The lifetime of the timing belt of a certain make of cars is normally distributed with mean 125,000 miles and standard deviation 10,000 miles.
a) Find the probability that a timing belt lasts until the car runs 140,000 miles.
b) The auto maker recommends that owners have the timing belt replaced when the mileage reaches 90,000 miles. What is the probability that the timing belt fails before the car reaches the manufacturer’s recommended mileage?
c) An owner of this type of car wants to take a chance and replace the timing belt at the 1st percentile of the distribution. What should be the mileage of the car when he has the timing belt replaced?

The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.

What is volume?

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a rectangular prism with 7.2cm,8.4cm,18cm

we know,

the volume is

V= l.b.w

here,

l= 7.2 cm

b= 8.4 cm

w= 18cm

i.e. V= 1088.64 cm^2

Hence, The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.

To learn more on volume click :

brainly.com/question/1578538

#SPJ1

Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

Given data :

60 mph for 3 hours = 180 miles

55 mph for 4 hours = 220 miles

Total distance covered = 220 + 180

Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

Learn more about Average speed refer to :

https://brainly.com/question/4931057

#SPJ4

Answer:

The slope of the function y = -2x - 3 is -2. This is calculated by taking the coefficient of the x-term and making it the numerator of a fraction, and making the constant term the denominator.

Step-by-step explanation:

mark as brainliest

The relationship between x and y is that x is equal to twice the value of y.

The relationship between x and y can be expressed as a logarithmic equation. The first equation states that Log(c) = X/2, where c is a constant. The second equation states that Log(c^2) = Y. We can solve for the relationship using the two equations given. For equation 1, we can isolate X on one side of the equation to get X = 2*Log(c). For equation 2, we can isolate Y on one side of the equation to get Y = Log(c^2). Plugging the expression for X into equation 2, we get Y = Log(c^2) = Log(c)*2 = 2*Log(c) = X. Therefore, the relationship between X and Y is X = Y.To calculate the relationship between x and y, we can use the power law equation, which states that c^(x/2) = c^y. This can be rewritten as x/2 = y, so we can conclude that the relationship between x and y is x = 2y. Therefore, the relationship between x and y is that x is equal to twice the value of y.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ4

The probability that she will choose a fruit snacks, put it back and choose a granola bar will be 5/36.

The number of sections that need to be colored purple will be 2.

The probability that she will choose a fruit snacks, put it back and choose a granola bar will be:

= 5/12 × 4 / 12

= 5 / 36

The number of sections that need to be colored purple will be 2. This will be:

= p(head) × P(purple)

= 1/2 × 2/8

= 1/8

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

49

Step-by-step explanation:

7x7 = 49

you can just square 7 in your calculator

The probability that it rains at least one of the days is 40%.

Given data :

Let D1 = the event that it will rain on today

D2 = the event that it will rain on tomorrow.

P(D1) = 40% = 0.4

P(D2) = 40% = 0.4

The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N.

P(D1) + P(D2) / 2 = 0.4 + 0.4 = 0.8 / 2 = 0.4 = 40%

Learn more about Probability refer to :

https://brainly.com/question/24756209

#SPJ4

.

The percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Let the percent of the real fruit in the first brand = x

Given that number of gallons of  real fruit in the first brand = 9 gallons

Given that percent of the real fruit in the second brand = 48%

Given that number of gallons of  real fruit in the second brand = 8 gallons

Given that  percent of the real fruit in the mixture = 30%

then number of gallons of  real fruit in the mixture = (9+8) = 17 gallons

Then we get equation:

[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]

9x+48(8)=30(17)

9x+384=510

9x=510-384

9x=126

x=126/9

x=14

Therefore, the percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14.

To learn more about percent visit : brainly.com/question/14699403

#SPJ4

The percentage of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14%.

Let the percentage of real fruit juice in the first brand = a

Given number of gallons of real fruit in first brand = 9 gallons

Given the percent of real fruit juice in the second brand = 48%

Given number of gallons of real fruit in second brand = 8 gallons

Given the percent of the real fruit in total mixture = 30%

Total mixture of gallons of real fruit = 17 gallons

a% of 9 + 48% of 8 = 30% of 17

9a+48(8)=30(17)

9a+384=510

9a=510-384

9a=126

a=14

Therefore the percent of real fruit in the first brand =a=14%

Learn more about percentage here:

https://brainly.com/question/29306119

#SPJ4

Answer:

Clearly this figure is delusional loser bs

D = 93º

E = 43.5º

F = 43.5º

DF = 40

DE = 40

EF = 58

Step-by-step explanation:

Assuming angles F and E are the same angle, then:

8x - 24 = 40

8x = 40 + 24

8x = 64

x = 8

6x + 10 =

6 * 8 + 10 =

48 + 10 =

58

Cut the triangle in half:

58 / 2 = 29

sin x = 29 / 40 = 0.725 =~ 46.5º

D = 46.5 * 2

D = 93º

180 - 93 = 87º

87 / 2 = 43.5º

The point on the x-axis that lies on the line passing through point C and parallel to line AB is (4, 0).

A line that is parallel to line AB and passes through point C has the same slope as line AB. The slope of line AB can be found using the formula:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

In this case, (x1, y1) = (negative 4, 0) and (x2, y2) = (2, negative 3).

Substituting these values into the formula, we get:

m = (-3 - 0) / (2 - -4) =  -3 / 6 = -1/2

Since the slope of line AB is -1/2,

the slope of the line through point C and parallel to line AB is also -1/2.

A line with slope -1/2 and passing through (negative 2, 2) has the equation:

y - 2 = -1/2 (x - -2),

Rearranging this equation to solve for y, we get:

y = -1/2 x + 2

The x-axis has y-coordinate 0, so substituting 0 for y in the equation, we get:

0 = -1/2 x + 2

Solving for x, we get:

x = 4

hence the point is (4, 0)

Learn more about parallel lines at:

https://brainly.com/question/24607467

#SPJ1

The range is 4.5, and it means that the data varies by a value of 4.5.

A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it.

The range is the difference between the largest and smallest values in a data set.

In this case, the largest value is 8 and the smallest value is 3.5,

so the range is 8 - 3.5 = 4.5.

This means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

Hence, The range is 4.5, and it means that the data varies by a value of 4.5.

Learn more about data set here:

brainly.com/question/19243813

#SPJ1

In exercises 1 and 2:

In exercise 3 and 4, the value of x is 6 and 9

Please refer to the attached picture below as the referrence

The scale factor of the two triangles can be calculated by comparing the smallest side of both triangle. We will use side AB on ABC and side HI on HIJ. The scale factor of the two triangles is:

AB = 36  = 4

HI       27       3

The congruent angles of the two triangles are

A = H

B = I

C = J

The ratio of corresponding side lengths are:

AB = 36  = 4

HI       27       3

BC  =  42   =  4  

IJ       31.5     3

CA  =     59   = 4

JH       44.25     3

The ratio of corresponding side lenghts is 3/4

The scale factor of the two trapesium can be calculated by comparing the smallest side of both triangle. We will use side XY on WXYZ and side TU on STUV. The scale factor of the two triangles is:

XY  = 4  = 2

TU      6     3

The congruent angles of the two triangles are

W = S

X = T

Y = U

Z = V

The ratio of corresponding side lengths are:

WX  =  7     = 2

ST      10.5     3

XY  = 4  = 2

TU      6     3

YZ =   7    =  2  

UV     10.5     3

ZW = 10 =  2

VS     15     3

The ratio of corresponding side lenghts is 2/3

We can find the ratio of corresponding side lengths using the gvien data. We name the small parallelogram as A and the large one as B.

Side A = 2 = 1.5

Side B     8      x

2x = 12

x = 6

We can divide the poligons into 2 proportionally similar triangle. We name the small triangle as triangle C and the large one as triangle D.

Side C = 6 = x

Side D     10    15

6 = x

10     15

3  =  x

5     15

45 = 5x

x = 9

Learn more about Congruent Angles here: brainly.com/question/5218184

#SPJ4

After simplifing [tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex] after dividing the value is [tex]2\frac{11}{14}[/tex]

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

The numerator of an improper fraction is bigger than the denominator. For instance, 2/3 is a valid fraction since its denominator is bigger than its numerator, but 3/2 is an improper fraction.

The mixed fractions are

[tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex]

The improper fractions are :

13/2 and 7/3

Dividing 13/2 by 7/3 we get the value :

(13/2)/(7/3) = 13/2 * 3/7 = 39/14 = [tex]2\frac{11}{14}[/tex]

To learn more about Fractions refer to :

https://brainly.com/question/20409294

#SPJ4

The region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have examined the numerous three-dimensional solids and shapes, such as cubes, cuboids, cylinders, cones, etc., in three-dimensional geometry.

The intersection points of y = 6−x^2 and y = 2 are given by the equation 6 − x^2 = 2, i.e., x^2 = 4, so x = −2 and x = 2.

The integration can be written as:

[tex]\int\limits^2_{-2} {\ \pi (y_t^2 - y_b^2) } \, dx \\\\\int\limits^2_{-2} {\ \pi((6 - x^2)^2 - 4)} \, dx \\\\\int\limits^2_{-2} {\ \pi (x^4 - 12x^2 + 32)^2} \, dx\\ \\= \pi [\frac{x^5}{5} - 4x^3 + 32x ]_{-2}^2\\\\= \frac{384 \pi}{5}[/tex]

Hence, the region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.

Learn more about volume here:

https://brainly.com/question/1578538

#SPJ4

The probability that it takes 10 circuit boards to be inspected before a defective board is found is approximately 0.16777216%.

The probability that it takes 10 circuit boards to be inspected before a defective board is found can be calculated using the cumulative distribution function (CDF) of the geometric distribution. The CDF of the geometric distribution is given by the formula:

[tex]CDF(k) = (1 - p)^{k-1} * p[/tex],

where p is the probability of success (in this case, the probability of finding a defective circuit board) and k is the number of trials (in this case, the number of circuit boards inspected). Since the probability of finding a defective circuit board is 0.02, we can calculate the CDF as follows:

CDF(10) = [tex](1 - 0.02)^{10-1}[/tex] * 0.02 = 0.0016777216 = 0.16777216%.

This means that the probability that it takes 10 circuit boards to be inspected before a defective board is found is approximately 0.16777216%.

Read more on probability :

https://brainly.com/question/24756209

#SPJ4

2x+4y+4z = 0 is an equation of a plane containing the line .

What's the plane's reply?

In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. The surface is level or flat, to put it another way.

                        A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.

Parallel line equation:  2x+4y+4z = d

Point ⟨−4,−3,4⟩ belong to this plane  2 * -4 + 4 * -3 + 4 * 4 = d; d = -4

So, this plane equation 2x+4y+4z = -4

Let check point when t = 1 we have point ⟨−4,4,−2⟩

We check now if it belong to plane: 2 * -4 + 4 *4 + 4 * -2 = 0, 0 = 0.

So, equation of plane  2x+4y+4z = 0

Learn more about A plane

brainly.com/question/27190150

#SPJ4

Side-Angle-Side postulate states that if two sides and the angle joining them of a triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.

therefore triangle ABC congruent triangle EDC

The corresponding sides of both triangles are congruent.

The corresponding angles have the same measure. That is, they are congruent.

First draw two triangle: ABC and CDE that meet the questions criteria.

triangle ABC and CDE

C is the midpoint of BD and AE

By using definition of midpoint AC congruent CE ; BC congruent CD

With the help of definition of vertical angles we can say angle BCA congruent angle DCE

Side-Angle-Side postulate states that if two sides and the angle joining them of a triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.

therefore triangle ABC congruent triangle EDC

To know more about Congruent Triangles visit brainly.com/question/12413243

#SPJ4

The statement is True. Mean normalization scales data to have a mean of 0, which allows the gradient descent algorithm to more quickly identify the optimum point.

Mean normalization is a feature scaling technique used to speed up the learning process of gradient descent algorithms. It works by mapping the values of a dataset to a range of [-1, 1], or [0, 1], by subtracting the mean from each data point and dividing by the standard deviation. This scaling process helps to reduce the impact of the outliers and normalize the data, allowing the gradient descent algorithm to more quickly converge on the optimal solution. This results in faster and more accurate models.

Learn more about Normalization: https://brainly.com/question/14531594

#SPJ4

Answer:

The y-intercept of the line of fit is 60, which means that a student who studies for 0 hours is predicted to earn 60% on the test. This indicates that there is a positive correlation between the amount of time a student spends studying and their grade on the test.

Step-by-step explanation:

Answer:

Give the guy brainliest he deserves it

Step-by-step explanation:

Answer:

41(2) or just 82

Step-by-step explanation:

First, you would combine like terms, 9* and 32* then you would time by 2.

By using parabola techniques to back up data, healthcare organizations can ensure that patient information is protected and secure.

The Health Insurance Portability and Accountability Act (HIPAA) sets standards for the privacy and security of patient information, and these standards are critical for protecting patient privacy when using an electronic health record (EHR).

There are two key administrative requirements that help to protect patient privacy in EHRs: access controls and data backup and storage.

Access controls determine who can access a patient's information and what level of access they have.

Access controls ensure that only authorized individuals can access patient information and prevent unauthorized access or misuse of information.

Data backup and storage involves backing up all patient information and storing it in a secure location to ensure that it is protected from unauthorized access, theft, or loss.

To know more about parabola here.

https://brainly.com/question/4074088

#SPJ4

A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

f(x)= -3x^2+4x+4

g(x)= x(-7x-7)

now,

f(x) + g(x)

=-3x^2+4x+4 +x(-7x-7)

= -10x^2 - 3x +4

Hence, A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).

To learn more on equation click:

brainly.com/question/29455032

#SPJ1

The cost function is C(t) = $46.25.

Companies frequently utilize the cost curve to reduce costs and increase production efficiency. A cost function is a function of input prices and output quantity whose value represents the cost of producing that output given those input prices.

The evaluation of marginal costs and sunk costs are only two examples of the many potential uses for this cost curve.

Given that,

Rental fee = $40

Additional fees= $6.25 per hour

So, cost function is $40+$6.25= $46.25

Thus, The cost function is C(t) = $46.25.

To know more about cost function visit: brainly.com/question/28394132

#SPJ4

The two possible non-zero values of k in terms of a and b for the given differential equation is √(-b/a) and -√(-b/a).

The characteristic equation of the differential equation is given by:

a*k^2 + b = 0

Solving for k, we get:

k = +/- sqrt(-b/a)

The general solution to the differential equation ay'' + by = 0 is given by

y = C1 * cos(sqrt(b/a) * t) + C2 * sin(sqrt(b/a) * t)

where C1 and C2 are constants determined by the initial conditions.

So, the two possible values of k in terms of a and b are:

k = ± √(b/a)

--The question is incomplete, answering to the question below--

"If the function y = sin(kt) solves the differential equation ay" + by = 0, where a, b > 0, what are the two possible values of k in terms of a and b?"

To know more on differential equation

https://brainly.com/question/29849976

#SPJ4

Frequency distributions can show absolute or relative frequencies, such as percentages or proportions.

Organizing and presenting frequency counts in a way that makes them easier to understand is done through frequency distributions, which are visual displays. Absolute or relative frequencies, such as percentages or proportions, can be displayed in frequency distributions.

The number of people in each category on the measuring scale is arranged by tabulation or graphic representation in a frequency distribution. The full data set can be simply viewed by the researcher thanks to this.

An ordered tabulation of how many people fall into each group on a scale of measurement is known as a frequency distribution. Both a table and a graph can be used to arrange a frequency distribution, although both display the same two components: 1.

To learn more about frequency distribution refer to:

https://brainly.com/question/27820465

#SPJ4

If the quadratic has x-intercepts of -3 and 5 the equation would be:

y=c(x+3)(x-5)

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, by creating one part as the mirror image of the other part.

First, we have to define the axis of symmetry.

The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.

We have x-intercepts of -3 and 5

In ordered to find the axis of symmetry we have to find their middle intercept

To find the axis of symmetry:

-3+5/2=2/2=1

So the axis of symmetry is x = 1

To know more about the axis of symmetry:

https://brainly.com/question/16654836

#SPJ4

Rhoxy is the chemical symbol for Rhodium (Rh).

Rhodium is a transition metal found in group 9 of the periodic table, and its atomic number is 45. Its atomic mass is 102.90550 g/mol. Its atomic radius is 1.36 angstroms and its oxidation state is +3.

Rhoxy can be calculated by taking the atomic mass of Rhodium and converting it to moles. This is done by dividing the atomic mass of Rhodium by the molar mass constant, which is 1.00794 g/mol. This results in 0.1022 moles of Rhodium. The formula for moles of a substance is n = m/M, where n is the moles, m is the mass of the substance, and M is the molar mass constant.

To calculate the amount of Rhoxy, divide the moles of Rhodium by Avogadro’s number (6.02 x 10^23). This results in 1.68 x 10^-24 moles of Rhoxy. The formula for this calculation is n = n/N, where n is the moles of the substance, and N is Avogadro’s number.

Learn more about Radius here:

https://brainly.com/question/24051825

#SPJ4

Complete question :

What is the symbol for Rhodium?

Answer:

1.4024390244 I hope that helps

The number of shirts that the debate club need to sell on order to break even would be = 17 T-shirts.

The total amount of money that the company producing the T-shirts will charge the club = $250

The total charge contains the following:

The amount to sell each T-Shirt. = $15 each.

The number of T-shirts that can be sold = 250/15 = 16.6

That is approximately = 17 T-shirts.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1