Find the length of side AC in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and

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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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.

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: 193

Step-by-step explanation:

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

Assuming second term is 9/(3²)?

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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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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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

In the binomial expression (x + y)^10, the term that will appear in the expansion of expression is ax^3y^7.

Binomial expression refers to the algebraic expression which contains two terms. These expressions are expanded using binomial theorem. According to the theorem, it is possible to expand the binomial (x + y)^n into a sum involving terms of the form ax^by^c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. Hence, for the given expression, the term which will appear in the expansion of binomial would have variables whose sum of power would be equal to the power of the expression i.e., the sum of the power would be 10. Hence, ax3y7 would appear in the expansion as the sum 3+7=10.

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Answer:

y=5x

Step-by-step explanation:

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 equivalent expression for the given expression is -2i(-8+4i).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 8 +16i.

The given expression can be written as 8(1+2i)

-2i(-8+4i)

= -2i×(-8)-(-2i)×4i

= 16i-8i²

= 16i-8(-1)

= 8+16i

Therefore, the equivalent expression is -2i(-8+4i).

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∠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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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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Answer:

Step-by-step explanation:het

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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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.

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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The null hypothesis is  H0: μ ≤ 68,800 for the  given  case of The owner of a football team claiming that the average attendance for games is 67,800.

Since we know that a null hypothesis (H0) shows that no significant variation exists between variables in other words it can be said that a single variable is much not different than its mean.  since from the above case we were given the information that The owner of a football team claims that the average attendance for games is 67,800. So, the null hypothesis the that the average attendance at games is less than or equal to 68,800.

H0: μ ≤ 68,800

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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?

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

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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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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The vector are quantity that has both magnitude and direction. they are normally visualized in graph.

A vector - values function F : R² ---> R² can be visualized as a vector field. At a point (x,y) , we plot a value of F(x,y) as a vector with the tail anchored as (x,y)

If we visualize the vector field it will look like an explosion emanating from the origin.

At each point (x,y) , the vector F(x,y) points precisely away from the origin.

If you drew the arrows to scale they would be as long as the distance to the origin but again the drawn arrows are shorter than the actual values of the vector field

The graph of a vector field is created by pointing arrows one at a time of substituting points into the plane to determine what error to draw at the point

The question is incomplete so, I have answered in general

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Answer:

(4,2) may be the answer

I guess!!

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 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 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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