Log base 28 of 7 plus log base 28 of 4

Answer: The slope of the line that passes through the points ( 9 , − 10 ) and ( 14 , 5) is 3.

Step-by-step explanation:

To calculate the slope of the line, we apply the following formula:

  \(\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}\)

where m is the slope of the line.

The points are:

         \(\boldsymbol{\sf{\diamond \ x_1=9, \ y_1=-10 }}\\ \\ \boldsymbol{\sf{\diamond \ x_2=14, \ y_2=5 }}\)

We substitute our data in the formula and solve, then

      \(\boldsymbol{\sf{m=\dfrac{5-(-10)}{14-9}=\dfrac{15}{5}=3 }}\)

The slope of the line that passes through the points ( 9 , − 10 ) and ( 14 , 5) is 3.

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What is the slope of the line that passes through the points (9 , -10 ) and (14 , 5)? Write your answer in simplest form.

From inspection on the given problem:

To calculate the slope of the line passing through the given points, we must use the formula below:

Substitute the given values into the slope formula and solve for m:

\( \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - (-10)}{14 - 9} = \dfrac{15}{5} = \pmb{3}}\)

Therefore, the slope of the line that passes through the given points is 3.

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The net force in the forward direction will be 9 Newton.

We have the coefficient of kinetic friction between the plastic legs of the desks and the tile is 0.3. The desks have a mass of 17 kg each. Mr. bob applies of a force of 60 N to the desk

We can write the equation for the net forward motion as -

F{net} = F{applied} - F{friction}

F{net} = F{applied}  - μ[k]N

F{net} = F{applied} - μ[k]mg

F{net} = 60 - 0.3 x 17 x 10

F{net} = 60 - 51

F{net} = 9 Newton

Therefore, the net force in the forward direction will be 9 Newton.

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Answer:

the correct answer is B

Step-by-step explanation:

Answer:

the second choise is the answer

Answer:

12

Step-by-step explanation:

Step 1:

50 = 14 + 3x         Equation

Step 2:

36 = 3x        Subtract 14 on both sides

Step 3:

x = 36 ÷ 3       Divide

Answer:

x = 12

Hope This Helps :)

Answer:

12

Step-by-step explanation:

50= 14 + 3x

-14   -14

36   = 3x

\(\frac{36}{3} =\frac{3}{3}\)

12 = x

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

multiplication and addition

Step-by-step explanation:

Answer: 11x + 12y

Step-by-step explanation:

Step 1: Just combine like terms

12x + 2y + - x + 10y

(12x + -x) + (2y + 10y)

= 11x + 12y

Answer:

you collect like terms

i.e 12x-x+2y+10y

13x+12y(sum)

In my front yard, there is a pine tree and a honey locust tree. every five years the pine tree produces pinecones. Every three years the honey locust tree produces bean pods. In 15 years this same situation will occur, were both pinecones and bean pods will produce.

A pine tree and honey locust tree are planted. Every five year pine tree produces pinecones and every three years the honey locust tree produces bean pods.

This year both the tress had pinecones and bean pods all over the yard.

So we need to tell when this same situation is going to occur.

For solving this we will use LCM method.

We will take the LCM of given figures that are-\(3 and 5\) years.

So the LCM of 3 and 5 is 15.

So this kind of situation will occur again in next 15 year.

Let us understand this question by simple method.

0 year- both pinecones and bean pods will produce.

1 year- nothing

2 year- nothing

3 year- bean pods

4 year- nothing

5 year- pinecones

6 year- bean pods

7 year- nothing

8 year- nothing

9 year- bean pods

10 year- pinecones

11 year- nothing

12 year- bean pods

13 year- nothing

14 year- nothing

15 year- bean pods and pinecones both.

Hence, in 15 year this same situation will occur, were both pinecones and bean pods will produce.

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Answer:29.04

Step-by-step explanation:

3.79+20.25=24.04

24.04+5=29.04

The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

Answer:

17.5 cm

Step-by-step explanation:

Multiply 0.7 by 25 to get 17.5 cm.

Hope it helped.

The Eurasian tectonic plate will travel 17.5 cm in 25 years.

Speed is the time rate at which an object is moving along a path,

The rate of the Eurasian tectonic plate is given as 0.7 cm per year. To find out how far the plate will travel in 25 years, we can use the formula:

distance = rate × time

Plugging in the values, we get:

distance = 0.7 cm/year × 25 years

distance = 17.5 cm

Therefore, the Eurasian tectonic plate will travel 17.5 cm in 25 years.

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Answer:

no

Step-by-step explanation:

The domain and the range of a graph are simply the possible x and y values of the graph.

Tatiana is incorrect, because she switched the x and y values

From the complete question (see attachment), we have the following observations.

This means that:

Tatiana's conclusion about the domain and the range of the graph is incorrect, because switched the values of the domain and the range

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The last cup contains 4 ounces of lemonade. Option (a) is correct.

Pam has 228 ounces of lemonade and she pours it into 8-ounce cups. To determine the amount of lemonade in the last cup, we divide the total amount of lemonade by the size of each cup.

228 ounces ÷ 8 ounces = 28 cups with a remainder of 4 ounces.

Since the last cup is not completely full, the remaining 4 ounces of lemonade are in the last cup. This means option (a), which states that there are 4 ounces in the last cup, is the correct answer.

By dividing the total amount of lemonade by the cup size and considering the remainder, we can determine the quantity of lemonade in the last cup, which in this case is 4 ounces.

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Answer: u = i- 100,000

Step-by-step explanation:

Hi, to answer this question we have to write an equation with  the information given:

Population of the United States = u

Population of India = i

Since the population of the United States, u, is about one hundred thousand less than the population of India, i, we have to subtract 100,000 (one hundred thousand) to the population of India (i). That expression must be equal to the population of United States (u).

Mathematically speaking:

u = i- 100,000

Feel free to ask for more if needed or if you did not understand something.  

Answer:

the x

Step-by-step explanation:

Looking at the x in an equation can reveal its shape. A linear graph can look like y=x, y=mx, y=mx+b (m being any number).

When you look at graphs that aren't linear, the x doesn't stand alone in the equation.

Parabolas have a y=x^2 equation. Cubic graphs are y=x^3. They have something attached to the x.

To see all the different kinds of equations and what their graphs look like you can search up "parent functions" and all the basic formulas show up.

The displacement of particle from r1 = (5.0î 4.5ĵ) cm to r2 = (−1.5î −2.0ĵ) cm is δr = -6.5î - 6.5ĵ cm.

The displacement of the particle is given by the vector difference between the final position and the initial position:

δr = r2 - r1

where r1 = (5.0î + 4.5ĵ) cm and r2 = (-1.5î - 2.0ĵ) cm.

So, we have:

δr = (-1.5î - 2.0ĵ) cm - (5.0î + 4.5ĵ) cm

δr = (-1.5 - 5.0)î + (-2.0 - 4.5)ĵ cm

δr = -6.5î - 6.5ĵ cm

Therefore, the displacement of particle by the method of vector difference between the final position and the initial position is δr = -6.5î - 6.5ĵ cm.

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The dependent variable in this study is the percentage of words correctly recalled.  The outcome is the % of words remembered, which was compared while studying in silence vs. with music.

The dependent variable in this study is the percentage of words correctly recalled by the participants. This variable is measured by comparing the words that the participants remembered after studying in silence to the words remembered after studying while listening to music. Dr. Majowski asks participants to study a list of words for two minutes; half of the participants study in silence and half study while listening to music. After studying the words, all participants are then asked to complete a set of mathematical problems for one minute. After this, each participant is asked to recall the words from the list they studied. Dr. Majowski then measures the percentage of words correctly recalled by each participant, which will provide an indication of the effect of music on memorization. This is the dependent variable in the study.

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Answer:

D

Step-by-step explanation:

To find the system of equations that is satisfied by the solution shown on the graph, we will simply need to find the equations of our two lines.

So, we will begin by finding the slope of each line and then proceed to find the entire equation.

Red Line:

To find the slope, we will first pick any two points from the red line.

Two sample points include (-5, 5) and (-4, 6).

The slope formula is given by:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Lett (-5, 5) be (x₁, y₁) and (-4, 6) be (x₂, y₂). Substitute:

\(\displaystyle m=\frac{6-5}{-4-(-5)}=\frac{1}{1}=1\)

Hence, the slope of the red line is 1.

Now, we can find the entire equation. We will use the slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

We know that the slope m is 1. Hence:

\(y=x+b\)

We need to find our y-intercept b. For the red line, we know that when x is -5, y is 5. Hence:

\((5)=(-5)+b\)

Solving for b yields:

\(b=10\)

Therefore, our entire equation is:

\(y=x+10\)

Blue Line:

Again, we will find the slope first.

Picking two points, we get (0, 6) and (1, 5).

Using the slope formula by letting (0, 6) be (x₁, y₁) and (1, 5) be (x₂, y₂), we acquire:

\(\displaystyle m=\frac{5-6}{1-0}=\frac{-1}{1}=-1\)

Hence, the slope of the blue line is -1.

Again, we can use the slope-intercept form:

\(y=mx+b\)

Fortunately, we already know the y-intercept in this case. Since we have the point (0, 6), the y-intercept b is 6.

Therefore, our equation is:

\(y=-x+6\)

So, our two equations are:

\(y=x+10\text{ and } y=-x+6\)

Our answers are in standard form, so we will convert the two equations to standard form. Standard form is given by:

\(Ax+By=C\)

Where A, B, and C are integers and A is positive.

For the first equation, we can subtract x from both sides to get:

\(-x+y=10\)

Since A should be positive, we multiply both sides to get:

\(x-y=-10\)

For the second equation, we can add x to both sides:

\(x+y=6\)

Hence, our two equations in standard form is:

\(x+y=6\text{ and } x-y=-10\)

Therefore, our final answer is D.

Answer: D x + y = 6 and x − y = -10

Step-by-step explanation:

In ANOVA, a main effect occurs when a factor significantly affects the outcome variable. This means that there is a statistically significant difference in the outcome variable across the different levels or categories of the factor being tested. For example, in a study comparing the effectiveness of different types of medication for a particular condition, a main effect would be present if the type of medication significantly affected the outcome (e.g. reduction in symptoms).

It is important to note that a main effect does not necessarily indicate the presence of an interaction between factors or outcomes. An interaction occurs when the effect of one factor on the outcome variable differs depending on the level or category of another factor. For example, in a study comparing the effectiveness of medication for a particular condition, an interaction might occur if the effect of the medication was different for men and women.

In summary, a main effect in ANOVA occurs when there is a significant difference in the outcome variable across the levels or categories of a factor being tested, while an interaction occurs when the effect of one factor on the outcome variable differs depending on the level or category of another factor.
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Answer:

d= 8 n=9

Step-by-step explanation:

The total thickness of all the components is 3/4 + 6/16 + t inches.

To find the smallest length of a bolt that will pass through all the given components, we need to determine the maximum thickness among them and then add it to the sum of their lengths.

The two pieces of tubing have thicknesses of 1/2 inch and 3/4 inch, respectively. Therefore, the maximum thickness among the tubing is 3/4 inch.

The two washers have thicknesses of 3/16 inch each. Since there are two washers, the total thickness of the washers is 2 * 3/16 = 6/16 inch.

The nut's thickness is not specified in the question, so let's call it t.

The total thickness of all the components is 3/4 + 6/16 + t inches.

To find the smallest length of the bolt, we need to add the total thickness to the sum of the lengths of the components. However, the lengths of the tubing, washers, and nut are not provided in the question.

If you provide the lengths of the tubing, washers, and nut, I can assist you further in determining the smallest length of the bolt.

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For each n ≥ 0, the natural filtration Gn satisfies Gn ⊆ Fn. show that for each n ≥ 0, Gn ⊆ Fn, we need to demonstrate that the natural filtration Gn is a subset of the filtering Fn.

The natural filtration Gn is defined as the sigma-algebra generated by the process {Xn}n≥1 up to time n. This means that Gn contains all the information available up to time n.

The filtering Fn, on the other hand, is defined as the sigma-algebra generated by the random variables {Xk}k≤n, which includes all the information up to and including time n.

Since Gn contains all the information up to time n and Fn includes all the information up to and including time n, it follows that Gn is a subset of Fn, i.e., Gn ⊆ Fn.

Therefore, for each n ≥ 0, the natural filtration Gn satisfies Gn ⊆ Fn.

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The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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The p-value is approximately 0.0359. Comparing the p-value to the given intervals, we can conclude that the p-value is 0.025 ≤ p-value < 0.05.

To calculate the test statistic for a hypothesis test of the population proportion, we can use the formula for a test statistic with a z-distribution:

Test statistic (z) = (P - p₀) / √(p₀(1 - p₀) / n)

Where:

P is the sample proportion (128/320 = 0.4)

p₀ is the hypothesized proportion (0.45)

n is the sample size (320)

Let's calculate the test statistic:

Test statistic (z) = (0.4 - 0.45) / √(0.45 * (1 - 0.45) / 320)

= (-0.05) / √(0.45 * 0.55 / 320)

= -0.05 / √(0.2475 / 320)

= -0.05 / √(0.0007734375)

= -0.05 / 0.0278125

≈ -1.796

Rounded to two decimal places, the test statistic is approximately -1.80.

To find the p-value, we need to find the area under the standard normal curve to the left of the test statistic (-1.80). We can consult the z-table to determine the p-value.

Based on the z-table, we find that the area to the left of -1.80 is approximately 0.0359.

Since the alternative hypothesis is p < 0.45, and the p-value represents the probability of observing a test statistic as extreme or more extreme than the one calculated under the null hypothesis, the p-value is the area to the left of the test statistic.

Therefore, the p-value is approximately 0.0359. Comparing the p-value to the given intervals, we can conclude that the p-value is 0.025 ≤ p-value < 0.05.

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In summary the equivalence relation on the set of real numbers is:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

To show that the relation {(x, y) | x − y ∈ Q} is an equivalence relation on the set of real numbers, we need to verify three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any real number x, we have x - x = 0, which is a rational number (0 ∈ Q). Therefore, (x, x) ∈ {(x, y) | x − y ∈ Q} for all x, and the relation is reflexive.

2. Symmetry: If (x, y) ∈ {(x, y) | x − y ∈ Q}, then x - y is a rational number. Since the negation of a rational number is still a rational number, -(x - y) = y - x is also a rational number. Therefore, (y, x) ∈ {(x, y) | x − y ∈ Q}, and the relation is symmetric.

3. Transitivity: If (x, y) ∈ {(x, y) | x − y ∈ Q} and (y, z) ∈ {(x, y) | x − y ∈ Q}, then x - y and y - z are both rational numbers. The sum of two rational numbers is also a rational number, so (x - y) + (y - z) = x - z is a rational number. Therefore, (x, z) ∈ {(x, y) | x − y ∈ Q}, and the relation is transitive.

Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on the set of real numbers.

Now, let's determine the equivalence classes [1], [1/2], and [π].

The equivalence class [1] consists of all real numbers x such that x - 1 ∈ Q. In other words, [1] = {x ∈ R | x - 1 ∈ Q}. This means that any real number x in the form x = 1 + q, where q is a rational number, belongs to [1].

Similarly, the equivalence class [1/2] consists of all real numbers x such that x - 1/2 ∈ Q. Therefore, [1/2] = {x ∈ R | x - 1/2 ∈ Q}, which means that any real number x in the form x = 1/2 + q, where q is a rational number, belongs to [1/2].

Finally, the equivalence class [π] consists of all real numbers x such that x - π ∈ Q. Thus, [π] = {x ∈ R | x - π ∈ Q}. This means that any real number x in the form x = π + q, where q is a rational number, belongs to [π].

In summary:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

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Answer:

Decisions help know what you believe in and in what you trust. It also expirements many new things. Some decisions end up being good one and correct ones.

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer: 3x +5

Step-by-step explanation:

Group the variables first 8x-5x is 3x. Then look at the numbers -2+7 is 5.

You can't combine letters and numbers so it's as far as you can go.

Answer:

80

Step-by-step explanation:

multiply both sides by 5

3x +50 = 4x -30

combine like terms

-x = -80

x = 80

Answer:

b is ur answer mate ....