A frame around a family portrait has a perimeter of 80 inches. The length is five less than twice the width. Find the length and width of the frame (in inches).

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

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Answer:

c = 8

Step-by-step explanation:

Using the Intersecting Chords Theorem, we can form the following equation and solve for c:

\(ab=cd\\(10)(8.8)=11c\\88=11c\\c=8\)

Answer: Choice D) x can be anything but 13

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

Explanation:

The domain of \((f \circ g)(x) = f(g(x))\) is the same as the domain of g(x)

The domain for g(x) is \(\{x|x \ne 13\}\) saying we can plug in any number we want as long as it's not 13. This is to avoid dividing by zero. The same domain applies for the composite function because

\(f(x) = x+7\\\\\\f(g(x)) = g(x)+7\\\\\\f(g(x)) = \frac{1}{x-13}+7\\\\\\(f \circ g)(x) = \frac{1}{x-13}+7\\\\\\\)

and we can see that we still need to kick out x = 13 from the domain to avoid the division by zero issue.

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Answer:

Step-by-step explanation:

Let the speed is x.

We have equation:

To solve we need to get rid of fraction:

Answer:

the last one, w-9

Step-by-step explanation:

plug in the given (9) for w and solve

Hope this helps :)

Answer:

Step-by-step explanation:

9-9=0 not 14

so w-9 is not a solution

Step-by-step explanation:

1. 95+78 as its asking how many bools all together. 173 books

2. 305-98 ita asking how many miles LEFT.

Answer:

1920 cm³

Step-by-step explanation:

V = w · h · l

V = 8 · 14 · 10

V = 1120 cm³

Now for the smaller one.

V = w · h · l

V = 8 · 10 · 10

V = 800 cm³

1120 cm³ + 800 cm³

1920 cm³

Answer:

1920 cm ^3

Step-by-step explanation:

find the volume of the 2 cuboids seperatly.

bigger one: LXWXH --> 8 X 14 X 10 = 1120

smaller one: LXWXH --> 10X10X8 = 800

add them up

1120 + 800 = 1920 cm

Hope this helps :D

Answer:

-7/4

Step-by-step explanation:

we can see that every time the value of x increases by 4, the value of y decreases by 7.

let's pick two sets of coordinates (first two will be fine).

that is (-4, 6) and (0, -1)

Slope = (change in y values) / (change in x values)

= (-1 - 6) / (0 - -4)

= -7 / (0 + 4)

= -7/4.

so our slope (gradient) is -7/4

Answer:5

Step-by-step explanation:

The range of the function g(x) = a[x], where a < 0, is y ≤ 0.

The function f(x) = [x], where [x] represents the greatest integer less than or equal to x, has a range of y ≤ 0. This means that the output of the function f(x) can be any number less than or equal to zero, including negative integers, zero, and non-negative fractions.

Consider the function g(x) = a[x], where a is a negative constant. When we multiply the input x by a the output of the function is also multiplied by a. Since a is negative, the sign of the output is flipped. Moreover, the output is an integer, as [x] is an integer for all x.

Here, the range of the function g(x) = a[x] is y ≤ 0.

This means that the output of the function g(x) can be any negative integer, zero, or any non-positive fraction, as these are the numbers that are less than or equal to zero.

Thus, the range of the function g(x) = a[x], where a < 0, is y ≤ 0.

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The length of the bases for the trapezoid are

shorter base is 3 in and the longer base is 7 in

The formula for area of trapezoid is

= 1/2 sum of bases * height

base of the trapezoid

20 = 1/2 sum of bases * 4

1/2 sum of bases = 5

sum of bases = 10

The relationship between the bases

longer base = 2 * shorter base + 1

sum of bases = longer base + shorter base

sum of bases = 2 * shorter base + 1 + shorter base

sum of bases = 3 shorter base + 1

substituting will result to

10 = 3 shorter base + 1

10 - 1 = 3 shorter base

9 = 3 shorter base

shorter base = 3 in

longer base = 2 * shorter base + 1

longer base = 2 * 3 + 1

longer base = 7 in

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Given:

Required:

We need to solve for x and identify if it is an extraneous solution.

Explanation:

First find the value of x

This solution is not extraneous, because extraneous solution emerage from solving the problem but are not actually valid solution fro initial problem.

With rounding , this solution is valid for the initial problem

Final answer:

A

Answer:

7x+63

Step-by-step explanation:

7(x + 9)

Expand the brackets.

7(x)+7(9)

Multiply the terms.

7x+63

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The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Using the substitution the system of equations y + 4 = x and 10x + 2y + 16 is solved to be

Substitution involves replacing a value with it's equal

The given equation include

y + 4 = x

10x + 2y + 16

substituting x = y + 4 into 10x + 2y + 16

10x + 2y + 16

= 10(y + 4) + 2y + 16

= 10y + 40 + 2y + 16

collecting like terms

= 12y + 16

12y = -16

y = -16/12

y = -4/3

substituting y = -4/3 into x = y + 4

x = -4/3 + 4

x = 8/3

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Answer:

70%

Step-by-step explanation:

I'm sorry but I don't really know how to explain it other than 70% of 30 is 21 so that means that 30% of the students turned their essay in on time.

(sorry for not being able to explain it but I hope it helped)

Answer: 70%

Step-by-step explanation:

there are 30 students in the class

to find 1 percent we will: 30/100=0.3

21 students completed the essay

21/03.=70 %

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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The coordinates for hector's position are (137.78, 47.72) for (x, y)

Tre's position as the point on the pitcher's mound (42.78, 42.78). Hector is approximately 95 feet away from the pitcher's mound horizontally (x axis).

We must solve for the correct x-coordinate because we already have the correct y-coordinate.

Now all that is required of you is to write down the coordinates.

The coordinates of Hector are (137.72, 47.78).

The coordinate values of a point on a graph can be represented by (x, y), with x being referred to as the abscissa, indicating the horizontal distance from the origin or x-axis, and y being referred to as the ordinate, signifying the vertical distance from the origin or the x-axis.

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Complete Question:

Hector was standing halfway between first and second base, at the grass line. The

grass line is 95 feet from the pitcher's mound.

6. Calculate the coordinates for Hector's position. [Note: We can assume that 95

feet is an approximately horizontal distance from the pitcher's mound to the grass

line.] (2 points: 1 for x, 1 for y)

Hector was standing at the coordinate ( __, _).

Answer:

  13.6 ft

Step-by-step explanation:

The geometric sequence of arc lengths can be described by ...

  f(n) = a·b^n

We have (n, f(n)) = (3, 20) and (7, 12). Using these values, we can find the common ratio (b):

  20 = a·b^3

  12 = a·b^7

Then ...

  12/20 = (a·b^7)/(a·b^3) = b^4 = 3/5

We want the 6th term, which we can get from the 7th term by multiplying by b^-1.

  b^(-1) = (b^4)^(-1/4) = (3/5)^(-1/4) = √(√(5/3)) ≈ 1.13622

Then the 6th swing had an arc length of ...

  f(6) = f(7)·b^-1

  f(6) = (12 ft)(1.13622) ≈ 13.63 ft ≈ 13.6 ft

To determine the total profit made by a potato chip manufacturer, we need to multiply the profit per bag by the number of bags sold and subtract the cost per bag.

The profit per bag is the difference between the selling price and the cost per bag, so we have:

Now, we can calculate the total profit for each option:

Therefore, the option that maximizes the profit is selling the bags at $1.50 each, with a total profit of $760,000.

Answer:

To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):

Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.

Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.

Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.

So, [(4r²t)³]² = 4096 * r^12 * t^6.

Step-by-step explanation:

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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The algebraic equation represents the words: Twenty percent of Tom's grade is 80 points would be 0.20x = 80. thus, option D is correct.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let the tom's grade represneted by x.

so,

Twenty percent of Tom's grade is 80 points means

20%x = 80

20x / 100 = 80

Or 0.20x = 80

Hence, algebraic equation represents the words: Twenty percent of Tom's grade is 80 points would be 0.20x = 80. thus, option D is correct.

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1