What is -110=-5(1+7v)

Answer:

Step-by-step explanation:

10x = 90

x = 9

RP = 9 - 4 = 5

\(P_{AEPR}\) = 20

Answer:

Explanation:

No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) \(n_{1}\)=628, \(p_{1}\)=7%, sample 2( 30 years old)\(n_{2}\)=2309, \(p_{2}\)=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

\(H_{0}:\)π1-π2=0

\(H_{1}:\)π1-π2≠0

α=0.05

Difference between proportions \(p_{1}-p_{2} =-0.04\)

\(p_{d}=0.07-0.11=-0.04\)

The pooled proportion needed to calculate standard error is:

\(p=(X_{1} -X_{2} )/(n_{1} +n_{2} )\)

=(44+254)/(628+2309)

=0.10146

The estimated standard error of difference between means is computed using the formula:

\(S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }\)

=\(\sqrt{0.101*0.899/628+0.101*0.899/2309}\)

=\(\sqrt{0.000143+0.00003}\)

=\(\sqrt{0.000173}\)

=0.01315

Z= Pd-(π1-π2)/\(S_{p_{1} -p_{2} }\)

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

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Question is incomplete as it also includes:

Significance level of 5%.

The slope means that the rate of change of height of the unmanned aerial vehicle after it begins its descent from cruising altitude is -0.2 ft/minutes.

The y-intercept means that the height before the descent was; 62 ft

The slope is the change in y-values divided by the corresponding change in x -values. Meanwhile, the y-intercept is the point at which x = 0 or where there graph crosses the y-axis.

In this case, the formula for the slope is;

Slope = (y2 - y1)/(x2 - x1)

Slope = (60 - 62)/(10 - 0)

Slope = -2/10

Slope = -0.2

From the table, the y-intercept is at y = 62

Thus, the slope means that the rate of change of height of the unmanned aerial vehicle after it begins its descent from cruising altitude is -0.2 ft/minutes

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The probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

To solve this problem, we need to use the Poisson process and the exponential distribution.

Let X be the number of arrivals in a 3-minute interval. Since customers arrive at a rate of 25 per hour, the expected number of arrivals in a 3-minute interval is:

λ = (25/60) x 3 = 1.25

Thus, X is Poisson distributed with parameter λ = 1.25.

Let Y be the service time for a customer. Since Linda serves a customer, on average, in 1.5 minutes, Y is exponentially distributed with parameter μ = 1/1.5 = 0.6667.

Let Z be the waiting time for a customer in the line. Z is the sum of X independent service times, so Z is gamma distributed with parameters X and μ.

We want to find the probability that Z is between 3 and 6 minutes:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

where f(x,y) is the joint probability density function of X and Y:

f(x,y) = (λ^x / x!) e^(-λ) μ e^(-μy) = (1.25^x / x!) e^(-1.9167) e^(-0.6667y)

Now we can evaluate the double integral:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

= ∫∫ (1.25^x / x!) e^(-1.9167) e^(-0.6667y) dx dy

= ∫ e^(-0.6667y) e^(-1.9167) ∑ (1.25^x / x!) dx dy (x=0 to ∞)

= e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

The sum in the integral is the Taylor series expansion of e^1.25, which is equal to e^1.25 = 3.4903.

Using a table of integrals or a computer software, we can evaluate the integral:

∫ e^(-0.6667y) e^(1.25) dy = (1/0.6667) (e^(1.25) - e^(-0.6667(6))) = 3.7225

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is:

P(3 ≤ Z ≤ 6) = e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

= e^(-1.9167) (3.7225) (3.4903) = 0.1658 or about 16.58% (rounded to four decimal places).

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

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Answer:

Ryan went down a total of 8 times

Step-by-step explanation:

He goes down 6 times 48/6 = 8

Answer:

If Maria uses 2 parts cream and 3 parts milk, then for every 2 parts of cream, she uses 3 parts of milk.

Since she uses 8 liters of cream, we can find the total volume of mixture by finding the equivalent volume of milk that she used.

To find the equivalent volume of milk, we multiply the volume of cream by the ratio of milk to cream:

8 liters * (3 parts milk) / (2 parts cream) = 12 liters

So Maria used 8 liters of cream and 12 liters of milk for a total volume of 20 liters.

The vectors u = \(\left(\begin{array}{ccc}Cost\\Sint\end{array}\right)\)     ,   v = \(\left(\begin{array}{ccc}Sint\\Cost\end{array}\right)\), are linearly independent, because the determinant is not 0.

The Vector "u" is =  \(\left(\begin{array}{ccc}Cost\\Sint\end{array}\right)\) , and the vector "v" is =  \(\left(\begin{array}{ccc}Sint\\Cost\end{array}\right)\).

If the value of matrix formed by two or more given vectors is zero(0) or

If determinant of matrix of given vectors is (0) zero, then the vectors can be called as linearly-dependent.

The matrix related to two vector "u" and vector "v" is given as :

⇒ \(\left[\begin{array}{ccc}Cost&Sint\\Sint&Cost\\\end{array}\right]\)

The value of this matrix can be calculated by finding the determinant of the matrix,

Which is : Cost×Cost - Sint×Sint

= Cos²t - Sin²t

= Cos(2t) ≠ 0,

Since the value is not zero, we can say that the vectors are linearly independent.

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The given question is incomplete, the complete question is

Determine whether or not the vector functions are linearly dependent.

u = \(\left(\begin{array}{ccc}Cost\\Sint\end{array}\right)\)     ,   v = \(\left(\begin{array}{ccc}Sint\\Cost\end{array}\right)\).

We determined the points of intersection, identified which function is on top in different intervals, and integrated the absolute difference between the functions over the interval [-3, 5].

To find the area of the region enclosed by the graphs of f(x) = x^2 - x - 5 and f(x) = x + 10, we need to determine the points of intersection between the two functions and integrate the absolute difference between them.

First, let's find the points of intersection by setting the two equations equal to each other:

x^2 - x - 5 = x + 10

Rearranging the equation, we get:

x^2 - 2x - 15 = 0

Factoring the quadratic equation, we have:

(x - 5)(x + 3) = 0

So the two points of intersection are x = 5 and x = -3.

Next, we need to determine which function is on top in the region

between these two intersection points.

For x < -3, the function f(x) = x + 10 is on top.

For -3 < x < 5, the function f(x) = x^2 - x - 5 is on top.

For x > 5, the function f(x) = x + 10 is on top.

To find the area, we integrate the absolute difference between the two functions over the interval [-3, 5].

∫[from -3 to 5] |(x^2 - x - 5) - (x + 10)| dx

Simplifying, we have:

∫[from -3 to 5] |x^2 - 2x - 15| dx

Now, we split the integral into two parts based on the intervals where the absolute value changes its sign.

∫[from -3 to 5] (x^2 - 2x - 15) dx + ∫[from -3 to 5] -(x^2 - 2x - 15) dx

Integrating each part separately, we obtain:

[(1/3)x^3 - x^2 - 15x] from -3 to 5 - [(1/3)x^3 - x^2 - 15x] from -3 to 5

Simplifying further, we get:

[(1/3)(5)^3 - (5)^2 - 15(5)] - [(1/3)(-3)^3 - (-3)^2 - 15(-3)]

Calculating the values, we find:

[125/3 - 25 - 75] - [-27/3 - 9 + 45/3]

The final result is the absolute value of the difference of these two values.

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Answer: He is correct

Step-by-step explanation:

25% is equal 25/100 which simplified to 1/4

The solution of the given problem of triangle comes out to be tan ∠A = 0.25.

Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners.

Here,

Since △ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.

Using the fact that tan ∠B = opposite/adjacent, we can set up a ratio using a common factor, x, for the opposite and adjacent sides of ∠B:

tan ∠B = 0.25 = opposite/adjacent = x/4x

Simplifying the right side, we get:

0.25 = x/4x = 1/4

Multiplying both sides by 4x, we get:

x = 4

So the opposite side of ∠B has length x = 4, and the adjacent side has length 4x = 16.

Using the Pythagorean theorem, we can find the length of the hypotenuse of △ABC:

c² = a² + b²

c² = 4²+ 16²

c² = 256

c = √256

c = 16

Now, we can use the fact that tan ∠A = opposite/adjacent to find tan ∠A:

tan ∠A = opposite/hypotenuse = 4/16 = 1/4

Therefore, tan ∠A = 0.25.

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Answer:

y= 3x + 1

Step-by-step explanation:solve for y

subtract 3x from the left  which leaves -y= -3x -1

then you have to take flip the signs or divide by -1  so it comes out to y=3x + 1

Answer:

y = 3x + 1

Step-by-step explanation:

Slope Intercept form is written out as the following:

y = mx + b

In order to convert "3x - y = -1", we first subtract 3x from both sides, giving us:

-y = -3x - 1

Since we have "-y", we multiply -1 on both sides.

-1(-y) = -1(-3x - 1)

Multiplying two negatives makes a positive, hence when we multiply -1 on both sides, it becomes this:

y = 3x + 1

So converting to the Slope Intercept form ends up being "y = 3x + 1"

a. P(-t0.025 ≤ T ≤ t0.025) = 0.95. b. the specific numerical values for t0.025 may vary based on the degrees of freedom (df) and the desired level of confidence.

(a) To find the value of t0.025 such that P(-t0.025 ≤ T ≤ t0.025) = 0.95, we need to look up the critical value in the t-distribution table or use statistical software.

Since we are looking for a two-tailed confidence interval with a total probability of 0.95, we divide the remaining probability (1 - 0.95 = 0.05) into two equal tails. Each tail will have a probability of 0.05/2 = 0.025

By consulting the t-distribution table or using software, we can find the critical value associated with the upper tail probability of 0.025 and degrees of freedom (df) equal to n - 1 = 9 - 1 = 8. Let's denote this critical value as t0.025.

Therefore, we find t0.025 such that P(-t0.025 ≤ T ≤ t0.025) = 0.95.

(b) To solve the inequality [-t0.025 ≤ T < t0.025] so that u is in the middle, we need to find the range of values for T that satisfies this condition.

Given the confidence interval is symmetric around the mean, we want to find the range that contains the central 95% of the t-distribution. We already found the critical values -t0.025 and t0.025 in part (a).

The solution to the inequality is -t0.025 ≤ T < t0.025. This range ensures that the population mean (u) will be within the central portion of the distribution, as the tails outside this range contain a cumulative probability of only 5% (0.025 on each side).

By selecting values of T within this range, we can be confident that the corresponding population mean will fall within the middle portion of the distribution.

It's important to note that the specific numerical values for t0.025 may vary based on the degrees of freedom (df) and the desired level of confidence.

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The inequality that represents the number d of dragonfly’s you must catch to earn a new high score, d> 1200.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

To set a new record, you must score at least

= 36,480 – 34,280

= 2,200 points.

When you have earned 35,000-34,280 points, you need 720 more to qualify for the bonus.

Total = 36,000 points after obtaining 720 dragonflies.

Bonus points = 1000 points.

As, we need more than 480 additional dragonflies to surpass your previous best.

So, The total of all the dragonflies shows that more than 1200 are required.

Then, the inequality is d> 1200.

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Step-by-step explanation:

It is worked out step by step.

Answer:

\(x=6, y=-2\)

Step-by-step explanation:

\(-2=3x-20 \\ \\ 3x=18 \\ \\ x=6 \\ \\ \therefore x=6, y=-2\)

Answer:

The answer is x = 6. If you want to solve the equation by inputting the x and y value, then take the x value and input it into the equation as well as the y value.

Step-by-step explanation:

To solve this equation, plug in the value equal to y and solve for x. The first thing you have to do is make the equation -2 = 4x - 20, since we already have the value for y which is given in the question. Then add 20 to both sides of the equation. We now have 18 = 3x, divide both sides by 3 and you have your answer.

Hence, X = 6.

Answer:

5p

Step-by-step explanation:

if p=7, 5p=35

Answer:

5p

Step-by-step explanation:

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

a) To find the probability that the television set lasts between 4 and 6 years, we need to calculate the integral of the density function f(x) over the interval [4, 6]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, we have:

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

b) To find the probability that the television set lasts at least 5 years, we need to calculate the integral of the density function f(x) over the interval [5, ∞). However, since the density function is zero for x ≥ 3, the integral over this interval is zero.

c) To find the probability that the television set lasts less than 2 years, we need to calculate the integral of the density function f(x) over the interval [0, 2]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, the integral becomes:

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

d) To find the probability that the television set lasts exactly 4.18 years, we need to evaluate the density function f(x) at x = 4.18. Plugging in the value of x into the density function, we get f(4.18) = 18(4.18) - 3.

e) To find the expected value of the number of years that the television set lasts, we need to calculate the integral of xf(x) over the entire range of x, which is [0, ∞). The expected value is given by:

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

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Answer:

domain = -11,-8,0,13 or the first coordinate

range    = 11,8,0,-13 or the second coordinate

Step-by-step explanation:

The difference between a formal and informal proof in arithmetics is that a formal proof uses equations, whereas an informal proof only uses text. That is option D.

A formal proof is defined as the concept used in arithmetics to show that the final answer to an expression obeys a particular rule of an equation or formula.

An informal proof is defined as the concept that shows the answer to a mathematical expression without the use of formula or derived equation.

Therefore, the difference between the formal and informal proof is that a formal proof uses equations, whereas an informal proof only uses text.

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Answer: perm will cost $48

Step-by-step explanation:

Let x be cost of haircut

So perm will cost her 2x

So

x + 2x + 5 = 77

3x = 72

x = 24

Perm will cost 2x24 = 48

Given an AR(1) process with drift X = α + βX_{t-1} + ε_t, where α = 2, β = 0.7, and ε_t ~ N(0, 1).To find the mean of the process, we note that the AR(1) process has a mean of μ = α / (1 - β).

So, the mean is 6.67, the variance is 5.41, the first three ACF are 0.68, 0.326, and 0.161, and the first three PACF are 0.7, -0.131, and 0.003.

So, substituting α = 2 and β = 0.7,

we have:μ = α / (1 - β)

= 2 / (1 - 0.7)

= 6.67

To find the variance, we note that the AR(1) process has a variance of σ^2 = (1 / (1 - β^2)).

So, substituting β = 0.7,

we have:σ^2 = (1 / (1 - β^2))

= (1 / (1 - 0.7^2))

= 5.41

To find the first three autocorrelation functions (ACF) and the first 3 partial autocorrelation functions (PACF), we can use the formulas:ρ(k) = β^kρ(1)and

ϕ(k) = β^k for k ≥ 1 and

ρ(0) = 1andϕ(0) = 1

To find the first three ACF, we can substitute k = 1, k = 2, and k = 3 into the formula:

ρ(k) = β^kρ(1) and use the fact that

ρ(1) = β / (1 - β^2).

So, we have:ρ(1) = β / (1 - β^2)

= 0.68ρ(2) = β^2ρ(1)

= (0.7)^2(0.68) = 0.326ρ(3)

= β^3ρ(1) = (0.7)^3(0.68)

= 0.161

To find the first three PACF, we can use the Durbin-Levinson algorithm: ϕ(1) = β = 0.7

ϕ(2) = (ρ(2) - ϕ(1)ρ(1)) / (1 - ϕ(1)^2)

= (0.326 - 0.7(0.68)) / (1 - 0.7^2) = -0.131

ϕ(3) = (ρ(3) - ϕ(1)ρ(2) - ϕ(2)ρ(1)) / (1 - ϕ(1)^2 - ϕ(2)^2)

= (0.161 - 0.7(0.326) - (-0.131)(0.68)) / (1 - 0.7^2 - (-0.131)^2) = 0.003

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The volume of the canister is 339.1 cubic inches.

The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.

Using the formula, we can calculate the volume of the canister as follows:

V = π×3²×12

V = 108×3.14

V = 339.1 cubic inches

Therefore, the volume of the canister is 339.1 cubic inches.

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Answer:

7. Option D

9. Option B

10. Option C

Step-by-step explanation:

Answer:

7. Option D

9. Option B

10. Option C

Mark as Brainliest!!!

To calculate Mr. Jones' pay for the week, we need to consider his regular pay for 40 hours and his overtime pay for the additional 5 hours he worked.

His regular pay for the week would be:

$26.50/hour x 40 hours = $1,060

To calculate his overtime pay, we need to first determine his overtime rate. His overtime rate is time-and-a-half, which means he earns one and a half times his regular pay rate for each hour of overtime. So, his overtime rate is:

1.5 x $26.50/hour = $39.75/hour

Now we can calculate his overtime pay for the week:

$39.75/hour x 5 hours = $198.75

To find his total pay for the week, we just need to add his regular pay and overtime pay:

$1,060 + $198.75 = $1,258.75

Therefore, Mr. Jones' total pay for the week in which he works 45 hours is $1,258.75.

Answer:

Yes

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction. In this case, the fraction is being expressed by a decimal. So therefore 7.29 is a rational number.

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Answer:

x = 4

Step-by-step explanation:

x + 7 = 11

=> x = 11 - 7

=> x = 4

Answer:

x = 4

Step-by-step explanation:

x + 7 = 11 ..... subtract by 7 on both sides

x + 7 - 7 = 11 - 7

x = 4

OR,

x + 7 = 11 .........bring the 7 on the other side changing its sign + to -

x = 11 - 7

x = 4

The margin of error in the report is 2.35 minutes.

The margin of error is a measure of the amount of uncertainty or error associated with a survey or study's results. It represents the range within which the true value of a population parameter is likely to lie, given the sample size and sampling method used. In this case, the report provides a range for the average amount of time a 10-year-old American child spends playing outdoors per day. The margin of error can be calculated as half the width of the confidence interval, which is (24.78 - 20.08)/2 = 2.35 minutes. This means that if the study were repeated many times, 95% of the time the true average time spent playing outdoors per day for 10-year-old American children would be within 2.35 minutes of the reported range.

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