What is the domain of the relation R = {(-1,1), (2,3), (4,5), (5,6)}?

Answer:

2m/s/s

Step-by-step explanation:

It was 0 m/s/s before, and now it is 10 / 5 = 2 m/s/s

The cost of wrapping both boxes would be = $1.13

Surface Area of a rectangular prism = 2 (lh +wh + lw )

where length = 0.6

width = 1

height =1.2

The surface area of Box A

= 2( 0.6×1.2+1×1.2+0.6×1)

= 2( 2.52)

= 5.04ft²

where length = 0.5

width = 1.6

height =1.6

Area = 2(0.5×1.6+1.6×1.6+0.5×1.6)

= 2(4.16)

= 8.32ft²

The total area of the boxes = 5.04+8.32 = 13.36

But 6.79 = 80 ft²

X = 13.36ft²

make X the subject of formula;

X = 13.36×6.79/80

X = 90.7144/80

X= $1.13

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(A) The petri dish has a radius of 9 cm and a diameter of 18 cm. We must integrate the density function over the circle's area to determine the number of organisms in the dish:

Number of organisms in dish = ∫₀⁹⁶πx² f(x) dx

(b)

I. Along the line of nutrients, we can cut the petri dish into thin, concentric rings with a width of x. Each slice will have an area of 2xxx and a radius of x.

ii. The density f(xi) multiplied by the area of the slice gives a rough estimate of the number of organisms in the ith slice:

Number of organisms in ith slice ≈ f(xi) * 2πxiΔx

iii. The number of organisms in each slice can be added together to obtain a Riemann sum, which can be used to estimate the total number of organisms in the petri dish:

where the total is calculated across all slices.

Total number of organisms ≈ ∑ᵢ f(xi) * 2πxiΔx

iv. We must take the limit as x approaches 0 to obtain an integral, which will allow us to determine the precise number of organisms in the petri dish:

Number of organisms in dish = ∫₀⁹ f(x) * 2πx dx

In this case, each slice has a width dx equal to its thickness as we integrate across the dish's radius. The radius of the circle at radius x determines the factor of 2x.

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Answer:

Step-by-step explanation:

Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.

We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:

x + 3x = 136

Simplifying this equation, we get:

4x = 136

Dividing both sides by 4, we get:

x = 34

This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:

3x = 3(34) = 102

So, 102 sodas were sold.

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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The Distance between Amanda and the rope is approximately 2317.9 ft.

Let's denote the distance between Amanda and the rope by x. Then, the distance between Jeremiah and the rope is 4000 - x (since they are separated by a horizontal distance of 4000 ft). We can use trigonometry to find the value of x.

First, let's consider Amanda's angle of elevation. We can see that the triangle formed by Amanda, the rope, and the helicopter is a right triangle with angle 60°. Therefore, we have:

tan(60°) = x/h

where h is the height of the helicopter above the ground. Solving for h, we get:

h = x/tan(60°)

Next, let's consider Jeremiah's angle of elevation. We can see that the triangle formed by Jeremiah, the rope, and the helicopter is also a right triangle, but with angle 30°. Therefore, we have:

tan(30°) = (4000 - x)/h

Substituting the expression for h that we obtained earlier, we get:

tan(30°) = (4000 - x)/(x/tan(60°))

Simplifying this expression, we get:

tan(30°) = (4000tan(60°) - x)/x

Solving for x, we get:

x = 4000tan(60°)/(tan(60°) + √3)

Using a calculator, we can evaluate this expression to get:

x ≈ 2317.9 ft

Therefore, the distance between Amanda and the rope is approximately 2317.9 ft.

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer: 5x^3+28x+8

Step-by-step explanation:

There are multiple steps to this:

First perform distributive property to each set of parentheses:

ie. 6x(x+5) = 6x*x + 6x*5= 6x^2+30x

6x^2+30x+8-2x-6x^2+5x^3

Combine like terms giving you your answer:

5x^3+28x+8

Hope this helps :)

Answer:

$5.02

Step-by-step explanation:

The unpaid balance method is a common method used by credit card companies to calculate finance charges. It determines the finance charge based on a portion of the previous balance you have not yet paid.

Equations to use:

\(\boxed{\begin{minipage}{9.7cm}\phantom{w}\\Periodic (monthly) rate = annual interest rate $\div$ 12\\\\Finance Charge = previous balance $\times$ periodic rate\\\\Unpaid Balance = previous balance + finance charge +\\\phantom{wwwwwwwwwww} new purchases - returns - payments\\\end{minipage}}\)

The periodic rate is the interest rate charged over a certain number of time periods. The interest on a credit card is usually calculated monthly, so if the annual interest rate is 21%, then the periodic (monthly) rate is:

\(\text{Periodic Rate}=\dfrac{21\%}{12}=1.75\%=0.0175\)

The unpaid balance is "last month's balance", which is $385.

Calculate the finance change by multiplying the previous balance (last month's balance) by the periodic rate:

\(\begin{aligned}\text{Finance change} &=\rm previous\; balance \times periodic\;rate \\&=\$385 \times 0.0175 \\&= \$6.7375\end{aligned}\)

Calculate the unpaid balance by subtracting the returns and payments from the sum of the previous balance, finance charge and new purchases:

\(\begin{aligned}\rm Unpaid \; Balance &= \rm previous\; balance + finance\;charge +new \;purchases\\&\phantom{=w}\rm - returns - payments\\&= \$385 + \$6.7375 + \$303 - \$158 - \$250 \\&= \$286.7375\end{aligned}\)

Finally, to calculate the current month's finance charge, multiply the unpaid balance by the periodic rate:

\(\begin{aligned}\text{Current month's finance charge}&=\rm unpaid \;balance\times periodic \;rate\\&=\$286.7375 \times 0.0175 \\&= \$5.02\; \text{(nearest cent)}\end{aligned}\)

Therefore, the current month's finance charge is $5.02 to the nearest cent.

T(x-7, y+1)

Step-by-step explanation:

Subtract the second number x and the second number y by the first x and the first y. x2-x1, y2-y1

the ratio of the side length of the smaller triangle to the side length of the larger triangle: the area of the smllest triangle is 64ft²

At the point when we have similar figures, its lengths have a constant ratio. For this situation, the ratio from the smallest to the biggest is:

r = 8/9

The areas of similar figures are connected with the square of the ratio of the lengths, that is:

\(r^{2}\) = \(A_{smallest \\\)/ \(B_{biggest\) =  \(A_{2} / A_{1}\)

\(A_{2}\) =  \(r^{2}A_{1} = (8/9)^{2}. 81ft^{2} = 64ft^{2}\)

In this way, the area of the smllest triangle is 64ft².

This means that the ratio of the lengths of the briefest side to the hypotenuse of any 30-60-90 right triangle is 1:2. Consequently, On the off chance that a triangle is a 30-60-90 right triangle, the ratio of the sides (short leg:long leg:hypotenuse) is 1:√3:2

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Answer:

Step-by-step explanation:

the value of b is 0.

the base with the power 0 is always 1

Given,

Rate of free fall = 216 km/h

Solution,

km/h to m/s is converted as follows :

\(216\ \dfrac{km}{h}=216\times \dfrac{1000\ m}{3600\ s}\\\\=60\ m/s\)

So, the rate of fall is 60 m/s.

If t = 20 s

Assume, initial velocity = 0

It will move under the action of gravity.

Using equation of motion,

\(h=ut+\dfrac{1}{2}gt^2\\\\h=0+\dfrac{1}{2}\times 10\times 20^2\\\\h=2000\ m\)

Hence, this is all for the solution.

The least common multiple of 10, 25 and 30 is 150.

Hope this helps ! :)

Answer:

35 oz

Step-by-step explanation:

cashew is 5×3 = 15

almonds 5

peanuts 5+10= 15

15+15+5 = 35 oz

Answer:

thing is im in middle school

dunno if i can do college stuff

sometimes i can do highschool

grab some snacks tho oh yeah here are your utensils️

Step-by-step explanation:

y > -12x + 9

Slope intercept form is y = mx + b where m is slope and b is the y intercept. Since this equation is an inequality, we will use the > instead of =.

We have to subtract 12x from both sides to get it on the opposite side as the y.

12x + y -12x > 9 - 12x

This leaves us with y > 9 - 12x

Then we rearrange the terms on the right side to get it in y > mx + b form leaving us with the following:

y > -12x + 9

Answer:

D. 286.5 in.^2

Step-by-step explanation:

3 X 7.5+ 3 X 11.5 + 3 X 7.5+ 11.5 X 3 + 7.5 X 11.5 + 7.5 X 11.5=

22.5 + 34.5 + 22.5 + 34.5 + 86.25 + 86.25=

total surface area= 286.5 in.^2

Answer:

D)

Step-by-step explanation:

Ok when i saw this ^5 that means the power of five i honestly don't know this is my best guess

Answer:

30.57%

Step-by-step explanation:

Dylan bought it for 3600.

Kirtim bought it from Dylan for 3600+205 = 3805

Aayush bought it from Kirtim for 4968.

that difference (profit for Kirtim) = 4968 - 3805 = 1163

Kirtim's initial 100% = 3805

1% = 100%/100 = 3805/100 = 38.05

now we want to know how many % in relation to his buying cost this 1163 selling profit is.

that means we need to see how often 1% fits into that amount.

%profit = profit / 1% cost = 1163 / 38.05 = 30.57%

=>

Kirtim made a profit of 30.57%.

Answer:

Subtraction Property of Equality

Step-by-step explanation:

you should subtract both side with 7 first.

Answer:

Either 2/3 or (0, 10/3)

Step-by-step explanation:

Use the slope formula to find the slope  

m = 2 /3

and the y-intercept

The value of  y  at the point where a curve crosses the y-axis.

(0, 10/3)

Answer:

Either 2/3 or (0, 10/3)

Step-by-step explanation:

Use the slope formula to find the slope  

m = 2 /3

and the y-intercept

The value of  y  at the point where a curve crosses the y-axis.

(0, 10/3)

Answer:

Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.

F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b

Answer:

\(274\,\text{in}^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)

Answer:

Step-by-step explanation:

You can observe a representation of this problem in the image attached.

Notice that the grass seed is gonna be put only in the green zone, out of the pond. So, we need to find each area and subtract them.

\(A_{garden}= 14 \times 9 =126 \ m^{2} \\A_{pond}=2.4 \times 3.8 = 9.12 \ m^{2}\)

The difference is

\(A_{seed}=126 - 9.12 = 116.88 \ m^{2}\)

Now, according to the problem, one box of grass seed covers 15 meters of the garden, let's divide this number with the seed area.

\(n=\frac{116.88}{15} \approx 7.792\)

Therefore, Kayla needs 8 boxes of grass seed to cover the whole garden without including the pond.

9514 1404 393

Answer:

Step-by-step explanation:

Occasionally, you're asked about limits at some point where a function is continuous. At such a point, the limit is simply the value of the function.

__

Here, you're asked about limits at values of x where the function has discontinuities. That is, you  must lift your pencil when you draw the function graph through that area.

The limit from the left (indicated by a superscript minus sign) is the point you end up at when you follow the graph left to right to the x-value of interest. In this graph, the left-limit at x=0 is -1, and the left-limit at x=2 is +2.

The limit from the right (indicated by a superscript plus sign) is the point you end up at when you follow the graph right to left to the x-value of interest. In this graph the right-limit at x=2 is 0, and the right-limit at x=0 is -2.

When the left- and right-limits are the same, the limit is said to exist. When they are different, we say the limit does not exist.

A function is "continuous" at a point if (a) the limit at that point exists (left- and right-limits are the same), and (b) the function is defined at that point to be the limit value.

Here, you will notice that the function value is the solid dot that is present on the vertical line where the discontinuity occurs. g(0) = -1, g(2) = 1.

__

With these things in mind, we can answer the questions as follows:

  \(\displaystyle\text{(a) }\lim_{t\to0^-}g(t)=-1\\\\\text{(b) }\lim_{t\to0^+}g(t)=-2\\\\\text{(c) }\lim_{t\to0}g(t)\quad\text{DNE}\\\\\text{(d) }\lim_{t\to2^-}g(t)=2\\\\\text{(e) }\lim_{t\to2^+}g(t)=0\\\\\text{(f) }\lim_{t\to2}g(t)\quad\text{DNE}\\\\\text{(g) }g(2)=1\)