Answer questions (a – f) based on the following graph.

Answer:

A) 30°

Step-by-step explanation:

All triangles angles add always to 180°, so we have two already 75° + 75° = 150° thus the angle is 30°

Answer:

m Is 30

Step-by-step explanation:

m is 30

because....the sum of angles in a triangle is 180

75+75+m =180

150+m=180

make m the subject of the formula

m=180-150

m=30

Answer:

500

Step-by-step explanation:

Mai has x/3 books if Tyler has x books.

Let's assume that Mai has y books and Tyler has 3 times as many books as Mai, which is given as x = 3y.

Therefore, the number of books that Mai has is given as y = x/3.

We can obtain the number of books Mai has in terms of x since we already know that Tyler has x books.

Tyler's number of books does not directly influence the number of books Mai has;

rather, Tyler's number of books is used to figure out how many books Mai has as per the given problem statement.

Answer:

Mai has x/3 books.

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Answer:

firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass

Step-by-step explanation:

To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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Answer:

The answer is 8

Step-by-step explanation:

Since there are 2 negative signs that cancel each other out and become a positive, another word for addition, or multiplication.

Answer:

You get a total of two hours of parking.

Step-by-step explanation:

First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!

Answer:

0.666666

Step-by-step explanation:

2/3

0.666666

The pathway for nociceptors (pain) and thermoreceptors (temperature) that travels up the contralateral side of the spinal column is known as the "spinothalamic tract."

The spinothalamic tract is a major pathway in the nervous system that carries sensory information related to pain and temperature from the body to the brain. It consists of a bundle of nerve fibers that originate in the spinal cord and ascend towards the thalamus, a region in the brain responsible for relaying sensory information.

In the case of nociceptors (pain) and thermoreceptors (temperature), the sensory signals are detected by specialized receptors in the peripheral nervous system, such as the skin, and are then transmitted to the spinal cord via sensory neurons. These sensory neurons cross over to the opposite side of the spinal cord shortly after entering, a process known as decussation. Once the sensory signals have crossed over, they ascend through the spinothalamic tract on the contralateral (opposite) side of the spinal column.

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The association between lung function (FEV) and age can be observed through the analysis of the provided output from R.

The output from R likely includes statistical measures such as correlation coefficients or regression analysis results to determine the relationship between FEV and age. These calculations can help quantify the association between the two variables. For example, a correlation coefficient can indicate the strength and direction of the relationship, where a positive value suggests a positive association between FEV and age.

Based on the provided output from R, it can be concluded that there is an association between lung function (FEV) and age. However, without the actual output or specific statistical measures, it is challenging to provide further details or draw more precise conclusions. It is important to consider that the association between FEV and age may not necessarily imply causation, as other factors such as lifestyle, health conditions, and genetics can also impact lung function. Further analysis and additional data would be necessary to fully understand the nature and significance of this association.

Overall, it is reasonable to conjecture that lung function (FEV) changes with age, but a comprehensive analysis of the provided output and additional research would be required to establish the precise relationship between the two variables.

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Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

How to find?

To find out how many cups of chocolate chips Rana has left, we need to subtract the amount she used in the cookie recipe from the amount she bought.

First, we need to convert both mixed numbers to improper fractions, so we can subtract them.

Three and three-fourths cups can be written as:

3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

Two and one-third cups can be written as:

2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}

Now, we can subtract:

\frac{15}{4} - \frac{7}{3} = \frac{45}{12} - \frac{28}{12} = \frac{17}{12}

Therefore, Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

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Answer:

the value of x°= 20°

explanation is in the picture attached below

hope it is helpful to you

The probability of a z-score less than 2.357 is 0.9906.

To use the normal approximation, we need to check that the sample size is sufficiently large and that the population proportion is not too close to 0 or 1. In this case, n*p = 58.5 and n*(1-p) = 19.5, which are both greater than 10, so the normal approximation is valid.

We can find the mean and standard deviation of the sampling distribution using the formulas mu = n*p = 58.5 and sigma = sqrt(n*p*(1-p)) = 4.031.

Then we can standardize X using the formula z = (X - mu)/sigma = (68 - 58.5)/4.031 = 2.357.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 2.357 is 0.9906.

Therefore, P(X < 68) = P(Z < 2.357) = 0.9906.

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Answer:

6/10

Step-by-step explanation:

30/50=3/5

3/5=3/5

15/25=3/5

3/5*2/2=6/10

The answer is (a): \($\mathbf{8 0 0 0}$\)

We have 20 options for each number. Each position is distinct from the others.

Thus, by counting the total number of options, \($=20^{3}=8000$\)

What is combination?

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Step-by-step explanation:

I) 9+9+9+9=36

Ii)radius is 4.5 L=2piR= 2pi(4.5)= 9pi

Iii) A=piR^2= pi(4.5)^2 = 20.5pi

IV) 9×9 =81

V) 81-20.5pi = 16.597

Answer:

this is a required answer.

In the given figure we have a circle with center J.

By definition, the radius is the distance from its center to a point located on the circle.

a) In the given figure, a radius is JI

A diameter is a chord that passes through the center of the circle and it is twice the radius.

b) A diameter is KL.

A chord is a segment that connects two points on a circle.

c) A chord is HM.

d) If the length of JI (remember this is a radius) is 2 units, then the length of KL is twice this value: 2*2units= 4 units.

Answer:

True

Step-by-step explanation:

it is 3/5. Than 6/10 is equal to 3/5. Than 9/15 is equal to 3/5.

Answer: True

Step-by-step explanation:

That is true because let's take the first point for example.

3 cups of almonds for 5 cups of oats.

3/5 of 5 is 3

So that's correct.

If you still aren't sure you should try that with a different point. Hmm how about :

9 cups of almonds for 15 cups of oats

3/5 of 15 = 45/5 = 9

That's correct as well.

Hope these helps!

Answer:

1) 8/10 or 4/5

2) 1/4

3) 7/8

4) 13/10 or 1  3/10

5) 1/6

Step-by-step explanation:

1) If the denominators are different numbers, you need to find the common denominator. 3/5 + 2/10: Since /5 is a factor of /10, then you can multiply /5 by 2. But if you change the denominator, the numerator needs to change too. 3/5 * 2 = 6/10. Now simply add both fractions. 6/10 + 2/10 = 8/10 or if you reduce; 4/5!

2) Now that you know that method, do the same with the next problem. 3/4 - 1/2: /2 *2=/4. 1/2*2=2/4. 3/4-2/4 = 1/4!

3) 3/4 + 1/8 = (3/4*2) + 1/8. 3/4*2= 6/8. 6/8+1/8=7/8

4) Now, you cannot multiply 2 by any number to get 5. So you need to find the lowest common denominator. You find this by adding each number that is the denominator by itself until you get the same sum. Example: /5+/5=/10.  /2+/2+/2+/2+/2=/10. Remember, whatever is done to the denominator is done to the numerator. /5*2 = /10, 4/*2=8/. And /2*5=/10, 1/*5=5. So now it would be 5/10+8/10= 13/10 which could be changed to 1  3/10

5) Use the same technique you used last time on this problem. 2/3-1/2= (2/3*2) - (1/2*3) =4/6 - 3/6= 1/6!

Answer:

Step-by-step explanation:

The first is if the corresponding angles, the angles that are on the same corner at each intersection, are equal, then the lines are parallel. The second is if the alternate interior angles, the angles that are on opposite sides of the transversal and inside the parallel lines, are equal, then the lines are parallel.

Given

Mike took a taxi from home to Airport. The taxi driver charged $6 as initial fees and $3 per mile and the total fare is $24.

Required

we need to find total number of miles he covered on this ride.

Explanation

Let total number of miles he travelled be x

Then total fare =6+3x

i.e

So total number of miles covered is 6 miles.

The equation of the line that passes through the point (2, 5) and (6, 7) is

y = (1/2)x + 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

We have,

The equation of a line passes through points (2, 5) and (6, 7).

The equation of a line can be written as:

y = mx + c ______(1)

Points (2, 5) and (6, 7) must satisfy line (1).

5 = 2m + c _____(A)

7 = 6m + c ______(B)

From (A),

c = 5 - 2m

Putting in (B).

7 = 6m + 5 - 2m

7 = 4m + 5

2 = 4m

m = 1/2

Putting in (A) we get,

5 = 2 x 1/2 + c

5 = 1 + c

c = 4

Now,

The equation of the line is:

y = (1/2)x + 4.

Thus,

The equation of the line that passes through the point (2, 5) and (6, 7) is

y = (1/2)x + 4.

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The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex

For the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).

Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.

In conclusion, the correct option is C.

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Answer:

your answer C.)11,779 feet

Step-by-step explanation:

also the other ch.at got max out....

Answer:

C.)11,779 feet

Step-by-step explanation:

I took the test and got it correct!

Answer:

2.08

Step-by-step explanation:

:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately) are the exact values of each indicated trigonometric function.

Given function value is `cos(β) = √11/6` where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

To find the exact value of each indicated trigonometric function, we need to first find sin(β), tan(β), cos(β), csc(β), sec(β), and cot(β) where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.

We know that `sin²(β) + cos²(β) = 1`.So, `sin(β) = ± √(1 - cos²(β))`Since `0˚ ≤ β ≤ 90˚`, `sin(β) = √(1 - cos²(β))`Now, `sin(β) = √(1 - (√11/6)²)`  = √(1 - 11/6)  = √(6/6 - 11/6)  = √(-5/6)

Since the value of β lies in the first quadrant, sin(β) is positive. Therefore, `sin(β) = √(5/6)`We also know that `tan(β) = sin(β)/cos(β)`.So, `tan(β) = (√(5/6))/((√11)/6)`

Now, `tan(β) = (6√5)/11`Similarly, we can find the values of all other trigonometric functions.a. sec(β) = `1/cos(β)` = `1/(√11/6)` = `6/√11` = `6/11`b. sin (β) = `√(5/6)` = `5/6`c. Cot(β) = `1/tan(β)` = `1/((6√5)/11)` = `11/(6√5)` = `(11/6) * (1/√5)` = `11/(6√5)` * `(√5/√5)` = `(11√5)/30` = `(11/5.48)` = `2.01` (approximately)d. Sin(β - 90˚) = `cos(β)` = `√11/6`

Therefore, the exact value of each indicated trigonometric function is:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately).

Therefore, the options (a), (b), (c), and (d) are (6/11), (25/36), (11/5), and (11/6) respectively.

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