1. find the difference 7 1/4 - 3 1/2 =

a. 3 3/4
b. 4 3/4
c. 3 1/2
d. 4 1/2

2. find the product and write it in simplest form 3/8 x 2/3

a. 9/16
b. 6/24
c. 2/8
d. 1/4

3. find the product and write it in simplest form 2 3/8 x 1 2/3

a. 2 6/24
b. 3 23/24
c. 3 3/4
d. 95/8

4. perform the division and write it in simplest form 7/10 ÷ 3/5

a. 35/30
b. 6/7
c. 21/60
d. 1 1/6

Answer:

The APY of the saving account is 4.048656%

Step-by-step explanation:

We know the formula for APY which is given by

[tex]APY=(1+\frac{r}{n} )^n-1[/tex]

here, r= interset rate =  3.9886% = 0.039886

n = compounding cycles = 4

On plugging these values in the above formula, we get

[tex]APY=(1+\frac{ 0.039886}{4} )^4-1[/tex]

On simplifying this we get

APY = 0.04048656 =4.048656%

Answer:

APY = 4.0486561%

Step-by-step explanation:

Given is the Annual Percentage Rate (APR) = 3.9886% compounded quarterly.

Suppose Principal amount, P = $1.

time, t = 1 year.

interest rate, r = 3.9886% = 0.039886

period of compounding, n = 4 (for quarterly).

Future value = P * (1 + r/n)^(nt)

FV = 1 * (1 + 0.039886/4)^(1*4) = 1.040486561

Annual Percentage Growth = (FV/P)*100 = (1.040486561 / 1) * 100 = 4.0486561%

Hence, Annual Percentage Yield (APY) = 4.0486561%

Answer: There are 82.5% after school students who are enrolled in his classes.

Step-by-step explanation:

Let the total number of students be 100

Percentage of students who need help in computer science = 30%

So, number of students who need help in computer science = 30

Percentage of students who need help in maths = 70%

So, number of students who need assistance in maths  = 70

Of the students who need help,

40% are enrolled in Mr. Ellis's class during the school day,

So, it means 60% are enrolled in his class after the school day.

Number of students who are enrolled in his class after the school day = 60

Number of students who need help in Maths is given by

[tex]\frac{70}{100}\times 60=42[/tex]

Of the students that need help in maths, percent of students are enrolled in his class during the day = 25%

So, number of students who need help in maths and enrolled in his class after school hours

[tex]\frac{75}{100}\times 42=31.5[/tex]

Number of students who need help in computer science and enrolled in his class after school hours

[tex]\frac{30}{100}\times 60=18[/tex]

Therefore, there are [tex]31.5+18=49.5[/tex] students who joined his class after school hours,

Percentage of the after students who are enrolled in Mr. Ellis's classes is given by

[tex]\frac{49.5}{60}\times 100=82.5\%[/tex]

Hence, there are 82.5% after school students who are enrolled in his classes.

29.5% of the after-school students are enrolled in Mr. Ellis's classes.

1. Calculate the percentage of students who need help in computer science and are enrolled in his class:

  - 30% of the students need help in computer science.

  - 40% of those students are enrolled in his class during the school day.

[tex]\[ \text{Percentage of students needing help in computer science and enrolled in his class} = 30\% \times 40\% = 0.3 \times 0.4 = 0.12 = 12\% \][/tex]

2. Calculate the percentage of students who need help in math and are enrolled in his class:

  - 70% of the students need help in math.

  - 25% of those students are enrolled in his class during the school day.

[tex]\[ \text{Percentage of students needing help in math and enrolled in his class} = 70\% \times 25\% = 0.7 \times 0.25 = 0.175 = 17.5\% \][/tex]

3. Combine the two percentages to find the total percentage of after-school students enrolled in his classes:

  - 12% of the total students are those who need help in computer science and are in his class.

  - 17.5% of the total students are those who need help in math and are in his class.

Thus, the total percentage of after-school students enrolled in Mr. Ellis's classes is:

[tex]\[12\% + 17.5\% = 29.5\%\][/tex]

Answer:

f(x)=(x−5)2−16

Set the polynomial equal to y

to find the properties of the parabola.

y=(x−5)2−16

Use the vertex form, y=a(x−h)2+k

, to determine the values of a, h, and k

.

a=1

h=5

k=−16

Since the value of a

is positive, the parabola opens up.

Opens Up

Find the vertex (h,k)

.

(5,−16)

Find p

, the distance from the vertex to the focus.

Tap for more steps...

14

Find the focus.

Tap for more steps...

(5,−634)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=5

Answer:

 x > -1 or x < -9

Step-by-step explanation:

(x + 5)^2 must be > 16 for f(x) to be positive.

(x + 5)^2 > 16

Taking square roots:-

x + 5 > 4

x > -1   (answer)

or x + 5 < -4

x  < -9 (answer)

Answer:

enrollment decreases by 14.34%.

Step-by-step explanation:

Given that number of students enrolled in 2000 = 823

Given that number of students enrolled in 2010 = 705

705 is less than 823 so that means number of students enrollment is decreasing.

Decrease = 823-705 = 118

Percent decrease is given by formula:

[tex]Percent =\frac{part}{whole}\cdot100 =\frac{118}{823}\cdot100= 14.3377885784[/tex]

which is approx 14.34%.

Hence final answer is that enrollment decreases by 14.34%

Put the coordinates of the point (1, 9) to the inequality y > 6x + 3:

9 > 6(1) + 3

9 > 6 + 3

9 > 9    FALSE

The difference in elevations between a scuba diver at -8 meters and a shark at -29 meters is calculated as: -8 - (-29) = 21 meters.

The subject in question involves finding the difference in elevations. In this context, the scuba diver is swimming at an elevation of -8 meters, and the shark is at -29 meters. To find the difference, we subtract the lower number (-8) from the higher number (-29).

However, due to the negative signs, the difference will be calculated as follows: -8 - (-29) = -8 + 29 = 21 meters. Therefore, the difference in elevations between the shark and the scuba diver is 21 meters.

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Answer:

44 hours

Step-by-step explanation:

Decreasing the people by a factor of 2 means we have 3 people

The job takes 6* 22 = 132 people hours

When we decrease the people, it will take more hours

132 people hours = 3 people * t hours

Divide each side by 3

132/3 = 3t/3

44 = t

It will take 44 hours

Answer:

7+2-5=f

Step-by-step explanation:

If he starts on the 7 floor, then he is seven above ground, and that would clarify as a positive number. He then goes up 2 floors, which means we would add 2 to the original number. Going down five would mean we would subtract, because he is getting closer to zero, which is ground level. F represents the floor he is on now.

Hope this helps! (Brainliest please!)

answer

4th floor

Step-by-step explanation:

7+2-5=4

Answer:9-16=-7

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

l x w = area

(x + 5) (3.4) = 51

x+5=15

x=10

plug back into the equation for length

(10+5) = 15

Answer:

y = 9x + 2

Step-by-step explanation:

The equation of a line with slope m and y-intercept b is

y = mx + b

If you were asked to write the equation of the line with slope = 9 and y-intercept = 2, then the equation is

y = 9x + 2

Answer:

y = 9x -2

Step-by-step explanation:

Answer:

We cannot find a solution to the system of equations.

a+b = 5.30

2a + 2b = 14

Step-by-step explanation:

Let a = the price of an apple

let b = price of an orange

a+b = 5.30

2a + 2b = 14

Multiply the first equation by 2

2a+ 2b = 10.60

Subtract the second equation

2a+2b = 10.60

-2a+2b = 14

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

0 = -3.40

This is never true  so there is no solution

Answer:

Can we find a unique price for an apple and an orange?

Choose 1 answer:

CORRECT (SELECTED)

No; the system has no solution.

Step-by-step explanation:

See attached!

Answer:

Step-by-step explanation:

2.) −$180/year

The average rate of change between Year 4 and Year 9 is -$180 per year.

A linear equation can be used to represent a non linear line. A linear equation is of the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the value of car after x years.

From the graph, at year 4, y = 2300, hence it is (4, 2300). At year 9, y = 1400, hence it is (9, 1400). Therefore:

[tex]Average\ rate\ of\ change=\frac{1400-2300}{9-4}= - 180[/tex]

Hence the average rate of change between Year 4 and Year 9 is -$180 per year.

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Answer:

I would pick the letter C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rules for Dilations. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure (called the image)

Answer:

D

Step-by-step explanation:

Answer:

1430 yards

Step-by-step explanation:

Note that [tex]1\text{ acre}=\dfrac{1}{640}\text{ square mile}.[/tex] Then

[tex]25\text{ acres}=\dfrac{25}{640}\text{ square mile}.[/tex]

If one side of the restangular field measures exactly [tex]\dfrac{1}{4}[/tex] mile, then let the second side be x miles and

[tex]\dfrac{25}{640}=\dfrac{1}{4}\cdot x,\\ \\x=\dfrac{\frac{25}{640}}{\frac{1}{4}}=\dfrac{25}{640}\cdot \dfrac{4}{1}=\dfrac{25}{160}=\dfrac{5}{32}\ mile.[/tex]

The perimeter of the rectangle will be

[tex]P=2\cdot \dfrac{1}{4}+2\cdot \dfrac{5}{32}=\dfrac{2\cdot 8+10}{32}=\dfrac{26}{32}=\dfrac{13}{16}\ mile.[/tex]

Since [tex]1\ mile=1760\ yards,[/tex] then [tex]\dfrac{13}{16}\ mile=\dfrac{13}{16}\cdot 1760=1430\ yards.[/tex]

To fence a 25-acre rectangular field with one side 1430 yards of fencing is needed.

To order fencing for a 25-acre, rectangular field, with one side measuring exactly  1/4 mile, we first need to determine the field's dimensions. Since a mile equals 1760 yards, one side of the field is

1/4 x 1760 = 440 yards.

Now, to find the other side, we use the area formula (Area = length x width).

The field is 25 acres, and 1 acre equals 4840 square yards. So the field has an area of 25 x 4840 square yards.

Let's denote the unknown side as 'width':

= 25 x 4840 = 440 x width

Width =  25 x 4840/ 440

= 275 yards

Now that we have both the length and the width, we can find the perimeter, which is the total length of fencing needed. The perimeter of a rectangle is 2  x (length + width).

Perimeter = 2 x (440 + 275) = 2 x 715

= 1430 yards

Therefore, to enclose the field completely, you would need 1430 yards of fencing.

The sllope-intercept form:

[tex]y=mx+b[/tex]

[tex]6y-12=14x[/tex]          add 12 to both sides

[tex]6y=14x+12[/tex]      divide both sides by 6

[tex]y=\dfrac{14}{6}x+\dfrac{12}{6}\\\\\boxed{y=\dfrac{7}{3}x+2}[/tex]

To change the equation 14x=6Y-12 into slope-intercept form, first isolate Y by adding 12 to both sides, then dividing by 6. This results in the equation Y = (7/3)x + 2.

The equation provided is 14x=6Y-12 and we need to transform it to slope-intercept form, which has a general format of y = mx + b, where m is the slope and b represents the y-intercept.

Let's start by isolating y in the equation:

So, the slope-intercept form of the given equation is Y = (7/3)x + 2.

Learn more about Slope-Intercept Form

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Answer:

She would have to do 219 haircuts in a month for the costs to be the same, which would be $428.

Step-by-step explanation:

To find this we take the costs of the first place.

$438

Next we can look at the costs of the second place using x as the number of haircuts she'd do.

2x

Now we can set the two equal to each other to find the number of cuts.

438 = 2x

219 = x

Carrie would pay $438 and perform 219 haircuts each month.

To find out how much Carrie would pay and how many haircuts that would be, we need to set up an equation.

Let's assume the number of haircuts per month is x.

For self-employment at The Belmont Salon, Carrie would pay a fixed monthly rent of $438, so her total cost would be $438.

For the franchise option, Carrie would pay $2 for every haircut. So the total cost would be 2x.

Setting up the equation: 438 = 2x

To solve for x, we divide both sides of the equation by 2:

x = 438 / 2 = 219

Therefore, Carrie would pay $438 and perform 219 haircuts each month.

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Answer:

p = 12

Step-by-step explanation:

add 2 to both sides of the equation

24 = 2p ( divide both sides by 2 )

p = 12

Answer: p=2

Step-by-step explanation:

22=2p-2

You add two to 22 which will give you 24

24=2p

You want to divide the 2 to get the letter by itself

12=2

Answer: Each book costs $9

Step-by-step explanation:

74-11 = 63

63 divided by 7 = 9

That's the answer

Answer: $9

Step-by-step explanation: 74 - 11 = 63. 63 divided by 7 equals 9. So each book cost $9

Answer: 3) 9 7/10 (C)

4) 26 1/12 pounds (A)

5) 17 5/6 miles (D)

Answer:

3. C

4. A

4. D

Step-by-step explanation:

3)

When adding two fractions, you must add them with the same denominator. This means finding the lowest common multiple of  10 and 5, which is 50. Simply multiply each fraction by the denominator of the opposite fraction:

[tex]\frac{4}{5} * 10 = \frac{40}{50}[/tex]

[tex]\frac{9}{10} * 5 = \frac{45}{50}[/tex]

Add the two fractions together:

[tex]\frac{40}{50} + \frac{45}{50} = \frac{85}{50}  = 1 \frac{35}{50} = 1 \frac{7}{10}[/tex]

7 + 1 + 1 + 7/10 = 9 7/10

4)

Again, make the denominator the same number by multiplying the fraction by the denominator of the other fraction:

[tex]\frac{3}{4} * 3 = \frac{9}{12}[/tex]

[tex]\frac{1}{3} * 4 = \frac{4}{12}[/tex]

9/12 + 4/12 = 13/12 = 1 1/12

10 + 15 + 1 + 1/12 = 26 1/12

5)

Again, multiply the fraction by the denominator of the opposite fraction:

[tex]\frac{1}{2} * 3 = \frac{3}{6}[/tex]

[tex]\frac{1}{3} * 2 = \frac{2}{6}[/tex]

3/6 + 2/6 = 5/5

7 + 6 + 4 + 5/6 = 17 5/6

Final answer:

To order the given fractions from least to greatest: 73/100, 2/5, 1/10, convert them to decimals and arrange them in increasing order: 0.1, 0.4, 0.73.

Explanation:

To order the numbers least to greatest, we compare their values. Let's convert these fractions to decimals first:

Now that we have the decimals, we can arrange them from least to greatest:

[tex]\left\{\begin{array}{ccc}2x+3y=12&|\text{multiply both sides by 2}\\-4x-6y=-24\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+6y=24\\-4x-6y=-24\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=0\qquad TRUE\\\\2x+3y=12\qquad\text{subtract 2x from both sides}\\\\3y=12-2x\qquad\text{divide both sides by 3}\\\\y=4-\dfrac{2}{3}x\\\\Answer:\ \text{It's the dependent system of equations}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=4-\dfrac{2}{3}x\end{array}\right[/tex]

Solving the system using elimination reveals that the two equations are dependent, resulting in infinitely many solutions since they represent the same line. There is no unique solution for x and y.

To solve the system of equations 2x + 3y = 12 and -4x - 6y = -24 using the elimination method, we aim to eliminate one variable by combining the equations. First, notice that the second equation is exactly -2 times the first equation. If we multiply the first equation by 2, we would have identical left-hand sides but with opposite signs, which would cancel out when added together.

Multiplying the first equation by 2 gives 4x + 6y = 24. Now, add this new equation to the second equation:

Adding them results in 0 = 0, which indicates that the two equations are dependent, and the system has infinitely many solutions. This is because each equation is a multiple of the other, and they both represent the same line. Therefore, we cannot isolate x or y to find a unique solution. The system is consistent and dependent.

Answer:

37

Step-by-step explanation:

a + b for a=24 and b=13

plug in

24 + 13

= 37

Answer:

a + b = 37

Step-by-step explanation:

substitute the values a = 24 and b = 13 into the expression

a + b =  24 + 13 = 37

A) -102 feet

She started at -38 feet. She then went -120 feet, so -38-120= -158. She then went +56 feet. -158+56=-102.

Answer:

The answer is A. -102

Step-by-step explanation:

If she started at 38 feet below sea level, we would describe it as -38. If she descended 120 feet deeper, than we subtract that from -38.

-38-120=-158

She is now 158 feet below sea level, or -158.

Then, if she climbs up 56 feet, we would add that to -158.

-158+56=-102

Answer:

1st blank is 0,14 dollars/1yuan, and 2nd blank is 1kg/2.2lb

Step-by-step explanation:

The tomatoes at the Chinese market would cost approximately $0.99 per pound, following the currency conversion rate from yuan to dollars and the weights conversion rate from kilograms to pounds.

To find the cost in dollars per pound from yuan per kilogram, we should use both the conversion rate from yuan to dollars and the conversion rate from kilograms to pounds. In this case, we are given that 1 yuan is worth 0.14 dollars and that 1 kilogram is approximately 2.20462 pounds. Therefore, the cost in yuans per pound would be 15.65 yuan/kg divided by 2.20462 lbs/kg, which equals approximately 7.09 yuan/pound. After converting it to dollars, it'd be approximately 7.09 yuan/pound times 0.14 dollars/yuan which gives us approximately $0.99 per pound.

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Answer:

81/64  or 1 17/64

Step-by-step explanation:

A negative exponent means to flip the fraction

(8/9) ^-2

(9/8)^2

81/64

Changing this to a mixed number

1 17/64

Answer:

[tex]f(x) = 3 \cdot 0.2^x[/tex]

Step-by-step explanation:

[tex]f(x) = 3 \cdot 0.2^x[/tex]

Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is [tex]\mathbb{R}[/tex]

Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore [tex](0, \infty)[/tex].

Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.

Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.

Symmetry: It is clear to see the graph of f(x) has no symmetry.

Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe [tex]f(x-1) > f(x)[/tex] for all x in the domain.

The function is however bounded below by 0: no value of x in the domain exists which satisfies [tex]f(x) < 0[/tex].

Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)

Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: [tex]y=0[/tex].

End behaviour: As [tex]x \rightarrow \infty, f(x) \rightarrow 0[/tex]. As [tex]x \rightarrow -\infty, f(x) \rightarrow +\infty[/tex]

The function f(x) = 3*0.2^x is a decaying exponential function, with a domain of all real numbers and a range of (0, ∞). It is continuous, decreasing and has a horizontal asymptote at y=0.

The function f(x) = 3*0.2^x is an exponential function with a base of 0.2. Here we're multiplying the function by a coefficient of 3.

Domain: The domain of an exponential function is always all real numbers. So, the domain is (-∞, ∞).

Range: Since this is a decaying exponential function, the output will always be between 0 (which will never actually be reached) and positive infinity. So, the range is (0, ∞).

Continuity: An exponential function is always continuous, meaning there are no holes or jumps in the graph.

Increasing or Decreasing Behavior: Since the base of the exponential (0.2) is less than 1, this function is always decreasing.

Symmetry: Exponential functions are not symmetric.

Boundedness: This function is bounded below by 0.

Extrema: There are no maximum or minimum points in this function. However, it is worth noting that the function gets closer and closer to y=0 as x goes to infinity, but never reaches it. This is sometimes considered a minimum.

Asymptotes: An asymptote is a line that the graph approaches but never reaches. For this function, the x-axis, or y = 0, is the horizontal asymptote.

End behavior: As x approaches positive infinity, y approaches 0; as x approaches negative infinity, y approaches positive infinity.

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