Acceleration a in feet per second squared, distance traveled d in feet, velocity v in feet per second, and time t in seconds are related in the formula d=vt+1/2at².

b. If an object travels 2850 feet in 30 seconds with an initial velocity of 50 feet per second, what is the acceleration of the object? What property justifies your calculation?

Step-by-Step Explanation:

We know,

\( \cos(angle) = \frac{base}{hypotenuse} \)

Here, angle = 60°, base = 5, hypotenuse = x

Therefore,

\( \cos(60) = \frac{5}{x} \\ = > \frac{1}{2} = \frac{5}{x} \\ = > x = 5 \times 2 \\ = > x = 10\)

Answer:

10

Hope it helps.

The solution for x in triangle is,

⇒ x = 10

We have to given that;

A triangle is shown in figure.

Since, A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Now, We can use the trigonometry formula to find the value of x as;

⇒ cos a = Base / Hypotenuse

Substitute a = 60°, base = 5 , hypotenuse = x in above equation,

⇒ cos 60° = 5 / x

⇒ 1 / 2 = 5 / x

⇒ x = 5 × 2

⇒ x = 10

Thus, The solution for x in triangle is,

⇒ x = 10

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Answer:

1 pound?

Step-by-step explanation:

4/4 = 1 * 1 = 1

Strassen's algorithm is most effective when the matrices to be multiplied are sufficiently large (usually n > 32).

Strassen's nxn square matrix multiplication algorithm follows certain valid states. These states are given below:

i) Strassen uses divide and conqur approach.

ii) The algorithm only makes 7 recursive calls on sub problems that are roughly 1/4 the size of the original (sub problems are defined by n/2 & n/2).

iii) It improves on the runtime of brute force by a polynomial factor.

iv) The combining step of the algorithm runs in O(N^2) in the worst-case.

v) Worst-case O(N^log7) is considered to be valid.

Strassen's algorithm for matrix multiplication has revolutionized the field of matrix multiplication by enabling much faster multiplication of matrices.

Strassen's algorithm is superior to other algorithms for matrix multiplication in terms of the number of elementary arithmetic operations required.

Strassen's algorithm is most effective when the matrices to be multiplied are sufficiently large (usually n > 32).

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The parametrization of the tangent line to the function f(x) = ln(x) - 7/15x^3 at the point (1,-46/15) is r(t) = <1, -46/15> + t<1, -2/3>.

To find the tangent line at a point, we need the slope of the tangent line, which is the derivative of the function evaluated at that point. So, we first find the derivative of f(x):

f'(x) = 1/x - 7/5 x^2

Then, we evaluate f'(1) to find the slope at x = 1:

f'(1) = 1/1 - 7/5(1)^2 = -2/5

Thus, the slope of the tangent line is -2/5. We also know that the point of tangency is (1,-46/15), so we can use the point-slope form to find the equation of the tangent line:

y - (-46/15) = (-2/5)(x - 1)

Simplifying, we get:

y = (-2/5)x - 16/3

Now we can write the parametrization of the tangent line as r(t) = <1, -46/15> + t<1, -2/3>. This is because the direction vector of the tangent line is <1, -2/3>, which is the same as the slope of the line, and the point on the line is (1,-46/15).

So, to get the equation of the line in vector form, we start with the point <1, -46/15>, and add a scalar multiple of the direction vector <1, -2/3>. Thus, the parametrization of the tangent line is r(t) = <1, -46/15> + t<1, -2/3>.

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The parametrization of the tangent line to the function f(x) = ln(x) - 7/15x^3 at the point (1,-46/15) is r(t) = <1, -46/15> + t<1, -2/3>.

To find the tangent line at a point, we need the slope of the tangent line, which is the derivative of the function evaluated at that point. So, we first find the derivative of f(x):

f'(x) = 1/x - 7/5 x^2

Then, we evaluate f'(1) to find the slope at x = 1:

f'(1) = 1/1 - 7/5(1)^2 = -2/5

Thus, the slope of the tangent line is -2/5. We also know that the point of tangency is (1,-46/15), so we can use the point-slope form to find the equation of the tangent line:

y - (-46/15) = (-2/5)(x - 1)

Simplifying, we get:

y = (-2/5)x - 16/3

Now we can write the parametrization of the tangent line as r(t) = <1, -46/15> + t<1, -2/3>. This is because the direction vector of the tangent line is <1, -2/3>, which is the same as the slope of the line, and the point on the line is (1,-46/15).

So, to get the equation of the line in vector form, we start with the point <1, -46/15>, and add a scalar multiple of the direction vector <1, -2/3>. Thus, the parametrization of the tangent line is r(t) = <1, -46/15> + t<1, -2/3>.

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The coefficient of x⁷ in the given expression is 16.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is the expression [x³ + (4 / x²)]⁴.

[x³ + (4 / x²)]⁴ =  (x³ + 4x⁻²)⁴

                      = (x³ + 4x⁻²)² (x³ + 4x⁻²)²

                      = (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)  

                      = x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +

                         256x⁻⁸

Rearranging with like terms, we get,

                      = x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸

Hence the coefficient of x⁷ is 16.

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Answer:

1) √55 (choice A)

2) square root of 34 (√34)

3) square root of 51 (√51)

Step-by-step explanation:

a^2+b^2=c^2

a^2+3^2=8^2

a^2+9=64

a^2=55

a=√55

a^2+b^2=c^2

3^2+5^2=c^2

9+25=c^2

34=c^2

c=√34

a^2+b^2=c^2

7^2+b^2=10^2

49+b^2=100

b^2=51

b=√51

I, II, and III only are the correct options for statements about the coefficient of variation (CV).

Coefficient of variation (CV) is a measure of the degree of variation of a set of data points relative to the mean of the same data points. It is calculated as the ratio of the standard deviation of a data set to its mean, and then multiplied by 100% to get the percentage value. The CV is used to compare the variation of the risks of two or more assets that have different expected returns.

Therefore, it is particularly useful when dealing with datasets that have varying means, such as in finance. A lower CV implies that the data points in the dataset are closely clustered around the mean, while a higher CV implies that the data points are widely spread out from the mean. Thus, the higher the CV, the higher the risk, and the lower the CV, the lower the risk. Therefore, the correct option is I, II, and III only.

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True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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Answer:

Step-by-step explanation:

Here is what the mixed number looks like. \(W\frac{R}{D}\)

W- whole numbers (that is the integers)

R- remainder

D- denominator

If you ever want to convert an improper fraction to a mixed number, here are the steps.

Step 1: Use traditional division. How many does 3 goes into 7? 2 times with remainder, R=1 (how many is left over after dividing).

Step 2: Replace the unknowns with D=3

Note: the denominator always stays the same!

\(2\frac{1}{3}\)

To find the maximum likelihood estimator for theta, we need to first find the likelihood function by taking the product of the density function for each observation. Assuming we have n observations, the likelihood function is given by:

L(theta) = (1/theta^2) * Π[i=1 to n] (xi * e^(-xi/theta))

Taking the logarithm of the likelihood function and simplifying it, we get:

ln(L(theta)) = -2ln(theta) + Σ[i=1 to n] ln(xi) - Σ[i=1 to n] (xi/theta)

To find the maximum likelihood estimator for theta, we need to differentiate ln(L(theta)) with respect to theta and set it equal to zero. Solving for theta, we get:

θ = Σ[i=1 to n] xi / n

Therefore, the maximum likelihood estimator for theta is the sample mean of the n observations.

It is important to note that this estimator is unbiased and efficient, meaning that it has the smallest possible variance among all unbiased estimators. This makes it a desirable estimator for practical applications.

In conclusion, the maximum likelihood estimator for theta in the given probability density function is the sample mean of the n observations.

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The angle between the lines with slopes -1 and 0 is 45 degrees (or π/4 radians).

To find the angle between two lines given their slopes, we can use the formula:

θ = atan(|(m1 - m2) / (1 + m1 * m2)|)

where m1 and m2 are the slopes of the two lines.

In this case, we have two lines with slopes -1 and 0.

Let's calculate the angle:

θ = atan(|(-1 - 0) / (1 + (-1) * 0)|)

= atan(|-1 / 1|)

= atan(1)

The arctangent of 1 is 45 degrees (or π/4 radians).

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The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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Answer: She worked as a carpenter for 12 hours and a blacksmith for 18 hours.

Step-by-step explanation:

18*25 = 450

12*20 = 240

240 + 450 = 690

12 + 18 = 30.

Answer:

Continuous data are data which can take any values. Examples include time, height and weight. Because continuous data can take any value, there are an infinite number of possible outcomes.

Given

Number of questions in an english exam = 10

Find

Number of different sets of 4 questions are available.

Explanation

as we have given that a student must choose 4 of the 10 questions.

so , number of different set of 4 questions are available =

so ,

Final Answer

Hence , the number of different sets of 4 questions are available are 210

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

The actions of withdrawing $ from your checking account and depositing it into a savings account will affect the measures of money supply, M1 and M2, as follows:

M1: M1 is a measure of the narrowest definition of the money supply, which includes all currency (including coins), checking accounts, and travelers' checks. Withdrawing money from your checking account will reduce the amount of money in M1. However, depositing the funds into a savings account will not have any impact on M1 since savings accounts are not included in this measure of the money supply.

M2: M2 is a measure of the broader definition of the money supply, which includes M1 and all-time deposits, savings accounts, and money market securities with a value of less than $100,000. Depositing money into a savings account will increase the amount of money in M2, as savings accounts are included in this measure of the money supply. However, withdrawing money from a checking account will not have any impact on M2 as the decrease in M1 will be offset by the increase in savings accounts.

Therefore, In conclusion, withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

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Question Correction: Suppose you withdraw $6,000 from your checking account and use the funds to invest in a savings account at the bank. How will these actions affect M1 and M2?

A. M1 wil decrease and M2 wil not change

B. M1 and M2 will increase

C. M1 and M2 will not change.

D. M1 wil decrease and M2 will increase

The measure of the angle of the triangle is ∠Q = 72.1°

Given data ,

Let the triangle be represented as ΔQRS

Now , the measure of sides of the triangle are

SQ = 75 inches

And , RS = 23 inches

From the trigonometric relations , we get

cos θ = adjacent / hypotenuse

On simplifying , we get

cos Q = 23/75

cos Q = 0.3066667

Taking inverse on both sides , we get

The inverse of the cosine function is Q = cos⁻¹ ( 0.306667 )

Q = 72.14°

Hence , the angle is Q = 72.1°

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Answer:

Every time the input goes up by 1 the output increases by 10.

Step-by-step explanation:

Answer:

y=2/3x

Step-by-step explanation:

Answer:

The correct answer is:

It is a continuous random variable (C)

Step-by-step explanation:

Continuous Random Variables are variables that do not take on a distinct value. They take on values that are a range of different possibilities to infinity. In continuous random variables, the values cannot be counted. In this example, the time it takes for a light bulb to burn out can be any rational number which is greater than 0, up to infinity; for instance, it can be 24 hours, 24.5 hours, 30.8 hours, 51.2 hours etc. There is an infinite possibility of the time it takes for the bulb to burn out.

Discrete Random Variables are ones in which the variables take on distinct values and nothing in between. Here, the outcomes can be counted. For example if a coin is tossed, there are only two possibilities which can be the outcome and that is either head, or tail. The number of possible outcome is 2, and there is nothing inbetween head or tail.

Answer:

It’s C

(Gibberish words to so i can to 29 words)

hciejdgrifgirgrittrufifgeydifufgfidhfuvifgdudugcudydgdidhdhf

Hope this helped,if not, don’t hate.

Answer:

XZ = 2.5 BD

Step-by-step explanation:

Comparing the two triangles,

\(\frac{BD}{BC}\) = \(\frac{XZ}{XY}\)

\(\frac{6}{8}\) = \(\frac{XZ}{20}\)

⇒ XZ = \(\frac{20*6}{8}\)

         = 15

XZ = 15

So that,

BD:XZ = 6:15

           = 1:2.5

Therefore, the relationship between BD and XZ is XZ = 2.5 BD.

Answer:

Price increased=rs 52-1=rs 51

So therefore, increased%=51/1 x 100= 5100%

Step-by-step explanation:

Hope this helped!!!!!

The probability that the mean run time for the 40 runners is between 141 and 143 minutes is approximately 0.4394

Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

Mean is a measure of central tendency that represents the average value of a set of numbers.

According to the given information :

Using the Central Limit Theorem, we know that the sample mean follows a normal distribution with a mean of 142 and standard deviation of 8/√40 = 1.2649. To find the probability that X is between 141 and 143, we standardize the values:

z1 = (141 - 142) / 1.2649 = -0.7925

z2 = (143 - 142) / 1.2649 = 0.7925

Using a standard normal table or calculator, we can find the area between -0.7925 and 0.7925 to be 0.4394. Therefore, the probability that the mean run time for the 40 runners is between 141 and 143 minutes is approximately 0.4394.

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Therefore, the statement represents an exponential function.

The given statement, "The value of a coin collection has increased by 3.25% annually over the last 20 years" represents an exponential function.Exponential functions refer to the mathematical operations where a constant is raised to the power of the variable x and this variable is the input, and the exponential function is the output.The given statement represents the exponential function because the value of the coin collection is increasing by 3.25% every year, which means it is compounding. Compounding interest is an essential feature of an exponential function since it increases in a compound way. The formula for compound interest is given as:`A=P(1+(r/n))^nt`Where,A is the final amount,P is the principal amount,r is the annual interest rate,n is the number of times the interest is compounded per year,t is the time in years.The compound interest formula reflects the exponential growth model because of the exponent. Also, the coin collection's value is continuously growing and, the longer it takes, the more its value increases.Therefore, the statement represents an exponential function.

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Answer:

A and D choices (Plato)

Step-by-step explanation:

The upper boundary of the first equation is at x = 12, y = 0. With these values, this is the second equation:

100(12) − 200(0) = 1,200.

The lower boundary of the first equation is at x = 0, y = 12. With these values, this is the second equation:

100(0) − 200(12) = -2,400.

Both of these scores are possible in the game, so they are both viable.

Because the upper boundary is greater than 600, it suggests that you can still score 600 points and win the game even if you get one or two of the questions incorrect.

In fact, you could give 10 correct and 2 incorrect answers to score 600 points and still beat the champion, Kimberly, assuming she answers 15 correct and 5 incorrect to score 500 points.

Answer:

17/18

Step-by-step explanation:

okay this one is a bit different

you have to take the total number that are batwing-shaped (12) and the total number that are made of cotton (12) and then subtract the ones that are both batwing-shaped and made of cotton.

so 12+12-7 which is 17

then you put that over the total (18)

17/18 doesn't simplify

Answer:

Each strip is 117.6 cm

Step-by-step explanation:

I created a proportion of hearts to others.  On strip A there is 1 heart to 2 others and B there is 1 heart to 3 others.  I added them and got a proportion of 2 hearts to 5 others for both. With a total of 56 hearts, I set up a proportion to determine the total stickers

2/5=56/x

When I cross multiply, I get 2x=280 and x=140

so for the 56 total hearts, I have 140 others.  I added those to get the total stickers and got 196.  I multiplied that by 1.2cm and got 235.2 cm for both. Since both are the same size, just divide that by 2 and get 117.6 cm each.

Answer:

THE OTHER ANSWER IS WRONG

Step-by-step explanation:

90=20+6x-2

92=20+6x

72=6x

12=x

Hope this helps!

Step-by-step explanation:

first u need to pick a random coordinate to substitute the X . example 0

y = 2(0) + 1

y =1 , X= 0

X= 1

y= 2(1) + 1

y= 3, X= 1

then you continue this same process and again until u have at least two points to draw a straight line. it kinda depended if u want to fill the entire graph.