Solve for the values of x:

(2x-1)(x+4) = 0

Answer:

x = 23

Step-by-step explanation:

Sum of 25 and x = 48

25 + x = 48

Subtract 25 from both sides

25 - 25 cancels out

48 - 25 = 23

We would be left with x = 23

Answer:

\(x =23\)

Step-by-step explanation:

Sum of 25 and x

\(25 + x\)

Sum of 25 and x is 48

\(25 + x = 48\)

Now lets simply Solve the equation

\(25 + x = 48 \\ x = 48 - 25 \\ x =23\)

Hope this helps you.

Have a nice day!

27 well if you're asking that then

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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Answer:

B and a good one for me your photo is a complete collection

The shorter side of the fence would be approximately 133.33 feet long, and the longer side would be twice that length, which is approximately 266.67 feet long.

Let's assume the shorter side of the fence is x feet long. According to the given condition, the longer side will be twice as long, so its length will be 2x feet.

To calculate the total length of the fence, we add the lengths of both sides:

Total length = Shorter side length + Longer side length

Total length = x + 2x

Total length = 3x

Given that you have 400 feet of fence to work with, we can set up an equation:

3x = 400

To solve for x, we divide both sides of the equation by 3:

x = 400 / 3

x ≈ 133.33 feet

So, the shorter side of the fence would be approximately 133.33 feet long, and the longer side would be twice that length, which is approximately 266.67 feet long.

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Richard has a 1/5 probability of accurately answering all of the questions.

Probability is simply the possibility that something will happen.

When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

The study of events that fit into a probability distribution is known as statistics.

How likely something is to happen is determined by its probability.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

So, we know he probability formula which is:

P(E) = Favourable events/Total events

So, the correct answers are 10 and there are 10*5 total options.

Then, P(F) = 10 and P(T) = 10*5 = 50.

Now, insert values in the formula and calculate as follows:

P(E) = Favourable events/Total events

P(E) = 10/50

P(E) = 1/5

Therefore, Richard has a 1/5 probability of accurately answering all of the questions.

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Complete question:

Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended a class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.)

What is the probability that he will answer all questions correctly?

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of line Q

\(y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{10}{9}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is -10/9 and it passes through (9 , -3) for line R

\((\stackrel{x_1}{9}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{10}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{10}{9}}(x-\stackrel{x_1}{9}) \implies y +3= -\cfrac{10}{9} (x -9) \\\\\\ y+3=-\cfrac{10}{9}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{10}{9}x+7 \end{array}}\)

Answer:

A "rate" is a ratio involving a comparison of 2 quantities that have different unites of measurement. An example of this can be miles per hour or g/mL

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

A cylinder has two circles as its bases, and the diameter formula is:

2r = d

So if you plug in:

2r = 18

---    ---

2     2

r = 9

So it will be true.

Hope this helped.

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Answer:

Area= π(R^2-r^2)

Step-by-step explanation:

Although I can't find the attached file

Let the radius of the large circle be R

And the radius of the small circle be r

Area of large circle is

Area= πR^2

Area of small circle is

Area= πr^2

The difference is

Area= πR^2- πr^2

Area= π(R^2-r^2)

To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

Answer:

C. 8 miles per hour

Step-by-step explanation:

It takes Diego \(\frac{1}{8}\) of an hour to complete the lap = \(\frac{1}{8}\) x 1 hour = \(\frac{1}{8}\) hour

Distance of the track = 1 mile long

The speed of an object expresses the ratio of distance moved to time taken to cover the distance.

i.e speed = \(\frac{distance}{time taken}\)

           = \(\frac{1}{\frac{1}{8} }\)

           = 8

Speed = 8 mile per hour

Therefore, Diego's bike has a speed of 8 miles per hour.

Answer:D

Step-by-step explanation:

Therefore, the range of the relation 2x + y = 3 for the given domain {-3, 0, 6} is {9, 3, -9}.

To determine the range of the relation 2x + y = 3 for the given domain {-3, 0, 6}, we need to find the corresponding range values when we substitute each value from the domain into the equation.

Substituting -3 into the equation, we have 2(-3) + y = 3, which simplifies to -6 + y = 3. Solving for y, we get y = 9.

Substituting 0 into the equation, we have 2(0) + y = 3, which simplifies to y = 3.

Substituting 6 into the equation, we have 2(6) + y = 3, which simplifies to 12 + y = 3. Solving for y, we get y = -9.

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Answer:

8. Closest option is 8.1 Just saw your choices now!

Step-by-step explanation:

This is because if you do the work, you will get: 8.12403840464..... So, rounding, you'll get 8.

Hope that helps!

Therefore, the truth value of Proposition 2A is False.

To determine the truth value of Proposition 2A, let's substitute the given truth values for the variables:

A = True

B = True

X = False

Y = False

Now let's evaluate the truth value of each component of the proposition:

(X ⊃ A) • (B ⊃ ∼ Y):

(False ⊃ True) • (True ⊃ ∼ False)

(True ⊃ True) • (True ⊃ True)

True • True

True

(B ∨ Y) • (A ⊃ X):

(True ∨ False) • (True ⊃ False)

True • False

False

[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]:

True ⊃ False

False

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The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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(a) The probability of zero arrivals during the next minute is approximately 0.2231. (b) The probability of z service times less than or equal to a given value can be calculated using the exponential distribution formula.

(a) The probability of zero arrivals during the next minute can be calculated using the Poisson distribution with a rate of 1.5 per minute. Plugging in the rate λ = 1.5 and the number of arrivals k = 0 into the Poisson probability formula, we get P(X = 0) = e^(-λ) * (λ^k) / k! = e^(-1.5) * (1.5^0) / 0! = e^(-1.5) ≈ 0.2231.

(b) In the second part of the problem, the employee serves each customer in 1 minute on average, and the service times follow an exponential distribution. The probability of z service times less than or equal to a given value can be calculated using the exponential distribution. We can use the formula P(X ≤ z) = 1 - e^(-λz), where λ is the rate parameter of the exponential distribution. In this case, since the average service time is 1 minute, λ = 1. Plugging in z into the formula, we can calculate the desired probability.

Note: Since the specific value of z is not provided in the problem, we cannot provide an exact probability without knowing the value of z.

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The sum of the m integers between ai and aj is si - s(i-1) + s(i-1) - s(j-1) = si - sj, which is divisible by m since si, sj have same remainder. So, there exists a consecutive subsequence of the original sequence with a sum divisible by m, namely the integers between ai and aj.

We can prove this using the Pigeonhole Principle.

Consider the sequence of m integers a1, a2, ..., am. Let's compute the prefix sums of this sequence, which we'll denote by s0, s1, s2, ..., sm. That is, we define si = a1 + a2 + ... + ai-1 for i = 1, 2, ..., m, and s0 = 0.

Note that there are m + 1 prefix sums, but only m possible remainders when we divide a sum by m (namely, 0, 1, 2, ..., m-1).

Therefore, by the Pigeonhole Principle, at least two of the prefix sums must have the same remainder when divided by m. Let's say these are si and sj, where i < j.

Then, the sum of the m integers between ai and aj (inclusive) is si - s(i-1) + s(i-1) - s(j-1) = si - sj, which is divisible by m since si and sj have the same remainder when divided by m.

Therefore, there exists a consecutive subsequence of the original sequence with a sum divisible by m, namely the integers between ai and aj.

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Answer: A

Step-by-step explanation: true true true

Answer:

2(t-4)+1

2t-8+1

2t-7

Answer:

136 ft^2

Step-by-step explanation:

Surface area = 2 [ (l*w) + (l*h) + (w*h) ]

= 2 [ (8*3) + (8*4) + (4*3) ]

= 136 ft^2

Answer:

<A = 35 degrees

Step-by-step explanation:

<A = x

<B = 2x

<C = 2x + 5

X + 2x + 2x + 5 = 180 degrees

5x + 5 = 180

5x = 180 -5

x = 175/5

x = 35

Answer:

y = -5/2x + 8

Step-by-step explanation:

20x + 8y = 64​

-20x           -20x

---------------------------

8y = -20x + 64

/8           /8

----------------------------

y = -5/2 + 8  ------> slope intercept form

The equation of line in slope intercept form is y = ( -5/2 )x + 8 , where the slope is m = -5/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

20x + 8y = 64   be equation (1)

On simplifying the equation , we get

Subtracting 20x on both sides of the equation , we get

8y = -20x + 64

Divide by 8 on both sides of the equation , we get

y = ( -20/8 )x + 8

On further simplification , we get

y = ( -5/2 )x + 8

Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Hence , the equation of line is y = ( -5/2 )x + 8

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