Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.
Let the radius of the sphere be R.
So, the volume of the sphere is given by,
V = [tex]\frac{4}{3}\pi r^3[/tex]
Differentiating the above relation with respect to time 't' we get,
dV/dt = 4[tex]\pi r^2[/tex]. dr/dt
Given that, the change of radius (dr/dt) = 4 mm/s
When the diameter is 80 mm, then the radius = 80/2 = 40 mm
So the volume change when the diameter is 80 mm is given by,
dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s
Hence the volume increase in 802424.77 cubic mm/s.
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how does the symmetry of a parabolas hep you graph a quadratic function?
Answer:
It line splits the graph of a quadratic equation into two mirror image, or basically means every point on the parabola on one side of the axis will be a mirror image of the other side of the parabola.
np :d
What is the equation of the line in slope-intercept form?
pls help me!
Answer:
y = [tex]\frac{4}{3}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line
Please help me I am stuck on this
Step-by-step explanation:
when we say "a/b of c", we mean mathematically :
a/b × c
so,
a)
x = 1/5 × 15 = 15/5 = 3
b)
x = 3/4 × 48 = 3×48/4 = 3×12 = 36
Answer:
a) 3 b) 36Step-by-step explanation:
a) 1/5 of 15 = ?
→ 1/5 of 15
→ (1/5) × 15
→ 15/5 = 3
So, answer is 3.
b) 3/4 of 48 = ?
→ 3/4 of 48
→ (3/4) × 48
→ 144/4 = 36
So, answer is 36.
A toy company puts 25 toy cars in each box.
How many toy cars are in 1,000 boxes? Use the expression 25 × 1,000 to find the answer. Then, describe the value of 25 in the result.
A. 2,500
The place value of 25 increases by 1 place to the left.
B. 2,500
The place value of 25 increases by 2 places to the left.
C. 25,000
The place value of 25 increases by 3 places to the left.
D. 25,000
The place value of 25 increases by 4 places to the left.
The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.
How to calculate the value?It should be noted that place value is used to know the value of the numbers that are given in a data.
In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:
= 25 × 1000
= 25000
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If g(x)=8x^6 and f(x) = log4 (2x) then f(g(x)) = ?
Answer:
f(g(x))= log4(2(8x^6))
or log4(16x^6)
Step-by-step explanation:
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 7 minutes and you record the data point of (14,y), what is the value of y? Use slope to justify your answer.
The value of y which the slope formula is 34.
What is slope?Slope can be defined as the rate of change of a body.
To calculate the value of y, we use the formula below.
Formula:
ΔL/t = y/x........... Equation 1Where:
ΔL = Rise in the Level of watert = TimeFrom the question,
ΔL = 17 cmt = 7 minutesx = 14Substitute these values into equation 1 and solve for y
17/7 = y/14y = (17×14)/7y = 17×2y = 34Hence, the value of y is 34.
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7×25
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
175
how will convert it in mixes fraction when there is no division number
Use the given information to prove that x II y
Considering the figure < 4 ≅ < 5 alternate internal angles
What is the alternate internal angle theorem ?Alternate internal angle theorem is a theorem that holds true when in the occurrence of parallel lines and a transversal line.
Some of the theorems occurring at this stage include
alternate exterior anglescorresponding angles same side exterior anglesUsing the figure. alternate internal angle theorem proves that
< 4 ≅ < 5< 3 ≅ < 6This helps to complete the required proof that < 4 = < 5
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Tell whether x and y show a positive, negative, or no relationship.
The coordinates of x and y on the graph can not form a function.
x and y do not show any relationships.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates from the graph.
(2, 0)
(2, 1)
(-1, 2)
(1, 3)
(0, -1)
(2, -3)
(-1, -1)
(3, -2)
We can say that,
A function can not have one to many.
We have,
(2, 0), (2, 1), and (2, -3).
This means,
For x = 2, y = 0, 1, -3.
This is not possible.
Thus,
The coordinates of x and y on the graph can not form a function.
x and y do not show any relationships.
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rewrite the function g(x)=2x^2+16x+6 in vertex form by completing the square
The vertex form of the function g(x)= 2[tex]x^2[/tex]+16x+6 is g(x)= 2[tex](x+4)^2[/tex]-26.
What is vertex form of the function?
The function's maximum or lowest possible output is represented by the vertex of the quadratic function's graph. When viewing a graph, the vertex is the highest or lowest point on the parabola. Utilizing the vertex formula is the simplest technique to discover the vertex. It is simple to locate the vertex of the parabola using the vertex form of a quadratic equation. Y=a(xh)2+k is the definition of the generic vertex form, where h is the x-coordinate and k is the y-coordinate of the vertex.
Here the given function is ,
=> g(x) = 2[tex]x^2[/tex]+16x+6
=> g(x) = 2([tex]x^2+[/tex]8x+3)
=> g(x) = 2([tex]x^2+[/tex]8x+16-16+3)
=>g(x) = 2 [[tex](x+4)^2[/tex]-13]
=> g(x)= 2[tex](x+4)^2[/tex]-26
Therefore vertex form of the function is g(x)= 2[tex](x+4)^2[/tex]-26 and vertex is (-4,-26).
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Answer:
g(x)=2(x+4)^2-26
Has a minimum value of -26
Step-by-step explanation:
i got it right!
The measure of an angle is 60.5°. What is the measure of its supplementary angle?
Answer:
119.5
Step-by-step explanation:
Since supplementary is 180 degrees, 180-60.5=119.5
what is the answer what is the answer what is the step by step answer to learn to do it
The approximate percentage of sales tax is 1%
A gymnastics mat priced at $53.
A cost of mat after adding sales tax = $53.53
So, the tax amount would be,
53.53 - 53 = 0.53
We need to find the sales tax percentage.
Let x be the percentage of sales tax.
x = (0.53)/(53.53) * 100
x = 0.0099 * 100
x = 0.99%
x ≈ 1%
Therefore, the approximate percentage of sales tax is 1%
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A line has a slope of -2/3 and passes through the point (-3,8). What is the equation of the line?
A. y = -2/3 x + 6
B. y = -2/3 x + 8
C. y = 6x - 2/3
D. y = 8x - 2/3
Answer:
A
Step-by-step explanation:
What is the expected number of female children in a family with three children?
O 1
O 1.5
O 2
O 2.5
Using the probability, the expected number of female children in a family with three children is 1.5. The option 2 is correct.
In the given question, we have to find the expected number of female children in a family with three children.
The possibility of having girls in family is 0,1,2 or 3.
From the 8 possible sequences, only one of them give the possibility of 0 girls.
So the probability of 0 girls is 1/8.
There are total 3 ways of having 1 girl.
That is: GBB, BGB, and BBG.
Thus, the probability of 1 girl is 3/8.
Similarly checking for having 2 girls with probability 3/8
Having 3 girls with probability 1/8.
The predicted number of girls is calculated as a weighted average of all potential numbers, where a number's weight is determined by its likelihood of occurring.
The anticipated number of girls is therefore
= 1/8⋅0+3/8⋅1+3/8⋅2+1/8⋅3
= 0+3/8+6/8+3/8
=(3+6+3)/8
=12/8
=1.5
Hence, the expected number of female children in a family with three children is 1.5.
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2x + y = 1
-2y + 5z = -5
3x + 4z = -2
Answer:
y=5 x= -2 z=1 the procedure Is in the picture
as discussed in the wall street journal story, weighting is designed to adjust poll results to give more weight to people whose demographic characteristics are under-represented in the sample and less weight to people whose demographic characteristics are over-represented. think about how certain demographic groups might end up being under or over-represented (that is, there are too many or too few people in the sample from that group, compared to the population as a whole). weighting can therefore potentially help fix which types of bias? (check all that apply.)
Using the concepts of weighting, we got that demographic groups helps in fixing difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.
Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the employment, etc.
It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.
Hence, certain demographic groups might end up being under or over-represented means that there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.
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There are 24 students in mr. bonogofsky's math class, 5 - of these students earned an a on the geometry unit assessment. how many students earned an ap
Answer: 19
Step-by-step explanation:
Rodrigo is taking an SAT prep class at the Westminster Community Center. The community center is 3.1 miles away from Rodrigo's house. How far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles?
1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given,
The community center is 3.1 miles away from Rodrigo's house.
We need to find how far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
As given, 3 inches : 9.3 miles
1 mile = 3/9.3 inches
1 mile = 0.323 inches.
So let us multiply 3.1 with 0.323
3.1×0.323
1.0013 inches
Hence 1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
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Please help meee!!!!!!
The required value of "b" is 7, where the equation is y = -3x + 7.
As per the given table, we take the two points (9, 1) and (3,7).
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -3, y₁ = 16
x₂ = 1, y₂ = 4
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute the values in the above equation,
y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))
y - 16 = (-12/4)(x+3)
y - 16 = -3(x+3)
y - 16 = -3x - 9
y = -3x - 9 + 16
y = -3x + 7 ....(i)
Compare the given equation y = mx + b with the above equation, and we get
b = 7
Therefore, the required value of "b" is 7.
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Round 74.9963 to the nearest 10
The number 74.9963 would round down to 70
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to round 74.9963 to the nearest 10
We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.
The answer would be 70
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Two cards are drawn without replacement from an ordinary deck. Find the probability that the second is not a red card, given that the first is not a red card.
What is the conditional probability?
Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.
What is the likelihood of receiving two red cards without being replaced?The probability of drawing a second red in the event that this red is not changed is 9/15,
hence the probability of A is 10/16 * 9/15, or 0.375.
The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.To learn more about conditional probability refer to:
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What is the additive in verse of 16 5/7?
Answer:
the additive inverse of 16 5/7 IS 26/7
which expression correctly represents the area of triangle EFG?
a. 1/2 gf sin (F)
b. 1/2 ef sin (E)
c. 1/2 gf sin (G)
d. 1/2 ef sin (G)
1/2 ef sinG is the expression that correctly represents the area of triangle EFG. Select option d.
How to determine which expression correctly represents the area of triangle EFG?
Given: the triangle EFG as shown in the image
The formula for the Area of triangle is:
A = 1/2 × base(b) × height(h)
Area of EFG = 1/2 × f × h
Using trigonometric ratio:
sin G = h/e (opp. / hyp.)
h = e sin G
put h = g sin E into the Area of EFG:
Area of EFG = 1/2 × f × e sin G = 1/2 ef sin G
Therefore, the expression correctly represents the area of EFG is 1/2 ef sinG
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can someone please doordash me something like i will give brainly 5 stars and spotify premium just 10 dollars please
i gotchu what do u want
Put these numbers in order from greatest to least.
-24/40
0.5
66 6/15
66.2
-0.4
Answer:
First simplify the ones that need dividing
Step-by-step explanation:
So i got
-0.4, -0.6, 0.5, 4.44, 66.2
Hope this helps!
Maria's rectangular rug is twice as long as it is wide. The are of the rug is 76.88 square feet.
What is the perimeter of the rug?
The perimeter of the rug is 37.2
The first line says that the rug is twice as long as its width. If the width is taken as w and length is taken as l, we get an equation l= 2w. Since it is a rectangle, the area of the rectangle will be (length*width) which is equal to l*w.
Since l=2w, area = 2w*w = 2w^2. This is given equally to 76.88.
2w^2 = 76.88
w^2 = 38.44
w = 6.2
l = 2w = 2*6.2 = 12.4
Now, perimeter of rectangle is 2w+2l = 2*6.2 + 2*12.4 = 37.2
Hence the perimeter of the rug is 37.2
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Mr. fitzpatrick is taking his math class to see a pearl jam concert because they have worked so hard this week in class. he purchases 22 tickets for a total of $265. tickets cost $10 for students and $15 for adults. some students must pay adult prices because they are over 18 years of age. what are the number of student tickets purchased and the number of adult tickets purchased
Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.
It is given that Mr. Fitzpatrick bought 22 tickets
The tickets collectively cost him $265
The student tickets cost $10 while adult tickets cost $15
Let the no. of adult tickets sold be x
Let the no. of children's tickets sold be y
Therefore we get the equations
x + y = 22 [1]
15x + 10y = 265 [2]
or, 5x + 10x + 10y = 265
or, 5x + 10(x + y) = 265
from equation [1] we get
5x + 220 = 265
or, 5x = 265 - 220
or, 5x = 45
or, x = 9
Therefore,
y = 22 - 9
= 13
Therefore he bought 9 adult tickets and 13 children tickets.
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Select all statements that are true about a linear relationship that is also a propotional relationship
A) The graph passes through the origin
B) The graph does not pass through the origin
C) The constant of proportionality can be found using run/rise
D) The slope is the same as the constant os proportionality
D) The slope is the same as the unit rate
For all proportional relationships, the true statements are:
A, D, and E.
Which statements are true about a proportional relationship?
A proportional relationship between two variables x and y is written as:
y = k*x
Now let's analyze each of the given statements:
A) The origin is the point (0, 0).
If you evaluate the general equation in x = 0 you get:
y = k*0 = 0
So yes, this equation passes through the point (0, 0).
B) This is false, as we saw above.
C) The formula for the constant of proportionality is:
y = k*x
y/x = k
So we can see that k = rise/run
the statement is false.
D) Yes, this is true, a general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept, particularly if the y-intercept is zero, then we have a proportional relation.
E) Yes, slope, unit rate, constant of proportionality, are all equivalent terms for a proportional relation.
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Can someone please help !
[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]
If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.
Therefore the segments form the proportion:
[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]
BT is the midsegment of ΔMAH, therefore
[tex]HB=\dfrac{1}{2}HM[/tex]
DC is the midsegment of ΔBTH, therefore
[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]
Substitute:[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]
cross multiply
[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]
divide both sides by HM
[tex]\boxed{BT=21}[/tex]
[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]
cross multiply
[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]
divide both sides by HM
[tex]\boxed{DC=10.5}[/tex]
1. The retail price of grapes is $2.17 per pound. if a customer paid $8.68 for grapes, how many pounds did she buy?
