How many solutions does the equation - 4x + 6 = 6x - 2 have?

The interest rate on loan is 5.25%.

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Given, Principal amount=$125,000, time=10years, Interest=$65,625.

Let r be the rate of interest, on applying simplest interest formula

                                               I=P.r.t

Where P=principal amount, r=rate, t=time.

I=125,000 x r x10

65,625=125,000 x r x10

r=\(\frac{65,625}{125,000(10)}\)

r=0.0525

r=5.25%

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5x + 2y = 2120

x + y = 574

2y = 2120 - 5x

2y = 1148 - 2x

1148 - 2x = 2120 - 5x

-972 = -3x

x = 324

574 - 324 = y

y = 250

324 adult tickets sold, 250 student tickets sold

Answer:

24 peeps

Step-by-step explanation:

Answer:

b.28% of the patients tested received the medication and experienced a decrease in blood pressure

Answer:

The second one

Step-by-step explanation:

The total of patients is 100% wich is equivalent to 1.

● 0.5 of them received medication and ● 0.54 of them experienced a decrease in blood pressure.

The intersection of both is worth 0.28

So out of 1, 0.28 took medication and experienced a blood pressure decrease

Answer:48

Step-by-step explanation:

When the weight of the child changes, the amount of medication they receive will also change in proportion to their weight. For example, if the child's weight increases from 20 lbs to 40 lbs, they would need twice as many teaspoons of medicine; if their weight decreases from 20lbs to 10lbs, they would require one half as much medicine.

Answer:

You will need to find the ratio of how much medication to every 1 pound then you will see how much the child weighs then the number of teaspoons will change once the child has gained another 20 pounds.

Step-by-step explanation:

Answer:

d/x

Step-by-step explanation:

\(d=bx\\\frac{d}{x} =b\)

Answer:

r = 2.5

Step-by-step explanation:

U= π(r+h)

Where,

U = 16 1/2

h = 2 3/4

π = 3 1/7​

U= π(r+h)

16 1/2 = 3 1/7(r + 2 3/4)

33/2 = 22/7(r + 11/4)

33/2 = 22/7r + (22/7 * 11/4)

33/2 = 22/7r + 242/28

33/2 - 242/28 = 22/7r

(462-242) / 28 = 22/7r

220/28 = 22/7r

r = 220/28 ÷ 22/7

= 220/28 × 7/22

= (220 * 7) / (28 * 22)

= 1540/616

= 2.5

r = 2.5

A graph that represents the linear system of inequalities is shown in the image attached below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours coaching and number of hours at the printing shop respectively, and then translate the word problem into algebraic equation as follows:

Since Mason coaches a swim team for $15 per hour, works at a printing shop for $18 per hour and wants to earn at least $125, a linear inequality to describe this situation is given by:

15x + 18y ≥ 125.

Additionally, he cannot work for more than 20 hours a week;

x + y ≤ 20

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Answer:

f(x)=(5+a)/(a-1)

Step-by-step explanation:

input a+2 for x

f(x)=(a+5)/(a-1)

and no ur not dumb u just need practice :D

Answer:

-4 and 1/7 is your answer.

Step-by-step explanation:

\(f(x)=\frac{3}{19+2} -\sqrt{19-3}\)

The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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Answer:

a. 2007

b. 120,000

c. the amount of money raised each year is decreasing

Step-by-step explanation:

sorry if im wrong just pay very close attention to the graph

The volume of the composite space figure is approximately 2818.33 cubic cm.

To find the volume of the composite space figure, we need to add the volumes of the rectangular prism and the rectangular pyramid.

The rectangular prism has a length of 26 cm, a width of 5 cm, and a height of 14 cm. So its volume is:

V_prism = length x width x height

V_prism = 26 cm x 5 cm x 14 cm

V_prism = 1820 cubic cm

The rectangular pyramid has a height of 23 cm and a rectangular base with a length of 26 cm and a width of 5 cm. To find its volume, we need to first find its base area:

A_base = length x width

A_base = 26 cm x 5 cm

A_base = 130 square cm

Then, we can use the formula for the volume of a pyramid:

V_pyramid = (1/3) x base area x height

V_pyramid = (1/3) x 130 square cm x 23 cm

V_pyramid = 998.33 cubic cm (rounded to the nearest hundredth)

To find the total volume of the composite space figure, we add the volumes of the prism and the pyramid:

V_total = V_prism + V_pyramid

V_total = 1820 cubic cm + 998.33 cubic cm

V_total = 2818.33 cubic cm (rounded to the nearest hundredth)

Therefore, the volume of the composite space figure is approximately 2818.33 cubic cm.

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There is a maximum value of 6 located at (x, y) = (1, 6).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 12.

Rearranging the constraint, we get:

6x + y = 12,

or, y = 12 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(12 - 6x) = 12x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 12 - 12x ... (i)

Equating to 0, we get:

12 - 12x = 0,

or, 12x = 12,

or, x = 1.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.

The value of y, when x = 1 is,

y = 12 - 6x,

or, y = 12 - 6*1 = 6.

The value of f(x, y) when (x, y) = (1, 6) is,

f(x, y) = xy,

or, f(x, y) = 1*6 = 6.

Thus, there is a maximum value of 6 located at (x, y) = (1, 6).

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The provided question is incomplete. The complete question is:

"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.

Answer:

i think

-17x^2 +3x

.....

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5+5=10

Answer:

135

Step-by-step explanation:

this seems like a continuation of the question which was answered previously

we know angle AEB=135, using vertical angle theorem, AEB and CED are congruent, so CED=135

The solution of the given problem of probability comes out to be

a)0.35

b)0.3625

c)0.23125

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance integers can be represented by any number between 0 and 1, for which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) we can compute the integral of f(x) over the entire real line:

integral from -infinity to infinity of f(x) dx

= integral from -infinity to 3 of 0 dx + integral from 3 to 5 of (0.075x + 0.2) dx + integral from 5 to infinity of 0 dx

= (0.075/2)x² + 0.2x, evaluated from x=3 to x=5

= (0.075/2)(5²- 3²+ 0.2(5 - 3)= 0.35

Since the integral of f(x) over the entire real line is equal to 1, we have verified that the total area under the density curve is indeed 1.

(b) To calculate P(X ≤ 4), we can integrate the density function from x = 3 to x = 4:

P(X ≤ 4) = integral from 3 to 4 of (0.075x + 0.2)

dx = (0.075/2)x² + 0.2x,

evaluated from x=3 to x=4

= 0.3625

To compare this probability to P(X & lt; 4),

we can integrate the density function from x = 3 to x = 4:

P(X < 4) = integral from 3 to 4 of (0.075x + 0.2)

dx = (0.075/2) x²+ 0.2x,

evaluated from x=3 to x=4

= 0.3625

Since P(X ≤ 4) = P(X < 4) in this case, the two probabilities are equal.

(c) To calculate P(3.5 ≤ X ≤ 4.5), we can integrate the density function from x = 3.5 to x = 4.5:

P(3.5 ≤ X ≤ 4.5) = integral from 3.5 to 4.5 of (0.075x + 0.2)

dx = (0.075/2)x²+ 0.2x,

evaluated from x=3.5 to x=4.5

= 0.26875

To calculate P(X > 4.5), we can integrate the density function from x = 4.5 to x = 5:

P(X > 4.5) = integral from 4.5 to 5 of (0.075x + 0.2)

dx = (0.075/2)x²+ 0.2x,

evaluated from x=4.5 to x=5 = 0.23125

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Answer:

Over 3000 texts/mo

Step-by-step explanation:

A $30 + $1/100 texts

B $50

For option B to save money, you would have to send an additional $30 worth of texts

$30 * 100 texts = 3000

If you send more than 3000 texts per month, plan B will save you money compared to plan A.

To find out how many texts you would need to send per month for plan b to save you money, you need to compare the cost of both plans for the same number of texts.

Let's assume you send x number of texts per month.

For plan A, you would pay $20 per month plus $0.01 per text, so your total cost would be $20 + $0.01x.

For plan B, you would pay a flat fee of $50 per month, regardless of how many texts you send.

So to find out when plan B becomes cheaper than plan A, you need to solve the inequality:

$50 < $20 + $0.01x

Subtracting $20 from both sides gives:

$30 < $0.01x

Dividing both sides by $0.01 gives:

x > 3000

The calculation compares the total cost of both plans for a certain number of texts. Plan A has a fixed monthly fee of $20, and an additional cost of $0.01 per text. Plan B, on the other hand, has a flat monthly fee of $50 with unlimited texts. By setting these two costs equal to each other, you can solve for the number of texts that makes Plan B cheaper than Plan A. In this case, sending more than 3000 texts per month makes Plan B the cheaper option.

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When the car traveled 19 miles per hour faster than the truck then the average speed of the truck is 81 miles per hour, and the average speed of the car is 100 miles per hour.

A car and a truck left Washington D.C. traveling in opposite directions. The car traveled 19 miles per hour faster than the truck.

After 8 hours, the vehicles were 1448 miles apart. We need to find the average speed of each vehicle.

Let's assume the speed of the truck is x miles per hour.

Since the car is traveling 19 miles per hour faster, the speed of the car is (x + 19) miles per hour.

We know that distance = speed * time.

After 8 hours, the car has traveled a distance of (x + 19) * 8 miles, and the truck has traveled a distance of x * 8 miles.

The sum of these distances is equal to 1448 miles:

8(x + 19) + 8x = 1448

Simplifying the equation, we get:

8x + 152 + 8x = 1448

Combining like terms, we have:

16x + 152 = 1448

Subtracting 152 from both sides of the equation:

16x = 1296

Dividing both sides by 16:

x = 81

So, the speed of the truck is 81 miles per hour, and the speed of the car is (81 + 19) = 100 miles per hour.

Therefore, the average speed of the truck is 81 miles per hour, and the average speed of the car is 100 miles per hour.

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Step-by-step explanation:

Side length of the frame = √81 = 9 inches.

The value of x to the nearest hundredth is equal to 22.32 units.

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of x can be calculated as follows:

25(14 + 25) = 22(22 + x)

25(39) = 484 + 22x

975 = 484 + 22x

22x = 975 - 484

22x = 491

x = 22.32 units.

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The area of the triangle with the given vertices is approximately 13.95 square units.

To find the area of the triangle with the given vertices, we can use calculus to calculate the magnitude of the cross-product of two of its sides. Specifically, we can use the vectors formed by two pairs of vertices and take their cross-product to find the area.

Let's choose the vectors formed by the points (0,0) and (3,2) as well as (0,0) and (1,6). We'll call these vectors u and v, respectively:

u = <3, 2>

v = <1, 6>

To take the cross product of these vectors, we can use the formula:

|u x v| = |u| |v| sin(theta)

where |u| and |v| are the magnitudes of the vectors, and theta is the angle between them.

To find the angle between u and v, we can use the dot product formula:

u · v = |u| |v| cos(theta)

Solving for cos(theta), we get:

\($\cos(\theta) = \frac{\mathbf{u} \cdot \mathbf{v}}{\lvert\mathbf{u}\rvert \lvert\mathbf{v}\rvert} = \frac{(3 \cdot 1) + (2 \cdot 6)}{\sqrt{3^2 + 2^2} \sqrt{1^2 + 6^2}} = \frac{21}{\sqrt{13} \sqrt{37}}$\)

We can then use the Pythagorean identity to find sin(theta):

\($\sin(\theta) = \sqrt{1 - \cos^2(\theta)} = \sqrt{1 - \left(\frac{21}{\sqrt{13}\sqrt{37}}\right)^2}$\)

Finally, we can plug in the values we've found to the formula for the magnitude of the cross-product:

\($\lvert\mathbf{u} \times \mathbf{v}\rvert = \lvert\mathbf{u}\rvert \lvert\mathbf{v}\rvert \sin(\theta) = \sqrt{3^2 + 2^2} \sqrt{1^2 + 6^2} \sqrt{1 - \left(\frac{21}{\sqrt{13}\sqrt{37}}\right)^2}$\)

Evaluating this expression gives us the area of the triangle:

\($\lvert\mathbf{u} \times \mathbf{v}\rvert = 9 \sqrt{37} \sqrt{1 - \left(\frac{21}{\sqrt{13}\sqrt{37}}\right)^2} \approx 13.95$\)

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The mean absolute deviation of 0.08 ounces means that on average, the difference of the weight of the 48 eggs and the mean of 2.1 ounces is of 0.08 ounces.

The last bullet point is used to interpret the mean absolute deviation of 0.08 ounces in the context of this problem.

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The equation for the relationship between x (volume of flour in cups) and y (number of muffins) is y = 4x. This means that for every cup of flour used, Josiah can bake 4 muffins.

The equation for the proportional relationship between the volume of flour (x) and the number of muffins (y) that Josiah bakes can be written as y = kx, where k is the constant of proportionality. In this case, k represents the number of muffins that can be made with one cup of flour.

To solve for the constant of proportionality, we need more information. If Josiah bakes a known number of muffins using a certain amount of flour, we can use that data to find the value of k. For example, if Josiah bakes 12 muffins using 3 cups of flour, we can substitute these values into the equation:

12 = k * 3

To find k, we divide both sides of the equation by 3:

k = 12 / 3

k = 4

So, the equation for the relationship between x (volume of flour in cups) and y (number of muffins) is y = 4x. This means that for every cup of flour used, Josiah can bake 4 muffins.

In summary, the equation y = 4x represents the proportional relationship between the volume of flour (x) and the number of muffins (y) that Josiah bakes. The constant of proportionality, 4, indicates that for every cup of flour, Josiah can bake 4 muffins. This equation can be used to calculate the number of muffins Josiah can bake based on the amount of flour he has available or to determine the amount of flour needed to bake a desired number of muffins.

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Answer:

All real numbers

The interval from -infinity to infinity indicates that all real numbers are in the interval.

Real numbers include fractions, decimals, irrational numbers, etc., while integers do not. Integers are only the whole numbers.

Hope this helps!

Step-by-step explanation:

the area of a triangle is baseline×height/2.

the baseline is here 5.8 cm

and the height is given : 2.4 cm

so, the area is

5.8 × 2.4 / 2 = 5.8 × 1.2 = 6.96 cm²

Answer:

  9. (a) -4.58872425

  10. (a) -18.22610955

Step-by-step explanation:

You want the approximate value of f'(5.245) if f(x) = ln(3x) +sin(5x -4) -3 and the approximate value of f''(2.156) if f(x) = 2tan(x) +cos(2x) using h = 0.025 and 0.003, respectively.

The approximate value of f'(x) is the difference quotient ...

  f'(x) ≈ (f(x+h) -f(x))/h

For x=5.245 and h=0.025, this is ...

  f'(x) ≈ ((f(5.245 +0.025) -f(5.245))/0.025

The calculator screen in the first attachment shows the value of this is about ...

  f'(5.245) ≈ -4.58872425

For the second derivative, we use ...

  f'(x) ≈ ((f(x +h) -f(x))/h

  f''(x) = (f'(x -h) -f'(x))/h

The calculator screen in the second attachment shows the calculations and the final value of f''(2.156) as ...

  f''(2.156) ≈ -18.22610955

__

Additional comment

Note that the calculator must be set to radians mode.

<95141404393>

Answer:

2

Step-by-step explanation:

To find the x-intercept of the equation we have to substitute y = 0 in it.

=> 0 = 3x - 6

=> 3x = 6

=> x = 2

Therefore the line will meet x-axis at (2,0) which means it'll have x - intercept of 2 units.

If a shopper pays for 517 for a 470 camera after sales tax is added then sales tax percentage is 10%.

To find the sales tax percentage, we will follow these steps:

1. Determine the amount of sales tax paid.

2. Divide the sales tax amount by the original price of the camera.

3. Multiply the result by 100 to find the sales tax percentage.

Step 1: Determine the amount of sales tax paid.

Sales tax amount = Total amount paid - Original price of the camera

Sales tax amount = 517 - 470

Sales tax amount = 47

Step 2: Divide the sales tax amount by the original price of the camera.

Sales tax rate = Sales tax amount / Original price of the camera

Sales tax rate = 47 / 470

Step 3: Multiply the result by 100 to find the sales tax percentage.

Sales tax percentage = Sales tax rate * 100

Sales tax percentage = (47 / 470) * 100

Sales tax percentage ≈ 10%

So, the sales tax percentage is approximately 10%.

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