What are 10 multiples of 3?.

The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.

Given that,

85% of California people (428 out of 506 polled) believe that education is one of the state's most problems. For the true percentage of California adults who believe that education is one of the state's top problems, we want to build a 90% confidence interval.

We have to find the population proportion's 90% confidence interval.

We know that,

Let

n = 506, p = 0.85

90% Confidence interval :

At α = 0.1, two critical value, z base c = normal variable(0.1/2) = 1.645

Lower Bound = p - z base c×√(p ×(1- p)/n) = 0.85 - 1.645×√(0.85×0.15/506) = 0.824

Upper Bound = p + z base c×√(p ×(1- p)/n) = 0.85 + 1.645×√(0.85×0.15/506) = 0.876

0.824 < p < 0.876

Therefore, The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.

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The amount of zinc oxide need to be added to 450 g of 1.5% ointment to make a 11% zinc oxide ointment is 48 gram.

A fraction represent the number of parts in total or whole. Fraction is sometimes denoted in percentage, e.g. 20% means a fraction of 20/100.

In the given problem, let w is the amount of zinc oxide need to be added.

Original weight of Zinc oxide = 1.5% x 450 g

After adding w gram of zinc oxide, weight of zinc oxide = 1.5% x 450 + w

Original weight of ointment = 450 g

After adding w gram of zinc oxide, weight of ointment = 450 + w

Hence, the new fraction of zinc oxide:

(1.5% x 450 + w) / (450 + w) = 11%

1.5% x 450 + w = 11% x 450 + 11% w

9.5% x 450 = 89% w

w = 48

Hence, the amount of zinc oxide need to be added is 48 gram.

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The probability of a random sample of parts produced by this machine being exactly defective = 0.15

Step-by-step explanation:

Let the percentage of defective part be 12%

and the sample be out of 7 , 2 are defective.

P(X=x) = (e-λ λ x)/ x!   [ poisson distribution]

Since, 12%  defective parts is produced by one of the machines of the time.

μ= (12%×7)= 0.84

the number of defective product =2

Therefore ,

P(X=2) = 0.15

Thus the required probability becomes 0.15

In Statistics, Poisson distribution is one of the important topics. It is used for calculating the possibilities for an event with the average rate of value. Poisson distribution is a discrete probability distribution.

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Proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

The polynomial is given by

f(x) = [tex]x^3[/tex] - 6x + 1

We have to show that at least one zero lies in the given interval for the given polynomial using the intermediate value theorem

When the value of x = 2

Substitute the value of x in the polynomial

f(2) = (2)^3 - 6(2) + 1

= 8 - 12 + 1

= -3

When the value of x = 3

Substitute the value of x in the polynomial

f(3) = (3)^3 - 6(3) + 1

= 27 - 18 + 1

= 10

Here the value of f(2) is negative and the value of f(3)  is positive therefore there is at least one real zero between x = 1and x = 2

Hence, proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

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The number terms in the given expression is 3, they are 5xy, -3x and -82.

The given expression is 5xy-3x-82.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

In the given expression 5xy-3x-82, there are three terms, which are 5xy, -3x and -82.

Therefore, the number terms in the given expression is 3, they are 5xy, -3x and -82.

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Answer:

-5

Step-by-step explanation:

its because each term is being mutliplied by -5

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Answer:

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

[tex]\huge \boxed{\sf C}\\\\\\\displaystyle \sf Substituting\ x=0 \\\\3(0)-3y=12\\\\-3y=12\\\\Dividing\ each\ side\ by\ -3 \\\\\frac{-3y}{-3} =\frac{12}{-3} \\\\y=-4 \\\\\\Substituting\ y=0 \\\\3x-3(0)=12\\\\3x=12\\\\Dividing\ each\ side\ by\ 3 \\\\\frac{3x}{3} =\frac{12}{3} \\\\x=4[/tex]

The type of graph for a rational function is hyperbola

The parent function of a rational function is f(x)=1x and the graph is a hyperbola . The domain and range is the set of all real numbers except 0 . An excluded value in a rational function, is any x -value that makes the function value y undefined.

A hyperbola is an open curve with two branches, the intersection of a plane with both the halves of a double cone. The plane need not be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.

Therefore, Hyperbola is the type of graph for a rational function.

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The new profit per unit will be $7.

What are the aggregate prices?

The total amount of money required to create a product, provide a service, or carry out a project is referred to as the aggregate cost. The aggregate cost is also known as "total cost" because it includes all costs associated with the entire project or production.

We have,

aggregate prices + $3,

old profit of $4,

new profit?

Aggregate cost = total amount of money

new profit = old profit + increased price

new profit = 4 + 3

= 7

new profit = $7.

Hence, the new profit per unit will be $7.

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When the space is 63 feet², the rectangle is 7 ft wide and 9 feet long.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. The "space encompassed inside the perimeter or the boundary" of the specified form is what is referred to as a shape's area. Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here,

Let w be the width and l be the length of the rectangle,

The area of rectangle= 63 feet²

area=w*l

l=w+2

w(w+2)=63

w²+2w=63

w²+2w-63=0

w²+9w-7w-63=0

w(w+9)-7(w+9)=0

(w-7)(w+9)=0

w=-9, 7

width=7 feet

length= 9 feet

The width of rectangle is 7 feet and length of rectangle is 9 feet when area is 63 feet².

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To explain further for each of the scenarios on how to solve the problem and show your work (set up the numbers in the equation) is given under.

How many two-apple combos can you create when you have three apples?

We may use the following combination equation to solve this problem: C(n, k) is equal to n! / (k! * (n-k)!. In this instance, the number of apples is n=3, and k=2  apples in each combination). With these values entered into the formula, we obtain:

C(3, 2) = 3! / (2! * (3-2)!) = 3 / 2 = 1.5

Given that a combination is a collection of things chosen without respect to their order, the solution to this puzzle is 1.5. However, because you cannot eat half an apple, the real number of combinations of two apples that may be formed is one.

How many possible combinations of two novels can you create if you have four?

C(n, k)=n!/(k!*(n-k))!

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The total number of pieces that Preston's brother has left is 24.

What is the subtraction operation?

In mathematics, the operation of eliminating items from a collection is represented by the subtraction operation. The negative symbol (-) is used to denote subtraction.

Given, Preston and his brother collected 53 pieces of candy.

Each of them ate 5 pieces of candy.

And, Preston had 19 pieces left.

The number of candies Preston's brother have left = 53 - (5*2 + 19) = 24

Hence, the total number of pieces that Preston's brother has left is 24.

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Answer:

A triangle where the angles in the inside are 100 degrees, 40 degrees, and 40 degrees.

Step-by-step explanation:

The angles inside a triangle always add up to 180 degrees

And an obtuse triangle is a triangle whose biggest angle is bigger than 90 degrees

100 is biggest angle out of the three angles we're using to make the triangle and 100 is bigger than 90.

Adding the three angles we're using also makes 180 (100 + 40 + 40)

Answer:

Angle3 and Angle6

(also, Angle4 and Angle5)

Step-by-step explanation:

Alternate interior angles are between the parallel lines and also on opposite sides of the transversal.

If an environmentalist group wishes to measure the amount of dissolved oxygen per liter of water in a local stream, then the detailed solution is down below.

A dataset's variability is quantified by its standard deviation. It is determined by taking the square root of the variance, which is the sum of the squared deviations between each value in the dataset and its mean. How far a dataset's individual values deviate from its mean is determined by its standard deviation. A low standard deviation suggests that the dataset's values are close to the mean, whereas a large standard deviation suggests that the dataset's values are widely dispersed. When comparing the spread of two or more datasets, standard deviation is frequently utilised. It is a widely used statistical measure of dispersion.

How to solve?

a. The point estimate for the average amount of dissolved oxygen is 4.62 mg.

b. The distribution to use to construct the confidence interval is student-t.

c. Provide the values A - E for this problem on the following graph.

A. The sample mean is 4.62 mg.

B. The sample standard deviation is 0.92 mg.

C. The degrees of freedom for the student-t distribution is 45 - 1 = 44.

D. The t-value for a 90% confidence interval with 44 degrees of freedom is 1.699.

E. The error bound or margin of error is 0.92 mg * 1.699 = 1.57 mg.

d. The Confidence Interval is (4.62 - 1.57, 4.62 + 1.57) = (3.05, 6.19) mg, which means the error bound (or margin of error) is 1.57 mg.

e. The interpretation of this interval is that the environmentalists are confident that the true amount of dissolved oxygen in the stream is between 3.05 mg and 6.19 mg.

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A 36-month-old boy has the expected height, as an adult is 66 inches.

What is a linear equation?

A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.

We have,

The equation: y = 3.5x - 60,

The height of the 36-month-old boy is 36 inches,

we just need to use the value of x = 36 in the equation, and then we get the value of y:

y = 3.5x - 60

y = 3.5 * (36) - 60

y = 66 inches

Hence, his expected height, as an adult is 66 inches.

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In a case wherby Becky has a paper route and It takes her 50 minutes to deliver newspapers to her 40 customers  the unit rate in newspapers per minute is 4/5 customers per minutes.

The concept of raqte will be used, Rate can be described as the degree of something measured per unit of something else.

From the question,

50 minutes  will be used to deliver newspapers to her 40 customers, then thye rate can be written as 40 customers/ 50 minutes

This can be simplified as :

4 customers/5 minutes

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Step-by-step explanation:

Sin, Cos, and Tangent are the three common trig functions.

Sine, when given an angle, is a right triangle ratio between the opp side of the angle /hypotenuse(the side opposite of the right triangle),

SOH

Cosine, when given an angle, is a right triangle ratio between the adj side of the angle/hypotenus(the side opposite of the right triangle)

CAH

Tangent, when given an angle, is a right triangle ratio between the opp side of the angle/ adj side of the angle

TOA.

So

given an angle, alpha,

[tex] \sin( \alpha ) = \frac{o}{h} [/tex]

[tex] \cos( \alpha ) = \frac{a}{h} [/tex]

[tex] \tan( \alpha ) = \frac{o}{a} [/tex]

Problem 1, we know that the angle of reference is 53.1, the side adjacent to that angle is 30 cm, and we are trying to find x. and y.

Solving for x, the side length x is opposite of the angle 53.1

We have an angle, the adjacent side of the angle and the opposite side is what we are trying to find.

We use TAN

[tex] \tan(53.1) = \frac{x}{30} [/tex]

We know

[tex] \tan(53.1) = 1.33[/tex]

so

[tex]1.33 = \frac{x}{30} [/tex]

[tex]40 = x[/tex]

Now, since we know the side length of x, we have two ways to solve for y, which is the hypotenuse.

Remember the hypotenuse is the angle opposite of the 90° angle(right angle)

We could use Sine or Cosine

[tex] \sin( 53.1) = \frac{40}{y} [/tex]

[tex]0.8 = \frac{40}{y} [/tex]

[tex]y = \frac{40}{0.8} [/tex]

[tex]y= 50[/tex]

or

[tex] \cos(53.1) = \frac{30}{y} [/tex]

[tex]0.6 = \frac{30}{y} [/tex]

[tex]y = 50[/tex]

So x=40, y=50

2. Do the same steps above

Solving for x,

[tex] \sin(30) = \frac{x}{90} [/tex]

[tex]45 = x[/tex]

Solving for y,

[tex] \cos(30) = \frac{y}{90} [/tex]

cos(30)

[tex] \cos(30) = \frac{ \sqrt{3} }{2} [/tex]

so

[tex] \frac{ \sqrt{3} }{2} = \frac{y}{90} [/tex]

[tex]y = 45 \sqrt{3} = 77.942[/tex]

The probability of randomly selecting a male is dependent upon the gender distribution of the population from which the selection is made.

For example, if the population is evenly split between males and females, then the probability of randomly selecting a male would be 50%. Alternatively, if the population had more females than males, then the probability of selecting a male would be lower than 50%.

In general, the probability of randomly selecting a male is determined by the ratio of males to females in the population. For example, if there were twice as many females as males, then the probability of randomly selecting a male would be 33.3%. Similarly, if there were four times as many females as males, then the probability of randomly selecting a male would be 25%.

These probabilities can also be applied to specific populations. For example, the United States Census Bureau estimates that there are 101.8 males for every 100 females in the US population. Therefore, the probability of randomly selecting a male from the US population is approximately 50.9%.

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The inverse function of f(x) is [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}(13)[/tex] = 5

What is an inverse function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] One should not confuse (-1) with exponent or reciprocal here.

if f(x) = 3x - 2

setting y = 3x - 2 and making x the subject of the formulae,

we have

3x - 2 = y

3x = y + 2

x = [tex]\frac{y + 2}{3}[/tex]

replacing y with x and x with  [tex]f^{-1}[/tex](x)

[tex]f^{-1}[/tex](x) =   [tex]\frac{x + 2}{3}[/tex]

the value of  [tex]f^{-1}[/tex](13) , we substitute x = 13,

[tex]f^{-1}[/tex](13) = 13 + 2 / 3

[tex]f^{-1}[/tex](13) = 15/3

[tex]f^{-1}[/tex](13) = 5

In conclusion, the inverse function is  [tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex] and  [tex]f^{-1}[/tex](13) = 5

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Every linear equation represents a relationship between the x and y values, a table of values represents just a few of the line's points.

In the given question we have to explain about a linear equation in a table.

We can generate a table of values for any line since every linear equation represents a relationship between the x and y values. These are the only x and y values for the specified line that are accurate. In other words, a table of values represents just a few of the line's points.

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Answer:

6

Step-by-step explanation:

8 cube root is 2

there are 3 different lengths

3x2=6

The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.

Given that,

As seen in the spreadsheet file P05 63.xlsx, two gamblers engage in a game of wheel-based roulette. Each gambler lays four bets, but each uses a different strategy, as will be seen later. Use the probabilities to determine the distribution of each gambler's net earnings after four bets. Then calculate their net wins' mean and standard deviation. You can get going with the file.

We have to find the mean and standard deviation.

We know that,

In the picture we can see the complete table.

Here, we calculated probability as,

For example take a first row

P(red=4, black=0, green=0) = (18/37)⁴ + 0 + 0 = 0.056

So the mean is 65.0646 and standard deviation is 39.082.

Therefore, The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.

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The value of k should be less than 6.

Equation is defined as a relation that equates two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. A quadratic equation is of the form -

ax² + bx + c = 0.

Given is the quadratic equation as -

kx² - 2kx + 6 = 0

For no real roots, We can write -

b² - 4ac < 0

(-2k)² - 24k < 0

4k² - 24k < 0

k(4k - 24) < 0

k < 0 and 4k - 24 < 0

k < 0 and k < 6

k < 6

Therefore, the value of k should be less than 6.

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There are 8 zeroes at the end of [tex]20!^{2}[/tex]

Here, we are given an expression- [tex]20!^{2}[/tex]

To find the number of zeroes in any expression, we need to find the number of multiples of 10 in the expression.

10 is made up of 2 prime numbers, that are- 2 and 5

Thus, the number of multiples of 5 and 2 will give us the number of zeroes.

In 20!, the multiples of 5 will be- 5, 10, 15 and 20

⇒ there are total 4 multiples of 5 in 20!

Now, looking at the multiples of 2, we can see that there will definitely be more than 4 multiples, some of them are- 2, 4, 6, 8, 10 and so on

But since there are only 4 multiples of 5, there will be only 4 multiples of 10 and hence only 4 zeroes in the expansion of 20!

If we square 20!, the number of zeroes will also double and become 8

Thus, there are 8 zeroes at the end of [tex]20!^{2}[/tex]

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The number of different combination may a new car would have is 10 ways.

What is a combination in mathematics?

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

Given that there are 10 different options.

We have to choose one car.

So total number of combinations = [tex]^{10}C_1[/tex]

                                                       = 10!/(9!)(1!)

                                                       = 10 ways

Hence, the number of different combination may a new car would have is 10 ways.

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In 10 ways the combination of a new car can be installed as followed by the rules of Permutation combination.

what is Permutation combination ?

Putting things or numbers in order is the definition of a permutation. Combinations are a method of choosing elements such as numbers or objects from a collection or set of elements without regard to the elements' order.

Solution:

Given that the car are 10 different options.

We have to choose one car.

So total number of combinations = 10C1

                                                      = 10!/(9!)

                                                      = 10 ways

Therefore, In 10 ways the combination of a new car can be installed.

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The margin error is the amount that is added to and subtracted from a point estimate in order to create a confidence range for the population parameter.

The margin error, or error rate, in statistics refers to how inaccurate survey results utilizing random samples are. A larger statistical margin of error indicates a decreased likelihood of relying on a survey's or poll's results, indicating a decreased level of trust in the results' capacity to fairly represent a community. It is an essential tool for market research since it demonstrates the level of trust that should be placed by the researchers in survey results.

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The two numbers among them are such that one divides the other.

The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.

The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.

As per the question,

Let us divide the set into two sets,

                A   =   { 1, 3 . . . . . n }    and   B   =   { 2, 4 . . . . . . 2n }

A and B contain the same number of elements i.e. two sets have equal sizes. Element of B is one of the elements of A multiplied by 2 or elements of B multiplied by 2. So, if we remove the powers of 2 i.e we divide each element by [tex]2^{k}[/tex]. Then there exist another 2 sets [tex]A ^{'}[/tex] and [tex]B^{'}[/tex] such that [tex]A ^{'}[/tex] U [tex]B^{'}[/tex] = [tex]A ^{'}[/tex] .

By using the pigeonhole principle, [tex]A ^{'}[/tex] consists of n elements and we add +1 to it additionally.

Therefore, When we are given n + 1 numbers from set { 1, 2 . . . .  2n }, there are two numbers among them such that one divides the other.

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Answer:

”fih” weighs 56 ounces

Step-by-step explanation:

8p=f

f+p=63

f- fih

p- parakeet

p+8p=63

9p=63

/9.  /9

p=7

Parakeet weighs 7 ounces now to find the weight of the fih

8(7)=f

56=f

Fih weighs 56 ounces

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