Triangle A'B'C' is the image of AABC under a reflection. Given A(-2, 5), B(0, 9), C(3, 7), A'(5,-2), B'(9, 0), and C(7,3), what is the line of reflection?

Answer:

x = 6

Step-by-step explanation:

x + 2(4x-6) = 42

x + 8x - 12 = 42

9x = 42 + 12

9x = 54

9/9 x = 54/9

x = 6

The measures, using the normal distribution and the central limit theorem, are given as follows:

a) Probability of at least 4.03 ounces: 0.9192 = 91.92%.

b) Probability of 74% that it is between 4.04 ounces and 4.16 ounces.

c) Probability of 78% that it is greater than 4.06 ounces.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters regarding the amount of juice squeezed from these oranges are given as follows:

[tex]\mu = 4.10, \sigma = 0.2, n = 16, s = \frac{0.2}{\sqrt{16}} = 0.05/tex]

The probability that the sample mean amount of juice will be at least 4.03 ounces is one subtracted by the p-value of Z when X = 4.03, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (4.03 - 4.10)/0.05

Z = -1.4.

Z = -1.4 has a p-value of 0.0808.

1 - 0.0808 = 0.9192.

Considering the symmetry of the normal distribution, the middle 74% of the measures is bounded by:

Hence the lower bound is:

[tex]Z = \frac{X - \mu}{s}[/tex]

-1.125 = (X - 4.10)/0.05

X - 4.10 = -1.125 x 0.05

X = 4.04.

The upper bound is:

[tex]Z = \frac{X - \mu}{s}[/tex]

1.125 = (X - 4.10)/0.05

X - 4.10 = 1.125 x 0.05

X = 4.16.

The probability is ​78% that the sample mean amount of juice will be greater than the 22th percentile, which is X when Z = -0.77, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.77 = (X - 4.10)/0.05

X - 4.10 = -0.77 x 0.05

X = 4.06 ounces.

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If a waste bin is in the shape of a cylinder. the diameter of the base is 20cm and the height is 25cm. The volume of the waste bin is: 7,853.98 cm³.

Using this formula to find the volume

Volume (v) = π (d/2)² h

Where:

d= diameter =  20 cm

h = height =25 cm

Let plug in the formula

Volume (v) = π × (20/2)² × 25

Volume (v) = π × 100 × 25

Volume (v) = 7,853.98 cm³

Therefore 7,853.98 cm³ is the volume.

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The broker charged $100.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total shares = 1000

Price for each shares= $5.

So, the total price of 1000 shares= $5000

If broker is charging a flat percentage of 2% for a trade.

Then, the broker charged for 1000 trade

= 5000 x 0.02

= $100.

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The axis of symmetry of function y = -|x + 10| is at y = 0

Axis of symmetry is an imaginary straight line which divide the function into two equal parts.

Axis of symmetry creates a mirror image of other part.

If we fold the two parts then the parts will superimposed.

Given function,

y = -|x + 10|

is in form y = a |x - h| + k

here , (h, k) is vertex

Comparing the form to the given equation

(h, k) = (-10 , 0)

which means graph is opens upward

and a = -1

Hence, the equation of axis of symmetric is at y = 0

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Answer:

−16x − 20y + 17

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

(15x+3)° = 108 (vertically opposite angles)

15x = 108-3

15x = 105

x = 105/15

x =7

4 minutes is equivalent to 240 seconds.

There is 60 seconds in a minute.

60x4 = 240.

Answer:

240 Seconds.

Step-by-step explanation:

1 Minute is 60 Seconds, SO 4 x 60 = 240!

The quadratic functions in this problem are listed as follows:

The definition of a quadratic function is presented as follows:

y = ax² + bx + c.

In which the leading coefficient a has to assume a value different of zero.

Another format to represent a quadratic function is making the input variable y and the output variable x, which is an exchange of the conventional notation, hence:

x = ay² + by + c.

The non-quadratic functions in this problem are:

All the other functions are quadratic functions, as they have two as the highest exponent, with a leading coefficient different of zero.

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The critical values for the chi-square distribution, with a sample size of 4 and a confidence level of 98 percent, are of:

0.2971 and 13.2767.

The critical value for the chi-square distribution is obtained inserting these following information into a calculator:

In the context of this problem, with a sample size of 4 and a confidence level of 98 percent, the parameters are given as follows:

Inserting these information into the calculator, the critical values are given as follows:

0.2971 and 13.2767.

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Explanation:

We know the final price is $899 and $365 is constant price:

899 = 365 + 89x

We need to find x, the amount of hours, by simplifying:

534 = 89x

x= 6

6 hours of labor

Answer:

f(x) = -3x+1

Step-by-step explanation:

every straight graph has an equation f(x) = m * x + b

when the graph goes up when you look at it from left to right, m is a positive number. when it goes down, then m is negative.
the value of m you can read when you go 1 to the right and then count how many you need to go up/down to meet the graph. in this picture, you need to go down 3.
So m = -3
b is how many you habe to go up (+) or down (-) from the center point 0
so in this case you see on the picture that the graph is hitting the y line on 1

so your equation is -3x + 1

Answer: a) $78 per day

b) $21,352.50

Step-by-step explanation:

a) 60x10=600

600x0.13= $78 per day

b) 15x10=150

150x0.13=$19.50 per day

19.50x365= $7,117.50 per year (with a 15watts lightbulb)

$78x365=$28,470 per year (with a 60watts lightbulb)

$28,470-7,117.50= $21,352.50

Explanation:

To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:

a² + b² = c² (c is always hypotenuse)

So:

a² + 6² = 9²

a² = 9² - 6²

a² = 81 - 36

a² = 45

a = sqrt45

Now we do the same thing for the other triangle:

x² + 5² = sqrt45²

x² + 25 = 45

x² = 20

x = 2√5 or 4.5...

Step-by-step explanation:

Formula for distance travelled:

x= ut + 1/2at^2

x is 1.4km, convert this to m since acceleration is in m, = 1400m

u is initial velocity, in this case assume 0

a is acceleration, = 4m/s^2

t is unkown and what we want to find out

Substitute value into formula,

1400 = 0t + 1/2(4)t^2

1400 = 2t^2

t^2 = 1400/2

t^2 = 700

t = 26.458s

Formula for acceleration:

a = (v-u)/t

at= v-u

Substitute value,

4(26.458) = v - 0

v = 105.832 m/s

The equation that is used to find the length of the legs of the triangle is

0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0

The area of the triangle is 24 square feet.

We know that the area of a triangle is given by the formula

1/2 × base × height.

Now in the attached figure we can see that the length of the base is x feet

The height of the right-angled triangle is (x+2) feet.

So the area of the triangle will be:

area = 1/2 · (x) · (x+2)

or, area = 0.5x(x+2)

But the area of the triangle is 24 square feet. Therefore the Equation to find the legs will be 0.5x(x+2) = 24.

Now if we use the properties of Pythagoras theorem we can write the formula as

hypotenuse² =  sum of squares of legs

10² = x² + (x+2)²

Therefore we get the second equation.

Now simplifying the above equation we get:

10² = x² + (x+2)²

or, 2x² + 4x - 96 = 0

or, x² + 2x - 48 = 0

This is the third option.

Therefore the required equation are:

0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0 .

Disclaimer: The missing image of the triangle is attached below.

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The most appropriate design for the study would be the experiment. We must apply the new repellent to a group of 5 dogs and the popular repellent to another group of 5 dogs. This will allow us to establish if the new repellent is more effective.

The most appropriate research design for this case is the experiment because it will allow us to check if our hypothesis is true.

The research design of experiment should be implemented as follows. First of all we must apply the new repellent to a group of 5 dogs and in parallel, we must apply the popular repellent to another 5 dogs. After a while we must examine them to check the effects of the repellent.

In this way we will know if the new repellent is more effective than the popular repellent. Additionally, we can establish how effective it is taking into account that we used a population of 5 dogs.

This design would benefit my research because it allows me to establish whether my hypothesis is true. Additionally, it allows me to establish how much more effective one repellent is than the other.

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This is not a prime factorization.

The correct prime factorization is [tex]2^5*3*5^4*11^2[/tex]

=======================================================

Further Explanation:

The expression your teacher gave you is not a prime factorization because the 8 isn't prime.

8 = 2*2*2 = [tex]2^3[/tex]

If we replace 8 with [tex]2^3[/tex], then we go from

[tex]2^2*3*5^4*8*11^2[/tex]

to

[tex]2^2*3*5^4*2^3*11^2[/tex]

and that rearranges to

[tex]2^2*2^3*3*5^4*11^2[/tex]

Then we can simplify the [tex]2^2*2^3[/tex] portion to get [tex]2^5[/tex] since we add the exponents while keeping the base '2' the same.

We therefore end up with

[tex]2^5*3*5^4*11^2[/tex]

as the correct prime factorization. Each base (2,3,5,11) is a prime number.

---------------

As a check, use your calculator to type in

2^2*3*5^4*8*11^2

and also

2^5*3*5^4*11^2

and you should get the result of 7,260,000 each time. Since we get the same result, this confirms 2^2*3*5^4*8*11^2 = 2^5*3*5^4*11^2

A student ran 6% of the journey.

In this question, we have been given the distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres.

We know that 1 km = 1000 meters

So, 8 km = 8000 meters

So, the percent of the journey he ran,

480/8000 * 100

= 6%

Therefore, A student ran 6% of the journey.

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Answer:

[tex]\frac{19}{20}[/tex]

Step-by-step explanation:

0.45 can be written as  [tex]\frac{9}{20}[/tex] in fractional form and 0.5 can be written as [tex]\frac{1}{2}[/tex].

Whenever adding fractions you need like bases. To do this, multiply the 0.5 fraction by 10/10. This would get you [tex]\frac{10}{20}[/tex].

Adding fractions:

[tex]\frac{9}{20} + \frac{10}{20}[/tex]    ** only add the numerators and leave the denominator as is

= [tex]\frac{19}{20}[/tex]

The selling price per bag whose purchasing price is $2.57 and profit is 41% should be $4.52

What is selling price?

The amount a buyer pays for a good or service is known as the selling price. Selling price may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.

Given in the question,

Number of bags = 700

Purchase per bag = $2.57

Spoilage = 20%

Profit = 41%

Cost of 700 bags of onion = 700*2.57 = $1799

Spoilage of 20% = 700*20% = 140 bags, which means only 560 bags left to sell

Desired profit = 41 percent

Assume Selling Price be SP

Profit percentage = (560*SP - 1799)/1799

0.41 = (560*SP - 1799)/1799

SP = $4.52

Therefore, selling price is $4.53

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Answer:

42 rotten tomatoes would likely be found in 14 boxes.

Step-by-step explanation:

Since [tex]\frac{12}{4} = \frac{3}{1}[/tex] , there are 3 rotten tomatoes in every box.

[tex]\frac{3 * 14}{1 * 14} = \frac{42}{14}[/tex]

3 * 14 = 42, so 14 boxes contain 42 rotten tomatoes.

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

Let take the volume of a closed cylinder as V1.

And take the volume of a closed sphere as V2.

And the radius of the cylinder = radius of the sphere = r

Height of the cylinder = h

If height of the cylinder is four times the radius of the cylinder  which means h = 4r

Volume of the closed cylinder V1 = π × r^2 × h

if h = 4r

Then V1 = π × r × r × 4r

V1= 4π × r^3

Volume of the closed cylinder V1= 4π × r^3

Volume oh the sphere V2 = 4/3 × π × r^3

The ratio of the volume of the cylinder to the volume of the sphere

= V1 / V2 = V1 : V2

V1 : V2 = (4π × r^3) ÷ (4/3 × π × r^3)

V1 : V2 = 4 ÷ 4/3 = 4/1 × 3/4 = 3/1 = 3 : 1

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

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Answer:

98 m

Step-by-step explanation:

A = l * w

8624 = l * 88

l = 8624/88 = 98 m

True. You can look at the direction of the line and automatically know if the slope is a positive or negative number.

The linear equation with positive value of slope goes upwards from left to right and linear equation with negative value of slope goes downwards from left to right.

Thus, it is true that you can look at the direction of the line and automatically know if the slope is a positive or negative number.

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Answer:

D: (neg infinity, pos infinity)

R: [-2, pos infinity)

Step-by-step explanation:

Based on the average profit per game, the total money which this club should expect to earn by the end of the 10-game season is $80.21.

In order to determine a linear equation of the trend line (line of best fit) that models the data points contained in the table, we would have to use a scatter plot.

In this scenario, the number of games would be plotted on the x-axis of the scatter plot while the profit (in dollars) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data points in the table, a linear equation of the trend line is given by:

y = 8.23x - 2.09

By the end of the 10-game season, the average profit per game is given by:

y = 8.23x - 2.09

y = 8.23(10) - 2.09

y = 82.3 - 2.09

y = $80.21.

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Answer:

Step-by-step explanation:

7

Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure Kyle's blood pressure : 149.5

What is blood pressure?
Blood pressure (BP) is the force exerted by moving blood against blood vessel walls. The heart's action of pumping blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) above the atmospheric pressure in the immediate vicinity.

The z-score of a measure X in a set with mean and standard deviation is given by:

Z = (X - μ) / σ

The Z-score calculates the deviation of the measure from the mean in standard deviations. We look at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure exceeds X is calculated by deducting 1 from the p-value.

This issue involves that:
μ = 125
σ = 14
The z-score for Kyle's systolic blood pressure is 1.75, according to his physician.
He therefore has a 1.75 standard deviations higher systolic blood pressure than the mean.

Which of the following best describes how this standardized score should be interpreted?

Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure.

Calculate Kyle's blood pressure in part (b). (Enter a precise quantity as a decimal, fraction, or integer.)
If Z = 1.75, then this is X.

Z = (X - μ) / σ

1.75 = (X - 125) /  14

1.75 x 14 = (X - 125)

24.5 = X - 125

X = 24.5 + 125

X = 149.5

Hence, a) Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure.

b) Kyle's blood pressure is 149.5

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