(08.02 MC)
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The area of the triangle P’Q’R’ is 384 square units

The formula for calculating the area of a triangle is expressed as:

If the right triangle PQR has sides of length 6 units, 8 units, and 10 units is dilated by a scale factor of 4 units, hence:

Area of the triangle P’Q’R’ = 0.5(24)(32)

Area of the triangle P’Q’R’ = 384 square units

Hence the area of the triangle P’Q’R’ is 384 square units

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The value of the probability is 3.75.

It is a branch of mathematics. The possibility of the outcome of any random event is termed as probability. The range of the probability must be between o to 1. Here o indicates impossibility of an event and 1 indicates certainty. Probability can be expressed in proportions. Probability deals in finding the occurrence of an event. It is based on the possible chances of something that happen. Probability is of 3 types. They are:

1.Theoretical probability

2.Experimental probability

3.Axiomatic probability

P(N=2)=P(TT)=14

P(N=3)=P(HTT,THT)=28

P(N=4)=P(HHTT;HTHT;THHT)=316

P(N=5)=432

P(N=6)=1−14−28−316−432=316

E(N)=2(14)+3(28)+4(316)+5(432)+6(316)=154=3.75

The value of the probability up to 2 decimal places is 3.75

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Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

We have that Troya had 52000 people in 2010 and the population is increasing at a rate of 2 percent. If this growth rates continues the equation is,

Where x represents the number of years after 2010 and y represents the number of people x years after 2010.

Answer:

Why? Sorry I dont so that lol

Step-by-step explanation:

Have a nice day? <3

Answer:

answer would be -10 for x

Answer:

your answer is x= -10

Step-by-step explanation:

i cant put in the image from the calculator but i hope this still helps

if im wrong pls let me know

but if im right may i please be marked braniliest

Answer:

$41.05

Step-by-step explanation:

\(\frac{40}{100} =\frac{16.42}{x}\)

\(40x=1642\)

\(x=41.05\)

So, the original price is $41.05.

To compare the profiles of temperature and salinity for Argo Float 108683 in the Eastern Tropical North Pacific on April 16, 2012 (Profile 001) and April 16, 2016 (Profile 138), follow these steps:

Locate the data: Visit the Argo Data Management site (http://www.argodatamgt.org/) and search for Argo Float 108683 using the ArgosID. Download the data for the specific dates (April 16, 2012, and April 16, 2016).

Plot the graphs: Using a data analysis tool like Excel or Python, create plots of temperature with depth and salinity with depth for both profiles. Ensure that you label the axes and include units.
Compare the profiles: Examine the shapes of the temperature and salinity profiles for both years, focusing on the mixed layer depth and the main thermocline depths.

Based on general ocean circulation, we would expect temperature profiles in the Eastern Tropical North Pacific to show a well-mixed layer near the surface with a rapid temperature decrease below the mixed layer depth, leading to the main thermocline.

Differences between years could be attributed to several factors, such as variations in seasonal weather patterns, changes in ocean circulation, or anomalies like El Niño events. These factors could affect the mixed layer depth, main thermocline depths, and surface features, leading to differences in the temperature and salinity profiles for the two years.

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y =\((x/2)^2 + 1 or y = (x/2)^2 + 1\)

The curve represents a parabola opening upwards. It is symmetric about the y-axis.

Let's eliminate the parameter t and sketch the curves for each exercise:

1. x = t^2 + 2t, y = t + 1

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 + 2t = x

t = -1 ± √(x + 1)

Substituting the expression for t into the equation y = t + 1, we get:

y = (-1 ± √(x + 1)) + 1

y = -√(x + 1) or y = √(x + 1)

The curve represents two branches of a parabola opening upwards. It is symmetric about the y-axis.

2. x = cos(t), y = sin(t), (0, 2π]

Eliminating the parameter t, we obtain:

\(x^2 + y^2 = cos^2(t) + sin^2(t) \\= 1\)

The curve represents a circle centered at the origin with a radius of 1. It covers a full revolution (360 degrees or 2π) in the counterclockwise direction.

3. x = 2t + 4, y = t - 1

By eliminating the parameter t, we have:

t = (x - 4) / 2

Substituting this expression into the equation for y, we get:

y = ((x - 4) / 2) - 1

y = (x - 6) / 2

The curve represents a line with a slope of 1/2 and a y-intercept of -3. It is inclined upwards from left to right.

4. x = 3 - t, y = 2t - 3, 1.5 ≤ t ≤ 3

Eliminating the parameter t, we have:

t = 3 - x

Substituting this expression into the equation for y, we get:

y = 2(3 - x) - 3

y = 6 - 2x - 3

y = -2x + 3

The curve represents a line with a slope of -2 and a y-intercept of 3. It is inclined downwards from left to right.

\(5. x = 2t^2, y = t^4 + 1\)

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 = x/2

t = ±√(x/2)

Substituting the expressions for t into the equation y = t^4 + 1, we get:

y = (√(\(x/2))^4\) + 1 or y = (-√\((x/2))^4\) + 1

\(y = (x/2)^2 + 1 or y = (x/2)^2 + 1\)

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The angular diameter of an object is the measure of the object's apparent size as seen from a specific point. To calculate the distance to the object.

We can use the formula:

distance = size / angular size.

In this case, the angular diameter is given as 10 arc-seconds (which is a measure of angle) and the distance is 50,000 meters.

Plugging these values into the formula, we get: distance = 50,000 / 10 = 5,000 meters.

Therefore, the distance to the object is 5,000 meters.

Summary: The object with an angular diameter of 10 arc-seconds is located at a distance of 5,000 meters.

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Answer:

0.7x - 1.4 =-3.5

      +1.4   +1.4    Step one: add 1.4 to both sides to cancel out 1.4

0.7x = -2.1

----      -----         Step two: divide both sides by 0.7

0.7      0.7

x = -3              The answer is x = -3.

Answer:

B

Step-by-step explanation:

The value of function f'(-4) = 3/16.

To find f'(-4), we can use the quotient rule.

That is,

f'(x) = f(x)/g(x)
f'(-4) = (f(-4)*g'(-4) - g(-4)*f'(-4))/(g(-4))^2

Substituting in the given values, we get,
f'(-4) = (9*6 - 8*6)/(8)^2
f'(-4) = 3/16

Therefore, the value of function f'(-4) = 3/16.

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The value of function f'(-4) = 3/16.

To find f'(-4), we can use the quotient rule.

That is,

f'(x) = f(x)/g(x)
f'(-4) = (f(-4)*g'(-4) - g(-4)*f'(-4))/(g(-4))^2

Substituting in the given values, we get,
f'(-4) = (9*6 - 8*6)/(8)^2
f'(-4) = 3/16

Therefore, the value of function f'(-4) = 3/16.

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Appling percentages, if Ms. Lama marked the price of a a cosmetic items 25% above it's cost price and the cost price of the cosmetic items was Rs.4400 sold with 13% VAT, the selling price is $6,215.

The selling price is determined by increasing the cost price by the markup percentage and then the VAT percentage.

Cost price of the cosmetic items = Rs.4,400

Markup = 25%

Markup factor = 1.25 (1 + 0.25)

Marked up price = Rs.5,500 (Rs.4,400 x 1.25)

VAT = 13%

Markup ith VAT factor = 1.13 (1 + 0.13)

Selling price = Rs.6,215 (Rs.5,500 x 1.13)

Thus, Ms. Lama sold the cosmetic items at Rs.6,215, 13% VAT inclusive.

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The first city receives an average of 373.5 millimeters of rain each year.

Given that the second city receives an average of 240.9 millimeters of rain annually, we are told that the first city receives an average of 132.6 millimeters more rain than the second city. To find the average rainfall of the first city, we add this average difference to the rainfall of the second city.

Average rainfall of the first city = Average rainfall of the second city + Average difference

Average rainfall of the first city = 240.9 mm + 132.6 mm

Average rainfall of the first city = 373.5 mm

Thus, the first city receives an average of 373.5 millimeters of rain each year.

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Answer:

Perimeter of ΔDBC = 48 units

Step-by-step explanation:

It's given in he question,

ΔABD ~ ΔDBC

Therefore, by the definition of similar triangles,

Corresponding sides of both the triangle will be proportional.

\(\frac{AB}{DB}= \frac{BD}{BC}= \frac{AD}{DC}\)

\(\frac{9}{12}= \frac{12}{16}= \frac{AD}{DC}\)

\(\frac{3}{4}=\frac{AD}{DC}\)

AD = \(\frac{3}{4}DC\) ----------(1)

Since, perimeter of ΔABD = 36,

AB + BD + AD = 36

9 + 12 + AD = 36

AD = 36 - 21

AD = 15

From equation (1),

15 = \(\frac{3}{4}(DC)\)

DC = 20

Perimeter of ΔDBC = DB + BC + DC

                                = 12 + 16 + 20

                                = 48

Therefore, perimeter of ΔDBC = 48 units is the answer.

Answer:

median: 9

mean:11

mode: 7 or 9

range 13

Step-by-step explanation:

hope it helped!

Answer: B

Step-by-step explanation:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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Answer:

Disagree

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money

Step-by-step explanation:

The given expression for the hourly earnings of Regina, Phil and Joseph are as follows;

Regina: 6.50·h + 16

Phil: 3·(2.5·H + 5)

Joseph: 7.50·h + 10

The number of hours worked = h

The hourly earnings for Phil equated to the hourly earnings of Joseph gives;

3·(2.5·H + 5) = 7.50·h + 10

Simplifying we get;

3 × 2.5·h + 3 × 5 = 7.50·h + 10

7.5·h + 15 = 7.50·h + 10

Which gives

15 =  10 + 5 = 10 which is not correct.

Therefore, when both Phil and Joseph works the same number of hours, in the week, Phil will earn 5 units more Joseph

However, we have that, where Joseph works extra 5/7.5 or 2/3 hours more than Phil, every week, they will earn the same amount of money every week.

Therefore, it is possible for Phil and Joseph to earn the same amount of money when Joseph works extra 2/3 hours more than Phil which gives;

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money.

Answer:

x = 37 /8

Step-by-step explanation:

Answer:37/8

Step-by-step explanation:

1/8-(-5+3/4)=x+(-1/4)

or, 1/8+5-3/4=x-1/4

or, 41/8-3/4=x-1/4

or, 35/8=x-1/4 (taking LCM)

or, x=1/4+35/8

x=37/8

Plz mark me brainliest.

Answer:

x=4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

8x+6=13x-14

+14        +14

8x+20=13x

-8x      -8x

20=5x

20/5=4

5/5=1

4=x

I hope this helps! :D

Pls give thx and brainliest if I’m right ;)

The term "content loaded in a test of the hypotheses" refers to the data and information used to perform the hypothesis test, which in this case resulted in a calculated p-value of 0.03.

Based on the information provided, the calculated p-value of 0.03 is less than the level of significance of 2%. This means that the null hypothesis can be rejected and the alternative hypothesis can be accepted.

Therefore, the decision is to reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The term "content loaded in a test of the hypotheses" refers to the data and information used to perform the hypothesis test, which in this case resulted in a calculated p-value of 0.03.

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Answer:

$3575

Step-by-step explanation:

65000×0.055=3575

plzz mark me brainlest, need it to level up

h = kv is the formula connecting the height reached and the initial velocity

A variation is a relation between a set of values of one variable and a set of values of other variables.

From the information, the stone is thrown upwards, the height, h, it reaches is proportional to the square of the initial velocity, v.

Since the height, h is proportional to the square of the initial velocity, v.

We can write the formula as follows:

h α v

h = kv   (where k is constant of proportionality)

Therefore, the formula connecting the height reached and the initial velocity is h = kv  

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Answer:

1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.

2.

2 = a + b

3.

0 = 2a + b

4.

a = -2

b = 4

Step-by-step explanation:

the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.

1. that means that for x=1

3 - x = ax² + bx

so,

3 - 1 = a×1² + b×1 = a + b

2 = a + b

we have to use a=2 and b=3

2 = 2 + 3 = 5

2 is not equal 5, so the assumed equality is false, so the function is not continuous there.

2. point 1 gave us already the working relationship between a and b.

2 = a + b

only if that is true, is the function continuous at x=1.

3. now for x=2

5x - 10 = ax² + bx

5×2 - 10 = a×2² + b×2 = 4a + 2b

10 - 10 = 4a + 2b

0 = 4a + 2b

0 = 2a + b

4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.

so, they establish a system of 2 equations with 2 variables.

2 = a + b

0 = 2a + b

a = 2 - b

0 = 2×(2-b) + b = 4 - 2b + b = 4 - b

b = 4

therefore

a = 2 - 4 = -2

5. I cannot draw a graph here.

just use now the function

3 - x, x < 1

‐2x² +4x, 1 <= x < 2

5x - 10, x >= 2

a) The number 65 represents the constant speed of the car in miles per hour.

b) The car travels 97.5 miles in 1.5 hours.

c)  It takes the car 0.4 hours (or 24 minutes) to travel 26 miles at this speed.

Speed is the rate at which an object travels a certain distance in a given amount of time. It is expressed as distance traveled per unit of time, usually in miles per hour or meters per second.

a) The number 65 represents the constant speed of the car in miles per hour. This means that the car is traveling at a constant rate of 65 miles per hour regardless of the time it takes to travel that distance.

b) To find out how many miles the car travels in 1.5 hours, we simply substitute t = 1.5 into the equation and solve for d:

d = 65t

d = 65(1.5)

d = 97.5

Therefore, the car travels 97.5 miles in 1.5 hours.

c) To find out how long it takes the car to travel 26 miles at this speed, we again use the equation and solve for t:

d = 65t

26 = 65t

t = 26/65

t = 0.4 hours

Therefore, it takes the car 0.4 hours (or 24 minutes) to travel 26 miles at this speed

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Full Question:

Although part of your question is missing, you might be referring to this full question:

A car is traveling down a highway at a constant speed, described by the equation d=65td = 65 t, where d represents the distance, in miles, that the car travels at this speed in t hours.

a) What does the 65 tell us in this situation?

b) How many miles does the car travel in 1.5 hours?

c)How long does it take the car to travel 26 miles at this speed?

This statement is true

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring. Probability is the measure of the likelihood of a random event happening, and it is expressed as a number between 0 and 1, with 0 implying that the event would never occur and 1 implying that it is certain to happen.

The probability of an event happening is referred to as its likelihood. Probability can be expressed as a fraction, percentage, or decimal, and it is a vital tool in statistics. It is frequently utilized in mathematics to estimate real-world situations that involve random variables such as coin flips, weather patterns, stock market trends, and even sporting events.

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Rounded to three decimal places, the probability is approximately 0.457.

To find the probability that at least two bills must be selected to obtain a first $10 bill, we need to consider two scenarios.

Scenario 1: The first bill selected is a $10 bill. There are six $10 bills in the wallet, so the probability of selecting a $10 bill first is 6/15.

Scenario 2: The first bill selected is not a $10 bill. In this case, we need to calculate the probability of not selecting a $10 bill on the first draw, and then selecting a $10 bill on the second draw.

There are nine non-$10 bills in the wallet initially (3 $5 bills + 6 $1 bills), and there are a total of 14 bills left in the wallet after the first draw (15 bills - 1 non-$10 bill).

Therefore, the probability of not selecting a $10 bill on the first draw is 9/15, and the probability of selecting a $10 bill on the second draw is 6/14.

Multiplying these probabilities together, we get (9/15) * (6/14) = 54/210.

To obtain the final probability, we sum the probabilities from both scenarios: (6/15) + (54/210) = 16/35.

Rounded to three decimal places, the probability is approximately 0.457.

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Here are the properties on the left and their corresponding methods for showing that the property holds on the right:

Properties on the left:

Method for showing that the property holds on the right:

f is one-to-one

Show that f(a) = f(b) implies that a = b. f is onto

Show that for every b in B, there is an a in A such that f(a) = b. f is a bijection

Show that f is both one-to-one and onto. The given properties pertain to functions and set theory. Here, f(a) and f(b) are two elements in the function domain.

A function is said to be one-to-one if distinct elements in the domain have distinct images in the range. In contrast, a function is called onto if every element of the range is an image of at least one element in the domain.

A function is called a bijection if it is both one-to-one and onto, meaning that every element in both domains corresponds to a unique element in the other domain.

To show that a function satisfies one of these properties, we must perform a specific method of proof. These methods are as follows:

To prove that f is one-to-one, we must show that f(a) = f(b) implies that a = b.

To prove that f is onto, we must show that for every b in B, there is an a in A such that f(a) = b.

To prove that f is a bijection, we must show that f is both one-to-one and onto.

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