The line y = 3x - 6 is dilated by the scale factor k=3 and centered at the origin. What is the equation of the new


line


I’ll give brainliest

Answer:

11

Step-by-step explanation:

q^4=4

r=1

s^6=6

4+1+6=11

Answer:

Figure 1: 623.2 in²

Figure 2: 679.8 in²

Step-by-step explanation:

For a pyramid total surface area

= Base Area + Lateral Surface Area

Figure 1 is a triangular prism
It's base is an equilateral triangle with side = 20 in
Area of an equilateral triangle = \(\dfrac{\sqrt{3}}{4} a^2\) where \(a\) is the length of the base

So in figure 1, base area = area of equilateral triangle with side a = 20 in
\(\text{Base Area =} \dfrac{\sqrt{3}}{4} \cdot 20^2 \approx 173.2 \;in^2\)

Each lateral side is an isosceles triangle with base = 20 and height = 15
Area of each triangle

\(= \dfrac{1}{2} \cdot base \cdot height\)
\(= \dfrac{1}{2} \cdot 20 \cdot 15 \\\\= 150 \; in^2\)

There are three such lateral sides so total lateral area = 150 x 3 = 450 in²

Total surface area = 173.21 + 450 = 623.2 in²

Figure 2
This is a regular hexagonal pyramid

The base is a regular hexagon of side 10

Base area = Area of hexagon of side 10

Area of a regular hexagon with side a
\(= \dfrac{3\sqrt{3}}{4} a^2\)

Base area of Figure 2
\(= \dfrac{3\sqrt{3}}{4} 10^2\\\\\approx 259.8 \;in^2\)

The lateral surface consists of 6 isosceles triangles each with a base = 10 in and height = 14 in

Area of each isosceles triangle
\(= \dfrac{1}{2} \cdot 10 \cdot 14 \\\\= 70 \;in^2\)

Since there are 6 such lateral triangles, total lateral surface area
= 70 x 6 = 420 in²

So total surface area = base area + total lateral surface area
= 259.8 + 420 = 679.8 in²

Hello, this should help you out!

In this graph, the y values move up 3 units each. Therefore, the blue parabola underwent a translation of 3 units upward.

For further explanation, we see that (0,0) goes up to (0,3), meaning the graph shifted upwards 3 units. So, each y value is raised by positive 3 units!

I hope I was of assistance! #SpreadTheLove! <3

To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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To compute the effect size, we can use the formula:

ES = (|Ž - X|) / SD

where Ž is the mean for Group 1, X is the mean for Group 2, and SD is the standard deviation from either group as the given question.

Using the given values, we have:

Experiment 1: ES = (|78.6 - 73.4|) / 2 = 2.6

Experiment 2: ES = (|78.6 - 73.4|) / 4 = 1.3

Experiment 3: ES = (|78.6 - 73.4|) / 8 = 0.65

From the experiments 1, 2, 3, we can see that the standard deviation increases, the effect size decreases.

It means that the larger SD makes it harder to detect a meaningful difference between the two groups.

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Answer:

the answer would be f(x)=-5x+41

Step-by-step explanation:

you start by calculating the change in y (or f(x)) and dividing that by the change in x or y2-y1/x2-x1. the answer you should get is the slope (mx). from there you calculate the y intercept (b) by simply finding when x=0. now you put it all together, y=mx+b or f(x)=-5x+41

The probability of rolling an even number in at least one of the throws is 31/32 or approximately 0.969.

The probability of not rolling an even number in a single throw is 1/2, since there are three odd numbers and three even numbers on the die. Therefore, the probability of not rolling an even number in five independent throws is (1/2)^5 = 1/32.

The probability of rolling an even number in at least one of the throws is the complement of the probability of not rolling an even number in any of the five throws. So:

P(rolling an even number in at least one of the throws) = 1 - P(not rolling an even number in any of the five throws)

= 1 - (1/32)

= 31/32

Therefore, the probability of rolling an even number in at least one of the throws is 31/32 or approximately 0.969.

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Answer:

60:1

Step-by-step explanation:

60:1 = 366:x

60x = 366

x = 6.1

366 minutes is equivalent to 6.1 hours.

Convert 366 minutes to hours.

\(\boldsymbol{\sf{Therefore \ \to \ 366 \not{m}*\dfrac{1 \ hr}{60\not{m}}=6.1 \ hr }}\)

We conclude that a time of 366 minutes is equal to 6.1 hours

There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60=2.

Answer:

Where are the expressions??

Step-by-step explanation:

x + 2y + x + 2  simplified would be 2x+2y+2

Hope this helps :)

\( \large \sf \underline \bold { \color{violet}Given :}\)

\( \large \sf \underline \red{Now, \: By \: Avarage \: Speed \: = \frac{Distance}{Time} }\)

Its  average speed rounded to 1dp is 54.76 miles per hour.

Using this formula

Average speed=Distance/Time

Where:

Total Distance =230 miles

Time= 4.2 hours

Let plug in the formula

Average speed=230/4.2

Average speed=54.76

Inconclusion Its  average speed rounded to 1dp is 54.76 miles per hour.

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600 cactus wren nests the experimenter would expect to be in the entire 200-acre preserve.

To estimate the number of cactus wren nests in the entire 200-acre preserve, we can use the ratio of the area surveyed to the number of nests found.

Let's call the number of nests in the entire 200-acre preserve "N".

The ratio of the area surveyed to the number of nests found is:

2 acres / 6 nests = 200 acres / N nests

We can use this ratio to find the number of nests in the entire 200-acre preserve:

N nests = 200 acres * (6 nests / 2 acres)

N nests = 200 * 3

N nests = 600

So the experimenter would expect to find approximately 600 cactus wren nests in the entire 200-acre preserve, assuming that the habitat is fairly uniform.

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The college can select 20 groups of three students from the six interviewees for graduate assistantships.

A college plans to interview 6 students for possible offer of graduate assistantships. The college has three assistantships available.

The number of ways in which a college can select three students from the six interviewees for graduate assistantships can be calculated by the combination formula:

C(n, r) = (n!) / [(n - r)! r!],

where n = number of interviewees = 6 and r = number of graduate assistantships available = 3.

C(6, 3) = (6!) / [(6 - 3)! 3!]

C(6, 3) = (6 x 5 x 4 x 3!) / [(3 x 2 x 1) x (3 x 2 x 1)]

C(6, 3) = 20

Therefore, the college can select 20 groups of three students from the six interviewees for graduate assistantships.

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Answer:

1) m=2/3

2) b=10

3) x-int:(-15, 0)

4) y-int: (0, 10)

Our equation is:

\(y=\frac{2}{3}x+10\)

Step-by-step explanation:

To start, let’s find the equation of the line.

We can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

So, let’s substitute 2/3 for m and (-3, 8) for (x₁, y₁). This yields:

\(y-8=\frac{2}{3}(x-(-3))\)

Simplify:

\(y-8=\frac{2}{3}(x+3)\)

Distribute:

\(y-8=\frac{2}{3}x+2\)

Add 8 to both sides:

\(y=\frac{2}{3}x+10\)

This is in slope intercept form: y=mx+b.

Therefore, our m is 2/3 and our b is 10.

To find the x-intercept, we will substitute 0 for y and solve for x. Therefore:

\(0=\frac{2}{3}x+10\)

Subtract 10 from both sides:

\(-10=\frac{2}{3}x\)

Multiply both sides by 3/2. So:

\(x=-10(\frac{3}{2})=-30/2=-15\)

Therefore, the x-intercept is (-15, 0).

To find the y-intercept, we will substitute 0 for x and solve for y. Therefore:

\(y=\frac{2}{3}(0)+10=10\)

So, the y-intercept is (0, 10).

We will also graph it. See the attachment. To graph by hand, we can start at the y-intercept and go up two for every three to the right. Or, we can go down two for every three to the left. This should yield the following graph:

Answer:

The conditional relative frequency that someone is in high school, given that the person prefers to study without music, is about 0.56.  

If someone prefers to study music, the probability the person is in HS is about 44%.

Step-by-step explanation:

In the music column, we see that

total people who prefer to study with music =   153

high school students = 68

So, probability of high school students who study with music

= 68/153

= 0.44

= 44%.

College students = 85

Probability of college students who prefer to study with music

=  85/153

= 0.56

= 56%.

So, the correct statements are :

The conditional relative frequency that someone is in high school, given that the person prefers to study without music, is about 0.56.  

If someone prefers to study with music, the probability the person is in HS is about 44%.

Answer:

3 and 5

Step-by-step explanation:

2022

Answer:

√10.

___________________

Step-by-step explanation:

As you have not provided any options, the correct answer would be a value NOT between :

\(\sqrt{4}\) and \(\sqrt{5}\)

Or in decimal, between:

2 and 2.236

Hope this helps!

3birds would have=2(3)=6legs

Cats have:-

Each cat has 4legs.

Total cats:-

\(\\ \sf\longmapsto \dfrac{24}{4}=6cats\)

Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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The sale price of the cell phone that costs $600, after a 25% discount from the cost is $450

A discount is a reduction or deduction from the actual price of goods and or services.

The cost of the cell phone = $600

The percentage discount on the of the cell phone = 25%

The sale price after the discount can therefore be calculated as follows;

Sale price = ((100 - 25)/100) × $600 = $450

The sale price after the discount = $450

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Answer:

x = 7/9 or 0.78 as a decimal

Step-by-step explanation:

have a nice day!! :)

The best predicted value given that a person has an IQ of 91 is 94.03.

Here, we are given that-

sample size n = 20

sample mean for the independent value x = 100.39

sample mean for the dependent value y = 103.6

coefficient of correlation r = 0.925

The general expression for representing a linear model is given by-

y = β₀ + β₁x

where β₀ is the intercept and β₁ is the slope

For the above given case, the linear model will be given as-

y = -3.34 + 1.07x

where -3.34 is the intercept and 1.07 the slope.

To find the best predicted value when X = 91, we substitute the value of x as 91 in the equation as follows-

y = -3.34 + 1.07(91)

y = 94.03

Thus, the best predicted value given that a person has an IQ of 91 is 94.03.

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Answer:

  2.37×10^-11 milliliters

Step-by-step explanation:

The exponential model for decay is ...

  y = a·b^x

where 'a' is the initial value, 'b' is the decay factor, and x is the number of intervals over which the decay is taking place.

__

Here, you're given an initial value of a=500 mL.

The decay factor is 1 more than the decay rate, so is ...

  b = 1 -12% = 0.88

We are asked for the remaining amount after 240 intervals (breaths), so that will be ...

  y = 500·0.88^x

  y = 500·0.88^240 ≈ 2.37×10^-11 . . . . milliliters

__

Additional comment

That's about 640 million molecules of air--not very much. After 400 breaths, there is about 1 molecule of the original air remaining.

Step-by-step explanation:

hope it helps you

You move the decimal point over 2 spots to the right.

For example, the value 0.03 becomes 3%

Another example: 0.789 turns into 78.9%

Moving the decimal over 2 spots to the right is the same as multiplying by 100

The forecast for the number of accidents that will occur in the month of May is 110.

To find the trend equation for forecasting using the least-squares regression method, we need to perform a linear regression analysis on the given data.

Let's assign the variable x to represent the month number (1 for Jan, 2 for Feb, etc.) and y to represent the number of accidents.

Using the given data:

x: 1, 2, 3, 4

y: 30, 40, 60, 95

Step 1: Calculate the means of x (bar) and y (bar):

x(bar) = (1 + 2 + 3 + 4) / 4 = 2.5

y(bar) = (30 + 40 + 60 + 95) / 4 = 56.25

Step 2: Calculate the deviations from the means (dx and dy):

dx = x - x(bar)

= 1 - 2.5, 2 - 2.5, 3 - 2.5, 4 - 2.5

  = -1.5, -0.5, 0.5, 1.5

dy = y - ȳ = 30 - 56.25, 40 - 56.25, 60 - 56.25, 95 - 56.25

  = -26.25, -16.25, 3.75, 38.75

Step 3: Calculate the product of the deviations (dxdy):

dxdy = dx * dy

     = (-1.5) * (-26.25), (-0.5) * (-16.25), 0.5 * 3.75, 1.5 * 38.75

     = 39.375, 8.125, 1.875, 58.125

Step 4: Calculate the squared deviations (dx² and dy²):

dx² = dx * dx

    = (-1.5) * (-1.5), (-0.5) * (-0.5), 0.5 * 0.5, 1.5 * 1.5

    = 2.25, 0.25, 0.25, 2.25

dy² = dy * dy

    = (-26.25) * (-26.25), (-16.25) * (-16.25), 3.75 * 3.75, 38.75 * 38.75

    = 689.0625, 264.0625, 14.0625, 1503.125

Step 5: Calculate the sum of the squared deviations (Σdx² and Σdy²):

Σdx² = 2.25 + 0.25 + 0.25 + 2.25 = 5

Σdy² = 689.0625 + 264.0625 + 14.0625 + 1503.125 = 2470.3125

Step 6: Calculate the sum of the product of the deviations (Σdxdy):

Σdxdy = 39.375 + 8.125 + 1.875 + 58.125 = 107.5

Step 7: Calculate the slope (b):

b = Σdxdy / Σdx² = 107.5 / 5 = 21.5

Step 8: Calculate the y-intercept (a):

a = y(bar) - b * x(bar)

= 56.25 - 21.5 * 2.5

= 56.25 - 53.75

= 2.50

Therefore, the trend equation for forecasting is:

y = 2.50 + 21.50x

To find the forecast for the number of accidents in May (x = 5), substitute x = 5 into the equation:

y = 2.50 + 21.50 * 5

= 2.50 + 107.50

= 110

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Step-by-step explanation:

The plant Cuscuta derives its nutrition from the host plant by sending its root-like structures into the stem or roots of the host plant to absorb water, mineral salts and food from it. This type of nutrition is known as Parasitic Nutrition.

Answer:

The plant Cuscuta derives its nutrition from the host plant by sending its root-like structures into the stem or roots of the host plant to absorb water, mineral salts and food from it. This type of nutrition is known as Parasitic Nutrition.

The angles and arcs are as follows

5. Arc RS = < RQS

6. < 1 = arc AB

7. < KQL = arc KL

8. arc SVT = < SQT

9. 120/r

10. 123° r

the length of arc, s on a circle is given by the formula

s = r θ

where

r = radius of the circle

θ = angle in radians

9. in the figure we have that

s = 120

θ = s / r

θ = 120/r

10.

θ = 120

s = 120r

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Estimated proportion of the 73219 composite scores that would be at least 42 is 0.09823625 i.e. 0.10

Step-by-step explanation:
                                               
The observed data can be roughly classified as normally distributed data.  We will compute a three-standard deviation interval that contains 99.73% of the values.

Assume that random variable X represents the customers' composite scores.
: X~N  (u, σ² )    
The parameters' exact values are unknown to us. These are estimated using observed sample values.

Estimated mean is given by  
U=1/65 ∑ x^65=32
Estimated standard deviation is given by
σ=√1/64 ∑^65(x ^i -u)^2=7.741931
So, 3-standard deviation interval is given by
(u-3*σ, u-3 *σ)
=(32-3*7.741931+3*7.741931)
=(8.7742,55.2258)
           
The composite scores have integral values and cannot exceed 49. We must adjust the interval in light of these two facts..

So, most of the 73,129 composite scores would fall in the interval (8,49).

p(X>42)=P(X-u/σ>42-32/7.741931)                      
=p(Z>1.291667)
=0.09823625
Estimated proportion of the 73219 composite scores that would be at least 42 is 0.09823625 i.e. 0.10

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When we take the absolute value of a number, we always end up with a positive number (or zero). Whether the input was positive or negative (or zero), the output is always positive (or zero). For instance, | 3 | = 3, and | –3 | = 3 also.