Find the amount paid for the loan.

$4800 at 9.9% for 4 years

$

Answer:

Yes

Step-by-step explanation:

On my worksheet

Answer: Yes

Step-by-step explanation:

You asked if the line was linear not passing through the origin. The line is linear because it has a slope that is constant. Therefore, it will be drawn as a line, so it is linear.

We have to simplify the expression:

The second parenthesis has a "-" sign at the front. So, all the signs of each term within the parenthesis changes.

We have:

Now, we can simplify the expression by adding/subtracting like terms (terms whose variables and exponents are the same). This process of simplification is shown below:

Answer:

the first one

Step-by-step explanation:

i think that's the correct answer

The trend line is a good fit for the data.

The trend line is a good fit for the data because about half of the points lie above the line and half lie below the line. In addition, the points lie close to the line. The scatter plot is a graphical representation of the data where the values of two variables are plotted on a coordinate plane. In general, if a scatter plot shows a positive correlation between the variables, a trend line can be drawn to help represent the relationship.A trend line is a straight line that is used to represent the general trend of the data in a scatter plot.

The line is drawn such that the number of points above the line is equal to the number of points below the line. This helps to indicate the direction of the relationship between the two variables plotted on the coordinate plane. The closer the data points are to the trend line, the better the fit of the line. So, it can be concluded that the trend line is a good fit for the data.

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Answer:

Step-by-step explanation:

Hello, please consider the following.

\(x(t)=sin(t)\\\\dx=cos(t)dt\\\\\text{For x = }\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2} \text{ we have } t = \dfrac{\pi}{4}\)

So, we can write.

\(\displaystyle \int\limits^{\dfrac{1}{\sqrt{2}}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{1-sin^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{cos^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{cos(t)}} \, dt \\\\=\int\limits^{\dfrac{\pi}{4}}_0 {1} \, dt\\\\=\large \boxed{\sf \bf \dfrac{\pi}{4}}\)

Thank you

Answer:  \(\bold{\dfrac{\pi}{4}}\)

Step-by-step explanation:

Note the following integral formula:   \(\int\limits^a_b {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\sin^{-1}(x)\bigg|^a_b\)

We can rationalize the denominator to get: \(\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)=\dfrac{\sqrt2}{2}\)

*************************************************************************************

\(\int\limits^{\frac{\sqrt2}{2}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx \\\\\\=\sin^{-1}(x)\bigg|^{\frac{\sqrt2}{2}}_0\\\\\\= \sin^{-1}\bigg(\dfrac{\sqrt2}{2}\bigg)-\sin^{-1}(0)\\\\\\=\dfrac{\pi}{4}-0\pi\\\\\\=\large\boxed{\dfrac{\pi}{4}}\)

Answer:

14

Step-by-step explanation:

because 6+6 is 12 and add 2 is 14

The transitivity of divisibility theorem says that for all integers a, b, and c, if a divides b and b divides c, then a divides c. In other words, if a is a factor of b and b is a factor of c, then a is also a factor of c.

This theorem can be written as follows: If a | b and b | c, then a | c. For example, if a = 2, b = 6, and c = 12, we know that 2 | 6 and 6 | 12, so by the transitivity of divisibility theorem, we can conclude that 2 | 12.

The transitivity of divisibility is an important property of integers and is often used in number theory and other mathematical areas. It allows us to make inferences about the factors of numbers and the properties of divisibility, and is a useful tool in proofs involving divisibility and prime numbers.

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Given that a is in Quadrant 2 and sin(a) =, we need to calculate the value of a. However, the value of sin(a) is missing in the question.

Please provide the value of sin(a) to proceed further. Similarly, given that B is in Quadrant 1 and tan(B) = 1, we need to calculate the exact answers for sin(2/3), cos(26), and tan(23).Here are the steps to calculate the exact answers for sin(2/3), cos(26), and tan(23):Given that B is in Quadrant 1 and tan(B) = 1:Since

tan(B) = opposite / adjacent We can assume opposite side as x and adjacent side as 1. Therefore, we get:

Tan(B) = opposite / adjacent

=> 1 = x/1

=> x = 1 Hence, the opposite side in the right triangle is 1.

Now, we can use the Pythagorean Theorem to find the adjacent side. Using the Pythagorean Theorem, we get:

hypotenuse^2 = opposite^2 + adjacent^2

=> hypotenuse^2 = 1 + 1

=> hypotenuse = √2a.

sin(2a) = sin 16/9 Given that a is in Quadrant 2, the value of cos(a) is positive and sin(a) is negative.

sin(a) = -16/9

cos(a) = sqrt(1 - sin^2(a)

= sqrt(1 - (256/81))

= sqrt(25/81)

= 5/9cos(2a)

= cos^2(a) - sin^2(a)

= (5/9)^2 - (16/9)^2

= 25/81 - 256/81= -231/81

tan(2a) = (2tan(a))/(1 - tan^2(a)

)= 2 * (-16/9) / (1 - (-16/9)^2)

= -32/145 Given that B is in Quadrant 1 and

tan(B) = 1:b. cos(26)We know that

cos(90 - 26) = sin(26) and

sin(90 - 26) = cos(26)

cos(90 - 26) = sin(26)

= sin(64)= cos(26)c. tan(23) We can use the identity

tan(2x) = 2tan(x) / (1 - tan^2(x))

tan(2*23) = tan(46)

= 2tan(23) / (1 - tan^2(23))

=> 1/tan(46) = 2/tan(23) - tan(23)

=> tan(23)

= (2 / tan(46)) + tan(46) We know that

tan(90 - 46)

= cot(46)

= cot(44)

= 1/tan(44) Substituting this value, we get

tan(23) = (2 / (1/tan(44))) + (1/tan(44))

= 2tan(44) + tan(44)

= 3tan(44)

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The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.

In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.

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The null hypothesis (H0) is that the manufacturer's claimed mpg rating is correct and the alternative hypothesis (Ha) is that it is incorrect.

To test this, we need to conduct a hypothesis test using the sample mean and standard deviation. We can use a one-sample t-test since we have the sample mean and standard deviation.

The formula for the t-test is:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

In this case, the hypothesized mean is the manufacturer's claimed mpg rating of 53.2 mpg. The sample mean is 53.3 mpg, the standard deviation is 2.5 mpg, and the sample size is 25.

Plugging these values into the formula, we get:

t = (53.3 - 53.2) / (2.5 / sqrt(25)) = 0.2 / 0.5 = 0.4

To determine if this t-value is statistically significant at the 0.1 level, we need to compare it to the critical t-value for a one-tailed test with 24 degrees of freedom (sample size minus one). Using a t-table or calculator, we find the critical t-value to be 1.711.

Since our calculated t-value of 0.4 is less than the critical t-value of 1.711, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence at the 0.1 level to conclude that the cars have an incorrect manufacturer's mpg rating.

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The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

The equation of the graph is;

y = 4·x

Step-by-step explanation:

The coordinates of two points, (x₁, y₁), and (x₂, y₂) respectively on the straight line graph are;

(-3, 12), and (2, 8)

The slope, m, of the straight line graph is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Therefore, by substitution of the values, we have;

\(Slope, \, m =\dfrac{8-(-12)}{2-(-3)} = \dfrac{8 + 12}{2 + 3} =\dfrac{20}{5} = 4\)

The equation of the graph in point slope form is therefore;

(y - 8) = 4×(x - 2)

y = 4·x - 8 + 8 = 4·x

y = 4·x.

Answer:

Option C I guess

Step-by-step explanation:

Please Mark me brainlist

Answer:

C

Step-by-step explanation:

Real numbers are the collection of rational and irrational number , so it's option C.

If you like it so please mark me the brainliest

Answer:

Step-by-step explanation:

So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!

Let us assume the first consecutive positive integer as m. Therefore, second and third consecutive number would be (m + 1) and (m + 2) respectively.

Refer to the attachment now.

16.3 degrees is the angle that the ramp makes with the ground.

Draw a diagram: Draw a right-angled triangle with the ramp as the hypotenuse, the height of the truck as one of the other sides, and the horizontal distance from the bottom of the ramp to the truck as the other side.

Use trigonometry: We can use the trigonometric function tangent to find the angle the ramp makes with the ground. tan(theta) = opposite/adjacent = height of truck/horizontal distance

Let's substitute the given values:

tan(theta) = 6/21

Solve for theta: We can use the inverse tangent function to solve for theta.

theta = tan^-1(6/21)

theta ≈ 16.3 degrees

Therefore, the angle that the ramp makes with the ground is approximately 16.3 degrees.

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Sasha should use 2 desired outcomes in her probability calculation to determine that she has a 1/3 chance of winning the game.

To calculate Sasha's probability of winning, we need to determine how many desired outcomes she has. In this game, Sasha needs to spin a number higher than both of her friends' spins, which means she needs to spin a number greater than 1 and 4.

Let's analyze the spinner pictured. From the image, we can see that the spinner has numbers ranging from 1 to 6. Since Sasha needs to spin a number higher than 4, she has two options: 5 or 6.

Now, let's consider the desired outcomes. Sasha has two desired outcomes, which are spinning a 5 or spinning a 6. If she spins either of these numbers, she will have a number higher than both of her friends and win the game.

To calculate Sasha's probability of winning, we need to divide the number of desired outcomes by the total number of possible outcomes. In this case, the total number of possible outcomes is the number of sections on the spinner, which is 6.

Sasha's probability of winning is 2 desired outcomes divided by 6 total outcomes, which simplifies to 1/3.

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.

The translation transformation of the parent function in the graph, indicates that the equation for each of the specified graphs, using the form y = f(x - h) + k, are;

a. y = f(x) + 3

b. y = f(x - 3)

c. y = f(x - 1) + 2

A transformation of a function is a function that takes a specified function or graph and modifies them into another function or graph.

The points on the graph of the specified function f(x) in the diagram are; (0, 0), (1.5, 1), (-1.5, -1)

The graph is the graph of a periodic function, with an amplitude of (1 - (-1))/2 = 1, and a period of about 4.5

Therefore, we get;

a. The graph in part a consists of the parent function shifted up three units. The transformation that can be represented by the vertical shift of a function f(x) is; f(x) + a or f(x) - a

Therefore, the translation of the graph of the parent function is; f(x) + 3

b. The graph of the parent function in the graph in part b is shifted to the right two units, and the vertical translation is zero units, down or up.

The translation of the graph of a function by h units to the right or left can be indicated by an subtraction or addition of h units to the value of the input variable, therefore, the translation of the function in the graph of b is; y = f(x - 3) + 0 = f(x - 3)

c. The translation of the graph in part c are;

A vertical translation 2 units upwards

A horizontal translation 1 unit to the right

The equation representing the graph in part c is therefore; y = f(x - 1) + 2

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D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.

The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.

62% of women in the sample are the primary investor in their household.

Inference: Women in the United States are likely to be the primary investors in their households.

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Step-by-step explanation:

1) 3 – 36i = 9a + 4bi

3 = 9a => a = 3/9 = ⅓

-36 = 4b => b = -36/4 = -9

2) a – 15i = -7 – (2b-3)i

a = -7

-15 = -(2b-3)

2b-3 = 15

2b = 18

b = 18/2= 9

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

First, we need to figure out the amount the price increased.

50 - 40 = 10

The price of the yearbook this year increased $10.

Now, taking 10, we need to figure out what percent of 40 is 10.

10 ÷ 40 = 0.25

10 is %25 of 40.

Therefore, the price increase from last year to this year is %25.

The statement that accurately describes what Marisol should do next is that Marisol should go back and group the terms in Step1 as (6x³– 22x²) – (9x – 33) and it can be determined by using the factorization method.

Marisol grouped the terms and factored the GCF out of the groups of the polynomial \(\rm 6x^3- 22x^2- 9x + 33\).

To factor out the common GCF out of the group, the following steps should have been taken by Marisol.

Marisol grouped the terms and factored the GCF out of the groups of the,

To factor out the common GCF out of the group, the following steps should have been taken by Marisol following all the steps given below.

        \(\rm= 6x^3- 22x^2- 9x + 33\\\\= (6x^3-22x^2) - (9x-33)\)

        \(= (6x^3-22x^2) - (9x-33)\\\\= 2x^2(3x^2-11) -3(3x-11)\\\\= (2x^2-3) (3x-11)\)

Hence, The statement that accurately describes what Marisol should do next is that Marisol should go back and group the terms in Step1 as (6x³– 22x²) – (9x – 33).

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The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".

Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.

As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.

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Answer:

11 hours as a cashier

and 2 hours as a teacher

11 x 8 = 88

6 x 2 = 12

88 + 12 = 100

Step-by-step explanation:

The solution to the system equation  is (x, y, z, w) = (23, 12, 3, 1).

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

Here is a system of linear equations that represents the situation.

x +5y +10z +20w = 133 . . . total amount earned

x +y +z +w = 39 . . . . . . . . . total number of bills

y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s

x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s

_____

We can substitute for x and z in the first two equations:

... (2y-1) +5y +10(y/4) +20w = 133

... (2y-1) +y +(y/4) +w = 39

These simplify to

... 9.5y +20w = 134

... 3.25y +w = 40

Solving by your favorite method, you get

... y = 12

... w = 1

So the other values can be found to be

... x = 2·12 -1 = 23

... z = 12/4 = 3

hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).

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Answer:

See below

Step-by-step explanation:

The question is missing information:  " . . . how far would he go in an ???"

If the question is how far he would go in a [Pick a despised car model} ?  The answer is still 400.  The car would break down.

If the question is how far would he go in the same amount of time:

Whe the speed limit was 55, it would take Bob (55 miles/hr)*(X hr) = 400 miles

X = 7.273 hours to go 400 miles at 55 mph.

A speed limit of 70 mph would allow Bob the go:

    (70 miles/hour)*(7.272 hours) = 509.1 miles

To determine the probability that it would be more than 30 minutes before the next person is admitted to the hospital, we would need information about the admission process, such as the average rate of admissions or the distribution of inter-admission times.

However, if we assume that the time between admissions follows a continuous random distribution and is independent of the previous admission time, we can make some general assumptions.

Let's assume the time between admissions follows an exponential distribution with a mean of λ (lambda). The exponential distribution is commonly used to model the time between events that occur randomly and independently over time.

In this case, the probability that it would be more than 30 minutes before the next person is admitted can be calculated as the complement of the cumulative distribution function (CDF) of the exponential distribution at 30 minutes.

P(Time > 30 minutes) = 1 - CDF(30 minutes).

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Starting with the least likely event, the chances of a politician fulfilling all his or her campaign promises can be quite low due to the complexities of politics and the potential for unforeseen circumstances.

Next, while full moons are relatively common, they occur approximately once a month, making it more likely than the politician's scenario but less likely than the other events.

Rolling a die and getting a 6 has a higher likelihood as there is a 1 in 6 chance of rolling a 6 on a fair six-sided die. The safe arrival of a person in New York City from Chicago is more probable than the previous events but still has an element of uncertainty regarding the fate of their luggage.

Randomly selecting an ace from a regular deck of 52 playing cards has a higher probability compared to the previous events, as there are four aces in a deck. The likelihood increases further when randomly selecting the queen of hearts, which is only one specific card out of the 52-card deck.

Finally, selecting a black card from a regular deck has the highest probability among the listed events since there are 26 black cards in the deck, including all the clubs and spades.

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Answer:

n = 3

Step-by-step explanation:

To go from 20 to 1, you must divide 20 by 20. So, to find n, you must divide 60 by 20

There are 4845 different ways to select 16 questions out of a total of 20 questions on the exam.

To determine the number of different ways you can select 16 questions out of a total of 20 questions, we can use the concept of combinations.

In this case, we want to select 16 questions from a set of 20 questions, and the order in which we select them doesn't matter. This scenario can be represented by the combination formula.

The formula for combinations is given by:

C(n, k) = n! / (k!(n-k)!)

Where:

n is the total number of items in the set (20 questions)

k is the number of items to be selected (16 questions)

! denotes the factorial operation

Using the combination formula, we can calculate the number of different ways to select the questions:

C(20, 16) = 20! / (16!(20-16)!)

= 20! / (16!4!)

= (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)

= 4845

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The answers for these solutions to equation (x - 21)^2 = 25 are

x = 26

x =16

Picture proof

The value of x are 26 and 16.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra .

According to question

\((x - 21)^{2}\) = 25

(x-21) = ± 5

x-21 = +5   and x-21 = -5

x = 5+21    and x = -5+21

x= 26      and   x = 16

Hence, value of x are 26 and 16 .

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