Graph the system of equations to determine the solution.
y=1/2 x+3
2y = x +6

Answer: $3,842.1

Step-by-step explanation:

-$750.25 + $4,592.35 = $3,842.1

Answer:

Step-by-step explanation:

3/4 * 24 = (3*24)/4

18 = 72 : 4

18 = 18

Answer:

the length of the other leg is 13 units.

Step-by-step explanation:

The formula is:

a² + b² = c²

where a and b are the lengths of the legs and c is the length of the hypotenuse.

To find the length of the other leg, you can use the following steps1:

Identify the given values and plug them into the formula. In this case, you know that one leg is 9 units long and the hypotenuse is 16 units long. Let a = 9 and c = 16. Then you have:

9² + b² = 16²

Simplify and solve for b. To do this, you need to isolate b by subtracting 9² from both sides and then taking the square root of both sides. You get:

b² = 16² - 9² b² = 256 - 81 b² = 175 b = √175

Round to the nearest whole number. Since √175 is not a whole number, you need to round it to the nearest integer. You can use a calculator to find that √175 is approximately 13.23. The closest whole number is 13, so you round down.

Step-by-step explanation:

use Pythagorean theorem

c = 16

a = 9

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {b}^{2} = {16}^{2} \\ 81 + {b}^{2} = 256 \\ {b}^{2} = 175 \\ b \: = 13.22 \\ [/tex]

or you can round it to 13

Step-by-step explanation:

to get a we use cos and for b we use sin

so

cos(45°) =a/5√2....... when u criss cross it

a = cos(45°) × 5√2

a = √2/2 × 5√2

a= 5

sin(45) = b/5√2

b= sin(45) × 5√2

b = 5

In other way if u find the 1st side you r indirectly find the 2nd one which they are equal .

ANSWER

[tex] \frac{9}{4} + \frac{2}{8} \\ \\ = \frac{9 + 2}{4} \\ \\ = \frac{11}{4} \\ \\ = 2.75[/tex]

hope it helps

The actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

The margin of error in the report stating that a 10-year-old American child spends an average of 20.02 to 25.36 minutes playing outdoors per day can be calculated by subtracting the lower value from the higher value and dividing by 2. In this case, the margin of error is :

To find the margin of error, we need to calculate the halfway point between these two values.
(25.36 - 20.02) / 2 = 2.67

Therefore, the margin of error is approximately 2.67 minutes. This means that the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

Thus, the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

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Answer:

32 feet

Step-by-step explanation:

To do this, we can use the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In other words:

a^2 + b^2 = c^2

where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse.

Plugging in the given values, we get:

5^2 + 13^2 = c^2

25 + 169 = c^2

194 = c^2

c = sqrt(194)

Using a calculator, we can approximate c to be about 13.93 feet.

Therefore, the total amount of fencing needed for the entire animal pen is:

5 + 13 + 13.93

31.93 feet

Answer:Therefore, Shar needs 30 feet of fencing for the entire animal pen. So the answer is 30 feet.

Step-by-step explanation:

To find the length of the third side, we can use the Pythagorean theorem, which states that for a right triangle with legs a and b, and hypotenuse c:

a^2 + b^2 = c^2

In this case, the shortest side is 5 feet and the longest side is 13 feet, so we can set up the equation:

5^2 + b^2 = 13^2

Simplifying:

25 + b^2 = 169

b^2 = 144

b = 12

So the length of the third side is 12 feet. To find the total length of fencing needed, we add up the lengths of all three sides:

5 + 12 + 13 = 30

Therefore, Shar needs 30 feet of fencing for the entire animal pen. So the answer is 30 feet.

The probability of,

i) Given that there are 5 black retrievers, 3 brown hounds, and 4 black setters.

Total number of dogs = 5 + 3 + 4 = 12

Probability of getting a black retriever =

number of black retrievers / total number of dogs = 5/12.

Probability of getting a brown hound =

number of brown hounds / total number of dogs = 3/12.

Now, the probability of picking a black retriever and then a brown hound = probability of getting a black retriever x probability of getting a brown hound = 5/12 x 3/12 = 15/144.

ii) Given that there are 3 blue marbles and 2 red marbles.

Total number of marbles = 3 + 2 = 5

Probability of picking a blue marble =

number of blue marbles / total number of marbles = 3/5

Similarly, the probability of picking another blue marble is also = 3/15

Now, the probability of picking a blue marble at first, replacing it, and then picking another blue marble = 3/5 x 3/5 = 9/25.

From the above solution, we solved both problems.

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Repeating the 4 digit number is the same as multiplying by 10001, which factors into 73*137 (both prime). The only way 10001n does not have some other prime factor is if n also has only prime factors of of 73 and/or 137. Since 73*137 is 5 digit number, and both 137 and 73 have too few digits, the only product left is 73² = 5329.

The weight of the remaining paper is 5/12 pounds.

A ream of printer paper is a standard measure of paper quantity that typically consists of 500 sheets. The weight of a ream of paper depends on the type of paper and its thickness. In this problem, we are given that a ream of printer paper weighs 5 1/4 pounds.

Now, Adam used 1/3 of a ream to print flyers. We can find the weight of the paper Adam used by multiplying 1/3 of the weight of a ream of paper by its weight:

Weight of paper used = (1/3) x 5 1/4 pounds

Weight of paper used = (5/3) x (1 1/4) pounds

Weight of paper used = 6 7/12 pounds

To find the weight of the remaining paper, we need to subtract the weight of the paper used from the weight of the full ream:

Weight of remaining paper = Weight of full ream - Weight of paper used

Weight of remaining paper = 5 1/4 pounds - 6 7/12 pounds

Weight of remaining paper = (21/4) pounds - (79/12) pounds

Weight of remaining paper = (21/4) pounds - (6 7/12) pounds

Weight of remaining paper = (21/4) pounds - (6 7/12) pounds

Weight of remaining paper = (84/12) pounds - (79/12) pounds

Weight of remaining paper = (5/12) pounds

Therefore, the weight of the remaining paper is 5/12 pounds.

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The parent need to make an initial investment of about $12414.68 so as  to grow to $40,000 in 18 years.

The formula for one to use so as to get the future value of an initial investment P at a fixed annual interest rate r, continuously compounded for t years, is given below:

[tex]FV = P * e^r^t[/tex]

where:

A = Final amount ($40,000)

P = Initial investment

e = Euler's number (approximately 2.71828)

r = Interest rate (6.5% or 0.065)

t = Time period (18 years)

Note that  the parent wants the investment to go up to $40,000 in 18 years and there is a continuous interest rate of 6.5%.

Then it will be:

FV = $40,000

r = 0.065 ( 6.5%)

t = 18 years

We have to substitute the above values into the formula, so it will be:

[tex]$40,000 = P x e^(^0^.^0^6^5^ * ^1^8^)\\[/tex]

[tex]= $40,000/ e^(^0^.^0^6^5^ * ^1^8^)\\P= $40,000/ 2.71828^(^0^.^0^6^5^ * ^1^8^)\\ =$12414.68[/tex]

Therefore, the initial investment is $12414.68

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[tex] \sf \longrightarrow \: {x}^{2} + 3x - 4[/tex]

[tex] \sf \longrightarrow \: {x}^{2} + 4x - 1x - 4[/tex]

[tex] \sf \longrightarrow \: x(x + 4) \: - 1(x + 4)[/tex]

[tex] \sf \longrightarrow \: (x + 4) \: (x - 1) \\ [/tex]

Option C) (x + 4) (x - 1)

The factors of the expression x² + 3x - 4 are (x + 4) and (x - 1).

Option C is the correct answer.

We have,

To find the factors of the quadratic expression x² + 3x - 4, we can use either factoring by grouping or the quadratic formula.

In this case, we can factor it by splitting the middle term.

The expression is x² + 3x - 4.

Step 1:

Split the middle term (3x) into two terms whose product is equal to the product of the first and last coefficients (x² * -4 = -4x²) and whose sum is equal to the middle coefficient (3x).

The two terms are 4x and -x because 4x * -x = -4x² and 4x + (-x) = 3x.

Step 2:

Now, we rewrite the expression using the split terms:

x² + 4x - x - 4

Step 3:

Factor by grouping:

(x² + 4x) + (-x - 4)

Step 4:

Factor out the common terms from each group:

x(x + 4) - 1(x + 4)

Step 5:

Notice that both terms have a common factor of (x + 4):

(x + 4)(x - 1)

Thus,

The factors of the expression x² + 3x - 4 are (x + 4) and (x - 1).

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Mix fraction 3(6/10) written as a decimal is 3.6.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To write 3 6/10 as a decimal, we can first convert the mixed number to an improper fraction.

To do this, we multiply the whole number (3) by the denominator of the fraction (10) and add the numerator (6):

3 6/10 = (3 x 10 + 6)/10 = 36/10

Next, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

36/10 = (18 x 2)/(5 x 2) = 18/5

Now, we have an improper fraction.

To convert it to a decimal, we can divide the numerator by the denominator using long division or a calculator:

18 ÷ 5 = 3.6

Therefore,

3 6/10 written as a decimal is 3.6.

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By the principle of mathematical induction, the equation 2+7+12+17. +[5n-3]=n/2[5n-1] holds for all positive integers n.

To prove that the equation 2+7+12+17+...+[5n-3] = n/2[5n-1] holds for all positive integers n using mathematical induction, we need to show two things:

Base case: Prove that the equation holds for n=1.

Inductive step: Assume that the equation holds for n=k, and then show that it also holds for n=k+1.

Base case:

When n=1, we have:

2 = 1/2[5(1)-1]

2 = 1/2[4]

2 = 2

Therefore, the equation holds for n=1.

Inductive step:

Assume that the equation holds for n=k, i.e.,

2+7+12+17+...+[5k-3] = k/2[5k-1]

Now, we need to show that the equation also holds for n=k+1, i.e.,

2+7+12+17+...+[5(k+1)-3] = (k+1)/2[5(k+1)-1]

We can simplify the left-hand side of the equation as follows:

2+7+12+17+...+[5(k+1)-3] = [2+7+12+17+...+[5k-3]] + [5(k+1)-3]

Using the assumption from the inductive step, we can substitute k/2[5k-1] for the first part of the equation:

2+7+12+17+...+[5(k+1)-3] = k/2[5k-1] + [5(k+1)-3]

Simplifying the right-hand side of the equation:

2+7+12+17+...+[5(k+1)-3] = (5k² - k + 10k + 5) / 2

2+7+12+17+...+[5(k+1)-3] = (5k² + 9k + 5) / 2

2+7+12+17+...+[5(k+1)-3] = (k+1)/2[5(k+1)-1]

Therefore, the equation holds for n=k+1.

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Answer:

min=28

lower=34

median=39

upper=46.5

max=55

inter range=12.5

Step-by-step explanation:

Nice that the numbers are in order for you

The min is your smallest number = 28

To find the next part separate into 4 equal parts so you have 3 lines

The first line is between 34 and 34 the average of the 2 numbers is your lower quartile

lower quartile =34

middle line is your median between 39 and 39

median = 39

upper quartile is that 3rd line between 42 and 51 average is upper

upper quartile = (42+51)/2 = 46.5

max is the highest number = 55

Interquartile range is the difference between upper and lower = 12.5

Answer:

Step-by-step explanation:

Answer:

Hope this helps :)

Step-by-step explanation:

[tex]10^{27} =-5x[/tex]

The solution to the equation 3( 8p - 1 ) = -32 - 5 is p = -17/12

Given the equation in the question:

3( 8p - 1 ) = -32 - 5

To determine the solution, we simplify the left-hand side first by using the distributive property:

3(8p - 1)

3×8p -3×1

24p - 3

Now we can substitute this expression into the original equation:

24p - 3 = -32 - 5

Next, we'll add 3 to both sides:

24p = -32 - 5 + 3

24p = -34

Finally, we'll divide both sides by 24 to isolate p:

p = -34/24

Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor of 2, we get:

p = -17/12

Therefore, the solution is p = -17/12.

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Answer:

S = {1, 2, 3, 4, 5, 6, 7, 8} this is the answer

Step-by-step explanation:

Let's call the length of the base of the triangle "b". We know that the height of the triangle is double the length of the base, so the height can be written as "2b".

We also know that the area of the triangle is approximately 200 square feet. The formula for the area of a triangle is:

A = (1/2)bh

where A is the area, b is the length of the base, and h is the height.

We can substitute in the values we know:

200 = (1/2)bh

Since we know that h = 2b, we can substitute that in:

200 = (1/2)b(2b)

Simplifying:

200 = b^2

This is the equation we can use to find the length of the sign's base, b.

We can set the equation to: 200 = (1/2) × b × (2b)

To find the length of the sign's base, b, we can use the equation for the area of an isosceles triangle: A = (1/2)bh, where b is the length of the base and h is the height. Since we know that the height is double the length of the base, we can substitute 2b for h in the equation: A = (1/2)b(2b). Simplifying, we get A = b^2. Since we know that the area should be approximately 200 square feet, we can set A = 200 and solve for b: b^2 = 200. Taking the square root of both sides, we get b = 14.14 feet. Therefore, the length of the sign's base should be approximately 14.14 feet.

To find the equation for the length of the base of the sign, we'll use the formula for the area of a triangle, which is:

Area = (1/2) × base × height

Since the height of the triangle is double the length of its base (h = 2b), we can rewrite the equation as:

Area = (1/2) × b × (2b)

The owner of Trixie's Sweets and Treats wants the area of the sign to be approximately 200 square feet. So, we can set the equation to:

200 = (1/2) × b × (2b)

Now we have the equation that you can use to find the length of the sign's base, b.

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Answer:

300feet²

Step-by-step explanation:

Calculate the area of a parallelogram

A=b×h(b=base,h=height)

b=20feet,h=15feet

A=20feet×15feet=300feet²

So the area is 300 feet²

The idealized regression line is y = β₀ + β₁x + ε, and the least-squares regression line is Y = b₀ + b₁x. Four assumptions for regression inference are linearity, independence, homoscedasticity, and normality. The standard error of the regression slope is affected by the spread, sample size, and relationship strength. The formula for the standard error of the slope is SEb₁ = √[ Σ([tex]y_i - Y_i[/tex])² / (n-2) ] / √[ Σ([tex]x_i[/tex] - X)² ]. If there is no association between two variables, the slope of the regression line should be zero.

There are two equations commonly used in regression analysis: the idealized regression line and the least-squares regression line.

The equation for the idealized regression line is

y = β₀ + β₁x + ε

where

y is the dependent variable

x is the independent variable

β₀ is the intercept

β₁ is the slope

ε is the error term

The equation for the least-squares regression line is

Y = b₀ + b₁x

where

Y is the predicted value of y

x is the independent variable

b₀ is the intercept

b₁ is the slope

There are four assumptions and conditions that must be met in order to perform inference for regression

The relationship between the independent variable and dependent variables is called Linearity . To check linearity, plot the dependent variable against the independent variable and look for a straight-line pattern.

Independence, The observations are independent of each other. To check independence, ensure that there is no relationship between the residuals (the difference between the observed value and the predicted value) and any other variables.

The constant variance of errors across independent variable of all level is called homoscedasticity. To check homoscedasticity, plot the residuals against the predicted values and look for a consistent spread of points around zero.

Normality, The errors are normally distributed. To check normality, plot a histogram of the residuals and look for a roughly bell-shaped distribution.

The formula for the standard error for the slope is

SEb₁ = √[ Σ([tex]y_i[/tex]- [tex]Y_i[/tex])² / (n-2) ] / √[ Σ([tex]x_i[/tex] - X)² ]

where

[tex]y_i[/tex], observed value of variable which is dependent for the ith observation

[tex]Y_i[/tex] is the predicted value of the dependent variable for the ith observation

[tex]x_i[/tex], the observed value of variable which is independent for the ith observation

X is the mean of the independent variable

n is the sample size

The formula for the sampling distribution for regression slopes is

b₁ ~ N(β₁, σ² / Σ([tex]x_i[/tex] - X)²)

where

b₁, least-squares regression line's slope

β₁ is the true population slope

σ² is the variance of the errors

If there is no association between two variables, the slope of the regression line should be zero. it depicts that the variable which is independent has no effect on the variable which is dependent.

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The surface area of the triangular pyramid is approximately 684.77 square inches.

To find the surface area of the triangular pyramid, we need to calculate the area of each of its four triangular faces and then add them together.

First, we need to find the area of the equilateral triangular base. The area of an equilateral triangle with side length "s" is given by

Abase = ([tex]\sqrt{3/4}[/tex]) x [tex]s^{2}[/tex]

Substituting s = 19 inches, we get

Abase = ([tex]\sqrt{3/4}[/tex]) x [tex]19^{2}[/tex]

Abase = 166.89 square inches

Next, we need to find the area of each of the triangular faces. Each triangular face has base length 19 inches, and its height can be found using the Pythagorean theorem, since we know the slant height and the height of the equilateral triangle.

Let's call the height of the equilateral triangle "h". From the Pythagorean theorem, we know that

[tex]slant height^{2}[/tex] = (1/4) x [tex]s^{2}[/tex] + [tex]h^{2}[/tex]

Substituting s = 19 inches and slant height = 16 inches, we can solve for h

[tex]16^{2}[/tex] = (1/4) x [tex]19^{2}[/tex] + [tex]h^{2}[/tex]

256 = 90.25 + [tex]h^{2}[/tex]

h = 13.03 inches

Now we can calculate the area of each triangular face

Aface = (1/2) x base x height

Aface = (1/2) x 19 x 13.03

Aface = 123.69 square inches

Finally, we can calculate the surface area of the pyramid

Surface Area = Abase + 4 x Aface

Surface Area = 166.89 + 4 x 123.69

Surface Area = 684.77 square inches

Therefore, the surface area of the triangular pyramid is approximately 684.77 square inches.

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Result:

Taxable income of the individual = Rs. 420,000.

To calculate the taxable income, we will subtract the allowance from the individual's yearly income:

Given:

Yearly income = Rs. 4,44,000

Allowance Rs. 24,000

Taxable Income = Yearly Income - Allowance

Taxable Income = Rs. 4,44,000 - Rs. 24,000

Taxable Income = Rs. 420,000.

Therefore, the taxable income of the individual is Rs. 420,000.

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The triangles given are congruent.

Given are three triangles, we need to state their properties.

So, as we can see that the triangles are following the reflection transformation,

The red triangle is being reflected to form green triangle and green is reflected to form blue triangle.

Since, the reflection transformation forms congruent figures hence the triangles are congruent.

Hence, the triangles given are congruent.

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The probability of drawing a w both times would be C. 1 / 676.

The probability of rolling those numbers would be 3 / 36 = 1 / 12

.

Addressing the first inquiry, the chances of pulling out a w on the initial draw is 1/26. Armed with the knowledge that the alpha is subsequently reinstated, then there is also a probability of 1/26 to draw a w on the second try.

Subsequently, drawing a w both times entails a likelihood of (1/26) multiplied by (1/26), equaling 1/676.

For the subsequent enquiry, as each cube heave holds six potential outcomes, two such occasions result in 6 times 6, or 36 potential results. The odds for flicking a 6 on the very first cube is 1/6, and those for tossing an uneven number on the subsequently toss is 1/2 since three of the six numbers would be odd. For these two circumstances co-occurring together, the probability is reduced logically to (1/6) multiplied by (1/2), amounting to 1/12 in total.

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Answer:

-4.740

Step-by-step explanation:

sum if infinite geometric series

S= 243/5

Answer: [tex]x=\frac{15}{11}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} x-\frac{1}{3}x=x-1[/tex]

1. Find the common denominator, which is 15

2. Multiply each denominator to get 15

[tex]\frac{9}{15} x-\frac{5}{15}x=x-1[/tex]

3. Combine like terms

[tex]\frac{4}{15} x=x-1[/tex]

4. Subtract x from the right

[tex]\frac{4}{15} x-x=1[/tex]

5. Combine the terms

[tex]-\frac{11}{15} x=-1[/tex]

6. Multiply both sides by 15 to remove the fraction

[tex]-11x=-15[/tex]

7. Divide both sides by -11

[tex]x=\frac{15}{11}[/tex]

Mrs. Byers will need 29 yards of red fabric for each of the 5 costumes she is making, based on the equation 690 + 5r = 834

Let's assume that each costume requires "r" yards of red fabric.

Since Mrs. Byers is making 5 costumes, the total amount of red fabric she will need is 5r

We know that the total amount of blue fabric used in all 5 costumes is 834 yards, and each costume requires 138 yards of blue fabric. Therefore, we can write

5 × 138 = 690

The total amount of fabric used in all 5 costumes is

690 + 5r

We also know that the total amount of fabric used in all 5 costumes is 834 yards. Therefore, we can write

690 + 5r = 834

This is the equation we can use to determine how much red fabric "r" is needed for each costume.

To solve for "r," we can start by subtracting 690 from both sides

5r = 834 - 690

5r = 144

Finally, we can divide both sides by 5 to isolate "r"

r = 28.8

r ≈ 29 yards

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