5
1 point
Find VW.
T
3x
32
32
V x+8 W

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

A residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

The residual plot is a graphical tool used to assess the appropriateness of the line of best fit or the regression model for the data. It helps to examine the distribution and patterns of the residuals, which are the differences between the observed data points and the predicted values from the regression model.

In a residual plot, the horizontal axis typically represents the independent variable or the predicted values, while the vertical axis represents the residuals. The residuals are plotted as points or dots, and their pattern can provide insights into the line of best fit.

To determine if the line of best fit is appropriate, you would generally look for the following characteristics in the residual plot:

Randomness: The residuals should appear randomly scattered around the horizontal axis. If there is a clear pattern or structure in the residuals, it suggests that the line of best fit is not capturing all the important information in the data.

Constant variance: The spread of the residuals should remain relatively constant across the range of predicted values. If the spread of the residuals systematically increases or decreases as the predicted values change, it indicates heteroscedasticity, which means the variability of the errors is not constant. This suggests that the line of best fit may not be appropriate for the data.

Zero mean: The residuals should have a mean value close to zero. If the residuals consistently deviate above or below zero, it suggests a systematic bias in the line of best fit.

It's important to note that a residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

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Answer:

Sharon was driving 60 miles per hour.

Step-by-step explanation:

To solve this you must divide both the amount of miles (270) and the amount of hours (4.5) by the amount of hours so that way you can see how many miles per hour you are going.

4.5 / 4.5 = 1

270 / 4.5 = 60

This means that Sharon was driving 60 miles per hour.

Answer:

Step-by-step explanation:

56.1,12.1,23.6

Answer:

1,386

Step-by-step explanation:

guessed it in my head

The variance of the number of people placed on hold is 1.9.

Probability distribution A probability distribution is a function that maps all events or outcomes that can happen in an experiment to probabilities that summarize how likely they are to occur. The probabilities in a probability distribution must always meet the following conditions:

All probabilities must be nonnegative.

The sum of all probabilities must be equal to 1.If the probability distribution satisfies the above two conditions, it is a valid probability distribution. The table of probabilities given in the question satisfies the above two conditions. Therefore, it is a valid probability distribution.

The mean or expected value of a probability distribution is calculated by multiplying each outcome by its probability and adding all the products together.

The mean, μ, is given by:

μ = Σ(xi * P(xi)),where xi is the outcome and P(xi) is the probability of the outcome.

Using the values from the table, we have:

μ = (0 * 0.15) + (1 * 0.3) + (2 * 0.23) + (3 * 0.18) + (4 * 0.1) + (5 * 0.04)μ = 1.81

The mean number of people placed on hold is 1.81.

Standard deviation

The standard deviation of a probability distribution measures how spread out the outcomes are from the mean.

The standard deviation, σ, is given by:σ = sqrt(Σ(xi - μ)^2 * P(xi)),where xi is the outcome, μ is the mean, and P(xi) is the probability of the outcome.

Using the values from the table and the mean we just calculated, we have:

σ = √((0 - 1.81)^2 * 0.15 + (1 - 1.81)^2 * 0.3 + (2 - 1.81)^2 * 0.23 + (3 - 1.81)^2 * 0.18 + (4 - 1.81)^2 * 0.1 + (5 - 1.81)^2 * 0.04)σ = 1.38

The standard deviation of the number of people placed on hold is 1.38.

The variance of a probability distribution is the square of the standard deviation.

The variance, σ^2, is given by:σ^2 = Σ(xi - μ)^2 * P(xi),where xi is the outcome, μ is the mean, and P(xi) is the probability of the outcome.

Using the values from the table and the mean we just calculated, we have:

σ^2 = (0 - 1.81)^2 * 0.15 + (1 - 1.81)^2 * 0.3 + (2 - 1.81)^2 * 0.23 + (3 - 1.81)^2 * 0.18 + (4 - 1.81)^2 * 0.1 + (5 - 1.81)^2 * 0.04

σ^2 = 1.9

The variance of the number of people placed on hold is 1.9.

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Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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Answer:

4/8

Step-by-step explanation:

15 1/8 - 1/2(4/8) = 14 5/8

what is trigonometry

trigonometry is a very common branch of mathematics the word trigonometry means measurement of side of a triangle this branch of mathematics can be used to find the angle of a triangle knowing its side or to find the ratio of side of triangle knowing its angle

fact

Answer:

28°

Step-by-step explanation:

AB and CD are straight lines, all angles in a straight line add up to 180

Answer:

Answer:

11m(meters)

Step-by-step explanation:

A rectangular lot is 3 meters longer than its width. The area of the lot is 88 square

meters. Find the length of the lot.

Area of a rectangle = Length × Width

Length = 3 + W

Hence,

88m² = (3 + W) × W

88 = 3W + W²

W² + 3W - 88 = 0

We factorise

W² +11W - 8W - 88 = 0

W(W + 11) - 8(W + 11) = 0

(W - 8) (W + 11) = 0

W - 8 = 0

W = 8m

Hence, the width = 8m

Length = 3 + W

Length = 3 + 8m

= 11m(meters)

Answer:

The REAL answer is -50

Step-by-step explanation:

Step-by-step explanation:

A= (-2,1)

B= (2,-2)

C=(5,2)

slope = y1 - y2/ x1- x2

slope of

AB = -2-1/2-(-2)

= -3/4

BC= 2-(-2)/5-2

= 4/3

AC = -2-1/5-2

= -3/3

=-1

if ABC is a right triangle then AB should be perpendicular to BC

AB x BC = -1

LHS

=-3/4 x 4/3

=-1

= RHS

hence triangle ABC is a right triangle

Answer:

m = 55t

t = m/55

Step-by-step explanation:

According to the formula for calculating speed expressed as;

Speed = distance/time

Given;

Distance = 55mph

required:

distance as a function of t

time as a function of distance m

If distance is m and time is t

From the formula;

55 = m/t

m = 55t

Hence the equation to solve for miles m is m = 55t

To get t, we will cross multiply from 55 = m/t;

55t = m

Divide both sides by 55

55t/55 = m/55

t = m/55

Hence the equation to solve for time in hours is t = m/55

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Answer:

Step-by-step explanation:

The range is the set of second numbers of the ordered pairs.

  {-5, 1, 4, 5}

__

The domain is the set of first numbers of the ordered pairs.

  {-5, -3, 0, 2}

__

Additional comment

It is generally convenient to write the elements of a set in sorted order.

Answer:

2

Step-by-step explanation:

if you have one chip and add another chip then you have 2 chips

Answer:

The Merchant can Use All of His Beans Making 65 Bags Of House Blend , 30 Bags Of special Blend And 45 Bags Of Gourmet Blend .

Step-by-step explanation:

Abbreviation Used ( Colombian Bean = C , Kenyan Bean = K , French Roast Beans = F , House Blend = H , Special Blend = S , Gourmet Blend = G)

Now According to Question, We have 39kg of C , 15kg of K , 36kg of F

300gm in H + 200gm in S + 300gm in G = Total Colombian Beans(39000gm) ↔ Eq. 1

200gm in G + 200gm in S  = Total Kenyan Bean(15000gm) ↔ Eq. 2

300gm in H + 100gm in S + 300 in of G = Total FrenchRoast Beans(36000gm) ↔ Eq. 3

if we add all three Equations we get

600gm in H  + 500gm in S + 800gm in G = C+K+F(90000gm)↔Eq. 4

Now Subtract Eq. 1 - Eq. 3 We Get

100*S=3000

Total bag of Special Blend is 30

Now Put the value of S=30 in above equations(Eq. 1 & Eq. 4)

we get

3H+3G=330↔(eq. 5)  &   6H+8G=750↔(eq. 6)

solve these equation by subtracting (eq. 6 - 2*eq.5)

we get 2G=90  ⇔ Total bag of Gourmet Blend is 45

now By Putting G value in Eq. 6

We Get 6H=390 ⇔ Total bag of House Blend is 65

Let's find the average distance of a point in the solid ball of radius 2 to its center. We know that the solid ball of radius 2 is defined by the region Ω = {(x, y, z) : x² + y² + z² ≤ 4}.

To calculate the average distance of a point in this region to its center, we need to define a function f(x, y, z) which represents the distance from the point (x, y, z) to the origin (0, 0, 0). This function is given by:

f(x, y, z) = √(x² + y² + z²).

We can then use the formula for the average value of a function to find the average distance:f¯=1v∭Ωf(x,y,z)dxdydz.

Here, v is the volume of the region Ω, which is given by the formula for the volume of a ball: v = (4/3)πr³ = (4/3)π(2)³ = (32/3)π. Substituting in the function f(x, y, z), we have:f¯=1(32/3)π∭Ω√(x²+y²+z²)dxdydz.

We can simplify this integral by changing to spherical coordinates.

In spherical coordinates, we have:x = r sin θ cos φ,y = r sin θ sin φ,z = r cos θwhere r is the distance from the origin to the point (x, y, z), θ is the angle between the positive z-axis and the line connecting the origin to the point (x, y, z), and φ is the angle between the positive x-axis and the projection of the line connecting the origin to the point (x, y, z) onto the xy-plane.

The Jacobian of this transformation is r² sin θ. Using this, we can write the integral as:

f¯=1(32/3)π∫0²∫0π∫0²√(r²) r²sinθdrdθdφ=

f¯=1(32/3)π∫0²∫0π∫0² r³sinθdrdθdφ

f¯=1(32/3)π ∫0² r⁴/4 [from 0 to 2]

∫0π sinθ [from 0 to π] ∫0² dφ [from 0 to 2π]

Using this, we can evaluate the integral:

f¯=1(32/3)π ∫0² r⁴/4 dr ∫0π sinθ dθ ∫0²

dφ=1(32/3)π [r⁵/20] [from 0 to 2] [-cosθ] [from 0 to π] [φ]

[from 0 to 2π]=1(32/3)π [(2⁵/20) - (0)] [(-(-1) - (-1))] [(2π)] = 64/(15π)

The average distance of a point in the solid ball of radius 2 to its center is 64/(15π). Therefore, we have f¯ = 64/(15π).

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Answer:

Below

Step-by-step explanation:

Losing 27 % of value each year means it retains 73% each year

  we need to multiply 20 000 x  .73 x .73 x .73     ....  .73     (twelve times )

                  or   re-written as   20 000 * .73^12 = value =$ 458.04

The graph of the inequality y ≤ (x + 2)² is the graph (a)

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

(y\le(x+2)^2\)

Express properly

So, we have

y ≤ (x + 2)²

The above expression is a quadratic inequality with a less or equal to sign

This means that

The graph opens upward and the bottom part is shaded

Using the above as a guide, we have the following:

The graph of the inequality is the first graph

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(11) The measure of angle IGJ is  46⁰.

(12) The measure of arc JH is determined as 138⁰.

The measure of the arc or central angle indicated is calculated as follows;

(11) The measure of angle IGJ is calculated as follows;

m∠LGK =  arc angle LK (interior angle of intersecting secants)

m∠LGK = 48⁰

m∠HGI = m∠LGK = 48⁰ (vertical opposite angles are equal)

m∠IGJ + m∠HGI + m∠JGK = 180⁰  (sum of angles in a straight line)

m∠IGJ + 48⁰ + 86⁰ = 180

m∠IGJ = 180 - 134

m∠IGJ = 46⁰

(12) The measure of arc JH is calculated as follows;

arc JH = arc JI + arc IH

arc JI = arc FG

arc FG = 180 - 137⁰ (sum of angle in a straight line)

arc FG = 43⁰

arc FG = arc JI (vertical opposite angles are equal)

arc JH = arc JI + arc IH

arc JH = 43⁰ + 95⁰

arc JH = 138⁰

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Answer:

min=28

lower=34

median=39

upper=46.5

max=55

inter range=12.5

Step-by-step explanation:

Nice that the numbers are in order for you

The min is your smallest number = 28

To find the next part separate into 4 equal parts so you have 3 lines

The first line is between 34 and 34 the average of the 2 numbers is your lower quartile

lower quartile =34

middle line is your median between 39 and 39

median = 39

upper quartile is that 3rd line between 42 and 51 average is upper

upper quartile = (42+51)/2 = 46.5

max is the highest number = 55

Interquartile range is the difference between upper and lower = 12.5

Answer:

Step-by-step explanation:

2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

Given that,

TV viewers frequently doubt the validity of particular advertising. In an attempt to counter their critics, a large advertiser wants to determine the true proportion of consumers who believe what is depicted in ads. About 40% of individuals examined, according to preliminary studies, seem to believe what is depicted in advertisements.

We have to find what is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

We know that,

Let

Population proportion (p)= 0.40

Margin of error = 2% = 0.02

Confidence level = 95% = 0.95

α = 1- 0.95 = 0.05

α/2 = 0.025

Let's find out the Z critical value using excel for the 95% confidence level,

Use the following excel command.

= ABS(NORMSINV(α/2))

= ABS(NORMSINV(0.025))

We will get, Z critical value = 2.17009

Sample size (n) = p(1-p)×(Zα/2)/E

n = 0.40(1-0.40)({2.17009}÷{0.05})²

Sample size (n) = 2327

Therefore, 2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

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70.4 g of water are contained in 75.0 g of 6.10 aqueous solution of K3PO4. Therefore option D is correct.

To find the mass of water in the solution, we need to first find the mass of K3PO4 in the solution.

We can do this using the concentration of the solution, which is given as 6.10.

This means that there are 6.10 grams of K3PO4 for every 100 grams of solution.
To find the mass of K3PO4 in 75.0 grams of solution, we can use a proportion:
6.10 g K3PO4 / 100 g solution = x g K3PO4 / 75.0 g solution
Cross-multiplying gives:
(6.10 g K3PO4) * (75.0 g solution) = (100 g solution) * (x g K3PO4)
Solving for x gives:
x = (6.10 g K3PO4) * (75.0 g solution) / (100 g solution) = 4.575 g K3PO4

Now we can find the mass of water in the solution by subtracting the mass of K3PO4 from the total mass of the solution:
Mass of water = Total mass of solution - Mass of K3PO4
Mass of water = 75.0 g - 4.575 g = 70.425 g
Therefore, the answer is (d) 70.4 g of water are contained in 75.0 g of a 6.10 aqueous solution of K3PO4.

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