The expression which best represents the volume of the can in discuss as evaluated from the formula; V = π r² h and as required is; 6.75π.
What is the volume of the can as described?It follows from the task content that the volume of the can whose radius is; 1.5 inches and height is; 3 inches is to be determined.
It is noteworthy to know that the volume of a can often the shape of a cylinder is given by the formula;
Volume, V = π r² h.
where, radius, r = 1.5 in.
height, h = 3 in.
Therefore, we have that the volume of the can can be evaluated as;
Volume, V = π × ( 1.5 )² × 3
Volume, V = 6.75 π.
On this note, the best representation of the volume of a can having dimensions as described is; 6.75π.
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Identify the explicit formula for the sequence given by the following recursive formula:
(see picture below)
A) f(n) = 2 – 4(n – 1)
B) f(n) = –4 + 2(n – 1)
C) f(n) = 4 – 2(n – 1)
D) f(n) = –2 + 4(n – 1)
If f(n) = f(n - 1) + 4, then
f(n - 1) = f(n - 2) + 4
and substituting this into the first equation gives
f(n) = f(n - 2) + 2•4
Similarly,
f(n - 2) = f(n - 3) + 4
so that
f(n) = f(n - 3) + 3•4
and so on.
Note the pattern:
f(n) = f(n - k) + k•4
so that when k = n - 1, we have
f(n) = f(n - (n - 1)) + (n - 1)•4
or
f(n) = f(1) + 4 (n - 1)
so that
[D] f(n) = -2 + 4 (n - 1)
Luigi's Fine Dining charges $32.09 for its prix fixe meal plus $39.26 for every drink, d, you purchase. The equation that models the total cost (T) is T(d )= 39.26d + 32.09 Which value in the equation represents the rate of change?
A .. The number of drinks purchased
B .. $32.09
C .. $39.26
D .. $71.35
Answer:
C. $32.09, since it's not the fixed cost, it changes based on how much drinks are purchased.
How can you solve multistep equations that represent real world
scenarios?
Hi guys can u guys help me add 322 + 12
Answer:
334 is the answer
Step-by-step explanation:
you add them together
Answer:
334 is the right answer
Step-by-step explanation:
please mark me brainliest
on tuesday a local a hamburger shop sold a combined total of 448 hamburgers and cheeseburgers , the number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold on tuesday ?
simplify [tex]y^{-3}[/tex]
Find the exact value of tan π/12.
[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]
so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]
Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book
Answer:
Step-by-step explanation:
Let P be the number of pages
First day reads P/9 pages
Second day reads 24 pages
two days reading is P/5 (1 page read for every 4 pages left)
P/9 + 24 = P/5
P + 24(9) = 9P/5
5P + 24(9)(5) = 9P
1080 = 4P
P = 270 pages
There are 270 pages in this book.
Given that,
Emily reads a storybook the first day,
She reads 1/9 of the whole book, and on the second day, she reads 24 pages.
The ratio of the number of pages read to the remaining pages in the two days is 1:4.
We have to find
How many pages are there in this book?
According to the question,
Let, P is the number of pages,
The first day Emily reads p/9 pages of the whole book,
And the second day she read 24 pages.
The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.
Therefore,
The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days
[tex]\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages[/tex]
Hence, there are 270 pages in this book.
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Which equation represents this line in point-slope form?
A.
`(y + 4) = (4)/(3) (x + 3)`
B.
`(y −4) = -(4)/(3) (x +3)`
C.
`y= -(3)/(4)x`
D.
`4y− 3x = 0`
Answer:
The Answer is Option A or Option B
Step-by-step explanation:
First let's review what point slope form is.
[tex]y - y 1 = m(x - x1)[/tex]
To take a line and put it into point slope form you need to identify one of the points. In this case the point is either (-3, -4) or (-3, 4) but without a graph attached I cannot personally say which one it is.
You will also need to identify the slope of the line (m) based on the graph, so identify if the graph is ascending or descending. This alone can determine your answer
Again, there is no graph provided so it is up to you to determine if it is Option A or B.
I really hope this helps and you have a great rest of your day!
Note: I am not a professional educator so take my opinion carefully.
=)
order the expression from least to greatest
Answer:
So it would be 4, 11, 20
Step-by-step explanation:
[tex]11^1 = 11[/tex]
[tex]2^2 * 5 = 20[/tex]
[tex]8^2-60 =4[/tex]
I need help fast I forgot how to do this
Answer:
ABC & E are true statements about the graph
given parallelogram EFGH, where EF = 5x + 18, HE = 3x + 4 and the perimeter is 60, which value of GH
Given the perimeter of the parallelogram in the image below is 60, the value of GH will be: 23.
Recall:
Perimeter of a parallelogram = 2(a + b), where a is the side length and b is the base length.Opposite sides of a parallelogram are equal.Given the parallelogram as shown in the diagram below, where:
base (b) = EF = 5x + 18
side (a) = HE = 3x + 4
Perimeter = 60
Plug in the values into the formula:
60 = 2[(3x + 4) + (5x + 18)]
60 = 2[3x + 4 + 5x + 18]
60 = 2[8x + 22]
60 = 16x + 44
60 - 44 = 16x
16 = 16x
1 = x
x = 1
GH = EF = 5x + 18 (equal opposite sides of parallelogram)
GH = 5x + 18
Plug in the value of xGH = 5(1) + 18
GH = 23
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Write the word sentence as an equation. Then solve.
The difference of a number n and 3 is -7.
Answer:
n-3 = -7
n = -4
Step-by-step explanation:
(Meeting character limit)
Answer:
-4
Step-by-step explanation:
n - 3 = -7, n = -4
A scuba diver descends farther down into the ocean from an initial depth of 15.2 feet below sea level. The scuba diver descends at a constant rate for 212 minutes and reaches a depth no more than 46.7 feet below sea level.
What is the maximum rate, r, that the scuba diver may descend?
r≥241925
r≤12.6
r≤241925
r≥12.6
Answer:
r <= 12.6
Step-by-step explanation:
Let's calculate the rate at which he descends:
r = (46.7 - 15.2)/212 = 0.15 feet/minute
which expression is equivalent to (tan(θ/2))(sin θ)
Answer:
B) [tex]-1+cos\theta[/tex]
Step-by-step explanation:
[tex](tan(\frac{\theta}{2}))(-sin\theta)[/tex]
[tex](\frac{1-cos\theta}{sin\theta})(-sin\theta)[/tex]
[tex](\frac{-sin\theta+sin\theta cos\theta}{sin\theta})[/tex]
[tex]-1+cos\theta[/tex]
Therefore, option B is correct
Helpful Tips:
Half-Angle Formula: [tex]tan(\frac{\theta}{2})= \frac{1-cos\theta}{sin\theta}=\frac{sin\theta}{1+cos\theta}=\pm\sqrt{\frac{1+cos\theta}{2}}[/tex]
What is the temperature shown on
the thermometer?
A line has a slope of and passes through the point (4, 7). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
7=4m +c( y intercept)
Step-by-step explanation:
use the formula y= mx +c
Help, please
Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.
−5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3:negative five times x over negative five = fifty-three over negative five
Step 4: x = negative fifty-three over five
Answer:
The first step.
Step-by-step explanation:
what is x- 2 1/2 = 6 3/4
Answer:
3 2/2
Step-by-step explanation:
If 6 pounds of apples cost $4.80 what is the cost per 9 pounds
Answer:
Cost of 1 pound apple:4.80/6=2.4
cost of 9 pounds apple:2.4 ×9=21.6
Can someone help me with these 2 geometry questions?? Will mark brainiest :)
Answer:
Thats to hard Do it your self
You take a test with 25 questions. Your grade on the test was a 80%. How many questions did you get right?
Answer:
20 questions
Step-by-step explanation:
1.) Use the following equation:
[tex]\frac{x}{y}[/tex] = [tex]\frac{p}{100}[/tex]
2.) For this equation,
x is the # of test question you got righty is the total # of test questionsp is the grade you got on the test3.) Substitute
[tex]\frac{x}{25}[/tex] = [tex]\frac{80}{100}[/tex]
4.) Solve
[tex]\frac{x}{25}[/tex] = [tex]\frac{80}{100}[/tex]
[tex]\frac{x}{25}[/tex] = [tex]\frac{8}{10}[/tex]
[tex]\frac{x}{25}[/tex] = [tex]\frac{4}{5}[/tex]
5.) Cross Multiply
[tex]\frac{x}{25}[/tex] = [tex]\frac{4}{5}[/tex]
5x = 100
6.) Divide
5x = 100
x = 20
Therefore, you got 20 questions right.
A = $2100, P = $1600, t = 8
r = %
Answer:
I want to say 900 many sorry if it's wrong
16. Write an equation for the line that is parallel to the given line and passes through the given
(1 point)
point
y = 3x+7; (2, 10)
A. Y=3x + 11
B. y = 3x + 4
C. y=-3x+4
D. y=(-1/3)x+ 4
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
y = 3x + b
add in the desired point
10 = 3(2) + b
b = 4
B. y = 3x + 4
The radius of the circle shown below is 8 centimeters. What is the
approximate length of XY?
115
A. 50.3 cm
B. 16.1 cm
C. 8.0 cm
D. 64.2 cm
(fog) f(x) = 1/x g(x) square root x+3
Answer:
see the step below, but I'm not sure if this you want
Step-by-step explanation:
[tex](fog) = \frac{1}{ \sqrt{x + 3} } [/tex]
[tex](fog) = \frac{ \sqrt{ x + 3} }{x + 3} [/tex]
Examine the graphic organizer above. Which of the choices below BEST fills in the blank on the graphic organizer?
Houa is driving to a concert and needs to pay for parking. There is an
automatic fee of $8 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Houa have to pay for
parking if she left her car in the lot for 3 hours? How much total money would Houa have to pay if she left her car in the lot for 3 hours? How much would Houa have to pay if she left her car in the lot for t hours?
Cost of parking for 3 hours:
I
Cost of parking for t hours:
Step-by-step explanation:
let's create the corresponding equation.
it is linear, because the cost per hour is constant, no matter how many hours the car parks.
t is the variable indicating the amount of hours parking.
every hour costs $2.
and $8 is the starting value (we have to pay that, even if we have 0 hours parking time).
cost(t) = 2t + 8
so, the cost after 3 hours is
cost(3) = 2×3 + 8 = 6 + 8 = $14
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 52% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 5 customers at Anita's, exactly 4 order their food to go?
Round your response to at least three decimal places
Using the binomial distribution, it is found that there is a 0.1755 = 17.55% probability that, in a random sample of 5 customers at Anita's, exactly 4 order their food to go.
For each customer, there are only two possible outcomes, either they order their food to go, or they do not. The orders of each customer are independent of other customers, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
52% of its customers order their food to go, hence [tex]p = 0.52[/tex].Random sample of 5 customers, hence [tex]n = 5[/tex].The probability that exactly 4 order their food to go is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.52)^{4}.(0.48)^{1} = 0.1755[/tex]
0.1755 = 17.55% probability that, in a random sample of 5 customers at Anita's, exactly 4 order their food to go.
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A CD is on sale for $10.00. The sales tax rate is 6%. How much will the total cost be for the CD
Answer:
$10.06
Step-by-step explanation:
Tax rate = 6% , convert into 0.06
10 × 0.06 = 0.6
10 + 0.6 = 10.06