you walk to the subway station for your morning commute. given that you always leave your apartment at the same time, there is a probability of 1/2 that you will wait 3 minutes for the train and a probability of 1/2 that you will wait 7 minutes for the train. find the expected value of your wait time

The equivalent exponential expression for the radical expression [tex]\sqrt{2 + 3}[/tex]

is [tex](2 +3)^{\frac{1}{2} }[/tex].

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expression may not look the same but substituting the variables  will result to the same values.

Therefore, let's find the equivalent exponential expression for the radical expression can be found as follows:

[tex]\sqrt{2 + 3}[/tex]

Using exponential law,

[tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

Therefore,

[tex]\sqrt{2+3} = (2 +3)^{\frac{1}{2} }[/tex]

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The f-distribution's curve is positively skewed. Hence, the statement is true.

We have to check whether the statement is true and false.

The given statement is "The f-distribution's curve is positively skewed."

We can compare two populations using a F statistic thanks to the F distribution. The F distribution can be used to detect whether there is a significant difference in the variance between the means of two populations for ANOVA testing. Regression analysis can also make use of the F distribution to assess how well various models fit together.

The F distribution's graph is always positive and slanted to the right, while the form might vary based on the numerator and denominator degrees of freedom.

The f-distribution's curve is positively skewed. Hence, the statement is true.

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The only person that is correct with respect to the measurement of  ∠CEA of the congruent triangles is; Carlos

From the diagram attached, we are given that;

The measure of ∠CAE = 80°

∠BDE = 60°

Amy says that m∠CEA = 20°

Brent says that it is 30°

Carlos says that it is 40°

Debra says it is 50°

Now, by inspection, it is clear that ΔCAE is congruent to ΔBDE by SAS Congruency postulate and as such we can say that;

∠A = ∠B and ∠C = ∠D

Thus;

∠B = 80° and ∠C = 60°

Sum of angles in a triangle is 180 degrees and so;

∠CEA = 180 - (80 + 60)

∠CEA = 180 - 140

∠CEA = 40°

Which means that Carlos is correct.

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The coordinates of the vertices after a reflection over the line y = -5 is given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

The vertices of the original quadrilateral are given as follows:

T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).

The reflection line y = -5 is an horizontal line, meaning that after the reflection:

For example, the distance of the y-coordinate of the vertex U from -2 is of:

2 units above.

Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:

U'(2,-7).

Applying this rule for all the other vertices, they will be given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

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Function representing the sequence will be f(n) = (23 - 3n

The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....

Let n represents the number of term and f(n) the the term in the sequence.

Then we have to find the function that represents the sequence.

As we know explicit formula of an arithmetic sequence is given by

Or the function representing the sequence will be

f(n) = a + (n-1)d

where a represents first term of the sequence a = 20

and common difference d = 17-20 = (-3).

Now the function which represents this sequence will be

f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n

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When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.

A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.

Given,

Mean of the weights = 102.4 kg

Standard deviation = 13.9 kg

To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]

Where, [tex]\sigma[/tex]=standard deviation

n= number of reindeer

substitute the values in the formula,

[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]

Now,

[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]

from z-score table,

=0.1492

Thus, the probability the their mean weight is less than 100 kg is 0.1492.

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Your question is incomplete, here is the complete question.

The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg

if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?

Answer: 19.71 Million.

In order to regain the amount of water Joe losed during practice he should drink 10 cups of water.

A pound is equivalent to 453.59 mg, whereas a cup is equivalent to 236.59 ml.

You may roughly calculate that 2 cups equal 1 pound of water. The density should be 1 mg/ml if the fluid is mostly water.

The number of cups will be,

6 pounds * 453.59 (mg/pounds) * (1mg/ml) / (236.59 ml/cups)

= 10 cups .

Water is a crucial component for all living things, including people and other animals. Naturally, the water must go somewhere when it ascends the plant. Water loss will result from water evaporation (transpiration in plants)

Our breath, skin, urine, and sweat all cause water loss. A person's body will typically consume 2.5 L of water every day and expend the same amount. Your body will "inform you" you are thirsty and need to drink water if you get dehydrated (Figure 5). You have undoubtedly also noticed that when you drink less water, your pee is more concentrated.

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Adult tickets cost $8.25 and children ticket is $6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let adult tickets = a

Let children tickets = c

Since Johnny bought 4 adult tickets and 8 children tickets for $81. Leslie bought 2 adult

tickets and 2 children tickets for $28.50.

This will be:

4a + 8c = 81 ....i

2a + 2c = 28.50... ii

From equation ii a + c = 14.25

a = 14.25 - c

Put this into equation I

4a + 8c = 81 .

4(14.25 - c) + 8c = 81

57 - 4c + 8c = 81

4c = 81 - 57.

c = 6

Since a = 14.25 - c

a = 14.25 - 6.

a = 8.25

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Answer:All I know is that it’s not < or > but It might be ≤

Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.

[tex]\leq[/tex]

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

x^3 = 1,000,000  Find the cube root of 1,000,000

x^3 = 1.0x10^6     Using scientific notation, we can split the 1,000,000 into a 1.0 and a factor of 10*10*10*10*10*10 or 10^6

x = 1.0x10^2         The cube root of 1.0 is 1.0.  The cube root of 10^6 is found by dividing the exponent by 3:  10^2

The cube root of 1,000,000 is 1.0X10^2, or 100.

x = 100

Answer:

Van Dressler's total sales amount is $12,166.6666667

Step-by-step explanation:

3% = $365

365/3*100 =$12,166.6666667

The inequality to describe the possible side length for the third side is  5 < x ≤ 23.

What is the inequality of a triangle?

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.

The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

We have given,

Two sides of a triangle have lengths 9 and 14.

The third side is represented by x.

So by triangle inequality, we have the following inequality:

x ≤ 9 + 14

x ≤ 23

Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

14 - 9 < x

5 < x

Hence, the inequality to describe the possible side length for the third side is 5 < x ≤ 23.

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Answer:

Step-by-step explanation:

Hope it helps!

the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.

The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.

The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.

The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve

2y = 4√x

Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x

so, 4√x + 4x = 8

or,  √x + x = 2

or, √x = (2 - x)

or, x = (2 - x)²

or, x = x² - 4x + 4

or, x² - 5x + 4 = 0

or, ( x - 4) ( x - 1) = 0

or, x = 4, 1

when x = 4 then y = 2√4 = 4

when x = 1 then y = 2 √1 = 2

when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.

Thus, only intersection point is: (1,2)

This is the type (II) region.

So, integrate the region with respect to y.

Now, area =

= [tex]\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy[/tex]

= [tex]\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy[/tex]

= [tex]\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2[/tex]

= [tex]\frac{117}{12} - 6 + \frac{21}{4}[/tex]

= [tex]\frac{108}{12}[/tex]

= 9

Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.

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Mitchell's family will take 4 1/8 hours of time to cook the meat.

Maltiplication is reffered as adding multiple times. It is a one of the fundamental Mathematical operation. The symbol '×' used to denote the Maltiplication.

We use Multiplication to simplify the addition of the same number multiple times.

Here in this problem we use multiplication to solve the problem.

Here we have

Mitchell's family is slow cooking 2 and 3-fourths pounds of meat.

=> 2 and 3-fourth = 2 3/4 = 11/4 pounds of meat

The recipe says to cook the meat for 1 and a half hours per pound

For 1 pound of meat = 1 and 1/2 hours = 3/2 hours

The time required to cook 11/4 pounds = (11/4)(3/2) hours

= [tex]\frac{11}{4} (\frac{3}{2})[/tex] = [tex]\frac{33}{8}[/tex] = 4 (1/8) hours  

Therefore,

Mitchell's family will take 4 1/8 hours of time to cook the meat.

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The value of  h’(1) is = 22

How may the chain rule example be used?

Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.

Given that :

h(x) = 2f(x).g(x)

f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1

h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule

h’(1) = 2 f'(1)g(1) + g'(1)f(1)

= 2 * (4 * 2 + 1 * 3)

= 2* (11)

= 22

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The number of commercials and movies on which the songs were played are 5 and 2.respectively

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

The number of commercials is x, and the number of movies is y

The above parameters when represented as an equation is as follows

40x + 120y = 440

x = y + 3

Substitute x = y + 3 in 40x + 120y = 440

40(y + 3) + 120y = 440

Expand

40y + 120 + 120y = 440

Evaluate the like terms

160y = 320

Divide by 160

y = 2

Recall that

x = y + 3

So, we have

x = 2 + 3

x = 5

Hence, the number of commercials is 5 times

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The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

The point estimate of P, is defined as the proportion of successes in the sample.

P' = X/N ; where X = number of successes; N = total trials.

Here, N = 1000

According to the Child outlook file, number of "yes" = 240.

Hence, P' = 240/1000

P' = 0.24

Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

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The values (-7.5)-21.04 and (-7.5)+21.04 are not the same

A decimal can be defined as a number consisting of a whole number and also a fractional part.

These numbers are separated by a dot known as the decimal point

The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.

It is important to note the following operations;

From the information given, we have;

(-7.5)-21.04

Multiply the operation

+ 157. 8

Then,

(-7.5)+21.04

Multiply the operation

- 157. 8

Hence, the values are either negative or positive.

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On closely observing and solving the Probability it can be stated that  the batter will hit around 3 balls out of the next nine balls

What is Probability?

The ratio of the number of outcomes in an exhaustive collection of equally probable options that create a particular event to the entire number of conceivable outcomes.

Solution:

Average of Batter is 0.303 which means that the batter hits 303 shots of 1000 balls

So, in the next nine balls he will hit 9 * 303/1000 = 2.7 balls

Which means the batter will hit around 3 balls

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Answer:

Step-by-step explanation:

Rick should order part number G371-7 So the option A is the correct Answer

What is a part number ?

Part designs or materials are identified by part numbers, which are sometimes abbreviated as PN, P/N, part no., or part #. Its goal is to make referencing to that thing simpler. A part number clearly identifies a part design both inside and occasionally outside of a single organization. For instance, it is simpler to identify a screw as "HSC0424PP" rather than "Hardware, screw, machine, 4-40, 3/4" long, pan head, Phillips." The part number in this illustration is "HSC0424PP," which may be prefixed in database fields as "PN HSC0424PP" or "P/N HSC0424PP."

A serial number is a specific identifier of a specific instantiation of a part design, much as a part number identifies a component design (regardless of its instantiations). To put it another way, a part number designates each specific (physical) item as having been manufactured to a specific, original design;

As part number G371-7 fits perfectly to the desired requirement of float diameter of less than 8 inches, weigh more than 1 pound, and fit a 5/16-SAE spud connection that's why it is the correct answer

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Answer:

Step-by-step explanation

The slope intercept form is M=y2-y1 over x2-x1.

The answer for the equation is 12/3. 3 goes into 12 four times, so the answer is 4.

If the company has made 6732.16 in³ wax , Total number of candles made is 67

According to the question,

It is given that a wax candle is in cylindrical shape

Diameter of candle = 4 in

Radius will be = 4 / 2

=> 2 in

Height of each candles = 8 in

Company has used 6732.16 in³ of wax

We have to calculate number of candles company has made

Volume of cylinder = πr²h

Where r is radius and h is height

Substituting all the values,

Volume of candle = π (2)² (8)

=> V = 3.14 × 4 × 8   (putting π = 3.14)

=> V = 100.48

Therefore , Number of candles made = Total volume /volume of one candles

=> 6732.16 / 100.48

=> 67 candles are made by company

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ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)

steps

find the zeros JUST MEANS SOLVE FOR X

x⁴-2x²-16x-15=0

break it up

let u = x²

x⁴ = (x²)² = u²

-16x+u²-2u-15=0

hold off on -16x

u²-2u-15=0

what 2 numbers when multiplied give you -15 & when added give you -2?

-5 and 3

(u-5) (u+3)

-16x + (u-5) (u+3) = 0

go back x

-16x + (x²-5) (x²+3) = 0

factor -1 out

( looks horrible so far lol )

-1 ((- x²+ 5) (x²+3) + 16x) = 0

multiply (- x²+ 5) with ( x² + 3 )

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0

-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0

The equation of the line is y = x/4 + 13/2 .

A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

And here we have the slope,

m = 1/4

And (x₁ ,y₁)  =  (-2,6)

then the equation of line is

y - y₁ = m (x - x₁)

y - 6 = (1/4) (x +2)

y = x/4 + 13/2

Therefore, the equation is y = x/4 + 13/2.

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Answer:

x=8/9

Step-by-step explanation:

step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.

3x+-3x cancels itself out and 3x+6x=9x.

now, the equation looks like: 9x-7=1

step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.

7+-7 cancels itself out and 7+1=8.

now, the equation looks like 9x=8

step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".

9x/9= x, 8/9

so the answer is x=8/9

hope this helped!!