Rewrite 8 + 12 using the GCF and factoring.

2(2 + 6)
4(8 + 12)
4(2 + 3)
8(1 + 12)

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

To find the observed z value we have to use the principles to create a formula.

The formula for finding the value of z is

z = ( x - μ)/(σ/√n)

here,

x = sample mean

μ = population mean

σ = standard deviation of the population

n = sample size

for the given question the values are

x = 50

μ = 45

σ = 5

n = 1

staging the values in the formula

z = (50-45)/(5/√1)

z = 1

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

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No, the graph of a straight line need not always be a function.

The equation of a straight line is,

y = -mx + c

y = the y coordinate

x = the x coordinate

c = y-intercept of the line

m = slope of the line = tan(Ф)

Since the values of y are dependent on the values of x, the graph is a function. But for a line parallel to x-axis, the equation is,

y=a and x=0

That is, for any value of y, the value of x is 0

and for a line parallel to the y-axis, the equation is,

x=a and y=0

That is, for any value of x, the value of y is 0

The values of x and y don't depend on each other. Hence, the graphs of straight lines need not always be a function.

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Two of them have the same remaining. The proof using the pigeonhole principle is now complete.

When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.

If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.

So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.

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a)

Solution,

According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.

i.e. Left fuel = (1/2 + 3/4)/2 litres

Here,

1/2 of 40l = 1/2×40l

= 20l

3/4 of 40l = 3/4×40l

= 30l

Then,

Left fuel = (20l + 30l)/2

= 50l/2

= 25l

Consumed fuel = 40l - 25l

= 15l

Therefore,15 litres of petrol is used to travel 240km

b)

Solution,

Consumed fuel = 15l

Distance covered = 240km

Then,

Fuel consumption rate = 240km/15 l

= 16km/l

Therefore,the rate of petrol consumption is 16km/l of his car for this journey

Answer:

They are both factors of the logarithmic equation. The solutions to A and B are provided below.

Robert's time was 3 hours, and Wilbur's time was 1 hour and 30 minutes.

To determine the time taken by Robert and Wilbur, we need to use the formula:

Time = Distance / Speed

Since both Robert and Wilbur covered the same distance, we can equate their respective time formulas:

Distance / Robert's Speed = Distance / Wilbur's Speed

Simplifying the equation, we find:

Robert's Speed / Wilbur's Speed = Wilbur's Time / Robert's Time

Given that Robert's speed was 6 miles per hour and Wilbur's speed was 8 miles per hour, we can substitute these values into the equation:

6 / 8 = Wilbur's Time / (Wilbur's Time + 2)

Cross-multiplying and solving for Wilbur's Time, we get:

8(Wilbur's Time) = 6(Wilbur's Time + 2)

8Wilbur's Time = 6Wilbur's Time + 12

2Wilbur's Time = 12

Wilbur's Time = 6

Since Wilbur's time was given in hours and minutes, we convert 6 hours into 6 hours and 60 minutes. Therefore, Wilbur's time is 1 hour and 30 minutes.

To find Robert's time, we add 2 hours to Wilbur's time:

Robert's Time = Wilbur's Time + 2

Robert's Time = 1 hour and 30 minutes + 2 hours

Robert's Time = 3 hours

Thus, Robert's time was 3 hours, and Wilbur's time was 1 hour and 30 minutes.

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Answer:

Not a function

Step-by-step explanation:

Fails the vertical line test since there are multiple outputs that exist for single inputs.

Answer:

hm its not a function

Step-by-step explanation:

i alr did this one so youll get it right dw:) also bc the lines arent vertical

The intervals on which function f(x) = sin x -1 increasing or decreasing is (0, π/2) (B).



The given function is f(x) = sin x -1, 0 < x < 2 π.

A sinusoidal function is a function that can be written in the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d, where a, b, c, and d are constants.

The graph of the given function is a sine curve shifted downward by 1 unit.

The function is increasing on the interval (0, π/2) because the slope of the curve is positive on this interval.

The function is decreasing on the interval (π/2, 3π/2) because the slope of the curve is negative on this interval.

The function is increasing again on the interval (3π/2, 2π) because the slope of the curve is positive on this interval.

Therefore, the correct answer is option B. (0, π/2).

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The planet that has the larger mass is the planet B and the measurements in standard forms are

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

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

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The upper bound of the volume of water left in the fish tank is 60 liters.

33.81 fluid ounces make up one litre (US).

One litre of water would fill about one-fourth of a gallon water bottle. Also, you should be aware that there are two different kinds of ounces used globally to measure water volume: (1 litre = 33.814 US ounces).

The maximum allowable mistake can be added to the actual value to determine the upper bound of the amount of water still in the fish tank.

The maximum error for 90 litres, rounded to one significant figure, is half of the value of the last significant figure, or 5. Hence, the actual value of 90 litres might be either 85 or 95.

The largest potential inaccuracy for 30 litres, rounded to one significant figure, is likewise 5. Hence, the actual value of 30 litres might be 25 or 35.

We subtract the lower bound of the withdrawn volume from the higher bound of the original volume to determine the upper bound of the volume of water still present in the tank.

The upper bound of the volume of water left in the fish tank can be found by adding the half of the absolute uncertainty to the measured value of 60 liters (90 - 30):

Upper bound = 60 + 0.5 x 1 = 60.5 liters (rounded to 1 significant figure)

Therefore, the upper bound of the volume of water left in the fish tank is 60 liters.

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Answer:

37

Step-by-step explanation:

oh wait i was wrong look at the person above me plzzzz

Answer: $218.79

Step-by-step explanation:

$220 is the marked price.

You pay a 10 % discount. =>

1/10 x 220 = $22 discount.

Subtract this from your marked price to get  the remainder.

$220 - $22= $198.

There is a 10.5% service charge =>

10.5% of $198 = $20.79 for service charge.

Thus,

$198 + $20.79 = $218.79 which is the total pay for the ticket.

Hope this helps! :)

The total propagated uncertainty for the equation P = mgh is calculated to be approximately 9.6 ± 1.03 N. The largest source of uncertainty in this equation arises from the uncertainty in the value of g, which contributes ±1.86 N to the total uncertainty.

To find the total propagated uncertainty for P = mgh, we need to consider the individual uncertainties of the variables m, g, and h, and then combine them using the rules of error propagation.

The equation for P = mgh involves multiplication, so we use the rule that states the fractional uncertainties add in quadrature. The fractional uncertainties for m, g, and h are calculated by dividing their respective absolute uncertainties by their measured values.

For m = 5 ± 0.2 kg, the fractional uncertainty is 0.04, and for g = 9.8 ± 1.9 m/(s^2), it is 0.194. For h = 3 ± 0.1 m, the fractional uncertainty is 0.033.

Next, we multiply these fractional uncertainties by the values of mgh to obtain the individual propagated uncertainties for each variable. Multiplying mgh by the fractional uncertainties of m, g, and h gives us ±0.2 N, ±1.91 N, and ±0.1 N, respectively. To find the total propagated uncertainty, we add these individual uncertainties in quadrature: ±√((0.2 N)^2 + (1.91 N)^2 + (0.1 N)^2) = ±1.03 N.

The largest source of uncertainty in this equation is the uncertainty in the value of g, which contributes ±1.91 N to the total propagated uncertainty. This is because the uncertainty in g has the largest fractional uncertainty among the variables involved in the equation.

Therefore, the total propagated uncertainty for P = mgh is approximately 9.6 ± 1.03 N, with the largest source of uncertainty arising from the uncertainty in g, contributing ±1.86 N to the total uncertainty.

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Answer:

240

Step-by-step explanation:

From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.

Fraction of men at the recital = 4/10

Fraction of women at the recital = 6/10

The number of men performers that were in the dance recital will be:

= 4/10 × 600

= 240 men

Answer: 240 men

Step-by-step explanation:

From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.

Fraction of men at the recital = 4/10

Fraction of women at the recital = 6/10

The number of men performers that were in the dance recital will be:

= 4/10 × 600

= 240 men

Hope it helps

Answer:

I would think 10,700

Step-by-step explanation:

21.25 + 17.50 + 41.50 + 26.75 = 107

107 x 100 = 10,700

(I'm so sorry if I'm wrong)

Answer:

35 miles

Step-by-step explanation:

d=(70)(.5)

d=35 miles

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer: Answer A is correct :)

Step-by-step explanation:

If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation.

The sum of the triangle angles is 180°.

Hence, The sum of the triangle angles is 180°.

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A rotation which occurred using the origin as the center of rotation is a rotation of 90° clockwise.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise to the coordinate of triangle GHJ in order to determine the coordinate of the vertices H' of the image, triangle G’H’J’;

(x, y)                               →            (y, -x)

Coordinate H = (3, 3) → H' = (3, -(3)) = H' (3, -3)

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The angle between the string and the ground is decreasing at a rate of approximately 0.014 rad/s

The differential of V, ΔV = 4πr²Δr; Δr = 4.1 - 4 = 0.1in, and the r-value is 4in.

The calculation is as follows,ΔV = 4πr²Δr= 4π (4)² (0.1)≈ 20.1 cubic inches.

So, the change in volume is 20.1 cubic inches when the r-value is increased from 4 inches to 4.1 inches.

Given information: f(x) = 4Vx² + 24, x1 = 1.

First, we find the linear approximation at x1,  f(x) ≈ f(x1) + f'(x1)(x-x1)At x1 = 1, f(x1) = 4V(1)² + 24 = 4V + 24.

Since L(x) is the linear approximation to f(x), L(x1) = f(x1), so we have L(x) ≈ 4V + 24 + f'(x1)(x-x1)

Now, f'(x) = 8Vx, so f'(x1) = 8V.

Plugging in x = 1.1, we get, f(1.1) ≈ 4V + 24 + 8V(1.1-1)= 4V + 24 + 8V(0.1) = 4V + 0.8V + 24 = 4.8V + 24.

Hence, the linear approximation to f(x) = 4Vx² + 24 at x1 = 1 is L(x) ≈ 4V + 24 + 8V(x-1), and f(1.1) ≈ 4.8V + 24. The answer is 4.8V + 24.

Given,

The rate of the horizontal movement of the kite, dh/dt = 9 ft/s.

The length of the string is 140 feet.

The kite is 50 feet above the ground.

The height of the kite is h.

The angle between the string and the ground is θ.

The hypotenuse of the triangle is r.

Let's use trigonometry to relate the height of the kite and the angle between the string and the ground. tan θ = h/r Differentiate the above expression with respect to time t, sec²θ(dθ/dt) = (dh/dt)(r/h)

Substitute the given values to solve for (dθ/dt)sec²θ = (dh/dt)(r/h) = (9)(140)/h(secθ) = 1260/hsecθ = 1260/(50² + h²)secθ = 1260/(2500 + h²)dθ/dt = (dh/dt)(r/h)(cos²θ) = (9)(140)/(50)(2500 + h²)cos²θAt h = 50, dθ/dt = (9)(140)/(50)(2500 + 50²)cos²θ≈ 0.014 rad/s

Therefore, the angle between the string and the ground is decreasing at a rate of approximately 0.014 rad/s when 140 feet of string is out.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

22in

Step-by-step explanation:

Answer: 11/3

Step-by-step explanation:

Answer:

He needs 1 and 1/3 cups of pinapple juice when he uses 3 cups of orange juice.

Step-by-step explanation:

Orange Juice:

3 cups / 3/4 cups = 12/3 = 4

Pineapple Juice:

1/3 × 4 = 4/3 cups= 1  1/3 cups

Given problem;

   A = \(\pi\) r²

   Solve for π;

To solve for π implies that we make it the subject of the expression.

So;

       A = π r²

      Now multiply both sides by \(\frac{1}{r^{2} }\)

 So;

                A x \(\frac{1}{r^{2} }\)   = \(\pi\) x r² x \(\frac{1}{r^{2} }\)

              r² cancels out from the right side and leaves only π;

                  π = \(\frac{A}{r^{2} }\)

So    \(\pi = \frac{A}{r^{2} }\)

The greatest number from to which when 7 is added, the sum divides 90,105,224 without leaving a reminder is 8.

We can represent the greatest number  as  x, which implies that the greatest number that  when 7 is added it will divide the givn numbers without remainder, hence x +7 = hcf.

Then we can test for the factors of the given numbers on after the other as;

90  = (2 * 5 * 3 * 3)

105 = (5 * 3 * 7)

120 = (5 * 2 * 3 * 2 * 2)

Hence the hcf here can be expressed as 5 and 3  which is equivalent to 15

Then (x + 7) = 15

x = (15 - 7)

x = 8

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The future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

To calculate the future value (FV) of an investment of $10,000 at an interest rate of 6% per year, compounded annually, after 7 years, we can use the formula:

FV = P(1 + r)^n

Where:

P is the principal amount (initial investment) = $10,000

r is the interest rate per period = 6% = 0.06

n is the number of periods = 7

Plugging in the values, we have:

FV = $10,000(1 + 0.06)^7

Calculating the expression inside the parentheses first:

(1 + 0.06)^7 ≈ 1.41851

Now, multiply the principal amount by the calculated expression:

FV ≈ $10,000 * 1.41851 ≈ $14,185.10

Therefore, the future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

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The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.

Given that  

         3x + 3 - x + (-7) > 6

         3x - x > 6 + 7 - 3

         2x > 10

          x > 5

Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.

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The difference between 5x-2/4x and x-2/4x is (5x-2)/4x - (x-2)/4x, which can be simplified to (5x-x-2)/4x + 2/4x.

Combining like terms, this becomes 4x-2/4x, or (4x-2)/4x. The simplified expression is (2(2x-1))/4x. The numerator can be further simplified to (2(2x-1))/2(2x), which reduces to (2x-1)/2x. The difference between the two expressions, 5x - 2/4x and x - 2/4x, can be found by subtracting the second expression from the first.
Your expression: (5x - 2/4x) - (x - 2/4x)
First, you can combine the terms with the same denominator, which is 4x:
(5x - x) - (2/4x - 2/4x)
Next, simplify the terms in parentheses:
(4x) - (0)
The result is simply 4x. So, the difference between the two expressions is 4x.

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