if angle GHJ is an equilateral triangle, GH = 5x - 13, HJ = 11x - 61, and GJ = 7x - 29, find x and the
measure of each side. Draw and label a picture and show all work for full credit. (10 pts)

Answer:

16

Step-by-step explanation:

2 × | 6 + 2 |

= 2 × | 8 |

= 2 × 8

= 16

The probabilities, using the Poisson distribution, are given as follows:

11. A shark attack next year: 0.038.

12. More than one shark attack next year: 0.001.

13. At least one shark attack in the next 100 years: 0.982.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Considering that there have been 8 attacks in 200 years, the mean for n years is given as follows:

[tex]\mu = \frac{8n}{200}[/tex]

Hence the probability of one shark attack in the next year(n = 1, mean = 0.04) is given as follows:

[tex]P(X = 1) = \frac{e^{-0.04}(0.04)^{1}}{(1)!} = 0.038[/tex]

The probability of more than one shark attack is obtained as follows:

P(X > 1) = 1 - P(X ≤ 1)

In which:

P(X ≤ 1) = P(X = 0) + P(X = 1).

Then:

Thus:

P(X > 1) = 1 - (0.961 + 0.038) = 0.001.

For 100 years, the mean is of:

100 x 8/200 = 4.

Thus the probability of at least one attack is of:

P(X > 0) = 1 - e^(-4) = 0.982.

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The derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.

What is derivative?

dy/dx = d(5ˣ + e⁷) / dx

= 5ˣ ln 5 + 0

= 5ˣ ln 5

e⁷ is constant with respect to x , the derivative of e⁷ with respect to x is 0.

Hence, the derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.

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Step-by-step explanation:

{(3, 7), (3, 6), (5, 4), (4, 7)} Is not a function

{(1, 5), (3, 5), (4, 6), (6, 4)} is a function

{(2, 3), (4, 2), (4, 6), (5, 8)} is not a function

{(0, 4), (3, 2), (4, 2), (6, 5)} is a function

the flux of curI(F) through the surface area in the figure as with integral:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

First, we calculate the curl of F: curI(F) = (2z, -2x, 2y).

Next, we apply Stokes' Theorem to calculate the flux of curI(F) through the surface in the figure. We start by computing the line integral of F around the boundary of the surface. This is given by:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

We can now evaluate this line integral by splitting it into a sum of integrals:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

= 2∫x dx + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32∫dz + 4∫yz dz

= 2x^2/2 + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32z + 4yz^2/2

= x^2 + 4yz∫dx + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

Finally, we can evaluate the flux of curI(F) through the surface in the figure as:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

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Postage of the total cards is 20(.17w + .44) = 15.60 (word problem)

given, total no of cards = 20

cost of each card = .44

additional cost for each ounce = .17

total cards = 20(.17w + .44) = $15.60

Word Problems:

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The answer is 53

It is the process of substituting values of individual respective variables and solving using elementary arithmetic operations.

Given here, the expression as 8 - (m/n) + p² & substituting  the values as m=8 , n=2 , p=7 we get

8- 8/2 + 7² = 8-4+53

                  = 53

Hence, the final answer is equal to 53

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The function that has the least minimum value is the following function.

Function k(x).

From the graph given, looking at it's vertex, the minimum value of function f(x) is given as follows:

-7.

From the table given, the minimum value of function g(x) is given as follows:

-5, due to the symmetry from x = 0 to x = 2.

Function h(x) is defined as follows:

h(x) = 2(x - 1)².

Which has a minimum value of zero, as the y-coordinate of the vertex is not changed with the transformation.

Using a graphing calculator, as shown by the image at the end of the answer, the minimum value of function k(x) is given as follows:

-9.

Which is the least minimum value of all these functions.

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The root of a tree is the vertex from which all other vertices can be reached by following edges. The root of a tree is the only vertex that does not have an incoming edge.

In a rooted tree, a vertex is called a leaf if it has no children (i.e., it does not have any edges going out from it). Internal vertices are those that have children and are connected by edges to other vertices in the tree. If a vertex d is the root of a tree, the subgraph with d as its root is defined as the set of vertices that can be reached from d by traversing its edges, as well as the edges connecting them. The root is the only vertex that does not have an incoming edge, and all other vertices can be reached from the root.

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To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.

Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:

x0 = a

x1 = a + (b - a)/n

x2 = a + 2(b - a)/n

...

xn = b

The width of each subinterval is (b - a)/n.

We can then use these points to define the upper sum and lower sum as follows:

Upper sum = ∑ (b - a)/n * max(f(x))

Lower sum = ∑ (b - a)/n * min(f(x))

where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.

To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.

Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.

For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.

In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.

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The population standard deviation of {5, 8, 8, 5} is 3

The given population is

{5, 8, 8, 5}

The mean of the population = Sum of the terms /  Number of Terms

Find the values and substitute the values in the equation

Sum of terms = 5 + 8 + 8 +5

= 26

Number of terms = 4

The mean of the population= 26 / 4

= 6.5

The variance of the population = (5 - 6.5)^2 + (8 - 6.5)^2 + (8 - 6.5)^2 + (5 - 6.5)^2

= (-1.5)^2 + (1.5)^2 + 1.5^2 + (-1.5)^2

= 2.25 + 2.25 + 2.25 + 2.25

= 9

The standard deviation of the population  = [tex]\sqrt{9}[/tex]

= 3

Therefore, the standard deviation is 3

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As per the estimated percentage, the test statistic is 0.6167 or 61.67%

What is the percentage?

The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have given that in Arkansas than Virginia. the sample results show that rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.

And we need to find the test statistics.

While we looking into the given situation we have identified the following values,

=> H0 : p = 0.577

=> Ha : p ≠ 0.577

Now, we have estimated the proportion of stay-at-home residents in Arkansas is calculated as,

Here the Proportion of stay-at-home residents in Arkansas is written as,

=> p = 74/120 = 0.6167

Therefore, the test statistic is 0.6167.

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The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.

What is multiple regression?

A probit model is a type of regression in statistics where the dependant variable can only take two values.

We have:

Regress smoker on cubic polynomials of age

If we use linear probability model.

Here the data are missing, but we can say about the estimate that:

Only the estimate intercept is statistically significant at the 5% level is wrong,

Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.

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The cost of the boots is (b) $100

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

Markup rate = 50%

Markup price of the boot = $150

The cost of the boots can be calculated using the following equation

Markup price of the boot = cost of the boots * (1 + Markup rate)

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

150 = cost of the boots  * (1 + 50%)

This gives

150 = cost of the boots  * (1.5)

Divide by 1.5

cost of the boots = $100

Hence, the cost of the boots is $100

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Answer:

the degree is 6

Step-by-step explanation:

Answer:

.5648

Step-by-step explanation:

i am good at math :)

Answer:

= 56 + 0.048

= 56.048

Step-by-step explanation:

560 tenths + 48 thousandths

= 560 × 0.1 + 48 × 0.001

= 56 + 0.048

= 56.048

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Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.

Option (C) is the correct one.

Given, Two sides and an angle are given below.

we have to determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all.

If b = 5, c = 6 and B = 20 degrees in the triangle.

On using the concept of Laws of Sines, we get

sinA/a = sinB/b = sinC/c

sin 20°/5 = sin C/6

0.34/5 = sin C/6

0.007 = sin C/6

sin C = 0.042

C = 2.41

So, the angle C be 2.41 degrees.

which implies that no triangle can be formed or produced with the given data of the triangle.

Hence, No triangles are produced.

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Refer to the photo taken. Please rate :)

In the new graph, the price appears that is increase from 2002 to 2003 is 25% and 100%. Hence, option A is correct.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.

Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the data mentioned in the question,

Average cost to rent studio in 2002 = 400 and,

Average cost to rent studio in 2003 = 500

Then percent increase from year 2002 to 2003 will be,

% increase = (500 - 400)/400 × 100

% increase = 25%

Then, % increase from 2002 to 2003 is 25%,

(200 - 100)/100 × 100 = 100%.

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The probability of selecting a student that drink both coffee and tea is

1/10.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

From the algebra of sets, we know n(A∪B) = n(A) + n(B) - n(A∩B).

A university polls 200 students. 80 students drink tea, 140 drink coffee, and 30 drink neither.

Therefore,

200 = 140 = 80 - N(A∩B).

200 = 220 - N(A∩B).

N(A∩B) = 20.

So, out 0f 200 students 20 drink both.

Therefore the probability of students drink both is,

= 20/200.

= 1/10.

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Answer:

x=8

Step-by-step explanation:

Simplify 2(x+1)−x.

Simplify each term.2x+2−x=10

Subtract x from 2x.x+2=10

Move all terms not containing x to the right side of the equation.

Subtract 2

from both sides of the equation.x1−2

Subtract 2 from x = 10-2

subtract 2 from 10

hope that helps!

Answer:  8

Step-by-step explanation:

First, let's write out the equation:

2(x+1) - x = 10

So, we need to find the value of x.

Let's take an estimate of what x could be.

So, we know it has to be 5-10, because that is over when we add x to one, then multiply by 2.

So, numbers 5-7 couldn't be it, because the value of x is lower than 10. So, we have to guess if it's 8 or 9

Let's use both numbers to solve if it's correct:

2(8+1) - 8 =10

18 - 8 = 10

or

2(9+1) - 8 =10

20 - 8 = 12

So, we have 8 as our answer.

So, x = 8

The total hours worked is 40 hours, the total wage for the week is $238, the Total tax is 12.15%, and the paycheck after taxes is $209.44

Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses.

Given:

Pay Rate: $5.95 per hour,

Hours Worked: M-8, T-7, W-8, T-9, F-8,

FICA Tax (7.65 %),

State Income Tax (at 3%),

City Income Tax (1.5%),

Calculate the total working hours as shown below,

Total working hours = 8 + 7 + 8 + 9 + 8 = 40 hours

Calculate the total tax,

Total tax = 7.65 + 3 + 1.5 = 12.15%

Calculate total wage,

Total wage =  no of hours × 5.95

Total wage = 40 × 5.95 = $238

Paycheck after-tax deduction = Total wage - 12.15 % of $238

Paycheck after-tax deduction = 238 - 28.56

Paycheck after-tax deduction = $209.44

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Answer:

See Attached Images

Step-by-step explanation:

First, draw the lines without < or > signs, just use equals signs:

3x + y = -3

y = -3x - 3 (slope of -3, y-intercept at (0,-3) )

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 4

Now shade the region above and including line (1) and below and including line (2).

Note for similair problems: If you have to multiply or divide by a negative number when solving for y, remember to flip the < or > sign to the other one when determining where to shade on the graph.

A commuter passes through two traffic lights on their way to and from work. Let X1 represent the number of lights the commuter must stop at while traveling to work, and X2 represent the number of lights he must stop at. stop when returning from work. It is connected to the population mean.

a) P(To=0) = 0.2*0.2 = 0.04

P(To=1) = 0.2*0.4 + 0.4*0.2 = 0.24

P(To=2) = 0.4*0.4 + 0.2*0.2 + 0.4*0.2 = 0.36

P(To=3) = 0.2*0.4 + 0.4*0.4 = 0.24

P(To=4) = 0.2*0.2 = 0.04

b) µTo = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 = 2

It is equal to the population mean µ.

c) sTo2 = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 = 0.56

It is equal to the population variance s2.

d) E(To) = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 + 5*0 + 6*0 + 7*0 + 8*0 = 2

V(To) = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 + (5-2)2*0 + (6-2)2*0 + (7-2)2*0 + (8-2)2*0 = 0.56

e) P(To = 8) = 0

P(To = 7) = 0.2*0.2*0.2*0.2 = 0.0016

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The graph of the polynomial is given below.

The interval of the polynomial is

(-∞, 3) U (-3, -1) U (-1, ∞).

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

f(x) = x³ + 4x² + 3x

The graph of this polynomial is given below.

The interval of the graph are:

(-∞, 3) U (-3, -1) U (-1, ∞)

Thus,

The graph is given below.

The interval of the graph is (-∞, 3) U (-3, -1) U (-1, ∞).

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Therefore for computing the annual return we simply fund with coupon rate in percentage is 90 dollar

What is a percent simple definition?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

The additional sum of money over the principal sum of deposit or loan is called compound interest.

The yearly return on $ 3 ,000 investment will be $90.

This can be estimated as:

Investment = $3,000

Coupon rate in percentage = 3%

The computation of yearly return can be estimated as:

= $3,000 × 3%

= $90

Therefore for computing the annual return we simply fund with coupon rate in percentage.

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The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).

The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..

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The area of a rhombus is --336[tex]in^{2}[/tex]

A rhombus is a type of parallelogram where all the sides are equal in length. opposite sides of a rhombus are parallel to each other and opposite angles are equal.

The diagonals of a rhombus bisect each other at the right angle.

let, another diagonal of a rhombus is -b in

another diagonal of a rhombus, b = [tex]\sqrt{4x^{2} -a^{2} }[/tex]

                  = [tex]\sqrt{4*25^{2} - 14^{2} }[/tex]

                  =[tex]\sqrt{4*625 - 196}[/tex]

                  =[tex]\sqrt{2500 - 196}[/tex]

                 = [tex]\sqrt{2304}[/tex]

                 = 48 in

Area of the rhombus (A) = [tex]\frac{a * b }{2}[/tex]

                                       = [tex]\frac{14 * 48 }{2}[/tex] [tex]in^{2}[/tex]

                                       = 7 * 48 [tex]in^{2}[/tex]

                                      = 336 [tex]in^{2}[/tex]

The area of a rhombus is --336[tex]in^{2}[/tex]

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