6,318÷78 in long division

Answer:

x=16/3

x=5 1/3

x=5,3333333.....

Step-by-step explanation:

x+2/3= 6

x= 6-2/3

x=16/3

x= 5 1/3

x=5,33333333333......

I hope this will help you

Answer:

i dont get it?

Step-by-step explanation:

yes a right angle is 90^o

1. 177.441177

2. 354.882354

3. 118.294118

4. 473.176472

5. 236.588236

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the  the point in time where the cost of installing either will be the same.

Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.

We have two linear equations given,

C = 100t + 5000 and C = 75t + 7000.

The point of intersection of these linear equations will be when both the equations are equal.

100t + 5000 = 75t + 7000

100t - 75t = 7000 - 5000

25t = 2000

t = 2000/25

t = 80

This is the point in time where the cost of installing either will be the same, that is after 80 months.

Cost of installing = (100 × 80 ) + 5000 = 13,000

Or                         = (75 × 80) + 7000 = 13000

Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.

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Answer:

y = -31/5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 2x - 7

5x + 2 = 4

Step 2: Solve for x

Step 3: Solve for y

Answer:

$ 600

Step-by-step explanation:

From the question given above, the following data were obtained:

Principal (P) = $ 3000

Time (T) = 5 years

Rate (R) = 4%

Interest (I) =?

The total interest he will receive can be obtained as follow:

I = PTR/100

I = 3000 × 5 × 4 / 100

I = 60000 / 100

I = $ 600

Thus, the total interest he will receive is $ 600

The amount of $600 received by Prince Charming on the investment of $3000 for 5 years.

Prince Charming invests $3000, thus the principal amount is $3000.

He invest the same amount for 5 years, thus time we have to paid on this principal is 5 years.

The rate for which the principal amount increase is 4 %.

The formulated way to represent the simple interest (I) after passing t years of time, at a rate of r % and having a principal amount of P is mentioned below.

\(I=\dfrac{P \times r \times t}{100}\)

Substitute the given values in the above formula to calculate simple interest.

\(\begin{aligned}I&=\dfrac{3000 \times 4 \times 5}{100}\\&=600 \end{aligned}\)

Thus, the amount of $600 received by Prince Charming on the investment of $3000 for 5 years.

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Answer:

300%

Step-by-step explanation:

because 9/3×100=900/3=300 so it is 300%

Answer:

300%

Step-by-step explanation:

9/3 * 100%

900%/3 = 300%

Answer:

An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Only 2 of the 11 companies were planning to increase their workforce

This means that \(n = 11, \pi = \frac{2}{11} = 0.182\)

80% confidence level

So \(\alpha = 0.2\), z is the value of Z that has a pvalue of \(1 - \frac{0.2}{2} = 0.9\), so \(Z = 1.28\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 - 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.033\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 + 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.331\)

An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.

WE WILL FIRST FIND THE SLOPE BETWEEN THE POINTS

\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{6 - 2}{2 - 4} \\ m = \frac{4}{ - 2} \\ m = - 2\)

I WILL USE POINT (2,6) TO GET THE VALUE OF c

\(6 = - 2(2) + c \\ 6 = - 4 + c \\ c = 6 + 4 \\ c = 10\)

since the general equation of a straight line is given by y=mx+c

\(y = - 2x + 10\)

ATTACHED IS THE SOLUTION

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Find the gradient of the line first.

Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.

Gradient = (6-2) ÷ (2-4) = -2

Eqn is y = -2x + c

Substitute either one of the coordinates of the points into the equation to find c.

2 = -2(4) + c

c = 10

Equation of the line is y = -2x + 10

The coordinates of point R after the dilation are (-9, 12).

What is dilation?

A dilation is a transformation that stretches or shrinks a figure. In a dilation with scale factor k, each point in the figure is multiplied by k.

The center of dilation is a fixed point in the plane. Based on the scale factor and the center of dilation, the dilation transformation is defined.

If the scale factor is more than 1, then the image stretches.

If the scale factor is between 0 and 1, then the image shrinks.

To find the coordinates of point R(-3, 4) after a dilation with scale factor 3, we can apply the dilation to the coordinates of the point:

R' = (3*-3, 3*4)

R' = (-9, 12)

Hence, the coordinates of point R after the dilation are (-9, 12).

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Answer:

\(3\sqrt{22}\)

Step-by-step explanation:

The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)

Multiply

The value of the equation f(x) = 2.5x - 10.5 and g(x) = 64(0.5x) are calculated as x = 2: f(x) = 2.5(2) - 10.5 = -5.5 and g(x) = 64(0.5(2)) = 64.

The substitution method is a quick and easy way to identify the variables' solutions to a set of linear equations. It entails, as the name implies, determining the value of the x-variable in terms of the y-variable from the first equation, and then substituting or replacing the value of the x-variable in the second equation. So, we may solve the equation and determine the value of the y-variable. Finally, we can use any of the above equations with the value of y to determine x. It is also possible to solve for x first, then for y, in the opposite order.

The given equation are f(x) = 2.5x - 10.5 and g(x) = 64(0.5x).

Substituting the value of x we have the value in the table as follows:

x = 2:

f(x) = 2.5(2) - 10.5 and g(x) = 64(0.5(2))

f(x) = -5.5                     g(x) = 64

For x = 3:

f(x) = 2.5(3) - 10.5 and g(x) = 64(0.5(3))

f(x) = -3                         g(x) = 96

For x = 4:

f(x) = 2.5(4) - 10.5 and g(x) = 64(0.5(4))

f(x) = -0.5                     g(x) = 128

For x = 5:

f(x) = 2.5(5) - 10.5 and g(x) = 64(0.5(5))

f(x) = 2                          g(x) = 160

For x = 6:

f(x) = 2.5(6) - 10.5 and g(x) = 64(0.5(6))

f(x) = 4.5                       g(x) = 192

Hence, the value of the equation f(x) = 2.5x - 10.5 and g(x) = 64(0.5x) are calculated as x = 2: f(x) = 2.5(2) - 10.5 = -5.5 and g(x) = 64(0.5(2)) = 64.

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The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Answer:

  (x, y) = {(-2, -3), (2, 5)}

Step-by-step explanation:

You want to solve the system of equations y=x²+2x-3 and y=2x+1.

The two expressions for y can be equated, and the resulting equation put in standard form.

  x² +2x -3 = 2x +1

  x² -4 = 0 . . . . . . . . . . subtract (2x+1)

  (x -2)(x +2) = 0 . . . . . factor

Values of x that make the factors zero are 2 and -2.

Corresponding values of y are ...

  y = 2x +1 = 2(2) +1 = 5

  y = 2(-2) +1 = -3

Solutions are ...

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Answer:

Answer is a

Step-by-step explanation:

I don't want to explain

you can look at the graph when Y = 0 and the value of X on this point is the solution

so, the solution is

x=-6 and x=3

because is the moment the graph touches the Y axis or y is equal 0

7)

Given data:

The given expresson is a=7.7x10^15-(9.9x10^13)

The given expression can be written as,

a=770x10^13-9.9x10^13

=(770-9.9)x10^13

=760.1x10^13.

8)

Given data:

The given expresson is b=8.9x10^5-(6.5)x10^6

The given expression can be written as,

b=8.9x10^5-65x10^5

=(8.9-65)x10^5

=-56.1x10^5

The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

\(a(9 {a}^{2} b + ba)\)

hope it's helpful ❤❤❤❤❤❤❤

THANK YOU.

Answer:

Step-by-step explanation:

Given

Total Number of Cards = 52

Required

Probability of not picking a spade

Let P(S) represents the probability of picking a spade;

\(P(S) = \frac{n(S)}{Total}\)

Where n(S) is the number of spades

\(n(S) = 13\)

Substitute \(n(S) = 13\) and 52 for Total

\(P(S) = \frac{13}{52}\)

\(P(S) = \frac{1}{4}\)

Let P(S') represents the probability of not picking a spade

In probability;

\(P(S) + P(S') = 1\)

Substitute \(P(S) = \frac{1}{4}\)

\(\frac{1}{4} + P(S') = 1\)

\(P(S') = 1 - \frac{1}{4}\)

\(P(S') = \frac{4-1}{4}\)

\(P(S') = \frac{3}{4}\)

\(P(S') = 0.75\)

Hence, the probability of not selecting a spade is 3/4 or 0.75

The soccer ball is above 15 feet between 0.25 seconds and 1 second.

To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.

Given the quadratic function h(t) = -16t² + 20t + 11, we can rewrite the inequality as follows:

-16t² + 20t + 11 > 15

Subtracting 15 from both sides:

-16t² + 20t - 4 > 0

Simplifying further:

-16t² + 20t - 4 = -4(4t² - 5t + 1) = -4(t - 1)(4t - 1) > 0

Now, we can solve for t by finding the values that make the inequality true. We have two factors: (t - 1) and (4t - 1).

Setting each factor greater than zero and solving for t:

t - 1 > 0 => t > 1

4t - 1 > 0 => 4t > 1 => t > 1/4

So, we have t > 1 and t > 1/4. To satisfy both conditions, t must be greater than the maximum of 1 and 1/4, which is 1.

Therefore, the soccer ball is above 15 feet for t > 1 second.

The correct answer is:

C. The soccer ball is above 15 feet between 0.25 seconds and 1 second.

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