Write the equation of a cubic polynomial in standard form with root at 1 and double root at -5, passing through the point (3,32).

Answer:

Step-by-step explanation:

The x component of a function is domain and the y component is range of a function . For example -                                                                                                   R1={(3,4),(5,6),(7,9)}                                                                                                                  The domain of R1 ={3,5,7}                                                                                                                                                                                                                                     The range of R1={4,6,9}

The angle of inclination to the nearest degree is 13°.

The angle of inclination is the angle between the ramp and the ground, and we can use trigonometry to find this angle. Specifically, we can use the inverse tangent function to find the angle whose tangent is the ratio of the height to the base of the ramp.

The tangent of the angle of inclination is the ratio of the rise (height) to the run (length) of the ramp. In this case, the rise is 0.9 m and the run is 4.1 m, so the tangent of the angle of inclination is:

tan θ = 0.9/4.1

We can use a calculator to find the inverse tangent of this ratio:

θ = tan⁻¹(0.9/4.1) ≈ 12.75°

Therefore, the angle of inclination to the nearest degree is 13°.

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Harper would have $8,817 in her account.

To find out how much money Harper would have in her account when Alyssa's money has tripled in value.

We need to calculate the future value of Alyssa's investment and then find the corresponding value for Harper's investment.

The formula for calculating the future value with compound interest is:

Future Value = Principal * (1 + \((interest \hspace{1mm} rate / number of \hspace{1mm} compounding \hspace{1mm} periods))^{(number \hspace{1mm} of compounding \hspace{1mm} periods \times time)}\)

In this case, Alyssa's principal is $5,700, the interest rate is 5 1/4% (or 5.25% as a decimal), and the compounding is daily.

The time it takes for Alyssa's investment to triple in value is not given, so we'll need to determine it.

Let's assume it takes t years for Alyssa's investment to triple. We can use the formula for compound interest to find the value of t:

$\(5,700 * (1 + 0.0525/365)^{(365t)}\) = $5,700 * 3

Simplifying the equation, we have:

\((1 + 0.0525/365)^{(365t)} = 3\)

Take the natural logarithm of both sides:

\(ln[(1 + 0.0525/365)^{(365t)}] = ln(3)\)

365t * ln(1 + 0.0525/365) = ln(3)

Solve for t:

t = ln(3) / (365 * ln(1 + 0.0525/365))

Using a calculator, we find that t is approximately 7.587 years.

Now we can calculate the future value of Alyssa's investment:

Future Value of Alyssa's Investment = $\(5,700 * (1 + 0.0525/365)^{(365 * 7.587)}\)

To find out how much money Harper would have in her account when Alyssa's money has tripled, we need to calculate the future value of Harper's investment with continuous compounding.

The formula for continuous compound interest is:

Future Value = \(Principal * e^{(interest rate\hspace {1mm} \times time)}\)

In this case, Harper's principal is also $5,700, and the interest rate is 5 3/4% (or 5.75% as a decimal). The time will be the same as it took for Alyssa's investment to triple, which is approximately 7.587 years.

Future Value of Harper's Investment =\($5,700 * e^(0.0575 * 7.587)\)

Using a calculator, we can calculate the approximate future value of Harper's investment.

Calculating the expression $\(5,700 * e^{(0.0575 * 7.587)},\) we get:

$\(5,700 * e^{(0.4372375)}\) ≈ $5,700 * 1.548366 ≈ $8,817

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Answer:

um hi?

Step-by-step explanation:

Answer:

x = ± 2/3

Step-by-step explanation:

9x^2 = 4

Divide each side by 9

9/9x^2 = 4/9

x^2 = 4/9

Take the square root of each side

x = ±sqrt(4/9)

x = ± 2/3

9x^2=4

/9       /9

x^2=4/9

sqrt both sides

x=+/-\(\sqrt{4/9}\)

x=+/-(\(\frac{\sqrt{4} }{\sqrt{9} }\))

x=+/-2/3

Answer:

x=2/3, x=-2/3

The answer of the given question is inferential statistics.

The mathematical procedures used to assume or understand predictions about the whole population, based on the data collected from a random sample selected from the population, are called inferential statistics.

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The mathematical procedures used to assume or understand predictions about the whole population based on data collected from a random sample selected from the population are called statistical inference techniques.

Statistical inference involves drawing conclusions, making predictions, and testing hypotheses about population parameters based on sample data. These techniques include methods such as estimation, hypothesis testing, confidence intervals, and regression analysis.

By using statistical inference, we can generalize findings from the sample to make inferences about the larger population, allowing us to make informed decisions and draw meaningful conclusions based on the available data.

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Answer:

We know that at 6:00 they are 180 degrees from each other. Every minute, the hour hand moves 1/2 of a degree, and the minute hand moves 6 degrees. So in 48 minutes, the hour hand moves 24 degrees and the minute hand moves 288 degrees. 288-180-24=84. So, 84 degrees.

Answer : A=abs((30*6) - (5.5*48)), solve for A A = 84 Degrees.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2000 * .125/12 = $20.83

at $100 remaining balance = $1920.81

at $75 remaining balance   = $1945.81

Answer:

Hello! answer: 250

Step-by-step explanation:

10 × 5 = 50

10 × 5 = 50

10 × 5 = 50

10 × 5 = 50

5 × 5 = 25

5 × 5 = 25

50 × 4 = 200

200 + 25 + 25 = 250 the total surface area is 250 hope that helps!

answer:

52

explanation:

52 is the highest shared factor of the two numbers.

52*5=260

52*7=364

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Answer:

The two cones are aligned on edge to edge so that the total volume of the hourglass becomes 2∗13πr2h

Step-by-step explanation:

a) When the sand has y units left in the upper cone the height of the cone becomes y, the radius remains 1cm.Now let's take the right triangle In the upper coneAnd by similar triangles property we found that the radius of the cone in which the amount of sand is left is y3 unitsNow the volume of the sand in the remaining part of the upper cone isπy32y which gives πy327Now if we apply the same similar triangle property with the cone in the below we find that the radius of the part it has filled up remains the same as y3unitsSo the volume it has filled is (3-y) from the top cone which says that the volume filled on the bottom cone has a height of (3-y)So therefore the volume of the frustum which it has filled up isπ3h(R2+r2+rR) {Is the volume of the frustum with two radii r and R with a height h}i.eπ3(3−y)(12+(y/3)2+(y/3))So now the total volume of the hourglass in terms of y is π3(3−y)(12+(y/3)2+(y/3))+πy327b) The next question tells us that when the height of the sand in the below cone reaches up a height of h centimetreswhich is exactly 3-y in the previous questionso substituting y = h-3 in the previous question we'll find the volume of the hourglass in terms of hπ(h−3)327+π3(6−h)(12+((h−3)/3)2+((h−3)/3)) .c) Total volume of the hourglass isV=V1+V2⇒3π4=πy327+π−π27(3−h)3Putting h=1We have the value of y as⇒3π4=π27y3+π+π278..............(1)⇒y=(54)13Differentiating the first equation with respect to t we have0=π9y2dydt+π9(3−h)2dhdtPutting values that dydt=−0.14inches/sec at h =1 and for ⇒y=(54)13We have0=π9(54)132∗(−0.14)+π922dhdt⇒0.1956π9=4π9dhdt⇒dhdt=0.19564⇒dhdt=0.0489

Answer: b. Simon should chose option a. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

Statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The probability that the sum of the rolls is a prime number:

P(sum is prime) = 15/36 =0.416

Expected number of points = 0.416×15 =6.25

Probability that f the sum of the rolls is a multiple of 3,

P(sum of rolls is multiple of 3) = 12/36 = 0.33

Expected number of points = 0.33×12 = 3.96

Thus, statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

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Answer:

y = x + 22

Graph is also attached

Step-by-step explanation:

slope-intercept form: y = mx + b

2y - 2x = 44

    + 2x   + 2x

2y = 2x + 44

\(\frac{2y}{2}=\frac{2x+44}{2}\)

y = x + 22

Hope this helps!

Answer:

15/8

Hope it helps

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Thank you

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Two vectors in ℝ⁴ are orthogonal if their dot product is zero.

Two vectors in ℝ⁴ are said to be orthogonal if their dot product is zero. The dot product of two vectors measures the similarity or alignment between them. When the dot product is zero, it signifies that the vectors are perpendicular to each other and do not share any common direction.

Geometrically, orthogonality between two vectors in ℝ⁴ means that they are linearly independent and span different directions in four-dimensional space. It implies that there is no projection of one vector onto the other, and they are completely perpendicular to each other.

The concept of orthogonality is fundamental in many areas of mathematics, physics, and engineering. In linear algebra, orthogonal vectors play a crucial role in defining orthogonal bases and orthogonal projections. They also have applications in vector calculus, where they are used to define gradients and normal vectors. In physics, orthogonal vectors are relevant in studying forces, velocities, and geometric transformations. Overall, understanding orthogonality is essential for analyzing vector relationships and geometric properties in multi-dimensional spaces.

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The factored form of a quadratic function is  (x + a)(x+ b).

In math the term quadratic function is defined as a polynomial function of degree 2.

Here we have to find the process to convert the quadratic equation into the factored form.

As per the definition of quadratic equation, we all know that the standard form of the quadratic equation s written as,

=> y = ax² + bx + c

As we all know that factorization of quadratic equations can be done using different methods such as splitting the middle term or by using the quadratic formula or by completing the squares, etc.

Here we spilt the middle term then the expression is written as,

=> (x + a) (x + b)

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The first digit must be 1. The remaining seven ones must be either 0 or 1.

Therefore, there can be formed \(2^7=128\) different numbers.

DM is congruent to line CM because CDM is congruent to triangle CBM using the SAS congruence criteria for triangles.

Draw a diagram of the rectangle ABCD with M as the midpoint of AB. Draw lines CM and DM ( refer to the attached image). Since AB is a line segment, we know that AM is congruent to MB (because M is the midpoint of AB). Since ABCD is a rectangle, we know that AB is parallel to CD, and AD is parallel to BC. Thus, we have two pairs of parallel lines: AB and CD, and AD and BC.

Using the fact that opposite sides of a rectangle are congruent, we have CD = AB. Now, we have a pair of congruent sides (DM and CM) that are opposite each other in triangle CDM and CBM respectively. We also have another pair of congruent sides (CD and AB) that are opposite each other in both triangles. Finally, we know that the angle CMD is congruent to the angle CMB because they are vertical angles. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle CDM is congruent to triangle CBM.

Therefore, line DM is congruent to line CM by SAS congruence criteria.

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Answer:

Find the value of t0.05 for a t-distribution with 9 degrees of freedom. round your answer to three decimal places, if necessary.

Step-by-step explanation:

Find the value of t0.05 for a t-distribution with 9 degrees of freedom. round your answer to three decimal places, if necessary.

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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Answer:

x=3√5

Step-by-step explanation:

This is a right angle triangle

So the equation is

2²+x²=7²

x=√7²-2²

x=3√5

Answer:

x=3√5

Step-by-step explanation:

Answer:128391389708714902787902717138123712839113791380138477356798123102745374213809129830192382910830198913813091831923841209381036592387141283902171283041287841830214801274123092184091237040283921840912809184091830471938047019340912793018240812040148014819083017409180914727484911111111111111111111111111111111111122222222222222222222222222222222222222222222222222222223333333333333333333333333333333333333333333333333333333333344444444444444444444444444

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since each person forwards to email to 3 other people, the expression for the number of additional people who received it after rounds (including Elijah) is We can rewrite this as

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

In this scenario, if a computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is $470, and its value 3 years later would be $1410.

The straight-line method of depreciation is a method of calculating the decline in value of an asset over time. Using this method, an asset's value is spread evenly over its useful life.

In this scenario, if the computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is ($2350 / 5) = $470.

Three years later, the computer's value would be $2350 - ($470 x 3) = $1410. This is because the value of the computer is decreasing by $470 per year, and after three years, the total amount of depreciation would be $470 x 3 = $1410.

It's important to note that the straight-line method of depreciation is a simple method and it does not reflect the real-world scenario in which assets may have a higher value of depreciation in the initial years and less in the later years. But it's easy to calculate and use.

In conclusion, if an asset is depreciated using the straight-line method, its value decreases evenly over its useful life. It's important for businesses to understand the various methods of depreciation and choose the one that best suits their needs.

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The standard equation of the circle will be (x+5)²+(y+5)²= 145

The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.

formula for the midpoint

= ((x1+x2)/2, (y1+y2)/2)

Given points are - (3, 4), (−13, −14)

The circle's center is at (-5,-5)

Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.

The distance between a point on the circle and the circle's center in order to get the radius.

Therefore, let's calculate the distance between (-5, -5) and (-13,-14)

Radius R = √((-13+5)²+(-14+5)²) using the distance formula.

= 12.04

equation will be -

(x+5)²+(y+5)²= 145

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Chaneece did not find the correct solution

From the question, we have the following parameters that can be used in our computation:

x and y are the integers

So, we have

x + y ≤ 40

x - y ≥ 20

Add the equations

So, we have

2x = 60

Divide

x = 30

Next, we have

30 + y ≤ 40

So, we have

y ≤ 10

This means that

x = 30 or between 20 and 30

y = 10 or between 0 and 10

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