A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 540.08 yd. What is the surface area of the sphere? Use 3.14 for pi.

Answer:

75 gophers (about)

Step-by-step explanation:

We will use continuous compounding interest formula:

[tex]P(t)=P_0e^{rt}[/tex]

Where

P(t) is final value (at time t)

P_0 is initial value

r is the compounding rate

t is the time period

Given:

P(t) = 78

r is 1.5% or 1.5/100 = 0.015

t is 3

We solve for P_0, what we want, using algebra as shown below:

[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]

So, the initial population was 75 gophers.

The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.

To solve this problem, we can use the following exponential growth function:

P(t) = P_0 * e^(rt)

where:

P(t) is the population at time t

P_0 is the initial population

r is the annual growth rate

t is the time in years

We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.

So, we can plug in the following values into the exponential growth function:

P(3) = 78 = P_0 * e^(0.015 * 3)

Dividing both sides by e^(0.015 * 3), we get:

P_0 = 78 / e^(0.015 * 3)

Using a calculator, we can evaluate P_0 to be approximately 75.0.

Rounding up to the nearest whole number, we get an initial population of 75 gophers.

For such more question on function

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Answer:

The population will reach 20,400 after 6 years.

Step-by-step explanation:

Exponential function:

[tex]y(t)=y_0(1+r)^t[/tex]

y(t)= Population after t years

[tex]y_0[/tex] = initial population

r= rate of grow

t= time.

A town has a population of 17,000 and grows at a rate 3% every year.

y(t)= 20,400, [tex]y_0[/tex] = 17,000, r=3%=0.03, t=?

[tex]20,400=17,000(1+0.03)^t[/tex]

[tex]\Rightarrow \frac{20,400}{17,000}=(1.03)^t[/tex]

[tex]\Rightarrow \frac{102}{85}=(1.03)^t[/tex]

Taking ln function both sides

[tex]\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|[/tex]

[tex]\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|[/tex]

[tex]\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}[/tex]

⇒ t = 6 year.

The population will reach 20,400 after 6 years.

Answer:

6

Step-by-step explanation:

deltamath

Answer: 12inches

Step-by-step explanation:

Area of a circle= 113.04square inches

Area of a circle =pir^2

Pi=3.14

R=?

So we are looking for the radius and from there we will get the diameter

Area=pir^2

113.04=3.14×r^2

R^2= 113.04/3.14

R^2=36

R=square root of 36

R= 6

Diameter =2r

Diameter = 2×6

Diameter = 12inches

Answer:

12 inches

Step-by-step explanation:

3.14 × r² = 113.04

r² = 36

r = 6

Diameter = 2r = 12

Given:

θ = 54°

Radius = 10 in

To find:

The arc length of PQ

Solution:

Arc length formula:

[tex]$\text{Arc length}=2 \pi r\left(\frac{\theta}{360^\circ}\right)[/tex]

[tex]$\text{Arc length}=2 \times 3.14 \times 10\left(\frac{54^\circ}{360^\circ}\right)[/tex]

                 = 9.42 in

The arc length of PQ is 9.42 inches.

Answer:

y = 40 degrees can i have branliest

Step-by-step explanation:

All angles in a triangle add up to 180

180 - 50 = 130

3y + 10 = 130

3y = 120

y = 40

Answer:

c

Step-by-step explanation:

m = the number of miles driven

Company A cost = 76    

[they charge $76 for unlimited mileage, so they don't charge by the miles driven]

Company B cost =  0.70m + 55  

[they charge an initial fee of $55 plus $0.70 per mile(m)]

For what mileages will Company A charge less than Company B?

Company A cost < Company B cost  ----->   76 < 0.70m + 55      

To solve for m, isolate/get the variable "m" by itself in the inequality:

76 < 0.70m + 55     Subtract 55 on both sides

76 - 55 < 0.70m + 55 - 55

21 < 0.70m     Divide 0.70 on both sides to get "m" by itself

[tex]\frac{21}{0.70} <\frac{0.70m}{0.70}[/tex]

30 < m      [m is any number greater than 30]

Company A will charge less than Company B for mileages over/greater than 30.

Final answer:

Company A will charge less than Company B when more than 30 miles are driven; the inequality used to determine this is 76 < 55 + 0.70m, and after solving, it shows that m > 30.

Explanation:

To find out for what mileages Company A will charge less than Company B, we need to set up an inequality based on the given price structures for both companies:

Company A charges a flat rate of $76 per day, regardless of mileage.

Company B charges an initial fee of $55 plus $0.70 per mile driven.

The inequality to represent this scenario is:

76 < 55 + 0.70m

To solve for m (the number of miles driven), we subtract 55 from both sides:

21 < 0.70m

Then, divide both sides by 0.70 to isolate m:

m > 30

So, Company A will charge less than Company B when Bob drives more than 30 miles.

The slope-intercept form of the equation 4x + 3y = -3 is y = -4/3x - 1. The slope of the line is -4/3 and the y-intercept is -1.

The question asks to convert the equation 4x + 3y = -3 into slope-intercept form, and simplify all fractions. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

To transform the given equation into this form, we need to express it in terms of y. Here are the steps:

In this equation, the term -4/3 is the slope and the -1 is the y-intercept. That means the line decreases for every 4 units in the y-axis when it increases 3 units in the x-axis.

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Answer:

400

Step-by-step explanation:

1 hour = 5 pieces • $2

1 hour = $10 bcas each piece you make is $2

40 hours = $400 because you get $10 per week

You earn $400 per week

Answer:

$400

Step-by-step explanation:

S x H  = (1 x 5 x 2) x 40

S x H  = (1 x 10)  x 40

S x H  = 10 x 40

S  =  400

S  = $400    H = 40

Answer:

6 7/8

Step-by-step explanation:

Since 1 cup of rice is added to 2 3/4 water

We are to determine the Amount of water to be to 2 1/2 cups of rice

Let the unknown number for water be x

So let's solve

1 cup of rice=11/4 water

5/2 cup of rice=x water

Cross multiply

x=5/2×11/4

x=55/8

X=6 7/8

Therefore,6 7/8 water is needed

Answer:

d-(9,1)

Step-by-step explanation:

Answer:

(9,1)

Step-by-step explanation:

correct on edge

Step-by-step explanation:

According to BODMAS

the first way to evaluate the expression is starting from brackets.,

=3 * 9 -27 / 9

= 3 * 9 - 3

= 27- 3

=24

Answer:

Parenthesis.

Step-by-step explanation:

Parenthesis

Exponent

Multiply or

Divide

Add or

Subtract

PEMDAS is the order to solve expressions like so.

Step-by-step explanation:

M is the mid point of AB

here given A ( - 7 , -7) and M ( -6 , -1) Let the coordinates of point B be ( x1, y1)

Now

( - 6 , -1 ) = {( x1 - 7)/ 2 , ( y1 - 7) / 2}

Equating

-6 = x1 -7 -1 = y1 - 7

2. 2

-12 = x1 - 7. -2 = y1 - 7

x1 = -12 +7. y1 = -2 +7

Therefore x1 = - 5. Therefore y1 = 5

Therefore the coordinates of B is ( -5 , 5)

Answer:

the coordinates of B is ( -5 , 5)

Step-by-step explanation:

The volume of the pyramid is  167.6 cube inch (approx).

Step-by-step explanation:

Given,

Each length (l) of the base of the pyramid = 8.3 in

Height(h) of the pyramid = 7.3 in

To find the volume of the pyramid.

Formula

Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height

Area of the base = l²

Now,

The volume of the pyramid =  [tex]\frac{1}{3}[/tex]×l²×h

=  [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)

The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.

To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.

Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.

We can see that b1 = 18, b2 = 24, and h = 5

So, we can just substitute these in.

A = 1/2(18 + 24)5

A = 1/2 * 42 * 5

A = 21 * 5

A = 105

So, the answer is C. 105 sq cm

Answer:

105

Step-by-step explanation:

you just have to plug in your variables

[tex]-15x^2y^2+25xy^2=5xy^2(-3x+5)\:or\:-5xy^2(3x-5)[/tex]

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Answer:

3g

Step-by-step explanation:

Since 5p=3g

5p=x

So let's solve by cross multiplying

5px=3g×5p

5px=15gp

Divide both sides by 5p

x=3g

Therefore the final answer is 3g

Answer:

The length of the sides is 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Since the diagonal divide a square into 2 45-45-90 triangles:

The diagonal is the hypotenuse of the triangle

Divide 16 by [tex]\sqrt{2}[/tex] and you will get 8[tex]\sqrt{2}[/tex].

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Answer:

J

Step-by-step explanation:

As you can see, the peak occurs at (2,6). That means that all values below 6 are in the range.

Answer:

Step-by-step explanation:

The division problems 123.4/9.2 and 71.9/6.5 have an estimated quotient of 12 by considering 123.4 as 120, 9.2 as 10, 71.9 as 70, and 6.5 as 6.

The division problems with an estimated quotient of around 12 will be the ones where you divide a number close to 120 by 10. In this case, it comes to be 123.4/9.2 and 71.9/6.5. To estimate the quotient, you can consider 123.4 as approximately 120 and 9.2 as approximately 10. Similarly, 71.9 can be considered as approximately 70 and 6.5 as approximately 6. When you divide these estimate numbers, both quotients are close to 12.

Estimation is a useful skill in Mathematics that allows you to simplify complex problems and get close to the exact answer. It's particularly helpful in situations where you only need a rough estimate and not the exact figure.

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60.56 square feet, the area of the semicircles equates to 12.56 and the rectangle area is 48 so all you have to do is add them

Answer:

It is 60.56 ft2

Step-by-step explanation:

Hope this helps

Answer:

Approximately 53

Step-by-step explanation:

92% of 53 is 48.76, there is no way to use a whole number and get exactly 48, which is why it is approximately

hope this helps

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brainliest is appreciated :)))))

Answer:

14

Step-by-step explanation:

The diameter of a circle is twice the radius

d = 2*r

d = 2*7

d =14 m

Answer:

diameter = 14

Step-by-step explanation:

given that the radius of a circle = 7m

diameter = ?

recall that the formulae for finding the diamer = 2 x radius

diameter = 2 x 7

diameter = 14

Answer:

f (-2)=(-2)-2

= -4

By putting value of x= -2 in f (x)

Answer:

[tex]\huge\boxed{\dfrac{2}{16}=12.5\%}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\dfrac{2}{16}=\dfrac{2:2}{16:2}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{8}\cdot100\%=\dfrac{100}{8}\%=12.5\%\\\\\text{Other method.}\\\\\dfrac{1}{8}=\dfrac{1\cdot125}{8\cdot125}=\dfrac{125}{1000}=\dfrac{125:10}{1000:10}=\dfrac{12.5}{100}=12.5\%[/tex]

(6x-3)+(7x-7)

Hope I helped :d

Answer:

[tex]4x^{2} +x+2[/tex]

Answer:

$3.94

Step-by-step explanation:

You will need to use the compound interest formula for this.

[tex]P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate

n = number of times compounded annually

t = time

Your equation will look like this:

[tex]3.31(1+\frac{.0088}{1} )^{20}[/tex] = 3.94