How does using visual models
help us understand dividing
fractions by whole numbers?

Answer:

She needed a minimum of 600 voters

Step-by-step explanation:

1800/3 = 600

Helping in the name of Jesus.

The system of inequalities's point (4,8), where an is the number of apples and 8 is the number of peaches.

A pair of expresses or values that is neither equal in mathematics is referred to as an inequality. Thus, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are distinct things. Use the same equal symbol most frequently when two quantities are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two faces until only the variables are left, many straightforward inequalities can be solved. However, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

given

The following will be the solution to the expressions:-

0.75a + 1.5y = 15

a + y ≥ 12

To determine the values of a and y, solve both equations.

0.75a + 1.5(12 - a) = 15

0.75a + 18 - 1.5a = 15

-0.75a = -18 + 15

-0.75a = -3

a = 4

y = 12 - 4 = 8

The system of inequalities's point (4,8), where an is the number of apples and 8 is the number of peaches.

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Answer:

1073.45 in²

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The equation to solve for the area of a circle is:

But wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:

Now that we know this, we can insert 37 in for the diameter:

So, the radius of the circle is 18.5 inches.

Inserting 18.5 into the expression for the radius:

Using 3.14 for pi:

Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².

Answer:

9

Step-by-step explanation:

possible products:

9 x 2

If you add you get 11

6 x 3

If you add you get 9

The entire ocular micrometer ruler be in millimeters 2.3mm

For the scanning objective (4X),

the objective is the scanning power, The, power is 4X and the Diameter in mm is 2.3mm

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The value of XZ is given by 26.

Given that the triangles RST and XYZ are congruent to each other.

So, RS = XY, since corresponding parts of Congruent triangles are equal.

Given also that,

RS = 11x-1

XY = 9x+5

XZ = 7x+5

So, RS = XY gives

11x-1 = 9x+5

11x-9x = 5+1

2x = 6

x = 6/2

x = 3

Substituting the value of x in the value of XZ is given by,

XZ = 7x+5 = 7*3+5 = 21+5 = 26

Hence the value of XZ is 26.

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Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:

m = 2/3

Step-by-step explanation:

Answer:

\( \frac{2}{3} \)

Step-by-step explanation:

slope is

\( m = \frac{rise}{run} = \frac{y 2 - y1}{x2 - x1} \)

(0,0) & (3,2)

\( m = \frac{2 - 0}{3 - 0} = \frac{2}{3} \)

9514 1404 393

Answer:

  2 hours 30 minutes

Step-by-step explanation:

Effort is measured in people-hours per house. Here, the effort to deliver one leaflet is ...

  (3 people)(2.5 hours)/(270 houses) = 1/36 people-hours/house

Then the number of hours (h) for 5 people and 450 houses is ...

  (5 people)(h hours)/(450 houses) = 1/36 people-hours/house

  h = (1/36)(450/5) = 2.5

It will take 2 hours 30 minutes to deliver to 450 houses.

_____

Alternate solution

The time is (assumed) inversely proportional to the number of people, so increasing the number of people from 3 to 5 multiplies the time by 3/5. The time is proportional to the number of houses, so increasing the number of houses from 270 to 450 multiplies the time by 450/270 = 5/3. The time for the second task is (3/5)(5/3) = 1 times the time for the first task.

2 1/2 hours is 2 hours 30 minutes.

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:1333.3 Contiuous

Step-by-step explanation:

 .

4000/3,=1333.3x1,=1333.3

 I'm not sure

The explicit formula for the geometric sequence would be \(a_n =10000.87\times (0.95)^{n-1}\).

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given:

         \(a_4=8573.75\\\\a_6=7731.81\)

Now by using the formula for the nth term of a GP, we get

           \(a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3\)

Now for n = 6, we get

           \(a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5\)

Now divide we get

\(\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95\)

Now we can get the value of a,

        \(8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87\)

So we can prepare the explicit formula as

            \(a_n =10000.87\times (0.95)^{n-1}\)

Hence, the explicit formula for the geometric sequence would be \(a_n =10000.87\times (0.95)^{n-1}\).

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Answer:

Step-by-step explanation:

the first line has y-intercept = 5 and slope = -3, and the second line has y-intercept = 2 and slope = 1.

Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.

Answer:

the second option.

\(-3\leq x\leq 0\)

Step-by-step explanation:

Answer:

JC = 32

Step-by-step explanation:

From the diagram

JC + CA = JA , thus

JC + 17 = 49 ( subtract 17 from both sides )

JC = 32

The length of the segment JC is 32.

We have,

From the number line,

JA = 49

CA = 17

Now,

JA = JC + CA _______(A)

Substituting the values in (A).

JA = JC + CA

49 = JC + 17

Subtracting 17 on both sides.

JC = 49 - 17

JC = 32

Thus,

The length of the segment JC is 32.

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< TSU = 4y + 11 = 23 degrees

What does angle relationship mean?

We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles

we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5

SU bisects < TSV

=>    < TSU = < USV

4y + 11 = 6y + 5

-2y = -6

y = 3

< TSU = 4y + 11 = 23 degrees   ( put the value of y=3)

∠USV = 6y + 5 = 23 degrees      ( put the value of y=3)

Hence ,< TSU = 4y + 11 = 23 degrees

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Using the normal distribution, it is found that the z-scores are:

a) z = -1.5

b) z = 1.9

c) z = 0

In normal distribution with mean 'μ' and the standard deviation 'σ', the z-score of a measure X is given by:

z = x-μ/σ

It measures how many standard deviations the measure is from the mean, either above the mean(positive z-score), or below(negative z-score).

For first blank: 1.5 standard deviations below the mean, hence z = -1.5.

For second blank: 1.9 standard deviations below the mean, hence z = 1.9.

For third blank: The mean is 0 standard deviations from itself, hence z = 0.

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In your fourth year on the job, you can expect to earn $41,327.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that;

In this case, P = 34,000, r = 0.05, and n = 4.

Plugging these values into the formula, we get:

A = 34,000(1 + 0.05)^4

A = 34,000(1.05)^4

A = 34,000(1.2155)

A = 41,327

Therefore, by the simple interest the answer will be $41,327.

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After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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Answer:

D. The inequality sign always opens up to the smaller number.

Step-by-step explanation:

Well if A says sign always opens up to larger number and D says sign always opens up to smaller number so 1 of them must be false. Inequality signs always open up to greater number so the answer is D.

Answer:

21) 4

because -13-(-17) when 2 negatives are next to each other they cancel out and turn into positives the just -13+17

And 22 is 33 because the 2 negatives cancel out and turn into positives so 23+9

I am sorry but the rest I can't solve

Step-by-step explanation:

Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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Answer: 1 3/4 = 3/4 + 3/4 + 1/4, or 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4

Step-by-step explanation:

Answer:

16.666667 %

Step-by-step explanation:

1800 - 1500 = 300

x : 100 = 300 : 1800

x = 300 · 100 / 1800

x = 300/ 18

x = 100/6

x = 16.666667 %