What is the length of the hypotenuse of the triangle?

A)8cm
B)5cm
C)3cm
D)2cm

Answer:

The slope of the line is -1/4. To find the slope of the line, we can use the formula m = (y2 - y1)/(x2 - x1). In this case, y2 = 2, y1 = 3, x2 = 4, and x1 = 0. Plugging these values into the formula gives us m = (2 - 3)/(4 - 0) = -1/4.

The p-value for this test is 0.012, which is the probability of observing a sample mean as extreme as 380 (or more extreme) if the null hypothesis were true.

If the significance level of the test was α = 0.05, for example, we would reject the null hypothesis since the p-value (0.012) is less than the significance level.

To find the p-value for this test, we first need to determine the appropriate test statistic. Since we do not know the population standard deviation, we will use a t-test. The test statistic is calculated as:

t = (X - μ) / (s / √n)

Where X is the sample mean, μ is the null hypothesis population mean, s is the sample standard deviation, and n is the sample size.

In this case, the null hypothesis might be that μ = 400 (for example, if we were testing whether the mean weight of a certain type of fruit was 400 grams). Using the given sample information, we can calculate the t statistic as:

t = (380 - 400) / (39 / √18) = -2.82

Next, we need to find the corresponding p-value from the t-distribution table. Looking at the table with 17 degrees of freedom (since n - 1 = 18 - 1 = 17), we find that the p-value for a two-tailed test with a t-value of -2.82 is approximately 0.012.

To learn more about probability  visit;

https://brainly.com/question/30034780

#SPJ11

If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, 1 280 000 000 different ways are possible.

Therefore option B is correct.

In this scenario we apply our  knowledge of probability to find the phone number, so:

We can establish the following facts:

Therefore, if we calculate the possibilities of occurrence, we have:

8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000

Learn  more about probability at:

brainly.com/question/795909

#SPJ1

Yes, Both triangles ABC and DEF are congruent.

Given that;

To show that, all steps for triangles ABC and DEF are congruent.

Now, By given figure of the triangle;

⇒ ∠ C = 90°

⇒ ∠ F = 90°

And, Distance between B and C and E and F are equal to each other.

And, Also, Distance DF = AC

Hence, By SAS congruency;

Both triangles ABC and DEF are congruent.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

The calculated value of the car 5 years after its purchase is 7250

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

Equation of line of fit is y = -750x + 11000

The value of a car 5 years after its purchase means that the value of x is 5

i.e. x = 5

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

y = -750 * 5 + 11000

Evaluate

y = 7250

Hence, the value of a car 5 years after its purchase is 7250

Read more about linear regression at

https://brainly.com/question/26755306

#SPJ1

The height of the cone is 4cm

The parameters given in the question are

volume= 36

radius= 3

The formula for calculating the height of a cone is

height= 3(v/πr²)

= 3(36/3.14×3²)

= 3(36/28.26)

= 3(1.273)

= 3.8

⇒4

Hence the height of the cone is 4 cm

Read more on height here

https://brainly.com/question/27695078

#SPJ1

Answer: $1.74 worth of coins

Step-by-step explanation:

Let's say Tom throws x amount of money in coins on the table. Then Joe throws twice as much, which is 2x.

The total value of coins on the table is $5.22, so we can write an equation:

x + 2x = 5.22

Simplifying the equation, we get:

3x = 5.22

Dividing both sides by 3, we get:

x = 1.74

Therefore, Tom threw $1.74 worth of coins on the table.

Answer:

720.33 square inches.

Step-by-step explanation:

To find the amount of leather needed to create the travel case, you need to find the surface area of the cylinder. The surface area of a cylinder is given by the formula:

SA=2πr2+2πrh

where r is the radius of the base and h is the height of the cylinder. In this case, the radius is half of the diameter, so r = 17/2 = 8.5 inches. The height is given as 5 inches. Using π = 3.14, we can plug in these values and get:

SA=2×3.14×8.52+2×3.14×8.5×5

SA=452.38+267.95

SA=720.33

Therefore, the amount of leather needed is approximately 720.33 square inches. The closest answer is C. 720.63 square inches.

Answer:

720.63 square inches

To find the surface area of the cylindrical travel case, we need to add the areas of the two circular bases and the lateral surface area.

The diameter of the circular bases is given as 17 inches, so the radius is 17/2 = 8.5 inches. Using the formula for the area of a circle, we can find the area of one base:

Area of one base = πr^2 = 3.14 x 8.5^2 = 226.96 square inches

Since there are two circular bases, the total area of both bases is:

Total area of both bases = 2 x 226.96 = 453.92 square inches

The lateral surface area is a rectangle with height 5 inches and length equal to the circumference of the circular base. We can find the circumference using the formula:

Circumference = 2πr = 2 x 3.14 x 8.5 = 53.38 inches

So, the lateral surface area is:

Lateral surface area = height x circumference = 5 x 53.38 = 266.9 square inches

Therefore, the total surface area of the cylindrical travel case is:

Total surface area = 453.92 + 266.9 = 720.82 square inches (rounded to two decimal places)

So, the answer is approximately 720.63 square inches (rounded to two decimal places).

g(x) is a translation of f(x), and it can be written as:

g(x) = f(x + 2)

So f(x) is the graphed function and g(x) is the one in the table. We can see that the slopes of both functions are 2, so there is no change in the slope nor any type of reflection.

This means that we have a translation.

Now, comparing values:

f(0) = 1   and g(0) =5

f(1) = 3   and g(1) = 7

and so on.

in any of the values we can see that g(x) is 4 units above f(x), then there are two possible transformations:

g(x) = f(x) + 4

g(x) = f(x + 2)

(The +2 in the argument is equivalent because of the slope of 2, when we take that product we will get a 4)

Thus the correct option is the second one.

Laern moer about translations at:

https://brainly.com/question/24850937

#SPJ1

Answer:

Step-by-step explanation:

I haven't answered because I'm thrown off by (x-1) in exponent but typically the ratio is the base.

The exponent is base with exponent (here  not sure if it's from parent or with(x-1 ) depends on professor.

and y int comes from plugging in x=0

       Exponential Function            Ratio          y-int

A          [tex]3^{x-1}[/tex]                                         3             -2/3

B           [tex]2^{x-1}[/tex]                                        2            45/2

C        [tex].1^{x-1}[/tex]                                        .1 or 1/10       12340

D      [tex](1/2)^{x-1}[/tex]                                  1/2                     -10

I'm positive about y-int and pretty sure about ratio and iffy about ex. function.  

Hope this helps.

Keisha sold 48 gallons of basic paint and 92 gallons of premium paint last weekend.

Let's denote the number of premium paint gallons sold by "x" and the number of standard paint gallons sold by "y".

According to the problem statement, we have:

[tex]x = 2y - 4[/tex] (the number of standard paint gallons sold was four less than twice as many premium gallons sold)

The total sales revenue from paint sales can be expressed as:

[tex]40.5x + 24.5y = 4914[/tex]

We can substitute x in the second equation with 2y - 4:

40.5(2y - 4) + 24.5y = 4914

Simplifying and solving for y, we get:

[tex]81y - 162 + 24.5y = 4914\\105.5y = 5076\\y = 48[/tex]

Substituting y in the equation [tex]x = 2y - 4[/tex], we get:

[tex]x = 2(48) - 4\\x = 92[/tex]

Therefore, last weekend, Keisha sold 48 gallons of normal paint and 92 gallons of premium paint.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

Answer:

The formula for the area of a circle is A=pir^2. A stands for the area, r is the radius. Ignore the pi, you don't need that. Just take the radius^2 and multiply it. For example, if I had A=pi5^2, my answer would be A=25pi, because 5^2=25. :)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The area of a circle is:

[tex]A=\pi r^{2}[/tex] in terms of pi

with [tex]\pi[/tex] being 3.14..., r being radius, and ²-ing the radius.

Hope this helps! :)

Answer:

$66.24

Step-by-step explanation:

The area of Vince's porch is:

8 feet x 12 feet = 96 square feet

To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:

96 square feet x $0.69 per square foot = $66.24

So it will cost $66.24 to buy enough stain for the whole porch.

Answer:

[tex]v(t) = 10500( {.86}^{t} )[/tex]

Answer: Euclid

Step-by-step explanation:

Answer:  4

Which geometer developed the deductive reasoning method for geometric proofs that is used today?

1.  Rene Descartes

2. Pythagoras

3. Girard Desargues

4. Euclid

Deductive reasoning, unlike inductive reasoning, is a valid form of proof.  Euclid using his definitions, common notions and postulates as an axiomatic system, was able to produce deductive proofs of a number of important geometric propositions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is:

The theoretical probability of pulling a brown marble from the bag is 10/40 or 1/4, which is equivalent to 25%. This is because there are 10 brown marbles out of 40 total marbles in the bag.

The experimental probability of pulling a brown marble is 13/40 or 0.325, which is equivalent to 32.5%. This is because the student pulled a brown marble 13 times out of 40 total trials.

Therefore, the correct answer is: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

To show that dy/dx = 1 - x·ln(x)/x·e^x, we shall first find the derivative of y with respect to x using the chain rule and the quotient rule.

According to the Quotient Rule, the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Given the equation: y = ln(x)/e^x

First, apply the quotient rule to differentiate y = ln(x)/e^x

dy/dx = [(e^x)(d/dx)(ln(x)) - (ln(x))(d/dx)(e^x)] / (e^x)^2

Next, differentiate ln(x) using the chain rule

(d/dx)(ln(x)) = 1/x

Next, differentiate e^x using the chain rule

(d/dx)(e^x) = e^x

Then, substitute the derivatives of ln(x) and e^x back into the quotient rule expression

dy/dx = [(e^x)(1/x) - (ln(x))(e^x)] / (e^x)^2

Simplify the expression:

dy/dx = (e^x/x - ln(x)e^x) / e^(2x)

Next, multiply the numerator and denominator by x

dy/dx = (xe^x/x^2 - ln(x)e^x/x) / (xe^(2x)/x^2)

Then, simplify the expression

dy/dx = (e^x/x - ln(x)e^x/x) / (xe^(2x)/x^2)

And multiply the numerator and denominator by x^2

dy/dx = (xe^x - xln(x)e^x) / (xe^(2x))

Next, factor out e^x from the numerator

dy/dx = e^x (x - xln(x)) / (xe^(2x))

And simplify the numerator

dy/dx = e^x (x(1 - ln(x))) / (xe^(2x))

Next, simplify further

dy/dx = (x - xln(x)) / (xe^(x))

Finally, rearrange the terms

dy/dx = 1 - xln(x) / xe^(x)

Therefore, the derivative of y with respect to x is given by dy/dx = 1 - xln(x)/xe^(x).

Read more about the Quotient Rule at brainly.com/question/30278964

#SPJ1

Answer:133.4

Step-by-step explanation:

The number of middle school students prefer the Documentaries television genre is108.

To get that, we need to multiply the total number of students by the correspondent percentage (in decimal form).

We know that there are 450 students, and 24%  (just add the other percentages, and 24% is the amount missing to reach 100%) like the documentaries.

That percentage in decimal form is 24%/100% = 0.24

Then the estimation will be:

450*0.24 = 108

So that is the correct answer.

LEarn more about percentages at:

https://brainly.com/question/843074

#SPJ1

Answer:

d

Step-by-step explanation:

The transformations are matched as follows

f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

f(x) = eˣ to the graph of g(x ) = -eˣ - 4

f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

f(x) = eˣ to the graph of g(x ) = -eˣ - 4

Translation transformation refers to the movement of an object or figure in a straight line without rotation or distortion in this transformation all points of an object or shape move parallel and in the same direction

The negative sign in g(x) = -eˣ - 4 lead to reflection while the -4 is a translation 4 units downwards.

For the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

The +1 represents a vertical shift up by 1 unit and Horizontal shift left is represented by +5

Learn more about transformation at

https://brainly.com/question/4289712

#SPJ1

To get a result of 4 on the numerical expression, Barry added 4 to the expression on the number line. So, the correct answer is C).

The expression involves adding up the values at different points on the number line. We can see that the value at the point labeled "x" is the missing value that needs to be found.

By adding up the values at each point, we get the following equation

-5 + (-3) + x - (-7) = 1

Simplifying this equation gives

-5 - 3 + x + 7 = 1

Simplifying further

-x = -4

Solving for x, we get

x = 4

Therefore, the value of x that Barry added to the expression on the number line to get a result of 4 is 4. So, the correct option is C).

To know more about number line:

https://brainly.com/question/16191404

#SPJ1

--The given question is incomplete, the complete question is given

" Barry used a number line to simplify a numerical expression on a math test. Which number did Barry add to get a result of 4 on the numerical expression he simplified? A –14, B −6, C 4, D 14 "--

The original recipe requires 6 cups of flour and 4 cups of water. If the water is reduced to 2 cups, then 3 cups of flour should be used, found by setting up a proportion.

The recipe calls for 6 cups of flour and 4 cups of water.

To decrease the amount of water used to 2 cups, we can set up a proportion

(flour)/(water) = (6)/(4) = (x)/(2)

where x is the amount of flour needed when 2 cups of water are used.

Simplifying this proportion, we get

4x = 12

Dividing both sides by 4, we get

x = 3

Therefore, when the recipe uses 2 cups of water, 3 cups of flour should be used.

To know more about amount of water:

https://brainly.com/question/26211317

#SPJ1

The 95% confidence interval estimate for the population proportion of car deals that used 0% financing is (0.1612, 0.2308). So, the correct option is (b).

To construct a confidence interval estimate for the population proportion of car deals that used 0% financing, we can use the formula

CI = p ± z√((p(1-p))/n)

where

p = sample proportion = 98/500 = 0.196

n = sample size = 500

z = z-score for the desired level of confidence, which is 95% in this case. From a standard normal distribution table, the z-score corresponding to 95% confidence level is approximately 1.96.

Substituting the values, we get

CI = 0.196 ± 1.96√((0.196(1-0.196))/500)

= (0.1612, 0.2308)

Therefore, the 95% confidence interval estimate is (0.1612, 0.2308).

The correct answer is (b).

To know more about confidence interval:

https://brainly.com/question/29680703

#SPJ4

In the case of Alicia, The single net increase is 5.821% of the original price.

Alicia is buying shoes at a department store that offers a 15% discount on all shoes. Additionally, she has a store card that gives her another 5% discount. However, at checkout, the cashier tells her that there will be two increases, one of 2% for commissions and another of 18% for general sales tax. To determine if there is a net discount or increase, we need to calculate the total discount and total increase separately and compare them.

First, let's calculate the total discount:

Next, let's calculate the total increase:

If the total discount is greater than the total increase, then there is a net discount. If the total increase is greater than the total discount, then there is a net increase.

Therefore, we need to compare:

Simplifying both expressions, we get:

Since 1.0506 x Original Price is greater than 0.20 x Original Price, we can conclude that there is a net increase.

To calculate the amount of the single net increase, we can subtract the discounted price from the increased price:

Simplifying the expression, we get:

Therefore, the single net increase is 5.821% of the original price.

Learn More about discount

https://brainly.com/question/23865811

#SPJ4

Complete Question:

Alicia will buy shoes in a department store that advertises a 15% discount on all shoes, plus she has the store card and therefore they will give her another 5% discount. When paying: the cashier tells you that they will make 2 increases, one of 2% for commissions and the other of 18% for general sales tax. Determine if it is the case, how much is the discount or single increase?

The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.

The given trigonometric identity is,

(sin(x) + tan(x))/sin(x).

We know that tan(x) = sin(x)/cos(x), so we can substitute that in:

sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)

We can simplify the fraction in the numerator:

sin(x)/ sin(x) + sin(x)/sin(x)cos(x)

We know that sin(x)/sin(x) = 1, so we can simplify further:

1+ 1/cos(x)

We know that 1/cos(x) = sec(x), so we can substitute that in:

1 + sec(x).

Now we have the same expression as the right-hand side of the identity, so we have proven that:

sin(x) + tan(x)/sin(x) = 1 + sec(x)

Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.

To learn more about trigonometric identities;

https://brainly.com/question/24377281

#SPJ1

The scale factor used. in the dilation is 1/3

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

The scale factor is calculated as

Scale factor  = A'/A

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

Scale factor  = (-1, -1)'/(-3, -3)

Evaluate

Scale factor  = 1/3

Hence, the scale factor  = 1/3

read more about scale factor  at

https://brainly.com/question/29229124

#SPJ1

Step-by-step explanation:

we know the area A = B

10(6 + x) = A

5(15.5 + x) = B

A = B

10(6 + x) = 5(15.5 + x)

solve for x to get

x = 3.5

Add up to get the perimeter is 80

Mark Me Brainliest!

Answer:

Step-by-step explanation:

Given 3 points, you want the fourth point that defines a rectangle. Then you want the length, width, and area of the rectangle. {(3, 2), (3, -3), (-5, -3)}

A rectangle is a quadrilateral (4-sided polygon) with opposite sides the same length and parallel, and all corners 90°.

We can name the given points A(3, 2), B(3, -3), and C(-5, -3).

When you plot the given points, you can imagine they form a right triangle with the right angle at B. The missing sides of the rectangle are ...

A line parallel to BC through A, and a line parallel to AB through C.

The equation of the first line is y = 2, and the equation of the second line is x = -5. These two lines meet at the point (x, y) = (-5, 2)

The missing point is (-5, 2).

We generally think of "length" as being the longer dimension of the figure. Here, the points B and C are farther apart than the points A and B. The distance between those points is the difference of their x-coordinates:

  length = 3 -(-5) = 8

The length of the rectangle is 8 units.

As with length, we can determine the distance between points A and B as the difference of their y-coordinates:

  width = 2 -(-3) = 5

The width of the rectangle is 5 units.

The area of a rectangle is the product of its length and width:

  A = LW

  A = (8)(5) = 40 . . . . square units

The area of the rectangle is 40 square units.

__

Additional comment

When the sides of the rectangle are on grid lines, as here, finding the missing point and the various lengths is pretty easy.

You will notice that there are two different x-coordinates and two different y-coordinates among the four points. The four points are those coordinates in every combination. One way to find the missing point is to find the missing combination. The side lengths are the difference between x-coordinates and the difference between y-coordinates. (This works for rectangles aligned to the grid.)

When the sides are skew with respect to the grid lines, a different strategy for locating the missing point and for finding side lengths is required. That strategy can make use of the fact that the diagonals cross at their midpoints, and the length is given by the distance formula.

<95141404393>

Step-by-step explanation:

3^x eventually gets larger......it has exponential growth....the other is only linear growth