Item 25 The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function. 0 1 2 3 4 5 6 7 8 9 10

Answer:

Probability of (one club and one heart) = 0.1275 (Approx)

Step-by-step explanation:

Given:

Total number of cards = 52

Each suits = 13

FInd:

Probability of (one club and one heart)

Computation:

Probability of one club = 13 / 52

Probability of one heart = 13 / 51

Probability of (one club and one heart) = 2 [(13/52)(13/51)]

Probability of (one club and one heart) = 0.1275 (Approx)

Answer:

D. 0.1275

Step-by-step explanation:

Justo took the Pre-Test on Edg (2020-2021)!!

Answer:

$76

Step-by-step explanation:

$38 + $38 = $76

Answer:

1/3

Step-by-step explanation:

There are three elements that are intersecting: 5, 14, 22

Probability of choosing an item is 1/3

Answer:

-2

Step-by-step explanation:

The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:

[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]

Given that a line JK, with  Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:

[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]

Line segments can be divided into equal or unequal ratios

The x coordinate of the segment is -2

The coordinates of points J and K are given as:

[tex]J = (-6,-2)[/tex]

[tex]K = (8,-9)[/tex]

The ratio is given as:

[tex]m : n =2 : 5[/tex]

The x-coordinate is then calculated using:

[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]

So, we have:

[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]

[tex]x = (\frac{2}{7}) (14) -6[/tex]

Expand

[tex]x = (2) (2) -6[/tex]

Open bracket

[tex]x = 4 -6[/tex]

Subtract 6 from 4

[tex]x = -2[/tex]

Hence, the x coordinate of the segment is -2

Read more about line ratios at:.

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Answer:

Step-by-step explanation:

Question:

7^1/5

The number given has an exponent of a fraction: fraction exponent = 1/5

Since the top is one, the number 7 stays the same. = 7^1 = 7

The bottom is a 5. This means it is to the fifth root.

Answer = D

Hope this helped,

Kavitha

Answer: If 36/7 is one of the options, choose that one.

If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.

Step-by-step explanation: 7 is equal to 35/5 because 7×5=35

Add 1/5 and you end up with 36/5. A Common rational number.

7^(1/5) = the 5th root of 7. A very small irrational number!

Answer: 180

Step-by-step explanation:

Let the tons of ice the ship was carrying when it set sail be y.

We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.

This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:

2/3 × y = 120

2y/3 = 120

2y = 120 × 3

2y = 360

y = 360/2

y = 180

The ship was carrying 180 tons of ice when it set sail

Answer:

This is NOT a one solution problem.

Step-by-step explanation:

Group all terms with a c in it to the left of the equal sign, and group all numbers to the right of the equal sign.

5.7c-1.5+3.2c=7.8c-1.5+1.1c

5.7c + 3.2c - 7.8c - 1.1c = - 1.5 + 1.5

8.9c - 8.9c = 0

0 = 0

No matter which number you substitute for c, it will always be true. Since you can find infinity of solutions, this is NOT a one solution problem.

Answer:

C. 1/3

Step-by-step explanation:

Given:

Number of colors listed (Successful Outcome)

Red 1

Yellow 1

Purple 1

Total or Possible outcome= 3

Required:

What is the theoretical probability that it stops on the red sector on the last spin?

Formula:

Probability= Successful outcome ÷ Possible outcome

Solution:

Probability of the spinner stoping on red.

Probability= Successful outcome ÷ Possible outcome

Probability=1÷3

Probability=1/3

Hope it helps ;) ❤❤❤

The theoretical probability that spinner stops on the red sector on the last spin is option (C)  [tex]\frac{1}{3}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given,

A spinner is separated into 3 equal parts.

Then Mary spins the spinner 6 times.

What is the theoretical probability that it stops on the red sector on the last spin.  So only last spin is important, outcomes of first 5 spin is not important and it is independent.

Probability = Number of favorable outcome / Number of Total outcome

Probability (Red sector) =  [tex]\frac{1}{3}[/tex]

Hence, the theoretical probability that spinner stops on the red sector on the last spin is  option (C)  [tex]\frac{1}{3}[/tex]

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Answer:

second one

Step-by-step explanation:

Answer:

[tex]\boxed{\sf LM = 11}[/tex]

Step-by-step explanation:

According to trapezoid mid-segment theorem:

[tex]LM = \frac{QR+ST}{2}\\ Given \ that\ QR = 9, ST = 13[/tex]

[tex]\sf LM = \frac{9+13}{2}[/tex]

LM = 22/2

LM = 11

Answer:

2,666.67 L of water

Step-by-step explanation:

Solve for W:

1) 3200 = 2400 + 0.3w

2) 800 = 0.3w

Divide both sides by 0.3 to get the variable alone

3) (800)/0.3 = (0.3w)/0.3

4) w = 2,666.67 L

Answer:

y = -3

Step-by-step explanation:

y + 3 = 7(2 - 2)

y + 3 = 0

Subtract 3 from both sides

y + 3 - 3 = 0 - 3

y = -3

Answer:

  7x - y = 17

Step-by-step explanation:

Maybe you want the standard form of the point-slope equation ...

  y +3 = 7(x -2)

__

  y + 3 = 7x -14 . . . . . eliminate parentheses

  17 = 7x -y . . . . . . . . add 14-y

  7x - y = 17

Answer:

Step-by-step explanation:

y = 2x + 4a/6b   y=(12xb+4b )/6b

6yb=12x+4a

a=(-12xb+6yb)/4=

a=3yb/2 -3xb

x=y/2-a/3b

b=2a/(3y-6x)

the solution is for every variable

Answer:

37.5 cm

Step-by-step explanation:

See attached for reference.

let the diagonal be x,

By Pythagorean formula:

x² = (22.5)² + (30)²

x = √[(22.5)² + (30)²]

x = 37.5 cm

Answer:

11 /13 = t

Step-by-step explanation:

5/13  = t -6/13

Add 6/13 to each side

5/13 + 6/13  = t -6/13+ 6/13

11 /13 = t

Answer:

[tex]t=\frac{11}{13}[/tex]

Step-by-step explanation:

[tex]\frac{5}{13} = t -\frac{6}{13}[/tex]

Add [tex]\frac{6}{13}[/tex] to both sides.

[tex]\frac{5}{13} + \frac{6}{13} = t -\frac{6}{13} + \frac{6}{13}[/tex]

[tex]\frac{11}{13} =t[/tex]

Answer:

  0 < x < 3/2

Step-by-step explanation:

The dimensions are positive when ...

  18 -2x > 0   ⇒   x < 9

  3 -2x > 0   ⇒   x < 3/2

  x > 0

So, the values of x where the model makes sense are ...

  0 < x < 3/2

By the factor theorem,

[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]

Now,

[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]

[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]

So we have

[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]

The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.

If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then

Sum of the roots = [tex]\frac{-b}{a}[/tex]

And,

Product of the roots = [tex]\frac{c}{a}[/tex]

According to the given question.

We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]

On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].

We get

[tex]a = 3\\b = 5\\and\\c = 7[/tex]

Also, u and v are the solutions of the quadratic equation.

⇒ u and v are the roots of the given quadratic equation.

Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].

And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].

Therefore,

[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)

[tex]uv=\frac{7}{3}[/tex]   ....(iii)       (product of the roots)

Now,

[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex]                    ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])

Therefore,

[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex]         (from (i) and (ii))

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]

Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

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Answer:

Step-by-step explanation:

The gray shadowed area is below descending function and the line is dashed.

It means coefficient x is m<0 and the sign of inequality is y <  

So the inequality wich  fit it is  y < -1/2x + 2

The blue shadowed area is above ascending function and the line is uninterrupted.

It means coefficient x is m>0 and the sign of inequality is y ≥

So the second inequality of system (y ≥ 3x - 1)  also match.

The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

The standard equation of a line is expressed as y = mx + b;

For the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):

m = 5+1/2-0

m= 6/2

m = 3

The equation of the line is y = 3x - 1

Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1

For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):

m = 0-2/4-0

m= -2/4

m = -1/2

The equation of the line is y = -1/2x + 2

Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2

Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

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Answer:

x = 3.

Step-by-step explanation:

In this case, the x-value never changes, no matter the value of the y. So, x will always equal 3. Your equation is x = 3.

Hope this helps!

Answer:

x=3

Step-by-step explanation:

Answer:

[tex]\boxed{-4.1x-11y}[/tex]

Step-by-step explanation:

[tex](-12.7y-3.1x) + 5.9y-(4.2y + x)[/tex]

Expand brackets.

[tex]-12.7y-3.1x+ 5.9y-4.2y - x[/tex]

Combining like terms.

[tex]- x-3.1x-12.7y+ 5.9y-4.2y[/tex]

[tex]-4.1x-11y[/tex]

Answer:

[tex] \boxed{\red{ - 11y - 4.1x}}[/tex]

Step-by-step explanation:

[tex] (- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x[/tex]

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (2, - 1), thus

y - (- 1) = - 5(x - 2) , that is

y + 1 = - 5(x - 2) → C

Answer:

Option C is the correct option

Step-by-step explanation:

The general form of point slope form of line is :

[tex]y - y1 =m ( x - x1)[/tex]

Where ( x1 , y1 ) is one point on the line and m is the slope.

In the given problem,

The slope of line ( m ) = - 5

One point on the line = ( x1 , y1 ) = ( 2 , -1 )

The point slope form of the line is:

y - ( - 1 ) = - 5 ( x - 2 )

y + 1 = - 5 ( x - 2 )

Hope this helps..

Best regards!!

Answer: Zak - Resp after 24 months = $4,344.00

              Zak - Technology Fund after 24 months = $1,102.98

              Zak's Technology Fund has enough money to buy a laptop.

              Zak's Savings (Resp) will last less than 6 months

Step-by-step explanation for Zak:

January - June 2019

$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $12,240)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $5486.40(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                               Other Expenses: $5,212.08

July - December 2019 (excluding August)

$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income

Taxable Income is $6400 - $960 = $5440    (Annual Income $11,560)

→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income

Tech Fund (5%): $4916.80(0.05) = $245.84

Food Expense (30%): $4916.80(0.3) = $1,475.04

Clothing Expense (30%): $4916.80(0.3) = $1,475.04

Entertainment Expense (25%): $4916.80(0.25) = $1,229.20

Miscellaneous Expense (10%): $4916.80(0.1) = $491.68      

                                              Other Expenses: $4,670.96

January - June 2020

$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income

Taxable Income is $8160 - $1224 = $6936    (Annual Income $13,872)

→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income

Tech Fund (5%): $6169.92(0.05) = $308.50

Food Expense (30%): $6169.92(0.3) = $1,850.98

Clothing Expense (30%): $6169.92(0.3) = $1,850.98

Entertainment Expense (25%): $6169.92(0.25) = $1,542.48

Miscellaneous Expense (10%): $6169.92(0.1) = $616.98      

                                               Other Expenses: $5,861.42

July - December 2020 (excluding August)

$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $13,056)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $4916.80(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                              Other Expenses: $5,212.08

[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}[/tex]

Answer: x = -12

Step-by-step explanation:

-1/2x=6

Divide by -1/2

x = -12

Hope it helps <3

Answer:

Option (C)

Step-by-step explanation:

Given formula of a line passing through [tex](x_1, y_1)[/tex] and slope 'm' is,

[tex]y-y_1=m(x-x_1)[/tex]

Further solving this equation,

[tex]y-y_1=mx-mx_1[/tex] [By distributive property]

[tex]y-y_1+mx_1=(mx-mx_1)+mx_1[/tex] [By adding [tex]mx_1[/tex] on both the sides]

[tex]y-y_1+mx_1=mx[/tex]

[tex]\frac{y-y_1-mx_1}{m}=\frac{mx}{m}[/tex] [Divide the equation by m]

[tex]\frac{y-y_1}{m}-x_1=x[/tex]

Therefore, Option (C) will be the answer.

Answer:

-7/6

Step-by-step explanation:

If a = 1/2 and b = -3/7, then your given:

1/2 divided by -3/7=

-7/2*3=

-7/6

Sorry if its a bit unclears

Answer:

[tex]\frac{7}{-6}[/tex]

Step-by-step explanation:

To do this you are basically dividing the fractions so when you set up the equation it will look like this [tex]\frac{1}{2}/\frac{-3}{7}[/tex] now that we have this we will take the reciprocal of -3/7 which is 7/-3 and than multiply the 2 fractions we we get 7/-6

Answer:

Step-by-step explanation:

The < symbol does not include the "or equal to" case, so will be graphed with an open circle at the boundary. x < 4 means that values of x less than 4 will be shaded, and there will be an open circle at x=4. Graph B shows this.

__

4 ≤ x means there will be a solid dot at x=4, and values of x greater than 4 will be shaded. Graph A shows this.

Answer: B & A

Step-by-step explanation:

Answer:

[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]

The maximum amount of sand that can be stored in this structure is 1675.52 m³.

Step-by-step explanation:

The volume of a conical-shaped structure is given by

[tex]V = \frac{1}{3} (\pi \cdot r^2 \cdot h)[/tex]

Where r is the radius and h is the height of the structure.

We are given that

radius = 10m

height = 16m

Substituting the above values into the formula, we get

[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]

Therefore, the maximum amount of sand th can be stored in this structure is 1675.52 m³.

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

6 is the best estimate.

Step-by-step explanation:

(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.

Choose 6 as your best approximation.