A company establishes a sinking fund to pay a debt of $150,000 due in 4 years. At the beginning of each six-month period, they deposit $R in an account paying 9%, compounded semi-annually. How big must the payments be to pay the debt on time? ANSWER: ____dollars

Answer:

70m3

Step-by-step explanation:

5:2

The 2 represents the smaller cylinder. The smaller cylinder=28

To find out how much 1 is we can divide 28 by 2 and that =14. So in the ratio 1=14 and as seen on the left side we have 5    1's. So 14 times 5= 70

Have a nice day :-)

Answer:

(3x + 5) and (x - 6).

Step-by-step explanation:

There are 330 ways to choose 4 books from a collection of 11 books.


To solve this problem, we need to use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).

In this case, we have n = 11 (the total number of books) and r = 4 (the number of books to choose). Plugging these values into the formula, we get:
C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8 * 7!)/ (4! * 7!)
= (11 * 10 * 9 * 8)/ (4 * 3 * 2 * 1)
= 330

So there are 330 ways to choose 4 books from a collection of 11 books.

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Triangle ABC and ADC are similar if BE is parallel to CD.

What does a triangle similarity mean?

Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.

What is the triangle Theorem's similarity?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We are given that BE is parallel to CD.

As per the theorem of similarity, the two triangles are similar when the a line segment of the triangle is parallel to that of another triangle.

So, from this we get that the Triangle ABC and ADC are similar.

Hence, Triangle ABC and ADC are similar.

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The given set of vectors in R4 is linearly independent and  the vector u as a linear combination of the vectors v1, v2, and v3  can be written as u = (7,12,22)

a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.

First, let's form the matrix using the vectors:

| 1 0 -1 0 |
| 1 1 0  2 |
| 0 3  1 -2 |
| 0 1 -1  2 |

Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:

| 1 0 -1 0  |
| 0 1  1 -2 |
| 0 0  4 -6 |
| 0 0  0  4 |

The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.

b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:

u = av1 + bv2 + cv3

This gives us the following system of equations:

10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c

We can use Gaussian elimination to solve this system of equations:

| 2  1 -2 | | a | = | 10 |
| 3  2  2 | | b | = |  1 |
| 5  4  3 | | c | = |  4 |

After reducing the matrix to row echelon form, we get:

| 1 0  1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0  0 | | c | = | 0 |

From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:

a = 2
b = 3

Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:

u = 2v1 + 3v2 + 0v3

u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)

u = (4,6,10) + (3,6,12) + (0,0,0)

u = (7,12,22)

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Answer:

I think the answer is x= 5, -1

Answer:

i got x= 5,-1

Step-by-step explanation:

i hope this helps and have a good day

-13 is the  value of b in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                              Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

y = 6x + 4

 y = mx + c

is a straight line  of gradient of c.

  m = 6

y = 6x + c

the line passes through points(x,y) where x = 3 and y = 5

      5 = 6 * 3 + c

        c = 5 - 18

         c = -13

         y = 6x - 13

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Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.

Step-by-step explanation: Let's use the following variables to represent the price of each item:

c: price of a cup of coffee (in dollars)

b: price of a bagel (in dollars)

From the problem statement, we know that:

b = c + 1 (a bagel costs $1 more than a cup of coffee)

We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:

4c + 6b = 31

Now we can substitute the first equation into the second equation to eliminate b:

4c + 6(c + 1) = 31

Simplifying this equation, we get:

10c + 6 = 31

Subtracting 6 from both sides, we get:

10c = 25

Dividing both sides by 10, we get:

c = 2.5

Now we can use the first equation to find the value of b:

b = c + 1 = 2.5 + 1 = 3.5

Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.

The number 19 is the solution of the equation n-7=12.

The equation given is n-7=12. To find the solution, we need to isolate the variable n on one side of the equation. We can do this by adding 7 to both sides of the equation. This gives us:

n-7+7=12+7

Simplifying the equation gives us:

n=19

Now, we can check which numbers in the set {17,19,21} are solutions of the equation. The only number that satisfies the equation is 19. Therefore, the solution of the equation is 19.

Answer: The number 19 is the solution of the equation n-7=12.

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The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:

L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)

Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:

L(p) = p^k * (1-p)^(n-k)

where k is the number of heads in the sequence and n-k is the number of tails.

To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:

dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0

Solving for p, we get:

p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.

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Answer:

The expression a[(9b-c)+z] can be simplified using the distributive property of multiplication. The distributive property states that:

a(b + c) = ab + ac

Using this property, we can distribute the a to the terms inside the brackets:

a[(9b-c)+z] = a(9b-c) + az

Now, we can distribute the a again to get:

a(9b-c) + az = 9ab - ac + az

Therefore, the expression a[(9b-c)+z] is equivalent to 9ab - ac + az.

Answer:

Step-by-step explanation: Equivalent to 9ab - ac + az.

Answer:

Step-by-step explanation:

Check the picture below.

The expected number of defective batteries out of 15,000 batteries is of:

83.3.

Then this expected amount is compared to the number of different batteries of the other companies.

The number of defective batteries is obtained applying the proportions in the context of the problem.

Company C had 60 defective batteries out of 10,800, hence the proportion of defective batteries is of:

60/10,800.

Out of 15,000 batteries, the expected number of defective batteries is of:

60/10,800 x 15,000 = 83.3.

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Answer:

Answer:

Most poison dart frogs are brightly colored, displaying aposematic patterns to warn potential predators. Their bright coloration is associated with their toxicity and levels of alkaloids. ... Poison dart frogs are an example of an aposematic organism.

Hostas for Full Sun

In general, yellow or gold hostas tolerate partially sunny location without losing their vibrant yellow color. About two hours of daily sun exposure will keep these yellow or golden beauties looking their best. Aim for morning sun to avoid burned leaves.

hope this helps

Step-by-step explanation:

Hope this is the right answer Have a good day!

have a good day

Answer:

55%

Step-by-step explanation:

When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.

Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

What is liability ?

Liability refers to an obligation or debt that an individual, company, or organization owes to another party. In accounting and finance, liabilities are generally classified as current or long-term and can include items such as loans, mortgages, accounts payable, taxes owed, and salaries payable.

The following options would be considered a liability:

Student loan

Money you owe your parents

Mortgage payment

Car payment

Investments and retirement funds would not be considered liabilities as they are assets.

Therefore, Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

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The value of the sample variance and the sample standard deviation for the given data is equal to 47.4 and 6.9 respectively.

Data values are,

23, 12, 5, 9,8

Number of observations 'n' = 5

Mean = ( sum of all the observations ) / ( number of observations)

         = (23 + 12 + 5 + 9 + 8) / 5

         = 57 /5

         = 11.4

Deviations of each data point from the mean,

(23 - 11.4) = 11.6

(12 - 11.4) = 0.6

(5 - 11.4) = -6.4

(9 - 11.4) = -2.4

(8 - 11.4) = -3.4

Square each deviation is equal to,

11.6² = 134.56

0.6² = 0.36

(-6.4)² = 40.96

(-2.4)² = 5.76

(-3.4)² = 11.56

Sample Variance = ( Sum of squared deviation )/ ( n - 1)

⇒Sample Variance = (134.56 + 0.36 + 40.96 + 5.76 + 11.56) / (5-1)

⇒Sample Variance = 47.35

⇒Sample Variance = 47.4(rounded to one decimal place)

Now,

Standard deviation = √variance

Substitute the value we get,

⇒ Standard Deviation = √(47.35)

⇒ Standard Deviation = 6.9 (rounded to one decimal place)

Therefore, the sample variance is 47.4 and the sample standard deviation is 6.9.

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The above question is incomplete, the complete question is:

Calculate the sample variance and the sample standard deviation for the given data. Provide your sample standard deviation answer precise to one decimal place.

23, 12, 5, 9,8

The height of the cylinder is approximately 2.45 inches.

Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

1 and 1/16 = π(1/4)²h

Simplifying and solving for h, we get:

h = (1 and 1/16) / (π(1/4)²)

h = (17/16) / (π/16)

h = 17/π

Approximating using π = 22/7, we get:

h ≈ 17 / (22/7)

h ≈ 2.45 inches (rounded to two decimal places)

Therefore, the height of the cylinder is approximately 2.45 inches

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Answer:

-1 and 0

Step-by-step explanation:

This is a set of simultaneous equations. To solve them, you need to substitute one into the other. The easiest way to do this would be to rearrange x - y = -6 to make x the subject:

x = -6 + y

x = y - 6

Now we can substitute this equation into y = -x^2 + 5x + 6:

y = -(y - 6)^2 + 5(y - 6) + 6

Now simplify this equation, and rearrange to make it equal to 0:

y = -y^2 + 12y - 36 + 6

y = -y^2 + 12y - 30

0 = -y^2 + 12y - y - 30

-y^2 + 11y - 30 = 0

Now solve this quadratic equation to obtain two solutions:

y = 5, y = 6

Now substitute these values back into one of the starting equations to find the respective values for x:

When y = 5:

x - 5 = -6

x = -1

When y = 6

x - 6 = -6

x = 0

Therefore, the x solutions are -1 and 0.

Answer:

Step-by-step explanation:

I'm assuming you mean is the number 90 a rational number. The answer is that yes, it is a rational number.

Let me explain:

Under all the possible numbers, there is a taxonomy to organize these types of numbers. It goes down a list from:

- all numbers, which is divided into two groups; complex and real

Under real numbers, there's rational and irrational:

Under rational, there's integers and fractions

Under integers, there's whole numbers and negative

Under whole numbers, there's natural numbers and 0 (yes, zero).

90 falls under natural numbers, which means it is also a rational number. Hope this helps!

The final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.

To find the quotient of (28[tex]x^{5}[/tex]-8[tex]x^{4}[/tex]+40[tex]x^{(2)[/tex])/(4[tex]x^{3}[/tex]), we need to divide each term in the numerator by the denominator.

First, we divide 28[tex]x^{5}[/tex] by 4[tex]x^{3}[/tex]:

(28[tex]x^{5}[/tex])/(4[tex]x^{3}[/tex]) = (28/4)[tex]x^{(5-3)[/tex] = 7[tex]x^{2}[/tex]

Next, we divide -8[tex]x^{4}[/tex] by 4[tex]x^{3}[/tex]:

(-8[tex]x^{4}[/tex])/(4[tex]x^{3}[/tex]) = (-8/4)[tex]x^{(4-3)[/tex] = -2x

Finally, we divide 40[tex]x^{2}[/tex] by 4[tex]x^{3}[/tex]:

(40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = (40/4)[tex]x^{(2-3)[/tex] = 10[tex]x^{(-1)[/tex] = 10/x

Putting it all together, we get:

(28[tex]x^{5}[/tex] - 8[tex]x^{4}[/tex] + 40[tex]x^{2}[/tex])/(4[tex]x^{3}[/tex]) = 7[tex]x^{2}[/tex] - 2x + 10/x

Therefore, the final answer in simplest form is 7[tex]x^{2}[/tex] - 2x + 10/x.

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The expression that is equivalent to the given expression, 8x + 4, is 4(2x +1)

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is:

8x + 4

To determine the expression that is equivalent to the given expression, we will factorize the given expression.

First, we will determine the Greatest common factor (GCF) of the terms in the expression.

The terms in the expression are 8x and 4

The GCF of 8x and 4 is 4

Thus,

We can factor the expression as shown below:

8x + 4

4(2x + 1)

Hence, the expression is 4(2x + 1)

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Answer:

in all 240

60 chose blue

72 chose red

36 chose orange

7 chose purple

10 chose green

7 chose other

Step-by-step explanation:

48 x 5 = 240

48 = 20%

20% x 5 = 100%

The probability of rolling a dice less than 3 times is 17/100.

It is a branch of mathematics that deals with the occurrence of a random event.

The total no of times rolling = 200

The probability of rolling 1 = 17 times

And, The probability of rolling 2 = 17 times

So, the probability of rollng a dice less than 3 times is

17+17/200

34/200

17/100

Hence, the probability of rolling a dice less than 3 times is 17/100.

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Answer:

45

Step-by-step explanation:

3² · (12-2) ÷ 2

= 9 · (10) ÷ 2

= 90 ÷ 2

= 45

So, the answer is 45

Answer: 135

Step-by-step explanation: use a calculator/online calculator

The factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

To write the polynomial p(z) in factored form as a product of linear and quadratic expressions using integer coefficients only, we need to find the other zeros of the polynomial.

Since one of the zeros is a complex number, z = -1 + 6i, the other complex zero will be its conjugate, z = -1 - 6i. This is because complex zeros of polynomials with real coefficients always come in conjugate pairs.

Now, we can write the quadratic expression that has these two complex zeros as

(z - (-1 + 6i))(z - (-1 - 6i)) = (z + 1 - 6i)(z + 1 + 6i) = (z + 1)^(2) - (6i)^(2) = z^(2) + 2z + 1 - 36i^(2) = z^(2) + 2z + 37.

Since the polynomial p(z) is of degree 3, there must be one more zero, which we can find by dividing p(z) by the quadratic expression we just found:

p(z)/(z^(2) + 2z + 37) = 2z^(3)/(z^(2) + 2z + 37) - z^(2)/(z^(2) + 2z + 37) + 64z/(z^(2) + 2z + 37) - 185/(z^(2) + 2z + 37) = 2z - 5

So the other zero is z = 5/2.

Now,
p(z) = 2(z - 5/2)(z^(2) + 2z + 37) = (2z - 5)(z^(2) + 2z + 37)

So the factored form of the polynomial is p(z) = (2z - 5)(z^(2) + 2z + 37).

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The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.

Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.

Therefore, the correct answer is option b. Ordinal data.

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The required foci of the ellipse are also at (-4, -3).

To find the foci of the ellipse defined by the equation:

[tex]\dfrac{(x+4)^2}{4}+\dfrac{(y+3)^2}{9}=1[/tex]

We need to identify the values of 'a' and 'b' from the equation, where 'a' is the semi-major axis, and 'b' is the semi-minor axis of the ellipse.

The general equation of an ellipse centered at (h, k) is given by:

[tex]\dfrac{(x - h)^2}{ a^2} + \dfrac{(y - k)^2}{ b^2} = 1[/tex]

Comparing this with the given equation, we can see that the center of the ellipse is at (-4, -3), so (h, k) = (-4, -3).

Next, we find 'a' and 'b':

For the x-term: a² = 4

a = √4

a = 2

For the y-term: b² = 9

b = √9

b = 3

So, the semi-major axis 'a' is 2 units, and the semi-minor axis 'b' is 3 units.

Now, the distance from the center of the ellipse to the foci is given by:

[tex]c = \sqrt{(a^2 - b^2)[/tex]

[tex]c = \sqrt{(2^2 - 3^2)[/tex]

[tex]c=\sqrt{-5[/tex]

The distance is imaginary, which means the foci are not real, and the ellipse is degenerate. A degenerate ellipse is essentially a circle. Since we have a degenerate ellipse, the foci coincide with the center of the ellipse.

Therefore, the foci of the ellipse are also at (-4, -3).

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Answer:

If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:

t = kc

We can find the value of k by using the given information that 5 climbs cost $52.50:

52.50 = k(5)

Solving for k, we get:

k = 10.50

Therefore, the equation that represents the total cost, t, of c climbs is:

t = 10.50c