Find the surface area of
the prism.

Answer:

Perimeter: 18.28

Area: 22.28

Step-by-step explanation:

1. Approach

An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.

2. Find the circumference of the semi-circle

The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,

C = 2(pi)r

Since a semi-circle is half of a circle, the formula to find its circumference is the following,

C = (pi)

Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;

C = (pi)r

C = (pi)2

C ~ 6.28

3. Find the area of the semi-circle

The formula to find the area of a circle is as follows,

A = (\pi)(r^2)

As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle

A = ((pi)r^2)/(2)

The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;

A = ((pi)r^2)/(2)

A = ((pi)(2^2))/(2)

A = (pi)2

A = 6.28

4. Find the area and perimeter of the square,

The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;

P = 4+4+4

P = 12

The area of a square can be found by multiplying the length by the width of the square.

A = l*w

Substitute,

A = 4*4

A=16

5. Find the area and the perimeter of the figure,

To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;

A = C+P

A = 6.28+12

A = 18.28

To find the area of the figure, add the value of the area of the circle to the area of the square;

A = 6.28+16

A = 22.28

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

285 mi

Step-by-step explanation:

We can see that for every gallon, Josh drives 30 more miles. This means that he will drive 30*9.5 mi.

30*9.5 = 285

Answer:

12 and 12.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

36*12*6+12*24*3=3456

Answer:

3456

Step-by-step explanation:

36*12*6 + 24*12*3

just add up the two volumes

Answer:

I searched the q and this is what I found

Step-by-step explanation:

Explanation: Number greater than 4 are 5 and 6 . So required probability is 26=13.

Answer:

quadrilateral graph I think if you get the answer please inform me

Answer:

A

Step-by-step explanation:

edge 2023

Answer:

It's 4 miles East from the store.

Step-by-step explanation:

6 miles east - 2 miles west = 4 miles East

Displacement for north and south should cancel out since they are equal to each other.

Answer:

there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Step-by-step explanation:

Given the data in the question;

Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,

t is the number of months since January.

Now, we use a cosine curve to model this scenario

Vertical shift will be;

D = ( 6 + 14 ) / 2 = 20 / 2

D = 10

Next is the Amplitude;

|A| = ( 6 - 14 ) / 2

|A| = 4

Now, the horizontal stretch factor will be;

B = 2π / 12

B = π/6

Hence;

S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1

Now we find when there will be less than 9 million square meters of sea ice;

S(t) = 9

so we have

9 = 4cos( π/6 × (t-2) ) + 10

9 - 10 = 4cos( π/6 × (t-2) )

-1 = 4cos( π/6 × (t-2) )

-1/4 = cos( π/6 × (t-2) )

so we have;

cos⁻¹( -1/4 ) = π/6 × (t₁-2)  -------- let this be equation 2

2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2)  -------- let this be equation 3

so we solve equation 2 and 3

we have'

t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )

t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - 104.4775 )

t₁ - t₂ = 6/π × ( π - 104.4775 )  

t₁ - t₂ = 5.035

therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

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

Explanation:

a = 9 = first term

r = -2 = common ratio

We multiply each term by -2 to generate the next term

The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)

If you tried plugging in say n = 2, you should find that,

9(-2)^(n-1)

9(-2)^(2-1)

9(-2)^1

9(-2)

-18

So that confirms the second term. I'll let you try the other values of n to confirm it further.

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

From here, you plug in n = 10 to find the tenth term

9(-2)^(n-1)

9(-2)^(10-1)

9(-2)^9

9(-512)

-4608

Answer:

16 people

Step-by-step explanation:

35.75 times 16 is 572, times 17 is 607.75, he only has 600 and he cant have a fraction of a person, so he can have 16 people

Answer:

18m

Step-by-step explanation:

Width= 432m2 ÷ 24m

= 18m

Answer:

Step-by-step explanation:

432m^2 / 24m = 18 m is the width of the garden plot

Answer:

Option B

Step-by-step explanation:

Options for the given question -

A. A histogram

B. A cumulative frequency table

C. A pie chart

D. A frequency polygon

Solution

Option B is correct

The data represents the frequency value for a given interval and hence it represents the cumulative form of frequency distribution.

Answer:

f(x)= -25x+4

y-inter x=0

y= -25(0)+4

=4

x-inter y=0

0= -25x+4

-4= -25x

x=4/25

Answer:

32.5 feet long and 20 feet wide

Step-by-step explanation:

To solve for the length first, you have it measured as 26 in long and each 4 in is 5 ft so you can go ahead and divide 26 in by 4 in and that gives you 6.5 in so what we did was figure out how many 4 in were in 26 in and therefore we have a 6.5 and so just to match that to the 5 ft per each 4 in (in this case we have 6.5) so we multiply 6.5*5 and that equals 32.5 ft which is the length of the garden bed.

Next we are going to solve for the width which is 16 in wide in the scale and so again each 4 in is 5 ft so here again we're going to divide 16 in by 4 in and that equals 4 in and so again each 4 in is 5 ft so we're going to go ahead and multiply 4 * 5 and that gets you 20 ft which is the width of the garden bed.

Answer:

UW ≈ 6.55 ≈ 7

Step-by-step explanation:

cos (35) = adjacent/hypotenuse

cos(35) = UW/VW

cos(35) = UW/8

8*cos(35) = UW

UW ≈ 6.55

Hope this helped! <3

Answer: b) f(m)

Step-by-step explanation:

Answer:

I don know that language so I can not help sorry

Answer:

3/4 es MAYOR!

Step-by-step explanation:

5/16 es menor que 1/2.

3/4 es mayor que 1/2.

Step-by-step explanation:

15 may be

HOPE IT HELP U ...

Answer:

A. $15 is the mode.

Step-by-step explanation:

In order to answer this question, we need to know the definition of mode. "The mode of a set of numbers is the number that occurs the most" Since out of the four numbers, the one that appears the most is $15, then $15 is the mode.

Answer:115

Step-by-step explanation:

There is 4 X so you use 360- (11+1) which is 348 and now divide by 4 which is now 87

Answer:

42

Step-by-step explanation:

3x+1+x+11 = 180

4x+12 = 180

4x= 180-12

4x=168

x = 168/4

x = 42

Answer:

(My answers are not rounded!)

Problem A:

Area: 285 cm^2

Perimeter: 70 cm

Problem B:

Area: 30 m^2

Perimeter: 30 m

Problem C:

Area: 28 m^2

Perimeter: 24 m

Problem D:

Lateral Area: 150 in^2

2 (l + w) h

= 2 (11 + 4) 5

= 2(15)5

= 30(5)

= 150

Surface Area: 238 in^2

2 (lw + hl + hw)

2 (11 x 4 + 11 x 5 + 5 x 4)

= 2 ( 44 + 55 + 20)

= 2 (119)

= 238

Volume: 220 in^3

Length x width x height (rectangular prism)

use formula: 11 x 5 x 4 = 220

Problem E:

Area: 379.94 m^2

Formula: πr^2 (circle)

3.14(11^2)

= 3.14(121)

= 379.94

Circumference: 69.08 m

Formula: 2πr

= 2(3.14)11

= 6.28(11)

=69.08

Problem F:

Area: 49 m^2

length x width

7 x 7 = 49

Perimeter: 28 m

2 (l + w)

= 2 (7 + 7)

= 2(14)

= 28

Problem G:

Area: 1,056 cm^2

length x width

48 x 22 = 1,056

Perimeter: 140 cm

2 (l + w)

2 (48 + 22)

2(70)

=140

Problem H:

Lateral Area: 94.2 in^2

2πrh

= 2(3.14) x 1.5(10)

= 6.28 x 15

= 94.2

Surface Area: 108.33 in^2

2πrh+2πr2

=2(3.14) 1.5(10) + 2(3.14) 1.5^2

= 108.33

Volume: 70.65 in^3

πr2h

= 3.14(1.5^2) 10

= 3.14(2.25) 10

= (7.065) 10

= 70.65

Answer:

8h+(-5.9d)-17+4d-3.4h

8h-5.9d-17+4d-3.4h

group the like terms

8h-3.4h+4d-5.9d-17

4.6h-1.9d-17

Step-by-step explanation:

9514 1404 393

Answer:

  The quadratic function has two distinct real zeros.

Step-by-step explanation:

The fundamental theorem of algebra says the number of zeros is equal to the degree of the polynomial. A quadratic (2nd degree) will have two zeros.

We are given that the function has two x-intercepts (real zeros), so we can conclude ...

  The quadratic function has two distinct real zeros.

Answer:

[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]

Step-by-step explanation:

The area a total of 4+3+6+5=18 balls, consisting of:

After a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:

Therefore, the probability of drawing another green one is:

[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]

Answer:

966 feet

Step-by-step explanation:

First, we can see that we have the velocity function given, a base value for the height, and need to figure out the change in height. We also know that velocity is the derivative of position/height. Thus, we can find the integral of the velocity to find an equation for the height.

[tex]\int\limits^1_0 {-34t+291} \, dt\\[/tex]

Use the exponent rule to turn -34t into -17t² and 291 into 291t to get our result as

-17t²+291t + C = height (h)

When t=0, we know that our height (h) is 6, so C = 6, making our equation

-17t²+291t + 6

To find the change between 1 second and 8 seconds, we can plug 1 and 8 in for t, and find the difference between those values, which is

(-17(8)²+291(8) + 6) - ( -17(1)²+291(1) + 6 )

= 1246 - 280

= 966

Note that we did final value (t = 8) - initial value (t=1), not the other way around

The change in height, between 1 second and 8 seconds, is therefore 966 feet

Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times

Step-by-step explanation:

The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.

The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.

hence, option B is correct

Answer:

a. 0.94 = 94% probability that the firm will make at least one hire.

b. The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.

Step-by-step explanation:

There is only a 6% chance that it will not make any hires

This means that P(X = 0) = 0.06.

16% chance that it will make all three hires.

This means that [tex]P(X = 3) = 0.16[/tex]

60% chance of hiring at least two candidates.

This means that:

[tex]P(X = 2) + P(X = 3) = 0.6[/tex]

[tex]P(X = 2) + 0.16 = 0.6[/tex]

[tex]P(X = 2) = 0.44[/tex]

Probability of one hire:

The sum of all probabilities, from no hires to three hires, is 1. So

[tex]P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1[/tex]

[tex]0.06 + P(X = 1) + 0.16 + 0.44 = 1[/tex]

[tex]P(X = 1) = 0.66 = 1[/tex]

[tex]P(X = 1) = 0.34[/tex]

a. What is the probability that the firm will make at least one hire?

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.06 = 0.94[/tex]

0.94 = 94% probability that the firm will make at least one hire.

b. Find the expected value and the standard deviation of the number of hires.

Expected value:

[tex]E(X) = 0.06*0 + 0.34*1 + 0.44*2 + 0.16*3 = 1.7[/tex]

Standard deviation:

[tex]S(X) = \sqrt{0.06*(0-1.7)^2 + 0.34*(1-1.7)^2 + 0.44*(2-1.7)^2 + 0.16*(3-1.7)^2} = 0.8062[/tex]

The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.