The figure to the right shows the graph y= 3^-x and three inscribed rectangles. What is the sum of the areas of the rectangles?

Answer:

circumference of circular track =2πR

R = 50/2 = 25m

circumference = 2 × 22/7 × (25) = 157.14 ≈ 157m

No. of rounds made = 10

total distance covered = 157 × 10 = 1570m

Option 3) 1570 is correct

Answer:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Step-by-step explanation:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Answer:

y=3/x^3

Step-by-step explanation:

y = k / x^3

24 = k / 1/2^3

Cross Multiply:

24 × 1/2^3 = k

3 = k

Since k is 3, then:

y=3/x^3

Answer:

y = \(\frac{3}{x^3}\)

Step-by-step explanation:

Given y is inversely proportional to x³ then the equation relating them is

y = \(\frac{k}{x^3}\) ← k is constant of proportion

To find k use the condition when x = \(\frac{1}{2}\) , y = 24

24 = \(\frac{k}{(\frac{1}{2}) ^{3} }\) = \(\frac{k}{\frac{1}{8} }\) = 8k ( divide both sides by 8 )

3 = k

y = \(\frac{3}{x^3}\) ← equation of proportion

Answer:

2/5 is greater than 3/8, so 25 2/5 is greater

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 5 and 8 is 40

Next, find the equivalent fraction of both fractional numbers with denominator 40

For the 1st fraction, since 5 × 8 = 40,

2/5

=

2 × 8

5 × 8

=

16/40

Likewise, for the 2nd fraction, since 8 × 5 = 40,

3/8

=

3 × 5

8 × 5

=

15/40

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/40 > 15/ 40 or 2/5 > 3/8

Answer:

To solve the inequality |h + 3| < 5, we need to consider two cases, depending on whether the expression inside the absolute value bars is positive or negative:

Case 1: h + 3 >= 0

If h + 3 >= 0, then we can remove the absolute value bars without changing the inequality:

h + 3 < 5

Subtracting 3 from both sides, we get:

h < 2

So the solution for this case is h < 2.

Case 2: h + 3 < 0

If h + 3 < 0, then the inequality becomes:

-(h + 3) < 5

Multiplying both sides by -1 (and reversing the inequality), we get:

h + 3 > -5

Subtracting 3 from both sides, we get:

h > -8

So the solution for this case is h > -8.

Putting these two solutions together, we have:

-8 < h < 2

Therefore, the solution set in set-builder notation is:

{h | -8 < h < 2}

Answer:

I dont need

Step-by-step explanation:

what to convert

Answer:

127°

Step-by-step explanation:

First, add everything together.

112 + 133 + 128 + 100 + 120 = 593

Then. subtract 720 - 593

720 - 593 = 127

So, the missing angle is 127°

Have a great day!

Answer:

127°

Step-by-step explanation:

First, add everything together.

112 + 133 + 128 + 100 + 120 = 593

Then. subtract 720 - 593

720 - 593 = 127

So, the missing angle is 127°

Hope this helps you out

Answer: 3/4 pi

Step-by-step explanation:

Answer: Volume of the golf ball = 1.333π

Step-by-step explanation: Half the diameter = Radius (1 inch)

V=4/3π r³

V = 4/3π x 1³

V = 1.333π

Length of line XY is 12cm

We apply the mid-segment of trapezoid theorem:

Length of line XY is 12cm

An exponential function best model Jack's profits based on data collected so far.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

For this problem, we have that the profits increase at an approximately multiplicative rate, hence an exponential functions best models the profit.

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The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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The total number of left cosets of h in Z is n.

Here, Z represents the set of all integers and h = {0, 6n, 62n, 63n, . . .} is a subgroup of Z.

To find the left cosets of h in Z, we need to consider the elements of Z that are not already in h and then form the left cosets by adding elements of h to these elements.

Let's consider an integer a that is not in h. Then a can be written as:

a = 6qn + r, where 0 ≤ r < 6n

Now, we can form the left coset of h containing a by adding elements of h to a. That is:

a + h = {a + 0, a + 6n, a + 62n, a + 63n, ...}

Notice that adding any multiple of 6n to a will not change the left coset. Therefore, we can write:

a + h = {a + 6kn : k is an integer}

So, the left cosets of h in Z are of the form {6kn : k is an integer}. There are n different such cosets, because there are n different residue classes modulo 6n.

Therefore, the total number of left cosets of h in Z is n.

Note: A left coset of a subgroup H in a group G is a set of the form {ah : h ∈ H}, where a is an element of G.

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Step-by-step explanation:

A(2,0)=A'(2,0)

B(4,-1)=B'(0,0)

C(1,-3)=C'(2,3)

Using translation concepts, the coordinates of the image of the triangle are given as follows:

A'(0,2), B'(1,4), C'(3, 1).

What is a translation?

A translation is represented by a difference in the graph of function , follows to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a 90° counterclockwise rotation about the origin is given as follows:

(x,y) -> (-y,x).

Hence the coordinates of the image of the triangle are given as follows:

A': (2,0) -> (0, 2).

B': (4,-1) -> (1,4).

C': (1, -3) -> (3, 1).

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Answer:

The line shape will be reflected over line y = -x

Step-by-step explanation:

If you were to draw these lines and reflect the image, the image will show as being reflected into quadrant 3.

Answer:

77

Step-by-step explanation:

Answer:

x = 12√2

y = 12√2

Step-by-step explanation:

By applying cosine rule in the given triangle,

cos(45)° = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

\(\frac{1}{\sqrt{2}}=\frac{y}{24}\)

y = \(\frac{24}{\sqrt{2}}\)

y = \(12\sqrt{2}\)

By applying sine rule in the given triangle,

sin(45°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

\(\frac{1}{\sqrt{2}}=\frac{x}{24}\)

x = \(\frac{24}{\sqrt{2}}\)

x = \(12\sqrt{2}\)

B and C

Right pyramid has 8, Right triangular prism has 9

The means for groups A, B, and C are 4, 6, and 8, respectively. The omega-squared is 0.25.

The Omega-squared calculation is used to determine how much variance is explained by a specific component or therapy. It is represented as 2 and ranges from 0 to 1, with higher values indicating a greater relationship between the independent and dependent variables.

Omega-squared is calculated as follows:

                        ω2=SSBetween / SSTotalSSWithin

                             = SSTotal - SS Between

where SSTotal is the entire variance's sum of squares. Between and Within are the sums of the squares within and between the groups, respectively.

The following formula can be used to find the sum of squares between the groups:

                       SSTotal = SSBetween + SSWithinSSTotal

                                     = (nA + nB + nC - 1) × (σA² + σB² +σC²)SSBetween

                                     = SSTotal - SS Within SS Between

                                     = (3 - 1) × (42 + 62 + 82) - 120SSBetween

                                     = 80 Next,

  You can compute the total variance as follows:

                     SSTotal = SSWithin + SSBetweenSSTotal

                                   = 120 + 80SSTotal

                                    = 200

      Omega-squared can now be calculated as follows:

                    ω2 = SSBetween / SSTotalω2

                          = 80/200ω2

                          =0.4

      Omega-squared therefore has a value of 0.25.

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Answer:

50cm or 500mm

Step-by-step explanation:

There are 4 base edges and 4 lateral edges, therefore, multiply the number for both edges by 4 and add.

Considering the fact that we were given two units of measurement, millimeters and centimeters, but we know that there are 10mm (millimeters) in a cm (centimeter) , we can just divide 55 by 10 to get 5.5.

¦

Therefore;

5.5 x 4 = 22

7 x 4 = 28

28 + 22 = 50cm

The diagram can be drawn in order to assist in answering the question.

Its value is 1 ..

please mark me as branlist

Answer:

1

Any number raised to the power 0 is 1

Answer:

○ f(x) = x² + 3x - 37

Step-by-step explanation:

Based on the given data in the table, we can observe that the function values (f(x)) correspond to different x-values. To determine the polynomial function represented by the data, we need to find the pattern or relationship between the x-values and the corresponding f(x) values.

Looking at the data, we can see that the x-values are increasing by 1 each time, and the corresponding f(x) values seem to be following a pattern. Let's analyze the data:

x | f(x)

--+-----

-8 | -35

-3 | -17

5 | 6

1 | 2

6 | 3

2 | 2

1 | 1

6 | 7

7 | 37

From the given data, it appears that the polynomial function represented by the data is:

f(x) = x² + 3x - 7

None of the provided options exactly matches this polynomial function, but the closest option is:

○ f(x) = x² + 3x - 37

So, the closest function represented by the data is f(x) = x² + 3x - 37.

Answer:

To work out the percentage, all you have to do is divide the first subject by the second and multiply that by 100%.

In other words, \(\frac{\$10}{\$10} \cdot 100\%\)

= \(1 \cdot 100\%\)

= \(100\%\).

Step-by-step explanation:

Hope this helped!

Linear equation , quadratic equation and polynomial equation are the three types of equation.

1. Linear Equations: These equations have one or more variables and can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

2. Quadratic Equations: These equations have one variable and can be written in the form of ax^2 + bx + c = 0, where a, b and c are constants.

3. Polynomial Equations: These equations have one or more variables and can be written in the form of a polynomial, such as ax^n + bx^n-1 + ... + c = 0, where a, b, c, and n are constants.

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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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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The statement, "A p-value for correlation which is statistically significant implies the correlation is due to random chance" will be; FALSE.

Since the p-value is statistically significant, it indicates that the correlation is not due to random chance but rather has a true association.

However, the p-value refers to the probability of obtaining the observed result due to chance alone.

Correlation means that the relationship between two variables and correlation coefficient is used to measure the strength and direction of the relationship between the two variables.

We can conclude that a statistically significant p-value indicates that the correlation between two variables is not due to random chance but rather has a true association.

The statement that "p-value for correlation which is statistically significant implies the correlation is due to random chance" is false.

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The complete question is;

A p-value for correlation that is statistically significant implies the correlation is due to random chance. True or False.

Yes, the equation C-1(A+X)B-1=In has a solution, X. To find the solution, first use C-1(A+X)B-1=In to simplify to C-1 AB-1=In+X. Next, use matrix multiplication to expand C-1AB-1 to In+X = AC-1B-1-B-1C-1. Subtract In from both sides of the equation to get X=AC-1B-1-B-1C-1-In. This is the solution for X, where A, B, and C are nan invertible matrices.

Given that A, B, and C are invertible nan matrices, we have to check if the equation C-1(A+X)B-1=In has a solution or not, and if there is a solution, we have to find X.

Let's solve it. Let's multiply both sides of the equation by B and C, respectively, we get C-1(A+X)B-1B = IB and C-1(A+X) = B. Now, we have to multiply both sides by C on the left, so we get C*C-1(A+X) = CB, which becomes A+X = CB.

Now we have to multiply both sides by B-1 on the right, so we get A + XBB-1 = CBB-1, which becomes A + XB-1 = CB-1.Now, we have to multiply both sides by C-1 on the left, so we get C-1A + C-1XB-1 = I.

Now, we have to multiply both sides by B and C, respectively, which results in C-1AC-1B + XC-1B = B. Finally, X = B(C-1AC-1B)B-1 - C-1B + I. We know that if A and B are matrices of the same order, then (AB)-1 = B-1A-1. By using this property, we can write the solution as X = B-1(A-1 + C-1)-1B-1 - C-1B + I. So, the solution exists for the given equation.

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Answer:

-t + 4.5>7

Step-by-step explanation:

-18 = t

-t = 18

18+4.5 = 22.5

22.5>7

Boom

hope it helps :)