Divide.
(x²+7x+7)÷(x+4)
Your answer should give the quotient and the remainder.

The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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Answer:

1=125

2=55

3=55

4=125

5=125

6=55

7=55

8=125

Step-by-step explanation:

Answer:

y=10(3/4)^x

10 and 3/4

Step-by-step explanation:

Answer:

y=1/3x+2 2/3

Step-by-step explanation:

1/2x-2/3y=4

-2/3y=-1/2x+4

y=1/3x+2 2/3

Answer:

3x - 4y = 24

Step-by-step explanation:

The standard form of linear equation is Ax + By = C where A, B, and C are integers; A and B ≠ 0; and A is non-negative.  Decimals and fractions are not considered as integers.

Given the linear equation, ½x - ⅔y = 4:

We can eliminate the fractions by multiplying both sides by 6:

6(½x - ⅔y) = 4(6)

(6)(½x) - (6)(⅔y) = 24

3x - 4y = 24  ⇒ This is the standard form of the given equation where A = 3, B = -4, and C = 24.

Answer:

40 miles per hour and .025 hours per mile

Step-by-step explanation:

480/12=40

12/480 = .025

The given equation is 2x-2 = 9, x = 5.5.

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal. Any angle we draw between any two locations along a straight line will always be a 180-degree angle.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A linear equation is an equation of a straight line, written in one variable.

(a).The desired equation is,  2x-2 = 9

(b). After solving, We get  x = 5.5

(a). Let us consider, number is x

According to given statements,

First double it,   2x

Now, subtract 2, We get  2x - 2

Since, this is equal to 9.

So that,2x-2=9 is the desired equation.

(b) Now, we have to solve above equation.

   2x-2=9

    x=11/2

    x=5.5

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Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:

They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.

The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.

For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.

To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.

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Answer:

1. Yes, SAS

2. Yes, SSS

3. they not simular

4. Yes, SAS

4. Yes, AA

Step-by-step explanation:

An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t. Yes, the relationship is proportional.

An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t.

Where, A is total amount,

P is amount which Terry deposit,

r is rate of interest,

and t is number of years.

Yes, the relationship is proportional.

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Answer:

21920

Step-by-step explanation:

Answer:

21,920

Step-by-step explanation:

Work uploaded below :)

Answer:

a) \(\mathbf{ f(g(x))=x+2\sqrt{x} +1}\)

b) \(\mathbf{f(g(9))=16}\)

Step-by-step explanation:

We are given:

\(f(x)=(x-2)^2\\g(x)=\sqrt{x} +3\)

We need to find  \(a) f(g(x))\\b) f(g(9))\)

a) First finding: \(f(g(x))\)

It can be found by putting the value of g(x) into f(x)

We are given:

\(f(x)=(x-2)^2\\Put\:x=g(x)\:i.e. \: x= \sqrt{x} +3\\f(g(x))=(\sqrt{x} +3-2)^2\\Now\: solving:\\f(g(x))=(\sqrt{x} +1)^2\\Using\:formula\:\mathbf{(a+b)^2=a^2+2ab+b^2}\\f(g(x))=(\sqrt{x})^2+2(\sqrt{x} )(1)+(1)^2\\ f(g(x))=x+2\sqrt{x} +1\)

SO, we get: \(\mathbf{ f(g(x))=x+2\sqrt{x} +1}\)

b) Now finding: \(f(g(9))\)

It can be found by putting x=9 in f(g(x))

We have:

\(f(g(x))=x+2\sqrt{x} +1\\Put\:x=9\\f(g(9))=9+2\sqrt{9}+1\\We\:know\: \sqrt{9}=3\\ f(g(9))=9+2(3)+1\\f(g(9))=9+6+1\\f(g(9))=16\)

So, we get: \(\mathbf{f(g(9))=16}\)

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The circulation of the vector field G around the given square in the yz-plane is i * [(18 + 12k) * 6], where k represents an unspecified constant.

To evaluate the circulation of the vector field G = xyi + zj + 2yk* around the given square, we can use Stokes' theorem.

Stokes' theorem states that the circulation of a vector field around a closed curve is equal to the surface integral of the curl of the vector field over any surface bounded by the curve.

In this case, the square is lying in the yz-plane and has a side length of 6, centered at the origin. The square is oriented counterclockwise when viewed from the positive x-axis.

The surface bounded by the square in the yz-plane is a rectangle with sides of length 6 and 6.

The curl of the vector field G is given by:

curl(G) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂P/∂x)j + (∂P/∂y - ∂R/∂x)kwhere P = xy, Q = 0, and R = 2y.

Taking the partial derivatives, we have:

∂P/∂x = y

∂P/∂y = x

∂P/∂z = 0

∂Q/∂x = 0

∂Q/∂y = 0

∂Q/∂z = 0

∂R/∂x = 0

∂R/∂y = 2

∂R/∂z = 0

Therefore, the curl of G simplifies to:

curl(G) = xi + 2kj

Now, we need to calculate the surface integral of curl(G) over the rectangular surface bounded by the square.

The surface integral is given by:

∬S curl(G) · dS

Since the surface is a rectangle lying in the yz-plane, the normal vector of the surface is in the x-direction, i.e., n = i.

The magnitude of the normal vector is |n| = 1.

The surface integral simplifies to:

∬S curl(G) · dS = ∬S (curl(G) · n) dS

Since the normal vector is constant and equal to i, we can pull it out of the integral:

∬S curl(G) · dS = i ∬S (curl(G)) dS

The rectangular surface has dimensions 6 x 6, so the area of the surface is 36 square units.

Now, evaluating the surface integral:

∬S curl(G) · dS = i ∬S (xi + 2kj) dS = i ∬S (x + 2k) dS

Integrating over the rectangular surface:

∬S curl(G) · dS = i ∫(0 to 6) ∫(0 to 6) (x + 2k) dx dy

Integrating with respect to x:

∬S curl(G) · dS = i ∫(0 to 6) [(x^2/2 + 2kx)] (0 to 6) dy

= i ∫(0 to 6) (18 + 12k) dy

= i [(18 + 12k) * 6]

Therefore, the circulation of G around the given square is i * [(18 + 12k) * 6]

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The amount of money I would repay in the first month is $166.67.

The amount of money I would repay in the second month is $166.67.

The amount of money I would repay in the third month is $166.66.

In order to determine the money that would be repaid each of the first two months, multiply 1/3 by the amount of the loan.

1/3 x $500 = $166.67

Amount to be repaid in the third month = $500 - (166.67 x 2) = $166.66

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

Debit Income Summary $23,000; credit Owner Capital $23,000.

The entry to close the income summary account will be to debit the Income Summary by $23,000 and credit the Owner Capital account by $23,000. This entry transfers the net income or loss from the income summary account to the owner's capital account. Since the income summary account has a debit balance of $23,000, it means that expenses exceeded revenues, resulting in a net loss. By crediting the Owner Capital account, the loss is allocated to the owner's equity, reducing their capital by the amount of the loss.

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The minimum possible probability that chip A is defective can be calculated using conditional probability. Given that chips (A, B) and (A, C) are tested defective, the minimum possible probability that chip A is defective is 1/3.

Let's consider the different possibilities for the status of chips A, B, and C.

Case 1: Chip A is defective.

In this case, both (A, B) and (A, C) are tested defective as stated in the problem.

Case 2: Chip B is defective.

In this case, (A, B) is tested defective, but (A, C) is not tested defective.

Case 3: Chip C is defective.

In this case, (A, C) is tested defective, but (A, B) is not tested defective.

Case 4: Neither chip A, B, nor C is defective.

In this case, neither (A, B) nor (A, C) are tested defective.

From the given information, we know that at least one of the pairs (A, B) and (A, C) is tested defective. Therefore, we can eliminate Case 4, as it contradicts the given data.

Among the remaining cases (Case 1, Case 2, and Case 3), only Case 1 satisfies the condition where both (A, B) and (A, C) are tested defective.

Hence, the minimum possible probability that chip A is defective is the probability of Case 1 occurring, which is 1/3.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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Answer: I'm 90% sure that the S inside the angle is spatial points

The full Definition of the symbol combination is approximately equal to Spatial points?

Step-by-step explanation:

I searched s inside angle symbol and these are my results. "The angle symbol is a mathematical symbol that is placed ahead of character s, usually uppercase italic letters representing spatial points, to describe a geometric angle formed by the intersection of two lines, line segments, or rays."   I'm sorry if I'm wrong.

Step-by-step explanation:

=

38.64=9.2h/2

=

38.64=4.6h

=

h = 38.64/4.6

h = 8.4

thats it

Step-by-step explanation:

\(\dfrac{\left(x^2-\frac{1}{y^2}\right)^x\left(x-\frac{1}{y}\right)^{y-x}}{\left(y^2-\frac{1}{x^2}\right)^y\left(y+\frac{1}{x}\right)^{x-y}}\\\\=\dfrac{\left(\frac{x^2y^2-1}{y^2}\right)^x\left(\frac{xy}{y}-\frac{1}{y}\right)^{y-x}}{\left(\frac{x^2y^2}{x^2}\right)^y\left(\frac{xy}{x}+\frac{1}{x}\right)^{x-y}}\)

\(=\dfrac{\left(\frac{x^2y^2-1}{y^2}\right)^x\left(\frac{xy-1}{y}\right)^y\left(\frac{xy-1}{y}\right)^{-x}}{\left(\frac{x^2y^2}{x^2}\right)^y\left(\frac{xy+1}{x}\right)^x\left(\frac{xy+1}{x}\right)^{-y}}\\\\=\dfrac{\left(\frac{x^2y^2-1}{y^2}\right)^x\left(\frac{xy-1}{y}\right)^y\left(\frac{y}{xy-1}\right)^x}{\left(\frac{x^2y^2-1}{x^2}\right)^y\left(\frac{xy+1}{x}\right)^x\left(\frac{x}{xy+1}\right)^y}\)

\(=\left(\dfrac{x^2y^2-1}{y^2}\cdot\dfrac{y}{xy-1}\cdot\dfrac{x}{xy+1}\right)^x\left(\dfrac{xy-1}{y}\cdot\dfrac{x^2}{x^2y^2-1}\cdot\dfrac{xy+1}{x}\right)^y\)

\(=\left(\dfrac{(xy-1)(xy+1)xy}{y^2(xy-1)(xy+1)}\right)^x\left(\dfrac{x^2(xy-1)(xy+1)}{xy(xy-1)(xy+1)}\right)^y\\\\=\left(\dfrac{x}{y}\right)^x\left(\dfrac{x}{y}\right)^y=\left(\dfrac{x}{y}\right)^{x+y}\)

Used:

\(a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\(a\cdot b)^n=a^n\cdot b^n\\\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\a^2-b^2=(a-b)(a+b)\\\\a^n\cdot a^m=a^{n+m}\)

Answer:

Step-by-step explanation:

Answer:ee

Step-by-step explanation:

sus Answer:oo

Step-by-step explanation:

sus Answer:aa

Step-by-step explanation:

sus

The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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The integral ∫(5x^2 + 5x - 12) / (x^3 + 4x^2) dx, we use partial fraction decomposition to rewrite the integrand as -3/x - (13/6)/x^2 + (1/6)/(x^2 + 4). Then, we integrate each term and obtain the evaluated integral: -3ln|x| + 13/(6x) + (1/12)arctan(x/2) + C.

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Answer:

72 ÷ 8 = t

Step-by-step explanation:

To find out how many times 8 fits in 72, you need to divide 72 by 8.

This is a division problem.

To find the number of jars needed, divide 72 by 8.

Answer: 72 ÷ 8 = t

Answer:

18

Step-by-step explanation:

The equation for finding the length between two points is:

where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).

We assign A to be point 1 and B be point 2

Therefore,

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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