Which property justifies this statement?
If 12 = 1 +5, then 2 +5= 12.

Answer:

10.5in

Step-by-step explanation:

first we make a ratio of sides PO:CD

this is to give us the general length ratio between the two shapes

the ratio is 12:16

upon simplifying we get 3:4

now that we got our general ratio we have to create the ratio between DA and MP , MP:14

now we compare it to the general formula

3:4

MP:14

next we cross multiply

4MP=42

then solve for MP

=42/4

=10.5

To solve this expression we have to add 2 to both sides of the equation:

So, the correct option is: B: 5.5

To find the derivative of the function f(x) = 2e^x + 5x - ln(x), we can apply the rules of differentiation.  here, f'(x) =\(2e^x + 5 - 1/x.\)

The derivative of each term can be calculated separately using the following rules:

d/dx(e^x) = e^x (derivative of e^x is e^x itself)

d/dx(5x) = 5 (derivative of 5x with respect to x is 5)

d/dx(ln(x)) = 1/x (derivative of ln(x) with respect to x is 1/x)

Therefore, the derivative of f(x) is:

f'(x) = \(d/dx(2e^x) + d/dx(5x) - d/dx(ln(x))\)

     =\(2e^x + 5 - 1/x\)

So, f'(x) =\(2e^x + 5 - 1/x.\).

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Answer:

20 ft

Step-by-step explanation:

Since we assume the triangles are similar, therefore, the ratio of their corresponding sides will be the same.

Height of the bigger triangle corresponds to height of the person

Distance of the person from street light + shadow of the person corresponds to the length of the shadow of the person

Therefore, the ratio of the corresponding sides of the triangles would be:

Height of bigger triangle : height of the person = Distance of the person from street light + shadow of the person : length of the shadow of the person

Thus:

h : 6 = 28 + 12 : 12

h : 6 = 40 : 12

h/6 = 40/12

Cross multiply

12h = 40*6

12h = 240

Divide both sides by 12

12h/12 = 240/12

h = 20

Height of the street light = 20 ft

Answer:

10 months

Step-by-step explanation:

Step one

Given

Chuck has $500

Chuckle wants to save $100 monthly

Let the number of months be x

And the total be y

So

Y=500+100x--------1

Holy has $500

Chuckle wants to save $500 monthly

Let the number of months be x

And the total be y

So

Y=1000+50x--------2

Equate 1 and 2

500+100x=1000+50x

1000-500=100x-50x

500=50x

x=500/50

x=10

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Answer:  x = 0  y = –3

Step-by-step explanation:

We can solve this system by substitution.

use the second equation as a value for x.

Then substitute that value  in place of x in the first equation and solve for y.

6x - 5y = 15 becomes

6(y + 3) - 5y = 15  Distribute 6 × parentheses

6y + 18 - 5y = 15 combine like terms

6y -5y + 18 = 15

y + 18 = 15   Subtract 18 from both sides.

y =15 -18

y = –3

Use this value for y in either equation to solve for x

6x - 5(-3) = 15

6x + 15 = 15    Subtract 15 from both sides, divide by 6 (seems silly!)

x = 0

OR in he second equation,

x = -3 + 3  

Again, x = 0

The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

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Answer:

$3.08

Step-by-step explanation:

\(2.29(1.025)^{12} \approx \$3.08\)

Answer:

should be the first one

Step-by-step explanation:

any point connected

Answer:

The answer is:

line segment D

Step-by-step explanation:

Points: A, B, C, D Line segments: Bar (AB), Bar (AC), Bar (BD)

Answer:

\(\huge\boxed{\sqrt[3]{c^4}=c^\frac{4}{3}}\)

Step-by-step explanation:

\(\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\text{therefore}\\\\\sqrt[3]{c^4}=c^\frac{4}{3}\)

The statement you provided mentions two separate events involving different companies lower rates

1. Hertz runs a sale: Hertz, a car rental company, is having a sale. This implies that they are offering in  discounted prices or promotional deals on their rental services.

2. Avis buys new cars and Budget lowers rates: Avis, another car rental company, is purchasing that  new cars to add to their fleet. On the other hand, Budget, yet another car rental   the company, is reducing their rental rates.

These events indicate of independent actions taken by the respective companies and are not directly connected to each other.

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The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Answer:

C)2(x-3)(x+3)

Step-by-step explanation:

Answer:

both have equal.............

The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

The Gompertz function is a solution of the differential equation:

dP/dt = c ln(K/P) P

where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.

To solve this differential equation, we can use separation of variables:

dP/P ln(K/P) = c dt

Integrating both sides, we get:

∫ dP/P ln(K/P) = ∫ c dt

Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:

-∫ du/u = -ln|u| = -ln|ln(K/P)|

The right-hand side is just:

c t + C

where C is an arbitrary constant of integration.

Putting these together, we get:

-ln|ln(K/P)| = ct + C

Taking the exponential of both sides, we get:

|ln(K/P)| = e^(-ct-C)

Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:

ln(K/P) = e^(-ct-C)

Solving for P, we get:

P = K e^(-e^(-ct-C))

This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

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Answer: ten thousands place

Step-by-step explanation:

The number 7 in 78,180 is in the thousands place. :)

Answer:

70,000

Step-by-step explanation:

because if u take the other numbers and replace it with 0s it will be 70,000

The mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.

To calculate the mean weight for each group (xa and xb), follow these steps:

1. Add up all the weights of group a and divide by the total number of data points in group a to find the mean weight (xa).
2. Repeat the same process for group b, adding up all the weights and dividing by the total number of data points to find the mean weight (xb).
3. Finally, subtract the mean of group b (xb) from the mean of group a (xa) to find the difference between the two means (xa - xb).

In summary, to find the mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.

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Given:

Find-:

Select the graph that best describes the inequalities and system of inequalities.

Explanation-:

Graph of first inequality is:

Graph of the second inequality:

So the graph of inequality.



Fred is using a visual representation of his weight loss goals by placing 20 one-pound boxes of lard in the refrigerator. He removes one box each time he successfully loses a pound.

Fred's approach of placing one-pound boxes of lard in the refrigerator and removing them as he loses weight serves as a visual representation of his weight loss goals. By placing 20 boxes initially, he symbolizes his desire to lose 20 pounds. Each time Fred successfully loses a pound, he removes one box, visually tracking his progress. This method can provide motivation and a tangible representation of his accomplishments, making his weight loss journey more concrete and achievable.

Using visual aids or symbols can be a helpful strategy in reaching goals, including weight loss. It allows individuals to have a clear visual reminder of their progress and acts as a motivating factor. By physically removing a box of lard each time he loses weight, Fred experiences a sense of accomplishment and sees the physical evidence of his efforts. This approach can help individuals stay focused, track their progress, and stay motivated throughout their weight loss journey.

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Answer:

θ =  5.6251 + n*2π

Step-by-step explanation:

Given the expression

18cos(10x)+2=10

18cos(10x) = 10 -2

18cos(10x) = 8

cos(10x) = 8/18

cos(10x) = 5/9

10x = arccos(5/9)

10x = 56.251

x = 56.251/10

x = 5.6251

For cos theta

θ=cos^-1a+n*2π

θ = 5.6251 + n*2π

Answer:

4th is correct

Step-by-step explanation:

As the object moves in forword direction

so F2 must have great magnitude.

HOPE THIS HELP YOU FOR ANY QUESTION PLEASE ASK ME

Alpha one is equal to two is the null hypothesis and the alternate hypothesis says at least one pair is different.

Classification modes X is alpha + ц T and X is ц T + alpha

Therefore , P  value is 01.0197

Therefore, This value is smaller than 0.0 , this is the decision rule.

The null hypothesis will be rejected at that point since there is enough data to say that the therapy had a meaningful impact.

The null hypothesis means that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.

The alternate hypothesis means that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either Ha or by H1.

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The difference between the 2 in the tens place and 2 to its left column in the given number 2,222.222 is 180.

According to the number system, a number can be written in its expanded form according to their pace value in the chart.

2,222.222 can be written as 2×1000+2×100+2×10+2X1+2×1/10+2×1/100+2×1/1000

The place value of 2 in the tens place in given number 2,222.222 = 20

The place value of 2 in its left column in the given number 2,222.22  = 200

Difference between the place of 2 in tens place and 2 in its left column

= 200 - 20

= 180

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Answer: i don't get it

Step-by-step explanation:

Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

According to given,

p = 0.12 (success)

q = 1 - 0.12

  = 0.88 (failure)

x = 7

By applying binomial probability distribution we get -

P(x) = nCx.p^x.q^(n-x)

⇒ P(x=7) = nC7.(0.12)^7.(0.88)^(n-7)

Also given,

Probability of 7 successful trials = 0.77

Thus,

nC7.(0.12)^7.(0.88)^(n-7) = 0.77

⇒ n!/(7! (n-7)!).(0.12)^7.(0.88)^(n-7) = 0.77

⇒ n!/(7! (n-7)!).(0.88)^n = 0.77 * (0.88/0.12)^7

⇒ n!/(7! (n-7)!).(0.88)^n = 878214.711

⇒ n = 130

Thus, the number of calls needed to ensure that there is a probability of at least 0.77 of obtaining 7 or more successful calls is 130.

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Disclaimer : This question provided is incomplete, the complete question is given below

Question : A telephone call centre where people place marketing calls to customers has a probability of success of 0.12. Find the number of calls needed to ensure that there is a probability of at least 0.77 of obtaining 7 or more successful calls.

Answer:

Step-by-step explanation:

\(4-2b^2 +3c\\b =2\\c = -1\\4-2(2)^2 +3(-1)\\4- 2(4) -3\\4-8-3\\= -7\)

Answer:

-7

Step-by-step explanation:

Sub in the numbers

4 - 2(2)2+ 3(-1)

4 - 8 + (-3)

 = -7