Find the surface area of the composite figure.
5 cm
10 cm
4 cm
5 cm
SA =
10 cm
-8 cm
4 cm
12 cm
[?] cm²
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Answer:

g and f are inverse functions because g(f(x)) = f(g(x)) = x

Step-by-step explanation:

Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]

Now, let's find g(f(x)):

[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

[tex]f(x)=y=7x-6[/tex]

Swap x and y:

[tex]x=7y-6[/tex]

Solve for y:

[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]

Notice that we got g, which means f and g are inverse.

Answer:

[tex]a_n=(-2)^{n-1}[/tex]

Step-by-step explanation:

So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values

Plug known values in:

[tex]-8 = a_1(-2)^{4-1}[/tex]

Subtract the values in the exponent

[tex]-8 = a_1(-2)^3[/tex]

Simplify the exponent

[tex]-8 = a_1 (-8)[/tex]

Divide both sides by -8

[tex]1=a_1[/tex]

So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]

The surface area of prism 1 is 36 cm²

From the question, we are to calculate the surface area of prism 1

From the given information, we have that the two hexagon-based prism are similar

Since the shapes are similar, we can write that

(Length of a side in prism 1)² / (Length of the similar side in prism 2)² =

Area of prism 1 / Area of prism 2

From the given information,

Length of a side in prism 1 = 3 cm

Length of the similar side in prism 2 = 8 cm

Area of prism 2 = 256 cm²

Thus,

3² / 8² = Area of prism 1  / 256

Area of prism 1 = (256 × 3²)/ 8²

Area of prism 1 = (256 × 9)/ 64

Area of prism 1 = (2304)/ 64

Area of prism 1 = 36 cm²

Hence, the surface area of prism 1 is 36 cm²

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The measure of the smallest side of the triangle is 10 inches

A triangle is a shape that has 3 sides and angles. The perimeter of a shape is defined as the sum of the sides of the figure.

Let the length of the smallest side be x

If one side is 5 inches longer than the smallest side, then;

L1 = x + 5

If another side is 1 inch less than twice the smallest side, then;

L2 = 2x - 1

Take the sum to have:

x+x+5+2x-1 = 44

4x+4= 44

Subtract 4 from both sides

4x =44 - 4

4x = 40

Divide both sides by 4

x = 40/4

x = 10

Hence the measure of the smallest side of the triangle is 10 inches

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Answer:

15 triangles.

Step-by-step explanation:

just count them eventually you will reach there.

Common significance levels are 0.01 and 0.05. Because the observations in the sample do not come from a random pool, it is impossible to conduct a test based on a population percentage by utilizing the normal approximation approach. This is further explained below.

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, Both 0.01 and 0.05 are considered to be significant values. It is not feasible to perform a test based on a population percentage using the normal approximation technique because the observations in the sample do not originate from a random pool. This makes it impossible to utilize the normal approximation approach.

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After a special medicine is introduced into a petri dish full of bacteria, Every second, the number of harmful bacteria remaining in the body decays by a factor of 0.97

Generally, a kind of unicellular bacteria that has characteristics with many disease-causing organisms, such as having a cell wall but lacking organelles and an organized nucleus.

In conclusion, When a certain medication is put into a petri dish that is full of bacteria, the amount of pathogenic bacteria that are still present in the body decreases by a factor of 0.97 every single second.

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The tangent in the unit circle is equal to 0.334.

In trigonometry, unit circles are representations of a circle with radius 1 and centered at the origin of a Cartesian plane commonly use to estimate and understand angles and trigonometric functions related to them.

Angles are generated by line segments whose coordinates are of the form (x, y), where x is the position of the terminal point along the x-axis and y is the position of the terminal point along the y-axis.

In addition, the tangent of the angle generated in a unit angle is defined by the following equation:

tan θ = y / x     (1)

If we know that x = - 0.9483 and y = - 0.3173, then the tangent of the angle generated in the unit circle is:

tan θ = (- 0.3173)/(- 0.9483)

tan θ = 0.334

The tangent in the unit circle is equal to 0.334.

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The area of the reduced rug is 25 square feet

The dimensions are given as:

Length = 12.5 feet

Width = 10 feet

The area is calculated as:
Area = Length * Width

So, we have:

Area = 12.5 * 10

Evaluate

Area = 125

When reduced by one-fifth, we have:

Area =1/5 * 125

Evaluate

Area = 25

Hence, the area of the reduced rug is 25 square feet

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The amount  Tyshawn earn per hour is $13.5

Fractions are written as a ratio of two integers

If after working 80 hours at his job, Tyshawn earned a total of $1080, then;

80 hrs = $1080

In order to calculate the amount earned per hour

Amount per hour = 1080/80

Amount per hour = $13.5

Hence the amount  Tyshawn earn per hour is $13.5

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The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.

The z-score for the hypothesis test is calculated by,

z-score = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.

It is given  that,

Sample size n = 30

Population mean μ = 9.7

Sample mean X = 10.1

Standard deviation σ = 1.8

So, the z-score is

= (10.1 - 9.7)/(1.8/√30)

= 0.4/0.328

= 1.219 ≅ 1.22

Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.

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Area of the entire rectangle is x² + 11x + 30. This can be obtained by adding area of each square.

Method 1

Area of rectangle = length × width  

Area of entire rectangle = x² + 5x + 6x + 30 = x² + 11x + 30

Method 2

Area of entire rectangle = length × width

                                   = (x+6)×(x+5)    

                                  = x² + (6+5)x + (6×5)        [∵(x+a)(x+b) =x² + (a+b)x + ab]

                                    = x² + 11x + 30

Hence area of the entire rectangle is x² + 11x + 30.

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Answer:

y is 7, x is 14

Step-by-step explanation:

This is a 30-60-90 triangle,

The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,

The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle

So y is

[tex] \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y[/tex]

Then, that means x is

[tex]7 \times 2 = 14[/tex]

The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

H0: u = 24000

H1: u > 24000

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

[tex]t = \frac{x-u}{s/\sqrt{n} }[/tex]

When we out in the values we would have

[tex]t = \frac{27500-24000}{2400/\sqrt{84} }[/tex]

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

=  ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

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Using the Heron's formula, the area of the triangle is: D. 95 square inches.

Area = √[s(s - a)(s - b)(s - c)] where s is half the perimeter, or (a + b + c)/2.

Given the following:

s = semi-perimeter = 1/2(50) = 25 in.

a = length of side a = 22 in.

b = length of side b = 13 in.

c = length of side c = 50 - 22 - 13 = 15 in.

Plug in the values

Area = √[25(25 - 22)(25 - 13)(25 - 15)]

Area = √[25(3)(12)(10)]

Area ≈ 95 square inches.

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Answer:

d

Step-by-step explanation:

Answer:

x = 5/3

Step-by-step explanation:

3x = xy - 55

3x = x*6 - 5

3x = 6x - 5

3x = 5

x = 5/3

Answer:

t=-6

Step-by-step explanation:

The expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.

A rational number is simply any integer, terminating decimal/repeating decimal or fraction.

1) √6 + √9 = √6 + 3 → Not rational

2) √64 + 6/11 = 94/11 → Rational number

3) √36 + √21 = 6 + √21 → Not rational

4) √16 + √169 = 17 → Rational number

5) 17.4343434343434343 + √49 = 24.43434343 → Rational number

6) √44 + √25 = 2√11 + 5 → Not rational

Therefore, the expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.

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There might be 18 colored papers.

colored papers to white papers:

3:8

48 white papers

8x6 = 48

Then 3x6= 18

There might be 18 colored papers.

Ratios evaluate numbers, normally through dividing them. in case you are evaluating one facts factor (A) to another statistics factor (B), your formulation might be A/B. this indicates you are dividing data A by using information B. for example, if A is 5 and B is 10, your ratio will be 5/10.

In mathematics, a ratio indicates how many times one quantity incorporates some other. for instance, if there are 8 oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6. further, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the full amount of fruit is 8:14.

Ratios can be absolutely simplified just like fractions. To simplify a ratio, divide all the numbers in the ratio through the same wide variety until they can not be divided anymore.

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Answer:

The correct answer is beef

Step-by-step explanation:

I took the quiz and got it correct

Answer: [tex]x=8, y=2\sqrt 2[/tex]

Step-by-step explanation:

By the Pythagorean theorem, x=8.

So, by the geometric mean theorem,

[tex]y^2 = (6)(2)=8\\\\y=2\sqrt{2}[/tex]

Answer:

(2, - 1 )

Step-by-step explanation:

4x - 9y = 17 → (1)

6x - 5y = 17 → (2)

multiplying (1) by 6 and (2) by - 4 and adding will eliminate x

24x - 54y = 102 → (3)

- 24x + 20y = - 68 → (4)

add (3) and (4) term by term to eliminate x

0 - 34y = 34

- 34y = 34 ( divide both sides by - 34 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

4x - 9(- 1) = 17

4x + 9 = 17 ( subtract 9 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is (2, - 1 )

Answer:

12-24-36-48-60

if I'm wrong I will try to get back to you and right my wrong

There is no change in the temperature.

To find how much temperature is changed:

Let, 'F' be the temperature.

Temperature decreased by [tex]33\frac{1}{3}[/tex]%.

F × (1-.33333) = Temperature increases by 50%.

(F × (1-.33333)(1.50)) = F =  No net change, right back to the original temperature F.

Therefore, there is no change in the temperature.

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There are 9 positive integers with 1 digit (1 - 9).

There are 90 integers with 2 digits (10 - 99).

There are 900 integers with 3 digits (100 - 999).

There are 9000 integers with 4 digits (1000 - 9999).

And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.

Now,

1000 = 9 + 900 + 91

so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.

The coordinates of your position are (6, 0, -4).

Using a proportional relationship, the scaled distances, in sheets of toilet paper, are given as follows:

The real distances are missing, and they are given in the table at the end of the answer.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the constant for the Scaled Distances as a function of the Real Distances is given as follows:

k = 5/149.6 = 7.6/227.9 = 0.03334795963.

Hence, the relationship for the Scaled Distances is given by:

S = 0.03334795963R

In which R is the real distance.

Then the scaled distances for the planets are given as follows:

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Answer:

edmentum/plato hope this can help someone :)

Step-by-step explanation:

Answer:

150 minutes

Step-by-step explanation:

If Anna read 75% of her 300-page book, then she has already read:

300 × 75%

= 300×0.75

= 225

225 pages.

If Anna has already read 225 pages, then she has:

300 - 225 = 75

75 pages left still to read.

If Anna reads 2 minutes per page, then she has

75 × 2 = 150 minutes.

She has 150 minutes of reading left to finish her book.

By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!

2 photos will not be displayed

The given parameters are:

Photos = 17

Rows = 3

Divide 17 by 3 and take note of the remainder

Photos left = 17/3

This gives

Photos left = 5 remainder 2

Hence, 2 photos will not be displayed

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