You deposit $880 in a savings account paying 4% simple interest.


How much interest will you earn in 5 years?

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

(A) A person's chance of experiencing neither symptom is 30%. (b) Seventy percent of people are likely to experience at least one symptom. (c) If a person has symptom B, there is a 25% chance that they will also have both symptoms.

(A) The individual exhibits neither symptom:

Let's write P(A) for the likelihood of having symptom A and P(B) for the likelihood of having symptom B. Given that 20% of people only have symptom A, 40% only have symptom B, and 10% only have both symptoms, the likelihood of having neither symptom can be determined as follows:

100% - P(A) - P(B) - P(both symptoms) - P(neither symptom)

P(none of the symptoms) = 100% – 20% – 40% – 10% = 30%

As a result, there is a 30% chance that a randomly selected person will exhibit neither symptom.

(b) At least one symptom is present in the person.

We can use the complement rule to calculate the likelihood that at least one symptom will be present. Neither symptom is the opposite of having at least one symptom. Because of this, P(at least one symptom) = 1 - P(neither symptom), and P(at least one symptom) = 1 - 0.30 = 0.70.

Therefore, there is a 70% chance that a randomly selected individual has at least one symptom.

(c) The person has both symptoms, given that they have symptom B:

To calculate this conditional probability, we use the formula:

P(both symptoms | symptom B) is equal to the product of P(both symptoms and symptom B) / P(symptom B).

We are informed that 40% of people only have symptom B whereas 10% have both symptoms. P(both symptoms | symptom B) = (10% / 40%) = 0.25 as a result.

Given that they have symptom B, a randomly selected person has a 25% chance of having both symptoms.

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The transformation of the points and shapes after being transformed are calculated below

The coordinates of B in the figure is

B = (5, 1)

A translation of (x-4, y-3) means

B' = (5 - 4, 1 - 3)

B' = (1, -2)

Here, we have the following corresponding points

Pre = (2, 1)

Image = (-1, 2)

This represents

(x, y) = (-y, x)

This represents (d) 270° clockwise rotation

Given that the smaller figure is gotten from a bigger figure

Then the dilation is a reduction and the scale factor could be 1/2 or 1/4

We have

P = (3, -2) and S = (4, -5)

For the first transformation, we have

(x - 2, y)

P' = (1, -2) and S' = (2, -5)

For the second, we have

P'' = (1, 2) and S'' = (2, 5)

Here, we have

A = (-2, -5)

This means that the new ordered pair of point A is

A' = (-2, -5) * 1/2

A' = (-1, -2.5)

Hence, the new ordered pair of point A is (-1, -2.5)

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(tan(x) + cot(x)) / (tan(x) - cot(x)) = (tan²(x) + 1) / (tan²(x) - 1)

… = (sin²(x) + cos²(x)) / (sin²(x) - cos²(x))

… = -1/cos(2x)

Then as x approaches π/2, the limit is -1/cos(2•π/2) = -sec(π) = 1.

Answer:

y = 4x^2 + 5 has the narrowest graph.

Step-by-step explanation:

The larger the coefficient of x^2 is, the narrower the graph will be.  Thus:

y = 4x^2 + 5 has the narrowest graph.

In this case, the probability is given by the following expression:

Probability = number of pink marbles / total number of marbles

There are 3 pink marbles out of 14 marbles, then we get:

Probability = 3/14

Then, the probability of getting a pink marble is 3/14

Answer:

y=1262 /63 or y=20 and 2/63

Step-by-step explanation:

plug 21 into the equation to get y=2/3(21)+20

Answer:

I believe 70

Step-by-step explanation:

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

The random variable follows a continuous uniform distribution between 20 and 50.

The continuous uniform distribution is a probability distribution where all values within a specified range are equally likely to occur. In this case, the random variable follows a continuous uniform distribution between 20 and 50. To calculate the probabilities for this distribution, we can use the properties of the uniform distribution.

P(x ≤ 25):

To find this probability, we need to calculate the proportion of the range from 20 to 50 that lies below or equal to 25. Since the distribution is uniform, the probability is equal to the ratio of the length of the range below or equal to 25 to the length of the entire range.

Length of the range below or equal to 25 = 25 - 20 = 5

Length of the entire range = 50 - 20 = 30

P(x ≤ 25) = (Length of the range below or equal to 25) / (Length of the entire range) = 5 / 30 = 1/6 ≈ 0.1667

Therefore, P(x ≤ 25) is approximately 0.1667 or 16.67%.

P(x ≤ 30):

Using a similar approach, we calculate the probability of the range below or equal to 30.

Length of the range below or equal to 30 = 30 - 20 = 10

P(x ≤ 30) = (Length of the range below or equal to 30) / (Length of the entire range) = 10 / 30 = 1/3 ≈ 0.3333

Therefore, P(x ≤ 30) is approximately 0.3333 or 33.33%.

P(24 ≤ x ≤ 35):

To find this probability, we need to calculate the proportion of the range from 20 to 50 that lies between 24 and 35.

Length of the range between 24 and 35 = 35 - 24 = 11

P(24 ≤ x ≤ 35) = (Length of the range between 24 and 35) / (Length of the entire range) = 11 / 30 ≈ 0.3667

Therefore, P(24 ≤ x ≤ 35) is approximately 0.3667 or 36.67%.

P(x = 28):

Since the continuous uniform distribution is continuous, the probability of a single point is zero. Therefore, P(x = 28) is equal to zero.

In summary:

P(x ≤ 25) ≈ 0.1667 or 16.67%

P(x ≤ 30) ≈ 0.3333 or 33.33%

P(24 ≤ x ≤ 35) ≈ 0.3667 or 36.67%

P(x = 28) = 0

These probabilities are calculated based on the assumption that the random variable follows a continuous uniform distribution between 20 and 50.

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Answer:

\(The \ equation \ in \ point \ and \ slope \ form \ is; \ y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)

Step-by-step explanation:

The coordinates of the points through which the line passes are (1, 3) and (5, 1)

The slope, m, of a line given the coordinates of two known points on the line, (x₁, y₁), (x₂, y₂) can be found as follows;

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

The slope of the given line is therefore \(m =\dfrac{1-3}{5-1} = \dfrac{-2}{4} = -\dfrac{1}{2}\)

The equation of the line in point and slope form is therefore, y - y₁ = m·(x - x₁) or y - y₂ = m·(x - x₂)

Therefore, by substituting the known values, we have the equation in point and slope form as follows;

\(y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)

Answer:  27x² - 15xy - 24xz + 15yz - 3z².

Answer:

Step-by-step explanation:

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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In statistical analysis, a hypothesis refers to a tentative explanation or prediction that is based on limited evidence and is subject to further investigation and testing. It is a statement that can be either true or false, and is typically formulated in such a way that it can be tested using statistical methods.

The hypothesis is often used to guide the research process, to help identify potential patterns or relationships in the data, and to evaluate the significance of the results.

Overall, the hypothesis plays a critical role in statistical analysis, as it provides a framework for understanding and interpreting data, and helps to ensure that research findings are reliable and valid.

A hypothesis in the context of statistical analysis is a tentative explanation or prediction about the relationship between two or more variables, which is subject to testing and empirical evaluation using statistical methods.

It is a statement that can be either true or false, and it is usually formulated in terms of the expected direction and strength of the relationship between the variables of interest.

The hypothesis is typically derived from existing theory, prior research, or common sense, and it serves as a guide for the collection, analysis, and interpretation of data in a scientific study.

The process of testing a hypothesis involves setting up null and alternative hypotheses, selecting an appropriate statistical test, collecting and analyzing data, and drawing conclusions based on the results of the analysis.

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The average rate of change over the interval x = 3 and x = 7 is 30

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The equation is given as

g(x) = 2ˣ - 1

The interval is given as:

x = 3 and x = 7

Start by calculating g(3) and g(7)

So, we have

g(3) = 2³ - 1 = 7

g(7) = 2⁷ - 1 = 127

So, the average rate over these intervals is calculated as:

Average rate = [g(b) - g(a)]/[b - a]

This gives

Average rate = [g(7) - g(3)]/[7 - 3]

Substitute known values

Average rate = [127 - 7]/[7 - 3]

Simplify

Average rate = 120/4

Average rate = 30

Hence, the average rate of change is 30

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Answer:

2635*'fhhdgjvsvaksgwksygwi at gwjsksgeieh egg ejei

The identities among the given options are:

B. (sin x + cos x)² = 1 + sin 2x

C. sin 6x = 2 sin 3x cos 3x

Therefore, options B and C are the identities.

Among the given options, the identities are as follows:

B. (sin x + cos x)² = 1 + sin 2x

C. sin 6x = 2 sin 3x cos 3x

Let's examine each option:

A. This equation is not an identity since it does not hold true for all values of x.

B. This equation is an identity.

It is known as the Pythagorean Identity, which states that the square of the sum of sine and cosine is equal to 1 plus the sine of twice the angle.

C. This equation is also an identity. It is derived from the double angle formula for sine, which states that sin(2x) = 2sin(x)cos(x).

By substituting 3x for x, we get sin(6x) = 2sin(3x)cos(3x), which is the given equation.

D. The equation given here, "4 cos x sec x = tan x," is not an identity since it does not hold true for all values of x.

To summarize, the identities among the given options are B. (sin x + cos x)² = 1 + sin 2x and C. sin 6x = 2 sin 3x cos 3x.

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Answer:

\(n^4\)

Step-by-step explanation:

So we have:

\(n^{-2}\cdot n^6\)

We can use the following property:

\(x^a\cdot x^b=x^{a+b}\)

Thus, our expression is equivalent to:

\(=n^{-2+6}\)

Add:

\(=n^4\)

And we're done!

n2

i have taken something like this before!

The values of the coefficients is y = 1 - x^2/3 + x^4/30 - x^6/630 + ... and this is the general solution to the differential equation.

To use the power series method to determine the general solution to the equation (1-x^2)y'' - xy' + 4y = 0, we assume that the solution y can be written as a power series:

y = a0 + a1x + a2x^2 + ...

Then, we differentiate y to obtain:

y' = a1 + 2a2x + 3a3x^2 + ...

And differentiate again to get:

y'' = 2a2 + 6a3x + 12a4x^2 + ...

Substituting these expressions into the original equation and collecting terms with the same powers of x, we get:

[(2)(-1)a0 + 4a2] + [(6)(-1)a1 + 12a3]x + [(12)(-1)a2 + 20a4]x^2 + ... - x[a1 + 4a0 + 16a2 + ...] = 0

Since this equation must hold for all x, we equate the coefficients of each power of x to zero:

(2)(-1)a0 + 4a2 = 0

(6)(-1)a1 + 12a3 - a1 - 4a0 = 0

(12)(-1)a2 + 20a4 + 4a2 - 16a0 = 0

...

Solving these equations recursively, we can obtain the coefficients a0, a1, a2, a3, a4, ... and hence obtain the power series solution y.

In this case, we can simplify the recursive equations by using the fact that a1 = (4a0)/(1!), a2 = (6a1 - 12a3)/(2!), a3 = (6a2 - 20a4)/(3!), and so on. Substituting these expressions into the equation for a0 and simplifying, we get:

a0 = 1

Using this as the starting point, we can compute the other coefficients recursively:

a1 = 0

a2 = -1/3

a3 = 0

a4 = 1/30

a5 = 0

a6 = -1/630

...

Thus, the power series solution to the equation (1-x^2)y'' - xy' + 4y = 0 is:

y = a0 + a1x + a2x^2 + a3x^3 + a4x^4 + a5x^5 + a6x^6 + ...

Substituting the values of the coefficients, we obtain:

y = 1 - x^2/3 + x^4/30 - x^6/630 + ...

This is the general solution to the differential equation.

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Answer:

21 weeks or 5 months 1 week (7 days) to save 1250

Step-by-step explanation:

1250-200 (the amount he has)

1050 which is what he needs to save for

1050/50 = 21

Answer:

caca

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

(0)(8)(3+1−4)

=0(3+1−4)

=0(4−4)

=(0)(0)

=0

When we reflect a point across an axis, the distance between the point and the axis stays the same, but is flipped to the opposite side.  

We know that the coordinates of point A are (4,1), the coordinates of point B are (6,3), and the coordinates of point C are (2,4).  

In this case, Triangle ABC is a reflection of point A'B'C' across the y-axis.  

=  reflection across the y-axis

Answer:

Producer's surplus = (1/2) x (2) x (10) = 10

Step-by-step explanation:

To find the producer's surplus, we need to first determine the equilibrium quantity and price at which the supply and demand functions intersect.

Setting the supply function S(x) equal to the demand function D(x) and solving for x, we get:

4x + 2 = 14 - x^2

Rearranging and simplifying, we get a quadratic equation in standard form:

x^2 + 4x - 12 = 0

Using the quadratic formula, we get:

x = (-4 ± √(4^2 - 4(1)(-12))) / (2(1))

x = (-4 ± √64) / 2

x = -2 ± 4

x = -6 or x = 2

Since we're interested in a positive quantity, we'll take x = 2 as the equilibrium quantity.

To find the equilibrium price, we substitute x = 2 into either the supply or demand function:

D(2) = 14 - 2^2 = 10

So the equilibrium price is P = 10.

The producer's surplus is the area above the supply curve and below the equilibrium price. Since the supply function is linear, we can find the producer's surplus by calculating the area of a triangle with base x = 2 and height S(2) = 10:

Producer's surplus = (1/2) x (2) x (10) = 10

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Answer:

Acute, right angle, obtuse, reflex

Step-by-step explanation:

Answer:

Acute

right angle

obtuse

reflex angle

Step-by-step explanation:

Answer:

y = 476^x

Step-by-step explanation:

y = 250(1.904)^×

y = 476^x

Hope this helps, thank you !!

Answer:

Loading. . .

Step-by-step explanation:

Answer:

$490 is the retail price

Step-by-step explanation:

75% = \(\frac{3}{4}\)

\(\frac{280}{4} = 70\)

\(70(3)=210\)

\(280+210=490\)

The retail price will be; 490 dollar.

Markup is the amount that will be increased in the original price of the considered thing.

Markdown is the amount that will be decreased from the original price of the considered thing.

Think of "up" and "down" as increasing and decreasing prices respectively.

We are given that Haas Door Co. produces truck dock door seals. Their 9' × 10' seal costs $280 to produce.

The mark-up rate = 75% of the cost to produce.

Retail price = cost price + 75 % of cost price

Therefore,

Retail price = 280 + 75 % of 280

Retail price = 280 + 0.75 x 280

Retail price = 280 + 210

Retail price = 490

Thus, retail price is $ 490

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Answer:

b)

Step-by-step explanation:

i hope this help you