what is the probability that out of ten randomly selected 30 year olds in 1970. at least one did not earn more than his or her parents at age 30

Answer:

38 full batch with a remainder of 3

Step-by-step explanation:

18*7 + 15*7 = 231

231/6 = 38 r3

A pair of vertical angles is; Angle 1 and Angle 4

A pair of supplementary angles are; Angle 2 and angle 1

Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.

Two angles are defined as adjacent angles when they share the common vertex and side.

Two angles are defined as supplementary angles if they sum up to 180 degrees.

By those definitions above, we can say that;

Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.

We can also say that;

Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.

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On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.

        [tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]

Given is the function, as follows -

f(x) = (x²/15 + 6x - 9x²/{3/2})

The given function is -

f(x) = (x²/15 + 6x - 9x²/{3/2})

∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx

∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx

∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃

∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}

∫f(x) = x³/45) + (3x²) - (2x³) + C                  (C = C₁ + C₂ + C₃)

Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.

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Your answer would be x = 2 ± √2

Step-By-Step Solution:

Step one:

9x² - 36x + 32 = 14

Step two:

9x² - 36x + 32 - 14 = 14 - 14

9x² - 36x + 18 = 0

Now we use the quadratic formula.

Step three:

Plug the numbers into the quadratic formula.

x = [tex]\frac{-b±\sqrt{b^{2} - 4ac } }{2a}[/tex]

x = [tex]\frac{-(-36 ± \sqrt{(-36^{2})-4(9)(18 } )}{2(9)}[/tex]

x = [tex]\frac{36 ± \sqrt{648} }{18}[/tex]

x = 2 + √2 or x = 2 - √2

Answer:

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

Given equation:

Solve it in below steps:

The circumference of the circle is 25.12 inches

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

Radius = 4 inches

The circumference of a circle can be calculated using

C = 2πr

Substitute the known values in the above equation, so, we have the following representation

C = 2 * 3.14 * 4

Evaluate

C = 25.12

Hence, the circumference is 25.12 inches

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We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.

Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.

Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.

There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.

On the other hand, there are some sets which have no solution, and they are called inconsistent.

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There are 30 questions for 2 points and 10 questions for 4 point.

What is elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.

Given that, the total number of equations is 40. Total point on the paper is 100 points.

There are two types questions, one type question contains 2 points and other type question contains 4 points.

Assume that, there are x questions for 2 points and y questions for 4 points.

The total number of questions is x + y.

The total point is 2x + 4y.

Therefore,

x + y = 40  ......(i)

2x + 4y = 100  .....(ii)

Multiply 2 with equation (i)

2x + 2y = 80

2x + 4y = 100

___________

       -2y = -20

Divide both sides by -2:

y = 10

Putting y = 10 in equation (i)

x + 10 = 40

x = 30

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Answer:

x weigh of ball

2x+40=160

2x=120

x=60g

The solution is 60 grams

The size of each of the balls is given by the equation x = 60 grams

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the size of the balls be represented as = x

The number of balls = 2

So , the total size of the balls = 2x

Now , the equation will be

The weight of all the elements = 160 grams   equation (1)

The weight is balanced by = 40 grams + 2x   equation (2)

Now , equation (1) = equation (2)

Substituting the values in the equation , we get

160 = 2x + 40

On simplifying the equation , we get

Subtracting 40 on both sides of the equation , we get

2x = 120

Divide by 2 on both sides of the equation , we get

x = 60 grams

Therefore , the value of x is 60 grams

Hence , the size of the ball is 60 grams

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The distance between two buoys by the trigonometric function will be 175.48 feet.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

As per the given situation is making a right angle triangle.

By tan trigonometric function,

tan21.3° = BC/450

BC = 175.48 feet

Hence "According to the trigonometric function, there will be 175.48 feet between two buoys.".

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The rate at which the radius is increasing is; 0.006 in/min

We are given that the formula for the volume of  a spherical balloon is;

V = ⁴/₃πr³

where r is the radius

The volume is increasing at the constant rate of 0.78 inches per minute. Thus;

dV/dt = 0.78

Now, differentiating with respect to t gives;

dV/dt = ⁴/₃(3πr²)(dr/dt)

At radius of 3.2 inches, we have;

0.78 = 4π * 3.2² * dr/dt

dr/dt = 0.78/(4π * 3.2²)

dr/dt = 0.006 in/min

This is therefore the rate at which the radius is increasing.

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Answer:

its A

Step-by-step explanation:

Ben

Answer:

3900 is decreased.$74100 is new value

Step-by-step explanation:

5% of 78000 subtracted by 78000...

Answer:

First second and third

Step-by-step explanation:

A function can only have one output for every input

Answer:

2, 3, 4

Step-by-step explanation:

an input can only have 1 output

The Valdez family left at noon for a 4-hour trip to visit relative. They topped 1 hour time for lunch and 2 hour to visit an amusement park.The Valdez family would have arrived at their relative's house at 5 pm.

1. The Valdez family left at noon, so they had 12 hours to get to their relative's house.

2. They stopped for 1 hour for lunch, so they had 11 hours left.

3. They then stopped for 2 hours at the amusement park, so they had 9 hours left.

4. 9 hours later would be 9 pm.

5. However, since it is summer, the clocks are set to daylight savings time and it is currently one hour ahead, so the time is actually 5 pm.

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Answer:

i believe its 5+n ≤ -7

Step-by-step explanation:

the sum of 5 and a number(n) would be 5+n, and no more woukd be the  ≤  sign, which would lead to -7

Three of the seven phases of the impulse purchase cycle. The other phases include antecedent, search, and selection.

The impulse purchase cycle is a model that describes the process of making an impulsive purchase. It is typically divided into seven phases:

Antecedent: This phase is characterized by a need or desire for something. It can be triggered by a variety of factors, such as boredom, hunger, or a sudden craving for a particular product.

Search: In this phase, the consumer begins to actively search for a product that will satisfy their need or desire. They may search online or in physical stores, and they may consider various options before deciding on a product.

Selection: In this phase, the consumer narrows down their options and selects a specific product that they want to purchase. They may consider factors such as price, quality, and convenience when making their decision.

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Answer:

10 Guests

Step-by-step explanation:

200 - 75 = 125 (We need to find a number that will spend 125 dollars)

125 / 12.50 = 10

12.50 x 10 = 125

So the answer is 10

Answer:

l = 2.55 meters

Step-by-step explanation:

Tunnels are usually in cylinder shape

Surface Area of Cylinder:

l = s/(2πr)

l = 48/(2π(3))  ==> plug in known values

l = 48/(6π)

l = 8/π  

l = 2.546 meters

l = 2.546 meters

l = 2.55 meters

Answer:

4 quarts of milk will last her 8 days.

We can solve this by finding how many cups are in a quart.

1 quart=4 cups

4 quarts= 16 cups

Since Caroline drinks 2 cups a day, divide 16 by 2.

16/2=8

4 quarts will last her 8 days.

Hope this helps! :D

Step-by-step explanation:

Total no of racks in the store is 30 and grocery item is maximum.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.

Racks of confectionery items = 10

Racks of bread items = 5

Racks of grocery items = 15

The total no of racks in the departmental store is 30

Using the percentage formula we will calculate the percentage of each item

percentage of confectionery items rack =no. of confectionery racks/total no. of racks  x100

=10/30x100=33.33%

percentage of bread items rack = no. of bread racks/total no. of racks x 100

= 5/30x 100=16.66%

percentage of grocery items rack = no. of grocery racks/total no. of racks x 100

= 15/30 x 100 = 50%

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

We are given that the probability of selecting a yellow card is 3 times the probability of selecting a blue card, so we can write the following equation:

yellow = 3 * blue

We also know that the sum of the probabilities of selecting a red, yellow, or blue card must be equal to 1, so we can write the following equation:

red + yellow + blue = 1

Substituting the expression for yellow from the first equation into the second equation, we get:

red + 3 * blue + blue = 1

Combining like terms, we get:

red + 4 * blue = 1

We are given that the probability of selecting a red card is 1/9, so we can substitute this value into the equation:

1/9 + 4 * blue = 1

Solving for blue, we get:

blue = (1 - 1/9) / 4

blue = (8/9) / 4

blue = 2/9

Therefore, the probability of selecting a blue card on the first try is 2/9.

Answer:

To prove that 16^5+16^4 is divisible by 17 using factoring, first rewrite the expression 16^5+16^4 using the distributive law as 16^4*(16+1). Then, note that 16+1 is divisible by 17. Since 16^4 is also divisible by 17, the expression 16^4*(16+1) is also divisible by 17. Therefore, 16^5+16^4 is divisible by 17.

Answer:

all values less than -13

Step-by-step explanation:

3x + 5 < 2x - 8

3x + 5 - 5 = 2x - 8 - 5  ==> isolate x by subtracting 5 on both sides

3x < 2x - 13  ==> simplify

3x - 2x < 2x - 2x - 13  ==> subtract 2x from both sides to move x to the left

                                         side of the inequality

x < -13  ==> simplify

Hence, the answer is all values less than -13.

The resulting sampling technique is Stratified sampling.

As in the concept of statistical study, sampling methods refer to how we select members from the population to be in the study and if a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.

Here we need to find the type of sampling method.

Here the Stratified random sampling involves classifying the units of the population into different strata.

And the give units in each stratum should possess similar characteristics which then allows the researcher to pick a sample from each.

Then the stratified sampling approach can be divided into proportionate stratified sampling and disproportionate stratified sampling

Therefore, these method is employed in cases where the population is heterogeneous.

So, option (b) is correct.

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Answer:

Area :153.86 m

Circumference: 43.96 m

Step-by-step explanation:

Area: 3.14 x r^2

or, A= 3.14 x 7^2

Therefore, A= 153.86m

Circumference: 2 x 3.14 x r

or, C= 2 x 3.14 x 7

Therefore, C= 43.96 m

Hope this helps:)

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The centroid of the region in the first quadrant bounded by the given curves is (81/170, 81/170).

In the given question, we have to find the centroid of the region in the first quadrant bounded by the given curves.

The given curves are:

y = x^8, x = y^8

We can write the curves as

y = x^8...........................(1)

y = x^{1/8}.......................(2)

Now putting the value of y from equation 1 in equation 2, we get

x^8 = x^{1/8}

Now simplifying,

x^{64} = x

x^{64}-x = 0

x(x^{63} - 1) = 0

After equating equal to zero,

x = 0, x = 1

My = [tex]\int_{a\rightarrow b}x[f(x)-g(x)]dx[/tex]

My = [tex]\int_{0}^{1}x[x^{1/8} - x^{8}]dx[/tex]

My = [tex]\int_{0}^{1}[x^{9/8} - x^{9}]dx[/tex]

My = [tex][(8/17)x^{17/8} - (1/10)x^{10}]_{0}^{1}[/tex]

My = (8/17)-(1/10)

My = 63/170

Mx = 1/2[tex]\int_{a\rightarrow b}[(f(x))^2-(g(x))^2]dx[/tex]

Mx = 1/2[tex]\int^{1}_{0}[x^{1/4} - x^{16}]dx[/tex]

Mx = 1/2 [tex][(4/5)x^{5/4} - (1/17)x^{17}]^{1}_{0}[/tex]

Mx = (1/2)[(4/5)- (1/17)]

Mx = 63/170

M = [tex]\int_{a\rightarrow b}[f(x)-g(x)]dx[/tex]

M = [tex]\int^{1}_{0}[x^{1/8} - x^{8}] dx[/tex]

M = [tex][(8/9)x^{9/8} - (1/9)x^{9}]^{1}_{0}[/tex]

M = [(8/9) - (1/9)]

M =7/9

Center of mass(x',y') = (My/M, Mx/M)

Center of mass(x',y') = ((63/170)/(7/9), (63/170)/(7/9))

Center of mass(x',y') = (81/170, 81/170)

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The first quartile of miles driven is 218 miles.

Quartiles are three values ​​that divide the sorted data into four parts, each of which has the same observation value.

The four quarters that divide the dataset into quartiles are:

Let's arrange the data in an order:

211,212,218,223,231,233,245,261,278,299

Since the data has 10 observation, for which the median will be simply the average of two middle terms i.e.5th and 6th term dividing the data in two halves.

Median: 232

First half: 211,212,218,223,231

Second half: 233,245,261,278,299

As, quartiles are the medians of each half,

First quartile: 218

Third quartile: 261

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Answer:

[tex]6x + 6x + 6 + x = 13x + 6[/tex]