The triangles are similar.
What s the value of x?

See the attachment for the problem to be answered.

The zeros of f(x)= x²-9 is +3 and -3

The zeros of f(x) = x²-16 is +4 and -4

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. Vertical Asymptotes.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Therefore when f(x) =0

x²-9 = 0

x² = 9

x =√9

x = ±3

therefore the zeros of x²-9 is ±3

The vertical asymptote is 0 and horizontal asymptote is infinity.

x²-16 = 0

x² = 16

x = √16

x = ±4

the vertical asymptote is 0 and horizontal asymptote is infinity.

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A. The probability of no nap is 0.390625, one nap is 0.234375 and two naps is 0.156250. B. The probability of zero naps is 0.152587890625, one nap is 0.3076171875, and two naps is 0.146484375. C. The probability of no nap is 0.02734375, one nap is 0.14453125, and two naps is 0.271484375. D. The probability of no naps decreases as the mean number of naps increases.

A. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of no nap (x=0) is 0.390625, one nap (x=1) is 0.234375, and two naps (x=2) is 0.156250.

B. We can calculate the probability of zero naps, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of zero naps (x=0) is 0.152587890625, one nap (x=1) is 0.3076171875, and two naps (x=2) is 0.146484375.

C. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is eight, so the probability of no nap (x=0) is 0.02734375, one nap (x=1) is 0.14453125, and two naps (x=2) is 0.271484375.

D. We can see from the answers in (b) and (c) that the probability of no naps decreases as the mean number of naps increases, suggesting that a Poisson random variable follows a decreasing probability distribution.

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The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.

How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:

(1 - 0.82)^5 = 0.00033124

So the probability that at least one system detects the theft is:

1 - 0.00033124 = 0.99966876

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The rounding off the value 0.1347 to the nearest tenth is 0.1

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.

Given, 0.1347 round to the nearest tenth

While rounding to the nearest tenth, the value after the digit has been noticed.

In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.

So, 0.1347 becomes 0.1

Hence, the required answer is 0.1

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Answer:

(- 12x ^ 2 + 8x + 27y)/(3x * y ^ 2)

Step-by-step explanation:

Answer: 258 envelopes

Step-by-step explanation:

The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.

The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.

So, in the equation y = rx, the value of r is the constant of proportionality.

In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.

For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.

In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.

In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.

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Answer:

-1/6

Step-by-step explanation:

To solve the inequality 4x-(6x+1)≤ 8x + 2(x-3), we can simplify both sides of the inequality and isolate x on one side:

4x - (6x + 1) ≤ 8x + 2(x-3)

4x - 6x - 1 ≤ 8x + 2x - 6

-2x - 1 ≤ 10x - 6

Subtract 10x from both sides:

-12x - 1 ≤ -6

Add 12x to both sides:

-1 ≤ 6x

Divide both sides by 6:

-1/6 ≤ x

The solution to the inequality is x ≥ -1/6. This means that x is greater than or equal to -1/6, so any value of x that is greater than or equal to -1/6 will satisfy the inequality.

The equation of line r is x = -3/2y + 5/2.

A line's equation is typically expressed in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. A line's equation expresses the y coordinate of any point on the line in terms of its x coordinate. In other terms, a line equation is a formula that can be used to compute the y coordinate of any point on a line given its x coordinate.

In the given question,

The equation of line r is y = -1/3x + 7.

Line r is perpendicular to line q, so the slopes of the two lines must be opposite reciprocals of one another. The slope of line q is 3, so the slope of line r must be -1/3.

To find the equation of line r, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

In line r, (x1, y1) is (1, 3). The slope, m, is -1/3.

Substituting values into the point-slope formula, we have y - 3 = -1/3(x - 1).

Solving for y, we have y = -1/3x + 7.

This equation is written in slope-intercept form, which is the form y = mx + b, where m is the slope and b is the y-intercept.

In line r, the slope is -1/3 and the y-intercept is 7.

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Answer:

162

Step-by-step explanation:

Whether the zero is in the ones position or the tens position, there are only 9 possibilities for each of the other two digits and they can occur (with possible repetition) in either order. That’s 81 for each zero position for a total of 162.

There are 171 three-digit numbers that have exactly one zero. The zero can be in either the tens or units places, yielding 90 and 81 possibilities respectively.

To determine how many 3-digit numbers have exactly one zero, we need to consider the possible placements of the zero. A 3-digit number has three positions: the hundreds place, tens place, and units place. The zero cannot be in the hundreds place, as that would make it a 2-digit number. So, the zero can only have two possible positions: the tens or units place.

For each case:

So, in total, we have 90 + 81 = 171 3-digit numbers with exactly one zero.

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The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

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I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

The estimated percentage of states with an average per capita income greater than 32.5 k  is:we need to use the ogive (cumulative frequency curve) to determine the percentage of states with an average per capita income greater than 32.5k.

Assuming that the ogive is a continuous curve, we can estimate the percentage by finding the value on the horizontal axis corresponding to the 50% mark on the vertical axis, and then subtracting it from 100%. From the graph, we can see that the 50% mark corresponds to a value of around 30 k, which is between the values for Oklahoma and Pennsylvania. To get a more accurate estimate, we can use linear interpolation between these two data points.

Let's assume that the values for Oklahoma and Pennsylvania are

(x₁,y₁) = (25k,40%) and (x₂,y₂) = (35k,60%)

respectively. Then the equation of the straight line connecting these two points is:

(y-y₁) =(y₂-y₁) / (x₂-x₁) * (x-x₁)

Substituting in the values gives:

y - 40 = (0.6 - 0.4)/(35 - 25) * (x - 25)

y - 40 = 0.02(x - 25)

y = 0.02x - 0.5

To find the value of x that corresponds to the 50% mark, we can set y = 50% and solve for x:

50 = 0.02x - 0.5

0.02x = 50.5

x = 2525

So the estimated value for x is 25.25k. Therefore, the estimated percentage of states with an average per capita income greater than 32.5k is:

scss

Copy code

100% - 40% - (10% * (32.5 - 25.25)/(30 - 25))

= 50.5%

Therefore, we estimate that about 50.5% of the states have an average per capita income greater than 32.5k.

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Answer:because

Step-by-step explanation:a

Answer: 0.56

Step-by-step explanation:

Answer: Y would be 4

If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.

The test static is 1.60 and the p-value is 0.1096, null hypothesis is not rejected and the population mean is not significantly  different from $1000.

Assuming normal distribution

N( μ₀ , σ )

In this case N ( 1000, 200)

From a random sample of 64 accounts we get:

n  = 64

x = sample mean      x = 1040

σ = standard deviation of the population     σ = 200

a) Test Hypothesis

Null Hypothesis               H₀          x =  μ₀ = 1000

Alternative Hypothesis    Hₐ          x ≠ μ₀    

The alternative hypothesis implies a two tail-test. Given that  n > 30 and σ is known we will use z-table

b) z(s) = ( x  - μ₀ ) / σ/√n

z(s) = ( 1040 - 1000 ) / 200/ √64

z(s) = 40*8/200

z(s) = 1.60

c) P-value for  z (score 1.6)     p-value = 0.1096

d) If significance level is 0.05  then  α = 0.05  and   α/2 = 0.025

p-value >  α/2        

Then  the z(s) < z(c)      1.6 < 1.96            where  z(c) is z score for α/2

Hence, null hypothesis is not rejected

e) We can claim that at 95 % (of Confidence Interval) the population mean is not significantly  different from $1000.

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Question is not complete. The complete question is :

A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000. 1. State the null and alternative hypothesis. 2. Compute the test statistic. 3. Compute the p-value. 4. Based on the p-value and the significance level of 0.05% make a decision regarding the hypotheses. 5. Interpret your results in the context of the problem.

Option A, which is 4 x 15 + 1 - 5 x 4 x 1, is the correct expression that is equal to 45 x 4 + 5.

To show this, we can simplify the expression as follows:

4 x 51 + 1 - 5 x 4 x 1

= 204 + 1 - 20

= 205 - 20

= 184

Then, we can check if 185 is equal to 45 x 4 + 5:

45 x 4 + 5

= 180 + 5

= 185

Since 185 is equal to 185, it is concluded that an expression that is "equal to" 45 x 4 + 5, is held by option A.

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Answer:

If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T  (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)

Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.

30+70=100

180-100=80

C=80

Step-by-step explanation:

The estimated quantity of dye left in a healthy pancreas 30 minutes after the injection, rounded to the closest hundredth of a grams, is 0.07 grams.

As per the question given,  

After the dye is injected, a healthy pancreas will secrete 4% of the remaining amount of dye each minute. Let's use exponential decay to model the amount of dye remaining in the pancreas over time.

The amount of dye remaining after t minutes can be expressed as:

R(t) = 0.3 * (1 - 0.04)^t

We want to find the amount of dye remaining after 30 minutes, so we can substitute t=30 into the equation and calculate:

R(30) = 0.3 * (1 - 0.04)^30

R(30) = 0.3 * (0.96)^30

R(30) = 0.3 * 0.2312

R(30) = 0.0694

Rounding to the nearest hundredth of a gram, the predicted amount of dye remaining in a healthy pancreas 30 minutes after the injection is 0.07 grams.

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Answer:

  0.09 g

Step-by-step explanation:

You want to know the amount remaining of 0.3 g of dye after 30 minutes if the amount decreases by 4% per minute.

The amount can be modeled by the exponential function ...

  q = a·b^t

where q is the quantity remaining, 'a' is the initial quantity, b is the growth factor per minute, and t is the number of minutes.

The growth factor is related to the growth rate by ...

  b = 1 + growth rate

Here, the growth rate is -4% per minute, so the growth factor is ...

  b = 1 +(-0.04) = 0.96

The initial quantity is 0.3 grams, so the remaining quantity after 30 minutes is ...

  q = 0.30·0.96^30 ≈ 0.08816 ≈ 0.09 . . . . grams

The amount of dye remaining after 30 minutes is predicted to be 0.09 g.

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Answer:

option A is the correct answer.

The length of the third side of ALMN is 20 units.

If AGHI and ALMN are similar, then their corresponding sides are proportional.

Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:

10/8 = 15/12 = x/16

To find x, we can cross-multiply and simplify:

15 × 16 = 12x

240 = 12x

x = 240/12

x = 20

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Answer:

resistant

because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.

Answer:

[tex]g(3) = 11[/tex]

Step-by-step explanation:

Greetings!!!

The given function

[tex] g(x) = x {}^{2} + 2[/tex]

What we are looking now is what will be the value when 3 is substituted in the variable x.

[tex]g(3) = (3) {}^{2} + 2[/tex]

Solve the expression

[tex]g(3) = 9 + 2[/tex]

Add the numbers

[tex]g(3) = 11[/tex]

Thus, the value of g(3)= 11

Hope it helps!!!

The value of the angle 'x' in the right-angle triangle will be 42.99°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'x' is given by the sine of the angle 'x'. Then we have

sin x = 15 / 22

sin x = 0.6818

sin x = sin 42.99°

x = 42.99°

The value of the angle 'x' in the right-angle triangle will be 42.99°.

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To prove QR ~ SR, Use SAS to show triangle PRQ is congruent to

triangle PRS.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given,  PR bisects ZQPS, PQ = 12 units, and PS = 12 units

Now, The two triangles formed PQR and PSR share the same side PR.

Also m∠SPR = m∠QPR, Therefore these two triangles are congruent, and hence QR ~ SR

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A total of 77 new flowers can be planted on the flower bed.

New flowers has to be planted in a circular flower bed that has a diameter of 14 ft.

Each one of the flower requires to square feet of the space.

The radius of the flower bed will be 7 feet.

The area of the flower bed can be calculated by using the formula,

A = πr²

Where r is the radius.

Put in the value of radius to find the area of the flower bed,

A = 3.14 x 7 x 7

A = 153.86 ft²

Now, let us say that N number of floors can be planted,

So,

N)(2) = 153.82

N = 76.93

So we can say that about 77 flowers can be planted on the flower bed.

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Answer: look it up frfr

Step-by-step explanation:

The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and

<k = 125 degree.

When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.

Given:

As, from the Figure

<h + 135 = 180 (Linear Pair)

<h = 180 - 135

<h = 45

and, <g = 135 (Vertical Opposite Angle)

Now, <m + 125 = 180 (Linear Pair)

<m = 180 - 125

<h = 55

and, <k = 125 (Vertical Opposite Angle)

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The following statements best explains the steps to solve the pair of equations graphically is Option D.

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

The first equation is:

y = -x +1

so the slope is -1, and the y-intercept is +1.

The second equation is:

 y = 2x +4

so the slope is 2, and the y-intercept is 4.

The slopes and intercepts are properly described in the last selection.

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The complete question:

A pair of linear equations is shown below:

y = -x + 1

y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)

On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of

Intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of

intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point

of intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of

intersection of the two lines as the solution.