Solution:
The volume of a container varies jointly with the square of its radius, r, and its height, h
Therefore,
[tex]v \propto r^2 h\\\\v = k \times r^2h -------- eqn\ 1[/tex]
The container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic centimeters
Substitute v = 377 and h = 10 and r = 6 in eqn 1
[tex]377 = k \times 6^2 \times 10\\\\377 = k \times 360\\\\k = 1.047 \approx 1.05[/tex]
What is the volume of a container with a radius of 4 centimeters and a height of 4 centimeters?
Substitute k = 1.05 and r = 4 and h = 4 in eqn 1
[tex]v = 1.05 \times 4^2 \times 4\\\\v = 1.05 \times 16 \times 4\\\\v = 67.2[/tex]
Thus volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter
trey has a peanut allergy, so he eats granola bars that are nut-free. a box of nut-free granola bars cost $4.50 after a 10% discount. what is the original price of the box of granola bars
The original price of the granola bars before the 10% discount was $5.00. To determine this, the given discounted price was divided by 0.90, which represents the price after a 10% reduction.
The original price of a box of nut-free granola bars before the discount can be calculated by reversing the 10% discount process. Since Trey paid $4.50 after the discount, we can represent the original price as x. The discount applied to x would be 0.10 times x (which is how a 10% discount is calculated), and the price after the discount is x minus the discount. So the equation to solve is x - 0.10x = $4.50.
Simplify this equation to find x:
0.90x = $4.50.
Now, divide both sides of the equation by 0.90 to find x:
x = $4.50 / 0.90.
x = $5.00.
Therefore, the original price of the box of granola bars before the 10% discount was $5.00.
168 is 70 percent of what number ?
Answer:
240
Step-by-step explanation:
Multiply 168 by 100 then divide by 70
(I NEED THIS ANSWERED QUICKLY! I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER!)
Reflect triangle LMN about the x-axis. Then translate the resulting triangle 2 units up.
What are the coordinates of the vertices of the final image?
A. L’(4, 2), M’(7, 9), and N’(1, 9)
B. L’(4, 4), M’(7, -11), and N’(1, -11)
C. L’(4, 4), M’(7, 11), and N’(1, 11)
D. L’(-4, 4), M’(7, -9), and N’(1, -9)
Answer:
The answer is C
B is reflection over the y-axis
Step-by-step explanation:
C. L’(4, 4), M’(7, 11), and N’(1, 11) are the coordinates of the vertices of the final image.
B is a reflection over the y-axis
What are the coordinates of the vertices of a cube?Any point (x, y, z) can consequently be written as a sum of factors at the parallelepiped with one vertex on the origin. on this coordinate gadget, we are able to outline the unit cube with the 8 corner points classified (zero, zero, zero), (1, zero, zero), (1, 1, 0), (0, 1, 0), (zero, zero, 1), (1, 0, 1), (1, 1, 1), and (0, 1, 1).
The coordinates of the vertices of a triangle are (x2,y2) and (x3,y3). the line becoming a member of the primary is divided in the ratio l: okay and the road becoming a member of this point of the department to the opposite angular point is then divided by the ratio m:k + l.
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You and a friend race each other. You give your friend a 50-foot head start. The distance y (in feet) your friend runs after x seconds is represented by the linear function y=14x+50. The table shows the distances you run.
a. Who runs at a faster rate? What is that rate?
response - correct
You run faster.
Question 2
The rate is
feet per second.
b. Write a linear function that relates your distance to the number of seconds. In the same coordinate plane, graph the linear functions that represent the distances of you and your friend.
y=
Question 3
Time (seconds)Distance (feet)
Question 4
c. For what distances will you win the race? Explain.
response - correct
You catch up to your friend after you run 190 feet, so you will be ahead of him for any distance greater than 190 feet. I just need the answer for question 4 plz.
Answer:
You catch up to your friend after you run 190 feet, so you will be ahead of him for any distance greater than 190 feet.
Step-by-step explanation:
Prove the divisibility of 16^5+2^15 by 33
Answer:
Both terms have a common factor of 2^15
Step-by-step explanation:
Make use of prime factorizations:
16^5+2^15=(2^4)^5+2^15=2^20+2^15
Both terms have a common factor of 2^15.
16^5+2^15=2^15(2^5+1)=2^15 x 33
The term [tex]16^5+2^{15}[/tex] is divisible by 33
We have to given [tex]16^5+2^{15}[/tex] is divisible by 33.
What is the meaning of prime factorization?Prime factorization is a way of expressing a number as a product of its prime factors
Make use of prime factorization
[tex]16^5+2^{15}=(2^4)^5+2^{15}[/tex]
[tex]=2^{20}+2^{15}[/tex]
factor out the term [tex]2^{15}[/tex] we get,
[tex]16^5+2^{15}=2^{15}(2^5+1)=2^{15} * 33[/tex]
Therefore the term [tex]16^5+2^{15}[/tex] is divisible by 33
Hence proved.
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−1.2·(−0.4−(−4.6)−(+4.7))
Answer:
-0.62
Step-by-step explanation:
Jaylynn draws a hen on graph paper using the scale shown below the hen has a length of 16 units in the drawing what is the height in centimeters of the actual hen
Answer:
Step-by-step explanation:
48
The soccer team is selling tubs of cookie dough and brownie mix. Elaina raised $75 by selling one tub of cookie dough and five tubs of brownie mix. Megan raised $141 by selling three tubs of cookie dough and eight tubs of brownie mix. How much is a tub of brownie mix?
The cost of one tub of brownie mix = $12
Step-by-step explanation:
Step 1 :
Let x represent one tub of cookie mix's cost and y represent one tub cookie mix's cost
Total amount raised by Elaine = $75
Number of cookie mix tub sold by Elaine = 1
Number of brownie mix tub sold by Elaine = 5
This can be represented by the equation
x + 5 y = 75 => x = 75 - 5y
Step 2 :
Total amount raised by Megan = $141
Number of cookie mix tub sold by Megan = 3
Number of brownie mix tub sold by Megan = 8
This can be represented by the equation
3 x + 8 y = 141
Step 3 :
Solving the equations obtained in the above steps we have ,
3 ( 75-5y) +8y = 141
225 - 15y + 8y = 141
-7y = -84 => y = 12
Step 4 :
Answer :
The cost of one tub of brownie mix is $12
Answer:
Step-by-step explanation:
12 dollars
Maricela was recently approved for an $18,000 loan for 5 years at an interest rate of 6.2%. Use the monthly payment formula to complete the
statement
M= (1 + 5* - 1
M= monthly payment
P= principal
r=interest rate
= number of years
Maricela's monthly payment for the loan iss
Answer:
top is wrong my teacher told me the answer its
349.67
Maricela's monthly payment for the loan using the monthly payment formula is; $349.67
What is the monthly payment?
We are given;
Principal; P = $18000
Interest Rate; r = 6.2% = 0.062
Number of years; t = 5 years
The formula to find the monthly payment is;
M = P[(r/n) * (1 + (r/n))^(nt)]/[((1 + (r/n))^(nt)) - 1]
Plugging in the relevant values gives;
M = 18000[(0.062/12) * (1 + (0.062/12))^(12 * 5)]/[((1 + (0.062/12))^(12 * 5)) - 1]
Solving this with a calculator gives us;
M = $349.67
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What is 6x729 and how would u do the math in the best way ?
6x729 equals 4374 and you get that by using a calculator that's how i would do it
350 is what percentage of 50?
Answer:
175
Step-by-step explanation:
Answer:
175%
Step-by-step explanation:
Divide 50 by 100 then multiply it by 350
50 ÷ 100 × 350 = 175
which statement is true for all similar figures PLZZ HELP ME I WILL MARK YOU AS THE BRAINLIST
A they have the same size and shape
B they have the same size but different shapes
C they have corresponding sides that are congruent
D they have corresponding angles that are congruent
Answer:
C they have corresponding sides that are congruent
Step-by-step explanation:
hope this helps
Find the sizes of the angles marked with a letter.
Why is my answer wrong?
Answer:
29.28 degrees.
Step-by-step explanation:
sin x / 16.2 = sin 49 / 25
Cross multiply:
25 sin x = 16.2 * sin 49
sin x = (16.2 * sin 49) / 25
sin x = 0.48905
x = 29.28 degrees.
Find the volume of a square prymaid with a base of 9 ft and a height of 14 ft
126 ft³
277 ft³
378 ft³
1134 ft³
Answer:
Volume of the Square pyramid [tex]=378.27 Feet^3[/tex]
Step-by-step explanation:
A Square pyramid is the pyramid whose base is in the shape of a Square.
Volume of a Square Pyramid:
[tex]BASE*BASE*\frac{HEIGHT}{3}[/tex]
[tex]Base= 9 feet[/tex] and
[tex]Height= 14 feet[/tex]
Volume of the square Pyramid:
=[tex]9*9*\frac{14}{3}[/tex]
[tex]=81*4.67[/tex]
[tex]=378.27 Feet^3[/tex]
The volume of the Square pyramid [tex]=378.27 Feet^3[/tex]
Is 10xyz^3 a monomial
Answer:
Yes, 10xyz^3 is a monomial.
Step-by-step explanation:
A monomial is an algebraic expression consisting of one term that can have multiple variables of different degrees within.
Kendra is babysitting her cousins, who are quintuplets. At snacktime, Kendra puts 5 plates on the table. She cuts apples into slices and places an equal number of slices on each cousin's plate. There is a total of 35 apples slices on the plates.
Which equation can you use to find the number of apple slices s on each plate?
Answer:
Kendra is watching over 5 children. She wants to be sure that they each have an even number of apple slices. There are 35 apple slices total. She wants to take 35 and put it equally into 5 groups.
Your equation would be 5s=35, where s would be the total amount of apple slices on each plate.
To solve this equation you would divide both sides by 5 to get 7. s=7 (35/5=7)
Each quintuplet would be 7 apple slices.
Hope this helps ;)
circle E, and are diameters. Angle BCA measures 53°.
Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to connect points B and C and points A and D. Angle B C A is 53 degrees.
What is the measure of arc AD?
53°
74°
106°
180°
Answer:
74°
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
Triangle EBC is an isosceles triangle (because has two equal sides EB=EC)
so
[tex]m\angle BCA=m\angle BCE=m\angle EBC=53^o[/tex]
Find the measure of angle BEC
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle BCE+m\angle EBC+m\angle BEC=180^o[/tex]
substitute the given values
[tex]53^o+53^o+m\angle BEC=180^o[/tex]
[tex]m\angle BEC=180^o-106^o=74^o[/tex]
Find the measure of angle AED
we know that
[tex]m\angle AED=m\angle BEC[/tex] ----> by vertical angles
so
[tex]m\angle AED=74^o[/tex]
Find the measure of arc AD
we know that
[tex]m\ arc\ AD=m\angle AED[/tex] -----> by central angle
therefore
[tex]m\ arc\ AD=74^o[/tex]
Answer:
The answer is B on Edge 2020`
Step-by-step explanation:
I did the exam
what is the P(T,H,T,H) on 4 flips of a coin?
i need help
Answer:
1/16
Step-by-step explanation:
Each coin flip is an independent event so the probabilities are independent
P(T,H,T,H) = P(T) P(H) P(T) P(H)
= 1/2 * 1/2 * 1/2 * 1/2
= 1/16
Which of the following is a statistical question?
A.
How many hours do students in Mr. Brown's class typically spend on homework?
B.
What is Andy’s shoe size?
C.
What is the room temperature of Charlie's house?
D.
How much did Ashley pay for her smart phone?
For which two values of T will D = 40? Round to the nearest tenth.
Answer:I believe it is 20
Un observador se acerca con una velocidad de 15m/s a un parlante estático que está emitiendo un sonido con una frecuencia de 297 Hz. ¿Cuál es la frecuencia percibida por el observador?
Answer:
310 Hz
Step-by-step explanation:
This is a spanish language mathematical question.
We translate this to english:
An observer approaches a static speaker at 15 meters per second. The speaker is emitting a sound with a frequency of 297 Hz. What is the frequency perceived by the observer?
Solution:
This can be solved using doppler effect formula. Which is:
[tex]f=(\frac{c}{c+V_s})f_0[/tex]
Where
f is the observed frequency (297 Hz)
c is the speed of sound (343 m/s)
[tex]V_s[/tex] is the velocity of source (given as 15)
[tex]f_0[/tex] is what we want to find
Now, substituting, we solve:
[tex]f=(\frac{c}{c+V_s})f_0\\297=(\frac{343}{343+15})f_0\\297=(0.9581)f_0\\f_0=309.99[/tex]
Rounding,
We can say the perceived frequency would be around 310 Hz
point (k, -3) lies on the line whose equation is x-2y=-2. What is the value of k?
Answer:
Substitute, y = -3 and x = k on the equation.
=> k - 2×(-3) = -2
=> k = -2 + (-6)
=> k = - 8
=================
HOPE U UNDERSTOODMARK AS BRAINLIEST ONEAny Doubts? Please COMMENT
The required value of the k is -8 for which the point (-8, -3) line on the equation of the line.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Point (k, -3) lies on the line whose equation is x-2y=-2.
Put x = k and y = -3 in the given equation of the line,
k - 2 (-3) = -2
k = -2 -6
k = -8
Thus, the required value of the k is -8 for which the point (-8, -3) line on the equation of the line.
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A hat costs $17.00 and is on sale for 30%. How much will be saved?
Step-by-step explanation:
70
---- × 17=$11.90(saved)(answer)
100
Suppose the diameter of a circle is \color{green}{6}6start color green, 6, end color green units. What is its circumference?
Answer:
C =18.84
Step-by-step explanation:
The circumference is given by
C = pi*d
C = 6pi
If we approximate pi by 3.14
C = 6*3.14
C =18.84
In the last election, Candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B receive? What is the equation for this problem and what is the answer to it?
Answer:
B receives 62000 votes
C receives 47000 votes
Step-by-step explanation:
Let C be the vote for candidate C
Let B be the vote for candidates D
Let the total vote be T. Therefore,
C + B = T (1)
But C receives 15000 votes fewer than B ie
C = B —15000 (2)
Total votes, T = 109000
Substituting the value of C and T into equation 1
C + B = T
B — 15000 + B = 109000
Collect like terms
B + B = 109000 + 15000
2B = 124000
Divide both side by the coefficient B i.e 2
B = 124000/2
B = 62000
Putting the value of B into equation 2;
C = B —15000
But B = 62000
C = 62000 — 15000
C = 47000
B receives 62000 votes
C receives 47000 votes
A binomial trial is one in which there are four possible outcomes.
A. True
B. False
Answer:
The answer is B: False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Find the minimum value of
C = 4x + 3y
Subject to the following constraints:
x 20
y20
2x + 3y > 6
3x – 2y = 9
x + 5y = 20
Final answer:
To find the minimum value of C given the constraints, one must plot these constraints, find the feasible region's vertices, evaluate C at each vertex, and select the minimum value obtained. The minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.
Explanation:
To find the minimum value of C = 4x + 3y subject to the given constraints, we need to first correct the constraints provided, as it seems there might be a misunderstanding in how they were presented. Assuming the constraints meant to be:
1. [tex]\(x \geq 0\)[/tex]
2. [tex]\(y \geq 0\)[/tex]
3. [tex]\(2x + 3y \geq 6\)[/tex]
4.[tex]\(3x - 2y = 9\)[/tex]
5.[tex]\(x + 5y = 20\)[/tex]
We will solve the system of equations (4) and (5) to find the values of x and y that satisfy these conditions, and then we will check if these values satisfy all other constraints including (3). If they do, we'll use these values to find C.
Solving the equations simultaneously:
From equation (4): 3x - 2y = 9
From equation (5): x + 5y = 20
Multiplying equation (5) by 3 to eliminate x, we get:
3(x + 5y) = 3(20)
3x + 15y = 60
Now, subtract equation (4) from this result to eliminate x:
3x + 15y - (3x - 2y) = 60 - 9
3x + 15y - 3x + 2y = 51
17y = 51
y = 3
Substitute y = 3 into equation (5) to find x:
x + 5(3) = 20
x + 15 = 20
x = 5
Now, check if [tex]\(x = 5\) and \(y = 3\) satisfy the constraint \(2x + 3y \geq 6\):[/tex]
[tex]\[2(5) + 3(3) \geq 6\][/tex]
[tex]\[10 + 9 \geq 6\][/tex]
[tex]\[19 \geq 6\] - This is true.[/tex]
Since x = 5 and y = 3 satisfy all the constraints, we can calculate \(C\):
C = 4x + 3y
C = 4(5) + 3(3)
C = 20 + 9
C = 29
Therefore, the minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.
How many solutions are there to this equation 3x(x-4)+5-x=2x-7
Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
x = 1x = 4__
To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
__
Alternate method
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
Tom has three pieces of wood. The length of the longest piece is 3/4 foot. The length of the shortest piece is 3/8 foot. What might be the length of the third piece of wood.
Answer:
[tex]\dfrac{3}{8}\text{ foot}<x<\dfrac{3}{4}\text{ foot}[/tex]
Step-by-step explanation:
We are given the following in the question:
There are three pieces of a wood.
Length of longest piece =
[tex]\dfrac{3}{4}\text{ foot}[/tex]
Length of shortest piece =
[tex]\dfrac{3}{8}\text{ foot}[/tex]
Let x be the length of the third piece.
Since the length of third piece lies between the length of the longest and the shortest piece of wood, thus, we use the following inequality to represent the length of the third piece.
Inequality:
[tex]\dfrac{3}{8}\text{ foot}<x<\dfrac{3}{4}\text{ foot}[/tex]
Solve for a
h = a/4
Answer:
a=4h
Steps:
4h=a swap the sides
a=4h
So , a=4h