1. In the diagram below, AB = AC, CB = CE,
BD = BE, BC = 9 cm and CD = 5 cm. FindAC.

Answer:

1.  \(-1\) \(\frac{1}{3}\)

2. \(-1\) \(\frac{1}{2}\)

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

4. \(1 \frac{3}{4}\)

-1 1/3 is the least of all the numbers. So, this is the first number.

-1 1/2 is the second least number. So, this is the second number.

1 1/2 is the third least number. So, this is the third number.

Finally, 1 3/4 is the greatest number, so it is the fourth number.

Hope this helps you!

The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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Answer: 20

Step-by-step explanation:

1. a/(-5) = 8

a = 8 * (-5) = -40

2. 8/b = -4

b = 8/(-4) = -2

3. a/b = (-40)/(-2) = 20

Answer:

20

Step-by-step explanation:

We can figure out a and b using the expressions below:

A/-5 = 8 (Multiply both sides by -5)

A = -40

8/B = -4 (Multiply both sides by B)

8 = -4*B (Divide both sides by -4)

-2 = B

We can then divide A by B (-40/-2) and get 20.

Answer:

x^7/6

7 square root x^6 would be x ^7/6

The expression can be written in the form of exponential form after applying the property of the integer exponent.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

\(=\rm \sqrt[7]{x^6}\)

After applying the property of the integer exponent:

\(= \ \rm {x^{6/7}}\)

Thus, the expression can be written in the form of exponential form after applying the property of the integer exponent.

The options are:

x^{6/7}

x^{7/6}

x^{6x7}

7x^{6}

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1.   he ate 1/4 of the bucket

2.   4 of the pool floaties are yellow.

3.   she paid 4$ for the cookies

4 .  3 members of the band play the drums

5.   45 minutes

Answer:

1.  Ansley eats 1/4 of the popcorn bucket

2. He bought 4 yellow floats

3. She pays 4 pounds for the cookies

4. 3 members of the band play the drums

5. They spent 45 minutes jumping on the trampoline

Step-by-step explanation:

If you would like the explanation, I can comment it below (≧∇≦)/ xx

Hope this helps! ♡

Answer:

$49950

Step-by-step explanation:

you do 45000(.11) which equals 4950. and then you add 4,950 to 45000, and then you get your answer

Answer:

3

Step-by-step explanation:

12*25=300/100=3

Answer:

△JKI is conruent to △TRS

Step-by-step explanation:

It is based on the order of the vertices.

Answer:

answers is option C

Step-by-step explanation:

answer option C

The graph of the equation y = 2.5x is the graph in Choice A where evidently, the slope of the graph is 2.5.

To determine which graph is the graph of the equation y = 2.5x;

We must know that the equation takes the slope-intercept form of the equation of a straight line;

By observation, the graph drawn in Choice A has a slope of 2.5.

This is evident when we set the value of x = 2, we consequently get the value of y = 5.

The graph of Choice A is has a point represented by the coordinates, (2,5).

Ultimately, the correct answer is Choice A.

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384,000 bacteria would be present at the end of 7 hours if it doubles itself every hour.

Initial number of bacteria=3000

Number of bacteria at the end = initial number of bacteria * (base)ⁿ

where, n= number of hours

Number of bacteria at the end=3000*2⁷

                                                    =3000*128

                                                     =384,000

Therefore, there will be 384000 bacteria at the end of seven hour if the bacteria doubles itself every hour.

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The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.

The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.

The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.

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The length of the larger bed is 22 feet. The length of the smaller bed is 13 feet.

Let the side of the larger square be x and that of the smaller square be y.

The area of the larger square is given by x².

The area of the smaller square is given by y².

According to the problem statement, we can derive two equations:

x² + y² = 653 (sum of the areas)

x² - y² = 315 (difference of the areas)

We can solve these two equations simultaneously to find the values of x and y.

x² + y² = 653 x² - y²

= 315

Adding these two equations, we get: 2x² = 968 x²

= 484 x

= 22 (since x cannot be negative)

Substituting x = 22 in one of the equations above, we get:

y² = 653 - x²y²

= 653 - 484 y²

= 169 y

= 13

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The conditions for conducting one-sample t-procedures are as follows:

1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.

2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.

3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.

4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.

5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.

It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.

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The rate at which the distance between the two cars is increasing two hours later is 52 mi/h.

To determine the rate of change of the distance between the cars, we can use the concept of relative velocity. Since one car is moving south and the other is moving west, their velocities are perpendicular to each other. Thus, we can use the Pythagorean theorem to find the distance between them at any given time.

After two hours, the southbound car would have traveled 48 mi/h * 2 h = 96 miles, and the westbound car would have traveled 20 mi/h * 2 h = 40 miles. Therefore, the distance between the cars is the hypotenuse of a right triangle with sides 96 miles and 40 miles.

Using the Pythagorean theorem, the distance between the cars is √(96^2 + 40^2) = √(9216 + 1600) = √10816 = 104 miles.

Since two hours have passed, the rate at which the distance is increasing is 104 miles / 2 hours = 52 mi/h. Therefore, the distance between the cars is increasing at a rate of 52 mi/h.

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Answer:

Step-by-step explanation:

The length of the rectangular backyard is represented by the polynomial 3x + 4 and the width is represented by the polynomial x - 1. To find the area, we can multiply the length and the width, which will give us the polynomial expression for the area.

So the polynomial that represents the area of the rectangular backyard is:

(3x + 4) * (x - 1) = 3x^2 + x - 4

If x = 6, then we can substitute this value into the polynomial expression for the area and find the area of the backyard:

3x^2 + x - 4 = 3(6)^2 + (6) - 4 = 108 square feet

So the area of the rectangular backyard when x = 6 is 108 square feet.

The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

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Answer:

37

Step-by-step explanation:

1. Answer:

They are not similar.

1. Step-by-step explanation:

They do not have a common "rule" or do not multiply/divide to get the sides.

2. Answer:

They are  similar.

2. Step-by-step explanation:

Each side is being divided by 5 to get the sides.

Have a great day/night!

Answer:

Both triangles are isosceles.

Let's determine the ratio of corresponding sides:

Ratios are different 3/4 ≠ 2/3, this indicates the corresponding angles are not equal.

The triangles are not similar.

Given two rectangles.

Let's find the ratio of corresponding sides:

Correct choice is:

Answer: 23

Step-by-step explanation:

Equation:

(25-12)x - 60 = 250

13x - 60 = 250

13x = 310

x = 23.8 (I Rounded)

Since x has to be a whole number in a real-world situation, the answer is 23.

Step-by-step explanation:

9 x 4=36 is the answer

hope this helps you

have a nice day:)

The statement that is true concerning the function of the table compared to the graph is that the graphed function has a greater maximum value. That is option D.

From the graph, the maximum value is =0.5 while the minimum value cannot be determined.

From the table the maximum value is -3 while the minimum value is -24.

Therefore, the statement that is true concerning the function of the table compared to the graph is that the graphed function has a greater maximum value.

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Answer:

9/2

Step-by-step explanation: I think it is the answer? I really don't know.

Option A (0,1,-1,1) is in the span of {(1,2,0,1),(1,1,1,0)}.

To determine which vector is in the span of {(1,2,0,1),(1,1,1,0)}, we need to find a linear combination of these two vectors that equals the given vector.

Let's start with option A: (0,1,-1,1). We need to find scalars (a,b) such that:

(a,b)*(1,2,0,1) + (a,b)*(1,1,1,0) = (0,1,-1,1)

Simplifying this equation, we get:

(a + b, 2a + b, a + b, b) = (0,1,-1,1)

We can set up a system of equations to solve for a and b:

a + b = 0
2a + b = 1
a + b = -1
b = 1

Solving this system, we get a = -1 and b = 1. So, option A can be written as a linear combination of the given vectors:

(-1,1)*(1,2,0,1) + (1,1)*(1,1,1,0) = (0,1,-1,1)

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Hi. you've asked an incomplete question. However, I provided some explanation about algebraic expressions and numerical expression.

Step-by-step explanation:

First, we may wonder: What is a numerical expression? In simple words, they are mathematical expressions that contain numbers and operations (like +, -, ÷, ×).

For example, 7+70, 90-10, 60÷10, 5×4 are numerical expressions.

While an algebraic expression on the other hand is a mathematical expression that contains at least one variable.

Variables are letters or symbols (like x, y, p, q, etc) that represent an unknown number or value in a mathematical expression.

For example, 7x+70, 90y-10 are algebraic expressions since they contain at least one variable.

Answer:

A

Step-by-step explanation:

Answer:

A is the answer

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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Answer:

1 gigabyte

Step-by-step explanation:

70-65.50=4.5

The maximum whole number of gigabytes of data she can use while staying within her budget 2 gigabytes.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now given that,

Flat cost per month = $65.50

Cost per gigabyte = $4

Let x be the total gigabytes she uses in a month.

Thus, Cost of gigabytes of month = 4x

So, total bill of the month = 65.50 + 4x

Now  since, Hannah wants to keep her bill under $70 per month

⇒ 65.50 + 4x ≤ 70

Subtracting 65.50 both the side we get,

4x ≤ 70 - 65.50

⇒ 4x ≤ 4.50

Dividing 4 both the side we get,

⇒ x ≤ 1.125

Since she has to pay for the whole gigabytes

⇒ x ≤ 2

which is the required gigabytes she can use to keep her bill $70.

Thus, the maximum whole number of gigabytes of data she can use while staying within her budget is 2 gigabytes.

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curve C in the first quadrant from (0, 2) to (√2, √2).

What is Quadrant?

Quadrant: Each of the four quarters of a circle or instrument used for angular measurements of altitude in astronomy and navigation, typically consisting of a graduated quarter circle and a sighting mechanism.

To integrate the function f(x, y) = x^2 - y over the given curve C: x^2 + y^2 = 4 in the first quadrant from (0, 2) to (√2, √2), we can parameterize the curve C and then evaluate the line integral.

We can parameterize the curve C as follows:

x = rcos(t)

y = rsin(t)

Since the curve is defined on the circle with radius 2, we have r = 2. Thus, the parameterization becomes:

x = 2cos(t)

y = 2sin(t)

To determine the limits of integration for t, we need to find the values of t that correspond to the given points on the curve.

For the starting point (0, 2), we have:

x = 2*cos(t) = 0

Solving for t, we find t = π/2.

For the ending point (√2, √2), we have:

x = 2*cos(t) = √2

Solving for t, we find t = π/4.

Now we can calculate the line integral of f(x, y) over C using the parameterization:

∫[C] f(x, y) ds = ∫[t=π/2 to t=π/4] (x^2 - y) ||r'(t)|| dt

where ||r'(t)|| represents the magnitude of the derivative of the vector function r(t) = (x(t), y(t)).

Let's calculate the derivatives:

x'(t) = -2sin(t)

y'(t) = 2cos(t)

Therefore, ||r'(t)|| = sqrt(x'(t)^2 + y'(t)^2) = sqrt((-2sin(t))^2 + (2cos(t))^2) = sqrt(4sin(t)^2 + 4cos(t)^2) = sqrt(4) = 2.

Substituting the parameterization, limits of integration, and ||r'(t)|| into the line integral, we have:

∫[C] f(x, y) ds = ∫[t=π/2 to t=π/4] (x^2 - y) ||r'(t)|| dt

= ∫[t=π/2 to t=π/4] ((2cos(t))^2 - 2sin(t)) * 2 dt

= 2∫[t=π/2 to t=π/4] (4cos(t)^2 - 2sin(t)) dt.

Now we can evaluate this definite integral to find the value of the line integral over the given curve C in the first quadrant from (0, 2) to (√2, √2).

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Answer:

positive 6 is the change in the sequence