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The value of 'x' in the given proportion [tex]\frac{14}{6}[/tex] = [tex]\frac{21}{x}[/tex] is x=9 ft . The values in the dropdown menu are:

14 x 1.5 = 21

6 x 1.5 =  9

What is proportion?

Ratio and fractions are the basis of proportion. When two ratios are equivalent, it is stated by a fraction in the form of a/b, ratio a:b, and then a proportion. Any two integers may be used here as a and b. An analysis of two numbers is a proportion.  Two sets of provided numbers are said to be directly proportional to one another if they change in two different ways, either rising or decreasing.

Given the dimensions of smaller triangle:

6 ft

14 ft

16 ft

Given the dimensions of smaller triangle:

x ft

21 ft

24 ft

Given Proportion or ratio of sides,

[tex]\frac{14}{6}[/tex] = [tex]\frac{21}{x}[/tex]

14 . x = 21 . 6

      x = [tex]\frac{21 . 6}{14}[/tex]

      x = [tex]\frac{126}{14}[/tex]

      x = 9

The missing dimensions of triangle = 9 ft

Now for the answers in dropdown menu, let's evaluate the ratios of corresponding sides:

[tex]\frac{9}{6}[/tex] = [tex]\frac{21}{14}[/tex]  = [tex]\frac{24}{16}[/tex] = 1.5

a)14 x 1.5 = 21

b)6 x 1.5 = 9

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Refer to the attachment for the options.

The range of all possible values for f(1) for a strictly convex function passing through (-2,5) and (2,9) is (5,8).

Since f(x) is strictly convex, we can use the property that any point on the graph of f(x) lies below the line segment connecting the endpoints of any subinterval. In particular, for any x-value between -2 and 2, the y-value of f(x) must be below the line segment connecting (-2,5) and (2,9).

Let's first find the equation of the line segment connecting (-2,5) and (2,9). We can use the point-slope form of a line

slope = (9 - 5) / (2 - (-2)) = 4/4 = 1

y - 5 = 1(x - (-2))

y - 5 = x + 2

y = x + 7

Now we know that for any x-value between -2 and 2, the y-value of f(x) must be below the line y = x + 7. We can use this to bound the possible range of values for f(1)

-2 < 1 < 2, so f(1) must be below the line connecting (-2,5) and (2,9) when x=1.

Plugging x=1 into the equation y = x + 7, we get y = 1 + 7 = 8. Therefore, f(1) must be less than 8.

We can also use the property of strict convexity to find the maximum possible value of f(1). Since f(x) is strictly convex, the line segment connecting (-2,5) and (2,9) must lie above the graph of f(x) for any x-value outside the interval [-2,2]. This means that the graph of f(x) must be below the line connecting (-2,5) and (2,9) for x < 1 and x > 1. In particular, this means that the slope of the tangent line to the graph of f(x) at x = 1 must be less than 1, since the tangent line must lie below the line y = x + 7.

Let's find the equation of the tangent line to the graph of f(x) at x = 1. We can use the point-slope form of a line and the fact that the slope of the tangent line is equal to the derivative of f(x) at x = 1

slope = f'(1)

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

(f(1) - 5)/3 = f'(1)

Now we need to find the maximum possible value of f(1) subject to the condition that f'(1) < 1. We can use the fact that f(x) passes through (-2,5) and (2,9) to find the equation of the secant line connecting these two points

slope = (9 - 5)/(2 - (-2)) = 4/4 = 1

y - 5 = 1(x - (-2))

y = x + 7

Since the slope of the secant line is 1, the slope of any tangent line to the graph of f(x) must be less than 1. This means that the maximum possible value of f'(1) is 1. Therefore,

(f(1) - 5)/3 < 1

f(1) - 5 < 3

f(1) < 8

Combining this with the earlier bound, we get

5 < f(1) < 8

Therefore, the range of all possible values for f(1) is (5,8).

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The given question is incomplete, the complete question is:

suppose f(x) is a function that has this property: for all real numbers a and b such that a<b , the portion of the graph of y = f(x) between x= a and x = b lies below the line segment whose endpoints are (a,f(a)) and (b,f(b)) . (a function with this property is called strictly convex.) given that f(x) passes through (-2,5) and (2,9) , what is the range of all possible values for f(1)  ?

In general, an appropriate null hypothesis is one that states there is no significant difference or relationship between two variables.

Therefore, out of the options given, the appropriate null hypothesis would be "selection was not a significant factor."
An appropriate null hypothesis is "Selection has no effect on the observed outcome. "it means that any differences observed in the data are due to chance, and not due to a specific selection process or factor. The null hypothesis serves as a starting point in statistical analysis, and researchers aim to either accept or reject it based on the evidence collected.

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The equation for the graph of g(x) in different conditions;

g(x) = 2|x|

g(x) = -2|x|

g(x) = -2|x| -3

g(x) = -2|x -1| -3

Now, Multiplying the function by a constant stretches the graph by that constant. Here, we want a stretch factor of 2,

g(x) = 2f(x) = 2|x|

Now Negating a function causes its graph to be reflected over the x-axis.

 g(x) = -2|x|

Then, Subtracting 3 from the function value shifts its location on a graph down by 3 units.

g(x) = -2|x| -3

Now, Subtracting a constant from the x-value causes the graph of the function to be shifted right by that amount.

 g(x) = -2|x -1| -3

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The correct answer is D. The graph is a downward parabola, which means it opens downwards and is decreasing. This occurs for all negative values of x, and is also decreasing for values of x close to zero.

A graph is a visual representation of data or information, typically shown using lines, bars, dots, or other symbols to illustrate relationships, trends, and patterns.

A parabola is a U-shaped curve that is symmetric and can be represented by a quadratic equation. It is a type of conic section and appears in many areas of mathematics and physics.

According to the given information:

The correct answer is D. The graph is a downward parabola, which means that it opens downwards and has a maximum point at the vertex. The vertex is located at x = 0, and since the graph is decreasing on both sides of the vertex, it means that it is decreasing when x < 0. As x approaches negative infinity, the graph becomes more and more steep, and as x approaches positive infinity, the graph becomes flatter and flatter. This behavior is typical of a quadratic function with a negative leading coefficient. In this case, the graph represents a situation where the dependent variable decreases as the independent variable increases up to a certain point, after which it starts increasing again.

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Answer: x = 1.

Step-by-step explanation: 1 - 2x = 5 - 6

To simplify, we first subtract 5 from both sides:

-4 - 2x = -6

Then we add 4 to both sides:

-2x = -2

Finally, we divide both sides by -2:

x = 1

The ratio of seventh-graders girls to seventh-grade students is 3 : 5

From the question, we have the following parameters that can be used in our computation:

40% of the seventh-grade students are boys

This means that

60% of the seventh-grade students are girls

So, we have

Girls to Students = 60% : 100%

Simplify

Girls to Students = 3 : 5

Hence, the ratio is 3 : 5

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When using a standard normal table or calculator, it becomes clear that the area under the standard normal curve to the right of z=1.0 is approximately 0.1587.

Similarly, with the aid of this table or calculator, one can further deduce that the region under the standard normal curve to the left of z=-1.25 is roughly equal to 0.1056, while the section to the right of z=1.25 shares the same probability of 0.1056. Therefore, their combined value equates to 0.2112.

Through utilizing a standard normal table or calculator:

a. The possibility of z being lower than 1.96 is approximately 0.9750.

b. The likelihood of z being greater than 1.28 is about 0.1003. (It's crucial to note that this differs from the area to the right of z=1.28, which includes the region all the way up to z=1.28.)

Suppose one wishes to determine the z-score that corresponds to an IQ score of 90. In that case, we employ the following formula:

z = (x - μ) / σ

Indicating that x is the IQ score, μ denotes the mean (100), and σ is the standard deviation (15). By entering in these variables, one derives:

z = (90 - 100) / 15 = -0.67

Thus, the corresponding z-score to an IQ score of 90 is -0.67.

If finding out what IQ score corresponds to a z-score of -1.45 while considering the previously mentioned formula, one would alter it as follows to solve for x:

x = μ + z * σ

After substitution, this produces:

x = 100 + (-1.45) * 15 = 78.25

Consequently, the IQ score corresponding to a z-score of -1.45 is 78.25.

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The sum and the differences of the fractions are 25/28 and 1/6

For the first fraction expression, we have

3/4 + 1/7

Express them using a common denominator

So, we have

3/4 = 21/28

1/7 = 4/28

So, we have

3/4 + 1/7 = 21/28 + 4/28

Evaluate the sum

3/4 + 1/7 = 25/28

Next, we have

5/6 - 2/3

Express them using a common denominator

So, we have

5/6 = 5/6

2/3 = 4/6

So, we have

5/6 - 2/3 = 5/6 - 4/6

Evaluate the difference

3/4 + 1/7 = 1/6

Hence, the solutions are 25/28 and 1/6

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The solution to the equation is x= -10 and y= 5.

We have Equations,

2x + 6y = 10............(1)

3x - 2y = -40............(2)

Now, solving equation (1) and (2) we get

2x + 6y = 10

9x - 6y = -120

+    +       +

__________

   11x = -110

      x = -10

and, 3(-10) - 2y= -40

-30 - 2y= -40

-2y = -10

y=5

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Answer:

To determine the value of f(-1), we need to substitute -1 for x in the function y = 7x+4 and then solve for y:

y = 7x + 4

f(-1) = 7(-1) + 4

f(-1) = -7 + 4

f(-1) = -3

Therefore, f(-1) = -3.

Answer:-f

Step-by-step explanation:

Answer: option 3 is correct

Step-by-step explanation: Simplify the expression.−8m^5z^6

Value of mean is, 40.2

Value of median is, 45

Value of mode is, 28

Value of range is, 25

Given that;

Data set is,

⇒ 28, 45, 53, 28, 47

Now, We can arrange into ascending order as;

⇒ 28, 28, 45, 47, 53

Hence, Value of mean is,

⇒ (28 + 28 + 45 + 47 + 53) / 5

⇒ 40.2

And, The value of median is,

⇒ (5 + 1) / 2

⇒ 6/2

⇒ 3rd term

⇒ 45

The value of mode =28

And, The value of range is,

⇒ 53 - 28

⇒ 25

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Answer:

Step-by-step explanation:

Interior Angle to a Circle Theorem.

X° = 1/2 (130° + 142°)

x° = 1/2 (272°)

x° = 136°

True interpretation of the p-value is option E: if H0 is true, the probability of observing another sample with an average as or more extreme as the data is 0.23.

a. False. The p-value, under the assumption that the null hypothesis is correct, is the likelihood of finding a sample mean that is equally extreme or more extreme than the observed sample mean. The likelihood that the null hypothesis is true or false is not represented by it.

b.  False. The population mean being greater than 10 oz is not immediately shown by the p-value of 0.23. Only the amount of evidence that refutes the assumption that the population mean is equal to 10 oz is indicated.

c.  False. The p-value is a measure of the strength of evidence against the null hypothesis rather than the population mean.

d.  False. Having a low p-value does not necessarily suggest that the population average is just barely above 10 oz; rather, it implies that there is substantial evidence that the null hypothesis is false. A measure of the effect's size, such as Cohen's d or confidence intervals, should be used to assess the magnitude of the effect.

e. True. The p-value is correctly interpreted in this way. In the event that the null hypothesis is correct, the p-value represents the likelihood that another sample will have averages that are equally or even more extreme than the data.

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Answer:

Step-by-step explanation:

The statement that gives a unit rate is "for every day, Trey's cat ate 1.5 cups". So correct answer is option B).

This statement represents the amount of cat food consumed per unit of time, which is 1.5 cups per day. A unit rate is a comparison of two measurements in which one of the numbers is 1, making it easier to compare different rates. So, the correct option is B).

In this case, the unit rate would be 1.5 cups per day. Option A and C are not unit rates because they express the amount of cat food consumed over a varying number of days, while option D is not a unit rate because it expresses the amount of cat food consumed in a fractional amount of a day.

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Statements that are true about plant (height) is a) The plant has grown a total of 4.77 cm in two weeks.

Statement a is true because the plant grew 2.8 cm in the first week and 1.97 cm in the second week, for a total of 4.77 cm in two weeks.

Statement b is false because the plant grew at a slower rate in the second week than the first week.

Statements c, d, and e cannot be determined from the given information as they are unrelated to the growth rate of the plant.

a) The plant has grown a total of 4.77 cm in two weeks (True)

b) The plant grew at a faster rate in the first week than the second week (False)

c) The plant will be 100 cm tall after 50 weeks (Cannot be determined from the given information)

d) The plant will require at least 5 cm of water per week to continue growing (Cannot be determined from the given information)

e) The plant will die if it doesn't receive enough sunlight each day (Cannot be determined from the given information)

Correct Question :

Kevin bought a new plant. The plant grows 2. 8 cm in the first week and 1. 97 CM the second week. Select all of the statements that are true about the plant.

a) The plant has grown a total of 4.77 cm in two weeks

b) The plant grew at a faster rate in the first week than the second week

c) The plant will be 100 cm tall after 50 weeks

d) The plant will require at least 5 cm of water per week to continue growing

e) The plant will die if it doesn't receive enough sunlight each day

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Answer: is 2.5

Step-by-step explanation:

I looked it up

Answer:

Volume of cube =a3=43=64 cm3.

Step-by-step explanation:

Answer is 64 cm3

The equation of the parabola as [tex](y-6)^2 = 12(x-0) or (y-6)^2 = 12x.[/tex]

Given an axis equation of y=6, focus at (0,6), and p=-3, this is a horizontal parabola with its vertex at (0,6).

Since p<0, it opens to the left.

The standard equation of a horizontal parabola with vertex (h,k) and distance p is [tex](y-k)^2 = -4p(x-h).[/tex]

Plugging in the values (h,k)=(0,6) and p=-3, we get the equation of the parabola as [tex](y-6)^2 = 12(x-0) or (y-6)^2 = 12x.[/tex]

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After 5 years, Account Y earns more interest than Account X, even though the annual interest rate is slightly higher for Account X.

To compare the interest earned on Account X and Account Y, we can use the following formulas

For Account X

Simple interest = P × r × t

Where P is the principal, r is the annual interest rate, and t is the time in years.

For Account Y

Compound interest = P × [tex](1 + r/n)^{nt}[/tex] - P

Where P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using the given information, let's say we invest $10,000 in both accounts for 5 years.

For Account X

Simple interest = 10,000 × 0.021 × 5 = $1,050

For Account Y

Compound interest = 10,000 × (1 + 0.024/1)⁵ - 10,000 = $1,268.24

So, after 5 years, Account Y earns more interest than Account X, even though the annual interest rate is slightly higher for Account X. This is because Account Y compounds the interest annually, which means the interest earned in each year is added to the principal, resulting in a higher total amount of interest earned over time.

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Answer:

x = 15 and x = 10

Step-by-step explanation:

To complete the square for the quadratic equation -10x² + 250x - 1500 = 0, follow these steps:

1. Divide the entire equation by the coefficient of x² to make the coefficient of x² equal to 1:

-10x² + 250x - 1500 = 0

Dividing by -10, we get:

x² - 25x + 150 = 0

2. Move the constant term (in this case, 150) to the right-hand side of the equation:

x² - 25x = -150

3. Add the square of half of the coefficient of x to both sides of the equation:

x² - 25x + (25/2)² = -150 + (25/2)²

Note that (25/2)² = 625/4.

x² - 25x + 625/4 = -150 + 625/4

4. Simplify the right-hand side of the equation:

x² - 25x + 625/4 = 25/4

5. Factor the left-hand side of the equation as a perfect square trinomial:

(x - 25/2)² = 25/4

6. Take the square root of both sides of the equation:

x - 25/2 = ±5/2

7. Solve for x:

x = (25 ± 5)/2

x = 15 or x = 10

Therefore, the solutions to the equation -10x² + 250x - 1500 = 0 are x = 15 and x = 10.

Answer:

Step-by-step explanation:

you hav to times it

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled. This model helps to identify the mathematical correlations between variables and provides a foundation for developing a more detailed and accurate mathematical model.

The modeling process begins with the framing of a mathematical model that shows the relationships between the various parts of the problem being modeled. This model is often based on data analysis and utilizes statistical techniques to establish correlations between the different variables in the problem. Ultimately, the goal of the modeling process is to create a predictive tool that can be used to make informed decisions about the problem at hand.

Process models involve graphically representing processes or functions that capture, manage, store, and distribute information between the system and its environment and physical objects. One type of process model is the flowchart (DFD). A data flow is a diagram that shows the movement of data between external sources and processes and the data stored in the system. While several different tools have been developed for modeling, we focus only on data streams as they are effective tools for modeling. While not all organizations use all analytical methods, including these methods such as data flow, they have a significant impact on the development process.

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Answer:

2327

Step-by-step explanation:

17,900 x 13 : 100 that's the answer I think

The jet airplane covers a distance of approximately 148.62 km in 14.0 minutes, given that it reached a speed of 637 km/h during the flight.

To find the distance covered by the jet airplane in 14.0 minutes, we need to use the formula:

distance = speed x time

First, we need to convert the speed from kilometers per hour to meters per minute, since time is given in minutes:

637 km/h = 637,000 m/h

1 hour = 60 minutes, so:

637,000 m/h ÷ 60 min/h = 10,616.67 m/min

Therefore, the speed of the airplane in meters per minute is approximately 10,616.67 m/min.

Now we can use the formula:

distance = speed x time

where time is given as 14.0 minutes:

distance = 10,616.67 m/min x 14.0 min

distance = 148,616.67 meters

To convert the distance to kilometers, we can divide by 1000:

distance = 148,616.67 m ÷ 1000 = 148.62 km

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Complete question is:

A jet airplane reaches 637. km/h on a certain flight. What distance does it cover in 14.0 min?

Answer:

4

Step-by-step explanation:

(4+2+7+4+3)/5 = 20/5 = 4

The mean is also known as the average. To find the mean/average, we add up all of the given numbers and then divide by the number of numbers we added up.

In this case, our numbers are 4, 2, 7, 4, and 3, and there are 5 numbers total.

Mean = (4 + 2 + 7 + 4 + 3) / 5

Mean = 20 / 5

Mean = 4

Answer: Mean = 4

Hope this helps!

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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The surface area of a pyramid is similar to finding the surface area of a cone as both compose of Area of base and LSA or CSA.

To derive the Surface Area of Pyramid

Total Surface Area (TSA of Pyramid)

= LSA of pyramid + Area of the base.

= (½)Pl + B Square units

and, to derive the Surface area of Cone

The total surface area is

= CSA of cone + Area of Base

= πrl + πr²

= πr(l +r)

So, both SA have Area of base and LSA or CSA

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