2. Grant works as a salesperson at a seasonal market. During the Christmas season, he
gets a 15 percent commission on every tree he sells. If he sold 12 trees today, with an
average sale price of $35 per tree, what amount of commission will he make?

Answer:

x=30

Step-by-step explanation:

8x - 3(2x-4) = 3(x-6)

first let's get rid of the brackets:

8x- 3·2x + 3·4 = 3x - 3·6

8x - 6x + 12 = 3x - 18

now group all the x terms and number terms

8x - 6x - 3x = -18 - 12

-x = -30

x = 30

Jesse Owen speed is 9.71 meters per seconds.

Speed is a scalar quantity that refers to "how fast an object is moving.

In other words, speed is the distance travelled per unit of time.

Therefore, it can be represented mathematically as follows:

speed = distance / time

Jesse Owen covers 100 meters dash for 10.3 seconds. Therefore, the speed he used for the race can be calculated as follows:

speed = distance / time

distance = 100 meters

time = 10.3 seconds

Hence,

speed = 100 / 10.3

speed = 9.70873786408

speed = 9.71 meters per seconds

Therefore, Jesse Owen speed is 9.71 meters per seconds.

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Answer:4(x - 1) - x = 3(x + 5) - 11

Step-by-step explanation:

Lily's work:

4(x – 1) – x = 3(x + 5) – 11

4x – 4 – x = 3x + 15 – 11

3x – 4 = 3x + 4

Her partial solution, 3x - 4 = 3x + 4, can be interpreted as a FALSE statement because 3x - 4 does NOT equal 3x + 4.

Since it is a false statement, the equation has no solution.

The number of the solution will be infinity. Then the correct option is D.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

4(x – 1) – x = 3(x + 5) – 11

Simplify the equation, we have

4x – 4 – x = 3x + 15 – 11

3x - 3x = 8

The variable x is eliminated.

Then the number of the solution will be infinity.

Then the correct option is D.

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Answer:

[tex]y = 6.495x + 6.495[/tex]

Step-by-step explanation:

Represent years with x and cost with y.

So, we have:

[tex](x_1,y_1)=(1,12.99)[/tex]

[tex](x_2,y_2)=(3,25.98)[/tex]

Required

Determine the slope intercept equation

First, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{25.98 - 12.99}{3 - 1}[/tex]

[tex]m = \frac{12.99}{2}[/tex]

[tex]m = 6.495[/tex]

The equation is then calculated as:

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

Where

[tex]m = 6.495[/tex]

[tex](x_1,y_1)=(1,12.99)[/tex]

[tex]y - 12.99 = 6.495(x - 1)[/tex]

[tex]y - 12.99 = 6.495x - 6.495[/tex]

Make y the subject

[tex]y = 6.495x - 6.495 + 12.99[/tex]

[tex]y = 6.495x + 6.495[/tex]

Answer:

32/3 servings

Step-by-step explanation:

4 / (3/8) =

(4/1) x (8/3) =

32/3

Answer:

the probability to flip a head is 50%

Step-by-step explanation:

I think.

Answer:

x = 6, y = 5

Step-by-step explanation:

Solve the following system:

{5 y - 6 x = -11 | (equation 1)

{-11 y + 6 x = -19 | (equation 2)

Add equation 1 to equation 2:

{-(6 x) + 5 y = -11 | (equation 1)

{0 x - 6 y = -30 | (equation 2)

Divide equation 2 by -6:

{-(6 x) + 5 y = -11 | (equation 1)

{0 x + y = 5 | (equation 2)

Subtract 5 × (equation 2) from equation 1:

{-(6 x) + 0 y = -36 | (equation 1)

{0 x + y = 5 | (equation 2)

Divide equation 1 by -6:

{x + 0 y = 6 | (equation 1)

{0 x + y = 5 | (equation 2)

Collect results:

Answer: {x = 6, y = 5

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Answerits the point that divides the segment into two congruent segments

Step-by-step explanation:

ex. D————-o————-G

The midpoint would be the O. Mid:means Middle

hehehe hope this helps

158.93 yd³ water it would take to completely fill the swimming pool.

Given that, a swimming pool has a volume of 32,100 gal and we have to find out that how many cubic yards of water it would take to completely fill the swimming pool.

1 cubic yard (yd³) ≈ 201.97 gallon (gal)

So, by using the conversion given above we can simply find the water in cubic yards that it would take to completely fill the swimming pool.

Volume of the swimming pool = 32,100 gal

and we know that, 1 cubic yard (yd³) ≈ 201.97 gallon (gal)

Now, we get

water needed in cubic yards to completely fill the swimming pool

= 32,100/201.97

= 158.93 yd³

Hence, 158.93 yd³ water it would take to completely fill the swimming pool.

Therefore, 158.93 yd³ is the required answer.

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Answer:

what am i supposed to be answering..?

Step-by-step explanation:

Answer:

21 minutes or 8:21 a.m

Step-by-step explanation:

6+15=21

Answer:

On a coordinate graph, make a point at (0, -1)

Move the point up 3 units and right 2 units, and make another point. Continue across the plane and draw the line connecting the dots.

Answer:

Step-by-step explanation:

The value of the probability is P(Large or Blue) = 7/10

The given parameters are represented on the table

Using the table parameters, we have

P(Large or Blue) = [(Large) + (Blue) - (Large and Blue)]/Total

This gives

P(Large or Blue) = ((17 + 8) + (17 +3) - 17)/(17 + 3 + 8 + 12)

This gives

P(Large or Blue) = 28/40

Simplify

P(Large or Blue) = 7/10

Hence, the value of the probability is P(Large or Blue) = 7/10

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Answer:

1,080

Step-by-step explanation:

QUICK MATH

Answer:

-15

Step-by-step explanation:

Replace c with 2,

(2)^2 -8(2) -3 =

4 - 16 -3 + -12

= -15

The length of the ladder is 58.31 inches and the angle made by the ladder with the ground is θ = 59.04°.

The distance between the ladder and the wall is 30 inches.

The height at which the ladder touches the wall is 50 inches from the ground.

Let x be the slant height when the ladder touches the wall.

Then, by using a Pythagorean theorem:

(Base)² + (Altitude)² = (Hypotenuse)²

(30)² + (50)² = x²

x² = 900 + 2500

x² = 3400 inches²

x = √[ 3400 inches²]

x = 10√34 inches

x = 58.31 inches

Then the angle made by the ladder with gound is :

tan (θ) = opposite / adjacent

tan (θ) = 50/30

tan (θ) = 5/3

θ = tan⁻¹ ( 5/3 )

θ = 59.04°

Therefore, the ladder is 58.31 inches long and the angle between the ground and the ladder is 59.04°.

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Answer:

B

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant is

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real irrational roots

• If b² - 4ac > 0 and a perfect square then 2 real rational roots

• If b² - 4ac = 0 then 1 real double root

• If b² - 4ac < 0 then 2 complex roots

Given

x² + 3x - 7 = 0 ← in standard form

with a = 1, b = 3, c = - 7 , then

b² - 4ac

= 3² - (4 × 1 × - 7) = 9 + 28 = 37

Since b² - 4ac > 0 then 2 real irrational roots

The length of the parking lot will be 212 yards

From the question, we are to determine what the length of the parking lot needs to be

From the given information, we have that

"A rectangular-shaped parking lot is to have a perimeter of 546 yards"

and

"the width must be 61 yards"

From the formula for perimeter of a rectangle,

P = 2(l +w)

Where P is the perimeter

l is the length

and w is the width

From the given information,

P = 546 yards

w = 61 yards

Putting the parameters into the equation,

546 = 2(l + 61)

546 = 2l + 122

2l = 546 - 122

2l = 424

l = 424/2

l = 212 yards

Hence, the length of the parking lot will be 212 yards

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Answer:

  1500z

Step-by-step explanation:

Given a bacteria population that is multiplied by z every hour, and the population after 2 hours is 1500, you want the population after 3 hours in terms of z.

The problem statement tells you the population is multiplied by z every hour. After 2 hours, the population is 800 +300 +400 = 1500. After 3 hours, that value will be multiplied by z:

  1500z . . . . . population after 3 hours

__

Additional comment

The given values of population tell us z = 1100/800 = 1.375 for the first hour, and z = 1500/1100 ≈ 1.364 for the second hour. The average value of z for the two-hour period is √(15/8) ≈ 1.369. The desired expression could be any of ...

Presumably z would have different values in each case, and we hesitate to predict what those values might be. Perhaps the population is being rounded to the nearest 10 or 100.

An exponential regression calculation models the population as ...

  p = 801.945×1.36812^t . . . . . . . z ≈ 1.36812

Using this formula, we get the given population numbers by rounding to the nearest 10.

Answer:4.16667

Step-by-step explanation: 1

Simplify —

3

Equation

0 - (— • (8 + —))

2 3

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 3 as the denominator :

8 8 • 3

8 = — = —————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

8 • 3 + 1 25

————————— = ——

3 3

Equation at the end of step

2

:

1 25

0 - (— • ——)

2 3

STEP

3

:

1

Simplify —

2

Equation at the end of step

3

:

1 25

0 - (— • ——)

2 3

STEP

4

:

Final result :

-25

——— = -4.16667

6

Terms and topics

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Answer:

y = 6

Step-by-step explanation:

(7y-8y)2+14=2

First, simplify the left side

7y - 8y = -y

2*-y = -2y

Now solve the equation

-2y + 14 = 2

Subtract 14 from both sides

-2y = -12

Take away the negative signs since both sides are negative

2y = 12

Divide both sides by 2

y = 6

(If the variable was x instead of y the variable would still equal 6)

Answer:

(a) B ∩ D' = {k}

(b)  (B ∪ D)' = {s}

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Part (a)

[tex]\begin{aligned}\sf B \cap D' & = \sf B \cap \left( \text{U}-D\right)\\ &= \sf \{k, q, x, y \} \cap \left(\{f, k, q, s, x, y, z \} - \{f, q, x, y, z \}\right)\\& = \sf \{k, q, x, y \} \cap \{ k, s \}\\ & = \sf \{k \}\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}\sf \left(B \cup D\right)' & = \sf \text{U}-\left(B \cup D\right)\\& = \sf \{f, k, q, s, x, y, z \}-\left(\{k, q, x, y\} \cup \{f, q, x, y, z\}\right)\\& = \sf \{f, k, q, s, x, y, z \}-\{ f, k, q, x, y, z\}\\& = \sf \{s\}\\\end{aligned}[/tex]

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Now we have to find,

→ B ∩ D'

→ (B ∪ D)'

Let's solve for the following sets,

a) B ∩ D' = ?

→ B ∩ D'

→ {k, q, x, y} ∩ ({f, k, q, s, x, y, z} - {f, q, x,y,z})

→ {k, q, x, y} ∩ {k, s} = {k}

Hence, the required set is {k}.

b) (B ∪ D)' = ?

→ B' ∩ D'

→ ({f, k, q, s, x, y, z} - {k, q, x, y}) ∩ ({f, k, q, s, x, y, z} - {f, q, x, y, z})

→ {f, s, z} ∩ {k, s} = {s}

Hence, the required set is {s}.

Answer:

4-2=2

Step-by-step explanation:

Answer:

7 mph

Step-by-step explanation:

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