(2 points) conditional probability. a fair coin is tossed twice. (a) (1 point) what is the probability of two heads if we know that the first toss is a head? (b) (1 point) what is the probability of two heads if we know that at least one toss is a head?

Answer:

25

Step-by-step explanation:

We already have our first value 36 and the second value 144. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1 Y =  36/ 144

By multiplying both numerator and denominator by 100 we will get:

STEP 2 Y =  36/ 144  ×  100/ 100 =  25/ 100

STEP 3 Y = 25

Finally, we have found the value of Y which is 25 and that is our answer.

If you want to use a calculator to find 36 is what percent of 144, simply enter 36 ÷ 144 × 100 and you will get your answer which is 25

There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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Answer:

156.4171429

Step-by-step explanation:

Hope this helps!

Answer:

tbh i rlly dont know how todo dat either

The correct option is c. 33%.

The job rate of industry’s percent increase from 2003 to 2013 is 33%.

The percentage increase would be the change between the final and initial values given as a percentage. We need the initial value and the enhanced (new) value to calculate the percentage.

In other words, % growth is a measurement of percent change that indicates the amount by which a quantity increases in magnitude, strength, or value.

If the % rise is negative, we might conclude that there is corresponding proportion reduction. Let's look at the percentage growth calculation now.

Now, according to the question;

Total Number of years = 10 years

Total number of new jobs created = 2.65 thousand x 10

                                                         = 26.5 thousand

                                                         = 26,500

Number of jobs in 2013 = 78,900 + 26,500

                                       = 105,400

Percentage increase = (105,400 - 78,900)/78,900 x 100

                                   = 26,500/78,900 x 100

                                   = 0.3359 x 100

                                    = 33.59%

Percentage increase = 33% (approx)

Therefore, the percentage increases in the job between 2003 and 2013 is 33%.

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Answer:

C

Step-by-step explanation:

Answer: \(171.4\%\)

Step-by-step explanation:

Given

Time is extended from 28 days to 76 days

The percentage increase is given by

\(\Rightarrow \dfrac{\text{New-original value}}{\text{original value}}\times 100\)

Putting values

\(\Rightarrow \dfrac{76-28}{28}\times 100=\dfrac{48}{28}\times 100\\\\\Rightarrow 171.4\%\)

Thus, the percentage increase in time is \(171.4\%\)

Answer:

165

Step-by-step explanation:

The area of the circle is approximately 4.52 square kilometers.

To find the area of a circle with radius 1.2 kilometers, we can use the formula:

Area = π × \(r^{2}\)

Plugging in the values we get:

Area = 3.14 ×\(1.2^{2}\)

Area = 3.14 × 1.44

Area = 4.5216

Rounding to the nearest hundredth, we get:

Area ≈ 4.52 square kilometers

The area of a circle is the measure of the region enclosed by the circle in a two-dimensional space. It is the amount of space inside the circle and is usually measured in square units, such as square meters, square feet, square centimeters, etc. The formula for calculating the area of a circle is A =\(\pi r^{2}\)

, where A is the area, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14. In simpler terms, the area of a circle is the total surface area of the circle, including the interior region, and is directly proportional to the square of its radius.

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the complete questionis :

determine the area of the solution, use 3.14 as \(\pi\)  value and round the answer to the nearest hunderedth.

a circle with radius 1.2km is shown

The interest rate required to get a total amount of $38,000.00 from compound interest on a principal of $22,000.00 compounded 1 times per year over 9 years is 9.0909 % per year.

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR .

r = n[(A/P)1/nt - 1]

r = 1 × [(38,000.00/22,000.00)1/(1)(9) - 1]

r = 0.0909090

Then convert r to R as a percentage

R = r × 100

R = 0.0909090 × 100

R = 9.0909 %/year

The interest rate required to get a total amount of $38,000.00 from compound interest on a principal of $22,000.00 compounded 1 times per year over 9 years is 9.0909 % per year.

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Answer: 6.1

Step-by-step explanation:

Answer:

∠DCB = 102°

Explanation:

∠CDB = ∠CBD

∠DCB = 180° - ∠CBD - ∠CDB

∠DCB = 180° - 39° - 39°

∠DCB = 102°

Answer:

Step-by-step explanation:

If the sum of two angles is one right angle or 90°, then one angle is said to be complementary of the other. Thus, 25° and 65°; θ° and (90 - θ)° are complementary to each other.

Suppose a rotating line rotates about O in the anti-clockwise sense and starting from its initial position

Answer:

Step-by-step explanation:

12 x 5 = 60 + 35 = 85, and we cannot go any higher without exceeding 100. However it would be different if it was a decimal. So for now the answer would be 5 classes added with the initial one time fee of 35 dollars.

Answer:

21

Step-by-step explanation:

f(x) =x^2 - 6x + 21

f(xl =0

Answer:

substitute 0 for x

f(0) = 0^2 - 6(0) + 21

0. = 0 - 0 + 21

0. = 21

Answer:

The answer is given below

Step-by-step explanation:

The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:

\(f(t)=\frac{3}{2}t\)

When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:

\(g(t)=3-\frac{3}{2}t\)

a)

\(f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles\)

\(g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\\)

b)

\(h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3\)

c)

According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0

\(h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3\)

This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0

Answer:

11/7

Step-by-step explanation:

(44-22)/(28-14)

= 22/14

= 11/7

hope this helped!

Answer:

y2-y1/ x2-x1 use this formula for solving questions

Answer:

Area is (x² - 9) units squared.

Step-by-step explanation:

• from difference of squares quadratic property:

\({ \boxed{ \rm{(a - b)(a + b) = ( {a}^{2} - {b}^{2}) }}}\)

→ a is x

→ b is 3

• Therefore:

\({ \tt{area = {x}^{2} - {3}^{2} }} \\ \\ { \tt{area = {x}^{2} - 9 }}\)

Answer:

1 135

2 80

3 145

4 45

Step-by-step explanation:

Thats the answer

.

.

.

Answer:that is already in slope intercept form

Step-by-step explanation:

Answer:

y = x + 17

Step-by-step explanation:

Given equation,

→ y = x + 17

Now we have to,

→ write it in slope-intercept form.

The slope-intercept form,

→ y = mx + b

Let's solve the given problem,

→ y = mx + b

→ y = x + 17

(It's already in slope-intercept form)

Hence, the answer is y = x + 17.

Answer:

A. Computer Company A’s predicted total sales for the year 2022 will be 3.78 billion dollars and Computer Company B’s predicted total sales for the year 2022 will be 2.45 billion dollars.

B. Computer Company A’s predicted total sales will reach 4.24 billion dollars in 2027.

Answer: A. Computer Company A’s total sales for the year of 2022 will be about 3.78 billion dollars and Computer Company B’s total sales for the year of 2022 will be about 2.45 billion dollars.

B. Computer Company A’s total sales will reach to about 4.24 billion dollars in around the year of 2027.

Answer:

16

Step-by-step explanation:

Answer:

x=80

Step-by-step explanation:

my god this should be easy and I thought I was a bit slow

If the measure of one interior angle be 160° then the sides of polygon be 18.

Given that the measure of one interior angle be 160°.

We are required to find the number of sides of polygon if the measure of one interior angle be 160°.

Polygon is basically a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The interior angle of polygon is given by :

Angle=(n-2)*180/n

160=(180n-360)/n

160n=180n-360

180n-160n=360

20n=360

n=18

Hence if the measure of one interior angle be 160° then the sides of polygon be 18.

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Answer:

16.58 feet

Step-by-step explanation:

a² + b² = c²

Think of this as a right triangle

The hypotenuse is 30, and one of the legs is 25

To find the other leg, subtract the square of the hypotenuse by the square of the given leg

30² - 25² = leg

900 - 625 = 275

Square root the answer to find the length of the missing leg

√275 = 16.583123951777

The leg is 16.58 ft.

We have the following table:

x -3 -2 -1 0 1 2 3

f(x) 2 3 6 3 -2 -0.5 1.25

f(2) - f(0) = 6 - 3 = 3

f(-3) + f(1) - f(0) = 2 + (-2) - 3 = -3

(f(3) + f(2)) / 2 = (1.25 + (-0.5)) / 2 = 0.375

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The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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\(4+25=2+25\)

They are equal because their sums both equal \(29\).

Answer:

4 + 25 is equal to 4 + 25

Step-by-step explanation:

they are equal because both of the equations are the same so that would mean both of the equations would be equal to each other

hope this helps

Answer:

A  22w = 1540

B Width = 70 feet

Length = 700 feet.

Step-by-step explanation:

A.  If the width is w then the length is 10w.

Perimeter = 2* (length + width) so

2(10w + w) = 1540

22w = 1540.

B.  22w = 1540

w = 1540 / 22

w = 70 feet.

l = 70 * 10 = 700. feet.

The probability that the random sample of 16 people in the elevator will exceed the weight limit is essentially 1. Rounded to 4 decimal places, the answer is 1.0000.

To answer this question, we need to use the central limit theorem, which states that for a large enough sample size, the sample mean will be approximately normally distributed regardless of the underlying population distribution.

In this case, we are given that the weight of students, faculty, and staff is approximately normally distributed with a mean weight of 150 pounds and a standard deviation of 27 pounds. We are also given that the elevator has a weight limit of 2500 pounds and a 16-person limit.

To find the probability that the random sample of 16 people in the elevator will exceed the weight limit, we first need to calculate the mean and standard deviation of the sample.

The mean weight of the sample can be calculated as:

mean = population mean = 150 pounds

The standard deviation of the sample can be calculated using the formula:

standard deviation = population standard deviation / √sample size

standard deviation = 27 / √16 = 6.75 pounds

Next, we need to calculate the z-score for the weight limit:

z = (weight limit - mean) / standard deviation

z = (2500 - 150) / 6.75 = 341.48

This z-score is extremely high, which indicates that the probability of the sample weight exceeding the weight limit is very close to 1 (i.e., almost certain).

To calculate the actual probability, we can look up the z-score in a standard normal distribution table or use a calculator. Using a calculator, we can find that the probability of a z-score of 341.48 or higher is essentially 1.

Therefore, the probability that the random sample of 16 people in the elevator will exceed the weight limit is essentially 1. Rounded to 4 decimal places, the answer is 1.0000.

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A polynomial is the mathematical expression of one or more algebraic terms where each consists of a constant that is multiplied by one or more variables raised to a nonnegative integral power.

Your information is incomplete. Therefore, an overview will be given. It should be noted that a polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.

For example, 3x+2x-5 is a polynomial.

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