I Need This One Also ASAP Plz

Y= x2 - 2 =7

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Using algebraic expression and equation, he invested $2000 in fund b.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Let x = amount he invested in fund b

If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

Solving for x,

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

$60 + 0.07x = $120 + 0.04x

0.07x - 0.04x = $120 - $60

0.03x = $60

x = $2000

amount he invested in fund b = $2000

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I don't know but i can help a little

Step-by-step explanation:

But If the slops are the same and the y-intercepts are different, the lines are parallel...

Step-by-step explanation:

in this situation

A+B =D

Answer:

20 mi/gal

Step-by-step explanation:

310/ 15.5 = 20

The approximate volume of the cone with a radius of 1.75 feet and a height of 2.1 feet is approximately 6.478875 cubic feet.

To calculate the approximate volume of a cone, you can use the formula:

Volume = (1/3) * π * r^2 * h,

where r represents the radius of the cone's base and h represents the height of the cone.

Given that the radius (r) is 1.75 feet and the height (h) is 2.1 feet, we can substitute these values into the formula:

Volume = (1/3) * π * (1.75)^2 * 2.1

To calculate the approximate volume, we'll use the value of π as approximately 3.14:

Volume ≈ (1/3) * 3.14 * (1.75)^2 * 2.1

Now, we can perform the calculations:

Volume ≈ (1/3) * 3.14 * 3.0625 * 2.1

≈ 1.047 * 3.0625 * 2.1

≈ 6.478875

Therefore, the approximate volume of the cone with a radius of 1.75 feet and a height of 2.1 feet is approximately 6.478875 cubic feet.

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Answer:

It is not linear

Step-by-step explanation:

Lemme see....

Answer:

Yes, ASA.

Step-by-step explanation:

The ASA, or Angle-Side-Angle Postulate, states that "If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent."

In this case, it is given that two pairs of angles are congruent:

1) ∠J ≅ ∠N (Given)

2) ∠K ≅ ∠M (Given)

One pair of side is also congruent:

1) JK ≅ NM

∴ Through ASA Postulate, ΔJLK ≅ ΔNOM.

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The standard error of the slope coefficient is 4.38, which is option c.

The standard error of the slope coefficient can be calculated using the formula:

standard error = (standard deviation of residuals) / sqrt(sum of squared deviations from mean of explanatory variable)

Since we don't have the standard deviation of residuals or the sum of squared deviations from mean of explanatory variable, we can use the t-statistic and degrees of freedom to find the standard error from a t-table or calculator. For this problem, with a t-statistic of 4.38 and 1 degree of freedom (since there is only one explanatory variable), we can find the standard error as follows:

standard error = t-value / square root of degrees of freedom
standard error = 4.38 / sqrt(1)
standard error = 4.38

Therefore, the standard error of the slope coefficient is 4.38, which is option c.

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The standard error of the slope coefficient is 0.52. The standard error of the slope coefficient can be calculated using the formula:

Standard Error = (Standard Deviation of Residuals) / √ (Sum of Squares of x - mean of x)

However, since the standard deviation of residuals and the sum of squares of x - mean of x are not given in the question, we need to use the t-statistic and the degrees of freedom (df) to find the standard error. The t-statistic for the slope coefficient is given as 4.38, which has a p-value of less than 0.01 (assuming a two-tailed test and a significance level of 0.05). This means that the slope coefficient is significantly different from zero at the 99% confidence level.

The formula for the t-statistic is:
t = (slope coefficient - null hypothesis value) / standard error

We can rearrange this formula to solve for the standard error:
standard error = (slope coefficient - null hypothesis value) / t

Assuming the null hypothesis is that the slope coefficient is zero (i.e., no relationship between STR and test score), the null hypothesis value is 0. Using the t-statistic of 4.38, we can calculate the standard error as: standard error = (-2.28 - 0) / 4.38 = -0.52

However, we need to take the absolute value of the standard error, since it cannot be negative. Therefore, the answer is: a. 0.52

Therefore, the standard error of the slope coefficient is 0.52.

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The investment will be worth approximately $1,546.45 at the end of 7 years. To calculate the value of the investment after 7 years, we can use the formula for compound interest:

Value = Principal * (1 + interest rate)^time

Given Data:

Principal (P) = $900

Annual Interest Rate (r) = 8% or 0.08

Number of years (t) = 7

Substituting the values into the formula, we have:

Value = $900 * (1 + 0.08)^7

Calculating the exponent:

(1 + 0.08)^7 = 1.08^7 ≈ 1.718279

Now we can calculate the value of the investment:

Value = $900 * 1.718279 ≈ $1,546.45

Therefore, the investment will be worth approximately $1,546.45 at the end of 7 years.

In this calculation, we used the compound interest formula, which takes into account the initial principal, the annual interest rate, and the number of compounding periods (in this case, 7 years). The interest is compounded annually, meaning that at the end of each year, the interest earned is added to the principal for the next year's calculation.

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Answer:

13

Step-by-step explanation:

13x75000=975000

Check for reasonableness...

975000/75000=13

So the answer is 13 gallons.

P.S. There will still be 25,000 drops left, which is 1/3 of a gallon.

Answer:

144 students

Step-by-step explanation:

24 × 6 = 144

hope it helps

Among the given options, the closest probability is 0.95, so the correct answer is e. 0.95.

To find the probability that a randomly selected first-year college student eats at least one meal on campus at least one day per week, we need to sum up the probabilities for X = 1, 2, 3, 4, 5, 6, and 7.

Adding up the probabilities for X = 1, 2, 3, 4, 5, 6, and 7, we get:

0.10 + 0.15 + 0.20 + 0.20 + 0.15 + 0.10 + 0.005 = 0.925

Therefore, the probability that a randomly selected first-year college student eats at least one meal on campus at least one day per week is 0.925.

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Answer:

perimeter of the following figure will be equal to 440 miles.

Step-by-step explanation:

perimeter refers to measure of total boundaries of a figure

hence perimeter will be the sum off all sides

so , P = 170 + 30 + 160 +80 = 440 miles

i hope u got it.

have a great day .

Two or more angles are said to be supplementary if and only if they add up to \(180^{o}\).

Thus the required statements and appropriate reasons are stated below:

Two lines are said to be perpendicular when the measure of the angle between them is a right angle. Thus all right angle is congruent.

Angles are said to be congruent if and only if they have equal measure.

Thus in the given question, it can be deduced that:

                     STATEMENT                             REASONS

1. AC ⊥ BD, <1 ≅ <4                                  Given

2. <BCA = \(90^{o}\), <DCA = \(90^{o}\)                       Definition of perpendicular lines

3. <BCA ≅ <DCA                                      Right angles are congruent

4. <BCA = <1 + <2                                     Angle addition property

5. <DCA = <3 + <4                                    Angle addition property

6. <1 + <2 = <3 + <4                                   Distributive property

7. <1 + <2 = <4 + <3                                    Substitution property

8. <2 ≅ <3                                                 Reflexive property

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The only number that is 10 times as much as 72 is 720.

To find the numbers that are 10 times as much as 72 or 1/10 of 72, we can perform the following calculations:

10 times 72 = 720

1/10 of 72 = 7.2

So, the numbers that are 10 times as much as 72 are 720.

The number 67 is not 10 times as much as 72 or 1/10 of 72. Therefore, it is not one of the numbers we are looking for.

On the other hand, 1/10 of 72 is 7.2, which is not one of the numbers we are looking for either.

Therefore, the only number that is 10 times as much as 72 is 720.

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complete question

Select all the numbers that are 10 times as much as 72, 67, or 1/10 of 72.

- 67

-46

-720

-480

The required probability for P(x<92) is 0.15866.

Given that,
Sample score = X =  92
Mean = μ = 98
Standard deviation = σ = 6
p(x ≤ 92 ) is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

z = (X - μ) / σ
z = (92 - 98) / 6
z = - 1

Now
Probability,
p(x < 92) = P(z = -1)
p(x < 92)  = 0.15866   (from z score table)

Thus, The required probability for P(x<92) is 0.15866.

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The tendency of group members to exert less effort when they work in groups than they would exert if they were acting alone is known as social loafing.

Social loafing is a common phenomenon that occurs when individuals feel that their individual effort will not significantly affect the group's overall performance or when they believe that other group members will compensate for their lack of effort.

This phenomenon can be observed in various group settings, such as in work teams, sports teams, and even in classroom group projects. The lack of accountability and the diffusion of responsibility that occur in groups can contribute to social loafing.

Social loafing can have negative consequences on group performance, as it can decrease the overall quality of the group's output and reduce motivation among group members.

To mitigate social loafing, it is important to establish clear roles and responsibilities for each group member and to provide regular feedback and recognition for individual contributions.

Additionally, creating a sense of collective identity and establishing group goals can also help to combat social loafing by promoting a sense of shared responsibility and commitment to the group's success.

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Answer:

1:4

Step-by-step explanation:

Answer:

  0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

  x^2 +y^2 = -xy

Factoring the expression of interest, we have ...

  x^3 -y^3 = (x -y)(x^2 +xy +y^2)

Substituting for xy using the first expression we found, this is ...

  x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0

The value of x^3 -y^3 is 0.

Answer:

.

Step-by-step explanation:

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check it bro

Step-by-step explanation:

t1= 2-3-6=-7

t2= 8-6-6=-4

t3=18-9-6=3

Answer:

T1 = -7, T2 = -4, T3 = 3

Step-by-step explanation:

For T1, substitute n for 1 and solve the equation. Then for T2, substitute n for 2 and solve the equation. Same goes for T3.

Answer:

12% i thinkkkk

Step-by-step explanation:

Answer:

12 percent

Step-by-step explanation:

Amy has ridden 12 percent so far. You can just set up a proportion for this probelm

1 Set up equation 3/25 = %/100

2 Solve the equation by multiply 3 and 100 then divide by 25.

3 Finally your answer should be 12.%

pls mark brainliest because i didnt waste your time

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given logarithmic expression

STEP 2: Find the value of x

State the rule of logarithm that applies

Apply the rule

Hence, the value of x is approximately 10.56

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The required graph has been attached below which represents the inequality x ≥ 11 on a number line.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

x ≥ 11

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout.

A number line is typically shown horizontally and can be extended indefinitely in any direction.

Thus, the graph has been attached below which represents the inequality on a number line.

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Answer:

x³ - 4x² + 6x - 24

Step-by-step explanation:

Given

(x² + 6)(x - 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x - 4) + 6(x - 4) ← distribute both parenthesis

= x³ - 4x² + 6x - 24

The vectors a₁ = (1, 0, -1), a₂ = (1, 1, 1), and a₃ = (3, 1, -1) are linearly dependent.

We have,

To determine if the vectors a₁ = (1, 0, -1), a₂ = (1, 1, 1), and a₃ = (3, 1, -1) are linearly dependent or linearly independent, we can follow these steps:

Step 1:

Form the matrix A by arranging the vectors a₁, a₂, and a₃ as columns:

A = [1 1 3; 0 1 1; -1 1 -1]

Step 2: Calculate the determinant of matrix A:

|A| = 1[(1)(-1)-(1)(1)] - 1[(0)(-1)-(1)(-1)] + 3[(0)(-1)-(1)(-1)]

= 1[-1-1] - 1[0 + 1] + 3[0 + 1]

= -2 - 1 + 3

= 0

Step 3:

Analyze the determinant value. If the determinant |A| is equal to zero, it indicates that the vectors a₁, a₂, and a₃ are linearly dependent. If the determinant is non-zero, the vectors are linearly independent.

Therefore,

The vectors a₁ = (1, 0, -1), a₂ = (1, 1, 1), and a₃ = (3, 1, -1) are linearly dependent.

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