A vehicle is randomly selected. Let T be the event that
the vehicle is a truck and A be the event that the
vehicle has all-wheel drive. What is the value of P(T°
and A)?
A)0.06
B)0.20
C)0.32
D)0.80

Using the bottom rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.

The image showing the two groups is as shown in the brainly link attached at the end.

From the attached file in the brainly link, we see that the shapes are grouped using the following criteria:

Using the above rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.

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Answer:

4(3)(-2) = -24

Answer:

C) -24

Step-by-step explanation:

Given the expression: 4xy

Substitute the values above for the variables and multiply:

4(3)(-2)

12(-2)

-24

Final answer: -24

Hope this helps!

Answer:

550 sq. cm

Step-by-step explanation:

Attached above (answer):-

Step-by-step explanation:

(x - h)² + (y - k)² = r²

with (h, k) being the center and r the radius.

in our case the center is (1, 3), the radius is 3.

so, the right answer is the third answer option

(x - 1)² + (y - 3)² = 9

Answer:

4080 cm³

Step-by-step explanation:

Figure is of a cuboid

Given length (l) = 30cm

breadth (b) = 17cm

height (h) = 8cm

Volume of cuboid = l.b.h

= 30 × 17 × 8

= 4080 cm³

The probability of selecting a multiple of 2 or a multiple of 7 is 11/20 or 0.55 or √0.3025.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of outcome = 20

Total number of favourable outcome (multiple of 2 or a multiple of 7):

E = {2, 4, 6, 7, 8, 10, 12, 14, 16, 18, 20}

n(E) = 11

The probability = 11/20 = 0.55 or

= √0.3025

Thus, the probability of selecting a multiple of 2 or a multiple of 7 is 11/20 or 0.55 or √0.3025.

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[tex]f(x)=x+10\\\\f(7)=(7)+10\\\\f(7)=17[/tex]

the answer is 17.

Answer:

The answer is 17, x±10 =10+7= 17

[tex]\huge\rm\underline{Answer}[/tex]

✧ Rational numbers are represented on the number line by dividing a unit into as many divisions as the denominator of the rational number

Here , Each unit is divided into 7 equal parts . It means denominator of the rational number is 7.

So , A represents -10/7

So , B represents -6/7

So , C represents 3/7

So , D represents 15/7

Hope it helps ~

Answer:

  3, 4

Step-by-step explanation:

The expanded form of the given product is found using the distributive property. An equivalent form can be found using the commutative property of multiplication.

__

  7(2 -3n) = 7(2) +7(-3n) = 14 -21n . . . . . . . matches 3

Swapping the factors gives ...

  7(2 -3n) = (2 -3n)·7 . . . . . . . . . . matches 4

__

About the other choices

1. The value is not the same as 14 -21n. It appears to have been the result of (more or less) adding 7 to the coefficients inside parentheses.

2. It is a common mistake to eliminate parentheses after applying the outside factor to the first term only. That seems to be what happened here. The distributive property says you apply the factor to all the terms inside parentheses.

5. The sum of terms (2 -3n) has been incorrectly replaced by the product of terms (2)(-3n).

Answer:

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this :  h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

[tex]\Leftrightarrow w=\frac{h-1}{2}[/tex]

now , if the door is 7 feet high then it’s width is equal to :

[tex]\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft[/tex]

Answer:

3 feet

Step-by-step explanation:

It mentions that the height of the door is 1 foot more than twice its width.

The width of a door of height 7 feet will be :

x^2 = (16)^2 + (16)^2

x^2 = 256 + 256

x^2 = 512

x = 16√2

Answer:

Nothing provided

Step-by-step explanation:

Answer:

300000

30000

3000

300

Step-by-step explanation:

Use the zero's trick for 10's.

The product of the given multiplications are 300000, 30000, 3000 and 300

Multiplication is when you take one number and add it together a number of times.

Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given that are four multiplication, 10000x30, 1000x30, 100x30 and 10x 30,

We know,

Multiplication by multiples of 10, 100, 1000, 10000:

We multiply the multiplicand by the non-zero digit of the multiplier. Then we add the same number of zero to the extreme right of the product as the multiplier has.

For example :-

26 × 10000 = 260000

524 × 10000 = 5240000

Therefore,

10000 x 30 = 300000

1000 x 30 = 30000

100 x 30 = 3000

10 x 30 = 300

Hence, the product of the given multiplications are 300000, 30000, 3000 and 300

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Answer:

Reese's Peanut Butter Cups: 10.8

York Peppermint Patties: 2.6

Step-by-step explanation:

Let Reese's Peanut Butter Cups be r and York Peppermint Patties y.

Step 1: Make equations.

1) If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.

[tex]3r + 6y = 48[/tex]

2) If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.

[tex]4r + 3y = 51[/tex]

Step 2: Solve the system of equations.

We have system of equations. I'll solve them by elimination.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 4r + 3y = 51[/tex]

Multiply the second equation with 2 so we'll get 6y.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 8r + 6y = 102[/tex]

Now let's subtract second equation from first and solve for r.

[tex]3r - 8r + 6y - 6y = 48 - 102\\-5r = -54\\r = \frac{-54}{-5}\\r = \$10.8[/tex]

To get y let's substitute the value of r in first equation.

[tex]3r + 6y = 48\\3 \cdot 10.8 + 6y = 48\\32.4 + 6y = 48\\6y = 15.6\\y = \$2.6[/tex]

Answer:

6. The number is [tex]-5[/tex]

7. The two numbers are [tex]10[/tex] and [tex]11[/tex]

Step-by-step explanation:

Question six can be re-worded to create the following expression:

[tex]-2=\frac{4x+10}{5}[/tex]

Solve for x to find the number:

[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]

Question seven can be solved by first listing the constraints (assuming x is smaller than y):

To get the numbers, we can create a system of linear equations. First, solve for [tex]y[/tex] in each expression:

[tex]y = x+1[/tex]

[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]

Solve for [tex]x[/tex]:

[tex]x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x[/tex]

Solve for [tex]y[/tex]:

[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]

Answer:

see explanation

Step-by-step explanation:

(6)

let n be the number then the sum of 4 times the number and 10 is 4n + 10

so

[tex]\frac{4n+10}{5}[/tex] = - 2 ( multiply both sides by 5 to clear the fraction )

4n + 10 = - 10 ( subtract 10 from both sides )

4n = - 20 ( divide both sides by 4 )

n = - 5

(7)

let the consecutive integers be n and n + 1 , then

3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side

3n = 2n + 2 - 8

3n = 2n - 6 ( subtract 2n from both sides )

n = - 6 and n + 1 = - 6 + 1 = - 5

the 2 integers are - 6 and - 5

Answer:

49 teachers

Step-by-step explanation:

By proportion, the number of teachers needed is found as follows:

6/102 = x/825 where x is the required number of teachers.

102x = 6*825

x = (6*825)/102

=  48.5

Answer:

Se necesitan 49 profesares

Step-by-step explanation:

Part A

The yard is a quadrilateral with the following corner points

I'll label those points A through D in the order presented above.

From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.

In short: side AB is 40 feet long.

The length of side BC is not as simple. We'll need the distance formula.

[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]

Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.

Use the distance formula again to find the distance from point C(40,50) to D(50,0)

[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.

We have these side lengths:

AB = 40

BC = 41.2311 (approximate)

CD = 50.9902 (approximate)

AD = 50

Add up those four sides and we'll get the perimeter of the quadrilateral.

AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213

===================================================

Part B

The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).

This 15 by 20 rectangle has an area of 15*20 = 300 square feet.

The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.

The area of the trapezoid is

A = h*(b1+b2)/2

A = 15*(20+35)/2

A = 412.5

That decimal value is exact.

Add it onto the area of the rectangle

412.5+300 = 712.5

Answer:

x = 10.9 cm

Step-by-step explanation:

Formula for a cone

Here, we are given :

Solving

Answer:

x ≈ 3.6 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = πr²h ( r is the radius and h the perpendicular height )

here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then

π × 3.5² × x = 140

π × 12.25x = 140 ( divide both sides by 12.25π )

x = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )

Answer:

Candy is 21 years old

Step-by-step explanation:

If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.

If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).

16+8+21=45

45÷3=15

Hope this helps!

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.

Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,

x = 2y                                    ...(1)

x - 5 = z                                 ...(2)

(x + y + z) / 3 = 15                  ...(3)

From equations (1), (2), and (3), then

x + x / 2 + x - 5 = 45

(5/2) x = 50

x = 20

Then the age Candy is calculated as,

z = 20 - 5

z = 15

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

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Answer: The median is 7 and the mode is 3

Step-by-step explanation:

Check the picture below.

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 48, \sigma = 8, Z = -3[/tex].

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-3 = \frac{X - 48}{8}[/tex]

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

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Answer:

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

Normal Probability Distribution

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the parameters are given as follows:

.

Hence:

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

Answer:

6.28 meters

Step-by-step explanation:

Circumference is the distance around the circle, given by:

C = pi•d

C = 3.14 • 2

C = 6.28 meters

Answer:

6.28 Meters

Step-by-step explanation:

2pi * r

= 2*3.14

= 6.28 Meters

Answer:

106 students

Step-by-step explanation:

If you take the 2 3/5 and covert it into a whole number by: 2×3+5 = 10

and then you have 96 girls so you add the whole number you got that is 10 and the 96 girls

=96+10= 106 students

⋆ ˚｡⋆୨୧˚hope this helped˚୨୧⋆｡˚ ⋆

Answer:

see explanation

Step-by-step explanation:

the standard form of a quadratic expression is ax² + bx + c ( a ≠ 0 )

(1)

(2x + 5)(x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

2x(x + 1) + 5(x + 1) ← distribute parenthesis

= 2x² + 2x + 5x + 5 ← collect like terms

= 2x² + 7x + 5 ← in standard form (a = 2, b = 7, c = 5 )

(2)

(x - 2)(x + 2)

= x(x + 2) - 2(x + 2) ← distribute parenthesis

= x² + 2x - 2x - 4 ← collect like terms

= x² - 4 ← in standard form (a = 1, b = 0, c = - 4 )

Answer:

m = [tex]\frac{1}{2}[/tex] , c = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

y + 2x = 4 ( subtract 2x from both sides )

y = - 2x + 4 ← in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (3, 4 ) into the partial equation

4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line

with m = [tex]\frac{1}{2}[/tex] and c = [tex]\frac{5}{2}[/tex]

Answer:

0.525 is the number.

X = Y/P%

X = 0.84/160%

p = 160%/100 = 1.6

X = 0.84/1.6

X = 0.525

Answer:

12/5 hours

Step-by-step explanation:

Let the total area to be painted be X

Let S be the rate at which Sally paints and J be the rate at which Joe paints

We have:
X/S = 4 hours (1)

X/J = 6 hours (2)

(1) ÷ (2) ==>
LHS = X/S ÷ X/j = X/S × J/X ==> J/S (3)
RHS = 4/6 = 2/3 (4)

From (3) and (4)
J/S = 2/3 or J =2/3 × S

If they both paint at the same time time taken is

X/(S+J)
S + J = S + 2/3 *S = 5/3S
So time taken for both of them to paint is X/(5/3)*S = X/S * 3/5
But we know from (1) that X/S = 4 so time taken = 4 * 3/5 = 12/5 hours