The area of a square-shaped rug is 81 sq feet. If the rug is 9 ft long, what is its perimeter? Explain.

Answer:

B) [tex]f(x)=-3(x+1)^2+2[/tex]

Step-by-step explanation:

Notice that the graph of the parabola opens downward. This tells us that the leading coefficient of the function must be negative. Hence, we can rule out answers A and D.

Also, notice that our vertex is [tex](h,k)\rightarrow(-1,2)[/tex], which when we plug into vertex form, we get [tex]y=a(x-h)^2+k\rightarrow y=a(x-(-1))^2+2\rightarrow y=a(x+1)^2+2[/tex].

This means that B is the correct function that represents the graph.

Answers:  

============================================================

Explanation:

Part 1

Sort the data values to get

51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100

Now let's say we had these intervals

Notice each interval is 9 units wide.

The 5 scores 51,54,58,60,60 are in the interval 51-60, which means the first interval has a bar that's 5 units tall.

The scores 62,70 are in the interval 61-70, which means the second bar is 2 units high.

Keep this process going to create the histogram shown below.

It looks like you have the right idea, but your class interval widths aren't the same each time.

Because the class interval widths can change, this means other histograms are possible. Just be sure to stick to one interval width.

-----------------------------------

Part 2

Set A = set of scores that are 70 or larger, i.e. those who passed

Set A = {70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}

Set B = set of all scores in the class

Set B = {51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}

There are 14 items in set A and 20 in set B

This means 14/20 = 7/10 of the students passed.

Answer:

B

Step-by-step explanation:

Since the y-intercept is -3 look for the graph that has the point (0,-3)

Sam’s operating expenses for last year given the gross profit and the net income is  $33,345.

Operating expense is the expense that a company incurs in the course of running its business. It is determined by subtracting net income from gross profit.

Operating expense =  gross profit - net income

$105,355 -  $72,010 = $33,345

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Answer:

B

Step-by-step explanation:

Answer:

39.25

Step-by-step explanation:

Area of circle is pi(3.14) times r^2.

Semi means half

So 3.14 times 5^2 = 78.5

Its a semi ciricle so its 78.5/2 which is 39.25

Answer:

The slope is 32 while the y-intercept is (0,-6)

Step-by-step explanation:

.......

Answer:

12.025

Step-by-step explanation:

h=v/(π*r square)

divide the volume of a cylinder by the amount of the radius squared multiplied by π(pi)

340÷(π×3square)

giving you 12.025

(original in calculator=12.02504014)

but it is 12.025

[tex]\stackrel{\textit{area of the great circle}}{A=\pi r^2}\hspace{5em}81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies 9=r \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{surface area of the sphere}}{SA=4\pi r^2}\hspace{5em}SA=4\pi (9)^2\implies SA=324\pi ~in^2[/tex]

Apple be A and blueberries be B

So

As per Venn diagram

#1

P(A)=12/24

P(B)=7/24

Add

#2.

n(AUB)

E=8+16=24

P(AUB)=16/24=2/3

Answer:

[tex]\sf a) \quad P(contains\:apple)+P(contains\:blueberry)=\dfrac{5}{6}[/tex]

[tex]\sf b) \quad P(contains\:apple\:or\:blueberry)=\dfrac{11}{15}[/tex]

c)    Not mutually exclusive events

Step-by-step explanation:

From inspection of the Venn diagram:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let A = contains apple

Let B = contains blueberry

[tex]\implies\sf P(A)=\dfrac{15}{30}=\dfrac{1}{2}[/tex]

[tex]\implies\sf P(B)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]

Part (a)

[tex]\begin{aligned} \implies \sf P(A)+P(B) & =\sf \dfrac{1}{2}+\dfrac{1}{3}\\\\ & = \sf \dfrac{3}{6}+\dfrac{2}{6}\\\\ & = \sf \dfrac{5}{6}\end{aligned}[/tex]

Part (b)

[tex]\textsf{Addition Law}: \quad\sf P(A\:or\: B) = P(A)+P(B)-P(A\:and\:B)[/tex]

Given:

[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]

[tex]\sf P(A\:and\:B)=\dfrac{3}{30}\quad \textsf{(where the circles overlap)}[/tex]

[tex]\begin{aligned}\implies \sf \sf P(A\:or\: B) &= \sf P(A)+P(B)-P(A\:and\:B)\\\\& =\sf \dfrac{5}{6}-\dfrac{3}{30}\\\\ & =\sf \dfrac{25}{30}-\dfrac{3}{30}\\\\ & =\sf \dfrac{22}{30}\\\\ & = \sf \dfrac{11}{15}\end{aligned}[/tex]

Or, we can simply read P(contains apple or blueberry) from the Venn diagram.  

P(A or B) is the total of the numbers inside the circles divided by the total number of smoothies:

[tex]\sf P(A\:or\:B) = \dfrac{12+3+7}{30}=\dfrac{22}{30}=\dfrac{11}{15}[/tex]

Part (c)

For two events, A and B, where A and B are mutually exclusive:

[tex]\sf P(A \: or \: B)=P(A)+P(B)[/tex]

Given:

[tex]\sf P(A)+P(B)=\dfrac{5}{6} \quad \textsf{(from part a)}[/tex]

[tex]\sf P(A\:or\:B)=\dfrac{11}{15} \quad \textsf{(from part b)}[/tex]

[tex]\sf As\:\dfrac{11}{15}\neq \dfrac{5}{6} \implies P(A \: or \: B)\neq P(A)+P(B)[/tex]

Therefore, choosing a smoothie containing apple and choosing a smoothie containing blueberry are NOT mutually exclusive events.

Answer:

y=3x-2

For plotting graph we have to put some x values in above equation then we get y Ans

when x=0,y=-2

when x=1,y=1

when x=2,y=4

when x=-1, y=-5

when x=-2, y=-8

Step-by-step explanation:

Answer:

y=3x-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

z - 7 ≥ 0

z ≥ 7

| z - 7 | = z - 7, z ≥ 7

| z - 7 | = -z + 7, z < 7

z - 9 ≥ 0

z ≥ 9

| z - 9 | = z - 9, z ≥ 9

| z - 9 | = -z + 9, z < 9

| z - 7 | = -z + 7

| z - 9 | = -z + 9

|z - 7| - |z - 9|

-z + 7 - (-z + 9)

-z + 7 + z - 9

= -2

A. Substitute x = 3 into the equation of the line of best fit.

B. Estimate of the inventory on day 3 is: 3 (in hundreds).

The equation of the line of best fit models the relationship between two variables, which can be used for making estimates or predictions.

The equation of the line of best fit given is: f(x) = -1/3x + 4, where:

A. To estimate the inventory after day 3, substitute x = 3 into the equation of the line of best fit.

B. Plug in x = 3 into f(x) = -1/3x + 4

f(3) = -1/3(3) + 4

f(3) = 3

Estimate of the inventory on day 3 is: 3 (in hundreds).

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Based on the correlation coefficient between sodium and the calories in the meal, we can say that there is a strong positive correlation, and it is not likely causal.

Correlation coefficients are used to show the strength of a correlation between two variables. They go from -1 to 1 and the closer to figure is to 1, the stronger the correlation between the two.

If the figure is close to 1 (instead of -1) as is the case here it means that there is a positive correlation.

Correlation however, does not mean causation which is why there is a strong positive correlation between Sodium and calories with a coefficient of 0.74, but its likely that this isn't causal.

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Answer:

Multiplying by 3 isolates x on one side of the equation.

Step-by-step explanation:

When solving an algebraic equation, you want to isolate the variable on

one side of the equation. By isolating the variable, you can see what the

variable is equal to.

Hope it helps, have a fantastic day.

Answer:

16.97

Step-by-step explanation:

Therefore b= 16.97

The new price of the shoe before taxes will be $ 35.75.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.

It cost Nike $55 to make the "Kyrie 5".

You just found a coupon for 35% off.

Then the new price of the shoe before taxes will be

⇒ (1 - 0.35) x 55

⇒ 0.65 x 55

⇒ $ 35.75

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Step-by-step explanation:

answer 3 is correct.

the result is clearly shifted (translated) and then enlarged (dilation).

the dimensions of the side lengths all follow the same scale factor (2).

The domain of the given relation will be { - 1,2,3,4}.

The domain of the function is defined as the set of all the possible values of the function.

So here we have the ordered pairs given as:-

{ (-1,- 6), (2, - 6), (3,5), (4,0), (4,7)}

Here the possible values for the input of the functions are { - 1,2,3,4}.

Therefore the domain of the given relation will be { - 1,2,3,4}.

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Answer: 64 m^3

Step-by-step explanation:

V=1/3*a^2*h

V = 1/3*64*3

V=64 m^3

Answer:

64 m³

Step-by-step explanation:

Formula

[tex]\textsf{Volume of a square based pyramid}=\dfrac{1}{3}a^2h[/tex]

where:

Given:

Substituting the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume}& =\dfrac{1}{3} \cdot 8^2 \cdot 3\\\\& = \dfrac{3}{3} \cdot 64\\\\& = 1 \cdot 64\\\\& = 64\:\sf m^3\end{aligned}[/tex]

Answer:

(15/360)*whatever the circumferance is

Step-by-step explanation:

Length of arc = 2π * radius * angle/360

And 2π * radius= circumference

Therefor we can replace that in the eqaution so we can do

circumference *angle/360=lengnth of arc

Answer:

To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:

V = l * w * h

In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:

21,904 ft3 = l * w * (8ft)

You are also told that the length is 2 times the width. Written as an equation, you would say that

l = 2w

Now, you can substitute that 2w for l to get the equation:

21,904 ft3 = (2w) * w * 8ft

We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that

21,904 ft3 = 2w2 * 8ft

Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get

2738 = 2w2

Then divide both sides by 2 to get

1369 = w2

Finally, for this portion, take the square root of 1369 to get

w = 37 feet.

But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.

The final answer is that the width of the pool is 37 feet and the length is 74 feet.

You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.

If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.

Step-by-step explanation:

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A, the difference between two cylinders with the same height and different radii.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Since the shape of a paper towel is like a cylinder, therefore, the composition that produces a solid with the same shape and dimensions as the roll of the paper towel is a difference between two cylinders with the same height and different radii.

Hence, the correct option is A.

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Answer :

[tex]\boxed{D) \sqrt{119} \: cm}[/tex]

Solution :

In the above figure, the line that is drawn from the centre of the given circle to the targent PQ is perpendicular to PQ.

And So, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get ,

[tex]\Longrightarrow\: OQ^2 = OP^2 + PQ^2[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: (12)^2 = 5^2+PQ^2[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ^2 = 144-25[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ^2 = 119[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\: PQ = \sqrt{119} [/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

So, option D) √119 cm is the length of PQ.

Answer:

132

Step-by-step explanation:

surface area of a triangular prism

132 ft is needed for the entire outside

its a 3 4 5 right triangle

10 is the height

Answer:

The correct answer is the last one, [tex]\frac{\pi }{6}[/tex].

Step-by-step explanation:

Assuming you need this urgently so I won't explain.

Hope this helps:) Goodluck!

Answer:

5π/6, 7π/6

Step-by-step explanation:

Solving :

cos⁻¹ (-[tex]\frac{\sqrt{3} }{2}[/tex])

cos⁻¹ (-cos30°)

cos 30° is negative in Quadrant II and Quadrant III

Value in QII :

Value in QIII :

The answer is 5π/6, 7π/6

Answer:

62

Step-by-step explanation:

all you do for this is take 496 and divide it by 8, which gives you 62, if you still need help explain I can reply with a step by step of showing how to divide

Answer:

5600x10=56000

56000=B ten thousands

Answer:

Ten Thousands

Step-by-step explanation:

5,600x10=56000

So the 5 will be in the ten thousand place if u get a chart/

ignore the numbers on the chart

Answer:

t = 8 days i saw it on a website if i recall its the answer

Step-by-step explanation:

speed = distance/time

4 P = 1 House / 10 Days

P = 1 House / 40 Days

Let T = Time it takes for five painters.

5 P = 1 House / T

5(1/40) = 1 /T

1/8 = 1 /T

T = 8 Days

Answer:

Step-by-step explanation:

5x-2y-12=0

5x-2y+12-12=0+12

5x-2y=12

5x-5x-2y=12-5x

-2y=12-5x

(-2y)/-2=(12-5x)/-2

y=5/2x-6

slope= 5/2x up 5 over 2

y-intercept is -6

Answer:

x = 0.7401 ± 0.7401i, x = 0

Step-by-step explanation:

(6 • (x^2)) +  5x^6  = 0

(2•3x^2) +  5x^6  = 0

5x^6 + 6x^2 = x^2 • (5x^4 + 6)

x^2 • (5x^4 + 6) = 0

x^4 = -6/5 = -1.200

x  =  ∜ -6/5

⇒ Proven by the equations, there are no real solutions, so we can use imaginary i, or zero as our answer.

→ x = 0

→ x = 0.7401 ± 0.7401i