For each relation, decide whether or not it is a function.

Answer:

13.5

Step-by-step explanation:

Answer: 13.5

Step-by-step explanation:

just use the calculator

Answer:

5. [tex]P = 11.2 cm[/tex], [tex]A=7.8cm^2[/tex]

6.[tex]P = (4x -28) yds[/tex], [tex]A= (x-7)yds^2[/tex]

Step-by-step explanation:

5) Because the figure is a square then the diagonal splits the shape into two isosceles right triangles then the triangles are 45° 45° 90° triangles and the rule for such triangle is that the hypotenuse(in this case 4) is equal to a leg ·√2  so to find the leg we divide the hypotenuse by √2 so

4/√2 which is approximately 2.83 which when rounded to the nearest tenth is 2.8

so x = 2.8 cm

And because the figure is a square the perimeter is the length if a side times four so

P= 2.8(4)

P = 11.2 cm

A= 2.8(2.8)

A = 7.84cm^2 which when rounded to the nearest tenth is 7.8cm^2

6) This figure is also a square so the same rules apply for finding perimeter and area so

P = 4(x-7)

P = 4x - 28

P = (4x -28) yds

A = (x - 7)(x-7) which would just be A=(x-7)yds^2 or we could expand our answer

Use the FOIL method

x^2 -7x -7x + 49

Combine like terms

x^2 -14x +49

The probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.

Probability is the study of the chances of particular outcomes in a set of given circumstances. It is used to measure the likelihood of an event occurring, and it is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can also be expressed as percentages, fractions, or decimals. Probability is used in many fields, including mathematics, finance, engineering, and science.

P(B) = 0.20

P(-B) = 0.80

P(No Play | B) = 0.20

P(No Play | -B) = 0.95

a) P(No Play) = P(No Play | B)*P(B) + P(No Play | -B)*P(-B)

= 0.20*0.20 + 0.95*0.80 = 0.76

b) P(Store Bought | No Play) = P(No Play | B)*P(B) / P(No Play)

= 0.20*0.20 / 0.76 = 0.1053

From the tree diagram, the probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.

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Answer:

$5,149.44

Step-by-step explanation:

To calculate the compound amount and interest on a loan of ​$10800 compounded annually for four years at 10%, we can use the formula:

A = P(1 + r)^t

where A is the compound amount, P is the principal (the initial loan amount), r is the interest rate (as a decimal), and t is the number of years.

In this case, P = $10800, r = 0.10 (10% as a decimal), and t = 4. Substituting these values into the formula, we get:

A = $10800(1 + 0.10)^4

A = $10800(1.10)^4

A = $15,949.44

Therefore, the compound amount after four years is $15,949.44.

To calculate the interest, we can subtract the principal from the compound amount:

Interest = $15,949.44 - $10,800

Interest = $5,149.44

Therefore, the interest on the loan is $5,149.44.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10800\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 10800\left(1+\frac{0.10}{1}\right)^{1\cdot 4} \implies \boxed{A = 15812.28} ~\hfill \underset{ earned~interest }{\stackrel{ 15812~~ - ~~10800 }{\boxed{5012}}}[/tex]

Answer:

A and E

Step-by-step explanation:

A. -4 (2x - 1) = -8x + 4

B. 4 (2x - 1) = 8x - 4

C. 4x (2 - 1) = 8x - 4

D. 4x (2x + 1) = 8x² + 4x

E. 4 (-2x + 1) = -8x +4

F. 4 (2x + 1) = 8x + 4

The probability from the t distribution is 0.8999 and the value of c is 1.77

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

Degrees of freedom = 15

Using a graphing calculator, we have

P(t ≥ -1.34) = 1 - 0.1001

So, we have

P(t ≥ -1.34) = 0.8999

Calculating the value of c, we have

P(-c < t < c) = 0.95

At a degree of freedom of 13, we have

c = 1.77

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R'(-3, 2), S'(-5, -2), T'(-6, 0) is the correct answer for the given problem.

To reflect a point over the y-axis, we negate its x-coordinate.

Using this rule, the coordinates of the image of R, S, and T after reflecting the triangle over the y-axis are:

R'(-3, 2) (negate the x-coordinate of R)

S'(-5, -2) (negate the x-coordinate of S)

T'(-6, 0) (negate the x-coordinate of T)

Therefore, the correct answer is: R'(-3, 2), S'(-5, -2), T'(-6, 0).

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Answer:

$3267

Step-by-step explanation:

$121000 × $2970/$110000

= 11 × 297

= $3267

The taxes on the house with an assessment of $121000 are $3267

Answer:

  $3267

Step-by-step explanation:

You want to know the taxes on a house assessed at $121000 if the taxes on a house assessed at $110000 are $2970.

The taxes are proportional to the house value, so if the house value goes up by a factor of 121000/110000, so do the taxes. The taxes will be ...

  (121000/110000)·$2970 = $3267

The taxes on the house with an assessment of $121,000 are $3267.

__

Additional comment

You could go to the trouble to find the tax rate, which is ...

  rate = $2970/$110000 = 0.027

This can be described as 27 mils, 27‰, or $27 per thousand.

Multiplying this rate by the higher assessed value shows the taxes are ...

  0.027 × $121000 = $3267

We don't really need to know the tax rate. All we need to know is that the house with the 10% higher value will have 10% higher taxes.

In order to simulate the amount of bullseyes that Grace will strike during her upcoming turn, we can carry out the following steps:

Set up a loop which will execute the simulation for a predetermined number of rounds. Let's say that we wish to conduct 10,000 rounds as an example.

Within each cycle of the loop, mimic every round by generating 5 random numbers between 0 and 1 – signifying the likelihood of hitting a bullseye with each projectile.

For each round, accumulate the total number of bullseyes achieved by summing together the resultant quantity of times when the generated figure is less than or equivalent to 2/3.

Subsequent to the successful running of the simulation through the 10,000 rounds, calculate the average number of bullseyes struck in per round basis by dividing the complete amount of bullseyes hit with 10,000.

Finally, express the projected amount of bullseyes that Grace is anticipated to hit within her successive turn, by stating the average attained from step 4.

Consequently, with judicious repeating of multiple rounds, our calculation can factor in the differential element instinctive within this process and finally acquire a more precise tally of the estimated number of bullseyes Grace could potentially hit during her impending turn.

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Volume of pyramid = lwh/3
V = (7/3) x (15/2) x (24/5) / 3
V = (2520/30) / 3
V = 28cm^3

Answer:

Single payment Variable annuity

The value of θ for the given equation is θ = 54.74°.

The inverse cosine function (arccos) has a range of 0 to arccos(x), where x is a real number in the range of -1 to 1. An angle in radians between 0 and, which measures the angle between the x-axis and the terminal side of a unit circle that crosses the line between the origin and the point (x, y), is the result of the inverse cosine function. To put it another way, the inverse cosine function returns the angle whose cosine is equal to a specified value x.

The given equation is 4sec(θ) - 7 = 0:

Now, isolating the value of sec(θ) we have:

4sec(θ) = 7

sec(θ) = 7/4

Now, converting into cos we have:

cos(θ) = 4/7

θ = arccos(4/7)

θ = 54.74°

Hence, the value of theta for the given equation is θ = 54.74°.

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Answer:

trying not to get too much

Step-by-step explanation:

j and

The length of AB, x is 2.414 units.

Let's call the length of the square's side x. Then, the hypotenuse of each triangle is the diagonal of the square, which has length x√2.

Let's consider one of these triangles, say triangle APC. We can use the Pythagorean theorem to find the length of PC:

PC² = AP² + AC²

PC² = 1² + x²

PC = √(1+x²)

Since triangle APC is isosceles, we know that angle APC is 45 degrees. Therefore, angle CPB is also 45 degrees, since it is the supplement of angle APC. Similarly, angle BPC is 90 degrees, since it is the sum of angles CPB and BPA.

We can now use the sine rule in triangle BPC to find the length of BP:

sin(BPC) / BP = sin(CPB) / x√2

sin(90°) / BP = sin(45°) / x√2

BP = x / √2

Since AP = BP = CP = 1, we have:

1 + x / √2 + √(1+x²) = x

Solving this equation for x gives:

x ≈ 2.414

Therefore, the length of AB is approximately 2.414 units.

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The statement proposes  that for any subset X of a group G, there exists a unique smallest subgroup H of G that contains X.

We must take into consideration the collection of all subgroups of G that contain X in order to get the smallest subgroup of G that contains X.

Given that G is included in the collection, it is not empty.

The smallest subgroup of G that contains X is then obtained by taking the intersection of all the subgroups in the said  collection.

The subgroup contains X and is contained in every other subgroup of G that contains X because the intersection of subgroups may not be immediately apparent or simple to compute.

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The p value is: 13.1578

P-value is calculated as P (Z> Test statistics) in a right-tailed test. P-value is generally compared with 5% but it is a misconception that if p is less than 0.05, then there is sufficient evidence to reject the null hypothesis whereas it is always considered with the significance level.

We have the information:

[tex]H_0:p=0.4\\\\H_1:p > 0.4[/tex]

n = 100

[tex]\alpha =0.05[/tex]

x = 45

The sample proportion is given as:

[tex]p_0=\frac{x}{n}\\ \\p_0=\frac{45}{100}\\ \\p_0=0.45[/tex]

[tex]np_0(1-p_0)= 100(0.45)(0.55)[/tex]

                  = 24.75 > 10

The test statistics value is calculated as:

[tex]z=\frac{p_0-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

 = [tex]\frac{0.45-0.4}{\sqrt{\frac{0.4(1-0.4)}{100} } }[/tex]

 = 0.05/0.0038

 = 13.1578

The p value is: 13.1578

Now, Put z value in bracket and p value will be found.

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The probability that two red and two blue balls were transferred from the first urn to the second urn is 0.27 (approx).

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is a mathematical concept that ranges from 0 (indicating an impossible event) to 1 (indicating a certain event).

Let R1 be the event that the first ball drawn from the first urn is red, and let B1 be the event that the first ball drawn from the first urn is blue. Similarly, let R2 and B2 be the events that the second and third balls drawn from the first urn are red and blue, respectively. Finally, let B be the event that a blue ball is drawn from the second urn.

We want to find P(R2=2, B2=2 | B), the probability that two red and two blue balls were transferred from the first urn to the second urn, given that a blue ball was drawn from the second urn.

By Bayes' theorem, we have:

P(R2=2, B2=2 | B) = P(B | R2=2, B2=2) * P(R2=2, B2=2) / P(B)

To find each of these probabilities, we can use the following:

P(R2=2, B2=2) = (5 choose 2) * (3 choose 2) / (8 choose 4) = 15/56, which is the probability of selecting 2 red and 2 blue balls from the first urn.

P(B | R2=2, B2=2) = 2/4 = 1/2, which is the probability of drawing a blue ball from the second urn, given that 2 red and 2 blue balls were transferred from the first urn.

P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2), which is the total probability of drawing a blue ball from the second urn.

To find P(R2=0, B2=4), we need to use the complement rule:

P(R2=0, B2=4) = 1 - P(R2=1, B2=3) - P(R2=2, B2=2)

To find P(R2=1, B2=3), we can use:

P(R2=1, B2=3) = (5 choose 1) * (3 choose 3) / (8 choose 4) = 5/56

Substituting all these values into Bayes' theorem, we get:

P(R2=2, B2=2 | B) = (1/2) * (15/56) / P(B)

To find P(B), we can use the law of total probability:

P(B) = P(B | R2=0, B2=4) * P(R2=0, B2=4) + P(B | R2=1, B2=3) * P(R2=1, B2=3) + P(B | R2=2, B2=2) * P(R2=2, B2=2)

Substituting the values we found earlier, we get:

P(B) = (0/4) * (1 - 5/56 - 15/56) + (1/4) * 5/56 + (2/4) * 1/2 = 0.27 (approx)

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Check the picture below.

If y = 3, we can see that there are again two values of x that satisfy the equation: x = 0 and x = 4. This is because the graph intersects the horizontal line at y = 3 at two points.

A mathematical statement used to describe the relationship between the variables that make up a graph is called an equation.

To put it another way, a graph equation is a formula that can be applied to either build the graph or identify certain points on the graph.

Using the graph of the equation y = -|x - 2| + 2, we can find all the values of x for a given value of y by looking at where the graph intersects the horizontal line at y.

For example, if y = 1, we can see from the graph that there are two values of x that satisfy the equation: x = 3 and x = 1. This is because the graph intersects the horizontal line at y = 1 at two points.

If y = 2, we can see that there is only one value of x that satisfies the equation: x = 2. This is because the vertex of the absolute value function is at (2, 2), and the graph is reflected below the x-axis, so it only intersects the horizontal line at y = 2 at one point.

We can repeat this process for any value of y to find the corresponding values of x that satisfy the equation.

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Answer:

Step-by-step explanation:

h = how old the house is right now

so right now Mark and Lynne are paying the house off, the house as we speak is "h" years old, it happens that Mark and Lynne are going to be paying the whole house in 18 years from now, so by then the house will be whatever years is now, or "h", plus 18 years, so when Mark and Lynne are done paying for it, the house will be "h + 18" years old.

Now, if the house in 18 years is going to be 4 times as old as it's right now, well, hell right now is "h" years old, 4 times that much is just "4h" years, so we can say

[tex]\stackrel{\textit{18 years from now}}{h+18}~~ = ~~\stackrel{\textit{18 years from now}}{4h}\implies 18=3h\implies \cfrac{18}{3}=h\implies 6=h[/tex]

Answer:

the vertex form of the given quadratic expression is:

y = 3(x + 8/3)^2 - 4/3

Step-by-step explanation:

To write the given quadratic expression 3x^2+16x+20 in vertex form, we need to complete the square.

Step 1: Factor out the coefficient of x^2:

3(x^2 + (16/3)x) + 20

Step 2: Take half of the coefficient of x and square it:

(16/3)/2 = 8/3

(8/3)^2 = 64/9

Step 3: Add and subtract the result from step 2 inside the parentheses:

3(x^2 + (16/3)x + 64/9 - 64/9) + 20

Step 4: Simplify inside the parentheses and factor:

3[(x + 8/3)^2 - 64/9] + 20

Step 5: Simplify the constant term:

3(x + 8/3)^2 - 4/3

Therefore, the vertex form of the given quadratic expression is:

y = 3(x + 8/3)^2 - 4/3

Answer:

The answer should be P'(-3,-7), Q(-9,3), and R'(-4,1) which is D.

Step-by-step explanation:

The percentile for the data value 121 in the given data set is 75th percentile.

To find the percentile for the data value 121 in the given data set, we need to follow these steps:

Step 1, Sort the data set in ascending order.

111 111 112 113 113 115 115 115 117 118 119 119 121 123 127 129

Step 2, Calculate the rank of the data value 121 in the sorted data set.

The rank of 121 is the position of 121 in the sorted data set. Counting from left to right, we see that 121 is the 12th value in the sorted data set.

Step 3, Calculate the percentile rank.

Percentile rank = (Rank of the data value / Total number of data values) x 100

In this case, the total number of data values is 16. Therefore,

Percentile rank = (12/16) x 100 = 75

This means that 75% of the data values in the set are less than or equal to 121.

Correct Question :

Find the percentile for the data values. Data set:115 127 119 113 121 123 113 111 118 115 119 129 111 115 117 112; data value:121

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Answer:

Please mark me the brainliest. It took me a lot of time to answer this question.

Step-by-step explanation:

To solve this problem, we can use trigonometry. We know that the length of the train track through the mountain is 1600 feet and that the angle it makes with the horizontal is 1.1. Let's call the change in elevation from one end of the tunnel to the other "h".

We can use the tangent function to find "h", which is defined as the opposite side (the change in elevation) divided by the adjacent side (the length of the train track through the mountain). In this case, the tangent of the angle 1.1 is equal to h divided by 1600:

tan(1.1) = h/1600

To solve for "h", we can multiply both sides by 1600:

h = 1600 * tan(1.1)

Using a calculator, we can find that tan(1.1) is approximately 0.0192. Therefore:

h = 1600 * 0.0192

h = 30.72 feet

So the change in elevation from one end of the tunnel to the other is approximately 30.72 feet.

The solutions of the inequalities are s≤2 and s>7 respectively

The given inequalities are 2s +3≤7 OR 3s +5> 26

We have to find the solutions

2s +3≤7

Subtract 3 from both sides

2s≤4

Divide both sides by 2

s≤2

Now inequality 3s +5> 26

Subtract 5 from both sides

3s>21

s>7

Hence, the solutions of the inequalities are s≤2 and s>7 respectively.

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The average of all your quiz scores which is also called the mean would be 90.

Since we know that average or mean can be calculated by dividing the sum of observations by the number of observations.

Average = Sum of observations/the number of observations

We are given that the following scores in your math quizzes (80,85,90,95,100).

Therefore,

Average = Sum of observations/the number of observations

Average = 80 + 85 + 90 + 95 + 100 / 5

Average = 450/5

Average = 90

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Decreasing confidence level or increasing sample size decreases width of confidence interval. Undercoverage cannot be adjusted after sampling.

Define sampling ?

Sampling is the process of selecting a subset of individuals or units from a larger population to estimate characteristics of the population.

(a) If the confidence level were decreased from 95% to 90%, the width of the interval would decrease. This is because a lower confidence level requires a smaller margin of error, which is the product of the critical value and the standard error of the proportion.

(b) If the sample size were increased from 50 to 200 students, the width of the interval would decrease. This is because as the sample size increases, the standard error of the proportion decreases, resulting in a smaller margin of error and a narrower confidence interval.

(c) The physician cannot adjust the confidence interval to take undercoverage into account after the sample has been collected. Undercoverage is a type of sampling bias that occurs when some members of the population are less likely to be included in the sample than others. Adjusting the confidence interval would require information about the characteristics of the missing 30% of freshmen, which is unknown. The best way to address undercoverage is to try to improve the sampling method in future studies, such as by using stratified sampling to ensure that all subgroups of the population are represented in the sample.

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Answer:

14336

Step-by-step explanation:

the general term is:

s(n) = 7*(2)^(n-1)

you can check it by plugging in some number:

s(3) = 7*2^(3-1) = 7*4 = 28

s(4) = 7*2^(4-1) = 7*8 = 56

The 12th term is:

s(12) = 7*2^(12-1) = 7*2^11 = 7*2048 = 14336

Answer: 185

Step-by-step explanation:

231-46=185

Answer: 185

Step-by-step explanation:

231-46