In ΔUVW,
U
W
‾
UW
is extended through point W to point X,
m
∠
U
V
W
=
(
3
x
+
4
)
∘
m∠UVW=(3x+4)
∘
,
m
∠
V
W
X
=
(
8
x
−
12
)
∘
m∠VWX=(8x−12)
∘
, and
m
∠
W
U
V
=
(
x
+
20
)
∘
m∠WUV=(x+20)
∘
. What is the value of
x
?
x?

Answer:

Step-by-step explanation:

?

Answer:

[tex]\huge\boxed{\sf 1}[/tex]

Step-by-step explanation:

f(x) = 3x - 4

Put x = 3

f(3) = 3(3) - 4

f(3) = 9 - 4

Also,

g(x) = x²

Put x = 2

g(2) = (2)²

Subtract Eq. (2) from Eq. (1)

= 5 - 4

[tex]\rule[225]{225}{2}[/tex]

Answer:

F(3) -g(2) = 1

Step-by-step explanation:

F(3)= 3(3) -4= 5

g(2)= [tex]2^{2}[/tex] = 4

f(3) -g(2)= 5-4 =1

The required simplified value of the given expression is x = 0.67.

Given that,
To determine the simplified solution of the expression, [tex]\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right][/tex]

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

In order to simplify the given expression, we have to transpose the number across the equal sign as exponents numbers tobe either side and constant on the other side.

[tex]=\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right]\\=\left(\left(3\sqrt{3}\right)^x\right)^{-1}+1=\frac{1}{3}\left[\left(\left(3\sqrt{3}\right)^x\right)^2-5\right]\\= 2 / 3\\= 0.67[/tex]

Thus, the required simplified value of the given expression is x = 0.67.

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Therefore, by using trigonometry and ratios of trigonometry the height of the airplane is 426 feet.

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometric functions (also known as circular functions) include the cosecant, cosine, cotangent, secant, sine, and tangent.

With this drawing, we can see that this is a right triangle, which can be solved using some trigonometry. To solve the height, we must use the tangent:

for the diagram see the image.

[tex]tanA = \frac{opposite}{adjecent} \\tan (12) = \frac{opposite}{adjecent} \\\frac{0.213}{1} = \frac{height}{2000}\\height = 2000(0.213)\\\\[/tex]

height = 426 feet

Therefore, the height of the airplane is 426 feet.

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By using the quadratic equation that can be written with the given information:

x² -7x + 10 = (x - 5)*(x - a)

We will see that the length is:

L  = x - 2

Remember that for a rectangle of length L and width W, the area is given by the product:

A = L*W

Here we know that:

The area is: x² -7x + 10

The width is: x -5

The length will be another factor of the quadratic equation, and we know that it should be of the form:

(x - a)

Using the area formula, we will get:

x² -7x + 10 = (x - 5)*(x - a)

Expanding the right side we get:

x² -7x + 10 = x² -5x -ax + 5a

x² -7x + 10 = x² + (-5 - a)*x + 5a

Comparing like terms, we can see that:

-5 - a = -7

5a = 10

The solution of both of these is:

a = 7 - 5 = 2

a = 10/5 = 2

Then the length of the rectangle is:

L = (x - 2)

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If 675 workers work for 3 hours and can produce 11198.25 widgets then the constant of proportionality is  5.53 .

In the question,

it is given that ,  

the number of widgets production varies with the  number of workers and the time that they have worked ,

let the number of workers be "w" and

let the number of time they worked be "t" ,

let the number of widgets produced be "n".

So , the equation becomes

n ∝ w × t

n = k × t × w

Substituting the values of w  = 675 , t = 3 and n = 11198.25

we get ,

11198.25 = k × ×675 × 3

k = 11198.25/2025

k = 5.53

Therefore , the constant of proportionality is 5.53  .

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At n = 75 the value of 3/5 * n will be 45

What is Fraction?

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction denotes the number of components of a specific size.

Solution:

Since we are given that 3/5 of n is 45

We can for an equation as 3/5 * n = 45

and to solve this we neeed to use cross multiplication method for the same

Cross Multiplication

n = 45*5/3

n = 15*5

n = 75

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Answer:

2/3

Step-by-step explanation:

To find slope, we have:

change in y /(over) change in x

1-(-3) = 4, and -2-(-8) = 6, so 4/6 = 2/3, which is our answer.

The new equation of the function y = 2^x + 4 shifted 10 units to the left is y = 2^(x-10) + 4

translation moves a shape left, right, up, or down but does not turn. The translated shapes (or the image) appear to be the same size as the original shape, indicating that they are congruent.

Since the function is shifted 10 units to the left, it means the x coordinate of the function is reduced by 10.  making the exponent (x) to become (x - 10)

So the function's new equation is y = 2^(x-10) + 4

In conclusion, the new equation is  y = 2^(x-10) + 4

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51.6is the likelihood of the given sample.

Explanation:

P (X) is equal to n/N,

155/3 = 51.6.

The likelihood of choosing at random a mammal species that is not present in either North America or Europe is 51.6.

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51.6 is the likelihood of the given sample.

A population unit's likelihood of being included in a sample obtained using probability sampling is known as probability of selection.

Interpretation, each subgroup of a population is assigned a probability of being chosen in the sample according to the sampling design.

P (X) is equal to n/N, where n is the number of favorable outcomes and n is the total number of outcomes that are feasible.

(N-n/N-(n-1)). The probability P is given here, along with the sample size n and the population N. The result will be P = n/N if 1-(N-n/n) is now cancelled. Additionally, it is required that a sample have a possibility of being chosen more than once: P = 1-(1-(1/N)) n.      

P (X) is equal to n/N,

155/3 = 51.6.

The likelihood of choosing at random a mammal species that is not present in either North America or Europe is 51.6.

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Answer: hypotenuse and leg of one right triangle

Step-by-step explanation:

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Answer:

[tex]2 \sqrt[]{7} , and -2\sqrt[]{7}[/tex]

Step-by-step explanation:

or:

x=5.29150262…,−5.29150262

Yes, 1 is the first square number.

What is a square number?

A square number, sometimes known as a perfect square, is an integer that is an integer squared; in other words, it is the result of multiplying an integer by itself. Because it equals 3² and can be represented as 3 *3, the number 9 is an example of a square number.

Given that 1 x 1 equals 1, the initial square number is 1.

Due to the fact that 3  x 3 = 9, the third square number is 9, and so forth. Following are the first fifteen square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, and 225.

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In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time.

A simulation is a model that replicates how a current or proposed system functions, offering evidence for decision-making by allowing the testing of various scenarios or process improvements. A more immersive experience can be had by combining this with virtual reality technology.

The fundamental goal of simulation is to illuminate the underlying processes that regulate a system's behavior. A system's future behavior can be predicted (forecasted) using simulation, and you can use it to figure out how to influence that behavior in the future.

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(a) The first four terms of the geometric sequence are 3, 9, 27, 81.

(b) The product of any two terms of the sequence is present in the sequence.

A geometric sequence is one where each phrase is obtained by multiplying the term before it by the same number.

Formula to find nth term of geometric sequence is aₙ = a₁ rⁿ⁻¹. The common ratio is expressed as the value r.

Given that,

The nth term of the geometric sequence uₙ = 3ⁿ.

(a)

The first term of the sequence u₁ = 3¹

Second term of the sequence u₂ = 3² = 9

Third term of the sequence u₃ = 3³ = 27

And the fourth term of the sequence u₄ = 3⁴ = 81

The four terms of the sequence are 3, 9, 27, 81.

(b)

To prove that product of two term is also present in the sequence.

Product of first two terms = 3 x 3² = 3 x 9 = 27

27 is present in the sequence.

Further, product of next two terms,

9 x 27 = 243 = 3⁵

3⁵ will also present in the sequence.

Therefore, product of any two terms is present in the sequence.

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The difference between the largest and smallest geometric numbers is 840.

Assume that the largest geometric number starts with a 9.

We know that the common ratio must be a rational of the form k/3 for some integer k, because a whole number should be attained for the 3rd term as well. When k = 1, the number is 931.

When k = 2, the number is 964. When k = 3, we get 999, but the integers must be distinct.

By the same logic, the smallest geometric number is 124.

The largest geometric number is 964 and the smallest is 124. Thus the difference is 964 - 124 = 840.

Hence, the difference between the largest and smallest geometric numbers is 840.

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Answer: Red.

Step-by-step explanation:

There are 10 marbles of each colour as described here: 'A bag contains the same number of each of four different colors of marbles.' The theoretical probability of drawing any marble of a select colour is 1/4. The red marble was drawn 10 times, making it fit this 1/4 theoretical probability.

The answer to this Question based on probability is 0.1

What is Probability?

Probability is the measure of the likelihood of a certain event or outcome happening. It is expressed as a number between 0 and 1, where 0 means the outcome or event is impossible and 1 means the outcome or event is certain. Probability can be used to calculate the chances of certain outcomes occurring in a variety of situations. Probability can be used to determine the likelihood of events happening in games of chance, in business and finance decisions, in science and medicine, and in a variety of other contexts. Probability can also be used to help us make decisions and understand the relationships between different events.

to calculate the probability of getting show of size 8 we just need to calculate how many favourable cases are and here we can see it is 1 only
now we will calculate total cases that are 10 here
so we are ready with our answer that probability  = 1/10 = 0.1

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129 many music on his Computer if Jan has 516 when on Jan's computer, there are four times as many songs as there are on Ian's.

Given that,

On Jan's computer, there are four times as many songs as there are on Ian's.

We have to find Ian has how many music on his Computer if Jan has 516.

We know that,

Let x  be the number of songs lan has.

Since Jan has 4 times as many songs than lan then multiply x by 4.

Then equate this expression to 516.

4x=516

Divide 4 on both sides

4x/4=516/4

x=129

Therefore, 129 many music on his Computer if Jan has 516 when on Jan's computer, there are four times as many songs as there are on Ian's.

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Answer:

x = -136

Step-by-step explanation:

x + 2 =  7/8 x -15   Multiply all the way through by 8

8x + 16 = 7x -120  Subtract 7x from both sides

x + 16 = -120  Subtract 16 from both sides

x =  -136

Answer:

337 = 3

Step-by-step explanation:

Multiply by LCM

337 = 3

and the sides are not equal so I guess there is no answer but

337 = 3

Answer:

13 Hurdles

Step-by-step explanation:

If a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile then there are 13 such hurdles after solving all the fractions.

Given that a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile.

We are required to find the number of hurdles. All the values are given in fractions.

Ability of horse to gallop=7+3/7

=(49+3)/7

=52/7

Distance between two hurdles=4/7

Number of hurdles=52/7/4/7

=52*7/4*7

=52/4

=13 hurdles

Hence if a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile then there are 13 such hurdles after solving all the fractions.

If the level of significance is 10 %, then the potential type of statistical error is type II error.

What is statical error?

The term "error" (also known as "statistical error") refers to the discrepancy between a value obtained through a data gathering procedure and the population's "actual" value. The data are less representative of the population the higher the inaccuracy.

In the given test,

The p-value = 0.24

Level of significance (a) = 0.10

Here,

0.24 > 0.10

P-value > level of significance

Therefore, We failed to reject the null hypothesis that is actually false

This is type II error,

The type II error occurs when one fails to reject a null hypothesis that is actually false itself.

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The probability that a zoomy express bus arrives as schedule if it departs as schedule is 0.85.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty. An event's likelihood of occurring increases with its probability.

now , let D = depart on time and A = arrives on time

given that ,

P(D) = 80% = 0.80

P(A∩D) = 68% = 0.68

P(A/D) = [tex]\frac{0.68}{0.80}[/tex]

           =  [tex]\frac{68}{80}[/tex]

           =  [tex]\frac{17}{20}[/tex]

           =  0.85

Hence , the probability is 0.85.

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To ensure the sample is representative of the population as a whole, try to use some random samples.

A sample refers to a small quantity that is examined to get the knowledge of how the whole product/population will be.

Now, we need feedback from our clients. To ensure that our sample is representative of the population as a whole, we should include clients with different attributes.

Like, choosing 10 clients all living in the same place, same gender, and same age group will be the worse sample.

The best way to do this is to select samples randomly, ensuring that our sample includes people with different ages, gender, height, disabilities(if any) and statuses, etc.

So, A randomized sample is the best for ensuring that the sample is representative of the population as a whole.

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The expression for savings after t years, based on the principle amount and annual interest rate is 3000 + 105t.

The formula to be used for computation of savings is -

Interest = (Principal × Rate of interest × Time)/100

Keep the values in formula -

Interest = (3000 × 3.5 × t)/100

Performing division and multiplication

Interest = 10,500t/100

Performing division on Right Hand Side of the equation to find the interest

Interest = 105t

Now, savings will be sum of amount and the interest earned

Savings = 3000 + 105t

Thus, the savings will be 3000 + 105t.

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