Let a € (-1,1). Evaluate TT cos 20 de. 1-2a cos 0 + a2 d0

Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

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Answer:

4.1

Step-by-step explanation:

You would first subtract 55.50 from 71.90 which leaves you with 16.4,

Then you would divide 16.4 by 4 to find how many gigabytes she could use which gives you 4.1

Hope this helped

Answer:

4.1

Step-by-step explanation:

If three pencils, each measuring one foot in length, are laid end to end touching, the total distance covered by the row would be 3 feet.

Since each pencil is 1 foot long, when three pencils are laid end to end, they form a row that is 3 feet long. The key information here is that the pencils are touching, which means there are no gaps between them. Therefore, the row would extend for a total distance of 3 feet.

In this scenario, the correct answer is option a, 3 ft. The row would not extend beyond 3 feet because there are only three pencils, each measuring one foot in length. If there were more pencils or if they were not touching end to end, the total distance covered by the row would be different. However, based on the given information, the row formed by the three one-foot-long pencils would have a length of 3 feet.

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A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Divide each term in the bracket by 4:

=  

3

x

−

2

Explanation:

Multiplying by  

1

4

is the same as dividing by 4. - You are finding a quarter of something.

To find a quarter of the bracket, divide each coefficient by 4.

You will get two unlike terms so you will not be able to simplify them.

This is the reason why you cannot simplify inside the original bracket either.

Step-by-step explanation:

Answer:

Angle C is the opposite angle of AB

Side AB is opposite to angle ∠ACB in triangle ABC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given rectangle, AC is the diagonal

ABC and ADC are two right triangles.

We have to find the angle which is opposite to the side AB.

The angle opposite to side AB is angle C.

In the option we have angle ∠ACB.

Hence, Side AB is opposite to angle ∠ACB in triangle ABC

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c = 22.3 km

Step-by-step explanation:

You can solve this problem using cosine law:

\( {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos( \gamma ) \)

where a and b are the legs of the triangle, c is the unknown length and the angle gamma is the angle opposite length c. We know that

a = 50 km

b= 52.4 km

gamma = 25°

c^2 = (50 km)^2 + (52.4 km)^2 -2(50)(52.4)cos25°

= 496.707 km^2

or

c = 22.3 km

Using the zero product, the solutions to the equation x² + x - 30 = 12 are  A. x=-7 or x=6

From the question, we have the following parameters that can be used in our computation:

x^2 + x - 30 = 12

Express the exponent as a proper superscript

So, we have the following representation

x² + x - 30 = 12

Subtract 12 from both sides

This gives

x² + x - 42 = 0

Expand

x² + 7x -6x - 42 = 0

When the equation is factored, we have

(x +_7)(x - 6) = 0

Solve for x

x = -7 and x = 6

Hence, the solutions are x = -7 and x = 6

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The probability that each of the balls will be of a different color is approximately 0.084.

To calculate the probability that each of the balls will be of a different color, we need to consider all possible combinations of 3 balls from the urn. There are a total of 19 balls in the urn, so there are 19 choose 3, or 19!/(3! * (19-3)!) = 191817/3! = 969 possible combinations.

Of these 969 combinations, there are

5 choose 1 * 6 choose 1 * 8 choose 1 = 5 * 6 * 8 = 240 combinations where each of the 3 balls is of a different color. So, the probability that each of the balls will be of a different color is 240/969 = 0.084, or approximately 0.084.

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Answer:

4/10

Step-by-step explanation:

This is because 4 water bottler are distributed to 10 girls

Answer:

2/5 of a bottle

Step-by-step explanation:

since there are 10 girls sharing 4 bottles of water, the equation is 4/10. This fraction can be further simplified into 2/5 and that's the answer. Hope this helps. :)

Answer: sales tax rate

Step-by-step explanation: p being the price and you mutiply 0.0635 by price to get the total

Lori will make more than Darryl, then the after 10 years Lori will have make $27.00 more in their account.

Darryl deposits into a savings = $1,500

Account that has a simple interest rate = 2.7%.

Lori deposits into a savings = $1,400

Account that has a simple interest rate = 3.8%.

Let us assume,

\(P_{1}\) = $1,500

\(r_{1}\) = 2.7%.

\(r_{1}\) =  2.7/100

\(r_{1}\) = 0.027

After 10 years = t = 10years

The formula to calculate simple interest is,

\(A_{1}\) = \(P_{1} (1+r_{1} t)\)           (Equation-1)

\(P_{1}\) = Principal amount

\(r_{1}\) = rate of interest ( in decimal )

t = time

First we calculate Darryl's deposit,

So we can substitute values in the equation-1,

\(A_{1}\) = 1,500(1 + 0.027×10)

\(A_{1}\) = 1,500 ( 1+0.27 )

\(A_{1}\) = 1,500 × 1.27

\(A_{1}\) = $1905

Now we will calculate Lori's deposit,

\(A_{2}\) = \(P_{2} (1+r_{2} t)\)                (Equation-2)

\(P_{2}\) = $1,400

\(r_{2}\) = 3.8%.

\(r_{2}\) =  3.8/100

\(r_{2}\) = 0.038

So we can substitute values in the equation-2,

\(A_{2}\) = 1,400 ( 1 + 0.038 × 10 )

\(A_{2}\) = 1,400 ( 1 + 0.38 )

\(A_{2}\) = 1,400 × 1.38

\(A_{2}\) = $1,932

Darryl will make money after 10 years = $1905

Lori will make money after 10 years = $1,932

Hence,

Lori will make more than Darryl,

Then the difference will be = 1,932 - 1,905 = $27

Therefore,

After 10 years Lori will have make $27.00 more in their account.

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Answer:

13x + 16

Step-by-step explanation:

Add the like terms together, like terms are terms that have the same variable or power. Ex. x and 4x are like terms, 4x and 4 are not. x^2 and x^3 are not like terms, x^2 and 2x^2 are like terms.

3+9+5x+4+8x

5x+8x+3+9+4

13x + 16

Answer: 290 miles

Step-by-step explanation:

Distance = speed × time

(65 × 1.5) + ( 55 × 3.5)

97.5 + 192.5

The relation that represents a function is the one in the top right.

Here we have some graphs of some relations, and we want to se which one of these is also a function.

A relation is a function only if each element in the domain (set of the inputs of the function) is mapped into only one of the elements in the range (set of the outputs of the function)

When we have a graph, we can check this with the vertical line test.

If we draw a vertical line over the graph of the relation, and it touches the graph of the relation in more than one point, then it is not a function.

If we do that, we  will see that the only graph that represents a function is the one in the top right position.

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Answer:

The vertex form of the quadratic:    y = (x - 1)² + 2

Coordinates of vertex:    (1, 2)

Step-by-step explanation:

\(y=x^2-2x+3\\\\y=x^2-2x+1+2\\\\y=(x-1)^2+2\)

The vertex form of an equation of the parabola is:  f(x) = a(x - h)² + k

where (h, k) is the vertex. So:

x - h = x - 1   ⇒   h = 1

+ k = +2     ⇒  k = 2

The simplification of the given fraction which is solved as a fraction would be =-13/12

A fraction is defined as the expression that represents the whole of a value in the form of a numerator and denominator.

The fraction given;

-8/24+ -18/24

The Lowest common denominator of the given fraction is 24

= -8-18/24

= -26/24

= -13/12

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We are given the equation below:

\( \large{ {p}^{2} = \frac{9}{36} }\)

Use the property below:

\( \large \boxed{ {x}^{2} = \frac{a}{b} \longrightarrow x = \pm \frac{ \sqrt{a} }{ \sqrt{b} } \: \: (a \geqslant 0 \: \: and \: \: b > 0)}\)

From the equation:

\( \large{p = \pm \frac{ \sqrt{9} }{ \sqrt{36} } } \\ \large{p = \pm \frac{3}{6} \longrightarrow p = \pm \frac{1}{2} }\)

Hence the answer is p = ± 1/2.

Answer

Both answers work. The second answer is in the plus-minus form.

Hope this helps! Let me know if you have any doubts.

Answer:

1/2

Step-by-step explanation:

we know that 1/4 of them failed, meaning that 3/4 of them passed.

1/3 of 3/4 is 1/4, meaning that 1/4 of the class got an A.

If 1/4 failed, and 1/4 passed with an A, that leaves 2/4 of the class that passed but didnt get an A, which simplifies to 1/2.

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Answer:

10 sqrt 3.

Step-by-step explanation:

sqrt30 = sqrt10 * sqrt 3

so sqrt30 * sqrt10

= sqrt10 * sqrt10 * sqrt3

= 10 sqrt 3.

Answer:d

Step-by-step explanation:

The annual growth factor represents the rate at which an investment grows each year. It is calculated by adding 1 to the growth rate expressed as a decimal.

In this case, the investment is growing by 7.5% each year. To express this as a decimal, we divide 7.5 by 100, which gives us 0.075. The annual growth factor is then calculated by adding 1 to the growth rate: 1 + 0.075 = 1.075.

Therefore, the annual growth factor is 1.075. This means that the investment grows by a factor of 1.075 each year, which corresponds to a 7.5% increase from the previous year's value.

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The approach to probability exemplified by the formula Probability of an Event = Number of favourable Outcomes / Total number of possible outcomes is the Classical approach to probability.

The Classical approach to probability is based on the assumption of equally likely outcomes and is often used when dealing with simple and well-defined experiments or situations. It involves counting the number of favorable outcomes (those that satisfy the desired condition) and dividing it by the total number of possible outcomes. This approach assumes that all outcomes have an equal chance of occurring.

In contrast, the Empirical approach involves conducting experiments or observations to gather data and estimate probabilities based on the observed frequencies. The Subjective approach relies on personal judgments or subjective assessments of probabilities based on individual beliefs or opinions.

Therefore, the correct answer is A) Classical approach.

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Answer:

a.36

Step-by-step explanation:

tie is not sure of winning or lose

so,5 tied may consider as lose too

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Factors.

1.) x^2-3x-10 = (x-5) (x+2)

2.)x^2-3x-18 = (x-6) (x+3)

Answer: -35/18

Step-by-step explanation: Hello!

The main thing that you need to know when dividing fractions is what the reciprocal is. Here is an example of finding the reciprocal:

1/2 divided by 2/3 = 1/2 x 3/2.

Basically, you flip the second fraction upside down (Put the number under the fraction line over the fraction line and put the number above the fraction line under the fraction line).  Then, you multiply the two fractions.  Then, you will find the answer.  Here is how to do that with the problem you have:

5/3 divided by (-6/7) = ?

After finding the reciprocal, you would get:

5/3 x (-7/6)

To find the answer, multiply the numerators together (5 and -7) and the denominators (3 and 6) together.

For the new numerator, you get -35.  For the new denominator, you get 18.  Put the new numerator above the fraction line and the new denominator below the fraction line.

The answer is:

-35/18

Answer:

-48-12g

Step-by-step explanation:

Use the distributive property to get your answer

Answer:

-48-12g

Step-by-step explanation:

-12 x 4 = -48

-12 x g = -12g

Put it all together: -48-12g