Lin has a drawing with an area of 20 in²

If she increases all the sides by a scale factor of 4, what will the new area be?

With a density function of p(x) = x³ - 5x + 7, the mass of the larger hockey puck is roughly 13.43. units.

To find the mass of the oversized hockey puck, we need to integrate the density function over the area of the object. Since the object is a disk with radius 2, we can integrate over a circle of radius 2 using polar coordinates.

The area element in polar coordinates is r dr dθ, so we can express the mass M of the object as:

M = ∫∫ p(x) dA

where dA = r dr dθ is the area element in polar coordinates.

To evaluate this integral, we need to express the density function p(x) in polar coordinates. Since x = r cosθ, we can substitute x = r cosθ into the expression for p(x) to get:

p(x) = (r cosθ)³ - 5(r cosθ) + 7

Simplifying this expression, we get:

p(r,θ) = r³ cos³θ - 5r cosθ + 7

Now we can integrate this expression over the circle of radius 2:

M = ∫∫ p(r,θ) r dr dθ, where r ranges from 0 to 2, and θ ranges from 0 to 2π.

Using polar coordinates, we can express the double integral as:

M = ∫0² ∫0²π r⁴ cos³θ - 5r²cosθ + 7r dr dθ

Solving this integral using standard techniques, we get:

M = (32π/5) - (20/3)

M = (32π/5) - (20/3)

M ≈ (32*3.14159/5) - (20/3)

M ≈ 20.106 - 6.667

M ≈ 13.439

Therefore, the mass of the oversized hockey puck with density function p(x) = x³ – 5x + 7 is approximately 13.43.

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Answer:

I think it's 27

because length is 3 times its width

Answer:

3/1

Step-by-step explanation:

In triangle ABC, the known side is AC, which is equal to 6. The corresponding side to AC from triangle DEF would be FD, which is equal to 2. You divide 6/2 in order to get 3/1.

Answer:

It is 16.666…

let 16.666 be x :

\(x = 16.666 - - - (i) \\ 100x = 1666.666 - - - (ii)\)

subtract (i) from (ii):

\(99x = 1650 \\ \\ x = \frac{1650}{99} = { \boxed{ \boxed{ \frac{50}{3} }}}\)

-12 + 5x = -24 + x

5x - x = -24 + 12

4x = -12

x = -12/4

x = -3

Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:

# Load HardyWeinberg package

library(HardyWeinberg)

# Load Mourant dataset

data(Mourant)

# Extract the genotype counts for the 206th row

counts <- Mourant[206, 2:4]

# Calculate the MLE of M allele frequency

mle <- hw_mle(counts)

# Extract the MLE of M allele frequency

mle_M <- mle$p[2]

Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.

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Answer:

x=129

Step-by-step explanation:

triangles are 180 degrees

180-35-94=51

now 180-51

129

Answer:

20 !

Step-by-step explanation:

80 + 20 = 100.

Answer:

B

Step-by-step explanation:

because B is 8/20 and it's not equivalent to 40/100

The set of side measurements that could be used to form a right triangle is

The problem is solved using the Pythagoras theorem is applicable to right triangle.  

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

the set of sides that adheres to this theorem can form a right triangle

plugging the values as in the problem  6, 8, 10

say side 10 = x

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10

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Answer: x = -2

Step-by-step explanation:---------------

The calculated acceleration at the time t = 1.1 is 43.36 ms⁻²

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

v (ms⁻¹) 43.1   47.7  52.1   56.4  60.8

t(s)         1.0      1.1     1.2      1.3   1.4

The acceleration is calculated as

a = v/t

At time t = 1.1, we have

v = 47.7

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

a = 47.7/1.1

Evaluate

a = 43.36

Hence, the acceleration is 43.36 ms⁻²

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Question

The velocity v at specified time t is recorded in the table below.

v (ms⁻¹) 43.1   47.7  52.1   56.4  60.8

t(s)         1.0      1.1     1.2      1.3   1.4

Find the acceleration at time t = 1.1

Answer:

(19/2.11/2) or (9.5,5.5)

Step-by-step explanation:

finding midpoint is simple, just add two x/y and divide by 2

x1=12

x2=7

(12+7)/2=19/2

y1=2

y2=9

(2+9)/2=11/2

your answer is above

9.5 and 5.5 is answer

Answer:

15:20

Step-by-step explanation:

3 + 4 = 7

35 / 7 = 5

5 x 3 = 15

5 x 4 = 20

Therefore the answer is 15:20

The three points on the given graph are the ones in the set below.

{(4, -1),  (-2, -3), (-5, 2)}

The coordinates of a point are writen as (x, y), where x is the value on the horizontal axis and y is the value on the vertical axis.

So the graph is just:

{(4, -1),  (-2, -3), (-5, 2)}

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Find the sides that are opposite, next to, and the hypotenuse of angle B in the triangle to determine its sine, cosine, and tangent. The values can then be determined using the aforementioned formulas.

The formula for the tangent of an x is tan x = sin x cos x, where tan x = sin x cos x.

The sine, cosine, and tangent of an angle in a right triangle are defined as follows:

Sine: The proportion of the length of the hypotenuse to the length of the side that faces the angle.

Cosine is the proportion of the adjacent side's length to the hypotenuse's length.

The length of the side directly across from the angle in relation to the length of the side directly across.

Identifying the triangle's opposing, adjacent, and hypotenuse sides will help you determine the sine, cosine, and tangent of angle A in a right triangle. The values can then be determined using the definitions above:

Angle A's sine equals its opposite or hypotenuse

Angle A's cosine equals its adjacent or hypotenuse.

Angle A's tangent is its opposite or adjacent.

Similar to this, you must determine the sides that are directly opposite, adjacent, and the hypotenuse of angle B in the triangle in order to get its sine, cosine, and tangent. The values can then be determined using the same formulas as above.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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For Ms Hurst:

Distance covered by her = Speed * time taken by her

Given:

Speed of Ms Hurst = 10miles/min

Time taken = 60 mins (since they both ran for 60minutes)

Substitute into the formula

Distance covered by Ms Hurst = 10mil/min * 60min

Distance covered by Ms Hurst = 600 miles

Hence Ms Hurst completed 600 miles

If the appropriate x value is known, a set of answer options can be predicted using a least squares regression line.

The ideal choice is (a)

A straight line that illustrates how a response variable, y, changes as an explanatory variable, x, changes is called a regression line (LSRL, or least squares regression line). The line is a mathematical model that can be used to foretell the value of y given a value for x. A response and an explanatory variable are necessary for regression.

According to, the universal least squares regression line.

y = a+ bX

Here,

Independent variable: X

Y is the dependent variable.

The slope (or regression) coefficient is b.

If a = intercept,

When the independent variable is known, the least square regression line's main objective is to forecast the value of the dependent variable.

The following is the proper interpretation:

If the appropriate x value is known, a least squares regression line can be employed to forecast the value of y.

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

Step-by-step explanation:

X( -9 , 2)  & Y(5 , -4)

\(distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\XY=\sqrt{(5-[-9])^{2}+(-4-2)^{2}}\\\\=\sqrt{(5+9)^{2}+(-6)^{2}}\\\\=\sqrt{(14)^{2}+(-6)^{2}}\\\\=\sqrt{196+36}\\\\=\sqrt{232}\\\\= 15.23\)

The Lindsey should save around $28,000 for the down payment. If she wants to expedite her savings, she can look into cutting down expenses or increasing her income.

Congratulations to Lindsey for being debt-free and having a fully funded emergency fund! As for her question, the down payment for a house usually ranges from 3% to 20% of the home's purchase price.

Based on Lindsey's desired home worth $140,000, the down payment can range from $4,200 (3%) to $28,000 (20%).

However, it's recommended to aim for a 20% down payment to avoid private mortgage insurance (PMI) and to lower monthly payments. Best of luck to Lindsey on her journey towards homeownership

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The value of the side length x is equal to 14 using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin45 = 7√2/x {opposite/hypotenuse}

√2/2 = 7√2/x {sin45 = √2/2}

x = 7√2 × 2/√2 {cross multiplication}

x = 7 × 2

x = 14

Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.

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Answer:

13- pretty sure its 122

14- 58

15- i think its 236?

Problem 13

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

Explanation:

It's not mentioned, but keep in mind that 1 foot is equivalent to 12 inches. This means that 48 inches is equal to 48/12 = 4 feet. So you must be 4 feet tall, or taller, to be able to ride the roller coaster.

To convert this to centimeters, we multiply by 30.48 to get 4*30.48 = 121.92 cm, which then rounds to 122 cm

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

Problem 14

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

Explanation:

1 gallon = 16 cups

Note how 240/16 = 15, which means we can multiply both sides of that equation above by 15 and we end up with

15*(1 gallon) = 15*(16 cups)

15 gallons = 240 cups

The water cooler is 15 gallons.

Multiply this by 3.8, since there are about 3.8 liters per gallon, and we end up with the answer of 3.8*15 = 57 liters

This answer is approximate since the 3.8 was approximate.

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

Problem 15

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

Explanation:

1 meter = 100 cm

6 meters = 600 cm (multiply both sides by 6)

1 cm = 0.39 inches

600*(1 cm) = 600*(0.39 inches)

600 cm = 234 inches

This answer is approximate because the 0.39 was approximate.

Answer:

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Step-by-step explanation:

We are given that

\(\angle ABC=85^{\circ}\)

Exterior angle=\(147^{\circ}\)

We have to find the value of x.

We know that

Exterior angle=Sum of opposite interior angles of triangle

Using the property

\(x+85=147\)

Subtract 85 from both sides we get

\(x=147-85\)

\(x=62\)

Option B is true.

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Answer:

its d

Step-by-step explanation:

the number 30 is not listed in the problem there that is info that is not there

The dog is playing with his chew toy!

Answer:

Explanation

Step-by-step explanation:

In general, dogs can run 15-20 mph

humans can run 6-8 mph

You are significantly slower than the dog,

the fastest human is around 27 miles per hour, unfortunately, even if you were this fast

the fastest dog can run 40 miles per hour as an estimate

even house cats can run at 30 mph maximum if they really wanted,

You have no chance of outrunning this dog, and barely a chance of outsmarting it if that option was available, in conclusion, the dog is chasing you at a speed of around 30 mph about 6-7x more than your own speed with no chance of outrunning it(the dog).

y=

5x+2y=5x+18

X+5-5+2=X+5-5+18

X=2. X=18