What is the scale of a drawing where an 8 foot wall is two inches long?

Answer:

x=2.5

Step-by-step explanation:

First, you need to expand the brackets.

51x-19.5=108

Next, you need to add 19.5 to both sides giving:

51x=127.5

Then finally, you need to divide both sides by 51.

x =2.5

x equal to 2.5 in this equation

An algebraic equation is a mathematical statement that contains two or more algebraic expressions that are set equal to each other. The algebraic expressions can contain variables, constants, and operators.

We have:

3(17x – 6.5) = 108

We can solve for the value of x as follow:

3(17x – 6.5) = 108

17x(3) - 6.5(3) = 108

51x - 19.5 = 108

51x = 108 + 19.5

51x = 127.5

x = 127.5/51

x = 2.5

Therefore, x equal to 2.5 in this equation

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Answer:

1/2, 5/4, 7/8

Step-by-step explanation:

to find it you can divide it on a calculator and then see the decimals and decide from least to greatest or you can reduce the fraction to its simplest form and then do the least fo greatest by looking at the denominator only

Answer:

1/2, 7/8, 5/4

Step-by-step explanation:

Answer: C... {y|y ≥ -1}

Step-by-step explanation:

f(x) is a quadratic equation with the x-side squared and a is positive which means that the graph of the function is a parabola facing up. The range of f(x) is given by {y|y ≥ k}, where k is the y-coordinate of the vertex.

in vertex form (h, k) = (-1, -11)

This meaning the range ={y|y ≥ -11}

Answer:

the answer is C

Step-by-step explanation:

Answer:

The value increases

Step-by-step explanation:

the smaller the divisor, the larger the quotient.

It increases I am taking the quiz right now and I checked.

Answer:

6x³ + 24x² + 18x - 12

Step-by-step explanation:

We require the product

(2x² + 4x - 2)(3x + 6)

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

2x²(3x + 6) + 4x(3x + 6) - 2(3x + 6) ← distribute all parenthesis

= 6x³ + 12x² + 12x² + 24x - 6x - 12 ← collect like terms

= 6x³ + 24x² + 18x - 12

I think that it might be C.

Answer:

The answer is  D.

Step-by-step explanation:

I got it right on the test

Answer:

In 1981, the Australian humpback whale population was 350

Po = Initial population = 350

rate of increase = 14% annually

P(t) = Po*(1.14)^t

P(t) = 350*(1.14)^t

Where

t = number of years that have passed since 1981

Year 2000

2000 - 1981 = 19 years

P(19) = 350*(1.14)^19

P(19) = 350*12.055

P(19) = 4219.49

P(19) ≈ 4219

Year 2018

2018 - 1981 = 37 years

P(37) = 350*(1.14)^37

P(37) = 350*127.4909

P(37) = 44621.84

P(37) ≈ 44622

There would be about  44622  humpback whales in the year 2018

Final answer:

To predict the Australian humpback whale population, an exponential growth model is used with equation P(t) = 350  [tex]imes (1 + 0.14)^t.[/tex] By substituting t with the number of years since 1981, we can estimate the population for any given year.

Explanation:

To write the equation for a function you could use to predict the number of humpback whales, we can use an exponential growth model because the population increases by a constant percentage rate each year. The general form of an exponential growth model is [tex]P(t) = P0 imes (1 + r)t,[/tex]where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the number of years since the initial time.

Given that the initial population in 1981 was 350 whales and the growth rate is 14% or 0.14, and taking t to be the number of years since 1981, the function to predict the number of whales in year t is:

[tex]P(t) = 350 imes (1 + 0.14)t[/tex]

For the number of whales in the year 2000, we substitute t with 19 (since 2000-1981=19), and for the year 2018 it would be 37 (since 2018-1981=37).

To predict the number of humpback whales in the year 2018, we use the function with t=37:

[tex]P(37) = 350 imes (1 + 0.14)37[/tex]

Calculating this, the result is rounded to the nearest whole number giving us the approximate whale population in 2018.

Could you comment the question so I could see it closer?

Answer:

Bank R

Step-by-step explanation:

Answer:

Bank R is the answer.

Step-by-step explanation:

Emma usually has about $1000 in her account at any given time during the month.

She usually visits the ATM twice a week and is interested in banking online options.

Bank R has 10 ATMs within a 5 mile radius of Emma’s home.

Bank S has 1 ATM 10 miles from Emma’s work.

Based on the availability of ATMs nearby, Emma should choose Bank R.

Answer: A.Lauren and Christy sold cookies for $0.50 each and glasses of lemonade for $1.10 each.

To get $17.20 you have to multiply the price of cookies by how many cookies you sold plus the cost of lemonade by how many glasses of lemonades were sold. Hope this helps!

Answer:

Saving account: A = 500(1 + 0.023t)

CD account: A = 500(1 + 0.018/12)^(12t)

Future value of saving account is $730

Future value of CD account is $716.47

She should choose the saving account

Step-by-step explanation:

* Lets revise the rules of simple and compound interest

- Simple Interest Equation (Principal + Interest)

 A = P(1 + rt)

- Where:

• A = Total amount (principal + interest)  future amount

• P = Principal Amount

• I = Interest Amount

• r = Rate of Interest per year in decimal; r = R/100

• t = Time Period involved  

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested for

* Now lets solve the problem

- Saving account:

# P = $500

# r = 2.3/100 = 0.023

# t = t

∴ A = 500(1 + 0.023t) ⇒ (1)

- CD account:

# P = $500

# r = 1.8/100 = 0.018

# n = 12

# t = t

∴ A = 500(1 + 0.018/12)^(12t) ⇒ (2)

* In case t = 20 years

- In equation (1)

# A = 500(1 + 0.023 × 20) = $730

- In equation (2)

# A = 500(1 + 0.018/12)^(12 × 20) = $716.47

* The future value of saving account is greater than the CD account

∴ She should choose the saving account

Answer:

The simplified result is: [tex]\frac{5a^3}{3}[/tex]

Step-by-step explanation:

[tex]a^2.\frac{a^{3}+a^2b }{5a}.\frac{25}{3b+3a}[/tex]

We need to solve the above equation.

We take a^2 common from a^3+a^2b

and we take 3 common from 3b+3a

Solving,

[tex]a^2\:\frac{a^2\left(a+b\right)\:}{5a}\frac{25}{3\left(b+a\right)}[/tex]

Since a+b = b+a we can cancel them with each other.

[tex]=a^2\:\frac{a^2}{5a}\frac{25}{3}\\=a^2\:\frac{a^2}{a}\frac{5}{3}\\=a^2\:a\:\frac{5}{3}\\=\frac{5a^3}{3}[/tex]

So, The simplified result is: [tex]\frac{5a^3}{3}[/tex]

The simplified expression is (5(a + b)) / (3a(b + 1)).

To simplify the given expression, we'll perform the indicated operation step by step:

a² * [(a³ + a²b) / 5a] * [25 / (3b + 3a)]

Step 1: Cancel common factors within each fraction:

a² * [(a³ + a²b) / (5a)] * [25 / (3(b + a))]

Step 2: Simplify further:

(a³ + a²b) * [25 / (5a * 3(b + a))]

Step 3: Factor out common terms:

(a²(a + b)) * [25 / (15a(b + a))]

Step 4: Cancel common factors between numerators and denominators:

(a + b) * (25 / (15a(b + a)))

Step 5: Simplify further:

(25(a + b)) / (15a(b + a))

Step 6: Factor out common terms again:

(25(a + b)) / (15a * a(b + 1))

Step 7: Cancel common factors:

(5(a + b)) / (3a(b + 1))

So, the simplified expression is (5(a + b)) / (3a(b + 1)).

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Answer:

B. $8 profit

Step-by-step explanation:

Loss is negative and profit is positive

Monday :      -11

Tuesday:     +18

Wednesday: -7

Thursday:    +8

                 ------------

                   +8

We have a profit of 8

Answer:

8

Step-by-step explanation:

Answer:

1.06t

Step-by-step explanation:

When the annual rate on a loan is 12% , which was represented using the expression 1.12t. Where t is the time. We are asked to write an expression that represents the 6 months interest rate applied. Assuming the rate of interest for 6 months be 6% half yearly, the expression for the same will be 1.06t

Answer:

1.06t

Step-by-step explanation:

When the annual rate on a loan is 12% , which was represented using the expression 1.12t. Where t is the time. We are asked to write an expression that represents the 6 months interest rate applied. Assuming the rate of interest for 6 months be 6% half yearly, the expression for the same will be 1.06t

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Solve the equation by inserting 7 for x.

Our equation is now y=2.5(7)-1.5

Multiply.

Y=17.5-1.5

Subtract

Y=16

The answer is D. 16

Hope this helps!

We just have to evaluate and compare the numbers:

[tex]4^3 = 64\\(-2)^5 = 32\\(-7)^2=49\\(-3)^4 = 81\\(-5)^2=25[/tex]

So, the only expression that exceeds 4^3 is (-3)^4

(-3)^4

Step-by-step explanation:

Answer:

Volume of larger ball = 220,781.3 cubic centimeters

Step-by-step explanation:

Let's use ratios to solve for the diameter of the larger ball first (let the diameter of larger ball be L)

[tex]\frac{LargerBall}{SmallerBall}=\frac{15}{11}=\frac{L}{55}\\11*L=15*55\\11*L=825\\L=\frac{825}{11}=75[/tex]

So, the diameter of the larger ball is 75 cm. We know radius is half of diameter, so radius of larger ball is (1/2)(75) = 37.5 cm

Ball is in the shape of a sphere, which has a formula for volume as:

[tex]V=\frac{4}{3}\pi r^3[/tex]

where V is the volume and r is the radius

now we simply plug in 37.5 into r and use 3.14 as π:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(3.14)(37.5)^3\\V=220,781.3[/tex]

Answer:

A 1:3

Step-by-step explanation:

Point P(-1, -12/5) partitions the line segment AB in the ratio of 2:1, which is calculated using the section formula in coordinate geometry.

To determine the ratio at which point P partitions AB, we can use the concept of section formula in coordinate geometry. The section formula states that if a point P(x, y) divides the line segment AB in the ratio m:n, then its coordinates are given by:

[tex]\[ x = \frac{mx_2 + nx_1}{m + n} \quad \text{and} \quad y = \frac{my_2 + ny_1}{m + n} \][/tex]

Substituting the given coordinates of A(-3, -4), B(2, 0), and P(-1, -12/5), we can form two equations with the unknowns m and n. Solving for m and n will give us the required ratio.

[tex]\[ -1 = \frac{m \cdot 2 + n \cdot (-3)}{m + n} \text{ and } (-\frac{12}{5}) = \frac{m \cdot 0 + n \cdot (-4)}{m + n} \][/tex]

Solving the equations, we find m = 2 and n = 1, meaning P divides AB in the ratio of 2:1, which is option B.

Answer:

Option D is correct .i.e., Most likely, the number of baseball cards in the deck is 27.Step-by-step explanation:we find probability of getting a Base ball card and compare it with probability of Baseball card from whole data.let,Total No. of Sports Cards in Data 1= 60and No. of Base ball card in Data 1 = xIn Data2,Jamie recorded data for 20 times⇒Total No. of cards in Data 2 = 20In which 9 cards are of Baseball and 11 cards are of Football.⇒ No. of Baseball card in Data 2 = 9Now by comparing,Therefore, Option D is correct .i.e., Most likely, the number of baseball cards in the deck is 27.

Step-by-step explanation:

Answer:

(C) The probability of buying bread and cheese is 0.12

Step-by-step explanation:

P(Event A) = 0.6

P(Event B) = 0.2

If Event A and Event B are independent,

Then P(Event A and Event B) = 0.6 x 0.2 = 0.12

A and B are independent events if:

 C.   The probability of buying bread and cheese is : 0.12

Two events  A and B are said to be independent.

                     if P(A∩B)=P(A)×P(B)

where P denote the probability of an event.

Here,

Event A= A shopper buys bread

and Event B=A shopper buys cheese

Also we have:

P(A)= 0.60 and P(B)= 0.20

If A and B are independent events then,

P(A∩B)=0.60×0.20

i.e.

P(A∩B)=0.12

i.e.If A and B are independent then the probability of buying bread and cheese is: 0.12

Also we know that:

P(A∪B)=P(A)+P(B)-P(A∩B)

If A and B are independent then,

P(A∪B)=0.60+0.20-0.12

i.e.

P(A∪B)=0.68

If A and B are independent then the probability of buying bread or cheese is: 0.68

Answer:

G=-8

Step-by-step explanation:

Answer:

G=-8

Step-by-step explanation:

Answer:

A.) is the best option

Step-by-step explanation:

Answer:Sorry about the sick day.The answer is simply Larry did the greatest.

Step-by-step explanation:First, subtract 54-14=41. Then, you multiply 41 times .25 since 25%=.25.This will give you 10.25.Finally, you subtract 41.00-10.25 to find out the remaining payment from Larry which is 37.50 dollars.Therefore, Larry paid the most.

Answer:

Lidea paid the most.

Answer:

0.00247

Step-by-step explanation:

Answer:

[tex]\large\boxed{2.47\times10^{-3}=0.00247}[/tex]

Step-by-step explanation:

METHOD 1:

[tex]\text{Use:}\ 10^{-n}=\dfrac{1}{10^n}\\\\2.47\times10^{-3}=2.47\times\dfrac{1}{10^3}=2.47\times\dfrac{1}{1000}=\dfrac{2.47}{1000}\\\\=\dfrac{2.47\times100}{1000\times100}=\dfrac{247}{100000}=0.00247[/tex]

METHOD 2:

[tex]a\times10^n\\\\\text{If}\ n<0\ \text{then move the comma n places to the left.}\\\text{If}\ n>0\ \text{then move the comma n places to the right.}[/tex]

[tex]\text{Therefore}\ 2.47\times10^{-3}=0\underbrace{.002}_{\leftarrow3}47[/tex]

For this case we have by definition, that the circumference of a circle is given by the following formula:

[tex]C = \pi * d[/tex]

Where:

d: Is the diameter of the circumference

So:

[tex]C = \pi * 25\\C = 78.5398[/tex]

Rounding to a decimal we have:

[tex]C = 78.5 \ yards[/tex]

ANswer:

[tex]C = 78.5 \ yards[/tex]

12 • 16 = 192

5 • 3.14 = 15.7 15.7/2= 7.85

192 + 7.85 = 199.85

The area of the objective is 199.85

Answer:

2.4 ft = height

Step-by-step explanation:

The formula for the volume of a pyramid is V = (1/3)(base area)(height).

Here V = 20 ft² = (1/3)(base area)(height).

Since the base area is (5 ft)², or 25 ft²,   20 ft² = (1/3)(25 ft²)(height),

(height) = (20 ft³) / ( [25/3] ft², or    60 ft³ / (25 ft²) = 2.4 ft = height

Answer:

2. the second alternative is correct

3. 24

Step-by-step explanation:

2.

In flipping a coin once, we can either land Heads, H or Tails, T. The sample space is thus;

{H,T}

In rolling a number cube labelled 1 to 6, we can roll a 1, 2, 3, 4, 5, or a 6. The sample space is thus;

{1, 2, 3, 4, 5, 6}

When we flip the coin and roll the number cube we shall combine the above sample spaces using the following logic;

We can roll the number cube and obtain a 1. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-1, T-1

We can roll the number cube and obtain a 2. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-2, T-2

Going on and on, we can roll the number cube and obtain a 6. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-6, T-6

We shall have a total of ;

6*2 = 12 possible outcomes

Therefore, the second alternative is correct

3.

The number of different lunch combinations that can be made from 3 sandwich choices, 2 side item choices and 4 beverage choices  if you choose one sandwich, one side and one beverage is ;

3*2*4= 24

We simply find the product of the number of choices under each category.

Answer:

confusing activities with accomplishments

Step-by-step explanation:

Answer:

confusing activities with accomplishments.

Step-by-step explanation:

the answers is a) nucleus, cytoplasm and ribosomes

Answer:

Try using A for your answer

Step-by-step explanation: