Which expression is equivalent

Answer:

12² = 144

12 to the power of 2 us equal to 144

Answer:

The area of the dog pen is 522 [tex]ft^2[/tex].    (feet squared)

The perimeter of the dog pen is 94 feet

Step-by-step explanation:

Area

Here is the formula for the area of a rectangle.

[tex]A=lw[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]A[/tex].

[tex]A=29*18\\A=522[/tex]

Perimeter

Here is the formula for the perimeter of a rectangle.

[tex]P=2w+2l[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]P[/tex].

[tex]P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94[/tex]

Based on the 2:5 quantity of concentrate and water, the amount of water required for 90 mililitres will be 225 mililitres of water.

Firstly we will be creating the ratio for the mentioned information. It will be as follows-

Amount of concentrate/Amount of water

The proportion will be -

2/5 = 90/Concentration of water

Concentration of water = 90×5/2

Now perform multiplication in numerator on Right Hand Side of the equation

Concentration of water = 450/2

Then work out the division on Right Hand Side of the equation

Concentration of water = 225 mililitres

Thus, the required amount of water is 225 mililitres.

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Answer:

$899.54

Step-by-step explanation:

To find the cost of sod for a trapezoid shaped yard, we need to first find the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid and b1 and b2 are the lengths of the bases.

Substituting the given values, we get:

Area = (1/2) * 46 ft * (78 ft + 111 ft)

= (1/2) * 46 ft * 189 ft

= 4274 ft^2

To find the cost of sod for this area, we need to multiply the area by the cost per square foot of sod. The cost will be:

Cost = 4274 ft^2 * $0.21/ft^2

= $899.54

So the cost of sod for this yard will be $899.54.

Based on this information, Gregory can make a valid conclusion.

Sampling methods are methods used to create a sample in for a survey. There are probability sampling methods as well as non probability sampling methods.

Given sampling method done by two students, Mike and Gregory, to choose a sample of students to survey the students interested in summer camp.

Names of students are listed in an alphabetical order.

Mike chooses the name of every student in 7th grade on the list and Gregory chooses the name of every 3rd student on the list.

The sampling of Mike will lead to sampling bias. Here the conclusion which can be made about the total population is weaker because only the students of particular class is attending. Conclusions may be more limited.

Whereas in the case of sampling of Gregory, he uses one of the probability sampling method called systematic sampling method. The sampling using probability sampling method is more convenient as it has less sampling bias as well as research bias.

Hence Gregory can make a valid conclusion in this case.

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The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

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To calculate log 10 on a calculator, you will typically use the "log" button. Depending on the type of calculator, you may need to enter the number 10 first, then hit the "log" button.

For example, if using a standard scientific calculator, you would enter 10, then hit the "log" button. On some calculators, you may need to hit the "10x" button first before hitting the "log" button.  On some graphing calculators, you may need to use the "log base" button. When using this button, you would enter 10 as the base and the number you are trying to calculate the log of.

In some cases, you may need to use the "ln" (natural log) button instead of the "log" button. In this case, you would need to use the conversion formula of "ln x = 2.303 log 10 x" to get the desired number.  Finally, some calculators may have an "antilog" button. This button will calculate the inverse of the logarithm or the power of 10 of a given number. To use this button, you would enter the number, then press the antilog button.

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Answer:25cm

Step-by-step explanation:area of triangle=1/2 × base× height

=1/2×10×5

= 25cm^2

Answer:

There are 47 dimes and 2 pennies.

Step-by-step explanation:

10¢ = 1 dime

$4.70 = 470 ¢

470 dimes = 47 dimes

and 2 pennies

Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

30100 of 84 = 30100 × 84Therefore, the answer is 25.2

If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.

Answer:

  see attached

Step-by-step explanation:

You want the graph of g(x) = -f(x-3), given the graph of the parent function f(x) = log₂(x).

The replacement of x with x-3 as the function argument causes the graph to be translated 3 units to the right.

The replacement of f(x) with -f(x) causes the graph to be reflected over the x-axis.

The translated, reflected graph is shown in blue in the attachment.

Three straight sides and three angles make up the shape of a triangle. The angles of a triangle can either be acute, right, or obtuse. An angle with three acute angles is a triangle where all three angles measure less than 90 degrees.

A triangle is a three-sided shape with three angles. The sum of the internal angles of a triangle is always 180 degrees. An angle is the amount of turn or change in direction between two lines. There are three types of angles, acute, right and obtuse. An acute angle is an angle which measures less than 90 degrees. A right angle is an angle which measures exactly 90 degrees, and an obtuse angle is an angle which measures more than 90 degrees. Therefore, an angle with three acute angles is a triangle where all three angles measure less than 90 degrees. A triangle with three acute angles is also known as an acute triangle. All three angles must add up to 180 degrees, so the measure of each angle must be less than 60 degrees.

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Answer:

[tex] \sf \: 7.31[/tex]

Step-by-step explanation:

Now we have to,

→ round a number to 2 decimal places.

The number is,

→ 7.3084

Let's solve the problem,

→ 7.3084

→ ≈ 7.308

→ [tex] \boxed{ \sf ≈ 7.31} [/tex]

→ ≈ 7.3

Hence, the answer is 7.31.

Answer:

The hundreds place

Step-by-step explanation:

143, first digit is , 1 is in the hundreds place

With 10 faces and 16 vertices, an octagonal prism is depicted.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.

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In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.

1. Look at the inequality and identify if the equation is an open or closed interval.

2. If it is an open interval, it will be represented by a dashed line on the graph.

3. If it is a closed interval, it will be represented by a solid line on the graph.

4. Determine the starting and ending points of the inequality, and plot them on the graph.

5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.

6. Shade the area of the graph that is represented by the inequality.

7. Label the graph with the inequality, the points, and the shading.

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The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95.

Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.

Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.

The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.

In this case:

μ = 505 mL (population mean)

σ = 10 mL (population standard deviation)

n = 16 (sample size)

The standard error (SE) of the sample mean is:

SE = σ/√n = 10/√16 = 10/4 = 2.5 mL

Now, we need to find the z-scores for 500 mL and 510 mL:

z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2

z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2

Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(z < -2) ≈ 0.0228

P(z < 2) ≈ 0.9772

Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:

P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544

So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95

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The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

population mean assumed to be 2925

sample mean = 2515

standard deviation of sample = 585.

sample size = 15

t-score is indicated because the standard deviation is taken from the sample rather than from the population.

t-score = (x - m) / s

x is the raw score

m is the raw mean of the population

s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.

degrees of freedom = 15 minus 1 = 14.

t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.

you need to know the confidence level.

at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.

since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

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Answer:

f(-7) = -33

Step-by-step explanation:

f(x) = − x² - 4x – 12

f(-7) = ?

We put -7 in for x and solve

f(-7) = -(-7)^2 -4(-7) - 12

f(-7) = -(49) + 28 - 12

f(-7) = -49 + 28 - 12

f(-7) = -33

The required probability as calculated from the data given above is found to be as 1 / 9.

Given,

The spinner is having the letters as A, B and C.

The possibility of getting any of these letters when the spinner is rolled is same.

Therefore , the sample space will be as follows ,

6 + 3 = 9

This is due to the fact a die has 6 sides.

Then the probability of getting a B will be ,  1/9

Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.

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The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).

Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:

y = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:

y = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)

f(x) = (x + 7) · (x - 3) · (x - r)

Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.

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Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

1) Number of 200 notes = 17,923,275

Number of 100 notes = 35,846,550

Number of 50 notes = 71,693,100

Number of 20 notes = 179,232,750

2) Number of 200 notes = 428,800

Number of 100 notes = 857,600

Number of 50 notes = 1,715,200

Number of 20 notes = 4,288,000

3) Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Ghana credits 200,100,50 and 20 notes.

Now,

Since, Ghana credits 200,100,50 and 20 notes.

1) Hence, To credit the amount 3584655000,

Number of 200 notes = 3584655000/200 = 17,923,275

Number of 100 notes =3584655000/100 = 35,846,550

Number of 50 notes =3584655000/50 = 71,693,100

Number of 20 notes = 3584655000/20 = 179,232,750

2) To credit the amount 85760000;

Number of 200 notes = 85760000/200 = 428,800

Number of 100 notes = 85760000/100 = 857,600

Number of 50 notes = 85760000/50 = 1,715,200

Number of 20 notes = 85760000/20 = 4,288,000

3) To credit the amount 146737000;

Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) To credit the amount 5555627000;

Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) To credit the amount 7777000;

Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

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For the given equations , the solutions are as follows :

(a) the equation [tex]6x + 8 = 7x + 13[/tex] has exactly one solution , and the solution is  .

(b) the equation [tex]6x + 8 = 2(3x + 4)[/tex] has Infinitely Many Solutions .

(c) the equation [tex]6x + 8 = 6x + 13[/tex] has No Solution .

Equation (a) ;

the equation is given as [tex]6x + 8 = 7x + 13[/tex] , we solve the equation further ,

we get ;

[tex]7x - 6x = 13 - 8[/tex] ;

[tex]x = 5[/tex] ;

So , the equation has exactly one solution and the solution is [tex]x = 5[/tex] .

Equation (b) ;

the equation is given as [tex]6x + 8 = 2(3x + 4)[/tex] , we solve equation further ,

we get ;

[tex]6x + 8 = 6x + 8[/tex] ;

On solving further ,

we have ;

[tex]8 = 8[/tex] ;

So , the equation has infinitely many solutions .

Equation (c) ;

the equation is given as [tex]6x + 8 = 6x + 13[/tex] , we solve equation further ,

we get ;

[tex]8 = 13[/tex] ;

and we know that [tex]8\neq 3[/tex] ,

So , the equation have No Solution .

The given question is incomplete , the complete question is

For each equation determine whether it has no solutions, exactly one solution, or is true . for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.

(a) 6x + 8 = 7x + 13

(b) 6x + 8 = 2(3x + 4)

(c) 6x + 8 = 6x + 13

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One cannot add themselves directly to Wikipedia as this can cause harm to the platform and community in a later run. As one can start adding content and details on the page based on their personal opinions.

Therefore we can say that  the answer is that we cannot edit or create our own Wikipedia page, because that would be a conflict of interest ,more on this later.

But the thing which one can do is to add themselves in the line ,to list themselves on Wikipedia’s repository of articles which are out there looking for creators who can help maintain the site.

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The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer:

u = 8

Step-by-step explanation:

calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )

m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives

[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )

10(u - 5) = 30 ( divide both sides by 10 )

u - 5 = 3 ( add 5 to both sides )

u = 8

Step-by-step explanation:

(u - 5)/(5 + 5)= 3/10

(u - 5)/10= 3/10

10u - 50 = 30

10u = 80

u = 8

The value of x in the triangle WXY is 19 degrees

An equation shows how two or more numbers and variables are related to each other.

From the question, we have the following parameters that can be used in our computation:

The triangle XYZ and the line YZ such that lie YZ and XW are parallel lines

Using the above as a guide, we have the following:

∠ZYW = ∠XWY (alternate angles are equal)

∠XWY = 2x (Given)

So, we have

∠XWY + ∠XYW + ∠YXW = 180° (the sum of angles in a triangle)

Substitute the known values in the above equation, so, we have the following representation

2x + (3x - 5) + 90 = 180

Open the brackets and solve

5x - 5 = 90

Evaluate the like terms

5x = 95

Divide both sides by 5

x = 19°

Hence, the value of x is 19°

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Answer:

1/4 of 60= 15

15+60=75

75 is 125% of 60

Step-by-step explanation:

Answer: D

Step-by-step explanation:

In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.

Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.

This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.

The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.

The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.

The domain of a function refers to the interval of the x values of the function.

In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.

To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.

The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.

Thus, the correct answer is option D, {x | −3 < x < 3}.

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