Find the missing side. 37° Z 25 z = [?] Round to the nearest tenth. Remember: SOHCAHTOA​

Answer:

y = [tex]\frac{-5}{4}[/tex]x - 30

Step-by-step explanation:

we will use the x = -40 and the y = 20 from the point given (-40,20).  The perpendicular slope would be the opposite reciprocal from the slope given.  The slope given is 4/5.  The reciprocal is 5/4 and the opposite would be -5/4

y = mx + b  Plug in what we know and solve for b

20 = [tex]\frac{-5}{4}[/tex] ( -40) + b

20 = [tex]\frac{-5}{4}[/tex] ·[tex]\frac{-40}{1}[/tex] + b

20 = [tex]\frac{200}{4}[/tex] + b

20 = 50 + b  Subtract 50 from both sides

20 - 50 = 50 - 50 + b

-30 = b

To write the equation we need the slope (m) ([tex]\frac{-5}{4}[/tex]) and the y-intercept (b) (-30)

y = mx + b

y = [tex]\frac{-5}{4}[/tex]x - 30

Helping in the name of Jesus.

The period of oscillation of the wave is 8 seconds

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle.

Period is measured in seconds and it is the inverse of frequency of the oscillation. This means that T = 1/f

where f is the frequency and T is the period.

An oscillation can also be called cycle or Revolution or vibration.

From the graph, the oscillating wave made a complete oscillation at 8 seconds.

Therefore the period of oscillation of the wave is 8 seconds.

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Answer:the space is 7 in the text below

Step-by-step explanation:

Answer:To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph. Here are some examples: y ≥ x2 + 3. graph {y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]} Although it is not 100% certain from just the graph, this graph does get wider and wider.

Step-by-step explanation:

For the function f(x) = logb(x) to be increasing, the value of the logarithmic base b must be greater than 1. To understand why this is the case, let's consider the definition of an increasing function

. A function is increasing if, as the input values increase, the corresponding output values also increase. In the case of logarithmic functions, the input values are positive real numbers (x > 0) and the output values are the logarithms of these numbers.

When the base b of the logarithm is greater than 1, the function f(x) = logb(x) exhibits an increasing behavior. This is because as the input values x increase, the logarithm of x also increases. In other words, the function "stretches out" the input values and maps them to larger output values as x increases.

On the other hand, when the base b is less than 1 (0 < b < 1), the logarithmic function f(x) = logb(x) becomes a decreasing function. In this case, as the input values x increase, the logarithm of x becomes more negative, resulting in decreasing output values.

Therefore, the values of b for which the function f(x) = logb(x) is increasing are when b > 1.

In summary, the logarithmic function f(x) = logb(x) is increasing when the base b is greater than 1.

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Answer:

a. The probability that this whole shipment will be accepted is the probability that none or only one of the 42 randomly selected tablets is defective.

b. The company will accept approximately 36.8% of the shipments and will reject approximately 63.2% of the shipments, so many shipments will be rejected.

Step-by-step explanation:

Given statement solution is :- "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)).

"f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)).

The expressions "F(g(x)) g(f(x))" and "f(g(x)) g(f(x))" are compositions of functions. The answer to the question posed would depend on the specific functions F(x) and g(x), as well as f(x) and g(x) in the second expression.

To provide a brief response:

For the expression "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)). The order of composition is F(g(x)) first, followed by g(f(x)).

For the expression "f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)). The order of composition is f(g(x)) first, followed by g(f(x)).

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Answer:

It looks to be -4, -2, 1, and 3

Answer:

There are infinitely many rational numbers between 6.1 and 6.3.

6.15 is an example.

Answer: 6.2

Step-by-step explanation:

6.2 is between 6.1 and 6.3 because 2 comes after 1.

The equation of the hyperbola with foci at (±3,0) and vertices at (±2,0) is[tex](x^2 / 4) - (y^2 / 5) = 1[/tex].

To find the equation of a hyperbola, we need to determine its center, vertices, and foci. In this case, we can observe that the hyperbola is centered at the origin (0, 0) since the foci and vertices lie along the x-axis.

Let's denote the distance between the center and each focus as c, and the distance between the center and each vertex as a. In this scenario, the foci are located at (±3, 0), and the vertices are at (±2, 0).

From the given information, we can deduce that c = 3 and a = 2. Now, we can calculate the value of b using the relationship between a, b, and c in a hyperbola:

[tex]c^2 = a^2 + b^2[/tex]

Plugging in the values, we have:

[tex]3^2 = 2^2 + b^2\\9 = 4 + b^2\\b^2 = 9 - 4\\b^2 = 5[/tex]

Now we have all the necessary values to write the equation of the hyperbola. Since the foci lie on the x-axis and the center is at the origin, the equation of the hyperbola in standard form is:

[tex](x^2 / a^2) - (y^2 / b^2) = 1[/tex]

Plugging in the values for a and b, we get:

[tex](x^2 / 2^2) - (y^2 / 5) = 1\\(x^2 / 4) - (y^2 / 5) = 1[/tex]

Therefore, the equation of the hyperbola with foci at (±3,0) and vertices at (±2,0) is[tex](x^2 / 4) - (y^2 / 5) = 1[/tex].

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Answer:

i dont know

Step-by-step explanation:

give proper diagram please

Domain: (-∞, ∞)

Range: [0, ∞)

Domain and range help describe the values that the function covers.

Domain

The domain of a function describes the x-values covered by a function. This means that any x-value that can be input into the function is part of the domain. The domain of this function is all real numbers. This is because any x-value could be input into the function and give an output. Additionally, the graph will continue for infinity and cover all x-values. In interval notation, the domain is (-∞, ∞). The domain for all quadratic functions is all real numbers, also written as (-∞, ∞).

Range

The range of a function describes the y-values covered by a function. Any y-values that are possible outputs are a part of the range. In this function, we can see that the parabola does not cover the positive y-values. So, the only possible outputs for the function are negative values. This means that our range will only be the negative values. In interval notation, the range is  [0, ∞). We use brackets to show that the 0 is included in the range. Since infinity cannot be included in a domain or range, we use parentheses.

The solutions for x are approximately x ≈ 7.888 and x ≈ -4.263.

To solve the equation, let's simplify the equation and then isolate the variable x.One of the properties of triangle Pythagorous theorem

The given equation is: 27^2 + (4x - 4)^2 = 36^2.

First, evaluate the exponents: 27^2 = 729 and 4^2 = 16.

Substituting these values back into the equation, we have: 729 + (4x - 4)^2 = 1296.

Next, simplify the equation further: 729 + (4x - 4)(4x - 4) = 1296.

Expanding the squared term: 729 + (16x^2 - 32x + 16) = 1296.

Combine like terms: 16x^2 - 32x + 729 + 16 = 1296.

Simplify further: 16x^2 - 32x + 745 = 1296.

Rearrange the equation: 16x^2 - 32x + 745 - 1296 = 0.

Combine like terms: 16x^2 - 32x - 551 = 0.

To solve the quadratic equation, we can either factor it or use the quadratic formula. However, this equation does not factor easily, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 16, b = -32, and c = -551.

Substituting these values into the quadratic formula:

x = (-(-32) ± √((-32)^2 - 4(16)(-551))) / (2(16)).

Simplifying further:

x = (32 ± √(1024 + 35328)) / 32.

x = (32 ± √(36352)) / 32.

x = (32 ± 190.413) / 32.

Therefore, the two possible solutions for x are:

x1 = (32 + 190.413) / 32 ≈ 7.888.

x2 = (32 - 190.413) / 32 ≈ -4.263.

Therefore, the solutions for x are approximately x ≈ 7.888 and x ≈ -4.263.

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The hip breadth for males that separates the smallest 99% from the largest 1% is determined to be 17.03 inches using the Z-score formula and percentile calculations.

According to the question, the engineers want to design seats in commercial aircraft that can accommodate at least 99% of all males. The mean and standard deviation of male hip breadth are 14.9 in. and 1.1 in., respectively.

To determine P99, we need to find the hip breadth for males that separates the smallest 99% from the largest 1%. The value of P99 can be determined using the Z-score formula, which is given by Z = (X - μ)/σ where X is the raw score, μ is the mean, σ is the standard deviation and Z is the standard score.

Since we are looking for the hip breadth for males that separates the smallest 99% from the largest 1%, we need to find the Z-score for the 99th percentile.

Using a Z-score table, we can find that the Z-score for the 99th percentile is 2.33. Substituting the given values into the Z-score formula, we get 2.33 = (X - 14.9)/1.1. Solving for X, we get:X = 2.33(1.1) + 14.9 = 17.03 inches

Therefore, the hip breadth for men that separates the smallest 99% from the largest 1% is 17.03 inches.

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Answer: 47 I think

Step-by-step explanation:

47+43=90

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

418

Step-by-step explanation:

-4.0(5+100)+80(5)+60

We will consider the '+' outside the bracket as the dividers.

Therefore,

=-0.4(105)+400+60

=-42+400+60

=358+60

=418

Answer:

65.56°

Step-by-step explanation:

Trigonometric ratios:

        Opposite side of x° is 11 cm and adjacent side of x° is 5 cm.

To find x°, we have to use Tan ratio.

           [tex]\boxed{\bf Tan \ x = \dfrac{opposite \ side \ of \ \angle x }{adjacent \ side \ of \angle x}}[/tex]

                       [tex]\sf = \dfrac{11}{5}\\\\ = 2.2[/tex]

                    [tex]\sf x = tan^{-1} \ 2.2\\\\ x = 65.56[/tex]

Answer:

To determine the probability that the whole shipment will be accepted, we need to calculate the probability that at most one battery does not meet specifications.

Given that 1% of the batteries do not meet specifications, it means that out of 5000 batteries, 0.01 * 5000 = 50 batteries do not meet specifications.

Now, using the binomial probability formula, we can calculate the probability of at most one battery not meeting specifications:

P(X ≤ 1) = P(X = 0) + P(X = 1)

Where X follows a binomial distribution with parameters n = 60 (sample size) and p = 50/5000 = 0.01 (probability of a battery not meeting specifications).

P(X = 0) = (60 choose 0) * (0.01)^0 * (1 - 0.01)^(60 - 0)

P(X = 1) = (60 choose 1) * (0.01)^1 * (1 - 0.01)^(60 - 1)

Calculating these probabilities:

P(X = 0) ≈ 0.301

P(X = 1) ≈ 0.401

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.301 + 0.401 ≈ 0.702

a. The probability that this whole shipment will be accepted is approximately 0.702.

b. The company will accept approximately 70.2% (0.702 * 100) of the shipments and will reject approximately 29.8% (100 - 70.2) of the shipments.

Answer:

To get the price of 1 each

$80.50÷7=

$11.50

To get the price of 10

$11.50×10

=$115

Answer:

Step-by-step explanation:

I think there is a typo in the question

Qn : let p(n) be  [tex]\sum\limits^n_{i = 1}{i2^i} = 2 + (n-1)2^{n+1} \;\;\;\;\;\;:n\geq 1[/tex]

When n = 1:

LHS: 1(2¹) = 2

RHS: 2 + (1 - 1)(2¹ ⁺ ¹) = 2

LHS = RHS

⇒ p(n) holds for n = 1

Let us assume that the proof holds for p(n): n = x

ie.

[tex]p(x): \sum\limits^x_{i = 1}{i2^i} = 2 + (x-1)2^{x+1}[/tex]

To prove that the proof holds for n = x+1

ie   [tex]p(x+1): \sum\limits^{x+1}_{i = 1}{i2^i} = 2 + (x)2^{x+2}[/tex]

Consider LHS

[tex]\sum\limits^{x+1}_{i = 1}{i2^i}\\\\= \sum\limits^{x}_{i = 1}{i2^i}+\sum\limits^{x+1}_{i = x+1}{i2^i}\\\\= p(x) + (x+1)2^{x+1}\\\\= 2 + (x-1)2^{x+1} + (x+1)2^{x+1}\\\\= 2 + 2^{x+1} (x-1 + x+1)\\\\= 2 + 2^{x+1} (2x)\\\\= 2 + (x)2^{x+2}\\\\= RHS[/tex]

Answer:

45

Step-by-step explanation:

Do the operation in parentheses first.

(45)(4 - 3) = (45)(1) = 45

Answer:

Step-by-step explanation:

The answer is 45.

Given,

[tex](45)(4-3)\\=(45)(1)\\=45[/tex]Using subtraction and multiplication rule.

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Answer:

Step-by-step explanation: f'(x)=0. Explanation: f'(x)=8x+2=0. critical value =−14. hope that helped.

[tex]\begin{gathered} \; \color{pink}{\frak{\qquad \: x - \dfrac{x - 1}{2} = 1 - \dfrac{x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{(2 \times x) - x - 1}{2} = \dfrac{(3 \times 1) - x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{2x - x - 1}{2} = \dfrac{3 - x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{x - 1}{2} = \dfrac{1 - x}{3}}} \\ \end{gathered}[/tex]

Cross Multiplying,,

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \dfrac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}[/tex]

Answer:

Step-by-step explanation:

To find the ratio of correct to incorrect answers on the test, we need to determine the number of correct and incorrect answers.

If you got 95% of the questions correct, it means you got 95% of 140 questions correct.

Number of correct answers = 95% of 140 = (95/100) * 140 = 133

To find the number of incorrect answers, subtract the number of correct answers from the total number of questions:

Number of incorrect answers = Total number of questions - Number of correct answers = 140 - 133 = 7

Therefore, the ratio of correct to incorrect answers on the test is 133:7, which is already in its lowest terms and cannot be simplified further.

Final result:

Of the 140 questions, you properly answered 133 of them, while 7 of them were incorrect. You have a 133:7 chance of winning because you provided the right answers.

Explanation:

We need to know how many questions were correctly and wrongly answered before we can fix this issue. You correctly answered 140 out of 140 questions, or 95 percent of them, giving you a total of 133 valid answers.

Thus, 133 correct answers out of 140 total questions equals 7 incorrect answers. As a result, the ratio of correct to incorrect answers is already very low at 133:7.

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The amount of carpet needed for the living room is three times greater than the amount of carpet needed for the bedroom.

To calculate the amount of carpet needed for each room, we need to consider the dimensions of the rooms. Let's assume the length of the bedroom is x units.
Since the living room is two times as long as the bedroom, its length will be 2x units.
Similarly, the width of the living room is one and a half times as wide as the bedroom. So, the width of the living room will be 1.5x units.
To find the area of each room, we multiply the length by the width.
The area of the bedroom is x units * x units = x^2 square units.
The area of the living room is 2x units * 1.5x units = 3x^2 square units.
The amount of carpet needed is directly proportional to the area of the room. Therefore, the amount of carpet needed for the living room is 3x^2 square units, while the amount needed for the bedroom is x^2 square units.
To find the difference, we divide the area of the living room by the area of the bedroom: 3x^2 / x^2 = 3.
Thus, the amount of carpet needed for the living room is three times greater than the amount needed for the bedroom.

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Answer: D

Step-by-step explanation:

we will multiply

4/7* 1/8

we will get 1/14

Answer:

Step-by-step explanation:
After reducing 4/7 of 1/8 to the lowest terms we get 1/14. Thus, option C is the answer.

For reducing a number to its lowest terms, first, we need to simplify the numbers to a more significant number, i.e. 4/7 of 1/8 means 4/7*1/8=4/56.

Now we know that 56 is a multiple of 4 when multiplied by 14. Hence, when we get it in the lowest term we would get 1/14

Sin(θ) is negative for θ ∈ (π, 3π/2) U (3π/2, 2π).

Cos(θ) is negative for θ ∈ (π/2, π) U (π, 3π/2).

To determine the values of θ for which sin(θ) is negative, we need to consider the unit circle and the quadrants in which sin(θ) takes negative values.

On the unit circle, sin(θ) represents the y-coordinate of the point corresponding to the angle θ. Sin(θ) is negative in the third and fourth quadrants of the unit circle.

In the third quadrant, the angle θ lies between π and 3π/2. In this quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) are negative.

In the fourth quadrant, the angle θ lies between 3π/2 and 2π. In this quadrant, the x-coordinate (cosine) is positive, but the y-coordinate (sine) is negative.

Therefore, the values of θ for which sin(θ) is negative are:

θ ∈ (π, 3π/2) U (3π/2, 2π)

Next, to determine the values of θ for which cos(θ) is negative, we again consider the unit circle and the quadrants in which cos(θ) takes negative values.

Cos(θ) represents the x-coordinate on the unit circle. Cos(θ) is negative in the second and third quadrants of the unit circle.

In the second quadrant, the angle θ lies between π/2 and π. In this quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) are negative.

In the third quadrant, the angle θ lies between π and 3π/2. In this quadrant, the x-coordinate (cosine) is negative, but the y-coordinate (sine) is positive.

Therefore, the values of θ for which cos(θ) is negative are:

θ ∈ (π/2, π) U (π, 3π/2)

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Answer:

Step-by-step explanation:

try (3,-1)

Answer:

Step-by-step explanation:

A rhombus has all equal sides and two parallel sides.

Notice how Point C is 2 units to left and 1 unit below Point D>

Thus, our missing point, A, should be 2 units to left of B and 1 unit below it.

We therefore get (1,3)

So the point is (1,3)

Answer:

-12

Step-by-step explanation:

3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =

= 3/5 * (1 + 4)^2 - (3)^3

= 3/5 * (5)^2 - 27

= 3/5 * 25 - 27

= 15 - 27

= -12