Determine if the given sides form a triangle.
3.3 m, 1.6 m, 0.2 m
Select the correct choice below, and fill in the answer box
to complete your choice.
(Type an integer or a decimal.)
A. Yes, because the sum of the lengths of the two
shorter sides is m, which is greater than the
length of the third side.
B. No, because the sum of the lengths of the two
shorter sides is m, which is less than the
length of the third side.
C. No, because the sum of the lengths of the two
shorter sides is
m, which is equal to the length
of the third side.

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

From the question, we have the following equations that can be used in our computation:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

The completed table of the functions and inverses can be presented as follows;

1. t(x) → a(x)

2. Q(x) → B(x)

3. G(x) → c(x)

4. f(x) → D(x)

5. y(x) → w(x)

6. e(x) → R(x)

7. U(x) → H(x)

8. P(x) → J(x)

9. m(x) → k(x)

10. S(x) → n(x)

Making x the subject of the given functions to find the inverse gives;

1. a(x) = 2•(x - 6)

Therefore;

x = (a(x)/2) + 6

t(x) = (x/2) + 6

Therefore;

2. G(x) = (1/4)•x²

4•G(x) = x²

x = 2•√(G(x))

3. B(x) = √(x)/4

4•B(x) = √(x)

x = 16•(B(x))²

Q(x) = 16•x²

Therefore;

4. D(x) = (x + 6)/2

x = 2•D(x) - 6

f(x) = 2•x - 6

Therefore;

5. y(x) = (4•x + 2)²

(√(y(x)) - 2)/4 = 4•x

w(x) = (√(x) - 2)/4

Therefore;

6. R(x) = (1/4)•(4•x)²

x = √(4•R(x))/4 = √(R(x))/2

e(x) = √(x)/2

Therefore;

7. H(x) = 2•x + 6

(H(x) - 6)/2 = H(x)/2 - 3

x = H(x)/2 - 3

U(x) = x/2 - 3

Therefore;

8. J(x) = (√(x + 2))/4

x = (4•J(x))² - 2

P(x) = (4•x)² - 2

Therefore;

9. k(x) = x/4 + 3

x = 4•(k(x) - 3) = 4•k(x) - 12

m(x) = 4•x - 12

Therefore;

10. n(x) = 4•(x + 3)

x = n(x)/4 - 3

S(x) = x/4 - 3

Therefore;

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The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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Answer:

95% of all students at private universities pay less than $58,302.5.

Step-by-step explanation:

Normal Probability Distribution:

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 of $50,900, standard deviation of $4,500

This means that \(\mu = 50900, \sigma = 4500\)

Ninety-five percent of all students at private universities pay less than what amount?

Pay less than the 95th percentile, and the amount is given by X when Z has a pvalue of 0.95, so X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 50900}{4500}\)

\(X - 50900 = 1.645*4500\)

\(X = 58302.5\)

95% of all students at private universities pay less than $58,302.5.

Answer:

83.25

Step-by-step explanation:

add all the numbers and divide by 8. 666/8 = 83.25

Answer:

83.25

Step-by-step explanation:

Mean = sum of all terms / number of terms

82+100+92+66+72+96+70+88 = 666

666 / 8 = 83.25

Answer:

the probability is 0.0202

Step-by-step explanation:

The computation is shown below:

Given that

The Average life span = 17 hours

Standard deviation = 0.8 hours

Sample = 30 batteries

Sample mean = 16.7 hours

Now based on the above information

The probability is

\(P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202\)

Hence, the probability is 0.0202

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

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

Explanation:

Utility is another way of saying happiness more or less. Marginal utility is getting that extra bit of satisfaction from buying/consuming one additional item. Saying the marginal utility is diminishing but not negative, means we have an increasing utility curve that has its rate of increase slow down. An example would be a log curve.

Inflation can be thought of as an expense. For example, if it costs $1 to get a loaf of bread one year, and then next year that cost jumps to $1.50 for that same loaf of bread, then the worker has effectively lost 50 cents on their paycheck. Zero inflation means there isn't any such expense. So in a way, this is like getting a raise.

Being paid more due to higher labor costs means that the worker gets even more money on top of the bonus money saved from zero inflation. These two aspects would provide a lot of incentive for the person to work more hours. Of course, there would be a point in which the marginal utility is far too small. In other words, the amount of additional money earned isn't worth the additional time spent working. This is likely when the worker would take time off, seek out a raise, or find some other job.

Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Step-by-step explanation:

Answer:you would use a demand chart

Step-by-step explanation:

Answer:

C. A demand schedule.

Step-by-step explanation:

The demand curve is a visual representation of how many units of a good or service will be bought at each possible price. It plots the relationship between quantity and price that's been calculated on the demand schedule, which is a table that shows exactly how many units of a good or service will be purchased at various prices.

As you can see in the chart below, the price is on the vertical (y) axis, and the quantity is on the horizontal (x) axis. This chart plots the conventional relationship between price and quantity. The lower the price, the higher the quantity demanded. As the price decreases from p0 to p1, the quantity increases from q0 to q1.

Key words and Phrases:

quantity, price, demand, good, service, demand curve, demand schedule

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Step-by-step explanation:

[taking alpha = a]

L.H.S.

(1-sin⁴a)/cos⁴a

= 1/cos⁴a-sin⁴a/cos⁴a

= sec⁴a-tan⁴a

= (sec²a+tan²a)(sec²a-tan²a)

= (1+tan²a+tan²)(1) [as sec²a=1+tan²a]

= 1+2tan²a

= R.H.S. [Proved]

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

I think it's 8 - ab but I'm not really sure

Answer:

0.29b =

Step-by-step explanation:

each banana costs .29 $ so if you replace b with any number, you would have the cost the certain quantity of bananas

Answer:

13 Compute using the 2 right angles, we know that m<FIG=90* and

The perimeter of the woods is 26 miles if each grid represents one mile in the figure.

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We know the perimeter of the rectangle = 2(length + width)

As we can see closely in the figure the perimeter of the wood is actually a perimeter of a rectangle if we shift vertical and horizontal lines to make it a complete rectangle.

Let's suppose each grid is expressing one mile.

So the length of the rectangle = 9 miles

The width of the rectangle = 4 miles

The perimeter of the woods  = 2(9+4) = 26 miles

Thus, the perimeter of the woods is 26 miles if each grid represents one mile in the figure.

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The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

234

Step-by-step explanation:

Answer:

B. 21

Step-by-step explanation:

3x7= 21 they both have this multiple in common

The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; \(x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}\)

The statements and reasons can be presented algebraically as follows;

Statements \({}\)                                          Reasons

\(x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}\)        Find a common denominator on the

                                                            right side of the equation

\(x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}\)                 Add the fractions together on the

                                                     \({}\)        right side of the equation

\((x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}\)                             Rewrite the perfect squared equation

                                                      \({}\)      to the left side of the equation as a

                                                        \({}\)    binomial squared

\(x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }\)                   Take the square root of both sides of  the

                                                    \({}\) equation

\(\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}\)                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

have a great day :) .!

Answer:

The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.

Step-by-step explanation:

Answer:

The scale factor is a proportional relationship.   The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship. Enlargements have a scale factor greater than 1.  Reductions have a scale factor between 0 and 1. The proportion should be preserved.

Hope this Helps!

Answer:

Step-by-step explanation:

take 32 degree as reference angle

using sine rule

sin 32=opposite/hypotenuse

0.52=x/13

0.52*13=x

6.76=x

Answer:

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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Answer:

The probability of flipping heads is 1/2 and the probability of picking a vowel is 4/10 or 2/5

The value of x is 30°.

What is the linear angle?

A linear angle refers to an angle whose measure is equal to 180 degrees. It is also known as a straight angle. In geometry, a linear angle is used to describe the relationship between two lines that form a straight line, i.e. they are parallel. The two lines are said to be supplementary to each other, meaning they add up to 180 degrees.

We have given,

The sum of the measures of ∠QRT and ∠TRS is 180°

∠QRT = (x-10)° and ∠TRS = (4x - 20)°

To find the value fo x =?

We know that,

By combing these two angles we get the linear angle.

so, A linear angle refers to an angle whose measure is equal to 180 degrees.

∠QRT + ∠TRS = 180°  

(x - 10)° + (4x - 20)° = 180°

by simplifying,

5x - 30° = 180°

5x = 180° - 30°

5x = 150

x = 150/5

x = 30°

Hence, the value of x is 30°.

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Answer:

0.148

Step-by-step explanation:

Answer:

the answer is 50.27 cm for your question

If a coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The amount of  each type that should be mixed in order to have 20 pounds of coffee that is worth ​$8.50 per​ pound is: 13  pounds $10.00 Gourmet coffee, 7 pounds $6.00 Cheap brand.

Gourmet coffee $10.00 ---- x pounds

Cheap brand $6.00 --- 20 - x pounds

Mixture $8.50 ---- 20

Total 20 pounds

10 x + 6 ( 20 - x ) = 8.50 × 20

10 x + 6 ( 20 - x ) = 170

10 x + 120 - 6 x = 170

Collect like terms

10 x - 6 x = 170 - -120

4 x = 50

Divide both side by 4x

x =50/4

x = 12.5

x = 13  pounds $10.00 Gourmet coffee

Cheap brand

20-x pounds

20-13

=7 pounds $6.00 Cheap brand

Therefore 13 pounds and 7 pounds should be mixed.

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The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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