A circles circumference
is approximately 76 cm.
Estimate the radius
diameter, and area of the
circle

If Mark and Doug work at the mall and their total number of combined hours was 13 more hours than Mark worked, The number of hours they work in total is 47 hours.

Let x represent the time Doug  worked

let 3x - 5 represent the number of hours Mark worked

Hence,

x + 3x - 5 = 3x -5 +13

4x-5=3x-5+13

4x-5=3x+8

Add 5 to both side

4x-5+5 =3x+8+5

simplify

4x =3x +13

subtract 3x from both side

4x -3x = 3x + 13 =3x

1x = 13

x =13/1

x =13 (Doug)

Hence,

3x -5 where x = 13

3 (13) -5

= 39 -5

= 34 hours (Mark)

Total hours

(Doug + Mark)

= 13 hours + 34 hours

= 47 hours

Therefore the total hours is 47 hours.

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Answer:

\(P = 48 in\),\(A= 120in^2\)

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

Answer:

The formula for calculating the surface area of a cuboid is as follows.

Surface Area of Cuboid = 2lw + 2lh + 2hw

Where,

Therefore,

Surface Area of Cuboid = (2 x 20 x 5) + (2 x 20 x 10) + (2 x 10 x 5)

                                         = 200 + 400 + 100

                                         = 700 \(cm^{2}\)

Answer:

b the area

Step-by-step explanation:

you will need to see if you have enough area for the microwave to fit

These are the transformed functions for each of the four transformations mentioned.

Vertical translation (shift) by k units: f(x) + k

Horizontal translation (shift) by h units: f(x - h)

Vertical stretch/compression by a factor of c: c * f(x)

Reflection across the x-axis: -f(x)

Replace k, h, and c with the desired values to obtain the specific transformed functions.
Here are four common types of transformations:
Vertical translation (shift) by k units: f(x) + k
Horizontal translation (shift) by h units: f(x - h)
Vertical stretch/compression by a factor of c: c * f(x)
Reflection across the x-axis: -f(x)
For the function f(x) = 2x + 3,

let's apply these transformations:
Vertical translation (shift) by k units: f(x) + k -> 2x + 3 + k (where k is the number of units shifted vertically)

Horizontal translation (shift) by h units: f(x - h) -> 2(x - h) + 3 (where h is the number of units shifted horizontally)
Vertical stretch/compression by a factor of c: c * f(x) -> c(2x + 3) (where c is the stretch/compression factor)
Reflection across the x-axis: -f(x) -> -(2x + 3).

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Answer:

Step-by-step explanation:

y + 4 = -2(x - 0)

y + 4 = -2x + 0

y = -2x - 4

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

8

Step-by-step explanation:

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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The equation of the circle with center (-4, 4) and passing through (-2, 4) is \((x + 4)^2 + (y - 4)^2 = 4.\)

We have,

To determine the equation of a circle, we need the center coordinates and the radius. The center coordinates are given as (-4, 4), and we have a point on the circle as (-2, 4).

The distance between the center (-4, 4) and the point on the circle (-2, 4) represents the radius of the circle.

Using the distance formula.

\(radius = √[(x_2 - x_1)^2 + (y_2 - y_1)^2]\\= \sqrt{(-2 - (-4))^2 + (4 - 4)^2}\\= \sqrt{2^2 + 0^2}\\= \sqrt{4}\\= 2\)

Now that we have the center coordinates (-4, 4) and the radius 2, we can write the equation of the circle in standard form:

\((x - h)^2 + (y - k)^2 = r^2\)

Substituting the values:

\((x - (-4))^2 + (y - 4)^2 = 2^2\\(x + 4)^2 + (y - 4)^2 = 4\)

Therefore,

The equation of the circle with center (-4, 4) and passing through (-2, 4) is \((x + 4)^2 + (y - 4)^2 = 4.\)

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Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve for f, we can cross-multiply the equation:

f/40 = 10/f

Multiplying both sides by 40f gives:

f^2 = 400

Taking the square root of both sides yields:

f = ±20

Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:

f = 20

Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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Answer:

13%

Step-by-step explanation:

338/2600

13/ 100

I hope it help

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer:

y=8

Step-by-step explanation:

4x8=32

Answer:

y=8

Step-by-step explanation:

Let's solve your equation step-by-step.

32=4y

Step 1: Flip the equation.

4y=32

Step 2: Divide both sides by 4.

4y/4=32/4

y=8

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

The price per foot is $3.09

A 3 yard roll of butcher paper costs $9.27

= 9.27/3

= $3.09

Hence the price per foot is $3.09

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Answer:

y = ¼x

Step-by-step explanation:

The slope-intercept form is y = mx + b where m = slope, and b = y-intercept.

In order to transform the given equation into its slope-intercept form, isolate the y by dividing both sides by 4:

4y = x

\(\frac{4y}{4} = \frac{1*x}{4}\)

y = ¼x + 0, or simply, y = ¼x.

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

x =-48.1

Step-by-step explanation:

-72 + 12 - 2.x = 23 + 13.2

Combine like terms

-60 -2x = 36.2

Add 60 to each side

-2x -60+60 = 36.2+60

-2x = 96.2

divide by -2

-2x/-2 = 96.2/-2

x =-48.1

Answer:

\( = - 48.1\)

Step-by-step explanation:

\( - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

0.325

Step-by-step explanation:

Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport

Given

Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325

Answer:

a) \( P(0<z<1.67)= P(z<1.67) -P(Z<0) = 0.953 -0.5=0.453\)

b) \( P(Z<-0.33) = 0.371\)

c) \( P(Z>0.33) =1-P(Z<0.33) = 1-0.629= 0.371\)

d) \( P(2<z<2.67)= P(z<2.67) -P(Z<2) = 0.996 -0.977=0.019\)

Step-by-step explanation:

Assuming the following questions:

a. Between 20 and 25 gallons

Let X the random variable that represent the sports drink consumption of a population, and for this case we know the distribution for X is given by:

\(X \sim N(20,3)\)  

Where \(\mu=20\) and \(\sigma=3\)

We are interested on this probability

\(P(20<X<25)\)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

\(z=\frac{x-\mu}{\sigma}\)

And if we find the z score for each limit we got:

\( z = \frac{20-20}{3}=0\)

\( z = \frac{25-20}{3}=1.67\)

And we can use the normal standard distirbution table and we got:

\( P(0<z<1.67)= P(z<1.67) -P(Z<0) = 0.953 -0.5=0.453\)

b. Less than 19 gallons

\( z = \frac{19-20}{3}=-0.33\)

And using the normal table we got:

\( P(Z<-0.33) = 0.371\)

c. More than 21 gallons

\( z = \frac{21-20}{3}=0.33\)

And using the normal table and the complement rule we got:

\( P(Z>0.33) =1-P(Z<0.33) = 1-0.629= 0.371\)

d. Between 26 and 28 gallons

\( z = \frac{26-20}{3}=2\)

\( z = \frac{28-20}{3}=2.67/tex]

And we can use the normal standard distirbution table and we got:

\( P(2<z<2.67)= P(z<2.67) -P(Z<2) = 0.996 -0.977=0.019\)

Answer:

From the origin, go left 2 then up 3

Step-by-step explanation:

negative x value means move left, positive y value means move up

Answer:

go left 2 and go up 3

Little note:

Hope this helps

Answer:

25

Step-by-step explanation:

-28+53

Hope this helps! :)

Answer:

Is there an image of the table with the data?

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Moores law that number of transistors per IC Prediction = 4,096,000 and Prediction = 25.6 trillion.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. For example, the probability of flipping a fair coin and getting heads is 0.5, while the probability of rolling a six on a fair six-sided die is 1/6 or approximately 0.1667.

In mathematical terms, probability is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. Probability theory is widely used in many fields, including statistics, finance, science, engineering, and economics, to help predict and analyze the likelihood of various outcomes and make informed decisions based on the probabilities involved.

According to the question:

Part a: Moore's Law predicts that the number of transistors per IC doubles every 18-24 months. Since 20 years is approximately 10 doublings (20/2), we can estimate the number of transistors in 1992 to be \(4,000 * 2^{10} = 4,096,000.\)

Prediction = 4,096,000

Part b: Based on the chart, the number of transistors per IC in 2016 appears to be around 10 billion \((1 * 10^{10})\)

Using Moore's Law, we can estimate the number of transistors per IC in 2040 to be \(1 * 10^{10} * 2^{24/18} = 25.6 * 10^{12} (or 25.6 trillion)\).

Prediction = 25.6 trillion

Part c: The prediction in Part b may not be entirely believable, as there are physical limits to the number of transistors that can be placed on a single chip. Moore's Law has been slowing down in recent years, with transistor density growth rates dropping below historic trends. Additionally, new technologies beyond traditional silicon-based chips may become necessary to continue improving transistor density at the same pace as in the past. Therefore, while the prediction is technically possible, it may not be achievable without significant breakthroughs in semiconductor technology.


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