Dave buys a basketball for $20 plus an 8% tax. Mel bought a football for $28 plus an 8% tax. Enter the difference that Dave and Mel paid, including tax. Round your answer to the nearest cent.

Answer:

3:5

Step-by-step explanation:

Please see attached picture for full solution. ( Unit method)

Rhonda must collect at least 240 stamps in order to reach her goal.

Step-by-step explanation:

Given,

Stamps Rhonda wants to collect = 575

Stamps already in collection = 335

Let,

d represents the number of stamps Rhonda needs to collect to achieve her goal.

Stamps to collect + Stamps already in collection ≥ 575

[tex]d+335\geq 575\\d\geq 575-335\\d\geq 240[/tex]

Rhonda must collect at least 240 stamps in order to reach her goal.

Keywords: inequality, addition

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When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = [tex]a^2[/tex]

6 is subtracted from the square of a number = [tex]a^2 - 6[/tex]

5 times the number = [tex]5 \times a[/tex]

So we can frame a equation as:

6 is subtracted from the square of a number = 5 times the number

[tex]a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0[/tex]

Let us solve the above quadratic equation

For a quadratic equation [tex]ax^2 + bx + c = 0[/tex] where [tex]a \neq 0[/tex]

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Here in this problem,

[tex]a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6[/tex]

Substituting the values in above quadratic formula, we get

[tex]\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}[/tex]

We have two solutions for "a"

[tex]\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}[/tex]

We have asked negative solution. So a = -1

Thus the negative solution is -1

To find the product for 2(2n + 3), use the distributive property to multiply 2 with each term inside the parentheses, resulting in 4n + 6.

The question asks to find the product for 2(2n + 3). To solve this, we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this rule to the given expression, we multiply 2 with each term inside the parentheses.

First, multiply 2 by 2n to get 4n. Next, multiply 2 by 3 to get 6. Therefore, the expression simplifies to 4n + 6.

We have successfully used the distributive property to find that the product of 2(2n + 3) is 4n + 6.

Answer:

  Car A: 40 mph

  Car B: 50 mph

Step-by-step explanation:

For the same travel time, the ratio of speeds is the same as the ratio of distances:

  (speed B)/(speed A) = 150/120 = 5/4

The difference in the (reduced) ratio units is 1, so 1 ratio unit corresponds to 10 mph. Multiplying the reduced ratio by 10 mph, we get ...

Speed B is 50 mph; speed A is 40 mph.

Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, [tex]x+y=22[/tex]----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

[tex]0.75x+0.40y=11.95[/tex]------------(2)

solve equation 1 and equation 2 for x and y.

From equation 1.

[tex]x+y=22[/tex]

[tex]y=22-x[/tex]----------------(3)

put y value in equation 2.

[tex]0.75x+0.4(22-x)=11.95[/tex]

[tex]0.75x+0.4\times 22-0.4x=11.95[/tex]

[tex]0.75x+8.8-0.4x=11.95[/tex]

[tex]0.75x-0.4x=11.95-8.8[/tex]

[tex]0.35x=3.15[/tex]

[tex]x=\frac{3.15}{0.35}[/tex]

[tex]x=9[/tex]

Now substitute x value in equation 3.

[tex]y=22-9[/tex]

[tex]y=13[/tex]

So, he buy 13 pencils.

The items are classified as M1, M2, or neither based on their liquidity and spendability. A line of credit and traveler's checks are neither M1 nor M2 as they are not actual money. Physical currency and money in a checking account are classified as M1, while money in a money market account is classified as M2.

M1 refers to the narrowest definition of the money supply, which includes only the most liquid forms of money that can be easily spent. M2 is a broader measure of the money supply and includes M1 as well as other less liquid forms of money. Neither refers to items that do not fit into either M1 or M2.

a. Your $5,000 line of credit on your Bank of America card is neither in M1 nor M2 as it is not actual money but a credit limit.

b. $50 dollars' worth of traveler's checks you have not used yet is neither in M1 nor M2 as they need to be exchanged for cash before they can be spent.

c. $1 in quarters in your pocket is in M1 as it is physical currency that can be spent.

d. $1200 in your checking account is in M1 as it is a liquid form of money that can be spent.

e. $2000 you have in a money market account is in M2 as it is a less liquid form of money that can be accessed but may have restrictions or penalties for withdrawal.

Answer:

Mutually exclusive,

[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]

Step-by-step explanation:

Please consider the complete question:

Determine if the scenario involves mutually exclusive or overlapping events. Then find the  probability.

A cooler contains twelve bottles of sports  drink: four lemon-lime flavored, four  orange flavored, and four fruit-punch  flavored. You randomly grab a bottle. It  is a lemon-lime or an orange.

Let us find probability of finding one lemon lime drink.

[tex]P(\text{Lemon-lime})=\frac{\text{Number of lemon lime drinks}}{\text{Total drinks}}[/tex]

[tex]P(\text{Lemon-lime})=\frac{4}{12}[/tex]

[tex]P(\text{Lemon-lime})=\frac{1}{3}[/tex]

Let us find probability of finding one orange drink.

[tex]P(\text{Orange})=\frac{\text{Number of orange drinks}}{\text{Total drinks}}[/tex]

[tex]P(\text{Orange})=\frac{4}{12}[/tex]

[tex]P(\text{Orange})=\frac{1}{3}[/tex]

Since probability of choosing a lemon lime doesn't effect probability of choosing orange drink, therefore, both events are mutually exclusive.

We know that probability of two mutually exclusive events is equal to the sum of both probabilities.

[tex]P(\text{Lemon-lime or orange})=P(\text{Lemon-lime})+P(\text{Orange})[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{1}{3}+\frac{1}{3}[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{1+1}{3}[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]

Therefore, the probability of choosing a lemon lime or orange is [tex]\frac{2}{3}[/tex].

Answer:

[tex]y=\frac{11}{5}[/tex]

Step-by-step explanation:

Given expression

[tex]\frac{1}{3}(y-2)-\frac{5}{6}(y+1)=\frac{3}{4}(y-3)-2[/tex]

To solve for [tex]y[/tex] for the given expression.

Solution:

We multiply each term with the least common multiple of the denominators of the fraction in order to remove fractions.

The multiples of the denominators are:

3 = 3,6,9,12,15

6 = 6,12

4 = 4,8,12

The least common multiple = 12.

Multiplying each term with 12.

[tex]12.\frac{1}{3}(y-2)-12.\frac{5}{6}(y+1)=12.\frac{3}{4}(y-3)-2(12)[/tex]

[tex]4(y-2)-10(y+1)=9(y-3)-24[/tex]

Using distribution.

[tex]4y-8-10y-10=9y-27-24[/tex]

Simplifying.

[tex]-6y-18=9y-51[/tex]

Adding [tex]6y[/tex] both sides.

[tex]-6y+6y-18=9y+6y-51[/tex]

[tex]-18=15y-51[/tex]

Adding 51 both sides.

[tex]-18+51=15y-51+51[/tex]

[tex]33=15y[/tex]

Dividing both sides by 15.

[tex]\frac{33}{15}=\frac{15y}{15}[/tex]

[tex]\frac{33}{15}=y[/tex]

Simplifying fractions.

[tex]\frac{11}{5}=y[/tex]

∴ [tex]y=\frac{11}{5}[/tex]  (Answer)

Option C

The explicit formula for the arithmetic sequence is [tex]a_n = 9 - 6n[/tex]

Solution:

Given that the arithmetic sequence is:

3, -3, -9, -15, -21, ...

To find: Explicit formula for the arithmetic sequence

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where [tex]a_n[/tex] is nth term of sequence

n is the term's location

[tex]a_1[/tex] is the first term of sequence

d is the common difference between terms

In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.

In the given sequence:

3, -3, -9, -15, -21, ...

[tex]a_1 = \text{ first term } = 3[/tex]

d = difference between any two terms in sequence

[tex]d = a_2 - a_1[/tex]

d = -3 - (3) = -6

Substituting the values in above formula,

[tex]a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n[/tex]

Thus the explicit formula to find any term in sequence is found

The expression for the total cost of bats and gloves is b*x + 5*y. To find the total cost when three bats are bought, you need to know the costs of a bat (x) and a glove (y), and substitute those into the expression.

Assume that the cost of a baseball bat is 'x' dollars and each glove costs 'y' dollars. The total cost can be calculated by making 'b' the number of bats and adding the cost of 5 gloves. Therefore, the expression representing the total cost is b*x + 5*y.

Now, if the coach bought 3 bats, and we're given the costs for a bat and a glove, we can substitute '3' for 'b', 'x' for the cost of a bat, and 'y' for the cost of a glove.

For example, if a bat is $50 (x=50) and a glove is $20 (y=20), the total cost would be: 3*50 + 5*20 = 250 dollars.

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Final answer:

The expression for total cost of baseball bats and gloves is 'b times the number of bats plus 5 times the cost of a glove', where 'b' represents the cost of a bat. In the bat and ball problem, if a bat costs $1 more than the ball and together they cost $1.10, the ball costs $0.05. For three bats, the total cost is $3.15.

Explanation:

The question posed is a classic algebra problem from mathematics often used to illustrate a common cognitive error. To write an expression for the total cost of the baseball bats and gloves, let the cost of each bat be represented by 'b' and assume each glove has a fixed cost 'g'. The expression is then b times the number of bats plus 5 times the cost of a glove. However, we require additional information regarding the cost of individual gloves to complete this expression.

Turning to the bat and ball problem, if a bat and ball together cost $1.10, and the bat costs $1 more than the ball, we can set up the following equations where 'x' is the cost of the ball:

x + (x + $1) = $1.10

2x + $1 = $1.10

2x = $1.10 - $1.00

2x = $0.10

x = $0.05

Thus, the ball costs $0.05 and the bat costs $1.05. Finding the cost of three bats, we simply multiply $1.05 by 3 to get $3.15.

Using [tex]a/b+c/b=(a+c)/b[/tex], we find that [tex]2/5+2/5=4/5[/tex].

Hope this helps.

Answer:

E

Step-by-step explanation:

There are 48 cards numbered from 1 to 48.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Multiples of 8: 8, 16, 24, 32, 40, 48

Multiples of 6 and 8: 24, 48.

Hence,

Total number of cards = 48,

Number of cards which are multiples of 6 and 8 = 2

The probability that the number card is a multiple of both 6 and 8 is

[tex]P=\dfrac{2}{48}=\dfrac{1}{24}[/tex]

Answer: Im assuming this is a true or false question anyways the answer would be false if it is

Step-by-step explanation:

Average rate of change is 0

Interpretation: The crop yield did not change from year 5 to year 15

Solution:

The function that models the yield is:

[tex]f(x) = -x^2 + 20x + 75[/tex]

The average rate of change of f(x) from x = a to x = b is given by the formula:

[tex]\text{ average rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]

Find and interpret the average rate of change from year 5 to year 15

[tex]f(5) = -(5)^2 + 20(5) + 75\\\\f(5) = -25 + 100 + 75\\\\f(5) = 150[/tex]

[tex]f(15) = - (15)^2 + 20(15) + 75\\\\f(15) = -225 + 300 + 75\\\\f(15) = 150[/tex]

Thus average rate of change:

[tex]\text {average rate of change}=\frac{f(15)-f(5)}{15-5}[/tex]

[tex]\text {average rate of change}=\frac{150-150}{10}=0[/tex]

Thus Average rate of change is 0

Interpretation: The crop yield did not change from year 5 to year 15.

Final answer:

The average rate of change in wheat yield from year 5 to year 15 is 0 pounds per acre per year, symbolizing that there was no change in the crop yield between these years.

Explanation:

To find the average rate of change of the wheat yield from year 5 to year 15, we will apply the function f(x) = −x² + 20x + 75 to these years and then calculate the rate of change. First, we'll find the yield for year 5 and year 15:

Next, we'll calculate the average rate of change using these yields:

Average rate of change = (f(15) - f(5)) / (15 - 5) = (150 - 150) / (10) = 0

Therefore, the crop yield did not change from year 5 to year 15. The function indicates that at both year 5 and year 15, the farmer's land yielded 150 pounds per acre, so the average rate of change in yield over this period is 0 pounds per acre per year.

Answer:

File is given in attachements .

Step-by-step explanation:

[tex]y = \sqrt[3]{x}  + 2[/tex] will pass through (0,2) and (-8,0) . Its shape will be as shown in the graph.

Answer:

Graph C

Step-by-step explanation:

Answer: 108

Step-by-step explanation:

Answer:

1) The slope of the line is [tex]m=\frac{5}{2}[/tex]  or  [tex]m=2.5[/tex]

2) The equation of the line is [tex]y=2.5x-4[/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

[tex]m=\frac{6-1}{4-2}[/tex]

[tex]m=\frac{5}{2}[/tex]

[tex]m=2.5[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=2.5[/tex]

[tex]point\ (2,1)[/tex]

substitute

[tex]y-1=2.5(x-2)[/tex]

Convert to slope intercept form

isolate the variable y

[tex]y-1=2.5x-5[/tex]

[tex]y=2.5x-5+1[/tex]

[tex]y=2.5x-4[/tex]

Answer:

n=6

Step-by-step explanation:

4(n+2)=2(n+10)

4n+8=2n+20

4n-2n+8=20

2n+8=20

2n=20-8

2n=12

n=12/2

n=6

Answer:

The graph is plotted below.

One ordered pair as solution is (0, 0).

Step-by-step explanation:

Given:

The inequality is given as:

[tex]y\geq x-5[/tex]

In order to plot it, we first replace '≥' by '=' sign. This gives,

[tex]y = x-5[/tex]

Now, we plot the above line. For that, we need the x and y intercepts.

At x-intercept, y = 0. So,

[tex]0=x-5\\x=5[/tex]

The point is (5, 0)

At y-intercept, x = 0. So,

[tex]y=0-5\\y=-5[/tex]

The point is (0, -5)

Now, plot these two points and draw a line passing through these two points. The graph is shown below.

Now, replace '=' by '≥' sign. Since, 'y' is greater than equal to 'x - 5'. So, the solution region is above the given including the values on the line.

Therefore, any ordered pair in the solution region is a solution of the given inequality. From the graph, one such ordered pair is (0, 0).

This can be verified from the inequality also.

[tex]0\geq 0-5\\0\geq -5(True)[/tex]

So, one ordered pair is (0, 0).

Answer:

1. f(2) = 6

2. Slope, m = [tex]$ \frac{7}{2} $[/tex]

Step-by-step explanation:

Problem 1:

Given f(x) = |3x|

To find f(2), substitute x = 2.

⇒ f(2) = |3(2)|

= |6|

= 6

Problem 2:

The given equation is: 2y = 7x + 8

The general equation of the line is: y = mx + c, where m is the slope of the line.

Therefore, we reduce the given equation to the general form of the line.

Dividing the given equation by 2, we get:

y = [tex]$ \frac{7}{2}x + \frac{8}{2} $[/tex]

[tex]$ \implies y = \frac{7}{2}x + 4 $[/tex]

Thus, slope, m = [tex]$ \frac{7}{2} $[/tex] which is the answer.

Problem 3:

Given with 14 gallons of gas, we can drive 392 miles.

The capacity of the tank if 14 gallons.

If 14 gallons can take us 392 miles, then 1 gallon of gas should take us: [tex]$ \frac{392}{14} $[/tex] miles.

= 28 miles/gallon of gas

Therefore, with 3.7 gallons of gas, we can travel 3.7 X 28 miles

= 103. 6 miles

x=-3

9x+2(3x+7)= -31

multiply the "3x" and the "7" by two (distributive property)

[="6x" and "7"]

add the "9x" and the "6x" [="15x"]

subtract "14" from"-31" [= "-45"]

divide "15x" from "-45"

="-3"

put the "-3" in for "x"

multiply 9(-3) [=-27]

multiply 3(-3) [=-9]

distribute the 2 to the "-9" and the "7" [="-18" and "14"]

add the "-18" and "14" [=-4]

add the "-27" and the "-4"

=-31 ✓

9x+2(3x)+2(7)= -31

9x+6x+14= -31

15x+14= -31

-14 -14

15x= -45

/15= /15

x= -3

9x+2(3x+7)= -31

9(-3)+2(3(-3)+7= -31

-27+2(-9+7)= -31

-27+(2(-9)+2(7))= -31

-27+(-18+14)= -31

-27+ (-4)= -31

-31= -31✓

Answer:

(0,-26)

Step-by-step explanation:

Write the equation of the line in the slope-intercept form:

1. The slope of the line is

[tex]\dfrac{-65-(-52)}{51-34}=-\dfrac{13}{17}[/tex]

2. The equation of the line is

[tex]y-(-52)=-\dfrac{13}{17}(x-34)\\ \\y+52=-\dfrac{13}{17}x+26\\ \\y=-\dfrac{13}{17}x-26[/tex]

Now, find the y-intercept, substitute x = 0:

[tex]y=-\dfrac{13}{17}\cdot 0-26\\ \\y=-26[/tex]

Answer: 7c ≤ 63

Ivan will buy at most 9 pounds of candy, which means that multiplying 9 by 7, the cost of the candy, will get your answer: 63. Plug these values into an inequality with a less than or equal to sign (≤) facing away from 63 and you're done!

The possible amounts Ivan will spend on candy can be represented as c ≤ 7.

Let's denote the amount Ivan will spend on candy as c. The cost of candy is $7 per pound, and Ivan will buy at most 9 pounds of candy. Therefore, the maximum amount he could spend on candy is 9 pounds multiplied by $7 per pound, which is 9c ≤ 63.

Since we are looking for possible amounts, we can rewrite this inequality as c ≤ 63/9, which simplifies to c ≤ 7.

So, the possible amounts Ivan will spend on candy are values less than or equal to $7.

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Answer:

G

Step-by-step explanation:

G = -2

-2 is greater than -4, yet, less than 0

The period will be the length for one cycle of the function.

answer: 10

Answer:

125

Step-by-step explanation:

26:4

Hope this helps!

An equivalent ratio to 13:2 can be found by multiplying or dividing both terms of the ratio by the same number. For instance, when both terms are multiplied by 2, the equivalent ratio is 26:4 because the proportion remains unchanged.

To find a ratio equivalent to 13:2, you need to multiply or divide both terms of the ratio by the same number. For example, if you multiply both terms of the ratio 13:2 by 2, you would get 26:4 which is an equivalent ratio. This is because the relationship or proportion between the two terms remains the same.

Here's the step-by-step calculation:

So, the ratio that is equivalent to 13:2 is 26:4.

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Rahul gets 12 paper clips.

Step-by-step explanation:

Given,

Paper clips Tian have = 56

He gives 3/4 of them to joe.

Joe gets = [tex]\frac{3}{4}*56=\frac{168}{4}[/tex]

Joe gets = 42 paper clips

He given 2/7 of received to Rahul.

Rahul gets = [tex]\frac{2}{7}*42=\frac{84}{7}[/tex]

Rahul gets = 12 paper clips

Rahul gets 12 paper clips.

Keywords: fraction, division

Learn more about fractions at:

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Answer:

50m

Step-by-step explanation:

Information from the question:

The length is 15m

The width is 10m

Length is represented by "l"

Width is represented by "w"

The perimeter is the total of its side lengths. A rectangle has four sides that are two lengths and two widths.

Use the formula for perimeter:

P = 2(l + w)            Put in the length and width measurements

P = 2(15m + 10m)    Add inside the brackets

P = 2(25m)        Multiply

P = 50m           Answer

Therefore the perimeter of the rectangular swimming pool is 50 meters.