Is x = 0 a valid potential solution to the equation log(x + 7) + log(x − 3) = 17?

Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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The Binomial probability of x = 3 for the given parameters is 0.2048

The Binomial probability relation can expressed as :

\(P(x) = nCx * p^{n} * q^{n-x}\)

where :

for x = 3

We substitute x into the equation thus :

P(x = 3) = 17C3 * (1/8)³ * (1 - 1/8)¹⁴

P(x = 3) = 0.2048

Therefore, the probability of x = 3 in the scenario given is 0.2048

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A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

y-7/ 12y+3

Step-by-step explanation:

Answer:

x = \(\frac{4}{5}\), y = \(\frac{1}{5}\)

Step-by-step explanation:

Express as 2 equations, that is

x + y = 1 → (1)

- x + 9y = 1 → (2)

Add the 2 equations term by term to eliminate x, that is

10y = 2 ( divide both sides by 10 )

y = \(\frac{2}{10}\) = \(\frac{1}{5}\)

Substitute this value into (1) and solve for x

x + \(\frac{1}{5}\) = 1 ( subtract \(\frac{1}{5}\) from both sides )

y = \(\frac{5}{5}\) - \(\frac{1}{5}\) = \(\frac{4}{5}\)

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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The area of the figure below is 96 mm².

The area of a shape is the amount of space occupied by a two dimensional figure.

From the diagram

Area of the triangle = (1/2) * base * height = (1/2) * (8 + 8) * 6 = 48 mm²

Area of the parallelogram = base * height = 8 * 6 = 48 mm²

Area of figure = 48 + 48 = 96 mm²

The area of the figure below is 96 mm².

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Answer:

b = −2

Step-by-step explanation:

1. Simplify −4 − b + 6 to 2 − b.

− b = 4

2. Subtract 2 from both sides.

−b = 4 − 2

3. Simplify 4 − 2 to 2.

−b = 2

4. Multiply both sides by −1.

b = −2

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

Answer:

Step-by-step explanation:

If you toss the coin 4 times, you get 2 * 2 * 2 * 2 possible outcomes, which is 16 outcomes.

There is only 1 outcome where P(x = 0) is possible and that would be

T T T T

one out of 16 is .0625. So

Answer: P(x = 0 )  = 0.0625

Answer:

P (x = 0)  1/16 = 0.0625

Step-by-step explanation:

We toss a fair coin 4 times.

HT HT HT HT      4/4   of each if TH TH TH TH etc..

HT HT HT TH     3/4

HT HT TH HT    3/4

HT HT TH TH    1/2

Let X count heads. Find P(X = 0) to nearest ten thousandth (4 decimal places).

P (x = 0)  1/16 = 0.0625

We cna find the average by multiplying a midpoint on one half findings on one side ie) 4/4 x 3/4 x 3/4 x 1/2  = 0.2813

Answer:

y = \(\frac{25x+22}{6}\)

Step-by-step explanation:

express the ratios in fractional form

\(\frac{5x+2}{y-2}\) = \(\frac{6}{5}\) ( cross- multiply )

6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides

6y - 12 = 25x + 10 ( add 12 to both sides )

6y = 25x + 22 ( divide both sides by 6 )

y = \(\frac{25x+22}{6}\)

Answer:

2 3/4

Step-by-step explanation:

So area is just base X height

3 X 11/12

2 3/4

Answer:

6

Step-by-step explanation:

tell me if I'm wrong:

b-bathroom

s-sweep

《in equation form》

s×3=18

18/3=6

so s=6

《explanation》

^ so you are going to divide 18 by 3 which gives you the answer 6^

Step-by-step explanation:

4*1 = 4

this indicates multiplication

8/9 = 0.88888888888 which when simplified would go back to 8/9 or .889

8 "over" 9 indicates division!

The following answers are given as:

2.1)

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

2.2)

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

2.3)

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

2.4)

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

6 teaspoons of vinegar = 15 teaspoons of olive oil.

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 2 on both sides.

2 teaspoons of vinegar = 5 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 8 on both sides.

8 teaspoons of vinegar = 20 teaspoons of olive oil.

Now,

Total number of teaspoons = 42

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 12 on both sides.

12 teaspoons of vinegar = 30 teaspoons of olive oil.

12 + 30 = 42 teaspoons

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 4 on both sides.

4 teaspoons of vinegar = 10 teaspoons of olive oil.

4 + 10 = 14 teaspoons

Thus,

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

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The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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The compound inequality representing the range for the skull size of cats is: 39.32 ≤ x ≤ 43.01.

To find the compound inequality that represents the range for the skull size of cats, we need to solve the given compound inequality:

8 ≤ 1.03x - 32.4 ≤ 12

Let's solve it step by step:

Add 32.4 to all parts of the compound inequality:

8 + 32.4 ≤ 1.03x - 32.4 + 32.4 ≤ 12 + 32.4

40.4 ≤ 1.03x ≤ 44.4

Divide all parts of the compound inequality by 1.03 (the coefficient of x):

40.4/1.03 ≤ (1.03x)/1.03 ≤ 44.4/1.03

39.32 ≤ x ≤ 43.01

Therefore, the range for the skull size of cats can be represented by the compound inequality:

39.32 ≤ x ≤ 43.01

Rounded to the nearest hundredth, the compound inequality representing the range for the skull size of cats is:

39.32 ≤ x ≤ 43.01

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Answer:

The restaurant bill before the service charge ​is: £69.55

Step-by-step explanation:

Service charge percentage = 8%

Total Bill including service charge = £75.60

Let us first determine the service amount using the formula

Service amount = 8% of 75.60

                          = 8/100 × 75.60

                          = £6.05

Thus, the restaurant bill before the service charge can be determined by subtracting the service amount from the total bill.

Restaurant bill before the service charge = Total Bill - Service amount

                                                                     = £75.60 - £6.05

                                                                      = £69.55

Therefore, the restaurant bill before the service charge ​is: £69.55

Answer:

One Rectangular Pan

Step-by-step explanation:

Part C cannot be answered since the dimensions of the pool are not given.  Please check the question.

The cake pans may be compared by calculating the volume of each shape:

Rectangular pan:  Volume = Length x Width x Height

  Volume Rectangle = (13")*(9")*(2") = 234 in^3

Round pan:  Volume = \(\pi r^{2} h\)

  Volume Round = (3.14)*(4")^2(2") = 100.5 in^3

Two round pans will hold 2*(100.5 in^3) or 201 in^3 of batter

One rectangular pan holds 234 in^3.

Go with the rectangular pan if you want more cake.

the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.

We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.

Now, consider the Discriminant of the polynomial, which is defined as the expression below:

Discriminant = b2 - 4ac

In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:

Discriminant = a2^2 - 4a0a3

Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

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Answer:

The value is  \(P(X > 3.30) = 0.12405\)

Step-by-step explanation:

From the question we are told that

   The mean GPA is  \(\mu = 3.25\)

   The standard deviation is \(\sigma = 0.75\)

    The sample size is  n  =  300

Generally the standard error of mean is mathematically represented as

     \(\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }\)

=>   \(\sigma_{\= x} = \frac{0.75}{\sqrt{300} }\)

=>   \(\sigma_{\= x} = 0.0433\)

Generally the  probability that a random sample of 300 students will have a mean GPA greater than 3.30 is mathematically represented as

     \(P(X > 3.30) = P(\frac{X - \mu}{\sigma_{\= x}} > \frac{3.30 -3.25}{ 0.0433} )\)

\(\frac{\= X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \= X )\)

    \(P(X > 3.30) = P(Z> 1.155 )\)

From the z table the probability of  (Z >  1.155 ) is

     \(P(Z> 1.155 ) = 0.12405\)

   \(P(X > 3.30) = 0.12405\)

Answer:

number 3 the answer

Step-by-step explanation:

im pretty sure its 0.19 because the sqyare root of 49 is 7. the square root of 1250 is 35.35

7/35.35=0.19

Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.

First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.

Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.

$18.50 ÷ $1.67 per avocado = 11.08 avocados.

Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.

Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:

$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.

Total spent:

$2.50 + $45.00 = $47.50

Total money had:

$21.00

Remaining money:

$0.00

Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

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It’s either C or D, but i’m pretty sure it’s C

In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

The compound interest model is based on the assumption that the initial capital obtain gains continuously in time. This model is represented by the following expression:

C' = C · (1 + r/100)ˣ     (1)

Where:

Please notice that a year consists in four quarters. If we know that C = 1200, r = 5.25 and x = 8, then the current capital is:

C' = 1200 · (1 + 5.25/100)⁸

C' = 1807

In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

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The unknown values in the triangle is calculated to be

PL = 14.3 cm

CY = 7.74

NY = 9.9 mm

LJ = 8.3

The unknown values in the triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

1. using Sin = opposite / hypotenuse - SOH

sin x = PL / PX

sin 54.25 = PL / 17.62

PL = sin 54.25 * 17.62

PL = 14.3 cm

2. using Tan = opposite / adjacent - TOA

tan 52.67 = CY / 5.9

tan 52.67 * 5.9 = CY

CY = 7.74

3. using Sin = opposite / hypotenuse - SOH

sin 33.06 = YC / NY

NY = 5.4 /  sin 33.06

NY = 9.9 mm

4. using Tan = opposite / adjacent - TOA

tan 55.05 = LJ / VJ

tan 55.05 * 5.8 = LJ

LJ = 8.3

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The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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