Answer:
domain: -5 < x ≤ 1range: -3 ≤ y ≤ 1is a functionStep-by-step explanation:
The domain of a relation is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.
The range of a relation is the set of values the dependent variable may have. It is the vertical extent of the graph.
A relation is a function if there is only one output value for any given input value. That is, a vertical line can intersect the graph in at most one place.
__
a)domainThis graph extends from x > -5 to x = 1. The domain is ...
-5 < x ≤ 1 . . . . . . . (-5, 1] in interval notation
rangeThis graph extends from y = -3 to y = 1. The left side of the graph does not include the point (-5, 1), but the right side includes the point (1, 1). So y = 1 is one of the output values of the relation. The range is ...
-3 ≤ y ≤ 1 . . . . . . . . [-3, 1] in interval notation
__
b)No vertical line crosses the graph in more than one place, so the relation shown is a function.
_____
Additional comment
Sometimes a relation is given as a table or a list of ordered pairs. If there are no repeated x-values (inputs), the relation is a function. Repeated x-(input) values usually have different output values, so violate the requirement that a function have only one output for each input.
From a cylinder of height of 24cm and base diameter 14cm, a cone having equal radius and height is hollowed out. Find the volume of the remaining solid of the cylinder.
Answer:
2463 cm^3
Step-by-step explanation:
Given that a cylinder of height of 24cm and base diameter 14cm, a cone having equal radius and height is hollowed out. Find the volume of the remaining solid of the cylinder.
Let first calculate the volume of the cylinder
V = πr^2h
Where the radius = 7 cm
V = π × 7^2 × 24
V = 3694.5 cm^3
Let's calculate the volume of a cone
V = 1/3πr^2h
V = 1/3 × π × 7^2 × 24
V = 1/3 × 3694.5
V = 1231.5 cm^3
To Find the volume of the remaining solid of the cylinder, minus the volume of a cone from the volume of a cylinder
Remaining volume V = 3694.5 - 1231.5
V = 2462.99 cm^3
V = 2463 cm^3 approximately
Find the surface area of the prism. Round to the nearest tenth if necessary.
Regular pentagon base
B≈61.94 cm2
Base length=6cm
Lateral edge=5cm
A regular pentagonal prism is shown. The length of the side of the pentagon is six centimeters. The height of the prism is five centimeters.
The surface area of the prism is 248.88 cm²
What is surface area of prism?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a prism is expressed as;
SA = 2B + ph
where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.
Base area = 61.94 cm²
height = 5cm
perimeter = 5 × 5 = 25cm
SA = 2 × 61.94 + 25 × 5
SA = 123.88+ 125
SA = 248.88 cm²
Therefore the surface area of the prism is 258.88 cm²
learn more about surface area of prism from
https://brainly.com/question/1297098
#SPJ1
Brainliest if correct
Answer:
y = 3
Step-by-step explanation:
Since x = 4
4 + y = 7
Subtract 4 from both sides of the equation
y + 4-4 = 7 -4
Simplify
y =3
[RevyBreeze]
help me fast rapidly is of khan academy:
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTthe area of a square is seasonal 25 cm Square calculate the length of a diagonal to one decimal place .
Answer:
The answer is 7.1cm to 1d.p
Step-by-step explanation:
Area of square =L²
25=L²
√L²=√25
L=5cm
hyp²=opp²+adj²
x²=5²+5²
x²=25+25
x²=50
√x²=√50
x=7.1cm to 1d.p
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
You ride your bike north for 100 m at a constant speed of 5 m/Your acceleration is ?
100 m at a constant speed of 5.
to find:the acceleration.
solution:\(a = \frac{v - u}{t} \)
\(a = \frac{100 - 100}{5} \)
\(a = 0.00m | {s}^{2} \)
Use the Standard Normal Table or technology to find the Z-score that corresponds to the following cumulative area.0.952
The cumulative area corresponds to the z-score is 1.67
What is the cumulative area?
The likelihood that a real-valued random variable, X, will assume a value less than or equal to x is represented by the cumulative distribution function of X, or simply by the distribution function of X, assessed at x.
Here, we have
Given: the following cumulative area is 0.952.
We have to find the Z-score that corresponds to the following cumulative area.
p(z<z)=0.952
p(z<1.67)=0.952
z=1.67 (from the standard normal table)
Hence, The cumulative area corresponds to the z-score is 1.67
To learn more about the cumulative area from the given link
https://brainly.com/question/28328377
#SPJ1
An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work.
The area of the circle created by the paint is given by the expression 4πt².
The area of the circle is 100π, which is approximately 314.16 in².
The circle will be at least 300 in² in 5 minutes. Yes.
To find the area of the canvas, we multiply the lengths of its sides:
Area = (3x + 5) × (2x + 1)
Expanding the expression:
Area = 6x² + 3x + 10x + 5
Combining like terms:
Area = 6x² + 13x + 5
The area of the canvas is given by the expression 6x² + 13x + 5.
Now, let's find the area of the circle created by the paint.
The area of a circle is given by the formula A = πr², where r represents the radius.
The radius is given by the spreading of paint, which is r(t) = 2t.
Substituting the value of r(t) into the formula, we have:
A[r(t)] = π(2t)²
Simplifying:
A[r(t)] = π(4t²)
A[r(t)] = 4πt²
Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.
Substitute t = 5 into the area formula:
A[r(5)] = 4π(5)²
A[r(5)] = 4π(25)
A[r(5)] = 100π
Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.
For similar questions on area of the circle
https://brainly.com/question/12269818
#SPJ8
7. A floor is covered by 800 tiles measuring 10 squared cm. How many square tiles of side 8 cm would be needed to cover the same floor?
Answer:
1000 tiles
Step-by-step explanation:
Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.
This one twelve less one fourth of a number
Answer:
True
Step-by-step explanation:
1/4 is greater than 1/12
Hope this helps
In January, a store sold a pack of collectible cards for $1.75. In February, they sold the same pack of collectible cards for $1.89. What is the percent of the increase?
Answer:
8%
Step-by-step explanation:
Step 1: Find the difference (increase) between the two costs
\(\$1.89 - \$1.75\\\\= 1.89 - 1.75\\\\= 0.14\)
Step 2: Divide the increase by the original cost
\(0.14 \div 1.75\\\\\frac{0.14}{1.75} \\\\= 0.08\)
Step 3: Convert the answer to percent
\(\frac{0.08}{1} \times \frac{x}{100}\)
Cross multiply
\(0.08 \times 100\\\\= 8 \\\\= 8\%\)
Therefore, 8% is the percent increase.
Which set of ordered pairs does NOT represent a function?
{(8,9), (-2,9), (7,5), (-4, – 7)}
{(-5, -7),(-5,4), (-2,-8),(3,5)}
{(8,0),(-4, -2), (7,1),(0,0)}
{(-8,3), (-5, – 7),(-4,5), (9,3)}
Answer:
{(-5, -7),(-5,4), (-2,-8),(3,5)}
Step-by-step explanation:
Functions can't use the same x-coordinate twice
15) You have an allowance of $15 per week. You are in a bowling league that costs $6.50 each week,
and you save at least $5.00 each week. How much will you have left to spend each week?
Answer:
3.50
Step-by-step explanation:
15-5-6.50 equals 3.50
— 7x — бу = — 15 Determine the intercepts of the line.
Answer:
see below
Step-by-step explanation:
— 7x — бу = — 15
To find the x intercept set y = 0 and solve for x
-7x - 0 = -15
-7x= -15
Divide by -7
-7x/-7 = -15/-7
x = 15/7
The x intercept is (15/7,0)
To find the y intercept set x = 0 and solve for y
o— бу = — 15
— бу= -15
Divide by -6
— бу/-6= -15/-6
у= 5/2
The y intercept is (0,5/2)
Suppose that X-N (2,6) is a normal distribution with mean 2 and standard deviation 6. What value of x has a z-score of three?
The value of x has a z-score of three is 20
How to determine the value of x?The given parameters are:
Mean = 2
Standard deviation = 6
z = 3
The z-score is calculated as:
\(z = \frac{x - \mu}{\sigma}\)
So, we have:
\(3 = \frac{x -2}{6}\)
Multiply through by 6
18 = x - 2
Add 2 to both sides
x = 20
Hence, the value of x has a z-score of three is 20
Read more about z-score at:
https://brainly.com/question/15016913
#SPJ1
You are given the great circle of a sphere is a length of 25 miles. What is the volume of the sphere
The volume of the sphere is approximately 3431.82 cubic miles.
To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.
C = 2πr
60 = 2πr
Divide both sides of the equation by 2π:
r = 60 / (2π)
r = 30 / π
Now that we have the radius, we can use the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(30/π)³
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)(27000/π²)
V = (4/3)(27000/9.87) (approximating π to 3.14)
V ≈ 3431.82 cubic miles
Therefore, the volume of the sphere is approximately 3431.82 cubic miles.
for such more question on volume
https://brainly.com/question/6204273
#SPJ8
Question
You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?
Sofia is investing $8,000 in an account paying 5.5% interest compounded quarterly.
What will Sofia's account balance be in 7 years?
The balance after 7 years is $11726.12
How to determine the balance in 7 years?The given parameters are:
Principal, P = 8000Interest rate, r = 5.5%Number of times compounded, n = 4Time, t = 7The amount is calculated as:
\(A = P(1 + \frac rn)^{nt}\)
So, we have
\(A = 8000 * (1 + \frac {5.5\%}4)^{4 * 7}\)
Evaluate the expression
A = 11726.12
Hence, the balance after 7 years is $11726.12
Read more about compound interest at:
https://brainly.com/question/24924853
#SPJ1
Complete the square to find
the vertex of this parabola.
x2 - 8x - y - 4 = 0
([?], [ ]
Answer:
-20
Step-by-step explanation:
Complete the square to find the vertex of this parablola x^2-8x-y-4=0 {the second one of -20; so 4,-20}
Step-by-step explanation:
The answer would be (4,-20)
Fill in 4 and -20
Ann had 48 fliers to post around town. Last week, she posted 1/3 of them. This week, she posted 1/4 of the remaining fliers. How many fliers has she still not posted?
Step-by-step explanation:
Ann posted 1/3 of the fliers last week, which means she posted:
1/3 x 48 = 16 fliers
This means that she has 48 - 16 = 32 fliers left to post.
This week, Ann posted 1/4 of the remaining fliers, which means she posted:
1/4 x 32 = 8 fliers
So she has 32 - 8 = 24 fliers still to post. Therefore, Ann has still not posted 24 fliers.
find by a digit to make the number divisible by 3 1234?
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
For more such questions on divisible
https://brainly.com/question/29373718
#SPJ8
Meena bought headphones online for $33. She used a coupon code to get a 20% discount. The website also applied a 5% processing fee to the price after the discount. How much was the processing fee? Round to the nearest cent.
discount = 20/100 * 33 =6.6
price after discount = 33 - 6.6 = 26.4
the possessing fee = 5/100 * 26.4 = 1.32 $
Which of the following is the graph of f(x) = 5 cos (2x)? Select one: a. graph with points 0, 5 and pi over 4, 0 and pi over 2, negative 5 and 3 pi over 4, 0 and pi, 5 b. graph with points at 0, 0 and pi over 4, negative 3 and pi over 2, 0 and 3 pi over 4, 3 and pi, 0 c. graph with points 0, negative 5 and pi over 4, 0 and pi over 2, 5 and 3 pi over 4, 0 and pi, negative 5 d. graph with points at 0, 5 and pi over 4, 2 and pi over 2, negative 1 and 3 pi over 4, 2 and pi, 5
The required graph has been attached below that represents the function f(x) = 5 cos (2x).
The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.
Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.
The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).
Thus, the graph has been attached below that represents the given function.
Learn more about Trigonometric functions here:
brainly.com/question/6904750
#SPJ1
On a boat tour there are half as many children as there are adults. There are 30 people on the tour. How many children are there?
Answer:
10 children
Step-by-step explanation:
Which property justifies the statement below? X(y+5)=xy+5x
160 O SHO) A person bought 6,852 Japanese you from Nepal Rastra Bank for Rs 6,320. find exchange rote between japanese yen and Nepali rupess.
The exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.
The exchange rate between Japanese Yen and Nepali Rupees is
1 JPY = 0.7184 NPR
Therefore, the exchange rate is 6,852 JPY = 6,320 NPR
Therefore, the exchange rate between Japanese Yen and Nepali Rupees is 0.7184 NPR per 1 JPY.
The exchange rate between Japanese Yen and Nepali Rupees is given by the following formula:
Exchange Rate = (Total Amount in Nepali Rupees/Total Number of Japanese Yen)
Exchange Rate = (Rs 6320/6852 Yens) = Rs 0.92 per Yen.
Therefore, the exchange rate between Japanese Yen and Nepali Rupees in this case is given by Rs 0.92 per Yen.
Learn more about money here:
https://brainly.com/question/22984856.
#SPJ1
A paralegal bills a law firm for 19.5 hours of work at a rate of £240 per hour. How much money has the paralegal earned from this job? Include units in your answer.
The money that the paralegal has earned for this work = £4680
What is the unitary approach for problem solving?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. This technique essentially involves determining the value of a unit from the value of a multiple.
Given, cost of work per hour = £ 240
Duration of work of a law firm = 19.5 hours
Money earned by paralegal for the work = (240*19.5) = £ 4680
Thus, the money that the paralegal has earned for this work = £4680
To learn more about this, tap on the link below:
https://brainly.com/question/28486225
#SPJ9
If using the method of completing the square to solve the quadratic equation x^2-19x+9=0x
2
−19x+9=0, which number would have to be added to "complete the square"?
The graph of y < 2 - 3is shown.
Which set contains only points that satisfy the inequality?
A (412) (1,5), (4), (5. 6))
B. 11. 10). (5.7) (4-13) (32)
OC (57).(3.10) (57) (1.4)
OD. 133 (4-1), (2, 3). (5.0))
Answer:Its letter b i think
Step-by-step explanation:
Ringo deposited some money into a savings account. He earned 4% interest. After 6 months he earned $21 in interest. How much money did he start with?
I NEED HELP PLEASE!!
Answer:
$1050
Step-by-step explanation:
I = PRT / 100
I = 21
P = ?
R = 4%
T = 6 months = 0.5 yr
P = 100I / RT
P = (100 * 21) / (4 * 0.5)
P = $1050