Consider the following equations. y=2x+7 2x+y=−7 y=12x−4 y=−2x+7 2y−x=−8 Which two equations represent a system of linear equations with infinitely many solutions? Responses y=12x−4 and 2y−x=−8 , y is equal to 1 half x minus 4 and 2 y minus x is equal to negative 8 y=−2x+7 and y=12x−4 y is equal to negative 2 x plus 7 and y is equal to 1 half x minus 4 2x+y=−7 and y=−2x+7 2 x plus y is equal to negative 7 and y is equal to negative 2 x plus 7 y=2x+7 and y=−2x+7

Your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.

To calculate the sum that your close relative has to contribute in a bond common finance to supply you with $18,000 per year, you wish to utilize the equation for the display esteem of an annuity.

PV = PMT * (1 - (1 + r)^(-n)) / r

where:

PV = display esteem

PMT = installment sum (in this case, $18,000 per year)

r = intrigued rate (3.0%)

n = number of periods (in this case, 1 year)

Substituting the values into the equation:

PV = $18,000 * (1 - (1 + 0.03)^(-1)) / 0.03

PV = $18,000 * (1 - 0.9709) / 0.03

PV = $18,000 * 0.0291 / 0.03

PV = $17,430

Subsequently, your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.

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Answer:

Yes, the bottom shelf is parallel to the middle shelf. Angle 6 measures 120°, so angles 6 and 11 are congruent alternate exterior angles.

The radius of the cylindrical cup is 6 centimeters.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given that the volume of the cylindrical cup is 1356.48 cubic centimeters and the height is 12 cm.

We can substitute these values into the formula and solve for the radius:

V = π × r² × h

r = √( V / (πh) )

r = √( 1356.48 / ( 3.14 × 12) )

r = 6 cm

Therefore, the radius is 6cm.

Option C) 6cm is the correct answer.

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The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 515, \sigma = 125[/tex]

The proportion of scores less than 675 is the p-value of Z when X = 675, hence:

Z = (675 - 515)/125

Z = 1.28

Z = 1.28 has a p-value of 0.8997.

Hence the percentage is 89.97%.

The proportion of scores greater than 550 is one subtracted by the p-value of Z when X = 550, hence:

Z = (550 - 515)/125

Z = 0.28

Z = 0.28 has a p-value of 0.6103.

1 - 0.6103  = 0.3897, hence the amount is given as follows:

E(X) = 1000 x 0.6103 = 610.

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Answer:

It's very simple you just subtract 432 and 129. And you get 303. Then you just multiple 303 by 5 and you get 1515.

1515

The 95% confidence interval of (-0.02, 0.16) mm for the median difference between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution means that we are 95% confident that the true median difference of healing in mm will exist within the confidence interval of (-0.02, 0.16).

The 95% confidence interval of (-0.02, 0.16) mm means that there is a 95% chance that the true median difference in healing between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution falls within this range. This means that 95% of all random samples drawn will exist within this confidence interval, and we can be confident that the methods used in this study have at least as much healing as was seen in the sample median difference of new tissue formed in mm. Therefore, with 96% confidence, we can say that the true median difference in healing between the two methods is somewhere within this range. Methods used to generate confidence intervals that bracket the true median difference will form confidence intervals that fit within the confidence interval of (-0.02, 0.16) we have calculated.

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The null and alternative hypothesis is represented by option A.

The test statistic is 0.153.

We want to test the claim that women and men have the same mean diastolic blood pressure.Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men.

The t-statistic value will be:

= (69.81 - 69.53) / (✓10.46²/26 + 11.24²/26)

=0.153

Since p-value for two tail test=0.879 which is greater than =0.05(0.879>0.05) So we do not reject H0.

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Answer:

26.5

Step-by-step explanation:

The formula for the area of a trapezoid is:

A = (1/2)h(b₁ + b₂)

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

Substituting the given values:

A = (1/2)(4.3 m)(9.2 m + 3.2 m)

A = (1/2)(4.3 m)(12.4 m)

A = 26.52 m²

Rounding to the nearest tenth:

A ≈ 26.5

Therefore, the area of the trapezoid is approximately 26.5 square meters.

Answer:

Step-by-step explanation:

You want to know what else Fernando needs to know to figure how much interest he will earn on $4000, if he has the interest rate.

There are two interest formulas. One is for simple interest, and one is for compound interest. So, one bit of information Fernando needs is whether interest is being compounded.

The formulas are ...

  I = P·r·t . . . . . . . simple interest

  I = P((1 +r/n)^(nt) -1) . . . . . . compound interest

If Fernando knows the invested amount P and the interest rate r, then he needs to know 'n' and 't' to be able to choose and use the correct interest formula.

Fernando needs to know ...

Step-by-step explanation:

Tan Φ = opposite leg / adjacent leg

tan 19 = height / 1500

1500 * tan 19 = height = 516 m    <==== must rise this much

I'm assuming you mean "How do I find the value of x such that the arc length of the circle defined by (10x-23) is 106?" So, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 and x ≈ 1.89.

To find the value of x such that the arc length of the circle defined by (10x-23) is 106, we can use the formula for the arc length of a circle:

Arc Length = θr

where θ is the central angle in radians, and r is the radius of the circle.

In this case, we know the arc length is 106, and we need to find the value of x such that the radius is defined by (10x-23). Let's call this radius r.

We can rearrange the formula to solve for the radius:

r = Arc Length / θ

We also know that the central angle in radians is equal to the arc length divided by the radius.

So we can write:

θ = Arc Length / r

Substituting in the values we have:

θ = 106 / (10x-23)

Now we can solve for x. We know that the central angle for a full circle is 2π radians, so the central angle for a circle with radius (10x-23) is:

θ = (2π)(10x-23)

Setting this equal to our previous expression for θ, we have:

106 / (10x-23) = (2π)(10x-23)

Solving for x:

106 = (2π)(10x-23)(10x-23)

106 = (2π)(100x^2 - 460x + 529)

53 = π(100x^2 - 460x + 529)

53/π = 100x^2 - 460x + 529

100x^2 - 460x + (529 - 53/π) = 0

We can solve this quadratic equation using the quadratic formula:

x = [460 ± sqrt(460^2 - 4(100)(529 - 53/π))] / (2(100))

x ≈ 2.71 or x ≈ 1.89

Therefore, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 or x ≈ 1.89.

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Answer:

3y+8x

Step-by-step explanation:

To solve this problem we first have to add similar terms

Adding like terms:

So let us add up the sides that have the same variable. Let us solve for the variable y first ->

[tex]4+y+2y-2\\\\(y+2y)+(4-2)\\\\3y+2[/tex]

Now we have the simplified form of the y. Now let us solve for x ->

[tex]6x+2+2x-4\\\\(6x + 2x) + (2 - 4)\\\\8x - 2[/tex]

Combine both expressions:

To combine these expressions we add the constants and leave the variables. (We do this because different variables cannot be added together)

[tex]8x - 2 +3y +2\\\\8x + 3y + (-2 + 2)\\\\8x+3y+0\\\\8x+3y[/tex]

So 3y + 8x is the asnwer

Answer:

B. A cube with side lengths of 2 feet has a volume of 8 cubic feet.

v(s) = s^3, so v(3) = 2^3= 8

Answer:

see attatched picture

Step-by-step explanation:

The minimum sample size required to construct a 95% confidence interval for the population mean is 16.

To determine the minimum sample size required to construct a 95% confidence interval for the population mean circumference of tennis balls within 0.05 inch, we need to use the formula for the margin of error:

Margin of error = Z* (σ/√n)

Where Z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Since we want a 95% confidence interval, Z* = 1.96 (from a standard normal distribution table).

We are given that σ = 0.10 inch and we want the margin of error to be 0.05 inch. Plugging in the values, we get:

0.05 = 1.96 * (0.10 / √n)

Solving for n, we get:

n = [(1.96 * 0.10) / 0.05]² = 15.36

We can't have a fractional sample size, so we round up to the nearest whole number. Therefore, the minimum sample size required is 16.

This means that the manufacturer needs to randomly select and measure the circumferences of at least 16 tennis balls to estimate the population mean circumference with 95% confidence and a margin of error of 0.05 inch.

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Answer: 14 and 14

Step-by-step explanation:

So u would Since 13 and 14 are both consecutive integers and their sum is 27, we have our answer.

[tex]9.31*10^5[/tex] gallons are the total gallons of water used by the water park after adding the new ride.

To express the total gallons of water used by the water park after adding the new ride in scientific notation, we need to add the two values together and then convert them to scientific notation.

[tex]8.8*10^5[/tex] gallons + 51,000 gallons = [tex]9.31*10^5[/tex] gallons

Therefore, the total gallons of water used by the water park after adding the new ride is [tex]9.31*10^5[/tex] gallons.

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The quadratic function with roots -9 and 7 is f(x) = x² + 2x - 63

First, recall that a quadratic function has the form:

f(x) = ax² + bx + c

where a, b, and c are constants.

Given the roots of the quadratic function:

-9 and 7
x = -9 and x = 7 are the two distinct solutions to the quadratic equation.

Hence:

x + 9 and x - 7 are the factors of the quadratic equation.

( x + 9 ) ( x - 7 )

Expanding this expression Using FOIL method:

x( x - 7 ) + 9( x - 7 )

x² - 7x + 9x - 63

Collect and add like terms

x² + 2x - 63

Therefore, the function is f(x) = x² + 2x - 63.

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The volume of the sports ball is 6286.28 cm³

A sphere is round, has no edges, and is a solid shape. Examples of a sphere include; The playing ball, balloon, and even light bulbs .

A sphere is a 3-dimensional shape ,and it's therefore a solid shape.

The volume of a sphere is expressed as;

V = 4/3 πr³

where r is the radius of the sphere and v is the volume.

the radius of the sphere is half the diameter.

D = 2r

r = 23/2 = 11.5

therefore ;

V = 4/3 × 3.14 × 11.5³

V = 18858.85/3

V = 6286.28 cm³ ( 2 decimal place)

Therefore the volume of the ball is 6286.28 cm³

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Answer:

Using guess and check, we can estimate the number of years it will take for the investment to grow to $10,000 as follows:

First, we'll assume that it will take 5 years for the investment to grow to $10,000.

After 5 years, the investment would grow to:

$6,500 x 1.03^5 = $7,960.35

Since this is still less than $10,000, we need to increase the number of years.

Next, we'll assume that it will take 10 years for the investment to grow to $10,000.

After 10 years, the investment would grow to:

$6,500 x 1.03^10 = $9,020.14

Since this is still less than $10,000, we need to increase the number of years again.

Finally, we'll assume that it will take 15 years for the investment to grow to $10,000.

After 15 years, the investment would grow to:

$6,500 x 1.03^15 = $10,005.58

Since this is slightly more than $10,000, we can estimate that it will take around 15 years for the investment to grow to $10,000.

Therefore, the estimated number of years it will take for the investment to grow to $10,000 is about 15 years.

If the number of papers is 56, the ratio of the total height in millimeters of 2 mm thick paper to the total height in millimeters of 23 mm thick paper is 2:23.

The ratio is the relative size of two comparable quantities, values, or numbers.

Ratios are computed as the quotients of one value (the numerator) and another (the denominator).

We can depict ratios as decimals, fractions, percentages, or in their standard forms (:).

The total height in millimeters of 2 mm thick paper = 112 mm (56 x 2)

The total height in millimeters of 23 mm thick papers = 1,288 mm (56 x 23)

Ratio = 0.0869 (112 ÷ 1,288) or 2/23 or 8.69%.

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Answer:

(-2, -6)

Step-by-step explanation:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

= (-3 + -1)/2, (-5 + -7)/2

= (-4/2), (-12/2)

= (-2, -6)

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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The number of miles that he would have saved instead would be = 8.6 miles

The amount of miles he traveled south = 7 miles

The amount of miles he traveled east = 5 miles

To calculate the number of miles he would have saved, the Pythagorean formula is used;

That is :

C² = a²+ b²

a = 7

b =5

c² = 7²+5²

= 49+25

= 74

c = √74

= 8.6 miles

Therefore, he would have travelled 8.6 miles instead of 12 miles.

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The graph of g(x) = √(x - 16) is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) =√x

Which has vertex at the origin.

The function g(x) = √(x - 16) is equivalent to g(x) = f(x - 16), which is a translation right 16 units of f(x), according to the graph presented at the end of the answer.

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The record long jump is 8 inches short of 10 yards.

We know that 1 yard is equal to 3 feet, so 10 yards is equal to 10 x 3 = 30 feet.

To find out how many inches short of 10 yards the record long jump is, we need to first convert 29 feet 4 inches to inches only.

We can do this by multiplying the number of feet by 12 (since there are 12 inches in a foot) and then adding the number of inches:

29 feet 4 inches = (29 x 12) + 4

= 348 + 4

= 352 inches

Now we can find out how many inches short of 10 yards the record long jump is:

30 feet = 30 x 12 = 360 inches

360 - 352 = 8

Therefore, the record long jump is 8 inches short of 10 yards.

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To find the percentage of Farmer Gibson's herd that remains after he sold 60 cows, we need to calculate the new total number of cows he has.

Number of cows remaining = Total number of cows - Number of cows sold

Number of cows remaining = 200 - 60

Number of cows remaining = 140

So, Farmer Gibson has 140 cows remaining in his herd.

To find the percentage of cows remaining, we can use the following formula:

Percentage = (Number remaining ÷ Total number) x 100

Plugging in the values we have:

Percentage = (140 ÷ 200) x 100

Percentage = 0.7 x 100

Percentage = 70%

Therefore, Farmer Gibson has 70% of his herd remaining after selling 60 cows.

~~~Harsha~~~

Answer:

  34.8°

Step-by-step explanation:

You want the angle opposite a side of length 8 cm in a right triangle with hypotenuse 14 cm.

The sine relation is the one of interest in this geometry:

  Sin = Opposite/Hypotenuse

  sin(x°) = (8 cm)/(14 cm)

The angle can be found using the inverse sine function:

  x° = arcsin(8/14) ≈ 34.8°

The size of the angle x° is 34.8°.

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