PLEASE HELP

Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities. (Round your answers to four decimal places.)

(a) P(x ≤ 60)

(b) P(x ≥ 50)

(c) P(50 ≤ x ≤ 60)

Answer:

Step-by-step explanation:

Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7

The graph shows that Becca walks five dogs at the end of the third month.

We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.

We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month .  We would now read off the graph to know the number of dogs that he walks after three months.

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Answer:

Diana has 40 books in her collection.

Step-by-step explanation:

We can set up the equation 4x + x = 200 to represent the total number of books in the collection, where x is the number of books in Diana's collection and 4x is the number of books in Teri's collection. Solving for x, we get 5x = 200, so x = 40. This means that Diana has 40 books in her collection.

Answer:

Teri has 160 books

Step-by-step explanation:

The value of [x] is equivalent to 9.72 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

The triangle similarity criteria are:

Given is a triangle as shown in the image.

The smaller triangle and the larger triangle are similar to each other. So, we can write -

3x - 4 = 10x - 72

- 4 + 72 = 10x - 3x

68 = 7x

x = 68/7

x = 9.72 units

Therefore, the value of [x] is equivalent to 9.72 units.

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Answer:

B

Step-by-step explanation:

2x + 2 + 5x + 3 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25°

Step-by-step explanation:

So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.

First, multiply both sides by 40

5/8*40=x

Express 5/8 * 40 as a single fraction.

5*40/8=x

Multiply 5 40 to get 200.

200/8=x

Divide 200 by 8 to get 25.

25=x

Swap sides so that all variable terms are on the left-hand side.

x=25

The triangle ABC is an isosceles triangle because AB = BC = √73

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

A(0, 0), B(3, 8), and C(6,0).

An isosceles triangle is any triangle that has two of its sides to be equal

So, we start by calculating the lengths of the sides using the distance equation represented as follows

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

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

AB = √[(0 - 3)² + (0 - 8)²]

AB = √73

AC = √[(0 - 6)² + (0 - 0)²]

AC = 6

BC = √[(3 - 6)² + (8 - 0)²]

BC = √73

Because AB = BC = √73, then the triangle is an isosceles triangle

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The binary representation of each of these hexadecimal numbers is given as follows:

a) 80E = 100000001110

b) 135AB = 00010011010110101011

c) ABBA = 1010101110111010

d) DEFACED = 1101111011111010110011101101

To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:

Then, for example:

80E hexadecimal = 100000001110.

As:

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From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.

Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

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Answer:

3

Step-by-step explanation:

on edge

Answer:

  x = 3

Step-by-step explanation:

You want the root of the polynomial equation x(x -2)(x +3) = 18.

A graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.

There are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.

Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...

  x = 18/((x -2)(x +3))

This can be graphed as two equations:

  y = x

  y = 18/((x -2)(x +3))

This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)

__

Additional comment

Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.

Answer:

D. x=4

Step-by-step explanation:

32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles

m<2=m<RQP

m<1=m<SQP

m<RQP+m<SQP=m<SQR

m<2+m<1=m<SQR

m<2+m<2=m<SQR

(2+7x)+(2+7x)=16x-4

2+7x+2+7x=16x-4

2+2+7x+7x=16x-4

4+14x=16x-4

4-4+14x=16x-4+4

4+4+14x=16x-4+4

14x+8=16x

14x-14x+8=16x-14x

8=2x

x=8/2

x=4 ==> D

Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.

The graph of the compound inequality can be seen in the image at the end.

Here we have a compound inequality which is:

4x + 7 ≤ -37

5x + 3 > -7

First we need to isolate x in both of these inequalities, on the first one we will get:

4x + 7 ≤ -37

4x ≤ -37 - 7

4x≤ -44

x ≤ -44/4

x ≤ -11

The other inequality gives:

5x + 3 > -7

5x > -7 - 3

5x > -10

x > -10/5

x > -2

So the compound inequality is:

x > -2

x ≤ -11

To graph this we need to have a open circle at x = -2, and we need to graph a line to the right. And a closed circle at x = -11 and a line that goes to the left.

The number line is below

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Confidence interval for the mean score of all students is (91.679, 98.321)

Given:

Sample mean = 95

Standard deviation = 6.6

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

We have to construct a 99% confidence interval for the mean score of all the students.

Sample Standard Error =

[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]

= 1.205

t-value for the 99% confidence interval = 2.756

(use the t-tables for this)

Margin of error = 2.756 x 1.205 = 3.321

If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.

So, for the 99% confidence interval:

(95 - 3.321, 95 + 3.321) = (91.679, 98.321)

This is the final confidence interval.

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Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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All solutions of the following system of linear inequalities are given-

B (6, 2), C (9, 9), D (8, 2)

For the stated question,

Therefore, the solutions of the following system of linear inequalities are-

B (6, 2), C (9, 9), D (8, 2).

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Answer:

Some points that are on this line are:

(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)

The minimum lateral surface area of the prism is approximately 1.194 square units.

The given base and height of the prism is y and x respectively.

Hence volume of the prism

V = 1/3 x²y

again 1/3 x²y  = 1/6

or, y = 1/2x²

The lateral surface area of the prism is given by :

F = √(4y²+x²)

By the equation 1 we get :

F = x √ (1/x⁴ + x²)

Now we will use differentiation:

[tex]\frac{df}{dx} = \frac{2x^6-1}{x^4(x^2+\frac{1}{x^2} )}[/tex]

Now for the critical points we have to take df/dx = 0

hence solving the equation for x we get :

[tex]x = (\frac{1}{2} )^{\frac{1}{6}}[/tex]

Hence the values of x is [tex](\frac{1}{2} )^{\frac{1}{6}}[/tex] and the value of y will be  [tex]\frac{1}{2^\frac{2}{3}}[/tex] units,

And the lateral surface are will be :

F (min ) = √(4y²+x²)

= √ (0.795 + 0.633)

= 1.194 square units

The approximate values of x and y are

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Using the concept of percentage, she earned a total of $1091 last week

A percentage is a number or ratio that can be expressed as a fraction of 100. 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. It is represented by the symbol “%”.

To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.

She received 3% commission on her sales and she made a sale of $29700.

Let's find 3% of 29700

3 / 100 = x / 29700

0.03 = x / 29700

x = 29700 * 0.03

x = 891

The amount she earns will be 891 + 200 = 1091

Janelle earned $1091 last week

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Step-by-step explanation:

x = second number

first number = x - 6

third number = 4x

x - 6 + x + 4x = 96

6x - 6 = 96

6x = 102

x = 102/6 = 17

first number = x - 6 = 17 - 6 = 11

second number = x = 17

third number = 4x = 4×17 = 68

The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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In order for mn to be even, m must be even or n must be an even number.

The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.

Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:

Let n and m be equal to 2a +1  and 2b + 1 respectively, then their product is:

                 (2a +1) (2b + 1) = 4ab + 2a + 2b + 1

                                       = 2(2ab +a + b) + 1

This shows that the expression 2(2ab +a + b) + 1  is of the form 2n +1,  thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.

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The number of minutes that will be used for commercials will be 20 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

If the radio program plays 40 minutes of music.

Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,

⇒ 60 - 40

⇒ 20 minutes

The number of minutes that will be utilized for plugs will be 20 minutes.

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The Total Income from this caster in the first year = $184,822 approximately

What is Total Income?

Total income is the sum of all earnings, save those specifically mentioned in Section 12 of this Act, that a person receives during a certain accounting period, before any deductions are taken into account.

Given that : f(t)=12,000e^0.04t (dollars per month)

We could calculate our twelve calculations and evaluate this function once a month, but it would take some time. Instead, we should keep in mind that a continuous function can be represented by an integral. This indicates that we can simplify our calculation by simply taking the integral of this function between 0 and 12.

∫₀¹² 12000e⁰·⁰⁴t dt

Since we will transform this integrand into something for which we have the antiderivative, we may utilise u-substitution to simplify the calculation of this integral.

u=0.04t

du=0.04

dt0.04(0)=0

0.04(12)=0.48

To get the substitute for d u, we must slightly modify our integrand. This can be accomplished by adding 0.04 inside and canceling it outside by its reciprocal. The Fundamental Theorem of Calculus will then be used to calculate this definite integral.

12000 (1/0.04) ∫₀¹² 0.04e⁰·⁰⁴t dt = 30000 ∫₀⁰·⁴⁸ e⁴du

30000[tex]e^{u}[/tex] | ₀ ⁰·⁴⁸

30000(1.61607 -1)

184822.32

Therefore, the total income over the first year is approximately $184,822.

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Answer:

show the whole question

Step-by-step explanation:

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.

We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08.  The unit price for each bottle will be: The bottle having the lower price will be:-

30-ounce bottle = $6.00

One ounce bottle = 30 / 6.00 = $5.00

and

24-ounce bottle = $4.08

One ounce bottle = $24/ 4.08 = $5.88

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

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After solving the equation, the value obtained for m ∠B will be equal to 132°.

An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.

Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.

As per the given information in the question,

The inside angle plus the external angle add up to 180°.

So,

m ∠B = (14x − 22)°

14x - 22° + 6x - 18° = 180°

14x + 6x - 22° - 18° = 180°

20x - 40° = 180°

20x = 180° + 40°

20x = 220°

x  = 220° / 20

x = 11°

Now, let's find m∠B.

m ∠B = (14x − 22)°

Put x = 11° in above equation,

m ∠B = (14(11) − 22)°

m ∠B = 154° - 22°

m ∠B = 132°.

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Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” 95% confidence interval for the poll is

(38.88%, 41.12%)

Generally, To construct a 95% confidence interval for the poll, we need to first calculate the margin of error. The margin of error for a poll is a measure of the precision of the estimate and is calculated based on the sample size, the level of confidence, and the standard deviation of the population.

In this case, the sample size is 500, the level of confidence is 95%, and the standard deviation of the population is unknown. We can approximate the standard deviation using the sample proportion of 40% as an estimate of the population proportion.

Using these values, the margin of error can be calculated as follows:

Margin of error = z * standard error

Where z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard error is calculated as:

Standard error = √(p * (1 - p) / n)

Where p is the sample proportion (40% in this case) and n is the sample size (500 in this case).

Substituting these values into the formula for the margin of error, we get:

Margin of error = 1.96 * √(0.4 * (1 - 0.4) / 500)

= 1.96 * sqrt(0.16 / 500)

= 1.96 * √(0.000032)

= 1.6 * 0.005656854

= 0.011168

So the margin of error for this poll is approximately 0.011168 or 1.12%.

To construct the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. The 95% confidence interval for the poll is, therefore:

40% ± 1.12%

= (38.88%, 41.12%)

This means that we can be 95% confident that the true population proportion of parents who would prefer to have their child taught by a male in grades K-2 lies within the interval between 38.88% and 41.12%.

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