Determine sin (A) and sin (B)

To solve for the remaining angles and side of the triangles, we can use the Law of Sines and the Law of Cosines.

Triangle 1: (where angle A is acute)

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

[tex]sin A / a = sin B / b[/tex]

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14°

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

Triangle 2 (where A is obtuse):

Given:

B = 50°

b = 5

a = 6

Using the Law of Sines:

sin A / a = sin B / b

sin A / 6 = sin 50° / 5

sin A = (6 x sin 50°) / 5

A = arcsin[(6 x sin 50°) / 5]

A ≈ 44.14° (rounded to the nearest hundredth)

Using the Law of Sines again:

sin C / c = sin B / b

sin C / c = sin 50° / 5

sin C = (c x sin 50°) / 5

Since A is obtuse, C = 180° - A - B

C ≈ 85.86° (rounded to the nearest hundredth)

Using the Law of Cosines:

c² = a² + b² - 2ab x cos C

c² = 6² + 5² - 2(6)(5) x cos C

c² = 36 + 25 - 60 x cos C

c² = 61 - 60 x cos C

c ≈ √(61 - 60 x cos C)

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The probability that Jess will win only the third game out of three games is 0.144, or 14.4%

To calculate the probability that Jess will win only the third game out of three games, we will use the concept of independent events. In this scenario, we have the following events:

1. Jess loses the first game.
2. Jess loses the second game.
3. Jess wins the third game.

Since the events are independent, we can calculate the probability of this specific sequence occurring by multiplying the probabilities of each individual event:

1. Probability of losing the first game: 1 - 0.4 = 0.6
2. Probability of losing the second game: 1 - 0.4 = 0.6
3. Probability of winning the third game: 0.4

Now, we multiply these probabilities together:

0.6 * 0.6 * 0.4 = 0.144

So, the probability that Jess will win only the third game out of three games is approximately 0.144, or 14.4% when rounded to three decimal places.

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The inverse function of f(x) is given as follows:

[tex]f^{-1}(x) = \sqrt{x}[/tex]

The function f(x) graphed in this problem is given as follows:

f(x) = x².

Using the notation y = f(x), we have that:

y = x².

To obtain the inverse, first we exchange y and x, hence:

x = y².

Finally, we must isolate the variable y, hence:

[tex]y = \pm \sqrt{x}[/tex]

[tex]y = \sqrt{x}[/tex] -> we take only the positive and the domain is the non-negative numbers.

Hence the inverse function is:

[tex]f^{-1}(x) = \sqrt{x}[/tex]

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Answer:

3667 miles driven

Step-by-step explanation:

2132 + 1535 = 3667

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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Answer:

x=335/336

Step-by-step explanation:

First of all, we open the parentheses. 17x+14 1/2-2 3/7+7x=36. Then, we subtract the mixed fractions. 14 1/2-2 3/7=12 1/14. Then, we add the x's. 17x+7x=24x. What we get is 12 1/14+24x=36. We have to subtract 12 1/14 on both sides. 24x=23 13/14. To find x, we do 23 13/14 divided by 24=335/336. x=335/336

Answer:

The mean distance to his friends' house is between 2 -3 blocks.

Step-by-step explanation:

1. Mean = Average.

Average = (n1+n2+n3....nx)/x

2. The average = 1+2+5+3+2+2+5+3/8

3. Therefore, the answer is 2.875, making the mean between 2 and 3

Answer:

The statement that supports the data is the mean distance to his friends' houses is in between 2 and 3 blocks.

Step-by-step explanation:

What is mean, median and mode?

Mean: The average of the given data points.

Median: The central point of the whole data set.

Mode: The number that occurs for the maximum times in the data set.

Given:

Karl records the number of city blocks from his house to each of his friends houses.

Data set for the number of city blocks to eight friends houses:

{1, 2, 5, 3, 2, 2, 5, 3}

The first option: it is given that the maximum number of blocks the Karl lives from his friend is 4, but according to the data set, the maximum number of house blocks should be 5.

Hence, this option is incorrect.

The second option: It is given that the mode shows that Karl has 3 friends who live 3 blocks from him, but according to the given data set Karl has 3 friends who lives 2 blocks from him. Hence the mode is 2.

Hence, this option is incorrect.

The third option: It is given that the minimum distance from Karl's house to a friend's is 2 blocks, but according to the given data set the minimum distance from Karl's house to a friend's is 1 block.

Hence, this option is incorrect.

The fourth option:  It is given that the mean distance to his friend's houses is in between 2 and 3 blocks.

We will find the mean for the given data set.

⇒ Mean = (Sum of all the data points) / (Total number of data points)

⇒ Mean = (1 + 2 + 5 + 3 + 2 + 2 + 5 + 3)/8

⇒ Mean = 23/8

⇒ Mean = 2.875

∴ The mean distance from Karl to his friend's houses is 2.875 which is in between 2 and 3.

Hence, this option is correct.

Therefore, the fourth option which says the mean distance between Karl and his friend's houses is in between 2 and 3 is correct.

[tex]-29~~,~~\stackrel{-29+7}{-22}~~,~~\stackrel{-22+7}{-15}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{d=+7} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-29\\ n=92\\ d=7 \end{cases} \\\\\\ a_{92}=-29+(92-1)7\implies a_{92}=-29+637\implies \boxed{a_{92}=608}[/tex]

The 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

The given data points are:

97.1, 98.1, 98, 97.7, 97.4, 99.3, 96.8

Step 1: Calculate the sample mean (µ):

µ = (97.1 + 98.1 + 98 + 97.7 + 97.4 + 99.3 + 96.8) / 7 ≈ 97.914

sample standard deviation (s):

≈ 0.839

Step 3: Calculate the standard error (SE):

SE = s / sqrt(n)

≈ 0.839 / sqrt(7) ≈ 0.317

Step 4: Find the t-value for a 90% confidence interval with 6 degrees of freedom (n - 1 = 7 - 1 = 6).

Using a t-distribution table  we find that the t-value is approximately 1.943.

Step 5: Calculate the margin of error (ME):

ME = t-value * SE

≈ 1.943 * 0.317 ≈ 0.615

Step 6: Calculate the confidence interval:

Lower limit = µ - ME ≈ 97.914 - 0.615 ≈ 97.299

Upper limit = µ + ME ≈ 97.914 + 0.615 ≈ 98.529

So, the 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

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Check the picture below.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{blue triangle} }{\cfrac{1}{2}(1)(2)}~~ + ~~\stackrel{ \textit{orange triangle} }{\cfrac{1}{2}(2)(1)}~~ + ~~\stackrel{ \textit{yellow rectangle} }{(2)(3)}~~ + ~~\stackrel{ \textit{purple triangle} }{\cfrac{1}{2}(3)(2)}} \\\\\\ 1+1+6+3\implies \text{\LARGE 11}[/tex]

Answer:

---------------------

Use the area formula:

We are given the circumference of the circle, which is C = 2πr.

So, we can set up an equation:

Now, we can plug this value of r into the area formula:

Therefore, the area of the circle is 42.25π or 132.73 square inches.

The 95% confidence interval for the population mean is (47.00, 48.90).

A sample of size n=78 is drawn from a normal population with a standard deviation of σ=5.1. The sample mean is x=47.95.

Using this information, we can estimate the population mean using the formula:

μ = x ± z*(σ/√n)

where μ is the population mean, x is the sample mean, z is the z-score for the desired level of confidence (e.g., 1.96 for a 95% confidence interval), σ is the population standard deviation, and n is the sample size.

Assuming a 95% confidence level, the z-score is 1.96. Plugging in the given values, we get:

μ = 47.95 ± 1.96*(5.1/√78)

Solving for the upper and lower bounds of the confidence interval, we get:

μ = 47.95 ± 0.95

So the 95% confidence interval for the population mean is (47.00, 48.90). This means that if we were to repeat this sampling process many times, we would expect the true population mean to fall within this interval 95% of the time.

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Answer:

b) Answers may vary, e.g., I would determine the x- and y-intercepts because I think it's easier. Lesson 1.1, page 12. 1. a) on the graph because if b) not on ...64 pages

Step-by-step explanation:

Determine the x and y intercept for each of the equations. Write your answer as a coordinate pair. If it does not have an intercept, explain your reasoning.

The correct probability is indeed 0.25 or 25%.

When heterozygous pink (Pp) and white (pp) flowers are crossed, the Punnett square can be used to determine the probability of offspring having white flowers:

     |   P     p

---------------

 P  |  PP   Pp

---------------

 p  |  Pp   pp

From the Punnett square, we can see that there are four possible combinations of alleles for the offspring: PP, Pp, Pp, and pp.

Out of these four possibilities, only one combination (pp) corresponds to the white flower trait.

Therefore, the probability of an offspring having white flowers is 1 out of 4.

In terms of probability, this can be expressed as:

Probability of white flowers = Number of favorable outcomes / Total number of possible outcomes.

= 1 / 4

= 0.25

So, the correct probability is indeed 0.25 or 25%.

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

Answer:

0.4

Step-by-step explanation:

Let A be the event of selecting a bead with two holes and B be the event of selecting a red bead. We are given P(A) = 0.5 and P(A and B) = 0.2. We need to find P(B|A), the probability of selecting a red bead given the bead has two holes.

By definition of conditional probability, we have:

P(B|A) = P(A and B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.2 / 0.5

Simplifying, we get:

P(B|A) = 0.4

Therefore, the probability of selecting a red bead given the bead has two holes is 0.4.

Answer: 0.2.

Step-by-step explanation:

The expression, in the end, is 10 x 3 = 30

i.e

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

We have,

We see that,

The number of tiles:

18, 24, 30,

This is an arithmetic sequence.

So,

The next term:

= 30 + 6

= 36

Now,

The length is a sequence in ascending order of the factor of the arithmetic sequence.

So,

30 is a factor of 2, 3, 5, 6, and 10.

This means,

The expression, in the end, is 10 x 3 = 30

So,

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

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No triangles can be constructed with the given side lengths.

As, The triangle inequality is a mathematical theorem that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds true:

a + b > c

Here, sides of triangle are 4cm, 5 cm and 9 cm.

So, 4 + 5 = 9

Thus, No triangles can be constructed with the given side lengths.

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Figure ABCD is translated 3 units right and 1 unit up.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Based on the information provided, we have the follwoing:

(x, y)                               →                  (x + h, y + k)

A (2, 3)                              →                  A' (5, 4).

5 = 2 + h

h = 5 - 2

h = 3 (3 units right).

4 = 3 + k

k = 4 - 3

k = -3 (1 unit up).

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Complete Question:

Describe the translation of figure ABCD. Complete the sentence to explain your answer.

Figure ABCD is translated  unit(s) right and  unit(s) up.

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

x = 7

Step-by-step explanation:

Product of powers rule:

[tex] a^m \times a^n = a^{m + n} [/tex]

When you multiply two powers with the same base, add the exponents.

[tex] 3^5 \times 3^2 = 3^x [/tex]

Apply the rule above to the left side.

[tex] 3^{5 + 2} = 3^x [/tex]

[tex] 3^7 = 3^x [/tex]

[tex] x = 7 [/tex]

The surface area of the cone is 553 cm².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the cone, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

Check Explanation

Step-by-step explanation:

The question is incomplete. But I can explain in a way that the full question can be easily solvable.

Note that the missing part of the question is percentage or fraction of the total college tuition cost that the scholarship covers.

For the sake of clarity, let us assume that the scholarship covers 60% of the total college tuition costs.

This means that Tamara still has to raise 40% of the total college tuition cost herself over the space of 2 years (24 months)

The total college tuition cost = $8240

Amount that Tamara still needs to raise = 40% × 8240 = $3296

She has to raise this amount over 2 years (24 months) on a monthly basis.

So, the amount she has to save monthly over 24 months = (3296/24) = $137.333

So, whatever the fraction or percentage of the total college tuition cost that the scholarship covers, just divide the rest of the college tuition cost after the scholarship has done its part (1 - fraction or 100% - percentage) by 24 months.

The answer is the amount that Tamara needs to save monthly.

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The distance from point A to point B is approximately 920 feet.

Let's call the distance from point A to point B as x.

From point A, the angle of elevation to the lighthouse's beacon-light is 8 degrees.

Using the tangent function to find the height of the lighthouse (h):

tan(8) = h/1083

h = 1083 tan(8) ≈ 157.6 feet

From point B, the angle of elevation to the lighthouse's beacon-light is 4 degrees.

Using the tangent function again to find the height of the lighthouse from point B (h'):

tan(4) = h'/(1083-x)

h' = (1083-x) tan(4) ≈ 78.6 - 0.07x

Since the height of the lighthouse should be the same from both points A and B, we can set h = h' and solve for x:

1083 tan(8) = (1083-x) tan(4)

x = 1083 - (157.6/tan(4)) ≈ 920 feet

Therefore, the distance from point A to point B is approximately 920 feet.

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Answer:

centimeters: 141

meters: 1.41

Step-by-step explanation:

1.16 m to cm is 116

116+25 = 141

25 cm to meters is 0.25

1.16+0.25 = 1.41

Answer:

[tex]\textsf{A.}\quad\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]

Step-by-step explanation:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \sec(3x+1)\; \text{d}x[/tex]

To evaluate the given integral, use the method of integration by substitution.

Let u = 3x + 1.

Find du/dx and rewrite it so that dx is on its own:

[tex]\dfrac{\text{d}u}{\text{d}x}=3 \implies \text{d}x=\dfrac{1}{3}\;\text{d}u[/tex]

Rewrite the original integral in terms of u and du and integrate:

[tex]\begin{aligned}\displaystyle \int \sec(3x+1)\; \text{d}x&=\int \dfrac{1}{3} \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3}\int \sec(u)\; \text{d}u\\\\&= \dfrac{1}{3} \ln \left|\sec(u)+\tan(u)\right|+\text{C}\end{aligned}[/tex]

Finally, replace u with the original substitution.

[tex]\dfrac{1}{3} \ln \left|\sec(3x+1)+\tan(3x+1)\right|+\text{C}[/tex]

Line segment PT ≅ line segment PT by the reflexive property.

ΔPRT ≅ ΔTVP by the SSS triangle congruence theorem

The SSS congruence theorem (side-side-side congruence theorem) states that if all three sides of one triangle are congruent to the corresponding three sides of another triangle, then both are considered congruent triangles.

According to the reflexive property, a line or angle is equal to itself, therefore, Line segment PT ≅ line segment PT by the reflexive property.

This also implies that both triangles have three pairs of corresponding sides that  congruent, therefore, ΔPRT ≅ ΔTVP.

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The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

We have,

To find the place value of the number in the thousand's place for the number obtained by adding 60 tens, 58 hundreds, and 685 ones, we can start by realizing that 60 tens are the same as 600, and 58 hundreds are the same as 5800.

Therefore, we have:

600 + 5800 + 685 = 7085

So the number is 7085.

The digit in the thousand's place is 0 since there is no digit in the thousand's place.

Therefore, the place value of the number in the thousand's place is 0.

To determine if the number is even or odd, we can look at the unit digit, which is 5.

Since 5 is an odd number,

The entire number is odd.

2.

The predecessor of a number is the number that comes before it, and the successor of a number is the number that comes after it.

To find the predecessor of a number, we subtract 1 from the number, and to find the successor, we add 1 to the number.

For example,

Let's say we want to find the predecessor and successor of the number 7.

The predecessor of 7 is 6, since 7 - 1 = 6.

The successor of 7 is 8, since 7 + 1 = 8.

In general,

For any number n, the predecessor is n - 1 and the successor is n + 1.

Thus,

The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

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