Step-by-step explanation:
We want to find how many miles per minute Joe runs. This means, we need to simplify the equation:
[tex]\frac{12 mi}{84 min}[/tex]
so that the number on the bottom is 1. How do we do that?
Simple.
Just divide 12 / 84
Answer:
Joe runs approx. 0.143 miles per minute.
Polynomial: 3x^4 + 5x - 4; Divisor: x - 1
Answer:
3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm
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Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
_____
Additional comment
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
Solve for x.
A. 8
B. 4
C. 10
D. 7
Answer:
D. 7
Step-by-step explanation:
Apply the secant-scant product theorem. Thus, based on the theorem, we have the following equation:
6(4 + 6) = 5(x + 5)
6(10) = 5x + 25
60 = 5x + 25
Subtract 30 from each side
60 - 25 = 5x + 25 - 30
35 = 5x
Divide both sides by 5
35/5 = 5x/5
7 = x
x = 7
Corinne solved the equation below:
5x = 95
5x − 5 = 95 − 5
x = 90
Is Corinne's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answer:
The solution is incorrect
Step-by-step explanation:
5x = 95
We need to do the opposite
We are multiplying x by 5 so we need to divide by 5
5x/5 = 95/5
x = 19
Corinne's solution is incorrect.
The mistake occurred when she subtracted 5 from both sides of the equation.
We have,
To solve the equation correctly, we need to isolate the variable x. Here are the correct steps:
Starting with the equation:
5x = 95
To isolate x, we divide both sides of the equation by 5:
(5x) / 5 = 95 / 5
x = 19
Thus,
The correct solution to the equation is x = 19.
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On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
Which answer explains the correct way to move the decimal to find the quotient of 14.6 ÷ 10,000?
three places to the right.
three places to the left.
four places to the left.
four places to the right
Answer:
Four places to the left.
Step-by-step explanation:
14.6/10000
=> 1.46/1000 [Shifted 1 decimal place after dividing by 10]
=> 0.146/100 [Shifted 1 decimal place after dividing by 10]
=> 0.0146/10 [Shifted 1 decimal place after dividing by 10]
=> 0.00146 [Shifted 1 decimal place after dividing by 10]
Number of decimal places = 1+1+1+1=4
Four places to the left.
In 2013, selected automobiles had an average cost of $16,000. The average cost of those same automobiles is now $20,000. What was the rate of increase for these automobiles between the two time periods
Answer:
25%
Step-by-step explanation:
The average cost of the automobile in 2013 is $16,000
The present cost now is $20,000
Therefore the rate of increase between the two automobiles can be calculated as follows
= 20,000-16,000/16,000
= 4,000/16,000
= 0.25×100
= 25%
Hence the rate of increase is 25%
50 POINTS PLEASE HELP ME
Hello!
f(g(x)) = 4 - 2 × (3x²) <=>
<=> f(g(x)) = 4 - 6x²
Answer: B. f(g(x)) = 4 - 6x²
Good luck! :)
Let we find the composition,
→ f(g(x)) = 4 (-2 × 3x²)
→ f(g(x)) = 4 -6x²
Hence, option (B) is the answer.
PLEASE HELP WILL MARK BRAINLIEST! Also please explain the answer
Answer:
Each triangle is a right triangle.
Step-by-step explanation:
You can see each one has one 90 degree corner.
Answer:
13. True
14. True
15. False
Step-by-step explanation:
By using the Pythagorean Theorem a^2+b^2=c^2, you can evaluate whether or not the triangles are right triangles.
13. 8^2+15^2=17^2 -> 64+225=289 -> TRUE
14. 50^2+120^2=130^2 -> 2500+14400=16900 -> TRUE
15. 12^2+35^2=36^2 -> 144+1225 =/=1296 -> FALSE
Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find B'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
The complement of set B denoted by B' is are {chocolate, strawberries, peanuts}
What is a Venn Diagram?A Venn diagram is a diagrammatic illustration showing the various components of a set in a diagram. The venn diagram for each set is usually enclosed in a circle and those circle(s) are inscribed in a rectangle known as the Universal Set.
A complement of a set is a set that is not from the Universal Set.
Let's assume that we use the initials of each word to represent them in a Venn diagram. Then;
Universal Set (U) = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream} Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}Let B = {vanilla, hot fudge, sprinkles, whipped cream}Let C = {chocolate, hot fudge, peanuts, whipped cream}The complement of Set B denoted at B' = {chocolate, strawberries, peanuts}
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Triangle A”B”C is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship of BC and B”C? PLEASE HELP
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Answer:
(b) BC = B"C"/3
Step-by-step explanation:
Choices A, C, D are all different ways of expressing the same relationship, and they are all incorrect.
B"C" is segment BC after dilation by a factor of 3, so it is 3 times as long as BC. That is, BC is 1/3 the length of B"C", choice B.
IBM issued 30-year bonds with an annual simple interest rate of 6.22%. Find the semiannual interest payment on a$5,000 bond.
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Answer:
$155.50
Step-by-step explanation:
The interest is given by the formula ...
I = Prt
where P is the principal earning interest at annual rate r for t years. The interest period here is 1/2 year.
I = $5000×0.0622×1/2 = $155.50
The semiannual interest payment is $155.50 on this bond.
For the parallelogram, if m∠2=4x+30 and m∠4=2x+70, find m∠3.
if D is the center of the circle below and AC measures 48, what is the mesure of ABC
Answer:
A. 24
Step-by-step explanation:
48/2=24. Hope this helps:)
The feet of the average adult woman are 24.6 cm long, and foot lengths are normally distributed. If 16% of adult women have feet that are shorter than 22 cm, approximately what percent of adult women have feet longer than 27.2 cm?
Answer:
Approximately 16% of adult women have feet longer than 27.2 cm.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The feet of the average adult woman are 24.6 cm long
This means that [tex]\mu = 24.6[/tex]
16% of adult women have feet that are shorter than 22 cm
This means that when [tex]X = 22[/tex], Z has a p-value of 0.16, so when [tex]X = 22, Z = -1[/tex]. We use this to find [tex]\sigma[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{22 - 24.6}{\sigma}[/tex]
[tex]-\sigma = -2.6[/tex]
[tex]\sigma = 2.6[/tex]
Approximately what percent of adult women have feet longer than 27.2 cm?
The proportion is 1 subtracted by the p-value of Z when X = 27.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.2 - 24.6}{2.6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16
0.16*100% = 16%.
Approximately 16% of adult women have feet longer than 27.2 cm.
Translate the following word phrase into an algebraic expression nine times the difference of five and y
Graph the function h(x) = -2x– 3.
Answer:
look below
Step-by-step explanation:
To graph the function h(x) = -2x - 3, we can plot points on a coordinate plane using the equation and then connect the points to form the graph.
To find the points, we can choose different values of x and substitute them into the equation to calculate the corresponding values of h(x). Let's select a few values for x:
When x = -2:
h(-2) = -2(-2) - 3 = 4 - 3 = 1
So we have the point (-2, 1).
When x = 0:
h(0) = -2(0) - 3 = 0 - 3 = -3
So we have the point (0, -3).
When x = 2:
h(2) = -2(2) - 3 = -4 - 3 = -7
So we have the point (2, -7).
Now, we can plot these points on a coordinate plane and connect them to form the graph of the function h(x) = -2x - 3.
The graph will show a straight line that passes through the points (-2, 1), (0, -3), and (2, -7). The line will have a negative slope of -2, meaning it slopes downward from left to right.
Here's a rough representation of the graph:
|
|
-7 | .
|
-3 |
| .
1 |
|____________________
-2 0 2
Please note that this graph is just an approximation, and for a more accurate graph, you may use graphing software or a graphing calculator.
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Find the common denominator 2/7 and 7/10
Answer:
70
Step-by-step explanation:
Finding the common denominator is really just finding the gcf of 7 and 10. The gcf of 7 and 10 is 70. So the common denominator is 70.
We are given both the slope and y-intercept so writing the equation in slope-intercept form is a breeze! Label both the slope and y-intercept and them substitute them into the general form of slope-intercept form. So, y=4x−3.
Answer:
below
Step-by-step explanation:
hope it is well understood?
The slope is 4 and y- intercept is 13
What is slope?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
Given
Slope
y = 4x-3
dy/dx = 4
slope = 4
intercepts y = 4(4) 3
y = 16-3
y = 13
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20 points & Mark brainliest
Help me with steps
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Answer:
A. 3.46
Step-by-step explanation:
The side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. You are given the short side GF of this triangle, so its long side is GH = GF·3.
Then the area of ΔGFH is ...
A = 1/2(GF)(GH) = 1/2(4)(4√3) = 8√3 ≈ 13.86 . . . . square units
__
Segment GI divides the area of ΔGFH in half, so that ΔGFI is half the above area. Segments GF, FI, IH, GI are all congruent, so segment GJ divides isosceles triangle GFI in half. That is. ΔGJI is half the area of ΔGFI, so is 1/4 the area of GFH.
Area of ΔGJI = (8√3)/4 = 2√3 ≈ 3.46 . . . square units
Your help would be very much appreciated I will mark you brainliest as well! :D
what is 2 1/2 divided by 1/3 {pls hurry the teacher is not letting us use brainly}
Answer:
7 1/2
Step-by-step explanation:
2 1/2 ÷ 1/3
Change to an improper fraction
(2*1+2)/2 ÷ 1/3
5/2 ÷1/3
Copy dot flip
5/2 * 3/1
15/2
Change to a mixed number
7 1/2
Select the correct answer from each drop-down menu?
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Answer:
second3firstisStep-by-step explanation:
We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.
"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."
Given the similarity statement
AJKL ANOP, what's the
corresponding side of ON ?
Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
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Answer:
(d) KJ
Step-by-step explanation:
The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.
The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.
convert the following decimals to a simplified fraction, showing all wok
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Have a nice day
Answer:
first let y=1.33 (with a _ on top of the threes after the decimal) then let 100y=133.33( with a _on top of the threes after the decimal)then subtract eq(ii) -eq(I) which is left side 100y-y= 99yright side 133.33-1.33=132then 99y=132then y=132/99 hence converted to fractionThe product of two numbers is 60 and thei r sum is it, find the Numbers
A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the proportion of left-handed golfers is 8%. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
Answer:
A sample of 997 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A previous study indicates that the proportion of left-handed golfers is 8%.
This means that [tex]\pi = 0.08[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
This is n for which M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2[/tex]
[tex]n = 996.3[/tex]
Rounding up:
A sample of 997 is needed.
Simplify and express the following as a rational number
[tex]( \frac { - 4 } { 3 } ) ^ { 8 } \div ( \frac { - 4 } { 3 } ) ^ { 12 }[/tex]
Answer:
81/256
Step-by-step explanation:
(-4/3)^8 divide (-4/3)^12
= (-4/3)^8-12
= (-4/3)^-4
= (3/-4)^4
=81/256
Answer:
The answer is 81/256
Step-by-step explanation:
The angles in a triangle represented by x, 3x, and 6x. What is the value of x?
A.20
B.30
C.18
D.36
Answer:
18
Step-by-step explanation:
The sum of the angles of a triangle is 180
x+3x+6x = 180
10x = 180
Divide by 10
10x/10 =180/10
x = 18
Given the functions below, find f(x) - g(x) f(x) = 2x + 5 g(x) = x^2 - 3x + 1
Answer:
One of these
Step-by-step explanation:
