Answer:
22 dimes
10 quarters
Step-by-step explanation:
$4.70 = 0.25(q + 9) + 0.1d
4.7 = 0.25q + 0.25(9) + 0.1d
4.7 = 0.25q + 2.25 + 0.1d
2.45 = 0.25q + 0.1d
24.5 = 2.5 + d
22 = d = 22 dimes
$4.70 = 0.25(q + 9) + 0.1(22)
4.70 = 0.25q + 0.25(9) + 2.2
4.70 = 0.25q + 2.25 + 2.2
4.70 = 0.25q + 2.25 + 2.2
4.70 = 0.25q + 4.45
0.25 = 0.25q
1 = q
1 q + 9 q = 10 quarters
Check:
$4.70 = 0.25(q + 9) + 0.1(d)
$4.70 = 0.25(1 + 9) + 0.1(22)
$4.70 = 0.25(10) + 0.1(22)
$4.70 = 2.5 + 2.2
$4.70 = 4.7
Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
How many ounces are in 4 gallons?
Answer:
512
Step-by-step explanation
128 ounces in a gallon times that by 4. ====== ....... 512.
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You are a school photographer taking individual and class pictures for 2 classes of 21 students each. On average, each individual picture takes 3 minutes and a class picture takes 10 minutes.About how long should it take you to get all of the pictures
Answer:
2h and 26 minutes
Step-by-step explanation:
21x2=42
42x3=126
2x10=20
126+20=146
146m=2h 26m
If you multiply a matrix and its inverse together, you will always get the identity
matrix.
True
False
Answer:
True
Step-by-step explanation:
If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I. And the point of the identity matrix is that IX = X for any matrix X (meaning "any matrix of the correct size", of course).
Answer:
Yes
Step-by-step explanation: And 1 is the identity, so called because 1x = x for any number x. It works the same way for matrices. If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I.
For a statistics project a community college student at Diablo Valley College decides to investigate cheating in two popular majors at DVC: business and nursing. She selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. The question about cheating is one of many other questions about college life.
When the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. Can the student proceed with the calculation of the confidence interval for the difference in population proportions?
Answer:
The student can proceed with the calculation of the confidence interval for the difference in population proportions. This is because, from the data she has, 3/4 of the Business students admitted to cheating while 1/2 of the Nursing students admitted to cheating also.
This is above the average number of students in her given sample size which is valid for extrapolation to the College Majors being investigated.
Step-by-step explanation:
To make the expression 4x−2+□(2x+4) equivalent to 2(6x+7), what must be the value in the box? PLSSSSS HELLPPP
Answer:
4 goes in the box
Step-by-step explanation:
The solution of the equation 4x − 2 + y(2x + 4) = 2(6x + 7) will be 4.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let the value inside the box be 'y'. Then the equation is given as,
4x − 2 + y(2x + 4) = 2(6x + 7)
Simplify the equation, then we have
4x − 2 + y(2x + 4) = 2(6x + 7)
4x − 2 + y(2x + 4) = 12x + 14
y(2x + 4) = 8x + 16
y = 4(2x + 4) / (2x + 4)
y = 4
The solution of the equation 4x − 2 + y(2x + 4) = 2(6x + 7) will be 4.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Can someone please help?
10times larger than 40
Answer:400
Step-by-step explanation:10×40=400
Answer:400
Step-by-step explanation:
Match the number with its opposite.
Match Term Definition
9.2 A) 2.9
−2.9 B) −9.2
−1.4 C) −4.1
4.1 D) 1.4
Answer:
9.2 - B
-2.9 - A
-1.4 - D
4.1 - C
Step-by-step explanation:hope this helps
Find the solution to the equation.
4(x + 7) = 38 i need it ASAP plzzz
Answer:
x = 2.5
or
x = 1/4
Step-by-step explanation:
watch the following steps:
4x + 28 = 38
4x = 38 - 28
4x = 10
x = 2.5
or
x = 1/4
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
2.5, maybe
Step-by-step explanation:
distribute 4 into x and 7
subtract 28 from both sides (28-28, 38-28)
divide 4 and 10
2.5
it seems odd...
Find the surface area of a triangular prism that has a height of 11 meters and the following triangular base. All
dimensions are in meters.
13.5
4
surface area =
m?
Answer:
3 is your answer took the test
Step-by-step explanation:
Answer:
S A = 146 m^2
Step-by-step explanation:
Use the multiplier method to increase £72 by 12%
You must show your working.
Answer:
£80.62
Step-by-step explanation:
100+12%=112%
112/100= 1.12
1.12*£72 =£80.62
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 36 x2 x dx
We need to find the integration of (36x²)x.dx .
We know,
[tex]\int x^n.dx = \dfrac{x^{n+1}}{n+1} +c[/tex]
Now,
[tex]I=\int {36x^2x} \, dx \\\\I=36\int x^3.dx\\ \\I=36\times \dfrac{x^4}{4}+c\\\\I=9x^4+c[/tex]
Therefore, the integration of (36x²)x.dx is [tex]9x^4+c[/tex] .
Hence, this is the required solution.
Name an equivalent ratio for One-half with a denominator of 8.
a. 4 Over 8
c. 5 Over 8
b. 1 Over 8
d. 3 Over 8
Answer:
it is A
Step-by-step explanation:
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
Answer:
it needs 234 grass seeds for the acre
q(x) = –2x+1
r.(x)=x²+2
Find the value of q (r (3)).
3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this
Answer:
93
Step-by-step explanation:
match the simplified expressions to an equivalent expression
Lex be a random variable that represents the pH of arterial plasma (le, acidity of the blood). For healthy adults, the mean of the distribution is - 7.4.1 A new drug for arthritis has
been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with
sample standard deviations - 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
USE SALT
(a) what is the level of significance?
what is the value of the sample test sisse? (Round your answer to three decimal places)
Answer:
2.304
Step-by-step explanation:
2.
Fifty people who watch television were recently
polled as to which type of program they preferred.
The results are shown in the table.
Television Survey
Type of Show Number
who watch
comedy
16
documentary 9
drama
12
musical
8
news
5
What percent of those surveyed preferred to watch
comedy shows?
Answer:
39.02%
or
39%
Step-by-step explanation:
Taylor is driving on the freeway at 55 miles per hour. What question finds her distance
Answer:
distance(miles) = number of hours driven * 55
Step-by-step explanation:
A, B, C, or D???? Please help! Thank you!
Answer:
Step-by-step explanation:
either the c or d
A can of fruit contains 411 grams. One gram is approximately 0.035 ounces. About how many ounces does the can contain?
Answer:
14.385 ounces
Step-by-step explanation:
Converting grams to ounces:
1g ----- 0.035 ounces
411g ----- ?
Since we multiply 411 to the left hand side, multiply the left hand side by 411 too.
411g
= 0.035(411) ounces
= 14.385 ounces
Thus, the can contains 14.385 ounces of fruit.
FIRST RIGHT GETS BRAINLIEST
Answer:
-1 + 7 =-8
Step-by-step explanation:
Answer:
-6, -7
Step-by-step explanation:
-1 + -6 = -7
W/4 -4=3
Solve the eqution pls!
Answer:
W=28
Step-by-step explanation:
(W/4)-4=3
(W/4)=7
W=28
A food truck sells tacos $1.25 a piece. The truck operator earned $360.00 last night.
How many tacos did the food truck sell last night?
28.8 tacos
288 tacos
300 tacos
2.88 tacos
Answer:
288
Step-by-step explanation:
Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.
Step 1
1.25 x = 360
x =is the amount of tacos sold.
Step 2
1.25 x = 360
/1.25 /1.25
to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.
Step 3
x = 288
we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer the amount of tacos sold=288
i hope this helps ;)
I need help ASAP please
A circle is 360 degrees so 360 = b + 96 + 209
360 = b + 305
b = 55 degrees.
priya changed the rate at which flowed through the faucet. write an equation that represents the relationship w of t and when it takes 3 minutes to fill the cooler with 1 gallon of water. Which of the following equations represent the relationship between w and t? select all that apply.
Answer:
i love you sm
Step-by-step explanation:
PLEASE HELP
Logan bought a baseball bat on a trip. The baseball bat is 29 inches long.
Logan thinks he can bring the baseball bat home in his suitcase. Is he correct? Use your understanding of the Pythagorean Theorem to explain your answer.
Answer:
Use a^2 + b^2 = c^2 and substitute
18^2 + 24^2 = c^2
Solve what we know
324 + 576 = c^2
324 + 576 = 900
Square root 900 to get C
sqrt of 900 equals 30
So, yes he can fit the baseball bat in his suitcase
Evaluate 2x+6y when x= -4/5 and y= 1/3 Write your answer as a fraction or mixed number in simplest form.
2/5 is a answer
in this we can se the answer is 2/5