The lateral area of a regular pentagonal pyramid is 75 square inches and the slant height is 10 inches. Find the length of each side of the base.
A) 15 in.
B) 14 in.
C) 7.5 in.
D) 3 in

The proportion of students who have at least one cat is 0.37

The correct option is : (D)

A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Total students samples=30

Students answered yes =11

The proportion of students who have at least one cat

= [tex]\frac{11}{30}[/tex]

= 0.367

≈ 0.37

Hence the proportion of students who have at least one cat is 0.37.

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Answer:

(- 2, - 1 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = 3x + 5 → (2)

Substitute y = 3x + 5 into (1)

3x + 5 = 2x + 3 ( subtract 2x from both sides )

x + 5 = 3 ( subtract 5 from both sides )

x = - 2

Substitute x = - 2 into either of the 2 equations and evaluate for y

Substituting into (1)

y = 2(- 2) + 3 = - 4 + 3 = - 1

solution is (- 2, - 1 )

Answer:

Graph the point at -1 on the y-axis, then the next at 4 on the x-axis, then connect them

This is the graph as in upload

Answer:

19.7°

Step-by-step explanation:

In ΔTUV, the measure of ∠V=90°, UV = 3.3 feet, and TU = 9.8 feet. Find the measure of ∠U to the nearest degree.

We make use of sine rule

TU/sin V = UV/sin U

9.8/sin 90 = 3.3/sin U

Cross Multiply

sin 90 × 3.3 = 9.8 × sin U

sin U = sin 90 × 3.3 /9.8

U = arc sin ( sin 90 × 3.3/9.8)

U = 19.7°

Answer:

3.002, 3.02, 3.03, 3.032, 3.2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

75ft

Step-by-step explanation:

We are to find the maximum height reached by the ball. This is expressed as;

H = u²sin²Ф/2g

u is the initial velocity = 80 ft./s.

Ф is the angle = 60degrees

g is the acceleration due to gravity = 32ft/s

Substitute

H =80²sin²60/2(32)

H = 6400sin²60/64

H = 100 (0.8660)²

H = 100*0.749956

H = 74.9956

H ≈ 75ft

Hence the ball has travelled 75ft apprximately

Answer:

-6 2/3

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

Answers:

x = angle MLN = 35 degrees

angle FLJ = 55 degrees

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

Explanation:

This problem is fairly tricky if you're not sure what to look for. A slight clue is that they've marked a red point that strangely doesn't have a label on it. It's a fairly small point but it's definitely there if you look closely. While this point's location isn't exactly what we want, we're fairly close. Start at point L and draw a ray through the center point P. Ray LP will intersect the circle at point A, as shown in the diagram below.

From here, draw segments FA and MA. Now notice that inscribed angle LMF = 55 and inscribed angle FAL both subtend the same arc. The term "subtend" basically means "cut off". This arc that the inscribed angles subtend is minor arc FL. A minor arc is where you travel the shorter path around the circle, which indicates its measure is less than 180 degrees.

Since inscribed angles LMF and FAL subtend the same minor arc, this makes the inscribed angles to be congruent.

In short: angle FAL is 55 degrees

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

Segment LA goes through the center P. Through Thales theorem, we know that inscribed angle LFA is 90 degrees. Consequently, we can determine that inscribed angle FLA is 90-55 = 35 degrees.

Segment JL is tangent to the circle, meaning that angle ALJ is 90 degrees. So angle FLJ is 90-35 = 55 degrees.

It's not a coincidence that angle FLJ, angle FAL, and angle LMF are the same measure.

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

We found that angle FAL was 55 degrees. Applying Thales theorem again shows that angle MAF is 90 degrees. Therefore, angle LAM is 90-55 = 35 degrees.

Focus now on triangle LMA. This is also a right triangle (Thales Theorem). The upper acute angle we found was angle LAM = 35, so the lower acute angle is ALM = 55.

Then we can find angle MLN = (angle ALN) - (angle ALM) = 90 - 55 = 35

In short, angle MLN = 35 degrees

Similar to the previous section, it is not a coincidence that angles LFM, LAM and MLN are the same measure.

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

As an alternative, since we know angle FLJ = 55, and angle FLM is 90 degrees, this means...

(angle FLJ)+(angle FLM) + (angle MLN) = 180

55 + 90 + angle MLN = 180

145 + angle MLN = 180

angle MLN = 180 - 145

angle MLN = 35 degrees

Answer:

960 cm³ I think it may be correct

Answer:

Step-by-step explanation:

The equation of this circle is (x - 2)^2 + (x + 3)^2 = 36.

The center of the circle is at (h, k):  (2, -3), and the radius, r, is 6.

Answer:

72 and -2

Step-by-step explanation:

x - y = 74

2x + 3y = 138

x - y = 74

y = x - 74

2x + 3(x - 74) = 138

2x + 3x - 222 = 138

5x = 360

x = 72

x - y = 74

72 - y = 74

-y = 2

y = -2

Answer:

12

Step-by-step explanation:

hi

Equation which describe relationship between total cost and number of t-shirt is    [tex]c(t)=75.93e^{0.06t}[/tex].

Data given are ,

Number of t-shirt (t)                  total cost c(t)

12                                            156

17                                             211

22                                            266

According to above table, exponential function best describes the relationship between the total cost, c(t), and the number of T-shirts, t.

Let,        [tex]c(t)=Ae^{kt}[/tex]

Substitute ,   t=12  and c(t) = 156

We get,     [tex]156=Ae^{12k}.......(1)[/tex]

Substitute ,  t=17 and c(t) = 211

We get,     [tex]211=Ae^{17k} ........(2)[/tex]

After solving above equations.

We get,    A = 75.93  and  k = 0.06

Thus,     [tex]c(t)=75.93e^{0.06t}[/tex]

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Answer:

30

Step-by-step explanation:

First, you have to convert 20% into a decimal.

Explanation:

20 ÷ 100 = 0.2

Now multiply 0.2 by 150

Explanation:

0.2 × 150 = 30.

Therefore, 20% of 150 is 30.

Answer:

16.50

Step-by-step explanation:

divide it to the upper thanks

Answer:

19

Step-by-step explanation:

hope this helps with the problem

Answer:

4. H0: u1= u2    Ha; u1≠ u2

5. The smaller value of p supports the null hypothesis.

Step-by-step explanation:

4. The null and alternate hypotheses are

H0: u1= u2   i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

Ha; u1≠ u2   i.e there a difference between the mean pinch strengthof the two surgeries

It can be written like this as well

H0: u1 -u2= 0   i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

Ha; u1 -u2≠ 0   i.e there a difference between the mean pinch strengthof the two surgeries

Part 5. The test having a p- value less than 0.05  tells that the null hypothesis cannot be rejected. Theres no evidence to reject the null hypothesis.

The smaller value of p supports the null hypothesis.

Answer: 36

Step-by-step explanation: using long division you take 11 divide into 398 so first, 11 goes into 39, 3 times

you have 6 left, so keep the 6 and drop down the other 6

next 11 goes into 66, 6 times making it 396/11= 36  

hope this helps

Answer:

36

Step-by-step explanation:

396 divided by 11 is equal to 36

      36

11/[tex]\sqrt{396\\}[/tex]

   - 33

      066

    -  66

         0

Answer:

x = 4/5

FILLER FILLER FILLER

Answer:

100 times

Step-by-step explanation:

you have a 3/6 chance of rolling less than 4 once

so you multiply 3/6 times 200- you get 600/6

you simplify 600/6 to 100

100 times is the answer.

Have a fantasical day.

Answer:

[tex]x = \frac{50 + 92}{2} = 71[/tex]

There have been more than 500 Iron Age bog bodies and skeletons recovered in Denmark alone, with additional finds made in Germany, the Netherlands, the United Kingdom, and Ireland. These discoveries date from between 800 B.C. and 200 A.D.

The term “quaking bog” refers to the unstable surface of the bog, which will sink slightly beneath a weight. Even the plants may be through to reach the water below. This is how both people and animals have drowned. If the peat is dense and spongy, non-floating bogs may also tremble.

here, we have,

Boggy body reports first appeared in the early 18th century. More than 1,850 bog remains were catalogued by the German scientist Alfred Dieck in 1965, however subsequent research showed that Dieck made many errors in his work.

Before cutting into the peat, ground-penetrating radar can be used to locate bodies and artifacts beneath the surface of bogs.

Therefore, people find bog bodies looking for peat for fuel. it's something along those lines.

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Answer:

Step-by-step explanation:

c circle

Answer:

Complementary, x=10

Step-by-step explanation:

Complementary angles mean they add up to 90 degrees.

So 29+(6x+1)=90.

30+6x=90

6x=60

x=10

Answer:

Complementary-------- x= 10

Step-by-step explanation:

only 90 degrees

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

3. 6x = 60

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

x= 10

Answer:

A cylinder

Step-by-step explanation:

When you rotate the rectangle you are make a circle but since its volume the original height of the rectangle is the height of the circle which would mean a cylinder.

Answer:

CYLINDER

Step-by-step explanation:

Answer:

z = 20 , x = 5

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

2 tickets

Step-by-step explanation:

a + c = 5

9a + 4c = 30

let a = 5-c

substitute:

9(5-c) + 4c = 30

45 - 9c + 4c = 30

45 - 5c = 30

-5c = -15

c = 3

a = 2