Eliminate the parameter.
x = one divided by two t, y = 3t^3 - 1
Answer choices:
y = three divided by eight t^3 - 1
y = 24x^3 - 1
y = 6x^3 - 1
y = 24x - 1
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Solve the triangle: α = 58°, a = 9, b = 15.
solve for y. triangle PQR is congruent to triangle DEF, PQ= 15, QR= 10, RP=8, and EF = 6y +4
someone help me, please :)
How much money must be deposited today to become $1300 in 20 years at 7.5% compounded continuously?
What are the zeros of f(x) = x2 + 3x – 10?
A. x = –5 and x = 2
B. x = 5 and x = 2
C. x = –5 and x = –2
D. x = 5 and x = –2
Find the equation of the line whose x-intercept is 8 and y-intercept is -2. write the equation in slope-intercept form.
The equation of the straight line whose x - intercept = 8 and
y - intercept = - 2 is y = x/4 - 2.
What is the slope intercept form of a straight line?
The slope - intercept form of a straight line is -
y = mx + c
Given is the equation of the line whose x-intercept is 8 and y-intercept is -2.
The given intercepts are -
x - intercept = 8
y - intercept = - 2
Then, the coordinates of the points through which the line passes are -
(0, -2) and (8, 0)
The slope of this line will be -
m = 0 - (- 2)/8 - 0
m = 2/8
m = 1/4
So the equation of the straight line will be -
y = x/4 - 2
Therefore, the equation of the straight line whose x - intercept = 8 and
y - intercept = - 2 is y = x/4 - 2.
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Subtract 8 + 7i from 4 − 16i. -4 − 23i 4 − 23i 4 + 9i 4 − 11i
Answer:
-4-23i
Step-by-step explanation:
Above answer didn't quite understand what the question was asking. It's asking to SUBTRACT 8+7i from 4-16i. So it would be written like this:
(4-16i) - (8+7i).
Simplify it from there and you'd get -4-23i
To subtract 8 + 7i from 4 - 16i, subtract the real parts and the imaginary parts separately, resulting in -4 - 23i.
Explanation:To subtract 8 + 7i from 4 − 16i, you treat the real and imaginary parts separately.
Subtract the real parts: 4 − 8 = −4.
Subtract the imaginary parts: (−16i) − (7i) = −16i − 7i = −23i.
Combine the results to get the final answer: −4 − 23i.
Therefore, subtracting 8 + 7i from 4 − 16i gives −4 − 23i.
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The mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.5%. assume that a sample size of 40 people was surveyed from the population an infinite number of times. 95% of the sample mean occurs between % and %. nextreset
If I’m 17 1/2 do I still have to wait a year to get my provisional license after I get my permit in Florida
Elizabeth brought a box of donuts to share. there are two-dozen (24) donuts in the box, all identical in size, shape, and color. six are jelly-filled, 6 are lemon-filled, and 12 are custard-filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two custard-filled donuts in a row.
In an origami class, the instructor tells the students to cut a square that has an area of 24 square inches. Kevin cuts a square with a side length of 4.80 inches. Which statement is true?
Answer:
The side length of the square Kevin cuts is slightly less than the length the instructor required
Can I get brainliest?
PLEASE HELP ME!!!! Thank you
I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how much of each type of milk should i use ?
The double lathe milk with 2 percent fat concentration, is made by
considering the concentration and amount of each constituent.
The amount of each type of milk to be used in the [tex]\dfrac{1}{3}[/tex] pint of double lathe
are;
[tex]\dfrac{2}{9}[/tex] pint of the 1 percent fat milk and [tex]\dfrac{1}{9}[/tex] pint of the 4 percent fat milk.Reasons:
Let x represent the amount of the milk that contains 1 percent fat in the
volume of the 2 percent fat milk.
Therefore, we have;
The amount of the 4 percent fat milk to be used = [tex]\dfrac{1}{3} - x[/tex]
[tex]Amount \ of \ fat = \dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{2}{100} \times \dfrac{1}{3} = \dfrac{2}{300}[/tex]
[tex]\dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{4 - 9 \cdot x}{300} = \dfrac{2}{300}[/tex]
Therefore;
4 - 9·x = 2
4 - 2 = 9·x
[tex]x = \dfrac{2}{9}[/tex]
The amount of the 1 percent fat milk to be used for the double lathe, x = [tex]\dfrac{2}{9}[/tex]
of a pint.
The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{3} - x[/tex]
Therefore;
The mount of the 4 percent fat milk = [tex]\dfrac{1}{3} - \dfrac{2}{9} =\dfrac{1}{9}[/tex]
The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{9}[/tex]
pint.
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I WILL MARK BRAINIEST 25 POINTS Find the area of trapezoid BCDE.
A) 12 5/8 in2
B) 13 7/8 in2
C) 16 1/8 in2
D) 18 5/6 in2
16. Supposes that y varies inversely with x and that y-10 whenx-7. Which of the following equations models this relationship?
A. Y=70x
B. Y=-10x
C. Y=x/70
D. Y=70/x
The equation that models this relation is y = 70/x. So, option (D) is the correct answer.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
For the given situation,
The values are y = 10 and x = 7
y varies inversely with x.
⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]
To remove proportionality we introduce a constant 'k'.
⇒ [tex]y=\frac{k}{x}[/tex]
Substitute the values of x and y,
⇒ [tex]10=\frac{k}{7}[/tex]
⇒ [tex]k=70[/tex]
Now substitute the value of k = 70 in y,
⇒ [tex]y = \frac{70}{x}[/tex]
Hence we can conclude that the equation that models this relation is y = 70/x. So, option (D) is the correct answer.
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The larger square has area of 400 square inches. the areas of the two squares have a ratio of 1:4. what is the side lengh of the smaller square?
Final answer:
To find the side length of the smaller square, we take the square root of the larger square's area (400 sq inches) to get 20 inches, then halve it to align with the 1:2 scale factor of the sides for a correct length of 10 inches.
Explanation:
To solve this problem, we first acknowledge that the ratio of the areas of the two squares is 1:4. Since area is a function of the side length squared, we look for a scale factor of the side length that when squared will give us this ratio. In this case, the scale factor is 1:2, meaning the side length of the smaller square is half that of the larger square.
The area of the larger square is given as 400 square inches. To find the side length, we take the square root of the area, which is 20 inches. Therefore, the side length of the smaller square is half of this, which is 10 inches. However, given that the statement seems to expect an 8-inch side for the larger square, there might be a misunderstanding in the problem, assuming that area scales directly with side length rather than its square. Nonetheless, based on area and scale factor, the correct side length is 10 inches.
A museum opened at 8:00am.In the first hour 350 people purchased admission tickets.In the second hour 20% more people purchased admission tickets than in the first hour.Each admission ticket cost 17.50. What was the total amount of money paid for all the tickets purchased in the first two hours?
8 MIN LEFT anyone know this?
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8
hours in the afternoon, how many hours does she work in the evening?
Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.
Given that:
[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]
We can convert the mixed number to an improper fraction:
[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]
So, [tex]\( A = \frac{41}{8} \)[/tex] hours.
The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:
[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]
Converting 1.75 to a fraction:
[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]
Now, the equation becomes:
[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]
Convert the improper fraction back to a mixed number:
[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]
Therefore, the waitress works:
[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
A cone and a cylinder have the same base and height, as shown below.
(please see attached picture)
The volume of the cylinder is 84(3.14) in^2 What can be concluded about the volume of the cone? Check all that apply.
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
The expression 84 (3.14)/2 finds the volume of the cone.
Answer with Step-by-step explanation:
We know that volume of a cylinder with radius r and height h is:
πr²h
and volume of cone with radius r and height h is:
πr²h/3
Volume of cone=Volume of cylinder/3 < Volume of cylinder
Volume of cylinder=84π in² where π=3.14
Volume of cone=84π/3 in²
= 84(3.14)/3 in²
Hence, correct options are:
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
the answer is: A, C, and D
An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond to the nearest tenth.
The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
What is the rectangular prism?In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.
Let,a be the length of the pond and b be the width of the pond.
The volume of the pond is;
[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]
The length of the pond is two times its width.
a = 2b
The area of the base = a × b
3000 = ab
ab = 3000
Substitute the value of a in equation 2
[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]
Substitute the value of b in equation 1
[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]
Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
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The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.
Explanation:To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.
Let's denote the width as w.
Since the length is two times the width, we can express the width as w and the length as 2w.
Therefore, the equation for the volume becomes:
2w × w × 24 = 72,000
48w^2 = 72,000
w^2 = 1,500
w ≈ 38.7
Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.
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Damien bowled 5 games, His scores were:
82, 83, 65, 84, 76.
What is Damien's mean bowling score?
Please hurry! On a time limit!
To find Damien's mean bowling score, we add up his scores and divide by the number of games played. The mean bowling score is 78.
Explanation:To calculate Damien's mean bowling score, we need to find the sum of all his scores and divide it by the total number of games played. Damien's scores are 82, 83, 65, 84, and 76.
Adding these scores together we get: 82 + 83 + 65 + 84 + 76 = 390.
Then, divide the sum by the total number of games played: 390 ÷ 5 = 78.
Therefore, Damien's mean bowling score is 78.
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How do you simplify x^2+y^2?
if you enjoy math and science, the career cluster that might be best for you is
Information Technology and Engineering
Step-by-step explanation:Mathematics is also a branch of Science. A person who is good in mathematics can take the analytical view of anything and convert ideas into practical form by using mathematical models. There are a lot of applications that can be used for converting analog models into digital models by using mathematics. So all of these models require mathematical backgrounds and engineers are the people who bring ideas to reality. The same is applied on IT field too.
In which situation would a savings account be the best investment to earn interest?
saving for retirement in 20 years
saving to buy a new car in three years
saving to buy a new house in seven years
saving to easily access the money when needed
Saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest
What is Investment?Investment is traditionally defined as the commitment of resources to achieve later benefits
An investment can be regarded as asset or item that is been gotten so as to generate income or appreciation.
It should be noted that appreciation serves as increase in the value of an asset over time.
To earn interest, it will be best to use savings account so that there could be easy access to the money when needed.
Hence, saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest
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The volume of a cone is 88π cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown below.
Step 1: 88π = 1/3 πr² (8)
Step 2: 88π = 8/3 πr²
Step 3: 8/3 (88) = r²
Step 4: 234.7 = r²
Step 5: 15.3 =r
What is Fatima's error?
- In step 4, Fatima did not find the correct value of 8/3 (88).
- In step 2, Fatima should not have multiplied 1/3 and 8.
- In step 3, Fatima did not multiply 88 by the reciprocal of 8/3
- In step 1, Fatima did not substitute the correct value for the height in the formula.
Answer:
step 3
Step-by-step explanation:
took test
a store is selling uniform shirts for 18.95 each. if samuel has a coupon for 1/4 off the price, how much would he pay for the shirt, excluding tax??
A jar contains nickels and pennies there are 56 coins in the jar in all the total value of he coins is $1.52 how many pennies are in the jar
One maid can clean the house in 3 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together?
The number of hours if they worked the job together will be 2 hours.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
One maid can clean the house in 3 hours. Another maid can do the job in 6 hours.
We know that work and time are inversely proportional to each other.
Let T be the total time taken. Then the equation will be
1/T = 1/3 + 1/6
1/T = (2 + 1) / 6
1/T = 3 / 6
T = 6 / 3
T = 2
The number of hours if they worked the job together will be 2 hours.
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