If y = x is compressed by a factor of 1/2 and translated up one unit, the new Function would be:

Answer:

The sum is 10s^2t-5st^2.  With two separate sections, it is a binomial, and since the sum of the powers of the variables is 2+1=3, it has a degree of 3.

Answer:

Never

Step-by-step explanation:

You are both running at the same speed in the same direction and start at the same time. You will always be 8 miles behind your friend and you will never catch up with him/her

The evaluated integral is: \(e^t i + t^5 j + (In(5t) t - t) k + C\)

To evaluate the integral \(\int (e^t i + 5t^4 j + In(5t) k) dt\), we integrate each component of the vector function separately, with respect to t:

\(\int e^t i dt = e^t i + C_1\)

\(\int 5t^4 j dt = t^5 j + C_2\)

\(\int In(5t) k dt = (In(5t) t - t) k + C_3\)

where C₁, C₂, and C₃ are constants of integration.

Therefore, the antiderivative of the vector function is:

\(\int (e^t i + 5t^4 j + In(5t) k) dt = e^t i + t^5 j + (In(5t) t - t) k + C\)

where C is a constant of integration that encompasses all three constants of integration.

Thus, the final answer is:

\(\int (e^t i + 5t^4 j + In(5t) k) dt = e^t i + t^5 j + (In(5t) t - t) k + C\)

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Answer:

180

Step-by-step explanation:

because im always right

Answer:

180 degrees

Step-by-step explanation:

All triangles have an interior angle sum of 180 degrees.

The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.

To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.

(3x³ - x² + 4) + (2x³ - 3x + 9)

Combine the like terms:

(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)

Simplify further:

5x³ - x² - 3x + 13

In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.

Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.

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\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(49)=y\implies \log_{10}(49)=y\implies 1.690196\approx y \\\\\\ \log_{10}(49)\approx 1.690196\implies \stackrel{\textit{then we can say}}{10^{1.690196}\approx 49}\)

sowwy I did change it into a mixed one

Answer:

no solutions

Step-by-step explanation:

y + 7 = y - 3 ( subtract 7 from both sides )

y = y - 10 ( subtract y from both sides )

0 = - 10 ← false statement

this false statement indicates the equation has no solution

Answer:

6, 4, 2, 0

Step-by-step explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula, that is

a₁ = 8 - 2(1) = 8 - 2 = 6

a₂ = 8 - 2(2) = 8 - 4 = 4

a₃ = 8 - 2(3) = 8 - 6 = 2

a₄ = 8 - 2(4) = 8 - 8 = 0

The first 4 terms are 6, 4, 2, 0

Answer:

3

Step-by-step explanation:

by the help of Prashant chettri

a) The magnitude of Pˉ is P.  b) The direction cosine of Pˉ with respect to the x-axis is 110/P.  c) The directional angle of Pˉ with respect to the z-axis is arctan(60/√(110^2+(-0.58P)^2)).

a) To find the magnitude of vector Pˉ, we use the formula for the magnitude of a vector in three dimensions, which is the square root of the sum of the squares of its components.

b) The direction cosine of a vector with respect to a specific axis is the ratio of the component of the vector along that axis to its magnitude. In this case, the x-component of Pˉ is 110, so the direction cosine with respect to the x-axis is 110 / P.

c) The directional angle of a vector with respect to a specific axis can be found using the arctan function. In this case, we use the y-component and z-component of Pˉ to find the angle between Pˉ and the z-axis.

Therefore, the magnitude of Pˉ is given by P, the direction cosine with respect to the x-axis is cos(θ_x), and the directional angle with respect to the z-axis is θ_z.

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h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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The probability that the mean contents of the 1024 sample cans is less than 11.994 ounces, is 0.055.

In the given question, a random sample of 1024 12-ounce cans of fruit nectar is drawn from among all cans produced in a run.

Prior experience has shown that the distribution of the contents has a mean of 12 ounces and a standard deviation of 0.12 ounce.

We have to find the probability that the mean contents of the 1024 sample cans is less than 11.994 ounces.

Given that,

Mean(μ) = 12

Standard Deviation(σ) = 0.12

n = 1024

So, μ = 12

σ/√n = 0.12/1024 = 0.00375

P( x<11.994) = P[(x-μ)/(σ/√n) < (11.994-12)/0.00375]

P( x<11.994) = P(z < -1.6)

(using z table)

P( x<11.994) = 0.055

Probability = 0.055

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Answer:  see proof below

Step-by-step explanation:

Use the following Power Reducing Identities:

\(\sin^3\theta= \dfrac{1+\cos 2\theta}{2}\\\\\\\cos^2\theta=\dfrac{3\sin \theta-\sin 3\theta}{4}\)

Use the following Product to Sum Identity:

\(\sin A \cdot \cos B = \dfrac{1}{2}\bigg[\sin (A + B) + \sin (A - B)\bigg]\)

Proof LHS → RHS

LHS:                           cos² Ф · sin³ Ф

\(\text{Power Reducing:}\qquad \bigg(\dfrac{1+\cos 2\theta}{2}\bigg)\bigg(\dfrac{3\sin \theta-\sin 3\theta}{4}\bigg)\)

\(\text{Expand:}\qquad \qquad \dfrac{1}{8}(3\sin \theta -\sin 3\theta +3\sin \theta\cdot cos 2\theta-\sin 3\theta \cdot \cos 2\theta)\)

\(\text{Product to Sum:}\\ \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin (\theta +2\theta) +\sin(\theta -2\theta)\bigg)-\dfrac{1}{2}\bigg(\sin (3\theta+2\theta) +\sin (3\theta-2\theta)\bigg)\bigg]\)

\(\text{Simplify:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta +\sin(-\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg]\)

\(\text{Cofunction:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta -\sin(\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg]\)

\(\text{Simplify:}\qquad \dfrac{1}{16}\bigg(6\sin \theta -2\sin 3\theta +3\sin 3\theta -3\sin(\theta)-2\sin 5\theta -2\sin \theta\bigg)\\\\\\.\qquad \qquad =\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)\)

\(\text{LHS=RHS:}\quad \dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)=\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)\quad \checkmark\)

Paige bought 32 songs in a month.

Let's break down the cost components in terms of an equation:

The monthly membership fee is $5.

The cost of each song is $0.10.

The total monthly cost is $8.20.

Let s represent the number of songs Paige purchases in a month.

The equation can be written as:

5 + 0.10s = 8.20

This equation represents the total cost of Paige's membership fee plus the cost of the songs she purchases, which equals the total monthly cost of $8.20.

To find the number of songs she bought, we can solve this equation for s.

Subtracting 5 from both sides:

0.10s = 8.20 - 5

0.10s = 3.20

Dividing both sides by 0.10:

s = 3.20 / 0.10

s = 32

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The quadratic formula, providing the solutions for any quadratic equation is \(x = (-b \pm \sqrt(b^2 - 4ac)) / (2a).\)

To derive the quadratic formula, we start with the quadratic equation in standard form: \(ax^2 + bx + c = 0\), where a, b, and c are constants and a ≠ 0.

Step 1: Divide the equation by 'a' to isolate the quadratic term:

\(x^2 + (b/a)x + c/a = 0.\)

Step 2: Move the constant term (c/a) to the right side:

\(x^2 + (b/a)x = -c/a.\)

Step 3: Add (b/2a)^2 to both sides of the equation to complete the square on the left side:

\(x^2 + (b/a)x + (b/2a)^2 = (b/2a)^2 - c/a.\)

Step 4: Simplify the right side:

\(x^2 + (b/a)x + (b^2/4a^2) = (b^2 - 4ac) / (4a^2).\)

Step 5: Factor the left side of the equation:

\((x + b/2a)^2 = (b^2 - 4ac) / (4a^2).\)

Step 6: Take the square root of both sides:

\(x + b/2a = \pm \sqrt((b^2 - 4ac) / (4a^2)).\)

Step 7: Simplify the right side:

\(x + b/2a = \pm \sqrt(b^2 - 4ac) / (2a).\)

Step 8: Finally, isolate 'x' by subtracting b/2a from both sides:

\(x = (-b \pm \sqrt(b^2 - 4ac)) / (2a).\)

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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The expected gestation period of this species with a 17-year life expectancy is approximately 430.2 days, rounded to one decimal place as needed.

A certain mammal has a life expectancy of about 17 years. To estimate the expected gestation period of this species, we can use the scatterplot provided, which shows Gestation Period (in days) vs. Life Expectancy (in years) for 18 species of mammals.

To determine if there is any evidence that an animal's gestation period is related to the animal's lifespan, we can look at the R-squared value provided, which is 86.5%. This indicates a strong positive correlation between gestation period and life expectancy.

To estimate the gestation period for the species with a 17-year life expectancy, we can use the provided linear regression equation:

Gestation = Constant + Coefficient * Life Expectancy

The given constant is 90.1808 and the coefficient is 20.

Gestation = 90.1808 + (20 * 17)

Gestation = 90.1808 + 340

Gestation ≈ 430.2 days

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Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

The number of hours lopudres will have to jog is .4 hours.

Lord wants to run at least 1.5 miles, and her pace is shown in the picture as 3.75 miles per hour, and the question asks us to construct an inequality expressing x for the amount of hours she would have to run. To meet this inequality, we'll need to apply how quickly or how many miles she wants to cover with how fast she's going to run, so we'll divide 1.5 miles by her rate of 3.75 miles per hour, and when you divide you'll get a number of hours, which comes out to 0.4 hours.

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Answer:

∠P ≅ ∠R

Step-by-step explanation:

We can see here two triangles , ∆ PQS and ∆ RQS.

To Prove :-

We can prove the given two triangles congruent then we can easily prove it out.

In ∆ PQS and ∆ RQS

Therefore by SAS congruence condition , both triangles are congruent .

Hence ,

Answer:

We conclude that:

X∩Y∩Z = {2, 4, 7, 9}

Step-by-step explanation:

What is the intersection of three sets:

We know that the intersection of three given sets represents the largest set which consists of all the elements that are common to all the sets.

What is the symbol of the intersection of the sets:

The intersection of sets is denoted by the symbol '∩'.

Determining the  intersection of the sets:

Given

X= {1,2,4,6,7,8,9}

Y= {1,2,3,4,7,9)

Z= {2,3,4,7,9)

Thus,

X∩Y∩Z = {2, 4, 7, 9}

Therefore, we conclude that:

X∩Y∩Z = {2, 4, 7, 9}

The classroom should have 28-42 pots.

To find the number of pots needed for a classroom, you first need to determine the total floor space in square feet. If the classroom has a length of 35 feet and a width of 40 feet, the total floor surface area is 35 feet * 40 feet = 1400 sq ft.

The scientist suggests providing two or three pots of flowers for every 100 sq ft of floor space. To find the number of pots needed for 1400 sq ft of floor space, you can divide 1400 sq ft by 100 sq ft/pot.

So 1400 sq ft / 100 sq ft/pot = 14 pots

The researcher suggests a minimum of 2 pots per 100 sq ft of floor space, therefore, the classroom needs at least 2 pots. The researcher also suggested a maximum of 3 pots per 100 sq ft of floor space,

Therefore, the classroom should have between 2 and 3 pots of flowers per 100 sq ft of floor space, which means that the classroom should have between 28 and 42 pots of flowers.

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Answer:

if we solve for y the answer is y= 2x+5

Answer:

Number of Adult tickets = 3

Number of student tickets = 4

Step-by-step explanation:

Let the number of Adults tickets = x

The number of students tickets = y

A. Specifically define variables for this system

x + y = 7...... Equation 1

They paid $6.50 for each adult ticket and $3.50 for each child's ticket.

$6.50 × x + $3.50 × y = $33.50

6.50x + 3.50y = 33.50.......Equation 2

B. Write a system of equations that reflects the relationships described in this situation

x + y = 7...... Equation 1

x = 7 - y

6.50x + 3.50y = 33.50.......Equation 2

6.50(7 - y) + 3.50y = 33.50

45.5 - 6.5y + 3.5y = 33.5

45.5 - 33.5 = 6.5y -3.5y

12 = 3y

y = 12/3

y = 4 tickets

x + y = 7...... Equation 1

x + 4 = 7

x = 7- 4

x = 3 tickets

Equation of a line:

9x - 7y = -63

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

Answer

x-intercept: −7; y-intercept: 9