if 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home?

The random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution:  

                    X ~ Exp( μ = 53)

Random Variable:

A random variable is a variable that can take many values. This is because random events can have multiple outcomes. So don't confuse random variables with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. A random variable, on the other hand, can have a range of values ​​that could be the result of a random experiment.

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X is 2 (1 + 1) and the maximum value is 12 (6 + 6). Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

According to the Question:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

            X ~ Exp( μ = 53)

But, also we can define the variable in terms of  like this:

            X ~ Exp (λ =1/λ =1/53)

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According to the given statement If each can sold in accounted for as to its cost Last in first out.

The average is determined by adding together all of the numbers as well as dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value. We constantly encounter the average computation in our daily lives.

The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or dispersion.

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The complete equation is  y =2x+7  after substituting the given values.

What is equation?

An equation is a condition on a variable such that two expressions in the variable should have equal value and  Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.

According to the question.

We have a table which shows the relation between x and y.

Let the missing term be a and b.

The the given equation becomes

y = ax+b

For finding the value of a and b.

Substitute x = 0 and y = 7 in equation y = ax + b.

7 = a(0) + b

b= 7

Again, substitute  x = 1 and y = 9 in the equation y = ax+ b

9 = a(1)+b

9 = a+7

a=9-7

a=2

substitute the value of a and b in the equation y = ax + b. we get ,

y = 2x+7

Therefore, the complete equation is y = 2x+7

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All of the true statements that have to do with the expression 8y+3x+5 are:

An expression in mathematics is made up of a mixture of variables, integers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

In the equation 5 is a constant, this is because the value would not have to change because it does not have a variable attached.

The terms of the expression are, 3x, 8 y and 5. This makes it a total of 3 terms in the expression.

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The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.

A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.

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On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles  in order to make renting from Company B a better deal

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so, we have -

Company A charges =  $35 per day

plus =  $0.45 per mile.

Company B charges =  $60 per day

plus  = $0.25 per mile.

McCall would need to drive 126 miles  in order to make renting from Company B a better deal

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a)  It is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.

b)It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05)  ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.

Now, According to the question:

Part (a) Step 1: Given Information

Given, p = 0.097

Formula used:

The expected value

μ = 1/p

Part (a) Step 2: Simplification

The number of independent trials required until first success is distributed geometrically.

A geometric distribution's expected value is

μ = 1/p = 1/0.097 = 10.3039

Hence, it is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.

Part (b) Step 1: Given Information

Given, p = 0.097

Formulae to be used

Geometric probability:

P(X = k) = [tex]q^k^-^1p = (1-p)^k^-^1p[/tex]

Addition rule:

P(A ∪ B) = P(A) + P(B)

Complement rule:

P(A°) = P(not A) = 1 - P(A)

Part (b) Step 2: Simplification

Consider, p = 0.097

Compute the binomial probability definition at k = 1, 2,and3....40  :

P(X = 1) = [tex](1 - 0.097)^1^-^1(0.097)[/tex] = 0.097

Using the complement rule:

P(X ≥ 40) = 1 - P(X ≤ 39) = 1 - 0.9813 = 0.0187 = 1.87%

It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05)  ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.

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The given question is incomplete, The complete question is:

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

The coordinate pair of the given solution of the system would be= (g, h) (1,-8).

Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.

4g + h = -4 ---->. eq 1

12g + 2h = -4 ----> eq 2

Make h the subject of formula;

h = -4 - 4g -----> eq 3

Substitute equation 3 into equation 2;

12g + 2( -4 - 4g) = -4

12g - 8 -8g = -4

4g -8 = -4

4g = -4 +8

4g = 4

g = 4/4= 1

Solve for g = 1 in equation 1;

4(1) + h = -4

4 + h = -4

h = -4-4

h = -8

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The exponential function that shows the relationship between y and t is y  = 220,000(1.062^t).

An exponential equation can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential equation is f(x) = e^x

Where:

The form of the exponential equation that can be used to determine the population after 1997 is:

FV = P (1 + r)^n

Where:

y=220,000 x ( 1+ 0.062)^t

y  = 220,000(1.062^t).

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The units digit of an integer every square of an integer ends with (=has a units digit) 0, 1, 4, 5, 6, or 9.

This question can be answered in a variety of ways. Finding squares with the unit digits 0, 4, 5, and 6 is one way to demonstrate by means of elimination that the answer must be 2. The reason this method works is that you're presuming one of the answers to this specific multiple-choice question is true, but it's not actually that fulfilling.

A more effective method is to note that any number has the form (10m+i) such that 0i9. By squaring, you may determine exactly which numbers are feasible units digits in a square by getting 100m2+20mi+i2, etc. in turn.

Every square of an integer should have the units digit (0, 1, 4, 5, 6, or 9) as its final value.

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By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)

In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:

1 / [1 / (x + 2) + 1 / (x + 3)]

Second, expand the denominator by addition of fractions with distinct denominator:

1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]

Third, use division of fractions:

[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]

Fourth, simplify both numerator and denominator:

(x² + 5 · x + 6) / (2 · x + 5)

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The probability of selecting a spade and then selecting a heart from a standard deck with replacement is 0.625.

When selecting two cards with replacement from a standard deck of 52 cards, the probability of selecting a specific card on the first draw does not affect the probability of selecting a specific card on the second draw. Therefore, we can simply multiply the probability of selecting one card of a specific suit by the probability of selecting a different card of a specific suit.

The probability of selecting a spade on the first draw is

13/52 = 1/4 = 0.25

since there are 13 spades in a deck of 52 cards.

The probability of selecting a heart on the second draw is also

13/52 = 1/4 = 0.25

since there are 13 hearts in a deck of 52 cards.

Therefore, the probability of selecting a spade and then selecting a heart is:

(0.25) * (0.25) = 0.0625

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The greatest possible error for 25 miles is 12.5 miles.

Half of the unit of measure to which a measurement is rounded is the largest possible error. The maximum error is 2 units when a measurement is taken to the nearest whole unit 4.

Given, A value of 25 miles.

Now, we know the greatest possible error is half of the unit of measure.

Therefore, The greatest possible error for 25 miles is,

= (25/2) miles.

= 12.5 miles.

As 12.5 miles is half the value of 25 miles.

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In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.

Here is a step-by-step process to solve an absolute value equation:

Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.

For example, |x| = 3 can be rewritten as x = 3 or x = -3

Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.

Solve each case separately.

Check your solutions by plugging them back into the original equation and making sure they are valid solutions.

Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.

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Answer:

  214.9°

Step-by-step explanation:

You want to know the angle of rotation that moves a point on a circle of 16 inch radius a distance of 5 feet.

The relation between the length of an arc and the central angle in radians is ...

  s = rθ

The distance of 5 ft is equal to 60 inches, so we have ...

  60 = 16θ

Solving for θ gives ...

  θ = 60/16 = 15/4 . . . . radians

The angle in radians can be converted to an angle in degrees by multiplying it by 180°/π:

  15/4 radians = (15/4)·(180°/π) ≈ 214.9°

The wheel turned through an angle of about 214.9°.

The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.

Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:

(h(2) - h(-2)) / (2 - (-2))

First, we have to find h(2) and h(-2) by substituting these values in the function:

h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5

h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5

So, the average rate of change is:

(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25

Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25

Answer:

30 degrees.

Step-by-step explanation:

2 cos x = √3

cos x = √3/2

x = 30.

The value of x is 15 units.

What are Corresponding  Angles ?

When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

For instance, angle p and angle w are the comparable angles in the image below.

Step-by-step explanation:

In the given triangle RSQ and ΔRST it is given that

∠RTS ≅ ∠SRQ ≅ 90°

∠RSQ is common in two triangles Δ RSQ and Δ RST.

Therefore two angles are equal so both the triangles are common.

From this property we opposite sides of the corresponding angles will be in the same ratio.

SR/SQ = ST/SR

x/(9 + 16) = 9/x

By cross multiplication on each side of the equation

x² = 25×9 = 225

x = √225 = 15

Therefore measurement of x is 15 units.

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The quiz should have 5 3-point number of questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.

3-point questions: 5

4-point questions: 3

5-point questions: 4

1. The total number of questions is 9.

2. The total number of points for the quiz is 35.

3. There should be 1 more 3-point question than 5-point questions.

4. So, 5 of the questions should be worth 3 points each, for a total of 15 points.

5. That leaves 4 points remaining.

6. 4 points can be achieved by having 3 4-point questions (12 points) and 4 5-point questions (20 points).

7. Therefore, the number of 3-point, 4-point, and 5-point questions should be 5, 3, and 4 respectively.

The quiz should have 5 3-point questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.

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As per the given points, the distance is 0.08 meter.

The term distance in math is known as the length of the line joining the two points.

Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.

Here we have to calculate the distance between the two point in  meter.

Let us consider that x be the distance between the two points.

As we know that in each side there is 4 centimeter distance.

Then the total distance between the two points,

=> 4 x 2 = 8 centimeter.

Then the meter equivalent is calculated as,

=> 8/100 = 0.08

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Answer:

there are 12 fourths in 3 .

The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.

P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356

P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)

P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)

P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144

Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

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Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y-value when x = 0).

we see that with every increase of x by 1 y increases by 3.

so, the slope "a" is 3.

to get b we use one of the given points, e.g. (1, 5) :

5 = 3×1 + b = 3 + b

b = 2

so, our function is

y = 3x + 2

Answer: d=162km

Step-by-step explanation:

the equation of this question is:

speed = distance / time

s=d/t

18=d/9

d=18*9

d=162km

Answer to Problem 13 is  34.5  

Answer to Problem 15 is  22.9  

==================================================

Work Shown for Problem 13

sin(x)/17 = sin(91)/30

sin(x) = 17*sin(91)/30

sin(x) = 0.56658036

x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)

x = 34.51210645 or x = 180-34.51210645

x = 34.51210645 or x = 145.48789355

x = 34.5 or x = 145.5

If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).

If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)

In short, x = 34.5 is valid while x = 145.5 is not valid.

Therefore, the only possible answer is   34.5  

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

Work Shown for Problem 15

sin(x)/20 = sin(119)/45

sin(x) = 20*sin(119)/45

sin(x) = 0.38871987

x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)

x = 22.87486940 or x = 180-22.87486940

x = 22.87486940 or x = 157.1251306

x = 22.9 or x = 157.1

If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.

If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1

The only possible answer is therefore   22.9  

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

Side notes:

the product of x and a factor not depending on x

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3x(m-6n)²

This expression contains two factors:

1 factor: 3x

2 factor: (m-6n)²

Hence the product of x and a factor not depending on x.

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If the two circle centered at P and Q with radius 10 and 8 respectively , and if the common external tangent intersects line PQ at R , then the length of QR is 72  .

The radius of the circle that is centered at P is = 10 ;

the radius of circle that is centered at Q is = 8 ;

the common external tangent intersects the line PQ at R ,

Let XYR be external tangent with X on the Circle with center P , and at point Y on circle with center Q .

we extend , the line PQ to point R ,

we get , that triangle XPR is similar to triangle YQR ,

it means that , [tex]\frac{RQ}{RP} =\frac{QY}{PX}[/tex] ;

let the length of RQ be = x , then

length of RP will be = [tex]x+18[/tex]  ;

we get ; [tex]\frac{x}{x+18} =\frac{8}{10}[/tex] ;

⇒ [tex]10x=8x+144[/tex] ;

⇒ [tex]2x=144[/tex] ;

⇒ [tex]x=72[/tex] .

Therefore , the length of QR is 72 .

The given question is incomplete , the complete question is

A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR .

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The completed table to show the member cost for different numbers of classes is :
No. of classes      Cost under old model              Cost under new model

        2                                   170                                            110

        4                                   200                                           170

        5                                    215                                           200

        6                                    230                                          230

        7                                    245                                           260

Assuming that the number of classes is x, then the formula to find the cost with a certain number of classes with the old model is:

= 15 x +  140 membership fee

4 classes :

= 15 x 4 + 140

= $ 200

5 classes :

= 15 x 5 + 140

= $ 215

6 classes :

= 15 x 6 + 140

= $ 230

7 classes :

= 15 x 7 + 140

= $ 245

Cost under new model would take the formula:

= 30 x + 50 membership fee

4 classes :

= 30 x 4 + 50

= $ 170

5 classes :

= 30 x 5 + 50

= $ 200

6 classes :

= 30 x 6 + 50

= $ 230

7 classes :

= 30 x 7 + 50

= $ 260

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Answer: [tex]4x^4 -3x^3 y+8x^2 y^2 -7xy^3[/tex]

Step-by-step explanation:

In standard form, the terms are arranged in order from highest to lowest exponent of the variable that comes first alphabetically.