exercise statement: the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi? use minitab how-to

Answer:

Step-by-step explanation:

right i think?

Part A:

After adding the meals tax we get the total bill as $27.32

Part B:

After adding the tip the total lunch cost was 432.24, hence the percentage of tip he gave is 18%

Tax

Meal plus tax = 25.3 + 8/100 * 25.3

Meal plus tax = 25.3 + 2.024             Round later. Find the total.

Meal plus tax = 27.324

Meal plus tax = 27.32 rounded to the nearest cent.

Tip

Total cost = $32.242

tip = 32.242 - 27.324

percentage of tip= 4.918

= 18%

Hence we get the required answers.

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Answer:

PQR is a right triangle

Step-by-step explanation:

slope of the line that contains PQ = 0

Because the line is parallel to x axis

slope of the line that contains QR

(5-1)/(-6+2) = 4/-4 = -1

slope of the line that contains PR
(1-5)/(-2-2) = -4/-4 = 1

PR and QR are perpendicular so the triangle is right

The smallest possible sum for this series is 20736 = 12^4.

Given:

A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power.

S = a + (a+2) + (a+4) + ... + (a+2*287) = 288(a+(a+574))/2 = 288(a+287)

288 = 2^5 * 3^2

smallest value of (a+287) that will make S = 288(a+287) a perfect fourth power is:

a + 287 = 2^3 * 3^2 = 72

a = −215

Smallest sum = 288*72 = 20736 = 12^4

Smallest odd integer in series = −215

−215 + −213 + −211 + ... + −1 + 1 + 3 + ... + 213 + 215 + ... + 359

= 20736 = 12^4.

Therefore the smallest possible sum for this series is 20736 = 12^4.

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The Answer is Han will cover 2.5 miles distance

What is distance ?

Distance is the total path covered by a object or person. As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river.

We need to find the distance run by Han after a half hour.

Han will cover a distance in 12 minutes=1 mile

Han will cover a distance in 1 minute= 1/12mile

Han runs distance in 30 minutes=30*1/12 miles

Hence, Han runs 2.5 miles after half hour.

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The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)

The graph represents the given parameter

On the graph, we have the following coordinate points

M = (-3, 4)

N = (2, 3)

O = (1, 1)

P = (-2, 2)

The rule of the reflection is given as:

Reflection across the x-axis

Mathematically, this is represented as

(x, y) ⇒ (x, -y)

When this is applied to the points, we have the following representation

M' = (-3, -4)

N' = (2, -3)

O' = (1, -1)

P' = (-2, -2)

Hence, the set of coordinates is (c)

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Using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.

So, if 'B' is the base and 'h' is the height of the pyramid,  its volume is V = (1/3) (Bh) cubic units.

Therefore, using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.

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If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, this phenomenon is called random phenomenon.

A phenomenon is random if individual outcomes are uncertain, but there is in spite of that, a regular distribution of outcomes in a great number of repetitions.

The probability of any outcome of a random phenomenon can be

described as the proportion of times the outcome would happen in a very lengthy chain of repetitions.

The outcome of any individual coin toss is random. But the outcome over many tosses is foreseeable, as long as the trials are individualistic (i.e., the outcome of a new coin flip is not impacted by the outcome of the preceding flip).

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Answer:

1 17/18

Step-by-step explanation:

4 2/3 / 2 2/5 =

= 14/3 / 12/5

= 14/3 × 5/12

= 70/36

= 35/18

= 1 17/18

4 2/3 divided by 2 2/5 results to 35/18.

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

Given:

4 2/3 divided by 2 2/5

So, 14/3 divided by 12/5

= 14/ 3 x 5/ 12

= 7/3 x 5/6

= 35/ 18

Hence, 4 2/3 divided by 2 2/5 results to 35/18.

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Answer:

11?

Step-by-step explanation:

since 8+3 = 11 won't each student get 11 because they equally share it and in total 11 x 8 = 88 so they have to share 11 blocks of clay.

The graph of the exponential function f(x) = (3/4)ˣ is attached below and this is also option A in the question given

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In the given function

f(x) = (3/4)ˣ,

we can use a graphing calculator to plot the graph while applying the values from the table of function.

Comparing the graph plotted and the options given, the answer is option A

Kindly find the attached graph below

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System of equations that models the situation is Option C . 2x+3y = 7.20 , 4x+3y = 8.80 and the price per pound for oranges is $1.40.

Given:

Part A

Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80.

Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.

2x + 3y = 7.20

4x + 2y = 8.80

Part B

on solving two equations:

2x + 3y = 7.20 and 4x + 2y = 8.80

2(2x + 3y) - 4x - 2y = 2*7.20 - 8.80

4x + 6y - 4x - 2y = 14.40 - 8.80

4y = 5.60

y = 5.60/4

= $1.40

hence price of oranges per pound is $1.40.

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Step-by-step explanation:

3900 if by hundreds

If by thousands 4000

The fraction 1/4th of the animals at the Jackson Zoo are monkeys.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

At the Jackson Zoo, 1/2 of the animals are primates

So if x is the total animals in that zoo, total primates are x/2.

Now out of them, 1/2 are monkeys i.e  1/2 of x/2

= x/4.

Hence 1/4 th fraction of the animals at the Jackson Zoo are monkeys.

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The equation is 51 = x + 120 × 0.30 that can find the monthly base fee charged by Chitchat wireless.

The equation representing the scenario will be formed through following components.

Total bill = monthly base fee + number of minutes × cost per minute

In the above mentioned equation, let us assume the monthly base fee to be x. Now, keep the values in formula to find the value of x.

51 = x + 120 × 0.30

Performing multiplication on Right Hand Side of the equation

51 = x + 36

Rewriting the equation according to x

x = 51 - 36

Performing subtraction on Right Hand Side of the equation

x = 15

Thus, the monthly base fee is $15.

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The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end[/tex]

Now, we will substitute the given function, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end[/tex]

Further, we will simplify this, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end[/tex]

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

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The number of solutions of the system of equations is given by:

Zero.

The number of solutions of a system of equations is obtained considering the coefficients and the constants of each side of the expression.

If the sides have different coefficients, then it will guarantee that the solution has only one solution, as there will be a division by a term different of zero.

If the sides have the same coefficients and then different constants, as is the case in this problem, the number of solutions is of zero, as a number different of zero will be divided by zero.

If the sides have the same coefficients and the same constants, then the number of solutions is of infinity, as the equivalent solution will be obtained with a division of zero by zero, that can be any value.

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For rolling four-sided die and a six-sided die, six-sided die have the lowest probability.

As per the state question-

Sample space for four-sided die = (1, 2, 3, 4).

Sample space for six-sided die = (1, 2, 3, 4, 5, 6).

The each outcome for the four-sided die will be 1/4 .

The each outcome for the six-sided die will be 1/6.

1/6 < 1/4

Thus, six-sided die have the lowest probability.

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The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6 to obtain a box with largest possible volume

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

Let S = length of the sides of the square cardboard sheet.  Let x = the side of each square cut from the corners.  The volume, V, of the box when the sheet is folded up is:

V = (S-2x)(S-2x)x = 4x3 - 4Sx2 + S2x

To find the maximum value, take the derivative of V wrt x, set it to zero, and solve for x:

V ' = dV/dx = 12x2 - 8Sx + S2

0 = 12x2 - 8Sx + S2

0 = (6x-S)(2x-S)

x = S/6 and S/2

To determine which is the max and which is the min, take the second derivative of V wrt x.

V'' = d2V/dx2 = 24x - 8S

At x = S/2, V'' = 24(S/2) - 8s = 4S. Since S>0, the point x=S/2 is a minimum. This makes sense because you have cut away the entire cardboard square.

At x = S/6, V'' = 24(S/6) - 8S = -4S < 0, so x = S/6 is the maximum

The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6

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The system of equation for each condition will be; 2a + 3c = 325.94 and

2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and

c = $46.99

A linear equation is an algebraic equation of the form y = mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

At an amusement park, the cost for an adult admission is a and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95 and all ticket prices include tax.

According to question,

2a + 3c = $325.94

4a + 2c = $256.95

2a + c = $162.97

Solving the equation by using elimination method, we get,

a = $57.99 and c = $46.99

Hence, The system of equation for each condition will be; 2a + 3c = 325.94 and 2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and c = $46.99

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The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.

We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.

Στ(B) = 0

τ(a) + τ(b) + τ(m1) + τ(m2) = 0

τ = r×F×sin(θ)

d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0

d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0

Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d

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The sentence, using the rational root theorem, is completed as follows:

If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.

The variables p and q are defined as follows:

Hence the blanks in this problem are completed, respectively, by:

Constant term and leading coefficent.

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Answer: 3)

Could you please mark me as "Brainliest"

Your answer is in bold below!

8.5 x 3 = 25.5

Answer: Her brother is 25.5 kg.

Step-by-step explanation:

If her brother is 3 times as heavy, we need to multiply 8.5 kg by 3.

8.5 kg times 3 is 25.5 kg.

The probability of getting a sum greater than 10 is 1/12.

From the question, we have

total outcomes = 6 ×6 = 36

Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3

Probability = 3/36

=1/12

The probability of getting a sum greater than 10 is 1/12.

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:210

Step-by-step explanation:

Answer:

3 times .. just multiply

The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

What is the area of a rectangle?

If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as

                  Area = Length * Breadth

The length of the screen is 11 in. and the breadth of the screen is 7 in.

Then the area of the screen,

            Area = length * breadth

                     =  11 * 7

                     = 77 square inches.

Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.

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