what is the perimeter of a rectangle

best answer of this equation is 10.772

Answer: 10.772

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

exact form:

x= 10 4/3

--------- (its a fraction)

2

decimal form: 10.77217345....

after that round to the nearest thousandth.

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

the answer is $26.38

Step-by-step explanation:

I hope this helps!

The maximum volume of the cylinder in exact form is; V_max = 2560π/27

Let us define the variables as:

Radius of cone = r

Radius of cylinder = x

Height of Cone = h

Height of Cylinder = y

The general equation for volume of the cylinder is;

V = πx²y  

Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:

Height of triangle above cylinder/Base of Triangle above cylinder   =   Height of full triangle/Base of full triangle

This gives;

(h - y)/2x  = h/2r

Making y the subject gives us;

h – y = hx/r

y =  h – hx/r

y = h(1 – x/r)

Plug in y into our Volume equation:

V(x) = πx²h(1 – x/r)

V(x) = πh(x²  - x³/r)

To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:

V'(x) = πh(2x  - 3x²/r)

V'(x) = 0

Thus;

(2x  - 3x²/r) = 0

x( 2r – 3x) = 0

Thus;

x = 0 or x = 2r/3

Put x = 2r/3 in our volume equation to find V_max

V_max  = πh((2r/3)² – (2r/3)³/r)

V_max = πh(4r²/9 - 8r²/27)

V_max = πh(12r²/27 - 8r²/27)

V_max = 4πhr²/27

Thus, at r = 8 and h = 10, we have;

V_max = 4π(10)8²/27

V_max = 2560π/27

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The area of a circle is pi x r^2

Area of full circle: 3.14 x 11^2

Area = 379.94 square miles.

To find the area of the bounded arc, multiply the full area by the fraction of a full circle the arc is:

379.94 x 300/360 = 316.62 square miles

Answer:

316.62 miles²

Step-by-step explanation:

Area of circle = 3.14 ×  r²

3.14 × 11²

= 379.94 (area of whole circle)

We need to find the area of the blue shaded sector.

300/360 × 379.94

= 316.62

Answer:

a. 160-24=g

b. 160-24=g

   -24

   136=g

c. 136

Answer:

the answer is (B) 10.

Step-by-step explanation:

To find the maximum possible number of spools that can be taken from the box without having at least 2 spools of each color, we need to find the maximum number of spools that can be taken without taking 2 spools of any one color.

The worst-case scenario is if we take all but one spool of one color, leaving only one spool of that color in the box. Then we can take all the spools of the other two colors, and one more spool of the first color, without having at least 2 spools of any one color.

So the maximum possible number of spools that can be taken is:

4 (red) + 5 (white) + 1 (green) = 10

Therefore, the answer is (B) 10.

The value of f(1) for function f(x) = x³ + x² f'(1) + x f"(2) + f"'(3) is 4

The given Function is f(x) = x³ + x² f'(1) + x f"(2) + f"'(3)

Differentiating both sides w.r.t x,

=> f'(x) = 3x² + 2x f(1) + f"(2) ----------------(1)

Putting x = 1

=> f'(1) = 3(1)+ 2 f(1) + f"(2)

=> f"(2) =  -3 - f'(1)

Again , differentiating equation (1) w.r.t x,

f"(x) = 6x + 2.f'(1) ---------------(2)

put x = 2,

f"(2) = 6(12)+ 2.f'(1)

=> f"(2) = 12+ 2.f'(1)  

Substitute f"(2) =  -3 - f'(1)

=> -3 - f'(1) =  12+ 2.f'(1)  

=> 3f'(1) = -15

=> f'(1) = -5

Differentiating the equation (2) w.r.t x

f"'(x) = 6

Putting x = 3,

=> f"'(3) = 6

Substituting the values in main function,

f(x) = x³ + x² (-5) + x(2) +6

Putting x = 1 ,

f(1) = (1)³ + (1)² (-5) + (2) +6

=> 4

I've answered the question in general as given question is incomplete

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The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

13 Percent of $140,000 is $18,200

0.13 times 140,000 :-)

The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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Simple Interest

The simple interest I for investment is calculated by:

I = P.r.t

Where P is the principal or initial amount of investment, r is the annual rate of interest, and t is the time the investment is under the period of simple interest.

The ending balance M is calculated as:

M = P + I

The data provided in the question is:

P = $7,400

r = 10,5% = 0.105

t = 6 months = 0.5 years

Calculate the interest:

I = $7,400 * 0.105 * 0.5

I = $388.50

Calculate the ending balance:

M = $7,400 + $388.50 = $7,788.50

The final balance is $7,788.50

Sure! Here is the previous response with all symbols turned into words:

A confidence interval is a range of values that is likely to contain the population mean with a certain level of confidence. The formula for a confidence interval for a population mean is given by: sample mean plus or minus critical value times (population standard deviation divided by the square root of sample size), where sample mean is the sample mean, critical value is the critical value for the desired level of confidence, population standard deviation is the population standard deviation and sample size is the sample size.

In this case, we are given a sample size of 766, a sample mean of 68.4 and a population standard deviation of 12.8. We are also asked to find the 99.5% confidence interval.

First, we need to find the critical value for a 99.5% confidence level. This can be done using a z-table or calculator. The critical value for a 99.5% confidence level is approximately 2.807.

Plugging these values into the formula gives us: 68.4 plus or minus 2.807 times (12.8 divided by the square root of 766) which is approximately equal to 68.4 plus or minus 1.289.

So, the 99.5% confidence interval for the population mean is 67.111 is less than population mean which is less than 69.689.

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

  12x³y²

Step-by-step explanation:

You want the product -2x (-3x²y)(2y).

An exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:

  x² = x·x

When the same factor appears a number of times in a product, an exponent can be used to represent that number.

  (-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)

The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...

  12x³y²

The length of a 30° arc of a circle with a radius of 6 feet is π feet.

What is circle ?

In geometry, a circle is a closed, two-dimensional figure that consists of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center). The distance across the circle through the center is called the diameter, which is equal to twice the radius.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, the circumference of this circle is:

C = 2π(6 feet) = 12π feet

Since a full circle is 360°, we can find the length of a 30° arc by multiplying the fraction of the circle represented by the arc by the circumference of the circle. In this case, the fraction of the circle represented by the 30° arc is:

30°÷360° = 1÷12

So the length of the 30° arc is:

(1÷12) × 12π feet = π feet

Therefore, the length of a 30° arc of a circle with a radius of 6 feet is π feet.

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Answer:

$440

Step-by-step explanation:

40 x 11 = your answer 440

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.

In an arithmetic series, the sum S of n terms is given by:

S = n/2 * (a + l)

where:

- n is the number of terms (which represents the number of students in this case),

- a is the first term (in this case, the first student's number, which would be 1), and

- l is the last term (in this case, the last student's number, which we don't know yet).

Given that S = Rs. 13225, we have:

13225 = n/2 * (1 + l)

Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:

13225 = n/2 * (1 + n)

Multiplying through by 2 to clear the fraction gives:

26450 = n * (1 + n)

Rearranging to a quadratic equation gives:

n^2 + n - 26450 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.

Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.

So, there were 163 students who donated money to the fund.

if 680,400kg pro' is burnt in 2.5mins

An equation can be driven to find how much pro' is burnt in 2 mins which is ( 2.5x = 680400 × 2 )

where x is the amount of pro' burnt in 2mins

2.5x = 1360800

divide both sides by 2.5

2.5x = 1360800

2.5 2.5

x = 544320

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer:

1.  This is a like term

24 = 24

2. This is not a like term

12x - 6 = 46

3. This is not a like term

33 = 5x + 43

4.This is a like term

1 = 1

5. This is not a like term

7x = -48

6. This is a like term

25 = 25

7. This is a like term

60 = 60

8. This is a like term

47 = 47

9.This is a like term

20.6 = 20.6

10.This is a like term

10 = 10

Step-by-step explanation:

1. 5x + 4x − 6x = 24

5x + 4x = 9x

9x - 6x = 24

3x = 24

We can replace x and turn it into an 8.

3(8) = 24

3 x 8 = 24

24 = 24

This is a like term.

2. 8x + 5 − 4x + 1 = 46

8x + 4x - 5 + 1 = 46

8x + 4x = 12x

12x - 5 + 1 = 46

5 + 1 = 6

12x - 6 = 46

We cannot replace the x with any number to get 46.

So this is not a like term.

3. 33 = 5(x + 8) + 3

5xX= 5x

5 x 8 = 40

33 = 5x + 40 + 3

40 + 3 = 43

33 = 5x + 43

We cannot replace any number with x and get 33.

This is not a like term.

4. 2x + 3(x − 8) = 1

3 x X = 3x

3 x 8 = 24

2x + 3x - 24 = 1

2x + 3x = 5x

5x - 24 = 1

We can replace the x with 5.

5(5) - 24 = 1

5 x 5 = 25

25 - 24 = 1

1 = 1

This is a like term

5. x + x − 2x + 4x = −48

x + x = 1x because x is always a 1

1x - 2x +4x  = -48

1x + 2x = 3x

4x + 3x = 7x

7x = -48

We cannot replace x with any number.

This is not a like term.

6. 2(x + 5) + 3x = 25

2 x X = 2x

2 x 5 = 10

2x + 10 + 3x = 25

2x + 3x + 10 = 25

2x + 3x = 5x

5x + 10 = 25

We can replace the x with a 3.

5(3) + 10 = 25

5 x 3 = 15

15 + 10 = 25

25 = 25

This is a like term.

7. 60 = 4(x + 3) + 2(x − 3)

4 x X = 4x

4 x 3 = 12

60 = 4x + 12 + 2(x - 3)

2 x X = 2x

2 x 3 = 6

60 = 4x + 12 + 2x - 6

60 = 4x +2x +12 - 6

4x - 2x = 2x

60 = 2x + 12 - 6

12 - 6 = 6

60 = 2x + 6

We can replace the x with a 33.

60 = 2(33) - 6

2 x 33 = 66

66 - 6 = 60

60 = 60

This is a like term.

8. 47 = 2(x + 3) + 3(x − 3)

2 x X = 2x

2 x 3 = 6

47 = 2x + 6 + 3(x - 3)

3 x X = 3x

3 x 3 = 9

47 = 2x + 6 + 3x - 9

47 = 2x + 3x + 6 - 9

2x + 3x =  5x

47 = 5x + 6 - 9

6 - 9 = -3

47 = 5x + -3

We can replace the x with a 10.

47 = 5(10) + -3

5 x 10 = 50

47 = 50 + -3

50 + -3 = 47

47 = 47

This is a like term.

9. −2(x + 1.4) − 1.8 = 20.6

-2 x X = -2x

-2 x 1.4 = -2.8

-2x + -2.8 - 1.8 = 20.6

-2.8 - 1.8 = -4.6

-2x + -4.6 = 20.6

We can replace x with a 8.

-2(8) + -4.6 = 20.6

-2 x 8 = -16

-16 + -4.6 = 20.6

20.6 = 20.6

This is a like term.

10. 8 − 2(x + 4) = 10

2 x X = 2x

2 x 4 = 8

8 - 2x + 8 = 10

8 - 8 + 2x = 10

8 - 8 = 0

0 + 2x = 10

We can replace x with 5.

0 + 2(5) = 10

2 x 5 = 10

0 + 10 = 10

10 = 10

This is a like term.

I hope this helped. I am sorry if you get this wrong. Have a wonderful day.

The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs

In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.

We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:

Fraction of bulbs not working = 2/40 = 0.05

Thus, number of bulbs not working in a sample of 1000 bulbs is:

0.05 * 1000 = 50 bulbs

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Answer:

B. y=4x+27

Step-by-step explanation:

Currently, this equation is written is point-slope form, so we need to change it to slope-intercept form, which looks like this: y=mx+b.

y+5=4(x+8)   Distribute.

y+5=4x+32   Subtract 5 on both sides.

  -5       -5

y=4x+27

Therefore, the answer is B.

Hope this helps and have a nice day ^^

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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