the volume of a box (V) varies directly with its length (l). if one of the boxes has a volume of 288 cubic inches and a length of 12 inches, what is the constant proportionality for the group of boxes

You would have 2/10 chance of choosing the sugar cookie then after you chosen it 5/9 chance of picking up a peanut butter cookie. I hope this helps

Answer:

1/9

Step-by-step explanation:

The total number of cookies is

2 sugar cookies+ 5 peanut butter cookies+ 3 chocolate chip cookies= 10

We want to take a sugar cookie

P(sugar cookie) = # sugar cookie/total cookies

                          = 2/10 = 1/5

Now we eat the cookie (not replacing it) so there are only 9 cookies

1 sugar cookies+ 5 peanut butter cookies+ 3 chocolate chip cookies= 9

Now we want a peanut butter cookie

P(peanut butter  cookie) = # peanut butter cookie/total cookies

                          = 5/9

To get the probability of both events happening, multiply them together

P( sugar, peanut) = 1/5 * 5/9

                            = 1/9

Answer:

Step-by-step explanation:

"the greatest value of n is 8" is signified by n ≤ 8.

This is a set, and also an inequality.

Answer:

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

We have the points (-7, 2) and (-8, -9). Substitute:

[tex]m=\dfrac{-9-2}{-8-(-7)}=\dfrac{-11}{-1}=11[/tex]

[tex]y-2=11(x-(-7))\\\\y-2=11(x+7)[/tex]

Convert to the standard form:

[tex]y-2=11(x+7)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y-2=11x+77[/tex]            add 2 to both sides

[tex]y=11x+79[/tex]           subtract 11x from both sides

[tex]-11x+y=79[/tex]        change the signs

[tex]11x-y=-79[/tex]

Answer:

12000 m³

Step-by-step explanation:

The volume (V) of a pyramid is calculated using the formula

V = [tex]\frac{1}{3}[/tex] × area of base × height, hence

V = [tex]\frac{1}{3}[/tex] × 900 × 40 = 300 × 40 = 12000 m³

Answer:

12000 no problem

Step-by-step explanation:

Volume=length×width×height

=5×3×6

=90 cu.ft

Answer:

Step-by-step explanation:

The formula of a volume of a rectangular solid (cuboid):

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have

[tex]l=5\ ft,\ w=3\ ft,\ h=6\ ft[/tex]

Substitute:

[tex]V=(5)(3)(6)=90\ ft^3[/tex]

52 divided by 4 then you’ll get 13

Answer:

3X(5+7)

Step-by-step explanation:

Because correctly is of this way:

3X(5+7)

and not so:

(3X5) + 7

Best regards

➷ You have written it the incorrect way.

Following the rules of PEMDAS, the multiplication would be carried out before the addition. This is not what is wanted

The question would want 3 times the SUM of 5 and 7.

To make sure you get the correct answer, you would have to write the expression slightly different

The correct way would be:

3(5 + 7)

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

$5.40

Step-by-step explanation:

To find the increase we need to consider our variables.

Current Rate = $4.50

Increase Percentage = 20% or 0.20

Now we can find the new rate by multiplying the Current Rate to the Increase Percentage and add it to the Current Rate again.

Total Price w/ Increase = ($4.50 x 0.20) + $4.50

Total Price w/ Increase = $0.90 + $4.50

Total Price w/ Increase = $5.40

I think the root of "3x + 1 = 7" is 2...

Answer:

The root of the equation is x=2.  

Step-by-step explanation:

Given : Equation [tex]3x+1=7[/tex]

To find : Solve for x?

Solution :

Step 1 - Write the equation

[tex]3x+1=7[/tex]

Step 2 - Subtract 1 both side,

[tex]3x+1-1=7-1[/tex]

[tex]3x=6[/tex]

Step 3 - Divide the equation by 3,

[tex]\frac{3x}{3}=\frac{6}{3}[/tex]

[tex]x=2[/tex]

Therefore, The root of the equation is x=2.  

You just need a calculator for these so there is no working

7)[tex]4.569245397*10^{-3}[/tex]

8)[tex]\frac{1}{2}[/tex]

9)0.5773502692

10)[tex]6.853838284*10^{-3}[/tex]

I am not sure for the rest, sorry havent done that far in school yet :)

Hope these helps :)

You need the Unit Circle to answer these questions! (attached)

7. Answer: [tex]\bold{\dfrac{\sqrt6-\sqrt2}{4}}[/tex]

Step-by-step explanation:

[tex]sin\dfrac{\pi}{12}=15^o\\\\\text{Since }15^o\text{ is not on the Unit Circle, you will need to use the difference}\\\text{formula for sin: sin(A - B) = sinAcosB - cosAsinB}\\\\sin15=sin(45-30)=\dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}=\dfrac{\sqrt6}{4}-\dfrac{\sqrt2}{4}=\boxed{\dfrac{\sqrt6-\sqrt2}{4}}[/tex]

8. Answer: 0

Step-by-step explanation:

The sum formula for cos is: cos (A + B) = cosA cosB - sinA sinB

Since we are given cos75° cos15° - sin75° sin15°, we can conclude that we are looking for cos (75° + 15°) = cos 90°.

The Unit Circle shows us that cos 90° = 0

9. Answer: [tex]\bold{\dfrac{\sqrt3}{3}}[/tex]

Step-by-step explanation:

The given expression is for tan (A + B).

tan (10° + 20°) = tan 30° = [tex]\dfrac{sin30^o}{cos30^o}=\dfrac{1}{\sqrt3}\implies\boxed{\dfrac{\sqrt3}{3}}[/tex]

10. Answer: [tex]\bold{\pm\dfrac{2-\sqrt2}{2}}[/tex]

Step-by-step explanation:

[tex]sin\dfrac{\pi}{8}=22.5^o=sin\dfrac{45^o}{2}\\\text{So we need to use the half-angle formula for sin:}\\\\sin\dfrac{\theta}{2}=\pm\sqrt\dfrac{1-cos\theta}{2}}\\\\sin\dfrac{45^o}{2}=\pm\sqrt\dfrac{1-cos45^o}{2}}=\pm\sqrt\dfrac{1-\frac{\sqrt2}{2}}{2}}=\pm\sqrt\dfrac{\frac{2}{2}-\frac{\sqrt2}{2}}{\frac{4}{2}}}=\boxed{\pm\dfrac{2-\sqrt2}{2}}[/tex]

11. TOO BLURRY TO SEE THE PROBLEM

12. Answer: [tex]\bold{\dfrac{7}{25}}[/tex]

Step-by-step explanation:

Quadrant II means that sin is positive and cos is negative.

[tex]sin\ x=\dfrac{3}{5}\implies cos\ x=-\dfrac{4}{5}\\\\cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{-4}{5}\bigg)^2-\bigg(\dfrac{3}{5}\bigg)^2\\\\.\qquad=\dfrac{16}{25}-\dfrac{9}{25}\\\\.\qquad=\boxed{\dfrac{7}{25}}[/tex]

Answer:

The value of y in the solution of the system is [tex]y=1[/tex]

Step-by-step explanation:

we have

[tex]y=3x-5[/tex] -----> equation A

[tex]6x+3y=15[/tex] -----> equation B

substitute equation A in equation B

[tex]6x+3(3x-5)=15[/tex]

[tex]6x+9x-15=15[/tex]

[tex]15x=15+15[/tex]

[tex]15x=30[/tex]

[tex]x=2[/tex]

Find the value of y

[tex]y=3(2)-5=1[/tex]

Answer:

59062.50

Step-by-step explanation:

Is means equals

9450 = 16% of a number

9450 = .16 N

divide by .16

9450/.16 = .16N/.16

59062.50 = N

The number is 59062.50

We want 100% of the number which is all of it

59062.50

7 is the answer

Area =length *breadth

Area =length *length

Area=49=x *x

[tex]49 = {x}^{2} \\ \sqrt{49} = x \\ x = 7[/tex]

your answer is 15 centimeters

Answer:

Step-by-step explanation:

The formula of a surface area of a rectangular prism l × w × h:

[tex]S.A.=2(lw+ih+wh)[/tex]

We have l = 5.5, w = 5 and h = 13. Substitute:

[tex]S.A.=2(5.5\cdot5+5.5\cdot13+5\cdot13)\\\\S.A.=2(27.5+71.5+65)\\\\S.A.=2(164)\\\\S.A.=328[/tex]

Answer:

(x - 15)(x + 3)

Step-by-step explanation:

Factors of 45 include 5 and 9, 3 and 15, 1 and 45, and so on.

Note that 3*15 =+45; this is not what we wanted.  Thus, try (-3)*15 = -45.

Do -3 and 15 combine to yield -12?  No.  Thus drop (-3)(15) and try (3)(-15).

Do 3 and -15 combine to yield -12?  YES

Therefore, the factored form of x² - 12x - 45 is (x - 15)(x + 3).

Answer:

y=3(x-1)^2-12

Step-by-step explanation:

Answer: I think 1 or 2

Answer:

4: 3 and 2

5: 1 and 4

Answer:

Step-by-step explanation:

The sqrt of 1/64 is 1/8, or 0.125.

1/4 is equivalent to 0.25.

0.2 repeating is 0.222222222222 ...

Least:  0.125

Middle:  0.25

Greatest:  0.222222222222 ...

The numbers from least to greatest are: square root of 1/64 (0.125), 0.2 repeating (0.222...), and 1/4 (0.25).

This problem requires an understanding of fractions and square roots to order the numbers correctly. Firstly, you have to calculate the square root of 1/64. The square root of 1/64 is 1/8 or 0.125. Then, let's consider the other numbers: 1/4 which is equal to 0.25, and 0.2 repeating which is actually equivalent to 0.222 continuing. Now we can order them from least to greatest: 1/8 (0.125), 0.2 repeating (0.222...), and 1/4 (0.25).

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Answer:

x = - 7, x = - 5

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

The factors are + 7 and + 5, since

7 × 5 = 35 and 7 + 5 = 12, hence

x² + 12x + 35 = 0 ← in standard form

(x + 7)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 5 = 0 ⇒ x = - 5

Answer:

.15 mph

Step-by-step explanation:

3 miles/ 20 hours or 3/20

Answer:

6 hours and 42 minutes (402 minutes)

Step-by-step explanation:

20 ÷ 3 = 6.7 hours

6.7 hours = 6 hours and 42 mins

To check if our answer is correct:

Do the inverse

6. 7 hours x 3 = 20.1

Round it to nearest whole number, 20

Answer:

[tex]3^{3}[/tex] = 27.

Step-by-step explanation:

3 to the third power ( [tex]3^{3}[/tex] ) is the same as :

3 x 3 x 3 which would equal :

3 x 3 = 9 x 3 = 27.

Hope this helps,

Davinia.

27

3 times.3 times 3

9 times 3

27

Answer:

X=2

Step-by-step explanation:

Answer:

y = -118 and x = 7

Step-by-step explanation:

I've attached a picture with my work.

Detailed steps on solving equations with variables y and x, including simplification and solving for the unknowns.

Solving the equation 64−(3y+8y+y)÷40=37:

Solving the equation 8,000÷(28x+4)−15 = 25:

48 and 81 basically you just have to multiply

Answer:

144 cubic inches

Step-by-step explanation:

We are given a diagram of a pyramid with length = 8 inches, height = 9 inches and width = 6 inches.

We are to find the volume of this pyramid.

We know that the formula of volume of a pyramid is given by:

[tex] \frac { l \times w \times h } { 3 } [/tex]

Substituting the given values in the above formula to get:

Volume of pyramid = [tex] \frac { 8 \times 6 \times 9 } { 3 } [/tex] [tex]=\frac{432}{3}[/tex] = 144 cubic inches

Answer:

Step-by-step explanation:

$300-$125=$175

Answer:

center:(4,-2)

Radius: 3 units

Step-by-step explanation:

The standard equation of a circle is given as [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius of the circle.

The given equation is [tex](x-4)^2+(y+2)^2=9[/tex].

We compare to the standard equation of the circle to get;

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

[tex]\Rightarrow -h=-4[/tex]

[tex]\Rightarrow h=4[/tex]

and

[tex]y-k=y+2[/tex]

[tex]\Rightarrow -k=2[/tex]

[tex]\Rightarrow k=-2[/tex]

Hence the center of the circle is (4,-2).

Also, we have [tex]r^2=9[/tex]

Therefore [tex]r=\sqrt{9}[/tex]

[tex]r=3[/tex] units.

Answer:

Center at (4,-2); radius: 3

Step-by-step explanation:

Answer:

step 4: Take the square root on both sides

√(x + 2)^2 = √10

step 5: Simplify

x + 2 = ±√10

Step 6: Solve for x

x = √10 - 2 and x = -√10 + 2

Step-by-step explanation:

Step 1: x^2 +4x = 6

Step 2: x^2 +4x +4 =  6+4

Step 3: (x +2)^2 = 10

The next 3 steps are:

step 4: Take the square root on both sides

√(x + 2)^2 = √10

step 5: Simplify

x + 2 = ±√10

Step 6: Solve for x

x = √10 - 2 and x = -√10 + 2

Hope this will helpful.

Thank you.

The solution of the given quadratic equation is,

x =  1.16 or -2+12i

The given expression is

x² +4x - 6 = 0,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

Then, after comparison,

a = 1, b = 4 and c = -6

Therefore the given equation is an quadratic equation,

We can write it apply quadrature formula:

x = (-b ± √(b²-4ac))/2a

  = (-4  ± √(16+24))/2

  = 1.16 or -2+12i

Hence,

x =  1.16 or -2+12i

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Answer:

x < -4

Step-by-step explanation:

To solve the inequality, use inverse operations.

-3x + 5 > 17

-3x > 17 - 5                    Subtract 5 from both sides.

-3x > 12                         Divide both sides by -3.

x < -4                             Flip the inequality sign since you divided by a negative.