The circumference of a circle is 119.32 kilometers. What is the circle's radius?

__________ km

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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Answer:

Area is  220 cm²

Step-by-step explanation:

Firstly divide the polygon into  rectangle and triangle

For rectangle  area

 Area = A  =  L × W = 11 × 18 = 198 cm²

For triangle

Area =  A =  1/2 bh = 1/2 × (15-11) × (18-7) = 1/2 × 4 ×11 = 44/2 = 22 cm²

Add them

     198 + 22 = 220cm²

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Answer: A: 234 grams

Step-by-step explanation:

The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

Here, we have,

Average population = 240

Standard deviation for the population; 3

Z-score can be calculated as ,

z = (x' - μ)/σ

The two z-score tables are as follows:

Positive Z Score Table: The observed value is greater than the average of all values.

An observed value that is below the mean of all values is shown by a negative Z score table.

Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.

Z-score is 1.96 at significance level 0.025.

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Getting close to a whole number results ,

x' = 246

Hence, The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

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Answer:

If it is a fair die then it should have 6 faces, each one having a number 1-6. The probability of landing on a single number is 1/6. Because the die is fair there should be an equal probability of landing on a number 1-6 giving you a probability of 1/6. However, if the number of times rolled is changed, then the answer would be multiplied or added (depending on the question).

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

1.) We don't reject the null

2.) We reject the Null

3.) We do not reject the null

Step-by-step explanation:

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0

A.)

Left tail , Z = - 1.32 ; α = 0.10

We can use the Pvalue calculator from Z score :

Pvalue = 0.934

Pvalue > α ; Hence, we fail to reject the null, H0

B.)

Right-tailed test, z = 2.46, α = 0.01

Pvalue from Zscore calculator ;

Pvalue = 0.0069

Pvalue < α ; Hence, we reject the null, H0

C.)

Two-tailed test, z = -1.68, α = 0.05

Pvalue from Zscore calculator ;

Pvalue = 0.093

Pvalue > α ; Hence, we fail to reject the null, H0

Answer:

The percentage that the coat was reduced is 25%.

Step-by-step explanation:

A percentage is always out of a factor of 100.

40 x 2.5 = 100

30 x 2.5 = 75

75/100 = 3/4

1/4 is missing, which is the percentage.

1/4 = 0.25, or 25%

Hope This Helps!

Answer:

(x + 3)(x + 4)

Step-by-step explanation:

(x + 3)(x + 4)

x^2 + 3x + 4x + 12

x^2 + 7x +12

Answer:

(x +3) (x+4)

Step-by-step explanation:

I took the test with this question, I hope this helps!

Answer- false, true, true, and false

Step-by-step explanation:

No, rectangle is not always a rhombus because in rectangle two opposite sides are equal in length, and all the angles in rectangle is right angled but it is not necessary in rhombus.

All rectangles are squares. False! A square has ALL sides equal, but a rectangle only has opposite sides equal. All trapezoids have only one pair of parallel sides.

A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.

If you have a quadrilateral with two pairs of parallel sides, you do not necessarily have a rhombus;

Answer:

x=26-19

=7

Your answer is 7

Answer:

6 kilometers

Step-by-step explanation:

1 kilometer = 1000 meters

6000/1000 = 6

6000 meters = 6 kilometers

Answer:

Step-by-step explanation:

To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:

11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:

1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.

2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:

2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.

ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:

10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.

123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:

1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.

Now, let's perform the arithmetic operations:

234 + 1090 + 2748 - 83 = 3989.

Therefore, the result of the given expression in decimal form is 3989.

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The statement about function g which is true is that: function g is exponential because g(x) changes by equal factors over equal intervals of x.

The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Slope = (40 - 10)/(2 - 1)

Slope = 30/1

Slope = 30

Slope = (160 - 40)/(3 - 2)

Slope = 120/1

Slope = 120.

Factor = 40/10 = 4

Factor = 160/40 = 4

Factor = 640/160 = 4.

Therefore, function g is exponential because g(x) changes by equal factors over equal intervals of x.

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Answer:

x-intercept: N/A (never crosses the x-axis)

y-intercept: (0, 20)

Step-by-step explanation:

hope this helps

Answer:

8 hours

Step-by-step explanation:

4 bunnies...... 10 hours

5 bunnies....... X hours

X=4 ×10 :5

X=40 :5

X=8 hours

\(12.5\) hours

The unitary method is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value.

Time taken by \(4\) bunnies to eat crops \(=10\) hours

Time taken by \(1\) bunny to eat crops \(=\frac{10}{4}\) hours

Time taken by \(5\) bunnies to eat crops \(=\frac{10}{4}\times 5\)

                                                              \(=12.5\) hours

So, \(5\) bunnies eat the same crops in \(\boldsymbol{12.5}\) hours.

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To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

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Answer:

Distance to grandparents' house

Step-by-step explanation:

distance = speed x time

time = distance/speed

y=60/x

y is time

x is speed

time = 60/speed

so 60 is distance to grandparents' house

Answer: Number 2

Step-by-step explanation: yes

Answer:

Step-by-step explanation:

The coordinates to which the portable irrigation system should be sent to water the area are:

(495.75, 672).

The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.

Hence the coordinates are given as follows:

Hence the x-coordinate of the point to which the system should be sent is:

x = (56 + 144 + 888 + 895)/4 = 495.75.

(the mean is given by the sum of the observations divided by the number of observations).

The y-coordinate of the point to which the system should be sent is:

y = (289 + 332 + 1012 + 1055)/4 = 672.

The area is given by the image at the end of the answer.

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Answer:

9, 15

Step-by-step explanation:

x = smaller number

y = larger number

system of equations:

x + y = 24

3x = 2y - 3

substitution method:

x = 24 - y

3(24 - y) = 2y - 3

72 - 3y = 2y - 3

72 = 5y - 3

75 = 5y

y = 15

x + 15 = 24

x = 9

The units and their matching quantity given by the formula are:

The units for speed are expressed as distance per time. For example, meters per second and kilometers per hour.

Volume is shown in cubic units while area is shown in square units. This is why an example of volume is cubic centimeters and area would be square meters.

Perimeter is just a sum of units so it will be shown without any powers.

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y = 2x

Comparing y=mx + b

m = 2

The y-intercet and x -intercept is at (0,0)

Find the hypotenuse using pythagoras theorem

hypotenuse² = adj² + opp²

= (-1)² + (-2)²

= 1 + 4

= 5

hypotenuse =√5

The six trigonometric values can be determined by applying the trigonometric ratio

sinθ = opp/ hyp

Rationalize

cosθ = adj / hyp

rationalize

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.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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the last one

Step-by-step explanation:

it is 40/100