A trapezoid has bases that measure 10 cm and 6 cm. The height of the figure is 15 cm. What is the area of the trapezoid?60 cm?90 cm?120 cm150 cm​

The equation of the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)

How to determine the graphed rational function

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

The graph

From the graph, we have vertical asymptotes at

x = 2 and x = -2

This means that the denominator of the function is

(x + 2)(x - 2)

Looking through the list of options, we have the function with a denominator of (x + 2)(x - 2) to be f(x) = (x + 1)/(x + 2)(x - 2)

Hence, the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)

The rational functions is graphed below is [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] (after dividing both the numerator and denominator by (x)). The correct answer is C.

1. Analyze the graph's behavior:
The graph has vertical asymptotes at x = -3 and x = 2. This means the denominator of rational function must have factors (x + 3) and (x - 2).
The graph intersects y-axis at (0, -1). when x = 0, function value is -1.
As x approaches positive / negative infinity, graph approaches line y = 0. The numerator's degree must be smaller than denominator degree.
2. Consider the answer choices:
Only option C, [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] has correct vertical asymptotes and a numerator degree of 1.
3. Verify the answer choice:
Let's substitute x = 0 into option C:
[tex]F(0) = \frac{(0 - 1)}{(0)(0 - 3)} = \frac{-1}{0} = -\infty[/tex]
This doesn't match the graph's behavior at x = 0. However, this is a common issue with rational functions when the numerator and denominator have a common factor. In this case, both the numerator and denominator have a factor of (x). Dividing both the numerator and denominator by (x) gives:
[tex]F(x) = \frac{\cancel{(x - 1)}}{\cancel{x}(x - 3)} = \frac{1}{(x - 3)}[/tex]
Now, let's substitute x = 0:
[tex]F(0) = \frac{1}{(0 - 3)} = -\frac{1}{3}[/tex]
This matches the graph's behavior at x = 0.

Complete and correct question:

Which of the following rational functions is graphed below?

[tex]A. F(x)=\frac{(x+1)}{(x+3)(x-2)}\\\\B. F(x)=\frac{(x-1)}{(x+2)^{2}}\\\\C. F(x)=\frac{(x-1)}{x(x-3)}\\[/tex]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= [tex]\pi r^2h[/tex]

According to the problem,

[tex]\pi r^2 h=25[/tex]

[tex]\Rightarrow h=\frac{25}{\pi r^2}[/tex]

The surface area of the base of the can is = [tex]\pi r^2[/tex]

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× [tex]\pi r^2[/tex])

The lateral surface area of the can is = [tex]2\pi rh[/tex]

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× [tex]2\pi rh[/tex])

                                                 [tex]=\$2.5 \pi r h[/tex]

Total cost of metal is C= 2.00 [tex]\pi r^2[/tex]+[tex]2.5 \pi r h[/tex]

Putting [tex]h=\frac{25}{\pi r^2}[/tex]

[tex]\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}[/tex]

[tex]\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}[/tex]

Differentiating with respect to r

[tex]C'=4\pi r- \frac{62.5}{ r^2}[/tex]

Again differentiating with respect to r

[tex]C''=4\pi + \frac{125}{ r^3}[/tex]

To find the minimize cost, we set C'=0

[tex]4\pi r- \frac{62.5}{ r^2}=0[/tex]

[tex]\Rightarrow 4\pi r=\frac{62.5}{ r^2}[/tex]

[tex]\Rightarrow r^3=\frac{62.5}{ 4\pi}[/tex]

⇒r=1.71

Now,

[tex]\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0[/tex]

When r=1.71 cm, the metal cost will be minimum.

Therefore,

[tex]h=\frac{25}{\pi\times 1.71^2}[/tex]

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

The radius should be approximately 1.7 cm, and the height should be approximately 2.77 cm.

We are to find the dimensions of a cylindrical can without a top that will minimize the cost while containing 25 cubic centimeters (cm³) of liquid.

The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height.

Given V = 25 cm³, we can express the height h in terms of the radius r:

h = V / (πr²) = 25 / (πr²)

The cost involves the lateral surface area (sides) and the bottom area:

Lateral surface area: As = 2πrh

Bottom area: Ab = πr²

Cost of the sides: $1.25 per square cm (let's denote the lateral cost by Cs)

Cs = 1.25 * 2πrh = 2.5πrh

Cost of the bottom: $2.00 per square cm (let's denote the bottom cost by Cb)

Cb = 2.00 * πr² = 2πr²

Total cost C is given by:

C = Cs + Cb = 2.5πrh + 2πr²

Substituting h = 25 / (πr²) into the total cost formula,

C = 2.5πr(25 / πr²) + 2πr² = 62.5 / r + 2πr²

To minimize the cost, we take the derivative of C with respect to r and set it to zero:

dC/dr = -62.5 / r² + 4πr = 0

Simplifying, we get:

4πr³ = 62.5

r³ = 62.5 / 4π = 4.978

r = ∛(4.978) ≈ 1.7 cm

Now, calculate the height h:

h = 25 / (π * 1.7²) ≈ 2.77 cm

Thus, the dimensions of the can that minimize the cost are approximately: radius = 1.7 cm and height = 2.77 cm.

Answer:

list all the statistics

Step-by-step explanation:

Answer:

5 ounce for $1.49 is you're answer.

Step-by-step explanation:

1.49/6 = 0.248 per oz

3.59/13 = 0.276 per oz

Answer:

(x-10) (x+1) =0

x=10                     x=-1

Step-by-step explanation:

x^2 -9x-10 =0

Factor

What two numbers multiply to -10 and add to -9

-10*1 = -10

-10+1=-9

(x-10) (x+1) =0

Using the zero product property

x-10 = 0             x+1=0

x-10+10=0+10       x+1-1=0-1

x=10                     x=-1

These are the x intercepts

Answer:

A. 0.09

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(x - h)² + (y - k)² = r²

x² + y² = r²

(-3)² + (-5)² = r²

r² = 34

x² + y² = 34

Answer:

x=500

Step-by-step explanation:

7/10=350/x

cross-multiply by multiplying 350 to 10 and multiply 7 to x.

example:

7•x

350•10

7x=3500

divide both sides by 7

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

x=500

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

Answer:

A. 191.54 ft²

B. $2011.17

Step-by-step explanation:

Part A involves multiplying to find the area of the living room using the formula to find the area of a rectangle.

A = b*h (original formula)

A = 15.7*12.2 (substitute values)

A = 191.54 (multiply)

The area of his living room is 191.54 ft²

Next, you need to multiply the number of ft² by the cost per ft² to find the cost to tile the living room

Cost = $10.50*191.54 (equation)

Cost = $2011.17 (multiply)

The total cost of tiling the living room would be $2011.17

Answer:

Step-by-step explanation:

Answer:

boardgamegeek.com/boardgame/245655/kings-dilemma

Step-by-step explanation:

The probability of rolling a factor of 8 with a six-sided die is 0.5 or 50%, as there are 3 favorable outcomes (1, 2, 4) out of 6 possible outcomes when rolling the die.

To find the probability of rolling factors of 8 with a fair, six-sided die, we first need to identify the factors of 8, which are 1, 2, 4, and 8. Of these, only 1, 2, and 4 are possible outcomes on a six-sided die. There are six possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), so the probability of rolling a factor of 8 is the number of favorable outcomes (where the result is a factor of 8) divided by the total number of possible outcomes.

The favorable outcomes for this probability event are {1, 2, 4}, hence there are 3 favorable outcomes. Thus, the probability of rolling a factor of 8 is:

P(rolling a factor of 8) = Number of favorable outcomes / Total number of possible outcomes

P(rolling a factor of 8) = 3 / 6

P(rolling a factor of 8) = 0.5

Therefore, the probability of rolling a factor of 8 is 0.5 or 50%.

Answer:

[tex]\frac{1}{5^{4}}[/tex] = [tex]\frac{1}{625}[/tex] = 0.0016

Step-by-step explanation:

I'm assuming you mean [tex]5^{-4}[/tex] (which could also be written as 5^-4, for future reference).

Negative exponents actually mean you'd use the term in the denominator, taking away the negative portion. It's difficult to explain in words, and is easier to see.

[tex]5^{-4}[/tex] = [tex]\frac{1}{5^{4}}[/tex]

Notice how the -4 changes to 4, and it becomes the denominator.

[tex]5^{4}[/tex] is also 625, so [tex]5^{-4}[/tex] is also 1/625, or the decimal version (0.0016).

I hope this helps!

Answer:

0.0217391304

Step-by-step explanation:

Answer:

1/46 gallons per mile

Step-by-step explanation:

Take the gallons used and divide by the number of miles driven  

5 gallons /230 miles

1/46 gallons per mile

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

(9+11)/2 = 10

Answer:

The letters of the word readers can be arranged in 1260 distinct ways.

Step-by-step explanation:

A word has n letters.

The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times

So the number of distincts ways the letters can be arranged is:

[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]

In this question:

Readers.

Has 7 letters.

E repeats twice.

R repeats twice.

So

[tex]N = \frac{7!}{2! \times 2!} = 1260[/tex]

The letters of the word readers can be arranged in 1260 distinct ways.

The word 'READERS' can be arranged in 1260 distinct ways, considering the repetition of letters.

The problem involves finding the number of distinct ways the letters in the word 'READERS' can be arranged. This is a topic in combinatorics, or counting, in mathematics.

The formula for the number of ways of arranging n objects where some objects are identical is n!/r1!r2!... where r1, r2, ... are the numbers of each type of similar object.

In the word 'READERS', there are 7 letters in total (n=7). Three of these letters are 'E', 'R' and 'R' (r1=2) and two of these letters are 'E' (r2=2).

The remaining letters 'A', 'D' and 'S' are all distinct (r3=1, r4=1 and r5=1). So, applying the formula, we get the number of distinct arrangements as 7!/(2!2!1!1!1!) = 1260.

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Answer:

1. Airspeed = 201.17 mph

2. Bearing  = 358.93⁰

Step-by-step explanation:

Given Data:

d = 700 mi

t = 3.5 hrs

speed of wind Vx = 10 mph

velocity of plane Vy = d/t

                                  = 700/3.5

                                  = 200 mph

1. Air speed (V) is calculated using the formula;

V² = V²x + V²y -2*Vx *Vy*cos∝

But ∝ = 338 - 180 = 158°

Substituting into the equation, we have

V² = 10² + 200² - 2*10*200*Cos 158

    = 40100 - 400 *(-0.92718)

    = 40100 + 370.872

 V²   = 40470.872

V = √40470.872

V = 201.17 mph

2. calculating the bearing using cosine rule, we have;

sin∅/Vx = sin∝/V

sin∅/10 = sin158/201.17

sin∅ = 10*sin 158/201.17

        = 3.746/201.17

       = 0.0186

∅ = sin⁻¹ 0.0186

   = 1.07

Therefore,

Bearing = 360 - 1.07

              = 358.93⁰

The airspeed is 201.17 mph and bearing is [tex]358.93^\circ[/tex] and this can be determined by using the vector form of velocity.

Given :

Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 ​mph.

To determine the airspeed the following formula can be used.

[tex]\rm V^2 = V^2_x +V^2_y-2V_xV_y cos \theta[/tex]    ---- (1)

where, [tex]\theta = 338-180 = 158^\circ[/tex], [tex]\rm V_y[/tex] is the velocity of the plane and [tex]\rm V_x[/tex] is the velocity of the wind.

Now, put the value of [tex]\rm V_y[/tex], [tex]\rm V_x[/tex] and [tex]\theta[/tex] in the equation (1).

[tex]\rm V^2 = 10^2+200^2+2\times 10\times 200\times cos158[/tex]

[tex]\rm V^2= 100 + 40000+4000(-0.9271)[/tex]

V = 201.17 mph

Now, using cosine rule:

[tex]\rm \dfrac{sin \alpha}{V_x}=\dfrac{sin \theta }{V}[/tex]

[tex]\rm \dfrac{sin\alpha }{10}=\dfrac{sin158}{201.17}[/tex]

[tex]\rm sin\alpha =10\times \dfrac{sin158}{201.17}[/tex]

[tex]\rm sin \alpha = \dfrac{3.746}{201.17}[/tex]

[tex]\rm sin\alpha =0.0186[/tex]

[tex]\alpha = 1.07^\circ[/tex]

Therefore, the bearing is given by 360 - 13.07 = [tex]358.93^\circ[/tex]

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Answer: 17.28

Step-by-step explanation:

18*12 =216*.02=4.32

18*12=216*.10=21.6

21.6-4.32=17.28

In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.

The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.

First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.

Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.

So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.

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Answer:

You don't need "models and equations"; if the denominator is the

same, just subtract the numerators.

Step-by-step explanation:

Answer:

The standard deviation of the sampling distribution of x overbar, denoted sigma subscript x overbar, is called the Standard Error of the Mean.

Step-by-step explanation:

Standard deviation of the sampling distribution, or sigma Subscript x overbar, is also known as the standard error of the mean. It represents how much the sample means deviate from the population mean. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size.

The standard deviation of the sampling distribution, represented by the symbol sigma Subscript x overbar is also known as the standard error of the mean. This term refers to the standard deviation of the population of all possible sample means from samples of a specific size.

The basic formula to calculate the standard deviation is Σ(x – μ)2 / N for the population and Σ(x – x)² / (n-1) for the sample. Greek symbol µ represents the population mean while 'x' is the sample mean.

The standard error can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). Thus, lesser the standard error, closer are the sample means to the population mean and vice versa. This is a very important concept in statistics as it allows one to estimate an unknown population parameter using sample data.

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Answer:

A decimal number can be divided in a decimal part, a whole part and the decimal point which separates the first two.

So, all numbers that are placed leftside of the decimal point can be classified in units, tens, hundreds, thousands, and so on. Basically, each value depends on a base of 10. This means that thousands are ten times more than hundreds, hundreds are ten times more than tens, tens are ten times more than units.

If we want to a specific value of the whole part in a decimal number, we just need to look units, tens, hundreds, thousands or millions.

For example, if we have the number 1235.8456, the whole part would be 1235, and the value of the numbers that are leftside of the decimal point is 1235 units.

Answer:

The name of the numbers that go to the left of the decimal point is INTEGERS. This is the whole number part of the decimal number.

Step-by-step explanation:

The english translation is

What is the name of the numbers that go to the left of the decimal point?

A number with decimal numbers has 3 parts.

- The whole number part that are to the left of the decimal point. This whole number part is called the INTEGER part.

- The decimal point. The decimal point separates the whole numbers part of the number on the left and the mantissa part that has numbers to the right of the decimal point.

- The numbers to the right of the decimal point constitute a value less than 1. This part of a decimal is called the MANTISSA.

Hope this Helps!!!

Answer: 5/3

Step-by-step explanation:

This is a trigonometry ratio. Tangent of a right angle triangle

Tan0° = opposite

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

adjacent.

Now from the question

Tan0° = 3/4 meaning that the opposite side is 3 while the adjacent side is 4. Going by the triple coordinate, when two of the sides of a right angle triangle are, 3 and 4, the third side should be 5, in other words you could as well use the Pythagoras theorem to find the other side which I believed you should be familiar with. Since the third side is known, the cosec could be calculated.

Cosec of an angle =

1/sine. From the question now,

Sine0° = opposite side

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

Hypothesis

= 3/5

Therefore

Cosec0° = 1/3/5

= 1

---

3/5

= 5/3

Answer: n=3

Step-by-step explanation: 5n+3=18

18-3=15

15/5=3

Answer:

Step-by-step explanation:

5n +3 =18

5n = 18- 3

5n = 15

Dividing through with 5

n =15/5

n = 3

Answer:

[tex] 22\sqrt 2 [/tex] cm

Step-by-step explanation:

[tex] in \: a \: 45 \degree - 45 \degree - 45 \degree \: \triangle \\ leg = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \therefore \: 22 = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \purple{ \bold{ \therefore \: hypotenuse = 22 \sqrt{2} cm}}[/tex]

Answer:

Find the degree of the equation to determine if linear.

"Not Linear"

Step-by-step explanation:

Answer:

  not linear, degree 2

Step-by-step explanation:

The degree of this equation is the highest sum of the exponents of the variables in any given term.

Here, there is one variable term. The variables are x and y. They each have an exponent of 1, so the degree of the variable term is 1+1 = 2.

Since the degree of the equation is not 1, it is not a linear equation.

Answer:

The value of test statistic is -2.736.

The type of alternate hypothesis is Left- tailed.

Step-by-step explanation:

We are given that Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV.

We have to test the hypothesis to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80.

Let p = population proportion of people who purchased the detergent because they had seen it advertised on TV.

SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is greater than or equal to 0.80}

Alternate Hypothesis, [tex]H_a[/tex] : p < 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80}

The test statistics that will be used here is One-sample z-proportion test;

                      T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of people who bought detergent because they saw it advertised on TV in a sample of 400 customers = [tex]\frac{296}{400}[/tex] = 0.74

           n = sample of customers = 400

SO, test statistics = [tex]\frac{0.74-0.80}{\sqrt{\frac{0.74(1-0.74)}{400} } }[/tex]

                               = -2.736

Therefore, the value of the test statistic for the test described above is -2.736.

And the type of alternative hypothesis is left-tailed because we have to determine whether the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80.

Final answer:

To test if the population proportion is less than 0.80, a hypothesis test can be conducted using the sample data. The test statistic can be calculated using the formula (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). Using the given information, the test statistic is approximately -5.00.

Explanation:

To test whether there is sufficient evidence to conclude that the population proportion of consumers who purchased the detergent because of TV advertisements is less than 0.80, we can conduct a hypothesis test using the sample data.

Null Hypothesis:

The proportion of consumers who bought the detergent because of TV advertisements is 0.80 or higher.

Alternative Hypothesis:

The proportion of consumers who bought the detergent because of TV advertisements is less than 0.80.

We can calculate the test statistic, which is also known as the z-score, using the formula:

test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)

Using the given information, the sample proportion is 296/400 = 0.74. The hypothesized proportion is 0.80, and the sample size is 400.

Plugging these values into the formula, we get:

test statistic = (0.74 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 400)

Calculating this expression, we find that the test statistic is approximately -5.00.

Answer:

B. t<2 hours

Step-by-step explanation:

If Tim has to mow his lawn in under two hours.

It means:

Tim must finish mowing the lawn before two hours, therefore t<2 is the correct option.

To express that Tim must mow his lawn in under two hours, the correct inequality is t < 2. This indicates that the time, t, must be less than two hours to complete the task. Option B.

To express the condition that Tim has to mow his lawn in under two hours as an inequality, we represent the time it takes to mow the lawn with the variable t. The inequality that represents the situation is t < 2, meaning the time must be less than two hours. This is conveyed using the less than symbol (<).

In the context of other example inequalities, such as t=0, which represents a starting time, and t=t+1, which indicates an increment of time, these are used to express discrete points or changes in time. However, to represent a range of time under a specific amount, we use an inequality like t < 2 to denote that the time taken should not exceed two hours, option B.

Answer:

The number at tenth place is 6. Therefore, I guess there's 6 tens.

Step-by-step explanation:

There are 6 tens in the number 49,869.

To find the number of tens, we look at the digit in the tens place, which is the second digit from the right.

4 is in ten thousand place.

9 is in thousand place.

8 is in hundred place.

6 is in ten place.

As the digit in the tens place is 6.

The digit 6 represents six groups of ten in the number.

So, in the number 49,869, there are 6 tens.

Therefore, the correct answer is that there are 6 tens in the number 49,869.

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Answer:

45 degrees

Step-by-step explanation:

Answer:

(52,20)

Step-by-step explanation:

Answer: B

(52, 20)

Step-by-step explanation: