help me plsssssssssssssss

Answer:

-1/2 and -3/4

Step-by-step explanation:

rational numbers are numbers that can be expressed in a fraction

The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

(a) 6 + 7(b - 1) = 5 + b

6 + 7b - 7 = 5 + b

7b - 1 = 5 + b

7b - b = 5 + 1

6b = 6

b = 1

(b) x/3 + 5 = 6 has the solution x = 3

as, 3/3 + 5 = 6

1 + 5 = 6

6 = 6

also, 9 - 3x = 0 has the solution x = 3

as, 9 - 3(3) = 0

9 - 9 = 0

0 = 0

also, 2x + 4 = 10 has the solution x = 3

as, 2(3) + 4 = 10

6 + 4 = 10

10 = 10

(c) 7x - 4 = 3x + 8

7x - 3x = 8 + 4

4x = 12

x = 3

(d) 6x - 9 = 15

6x = 15 + 9

6x = 24

x = 4

(e) 9 - x = 14/x has the solution x = 7

as, 9 - 7 = 14/7

2 = 2

also, 65 - 2x = 6x + 9 has the solution x = 7

as, 65 - 2(7) = 6(7) + 9

65 - 14 = 42 + 9

51 = 51

also, 3 + 4x = 5x - 4 has the solution x = 7

as, 3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Hence, The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

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a) The probability of randomly selecting a ball bearing with a diameter which exceeds 5.03mm is 4.78%.

b) The percentage of ball bearings will be discarded is 0.26%

c) We would expect to find approximately 78 faulty ball bearings in a batch of 30,000.

d)  We need to produce 30,008 ball bearings to fulfill the order for exactly 30,000 ball bearings.

e) If a small batch of 100 ball bearings are randomly and independently selected for quality control, then the probability that only 5 out of 100 ball bearings will be faulty is approximately 0.2195 or 21.95%.

a) To calculate the probability of randomly selecting a ball bearing with a diameter exceeding 5.03mm, we can use the normal distribution function with a mean of 5mm and a standard deviation of 0.02mm. The formula for the normal distribution function is:

f(x) = (1/σ√(2π)) * \(e^{-(x-\mu)^2\)/(2σ²))

Where μ is the mean, σ is the standard deviation, x is the value we want to find the probability for, e is the mathematical constant approximately equal to 2.71828, and π is the mathematical constant approximately equal to 3.14159.

We want to find the probability that x is greater than 5.03, so we need to find the area under the normal distribution curve to the right of 5.03. We can use a standard normal distribution table or calculator to find that the probability is approximately 0.0478 or 4.78%.

b) To determine the percentage of ball bearings that will be discarded due to their diameter being outside the range of 4.95mm to 5.05mm, we need to find the area under the normal distribution curve that falls outside of this range.

P(x < 4.95 or x > 5.05) = P(x < 4.95) + P(x > 5.05)

= (1/0.02√(2π)) * \(e^{(-((4.95-5)^2)}\)/(20.02²)) + (1/0.02√(2π)) * \(e^{(-((4.95-5)^2)}\)/(20.02²))

= 0.0013 + 0.0013

= 0.0026

Percentage of ball bearings that will be discarded = 0.0026 * 100%

= 0.26%

c) To find the expected number of faulty ball bearings in a batch of 30,000, we can use the mean and standard deviation of the normal distribution to calculate the expected value of the number of ball bearings that fall outside of the range of 4.95mm to 5.05mm.

We can calculate the expected value of the number of faulty ball bearings as follows:

E(X) = μ * n

= (P(x < 4.95 or x > 5.05)) * n

= 0.0026 * 30,000

= 78

d) To fulfill an order for exactly 30,000 ball bearings, we need to produce more than 30,000 ball bearings to account for the percentage of ball bearings that will be discarded. We can use the percentage of ball bearings that will be discarded (0.26%) from part (b) to calculate the total number of ball bearings that need to be produced. The formula is:

Total number of ball bearings needed = 30,000 / (1 - percentage of ball bearings that will be discarded)

= 30,000 / (1 - 0.0026)

= 30,007.8 (rounded up to the nearest whole number)

e) To find the probability that only 5 out of 100 ball bearings will be faulty, we can use the binomial distribution function.

In this case, n = 100, x = 5, and p is the probability that a ball bearing is faulty, which we can calculate using the probability from part (b) (0.0026).

f(5) = (¹⁰⁰C₅) * 0.0026⁵ * (1-0.0026)¹⁰⁰⁻⁵

= (100! / (5! * 95!)) * 0.0026^5 * 0.9974^95

= 0.2195 or 21.95%.

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Answer:

\(x(t) = 54t\)  and \(y(t) = 134(t - 3)\)

Step-by-step explanation:

Represent the swimmers with A and B

For Swimmer A:

\(Rate = 54m/min\)

For Swimmer B:

\(Rate = 134m/min\)

Required:

Write a parametric equation

For Swimmer A:

If swimmer A covers 54 meters in 1 minutes, then the swimmer covers 54t in t minutes

So, the function is:

\(x(t) = 54t\)

For Swimmer B:

If swimmer A covers t minutes, swimmer B swims for (t - 3) minutes because swimmer B starts 3 minutes later.

If in 1 minutes, swimmer B covers 134 minutes; In (t - 3) minutes, the swimmer covers 134(t - 3)

So, the rate is:

\(y(t) = 134(t + 3)\)

Hence, the parametric functions are:

\(x(t) = 54t\) and

\(y(t) = 134(t - 3)\)

Answer:

A on Edge

Step-by-step explanation:

Answer:

y-intercept is 30

Step-by-step explanation:

Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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Answer:

1/2 divided by 5

Step-by-step explanation:

Answer:

The first answer

Step-by-step explanation:

Answer:

2π² or 19.74

Step-by-step explanation:

Given r = π

Then:

or

To find the equation of the line tangent to the graph of f(x) = 4 - cos(x) at x = 0, we need to determine the slope of the tangent line and use the point-slope form of a linear equation.

The slope of the tangent line to a curve at a given point can be found by taking the derivative of the function at that point. The derivative of f(x) = 4 - cos(x) is f'(x) = sin(x). Evaluating f'(0) gives us f'(0) = sin(0) = 0.

Since the slope of the tangent line at x = 0 is 0, we know that the line is horizontal. The equation of a horizontal line can be written in the form y = c, where c is a constant. To find the value of c, we substitute x = 0 and y = f(0) into the equation of the function f(x). Plugging in x = 0, we get f(0) = 4 - cos(0) = 4 - 1 = 3.

Therefore, the equation of the tangent line to the graph of f(x) = 4 - cos(x) at x = 0 is y = 3. The line is horizontal and passes through the point (0, 3).

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In order to make one more kit with the remaining parts, you would need 1 more people marker and 1 more die using mathematical operations

Let's analyze the number of parts available and the requirements for each kit. To make a kit, you need 6 people markers, 3 six-sided dice, and 7 teleporter markers. From the available parts, you have 287 people markers, 143 six-sided dice, and 341 teleporter markers.

We can determine the maximum number of kits you can make by dividing the available quantity of each part by the number required per kit. For the people markers, you have enough to make 287 / 6 = 47 kits. For the six-sided dice, you have enough to make 143 / 3 = 47 kits as well. Finally, for the teleporter markers, you have enough to make 341 / 7 = 48 kits.

After making the maximum number of kits, you will have some remaining parts. To determine if you can make one more kit, you need to identify the part(s) for which you have the least availability. In this case, the limiting factor is the people marker, as you have only 287 available. Therefore, to make one more kit, you would need 1 more people marker. Additionally, since you have 143 six-sided dice available, you also need 1 more die to match the requirement. Therefore, the answer is A. 1 more people marker and 1 more die.

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The subset of real number that can be used to classify the number 5.33 is irrational number.

We know that 5.33 = 5 + 0.33 contains a decimal part which is 0.33 and 5 which is a whole number part.

Since 0.33 is the irrational or decimal part which makes 5 + 0.33 = 5.33 irrational since a rational number + an irrational number = irrational number.

Since an irrational number is a number which cannot be expressed as a ratio of two integers.

So, 5.33 is an irrational number.

So, the subset of real number that can be used to classify the number 5.33 is irrational number.

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Answer:

 \(0.2 + 0.9x\)

Step-by-step explanation:

Using BODMAS:

1) \(0.2(x + 1) + 0.7x\)  

2) \(0.2x + 0.2 +0.7x\)

3) \(0.2 + 0.7x +0.2x\)

4) \(0.2 + 0.9x\)

Step-by-step explanation:

9z-6+7z=16z-6

16z-6=16z-6

16z-16z=-6+6

0=0

Answer:

(2x + y) ( x + 2y)

Step-by-step explanation:

The temperature of the steam is 441.7 K.

A 1-m³ tank contains 2.1085 kg of steam at 0.6 MPa.

The gas constant, critical pressure, and critical temperature of steam are

R = 0.4615 kPa.m³/kg.K,

TCr = 647.1 K, and

PCr = 22.06 MPa.

Using data from the steam tables, let's find the temperature of the steam.

According to the steam table, the specific volume of the steam is 0.194 m³/kg at 0.6 MPa and 393.71 K. Since 1 m³ tank contains 2.1085 kg of steam, the total volume of steam is:

V = m/v

= (2.1085 kg)/(0.194 m³/kg)

= 10.8665 m³

The ideal gas equation of state is:

Pv = mRTor

T = PV/mR

Substituting the values we get:

T = (0.6 MPa)(10.8665 m³)/(2.1085 kg)(0.4615 kPa.m³/kg.K)

T = 441.7 K

Therefore, the temperature of the steam is 441.7 K.

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Answer:

=A is the answer of your question

Answer:

probability is the same

Let's assume that Horacio collected x dollars. Then Jack's collection was x+15.75 dollars. Rashad collected (1/3) x dollars. Thus, we can come up with the equation:

x + (x + 15.75) + (1/3)x = 126.35(5/3) x = 110.60x = $66Horacio collected 66 dollars Jack collected $81.75Rashad collected 1/3 of Horacio's amount which is $22Please note that the equation is used in order to find out the unknown values, it is a representation of the given information in a mathematical form. If-then moves are used to solve the equation. It is important to be familiar with these moves as they simplify and make the solution more manageable.

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Answer:

answer is d

Step-by-step explanation:

pretty ez

The area of the piece of cake that Marty eats is: 64π square inches * (1/8) = 8π square inches. the area of the piece of cake that Marty eats is 8π square inches.

To find the area of the piece of cake that Marty eats, we first need to calculate the area of the entire round cookie cake.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

Given that the diameter of the cake is 16 inches, the radius (r) is half the diameter, which is 16/2 = 8 inches.

So, the area of the entire round cookie cake is:

A = π(8)^2 = 64π square inches.

Since the cake is divided into 8 equal pieces, each piece represents 1/8th of the total area.

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Answer:

Explanation:

let the angle the ladder makes with the ground be θ

θ = cos⁻¹(3/20)

θ = cos⁻¹(0.15)

θ ≈ 81.37°

Answer:

38 degrees

Step-by-step explanation:

this is an isosceles triangle, meaning that the base angles are congruent.

the total triangle is equal to 180

so the equation would be: x=180 - (71+71)

evaluate:

x=180-142

x=38 degrees

Hope this helps :)

Answer:

there are 5 terms so it takes 5 days for the trip, im not sure.

Step-by-step explanation:

The value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)] where E is bounded by the parabolic cylinder z=16−y2z=16−y2 and the planes z=0,x=4, and x=−4.

To evaluate the triple integral ∭E \(x^8 e^y\) dV, where E is bounded by the parabolic cylinder z=16−y² and the planes z = 0,x = 4, and x = −4, we can use the cylindrical coordinate system. Here are the steps to solve the integral:

Write down the limits of integration for each variable:

For ρ, the radial distance from the z-axis, the limits are 0 to 4.

For φ, the angle in the xy-plane, the limits are 0 to 2π.

For z, the height, the limits are 0 to 16 - y² for the parabolic cylinder, and 0 to the plane z = 0.

Write the integral using cylindrical coordinates:

∭E \(x^8 e^y\) dV = ∫\(0^4\) ∫0²π ∫\(0^{(16-y^2)\) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

Evaluate the integral:

∫0²π ∫\(0^4\)(16-y²) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) dφ ∫\(0^{(16-y^2)}\)(\(\rho^{10\) \(e^y\)) dρ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [\((16-y^2)^{11}\) / 11 \(e^y\)] dy dφ

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [(\(16^{11}\) / 11) \(e^y\) - (11/11) y² (\(16^{10}\)) \(e^y\) + (55/11) \(y^4\) (\(16^9\)) \(e^y\) - ...] dφ

= ∫\(0^4\) (\(16^{11}\) / 11) \(e^y\) [(\(cos^8\) φ) (2π)] dy

= (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)]

Therefore, the value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)].

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(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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Answer:

One solution

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

4x + 3 = -5x + 21

4x + 5x = 21 - 3

9x = 18

Divide both sides by 9

9x / 9 = 18 / 9

x = 2

Hope it helps.

Answer: Two buildings are 26.3m apart. From the top of the shorter building the angle of elevation to the top of the taller building is 35.9 degrees and b = 26.3 tan(54.7) = 26.3 1.412 = 37.145

Step-by-step explanation:

A function for the area A of the enclosure in terms of w is A = W(750 - 2W).

The width w that would maximize the area is 187.5 feet.

The maximum area is equal to 70,312.5 square feet.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

From the information about the fencing (perimeter), we have:

P = L + 2W

750 = L + 2W

Making L the subject, we have:

L = 750 - 2W

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

A = W(750 - 2W).

A = 750W - 2W².

For the width that would maximize the area, we have:

Width, W = 750/4

Width, W = 187.5 feet.

L = 750 - 2W = 750 - 2(187.5) = 375 feet.

Maximum area = LW

Maximum area = 375 × 187.5

Maximum area = 70,312.5 square feet.

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1) Since in this pie chart, we have a budget. Let's locate the sectors for Housing, Insurance, and utilities

2) Enlisting them:

Housing: 24.8%

Insurance: 26.7%

Utilities: 12.9%

\%

So we can add them up:

Answer:

\(1. m_ADC=3x+10 and m~BC=2X-30,what is m™AC2. m2BDC=3(x-5) and m--BC=x+25,what is MZA3. m2A= 1/2 (x-10)and m_C=1/3 x+5,find m-BC4. if m(BC)=4x-6 and m_C=x+10,waht is m_BDC?\)

Step-by-step explanation: