A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid? ​

Answer:

  (1, 2) and (-1, -2)

Step-by-step explanation:

Since y = 2x, the first blank tells you

  2x = 2

  x = 1

____

Since the variables are squared, a negative solution is as good as a positive solution, so x = -1 and y = -2 will also work.

Answer:135.9

Step-by-step explanation:you just have to multiply

In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether [tex]x=10, \ y=-3, \ z=14[/tex] is the solution to this system, that is, the ordered triple [tex]P(x,y,z)[/tex] where three planes intersect.

The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:

[tex]First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation[/tex]

STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the [tex]x=10, \ y=-3, \ z=14[/tex] is not the solution to the system of equations.

The pic will help you

Good luck:))

The answer is

[tex]y = - 3x + \frac{18}{5} [/tex]

[tex]\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23\frac{1}{8}&1\\\\ x&17 \end{array}\implies \cfrac{23\frac{1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{23\cdot 8+1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{185}{8}}{x}=\cfrac{1}{17} \\\\\\ \cfrac{\frac{185}{8}}{\frac{x}{1}}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393\frac{1}{8}=x[/tex]

As given,

Number of sheets of paper put in the binder 8 days ago = 50 sheets

Current number of sheets left after 8 days = 2 sheets

So, number of sheets used in 8 days = [tex]50-2=48[/tex] sheets

As it is stated that the same number of sheets are used each day, so number of sheets used per day = [tex]\frac{48}{8}=6[/tex] sheets.

Hence, 6 sheets of paper were used each day.

Answer:

6

Step-by-step explanation:

Answer: the one that is not a magor epense catgortuy is c : transportation

Step-by-step explanation:

the answer is: C) transportation

➷ We know this:

3/7 = 27

You need to find the value of 1/7

To do this, divide by 3

27/3 = 9

1/7 = 9

Multiply this by 7 to get the total number of balls:

9 x 7 = 63

There are 63 balls.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The answer is divergent ⇒ answer (b)

Step-by-step explanation:

* The series is -5 + 25 + -125 + ........

- It is a geometric series with:

- first term a = -5 and common ratio r = 25/-5 = -5

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = -5

∴ IrI = 5

∴ IrI > 1

∴ The series is divergent

Answer:

one sample t-test will be appropriate in this case

Step-by-step explanation:

We are carrying out a hypothesis test of the mean with the population standard deviation being unknown. We shall estimate the population standard deviation with the sample equivalent, s in determining the value of the test-statistic.

Answer:

A left-tailed test

Step-by-step explanation:

I believe y = 41

Hope this helped!

The answer would be -21/4

Here’s how you solve it!

First move the variable to the left side which makes it change the sign to a negative

-4y➕1=22

Then you move the constant to the other side and change the sign

-4y=22-1

Now you subtract

22-1=21

-4y=21

Then divide both sides by -4

Then you are left with your answer

Y=-21/4

Hope this helps! :3

Answer:

-6,0,2

Step-by-step explanation:

f(x)=x(x−2)(x+6)

To find the zeros of the function, set the function equal to zero

0 =x(x−2)(x+6)

Using the zero product property

x=0  x-2 =0   x+6=0

Solve each equation

x=0  x=2    x=-6

There are three zero's

-6,0,2

Answer:

A = (x^2 - 2x - 8) m^2

Second option

Step-by-step explanation:

Area of rhombus = 1/2 d1 * d2

= 1/2(2x+4)(x-4)

= 1/2 (2x^2 -8x + 4x - 16)

= 1/2 (2x^2 - 4x - 16)

= x^2 - 2x - 8

Answer: first option.

Step-by-step explanation:

Find the common difference d of the arithmetic sequence:

[tex]d=a_n-a_{(n-1)}\\d=989-997\\d=-8[/tex]

Then the formula for the 101st term is the shown below:

[tex]a_n=a_1+(n-1)d[/tex]

Where:

[tex]a_1=997\\d=-8\\n=101[/tex]

Substitute values into the formula. Therefore, you obtain:

[tex]a_n=997+(101-1)(-8)=197[/tex]

Answer:

[tex]a_{101}=197[/tex]

Step-by-step explanation:

The first term of the sequence is

[tex]a_1=997[/tex]

The given sequence  is 997, 989, 981, ...

The common difference is

[tex]d=989-997=-8[/tex]

The nth ter of the sequence is

[tex]a_n=a_1+d(n-1)[/tex]

We plug in the first term and the common ratio to obtain;

[tex]a_n=997-8(n-1)[/tex]

[tex]a_n=997-8n+8[/tex]

[tex]a_n=1005-8n[/tex]

We substitute n=101 to get;

[tex]a_{101}=1005-8(101)[/tex]

[tex]a_{101}=197[/tex]

I guess that's f(x) = -3x^2+2

Well :

-3x^2+2=0

-3x^2=-2 / : (-3)

x^2= -2/-3

x^2= 2/3 / sqrt

x= +/ - sqrt(2)/sqrt(3)

We got the zero points.

x ~ +/- 0.81

f(0)= -3(0)^2 + 2

f(0)= 2

Mark three points:

(0.81;0)

(-0.81;0)

(0;2)

Connect with parabolic line and ya got a your graph

60 minutes = 1 hour

55 + 5 = 60 70 - 5 = 65 10:00

10:00 + 60 min = 11:00 65 - 60 = 5

11:00 + 5 min = 11:05

Bob finished mowing at 11:05

a^2+b^2=c^2 <----- the equation to find out sides for a right triangle

Every right triangle follows the pythagorean theorem: given the legs [tex]a[/tex] and [tex]b[/tex] and the hypothenuse [tex]c[/tex] we have

[tex]a^2+b^2=c^2 \implies c=\sqrt{a^2+b^2}[/tex]

In your case, a=3 and b=5, so we have

[tex]c=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}[/tex]

Answer:

It is a right triangle because if it contains a 90 degree angle (a right angle), it's  a right triangle.

Step-by-step explanation:

It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle

It's not C because

[tex](AB)_{1,1}=A_{1,c}B_{r,1}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2[/tex]

where [tex](AB)_{1,1}[/tex] denotes the element of [tex]AB[/tex] in row 1, column 1, [tex]A_{1,c}[/tex] denotes the first row of [tex]A[/tex], and [tex]B_{r,1}[/tex] denotes the first column of [tex]B[/tex].

It's not A because

[tex](AB)_{1,2}=A_{1,c}B_{r,2}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16[/tex]

It's not D because

[tex](AB)_{2,2}=A_{2,c}B_{r,2}=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46[/tex]

So B must be the correct answer (and it is).

Answer:

Last choice: 14 = (1/2)x(x - 12)

Step-by-step explanation:

base = x

height = x - 12

area = (1/2)bh

14 = (1/2)x(x - 12)

The answer is C. Thank Me Later ?

Answer:

The length is [tex]8\frac{1}{4}\ ft[/tex]

Step-by-step explanation:

we know that

The area of a rectangle is equal to

[tex]A=LW[/tex]

In this problem we have

[tex]A=53\frac{5}{8}\ ft^{2}[/tex]

[tex]W=6\frac{1}{2}\ ft[/tex]

convert to an improper fraction

[tex]A=53\frac{5}{8}=\frac{53*8+5}{8}=\frac{429}{8}\ ft^{2}[/tex]

[tex]W=6\frac{1}{2}=\frac{6*2+1}{2}=\frac{13}{2}\ ft[/tex]

substitute in the formula and solve for L

[tex]\frac{429}{8}=L\frac{13}{2}[/tex]

[tex]L=\frac{429*2}{8*13}=\frac{858}{104}\ ft[/tex]

Convert to mixed number

[tex]L=\frac{858}{104}=\frac{832}{104}+\frac{26}{104}=8\frac{1}{4}\ ft[/tex]

The length of the bathroom floor in this case is 8 1/4 feet.

The area of a rectangle is calculated by multiplying its length by its width. In this case, with the bathroom floor having an area of 53 5/8 square feet and a width of 6 1/2 feet, we can find the length as follows:

Area = Length x Width

53 5/8 = Length x 6 1/2

Length = 53 5/8 / 6 1/2

Length = 8 1/4 feet

Therefore, the length of the bathroom floor is 8 1/4 feet.

Answer:

This is called the independent variable.

Step-by-step explanation:

We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.

Answer:

Option A. 36

Step-by-step explanation:

Let

x-------> the number of boys

y------> the number of girls

we know that

[tex]x+y=42[/tex] -----> equation A

[tex]y=\sqrt{x}[/tex] -----> equation B

using a graphing tool to solve the system of equations

Remember that the solution is the intersection point both graphs

The solution is the point (36,6)

see the attached figure

therefore

The number of boys is 36

Answer:

54 square meters

Step-by-step explanation:

Similar figures have corresponding lengths as equal ratios.

Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]

this means the lengths of larger is 1.5 times lengths of smaller.

In terms of area, the scale factor is squared. Hence the scale factor for area is  [tex]k^2=(1.5)^2=2.25[/tex]

this means the area of larger is 2.25 times the area of smaller.

Now, Let area of smaller trapezoid be x so we can say:  [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]

to nearest square meter, x = 54 meters squared

Answer:

$ 11.36

Step-by-step explanation:

The advance cost​ him;

3.20 + 3.4% of 240

3.20 + (3.4/100)*240

3.20 + 8.16 = $ 11.36

Answer:

Step-by-step explanation:

$2345.20

The total cost price of the car is $2,345.2.

Given that, a car insurance company paid 1758.90 to repair a car that has been rear-ended. This was 75% of the total cost of the repair.

We need to find what was the total cost price of the car.

The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P. Selling Price: The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.

Let the total cost price be x.

Now, 75% of x=1758.90

⇒0.75×x=1758.90

⇒x=$2,345.2

Therefore, the total cost price of the car is $2,345.2.

To learn more about the cost price visit:

https://brainly.com/question/11027396.

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Answer:

163/500 = 0.326

Step-by-step Explanation:

Drawing a Venn diagram for this, we will have 3 circles.  One will represent rock, one will represent country, and one will represent jazz.

There are 11 students that like all 3 types of music.  This means the number 11 goes in the intersection of all 3 circles.

There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.

There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.

There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.

There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have

206-(11+19+16) = 206-(46) = 160 in just rock.

There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have

161-(11+19+11) = 161-(41) = 120 in just country.

There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have

118-(11+16+11) = 118-38 = 80 in just jazz.

This leaves

500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.

This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.

The probability that a randomly selected student likes neither rock nor country is;

P(R' ∩ C') = 0.326

Let us denote them as follows;

Number that like rock music be R

Number that like Country music be C

Number that like Jazz music be J

Thus, as we are given we have;

R = 206

C = 161

J = 118

R ∩ C = 30 - 11 = 19

R ∩ J = 27 - 11 = 16

C ∩ J = 22 - 11 = 11

R ∩ C ∩ J = 11

n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]

n(only jazz) = 118 - (16 + 11 + 11)

n(only J) = 80

n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]

n(only Rock) = 206 - (19 + 16 + 11)

n(only R) = 160

n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]

n(only country) = 161 - (19 + 11 + 11)

n(only C) = 120

Now, the number of students that like neither of the 3 music is;

A' ∩ B' ∩ C' =  500 - [(R ∩ C) + (R ∩ J) +  (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]

⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)

⇒ A' ∩ B' ∩ C' = 83

Thus, number of students that likes neither rock nor country is;

n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)

n(A' ∩ B') = 83 + 80

n(A' ∩ B') = 163

Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326

Read more at; https://brainly.com/question/8945385

Answer:

450

Step-by-step explanation:

To find an area of the triangle, you must first multiply the base and the height.