7.

Which expression is equivalent to 2r(2.5s + 10) - 3(r + 4) + s(r - 1)?

A. 6rs + 23r - 13

B

6rs + 17r - 13

С

6rs + 23r + S + 12

D

6rs + 17r - S - 12

Answer:

Step-by-step explanation:

If the population of the town last year was 2000 + x, then this year's population, after an increase of 25 people, can be represented by the expression:

(2000 + x) + 25

This means that when all 8 parts are arranged in a single row, probability there are 28 different conceivable configurations. Finley can have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces.

Finley features eight game pieces, each of which is entirely either all red or all black and simply differs in colour. This indicates that there are 28 distinct configurations that may be made using the 8 pieces arranged in a single row. Finley could have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces. This is due to the fact that the 8 pieces can be arranged in a variety of ways, and each arrangement will be deemed distinct as long as it contains at least one red and one black piece. For instance, the configuration could be as follows if there are 4 red and 4 black pieces: If there are four red pieces and four black pieces, for instance, the arrangement might be either black-red-black-red-black-red-red or red-black-red-black-red-black. No matter the configuration, there are a total of 28 arrangements.

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Answer:

x = 4√7

Step-by-step explanation:

You can use the pythagorean theorem which is a² + b² = c²

if you plug it in, it would be...

x² + 12² = 16²

x² + 144 = 256, subtract 144 to both sides

x² = 112, square root both sides to make x by itself.

x = 4√7  

Answer:

189.36 metres

Step-by-step explanation:

We can use trigonometry to solve this problem.

Let's draw a diagram to help visualize the situation:

```

          |

          |

          |90m

          |

          |

          |

-----------|--------------------

          x

```

We can see that the angle of depression is the angle formed by a horizontal line from the top of the cliff to the boat, and a line of sight from the top of the cliff to the boat. We can also see that the height of the cliff is 90 meters.

Using trigonometry, we can find the distance x between the boat and the foot of the cliff:

tan(26.2°) = opposite / adjacent

tan(26.2°) = 90 / x

To solve for x, we can rearrange the equation:

x = 90 / tan(26.2°)

x ≈ 189.36 meters

Therefore, the boat is approximately 189.36 meters from the foot of the cliff.

To find out when John, Maria, and Bruce will all go to the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 6, 8, and 12, which represents the number of days that will pass before they all meet at the clinic again.

First, we can list the multiples of each number until we find a common multiple:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, ...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

From these lists, we can see that the LCM of 6, 8, and 12 is 24. Therefore, John, Maria, and Bruce will all go to the clinic on the same day again in 24 days from February 17th, 2020.

To find out the exact date, we can add 24 days to February 17th, 2020:

February 17th + 24 days = March 12th, 2020

Therefore, John, Maria, and Bruce will all go to the clinic together again on March 12th, 2020.

Answer:

We can find the next time that John, Maria, and Bruce will all go to the clinic together by finding the least common multiple (LCM) of their visit frequencies.

The visit frequency of John is 6 days, Maria is 8 days, and Bruce is 12 days. To find the LCM, we can list out the multiples of each number until we find a common multiple:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...

From the lists above, we can see that the next time they will all go to the clinic together is on the 24th day, which is the least common multiple of 6, 8, and 12. Therefore, John, Maria, and Bruce will all go to the clinic together again on March 12th, 2020 (since February only has 29 days in a leap year).

Step-by-step explanation:

The length of the longer base of the trapezoid is TP = 13 units

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be A = 100 units²

Now , the length of the longer base b = 32 units

The length of the shorter base a = 8 units

Let the height of the trapezium be = h

Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

100 = ( 32 + 8 ) x h / 2

200 = 40h

Divide by 40 on both sides of the equation , we get

h = 5 units

Now , the height be PE , where E lies 12 units from T

Now , from the Pythagoras equation , we get

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

TP² = PE² + TE² , where PE is the height of the triangle

TP² = 5² + 12²

TP² = 169

Taking square roots on both sides of the equation , we get

TP = 13 units

Hence , the length of the trapezium is 13 units

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Answer: thus, 65% of the books were fictional.

Step-by-step explanation:

The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

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Answer: b) write an equation that you can use to get the amount of the tip. t= __ ($__)

Step-by-step explanation: You want to leave a 20% tip on a meal that cost $45.

First, convert the 20% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 20%) by 100%.So, the conversational term "20%" becomes 20% / 100% = 0.20 in terms of a real mathematical number.

Second, you need to find out what 20% of your $45 meal cost is.This is always done by multiplying 0.20 by $45.00, or

0.20 x $45.00=$9.00.

So, the amount of tip you are going to leave is $9.00.

This makes the total cost of your meal (to write on your charge)

$45.00 + $9.00 = $54.00.

I hope this helps <3

Answer:

a) $9

b) t = 20 × ($45) ÷ 100

c) $54

Step-by-step explanation:

So,

a) How much of a tip will they leave?

➵ (45 × 20) ÷ 100

➵ (900) ÷ 100

➵ $9

b) Write an equation that you can use to get the amount of the tip.

➵ t = 20 × ($45) ÷ 100

c) Ricardo's family paid $__ for dinner.

➵ Their total bill is $45 and the 20% tip

➵ $45 + $9

➵ $54

The equation given by Jill and Joel both are correct. Option C .

The line passing through the points (2, -1) and (-1, 14).

The equation of a line passing through a point \((x_1, y_1)\) is \(y-y_1=m (x-x_1)\) where m is the slope.

To find the slope m, using slope formula.

\(m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{14-(-1)}{-1-3} \\m=-5\)

Further simplify,

Substitute the values in the given formula.

\(y-y_1=m(x-x_1)\\y-(-1)=-5(x-2)\\y+1=-5(x-2)\)

Further simplify,

5x+y=9

Both the equations are correct.

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Answer:

B (56!)

Step-by-step explanation:

okay so you have to convert the inches to feet given the measurements

6.4(2.5)=16

4.8(2.5)=12

12+12+16+16=56

Answer:

perimeter = 56 feet

Step-by-step explanation:

4.8 in by 6.4 in

1 in = 2.5 ft

4.8 x 2.5 = 12

6.4 x 2.5 = 16

12 x 2 = 24

16 x 2 = 32

32 + 24 = 56

If a red ball is drawn at random from one of the urns, there is a higher probability (2/3) or 0.667 that it came from Urn A rather than Urn B. This suggests that Urn A is more likely to be the source of the red ball.

To calculate the probability that Urn A was chosen given that a red ball was drawn, we can use Bayes' theorem.

Let's denote the events:

A = Urn A was chosen

B = Urn B was chosen

R = A red ball was drawn

We want to find P(A|R), the probability that Urn A was chosen given that a red ball was drawn.

According to Bayes' theorem:

P(A|R) = (P(R|A) * P(A)) / P(R)

P(R|A) is the probability of drawing a red ball given that Urn A was chosen. Since Urn A has four red balls and four black balls, the probability of drawing a red ball from Urn A is 4/8 = 1/2.

P(A) is the prior probability of choosing Urn A, which is 0.5 since there is an equal chance of selecting either Urn A or B.

P(R) is the overall probability of drawing a red ball, which can be calculated by considering all possible scenarios:

P(R) = P(R|A) * P(A) + P(R|B) * P(B)

P(R|B) is the probability of drawing a red ball given that Urn B was chosen. Since Urn B has two red balls and six black balls, the probability of drawing a red ball from Urn B is 2/8 = 1/4.

P(B) is the prior probability of choosing Urn B, which is also 0.5.

Substituting the values into the equation:

P(R) = (1/2) * (1/2) + (1/4) * (1/2) = 3/8

Now we can calculate P(A|R) using Bayes' theorem:

P(A|R) = (P(R|A) * P(A)) / P(R) = (1/2 * 1/2) / (3/8) = 4/6 = 2/3

Therefore, the probability that Urn A was chosen given that a red ball was drawn is 2/3 or approximately 0.667.

In conclusion, if a red ball is drawn at random from one of the urns, there is a higher probability (2/3) that it came from Urn A rather than Urn B. This suggests that Urn A is more likely to be the source of the red ball.

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Answer:

1/3

Step-by-step explanation:

The simplest form of 2/6 is 1/3. You can do 2/6*.5/.5 to get 1/3

You can do other fractions such as 4/12, 8/24, as long as it the numerator maintains a ratio of 1:3

The values of k for which the function f(x, y, z) = kx² - kry + y² - 2yz - 22 has a nondegenerate local maximum at (0, 0, 0) are when k > 0.

To find the critical points of the function, we need to calculate the partial derivatives with respect to each variable:

∂f/∂x = 2kx ∂f/∂y = -kr + 2y - 2z ∂f/∂z = -2y

2kx = 0 => x = 0 (Equation 1) -kr + 2y - 2z = 0 => r = y - z (Equation 2) -2y = 0 => y = 0 (Equation 3)

From Equation 3, we can see that y = 0. Substituting this into Equation 2, we get:

r = 0 - z r = -z (Equation 4)

The Hessian matrix is given by:

H = | ∂²f/∂x² ∂²f/∂x∂y ∂²f/∂x∂z | | ∂²f/∂y∂x ∂²f/∂y² ∂²f/∂y∂z | | ∂²f/∂z∂x ∂²f/∂z∂y ∂²f/∂z² |

Calculating the second-order partial derivatives:

∂²f/∂x² = 2k ∂²f/∂y² = 2 ∂²f/∂z² = 0 ∂²f/∂x∂y = 0 ∂²f/∂y∂z = -2 ∂²f/∂z∂x = 0

Thus, the Hessian matrix becomes:

H = | 2k 0 0 | | 0 2 -2 | | 0 -2 0 |

D = ∂²f/∂x² ∂²f/∂y² ∂²f/∂z² + 2∂²f/∂x∂y ∂²f/∂y∂z ∂²f/∂z∂x - (∂²f/∂x² ∂²f/∂y∂z ∂²f/∂z∂x + ∂²f/∂y² ∂²f/∂z∂x ∂²f/∂x∂y ∂²f/∂z²)

Substituting the partial derivatives we calculated earlier:

D = (2k)(2)(0) + 2(0)(-2)(0) - (2k)(-2)(0) - (2)(0)(0) D = 0

If the determinant D is zero, the second derivative test is inconclusive. In such cases, we need to consider the eigenvalues of the Hessian matrix.

To find the eigenvalues, we solve the characteristic equation:

det(H - λI) = 0

where λ is the eigenvalue and I is the identity matrix. Substituting the values from the Hessian matrix:

| 2k-λ 0 0 | | 0 2-λ -2 | | 0 -2 -λ |

The characteristic equation becomes:

(2k - λ)((2 - λ)(-λ) - (-2)(0)) - (0)((2 - λ)(-2) - (0)(0)) = 0 (2k - λ)(λ² - 2λ) = 0

From this equation, we can see that one eigenvalue is (2k - λ) = 0, which implies λ = 2k.

For our case, we have one eigenvalue (λ = 2k). Thus, the sign of λ depends on the value of k.

When k < 0, the point (0, 0, 0) is a nondegenerate local minimum. When k = 0, the second derivative test is inconclusive, and further analysis would be required to determine the nature of the critical point.

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Answer:

each doll cost $35

Answer:

The dolls cost $35 dollars each

Step-by-step explanation:

Because $70 ÷ 2 dolls = $35 dollars each

(sorry if wrong!)

Answer:

98

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

start at 0 and move backwards 5(gives you -5) then move backwards 5 more(-10)

The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The given system of linear differential equations can be solved using the eigenvalue method and variation of parameters for the non-homogeneous case. By finding the eigenvalues and eigenvectors of the coefficient matrix, we can determine the general solution for the homogeneous part. Then, using the variation of parameters, we can find a particular solution for the non-homogeneous part. This approach allows us to obtain a complete solution to the system.

To solve the given system of linear differential equations, let's denote the variables as x₁, x₂, r₁, and r₂ respectively. In the first equation, we have:

d₁/dt = -61x₁ + 502x₂ + 22r₁ - 521r₂ + 42

By writing the system in matrix form, we obtain:

d/dt [x₁ x₂ r₁ r₂] = [-61 502 22 -521; -1 3 0 0; 3 2 -21 -1; 6 1 2 t]

To find the homogeneous solution, we consider the coefficient matrix [A] and find its eigenvalues. Solving the characteristic equation det([A] - λ[I]) = 0, we obtain the eigenvalues λ₁, λ₂, λ₃, and λ₄.

Next, we find the eigenvectors corresponding to each eigenvalue by solving the system ([A] - λ[I])v = 0. Let's denote the eigenvectors as v₁, v₂, v₃, and v₄. These vectors form the homogeneous solution:

x_h(t) = c₁v₁e^(λ₁t) + c₂v₂e^(λ₂t) + c₃v₃e^(λ₃t) + c₄v₄e^(λ₄t)

To determine the particular solution for the non-homogeneous part, we use the variation of parameters. We assume a particular solution in the form of:

x_p(t) = u₁(t)v₁e^(λ₁t) + u₂(t)v₂e^(λ₂t) + u₃(t)v₃e^(λ₃t) + u₄(t)v₄e^(λ₄t)

By substituting this into the original system of differential equations, we can solve for the functions u₁(t), u₂(t), u₃(t), and u₄(t). Once we have these functions, the particular solution is given by:

x_p(t) = u₁(t)v₁e^(λ₁t) + u₂(t)v₂e^(λ₂t) + u₃(t)v₃e^(λ₃t) + u₄(t)v₄e^(λ₄t)

Finally, the general solution to the system of differential equations is the sum of the homogeneous and particular solutions:

x(t) = x_h(t) + x_p(t)

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To determine the 95% energy bandwidth (B) of the signal g(t) = [0.5sinc²(0.5 t) cos(2 t)], we can apply Parseval's Theorem. Parseval's Theorem states that the total energy of a signal in the time domain is equal to the total energy of the signal in the frequency domain. Mathematically, it can be expressed as:

∫ |g(t)|² dt = ∫ |G(f)|² df

In this case, we want to find the frequency range within which 95% of the energy of the signal is concentrated. So we can rewrite the equation as: 0.95 * ∫ |g(t)|² dt = ∫ |G(f)|² df

Now, we need to evaluate the integral on both sides of the equation. Since the given signal is in the form of a product of two functions, we can separate the terms and evaluate them individually. By applying the Fourier transform properties and integrating, we can find the value of B.

For part (b), when we consider g(2t), the time domain signal is compressed by a factor of 2. This compression results in a corresponding expansion in the frequency domain. Therefore, the 95% energy bandwidth of g(2t) will be twice the value of B determined in part (a). This can be justified by considering the relationship between time and frequency domains in Fourier analysis, where time compression corresponds to frequency expansion and vice versa.

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How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

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Answer:

H=21ft

Step-by-step explanation:

Height=2•Area/Base

Area=126ft^2

Base=12ft.

H=2•126/12=21ft

H=21ft

Hope this helps :)

9514 1404 393

Answer:

  cos(20°)

Step-by-step explanation:

The angle difference formula for cosine is ...

  cos(α -β) = cos(α)cos(β) +sin(α)sin(β)

If we let α = 50° and β = 30° then this matches the given expression:

  cos(50° -30°) = cos(50°)cos(30°) +sin(50°)sin(30°) = cos(20°)

Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.

We get,

a)  \($\sum_{n=0}^{\infty}$\)

Infinity

b)  \($\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$\)

\(\sum_{n=1}^{\infty} \frac{4}{2^n}\)

\(& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\\)

\(& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\\)

\(& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)\)

\(& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\\)

\(& =4\left(2-\frac{1}{2^0}\right)\)

Then we get,

=4

c) \($\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$\)

\($\sum_{n=1}^{\infty} \frac{7}{10^n}\)

\(& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\\)

\(& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\\)

\(& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)\)

\(& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\\)

\(& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)\)

Simplify

\($7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$\)

= 7/9

Therefore,

a) infinity, b) =4, and c) = 7/9

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Answer:

m=1/5

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Six times negative three is negative eighteen and that plus four is negative 14

An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value.

Solution A,

p - 1 = 5p + 3p - 8

(Combine like terms on the right side)

p - 1 = 8p - 8

(Subtract p from both sides)

-1 = 7p - 8

(Add 8 to both sides)

7p = 7

(Divide both sides by 7)

p = 1

Solution B,

5n + 34 = -2(1 - 7n)

(Distribute the negative sign to both terms in parentheses)

5n + 34 = -2 + 14n

(Combine like terms on the right side)

34 = -2 + 9n

(Subtract 14n from both sides)

36 = 9n

(Divide both sides by 9)

n = 4

Solution C,

3x - 2 = 3x + 5

(Subtract 3x from both sides)

-2 = 5

(This is not possible since there is no value of x that would make this equation true. Therefore, there is no solution to this equation.)

Solution D,

4(2x - 8) = 8(x - 4)

(Distribute the 4 on the left side and the 8 on the right side)

8x - 32 = 8x - 32

(Combine like terms)

0 = 0

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The new area of the parallelogram is 207 cm², the area of a parallelogram is calculated by multiplying the base by the height. In this problem, the base is 18 cm and the height is 23 cm.

So, the original area of the parallelogram is 18 * 23 = 414 cm².If the base is decreased by 50%, the new base will be 18 / 2 = 9 cm. The new area of the parallelogram is then 9 * 23 = 207 cm².

Here are some additional explanations:

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The annual interest rate of the bank account is 3.1%.

Given:

After 5 years there is $673.40 in the account.

After 8 years there is $737.90 in the account.

Let x and A be the annual interest rate and Amount at first.

A(1+x)^5 = 673.40

A(1+x)^8 = 737.99

A(1+x)^8 / A(1+x)^5 = 737.99/673.40

(1+x)^3 = 1.0959

1+x = \(\sqrt[3]{1.0959}\)

x = 0.3099

x ≈ 0.031

x = 3.1%

Therefore The annual interest rate of the bank account is 3.1%.

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