Find the area of each shape

Answer:

20807508

Step-by-step explanation:20807508

The number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

A region's size on a plane or curved surface is expressed by a measurement known as an area. Unlike the area of a plane region or plane area, which refers to the area of a shape or planar lamina, surface area describes the area of an open surface or the boundary of a three-dimensional object.

Given:

A sheet of the card is 20 centimeters by 30 centimeters,

The diameter of a badge, d = 60 mm or 6 cm,

Calculate the area of the sheet as shown below,

\(Area = length \times width\)

Area = 20 × 30 = 600 cm²

Calculate the area of the badge as shown below,

\(Area = \pi d^2 / 4\)

Area = 3.14 × 6² / 4

Area = 28.26 cm²

To calculate the number of badges\(No\ of\ badges = Area\ of \ sheet / Area \ of badge\), use the formula given below,

Number of badges = 600 cm² / 28.26 cm²

Number of badges = 21.23 or 21

Therefore, the number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

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The time that the ball traveled is given as follows:

1.5 seconds.

The quadratic function determining the ball's height after t seconds is given as follows:

H(t) = -16t² + 24t.

The roots of the quadratic function in this problem are given as follows:

-16t² + 24t = 0.

16t² - 24t = 0

8t(2t - 3) = 0.

Hence we apply the factor theorem as follows:

Hence the time is given as follows:

1.5 - 0 = 1.5 seconds.

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Answer:

The pvalue of 0.0113 < 0.05 means that there is sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

Step-by-step explanation:

The null hypothesis is:

\(H_{0} = 28\)

The alternate hypotesis is:

\(H_{1} < 28\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

A recent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to find another position.

This means that \(n = 50, X = 26\)

Assume the population standard deviation is 6.2 weeks.

This means that \(\sigma = 6.2\)

Does the data provide sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

We have to find the pvalue of Z, looking at the z-table, when \(\mu = 28\). It if is lower than 0.05, it provides evidence.

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{26 - 28}{\frac{6.2}{\sqrt{50}}}\)

\(z = -2.28\)

\(z = -2.28\) has a pvalue of 0.0113 < 0.05.

The pvalue of 0.0113 < 0.05 means that there is sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

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The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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Step-by-step explanation:

Hey there!

Look explanation in picture.

Hope it helps....

Therefore, the weight is rising at a rate of 21/2 feet per second when the worker has walked 10 feet, and at a rate of 15/2 feet per second when the worker has walked 30 feet.

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables, which represent unknown values that we want to solve for. An equation can be represented using mathematical symbols and notation, such as the equals sign (=), plus sign (+), minus sign (-), multiplication sign (×), and division sign (÷).

Here,

This is a related rates problem. Let's start by labeling the variables:

Let x be the distance between the worker and the weight (in feet).

Let y be the length of the rope from the pulley to the worker (in feet).

Let z be the distance from the weight to the ceiling (in feet).

Let v be the speed of the weight rising (in feet per second).

Let w be the speed of the worker walking (in feet per second).

From the problem statement, we know that x + y + z = 80, and we want to find dv/dt when w = 2 and x = 10 or x = 30. To solve for v, we need to find an equation that relates the variables x, y, z, and v. Notice that as the worker walks away, the length of the rope from the pulley to the weight remains constant, so we have:

y² = z² - x²

Taking the derivative of both sides with respect to time t, we get:

2y (dy/dt) = 2z (dz/dt) - 2x (dx/dt)

Now we can use the fact that x + y + z = 80 to eliminate y, giving:

2z (dz/dt) - 2x (dx/dt) = 2y (dy/dt) = 2(80 - x - z) (dy/dt)

Simplifying, we get:

z (dz/dt) - x (dx/dt) = (80 - x - z) (dy/dt)

Finally, we can solve for dv/dt by plugging in the given values for w and x, and solving for v:

When x = 10:

z = 40, dx/dt = -2, w = 2

40 (dz/dt) - 10 (-2) = (80 - 10 - 40) (2)

dz/dt = 21/2

v = dz/dt = 21/2 feet per second

When x = 30:

z = 40, dx/dt = -2, w = 2

40 (dz/dt) - 30 (-2) = (80 - 30 - 40) (2)

dz/dt = 15/2

v = dz/dt = 15/2 feet per second

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Answer:

88 square cm

Step-by-step explanation:

Surface area of down rectangular prism:

      l = 6cm ; w = 3 cm & h = 2 cm

   \(\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}\)

                                                                       = 2*(6*3 + 3*2 + 2*6)

                                                                        = 2* (18 + 6 + 12)

                                                                         = 2 * 36

                                                                          = 72 cm²

Lateral surface area of the top rectangular prism:

    l = 3 cm

    w = 1 cm

     h =  4 - 2 = 2 cm

         LSA = 2h( l + w)

                = 2*2 *( 3 + 1)

                 = 4 * 4

                 = 16 cm²

Surface area of the shape = 72 + 16

                                              = 88 cm²

Answer:

a = 88 cm2

Step-by-step explanation:

\(a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15\)

\(a=88cm^{2}\)  

Hope this helps

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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The required, one of them should change the position of the block from horizontal to vertical and then combine the structure together.

3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.

Here,
Since Velma and Cruce the separate buildings one of them made the building by placing blocks horizontally and the other made the building by placing blocks vertically, So one of them must change their way of building.

Therefore, required, one of them should change the position of the block from horizontal to vertical and then combine the structure together.

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Answer:

\(4m(m {}^{2} + 3xm {}^{2} - 2m - 6)\)

Step-by-step explanation:

\(1. \: gcf = 4m \\ 2. \: 4m( \frac{4m {}^{3} }{4m} + \frac{12xm {}^{3} }{4m} + \frac{ - 8m {}^{2} }{4m} + \frac{ - 24m}{4m} ) \\ 3. \: 4m(m {}^{2} + 3xm {}^{2} - 2m - 6)\)

Answer: < or >

Step-by-step explanation:

Answer:

Angle 1 is 127°

∠2 is 53°

∠3 is 127°

∠4 is 53°

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Heather's account balance will be approximately $4,179.60 after 9 years if the interest is compounded 4 times each year.

Interest is the cost of borrowing money or the compensation received for lending money. It is usually expressed as a percentage of the amount borrowed or lent, and it is calculated based on the principal (the initial amount borrowed or lent), the interest rate, and the time period for which the money is borrowed or lent.

Compounding refers to the process of earning interest on both the principal amount and the accumulated interest earned over time. In other words, it is the interest earned on interest.When interest is compounded, the interest earned in each compounding period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.

In the given question,

We can use the formula for compound interest to find Heather's account balance after 9 years:

A = P * (1 + r/n)^(n*t)

where A is the account balance, P is the principal (initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:

A = 2975 * (1 + 0.035/4)⁴ˣ⁹

Simplifying this expression, we get:

A = 2975 * (1.00875)³⁶

Using a calculator or a computer, we can evaluate this expression to get:

A ≈ $4,179.60

Therefore, Heather's account balance will be approximately $4,179.60 after 9 years if the interest is compounded 4 times each year.

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

Answer:

The first blank is the less than symbol (<)

The second blank is the greater than symbol (>)

Step-by-step explanation:

It looks like you are comparing the left side of the equation to the right side.

If we look at the first unknown, we can multiply out the numbers on the left side to see if it's equal to the right side.

\(2^2 * 4^2 = 64\)

while the right side is this:

\(8^4 = 4096\)

we can see that one side is clearly bigger than the other side. Thus, we would use the less than symbol in this case as 64 is less than 4096:

\(2^2 * 4^2 < 8^4\)

\(64 < 4096\)

We can do the same for the second unknown as well:

\(2^4 * 4^2 = 256\\8^2 = 64\)

In this case, we can see that the left side is bigger than the right side. Thus, we will use the greater than symbol as 256 is greater than 64:

\(2^4*4*2 > 8^2\\256 > 64\)

Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

Answer:

(x+1) (x+6)/(x+7) (x+8)

X+1=0 so x=-1 and -6 respectively on the

x+7=0 so x=-7 and -8 in the

1denominator

Step-by-step explanation:

answer x<-1 and x<-6/

x<-7 x<

The measure of angle O is 56 and the value of m and n are 8.1 in and 14.5 in respectively.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The longest side is hypotenuse and it is the side facing the right angle. The other two sides are opposite and adjascent.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan,(tetha) = opp/adj

angle O = 180-(90+34)

= 180- 124

= 56°

To find m,

Tan 34 = m/12

m = Tan34 × 12

m = 8.1 in

using Pythagoras theorem to find n,

n= √8.1²+12²

n = √65.61+144

n = √209.61

= 14.5 in

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Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

The absolute minimum value is -8 and the absolute maximum value is 1.

Generally, To find the absolute extreme values of a function, you need to find its local extreme values (also called relative extreme values) and its global extreme values (also called absolute extreme values).

To find the local extreme values of a function, you can take the derivative of the function and set it equal to 0. This will give you the points at which the function has a local extreme value. For the function f(x) = x^3, the derivative is f'(x) = 3x^2. Setting f'(x) = 0 and solving for x gives us x = 0.

To find the global extreme values of a function, you also need to consider the values of the function at the endpoint of the interval. In this case, the interval is [-2, 1], so you need to find the values of f(-2) and f(1).

Plugging in these values gives us:

f(-2) = (-2)^3 = -8 f(1) = 1^3 = 1

So the absolute extreme values of f(x) = x^3 on the interval [-2, 1] are f(-2) = -8 and f(1) = 1.

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