Neil had $146.82 in his checking account. He deposited $84.27 and wrote a check for $19.12. Then, he wrote another check for $31.86. Which most closely estimates how much money remains in Neil's account?

Answer:

9 is 15% of 60. Eme can use that to her advantage because she can figure out how much 1% is and multiply it by 15

Step-by-step explanation:

x = age of the son

y = age of the father

x + y = 44

y = 2x

Substitute our second equation into our first equation.

x + 2x = 44. Combine the like terms.

3x = 44. Divide each side by 3

x = 44/3 or 14.7.

Substitute 44/3 into x for our second equation to find y

y = 2(44/3). Multiply 2 by 44/3

y = 88/3 or 29.3

Answer:

\(1.47 * 10^{-3}\)

Step-by-step explanation:

So I think standard form is basically scientific notation.

\(1.47 * 10^{-3}\)

Let me know if this is wrong

C. F-test statistic for testing the validity of the regression equation.

In multiple regression analysis, the ratio of MSR (Mean Square Regression) to MSE (Mean Square Error) is used to calculate the F-test statistic.

This statistic is used to test the overall validity of the regression equation, determining whether the regression model as a whole is statistically significant in explaining the variation in the dependent variable.

The F-test assesses whether the regression model as a whole provides a significant improvement over the null model (a model with no independent variables).

A large F-statistic indicates that the regression equation is statistically significant, implying that at least one of the independent variables has a significant effect on the dependent variable.

Therefore, option C, the F-test statistic for testing the validity of the regression equation, is the correct answer.

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Answer:

no

Step-by-step explanation:

100 + 75x > 700: This inequality represents the condition where Lawrence charges clients more than $700.

Let's represent the typical number of hours worked by Lawrence as "x" (in hours). Based on the information provided, we can set up the inequality to represent the range of fees charged by Lawrence: 100 + 75x < 250 or 100 + 75x > 700. Let's explain these inequalities: 100 + 75x < 250: This inequality represents the condition where Lawrence charges clients less than $250. The initial fee of $100 plus the product of $75 per hour (75x) should be less than $250.

100 + 75x > 700: This inequality represents the condition where Lawrence charges clients more than $700. The initial fee of $100 plus the product of $75 per hour (75x) should be greater than $700. These inequalities provide the boundaries for the range of fees charged by Lawrence, based on the number of hours worked (x). The exact value of "x" that satisfies either inequality depends on the specific rates charged by Lawrence and would need further information to determine.

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Answer:

2.26 feet

Step-by-step explanation:

400/25=16

16/3.14=5.0955

5.0955^2=2.257

The distribution of the sample mean diameter of the concrete columns follows a normal distribution with a mean of 8.25 inches and a standard deviation of 0.1 inch. To calculate probabilities, we can use the properties of the normal distribution.

In this problem, we are given that the mean diameter of all columns is 8.25 inches with a standard deviation of 0.1 inch. Since the sample size is relatively large (n = 35), we can approximate the distribution of the sample mean using the Central Limit Theorem. According to the theorem, the sample mean will follow a normal distribution with a mean equal to the population mean (8.25 inches) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (0.1 inch / sqrt(35)).

To find the probability that the sample mean diameter will be greater than 8 inches, we can standardize the value using the z-score formula: z = (x - μ) / (σ / sqrt(n)), where x is the desired value, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, x = 8, μ = 8.25, σ = 0.1, and n = 35. Calculating the z-score and looking up the corresponding probability in the standard normal distribution table, we find the probability to be approximately 0.8944, or 89.44%.

To find the probability that the sample mean diameter will be between 8.2 and 8.4 inches, we can standardize both values and subtract the corresponding probabilities. Using the z-score formula for each value and looking up the probabilities in the standard normal distribution table, we find the probability to be approximately 0.3694, or 36.94%.

If the standard deviation is 0.15 inch instead of 0.1 inch, the standard deviation for the sample mean would be 0.15 inch / sqrt(35). To calculate probabilities using this value, we would use the same formulas and methods as described above, but with the updated standard deviation.

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Answer:

11.1111

Step-by-step explanation:

11.1111 is 52 degrees Fahrenheit in Celsius by unit conversion.

What is  unit conversion ?

The same feature is expressed in a different unit of measurement through a unit conversion. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles. The units of a measured quantity can be changed without changing the value using a conversion factor, which is an expression representing the connection between units.

                              The numerator and denominator of a conversion ratio (also known as a unit factor) have the same value whether represented in various units, and the ratio itself always equals one (1).

1 °F    =  -17.2222 °C

(52°F − 32) × 5/9 = 11.111 °C

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Answer:

They travel 5/18 in one hour

Step-by-step explanation:

Answer:

In an hour the car can cover 5/18 of the distance

The constant of proportionality for the ratio of price to number of bouquets from the table is 3.

The constant of proportionality is the ratio of the y value to the x value. That is:

constant of proportionality(k) = y/x

In this case,

y = price

x = number of bouquets

To find the constant of proportionality for the table, just pick any corresponding number of bouquets (x) and price (y) values on the table and find the ratio. Thus:

Constant of proportionality (k) = y/x

Constant of proportionality = 9/3 = 3

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Complete Question

See image attached

The value of θ is the angle whose cosine is 7/8, which is approximately 28.955 degrees or 0.506 radians

We can begin by simplifying the equation using algebraic operations:

(6cos(θ)+1)/5 = (8cos(θ)-2)/4

Multiplying both sides by 20, we get:

4(6cos(θ)+1) = 5(8cos(θ)-2)

Expanding the brackets, we get:

24cos(θ) + 4 = 40cos(θ) - 10

Moving all the terms with cos(θ) to one side and all the constants to the other side, we get:

24cos(θ) - 40cos(θ) = -10 - 4

-16cos(θ) = -14

Dividing both sides by -16, we get:

cos(θ) = 7/8

Therefore, the value of θ is the angle whose cosine is 7/8, which is approximately 28.955 degrees or 0.506 radians

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Answer:

x(x-1)

Step-by-step explanation:

\(x^{2} -x\)

look for what both functions share, they both share an x,

which you can factor out,

x(x-1)

and you have your answer :)

In the absence of more information about the problem, it's difficult to determine whether a negative solution would be acceptable. However, we can consider some general guidelines

The detailed answer are following :-

a) The reasonableness of the answer depends on the context of the problem and the units used. Without knowing these details, it's difficult to determine if the answer found is reasonable. However, if we assume that the units are appropriate for the problem and the context is well-defined, then we can evaluate whether the answer seems reasonable. In general, a reasonable answer should make sense given the problem statement and any constraints or limitations provided. If the answer is consistent with our expectations, based on our knowledge of the problem, then it's likely to be reasonable. Conversely, if the answer seems too large or too small, it may indicate an error in the calculation or an unrealistic assumption.

b) In general, a negative solution may or may not be acceptable depending on the problem's context. In some situations, negative solutions are perfectly valid, while in others, they may not make sense. For example, if we're solving a physics problem that involves distance, a negative distance would not be physically meaningful. However, if we're solving an equation that represents a balance sheet or financial statement, negative solutions might be acceptable, as they can represent losses or debts owed.

In the absence of more information about the problem, it's difficult to determine whether a negative solution would be acceptable. However, we can consider some general guidelines. If the problem involves physical quantities that cannot be negative, such as time, distance, or mass, a negative solution is likely to be unreasonable. On the other hand, if the problem involves variables that can take on negative values, such as temperature, profit, or debt, then a negative solution may be acceptable. Ultimately, the reasonableness of a negative solution depends on the context of the problem and the assumptions made.

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Step-by-step explanation:

\( \red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}\)

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

\( \rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}} \)

Since, we know that,

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

\( \red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}} \)

\(\rule{200}{3}\)

\( \sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}} \)

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

\( \rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}} \)

Where,

Therefore,

\( \sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}} \)

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

\( \rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}} \)

\(\rule{200}{3}\)

\( \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}} \)

∴ Hence, the required answer is 17/7.

Answer:

128

Step-by-step explanation:

Answer:

X = -6, y = 8.

Step-by-step explanation:

Rearrange the second equation to the form ax + by = c

x + 2y = 10

2x - y = -20

Multiply equation 1 by -2

-2x - 4y = -20

Adding this to the second equation

-5y = -40

Y = 8.

Now substitute x = 8 into equation 1

X + 2(8) = 10

X = -6.

Answer: a. (-2, -2)

Step-by-step explanation:

The point at which the two lines intersects is at (-2, -2), which is the solution.

Answer:

Ok Sorry but please tell me how r u seeing my comments so fast?

Step-by-step explanation:

Answer:

d. $34.94

Step-by-step explanation:

the monthly finance charge = (24 * 145.59) /100 = $34.94

The orthonormal set derived from the original set {(−1, 4), (8, 2)} is {(1/√2, 1/√2), (138/√3280, 34/√3280)}.

To normalize the set {(−1, 4), (8, 2)} and produce an orthonormal set, we follow the steps of the Gram-Schmidt process. The Gram-Schmidt process is a method that allows us to orthogonalize and normalize a set of vectors.

Let's denote the given vectors as v1 = (−1, 4) and v2 = (8, 2).

Step 1: Orthogonalization

We start by finding an orthogonal vector to v1. We can choose any vector that is not collinear with v1. Let's choose w1 = (1, 1) as an orthogonal vector to v1.

Next, we subtract the projection of v2 onto v1 from v2 to obtain a new vector that is orthogonal to v1. Let's calculate this projection:

projv1(v2) = (v2 · v1) / (v1 · v1) * v1

where · represents the dot product.

projv1(v2) = ((8, 2) · (−1, 4)) / ((−1, 4) · (−1, 4)) * (−1, 4)

projv1(v2) = (−4 + 8) / (1 + 16) * (−1, 4)

projv1(v2) = 4 / 17 * (−1, 4)

projv1(v2) = (−4/17, 16/17)

Now, we can find the orthogonal vector w2 by subtracting the projection from v2:

w2 = v2 - projv1(v2)

w2 = (8, 2) - (−4/17, 16/17)

w2 = (8 + 4/17, 2 - 16/17)

w2 = (138/17, 34/17)

Step 2: Normalization

To normalize the orthogonal vectors w1 and w2, we divide each vector by its magnitude.

w1_normalized = w1 / ||w1||

w1_normalized = (1, 1) / √(1^2 + 1^2)

w1_normalized = (1/√2, 1/√2)

w2_normalized = w2 / ||w2||

w2_normalized = (138/17, 34/17) / √((138/17)^2 + (34/17)^2)

w2_normalized = (138/√3280, 34/√3280)

Finally, we have obtained an orthonormal set from the original set:

{(1/√2, 1/√2), (138/√3280, 34/√3280)}

Interpretation: These vectors are both orthogonal and normalized, meaning they form a set where each vector has a magnitude of 1 and is orthogonal to each other vector in the set.

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The  two possible solutions to A XYZ, Y = 60.5°, x = 15.2 cm, y = 14 cm are:

X ≈ 85.86°, Y = 60.5°, Z ≈ 59.64°, x = 15.2 cm, y = 14 cm, z ≈ 9.05 cm

X ≈ 94.14°, Y = 60.5°, Z ≈ 59.64°, x = 15.2 cm, y = 14 cm, z ≈ 29.53 cm

To solve triangle XYZ,

We can use the Law of Sines and Law of Cosines:

First, we can use the Law of Sines to find angle Z:

sin(Z)/14 = sin(60.5)/15.2

sin(Z) = (14/15.2)*sin(60.5)

Z ≈ 59.64°

Now we can use the Law of Cosines to find the length of side z:

z² = 14² + 15.2² - 2(14)(15.2)cos(59.64)

z ≈ 9.05 cm or z ≈ 29.53 cm

For the first solution, z = 9.05 cm:

Now we can use the Law of Sines again to find angle X:

sin(X)/15.2 = sin(59.64)/9.05

sin(X) = (15.2/9.05)*sin(59.64)

X ≈ 85.86°

For the second solution, we use the supplementary angle to angle X:

X = 180 - 85.86 = 94.14°

Now we can use the Law of Sines again to find the length of the second solution for side z:

sin(Z)/14 = sin(60.5)/15.2

sin(Z) = (14/15.2)*sin(60.5)

Z ≈ 59.64°

z² = 14² + 15.2² - 2(14)(15.2)cos(59.64)

z ≈ 29.53 cm

Therefore, the two possible solutions for triangle XYZ are:

X ≈ 85.86°, Y = 60.5°, Z ≈ 59.64°, x = 15.2 cm, y = 14 cm, z ≈ 9.05 cm

X ≈ 94.14°, Y = 60.5°, Z ≈ 59.64°, x = 15.2 cm, y = 14 cm, z ≈ 29.53 cm

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Expression which is used to represent the greatest common factor and the distributive property for calculating ( 27 + 36 ) is 9 ( 3+ 4).

As given in the question,

Given expression is equal to :

(27 + 36)

Expression which represents greatest common factor and the distributive property is given by

Factors of

27 = 3 × 3 ×3

36 = 2 × 2 × 3 × 3

Greatest common factor of 27 and 36 = 3 × 3

                                                            = 9

Now,

(27 + 36 )

= (3 × 3 ×3 + 2 × 2 × 3 × 3 )

= 9 ( 3 + 4)

Distributive property present multiplication over addition

A(B+C) = AB + AC

Therefore, expression which is used to represent the greatest common factor and the distributive property for calculating ( 27 + 36 ) is equal to 9 ( 3+ 4).

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Answer:the answer is -0.5 pound(s)

Step-by-step explanation:

Negative values means the cat's weight decreased from the previous month.

Positive values means the cat's weight increased from the previous month.

We want how much change in the last 3 months cat had gone though. We simply add up the changes.

-0.7 + 0.5 - 0.3 = -0.5

This means the cat's total weight change in all three months is decrease of 0.5 pounds.

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

A polynomial is a mathematical expression consisting of variables , constants and mathematical operators.

The standard form of a polynomial is

\(\rm a_1x^n +a_2x^{n-1}+............+a_0\)

The only equation that is in its standard form or in other words

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

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1. like terms are basically terms that have the same variables and powers. 

2. We call terms "like terms" if 2 numbers have the same variables.

3. Polynomials form a system similar to the system of integers, in that polynomials are closed under the operations of addition, subtraction, and multiplication. Polynomials will be closed under an operation if the operation produces another polynomial. Polynomials are closed under subtraction.

Answer: The line is y=-3x+3

Step-by-step explanation:

Its decreasing by 3 shown in the line so it would -3 and the equation for the  line would be y=-3x+3 as you said.

Answer:

7x + 30z

Step-by-step explanation:

7x +(5*6)z

= 7x + 30z