Sam has $40. He buys a book for $12.99 and a puzzle for $15.49.
Which equations can be used to find how much money Sam has left?
Select all that apply.
A. $40 – $28.48 = $11.52
B. $40 + $12.99 = $52.99
C.$15.49 – $12.99 = $2.50
D. $12.99 + $15.49 = $28.48
E. $40 – $2.50 = $37.50

Answer:

Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

Step-by-step explanation:

Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.

Since we want to make 30 liters of a 10% solution, we can set up the following equations:

Equation 1: x + y = 30 (total volume equation)

Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)

From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:

(0.06(30 - y) + 0.15y) / 30 = 0.10

Simplifying the equation gives:

(1.8 - 0.06y + 0.15y) / 30 = 0.10

1.8 + 0.09y = 3

0.09y = 1.2

y ≈ 13.33

Substituting y back into Equation 1, we find:

x + 13.33 = 30

x ≈ 16.67

Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

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Answer:

x= 4+5i

Step-by-step explanation:

The values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.

Given is a quadratic equation, x²-8x+41 = 0, we need to find the values of x,

Since, 41 is a prime number, which can not be factorized so, we will use quadratic formula,

x = [-b ± √(b²-4ac)] / 2a

Here, a = 1, b = -8, c = 41

Therefore,

x = [8 ± √(8²-4(41))] / 2

= [8 ± √(64-164)] / 2

= [8 ± √(-100)] / 2

= [8 ± 10i] / 2

= [4 ± 5i]

Therefore, x = 4+5i or x = 4-5i

Hence, the values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

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Answer:

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Expanding the given expressions:

1. (3x+2)(4x-5) = 12x^2 - 15x + 8x - 10 = 12x^2 - 7x - 10

2. (5x-2)(2x+7) = 10x^2 + 35x - 4x - 14 = 10x^2 + 31x - 14

3. (x-4)(3x-y+3) = 3x^2 - xy + 3x - 12x + 4y - 12 = 3x^2 - xy - 9x + 4y - 12

4. (2y-1)(2y+1)(4y^2 +1) = (4y^2 - 1)(4y^2 + 1) = 16y^4 - 1

5. (3x-3)(8x+1) = 24x^2 + 3x - 24x - 3 = 24x^2 - 21x - 3

6. (-m-3)(2m-4) = -2m^2 + 4m + 6m - 12 = -2m^2 + 10m - 12

7. (5d-12)(3d+1) = 15d^2 + 5d - 36d - 12 = 15d^2 - 31d - 12

8. (3x^2+2x)(4x-1) = 12x^3 - 3x^2 + 8x^2 - 2x = 12x^3 + 5x^2 - 2x

9. (3t-13)(2t+2) = 6t^2 + 6t - 26t - 26 = 6t^2 - 20t - 26

10. (4a-2b)(12a+6b) = 48a^2 + 24ab - 24ab - 12b^2 = 48a^2 - 12b^2

Each of the expressions has been simplified and solved by using properties of exponents as shown below.

In Mathematics and Geometry, an exponent is a mathematical operation that is written as an algebraic expression, so as to raise a quantity to the power of another.

Therefore, an exponent can be modeled by the following mathematical expression;

bⁿ

Where:

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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Answer:

5x-2

Step-by-step explanation:

(× + 5) + (4×-7) subtract the numbers x-2+4×

Answer:

x=\(\frac{695}{251}\)

or

x= 2\(\frac{193}{251}\)

Step-by-step explanation:

The average rate of change on the given interval is R = 3/2

To find the average rate of change on an interval [a, b], we need to use the formula:

R = (f(b) - f(a))/(b - a)

Here we have:

\(f(x) = 2^x + 1\)

And the interval is [0, 2]

Then:

\(f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5\)

Then we will get.

R = (5 - 2)/(2 - 0) = 3/2

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Answer:

1/2x+3/4y=10

ANS:

x=

−3

2

y+20

Let's solve for x.

1

12

12x+

12x+3

12x+34

12x+34y=10

Step 1: Add (-3)/4y to both sides.

1

12

12x+

12x+3

12x+34

12x+34y+

12x+34y+−3

12x+34y+−34

12x+34y+−34y=10+

12x+34y+−34y=10+−3

12x+34y+−34y=10+−34

12x+34y+−34y=10+−34y

12x+34y+−34y=10+−34y1

12x+34y+−34y=10+−34y12

12x+34y+−34y=10+−34y12x=

12x+34y+−34y=10+−34y12x=−3

12x+34y+−34y=10+−34y12x=−34

12x+34y+−34y=10+−34y12x=−34y+10

Step 2: Divide both sides by 1/2.

1

2

x

x1

x12

x12=

x12=−3

x12=−34

x12=−34y+10

x12=−34y+101

x12=−34y+1012

x12=−34y+1012x=

x12=−34y+1012x=−3

x12=−34y+1012x=−32

x12=−34y+1012x=−32y+20

Answer:

Answer:x=

Answer:x=−3

Answer:x=−32

Answer:x=−32y+20

question

Answer:

The answer is probably c

Step-by-step explanation:

its deducted by the x axis

Answer:

B

Step-by-step explanation:

Answer:

1 1/6 multiply 1/2 x 3/3 and 2/3x 2/2 then you 3/6 + 4/6 to get your answer

Answer: 5/13 of the cousins are male.

Step-by-step explanation:

If there are 26 cousins and sixteen are female, then subtract 16 from the total to find how many are male then divide it  by the total.

26 - 16 = 10    so 10 of them are male.

10/26 = simplifies to 5/13

Check:

\(\frac{5}{13}*\frac{26}{1}\) =     \(\frac{130}{13}\) = 10

Answer: \(y=5x^{2} + 4x +270\)

Step-by-step explanation:

The registration fee for a used car is 0.8 percent of sale price price os $5800 is $46.4.

Given the registration fees is the 0.8 percentage of the sale price then the registration fees is :

fees = 0.8% of $5,800,

fees = 5800 * 0.8/100,

fees = 58*0.8,

fees =  $46.4

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Therefore, the image of the point (5, -6) after a rotation of 90 degrees counterclockwise about the origin is (6, 5).  Thus, the correct answer is (6, 5).

To find the image of a point after a rotation of 90 degrees counterclockwise about the origin, we can use the rotation matrix.

Let's consider the point (5, -6). The rotation matrix for a counterclockwise rotation of 90 degrees is:

[ 0 -1 ]

[ 1  0 ]

To apply the rotation matrix, we multiply it by the coordinates of the point:

[ 0 -1 ]   [ 5 ]

[ 1  0 ] * [-6 ]

This gives us:

[ (0 * 5) + (-1 * -6) ]

[ (1 * 5) + (0 * -6) ]

Simplifying the expression, we get:

[ 6 ]

[ 5 ]

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Answer:

The circumference of original circle is, The area of original circle is, The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle. Therefore the radius of new circle is 4 ft and the statement A is true.

Answer:

Step-b 4.55 g/cmy-step explanation:

The average rate of water usage over the interval 0 < t < 5 is approximately 446.86 gallons per hour.

To find the average rate of water usage, we need to calculate the total amount of water used over the given interval and divide it by the length of the interval. The average rate is the ratio of the total water usage to the duration.

The integral of the rate function W(t) over the interval [0, 5] gives us the total amount of water used:

∫[0,5] 16te^t dt = [16te^t - 16e^t] evaluated from t = 0 to t = 5 = (16(5e^5 - e^5) - 16e^5) - (16(0 - 1) - 16) = 16(5e^5 - 1) - 16e^5 + 16 = 80e^5 - 16e^5 + 16 = 64e^5 + 16.

The length of the interval is 5 - 0 = 5.

Dividing the total amount of water used by the interval length:

Average rate = (64e^5 + 16) / 5 ≈ 446.86 gallons per hour.

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A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.

A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance

R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated

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If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased.

When there are omitted variables that are correlated with the variable of interest (in this case, years of schooling), the OLS estimator becomes biased. This means that the estimate of the effect of years of schooling on income is no longer accurate or unbiased. Therefore, researcher B's regression results may not provide a true estimate of the effect of education on wages due to the potential bias caused by the omitted variables.

Your answer: If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased. This is because the unobserved factors like motivation and work_ethic would be correlated with the variable of interest, educi, which can lead to biased estimates in the regression analysis.

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Answer:

2

Step-by-step explanation:

Add 1.5 to both sides:

5/2x-1.5+1.5=3.5+1.5

5/2x=5

Multiply both sides by 2/5

(2/5)*(5/2x)=(2/5)*(5)

Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

Answer:

not sure but I think it is this

The value of t will be  t ≥ 6 or t ∈ [ 6 , α ) .

Given,

-2t + 5 ≥ -7

Now,

Solving the inequality,

-2t + 5 ≥ -7

Take 5 from LHS of inequality to RHS of inequality .

-2t ≥ -12

The negative signs from both sides are eliminated .

2t ≥ 12

t≥ 12/2

t≥ 6 .

Thus the value of inequality will be t ≥ 6 .

Thus option C will be correct .

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Answer:

28 oz. for $2.24 cost most per ounce

$12.5 per oz

Step-by-step explanation:

Find the cost per ounce by dividing the total oz by cost of the total oz

60 oz. of peanut butter for $5.40

Cost per the ounce = 60 oz / $5.40

= $11.11 per oz

28 oz. for $2.24

Cost of peanut butter per ounce = 28 oz / $2.24

= $12.5 per oz

16 oz. for $1.76?

Cost of peanut butter per ounce = 16 oz / $1.76

= $9.10 per oz

28 oz. for $2.24 cost most per ounce

The present value of the cash flows is approximately $11,754.04.

To calculate the present value of the cash flows, we need to discount each cash flow to its present value using the appropriate discount rate. The present value (PV) can be calculated using the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + ... + CFn / (1 + r)^n

where CF is the cash flow and r is the discount rate.

Using the given discount rate of 9.89 percent per year, we can calculate the present value as follows:

PV = 2,200 / (1 + 0.0989)^1 + 2,600 / (1 + 0.0989)^2 + 4,800 / (1 + 0.0989)^3 + 5,400 / (1 + 0.0989)^4

Calculating each term and summing them up:

PV = 2,200 / 1.0989 + 2,600 / 1.0989^2 + 4,800 / 1.0989^3 + 5,400 / 1.0989^4

PV ≈ 1,999.64 + 2,271.89 + 3,622.82 + 3,860.69

PV ≈ 11,754.04

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Answer:

C I think

Step-by-step explanation:

Option a) Never. A correlation coefficient based on an observational study cannot be used to support a claim of cause and effect, regardless of its value or the characteristics of the scatterplot.

Correlation does not imply causation, which means that even if two variables are strongly correlated, it does not necessarily mean that one causes the other. There may be other variables or factors that are responsible for the observed correlation, and a causal relationship cannot be established from observational data alone. To establish causality, experimental studies are typically needed, where the potential cause is manipulated and the effect is measured.

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The y-intercept of the linear equation of best fit, considering the slope and the means, is of -60.428.

A linear function is modeled by:

y = mx + b

In which:

For a line of best-fit, the y-intercept is given by:

\(b = \overline{y} - m\overline{x}\)

The parameters in this problem are given as follows:

\(m = 4.915, \overline{x} = 14.347, \overline{y} = 10.088\)

Then:

\(b = 10.088 - 4.915(14.347) = -60.428\)

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