To purchase $13200 worth of machinery for her business, Nicole made a down payment of 1200 and took out a business loan for the rest. After 3 years of paying monthly payments of 365.07, she finally paid off the loan.


(a) What was the total amount Nicole ended up paying for the machinery (including the down payment and monthly payments)?

(b) How much interest did Nicole pay on the loan?

Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

Therefore, the generating function of (x+4)^4 is:

[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

The associated sequence can be read off by finding the coefficients of each power of x:

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256

Therefore, the generating function of (x+4)^4 is:

G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256

The associated sequence can be read off by finding the coefficients of each power of x:

The coefficient of x^k is the k-th term of the sequence.

In this case, the sequence is given by the coefficients of G(x):

a₀ = 256

a₁ = 256

a₂ = 96

a₃ = 16

a₄ = 1

Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

Learn more on binomial theorem here;

https://brainly.com/question/24756209

#SPJ1

Answer:

The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.

To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.

As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.

As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.

Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.

Answer:

3x(x - 4y)

Step-by-step explanation:

3x² - 12xy ← factor out 3x from each term

= 3x(x- 4y)

The open circle at 3 indicates that 3 is not included in the solution set. This inequality can be read as "X is less than 5" or "X is strictly less than 5."

In mathematics, an expression is a combination of numbers, symbols, and operators that represents a value. Expressions can be as simple as a single number or variable, or they can be complex combinations of mathematical operations. For example, 2 + 3 is a simple expression that represents the value 5, while (2 + 3) x 4 - 1 is a more complex expression that represents the value 19. Expressions can be evaluated or simplified using the rules of arithmetic and algebra.

Here,

1. Simplify:

3(4x-2)+ 7X (2-1) + 4 (6+4)+(-8)

Multiplying inside the parentheses first:

12x - 6 + 7x + 4 + 40 - 8

Combining like terms:

19x + 30

Final answer: 19x + 30

2. Graph:

3 > X

This is a simple inequality in one variable (X). To graph it on a number line, we first draw a dot at 3 (since the inequality is strict), and then shade all values less than 3:

<=========o---

The open circle at 3 indicates that 3 is not included in the solution set.

3. Write the inequality:

X < 5

This is a simple inequality in one variable (X). The inequality sign is "less than," and the number on the right-hand side is 5. This inequality can be read as "X is less than 5" or "X is strictly less than 5."

4. Solve for x:

3x - 7 = 42

Adding 7 to both sides to isolate the variable:

3x = 49

Dividing both sides by 3 to solve for x:

x = 16.33 (rounded to two decimal places)

Final answer: x = 16.3

5. Find 32% of $542.50:

To find 32% of $542.50, we can use the formula:

percent * amount = part

where "percent" is the percentage expressed as a decimal, "amount" is the whole amount, and "part" is the result we're looking for.In this case, we have:

0.32 * $542.50 = part

Multiplying:

$173.60 = part

Final answer: $173.60

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

Therefore , the solution of the given problem of standard deviation comes out to be option C with n = 1,000 and p near to 1/2 is the right response.

Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.

Here,

The following algorithm determines the standard deviation of the sampling distribution of a sample proportion p:

=> √((p*(1-p))/n)

where n is the sample size, and p is the population percentage.

For the sampling distribution of a sample proportion p,

the pair of sample number n and population proportion p that would result in the highest standard deviation is:

=>n =1,000, and p is almost half.

Because p=1/2

yields the highest possible value of the expression (p*(1-p)), a bigger sample size will result in a smaller standard deviation.

The standard deviations will be lower for the other choices, which have smaller sample sizes or extreme values of p.

Therefore, (C) with n = 1,000 and p near to 1/2 is the right response.

To know more about standard deviation visit :-

brainly.com/question/13673183

#SPJ1

Answer: We are given that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

To find the probability of obtaining a reading between 0°C and 1.08°C, we need to calculate the z-scores for these values using the formula:

z = (x - mu) / sigma

where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.

For x = 0°C, we have:

z1 = (0 - 0) / 1.00 = 0

For x = 1.08°C, we have:

z2 = (1.08 - 0) / 1.00 = 1.08

Using a standard normal table or a calculator, we can find the probability of obtaining a z-score between 0 and 1.08.

Using a standard normal table or a calculator, we find that the probability of obtaining a z-score between 0 and 1.08 is 0.3583.

Therefore, the probability of obtaining a reading between 0°C and 1.08°C is 0.3583, rounded to 4 decimal places.

Step-by-step explanation:

The scale of the map in the question is 1 inch = 50 miles.

A scale in a map is a relation that tells us how many units each unit in the map represents. In this case, we know that the distance between two points A and B on the map is 5 inches, while the actual distance between these two places is 250 miles.

Then we start with the relation:

5 inches = 250 miles.

But to get the scale of the map we need to see how many miles one inch represents in the map, then we can divide both sides of the equation by 5 to geT:

5 in = 250 mi

1 in = 250mi/5

1 in = 50 mi

The scale of the map is 1 inch to 50 miles.

Learn more about maps and scales at:

https://brainly.com/question/105644

#SPJ1

The probability of obtaining a reading less than 0.35° C is approximately 35%.

Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.

The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.

To solve this problem, we must use the z-score formula to standardise the value:

[tex]$Z = \frac{x - \mu}{\sigma}[/tex]

Z = standard score

x = observed value

[tex]\mu[/tex] = mean of the sample

[tex]\sigma[/tex] = standard deviation of the sample

Here

x = 0.35° C

[tex]\mu[/tex] = 0° C

[tex]\sigma[/tex] = 1.00°C

Using the values on the formula:

[tex]$Z = \frac{0.35 - 0}{1}[/tex]

Z = 0.35

The probability of obtaining a reading less than 0.35° C is approximately 35%.

To know more about probability visit:

brainly.com/question/30719832

#SPJ1

Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

Tom's fortnightly income is $3000.

In mathematics, an average is a measure that represents the central or typical value of a set of numbers. There are several types of averages commonly used, including the mean, median, and mode.

To calculate Tom's fortnightly income, we need to divide his yearly salary by the number of fortnights in a year:

Fortnightly income = Yearly salary / Number of fortnights in a year

Fortnightly income = $78000 / 26 = $3000

Therefore, Tom's fortnightly income is $3000.

To know more about average and given link below -brainly.com/question/24057012

#SPJ4

question - Calculate the  Tom's fortnightly income and yearly salary by the number of fortnights in a year .

The standard normal areas are given as follows:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the second bullet point, the areas are given as follows:

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12

The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.

According to the intermediate value theorem,

since g(x) is a continuous function on the closed interval [1, 6]

since g(1) = 18 is greater than 12, and

g(6) = 11 is less than 12,

there must be at least one value c between 1 and 6 where g(c) = 12.

Therefore, we can conclude that a value of c does exist such that g(c) = 12.

Learn more about intermediate value theorem at:

https://brainly.com/question/30557318

#SPJ1

To sketch the phase plane and trajectories of both populations in the competing species model, plot the population of one species on the x-axis and the population of the other species on the y-axis. Then, plot the isoclines and use them to determine the direction and stability of the population trajectories.

The competing species model is a system of two differential equations that describe the population dynamics of two species competing for the same resources. To sketch the phase plane and trajectories, plot the population of one species on the x-axis and the population of the other species on the y-axis. Then, plot the isoclines, which are curves that represent the values of one species' population at which the other species' population does not change.

The isoclines are found by setting each differential equation to zero and solving for one population in terms of the other. For example, the isocline for species 1 is found by setting dN1/dt = 0 and solving for N2. The resulting equation gives the values of N2 at which the population of species 1 does not change. Plotting these curves on the phase plane divides it into regions where the population of each species increases or decreases.

The direction and stability of the population trajectories can be determined by analyzing the slope of the vector field, which represents the rate of change of the population at each point in the phase plane. Trajectories move in the direction of the vector field, and their stability depends on the curvature of the isoclines. If the isoclines intersect at a single point, it is a stable equilibrium where both populations coexist. If they intersect at multiple points, the stable equilibrium depends on the initial conditions of the populations. If they do not intersect, one species will eventually drive the other to extinction.

To know more on competing species model

https://brainly.com/question/15100592

#SPJ4

--The question is incomplete, answering to the question below--

"Consider the competing species model, how to sketch the phase plane and the trajectories of both population"

Answer: 6y + 6

Step-by-step explanation:

To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):

First, we simplify the expression within parentheses, working from the inside out:

6(-1/2+4) = 6(7/2) = 21

Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:

8(3/4y -2) = 6y - 16

Finally, we combine the simplified terms:

8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6

Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.

Answer:

A. To find the derivative of h(x), we can use the chain rule:

h(x) = a(-2x + 1)^5 - b

h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4

To find the second derivative, we can again use the chain rule:

h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3

B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.

C. To find the critical points, we need to find where h'(x) = 0:

h'(x) = -10a(-2x + 1)^4 = 0

-2x + 1 = 0

x = 1/2

Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.

Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

What is parabola?

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function.

Assuming you meant [tex]f(x) = -x^2 + 7[/tex], here's how you can graph the parabola using the parabola tool:

Find the vertex

The vertex of the parabola is located at the point (-b/2a, f(-b/2a)), where a is the coefficient of the [tex]x^2[/tex] term and b is the coefficient of the x term. In this case, a = -1 and b = 0, so the vertex is located at the point (0, 7).

Plot the vertex

Using the parabola tool, plot the vertex at the point (0, 7).

Plot a second point

To plot a second point, you can choose any x value and find the corresponding y value using the quadratic function. For example, if you choose x = 2, then [tex]f(2) = -2^2 + 7 = 3[/tex]. So the second point is located at (2, 3).

Therefore, Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

To learn more about parabola from the given link:

https://brainly.com/question/21685473

#SPJ1

Complete Question:

Use the parabola tool to graph the quadratic function.

f(x) = -√² +7

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Graph D of the given function has the smallest value for b.

As per name signifies, exponents are used in exponential functions. But take note that an exponential function does not have a constant as its base and a variable as its exponent. One of the following forms can be used for an exponential function.

f (x) = aˣ

y=f(x) >0

f(x)=abˣ , where a>0

So, f(x)=abˣ

When, b<1 f(x) decreases

When, b>1 f(x) increases and the larger the b the steeper the graph

So, graph of D is increasing and is steepest

So, graph D has the smallest value for b.

To know more about variable, visit

https://brainly.com/question/17344045

#SPJ1

The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

The shape of an equilateral triangle is an equilateral triangle.

The word "Equilateral" is formed by combining two words. H. "Equi" means equal, "lateral" means side.

Equilateral triangles are also called regular polygons or equilateral triangles because all sides are equal.

In geometry, an equilateral triangle is a triangle with all sides of equal length.

Three sides are equal, so three angles on the same side are equal. Therefore, it is also called an equilateral triangle with each angle of 60 degrees.

Like other types of triangles, equilateral triangles have formulas for area, perimeter, and height. 

According to our question-

AB=OA=BO= 9CM

ONQ-AOB/ONQ*100

PUTTING VALUES

60.3%

Hence, The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

learn more about equilateral triangle click here:

https://brainly.com/question/17264112

#SPJ1

Answer:

Step-by-step explanation:

To calculate the interest earned by Linda for the first year, we can use the formula:

A = P(1 + r/n)^(nt)

Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

For the first year, we have:

A = $50,000(1 + 0.06/1)^(1*1) = $53,000

So, the interest earned by Linda for the first year is:

Interest = $53,000 - $50,000 = $3,000

For the second year, we can use the same formula with t = 2:

A = $50,000(1 + 0.06/1)^(1*2) = $56,180

Interest = $56,180 - $53,000 = $3,180

For the third year, we can use the same formula with t = 3:

A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80

Interest = $59,468.80 - $56,180 = $3,288.80

Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:

Interest = Prt

Where P is the principal amount, r is the annual interest rate, and t is the time in years.

For the first year, we have:

Interest = $50,0000.061 = $3,000

For the second year, we have:

Interest = $50,0000.061 = $3,000

For the third year, we have:

Interest = $50,0000.061 = $3,000

As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:

Linda earns more.

Answer:

Linda earns $9550.8 interest and bob earns $9000 interest

Step-by-step explanation:

Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal

interest= 50,000(1+6/100)³

=59550.8 - 50000

Linda earns $9550.8 interest in 3 years.

bob takes simple interest: S.I = prt/100

interest = 50,000*6*3/100

Bob earns $9000 in 3 years.

thus, Linda earns more interest than bob.

The relative maximum of the function is (0, 4), and the relative minimum is (6, -152).

To find the relative extrema of the function f(x) = x^4 - 8x^3 + 4, we first take the derivative of the function:

f'(x) = 4x^3 - 24x^2

Then we set f'(x) = 0 to find the critical points:

4x^3 - 24x^2 = 0

4x^2(x - 6) = 0

This gives us two critical points: x = 0 and x = 6.

Next, we find the second derivative of f(x):

f''(x) = 12x^2 - 48x

We can use the Second-Derivative Test to determine the nature of the critical points.

For x = 0, we have:

f''(0) = 0 - 0 = 0

This tells us that the Second-Derivative Test is inconclusive at x = 0.

For x = 6, we have:

f''(6) = 12(6)^2 - 48(6) = 0

Since the second derivative is zero at x = 6, we cannot use the Second-Derivative Test to determine the nature of the critical point at x = 6.

To determine whether the critical points are relative maxima or minima, we can use the first derivative test or examine the behavior of the function around the critical points.

For x < 0, f'(x) < 0, so the function is decreasing.

For 0 < x < 6, f'(x) > 0, so the function is increasing.

For x > 6, f'(x) < 0, so the function is decreasing.

Therefore, we can conclude that the critical point at x = 0 is a relative maximum and the critical point at x = 6 is a relative minimum.

To know more about relative maxima and minima:

https://brainly.com/question/6422517

#SPJ4

(a) The function x as a function of t is t = 250ln(499x/998)

(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.

(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate

dt/dx = kx(N−x)

dt/(N-x) = kx dx

Integrating both sides, we get

t = -1/k × ln(N-x) - 1/k × ln(x) + C

where C is the constant of integration.

To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:

0 = -1/k * ln(N-2) - 1/k * ln(2) + C

C = 1/k * ln(N-2) + 1/k * ln(2)

Substituting C back into the equation, we get:

t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)

Simplifying, we get

t = 1/k * [ln((N-2)x/(2(N-x)))]

Substituting k=1/250 and N=1000, we get:

t = 250ln(499x/998)

(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get

t = 250ln(499(500)/998) = 250ln(249/499)

t ≈ 109.86

Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.

Learn more about differential equation here

brainly.com/question/29199325

#SPJ4

The Sunday game brought in $2232.50, while the Thursday game brought in $1832.00.

A company's income, costs, and profit are compiled in a profit and loss (P&L) statement, a financial report. It provides information to investors and other interested parties about a company's operations and financial viability.

The issue informs us that the combined revenue from the two games was $4064.50.

S + (S - 400.50) = 4064.50

Simplifying the left side, we get:

2S - 400.50 = 4064.50

Adding 400.50 to both sides, we get:

2S = 4465

Dividing both sides by 2, we get:

S = 2232.50

So the Sunday game generated $2232.50, and the Thursday game generated $2232.50 - $400.50 = $1832.00.

To know more about brought visit:-

https://brainly.com/question/28646782

#SPJ1

Accοrding tο the half-life fοrmula, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.

Expοnential decay is a mathematical prοcess in which a quantity decreases οver time in a manner prοpοrtiοnal tο its current value. This means that the rate οf decay is prοpοrtiοnal tο the amοunt οf the substance remaining, and as the amοunt οf the substance decreases, the rate οf decay alsο decreases. The fοrmula fοr expοnential decay is οften written as:

N(t) = N₀ *[tex]e^{(-kt)[/tex]

where N(t) is the amοunt οf substance remaining at time t, N₀ is the initial amοunt οf the substance, k is the decay cοnstant, and e is the base οf the natural lοgarithm.

The half-life οf radium is apprοximately 1590 years, which means that after 1590 years, half οf the οriginal radium will have decayed. Therefοre, we can use the half-life fοrmula tο find the amοunt οf time it wοuld take fοr 1/7 οf the radium tο decay:

N = N₀[tex]* (1/2)^{(t/t1/2)[/tex]

where N is the final amοunt (1/7 οf the οriginal amοunt), N0 is the initial amοunt, t is the time elapsed, and t1/2 is the half-life.

We can rearrange this fοrmula tο sοlve fοr t:

t = t1/2 * lοg2(N₀/N)

t = 1590 years * lοg2(7)

t ≈ 4975 years

Therefοre, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.

To know more about exponential Decay visit:

brainly.com/question/2193799

#SPJ1

If we round up, we get x = 12, which means that 12 students took history and 36 students took mathematics.

A Venn diagram is a graphical representation of sets, often used to show relationships between different sets of data. It consists of one or more circles, where each circle represents a set. The circles are usually overlapping to show the relationships between the sets. The region where the circles overlap represents the elements that belong to both sets. The non-overlapping parts of each circle represent the elements that belong to only one of the sets.

Here,

A. To illustrate the data on a Venn diagram, we need to draw two overlapping circles, one for history and one for mathematics. We can label the regions as follows:

The region where the circles overlap represents the students who took both history and mathematics.

The region outside both circles represents the students who did not take either history or mathematics.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history.

In this diagram, let's assume that x students took history and 3x students took mathematics. Then the total number of students who took the examination is x + 3x = 4x. We can label the regions on the diagram accordingly:

The region where the circles overlap represents the students who took both history and mathematics. Since there are 3x students who took mathematics, and all of them are included in the overlap region, the number of students who took both is 3x.

The region outside both circles represents the students who did not take either history or mathematics. Since there are 46 students in total, and 4x of them took the examination, the number of students who did not take either is 46 - 4x.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics. Since x students took history, and 3x took mathematics, the number of students who took history but not mathematics is x - 3x = -2x. However, since we cannot have a negative number of students, we can assume that this region is empty.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history. Since there are 3x students who took mathematics, and some of them also took history, the number of students who took mathematics but not history is 3x - 3x = 0. Therefore, this region is also empty.

B. We know that the total number of students who took the examination is 46. Therefore, we have:

x + 3x = 46

4x = 46

x = 11.5

However, since x represents the number of students who took history, it must be a whole number. Therefore, we can round x up or down to the nearest whole number. If we round down, we get x = 11, which means that 11 students took history and 33 students took mathematics.

To know more about venn diagram,

https://brainly.com/question/29301560

#SPJ1

The difference in length between the two pieces of scrap wood is 7/8 inches.

To get the difference we just need to take the difference between the two lenghs.

Remember that we only have pieces of scraph wood if we have an "x" over the correspondent value in the line diagram.

By looking at it we can see that the longest pice measures 5 inches, while the shortest one (there are two of these) measure (4 + 1/8) inches.

The difference is:

5 - (4 + 1/8) = 7/8

The longest piece is 7/8 inches longer.

Learn more about differences at:

https://brainly.com/question/17695139

#SPJ1

Answer:

Step-by-step explanation:

2

Probability that precisely 5 people will respond that they would feel comfortable is 0.0808

Probability that more than 5 people will respond that they would feel comfortable is0.1061

Probability that at most 5 people will respond that they would feel comfortable is 0.9747

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence.

35 percent of households claim that having $50,000 in savings would make them feel comfortable. Ask 8 homes that were chosen at random if they would feel comfortable if they had $50,000 in savings.

Binomial conundrum with p(secure) = 0.35 and n = 8.

the likelihood that the number of people who claim they would feel comfortable is

(a) The number exactly five is equal to ⁸C₅ (0.35)5×(0.65)×3=binompdf(8,0.35,5) = 0.0808.

(b) more than five = 1 - binomcdf(8,0.35,4) = 0.1061

(c) at most five = binomcdf(8,0.35,5) = 0.9747.

to know more about  forecast, visit:

https://brainly.com/question/28839529

#SPJ1

Answer: $2,162.06

Step-by-step explanation:

To calculate the total monthly payment to the bank, we need to add up the monthly mortgage payment, the monthly portion of the semi-annual property tax bill, and the monthly portion of the annual homeowner's insurance bill.

First, we need to find the monthly portion of the semi-annual property tax bill. To do this, we divide the semi-annual property tax bill by 6 (since there are 6 months in half a year):

Monthly property tax payment = Semi-annual property tax bill / 6

Monthly property tax payment = $3,239 / 6

Monthly property tax payment = $539.83

Next, we need to find the monthly portion of the annual homeowner's insurance bill. To do this, we divide the annual homeowner's insurance bill by 12 (since there are 12 months in a year):

Monthly homeowner's insurance payment = Annual homeowner's insurance bill / 12

Monthly homeowner's insurance payment = $980 / 12

Monthly homeowner's insurance payment = $81.67

Now we can add up the monthly mortgage payment, the monthly property tax payment, and the monthly homeowner's insurance payment to find the total monthly payment to the bank:

Total monthly payment = Monthly mortgage payment + Monthly property tax payment + Monthly homeowner's insurance payment

Total monthly payment = $1,711.22 + $539.83 + $81.67

Total monthly payment = $2,332.72

Therefore, the Dotkoms pay the bank $2,332.72 each month.

Answer:

Step-by-step explanation:

Using proportions, it is found that they pay the bank $2332.72 each month.

What is a proportion?

A proportion is a fraction of a total amount.

Using proportions, it is found that they pay the bank $2332.72 each month.

What is a proportion?

A proportion is a fraction of a total amount.

Their payments are given by:

Monthly mortgage of $1,711.22.

Semi-annual property tax bill is $3,239, that is, it is paid every 6 months, hence 3239/6 = $539.83.

Answer:

Step-by-step explanation:

To find the current price index number using the 1975 price of 56.7 cents as the reference value, we can use the formula:

Price Index = (Current Price / Base Price) x 100

Where "Current Price" is the current cost of gasoline, and "Base Price" is the 1975 price of 56.7 cents.

Substituting the values given in the problem, we get:

Price Index = ($2.93 / $0.567) x 100

Price Index = 516.899

Therefore, the current price index number, using the 1975 price of 56.7 cents as the reference value, is 516.899.