And that includes the point (-5’2) has a slope of -4. what is its equation in point slope form?

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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Answer:

$3,480

Step-by-step explanation:

You multiply the amount she makes per hour by how many hours she works in a month.

11.60 × 300 = 3,480

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

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

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

The answer is 72.

Step-by-step explanation:

You have to put in the values of a and b into the expressions :

\( {a}^{2} {b}^{3} - {(ab)}^{2} \)

\(let \: a \: = - 2 \\ let \: b = 3\)

\( {( - 2)}^{2} \times {(3)}^{3} - {( - 2 \times 3)}^{2} \)

\( = 4 \times 27 - { (- 6)}^{2} \)

\( = 108 - 36\)

\( = 72\)

Answer:

Step-by-step explanation: Its "C" Or The 3rd Option

The change in temperature is 33°F.

According to the question we have been given that there are two temperature readings which are, -18°F and 15°F.

We need to find the change in temperature that is we need to find the difference. And for that we will use distance formula.

The formula to find the distance between the two numbers p and q is

                                    = |p-q|

Here , p = -18°F  and q = 15°F

Putting the required values in the above formula we get

                     = |-18 - 15| °F

                     = |-33| °F

                     = 33°F

Hence the change in temperature is 33°F.

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Answer:

a- (4,4)  b- (3,2)  c- (1,3)  d- (3,3)  e-(2,3)  f- (1,2)  g-(1,1)  f -(1,2)

Step-by-step explanation:

not sure but i think we're finding the coordinates of the letters.

The Bank discount and proceeds of the given information is:

$2365.27 and $47634.73 respectively.

Given the face value is $50,000

Discount rate = 13%

No.of term days = April 5 to August 14

= 131 days.

Bank discount = ?

Proceeds = ?

First calculate the bank discount using the formula:

Bank discount = face value × discount rate × time

Bank discount = $50,000 × 0.13 × 131/360

= 50,000×0.13×0.36388

= $2365.27

now calculate the proceeds using the formula :

Proceeds = face value - bank discount

= 50,000 - 2365.27

= $47634.73

Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.

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Answer:

c. 4

Step-by-step explanation:

see how many cubes are already there. Then, subtract that answe from 12 to get how many you need.

Answer:

Count the units in total shown here:

There are 2 units both in the back and front.

So double of 2 means 4 units, there are 4 units on the back and front.

Now count the units between them:

There are 4 units across from them.

Add the units together:

4 + 4

= 8, there are 8 units in total shown in this figure.

But, we need to find how many more units should be added to these 8 units to get a result of 12 units altogether.

So, subtract the 8 units from the 12 units to get the remaining units you would need to add to 8 units to get 12.

12 - 8

= 4, you would need 4 more units so that this figure would have a volume of 12.

The average pay-per-hour of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.

Therefore, the new salary will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 hours per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total earnings for the year will be:

= 2163 × 12 months

= 25956

The average pay-per-hour of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

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The result provides convincing evidence that the tsa officers did not carrry out a truly random sample.

A simple random sample is a subset of a statistical population in which each member has an equal chance of being selected.

In statistics, a simple random sample is a subset of individuals picked at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.

In this case, it's important to note that the fact that all the people chosen were first class members means that it was bias and not a random sampling.

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Answer:

8.513

Step-by-step explanation:

To round 8.51348424552 to 3 decimal places, we look at the digit in the fourth decimal place, which is digit 4. Since the digit 4 is less than 5, we don't need to round up the previous digit. Therefore, the rounded value is 8.513.

In this case, the digit in the third decimal place, which is 3, remains unchanged. The purpose of rounding to 3 decimal places is to have a value that is accurate to the nearest thousandth. So, by rounding 8.51348424552 to 3 decimal places, we obtain 8.513 as the result.

Answer:

BD is congruent to BC. BD=BC

BD = 5x – 26, BC = 2x + 1, and AC = 43

To find out , we need to find  BC first . For that we have to find out x

WE know that BD=BC, using that we solve for x

Now we plug in 9 for x  and find out BC

BC=2x+1

BC=2(9)+1

BC=19

We know AC= 43

AC=AB +AC

43=AB+19

subtract 19

AB = 24

Step-by-step explanation:

hope that helps>3

The pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

When working with a set of pulse rates that are normally distributed, we can use the Empirical Rule to determine the pulse rates that are within 1 standard deviation of the mean. According to the Empirical Rule, approximately 68% of the data falls within 1 standard deviation of the mean.

To find the pulse rates that are within 1 standard deviation of the mean, we need to first find the mean and standard deviation of the pulse rates. After we have these values, we can determine the range of pulse rates that fall within one standard deviation of the mean.

To calculate the percentage of the total that represents those rates, we can use the formula: Percentage = (Number of data points within 1 standard deviation / Total number of data points) x 100.

For example, let's say the mean pulse rate is 72 beats per minute and the standard deviation is 8 beats per minute. Using the Empirical Rule, we know that approximately 68% of the pulse rates fall within one standard deviation of the mean. This means that the pulse rates that fall within one standard deviation of the mean are between 64 and 80 beats per minute.

To find the percentage of the total that represents those rates, we need to count the number of data points within that range. If we assume that we have 1000 data points, then the number of data points within the range of 64 to 80 beats per minute is approximately 680. Therefore, the percentage of the total that represents those rates is:

Percentage = (680/1000) x 100

Percentage = 68%

Therefore, the pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

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This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

According to the statement

we have given that the one statement and we have to tell that the those statement is true or false after analyzing it.

So,

In C++ 11 is  a programming language which is used to write the coding. And in this language you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

Because in the coding it is not possible that the you can make loop without declare the random variable in the loop.

Due to this reasons without declare the variable it is not possible.

So, This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

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Answer:

an = 99 + a25

=99 + a + 24d

=99 + 3 +24 * 12

= 390

Answer:

34th term

Step-by-step explanation:

the nth term of an AP is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and d = a₂ - a₁ = 14 - 3 = 11 , then

\(a_{n}\) = 3 + 11(n - 1) = 3 + 11n - 11 = 11n - 8

substitute n = 25 into the rule to find a₂₅ , that is

a₂₅ = 11(25) - 8 = 275 - 8 = 267

then 99 more than this is 267 + 99 = 366

equate 11n - 8 to 366 and solve for n

11n - 8 = 366 ( add 8 to both sides )

11n = 374 ( divide both sides by 11 )

n = 34

then the 34th term is 99 more than the 25th term

Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

Step-by-step explanation: trust me

The speed of the man's shadow's tip at a distance of 10 feet from the light's base is given by dy/dt = 10 ft/s.

AB is equal to 15 feet in height.

Man's height in CD is 6 feet.

From the diagram attached, if BE = y, we may use the ratio of related triangles to obtain,

15/y = 6/(y - x) (y - x)

to obtain, cross-multiply;

15(y - x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

To get, multiply both sides by 3.

3y = 5x

separating the two sides according to t provides;

dy = dt + dx = 3.

(5/3)(dx/dt dy/dt)

putting yields for dx/dt at 6 ft/s;

dy/dt = (5/3)(6) (6)

dy/dt equals 10 ft/s

One of the many real-world applications of trigonometry is the study of heights and distance. The terms height and distance are frequently used while discussing the applications of trigonometry.

The following ideas are incorporated in the trigonometry application for height and distance:

Measurement of the separation between two heavenly bodies

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The two numbers are 3 and 11 respectively

From the information given, we have that

The first number is x

The second number is y

Also,

2x - y = -5

x + y = 14

Make 'x' the subject from equation 2

x = 14 - y

Make 'x' the subject

2(14-y) - y = -5

28 - 2y - y= -5

collect like terms

-3y = -33

y = 11

Substitute the values

x = 3

Hence, the values are 3 and 11

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Trigonometry is an important branch of mathematics that deals with the relationships between the sides and angles of triangles. It has many real-world applications in fields such as physics, engineering, and architecture. In this answer, I will provide a brief overview of some key concepts in trigonometry that are typically covered in a high school junior-level course.

One of the most important concepts in trigonometry is the unit circle. This is a circle with a radius of 1 unit that is centered at the origin of a coordinate plane. The unit circle is used to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.

To understand the trigonometric functions, we must first define some key terms. The hypotenuse of a right triangle is the side opposite the right angle. The opposite side is the side opposite the angle of interest, and the adjacent side is the side that is adjacent to both the angle of interest and the right angle.

Using the unit circle, we can define the sine and cosine of an angle as the y- and x-coordinates of the point on the unit circle that corresponds to the angle. The tangent of an angle is the ratio of the opposite side to the adjacent side. The cosecant, secant, and cotangent functions are simply the reciprocals of the sine, cosine, and tangent functions, respectively.

Trigonometric functions can be used to solve problems involving right triangles, such as finding missing side lengths or angles. They can also be used to model periodic phenomena, such as waves or oscillations.

In summary, trigonometry is a fascinating and useful branch of mathematics that has many applications in the real world. By understanding the key concepts of the unit circle and the trigonometric functions, students can develop a deeper appreciation for the beauty and utility of mathematics.

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Answer:

B

Step-by-step explanation:

15.125/4 and then multiply that by three. 11.344

Estimated values: Damping ratio = 0.15, Natural frequency = 21.2 rad/s, k = 41667 N/m, m = 92.7 kg, c = 582 N-s/m.

Here are the estimated values of m, c, and k:

Damping ratio: 0.15

Natural frequency: 21.2 rad/s

Value of k: 41667 N/m

Value of m: 92.7 kg

Value of c: 582 N-s/m

To estimate these values, we can use the following steps:

1. The damping ratio can be estimated by looking at the time it takes for the system to reach its final value after a step input. In this case, the system reaches its final value after about 1.1 seconds.

The damping ratio is related to the time it takes to reach the final value by the following equation:

\(\zeta = (1 - e^(-t/\tau))^(1/2)\)

where\(\tau\) is the time constant.  In this case, τ is about 0.1 seconds. Plugging in these values, we get a damping ratio of 0.15.

2. The natural frequency can be estimated by looking at the frequency of the oscillations in the step response. In this case, the frequency of the oscillations is about 21.2 rad/s.

3. The value of k can be estimated by multiplying the mass by the square of the natural frequency. In this case, k is about 41667 N/m.

4. The value of c can be estimated by dividing the damping coefficient by the mass. In this case, c is about 582 N-s/m.

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The complete question is:

The given figure shows the response of a system to a step input of magnitude 1000 N. The equation of motion is më + cả + kx = f(t) Estimate the values of m, c, and k. 0.04 0.036 0.032 0.028 0.024 0.02 0.016 0.012 0.008 0.004 0 O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Time (s) The damping ratio is determined to be The natural frequency is determined to be The value of k is determined to be rad/s. N/m. The value of m is determined to be kg. The value of cis determined to be N-s/m.

Answer:

Length of one side of garage = 58 ft

Length of one side + 50% = 87 ft

Percent increase in the length of one side 50% was added to the new length

Step-by-step explanation:

To find one side - Garage is a square, meaning all 4 sides are equal

To find new length of one side - If 50% is added, that means half the original amount was added.

Answer:

?

Step-by-step explanation:

The value x in the formula represents the value of each observation of the data-set.

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Therefore, the bond will sell at approximately $761.90.

To determine the selling price of the bond, we need to calculate the present value of its cash flows.

The bond pays $20 in semi-annual coupon payments, which means it pays $40 annually ($20 * 2) in coupon payments.

The current yield of 5.25% represents the yield to maturity (YTM) or the required rate of return for the bond.

To calculate the present value, we can use the formula for the present value of an annuity:

Present Value = Coupon Payment / YTM

In this case, the Coupon Payment is $40 and the YTM is 5.25% or 0.0525.

Present Value = $40 / 0.0525

Calculating the present value:

Present Value ≈ $761.90

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The percentage of people that spend between 41 and 56 minutes watching TV shows on this streaming service is: 13.5%

The formula for the z-score here is:

z = (x' - μ)/σ

where:

x' is sample mean

μ is population mean

σ is standard deviation

Thus, for:

σ = 15

μ  = 71

x' = 41, we have:

z = (41 - 71)/15

z = -30/5

z = -6

for:

σ = 15

μ  = 71

x' = 56, we have:

z = (56 - 71)/15

z = -15/5

z = -3

From online p-value from 2 z-scores calculator, we have the p-value as:

P(-6 < z < -3) = 0.135

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Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

Since all three principles of experimental design are likely to have been used in the study described, Therefore option D is correct.

All of the above are principles of experimental design. Randomization helps to ensure that groups are similar in all aspects except for the treatment received, reducing the effects of confounding variables. Replication allows for assessing the variability and consistency of results. Blinding reduces the risk of bias by preventing participants or researchers from knowing which treatment was received. The study described in the question uses all of these principles of experimental design.

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