A semi-circle with a diameter of 6 cm sits on top of an isosceles trapezoid. Find the area of the entire figure.

Answer:

[tex]\frac{8-\sqrt{6} }{2}[/tex]

Step-by-step explanation:

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which in this is 2 - √6.

We can write the expression:

[tex]\frac{3\sqrt{6}+5 }{2+\sqrt{6}} *\frac{2-\sqrt{6}}{2-\sqrt{6} }[/tex]

We can use the special product of the difference of squares to simplify the denominator:

[tex](2 + \sqrt{6})(2-\sqrt{6}) = 2^2 - (\sqrt{6})^2 =4 - 6 = -2[/tex]

We can use distributive for the numerator:

[tex](3\sqrt{6}+5)(2-\sqrt{6})=6\sqrt{6} -18+ 10-5\sqrt{6} =\sqrt{6} -8[/tex]

Now we can rewrite the fraction:

[tex]\frac{\sqrt{6}-8 }{-2} =\frac{8-\sqrt{6} }{2}[/tex]

Answer:

1. 8 + t

2. g/15

3. 5b

4. 32 - x

Step-by-step explanation:

1. the sum of 8 and t

8 + t

2. the quotient of g and 15

g/15

3. the product of 5 and b

5b

4. the difference of 32 and x

32 - x

Answer:

V = 30 cubic inches

Step-by-step explanation:

Given:

height (h) = 10 in.

Base area (B) = 9 in.²

Required:

Volume of the pyramid

Solution:

Formula for finding volume of triangular pyramid = ⅓(B)(h)

Plug in the values

V = ⅓(9)(10)

V = (3)(10)

V = 30 cubic inches

Answer:

☄ [tex] \large{ \tt{EXPLANATION}} : [/tex]

[tex] \large{ \tt{↬When \: x = - 1 ,\: f( - 1) = - 1 + 5 = \boxed{ \underline{ {4}}}}}[/tex]

[tex] \boxed{ \boxed{ \tt{OUR\: FINAL \: ANSWER : \boxed{ \bf{4}}}}}[/tex]

✺ Success can never be achieved by , " I'll do it tommorrow " kind of people !

ツ Hope I helped! ♡

☼ Have a wonderful day / evening ! ☃

# StayInAndExplore ! ☂

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

2.    4.88 feet

Step-by-step explanation:

cos∅ = adj/hyp

cos71 = adj/15

adj = 15*cos71

adj = 4.88

Answer:

0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean and standard deviation of 486.9 and 24.01, respectively.

This means that [tex]\mu = 486.9, \sigma = 24.01[/tex]

What is the probability that on a given day the supermarket will sell between 477 and 525 gallons of milk?

This is the p-value of Z when X = 525 subtracted by the p-value of Z when X = 477.

X = 525

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{525 - 486.9}{24.01}[/tex]

[tex]Z = 1.59[/tex]

[tex]Z = 1.59[/tex] has a p-value of 0.9441

X = 477

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{477 - 486.9}{24.01}[/tex]

[tex]Z = -0.41[/tex]

[tex]Z = -0.41[/tex] has a p-value of 0.3409

0.9441 - 0.3409 = 0.6032

0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk

Answer:

4

Step-by-step explanation:

The value of the probability P(A or B) is 0.77

The given parameters are:

P(A) = 0.64

P(B) = 0.25

P(A and B) = 0.12

The probability is then calculated as

P(A or B) = P(A) + P(B) - P(A and B)

Substitute the known values in the above equation

P(A or B) = 0.64 + 0.25 - 0.12

Evaluate the like terms

P(A or B) = 0.77

Hence, the value of the probability P(A or B) is 0.77

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

Given:

The vertices of the triangle ABC are A(2,3), B(-4,4), C(-1,-3).

Translation: [tex](x,y)\to (x+2,y)[/tex]

Reflection: in the x-axis.

To find:

The graph of the image.

Solution:

The vertices of the triangle ABC are A(2,3), B(-4,4), C(-1,-3).

The rule of translation is:

[tex](x,y)\to (x+2,y)[/tex]

The points after translations are:

[tex]A(2,3)\to A'(2+2,3)[/tex]

[tex]A(2,3)\to A'(4,3)[/tex]

[tex]B(-4,4)\to B'(-4+2,4)[/tex]

[tex]B(-4,4)\to B'(-2,4)[/tex]

[tex]C(-1,-3)\to C'(-1+2,-3)[/tex]

[tex]C(-1,-3)\to C'(1,-3)[/tex]

After that the figure is reflected across the x-axis. So, the rule of reflection is:

[tex](x,y)\to (x,-y)[/tex]

[tex]A'(4,3)\to A''(4,-3)[/tex]

[tex]B'(-2,4)\to B''(-2,-4)[/tex]

[tex]C'(1,-3)\to C''(1,3)[/tex]

The vertices of image are A''(4,-3), B''(-2,-4), C''(1,3).

Answer:

36 cubes

Step-by-step explanation:

the pic is up there

Step-by-step explanation:

a² - 25b² can be expressed as a² - (5²)b²

this gives us: a² - (5b)²

using difference of two squares, we have:

(a - 5b)(a + 5b)

Since this bakery sells 12 gourmet orange zest cupcakes for $36.00, all the statements that are true include the following:

A. $3.00/1 is a unit rate for the cost per cupcake.

B. Using the same rate, the bakery can sell 2 dozen cupcakes for $72.00.

C. 36/12 represents the ratio of $36.00 for 12 cupcakes.

First of all, we would determine the unit rate for the cost per cupcake by using the following mathematical expression;

Unit rate = Cost of cupcake/number of cupcakes

Substituting the given parameters into the unit rate formula, we have the following;

Unit rate = $36.00/12

Unit rate = $3.00.

This ultimately implies that, the unit rate for the cost per cupcake is equal to $3.00.

Note: 1 dozen is equal to 12 pieces.

For the cost of 2 dozen cupcakes, we have the following:

Cost of 2 dozen cupcakes = 12 × 2 × 3

Cost of 2 dozen cupcakes = $72.00.

For the cost of 8 cupcakes, we have the following:

Cost of 8 cupcakes = 8 × 3

Cost of 8 cupcakes = $24.00.

For the cost of 6 cupcakes, we have the following:

Cost of 6 cupcakes = 6 × 3

Cost of 6 cupcakes = $18.00.

Read more on ratios here: brainly.com/question/27817533

#SPJ1

Complete Question:

A bakery sells 12 gourmet orange-zest cupcakes for $36.00. Select all the statements that are true.

$3.00/1 is a unit rate for the cost per cupcake.

Using the same rate, the bakery can sell 2 dozen cupcakes for $72.00.

36/12 represents the ratio of $36.00 for 12 cupcakes.

Using the same rate, it would cost $24.50 for 8 cupcakes.

Using the same rate, the bakery can sell 6 cupcakes for $20.00.

Answer: the answer is the third one

Step-by-step explanation:

well first of all how u get 3is because u have to divide 6 by 2 or u have todo the square root of 6 and 2 and u get 3

Answer:

x=1, y=2

Step-by-step explanation:

Answer:mean

Step-by-step explanation: I am also not sure because I been looking for the anwser to this but I think it’s mean

Answer:

Number of tile need = 300 tiles

Step-by-step explanation:

Given:

Dimensions of floor = 3 m by 4 m

Perimeter of square tile = 80 cm

Find:

Number of tile need

Computation:

Perimeter of square tile = 4(Side)

80 = 4(Side of tile)

Side of tile = 80 / 4

Side of tile = 20 cm

Side of tile = 0.2 meter

Area of tile = 0.2 x 0.2

Area of tile = 0.04

Area of floor = 3 x 4

Side of tile = 12 square meter

Number of tile need = 12 / 0.04

Number of tile need = 300 tiles

Answer:

WVAD

Step-by-step explanation:

wdvvvvavdv

Answer:

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Given the following data;

Present value, P = $300

Interest rate, r = 8%

Number of times, n = 1/4

Note: Future value = 2 * P = 2*300 = $600

Compound interest is generally calculated based on the interest rate on a loan, principal and the accumulated interest gained from previous periods. This interest is compounded for a certain number of times such as daily, weekly, quarterly or annually.

To find how long she would have to invest her money in order to double it, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Answer:

C. It has four congruent angles.

Step-by-step explanation:

=======================================================

Explanation:

A) This statement is true, so we can rule it out. A rhombus by definition has four sides the same length. Think of a square but the sides can be slanted or the angles could be something different from 90 degrees.

B) This statement is true. The opposite sides of a rhombus are always parallel. Any rhombus is always a parallelogram, but not the other way around.

C) False. This is the answer. We could have a square, and in which case we have four congruent angles. But we could slant the sides and have the angles be something else. All that matters is that all four sides are the same length.

D) True. Any rhombus is a parallelogram as mentioned in part B. However, some parallelograms are not a rhombus. Consider any rectangle in which the length and width are not the same. The sides are parallel, but we don't have all four sides the same length.

Answer:

41.8°

Step-by-step explanation:

Opposite angles are equal.

Answer:

41.8 degrees

Step-by-step explanation:

They are vertical angles, meaning they are the same, just opposite one another.

Given :

A man 1.30 m tall is on a top of a building. He observed a car on the road at an angle of 60 degrees if the building is 30 m high.

To Find :

How far is the car from the building.

Solution :

Let, distance between car and the building is x m.

So,

[tex]tan \ \theta = \dfrac{height\ of\ building + height\ of\ man}{distance \ between \ car \ and \ building}\\\\tan \ 60^o = \dfrac{30+1.3}{x}\\\\x = \dfrac{31.3}{1.73}\ m\\\\x = 18.09\ m[/tex]

Hence, this is the required solution.

Answer:

A) 48

Step-by-step explanation:

Given:

b = 16

c = 20

Pythagorean thm:

a² + b² = c²

a² + 16² = 20²

a² + 256 = 400

a² = 144

a = 12

To find perimeter:

P = a + b + c

P = 12 + 16 + 20

P = 48

Answer:

I diminished the amount that

Step-by-step explanation:

Answer:

-2.00

Step-by-step explanation:

Applying,

Z = (x-μ)/σ.................. Equation 1

Where Z =  Michelle z-score, x = Michelle score, μ = mean of the score, σ = Standard deviation of the score.

From the question,

Given: x = 48, μ = 70, σ = 11

Substitute these values into equation 1

Z = (48-70)/11

Z = -22/11

Z = -2.00

Hence Michelle's z-score is -2.00