Juan bought a used bike from his uncle $20.6 each month for 2 years. What was the total amount Juan paid for the bike?

3.5

Step-by-step explanation:

let the number is x:

x(2)-3=4

2x-3=4

2x=4+3

2x/2=7/2

x=3.5

If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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f(c) = 7 for at least one c in the open interval (-13, -5).

The correct answer is "f(c) = 7 for at least one c in the open interval (-13, -5)."

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and it takes on two values, say y1 and y2, then it must also take on every value between y1 and y2.

In this case, we have f(-13) = 4 and f(-5) = 11. The function f is continuous on the closed interval [-13, -5]. Since 4 is less than 7 and 11 is greater than 7, by the Intermediate Value Theorem, there must exist at least one point c in the open interval (-13, -5) where f(c) = 7.

Therefore, the correct statement is "f(c) = 7 for at least one c in the open interval (-13, -5)."

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Answer:

\(x=1,y=3,z=1\)

Step-by-step explanation:

\(4x-4y+4z=-4\)

\(4x=-4+4y-4z\)

\(x=-1+y-z\)

Substitute  \(x=-1+y-z\) into second equation:

\(4\left(-1+y-z\right)+y-2z=5\)

\(-4+4y-4z+y-2z=5\)

\(5y-6z-4=5\)

\(y=\frac{6z+9}{5}\)

Substitute \(x=-1+y-z\) and \(y=\frac{6z+9}{5}\) into the third equation:

\(\frac{-41z-54}{5}+3=-16\)

\(-41z-54=-95\)

\(z=1\)

Substitute \(z=1\) into \(y=\frac{6z+9}{5}\):

\(y=3\)

Plug in y and z values into \(x=-1+y-z\):

\(x=1\)

Answer:

Step-by-step explanation:

3.4 times 2 is 6.8

pemdas for the second one. 2 times 6 is 12. 33+10-12, 31

102/22

4.3636

Answer:

1: 6.8

Work: 3.4 divided by 2 equals 6.8

2: 246

Work: 33 plus 10 minus 2 times 6 equals 246

3: 4

Work: 102 divided by 22 equals 4

Step-by-step explanation: I hope this helps! :)

The numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have:

The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2

The numbers are:

12, 17, 22, 27, 32, 37, 42, 47

By description method:

1      2     3    4      5     6      7      8  

12   17   22   27    32    37   42    47  

By set builder form:

s = {12, 17, 22, 27, 32, 37, 42, 47}

Thus, the numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

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If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

$23.75

Step-by-step explanation:

divide $28.50 by 6 to find the price for 1 bag which is $4.75 then multiply $4.75 by 5 and that equals $23.75

Answer:

If I did the math correctly, the answer would be $23.75.

Have a good day! :D

Step-by-step explanation:

28.50 ÷ 6 = $4.75

So, 1 bag would cost $4.75.

4.75 x 5 = $23.75

Answer:

Step-by-step explanation:

false true true false

Answer:

false true true and false

Step-by-step explanation:

Answer:

X=25

Step-by-step explanation:

Since these 2 angles are vertically opposite angles so they are equal. (rule)

75°=(4x-25°)

75° + 25° = 4x

100=4x

X=100/4 = 25

___________

Hope this helps...

Given:

Hazelnuts sells for $6.50/pound and peanuts nuts sells for $4.70/pound

Let the number of pounds of Hazelnuts be x and the number of pounds of peanut nuts be y

The company wants a 36 pound mixture. We can write this mathematically as:

The mixture sells for $5.40 per pound. We can write this mathematically as:

Solving the equations simultaneously using a graphical approach.

Using a graphing tool, the graph of the equations is shown below:

The point of intersection of the lines is (14, 22)

We can conclude that the company would need 14 pounds of

C is the most accurate one i guess

Answer:

D=(-1, -2)=(xd, yd); xd=-1, yd=-2→A'=(yd, -xd)=(-2, -(-1))→A'=(-2, 1)

E=(0, -1)=(xe, ye); xe=0, ye=-1→B'=(ye, -xe)=(-1, -0)→B'=(-1, 0)

F=(0, 1)=(xf, yf); xf=0, yf=1→C'=(yf, -xf)=(1, -0)→C'=(1, 0)

Step-by-step explanation:

pls give creds to Professor1994

3.2128 is a rational number because you can not make it into a fraction/ratio

The value of θ after solving trigonometric function cosine will be 41.4°.

What are trigonometric functions?

Trigonometric functions are mathematical functions that link right triangle angles to side lengths. Sine (sin), cosine (cos), and tangent (tan) are the most often used trigonometric functions, although there are also inverse trigonometric functions, hyperbolic trigonometric functions, and other related functions.

Trigonometric functions are employed in many different fields, including physics, engineering, navigation, and surveying.

Now,

We can use the inverse cosine function (also known as arccosine or cos⁻¹) to solve for θ:

Cos θ=0.75

θ = cos⁻¹(0.75)

θ =41.4°

We find that θ ≈ 41.4 degrees.

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The equation of the tangent line to the graph of f at x = 0 is y = 25x.

The equation of the tangent line to the graph of f at the indicated x value can be found by taking the derivative of the function f and evaluating it at the given x value.

The derivative of y = 5sin⁻¹(5x) can be obtained using the chain rule. Let's denote the derivative as f'(x). Then, the equation of the tangent line is given by y = f'(x)(x - x₀) + f(x₀), where x₀ is the given x value.

To find the derivative, we differentiate the function y = 5sin⁻¹(5x) with respect to x. Using the chain rule, we have:

f'(x) = d/dx [5sin⁻¹(5x)]

= 5 * d/dx [sin⁻¹(5x)]

= 5 * (1/√(1 - (5x)²)) * d/dx [5x]

= 5 * (1/√(1 - 25x²)) * 5

Simplifying this expression, we have:

f'(x) = 25/√(1 - 25x²)

Now, substituting x = 0 into the equation, we have x₀ = 0:

f'(0) = 25/√(1 - 25(0)²)

= 25

Therefore, the equation of the tangent line is given by y = 25(x - 0) + 5sin⁻¹(5(0)), which simplifies to y = 25x.

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We can find the general solution to the exponential growth model ODE by either method. The given statement is True.

The exponential growth model ODE dy/dt = ky, where k is a constant, can be solved using both linear and separable ODE methods.

As a linear ODE, we can rewrite the equation in the form:

dy/dt - ky = 0

Then, we can find the integrating factor by multiplying both sides by e^(-kt), giving:

e^(-kt) dy/dt - ke^(-kt) y = 0

The left-hand side is now in the form of the product rule for the derivative of a product, so we can integrate both sides with respect to t to obtain:

e^(-kt) y = C

where C is a constant of integration. Solving for y gives the general solution:

y(t) = Ce^(kt)

As a separable ODE, we can rewrite the equation as:

dy/y = k dt

Then, we can integrate both sides to obtain:

ln|y| = kt + C

where C is a constant of integration. Exponentiating both sides gives:

|y| = e^(kt+C) = Ce^kt

where C is a positive constant determined by the initial condition y(0) = y0. Thus, the general solution is:

y(t) = Ce^(kt) or y(t) = -Ce^(kt) depending on the sign of y0.

Therefore, we can find the general solution to the exponential growth model ODE by either method.

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Answer:

roots are [(5 - \(\sqrt{73}\)) / 4] and [(5 + \(\sqrt{73}\)) / 4]

Step-by-step explanation:

[-b ± √b² - (4ac)] ÷2a

2x² - 5x - 6 = 0

a = 2

b = -5

c = -6

[5 ± √5² - 4(2)(-6)] ÷ 2(2)

[5 ± √25 - (-48)] ÷ 4

[5 ± √73] ÷ 4

Answer:

y=-2/7x-61/7

Step-by-step explanation:

convert to slope intercept form

2x+7y=9

7y=-2x+9

y=-2/7x+9/7

slope is -2/7

-7-2/7=-51/7

y=-2/7x-61/7

Answer:

\(y=-\frac{2}{7}x-\frac{51}{7}\)

Step-by-step explanation:

Hi there!

We are given the line 2x+7y=9

We want to find the equation of the line that contains the point (-1, -7), and that is parallel to the equation above

Parallel lines have the same slopes.

So we need to find the slope of 2x+7y=9

One way to do this is to convert 2x+7y=9, which is currently in standard form (ax+by=c) into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

In slope-intercept form, y is isolated by itself, so let's start by moving 2x to the other side (it removes it from the left side)

2x+7y=9
-2x      -2x

____________
7y=-2x+9

Now divide both sides by 7

\(y=-\frac{2}{7} x + \frac{9}{7}\)

in this equation, -2/7 is in the place of where m should be. This means that -2/7 is the slope of this line.

It is also the slope of the line parallel to it.

The instructions want us to write this equation in slope-intercept form, so let's plug -2/7 as m into the formula.

Here is the equation of the line so far:

\(y=-\frac{2}{7}x + b\)

Now we need to find b.

As the equation contains the point (-1, -7), we can use it to help solve for b.

Substitute -1 as x and -7 as y into the equation

\(-7=-\frac{2}{7}(-1) + b\)

Multiply

\(-7=\frac{2}{7} + b\)

Subtract 2/7 from both sides

\(-\frac{51}{7} = b\)

Substitute -51/7 as b in the equation

\(y=-\frac{2}{7}x-\frac{51}{7}\)

Hope this helps!

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Given:

5× ______ = - 35

• -35/5

• -7

5 x -7 = -35

Answer:

The answer is 7

Step-by-step explanation:

Divide each term in 5x=-35 by 5 and simplify.x=−7

Answer:

Step-by-step explanation:

When you multiply two exponents with the same exact base, you simply add the exponents. With the left side, you can add together 6 and 'x' to get:

\(7^6^+^x=7^1^2\)

Both sides of the equation are equal. That is what an equation is saying. Therefore, if the bases of the exponent are the same, then the powers absolutely must equal each other. Therefore:

\(x+6=12\)

\(x=6\)

Answer:

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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The simplified mοnοmial is \(-9x^9y^5\).

In algebra, a mοnοmial is an expressiοn that has a single term, with variables and a cοefficient. Fοr example, 2xy is a mοnοmial since it is a single term, has twο variables, and οne cοefficient. Mοnοmials are the building blοcks οf pοlynοmials and are called 'terms' when they are a part οf larger pοlynοmials. In οther wοrds, each term in a pοlynοmial is a mοnοmial.

Mοnοmial is defined as an expressiοn that has a single nοn-zerο term. It cοnsists οf different parts like the variable, the cοefficient, and its degree. The variables in a mοnοmial are the letters present in it. The cοefficients are the numbers that are multiplied by the variables οf the mοnοmial. The degree οf a mοnοmial is the sum οf the expοnents οf all the variables.

When we multiply mοnοmials with the same base, we add their expοnents. Using this prοperty, we can simplify the expressiοn as fοllοws:

\((-8x^4y^3)(2x^5y^2)+7x^9y^5\)

\(= (-8 * 2)(x^4 * x^5)(y^3 * y^2) + 7x^9y^5\)

\(= -16x^9y^5 + 7x^9y^5\)

\(= (7 - 16)x^9y^5\)

\(= -9x^9y^5\)

Therefοre, the simplified mοnοmial is \(-9x^9y^5\).

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Answer:

\( \boxed{f(10) \: is \: 70}\)

Step-by-step explanation:

\(f(x) = { - x}^{2} - 3x\)

Find f(10) ?

\(f(x) = { - x}^{2} - 3x\)

Substitute x = 10

\(f(10) = { (- 10})^{2} - 3(10)\)

\(f(10) = 100 - 30\)

\(f(10) = 70\)

__________________________

Answer:

4.3 inches

Step-by-step explanation:

1. Add all of the inches together

3.44 + 5.07 = 8.51

8.51 + 4.28 = 12.79

2. Divide 12.79 by how many months are included

12.79/3 = 4.263 (3 is repeating)

3. Round to the nearest tenth

4.263 -> 4.3

Answer:

Step-by-step explanation:

→ \(\frac{(7x^2-40x+52)}{(x^2-6x+9)}\)

→ \(\frac{7x^2-40x+52}{x^2-2.3x+(3)^2}\)

→  \(\frac{7x^2-40x+52}{(x-3)^2}\)

So, your answer is C

\(----------\)

hope it helps...

have a great day!!

The partial fractions is to start with the simplified, and "decompose" the expression into initial polynomial fractions, and the calculation is as follows:

\(\to \frac{7x^2-40x+52}{x^2-6x+9}\\\\\to \frac{7x^2-40x+52}{x^2-(3x-3x)+9}\\\\\to \frac{7x^2-40x+52}{x^2-3x+3x+9}\\\\\to \frac{7x^2-40x+52}{x(x-3)+3(x+3)}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to A+ \frac{B}{(x-3)}+\frac{C}{(x-3)^2}\\\\\)

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Answer:

Step-by-step explanation:

Given the inequality (x²– 4)(x² – 10) < 0, we are to find the number of integers that satisfies the inequality

From (x²– 4)(x² – 10) < 0, (x²– 4)< 0 and (x² – 10) < 0

For (x²– 4)< 0;

x²<4

take the square root of both sides;

√x²<√4

x < ±2

x<2 and x<-2

Similarly for (x²– 10)< 0;

x²<10

take the square root of both sides;

√x²<±√10

x < ±√10

x<√10 and x<-√10

Note that √10 is not an integer but an irrational number. An integer should be a negative or positive whole number. Therefore the amount of integers that satisfies the equation is 2 i.e 2 and -2

Answer:

B - 2

Step-by-step explanation:

Edg2020

a. The linear correlation: r = 0.950.

b. Does there appear to be a significant correlation: A. yes.

c. The regression equation is y = 0.16297x - 2.3772.

d. If the amount of the bill is $45, the best prediction for the amount of the tip is $4.957.

e. According to the regression equation, for every $5 increase in the bill, the tip should increase by $0.815.

In this scenario, the bill amount (x) would be plotted on the x-axis of the scatter plot while the tip amount (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot which models the relationship between the bill amount (x) and the tip amount (y), the correlation coefficient is given by:

y = 0.16297x - 2.3772

Correlation coefficient, r = 0.9494535642 ≈ 0.950.

Part b.

In this context, we can logically deduce that there is a significant correlation between the data because the correlation coefficient (r) is is greater than 0.7 but less than 1;

0.7＜|r| ≤ 1.0   (strong correlation)

Part c.

Based on the scatter plot, the linear regression equation is given by:

y = 0.16297x - 2.3772

Part d.

The best prediction for the amount of the tip when the amount of the bill is $45 is given by:

y = 0.16297(45) - 2.3772

y = $4.957.

Part e.

For every $5 increase in the bill, the tip can be calculated as follows;

y = 0.16297(5)

y = $0.815.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.