What is the volume of a cube with a side length of 1/4 inch?

Answer:its 1.4>1.3

Step-by-step explanation:I THINK ITS 1.4>1.3

On solving the provided question we can say that at a simple 12% annual percentage rate, it would take approximately 6 years for capital to double.

In mathematics, a ratio or number expressed as a percentage of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." Nonetheless, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100.

The annual rate of return is 12%, so we can calculate:

Time to double = 72 / 12 = 6 years

Therefore, at a simple 12% annual rate, it would take approximately 6 years for capital to double.

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The correct question is -

How long does it take for capital to double at a simple 12% annual rate?

Answer:

[tex]x < -3\text{ or }x > 3[/tex]

Step-by-step explanation:

[tex]|1-2x|-4 > 1\\|1-2x| > 5\\\\1-2x > 5\\-2x > 6\\x < -3\\\\1-2x < -5\\-2x < -6\\x > 3[/tex]

We can be 99% confident that the true difference between the proportion of men and women who favor Mr. Singleton as a candidate is between 0.059 and 0.219.

Step 1: Determine the values of the [tex]\mathrm{\hat p_1}[/tex] and [tex]\mathrm{\hat p_2}[/tex] sample proportions.

The percentage of men who, on average, support Mr. Singleton is:

[tex]\mathrm{\hat p_1}[/tex]  = [tex]\dfrac{282}{659}[/tex], or around 0.428

The percentage of women who favour Mr. Singleton, as a sample, is:

[tex]\mathrm{\hat p_2}[/tex] = [tex]\dfrac{182}{629}[/tex], or around 0.289

Locate the critical value that must be utilised to build the confidence interval in step 2.

The level of significance is [tex]\alpha[/tex] = 0.01/2 = 0.005 (divided by 2 because it's a two-tailed test) because we want to determine a 99% confidence interval. The critical value for a z-score with  [tex]\alpha[/tex] = 0.005 is roughly 2.576 when using a table or calculator.

Step 3: Determine the standard error's value.

The standard error of the difference between two sample proportions is calculated as follows:

[tex]\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}[/tex]

When we enter the values from the issue, we obtain:

[tex]\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }[/tex]

Create the 99% confidence interval in step four.

We may create the confidence interval using the sample proportions, critical value, and standard error:

[tex]\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}[/tex]

When we change the values, we obtain:

2.576, × 0.031, = (0.428 - 0.289).

If we simplify, we get:

[tex]$$0.139 \pm \ 0.08$$[/tex].

3. Find the value of the standard error.

The following formula is used to compute the standard error of the difference between two sample proportions:

[tex]\mathrm{SE = \sqrt{\dfrac{\hatp_1}{SE}} = (\hat p_1 - \hat p_2) (\hat p_1 - \hat p_1) }[/tex]

[tex]\mathrm{(\Hat p 2-\Hat p 2) + n_1 + \frac {\hat p_2}{1}}[/tex]

When we type in the issue's values, we get:

[tex]$ \mathrm{\sqrt{(\frac{1-0.428}{0.659}) + \frac{1-0.288}{0.629}) }= about \ 0.031 \ for \ SE (\hat p_1 - \hat p_2)}[/tex]

In step four, calculate the 99% confidence interval.

With the sample proportions, critical value, and standard error, we can calculate the confidence interval:

[tex]\mathrm{SE(\hat p_1 - \hat p_2) 1:00 \ p.m. \ to \ 2:00 \ p.m. \ z \ \alpha \ 2}[/tex]

When the values are changed, we get the following result: [tex]$2.576 \times 0.031 = (0.428 - 0.289)$$[/tex]

Simplifying, we obtain: [tex]$$0.139 \pm \ 0.08$$[/tex].

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Answer:

true

Step-by-step explanation:

cause I’ve done this before

Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

Mathematical relationships between two variables that have a constant multiple of one another are known as proportional relationships. This implies that when one variable rises or falls by a particular factor, the other variable rises or falls by the same amount as well.

In other words, a straight line on a graph that runs through the origin (0, 0) can be used to illustrate a proportionate connection. This is due to the fact that they are proportional, therefore when one variable is equal to zero, the other variable must likewise be zero.

To graph the linear relationship between the number of stuffed animals, x, and the number of action figures, y, we can use the two given data points: (20, 15) and (60, 45).

First, we can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (20, 15) and (x2, y2) = (60, 45)

slope = (45 - 15) / (60 - 20) = 30 / 40 = 0.75

Next, we can use the point-slope form of the equation of a line to write the equation of the line that passes through the two points:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) = (20, 15)

y - 15 = 0.75(x - 20)

y - 15 = 0.75x - 15

y = 0.75x

Now we can graph the line by plotting the two given points and drawing a straight line passing through them:

Linear relationship graph

Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional, since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

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the APR for this loan is approximately 14.27%.

To find the APR for this loan, we can use the formula:

APR = (2 * n * F) / (P * (n + 1))

where:

n = number of payments (24 in this case)

F = finance charge per $100 financed ($11.45 in this case)

P = amount financed per $100 (which we don't know yet)

We need to solve for P to be able to use the formula. We know that the finance charge is $11.45 for every $100 financed, so we can set up the equation:

11.45 = F / P

where F is the finance charge per $100 financed and P is the amount financed per $100.

Solving for P, we get:

P = F / 11.45

P = 100 * (11.45 / 100)

P = $1,000

So the amount financed is $1,000.

Now we can substitute the values into the APR formula:

APR = (2 * n * F) / (P * (n + 1))

APR = (2 * 24 * 11.45) / (1000 * (24 + 1))

APR = 0.1427 or 14.27%

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The value of ø  in the given equation ø sin(ø-30)=cosø is 60 - 2πn, where n is an integer

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can solve this equation using trigonometric identities.

We know that sin(ø - 30) = cos(90 - (ø - 30)) = cos(120 - ø).

So, the equation becomes:

cos(120 - ø) = cosø

Using the identity cos(A) = cos(B) if and only if A = ±B + 2πn, where n is an integer, we get:

120 - ø = ±ø + 2πn

Simplifying and solving for ø, we get:

ø = 60 ± 2πn

So, the solutions are:

ø = 60 + 2πn, where n is an integer or

ø = 60 - 2πn, where n is an integer

Hence, the value of ø  in the given equation ø sin(ø-30)=cosø is 60 - 2πn, where n is an integer

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Square root of 8 plus square root of 1 equal 3.82842712

Algebraic integers

The square roots of an integer are algebraic integers —more specifically quadratic integers. The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors.

⇒ 3.8 rounded.

⇒ = 3.82842712

Hence, Square root of 8 plus square root of 1 equal 3.82842712

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The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Since the diameter of the garden is 42m, the radius is half of that, which is:

r = 42m / 2 = 21m

The circumference of the circular garden is therefore:

C = 2πr = 2π(21m) = 42πm

If the gardener makes 4 rounds of the fence, he will need to purchase 4 times the circumference of the garden in barbed wire. Therefore, the length of barbed wire he needs to purchase is:

4 x 42πm = 168πm

This is approximately equal to 527.79m, if we use the value of π to two decimal places.

Answer:

528 M

Step-by-step explanation:

CIRCUMFERENCE OF GARDEN= 2 pi r

r=42/2 =21

circumference = 2x (22/7) x21

=132 m

To make 4 rounds= 4 x 132 = 528m

Your statement is partially correct congruent .

Two triangles are similar if they have all three corresponding angles congruent or equal in measure, or if they have two corresponding angles congruent and the corresponding sides are in proportion (i.e., the ratio of the length of one side to the length of the corresponding side in the other triangle is constant). This is known as the Angle-Angle Similarity Theorem (AA Similarity), or the Angle-Side-Angle Similarity Theorem (ASA Similarity).

It is important to note that if only one pair of corresponding angles is congruent, the triangles are not necessarily similar. For example, two right triangles with one acute angle congruent are not necessarily similar, since the other acute angles are not congruent. Similarly, if two triangles have all three sides in proportion, they are not necessarily similar unless all three corresponding angles are also congruent.

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Answer:

he probability of Violeta pulling out a green marble is 0.3 or 30%.

Step-by-step explanation:

he probability of pulling out a green marble is the number of green marbles divided by the total number of marbles in the bag:

P(green marble) = number of green marbles / total number of marbles

In this case, there are 6 green marbles and 14 pink marbles, so the total number of marbles is:

total number of marbles = 6 + 14 = 20

Therefore, the probability of pulling out a green marble is:

P(green marble) = 6 / 20 = 3/10 = 0.3

So the probability of Violeta pulling out a green marble is 0.3 or 30%.

Answer:

===================================================

Work Shown:

x = amount invested at 9%

y = amount invested at 3%

x+y = 2300 invested total, which solves to y = 2300-x

0.09x+0.03y = 189 dollars of total profit

Applying substitution to solve.

0.09x+0.03y = 189

0.09x+0.03(y) = 189

0.09x+0.03(2300-x) = 189

0.09x+69-0.03x = 189

0.06x+69 = 189

0.06x = 189-69

0.06x = 120

x = 120/0.06

x = 2000

y = 2300-x = 2300-2000 = 300

The solution as an ordered pair is (x, y) = (2000, 300)

Therefore, $2000 was invested at 9%, and $300 was invested at 3%.

Answer:

Step-by-step explanation:

The two numbers that multiply to -140 also have to add to -13, so that means that the larger of the two numbers needs to be negative, and the other number positive.

7 x -20 = -140

7 - 20 = -13

The cosine equation of the function is y = 5cos (x + π/4) + (4).

What is the cosine function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

y = A cos (Bx - C) + D

A (amplitude) = max - D

B = Period/2π  --->   Period is the distance from max to next max

C = B · Phase Shift  ---> Phase shift is the distance from the y-axis to the max

D (vertical shift) = (max + min)/2

Maximum = 9, minimum = -1

A = (maximum-minimum)/2 = (9 - -1)/2 = 10/2 = 5

Vertical shift = maximum - A = 9 - 5 = 4

The maximum occurs at x = -π/4, and

for the original function (without shift), the maximum occurs at x = 0

So, the horizontal shift = 0 - (-π/4) = π/4

Hence, the cosine equation of the function is y = 5cos (x + π/4) + (4).

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Answer:$728

Step-by-step explanation: 4 percent increase= 104% which is x1.04

=700*1.04  

Answer:

y = (12 / (25/12)^7) * (25/12)^x

Step-by-step explanation:

To write an exponential model given two points, we can use the general form of an exponential function:

y = ab^x

where y is the dependent variable, x is the independent variable, b is the base or growth factor, and a is the initial value when x = 0.

Using the two given points, we can form a system of equations:

12 = ab^7 (1)

25 = ab^8 (2)

Dividing equation (2) by equation (1), we get:

25/12 = b^(8-7) = b

So the base of the exponential function is b = 25/12.

To find the initial value a, we can substitute b into either of the original equations. Let's use equation (1):

12 = a(25/12)^7

Simplifying, we get:

a = 12 / (25/12)^7

Therefore, the exponential model that fits the given points is:

y = (12 / (25/12)^7) * (25/12)^x

Answer:

middle set of data

Step-by-step explanation:

Answer:

180 + t = 267

Step-by-step explanation:

180 and t more is the same as adding t to 180.

"is" means equals

The scatterplot shows the weakest positive linear association is (a)

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

The graphs

A good line of best fit would have equal number of points on either sides

Using the images as a guide, we can see that:

Graph (a) and (b) have a positive linear association while graph (a) have the least number of points that appear to be on a straight line

This means that the line with the weakest is (a)

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Using arithmetic operations the individual would save approximately 76.36 gallons of gas per year by switching to a hybrid car for their commute.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Let's first calculate the annual distance driven by the individual to work.

Use arithmetic operation of multiplication.

Annual distance driven = 60 miles/week x 50 weeks/year = 3000 miles/year

Now, let's calculate how much gas the individual would use for their commute in their current car.

Use arithmetic operation of division.

Gas used in current car = (Annual distance driven) / (Miles per gallon of current car)

Gas used in current car = 3000 miles/year / 22 miles/gallon = 136.36 gallons/year

Next, let's calculate how much gas the individual would use for their commute in a hybrid car.

Use arithmetic operation of division.

Gas used in hybrid car = (Annual distance driven) / (Miles per gallon of hybrid car)

Gas used in hybrid car = 3000 miles/year / 50 miles/gallon = 60 gallons/year

Finally, let's calculate how much gas the individual would save by switching to a hybrid car.

Use arithmetic operation of subtraction.

Gas saved = Gas used in current car - Gas used in hybrid car

Gas saved = 136.36 gallons/year - 60 gallons/year = 76.36 gallons/year

Therefore, the amount of gas value saved is 76.36 gallons of gas per year.

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An individual has been driving a passenger vehicle to work, averaging 60 miles a week in a car that averages 22 miles per gallon. The individual plans to purchase a hybrid vehicle that averages 50 miles per gallon. If the individual drives to work 50 weeks a year, how much gas will they save if they switch to a hybrid vehicle for their commute?

Answer:0.047

Step-by-step explanation: This is actually easy  you need to divide using long division and put the numbers of the division that you use to subtract and then you get the answer.

The solution to the given inequality w > 2w - 9 is w < 9.

Inequality is defined as mathematical pieces of information that have a minimum of two terms including variables or numbers that are not equal.

The "inequality" is given in the question, as follows:

w > 2w - 9

We have to solve the above inequality for w.

⇒ w > 2w - 9

Rearrange the term of variable w in the above inequality,

⇒ w - 2w > - 9

Apply the subtraction operation and solve for w:

⇒ - w > - 9

Multiply the negative sign and flip the sign of inequality:

⇒ w < 9

Thus, the solution to the given inequality is w < 9.

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Answer:

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

From the above equation given in the question , we get that g(x)  have a value of 3x.

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

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The speed of the satellite around the earth in miles per hour is 8659.09 miles per hour.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is important to determine the quantity of any object.

A same quantity can have more than one type of measurement which can be converted to each other.

Given,

Speed of the satellite in feet per second = 12700 feet per second (ft/s)

We have,

5280 feet = 1 mile

1 feet = 1/5280 mile

12700 feet = 12700/ 5280 miles

Also,

60 minute = 1 hour

1 minute = 1/60 hour

60 seconds = 1 minute = 1/60 hour

1 second = 1/3600 hour

12700 feet per second =  12700/ 5280 miles ÷ 1/3600 hour

                                      = 8659.09 miles per hour.

Hence the speed converted is 8659.09 miles per hour.

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Answer:

13x-16

Step-by-step explanation:

I am assuming that you mean 5*(2 + 2x − 3) − (2*2 − 3x + 7).

That equals 10x-5+3x-11=13x-16

This expression gives the mean number of coupons you will need to collect before you have a complete set, given that each coupon obtained is equally likely to be any one of the c types.

In general, probability is a measure of the likelihood that a certain event or outcome will occur. It is a branch of mathematics concerned with analyzing and quantifying uncertainty. In formal terms, the probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities between 0 and 1 represent the degree of uncertainty associated with the event.

Here,

The probability that the first n coupons collected do not form a complete set can be found as follows:

Let S be the event that the first n coupons do not form a complete set, and let Ci be the event that the i-th coupon collected is a new type (i.e., a coupon of a type that has not been collected before).

Then, the event S can be expressed as the intersection of the events C1, C2, ..., Cn, where each Ci is independent of the others and has probability (c-i+1)/c of occurring. This is because there are c-i+1 types of coupons remaining after i-1 types have been collected, and each of these types is equally likely to be the next coupon collected.

So, the probability of S can be calculated as:

P(S) = P(C1 ∩ C2 ∩ ... ∩ Cn) = P(C1) × P(C2) × ... × P(Cn)

= (c-1)/c × (c-2)/c × ... × (c-n+1)/c

= Π(i=1 to n) (c-i+1)/c

To deduce an expression for the mean number of coupons you will need to collect before you have a complete set, let X be the random variable representing the number of coupons collected until a complete set is obtained. Then, the expected value of X can be calculated using the formula:

E(X) = Σ(k=1 to c) P(X ≥ k)

This formula sums the probabilities of all possible numbers of coupons collected until a complete set is obtained, weighted by their respective probabilities.

Note that P(X ≥ k) is the probability that a complete set has not been obtained after k-1 coupons have been collected, which is equal to the probability of the event S above. So, we can substitute the expression for P(S) into the formula for E(X) to get:

E(X) = Σ(k=1 to c) P(X ≥ k)

= Σ(k=1 to c) Π(i=1 to k-1) (c-i+1)/c

= Σ(k=1 to c) Π(i=0 to k-2) (c-i)/c

= Σ(k=0 to c-1) Π(i=0 to k-1) (c-i)/c (by changing the index of summation)

= Σ(k=0 to c-1) (c-k)/cˣ

= c Σ(k=0 to c-1) (1/c)ˣ - Σ(k=0 to c-1) (k/c)ˣ

= c (1 - (1/c)ˣ)/(1 - 1/c) - B(c, 1/c)

where B(c, 1/c) is the sum of the first c terms of the series (k/c)ˣ.

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The number of each denomination is: 13 of the $10-dollars bills.

Let x be number of the $20 dollars bills. Then, the number of the $10 dollars bills is (x+2), according to the condition.

The money equation will then be:

20x + 10*(x+2) = 350

Now, solve for x.  

20x + 10x + 20 = 350

30x = 350 -20

30x = 330

x = 330/30

x = 11

So, 11 of the $20 dollars bills and 11 +2 = 13 of the $10-dollars bills.

Full question "Part of the proceeds from a garage sale was ​$350 worth of ​$10 and ​$20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.

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The required turtle's speed is 12/5 miles per hour, as of the given condition.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
To find the turtle's speed in miles per hour, we need to convert the fraction of miles traveled in a fraction of an hour to miles per hour.

First, we can simplify the fraction 3/5 by dividing the numerator and denominator by 1/4,

speed = distance/time

Substitute the value in the above expression,
Speed = 3/5 / [1/4]
Speed = 12/5

Therefore, the turtle's speed is 12/5 miles per hour.

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