Image: ( A regular hexagon has an apothem of 4 and a side length of
8√3 /3 Its area is:_____)

Answer

A) 16√3 sq units
B) 48√3 sq units
C) 64√sq units
D) 32√3 sq units

Answer:

There are 36 dogs in the shelter.

Step-by-step explanation:

(Draw a model)

(3 boxes for dogs and 7 boxes for cats)

10 units = 120

1 unit = 120÷10

= 12

3 units = 12×3

= 36

(I hope you understand the question. A gentle reminder, always draw the model according to the ratio. From there you will understand.)

Answer:

The answer is 1 : 3 : 2

Step-by-step explanation:

First, you have to make them into same unit by converting it into km or m :

1 km = 1000 m

0.007 km = 7 m

0.021 km = 21 m

7 : 21 : 14

OR

14 m = 0.014 km

Then you can simplify it by 7 :

m,

7 : 21 : 14

= 1 : 3 : 2

OR

km,

0.007 : 0.021 : 0.014

= 0.001 : 0.003 : 0.002

= 1 : 3 : 2

(take note: in ratio, it is better to put it in whole number form rather than decimal form)

Step-by-step explanation:

a(n) = a ( n - 1) - 17

a(1) = 20

a(2) = a ( 2 - 1) - 17

= a (1) - 17

= 20 - 17

= 3

Now

a(3) = a ( 3 - 1 ) - 17

= a (2) - 17

= 3 - 17

= - 14

Hope it will help you.

Answer:

The best interpretation of one of the values of the function is that the rate  increases by 12% each day.

Step-by-step explanation:

Given:

F(x)=245(1.12)^x

To Find:

statement is the best interpretation of one of the values of the function

Solution:

Depending upon the values given the statement can be developed

As the function is itself the exponential growth structure ,

In this the statement ,Growth can be significantly depends on all factor

Such as time period initial value and rate.

But here the formula is simplified as ,

[tex]P=A(1+r)^t[/tex]

Here A= initial value r=rate and t =time period

Here A=245 and 1+r=1.12

i.e r=0.12 i.e 12%

Hence the rate give the best interpretation and more information about the function and scenario.

The function f(x)=245(1.12)^x models the exponential growth of bacteria in a sample over x days, with the base 245 being the initial number and 1.12 representing the daily growth rate.

The function f(x)=245(1.12)^x describes the exponential growth of bacteria, where the base number (245) represents the initial amount of bacteria and 1.12 indicates the growth rate per day.

For example, if we want to determine the number of bacteria at the end of the first day (x=1), we substitute 1 into the function to get f(1)=245(1.12)^1, which would give us the total number of bacteria at the end of day one.

The exponent x stands for the number of days and shows how the population grows at an increasing rate over time, which is a signature characteristic of an exponential function in a context like bacterial growth.

Answer:

its D the last one i just took the assignment

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

I took the assignment.

Answer:

The correct answer is 52 squats.

Step-by-step explanation:

An exercise routine requires 24 crunches for every 16 squats.

Therefore the routine would require 1 crunch for every [tex]\frac{16}{24}[/tex] squats.

And by the use of unitary method, the routine would require 78 crunches for every [tex]\frac{16}{24}[/tex] × 78 squats = 52 squats.

Thus for every 78 crunches attempted, the exercise routine would requires 52 squats to be done.

Given:

Desmond deposits $ 50 monthly.

Yearly he deposits = $50×12 = $ 600

Rate of interest compounded monthly = 4.7%

To find the amount he will receive after 10 years and the rate of change the value of his account after 10 years.

Formula

[tex]A = P(1+\frac{r}{(n)(100)} )^{nt}[/tex]

where,

A be the final amount

P be the principal

r be the rate of interest

t be the time and

n be the number of times the interest is compounded.

Now,

Taking,

P = 600, r = 4.7, n = 12, t = 10 we get,

[tex]A = 600(1+\frac{4.7}{(12)(100)}) ^{(12)(10)}[/tex]

or, [tex]A = 600(1.0039)^{120}[/tex]

or, [tex]A = 959.1[/tex]

Now,

At starting he has $ 600

At the end of 10 years he will be having $ 959.1

So,

The amount of change in his account = $ (959.1-600) = $ 359.1

Therefore the rate of change = [tex](\frac{359.1}{600} )(100) %[/tex]

= 59.85%

Hence,

a) His account will contain $ 959.1 after 10 years.

b) The rate of change in his account is 59.85% after 10 years.

Answer:

Step-by-step explanation:

Well first you have to find what the total amount of all the interior angles. In Oder to do that you count how many sides the shape has the subtract two from that number. Take the number you get from that and multiply it by 180. That number is total amount of all the interior angles including the angle x. Take the angles you do know and add them together. Take the number you get from that and subtract it from the total amount of all interior angles. The number you get from that is your answer. The answer to this problem is 103.

The value of angle x in a pentagon is 103 degrees.

In a pentagon, the sum of the interior angles is always 540 degrees. To find the value of angle x, we can subtract the given angles from 540 degrees and then divide by the number of missing angles.

Given angles: 117, 100, 105, 115

Sum of given angles: 117 + 100 + 105 + 115 = 437 degrees

Sum of missing angles: 540 - 437 = 103 degrees

Since there is only one missing angle x in the pentagon, the value of x must be 103 degrees.

Answer:

The answer to your question is t = 1.3 s

Step-by-step explanation:

Data

Equation    h(t) = -4.9t² + v₀t + h₀

v₀ = 0 m/s

h₀ = 8 m

t = ?

h = 0 m

Process

1.- Substitute the values in the formula

                  0 = -4.9t² + 0t + 8

2.- Simplification

                  0 = -4.9t² + 8

3.- Solve for t

                 4.9t² = 8

                      t² = 8/4.9

                      t² = 1.63

4.- Result

                      t = 1.27 ≈ 1.3 s

Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.

To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.

In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.

Answer:

[tex]\pi \: = \frac{22}{7} \: \: \: \: or \: \: \: \: \: \: 3.14 \\ \\ [/tex]

Answer:

0.3694

Step-by-step explanation:

In this question, we are asked to calculate the probability that a golfer scored at least 74 if she played on a particular day.

Given that ,

mean = µ = 73

standard deviation = σ = 3

P(x > 74) = 1 - P(x<74 )

= 1 - P[(x -µ) / σ < (74 -73) /3 ]

= 1 - P(z <0.3333 )

Using z table

= 1 - 0.6305

= 0.3694

probability= 0.3694

To find the probability of a golfer scoring at least 74 on a course with a mean score of 73 and a standard deviation of 3, we calculate the z-score for 74, find the corresponding probability in the z-table, and subtract this from 1 to get the upper tail probability. The probability is approximately 37%.

The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. We want to find the probability that a golfer scores at least 74. This is a question of statistics and specifically involves the concept of the normal distribution and calculating z-scores.

Firstly, we need to calculate the z-score for the score of 74. The z-score is calculated as (X-μ)/σ, where X is the score we are interested, μ is the mean, and σ is the standard deviation. Substituting the given values, (74 - 73) / 3 gives a z-score of approximately 0.33.

Then, to find the probability that a score is at least 74, we need to find the proportion of data to the right of this z-score in a standard normal distribution. This is known as the 'upper tail'. We subtract the z-score from 1 because the total probability under the normal curve is 1. If we look up 0.33 in the z-table, we get a value of 0.6293. Subtracting this value from 1 gives us 0.3707.

Therefore, the probability that a golfer scores at least 74 on this course is approximately 0.37 or 37%.

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Answer:

1/9= 2/18=3/27=4/36

Step-by-step explanation:

To find equivalent ratios to 1/9, both the numerator and the denominator are multiplied by the same number. Thus, 2/18, 3/27, and 4/36 are all equivalent ratios to 1/9.

Ratios are equivalent if they represent the same relationship between numbers. To find equivalent ratios for 1/9, you need to multiply both the numerator and the denominator by the same number. Here are three examples:

So, 2/18, 3/27, and 4/36 are ratios equivalent to 1/9.

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Answer: C.

Simple random sampling

Step-by-step explanation:

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

Answer:

C

Step-by-step explanation:

The computer randomly selects 500 names without any bias, Thus, it is simple random sampling because each name has equal chance of getting selected.

Answer:

I believe it is

x = -3/2 (-1.5)

y = 4

Answer:

A) 4x + 3y = 6

B) -4x + 2y = 14

Add the equations

5 y = 20

y = 4

Putting y into A)

A) 4x + 3*4 = 6

A) 4x = -6

x = -1.5

Step-by-step explanation:

Answer:

$48 green tokens

Step-by-step explanation:

please check the attached file for explanation

Answer:

48

Step-by-step explanation:

The original value of the house when it was purchased was $450,000.

Let us assume the original value of the house was x. This means that the house has increased by 38% from x to become $621,000.

In order to find the original value therefore, you can use the formula:

Original value + (Original value x Increase) = Current price

x + (38% × x) = 621,000

1.38x = 621,000

x = 621,000 / 1.38

= $450,000

In conclusion, the original value was $450,000.

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Final answer:

The original purchase price of the house was $450,000.

Explanation:

To find the original value of the house before it increased in value, we must first understand that the current value represents 138% of the original value, since the house has increased in value by 38%. This is because the original value is 100%, and the increase is 38%, making the total 138%. Therefore, the equation to find the original purchase price (which we can call 'P') is:

P * 138% = $621,000

We can rewrite this as:

P * 1.38 = $621,000

To solve for P, we divide both sides of the equation by 1.38:

P = $621,000 / 1.38

Now, doing the division:

P = $450,000

So, the house was originally purchased for $450,000 before it increased by 38% to its current value of $621,000.

Please consider the complete question.

A parking lot in the shape of a trapezoid has an area of 12,052.1 square meters. The length of one base is 82.4 meters and the length of the base is 108.6 meters. What is the width of the parking lot

We will use area of trapezoid to formula to solve our given problem.

[tex]\text{Area of trapezoid}=\frac{1}{2}(a+b)\times h[/tex], where

a and b represents parallel sides of trapezoid,

h = height of trapezoid.

Width of the trapezoid will be equal to height.

Upon substituting our given values in above formula, we will get:

[tex]12,052.1=\frac{1}{2}(82.4+108.6)\times h[/tex]

[tex]12,052.1\cdot 2=2\cdot \frac{1}{2}(82.4+108.6)\times h[/tex]

[tex]24104.2=(191)\times h[/tex]

[tex]\frac{24104.2}{191}=\frac{(191)\times h}{191}[/tex]

[tex]126.2=h[/tex]

Therefore, the width of the parking lot is 126.2 meters.

By proving triangle HKE and triangle GKF congruent, it is proved EG bisects HF and HF bisects EG.

Given that, parallelogram EFGH.

Prove that, EG bisects HF and HF bisects EG.

Parallelogram EFGH with diagonals EG and HF intersecting at point K.

Proof:

Consider, ΔHKE and ΔGKF

∠HKE=∠GKF (Vertically opposite angles are equal)

∠FHE=∠GFH ( Alternate angles between the parallel line EF and HG)

∠GEH=∠FGE ( Alternate angles between the parallel line EF and HG)

By AAA congruency, ΔHKE and ΔGKF are congruent

By CPCT,

KE=GK

JF=HK

So, EG bisects HF and HF bisects EG.

Hence, proved.

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Final answer:

To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH, we can use the statements and reasons provided.

Explanation:

To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH with diagonals EG and HF intersecting at point K, we can use the following statements and reasons:

Answer: 10.2

Step-by-step explanation:

Area of a circle is

A= pixr^2

327= 3.14r^2

Divide by 3.14

= 104.14

Get the sq rat of 104.14

= 10.2

The midpoint of a line segment is given by the formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2). After applying this formula to the given options, the correct midpoint is (p, r).

The midpoint of a line segment with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Applying this formula to the given options:

After substituting the values, we find that the correct answer is Option C: (p, r).

Answer:

Pyramids are triangular in shape with a sided shape, whereas cones have circular bases that merely adjoin at a point.

Step-by-step explanation:

Answer:

A pyramid is a cone with a polygonal base ;)

Answer:

6 pineapple, 6 melons, 8 grapefruits

Step-by-step explanation:

3.25P + 2.75M + 0.5G = 40

P = M

6M + 0.5G = 40

Let M = 6

6(6) + 0.5G = 40

0.5G = 4

G = 8

P = 6

M = 6

G = 8

Answer:

A) 1/2 - there are 2 sides - just as likely to occur as not to occur

B) 0% - it's never going to happen (impossible)

C) 0/0 - it's never going to happen (impossible)

D) 1/2 simplified from 2/4 - that was 2 out of the four balls. - just as likely to occur as not to occur

Answer:

b. g(x) only

Step-by-step explanation:

Answer:

30:15 (simplified is 2:1)

Step-by-step explanation:

Out of the 45 times Eric flipped a coin, 30 of them landed on heads. Tails is the the only other probable occurance, so since we know that there are 15 trials left, this means that the coin landed on tails 15 times. This would give a heads to tails ratio of 30:15, but the simplified ratio would be 2:1, because that's the smallest it can be divided evenly.

45-30=15

30:15=2:1

Answer:

j = 12

Step-by-step explanation:

Quotient means the answer when you divide the dividend by the divisor.

In this example, we are dividing 36 by 3, so 36 = dividend, 3 = divisor.

36 / 3 = 12. See the attachment if you need extra help on long division!

Answer:

It is 12

Step-by-step explanation:

So first you divide 36 by 3. So 3 goes into 3 once. Now 3 goes into 6 twice so there you have it

Answer:

Heres the anwser my man 128

Step-by-step explanation:

hope you got it right.

Answer:

B.14 m

Step-by-step explanation:

We are given that

Height of tree=12 m

[tex]\theta=40^{\circ}[/tex]

We have to find the distance between the spotlight and the base of tree.

In triangle ABC

AB=12 m

[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]

Using the formula

[tex]tan 40=\frac{AB}{BC}=\frac{12}{BC}[/tex]

[tex]BC=\frac{12}{tan 40}=14.3\approx 14 m[/tex]

Hence, option B is true.

Answer:

14m

Step-by-step explanation:

I took the test

Answer:15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

5=1

10=2

15=3