y=4x-1
if the value of y is 1 what is x

The solutions are;

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

Given;

Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.

(a) 80% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.

The critical value with a level of significance is 1.28.

α = 1 - 0.80 = 0.20

α/2 = 0.10

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

(b) 98% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.

The critical value with a level of significance is 2.33.

α = 1 - 0.98 = 0.02

α/2 = 0.01

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747

(C) 90% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.

The critical value with a level of significance is 1.64.

α = 1 - 0.90 = 0.10

α/2 = 0.05

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

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Answer:

9x+3

Step-by-step explanation:

first you add common variables like 7x plus 2x and get 9x. since 3 does't have a common variable it is just 3 therefor you answer would be 9x+3

Starting : 7x+2x+3

combine like terms 7x+2x=9x

youre left with 9x+3                     

Ralph will store 3/20 gallons of paint in each container.

Explain gallons

Gallons are a unit of measurement commonly used for liquids, especially in the United States. One gallon is equal to 128 fluid ounces or approximately 3.785 liters. It is used to measure the volume of liquids such as gasoline, milk, and water, and is often used in cooking, construction, and manufacturing industries.

According to the given information

To divide 3/4 gallons of paint equally among 5 containers, we need to perform the division (3/4)/5:

(3/4)/5 = 3/4 × 1/5 = 3/20

Therefore, Ralph will store 3/20 gallons of paint in each container.

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Answer:

Step-by-step explanation

To find the answer you would have to divide 3/4 gallons of paint equally among 5 containers, we need to perform the division (3/4)/5:

(3/4)/5 = 3/4 × 1/5 = 3/20

Ralph will store 3/20 gallons of paint in each container.

Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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We use the quadratic formula to find the roots of the quadratic equation.

The quadratic equation is given below:

f(x) = a\(x^{2}\) + bx + c = 0 where a, b, c

The system of equations used to find roots of equation is y = 12\(x^{3}\)-5x and y=2\(x^{2}\)+x+6.The given equation will be,12\(x^{3}\)-5x=2\(x^{2}\) + x + 6.

Now we take the root of equation into two parts:

1. Left-hand side

2. Right-hand side

Equation no.1 : 12\(x^{3}\)-5x=0

Equation no.2: 2\(x^{2}\)+x+6=0

Now we contains system of equation 0 with y.

So, the equation will be:

12\(x^{3}\)-5x=y

2\(x^{2}\)+x+6=y

However,system of equations can be used to find the roots of the equation 12\(x^{3}\)-5x=2\(x^{2}\)+x+6 is:
y = 12\(x^{3}\)-5x and y = 2\(x^{2}\)+x+6

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The length of the midsegment of the trapezoid is 8 units

Trapezoid

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides of the trapezoid and is parallel to the pair of parallel sides.

In this problem

The two non-parallel sides of the trapezoid are AD and BC

Step 1

Find the midpoint side of AD

Let

E the midpoint AD

A ( 2,4 ) D (-2,-1)

Find the x-coordinate of the midpoint AD

\(x = \frac{2-2}{2} = 0\)

Find the y-coordinate of the midpoint AD

\(y = \frac{4 - 1}{2} = 1.5\)

the point E is equal to (0, 1.5 )

Step 2

Find the midpoint side of BC

Let

F the midpoint BC

\(B ( 7,4) C ( 9, -1)\)

Find the x-coordinate of the midpoint BC

\(x = \frac{9+2}{7} = 8\)

Find the y-coordinate of the midpoint BC

\(y = \frac{4 - 1}{2} = 1.5\)

The point F is equal to ( 8 , 1.5 )

Step 3

Find the distance EF

Know that

The formula to calculate the distance between two points is equal to

\(d = \sqrt{(y2 - y1)^{2}+ (x2 -x1)^{2} }\)

we have

E ( 0 ,1.5) F ( 8, 1.5)

substitute the values

\(d = \sqrt{(1.5 - 1.5)^{2} + (8-0 )^{2} }\)

d = 8 units

Therefore

The length of the midsegment of the trapezoid is 8 units

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Answer:

-0.5774

Step-by-step explanation:

Tan 150 degrees is the value of tangent trigonometric function for an angle equal to 150 degrees. The value of tan 150° is -1/√3 or -0.5774 (approx).

According to the given statement This integral will give you the volume of the solid..

To find the volume of the solid obtained by rotating the region bounded by the curves 2x = y² and x = 0, we can use the method of cylindrical shells.

First, let's graph the given curves to visualize the region. The curve 2x = y² is a parabola opening to the right, and the line x = 0 is the y-axis.
Next, we need to find the limits of integration. From the given information, we know that x ranges from 0 to some value. To find this value, we set the equations equal to each other and solve for x:

2x = y²
x = y²/2

Since x cannot be negative, we take the positive square root of both sides:
√x = y/√2
√2x = y

So, the limits of integration for y are √2x and 0, and the limits of integration for x are from 0 to some value.

To set up the integral for the volume, we use the formula:

V = ∫[a, b] 2πrh dx

where r is the distance from the axis of rotation to the curve (in this case, the x-axis), and h is the height of the cylindrical shell.

In this case, the radius r is x, and the height h is given by the difference between the y-values of the curves at a particular x-value:

h = √2x - 0

Plugging these values into the integral, we get:

V = ∫[0, b] 2πx(√2x - 0) dx

Simplifying this integral will give you the volume of the solid.

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To find the volume of the solid obtained by rotating the region bounded by the given curves \(\(2x = y^2\) and \(x = 0\)\), we can use the method of cylindrical shells. The volume can be calculated using the integral:

\(\[v = \int_{0}^{2} 2\pi x\sqrt{2x} \, dx\]\)

The given curves are \(\(2x = y^2\) and \(x = 0\).\) We want to rotate the region bounded by these curves about the y-axis to form a solid.

To use the method of cylindrical shells, we divide the region into thin cylindrical shells. The radius of each shell is the x-coordinate, which is x, and the height is the difference between the y-values on the curve, which is \(\(\sqrt{2x}\)\).

Now, we set up the integral. The integral represents the sum of the volumes of all the cylindrical shells. The integral is evaluated over the range from x = 0 to x = 2, as determined by the bounds of the region.

Evaluating the integral gives us the volume of the solid:

\(\[v = 2\pi\int_{0}^{2} x^{3/2} \, dx\]\)

Integrating this expression yields:

\(\[v = 2\pi\left[\frac{2}{5}x^{5/2}\right]_{0}^{2}\]\)

Evaluating the limits of integration, we get:

\(\[v = 2\pi\left[\frac{2}{5}(2)^{5/2} - \frac{2}{5}(0)^{5/2}\right]\]\)

Simplifying this expression gives us the volume v of the solid.

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Answer:

100,000

Step-by-step explanation:

100,000 is in the middle of 130,000 and 600,000 cuz it's not even is gonna be a mix fraction

The expected number of radiation induced cancers according to the linear no threshold model of cancer induction is 500

Radiation is defined as the energy that comes from a source and travels through space at the speed of light.

Here we have given that 1,000,000 people are exposed to 10 msv and here we need to find the  the expected number of radiation induced cancers according to the linear no threshold model of cancer induction.

As we all know that the amount of dose depends on the type of x-ray examination. A CT examination with an effective dose of 10 milli Sieverts

And it may be associated with an increase in the possibility of fatal cancer of approximately 1 chance in 2000.

therefore, here we have the total number as 1,000,000

Then the expected number if calculated as,

=> 1,000,000/2000

=> 500

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24kx = 6

kx = 6/24

kx = 1/4

x = 1/4/k

x = 1/4k

A) X = 1/4k or the first option.

Addie taken advantage of coupons.

What is advantage of coupons ?

Coupons can help introduce new product lines and encourage customers to try a more profitable brand or service. Coupons can also help attract existing customers to come back to your store. The biggest con of using coupons is that they cost businesses money and may lead to lower profit for that sale.

In this he went to the mall to buy grocery item and he found lot of things from his week coupons and bought by coupons.

And he got many benefits from the coupons which he will never forget, this is a very big advantage of the coupons.

So we can say that

Addie taken advantage of coupons.

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Answer:

The value of \(r\) is 24 cm.

Option C. 24 cm

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the missing side.

Here is the formula for the Pythagorean theorem.

\(a^2+b^2=c^2\)

\(a\) and \(b\) are the legs of the triangle

\(c\) is the hypotenuse

In this example we are given the value of 1 leg and the hypotenuse.

Knowing 2 of the 3 sides, we can evaluate the missing leg.

Let \(a=r\)

We are given

\(b=10\\c=26\)

Inserting our values into the Pythagorean theorem gives us

\(r^2+10^2=26^2\)

Lets solve for \(r\).

\(r^2+10^2=26^2\)

Evaluate \(10^2\).

\(r^2+100=26^2\)

Evaluate \(26^2\).

\(r^2+100=676\)

Subtract \(100\) from both sides of the equation.

\(r^2=576\)

Take the square root of both sides to eliminate the exponent.

\(r=\sqrt{576}\)

\(r=24\)

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Ayana's car was at the shop for 38 minutes for the oil change.

Here we are given that Ayana dropped her car at the shop at 19 minutes to noon for an oil change.

When the time is said with the word "to", it means that we need to subtract the minutes from hours to get the actual time.

Therefore, 19 minutes to noon would be

12 : 00 - 19 minutes

= 11 : 41 a.m

Now, she picked her car up 29 minutes past noon. Since the word past has been used, we need to add up the hours and minutes mentioned hence we get

12 : 00 + 19 minutes

= 12 : 19 p.m

Now we need to find the time the car was at the shop. For this, we will subtract the time the car came in the shop from the time at which the car left the shop.

Hence we get

12 : 19 - 11 : 41

Now clearly, 19 > 41, hence we will carry over 60 mnutes from the hoyrs to get

11 : 79 - 11 : 41

= 38 minutes.

Hence, Ayana's car was at the shop for 38 minutes for the oil change.

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Using 90% confidence interval, the estimated mean winnings for all the players on the Jeopardy quiz show would fall between $26,638.11 lower confidence level and $32,586.69 upper confidence level.

To estimate the mean winnings for all the players on the television quiz show Jeopardy with a 90% confidence level, we can use the given random sample of winners' winnings.

First, let's calculate the sample mean (x) and sample standard deviation (s) from the provided data:

Sample mean (x) = (21689 + 34491 + 16742 + 34252 + 17405 + 34178 + 30563 + 25095 + 18087 + 34644 + 22265 + 22093 + 33404 + 31895 + 24051) / 15

Sample mean = 29612.4

Sample standard deviation (s) = √(((21689 - x)² + (34491 - x)² + ... + (24051 - x)²) / (15 - 1))

S.D = √((531250086.4) / 14)

S.D = √6540.24

Next, we can calculate the upper and lower confidence limits (UCL and LCL) using the formula:

UCL = x + (t * (s / √(n)))

LCL = x - (t * (s / √(n)))

where:

Since the sample size is 15, the degrees of freedom (df) is 15 - 1 = 14. Using a t-table or statistical software, the critical value for a 90% confidence level with df = 14 is approximately 1.761.

Plugging in the values, we have:

UCL = 29612.4 + (1.761 * (6540.24 / √(15)))

UCL= 29612.4 + (1.761 * 1689.31)

UCL = 29612.4 + 2974.29

UCL = 32586.69

LCL = 29612.4 - (1.761 * (6540.24 / √(15)))

LCL = 29612.4 - (1.761 * 1689.31)

LCL = 29612.4 - 2974.29

LCL = 26638.11

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To find the relative extrema of the function g(x) = (1/5)x^5 - x, we need to find the critical points and determine their nature by analyzing the sign changes of the derivative.

First, let's find the derivative of g(x) with respect to x:

g'(x) = d/dx [(1/5)x^5 - x]

      = (1/5) * d/dx (x^5) - d/dx (x)

      = (1/5) * 5x^4 - 1

      = x^4 - 1

To find the critical points, we set g'(x) equal to zero and solve for x:

x^4 - 1 = 0

We can factor this equation as a difference of squares:

(x^2 - 1)(x^2 + 1) = 0

Setting each factor equal to zero, we have:

x^2 - 1 = 0  -->  x^2 = 1  -->  x = ±1

x^2 + 1 = 0  -->  x^2 = -1 (No real solutions)

Therefore, the critical points are x = -1 and x = 1.

Now, let's analyze the sign changes of the derivative g'(x) to determine the nature of the extrema:

For x < -1, g'(x) = (-) - 1 = -1 < 0, indicating a decreasing slope.

For -1 < x < 1, g'(x) = (+) - 1 = -1 < 0, indicating a decreasing slope.

For x > 1, g'(x) = (+) - 1 = 1 > 0, indicating an increasing slope.

From this analysis, we can determine the nature of the relative extrema:

At x = -1, we have a relative maximum.

At x = 1, we have a relative minimum.

Therefore, the relative extrema of the function g(x) = (1/5)x^5 - x are:

Relative maximum at x = -1

Relative minimum at x = 1

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Answer:

62.8318531

10 x 2 = 20 so 20 is the diameter

20 x pi = 62.8318531

Hope this helps

Step-by-step explanation:

The exact circumference of a circle that has a radius of 10 cm is 62.8318531

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Given that circle that has a radius of 10 cm

The circumference is given by

C = 2πr

  = 2π10

   = 20π

10 x 2 = 20

Therefore, 20 is the diameter

So, 20 x π = 62.8318531

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The function f is continuous on a closed interval [a, b], differentiable on (a, b), and f has n zeros on [a, b], then f' has at least n - 1 zeros on [a, b].

Rolle's theorem is a fundamental result in differential calculus that states the following:

If a function f(x) is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in the open interval (a, b) such that f'(c) = 0.

Step 1: Base Case

Let's start with the base case where n = 1, meaning f has one zero on [a, b].

In this case, f(x) = 0 for some x in [a, b].

Since f is continuous on [a, b] and differentiable on (a, b), we can apply Rolle's theorem. This implies that there exists at least one point c in (a, b) such that f'(c) = 0.

Therefore, the statement holds for the base case.

Step 2: Inductive Hypothesis

Assume that the statement holds for some positive integer k, where k >= 1. This means that if f has k zeros on [a, b], then f' has at least k - 1 zeros on [a, b].

Step 3: Inductive

We need to prove that the statement holds for k + 1 zeros. Let f have k + 1 zeros on [a, b]. This means there exist k + 1 distinct points x1, x2, ..., x(k+1) in [a, b] such that f(x1) = f(x2) = ... = f(x(k+1)) = 0.

Consider the function g(x) = f(x) / (x - x1)(x - x2)...(x - x(k+1)). Since f is continuous on [a, b] and differentiable on (a, b), and the denominator of g(x) does not vanish on [a, b] due to the distinctness of the points x1, x2, ..., x(k+1), we can apply Rolle's theorem to g(x).

Rolle's theorem implies that there exists at least one point d in (a, b) such that g'(d) = 0. Now, let's expand g'(x):

g'(x) = f'(x) / (x - x1)(x - x2)...(x - x(k+1))

      - f(x)[(1 / (x - x1)^2) + (1 / (x - x2)^2) + ... + (1 / (x - x(k+1))^2)]

Since g'(d) = 0, we have:

0 = f'(d) / (d - x1)(d - x2)...(d - x(k+1))

   - f(d)[(1 / (d - x1)^2) + (1 / (d - x2)^2) + ... + (1 / (d - x(k+1))^2)]

Since the points x1, x2, ..., x(k+1) are distinct, the denominator (d - xi) for each term in the second part of the equation is non-zero. Therefore, for the above equation to hold, we must have f'(d) = 0.

Thus, we have shown that if f has k + 1 zeros on [a, b], then f' has at least k zeros on [a, b].

Step 4: Conclusion

By mathematical induction, we have proved that if f is continuous on a closed interval [a, b], differentiable on (a, b), and f has n zeros on [a, b], then f' has at least n - 1 zeros on [a, b].

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After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

Given that,

The half-life of curium-243 is 28.5 days.

We have to find how many grams of curium-243 will be left in a sample with 5.6 grams after 12 days.

We know that,

The formula is

A(t) = A₀(1/2\()^{t/h}\)

Here,

t= 12 days, half life,

h =28.5 days .

And the initial value, A(0)=5.6 grams

So we will get

A(t) = 5.6(1/2\()^{12/28.5}\)

A(t) = 5.6×0.747 = 4.2 grams

Therefore, After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

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Answer:

y = 3x - 5

Step-by-step explanation

Answer:

Y = 3x - 5

Step-by-step explanation:

6x - 2y = 10

-2y = -6x + 10

y = 3x - 5

Answer:

c

Step-by-step explanation:

Answer:

Sometimes, it is true

Step-by-step explanation:

The L. C. M of two numbers could be the product of the two Given numbers. This happens sometimes but not always. For instance, the Lowest Common. Multiple of 4 and 5 is 20

4 : 4, 8, 12, 16, 20, 24, 28, 32

5 : 5, 10, 15, 20, 25,...

L. C. M = 20 ; 4 * 5 = 20

However, L. C. M of 4 and 8

4 : 4, 8, 12, 16, 20, 24, 28, 32

8 : 8, 16, 24, 32, 40

L.C.M = 8 ; 4 * 8 = 32

HENCE, L. C. M could be the product of the 2 numbers sometimes and it may not in other scenarios.

Answer:

50minutes or 5/6hr

Step-by-step explanation:

Speed of Man is 10km/hr

or 10km/60min = 1km/6min.

5km can be distributed in five parts as like

1+1+1+1+1

So time taken, 6+5+6+5+6+5+6+5+6 = 50min.

Ans will be 50min or 5/6hr

Answer:Just click on the lines that it tells you to do and that should be your answer... I know that wasn't very helpful but I'm not to positive about my answer or what it is.

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

3x=4-1

3x=3

x=1

Total time(arithmetic) taken by app to show nearest charging port will be 30 seconds.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.

Main body:

As the driving directions algorithm requires searching through many possible routes to calculate the optimal route. the other operations, like incrementing the index and comparing the distances, take only a few nanoseconds.

Hence total time will be 30 seconds.

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Answer:

43

Step-by-step explanation:

AM must be a half of AB, because M is the midpoint of AB.

AM = 1/2AB

2x + 9 = 1/2(8x - 50)

Distribute 1/2 to (8x - 50).

2x + 9 = 4x - 25

Subtract 2x from both sides.

9 = 2x - 25

Add 25 to both sides.

34 = 2x

Divide both sides by 2.

x = 17

Now plug x into AM = 2x + 9.

AM = 2(17) + 9

AM = 34 + 9

AM = 43