suppose a house painter rests a 20-foot ladder against a building, then decides the ladder needs to rest 1 foot higher against the building.Will moving the ladder 1 foot towards the building do the job?If it needs to be 2 feet lower, will moving the ladder 2 feet away from the building do the trick? Let's investigate

The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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The exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

The exact value of the following trig expression tan(11pi/12) can be found using trig identities and the special points on the unit circle.

First, we can use the double angle formula for tangent:

tan(2x) = 2tan(x)/(1-tan^2(x))

We can then use this formula to rewrite the given expression:

tan(11pi/12) = tan(2*11pi/24) = 2tan(11pi/24)/(1-tan^2(11pi/24))

Next, we can use the sum formula for tangent to rewrite the expression in the numerator:

tan(11pi/24) = tan(7pi/24 + 4pi/24) = (tan(7pi/24) + tan(4pi/24))/(1-tan(7pi/24)*tan(4pi/24))

We can then use the special points on the unit circle to find the exact values of these expressions:

tan(7pi/24) = tan(pi/3 + pi/8) = (tan(pi/3) + tan(pi/8))/(1-tan(pi/3)*tan(pi/8)) = (sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))

tan(4pi/24) = tan(pi/6) = sqrt(3)/3

Plugging these values back into the original expression, we get:

tan(11pi/12) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(1-(sqrt(3)/3)^2) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(8/9) = (2(sqrt(3) + sqrt(2-sqrt(2))))*(9/(8-9sqrt(3)*sqrt(2-sqrt(2))))

Simplifying further, we get:

tan(11pi/12) = (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2)))

Therefore, the exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

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If Allister’s father measures 180 cm, then the height of Allister would be 150 cm

Let us assume that 'h' represents the height of Allister and 'm' represents the height of Allister’s father.

Here, Allister’s father is 120% of Allister’s height.

This means that m is 120 percent of 'h'

Using the formula of percentage,

m = 120% of h

m = 120/100 × h

m = 6h/5

But Allister’s father actually measures 180 cm

This means m = 180

so , 180 = 6h/5

We solve this equation to find the value of h.

⇒ h = 180 × 5/6

⇒ h = 150 cm

Therefore, Allister's height = 150 cm.

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The complete question is:

Allister’s father is 120% of Allister’s height. If his father measures 180 cm, how tall is Allister?

Answer:

The two numbers are 90 and 59

Step-by-step explanation:

Let's call the two numbers x and y.

From the problem statement, we know that:

x + y = 149 (the sum of two numbers is 149)

x - y = 31 (the difference of the two numbers is 31)

To solve for x and y, we can use the method of elimination. Adding the two equations together eliminates the y term:

(x + y) + (x - y) = 149 + 31

2x = 180

x = 90

Substituting x = 90 into one of the original equations, we can solve for y:

x + y = 149

90 + y = 149

y = 59

Therefore, the two numbers are 90 and 59.

The percent of powdered sugar in mixture B is 25.82%.

To solve this problem, we can use a table to organize the information and find the percent of powdered sugar in mixture B.

MixturePoundsPercent Powdered SugarPounds of Powdered SugarA520%1B11x%0.11xTotal1624%3.84

From the table, we can create an equation to find the percent of powdered sugar in mixture B:

1 + 0.11x = 3.84

Solving for x:

0.11x = 2.84

x = 25.82%

Therefore, the percent of powdered sugar in mixture B is 25.82%.

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Answer:

C

Step-by-step explanation:

They are not proportional

If 3 pie cost $12, one pie will be $4

If 10 pie cost $25, then 1 pie is $2.5

$4 is not proportional to $2.5

Hence 12/3 is not proportional to 25/10

Answer:

option (1)

Step-by-step explanation:

rearrange making x the subject, then x is the inverse

y = [tex]\frac{3}{2}[/tex] x ( multiply both sides by 2 to clear the fraction )

2y = 3x ( isolate x by dividing both sides by 3 )

[tex]\frac{2}{3}[/tex] y = x

change y back into terms of x , then inverse is

[tex]f^{-1}[/tex] (x) = [tex]\frac{2}{3}[/tex] x , or

y = [tex]\frac{2}{3}[/tex] x

Using the unitary method, we found that one yellow token is worth 13.57 points and one blue token is worth 8.57 points.

Let's first find the value of one yellow token. We know that Jillian has collected 7 yellow tokens and has a total of 95 points. Therefore, the value of 1 yellow token can be found using the unitary method as follows:

1 yellow token = 95 / 7

1 yellow token = 13.57

Therefore, one yellow token is worth 13.57 points.

Therefore, the value of 4 blue tokens can be found using the unitary method as follows:

4 blue tokens = 75 - (3 x 13.57)

4 blue tokens = 34.29

Now, we know that 4 blue tokens are worth 34.29 points. To find the value of one blue token, we can use the unitary method again as follows:

1 blue token = 34.29 / 4

1 blue token = 8.57

Therefore, one blue token is worth 8.57 points.

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Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.

H0: μ = $250,000

Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.

Ha: μ > $250,000

The null hypothesis assumes that there has been no change in the median price since 2018, while the alternative hypothesis assumes that the median price has increased. The alternative hypothesis is one-sided, as the broker is interested in testing whether the price has increased, rather than testing whether there has been any change (i.e., a two-sided test).

The null and alternative hypotheses for the scenario can be stated as follows:

Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.

H0: μ = $250,000

Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.

Ha: μ > $250,000

In the above hypotheses, μ represents the population median price of single-family homes in the town.

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Step-by-step explanation:

remember,

100% = 1

1% = 100%/100 = 1/100 = 0.01

as decimal

2/5 % = 1% × 2/5 = 0.01 × 0.4 = 0.004

as fraction

1% × 2/5 = 1/100 × 2/5 = 2/500 = 1/250

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:

(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.

Red ball percentage equals (25/100) times 100%

25% of the balls are crimson.

given

You can compute the cost as follows:

Loss is calculated as Initial Price - Selling Price ($210 - $139).

Loss = $71

We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:

(Loss / Original price) times 100 equals the percentage of loss.

($71 / $210) times 100 equals the percentage loss.

Loss as a percentage: 33.81%

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

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The probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869. The probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597.

To answer this question, we need to use the central limit theorem. The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, the sample size is 289 students.

First, we need to calculate the standard error of the mean. The standard error of the mean is the standard deviation of the distribution of sample means. It is calculated as:

SE = σ/√n

Where σ is the standard deviation of the population and n is the sample size. In this case, σ = 187 and n = 289. So, the standard error of the mean is:

SE = 187/√289 = 11.04

Next, we need to calculate the z-score for each of the two scenarios. The z-score is a measure of how many standard deviations away from the mean a data point is. It is calculated as:

z = (x - μ)/SE

Where x is the data point, μ is the population mean, and SE is the standard error of the mean. In the first scenario, x = 621, μ = 606, and SE = 11.04. So, the z-score is:

z = (621 - 606)/11.04 = 1.36

In the second scenario, x = 595, μ = 606, and SE = 11.04. So, the z-score is:

z = (595 - 606)/11.04 = -0.996

Now, we can use the z-score to find the probability. The probability that a random sample of 289 students will have a mean score of more than 621 is:

P(z > 1.36) = 0.0869

The probability that a random sample of 289 students will have a mean score of less than 595 is:

P(z < -0.996) = 0.1597

So, the probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869 (rounded to four decimal places) and the probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597 (rounded to four decimal places).

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Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.

To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).

Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.

Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.

Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.

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The expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

We can use the properties of logarithms to expand the expression as follows:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]ln(x^2) - ln(y^5/2)[/tex]

Next, we can simplify each logarithm using the property that log(a^b) = b log(a):

[tex]ln(x^2) - ln(y^5/2)[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

Hence, the expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

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In the following question, among the various parts to solve- a- "x = [[3/2x3-3/2x3x3]]", b- the dimension of the solution set of Ax = 3x is 1.

(a) To find all solutions of the equation system Ax = 3x, we need to solve the following system of linear equations:

(3 4 3) (x1) (3x1)

(2 5 3) (x2) = (3x2)

(0 2 6) (x3) (3x3)

This can be written as (A - 3I)x = 0, where I is the identity matrix. To find the solutions, we need to find the null space of A - 3I.

(A - 3I) = [[0 4 3 2 2 3 0 2 3]]

To find the null space of this matrix, we row-reduce it to obtain:

[[1 0 -3/2 0 1 3/2 0 0 0]]

The last row tells us that x3 is a free variable, while the first two rows give us:

x1 = (3/2)x3

x2 = (-3/2)x3

Therefore, the general solution to Ax = 3x is:

x = [[3/2x3-3/2x3x3]]

where x3 is any real number.

(b) We can speak about the dimension of the solution set of Ax = 3x because it is a linear homogeneous equation. In this case, the solution set is a subspace of the vector space R^3, and the dimension of this subspace is the number of linearly independent solutions. Since we have one free variable in the solution, the set of solutions is a line in R^3, and its dimension is 1. Therefore, the dimension of the solution set of Ax = 3x is 1.

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To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.

The meaningful numbers in a number are known as significant figures, also known as significant digits. They are the digits that indicate the level of measurement uncertainty and add to the precision of a number. In other words, important figures are one digit that is either uncertain or estimated in addition to the digits that are known for sure.

given

Repeating digits are represented using the bar notation.

We must recognise the repetitive pattern in the decimal before we can represent 2.2616161 as a repeating decimal using bar notation.

The repetitive pattern is 6161, as can be seen by looking at the decimal. As a result, we can write 2.2616161 as:

2.26 16161...

To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.

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Answer below

Step-by-step explanation:

For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2

The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6

Answer: 29%

Step-by-step explanation:

109/360=.294 Then move the decimal to make it a percent

The dosage of Jack and Jill is obtained using geometric series formula which is 500 mg and 225 mg respectively.

What is geometric series?

A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.

Let's start by finding the amount of medication that Jack takes in total.

Each hour, Jack takes a dosage that is 80% of the previous dosage (since it drops by 20%).

So his dosages form a geometric sequence with first term 100 and common ratio 0.8 -

100, 80, 64, 51.2, 40.96, ...

The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by -

sum = a / (1 - r)

In this case, a = 100 and r = 0.8, so the sum is -

sum = 100 / (1 - 0.8) = 500

Therefore, Jack takes a total of 500 mg of medication.

Now let's find the original dosage for Jill.

If Jill takes half the amount of medication that Jack eventually took, then she takes -

500 / 2 = 250 mg

Let's call Jill's original dosage x.

Then her dosages form a geometric sequence with first term x and common ratio 0.7 (since it drops by 30%).

The sum of this sequence must be 250.

x + 0.7x + 0.49x + 0.343x + ... = 250

This is an infinite geometric series with first term x and common ratio 0.7, so we can use the formula for the sum of an infinite geometric series -

sum = x / (1 - 0.7) = x / 0.3

Simplifying the equation from before -

x / 0.3 × (1 + 0.7 + 0.49 + 0.343 + ...) = 250

x / 0.3 × (1 / (1 - 0.7)) = 250

x / 0.3 × 3.333... = 250

x = 250 / 1.111... = 225

Therefore, Jill's original dosage was 225 mg.

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Answer:-12&-8

Step-by-step explanation:

since 3x is negative the -12 and -8 become positive to combine with 5 to either become 41 or 37

Kim Chung owes $176 in federal income taxes.

What is the interest?

In finance, interest refers to the fee that a borrower pays to a lender for the use of money or assets. It is a cost of borrowing money, usually expressed as a percentage of the principal amount borrowed (or invested).

To calculate the federal income tax owed by Kim Chung, we need to first determine his taxable income.

Kim Chung's taxable income is calculated as follows:

Total Income = $2,897 (wages) + $57 (interest) = $2,954

Adjustments = $0

Adjusted Gross Income (AGI) = Total Income - Adjustments = $2,954 - $0 = $2,954

Since Kim Chung's parents claim him as a dependent, his standard deduction for tax year 2022 is $1,150.

Taxable Income = AGI - Standard Deduction = $2,954 - $1,150 = $1,804

To determine the federal income tax owed, we need to use the tax tables provided by the IRS for tax year 2022.

According to the tax tables, the tax on $1,804 of taxable income is $176.

Therefore, Kim Chung owes $176 in federal income taxes.

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Answer:

21.5

Step-by-step explanation:

The stopping distance for a car traveling at 50 mph is 208.3 feet.

We can set up a proportion using the given information and the formula for stopping distance:

D = k s²

where D is the stopping distance, s is the speed of the car, and k is a constant of proportionality.

Using the given information, we can solve for k:

75 = k * 30²

k = 75 / (30²) = 0.0833

Now we can use this value of k to find the stopping distance for a speed of 50 mph:

D = 0.0833 * 50² = 208.3 feet

Therefore, the stopping distance for a car traveling at 50 mph is 208.3 feet.

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Answer:

If it costs 5% of $75  it would be $3.75

If it is 5% off $75 it would be $71.25

How we find the answer.

To find 10% of an item you move the decimal point once to the right

If we do this to 75.00 it would be 7.500

We can remove the two 0's

7.5

We are not looking for 10% though we are looking for 5%

Half of 10 = 5 so half 7.5

3.75 is 5% of 75

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

Now if we want to find out 5%  off of 75 we subtract

75.00 - 3.75

71.25

Hope i could help

Answer:

$3.75

Step-by-step explanation:

If the item was on sale and cost 5% of its original price, to find the answer we would have to find 5% of 75 and to do this we have to do 5 ÷ 100 × 75

This means that the price would be $3.75

Hope this helps, have a lovely day! :)

The simple  interest values are all wrong

Simple Interest (S.I) is a method of charging or yielding a specific percentage on the principal amount borrowed/deposited in a particular period. It is calculated using the formula

SI = (Principal*Rate*Time)/100,

a) SI = (450*25.2*3)/100,

SI = %70.2

2) SI = (Principal*Rate*Time)/100,

SI = (250*3.75*5)/100,

$46.875

(3) SI = (Principal*Rate*Time)/100,

SI = (1800*2.1*2)/100,

SI = $75.6

4) SI = (Principal*Rate*Time)/100,

SI = (1500*2.9*2)/100,

SI = $87

5) SI = (Principal*Rate*Time)/100,

SI = (50*1.9*10)/100,

SI =$9.5

6) SI = (Principal*Rate*Time)/100,

SI = (8*0.7*300)/100,

SI = $16.8

7) SI = (Principal*Rate*Time)/100,

SI = (125*2.03*4)/100,

SI = $10.15

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According to the question the resulting table would have 109 rows.

Table is a piece of furniture with a flat top and one or more legs, used as a surface for working at, eating from or on which to place things. Tables come in a variety of materials, shapes, and sizes and are used in many different settings, including homes, offices, and commercial establishments.

This is because all 90 players who played for 1 day would be joined, plus the 10 players who played across 2 days. Of the 90 players who played for 1 day, 82 would have 1 row each from the join, 7 would have 2 rows from the join, and 1 would have 0 rows from the join (since it was not in Table B). Of the 10 players who played across 2 days, 9 would have 1 row each from the join, and 1 would have 2 rows from the join. This adds up to a total of 109 rows.

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[tex]y =ax+b[/tex]

[tex]x = 0 \iff a(0) + b = 3 \implies b = 3[/tex]

[tex]x = 1 \iff a(1) + 3 = 5 \implies a = 2\\[/tex]

[tex]\implies \bf y = 2x + 3[/tex]

___________

[tex]x = 2 \iff 2(2) + 3 = 4 + 3 = 7[/tex]

[tex]x = 3 \iff 2(3) + 3 = 6 + 3 = 9[/tex]

The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.

Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.

Nοw,

Given statement can be written as

Twο times=2x

six less than 2 times=2x-6

is nο mοre than 17= 2x-6≤17

where x is the number.

Hence,

          The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

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The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

What is Subtraction?

One of the four arithmetic operations, along with addition, multiplication, and division, is subtraction, which is denoted by the minus sign. The operation of subtraction represents the removal of items from a collection. In the adjacent image, for instance, there are 5 2 peaches, which means 5 peaches with 2 subtracted, making a total of 3 peaches.

As a result, 5 minus 2 equals 3, or the difference between 5 and 2. Although subtraction is most often used in mathematics with natural numbers, it can also be used with other types of objects, such as negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices, to remove or decrease physical and abstract quantities.

The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

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