Solve: 3 - 2k - 3k = -12
What does K equal?
K =

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:

Circle 1

28.269 ÷ 9 = 3.141

Circle 2

25.126 ÷ 8 = 3.14075

Circle

37.686 ÷ 12 = 3.1405

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Answer:

8.25+50

Step-by-step explanation:

Answer:

x=\(\frac{3}{2}\) and x=\(\frac{1}{6}\)

Step-by-step explanation:

\(\sqrt{36x^2-60x+25}=4\)

=> \(\sqrt{36x^2-60x+25}^{2} =4^{2}\)

=> \({36x^2-60x+25}=16\)

=> \(36x^2-60x+25-16=16-16\)

=> \(36x^2-60x+9=0\)

=> \(x_{1,\:2}=\frac{-\left(-60\right)\pm \sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}}{2\cdot \:36}\\\\\sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}=48\)

=> \(x_{1,\:2}=\frac{-\left(-60\right)\pm \:48}{2\cdot \:36}\)

=>\(x_{1} = \frac{-\left(-60\right)+48}{2\cdot \:36}\\\\x_{1}=\frac{60+48}{2\cdot \:36}\\\\x_{1}=\frac{108}{72} \\\\\\x_{1}=\frac{3}{2}\\\)

=> \(x_{2}=\frac{-\left(-60\right)-48}{2\cdot \:36}\\\\x_{2} =\frac{60-48}{2\cdot \:36}\\\\x_{2}=\frac{12}{2\cdot \:36}\\\\\x_{2}=\frac{12}{72}\\\\x_{2}=\frac{1}{6}\)

To evaluate the surface integral of f(x,y,z) dS over the given surface, the first step is to set up the surface integral as a double integral over a region R in the xy-plane. To do this, we can express f(x,y,z) in terms of two parameters, u and v, as f(u,v). Then, the surface integral is expressed as follows:
Integral f(u,v) dS = Integral Integral f(u,v) dA,
where A is the area of the region R in the xy-plane.

For the given surface, we can express the equation of the cone as z2 = (x2 +y2), for 0≤z≤8. To parameterize this equation, we can set u = x and v = y, and express x and y in terms of z as follows:
x = rcosθ and y = rsinθ.
Therefore, the double integral of f(u,v) dA can be expressed as:
Integral Integral f(u,v) dA = Integral Integral f(r cosθ,r sinθ) rdrdθ,
where 0≤r≤5 and 0≤θ≤2π.
Finally, substituting f(x,y,z) with 4x and evaluating the integral, we obtain the surface area of the given cone as A = 80π.
In conclusion, the surface integral of f(x,y,z) dS over the given cone is 80π.

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If a case-control study were conducted to investigate the relationship between an exposure and a rare disease like neck cancer, the most likely relative measure that would be estimated is the odds ratio.

This is because the prevalence of neck cancer in the general population is low, which means that the incidence rate is also low. As a result, it is difficult to calculate the relative risk directly in a case-control study. Instead, the odds ratio is used as a measure of association between the exposure and the disease outcome.

The odds ratio is calculated by comparing the odds of exposure in cases to the odds of exposure in controls. The odds ratio can provide an estimate of the strength and direction of the association between the exposure and the disease outcome in the population being studied.

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Answer:

x=176.78

y=262.28

z=176.77

There is not enough evidence to support the claim made by the pit crew at α = 0.01.

From the question above, that n = 32, sample mean (X) = 12.9 seconds, standard deviation (s) = 0.19 seconds and level of significance (α) = 0.01

We need to check whether there is enough evidence to support the claim made by the pit crew at α = 0.01.

That means, we need to test the following hypotheses:

Null hypothesis: H₀: μ ≥ 13 (The mean pit stop time is greater than or equal to 13 seconds)

Alternate hypothesis: H1: μ < 13 (The mean pit stop time is less than 13 seconds)

This is a one-tailed test with the rejection region on the left side of the distribution. The critical value can be found using the t-distribution table with (n - 1) degrees of freedom at α = 0.01.

The degree of freedom is (n - 1) = 32 - 1 = 31

From the t-distribution table with 31 degrees of freedom and α = 0.01, we get the critical value t = -2.479.

The test statistic can be calculated using the formula:t = (X - μ) / (s / sqrt(n))

Substituting the given values, we get

t = (12.9 - 13) / (0.19 / sqrt(32))

t = -1.216

The calculated test statistic is -1.216.

It falls outside the rejection region (-2.479 to -∞) and therefore, we fail to reject the null hypothesis.

Therefore, there is not enough evidence to support the claim made by the pit crew at α = 0.01.

Your question is incomplete but most probably your full question was:

In auto racing, a pit crew claims that its mean pit stop time (for 4 new tires and fuel) is less than 13 seconds. A random selection of 32 pit stop times has a sample mean of 12.9 seconds and a standard deviation of 0.19 second.

Is there enough evidence to support the claim at α = 0.01?

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Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

\(\rm (x-h)^2+(y-k)^2=r^2\)

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

\(\rm (x+1)^2+(y-3)^2=r^2\)

Put the point on the circle equation to get the radius of the circle:

\(\rm (-10+1)^2+(1-3)^2=r^2\)

\(\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units\)

Equation of circle is:

\(\rm (x+1)^2+(y-3)^2=85\)

Now put the point J(-3, 12 ) in the circle equation:

\(\rm (-3+1)^2+(12-3)^2=85\)

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

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The calculated volume of the model space is 1657.92 cubic inches

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

The model space made from:

The volume of the model space is calculated as

Volume = Cone + Cylinder + Hemisphere

Using the volume formulas, we have

Volume = 1/3πr²h + πr²h + 2/3πr³

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 3.14 * 6² * 8 + 3.14 * 6² * 8 + 2/3 * 3.14 * 6³

Evaluate

Volume = 1657.92

Hence, the volume of the model space is 1657.92 cubic inches

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Answer: 75.95cm

Step-by-step explanation:

speed = 4.9cm/sec

time = 15.5 sec

d = speed • time = 4.9 • 15.5 = 75.95 cm

The airline might choose cluster random sampling in this case.

Cluster Sampling:

It is a sampling method where the entire population under study is divided into homogeneous groups called clusters. The clusters are externally homogeneous and internally heterogeneous.

Simple Random Sampling:

It is a sampling technique where every unit in the population has an equal chance of being selected in the sample and the samples are selected at random. The airline wants to survey 500 passengers on this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster.

Cluster sampling involves fewer resources for sampling compared to simple random sampling.

Here, the population under study is people travelling the flight which is externally homogeneous.

The people travelling in the flight are classified into three groups namely first class (most expensive), business class, and economy class (least expensive) which is internally heterogeneous. More number of persons can be included in the survey which acts as a good representative of the entire population. Thus, cluster sampling is suitable for this study. Simple random sampling may result in an unequal number of persons in each class if the persons are surveyed at random. So, cluster sampling better suits the scenario than simple random sampling.

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An equation that represents the population of the bacteria at time x is y = 500(1.047)^x.

The bacteria grows at an exponential rate. An exponential growth rate means that the growth rate of the bacteria would increase overtime.

The general form of exponential equation is f(x) = \(e^{x}\)

Where:

The future population of the bacteria can be represented with:

FV = P(1 + r)^x

Where:

y = 500(1 + 0.047)^x

y = 500(1.047)^x.

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C' would be (-1,7), Triangle Illustrations Triangles are three-sided polygons with three vertices.

Therefore,

'a' unit up = (x,y)  ⇒(x, y + a)

'a' unit down = (x,y) ⇒(x, y - a)

'a' unit left = (x,y) ⇒(x - a, y)

'a' unit right = (x,y) ⇒(x + a, y)

Given,

(x,y) ⇒(x-3),(y+8)

Simplifying,

C(2,-1)⇒C'(2-3, -1+8)

= C'(-1,7)

D(7,-4) ⇒ D'(7-3, -4+8)

= D'(4,4)

E(4,-6) ⇒ E'(4-4, -6+8)

= E'(0,2)

Hence, C'= (-1,7)

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The answer is associative property

this allows us to rearrange the grouping or grouping symbols and not the order of operation.

an eaxample is

Answer:

[0,infinity)

Step-by-step explanation:

Since it's a modulus function, f(x) will have a range of [0,infinity). Use desmos for graphing it

Answer:

Shirley bought a fax machine and sells to Devi at a profit of 25% on the cost price.

Shirley buy price:: x

Devi buy price:: 1.25x

Devi sells the fax machine to Amirah at a loss of 250 on the price which she buys it from Shirley.

Amirah buy price = 1.25x -250

if Amirah pays $360 for the fax machine,how much did Shirley pay for it?

Equation:

1.25x - 250 = 360

1.25x = 360 + 250

x = 610 / 1.25

x = 488

Ans: x = $488 (Price Shirley paid)

Answer: 2

Step-by-step explanation: When we talk about rate change, we are talking about the slope!

The slope is 2x which means the rate change is rise 2 and run over 1.

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Check the picture below.

so if we peel off the cylinder, we end up with that, hmmm how long is the width?  well, we know the circular bases have a diameter of 9mm, so half that is its radius or 4.5mm, and if we peel off the circle, we'll end up with a long line whose length is its perimeter or namely its circumference, which oddly enough is the length of the width

\(\textit{Circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies C=2\pi (4.5)\implies C=9\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Lateral Area}}{\stackrel{width}{(9\pi )} \stackrel{height}{(17)}} \implies {\Large \begin{array}{llll} 153\pi \end{array}} ~mm^2\)

Answer:

-2/15

Step-by-step explanation:

1. Change the denominator.

1/5 = 3/15

3/15 = 5/15

3/15 - 5/15 = -2/15

Answer:

6 ; 10

18 ; 162

Step-by-step explanation:

Recall :

Rate of change = Slope = Rise / Run = (y2 - y1) / (x2-x1)

2nd point is (1, 7)

3rd point is (2, 13)

Rate of change = (13 - 7) /(2 - 1)  = 6 /1 = 6

3rd and 4th point :

(2, 13)

(3, 23)

Rate of change = (23 - 13) / (3 - 2) = 10 /1 = 10

PART B:

(2, 11) ; (3, 29)

Rate of change = (29 - 11) / (3 - 1) = 18 /1 = 18

(4, 83)

(5, 245)

Rate of change = (245 - 83) /  (5-4) = 162 / 1 = 162

Yes, g has a maximum and minimum on the set S.

Since S is a closed and bounded interval, by the Extreme Value Theorem, any continuous function on S will have both a maximum and minimum value. Therefore, g, defined on S, will have both a maximum and minimum value.

To find the global maxima and minima of g on the set S, we need to analyze the function g(x). However, since no specific function is defined for g, we cannot determine the exact maxima and minima values without further information. We can make some general observations about g(x) on S. Firstly, since S includes both negative and positive values, g(x) could be a piecewise function that changes at x = 0. Secondly, the behavior of g(x) will depend on the specific function used to define it. For example, if g(x) = x^2, then g(x) will have a minimum value of 0 at x = 0 and a maximum value of 100 at x = 10 or x = -10. Similarly, if g(x) = -x^3, then g(x) will have a maximum value of 1000 at x = 10 and a minimum value of -1000 at x = -10.

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Answer:

Graph D

Step-by-step explanation:

To have the highest correlation coeffient, you would want the data points to be as close as possible to one another which is represents in graph d in whcih a best fit line could be added easily

Answer:

D

Step-by-step explanation:

The space between the dots on the scatt plot determines the correlation coefficient. Random lines across the graph is a coefficient of 0. A straight line has a coefficient of 1.

The smaller the amount of space between dots, the higher the correlation coefficient.

Answer:

3092-927=2165

Step-by-step explanation:

12-7= 5, except not 12 'cause 1-2 doesn't equal 6. 8 does, so carry the 1, 92. 3 something minus 9 equals something-ety 1, 30-9=21, so.

3092-927=2165

Or something like that.

A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as 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;

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

Ordered pair B' (-2, 1)   →          E (1, 2)

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One angle measures (2x - 3)°.

The other angle measures (x + 9)°.

Since the angles are congruent, we can set up the equation:

2x - 3 = x + 9

2x - x - 3 = x + 9 - x

x - 3 = 9

x = 12

Now that we have found the value of x, we can substitute it back into one of the angle measures to find the measure of one of the angles.

Using the expression (2x - 3)°:

Angle measure = (2(12) - 3)°

Angle measure = (24 - 3)°

Angle measure = 21°

Therefore, one of the angles measures 21°.

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In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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