemisphere how does the volume of the hemisphere compare with the volume of the sphere
Answer:
It is greater than the volume of the sphere
Step-by-step explanation:
Which right triangular prism has the greatest volume?
Answer:
So Prism D has the greatest volume.
Step-by-step explanation:
Since volume of a triangular prism = A × h
where A = Area of base of prism
h = height
For prism (A) ⇒ Volume = ( 6 × 7 ) × 9
= 42 × 9 = 378m³
Prism (B) ⇒ Volume = ( 5 × 6 ) × 13
= 30 × 13 = 390m³
Prism (C) ⇒ Volume = ( 11 × 8 ) × 8
= 88 × 8 = 704m³
Prism (D) ⇒ Volume = ( 10 × 8 ) × 9
= 80 × 9 = 720m³
So prism D has the maximum volume.
What is the approximate volume of a cylinder with a radius of 8 cm and height of 5 cm?
A. 62.8
B. 251.2
C. 25.1
D. 502.4
E. 1004.8
A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n - 1)(8) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula? A. 5 B. 3 C. 8 D. 24
What is the slope of the line that passes through the points (-4, 6) and (2, 4)?
A. -3
B. -1/3
C. 1/3
D. 3
Solve the system of equations using any method. 6x + 4y = −8 4x − 2y = 2 A) ( 11 7 , 2 7 ) B) ( 2 7 , 11 7 ) C) (− 2 7 , 11 7 ) D) (− 2 7 , − 11 7 )
Write as a mixed fraction: 22 / 3
The fraction 22/3 can be written as the mixed fraction 7 1/3.
We have,
To write the fraction 22/3 as a mixed fraction, we need to divide the numerator (22) by the denominator (3) and express the result as a whole number plus a proper fraction.
When we divide 22 by 3, we get a quotient of 7 and a remainder of 1.
The quotient represents the whole number part, and the remainder becomes the numerator of the proper fraction.
Thus,
22/3 can be written as the mixed fraction 7 1/3.
This means that we have 7 whole units and an additional 1/3 unit.
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1. a stockholder owns 381.881 shares. by the end of the year, he had increased his number of shares by 14.814. what is the total number of shares owned by the stockholder?
2. last week a sales representative earned a salary of $412.56 and a commission of $72.48. how much did she earn in all?
3.joan deposited a check for $48.51 in her checking account. if the previous balance was $381.49, how much money does joan now have in the account?
write the equations for the basic absolute value equation y=|x-h|+k under the given transformations:
1. shift 1 unit to the right and up 2 units
2. shift 3 units to the left and 7 units down
3. vertical shrink by a factor of 1/3
4. vertical stretch by a factor of 3