Solve the following equation for
b
b. Be sure to take into account whether a letter is capitalized or not.

Answer:

1. Option D. 15x²

2. Option C. 3

Step-by-step explanation:

1. Determination of the area of one section.

Length (L) of one section = 25x/5 = 5x

Width (W) of one section = 3x

Area (A) of one section =?

The area of one section can be obtained as follow:

Area (A) = Length (L) × Width (W)

A = L × W

A = 5x * 3x

A = 15x²

Thus, the area of one section is 15x²

2. Determination of the expressions that are equivalent to (p²)³.

We'll begin by simplifying (p²)³. This can be obtained as follow:

(p²)³ = p²*³

(p²)³ = p⁶

Next we shall compare each expression given in the question above to see which will be the same as p⁶.

p × p × p × p × p × p = p¹⁺¹⁺¹⁺¹⁺¹⁺¹

p × p × p × p × p × p = p⁶

p² × p² × p² = p²⁺²⁺²

p² × p² × p² = p⁶

p² × p³ = p²⁺³

p² × p³ = p⁵

Thus,

p² × p³ ≠ p⁶

p⁵ ≠ p⁶

p⁶ = p⁶

SUMMARY

p × p × p × p × p × p = p⁶ = (p²)³

p² × p² × p² = p⁶ = (p²)³

p⁶ = (p²)³

Therefore, 3 expressions are equivalent to (p²)³. Option C gives the correct answer to the question.

Answer:

[tex]M_{st} = (\frac{-2+4}{2}, \frac{-4+6}{2})[/tex]  

[tex]M_{st}=(\frac{2}{2}, \frac{2}{2} )[/tex]

[tex]M_{st}=(1, 1)[/tex]

[tex]M_{cd}=(\frac{-6+4}{2} , \frac{10-8}{2} )[/tex]

[tex]M_{cd}=(\frac{-2}{2} , \frac{2}{2} )[/tex]

[tex]M_{cd}=(-1, 1)[/tex]

Answer:

0.375 dollars

Step-by-step explanation:

1 pound = 16 oz

1 oz = 1/16 pound

2 oz = 2/16

2/16 * 3 = 0.375

Answer: 125.6 ml

Step-by-step explanation:

V = (3.14) (2^2) (10)

V = (3.14) (4)(10)

V= 125.6 cm^3

1 cubic centimeter = 1 milliliter

Answer:

17

Step-by-step explanation:

h(x) = x^2 + 2x + 2​

Let x = -5

h(-5) = (-5)^2 + 2(-5) + 2​

      = 25 -10 +2

    = 17

Answer: The answer is 125 degree(third option)

Step-by-step explanation:

x + 55 = 180 {being co interior angles}

or, x = 180 - 55

so, x = 125

Step-by-step explanation:

The time dilation formula is given by

[tex]F(t) = \dfrac{t}{\sqrt{1-v^2}}[/tex]

where t is the time measured by the moving observer and F(t) is the time measured by the stationary earth-bound observer and v is the velocity of the moving observer expressed as a fraction of the speed of light.

a) If the observer is moving at 80% of the speed of light and observes an event that lasts for 1 second, a stationary observer will see the same event occurring over a time period of

[tex]F(t) = \dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}}[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}} =\dfrac{1\:\text{s}}{\sqrt{1-(0.64)}}[/tex]

[tex]\:\:\:\:\:\:\:=1.67\:\text{s}[/tex]

This means that any event observed by this moving observer will be seen by a stationary observer to occur 67% longer.

b) Given:

t = 1 second

F(t) = 2 seconds

We need to find the speed of the observer such that an event seen by this observer will occur twice as long as seen by a stationary observer. Move the term containing the radical to the left side so the equation becomes

[tex]\sqrt{1-v^2} = \dfrac{t}{F(t)}[/tex]

Take the square of both sides, we get

[tex]1 - v^2 =\dfrac{t^2}{F^2(t)}[/tex]

Solving for v, we get

[tex]v^2 = 1 - \dfrac{t^2}{F^2(t)}[/tex]

or

[tex]v = \sqrt{1 - \dfrac{t^2}{F^2(t)}}[/tex]

Putting in the values for t and F(t) we get

[tex]v = \sqrt{1 - \dfrac{(1\:\text{s})^2}{(2\:\text{s})^2}}[/tex]

[tex]v = \sqrt{1 - \dfrac{1}{4}} = \sqrt{0.75}[/tex]

[tex]\:\:\:\:=0.866[/tex]

This means that the observer must moves at 86.6% of the speed of light.

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]

What is the probability that today is Monday?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]

0.0286 = 2.86% probability that today is Monday.

Answer:

90

Step-by-step explanation:

5x – 2y + (7x – y)

Combine like terms

12x -3y

Let x = 7 and y = -2

12(7) -3(-2)

84 +6

90

Answer:

90

Step-by-step explanation:

Hi there!

We are given this expression:

5x-2y+(7x-y) and we want to evaluate it if x=7 and y=-2

First, let's combine like terms, as that will make it easier for when we substitute the values into the expression

Open up the parentheses

5x-2y+7x-y

Combine like terms

12x-3y

Now substitute 7 as x and -2 as y into the expression

12(7)-3(-2)

Multiply

84+6

Add

90

Hope this helps!

There would likely be no relationship between first name and height of a person in a random sample.

Hope this helps :)

Answer: it’s B. I answered it right now and it said it was correct.

Step-by-step explanation:

McDonald’s fry’s are better than jack in the box’s fry’s.

x=3

Step-by-step explanation:

x+2=5

x=5-2

x=3

Answer:

d) Asking questions to make sure they understand what's being said

Step-by-step explanation:

Asking questions is important for learning and clears up any confusion.

Answer:

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 4 - 1 = 3

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm

The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

Answer:

270.47625

Step-by-step explanation:

249 is the original price

(249/100) · 8.625 = 21.47625 the tax total

249 + 21.47625 = 270.47625

Answer:

$48

Explanation:

> 50 x .20 = $10

$50 + $10= $60

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

> 60 x .20 = $12

$60 - $12= $48

Answer: See below

Step-by-step explanation:

Answer:

Answer below

Step-by-step explanation:

Answer:

Abdul's tank can hold 27 gallons of gas.

Step-by-step explanation:

Given that Abdul's gas tank is 1/3 full, and after he buys 12 gallons of gas, it is 7/9 full, to determine how many gallons can Abdul's tank hold the following calculation must be performed:

1/3 = 0.3333

7/9 = 0.7777

0.777 - 0.333 = 0.444

0.444 = 12

1 = X

12 / 0.444 = X

27 = X

Therefore, Abdul's tank can hold 27 gallons of gas.

Answer:

y  ≤  9

Step-by-step explanation:

3y - 11 ≤ 2y - 2

Subtract 2y from each side

3y-2y - 11 ≤ 2y-2y - 2

y - 11 ≤  - 2

Add 11 to each side

y - 11+11 ≤  - 2+11

y  ≤  9

Answer:

[tex]y \leqslant 9[/tex]

Step-by-step explanation:

[tex]3y - 11 \leqslant 2y - 2 \\ 3y - 2y \leqslant 11 - 2 \\ y \leqslant 9[/tex]

Let S and T denote the two finite sums,

S = 1 + x + x ² + x ³ + … + x ᴺ

T = 1 - x + x ² - x ³ + … + (-x) ᴺ

• If both S = 8 and T = 8 as N goes to infinity:

Then

xS = x + x ² + x ³ + x ⁴ + … + x ᴺ⁺¹

-xT = -x + x ² - x ³ + x ⁴ + … + (-x) ᴺ⁺¹

so that

S - xS = 1 - x ᴺ⁺¹   ==>   S = (1 - x ᴺ⁺¹)/(1 - x)

and similarly,

T = (1 - (-x) ᴺ⁺¹)/(1 + x)

For both sums, so long as |x| < 1, we have

lim [N → ∞] S = 1/(1 - x)

lim [N → ∞] T = 1/(1 + x)

Then if both sums converge to 8, this happens for

S : 1/(1 - x) = 8   ==>   x = 7/8

T : 1/(1 + x) = 8   ==>   x = -7/8

• If the sum S + T = 8 as N goes to infinity:

From the previous results, we have

1/(1 - x) + 1/(1 + x) = 8   ==>   x = ±√3/2

9514 1404 393

Answer:

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

Step-by-step explanation:

The only relation with no repeated x-values is the first one. The first relation is a function.

Answer:

18

Step-by-step explanation:

6^2 plus 3^2 = 324, square root 324 =18

Answer:

[tex]\sqrt{45}[/tex]

Step-by-step explanation:

The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.

Therefore, we have:

[tex]6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}[/tex]

Answer:

240000

Step-by-step explanation:

Represent the exponential equation.

[tex]10000 (5 {t}^{ \frac{2}{3} } + 4) = [/tex]

Replace 8 with t

[tex]10000(5(8) {}^{ \frac{2}{3} } + 4)[/tex]

[tex]10000(5 \times 4 + 4) [/tex]

[tex]10000(24) = 240000[/tex]

The population of the town after 8 month will be 2,40,000.

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Let P be the population of the town after 8 months

According to the given question

The current population of the town = 10,000.

Also, the population of the town is changing at the rate of [tex]4+5t^{\frac{2}{3} }[/tex].

Therefore, the population of the town after 8 month is given by the exponential function

[tex]P = 10000(4+5t^{\frac{2}{3} } )[/tex]

Substitute t =8 in the above equation

⇒[tex]P = 10000(4 + 5(8)^{\frac{2}{3} } )[/tex]

⇒[tex]P = 10000(4 + 5(2^{3}) ^{\frac{2}{3} } )[/tex]

⇒[tex]P = 10000(4+5(4))[/tex]

⇒[tex]P = 10000(24)[/tex]

⇒[tex]P = 240000[/tex]

Hence, the population of the town after 8 month will be 2,40,000.

Find out more information about exponential growth here:

https://brainly.com/question/11487261

#SPJ2

Answer:

35

Step-by-step explanation:

35 because the two angles are added 22 and 123 = 145. 145-180=35

9514 1404 393

Answer:

  2.64 gallons

Step-by-step explanation:

Each gallon costs $3.79, so the number of gallons that can be bought with $10 is ...

  $10/($3.79/gal) = (10/3.79) gal ≈ 2.6385 gal ≈ 2.64 gallons

Answer:

the answer is x because its small

Answer:

Step-by-step explanation:

It’s Xy

Answer:

1

Step-by-step explanation:

Cosine is a trigonometric function that is represented by adjacent divided by the hypotenuse. The side adjacent to angle A is AC and the hypotenuse is AB, so we can say cos(A) = [tex]\frac{AC}{AB}[/tex]. We can do the same for angle B. The side adjacent to it is BC, and the hypotenuse is again AB. So, we can say

cos(B) = [tex]\frac{BC}{AB}[/tex]. We are solving for [tex]\frac{cosA}{cosB}[/tex], so we can substitute the value of those two and solve:

[tex]\frac{\frac{AC}{AB}}{\frac{BC}{AB} }[/tex]

[tex]\frac{AC}{AB} * \frac{AB}{BC} = \frac{AC}{BC}[/tex]

AC is given to be 3 and BC is also 3, so [tex]\frac{AC}{BC}[/tex] is [tex]\frac{3}{3}[/tex] which is just 1.

Using the points stated in the original problem, I have determined the lines for the graph.  

f(x)=3x-1

g(x)= 3x+17

Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts. (to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)

Horizontal shifts move the line either to the left or to the right.  Vertical shifts move the line either up or down.

If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.  

If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.  

So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))

The vertical shift is g(x)=f(x) +18

The horizontal shift is g(x)=f(x-6)

Answer:

The vertical shift is g(x)=f(x) +18

The horizontal shift is g(x)=f(x-6)

Step-by-step explanation:

Answer:

(i) 4 interviewers

(ii) 3 interviewers