write four solutions for the following equation 4x+7y=12

we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

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Answer:

  (d)  44°

Step-by-step explanation:

You want the angle whose sine is 0.6947.

The arcsine function of your calculator can tell you what this is:

  arcsin(0.6947) ≈ 44°

__

Additional comment

The calculator mode must be set to "degrees."

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Answer:

2a^2 - a + 2 = 0

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Answer:

não sei nam mano foi mal ai

vei kskksksksk

Step-by-step explanation:

The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

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Answer: basically a rising straight line that goes through the origin

Step-by-step explanation:

Answer:

i thig it is hj

Step-by-step explanation:

jk

Each factor can be used more than once, but not all factors will be used x^3-6x^2-9x+54

The completely factored polynomial is (x - 6)(x + 3)(x - 3).

However, I can help you understand and factor the given polynomial: x3 = 6x2 + 9x + 54.

To factor the polynomial, we will follow these steps:

1. Look for a common factor among all terms.
2. If there isn't a common factor, check for possible factorization methods like grouping or factoring by special patterns.

Step 1:
There's no common factor among all terms.

Step 2:
Let's try factoring by grouping. Group the terms in pairs: (x3 + 6x2) + (-9x + 54)

Now, find the greatest common factor (GCF) in each pair and factor it out:

x^2(x - 6) - 9(x - 6)

Notice that both terms have a common factor of (x minus 6). Factor it out.

(x - 6)(x^2 - 9)

Now, you can see that the second factor (x2 - 9) is a difference of squares, which can be factored further:

(x - 6)(x + 3)(x - 3)

So, the completely factored polynomial is (x - 6)(x + 3)(x - 3).

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Answer:

Step-by-step explanation:

8. subtract 78 from both sides so you get r=-93

10. divide both sides by 8 so you get j=12

11. divide both sides by -13 so its z=3

12.divide both sides by 15 so its m=-12

13. divide both sides by 27 to get r=9

14. multiply both sides by 9 (9/1) to get y=-72

15. multiply both sides by 12 to get -j=-96 then divide it by - to get j=96

16. multiply it by 15/1 so its a by itself and then use cross multiplication to simplify it so 4/5 x 15/1 so 15 becomes 3 and 5 becomes 1 so its 4x3 which is 12 so a=12

17. g=6

18. q=4

Answer:

Area of geometric figures mentioned calculated.

Step-by-step explanation:

Square Perimeter = 4 x sides of square = 20. So, each equal side of square = 20 / 4 = 5

Area of square = ( Side )^2 = ( 5 )^2 = 25

Area of triangle = 1/2 (Base) (Height) = 1/2 x 3 x 3.5 = 5.25

The recorded time that is most precise among the four different clocks used to time an event is 55.254 seconds. This is because the recording of this time has the highest decimal precision compared to the other three options.

Precision refers to the degree of accuracy of a measurement, calculation, or specification. It's related to the number of digits used to record or express a quantity, and it's a reflection of uncertainty associated with a measurement or calculation. The greater the precision, the more significant digits are recorded. For example, the result of a calculation could be stated as 1.23 or 1.234, or 1.2345 depending on the degree of precision necessary or desired.

To determine which one is the most precise, you can look at the number of decimal places or digits after the decimal point. The option with the most number of decimal places is 55.254 s, which has three decimal places, while the other options have either one or two decimal places. The general rule for determining precision is to look at the smallest division on the scale of the measuring instrument. In this case, it is not given what type of clocks were used, so we cannot determine the smallest division of each clock. However, since 55.254 s has the most decimal places, it is the most precise recording among the four options.

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Answer:

Step-by-step explanation:

Rotating (2,-6) 90 degrees results in (6,2)

The area of a square is 14 times larger than the area of a triangle, so the length of a side of the square is 49 inches. The area of the triangle is 1/2  base  height, while the area of the square is 14 times larger.

Given, The area of a square is 14 times as large as the area of a triangle One side of the triangle is 7 inches long, and the altitude to that side is the same length as a side of the square. We need to find the length of a side of the square. Area of the triangle = 1/2 × base × height We know the base = 7 in and the height is equal to the side of the square. Let's say the side of the square is x. Area of the triangle = 1/2 × 7 in × x in = 7x/2 in²Area of the square = x²Given, the area of a square is 14 times as large as the area of a triangle.=> x² = 14(7x/2) in²=> x² = 49x in²=> x = 49 in Therefore, the length of a side of the square is 49 inches.

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Explanation

Step 1

Let x represents the number of hours

Let y represents the rate of the company

and

cost per hour = $3

so, the total cost per time is

cost per time= 3* number of hours

cost per time==3x

now, the company charges a $5 boarding rate

so, the rate is

I hope this helps you

Answer: 5(7) over x

Step-by-step explanation:

Answer:

576 (square yards)

Step-by-step explanation:

length of slanted height of triangle = √(6² + 8²)

= √100

= 10.

surface area = area of 2 triangle faces + area of 3 lengths

= 2 (1/2 X 12 X 8) + 3 (10 X 16)

= 576 (square yards)

Answer:

1 notebook $2.39

Step-by-step explanation:

n=notebook     b= binder

6n +2b =23.52

3n +4b = 25.53

MULTIPLY THE FIRST BY -2 AND ADD BOTH

-12n -4b = -47.04

3n + 4b = 25.53

(b is eliminated since 4b -4b=0)

-9n =  -21.51

9n = 21.51

n = 2.39

Answer:2

Step-by-step explanation:

59 to 1 sig. fig= 60

25 to 1 sig fig = 30

Therefore, 60/30 =2

Hope this helps :)

Answer:

2

Step-by-step explanation:

divide the numbers. then find the left furthest critical number.

count to the rifht by desired sig fig. use decimal to mark a place of significant zeros.

Answer:

C=0

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The expression  (x²)5 is simplified using the exponent properties to  5x².

Index forms of a number can be defined as the number written in the form of an exponential expression.

To be a single number that is raised to another number.

Numbers too large or small are written in index forms, since the law of exponents states the following;

Exponents of numbers are to be added when numbers are multiplied

We are Given the expression;

(x²)5

Using the law of exponents, we have;

5x²

Thus, the expression is simplified using the exponent properties to  5x²

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The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

There are two types of proportions.

1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.

2) Inverse Proportion - describes the indirect relationship between two quantities.  It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.

According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.

y = k/x

let y = a body's weight

x = square of its distance from the center of the earth

Solving for the proportionality constant, k.

y = k/x

12 = k / (5000^2)

k = 12 x 25, 000, 000

k = 300, 000, 000

The equation for the relationship in the problem can now be represented by:

y = 300,000,000/x

where

y = a body's weight

x = square of its distance from the center of the earth

Evaluating the new equation where x = square of 10,000:

y = 300,000,000/x

y = 300,000,00/(100,000,000)

y = 3

Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

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Therefore, the first partial derivatives of the function z = x sin(xy) are: Әz/Әx = sin(xy) + x * cos(xy) * y; Әz/Әy = \(x^2\)* cos(xy).

To find the first partial derivatives of the function z = x sin(xy) with respect to x and y, we differentiate the function with respect to each variable separately while treating the other variable as a constant.

Partial derivative with respect to x (Әz/Әx):

To find Әz/Әx, we differentiate the function z = x sin(xy) with respect to x while treating y as a constant.

Әz/Әx = sin(xy) + x * cos(xy) * y

Partial derivative with respect to y (Әz/Әy):

To find Әz/Әy, we differentiate the function z = x sin(xy) with respect to y while treating x as a constant.

Әz/Әy = x * cos(xy) * x

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Margo borrows $700 (P), the interest rate is 8% (0.08 as a decimal), and the time is 7 months, which is equivalent to 7/12 of a year (approximately 0.583 years).

Margo borrowed $700 and agreed to pay it back with 8% annual interest after 7 months. In order to calculate the amount of interest she will pay, we need to use the following formula: Interest = Principal x Rate x Time. Here, the principal is $700, the rate is 8%, and the time is 7/12 (as 7 months is equivalent to 7/12 of a year). So, we can plug in these values to get: Interest = $700 x 0.08 x (7/12)
Interest = $28
Therefore, Margo will pay $28 in interest.

Margo borrowed $700 and agreed to pay it back with 8% annual interest after 7 months. To calculate the amount of interest she will pay, we use the formula Interest = Principal x Rate x Time. Plugging in the values, we get Interest = $700 x 0.08 x (7/12), which equals $28. In summary, Margo will pay $28 in interest on her $700 loan.

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The inequality 2(x+6)<30 is sometimes true, specifically when x is less than 9. It is false for values of x equal to or greater than 9.

The inequality 2(x+6)<30 is sometimes true, depending on the value of x.

To determine the values of x for which the inequality is true, let's solve it step by step:

1. Distribute the 2 to both terms inside the parentheses:
2x + 12 < 30

2. Subtract 12 from both sides of the inequality to isolate the variable:
2x < 30 - 12
2x < 18

3. Divide both sides of the inequality by 2 to solve for x:
x < 18/2
x < 9

Therefore, the inequality is true when x is any value less than 9. For example, if x is 8, the inequality would be true: 2(8+6) = 28, which is less than 30.

However, if x is 9 or any value greater than 9, the inequality would be false.

In summary, the inequality 2(x+6)<30 is sometimes true, specifically when x is less than 9. It is false for values of x equal to or greater than 9.

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Answer:

10

Step-by-step explanation:

Use the Pythagorean theorem: a^2+b^2=c^2 to find the hypotenuse

a=6

b=8

6^2+8^2=c^2

36+64=c^2

100=c^2

10=c

Hope this helps! :)

Answer:

10 cm.

Step-by-step explanation:

By Pythagoras:

BC^2 = 6^2 + 8^2

BC^2 = 100

BC = 10.

The terminal-point P(x, y) on the unit circle for "t = 7π/6' is (-√3/2 , -1/2), and the labelled graph of "y = 3+cos(x)" is shown below.

We have to find the terminal-point for t = 7π/6.,

The angle is given to be 7π/6, which means in degree it's measure is 210 degrees, and since the circle is unit circle ,So, radius = 1

The value of x and y, for terminal-point can be calculated as:

x = r × cos(θ)  = 1 × cos(210°) = -√3/2,

y = r × sin(θ) = 1 × sin(210°) = -1/2,

So, the required terminal point will be = (-√3/2 , -1/2).

To sketch graph of function "y = 3+cos x",

We substitute the values, and plot them,

For x = -2π, we get y = 4, the point is (-2π, 4);

For x = -π, we get y = 2, the point is (-π, 2);

For x = 0, we get y = 4, the point is (0, 4);

For x = π, we get y = 2, the point is (π, 2);

For x = 2π, we get y = 4, the point is (2π, 4);

Therefore, the graph of these points is sketched below.

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The given question is incomplete, the complete question is

Find the terminal point P(x, y) on the unit circle determined by the given value of t. (Remember to show work to justify your answer.) t = 7π/6.

Sketch the graph of y = 3+cos x. Remember to label your axes carefully (with numbers) and to show the five points accurately.