2. Mateo graphs quadrilateral EFGH and then reflects it across the
line y = 2. How are the x-coordinates of corresponding points in
the image and the preimage related?

∠K≅∠T , KL/TU=JK/ST and  m∠J=m∠S are true .

Given:  △JKL∼△STU

When two triangles are similar , then their corresponding sides are proportional and Corresponding angles of one triangle is equal to corresponding angles of another Triangle.

The two Triangles can be similar by following Similarity axiom

1. AA

2. S A S

3. S S S

The Options are

→∠K≅∠T(  True) Corresponding angles are equal.

→JK≅ST (False)

→KL/TU=JK/ST (True) Because sides are proportional.

→JL=SU  (False)

→m∠J=m∠S (True)  Corresponding angles are equal.

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Usain bolt with a mass of 94 kg and speed 10m/s has kinetic energy 4700j

What is kinetic energy and what is its formula?

The energy that an object has as a result of motion is known as kinetic energy. It is described as the amount of effort required to move a mass-determined body from rest to the indicated velocity. The formula of kinetic energy is [tex]\frac{1}{2}mv^2[/tex]

We are given that the mass of usain bolt is 94 kg and that he runs at a speed of 10m/s

That means the value of m and v are 94 kg and 10 m/s respectively

Substituting the values in the formula we get

Kinetic energy = [tex]\frac{1}{2}94*10^2[/tex]

Kinetic energy = [tex]47*100\\[/tex]

Kinetic energy = [tex]4700 j[/tex]

Hence the kinetic energy of Usain bolt is 4700 j

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Answer:

Yes

Step-by-step explanation:

g(x) = 1/4 x

g(x) = x/4

f(x) = 4x

If you plugin f(x) in g(x) and g(x) into f(x), you should get x:

f(g(x))=

4(g(x)= => plugin g(x) for x in f(x)

4(x/4)=

4*x/4=x √

g(f(x))=

f(x)/4= ==> plugin f(x) for x in g(x)

4x/4 = x√

Hence, f(x) and g(x) are inverse of each other.

The probability that the sum of the numbers rolled is either even or a multiple of 5 is 61.11%.

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

Probability = Number of outcomes / Total number of outcomes

The total number of outcomes = 36

The number of outcomes whose sum is either even or a multiple of 5 = 22

The number of outcomes whose sum is either a multiple of 3 or 4 = 20

Now, the probability that the sum of the numbers rolled is either even or a multiple of 5 is,

Probability

= number of outcomes whose sum is either even or a multiple of 5 / total number of outcomes

= 22 / 36

= 11 / 18

= 0.61111

= 61.11%

Further, the probability that the sum of the numbers rolled is either a multiple of 3 or 4 is,

Probability

= number of outcomes whose sum of the numbers rolled is either a multiple of 3 or 4 / total number of outcomes

= 20 / 36

= 5/9

= 0.5555

= 55.55%

Hence, The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is 55.55%.

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Answer:

Hi, are you missing part of this question?

The temperature on the second day is 11°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the temperature on the second day be x.

Based on the information, temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up.

-4 + x = 7

Collect the like terms

x = 7 + 4..

x = 11

The temperature is 11°

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The temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up 7°. What is the Temperature on tue second day?

This is one way of writing a quadratic function:

[tex]f(x)= a(x-h)^2+k[/tex]

We're given:

[tex]f(x) = -6x^2 - 60x - 151[/tex]

To write a quadratic function in vertex form, we must complete the square.

⇒ Put parentheses around the first two terms containing x and x²:

[tex]f(x) = (-6x^2 - 60x) - 151[/tex]

⇒ Factor out -6 (keeping the x's in the parentheses):

[tex]f(x) = -6(x^2+10x) - 151[/tex]

⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.

[tex]f(x) = -6(x^2+10x+25) - 151[/tex]

⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:

[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]

⇒ Finally, complete the square.

[tex]f(x) = -6(x+5)^2 - 1[/tex]

[tex]f(x) = -6(x+5)^2 - 1[/tex]

Angle θ is equal to 0.56 radian.

What do you mean by inverse trignometry?

Inverse trigonometric functions are just the sine, cosine, tangent, cotangent, secant, and cosecant functions of the fundamental trigonometric functions. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions.

It is given that in right angle triangle, base of the triangle is 16 and height of the triangle is 10.

Now to find θ, from the given right angled triangle. Using the formula for tanθ

tanθ = P/B = 10/16 = 5/8

θ = [tex]tan^{-1}(5/8) = tan^{-1}(0.625) = 0.56[/tex] radian.

Therefore, angle θ is equal to 0.56 radian.

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The solution of the logarithm equation are as follows:

a. l = 100000

b. l = 1000000

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Let's solve the logarithm equation as follows:

a.

50  = 10 log₁₀ l

Using logarithm law,

50  = 10 log₁₀ l

50  = log₁₀ l¹⁰

10⁵⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

Hence,

l = 10⁵

Hence, the value of  l = 100000

b.

60 = 10 log₁₀ I

Using logarithm rule,

60 = 10 log₁₀ I

60 = log₁₀ l¹⁰

10⁶⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

l = 10⁶

Hence, the value of  l = 1000000

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The Z-value posted in part(c) for a confidence level of 74% is 1.150

The Confidence level in statistics denotes the likelihood that an estimate of the location of a statistical parameter (such as an arithmetic mean) in a sample survey will also hold true for the population.

Confidence levels must be determined before conducting a survey since they affect the poll's margin of error and necessary coverage. 90, 95, and 99% confidence intervals are widely employed in surveys.

A calculated statistic that was based on a sample would also be true for the entire population, within the established confidence level, with a 95% likelihood, if the confidence level were set at 95%.

Every confidence level has different z-value

In the question, We have to write the Z-value of 74% which is 1.15

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Answer: 6,845.9, or to whole number 6,846

Step-by-step explanation:

The probability of having a boy when a couple has six ​children is 63 / 64.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

A couple has six ​children, n = 6

The wanted event, p = 1 / 2

Calculate the probability of having a boy given by the following formula,

[tex]P(X) = nC_x px (1-p)n-x[/tex]

Here, [tex]X[/tex] = number of boys,

So,

P(X >= x) = 1 - P(X = 0)

P (X) = 1 - 6C₀ × (1 / 2) 0 × (1/2) 6

P (X) = 63 / 64

Therefore, the probability of having a boy when a couple has six ​children is 63 / 64.

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The rate at which water is draining when the water is  8 feet deep is calculated to be 2.54 ft³/ h

The vertex angle of the conical-shaped reservoir can be given as follows;

tan θ = R/H

Here R represents the radius and H illustrates the depth

so here we can say that the vertex angle will remain constant; therefore;

r/y = R/H

r/8 = 10/20

r = (10/20) × 8

r = 4

now for the volume, we can say;

V=1/3πr^2h

also, we can say;

r = y/2

Therefore here we will have;

V = 1/3π(y/2)^2y = 1/12 πy³

now for volume flow rate, we can determine as follows;

Q = dV/dt = 3/12πy²(dy/dt)

Q = 1/4 πy²v

Substituting the values as follows;

Q = 1/4 π(8)²(1/2)ft³/h

Q = 2.54 ft³/ h

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The correct option is option C i.e., current students are not included in the sample for the survey.

Current students are not required to participate in this survey because its main objective is to learn about respondents' career histories and starting salaries .

Survey could mean:

Research into humans and statistics.

A statistical survey is a technique for gathering numerical data on constituents of a population.

Type of survey

Cadastral surveyors provide paperwork, diagrams, plats, and maps to prove who owns the land.

Most of Western Canada is divided into one-square-mile pieces using the Dominion Land Survey technique for agricultural and other uses. Identifying and surveying land parcels in the United States using the Public Land Survey System.

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Applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers is GCD of that numbers .

Given :

You probably know the Fibonacci numbers 1 , 1 , 2 , 3 , 5 , 8 , ⋯ , where f n+2 = f n+1 + f n and we number as f 1 = 1,f 2 = 1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers .

Euclidean algorithm :

The Euclidean Algorithm is a technique for quickly finding the GCD of two integers .

GCD ( 1 , 2 )

2 = 1 * 2 + 0

GCD ( 1 , 0 )

hence GCD ( 1 , 2 ) is 1 .

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The area of the bridge(yellow part) is 297.9 m².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

From the given diagram the area of the bridge is the total area of the larger rectangle - the area of a semicircle - the area of the smaller rectangle.

We know the area of a rectangle is (length×width) and the area of a semicircle is (1/2)πr².

∴ The area of the bridge is = {(34×20) - (24×6.5) - (1/2)π(12)²} m².

= {680 - 156 - 226.1} m².

= 297.9 m².

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Alberto chooses the probability threshold needed for statistical significance and then use inferential statistics. This level layer is described known as the test's significance level.

The significance level refers to the threshold at which one may agree that an event was statistically significant.

To evaluate statistical significance, researchers utilize a measurement called the p-value: whereas if the p-value was lower than the significance level, the result is considered statistically significant. The implies as well as standard deviations of both the data samples determine the p-value.

The confidence level would be the inverse of the significance level and is computed as 1 minus the significance level.

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Answer:

y=5x

Step-by-step explanation:

a) The 95% confidence interval for the population standard deviation is given as follows: (5.25, 10.49).

b) Since the interval does not contain 3, yes, it contradicts the claim of the developer.

The bounds of the confidence interval for the variance are given as follows:

[tex]\frac{(n - 1)s^2}{\chi^{2}_{\frac{\alpha}{2}}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^{2}_{1 - \frac{\alpha}{2}}}[/tex]

The parameters are given as follows:

The critical values of the chi-square distribution with a confidence level of 95% and 18 - 1 = 17 df are given as follows:

7.5641 and 30.191.

Hence the lower bound of the interval for the variance is given as follows:

17 x 7²/30.191 = 27.59.

The upper bound of the interval is of:

17 x 7²/7.5641 = 110.13.

The standard deviation is the square root of the variance, hence the bounds are given as follows:

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Answer:

y=-4/3x+13

Step-by-step explanation:

formula:y=mx+b

you need to add 9 on both sides of the equation

so it's look like this:y-9=-4/3x+5

                                  +9          +9

so combine the like terms

y=-4/3x+13

Answer: Translation T = (x + 8, y + 4)

Step-by-step explanation:

The x coordinate moved to the right by 8 and the y coordinate moved up by 4.

Answer: 193

Step-by-step explanation:

(12 x 16) + 9/9 = 192 + 1 = 193

Assuming second term is 9/(3²)?

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS  is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.

Here,

Given:

we have to solve the system of equations given. .Each equation is added together to remove the variable Y.

2x + y = 4  

+

3x - y = 6

________

=> 5x =10

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

x =10 / 5 = 2

⇒ x=2

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The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

As a body travels a circular path, it has both a linear speed and an angular speed. The rate it travels on that path is the linear speed, and the rate it turns around the center of that path is the angular speed. The linear speed (v) and angular speed (ω) are related by the radius (r) or v = rω .

Given that ;

Radius = r = 50 ft

Frequency = f = 2 rev/min

The angular speed is the product of the angular displacement for one complete turn, namely 2π radians per revolution, and the frequency (f). That is, the angular speed is equal to ω = 2πf. Substituting this into the formula for linear speed (v), we get:

                                v = r (2πf)

                                    = (50 ft) ( 2π / rev) ( 2 rev/min)

                                    = 200π ft/min

                                    ≈ 628.2 ft/min

The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

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.

The correct options are;

a. The variables x and y also have a correlation close to 1 .

b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .

The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.

This mean that x and y are non linear correlated, but them are correlated.

For this type of data is used a non linear correlation technique know it as logarithm correlation.

Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.

So ,

The correct options are;

a. The variables x and y also have a correlation close to 1

b. A scatterplot of the variables log x andy shows a strong nonlinear pattern

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The length of AB is equal to 12cm

How to find the length of a triangle?

If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)

Leg b  = √(c² - a²)  if leg b is unknown.

The equation is c = √(a² + b²) for the hypotenuse c that is absent.

According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition. This indicates that a triangle with the dimensions 3, 4, and 9 is impossible because 3 + 4 =7 < 9.

a = √(c² - b²)

a=?,b=5,c=13

a=√169-25

a=12cm

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Answer:    If the algae in Lake Skinner doubles every day, then on the 15th day (halfway between the 1st and 30th) the lake will be covered halfway.

   If the algae doubles every day, then on January 26 it would have only doubled six times, meaning it would only cover 1/64 of the lake's surface. This is why your friend may be skeptical that the lake will be completely covered soon.

   The cleanup crew's efforts on January 29 were able to remove most of the algae, but by February 1 only 1% of the lake's surface was still covered. This means that while the problem has been greatly reduced, it is not completely solved and there may still be some risks to the fish in the lake. Continued monitoring and efforts to prevent future algae blooms may be necessary to fully protect Lake Skinner.

Step-by-step explanation:

Answer:

(4,2) may be the answer

I guess!!

Answer:

Step-by-step explanation:het