In the statements below, r and s represent integers. Is each statement always, sometimes, or never true? Explain.

a. A root of the equation 3x³ +rx²+s x+8=0 could be 5 .

Answer:

its x=24 hrhdjdjdndjrirjrjdjdhd

There are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom by permutation.

Permutation is the arrangement of objects when the order of arrangement matters.

Here the arrangement is done in 3! ways.

The formula used is

nPr= n!/(n-r)!

Here n=3, r=3

Therefore 3P3= 3!/ (3-3)!= 3!/ 0! =3!= 6 ways( since 0!=1 )

Alternatively,

When selecting a cone, there are six distinct possibilities if it matters which flavor is on top, which is in the middle, and which is on the bottom.

There are three options for the flavor that will be on top, followed by two options for the middle flavor, and then the remaining flavor for the bottom cone.

This gives you 3*2*1=6 possible cone arrangements.

Suppose we have three flavors: vanilla, chocolate, and strawberry.

If it is important which flavor is on top, which is in the middle, and which is on the bottom, there are only six distinct options that can be chosen for the cone. The six choices are:

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

v a n i l l a, s t r a w b e r r y, c h o c o l a t e

s t r a w b e r r y, c h o c o l a t e, v a n i l l a

s t r a w b e r r y, v a n i l l a, c h o c o l a t e

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

c h o c o l a t e, s t r a w b e r r y, vanilla

Therefore, there are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom.

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Answer:

A

Step-by-step explanation:

nsjsnsnsjsbsbjsbshshsbsjusbbbsjsj

A model that uses a system of symbols to represent a problem is called mathematical. Therefore, the correct option is (a) mathematical.

Mathematical modeling is a process of representing real-world systems or problems using mathematical language, symbols, and equations. It involves identifying the relevant variables, relationships, and constraints of a system and translating them into a mathematical form that can be manipulated and analyzed to gain insights and make predictions.

In a mathematical model, symbols are used to represent various components and parameters of the system, such as variables, constants, operators, and functions. These symbols can be combined and manipulated according to mathematical rules and principles to generate equations and formulas that describe the behavior of the system.

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Answer:

119 r 9

Step-by-step explanation:

Answer:

0$ or 3$

Step-by-step explanation:

If you are saying right now, then the answer would be zero. But, when we start, we can make and equation. Let's use J as John, A as Allen, and F and Frank. They all have n amount of money. Now, we work backwards: If A didn't give F 2$, then F now has n-2 and A has n+2. If J didn't give A 5$, then J would have n+5 and A would have n+2-5=n-3. The difference between those two is 8. Therefore, John has 8$ more.

Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

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Answer:

The last part.

Step-by-step explanation:

The error is only at the last part. Basically the answer part.

The answer should be —

\(13 \sqrt{5} \)

We don't multiply the square roots when adding or subtracting. That'd contradict the rules.

Here, we let the square root of five as x-term.

\( \sqrt{5} = x\)

\(4 \sqrt{5} + 9 \sqrt{5} = 4x + 9x\)

As we add up, we would get 13x. Thrn we convert x-term back to square root of five.

The answer would be —

\(13x \\ x = \sqrt{5} \\ 13 \sqrt{5} \)

Remember that we don't multiply the square roots when adding or subtracting.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

a times 12=300

Step-by-step explanation:

donated each month a should be 25. $25 times 12 equals 300

Answer:

C.  

a × 12 = 300

Step-by-step explanation:

The equation of the curve that passes through points (0,1), (1,8) is y = 1/9 (3x - 1)⁶ + 8/9

multiply dx on both sides, To shift it over. By doing this, we get

dy = 2 (kx - 1)⁵dx

Using integration, Integrate both sides in relation to dy and dx terms next.

dy = 2 (kx - 1)⁵dx

∫ dy = ∫ 2 (kx - 1)⁵dx

y = 2 ∫  (kx - 1)⁵dx

Here, a u-substitution is possible. Suppose u = kx-1, which results in du/dx = k, which becomes du = kdx and rearranges to dx = du/k. Consequently, the subsequent steps can look like, y = 2 ∫  (kx - 1)⁵dx

y = 2 ∫ u⁵ × du/k

y = 2/k ∫ u⁵ × du

y = 2/k ( 1/ 5 +1  u⁵⁺¹ + C )

y = 2/k ( 1/ 6 u⁶+ C )

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

Let's enter (x,y) = (0,1) and use a little algebra to find C. On the right, we'll see an equation in terms of k.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

1 = 2/k ( 1/ 6 (k × 0 - 1)⁶ + C )

1 = 2/k ( 1/ 6 + C )

k = 2 ( 1/ 6 + C )

k = 1/3 + 2C

3k = 1 + 6C

6C = 3k - 1

C = (3k - 1) / 6

Let's now insert that C value along with (x,y) = (1,8). After that, calculate k to obtain a precise number.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

8 = 2/k  ( 1/ 6 (k × 1 - 1)⁶ + ( 3k - 1 )/6 )

Find the root of the function using a graphing calculator. The x intercept is 3 and k is the input x. This would get you,  C = (3k - 1) / 6

C = (3 × 3 - 1) / 6

C = 8/6

C = 4/3

Therefore, y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

y = 2/3 ( 1/ 6 (3x - 1)⁶ + 4/3 )

y = 1/9 (3x - 1) ⁶ + 8/9 , hence the final equation.

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The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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Josh will pay a loan origination fee of $2,100 if the lender charges a fee of 0.75%.

To calculate the loan origination fee, we need to multiply the loan amount by the lender's fee percentage.

Loan origination fee = Loan amount x Lender's fee percentage

In this case, the loan amount is $280,000 and the lender's fee percentage is 0.75%.

Loan origination fee = $280,000 x 0.0075

Loan origination fee = $2,100

Therefore, Josh will have to pay a loan origination fee of $2,100.

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Answer:

ummmm j?:)

Step-by-step explanation:

(i) Rational numbers - A number which can be expressed as fraction, ratio or percentage is called as rational number

(ii)Irrational numbers - A number which is not rational, (i.e) cannot be expressed as a ratio or percentage is called as irrational number.

Since there are no common numbers in rational and irrational, they cannot be expressed as "G" option.

Real numbers are formed by the union of rational and irrational numbers.

Given a function \(\(f(x)\)\) as shown in the figure and another function

\(\(A(x)=\int_{n}^{x} f(t) d t\)\)We need to find: A local minimum of function

\(\(A(x)\) on \((0,6)\)\)The local maximum of function\(\(A(x)\) on \((0,6)\\))We need to find the derivative of the function \(A(x)\) to find the local minimum and local maximum on the interval\(\((0,6)\).\)

So,\(\(A(x)=\int_{n}^{x} f(t) d t\)\)Differentiating both sides with respect to

\(\(x\) \[\frac{d}{dx}(A(x))\)

=\(\frac{d}{dx}\left(\int_{n}^{x} f(t) d t\right)\\)]Applying the fundamental theorem of calculus

\(\[\frac{d}{dx}(A(x))\)

\(=f(x)\]\)So, we have

\(\[A'(x)=f(x)\]\)To find the local minimum and local maximum of the function, we need to check for the critical points on the interval\(\((0,6)\)\)Let's find the critical points:\(\(A'(x)=f(x)\)\)Critical points are obtained when

\(\(A'(x)=f(x)\)

\(=0\)\)

On the interval\(\((0,6)\)\), we can see that the function has two critical points; one at \(\(x=1\)\)and the other at

\(\(x=3\)\)Note that

\(\(f(x)=0\)\) at

\(\(x=1\)\)and

\(\(x=3\)\)From the given figure we can see that the graph is negative between

\(\(x=0\)\) to

\(\(x=1\)\), positive between

\(\(x=1\)\) to

\(\(x=3\)\) and negative between

\(\(x=3\)\) to

\(\(x=6\)\)Since the function changes its sign at the critical points, we can say that \(\(x=1\)\) is a local minimum and

\(\(x=3\)\) is a local maximum of the function\(\(A(x)\)\) on the interval

\(\((0,6)\)\)Therefore, the local minimum of the function on\(\((0,6)\)\) is at \(\(x=1\)\)The local maximum of the function on\(\((0,6)\)\) is at

\(\(x=3\).\)

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

4, 1, 2, 3

Step-by-step explanation:

let x = cost of 1 bar

cost of 75 bars = $65

cost of one bar => 75/75 = $65/75

x = $0.87

Answer:

4.  c = $0.97 rounded to the nearest hundredth

1.  Let c = cost of one bar

\(\textsf{2.} \quad 75c=\$65\)

\(\textsf{3.} \quad \dfrac{75}{75}c=\dfrac{\$65}{75}\)

Step-by-step explanation:

Step 1

Define the variable:

Step 2

Given that one box of 75 Toblerone chocolate bars costs $65:

Step 3

To find the cost of one Toblerone chocolate bar, divide both sides of the equation by 75:

Step 4

Simplify both sides of the equation and round the solution to the nearest hundredth:

Answer:

x= 1

Step-by-step explanation:

The value of y = -5x

Plug it in the equation of y + 4x = -1

So it becomes, -5x + 4x = -1

Combine like terms which are -5x and 4x which equals to -x

Eliminate the negative sign because x cannot be negative. Apply that to -1. It becomes 1.

Hope you find this helpful!

Answer:

Step-by-step explanation:

Equation 1: y = -5x

Equation 2: y + 4x = -1

Step 1. Substitute y in equation 2 using equation 1

You would get, -5x + 4x = -1

Step 2. Combine like terms

-x = -1

Step 3. Cross out the negatives

x = 1

Step 4. Substitute x in Equation 1 to get y

y = -5(1)

y = -5

Hope this helps :)

Have a great day!

Answer:

Point I and Point II may not need to be main points.

Ann's main points are not balanced.

Parallel structure will not work with Ann's speech topic.

Step-by-step explanation:

This division indicates that Ann prioritized Point III above Points I and II. Point III was allocated the most of Ann's time (75%), while Point I and II were each given 10% and 15%, respectively. This is a sign that Ann placed a higher priority on Point III.

In terms of the actual percentages, this could indicate a variety of things. It could mean that Ann felt Point III was more important than the other two points, or that Point III took more time to complete than the other two points. It could also mean that Ann was trying to achieve a specific ratio of her time dedicated to each point.
Regardless of the reasoning, this division of Ann's time shows that she placed a higher priority on Point III. This could mean that Point III was more important to her overall goal than the other two points, or that Point III required a larger amount of her time.

By understanding this division of Ann's time, we can gain insight into what she felt was important, and how she chose to prioritize her time. This can be used to better understand Ann's thought process and her overall goal.

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Answer:

An apple costs £0.25

A banana costs £0.34

Step-by-step explanation:

Let a be apples and b be bananas.

10a+5b=4.2

8a+10b=5.4

Solve for a:

10a+5b=4.2

Subtract 5b from both sides

10a=4.2-5b

Subtract 4.2 from both sides

10a-4.2= -5b

Multiply both sides by -1

-10a+4.2=5b

8a+10b=5.4

Subtract 10b from both sides

8a=5.4-10b

Subtract 5.4 from both sides

8a-5.4= -10b

Multiply both sides by -1

-8a+5.4= 10b

Divide both sides by 2

-4a+2.7=5b

Combine equations:

-4a+2.7= -10a+4.2

Add 10a to both sides

6a+2.7=4.2

Subtract 2.7 from both sides

6a=1.5

Divide both sides by 6

a=0.25

An apple costs £0.25

Solve for b:

10a+5b=4.2

Subtract 10a from both sides

5b= -10a+4.2

Subtract 4.2 from both sides

5b-4.2= -10a

Multiply both sides by -1

-5b+4.2=10a

8a+10b=5.4

Subtract 8a from both sides

10b= -8a+5.4

Subtract 5.4 from both sides

10b-5.4= -8a

Divide both sides by 4

2.5b-1.35= -2a

Multiply both sides by 5

12.5b-6.75= -10a

Multiply both sides by -1

-12.5b+6.75=10a

Combine equations:

-12.5b+6.75= -5b+4.2

Add 12.5b to both sides

6.75=7.5b+4.2

Subtract 4.2 from both sides

2.55=7.5b

7.5b=2.55

Divide both sides by 7.5

b=0.34

A banana costs £0.34

If you would like to check and see if it is true, (I already checked, it is) you can use the formulas I gave at the start of the explanation.

10a+5b=4.2

8a+10b=5.4

a=0.25

b=0.34

The answer is: A) The data support the researchers' belief that night owls have better dream recall than early birds. B) we can be 92% confident that the true difference in mean number of dreams recalled per week between night owls and early birds is between 1.87 and 2.63.

A) These are the alternative and null hypotheses:

H0: μE = μN (the mean number of dreams recalled each week is the same for early birds and night owls) (the mean number of dreams recalled per week is the same for early birds and night owls)

Ha: μE < μN (the mean number of dreams recalled each week is smaller for early birds than for night owls) (the mean number of dreams recalled per week is lower for early birds than for night owls)

Using the following formula, we can run a two-sample t-test with unequal variances:

t = [(sN2 / nN) + (sE2 / nE)] / sqrt[(xN - xE)]

where nN and nE are the sample sizes for night owls and early birds, respectively, and xN and sN and xE and sE are the sample means and standard deviations for night owls and early birds, respectively.

When we enter the values, we obtain:

t = (9.55 - 7.26) / sqrt[(5.88^2 / 100) + (6.94^2 / 100)] = 5.01

The data are consistent with the researchers' hypothesis that night owls are more capable of remembering their dreams than early birds.

B) We can use the following formula to determine the confidence interval:

CI is equal to (xN - xE) t/2 * sqrt[(sN / nN) + (sE / nE)].

where t/2 is the t-value for the required level of confidence and degrees of freedom, and xN, xE, sN, sE, nN, and nE are the same as previously (198 in this case).

With a t-value of 1.75 and a 92% confidence level (from a t-distribution with 198 degrees of freedom), we get:

CI is equal to (9.55 - 7.26) 1.75 * sqrt[(5.88 - + 6.94 / 100)] = (1.87, 2.63) (1.87, 2.63)

The genuine difference between night owls and early birds in terms of the average number of dreams recalled per week is therefore between 1.87 and 2.63, with a 92% confidence interval.

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Answer:

2/5, 0.85, 1 3/4, 22/7

Step-by-step explanation:

Lets change all of these to decimals so we can compare them.

2/5 = 4/10 = 0.4 = 0.40

0.85 is already ready to go.

1 3/4 = 1.75

22/7 = 3.142857...

So from smallest to biggest

.40, .85, 1.75, 3.14

Which are in their original form:

2/5, 0.85, 1 3/4, 22/7

Answer:

Step-by-step explanation: okay each hour she makes 120 cookies right then 2 hours would be 240 and three hours would be 360 and 4 would be 480 and 5 would be 600 hundred

The double integral of the given equation is 101.3π/4.

What is meant by integral?

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

The integrals of a function in two variables over a region in R², or the real number plane, are referred to as double integrals in mathematics.

The surface area of a 2D figure can be determined primarily using the double integral, which is indicated by the symbol "∫∫". By using double integration, we may quickly determine the area of a rectangular region. Double integration challenges will be easier to address if we are familiar with simple integration.

We are asked to find the double integral of

\(\int\int\limits_r \frac{4(1+x^2)}{1+y^2} dA,\),  where region r = {(x, y) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 1}

dA = dx.dy

We can then rewrite the equation as

\(\int\limits^4_0\int\limits^1_0 \frac{4(1+x^2)}{1+y^2} dydx\) = \(\int\limits^4_04(1+x^2)dx \ .\int\limits^1_0 \frac{1}{1+y^2} dy\)

For the first part,

\(\int\limits^4_04(1+x^2)dx = 4\int\limits^4_0(1+x^2)dx = 4[ x + x^3/3]\limits^4_0\)

                                                = 4 [ 4 + 4³/3] - 4[ 0] = 101.3

For the second part,

\(\int\limits^1_0 \frac{1}{1+y^2} dy\)

Take y = tan u

then dy = sec²(u) du

 Then the above equation becomes,

\(\int\limits^1_0 \frac{1}{1+tan^2(u)}. sec^2(u) du = \int\limits^1_0 \frac{1}{sec^2(u)}. sec^2(u) du\)  

                               = \(\int\limits^1_0 (1.du) = [u]^1_0\)

We know x = tan u

so u = tan⁻¹ x

Then the equation becomes

[tan⁻¹ x]¹₀ = [ tan⁻¹ 1 - tan⁻¹ 0] = π/4 - 0 = π/4

Therefore the double integral of the given equation is 101.3π/4.

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The sum of the values of f(x) is 3025.

The given function is \(f(x) = x^3\) over the integers 1, 2, 3,...10.

We have to find the sum of the values of f(x).

We are given the function as \(f(x) = x^3\) over the integers from 1 to 10.

Since the function is a polynomial function, the sum of its values can be calculated by finding the sum of its coefficients.

The sum of coefficients is nothing but the sum of the values of the function.

The sum of the values of f(x) is calculated as: f\((1) + f(2) + f(3) + .... + f(10)\\f(1) = 1^3 = 1\\f(2) = 2^3 = 8\\f(3) = 3^3 = 27\)

Similarly, \(f(4) = 4^3 = 64\\f(5) = 5^3 = 125\\f(6) = 6^3 = 216\\f(7) = 7^3= 343\\f(8) = 8^3 = 512\\f(9) = 9^3 = 729\\f(10) = 10^3 = 1000\)

Therefore, the sum of the values of \(f(x) = f(1) + f(2) + f(3) + .... + f(10) \\= 1 + 8 + 27 + 64 + 125 + 216 + 343 + 512 + 729 + 1000 \\= 3025\)

Therefore, the sum of the values of f(x) is 3025.

Note: It is important to remember that the sum of the values of a polynomial function over the integers can be found by adding up the coefficients.

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Answer:

Your range is A since that is the Y column

Step-by-step explanation: