IF YOU TRAVEL 82 km IN 40 MINS, WHAT IS YOUR SPEED IN km/h?

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = \(5x^5\)

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Only the first statement is false. The rest are true statements about the Central Limit Theorem.

The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.

It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.

The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.

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Compound interest is the interest based on the initial loan taken out and the interest accumulated with time

The amount owed at the end of 5 years is approximately $48,994.16

The known loan information are;

The loan principal amount, P = $30,000

The annual interest rate, r = 10%

The rate at which the interest is compounded = Every microsecond

Required:

The amount of money owed at the end of the five years

Solution:

The compound interest formula is presented as follows

\(A = P \times \left(1+\dfrac{r}{n} \right)^{n \times t}\)

Where;

Interest per period, i = r/n

t = The number of years = 5 years

Which gives;

The number of microseconds in a year, n = 3.15576 × 10¹³ microseconds

By plugging in the values, we get;

\(A = 30,000 \times \left(1+\dfrac{0.1}{3.15576 \times 10^{13}} \right)^{3.15576 \times 10^{13} \times 5} \approx 48,994.16\)

The amount owed at the end of 5 years ≈ $48,994.16

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The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Using z-scores, it is found that a scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.

The z-score of a measure X of a distribution with mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For the first scale, the parameters are given as follows:

\(X = 40, \mu = 37, \sigma = 6\)

Hence the z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (40 - 37)/6

Z = 0.5.

For the second scale, we want to find X when Z = 0.5, considering the following mean and standard deviation:

\(\mu = 50, \sigma = 10\)

Hence:

\(Z = \frac{X - \mu}{\sigma}\)

0.5 = (X - 50)/10

X - 50 = 5

X = 55.

A scale of 40 on the first scale is equivalent to a score of 55 in the new standardized scale.

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Answer:

The complete factored form of the equation is (x + 6)(x + 4).

Step-by-step explanation:

The first step in factoring this quadratic equation is to multiply the first term by the last term. Our first term is x² and our last terms is 24. Since x² does not have a coefficient, then we assume this number to be 1.

1 × 24 = 24

The next step is to find two factors that multiply together to get 24 and adds together to get our middle term which is 10.

Two factors that best show this is 4 and 6. So, let's plug them into our equation. Replace 10x with 4x + 6x.

x² + 4x + 6x + 24

Now, we group our first two terms together and our last two terms together.

(x² + 4x) + (6x + 24)

Next, we take the greatest common factor of each parentheses and factor them.

x(x + 4) + 6(x + 4)

Lastly, we factor the equation. You can know that you have factored the equation correctly when you have the same term in both parentheses.

So, the complete factor of the equation is (x + 6)(x + 4).

Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer:

Graph A best describes the given function

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

answer is .A

Step-by-step explanation:

Answer:

d or 4Step-by-step explanation:

Answer:

Multiply,Subtract,Add,Subtract

Step-by-step explanation: Easy, just think

Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

first option

Step-by-step explanation:

integers are like whole numbers but can also be negative

Answer:

A

Step-by-step explanation:

Answer: Solve for P: WR - 1 =R (1 – P) 10. ... Solve for B: A= 2B + C 12. ... 9. Solve for P: WR - 1 =R (1 – P).

Step-by-step explanation:

Answer:-111

and -99

Step-by-step explanation:

Answer:

-111 and -99 ( in order)

Step-by-step explanation:

Have a great day!

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

35x.25= 8.75 58x.05= 2.90 + .62 = 12.27 - 2.37 = 9.90

Step-by-step explanation:

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

The wall is 4 inches long on the blueprint

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Given :

3 ft is equal to 1 inch on blueprint

12  ft  is equal to 12/3 = 4 inches

The wall is 4 inches long on the blueprint

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Answer:

Step-by-step explanation:

Look at the picture.

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

DA = 25

Step-by-step explanation:

since the triangles are congruent, then corresponding sides are congruent, that is

DA = BA = 25

Answer:

2

Step-by-step explanation:

13*2=26

Answer:

the percent error in the student's measurement is 4.65%.

Step-by-step explanation:

The percent error can be calculated using the formula:

| (measured value - actual value) / actual value | * 100%

In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:

| (2.7 - 2.58) / 2.58 | * 100% = 4.65%

Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.

Therefore, the percent error in the student's measurement is 4.65%.

The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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Answer:

Step-by-step explanation:

Total amount of yogurts made by Stacy = 1.5 Litres

Volume of each cups to be filled with yogurts = 125mL = 125*10⁻³Litres

To get the number of cups Stacy can fill for her to exhaust 1.5Litres can be gotten using the relationship;

Number of cups = Total volume of yogurts made/Volume of each cup

Number of cups = 1.5/125*10⁻³

Number of cups = 1.5/0.125

Number of cups = 12 cups

Number of cups Stacy can fill is 12 cups

The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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Answer:

yellow

Step-by-step explanation:

bc blue