This is a multi-part Item. Make note of your answer(s) to this part for use in the remaining part(s).Kara and Nathan participated in a 60-minute maze race.Kara:32 minutesNathan:40 minutesPart AUse ratio notation and decimal notation to describe the relationship between Kara's time and the total time of the race.Enter the correct answers in the box. For the decimal, enter the digit that repeats 3 times.Hint(s): Write the ratio of Kara's time over the total time.Use long division to write the fraction as a decimal.ratio:decimal:

Given the system of equations

Solve by elimination method as shown below.

Multiply the first equation by 3 and subtract it from the second equation,

Then,

Use the value of y in the first equation,

Therefore, the answers are x=-5 and y=2, (x,y)=(-5,2)

Answer:

The number of blueberry muffins Jake sold.

Step-by-step explanation:

Since Jake sold $38 of muffins, we know that 3 pertains to Jake.

Y is the price of a blueberry muffin, so 3 must be how many blueberry muffins were sold.

The product of 6000 and 50 can be found below

Part A:

Given 900 dollars

Interest rate = 4.5%

Value at the end of 5 years

900 × 4.5% × 5 = $226.62

900 + 226.62 = 1,126.62

= 1,126.62 after 5 years

Part B: Given 900 dollars is placed in a saving account

interest rate = 4.5% semiannually (which means twice a year)

We need to find the value after 5 years

Since it's semiannually it's twice a year

5 × 2 = 10

900 × 4.5% (interest rate) × 10

900 × 4.5% × 10 = 510.29

510.29 + 900(intital amount) = 1,410.29

= $1,410.29 after 5 years

Step-by-step explanation:

you can use proportions to convert molecules to moles and then moles to grams.

To convert molecules to moles, use the Avogadro number (6,022 × 10²³ atoms)

The proportion is:

1 : Avogadro number = x : number of molecules

so

1 : 6,022 × 10²³ = x : 4,5 × 10²⁴

solve. x = 7,47 moles

From the moles you can get the grams of SO2. To find grams, first find the mass of SO2.

S = 32,06

O2 = (16×2) = 32

so mass of SO2 is 64,06

Now use the proportion:

mass of SO2 : 1 = moles : x

so

64,06 : 1 = 7,47 : x

solve. x = 0,11 grams

Since the profit equation has been given to us as

Where m is the number of megaphones sold.

Since m can only take integer values from zero and above.

When no megaphone was sold, p(m)=p(0)=-875

Therefore, the range is;

However p(m) is not all real numbers.

When 500 megaphones were sold, the profit is;

This is the correct range.

Therefore, the range is represented as;

Thus the correct option is a. II

Answer:

7 [tex]\frac{1}{73}[/tex]

Step-by-step explanation:

Set up a proportion

[tex]\frac{words}{minutes}[/tex] = [tex]\frac{words}{minutes}[/tex]

[tex]\frac{438}{6}[/tex] = [tex]\frac{512}{m}[/tex]  Cross multiply

438m = 6(512)

438 m = 3072  Divide both sides by 438

m = 7 [tex]\frac{1}{73}[/tex]

Answer:

y= -1/8x+3.5

Step-by-step explanation:

Plot your points and draw a line thru them. Find the slope: -1/8. Find the y-int: 3.5.

y = mx+b where x and y are variables, m is the slope and b is the y-int

y=-1/8x+3.5

Hope that helps

The way in which the given ordered pairs represent a function is: b. For every x value, there is only one y value - a function.

A function simply refers to a mathematical expression (equation) which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).

In this context, we can reasonably infer and logically deduce that these ordered pairs represent a function because it has different input variables (x-values) for different or the same output variables (y-values).

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Given

Set x=6; then,

If x=6, y=2

Step 1

Given;

Step 2

Thus;

Answer;

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾ is the explicit formula for the geometric sequence: 4, 20, 100, 500.

A geometric progression is simply a sequence of non-zero numbers, every term after the first can be determine by multiplying the previous number by a common ratio.

The nth term of a geometric sequence is expressed as;

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

Where a₁ is the first term, r is the common ratio and n is the number of terms.

Given the sequence in the question;

4, 20, 100, 500, ...

First determine the common ratio.

r = any term / previous term

r = 20/4

r = 5

Th first term in the sequence is 4.

Plug these into the geometric sequence formula and simply.

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

Therefore, the explicit formula for the sequence is aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

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According to the compound interest concept, the total amount he will be paid is  $8,864.73

Compound interest:

The general form of the compound interest is,

A = P(1 + r/n)ⁿˣ

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

R = Annual nominal interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

x = time in decimal years;

Given,

Ryan has an eight–year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually.

Here we need to find the total amount he will pay.

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)ⁿˣ

A = 6,000.00(1 + 0.05/1)⁽¹⁾⁽⁸⁾

A = 6,000.00(1 + 0.05)⁸

A = $8,864.73

Therefore, the total amount that he will pay is $ 8,864.73

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The order from least to greatest to satisfy the inequality  t < -3 is (-∞, -2).

For the given question,

The inequality is given as;

t < -3

For the inequality to be true the value of 't' must be less than -3.

Thus, the values will range between.

(-∞, -2)

Where, -∞ represents the least value and -2 shows the greatest value for 't'.

Thus, the order from least to greatest to satisfy the inequality  t < -3 is (-∞, -2).

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SOLUTION:

From the Z-score probability table;

P < 81 = 0.7123

CONCLUSION:

If one adult female is randomly selected, the probability that her pulse rate is less than 81 beats per minute is 0.7123

No, the sample of celebrities is not likely to be representative

Here, we should understand if the sample collected is likely to be representative or not

We need to understand what is meant by a representative sample or representative sampling

When a sampling is representative, it means that the sample that we have obtained looks like the population in which we are taking the sample from

Now, from what we have selected as a sample, we only considered the early comers while we have left out the late comers

What this mean in this case is that whatever sample we have is in fact not representative of the total

So we conclude that the sample of celebrities is not likely to be representative

Notice that the sequence has a common ratio of 4:

The n-th term of a sequence with first term equal to a and common ratio r is:

The first term of this sequence is 15 and the common ratio is 4, then the nth term is:

Substitute n=6 to find the 6th term:

Therefore, the 6th term of the sequence, is:

We have a sample of size n=250. They are normally distributed with mean 88 and standard deviation of 15.

We have to find how many values from the sample are expected to be below 78.

We can calculate the z-score for 78 as:

Then, we can calculate the percentage of values below 78 as the probability P(z<-0.67):

This percentage is independent of the sample size: it is the same percentage for 100 numbers, 250 numbers or 1000 numbers.

For 250, 63 numbers are expected to be below 78, as 0.25*250=63 approximately.

Answer: 25%

To answer how many Jugs would be needed to treat an are of 168 square feet, we can use proportional relationships:

In triangle, value of QS = 12 ft .

What is a triangle answer?

ΔPQR and ΔQSR ,

         QS/SR = PO/OS

           y/9 =      16/12

           12 *  y =  16 *  9

                y = 16 *  9 /12

                 y = 12

value of QS = 12ft

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The percent of eighth graders who voted for Luke is  64 %.

Given that:-

Number of eighth graders who voted for Luke = 192

Number of eighth graders who voted for Alice = 60

Number of eighth graders who voted for Chris = 48

Total number of eighth graders at Wilson Middle School = 300

We have to find the percent of eighth graders who voted for Luke.

We know that:-

Percent of eighth graders who voted for Luke =

(Number of eighth graders who voted for Luke/Total number of eighth graders)*100

Hence, we can write,

Percent of eighth graders who voted for Luke = (192/300)*100 = 64 %

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Yes. (-6) raised to -4 power equal -6 to the -4 power

What is exponentiation ?

Exponentiation is a mathematical operation, written as [tex]b^{n}[/tex], involving two numbers, the base b and the power n it is read as b raised to n.

We have asked that whether [tex](-6)^{-4}[/tex] is equal to [tex]-6^{-4}[/tex]

Now we solve both the sides to show that they are equal

[tex](-6)^{-4}=(\frac{-1}{6} )^{4}[/tex]

Now for the right hand side

[tex]-6^{-4} =\frac{-1}{6} ^{-4}[/tex]

Both the values are same

Hence, Yes. (-6) raised to -4 power equal -6 to the -4 power

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Answer:

√20 miles

Step-by-step explanation:

a² + b² = c²

                                           |

                     ?                    |   2 miles ↓

                                           |

          ------------------------------

                     ← 4 miles  

2² + 4² = c²

4 + 16 = c²

20 = c²

√20 = c

I hope this helps!

The length of the straight path they must run to get back to the starting line is 4.47 miles.

Displacement [x] of an object is the length of the straight line joining the initial and final position of the object. Mathematically, displacement can be written as-

Δx = x[2] - x[1]

Now -

Δx = vΔt              {[v] is velocity}

So we can write -

vΔt = x[2] - x[1]

Given are the runners at a cross-country meet such that they ran 2 miles to south and then 4 miles to west from the starting line.

We can find the straight path they must run to get back to the starting line using the Pythagoras theorem. The base will be equal to distance ran towards south and height will be equal to the distance ran towards west. The length of the hypotenuse will be equal to that of displacement or the straight path they must run to get back to the starting line. Using Pythagoras theorem -

[h]² = [b]² + [p]²

[h]² = (2 x 2) + (4 x 4)

[h]² = 4 + 16

[h]² = 20

[h] = 4.47 miles

Therefore, the length of the straight path they must run to get back to the starting line is 4.47 miles.

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Answer: m = -5 and b = -6

Given that 10x + 2y = -12

The slope - intercept form of equation is written as

y = mx + b

where m = slope and b = intercept

This equation can be re-arrange as

2y = -12 - 10x

2y = -10x - 12

Divide all through by 2

2y/2 = -10x/2 - 12/2

y = -5x - 6

From, y = mx + b

m = -5 and b = -6

The simple interest earned on $8,350 principal deposited for 6 years at an interest rate of 2.28% is $ 1, 141. 28

It is of great importance to know the formula for calculating the simple interest. It is expressed as;

I = PRT/100

Where;

Now, let's substitute the values into the formula, we have;

Simple interest, I = $8,350 × 2. 28 × 6/100

Multiply the denominators

Simple interest, I = 114228/100

Find the quotient

Simple interest, I = 1, 141. 28

Hence, the simple interest is $ 1, 141. 28

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Answer: x = 8

5x - 1 = 39

isolate and divide to get x

x = 8

We are given a data set and we are asked to write the model that fits the data. We notice that for each step of "x" the values of "y" increase by the same amount. That means that the data follow a linear model, therefore, we will use:

Where:

To determine the slope "m" we will use the following formula:

Where:

Are data points. From the table we choose the following points:

Now, we substitute in the equation for the slope:

Solving the operations:

Therefore, the slope is -7. Substituting in the equation of the line we get:

Now, we substitute one of the points to get the value of "b". We will substitute the value x = -8, y = 47, we get:

Solving the product:

Now we subtract 56 from both sides:

Now, we substitute the value of "b" in the equation of the line:

And thus we get the line equation.

The cost of manufacturing C(x) = 2658 in a day is $2658

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, it is given from the part A of solution :

the linear function that models the situation is C(x) = 75x + 1908

Now, for cost of manufacturing C(x) = 2658 the value of x will be :

C(x) = 75x + 1908

2658 = 75x + 1908

75x = 2658-1908

75x = 750

x = 10

Therefore, the cost of manufacturing C(x) = 2658 in a day is $2658

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Answer

Option Y is correct.

Explanation

We are told that the slope is multiplied by (1/2) and the y-intercept is increased by 3 units.

The original graph has a y-intercept (point where the graph crosses the y-axis) at point y = 1. Adding 3 units to that, changes the y-intercept to y = 4.

And that leaves options X and Y as viable answers.

But the original graph is positive sloping, and multiplying the slope by (1/2) only spreads the graph out more along the y-axis, it doesn't change the direction of the graph like option X has been changed to be negative sloping. This would only happen if the slope was multiplied by a negative number.

So, this leaves us with only Option Y as the viable answer.

And to be absolutely sure, we can go further and calculate the slope of the original graph and the graph in option Y.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For the original question,

(x₁, y₁) and (x₂, y₂) are (0, 1) and (-1, -1)

For the option Y,

(x₁, y₁) and (x₂, y₂) are (0, 4) and (-1, 3)

1 is indeed half of 2. This confrims our answer.

Hope this Helps!!!