Help 20 points!!!! Mathias

Answer:

\(\boxed {\boxed {\sf x \approx 105.3}}\)

Step-by-step explanation:

To solve for x, remember the right triangle trigonometry ratios (soh-cah-toa).

If we look at the angle given (θ), then we see that 36 is adjacent or next to the 70° angle. x is the hypotenuse because it is opposite the right angle. So, we have to use cosine (adjacent and hypotenuse).

\(cos (\theta)=\frac {adjacent}{hypotenuse}\)

\(cos(70)=\frac{36}{x}\)

Cross multiply. (Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator).

\(\frac{cos(70)}{1}=\frac{36}{x}\)

\(cos(70)*x= 36\)

Since we want to solve for x, we must isolate the variable. Divide both sides by the cosine of 70.

\(\frac{cos(70)*x}{cos(70)}=\frac{ 36}{cos(70)}\\x= 105.2569584\)

Round to the nearest tenth. The 5 in the hundredth place tells us to round the 2 to a 3.

\(x \approx 105.3\)

x is about 105.3

Answer:

1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder (or each of those is a counting number that can be multiplied by another counting number to make 12).

Step-by-step explanation:

hope this helps.

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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Answer:

your answer to your problem is D

Answer:

1.3

Step-by-step explanation:

just divide 31 by 24

This will give you the decimal: 1.291666667

Since the number 2 is right of the decimal point, it is in the tenths place.

Therefore, since the number next to the 2 is 9, you would round the 2 up and get 1.3 as your answer.

Answer:

Step-by-step explanation:

B

Step-by-step explanation:

given

\( \frac{7056}{x} = 42 \\ \\ 42x = 7056 \\ x = \frac{7056}{42} \\ = 168\)

also given

\( \frac{y}{112} = 8 \\ y = 8(112) \\ = 896\)

therefore

\( \frac{x}{y} = \frac{168}{896} \\ = \frac{3}{16} \)

The approximate 90% confidence interval for this situation is given as follows:

(70244, 70632).

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

From the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.645.

The parameters are given as follows:

\(\overline{x} = 70438, \sigma = 645.3, n = 30\)

The lower bound of the interval is given as follows:

\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)

The upper bound of the interval is given as follows:

\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)

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Answer:

-2 1/8

I think I'm not sure

The probability that in a given game the lions will score less than 3 goals is 0.80.

The probability distribution for the number of goals the lions soccer team makes per game is given below:

number of goals probability 0 0.30 1 0.35 2 0.15 3 0.10 4 0.10. The probability that in a given game the lions will score less than 3 goals is 0.80.

To find the probability that in a given game the lions will score less than 3 goals, we need to add up the probabilities for scoring 0, 1, or 2 goals.

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

We have the following probabilities:

P(0 goals) = 0.30

P(1 goal) = 0.35

P(2 goals) = 0.15

Therefore,

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

                                 = 0.30 + 0.35 + 0.15

                                 = 0.80

Thus, the probability that in a given game the lions will score less than 3 goals is 0.80.

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The system of transformation used to map ∆RST onto ∆UVW using algebraic notation is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).

Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Just the object's location changes during translation; its size stays the same.

Every point in a form, such as a triangle, rectangle, square, line, circle, and so on, will move by five units in the same direction if one point in the shape moves five units forward. If one point of a triangle travels four units to the left, all three points of the triangle should also move four units to the left.

From the figure we see that the coordinates of the points are:

R = (2, 3)

T = (-1, 0)

U = (1, -2.5)

W = (-0.5, -4)

The first transformation is that the ∆RST is translated down by 4 units.

(x, y) → (x, y - 4)

The second transformation is dilation, since the ∆UVW is smaller in size than the original image.

The distance between RT is:

d = √(-1 -2)² + (0 - 3)²

d = √9 + 9 = √18

The distance between UW is:

d = √(-0.5 - 1)² + (4 + 2.5)²

d = √2.25 + 42.25 = √44.5

The scale factor is:

SF = length of the original figure/ length of new image

SF = √18 / √44.5 = 6.6

Hence, the system of transformation used to map ∆RST onto ∆UVW is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).

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Using Trigonometry, the value of x in the right triangle is 17.1

Since we have a right angle triangle ; The angle L can be obtained thus ;

L = 180 - (90+67)

L = 23

Using Trigonometry:

Sin23° = opposite/ hypotenuse

Opposite= 6.7

hypotenuse= x

Sin23° = 6.7/x

x = 6.7/sin(23°)

x = 17.14

Therefore, the value of x to the nearest tenth is 17.1

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Answer:

4th one I believe, can I get support?

The percent of saline solution in brand B  is 10.83%

Let's assume that brand B has x gallons of the 100% saline solution.

The amount of salt in brand A is 18% of 6 gallons = 0.18 * 6 = 1.08 gallons.

When the two brands are mixed, the total volume of the mixture is 6 + x gallons, and the total amount of salt is 1.08 + x gallons.

Since the resulting mixture is 18 gallons of 8% saline solution, we can set up the equation:

(1.08 + x) / (6 + x) = 0.08

Solving for x, we get:

1.08 + x = 0.48 + 0.08x

0.92x = 0.6

x = 0.65

So, brand B has 0.65 gallons of the 100% saline solution.

Therefore, the percent of saline solution in brand B is:

0.65 / 6) * 100% = 10.83%, which rounded to the nearest whole number is 11%.

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The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

36×36=1296

27×27=729

1296-729=576

The answer is 567

The z-score of a person who scored 330 on the exam is approximately 2.7.

To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

z is the z-score

x is the raw score (330 in this case)

μ is the mean (195 in this case)

σ is the standard deviation (50 in this case)

Substituting the values into the formula, we get:

z = (330 - 195) / 50

z = 135 / 50

z = 2.7

The z-score of a person who scored 330 on the exam is 2.7.

The z-score measures the number of standard deviations a particular data point is away from the mean.

In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.

The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.

A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.

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Answer:

Step-by-step explanation:

Hope it helps! :)

Answer:

0.6

Step-by-step explanation:

hope this helps

Answer:

$6646

Step-by-step explanation:

C. The area of a rectangle is the product of its length and its width, so factoring the expression for the area will give the dimensions of the rectangle. The expressions for the dimensions of the rectangle are to be determined by factoring in the given area expression.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The area of a rectangle is given by the formula A = lw, where A is the area, l is the length, and w is the width of the rectangle.

To find possible dimensions of a rectangle with a given area, we can use factoring.

For example, if the area is 24, we can factor it as 24 = 2 x 2 x 2 x 3 or 24 = 4 x 6.

This means that a rectangle with an area of 24 could have dimensions of length 2 and width 12, length 4 and width 6, length 6 and width 4, or length 12 and width 2.

In this case, the question does not specify the value of the area, so we cannot find the dimensions of the rectangle.

we can still use factoring to find the possible dimensions of a rectangle with a given area, as shown in the example above.

Hence, The correct answer is:

C. The area of a rectangle is the product of its length and its width, so factoring the expression for the area will give the dimensions of the rectangle. The expressions for the dimensions of the rectangle are to be determined by factoring in the given area expression.

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$491

Explanation

Step 1

Let

Hoc income =16

Fiona was paid :

$9 an hour for 46 hours = $9*46=$414

$11 an hour for 7 hours = $11*7=$77

Step 2

the toal she earned is

Hence, the answer is $491

The density of mercury will be equal to 14 g/cm³.

It is given that the graduated cylinder holds exactly 22 ml and mercury used to fill the cylinder weighs 308 g.

We have to find out the density of the mercury.

What is the formula for density ?

The formula for density will be Density (D) = \(\frac{M}{V}\) , where M is mass / weight of the object and V is the volume of the object.

As per the question ;

Graduated cylinder holds 22ml.

∵ 1 ml = 1 cc or cm³

So ,

The volume of graduated cylinder = 22 cm³

The weight of mercury = 308g

We know that ;

Density of mercury = Weight / Volume

⇒ Density of mercury = \(\frac{308}{22}\)

⇒ Density of mercury = 14 g/cm³

Thus , the density of mercury will be equal to 14 g/cm³.

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The statement n² + 1 ≥ 2ⁿ, where n is an integer in [1, 4] is true statement.

The statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers is also true statement in all possible cases.

We have provide two statements and we have to prove them .

a) Consider the statement n² + 1 ≥ 2ⁿ where n is an integer in [1, 4].

For n= 1, we have n²+ 1 = 1 + 1= 2 and 2ⁿ = 2¹ = 1 so, 2≥ 2 then n² + 1 ≥ 2ⁿ.

For n = 2, we have n²+ 1 = 4+1 = 5 and 2ⁿ = 2² = 4 , so 5 > 4 then n² + 1 ≥ 2ⁿ.

For n = 3, we have n² + 1 = 9 + 1= 10 ≥ 8 =2³ =2ⁿ, then n² + 1 ≥ 2ⁿ.

For n = 4, we have, n²+1 = 16 + 1 = 17 > 16 = 2⁴ = 2ⁿ, so n² + 1 ≥ 2ⁿ.

In each case, we see n² +1 ≥ 2ⁿ Hence, the statement is proved.

b) Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers. Proof it by cases :

"a" is the minimum element if a is smaller than or equal to the other elements within the minimum statement: a ≤ min(b, c) or in other words a ≤b and a ≤ c.

The minimum of a and b then has to be equal to a (due to a ≤ b), min(a, b) = a

The minimum of a and c has to be equal to a (due to a ≤ c), min(min(a, b), c)

= min(a, c) = a

Thus we have shown in this case min(a. min (b.c))= min (min(a,b). c).

b is the minimum if b is smaller than or equal to the elements within minimum statement: b≤a and b≤min(b, c)

b is smaller than or equal to the minimum, if b is smaller than or equal to both of the terms expressed in the minimum.

b≤ b and b≤c

The minimum of a and b then has to be equal to b (due to b ≤ a), min(a,b) = b

The minimum of b and c has to be equal to b (due to b≤ c)

min(min(a, b), c) = min (b, c) = b

Thus we have shown in this case min(a, min (b, c)) = min (min(a,b), c).

c is the minimum if c is smaller than or equal to the elements within the minimum statement: c≤a and c< min(b, c)

c is smaller than or equal to the minimum, if c is smaller than or equal to both of the terms expressed in the minimum, c≤ b

c≤ c. Since c<a and c≤ b, c then also has to be smaller than or equal to the minimum of a and b, c≤ min(a, b). The minimum of min (a, b) and c has to be equal to c (due to c<min(a, b)), min(min(a, b), c) = c. Thus we have shown in this case min(a, min (b, c)) = min (min(a, b), c).

Conclusion : Since min(a, min(b, c)) = min (min(a, b), c) is true for all three possible cases, the statement is always true.

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Answer:

Step-by-step explanation:

Hey there,
Here's my reasoning regarding the problem:

Let's assume that the watch at the time it was lost was x years old.
When it was picked it was 3 times as old as it was when it was lost therefore it's currently 3x. The time between when it was lost and when it was found is 38 years. We can break this down into a simple algebraic formula:

3x - x = 38

2x = 38

x = 19

Answer:

14

Step-by-step explanation:

Answer:

B option 2

Step-by-step explanation:

I read the question

the correct answer is -28.8%

The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.

The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.

Therefore, let's represent the line with yellow point in slope intercept form.

Hence,

y = mx + b

where

Therefore, using (0, 2) and (6, 9).

m = 9 - 2 / 6 - 0

m = 7 / 6

Hence, let's find the y-intercept

y = 7 / 6 x + b

2 = 7 / 6(0) + b

b = 2

Therefore,

y = 7 / 6 x + 2.

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Answer:

Hope this may helps you

Answer:

36.87°  

Step-by-step explanation:

Assume the triangles are as in the diagram below.

∠BAC includes ∠DAE.

The measure of ∠BAE is 36.87°.

Answer:

36.87°

Step-by-step explanation:

i just had this question on edmentum and it was right.