A reflection of a figure can change which of the following.

A) Number

B) Size

C) Orientation

D) location

E) Shape


Please hurry

The simplified form of the given expression is 2a+b/2b+a.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is \(\frac{\frac{1}{a}+ \frac{2}{b} }{\frac{2}{a}+ \frac{1}{b} }\).

The expression can be simplified as follows

\(\frac{\frac{b+2a}{ab} }{\frac{2b+a}{ab} }\)

= 2a+b/2b+a

Therefore, the simplified form of the given expression is 2a+b/2b+a.

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Answer:

Step-by-step explanation:

The equation of a linear function:

y = mx + b

m - slope

b - y-intercept

x = 3 - it's a vertical line. It's not equation of a linear function

y = 16 - it's a horizontal line. It's an equation of a linear function

where m = 0, b = 16

y = -3x + 10 - it's an equation of a linear function

where m = -3, b = 10

y = 3x² + 1 - it's a quadratic function ( x² ).

Answer:

y = 16 and y = -3x + 10

Step-by-step explanation:

hello

Answer:

what the question there is no picture

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

just divide 600 by 30

20. because 600 divided by 30 is 20.

The maximum weight that the balloon can lift is 5020.31 Newtons.

We have to give that,

A 3.2 kg balloon is filled with helium with a density of 0.179 kg/m³.

And, the balloon is a sphere with a radius of 4.9 m.

Since The formula for the volume of a sphere is,

\(V = \dfrac{4}{3} \pi r^3\)

Here, \(g = 9.8 \text{m/s}\)

\(\rho_{air} = 1.225\) kg/m³

So, Buoyant force on the ballons is,

\(F_B = V \times \rho_{air} \times g\)

Substitute all the given values,

\(F_{B} = \dfrac{4}{3} \times\pi \times (4.9)^3 \times 1.225 \times 9.8\)

\(F_B = 5916.15 \text{N}\)

So, the maximum weight that the balloon can lift is calculated as,

\(W +M_b +V \times \rho_{He} \times g = F_B = V \times \rho_{air} \times g\)

\(W = F_B - (M_bg +V \times \rho_{He} \times g)\)

Where, \(M_b\) is the mass of balloons.

Substitute all the values,

\(W = 5916.15 - [(3.2 \times 9.8) + \dfrac{4}{3} \pi (4.9)^3 \times (0.179) \times(9.8)]\)

\(W = 5916.15 - 31.36 - 864.48\\\)

So, the maximum weight that the balloon can lift is,

\(W = 5020.31\)

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Answer:

The statement is true.

Step-by-step explanation:

Let us plug\(24=-4(8)-8\) in 8 for \(x\) and 24 for \(y\) in our equation: \(24 =-4 (8) - 8\).

Now we will solve in the order described by PEMDAS.

-4(8)=32

32-8=24

24=24

Thus, our statement is true.

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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Answer:

it should be 40º but it doesn't look like that's an option...

Step-by-step explanation:

so we know that the inside of a triangle is equal to 180º and for the triangle on the right we already have two angles. so we can add the angles (41 + 72 = 113) and then subtract that from 180 to find the missing angle.

180 - 113 = 67º

now we also know that vertical angles are congruent/the same. so the vertice that is connecting the two triangles is also 67º. we can do the same thing we did with the other triangle, add the angles up and subtract from 180.

67 + 73 = 140

180 - 140 = 40º

we know this is true because when you add all the angles up it equals 180.

67 + 73 = 140 + 40 = 180

44 would put it at 184º which is not correct, and 150 would put it at 290ª which is also not correct...

32% of the same people spend their time listening.

The total number of mentioned  people will be 100% or 1. Now, in the total people, the remaining ones who are not stated in the question, must be the listeners. Thus, calculating the remaining percentage of people, we will get the percentage of listeners in same people.

So, number of people who spend time speaking = 26%

Number of people who spend time speaking = \(\frac{26}{100}\)

Number of people who spend time speaking = 0.26

Number of people who spend time writing =  23%

Number of people who spend time writing = \(\frac{23}{100}\)

Number of people who spend time writing = 0.23

Number of people who spend time reading =  19%

Number of people who spend time reading = \(\frac{19}{100}\)

Number of people who spend time reading = 0.19

Total number of people involved in activities other than listening = 0.26 + 0.23 + 0.19

Total number of people involved in activities other than listening = 0.68

People who spend time listening = 1 - 0.68

People who spend time listening = 0.32

Percentage of people who spend time listening = 0.32 × 100

Percentage of people who spend time listening = 32%

Hence, 32% of the same people spend their time listening.

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Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

The region bounded by the curves y = 3x^2 - x^3 and y = 0 is sketched. The Method of Cylindrical Shells is appropriate for computing the volume. The volume is found to be 243π/10.

(a) Sketch of the graph of the region bounded by the curves y = 3x^2 - x^3 and y = 0:

The graph will consist of a curve representing y = 3x^2 - x^3, which intersects the x-axis at points (0, 0) and (3, 0), and the x-axis itself.

Here is a rough sketch of the graph:

      ^

       |         __

       |      _-'  '----.

       |   _-'           '-.

       |-'__________________'-__________> x

(b) Explanation of why the Method of Cylindrical Shells is appropriate:

The Method of Cylindrical Shells is appropriate for computing the volume of the solid generated by revolving the region because the region is bounded by vertical lines (x = 0 and x = 3) and is being revolved around a vertical axis (x = 4).

This method uses cylindrical shells, which are infinitesimally thin, vertical shells that enclose the region and can be integrated to find the volume.

(c) Computation of the volume:

To compute the volume of the solid generated by revolving the region about the line x = 4, we can use the Method of Cylindrical Shells. The volume is given by the integral:

V = ∫(2πx)(f(x) - g(x)) dx,

where f(x) represents the upper curve (y = 3x^2 - x^3), g(x) represents the lower curve (y = 0), and the integral is taken over the range of x from 0 to 3.

Substituting the functions into the formula, we have:

V = ∫(2πx)((3x^2 - x^3) - 0) dx

V = 2π ∫(3x^3 - x^4) dx.

Evaluating this integral, we get:

V = 2π [3/4 * x^4 - 1/5 * x^5] |[0, 3]

V = 2π [(3/4 * 3^4 - 1/5 * 3^5) - (3/4 * 0^4 - 1/5 * 0^5)]

V = 2π [(3/4 * 81 - 1/5 * 243) - (0 - 0)]

V = 2π [(243/4 - 243/5)]

V = 2π [243/20]

V = 243π/10.

Therefore, the volume of the solid generated by revolving the region bounded by the curves about the line x = 4 is 243π/10.

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The equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

The equation of a line in point-slope form is expressed as:

y-y0 = m(x-x0)

where:

m is the slope

(x0,y0) is the point on the line

The slope of the given line is as shown:

Slope = 2-(-4)/2-(-2)
Slope = 2+4/2+2
Slope = 6/4 = 3/2

Substitute the slope and the point

y - 1 = 3/2(x-(-3))

y - 1 = 3/2(x+3)

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

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The regression equation is a statistical tool that examines the relationship between college GPA (colgpai), high school GPA, and whether the student is a science major. By using the sample data of 50 students, the equation determines the relationship between college GPA and the independent variables - high school GPA and science major status.

The equation helps us understand the effect of high school GPA on college GPA, while also considering the influence of being a science major. It provides insight into how changes in these variables can impact a student's college performance. By analyzing the coefficients of the equation, we can determine the strength and direction of the relationship between the variables. This information is useful for predicting college GPA based on high school GPA and science major status. The regression equation allows researchers and analysts to study and understand the complex interplay between these factors and their influence on college success.

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[ ( 30 - 8 ) ÷ 2 + 2 ]

[ ( 22 ÷ 2 ) + 2 ]

[ ( 11 + 2 ) ]

[ 13 ]

The sixth decile for the given test scores is 82.

To find the sixth decile, we first need to find the corresponding percentile. The sixth decile represents the 60th percentile, meaning 60% of the data falls below this value.

First, we need to find the total number of data points:

n = 30

Next, we need to find the rank of the 60th percentile:

Rank = (60/100) * n

= 0.6 * 30

= 18

Now we need to find the corresponding value for the 18th rank. To do this, we need to sort the data in ascending order:

44 56 58 62 64 64 70 72 72 72 74 74 75 78 78 79 80 82 82 84 86 87 88 90 92 95 96 96 98 100

The value at the 18th rank is 82, which is the sixth decile for this dataset.

Therefore, the sixth decile for the given test scores is 82. Counting from the smallest value, we can see that the 18th value is 82.

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Answer:

Step-by-step explanation:

We can simplify (cross multiply) to get \(xy^2=wz\)

Then we easily simplify to get \(y=\sqrt{\frac{wz}{x}},\:y=-\sqrt{\frac{wz}{x}};\quad \:w\ne \:0,\:x\ne \:0\)

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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Answer:

A.)

Rise = 2

Run = 5

m = 2/5

B.)

Rise = 2

Run = - 4

m = - 1/2

C.)

Rise = 3

Run = 1

m = 3

Step-by-step explanation:

Rise = y2 - y1

Run = x2 - x1

Slope, m = Rise / Run

A.) (0,0) ; (5 2)

x1 = 0 ; y1 = 0

x2 = 5 ; y2 = 2

Rise = 2 - 0 = 2

Run = 5 - 0 = 5

m = 2/5

B.) (1, 2) ; (-3, 4)

x1 = 1 ; y1 = 2

x2 = - 3 ; y2 = 4

Rise = 4 - 2 = 2

Run = - 3 - 1 = - 4

m = 2/-4 = - 1/2

C.) (5,2) ; (6,5)

x1 = 5 ; y1 = 2

x2 = 6 ; y2 = 5

Rise = 5 - 2 = 3

Run = 6 - 5 = 1

m = 3/1 = 3

Since n = 1 is a positive integer for which the proposition is true, then p(1) is true.

Direct Proof:

Assume n is a positive integer.

Show that n²  ≥ n.

Substitute n = 1 into the equation n²  ≥ n

Solve the equation 1² ≥ 1

Show that 1² = 1, and 1 ≥ 1.

Therefore, n² ≥ n is true for n = 1.

This is an example of a direct proof, in which we start by assuming the statement is true for a particular value before using logical processes to demonstrate that it must be true for all values.

Before solving the problem, we made the assumption that n was a positive integer, added n = 1, and then proved that the assertion was accurate for n = 1. This establishes the statement's applicability to all positive numbers.

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Answer:

0 ft/sec

Step-by-step explanation:

He just dropped the hammer, so it's initial velocity is zero ft/sec.

Had he thrown the hammer down, the story would be different!

Answer:

I am sorry if this wrong. I believe the initial velocity is 20.

Step-by-step explanation:

My reasoning is because the -16t^2 is representing the time. The h for height we are trying find the height. So that leave us with the initial velocity 20.

I apologize if this wrong. Hope this helps!

Have a great day/night!

Answer:

9) 18.2

10) 59 degrees

11) 48.6 degrees

12) 25.8 degrees

13) 41.1 degrees

Step-by-step explanation:

number 9:

sine 60 = \(\frac{21}{x}\)

x = 18.18 ⇒ 18.2

number 10:

tan x = \(\frac{30}{18}\)

x = 59

number 11:

sine x = \(\frac{12}{16}\)

x = 48.59 ⇒ 48.6

number 12:

cos x = \(\frac{36}{40}\)

x = 25.8

number 13:

sine x = \(\frac{25}{38}\)

x = 41.1

Answer:

63 sandwiches

Step-by-step explanation:

Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter

They brought 7 loaves of bread

Each loaves have 18 slices

They used 2 slices each to make the sandwich

The first step is to calculate the total number of slices

Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows

= 7 ×18

= 126 slices

Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows

= 126/2

= 63

Hence 63 sandwiches were made for the shelter

The values of w typically vary, on average, from the mean of the distribution about 3.46.

The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

For a geometric(p = 0.25) distribution, the variance is computed here as:

Var(X) = (1 - p)/ p2 = (1 - 0.25) / 0.252 = 12

Therefore, the standard deviation is computed as:

= ✓(12) = 3.46 observations.

This is the standard deviation of the given distribution here.

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Answer:

see below

Step-by-step explanation:

We can write the length as w + 8 and since area is length * width our answer is w * (w + 8) = w² + 8w.

Answer:

1: draw a line across the circle, but not through point O

2: place the two points on the edge of the circle so that the space in between is about 1/3 of the circle. Label C and D.

3: draw two lines out from point O to the edge of the circle. 45 is half of 90. this means you can draw a 90 degree angle and divide it in half and remove the extra line. Label these E and F.

Answer:

V=36

Step-by-step explanation:

Having a rectangular pasture for the animals to graze in is something a farmer wants in order to start growing cows, horses, goats, and sheep. She has decided to purchase 7500 ft of fencing. 1875 square feet is the maximum possible area that each of the four pens will enclose.

The maximum possible area of each pen is 1875 square feet. To calculate this, first calculate the total area of the large rectangle that the farmer is enclosing. To do this, multiply the total length of the fencing (7500 feet) by the width of the fence (1 foot). This gives us 7500 square feet as the area of the large rectangle.

Next, divide the area of the large rectangle by 4 to get the area of each pen. This gives us 1875 square feet as the maximum area of each pen.

Total Area of Large Rectangle = 7500 ft x 1 ft = 7500 sq ft

Area of Each Pen = 7500 sq ft / 4 = 1875 sq ft

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We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

202500 is required deposit

Step-by-step explanation:

Based on the given conditions,

formulate:  225000  × 90 %  

Calculate the product or quotient: 202500  

get the result: 202500  

Answer: 202500

(Hope this helps can I pls have brainlist (crown)☺️)

With the mortgage 90 percent, the deposit required is $202500.

Given that, a luxury apartment is priced at $225000.

A bank offers a 90% mortgage.

A fixed-rate mortgage is a home loan option with a specific interest rate for the entire term of the loan.

Here, 90% of 225000

\(= \frac{90}{100} \times225000\)

\(=90\times2250\)

\(=202500\)

Therefore, the deposit required is $202500.

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Answer:

hard, stressful, sad

Step-by-step explanation:

Answer:

Obnoxious, boring, and irritated.