Solve x

1.6x+3=21

2.15(x - 5)=75

The area of the circle A and B is 86.54 inches and 124.62 mm

According to the statement

we have given that the radius of the circle A and b and we have to find the area of the given circle.

So, we know that the

The area enclosed by a circle of radius r is πr².

So, For area of the circle

For condition A :

diameter = 10.5 inches

then radius = 5.25

Area = πr²

Area = 3.14*27.56

Area = 86.54 inches

Now, For condition B :

radius = 6.3 mm

Area = πr²

Area = 3.14*39.69

Area = 124.62mm

So, The area of the circle A and B is 86.54 inches and 124.62 mm

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The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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Type I error says that we suppose that the null hypothesis exists rejected when in reality the null hypothesis was actually true.

Type II error says that we suppose that the null hypothesis exists taken when in fact the null hypothesis stood actually false.

In statistics, a Type I error exists as a false positive conclusion, while a Type II error exists as a false negative conclusion.

Making a statistical conclusion still applies uncertainties, so the risks of creating these errors exist unavoidable in hypothesis testing.

The probability of creating a Type I error exists at the significance level, or alpha (α), while the probability of making a Type II error exists at beta (β). These risks can be minimized through careful planning in your analysis design.

Examples of Type I and Type II error

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Answer:

  (d)  71°

Step-by-step explanation:

The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.

Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.

  sin(W/2) = Opposite/Hypotenuse

  sin(W/2) = (35/2)/(30) = 7/12

Using the inverse sine function, we find ...

  W/2 = arcsin(7/12) ≈ 35.685°

  W = 2×36.684° = 71.37°

  W ≈ 71°

The law of cosines tells you ...

  w² = u² +v² -2uv·cos(W)

Solving for W gives ...

  W = arccos((u² +v² -w²)/(2uv))

  W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°

  W ≈ 71°

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:

cos θ = - √[1 - (1 / csc θ)²]

If we know that csc θ = 2, then the exact of the cosine function is:

cos θ = -√[1 - (1 / 2)²]

cos θ = -√(3 / 4)

cos θ = -√3 / 2

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

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Answer:

6x + 4y = 16

Step-by-step explanation:

2(3x + 2y = 8)

2(3x + 2y) = 2(8)

6x + 4y = 16

Answer:

6x+4y=16

Step-by-step explanation:

2 (3x+2y=8)

2×3x+2×2y=2×8

=6x+4y=16 ans.

James is (B) 20 meters far from the finish line 9 seconds after the race has started.

To find the distance:

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

Answer:

true

Step-by-step explanation:

thats really it i believe its true

the unit price is $3 per pound, the correct option is the second one.

The unit price for the oranges is just the price for one pound of oranges.

Here we know that the price of 4 lb of oranges is $12, with that we want to get the cost of a single lb of oranges, so we can write:

4lb = $12

If we divide both sides by 4, then we get:

4lb/4 = $12/4

1lb = $3

This means that the price of 1 pound of oranges is $3, then the unit price is $3 per pound, the correct option is the second one.

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[tex](x-1) ^ { 3 } -(x-2) ^ { 2 } =1[/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x-2\right)^{2}=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x^{2}-4x+4\right)=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-x^{2}+4x-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-1-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5-1=0 [/tex]

[tex]x^{3}-4x^{2}+7x-6=0 [/tex]

[tex]±6,±3,±2,±1 [/tex]

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )

m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

Answer:

give it a try

Step-by-step explanation:

Okay. I'm gonna flip five coins, but I'm told the first coin is Tell there's no choice there at all. It is certain the first coin shows a tail and then I want to have four heads in a row. Okay, so one for tell which means certain getting ahead is a half chance. Again a half chance again a half and again a half So that you work out and it's 1/16. That's the answer. There's no choice about the foreheads. It just has to be head every time I said.

Answer:

30 km/h

Step-by-step explanation:

Let X km/h be the speed of the boat in still water

Let the distance covered each way be D km

Relative speed of boat downstream = X + 6

Relative speed of boat upstream = X - 6

Distance covered by boat when going downstream

D = 4(X + 6) = 4X + 24

Distance covered by boat upstream is the same as distance covered downstream
D = 6(X-6) = 6X -36

Setting the two X equations equal to each other gives us

6X - 36 = 4X + 24

Collecting like terms

6X - 4X = 24-(-36)

2X = 60

X = 30 km/hr which is the speed of boat in still water

Check

Downstream speed is 30+6 = 36 km/h and distance traveled downstream in 4 hours = 36 x 4 = 144km

Upstream speed is 30-6 = 24 km/h and it travels for 6 hours. Distance covered = 24 x 6 = 144 miles

So distance covered is same and hence check succeeds

Answer:

Exact form: 78√2 - 17√3 / 54

Decimal form: 1.49747766

Step-by-step explanation:

Rationalize and simplify the expression.

[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

[tex]y = a(1-r)^t[/tex]

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

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Answer: 24+12=36

Step-by-step explanation:

36= _+_

2x(2 times)

x

X+2x=36

3x=36

12

12+2(12)=36

12+24=36

Answer:

Step-by-step explanation:

From, the given word explanation try to create your own equation like

From, equation (1) solve for x

Substitute, equation (3) to equation (2).

If the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

Given that the model train has a scale of 1:3 and the real train is 12 feet tall.

We are required to find the height of the model train.

Ratio shows how many times one number contains another number. A ratio is the relationship in quantity  between two things. It expresses quantity of one thing in terms of another.

Ratio of model train to real train is 1 inches :3 inches.

Height of model train=12*1/4

=3 inches

Hence if the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

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Answer:

B

Step-by-step explanation:

B Rounded to nearest ten thousand

The attendance that aligns with rounding to 120,000 is B) 116,390.

To determine the possible attendance at the amusement park if it was rounded to the nearest ten thousand, we need to consider the rounding process.

When rounding to the nearest ten thousand, we look at the digit in the ten thousand place. If this digit is 5 or greater, we round up to the next ten thousand. If it is less than 5, we round down to the previous ten thousand.

In this case, the attendance was rounded to 120,000. To round to the nearest ten thousand, we look at the digit in the ten thousand place, which is 2. Since 2 is less than 5, we round down.

Therefore, the attendance at the amusement park could have been rounded to 120,000 people if it was rounded to the nearest ten thousand.

Among the given options, the attendance that aligns with rounding to 120,000 is B) 116,390.

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Answer: [tex]512a^{15}[/tex]

Step-by-step explanation:

[tex](a^5*2^3)^3[/tex]

First, lets solve the inside of the parenthesis

[tex](a^5*8)^3[/tex]

Now, distribute the power of 3 to both terms. Remember taking a power of an exponent is like multiplying them (in this case [tex](a^5)^3=a^{15}[/tex]

[tex]a^{15}*512[/tex]

Simplify

[tex]512a^{15}[/tex]

Answer:  [tex]\frac{1}{4}[/tex]

Work Shown:

[tex]\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)*\left(\frac{1}{2}\right) = \frac{1*1}{2*2} = \frac{1}{4}[/tex]

There is a maximum value of 6 located at (x, y) = (1, 6).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 12.

Rearranging the constraint, we get:

6x + y = 12,

or, y = 12 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(12 - 6x) = 12x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 12 - 12x ... (i)

Equating to 0, we get:

12 - 12x = 0,

or, 12x = 12,

or, x = 1.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.

The value of y, when x = 1 is,

y = 12 - 6x,

or, y = 12 - 6*1 = 6.

The value of f(x, y) when (x, y) = (1, 6) is,

f(x, y) = xy,

or, f(x, y) = 1*6 = 6.

Thus, there is a maximum value of 6 located at (x, y) = (1, 6).

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The provided question is incomplete. The complete question is:

"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.

The computation shows that the maximum number of pants per employee that can be washed each week is 6.

The maximum number of pants per employee that can be washed each week will be:

7 + 4.5x + 12 <= 46

4.5x <= 27

x <= 6

The maximum number is 6.

The maximum number of chef coats per employee that can be washed each week will be:

= 6 + 8

= 14

The maximum total number of items per employee that can be washed in a week will be:

= 6 + 14 = 20

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the ratio of the area of the triangle to the area of the rectangle is 1: 2

The formula for calculating the area of a triangle is;

Area of triangle = 1/ 2 base × height

The formula for area of a rectangle is;

Area of a rectangle = length ×  width

From the information given, we have;

Now, let's substitute the values;

Area of a triangle = 1/ 2 × 11 × 4

Area of a triangle = 44/ 2 = 22m²

Area of a rectangle = 11 × 4

Area of a rectangle = 44m²

The ratio of the area of the triangle to the area of the rectangle is

= 22: 44

= 1 : 2

Thus, the ratio of the area of the triangle to the area of the rectangle is 1: 2

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Answer:

11%

Step-by-step explanation:

Lets find the new price with the monthly installment.

5+6.50(10)=70

Now the percentage of increase.

Find difference

70-63=7

Divide by original

7/63=0.11

Multiply by 100

0.11*100=11.1

Rounds to approximately 11%

The polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

In this question,

We have been given the cartesian coordinate (-6, -1)

We need to convert given cartesian coordinate to polar coordinates.

We know that the polar coordinates is of the form (r, θ)

where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

and θ is the angle associated with the coordinates which is given by           θ =  [tex]tan^{-1}(\frac{y}{x} )[/tex]

The magnitude of the given polar coordinate is,

⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

⇒  r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]

⇒ r = [tex]\sqrt{36+ 1}[/tex]

⇒ r = [tex]\sqrt{37}[/tex]

⇒ r = 6.08

And the angle associated with the coordinate is,

⇒ θ =  [tex]tan^{-1}(\frac{-1}{-6} )[/tex]

⇒ θ =  [tex]tan^{-1}(0.167 )[/tex]

⇒ θ = 9.48°

⇒ θ = 0.0523π

So, the polar coordinate is (6.08, 0.0523π)

Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

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Yes, the correlation coefficient is statistically significance

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given,

Sample size, n = 4

Where ρ is the population correlation.

Then the number of degrees of freedom is, df = n-2 = 4-2 = 2

The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254

Here,

The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected

Suppose lr> re 0.254

Because on the sample correlation provided, we know that lrl = 0.835>=0.254.

Here, it is clear that the null hypothesis is rejected.

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The missing reason in step 8 is the substitution property.

It should be noted that according to substitution property, if x = y, then x can be substituted for y in any equation.

When a variable is equal to another variable, then the variables can be interchangeable.

In this case, the missing reason in step 8 is the substitution property.

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