Find the distance between the two points rounding to the nearest tenth (if necessary).
(-2, 5) \text{ and } (-8, -3)
(−2,5) and (−8,−3)

Answer:

11.9

Step-by-step explanation:

Pythagorean theorem:

\(a^2+b^2 = c^2\). where a and b are the sides and c is the hypotehnus (the side in front of the 90 degree angle)

\(22^2 + b^2 = 25^2\\484 + b^2 = 625\\b^2 = 625-484\\b^2 = 141\\b = \sqrt{141} \\b = 11.9\)

Answer:

11.9

Step-by-step explanation:

This is a right triangle so I can solve this with the pythagorean theorem.

Set up the equation 22²+x²=25² x would be the third side

Simplify, 484+x²=625

Subtract from both sides 484-484+x²=625-484

x²=141

Find the square root of 141 to get x

The square root of 141 is approximately 11.9 rounded to the nearest tenth.

Using  division we can infer that 50 pages will not be enough.

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number.

Timmy has 810 stamps.

Now each page can hold 16 stamps and he has 50 pages.

Now we will divide 810 by 16 to calculate the number of pages required to put all the stamps.

∴ 810 ÷ 16 = 50 remainder 10.

Therefore after completing the 50 pages there are 10 stamps left.

Hence from division we can infer that 50 pages will not be enough.

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Disclaimer : the complete question is :

Timmy has 810 stamps. He wants to organize them on pages that hold 16 stamps each. He has 50 pages. Does Timmy have enough pages to organize all his​ stamps?

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Answer:

D

Step-by-step explanation:

The decrease in losses is 3 and 3/5 is 60%

Answer:

D

Step-by-step explanation:

If you multiply 5 by 2, you get 10, I automatically view that as 100%, multiply 2 by 20(simplified for the 100 stance) you have 3 games won this season, multiply that by 20 and you have 60, give us a 60% decrease. Sorry if you don't understand, but hope this helps!

Answer:

the answer is 1.041

Step-by-step explanation:

you will do.... 12*8/100

The function to model the amount after the discount is x - 0.12x

The function to model the amount after the sales tax is x + 0.08x.

The rule for the composition function calculates the final price you pay Games Shop is x - 0.04x.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

12% = discount on purchases.

8%  = sales tax.

Now,

If the item cost $x

The function to model the amount after discount.

f(x) = x - (12/100)x = x - 0.12x

The function to model the amount after the sales tax.

g(x) = x + (8/100)x = x + 0.08x

Now,

The rule for the composition function calculates the final price you pay Games Shop.

= x + 0.08x - 0.12x

= x - 0.04x

Thus,

The function to model the amount after the discount is x - 0.12x

The function to model the amount after the sales tax is x + 0.08x.

The rule for the composition function calculates the final price you pay Games Shop is x - 0.04x.

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By solving the given equation f(x) = \(x^{2} +3x-40\), the zeroes are -3 and 5.

To solve the given equation we have to do the factorization.

What is factorization: Factorization is the method of writing numbers as the product of their factors or divisors.  In other words, we can say finding what to multiply together to get an expression.

To do the factorization, we have to follow the steps as shown below:

 \(x^{2} +3x-40\) \(= 0\)

\(-40 = 8 * -5\\\)                        [ multiplication of 8 and -5 is -40]

\(x^{2}+8x-5x -40\) \(= 0\)

\(x(x+8) -5(x+8)\) \(= 0\)

\((x-5)(x+8)\) \(= 0\)

\(x = 5\)   and  \(x = -8\)              [ The roots or zeroes]

From the above solution, we can conclude that the zeros of the given function \(x^{2} +3x-40\) are 5 and -8.

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Step-by-step explanation:

\( \sin(20) = 3 \div x\)

Multiply both sides with x :

\( x \times \sin(20) = 3\)

And divide both sides with sin(20) :

\(x = 3 \div \sin(20) = 8.771\)

Which gives us x=8,771

Answer:

AB = 6

Step-by-step explanation:

sin 20° = 3/?

\(\frac{1}{2}\) = \(\frac{3}{x}\)

cross-multiply: x = 6

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

A. The calculations for the measures of center are shown below.

B. The calculations for the measures of variability are shown below.

C. If you are interested in a larger class size, Mountain View School is a better choice for you.

In Mathematics and Geometry, the mean for a set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data based on the stem and leaf plot, we have the following for Mountain View;

Total class size, F(x) = 10+12+18+19+20+21+23+24+24+25+25+26+27+28+30

Total class size, F(x) = 332

Mean = 332/15

Mean = 22.13.

Median = 24

Mode = 24 and 25

For Bay Side school, we have:

Total class size, F(x) = 5+6+8+10+12+14+15+16+18+20+20+22+23+25+42

Total class size, F(x) = 256

Mean = 256/15

Mean = 17.07.

Median = 16

Mode = 16 and 20

Part B.

For Mountain View School:

Range = 30-12 = 18

Interquartile Range (IQR) = Q3-Q1 = 27-21 = 6

Variance = [(12-23)² + (18-23)² + ... + (30-23)²]/13 = 32.92

Standard Deviation = √(Variance) = 5.74

For Bay Side School:

Range = Highest number - Lowest number

Range = 42 - 5 = 37

Interquartile Range (IQR) = Q₃ - Q₁

Interquartile Range (IQR) = 22-10 = 12

Variance = δ²

Variance = [(5-17.4)² + (6-17.4)² + ........ + (42-17.4)²]/15

Variance = 194.16

Standard Deviation, δ = √(Variance)

Standard Deviation, δ = 13.93

Part C.

Based on the calculations above, we can logically deduce that Mountain View School is a better choice for anyone interested in a larger class size because its measures of center (mean and median class size) are higher than those of Bay Side School.

Conversely, we can logically deduce that Bay Side School is a better choice for anyone interested in a larger class size because its measures of variability (range and standard deviation) are higher than those of Mountain View School.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x is 12

Step-by-step explanation:

» From scalar properties:

\({ \tt{ \frac{FG}{FH} = \frac{AB}{AC} }} \\ \\ { \tt{ \frac{9}{6} = \frac{18}{x} }} \\ \\ { \tt{x = \frac{18 \times 6}{9} }} \\ \\ { \boxed{ \tt{ \: x = 12 \: }}}\)

Answer:

34 people voted for band 68 people voted for art and 88 people voted for Spanish this help

Step-by-step explanation:

Answer: 7$

Step-by-step explanation: 40-4= 36 | 3x5=15 | 36-15=21 | 21/3=7

Answer:

Step-by-step explanation:

same

Using the normal distribution, it is found that:

a) The pilot is at the 72th percentile.

b) 19.13% of pilots are unable to fly.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 72.6, \sigma = 2.7\).

Item a:

The percentile is the p-value of Z when X = 74.2, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{74.2 - 72.6}{2.7}\)

Z = 0.59

Z = 0.59 has a p-value of 0.7224.

72th percentile.

Item b:

The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:

X = 78:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{78 - 72.6}{2.7}\)

Z = 2

Z = 2 has a p-value of 0.9772.

X = 70:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{70 - 72.6}{2.7}\)

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.9772 - 0.1685 = 0.8087 = 80.87%.

Hence the percentage that is unable to fly is:

100 - 80.87 = 19.13%.

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Answer:

Yes

Step-by-step explanation

Lines are perpendicular when they have the reprocial slope with the opposite sign.

Yes, the lines having slopes 6 and -1/6 are perpendicular.

The slope of a line is a number that describes  the direction  of the line. The formula of calculating slope is calculated as under:

Slope=\((y_{2} -y_{1} )/(x_{2} -x_{1} )\).

We have been given that the slope of line A is 6 and slope of line B is -1/6.

Two lines are seem to be perpendicular to each other if the product of their slopes is equal to -1.

Product=slope of line A * Slope of line B

=6*(-1/6)

=-6/6

=-1

Hence the lines having slopes 6 and -1/6 are perpendicular to each other.

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Answer:

Angie drove to the beach. She kept track of the number of miles she traveled and the number of gallons of gas she used. Which method and reasoning can Angie use to calculate the gas mileage in miles per gallon?

A:435.7 miles • 12.42 gallons,

because multiplying a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

B:435.7 miles −12.42 gallons,

because subtracting a quantity with units of gallons from a quantity with units of miles gives a quantity with units of miles per gallon.

C:12.42 gallons ÷ 435.7 miles,

because dividing a quantity with units of gallons by a quantity with units of miles gives a quantity with units of miles per gallon.

D:435.7 miles ÷ 12.42 gallons,

because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

Step-by-step explanation:

Answer:

435.7 miles divided by 12.42 gallons

because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

Answer:

19.8

Step-by-step explanation:

Subtract 130.2 by 110.4

Answer:

1).6cm squared

2). 36 cm squared

3).787.5

(im not sure 3 is correct)

Step-by-step explanation:

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

12% of 7.99

=0.96$

so...

The cost after Markup

=7.99$+0.96$

answer/explanation:

carry out these steps: 12% of 7.99 = $0.96 and use fraction if u may like. therefore the new cost after the markup is $7.99 + $0.96 which is then equal to your final answer - $8.95!

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Let's find the slope (m) :

slope of given line is 5/3

now, let's plug the value of coordinates of a point lying on the line ( for example : (6 , 11) and slope (m) to find the y - intercept (c) :

value of y - intercept (c) = 1, so our equation will be :

The absolute maximum value of the function f(x, y) = \(x^2 + y^2 - 3y - xy\) on the solid disk \(x^2 + y^2\)≤ 9 is 18, achieved at the point (3, 0). The absolute minimum value is -9, achieved at the point (-3, 0).

To find the absolute maximum and minimum values of the function f(x, y) =\(x^2 + y^2 - 3y - xy\)on the solid disk \(x^2 + y^2\) ≤ 9, we need to consider the critical points inside the disk and the boundary of the disk.

First, let's find the critical points by taking the partial derivatives of f(x, y) with respect to x and y and setting them equal to zero:

\(\frac{\delta f}{\delta x}\) = 2x - y = 0 ...(1)

\(\frac{\delta f}{\delta y}\) = 2y - 3 - x = 0 ...(2)

Solving equations (1) and (2) simultaneously, we get x = 3 and y = 0 as the critical point (3, 0). Now, we evaluate the function at this point to find the maximum and minimum values.

f(3, 0) = \((3)^2 + (0)^2\) - 3(0) - (3)(0) = 9

So, the point (3, 0) gives us the absolute maximum value of 9.

Next, we consider the boundary of the solid disk\(x^2 + y^2\) ≤ 9, which is a circle with radius 3. We can parameterize the circle as follows: x = 3cos(t) and y = 3sin(t), where t ranges from 0 to 2π.

Substituting these values into the function f(x, y), we get:

=f(3cos(t), 3sin(t)) = \((3cos(t))^2 + (3sin(t))^2\) - 3(3sin(t)) - (3cos(t))(3sin(t))

= \(9cos^2(t) + 9sin^2(t)\) - 9sin(t) - 9cos(t)sin(t)

= 9 - 9sin(t)

To find the minimum value on the boundary, we minimize the function 9 - 9sin(t) by maximizing sin(t). The maximum value of sin(t) is 1, which occurs at t = \(\frac{\pi}{2}\) or t = \(\frac{3\pi}{2}\).

Substituting t = \(\frac{\pi}{2}\) and t = \(\frac{3\pi}{2}\) into the function, we get:

f(3cos(\(\frac{\pi}{2}\)), 3sin(\(\frac{\pi}{2}\))) = 9 - 9(1) = 0

f(3cos(\(\frac{3\pi}{2}\)), 3sin(\(\frac{3\pi}{2}\))) = 9 - 9(-1) = 18

Hence, the point (3cos(\(\frac{\pi}{2}\)), 3sin(\(\frac{\pi}{2}\))) = (0, 3) gives us the absolute minimum value of 0, and the point (3cos(\(\frac{3\pi}{2}\)), 3sin(\(\frac{3\pi}{2}\))) = (0, -3) gives us the absolute maximum value of 18 on the boundary.

In summary, the absolute maximum value of the function f(x, y) = \(x^2 + y^2\) - 3y - xy on the solid disk \(x^2 + y^2\) ≤ 9 is 18, achieved at the point (3, 0). The absolute minimum value is 0, achieved at the point (0, 3).

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Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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a. Find the graph in the attachment

b. As h increases, e tends to 90°

Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.

The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.

To plot the graph, we see that the function is the tangent function.

The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°

Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞

So, we plot h = 22tane for 0 ≤ e ≤ 90°

Find the graph in the attachment

From the graph, we seet that at high h or as h increases, e tends to 90°

So, as h increases, e tends to 90°

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Answer: 0.429

Step-by-step explanation: Use a calculator and put the fraction and hit enter to get it in decimal form. You should get a number like 0.42857142857 but the problem asks us to round to the nearest thousandth. Since there is a 5 in the ten-thousandth place, we must round up. Therefore, the final answer will be 0.429.

Answer:

x = 5, y = -2

Step-by-step explanation:

Given equations:

From the first equation we get:

Substitute x in the second equation, find y:

Find x:

Answer:

A) 3.5

Step-by-step explanation:

                4.3t + 6.8 = 8.4t - 7.55

         Subtract 8.4t from both sides,

              4.3t - 8.4t +6.8 = -7.55

        Combine like terms,

                      -4.1t  + 6.8 = -7.55

                  To isolate 't' first subtract 6.8 from both sides.

                   -4.1t  = -7.55 - 6.8

                   -4.1t  = -14.35

                Divide both sides by (-4.1)

                      t = -14.35 ÷ (-4.1)

                      t =  3.5

The additional operation which needed to make the expression equivalent to given expression is \(-\dfrac{3}{4} x\). Thus the option 3 is the correct option.

Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The equation given in the problem is,

\(\dfrac{5}{4} x+6\)

Let the equation is equation number 1.

This expression is to convert in the expression, which is,

\(\dfrac{1}{2}x+6\)

Let the above equation is equation number 2.

Let the additional operation which needed to make the expression equivalent to given expression is \(f(x)\).

As the addition of \(f(x)\) and equation 1 is equal to the equation 2. Therefore,

\(f(x)+\dfrac{5}{4} x+6=\dfrac{1}{2}x+6\)

Solve the equation as,

\(f(x)=\dfrac{1}{2}x+6-\dfrac{5}{4} x-6\\f(x)=\dfrac{1}{2}x-\dfrac{5}{4} x\\f(x)=\dfrac{2-5}{4} x\\f(x)=\dfrac{-3}{4} x\)

Hence, the additional operation which needed to make the expression equivalent to given expression is \(-\dfrac{3}{4} x\). Thus the option 3 is the correct option.

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Answer:

c                   the third one

Step-by-step explanation:

Based on this information, No, the university administration should not trust the professor because the study was not taken from a random sample of scholarship athletes. Hence option C is correct.

According to the mentioned question, a university professor investigates how the sample was gathered since he does not think that there is a true difference in the GPA of male and female scholarship athletes. His inquiry reveals that the study was exclusively distributed to the basketball teams' athletes.

According to this data, the university administration shouldn't believe the professor because the study's participant pool did not consist of a representative sample of scholarship athletes.

The sample may not be representative of all university scholarship athletes since the study solely looks at basketball players. This may skew the results and make it challenging to extrapolate the conclusions to the larger group of scholarship athletes.

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