50 students were asked what they did last night.
16 said they read a book, 41 said they watched television. If 7 said they
did neither how many
a) did both?
b) watched television. only?
c) read books only?​

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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The values of c and d which makes the provided equation of variable x and y true is 1 and 3 respectively.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

The variable  x is greater-than 0. Thus,

\(x > 0\)

The variable y greater-than-or-equal-to zero. Thus,

\(y\geq0\)

The given expression is attached in the image below, which is,

\(\sqrt{\dfrac{50x^6y^3}{9x^6}}={\dfrac{5y^c\sqrt{2y}}{dx}}\)

Cancel out x⁶ term and solve it further with

\(\sqrt{\dfrac{(25\times2)x^6(y^2\times y)}{(3^2)(x^6\times x^2)}}={\dfrac{5y^c\sqrt{2y}}{dx}}\\\sqrt{\dfrac{(5^2\times2)(y^2\times y)}{(3^2)(x^2)}}={\dfrac{5y^c\sqrt{2y}}{dx}}\\{\dfrac{(5y)\sqrt{(2y)}}{(3x)}}={\dfrac{5y^c\sqrt{2y}}{dx}}\)

Compare both the equation, we get,

\(5y=5y^c\\1=c\)

\(3x=dx\\3=d\)

Thus, the values of c and d which makes the provided equation of variable x and y true is 1 and 3 respectively.

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y = 3x - 4 can be written in fraction as (y + 4)/3x = 1

A fraction is a way to represent a part of a whole. It has two parts: a numerator (the top number) and a denominator (the bottom number).

The numerator represents the number of parts of the whole that are being considered, and the denominator represents the total number of parts in the whole.

y = 3x - 4 can also be written as:

y = 3x - 4

y + 4 = 3x

(y + 4)/3x = 1

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(i) The highest exponent on the variable x is 2. Therefore, the degree of the polynomial is 2. (ii) There are no x-intercepts for this polynomial. (iii) Since there are no x-intercepts, there is no intercept to be determined for this polynomial.

For the polynomial function \(y = x^2 + 169\):

(i) Degree of the polynomial:

The highest exponent on the variable x is 2. Therefore, the degree of the polynomial is 2.

(ii) All intercepts:

To find the intercepts, we set y = 0 and solve for x.

When y = 0:

\(x^2 + 169 = 0\)

This equation has no real solutions because the term x^2 is always non-negative, and adding 169 to it will result in a positive value. Therefore, there are no x-intercepts for this polynomial.

(iii) The intercept:

Since there are no x-intercepts, there is no intercept to be determined for this polynomial.

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The board is 3 1/6 feet left. The correct option is C.

To find out how much of the board is left, we need to subtract the length of the section that was cut off from the original length of the board:

6 2/3 - 3 1/2

To subtract these two mixed numbers, we need to find a common denominator. The smallest common denominator of 3 and 2 is 6:

Next, we can simplify the fractions,

62/3 - 3 1/2

= 20/3 - 7/2

= (40 - 21)/6

= 19/6

= 3 1/6 feet.

Therefore, the answer is C. 3 1/6 feet.

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Answer:

Below.

Step-by-step explanation:

This is a square based pyramid.

There are:

5 Faces (one on the base and 4 side faces)

8 edges.   ( 4 on base and 4 on side)

5 vertices   (4 on the base and one on the top)

Answer:

\(Faces~:~5\\Edges~:~8\\Vertices~:~5\)

Concept:

Here, we need to distinguish between face, edge, and vertex (plural: vertices)

A face is a single flat surface

An edge is a line segment between faces

A vertex is a corner

Please refer to the attachment below for a visual understanding

Solve:

Count the number of faces

1 + 4 = \(\Large\boxed{5~faces}\)

Count the number of edges

4 + 4 = \(\Large\boxed{8~edges}\)

Count the number of vertices

4 + 1 = \(\Large\boxed{5~vertices}\)

Hope this helps!! :)

Please let me know if you have any questions

(a) The probability that exactly 10 of the first 15 graded exam papers are from the second section can be calculated using the binomial distribution with n = 15 and p = 0.6,

where p is the probability that an exam paper is from the second section (since there are 30 students in the second section and 20 students in the first section, the probability that an exam paper is from the second section is 30/50 = 0.6). The answer is approximately 0.1804. This can be done using the binomial distribution formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k) where P(X = k) is the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in each trial, and (n choose k) is the binomial coefficient, which can be calculated as: (n choose k) = n! / (k! * (n-k)!)

To find the probability that at least 10 of the first 15 graded exam papers are from the second section, we can sum up the probabilities of getting exactly 10, 11, 12, 13, 14, or 15 exam papers from the second section. This can be done using the binomial distribution formula again, or by using a cumulative distribution function (CDF) for the binomial distribution. Using the CDF, we get: P(X >= 10) = 1 - P(X < 10) Using the binomial distribution formula, we get:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

P(X < 10) is approximately equal to 0.0013.

Therefore, P(X >= 10) = 1 - P(X < 10) is approximately equal to 0.9987.

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The maximum volume of the rectangular box is 975,000 cubic cm, and the minimum volume is 405,000 cubic cm.

Let's solve the problem step by step. We are given that the surface area of the rectangular box is 9000 square cm and the sum of the lengths of all edges is 520 cm. We need to find the maximum and minimum volumes of the box.

To find the maximum volume, we need to consider the case where the box is a cube. In a cube, all sides have equal lengths. Let's assume the length of each side is 'a'.

The surface area of a cube is given by 6a^2, and in this case, it is equal to 9000 square cm. So we have:

\(6a^2 = 9000\)

Dividing both sides by 6, we get:

\(a^2 = 1500\)

Taking the square root of both sides, we find:

\(a = \sqrt{1500} \\= 38.73 cm\)

The sum of the lengths of all edges of a cube is given by 12a, so we have:

12a = 12 * 38.73

= 464.76 cm

The maximum volume of the cube-shaped box is:

\(a^3 = 38.73^3\)

= 975,000 cubic cm.

To find the minimum volume, we need to consider the case where the box is not a cube. In this case, let's assume the lengths of the sides are 'x', 'y', and 'z'. We know that the sum of the lengths of all edges is 520 cm, so we have:

4(x + y + z) = 520

Dividing both sides by 4, we get:

x + y + z = 130

We need to maximize the volume of the box, which occurs when the sides are as unequal as possible.

In this case, let's assume x = y and z = 2x. Substituting these values into the equation above, we have:

2x + 2x + 2(2x) = 130

Simplifying, we get:

6x = 130

x = 21.67 cm

Substituting the values of x and z back into the equation, we find:

y = 21.67 cm and z = 43.33 cm

The minimum volume of the rectangular box is:

x * y * z = 21.67 * 21.67 * 43.33

= 405,000 cubic cm.

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Given Pauls age is three times barts age in 14 years pauls age will be twice as barts age, therefore, Bart is currently 14 years old, and Paul is currently 42 years old.

Let's assume that Bart's current age is x. Then, Paul's current age is 3x. In 14 years, Bart's age will be x + 14, and Paul's age will be 3x + 14. We know that Paul's age in 14 years will be twice Bart's age in 14 years. We can set up an equation to solve for x:

3x + 14 = 2(x + 14)

Simplifying this equation, we get:

3x + 14 = 2x + 28

x = 14

Therefore, Bart's current age is x = 14, and Paul's current age is 3x = 42.

To check our answer, we can verify that in 14 years, Paul's age will be twice Bart's age:

Paul's age in 14 years = 42 + 14 = 56

Bart's age in 14 years = 14 + 14 = 28

56 = 2(28)

Thus, our solution is correct. Bart is currently 14 years old, and Paul is currently 42 years old.

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120=!3÷!6

!2-!5=!3

to 120 modes

Answer:

Therefore, the actual building is 346.5 feet taller than the model. The answer is 346.5 feet.

Step-by-step explanation:

To find out how much taller the actual building is than the model, you can use the following formula: (Actual height - Model height) = Difference in height.Plugging in the given values, you get: (350 feet - 0.01*350 feet) = Difference in heightSimplifying this equation gives: (350 feet - 3.5 feet) = Difference in height

Using the empirical rule, we can determine that approximately 15.87% of IQ scores are at least 77.

According to the empirical rule, for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To find the percentage of IQ scores that are at least 77, we need to calculate the z-score for 77 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (77 - 101) / 12 = -24 / 12 = -2

Since 77 is 2 standard deviations below the mean, we know that approximately 95% - 2% = 15.87% of the IQ scores will be at least 77. Therefore, approximately 15.87% of IQ scores are at least 77, based on the empirical rule.

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The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

BMI - It's unhealthy. it looks like he eats too much. He is 15 years old, but his weight does not reflect his age. He needs to take a diet

What is BMI?

The body mass index (BMI) is a measurement based on a person's mass (weight) and height. The BMI is calculated by dividing the body weight by the square of the height, and it is expressed in kilogrammes per square metre (kg/m2) since weight is measured in kilogrammes and height is measured in metres. A table or chart that displays BMI as a function of mass as well as height using contour lines as well as colours for different BMI categories, and may use other units of measurement, may be used to calculate BMI. Based on tissue mass (muscle, fat, and bone) and height, the BMI is a practical guideline used to broadly classify a person as underweight, normal weight, overweight, or obese.

Hence, Mike is in the marginal overweight range.

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Answer:

-2

Step-by-step explanation:

You do "rise" over "run" (in this case, the rise is actually down)

so -2 "rise"

1 "run"

Answer:

Assuming the square and the semicircle aren't merged somehow, and we need to calculate their full area, we should take into account:

Area of a square:

(Side length)² = 22² = 484 square inches

Area of a circle with a diameter of 22inch:

3'14 · (radius)² = 3'14 · 11² = 379'94 square inches

Since we have half a circle, the total areas to add will be:

1/2 · 379'94 + 484 = 673'97

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The solution is, the previous salary is $40910.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

The total salary is $45000

Divide 10% by 100 to express the value as a decimal: 10/100= 0.1

Let x represent the previous salary.

If the previous salary was increased by 10% this means that they calculated the 10% of X and added it to the salary for the increase, symbolically:

x+0.1x=45000

1.1x=45000

x= 45000/1.1

x= 40909.09≅ $40910

Hence, The solution is, the previous salary is $40910.

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Answer:

1.) 9.32

2.) 4.82

Step-by-step explanation:

neat trick i learned that really helps: SOH-CAH-TOA

Sine (opposite, hypotenuse), Cosine (Adjacent, Hypotenuse), Tangent (Opposite, Adjacent)

1.)

sin(21) = x/26    <----------- multiply by 26 to get x by itself

26*sin(21) = x  <----------- multiply 26 by sin(21)

9.32 = x      <------ rounded answer

2.)

cos(64) = x/11      <------------ multiply by 11 to get x by itself

11*cos(64) = x      <---------------- multiply 11 by cos(64)

4.82 = x      <-------- rounded answer

Answer:

sir, this is a english app, search a spanish app

señor, esta es una aplicacion en ingles, busque una en español

Step-by-step explanation:

Brainly.lat

Answer:

A : 4.5

B: 1 4/5

E: 26

L:91

W: 5

H: 72.2

T: 11

M: 999

Step-by-step explanation:

hope this helps!!

Answer:

Step-by-step explanation:

First you want to divide 81 by 90%. You do this because 81 is the number you have and 90 is the percent you have.

81/90% = 90

Doing this will get you 90. This works for all percentages too.

Also you can check your answer by reversing this.

90 × 90% = 81

The probability that the flight would be delayed when it is raining = 0.79

Given that

the probability that it will rain is 0. 15

the probability that the flight will be delayed is 0. 11.

the probability that it will not rain and the flight will leave on time is 0. 75.

from the above

we can say that

the probability that the flight would be delayed when it is raining = 0.15 + 0.75 - 0.11

= 0.9- 0.11

= 0.79

The probability that the flight would be delayed when it is raining = 0.79

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Answer:

Amount

Rs 6345.30

Compound interest

Rs 1,345.30

Step-by-step explanation:

Here in this question, we are interested in calculating the amount and the compound interest on the value given.

To calculate the amount, we use the formula below;

A = P(1 + r/n)^nt

Where; A is the amount which we want to calculate

P is the principal which is Rs 5,000

r is the interest rate per annum = 10% = 10/100 = 0.1

n is the number of times per year in which it is compounded ( since it is annually, then it is 1)

t is the number of years which is 2.5 years( kindly know that 6 months is same 1/2 year , so 6 months is same as 0.5, and thus 2 years 6 months becomes 2.5 years)

now let’s substitute all these values;

A = 5000(1 + 0.1/1)^(1*2.5)

A = 5000(1 + 0.1)^2.5

A = 5000(1.1)^2.5

A = 6,345.2935314294

This is approximately Rs 6,345.30

The second part of the question asks to calculate compound interest

Mathematically ;compound interest = Amount - principal

= 6345.3 - 5000 = Rs 1,345.30

The standard form of a quadratic function is given by f(x) = ax^2 + bx + c.

To turn the given function into standard form, we need to expand and simplify the expression. Using the distributive property, we get:

f(x) = -0.089(x^2 - 6.6x - 90.266)

Next, we can distribute the -0.089:

f(x) = -0.089x^2 + 0.5874x + 8.033174

So the given function in standard form is:

f(x) = -0.089x^2 + 0.5874x + 8.033174

In standard form, the quadratic function is written as a polynomial in descending order of powers of x, where the coefficient of the x^2 term is non-negative.

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Answer:

P = 37.4 m

Step-by-step explanation:

let the third side of the triangle be x

using Pythagoras' identity in the right triangle.

x² + 7² = 16²

x² + 49 = 256 ( subtract 49 from both sides )

x² = 207 ( take square root of both sides )

x = \(\sqrt{207}\) ≈ 14.4 m ( to 1 decimal place )

the perimeter (P) is then the sum of the 3 sides

P = 7 + 16 + 14.4 = 37.4 m

In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

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Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.