what is the restriction in the determining if the given equation is a polynomial?

The tangential and normal components of the acceleration vector of r(t) = t i + t² j + 5t k are respectively 1 and 10.

To find the tangential and normal components of the acceleration vector, we first need to find the velocity and acceleration vectors. The velocity vector is the first derivative of the position vector:

The acceleration vector is the second derivative of the position vector:

Next, we need to find the unit tangent vector T(t) and unit normal vector N(t):

Finally, we can find the tangential and normal components of the acceleration vector by projecting a(t) onto T(t) and N(t):

Therefore, the tangential and normal components of the acceleration vector are respectively 1 and 10.

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Answer:

1/6

Step-by-step explanation:

1/6

The area of the original garden is 7200 square feet.

Given,

a rectangular garden has a length that is twice its width. the dimensions are increased so that the perimeter is doubled and the new shape is a square with an area of 3600 square feet.

we are asked to determine the area of the original garden = ?

let the width be x

and the length be 2x

area of the square = 3600 sq feet

Perimeter of the rectangle = 2(l+b)

⇒ 2(2x+x)

⇒ 2(3x)=6x

area of square = a²

a² = 3600

a = √3600

a = 60

now we get the width = 60

length = 2(60)

= 120

Now calculate the area of the rectangle:

= l×b

= 60 × 120

= 7200

hence we get the area as 7200 square feet.

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Answer:

Search Results

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A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

Step-by-step explanation:

Answer:

1 is FALSE

2 is TRUE

3 is FALSE

4 is FALSE

Step-by-step explanation:

1 is false because the blue marble is 2 only

2 is true because green marble has a 100% you get this.

3 is false because we din't have yellow marble

4 is false because red is has 10 marble so you get this red marbke is has 82% because red marble is 2nd most at the number of color

Answer:

The two clock will chime together in 75 minutes

Step-by-step explanation:

- The two clock will chime together in the multiples of 15 and 25

- Lets find the first common multiple of 15 and 25

∵ 15 = 5 × 3

∴ The prime factors of 15 are 3 and 5

∵ 25 = 5 × 5

∴ The prime factor of 25 is 5

∴ The lowest common multiple of 15 and 25 = 5 × 3 × 5 = 75

∴ The two clocks will chime together every 75 minutes

Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

Noah would need more cubes to fill the 1 1/2 inch cube because the cubes he is using have a smaller edge length than the cubes Lin is using. The larger the edge length of the cubes being used, the fewer number of cubes needed to fill a given space.

To see this, you can calculate the volume of the cube being filled by both Lin and Noah. The cube that Lin is filling has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Lin is using have a volume of (0.5)^3 = 0.125 cubic inches. So, Lin needs 3.375/0.125 = 27 cubes to fill the 1.5 inch cube.

The cube that Noah is filling also has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Noah is using have a volume of (0.25)^3 = 0.03125 cubic inches. So, Noah needs 3.375/0.03125 = 108 cubes to fill the 1.5 inch cube.

As we can see, Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.

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Sample size, n = 25One sample t-statistic = t = 1.12Null hypothesis, H0: µ = 64Alternative hypothesis, Ha: µ ≠ 64;

Two-tailed testNow, The P-value for the given data and check the conclusions at the 5% and 1% significance level.A) Calculation of P-valueThe P-value for the two-tailed test can be calculated using the following formula:P-value = 2 * (1 - T.DIST.2T(ABS(t), df))where T.DIST.2T is the two-tailed probability distribution function in Excel with degree of freedom, df = n - 1.P-value = 2 * (1 - T.DIST.2T(ABS(1.12), 24)) = 2 * (1 - 0.277) = 1.446At the 5% significance level, the P-value (0.01 < 0.05) is greater than the level of significance, so we fail to reject the null hypothesis.At the 1% significance level, the P-value (0.01 > 0.01) is less than the level of significance, so we reject the null hypothesis.B) Calculation of P-value for Ha: µ < 64Now, we need to redo question (a) using the alternative hypothesis, Ha: µ < 64; Left-tailed test.Since the null hypothesis states that the population mean is equal to 64, and the alternative hypothesis states that the population mean is less than 64, then the mean value of 64 is considered the “more favorable” hypothesis. Thus, the area under the left tail of the t-distribution is considered the P-value.P-value = T.DIST(t, df, 1)where T.DIST is the one-tailed probability distribution function in Excel with degree of freedom, df = n - 1.P-value = T.DIST(1.12, 24, 1) = 0.1402At the 5% and 1% significance level, the P-value (0.1402 > 0.05 and 0.1402 > 0.01) is greater than the level of significance, so we fail to reject the null hypothesis. Thus, we do not have sufficient evidence to support the claim that the population mean is less than 64.

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Answer:

g>-5

Step-by-step explanation:

Answer:

a. $63.00

b. $69.00

c. $75.00

d. $78.00

A

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The best method to estimate the size of a population of rabbits living in a large urban park is the Capture a set of rabbits, mark and release them, and then recapture a second set of rabbits, which is option C.

Later, a second sample of rabbits is captured, and the number of marked rabbits in this sample is recorded. The ratio of marked rabbits to the total number of rabbits in the second sample can be used to estimate the total population size.

The CMR method is considered one of the most accurate methods for estimating the size of a population of animals, as it accounts for the potential biases in other methods like counting individual animals within quadrants or along transects.

This method assumes that the marked and unmarked animals have an equal chance of being captured and that there is no migration or mortality between the two sampling periods.

In conclusion, the CMR method is the best option to estimate the size of a rabbit population in a large urban park as it is more accurate than other methods and accounts for potential biases in other methods. Therefore, correct option is C.

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The solution of the given differential equation is,

x^3y + 1/2ln(x) = e^(-x^4/4)

Given the differential equation,

(x+ x^(3)y)dx=(5−ln(x^(3)))dy

We need to verify whether the given differential equation is exact or not. If it is exact, we need to solve it.

Solution: We have,

(x+ x3y)dx=(5−lnx3)dy

Let M = x + x^3y,

N = 5 - ln(x^3).

The given differential equation can be written as,

M dx + N dy = 0

Now, the partial derivative of M with respect to y is,

M_y = x^3

On the other hand, the partial derivative of N with respect to x is,

N_x = (-3/x)

Now, we need to check whether these partial derivatives are equal or not.

If M_y = N_x, then the given differential equation is exact. We have,

M_y = x^3 and

N_x = (-3/x)

Clearly,M_y ≠ N_x

Hence, the given differential equation is not exact.

Therefore, we need to find an integrating factor I, such that

IM dx + IN dy = 0

is exact

.Let us find the integrating factor I.

Let, I = e^(∫(N_x - M_y)/M dx)

I = e^(∫(-3/x - x^3)/x dx)

I = e^(-3ln(x) - x^4/4)

I = 1/(x^3e^(x^4/4))

Now, let us multiply the given differential equation with the integrating factor I to make it exact.

I[(x+ x^3y)dx + (5−ln(x^3))dy] = 0

I(dx/dy) + [(5I/x^3) - (3x^2yI/x^3)]dx = 0

Simplifying, we get,

d/dy(x^3e^(x^4/4)) + 5e^(x^4/4)/x^3 = 0

This is a separable differential equation. So, we have,

d/dy(x^3e^(x^4/4)) = -5e^(x^4/4)/x^3

Integrating both sides, we get,

x^3e^(x^4/4) = C - ∫(5e^(x^4/4)/x^3) dy

x^3e^(x^4/4) = C - e^(x^4/4)/2 + D (where D is a constant of integration)

Therefore, the solution of the given differential equation is,

x^3y + 1/2ln(x) = e^(-x^4/4)

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The general solution to the given differential equation. The constant of integration is denoted by C.

To determine if the given differential equation is exact, we need to check if its coefficients satisfy the exactness condition:

∂M/∂y = ∂N/∂x

Let's examine the given differential equation:

(x + x³y)dx = (5 - ln(x³))dy

Taking the partial derivative of M = (x + x³y) with respect to y:

∂M/∂y = x³

Taking the partial derivative of N = (5 - ln(x³)) with respect to x:

∂N/∂x = -3x² / x³ = -3/x

Since ∂M/∂y = x³ ≠ ∂N/∂x = -3/x, the equation is not exact.

To solve the differential equation, we need to find an integrating factor (IF) that will make it exact.

The integrating factor is given by:

IF = e^(∫(∂N/∂x - ∂M/∂y)/N dx)

Substituting the values, we have:

IF = e^(∫(-3/x) dx)

= e^(-3ln(x))

= e^(ln(x⁻³))

= x⁻³

Now, we multiply the entire equation by the integrating factor (IF = x⁻³):

x⁻³(x + x³y)dx = x⁻³(5 - ln(x³))dy

Simplifying:

(x⁻² + y)dx = (5x⁻³ - ln(x³)x⁻³)dy

x⁻²dx + xydx = 5x⁻³dy - ln(x)dy

Taking the antiderivative with respect to x:

∫(x⁻²dx + xydx) = ∫(5x⁻³dy - ln(x)dy)

Applying the power rule and integration rules:

x⁻¹ + 1/2(x²y) = 5x⁻³y - ∫ln(x)dy

Rearranging:

x⁻¹ + 1/2(x²y) + ∫ln(x)dy = 5x⁻³y + C

Simplifying:

1/x + 1/2(x²y) + yln(x) = 5x⁻³y + C

That is the general solution to the given differential equation. The constant of integration is denoted by C.

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Answer:

pemdas

Step-by-step explanation:

PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Substitute 5 for x in the function f(x) = 2x + 7.

Option C is correct.

The answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

The Hardy-Weinberg equilibrium is a method for determining the frequency of certain genetic traits in a population. The following are the frequencies of the red hair (r) and non-red hair (R) alleles in the Norwegian population, according to the question: A) The total frequency of alleles is 1. If red hair (r) is found in approximately 4% of the people in Norway, then the frequency of the R allele must be 0.96 or 96%. R = 0.96 r = 0.04 B) The frequency of hetero zygotes in a population can be determined by multiplying the frequency of the R allele by the frequency of the r allele and then multiplying that number by 2.

Heterogeneous genotype = 2pq Here, p represents the frequency of the R allele, and q represents the frequency of the r allele. p = R = 0.96 q = r = 0.04 Therefore, 2pq = 2(0.96 x 0.04) = 0.077, or approximately 8%. C) In order for a child to have red hair, both parents must carry the r allele. If both parents are homozygous for the R allele, there is no chance that their child will have red hair. This means that the proportion of matings that cannot result in a child with red hair is (0.96 x 0.96) = 0.9216 or 92.16%.

Therefore, the answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

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Step-by-step explanation:

about 7% (not exactly 7%, just about)

Answer:

About 7% sodium.

The rest is information you may find important later.

For homemade chocolate chip cookies.

__________________________________________________________

Questions about percentage? Feel free to ask me in the comments box.

Answer:

34, 35, 36

Step-by-step explanation:

1st number = x

2nd number = x+1

3rd number = x+2

So the equation would be:

x+2(x+1)+(x+2)-7=133

x+2x+2+x+2-7=133

4x-3=133

4x=136

x=34

      Three consecutive numbers justifying the condition given in the statement will be 34, 35, 36.

Let three consecutive number are,

n, (n + 1), (n + 2)

First statement given,

" The sum of first number, twice the second number"

Expression for the statement → [n + 2(n + 1)]

Second statement → " 7 less than the third number"

Expression for the statement → (n + 2) - 7

Combine the expressions,

"The sum of first number, twice the second number and 7 less than the third number is 133"

Form the equation and simplify,

n + 2(n + 1) + (n + 2) - 7 = 133

n + 2n + 2 + n + 2 - 7 = 133

(n + 2n + n) + (2 + 2 - 7) = 133

4n - 3 = 144

4n = 136

n = 34

         Therefore, the numbers are,

                            1st number → n = 34

                            2nd number → (n + 1) = 35

                            3rd number → (n + 2) = 36

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A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

Answer:

The semi annual compound interest of a sum of money in 1 year and 2 years are Rs. 2100 and Rs. 4641 respectively, find the rate of interest and the sum.

Answer:5

Step-by-step explanation:

4565

Answer:

5 hourss

Step-by-step explanation:

197-32= 165

165/33

Answer:

5 hours

Step-by-step explanation:

Ralph earned $197 in total but with an initial fee of $32 so,

197 - 32 = 165

$165 is the amount he made from the hourly fee alone. So let's divide the total by the hourly fee.

165 ÷ 33 = 5.

So the job took 5 hours.

The different percentages are, 42%, 21% and 63%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolize it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Now, according to the given information, the double number line shows that 42 people watched Deon's new video today.

Now, we are to find,

100% of 42 people.

This is, (100/100)*42 = 42%.

Again, 50% of 42 people is,

(50/100)*42 = 21%.

Again, 150% of 42 people is,

(150/100)*42 = 63%.

Hence, the percentages are, 42%, 21% and 63%.

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Answer:

Answers are in the explaination.

Step-by-step explanation:

100% of 42 people answer is 42

50% of 42 people answer is 21

150% of 42 people answer is 63