47. For a certain type of computers, the length of time between charges of the battery is normally
distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of
these computers and wants to know the probability that the length of time will be between
40 and 70 hours.
A. .344
B. .656
C. .748
D. .908

Step-by-step explanation:

its -7.4

because each gap means 0.1

Therefore, using algebra, Laura is 14 years old and Juan is 21 years old.

Mathematical symbols and the rules for manipulating them are the focus of the discipline of study known as algebra. In order to express unknowable quantities, it makes use of symbols and variables as well as the study of mathematical equations and their characteristics. In algebra, numbers and mathematical operations are represented by letters and symbols in mathematical expressions and equations.

Let x be Laura's age and y be Juan's age.

Use the given information to set up two equations:

y = x + 7 (Juan is 7 years older than Laura)

xy = 294 (The product of their ages is 294 years)

Substitute the first equation into the second equation to get:

x(x + 7) = 294

Simplify the equation by expanding the left side:

x² + 7x = 294

Move all the terms to the left side of the equation:

x² + 7x - 294 = 0

Solve for x by factoring the left side of the equation or using the quadratic formula. Here, we'll use factoring:

(x + 21)(x - 14) = 0

This gives us two possible solutions for x: x = -21 or x = 14.

Since we're looking for age, we can discard the negative solution, x = -21.

Therefore, Laura's age is x = 14.

To find Juan's age, use the first equation and substitute the value of x:

y = x + 7

y = 14 + 7

y = 21

Therefore, Juan's age is y = 21.

So the ages we're talking about are Laura being 14 years old and Juan 21 years old.

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Your question is in Spanish. The English translation is:

Juan is 7 years older than Laura. The product of their ages is 294 years. What age numbers are we talking about?

Using combination, there are 424,110 ways to form a committee consisting of 4 teachers and 5 students.

This is a combination problem, as we are selecting a group of individuals from a larger set.

The number of ways to select 4 teachers from the 11 eligible teachers is:

C(11,4) = 11! / (4! * 7!) = 330

Similarly, the number of ways to select 5 students from the 13 eligible students is:

C(13,5) = 13! / (5! * 8!) = 1287

To find the total number of ways to form the committee, we need to multiply these two values:

330 * 1287 = 424,110

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The volume of prism P is calculated as: 16.55 cm³.

Similar figures are defined as those figures that the same shape, but the sizes are different.

The parameters given are:

- Prism P and prism Q are similar.

- Ratio of the surface area of the prism P to Q = 1 : 3

We also have:

Volume of prism Q = 86 cm³

Scale factor of height of the prism would be square root of surface area of the prism.

Scale factor of volume of the prism would be the cube of the height of the prism.

Let volume of prism P be V(P)

Let the volume of the prism Q be V(Q).

Thus:

V(P) / V(Q) = 1 / (√3)³

V(P) = V(Q) / (√3)³

      = 86 / (√3)³

      = 16.55 cm³

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There were about 204 principals in attendance.

The correct option is (A).

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data:

The total number of people in the recent conference = 875

The total number of people in one exhibit room = 60

Number of teachers in one exhibit room = 46

Number of principals in one exhibit room = 14

To find out the total number of exhibit rooms:

= Total number of people in the conference / total people in one room

= 875 ÷ 60

= 14.58 = 15 {rounding off to the nearest integer}

Number of principals in one exhibit room = 14

Total number of principals in the conference:

= Number of rooms × Principals in one room

= 15 × 14 = 210 which is equal to 204 {approximate answer}

There were about 204 principals in attendance.

Hence, There were about 204 principals in attendance.

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Answer:

19%

Step-by-step explanation:

First, find how many water bottles were manufactured in March:

4,100 x 1.07 = 4387

Add 500 to the March number

4387 + 500= 4887

Then divide the April number by February

4887/4100= 1.19195

This means that there is a 19 percent increase of water bottles manufactured from February to April

In the variation, the value of z is -6, when x = 10 and y = -7.

The value of z is calculated as follows;

x = ky/z

where;

k = xz/y

k = (20 x 6 ) / 14

k = 8.5714

In the variation, the value of z, when x = 10 and y = -7 is calculated as follows;

z = (ky) / x

z = (-8.5714 x 7 ) / (10)

z = -6

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The equivalent expression of the function using the distributive property is determined as  x² + 11x + 18.

The equivalent expression can be obtained by using distributive property as shown below;

The given expression = ( x + 2 ) ( x + 9 )

Using distributive property, we will have the following;

( x + 2 ) ( x + 9 ) = x ( x + 9 ) + 2 ( x + 9 )

x ( x + 9 ) + 2 ( x + 9 ) = x² + 9x + 2x + 18

x² + 9x + 2x + 18 = x² + 11x + 18

Thus, the equivalent expression is determined using  distributive property.

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The value of the standard form for the equation of a circle is,

⇒ (x - 5/2)² + (y - 9/2)² = (3/√2)²

We have to given that;

Circle have a diameter that has endpoints (- 2, 9) and (7, 0).

Hence, The radius of circle is,

We can find the distance the between given points as;

⇒ d = √(7 - (- 2))² + (0- 9)²

⇒ d = √81 + 81

⇒ d = 3√2

Hence, The radius of circle is,

⇒ r = 3√2/2

⇒ r = 3/√2

And, Center of the circle is,

⇒ (- 2 + 7 / 2, 9 + 0/2)

⇒ (5/2, 9/2)

Thus, The value of the standard form for the equation of a circle is,

⇒ (x - 5/2)² + (y - 9/2)² = (3/√2)²

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Answer:

8 sides and it's called an octagon.

Step-by-step explanation:

Let's begin by using the fact that the sum of the exterior angles of any polygon is always 360 degrees.

Let's call the measure of each interior angle "x". Then, you know that the measure of each exterior angle must be "x-90".

Using these expressions, you can find an equation for the sum of the exterior angles:

(number of sides) * (x-90) = 360

Simplifying this equation, you get:

number of sides = 360 / (x-90)

Now you just need to find a value of x that will make the number of sides an integer.

Since you know that the sum of the interior angles of any polygon is always (n-2)*180, where n is the number of sides, you can set up another equation:

(n-2)*180 = n*x

Simplifying this equation, you get:

n = 360 / (180-x)

You want both equations to give you an integer value of n, so you need to find a value of x that makes both denominators the same.

180-x = x-90

Solving for x, you get:

x = 135

Plugging this value of x into either equation gives you:

n = 360 / (180-135) = 360/45 = 8

So, the polygon has 8 sides and is called an octagon.

Answer:

The answer for x is 28°

Step-by-step explanation:

x+62=90°

x=90-62

x=28°

The area of the original figure is 9 times the area of the figure that results

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

Scale factor = 3

This means that the area scale factor is

Area scale factor = 3²

Evaluate the exponent

So, we have

Area scale factor = 9

This means that the area of the original figure is 9 times the area of the figure that results.

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The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

To solve for x in the measures of the exterior angles of a triangle, use the formula 180°=6x°+8x°+10x°. Rearranging to isolate x, we get x=180°/24x°=7.5. Therefore, x=7.5°.

Conclusion: The measures of the exterior angles of a triangle are 6x°, 8x°, and 10x°, and x equals 7.5°.

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The triangle has exterior angles measuring 90°, 120°, and 150° and value of x is 15.

What is Angle?

Angle is a figure formed by two straight lines or planes diverging from or meeting at a common point. It is a measure of the amount of rotation between two lines or planes and is usually measured in degrees or radians. Angles can be classified as right angles, acute angles, obtuse angles, straight angles, and reflex angles. Angles are also used in geometry to describe the shape of an object or the relationship between two lines or planes.

The sum of the exterior angles of any triangle is always 360 degrees.

Therefore, we can set up the equation: 6x° + 8x° + 10x° = 360°

Simplifying the left side of the equation, we get: 24x° = 360° Dividing both sides by 24, we get: x° = 15°

Therefore, the measures of the exterior angles of the triangle are: 6x° = 6(15°) = 90°

8x° = 8(15°) = 120°

10x° = 10(15°) = 150°

So the triangle has exterior angles measuring 90°, 120°, and 150°.

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Answer:

To find the lower bound of the mass of phosphorus in 1 liter of the fruit juice, we need to assume that all of the phosphorus is concentrated in just one liter of the juice. Therefore, the lower bound will be the mass of phosphorus in the entire bottle divided by the total volume of the bottle, which is 1.62 liters.

The mass of phosphorus per liter of juice is given by:

488 mg ÷ 1.62 L ≈ 301.2 mg/L

Rounding this to the nearest milligram, we get:

301 mg/L

Therefore, the lower bound of the mass of phosphorus in 1 liter of the fruit juice is approximately 301 mg.

The parallelogram with the given vertices is a,

7. None of the shapes.

8. Rectangle.

7. Parallelogram with vertices A(-2, -2), B(-3, 3), C(2, 0), D(-1, -5)

Using the distance formula,

AB = √(-3 + 2)² + (3 + 2)² = √1 + 25 = √26

BC = √(2 + 3)² + (0 - 3)² = √25 + 9 = √34

Adjacent sides are not equal.

So this is not a square or a rhombus.

AC = √(2 + 2)² + (0 + 2)² = √20

BD = √(-1 + 3)² + (-5 - 3)² = √68

This is not a rectangle since the diagonals are not equal.

8. L(-3, -4), M(3, 3), N(4, -3), O(-2, -2)

Using the distance formula,

LM = √36 + 49 = √85

MN = √1 + 36 = √37

Not a square or a rhombus.

LN = √49 + 1 = √50

MO = √25 + 25 = √50

Diagonals are equal, so it is a rectangle.

Hence the first one is none and the second one is a rectangle.

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(a)Probability of landing on A = 3/4 = 0.75 or 75%.

(b)The probability of the spinner landing on A or B is 100%, which means it is certain that the spinner will land on either A or B.

In part (a), we are asked to find the probability that the spinner will land on the letter A. The spinner has 4 sides and 3 of those sides have the letter A on them, so the probability of landing on A is 3/4. We can also express this probability as a percentage by multiplying 3/4 by 100%, which gives us 75%. Therefore, there is a 75% chance that the spinner will land on the letter A.

In part (b), we are asked to find the probability that the spinner will land on A or B. There are 4 sides on the spinner and 3 of them have the letter A, while only 1 of them has the letter B. To find the probability of landing on A or B, we add the number of sides with A or B, which gives us 3 + 1 = 4. Then, we divide this by the total number of sides on the spinner, which is 4. This gives us a probability of 4/4 or 1. We can also express this probability as a percentage by multiplying 1 by 100%, which gives us 100%. Therefore, there is a 100% chance that the spinner will land on either A or B.

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complete question:

Jenny spins a fair 4-sided spinner with the letters A B A and A on it

a) What is the probability that the spinner will land on A?

b) What is the probability that the spinner will land on A or B?​

The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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The volume of the composite object can be calculated as approximately: 285 ft³.

The composite object is composed of a cylinder and a rectangular prism, therefore:

The volume of the composite object = volume of cylinder + volume of rectangular prism

Volume of cylinder = πr²h

radius (r) = 1/2(4) = 2 ft

height (h) = 5 ft

Volume of cylinder = 3 * 2² * 5 = 60 ft³

Volume of rectangular prism = length * width * height

= 9 * 5 * 5

= 225 ft³

Volume of the composite object = 60 + 225 = 285 ft³.

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The price at which the company should sell its phones to get the maximum revenue is $250

Attaining peak yields is the preeminent rate of profits that a commerce or congregation can accumulate from its action, products, or amenities within a determined span.

It is where the firm or collective is accruing the most money achievable, harnessing its present facilities, marketplace appeal, pricing methods, along with other specifics.

In order to attain maximum revenue, an enterprise must focus on refining its sales and networking campaigns, developing its wares or services, determining and honing in on precise shoppers, and optimizing its expenses as well as costs efficaciously.

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Answer:

36.6°

Step-by-step explanation:

If angles W and X are complementary, this means that they add up to 90°.

If angle X equals 53.4°, then we can subtract 90-53.4 to get the measure of angle W.

90-53.4

=36.6

Angle W=36.6°

Hope this helps! :)

The probability that an answer is Ann's given that it is correct is 0.43 or 43%.

Where P(A|C) is the probability that the answer is Ann's given that it is correct, P(C|A) is the probability that the answer is correct given that it is Ann's, P(A) is the probability that the answer is Ann's, and P(C) is the probability that the answer is correct.

We can use Bayes' theorem to calculate the probability that an answer is Ann's, given that it is correct:

P(A|C) = P(C|A) * P(A) / P(C)

We are given that Brandon answered 80% of the questions correctly, so the probability that the answer is correct is:

P(C) = 0.8(0.6) + 0.85(0.4) = 0.79

where 0.6 is the probability that Brandon answers a question correctly (since 40% fail), and 0.4 is the probability that Ann answers a question correctly.

We are also given that Ann usually gets 85% of the questions right, so the probability that the answer is Ann's is:

P(A) = 0.4

Finally, the probability that an answer is correct given that it is Ann's is simply:

P(C|A) = 0.85

These values are what we obtain when we apply Bayes' theorem to them:

P(A|C) = P(C|A) * P(A) / P(C)

P(A|C) = 0.85 * 0.4 / 0.79

P(A|C) = 0.43

The Bayes theorem is a mathematical formula that estimates the likelihood that an event will occur based on knowledge of comparable events that have already occurred. It is named after Reverend Thomas Bayes, an 18th-century statistician, who first formulated it.

The theorem is based on the concept of conditional probability, which is the probability of an event occurring given that another event has already occurred. Bayes' theorem provides a way to update the probability of an event based on new evidence or information. The formula for Bayes' theorem is: P(A|B) = P(B|A) * P(A) / P(B), where P(A|B) is the probability of event A given event B has occurred, P(B|A) is the probability of event B given that A has occurred, P(A) is the prior probability of A occurring, and P(B) is the prior probability of B occurring.

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Answer:

x = 10 cm

Step-by-step explanation:

The total surface area of rectangular prism = [tex]2 (lb + bh + lh)[/tex]

Given,

l = x cm

b = 11 cm

h = 9 cm

TSA = 598 cm

Plugging in the values we get,

[tex]598 = 2(11x + 99 + 9x)\\20x = 299-99\\x = 10[/tex]

To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we substituted -3 for y and simplified. The first expression evaluates to 2, and the second evaluates to approximately -17.333.

To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we can simply substitute -3 for y in each expression and simplify

2(y+6)/3 = 2(-3+6)/3

Now, simplifying by simple subtraction and then multiply,

= 2(3)/3 = 6/3 = 2

Therefore, when y=-3, the value of 2(y+6)/3 is 2.

Now, substituting the value of y =-3

(4y+64)/(-3) = (4(-3)+64)/(-3) = (-12+64)/(-3) = 52/(-3) = -17.333...

Therefore, when y=-3, the value of (4y+64)/(-3) is approximately -17.333.

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The solution of the lines y = - x + 5 and y = 2x - 1 will be (2, 3).

Given that:

y = - x + 5

y = 2x - 1

The linear equation is given as,

y = mx + c

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

If the slopes are different then the system has one solution.

The lines are drawn on the graph. And the solution of the lines will be (2, 3).

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The quadratic function that could represent p is: [tex]p(x) = x^2 - 9[/tex].

What is quadratic function?

A quadratic function is a function that can be written in the form f(x) = [tex]ax^2 + bx + c[/tex], where a, b, and c are constants, and x is the variable. It is a type of polynomial function of degree 2, which means that the highest power of x in the equation is 2.

If the solutions to the quadratic equation p(x) = 0 are x = -3 and x = 3, we know that the factors of p(x) must be (x + 3) and (x - 3), since these are the expressions that yield zero when evaluated at -3 and 3, respectively. Therefore, a possible quadratic function p(x) that has these solutions is:

p(x) = (x + 3)(x - 3)

Expanding the expression using FOIL method, we get:

[tex]p(x) = x^2 - 9[/tex]

So, the quadratic function that could represent p is:

[tex]p(x) = x^2 - 9.[/tex]

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The required plant grew 9 centimeters in the sixth week.

Let x be the number of centimeters the plant grew in the sixth week.
To estimate x, we can use the formula for the mean (average) of a set of numbers:

mean = (sum of numbers) / (number of numbers)

We know the mean for 6 weeks is 9, so we can write:

9 = (13 + 6 + 10 + 5 + 11 + x) / 6

Multiplying both sides by 6, we get:

54 = 45 + x

Subtracting 45 from both sides, we get:

x = 9

Therefore, the plant grew 9 centimeters in the sixth week.

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In conducting a regression analysis, extrapolation is performed when one whishes to (A) predict beyond the limit of the sample

Extrapolation is the process of using a regression equation to make predictions beyond the range of the observed data. It involves extending the regression line or curve beyond the observed data points and predicting the values of the dependent variable for values of the independent variable that are outside the range of the observed data.

Determining cause and effect involves testing a hypothesis or theory about the relationship between variables. Lag variables are used as explanatory variables when there is reason to believe that the effects of a variable on the dependent variable are delayed or occur over time. Filling in gaps for missing observations involves imputing values for missing data points in the observed data set.

Therefore, the correct option is (A) predict beyond the limit of the sample.

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The given question is incomplete, the complete question is:

In conducting a regression analysis, extrapolation is performed when one whishes to :

A. predict beyond the limit of the sample

B. determine cause and effect

C. use a lag variable as an explanatory variable

D. fill in gaps for missing observations

Expressing the function F(2x - 1) in the form ax² + bx + c when F(x) = x² - 3x - 5 we get,

F(2x - 1) = 4x² - 10x - 3 and here  a = 4, b = -10 and c = -3

Given that the standard function is given by,

F(x) = x² - 3x - 5

We have to express the F(2x - 1) in the form ax² + bx + c.

In order to find F(2x - 1) we have to replace x with 2x - 1.

So, F(2x - 1) = (2x - 1)² - 3(2x - 1) - 5

F(2x - 1) = (2x)² + 1² - 2*2x*1 - 3*2x - 1*(-1) - 5

F(2x - 1) = 4x² + 1 - 4x - 6x + 1 - 5

F(2x - 1) = 4x² - 10x - 3

So comparing it with ax² + bx + c we get, a = 4, b = -10 and c = -3.

Hence, F(2x - 1) = 4x² - 10x - 3

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Answer: Gabriel is 10 years old.

Step-by-step explanation:

Let x represent Gabriel's age and x+2 represent Moussa's age.

x(x+2)=120

x^2+2x=120

x^2+2x-120=0

(Factor quadratic equation): (x-10)(x+12)=0

                                                  x=10, x=-12 --> (age can't be negative)

Gabriel is 10 years old.