Solve for p.
16 – 3p = 2/3p+5

Answer:

The correct answer is 2 inches.

Step-by-step explanation:

Let l inches and w inches be the length and width of a rectangle respectively.

According to the given problem, l - 8 = [tex]\frac{w}{2}[/tex].

Area of the rectangle is given to be, according to the question, 18 square inches.

Thus l × w = 18

⇒ l × (2l - 16) = 18

⇒ 2 [tex]l^{2}[/tex] - 16l - 18 = 0

⇒  [tex]l^{2}[/tex] - 8l - 9 = 0

⇒ ( l - 9) ( l + 1) = 0

The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.

Width of the rectangle is 2 inches.

Answer:

The coffee Leah has left in percentage is 68.18%

Step-by-step explanation:

Given data

Total available coffee = 22 ounces

Amount She took out = 7 ounces

Let us carry out a simple subtraction arithmetic to find out the remainder

Hence remaining coffee = 22-7= 15

To expressing the remainder as a percentage we have

(15/22)*100=0.6818*100

= 68.1818%

To the nearest hundredths we have

= 68.18%

Answer: 68.18%

Step-by-step explanation:

Leah has a 22 ounce coffee and she drinks 7 ounces of the coffee. This means she will have:

22 - 7 = 15 ounces left.

The percentage of ounces of coffee Leah has left of her coffee will be the number of ounces left divided by the total number of ounces of coffee multiplied by 100. This will be:

= 15/22 × 100

= 0.6818 × 100

= 68.18%

The percentage of coffee Leah has left is 68.18%.

Answer:

254.5 Inches Cubed

Step-by-step explanation:

Formula for Finding the Volume of a Cylinder: [tex]V=\pi r^2h[/tex]

The radius is 3 inches.

[tex]r=3[/tex]

The height is three times the radius.

Multiply the radius by three to get the height.

[tex]h=3*3\\h=9[/tex]

The height is 9 inches.

Use the formula to find the volume.

[tex]\pi (3)^29= \pi (9)9=81\pi[/tex]

The exact volume is 81[tex]\pi[/tex] inches cubed.

[tex]81 * \pi[/tex] ≈ 254.47

254.47 ≈ 254.5

The volume of the cylinder should be about 254.5 inches cubed.

Hello.

The angle shown for 1 (and 3) is ∠40.

A straight line is shown, which is 180°. So the measure of ∠4 is 140°

Answer: the school paid $80 for the book.

Step-by-step explanation:

Let x represent the amount that the school paid for the book.

Her school charges a lost book fee equal to 75% of the cost of the book. It means that the amount that the school would charge on a book that cost $x is

75/100 × x = 0.75 × x = 0.75x

Sarah received a notice stating that she owed the school $60 for he lost book. It means that

0.75x = 60

x = 60/0.75

x = $80

Answer:

13000=t720

Step-by-step explanation:

720 x t = 13000

The function that represents the number of gallons of water left in ​Bryant’s pool t hours after he starts draining is  13,000 - 720t.

A function assigns the value of each element of one set to the other specific element of another set.

Given Bryant’s pool contains 13,000 gallons of water. ​The maximum rate at ​which the city allows pools to be drained is 720 gallons per hour. Therefore, the equation can be written as,

Water left = 13,000 - 720t

Hence, the function that represents the number of gallons of water left in ​Bryant’s pool t hours after he starts draining is  13,000 - 720t.

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Answer:

25%

Step-by-step explanation:

Answer:

  B.  114 cm²

Step-by-step explanation:

You want to know the area of a complex shape consisting of a triangle and a semicircle.

The shape can be divided at the dotted line into two shapes whose areas you have formulas for:

Using the formulas for their areas, we find the area of each shape to be ...

  A = (1/2)πr² . . . . . . area of semicircle with radius r

  A = (1/2)π(5 cm)² = 25/2π cm² ≈ 39 cm²

  A = (1/2)bh . . . . . . area of triangle with base b and height h

  A = (1/2)(15 cm)(10 cm) = 75 cm²

The sum of the areas of the parts is ...

  total area = semicircle area + triangle area

  total area = 39 cm² +75 cm²

  total area = 114 cm²

The area of the complex shape is about 114 cm².

Given:

In ΔPQR, ∠Q = 90°

PQ = 8 cm

QR = 15 cm and

PR = 17 cm

To find the value of ∠P.

Formula

By Trigonometric ratio we get,

[tex]tan \theta=\frac{opp}{adj}[/tex]

Now let us take ∠P = θ

With respect to θ, QR be the opposite side and PQ be the adjacent side.

So,

tan θ = [tex]\frac{QR}{PQ}[/tex]

tan θ = [tex]\frac{15}{8}[/tex]

θ = [tex]tan^{-1} (\frac{15}{8} )[/tex]

θ = 61.93° (approx)

Hence, the value of ∠P is 61.93° (approx).

Answer:

61.93°

Step-by-step explanation:

Using cosine law:

15² = 8² + 17² - 2(8)(17)cosP

225 = 353 - 272cosP

cosP = 8/17

P = 61.92751306

x - 24 = 3 (-1) x

x - 24 = -3x

-24 = -4x

x = 6

Step-by-step explanation:

The number which decreased by 24 equals 3 times its opposite is 6

Let x represent the number to calculate

The opposite of the number is -x.

According to the problem, we have the following equation:

x - 24 = 3(-x)

Simplifying the equation:

x - 24 = -3x

Adding 3x to both sides:

4x - 24 = 0

Adding 24 to both sides:

4x = 24

Dividing both sides by 4:

x = 6

Hence, the number is 6.

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Answer:

6.5

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

First multiply 4 and 3. You can just add the negative after you multiply.

Use simple multiplication facts. So

4 x 3=12

So it will be -12

Then, do the same, but with 12 and 2.

12 x 2=24

So it will be -24

Final answer:

-24

Answer:39.3

Step-by-step explanation:

The volume of a right circular cone that has a height of 13 m and a base with a diameter of 3.4 m is 39.3 m^3

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

Right circular cone is the cone where the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

Given that right circular cone that has a height of 13 m and a base with a diameter of 3.4 m.

Volume can be calculated as;

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

V = 22/7×3.4×3.4×13×3.4/ 24

V = 39.3 m^3

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Answer:

-250

Step-by-step explanation:

I don't know for sure but I hope it's correct.

Answer:

-250

Step-by-step explanation:

Answer:

Step-by-step explanation:

C=Cupcakes

B=Brownies

$4.75 per cupcake...(4.75c)

$3.00 per brownies..(3b)

Leah has $65 only. ([tex]\leq[/tex] 65)

4.75c + 3b[tex]\leq[/tex] 65

Answer:

It’s c

Step-by-step explanation:

Answer:

horizontal and vertical

Step-by-step explanation:

if its the plus?

Answer:

3/2 π

Step-by-step explanation:

If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).

The circumference is measured in radians, where one round is 2π.

So 3/4 of 2π is 3/2 π.

In degrees, the answer is 3/4 of 360°, which is 270°.

Hope that was helpful.Thank you!!!

Answer:

Step-by-step explanation:

Answer:

30.10

Step-by-step explanation:

Answer:

23°

Step-by-step explanation:

We apply Pythagorean theorem to determine the missing length, Hypotenuse:

[tex]h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft[/tex]

This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:

-We apply the law of Sines;

[tex]\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\ h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree[/tex]

Hence, the angle of elevation is 23°

Answer:

1.25 m.

Step-by-step explanation:

Given,

Area of base = 1.2 m²

Number of gold fish = 6

Density of the tank should be = 4 fish/m³

Height of the tank= ?

4 fish = 1 m³

6 fish = 1.5 m³

Volume required for 6 fish is 1.5 m³

V = area of base x height

1.5 = 1.2 x h

h = 1.25 m

Hence, height of the tank is equal to 1.25 m.

Answer:

1.25

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

First, convert all dimensions to be uniform.

1ft=0.08333 ft

90ft=90*0.0833=7.5ft

40 ft=40*0.0833=3.33 ft

The diagonal of the vehicle will be

[tex]\sqrt 7.5^{2}+3.33^{2}=8.20738150149675\ approx 8.2 ft[/tex]

Since the diagonal of vehicle is smaller than 12 ft, the pipe can't fit unless divided into two equal parts.

Final answer:

The 12-foot pipe can fit inside the van due to its dimensions.

Explanation:

The pipe is 12 feet long, which is equivalent to 144 inches. The interior dimensions of the van are 90 inches in length, which is shorter than the length of the pipe,

40 inches in width, and 40 inches in height, providing enough width and height for the pipe to fit. Therefore, the pipe will fit inside the plumber's van comfortably.

Answer:

The selling price of the remote control car is $36.3

Step-by-step explanation:

In this question, we are tasked with calculating the selling price of the remote control car.

From the first part of the question, we were made to know that he applies a markup of 21% and luckily for us, we are told that the expression for the retail price given the markup is 1.21 c

This means 1.21 × the cost price of the remote car

Hence, to calculate the selling price, we simply substitute $30.00 for the value of c.

The selling price is thus 1.21(30) = $36.3

From the information given, the area of the circle is: "113 sq. cm".

The formula to find the area of a circle is πr².

Using the side as the radius of the circle, we can calculate the area of the base area.

Note;

r = 6

Thus,

A = π * 6²

A = (22/7) * 36

A = 3.14285714286 * 36

Hence, The area of the circle A = 113.142857143 or 113 sq. cm.

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Answer:

coefficient

Step by-step explanation:

Answer:

$91,749.04

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 2.3% into a decimal:

2.3% -> [tex]\frac{2.3}{100}[/tex] -> 0.023

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

[tex]A=65,000(1+\frac{0.023}{12})^{12(15)}[/tex]

[tex]A=91,749.04[/tex]

You will have $91,749.04 in 15 years.

The common ratio of the geometric sequence –1,-8, -64, ... is 8. This is calculated by dividing a term in the sequence by its preceding term and is same across all consecutive terms.

In a geometric sequence, the common ratio is found by dividing any term by its preceding term. Here, the sequence given is –1,-8, -64, ...

Let's calculate the ratio for this series: We divide the second term (-8) by the first term (-1), which is 8. Let's check it with the next terms, where we divide the third term (-64) by the second term (-8). We find the ratio to be 8 again.

Therefore, the common ratio of the given geometric sequence –1,-8, -64, ... is 8.

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The common ratio of the geometric sequence -1, -8, -64, ... is -8, which results from dividing any term of the sequence by its preceding term.

Geometric sequence: -1, -8, -64, ...

Common ratio:

To find the common ratio, we divide each term by its preceding term.

In this case, -8 ÷ (-1) = 8 and -64 ÷ (-8) = 8.

Therefore, the common ratio is 8.

Answer: his pay for the 4th year is $1453.16

Step-by-step explanation:

The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = $1,400

r = 1 + 1.25/100 = 1.0125

n = 4 years

The 4th term(year), T4 is

T4 = 1400 × 1.0125^(4 - 1)

T4 = 1400 × 1.0125^3

T4 = $1453.16

Using an exponential function, the rent Joe will have to pay for the fourth year, with a 1.25% annual increase, is approximately $1,453.38.

To calculate the rent Joe will have to pay for the fourth year of living in the apartment with an annual rent increase of 1.25%, we will use an exponential function. The general formula for compounded growth is given by:

Future Value = Present Value ×(1 + rate)number of periods

In Joe's case, the Present Value is the initial monthly rent of $1,400, the rate is 1.25% or 0.0125 when expressed as a decimal, and the number of periods is 3 years since we are calculating the rent at the start of the fourth year. Plugging these values into the formula:

Rent for the fourth year = $1,400 × (1 + 0.0125)3

Let's calculate that:

Rent for the fourth year = $1,400 × (1.0125)3

Rent for the fourth year approximately = $1,400 × 1.038128

$1,453.38

Hence, Joe will have to pay about $1,453.38 for the fourth year of rent.