Of 290 students in school,20%wear glasses. Is 75,95,58, or 119 a reasonable estimate for the number of students wearing glasses

{x| x is a natural number less than 7} ={1. 2. 3. 4. 5, 6}. The statement is true.

What is a natural number?

Natural numbers are all positive numbers that range from 1 to infinity and are consequently a part of the number system. Natural numbers are frequently referred to be counting numbers because they don't contain zero or negative numbers. They are a subset of real numbers that only contains positive integers and excludes all other types of numbers, such as negative, zero, fractional, and decimal.

It is in set builder form of set represenation.

A set consists of elements represented inside flower brackets { }.

Read as x such that x belongs to natural numbers less than 7.

Natural numbers starts from 1,2,3 .... to infinity.

Natural numbers less than 7 means

1,2,3,4,5,6

Represented in set as

{1,2,3,4,5,6}

Hence the statement is true.

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Answer:

Slope = -1

Step-by-step explanation:

I have assigned 7,3 as x2 and y2

and the other coordinates as x1 and y1

Then,

Use the slope formula

9 - 3 / 1 - 7

This would result in -1

Answer:

[9/5,∞)

Step-by-step explanation:

Rearrange variables to the left side of the equation: c ≥ 11/5-2/5

Calculate: c ≥ 9/5

Express solution set in interval notation: [9/5,∞)

Answer:

The letter "x" is often used in algebra to mean an unknown value. It is often called a "variable".

Example:

In x + 5 = 12, x is a variable, but we can work out its value if we try!

Answer:

Step-by-step explanation:

what is this

Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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Answer:

X >= 7

Step-by-step explanation:

7x + 8 >= 57

7x >= 57-8

7x >= 49

x >= 49/7

x >= 7

Answer:

x = ±10

Step-by-step explanation:

1) Subtract 10 from both sides.

\(-0.1 \times x^2=-10\)

2) Divide both sides by -0.1.

\(x^2=\frac{-10}{-0.1}\)

3) Simplify \(\frac{-10}{-0.1}\) to 100.

\(x^2=100\)

4) Take the square root of both sides.

\(x=\pm \sqrt{100}\)

5) Since 10 * 10 is 100, the square root of 100 is 10.

\(x=\pm10\)

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

\(0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70\)

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

\(s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }\)

Where \(X_{mean}\) is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate \((X - X_{mean})^2\)for each data point and sum up the values:

\((0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36\)

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

\(\sqrt{1.31} = 1.15\)

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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The value of x is 24 and different angles of hexagon will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.

We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).

Given the figure is hexagon,

the sum of angles of a hexagon is 720,

Upon adding the given angles,

mA = (7x-8)°

mB (4x+46)°

mC = (5x)

mD = (6x+12)°

mE = (x+7)°

mF = (5x-9)°

⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

⇒ 28x + 48 = 720

⇒ 28x = 672

⇒ x = 24

Therefore, the angles will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

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Answer:

20x + -10xy

Step-by-step explanation:

10x · 2 ⇒ 20x

10x · -y ⇒ -10xy

Therefore, it is 20x - 10xy.

Answer:

Check pdf

Step-by-step explanation:

(a) The probability that a point chosen randomly inside the rectangle is in the square is 0.6.

(b) The probability that a point chosen randomly inside the rectangle is outside the square is 0.4.

The probability that a point chosen randomly inside the rectangle is in each given shape is calculated as follows;

The area of the triangle is calculated as follows;

area = ¹/₂ x base x height

area = ¹/₂ x 4 x 5

area = 10 sq.units

The area of the rectangle is calculated as follows;

area = 4 x 4

area = 16 sq.units

The probability that a point chosen randomly inside the rectangle is in the square is calculated as;

P = outcome / total possible outcome

P = ( 10 ) / 16

P = 0.625 ≈ 0.6

The probability that a point chosen randomly inside the rectangle is outside the square;

P = 1 - p(inside)

P = 1 - 0.6

P = 0.4

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Answer: 9.46 grams

Step-by-step explanation:

Given: Number of muffins made in one batch = 1 dozen =12 ]

[ as 1 dozen = 12]

Also, in one batch the quantity of sugar = \(\dfrac14\) pound

As there are 454 grams of sugar in a pound.

So,  in one batch the quantity of sugar = \(\dfrac14\times454=113.5\ grams\)

i.e. in 12 muffins , there is 113.5 grams of sugar.

Then, in one muffin the quantity of sugar = (113.5 grams) ÷ 12

≈9.46 grams

Hence, there are 9.46 grams of sugar in 1 muffin.

Answer:

54

Step-by-step explanation:

1/6 × y = 9

y ÷ 6 = 9

y ÷ 6 × 6 = 9 × 6

y = 54

Answer:

1-b 2-c 3-a 4-d 5-d 6-a

Step-by-step explanation:

Answer:

\(L=\frac{1}{2}P-W\)

Step-by-step explanation:

Let's solve for L.

\(P=2L+2W\)

Step 1: Flip the equation.

\(2L+2W=P\)

Step 2: Add \(-2W\) to both sides.

\(2L+2W+-2W=P+-2W\)

\(2L=P-2W\)

Step 3: Divide both sides by \(2\).

\(\frac{2L}{2}=\frac{P-2W}{2}\)

\(L=\frac{1}{2}P-W\)

Answer:

\(L=\frac{1}{2}P-W\)

Answer:This would be option letter C

Step-by-step explanation:The diagram is a gram of external geofram so the position Is fFX(4) ^N

Answer:

D

Step-by-step explanation:

f(x)= -x^2+4

Draw graph of -x^2 and shift it 4 units above

Answer: the answer is B

Step-by-step explanation:

Answer:

56 and 62

Step-by-step explanation:

Answer:

Step-by-step explanation:

first, we need to convert the 15 feet of string that Daniel needs into inches. Since there are 12 inches in a foot, 15 feet is equivalent to 15 * 12 = 180 inches.

Since Daniel already has 28 inches of string, he still needs 180 - 28 = 152 inches of string to complete his project.

Received message. First, we need to convert the 15 feet of string that Daniel needs into inches. Since there are 12 inches in a foot, 15 feet is equivalent to 15 * 12 = **180 inches**. Since Daniel already has 28 inches of string, he still needs 180 - 28 = **152 inches** of string to complete his project.

Answer:

79.25 mm³

Step-by-step explanation:

The figure can be decomposed into 2 different half cylinders and a rectangular prism

Volume of the figure = volume of the smaller half cylinder + larger half cylinder + rectangular prism

✔️Volume of smaller half cylinder = ½(πr²h)

r = ½(2) = 1 mm

h = 5 mm

π = 3.14

Volume of smaller half cylinder = ½(3.14*1²*5)

= 7.85 mm³

✔️Volume of larger half cylinder = ½(πr²h)

r = ½(4) = 2 mm

h = 5 mm

π = 3.14

Volume of smaller half cylinder = ½(3.14*2²*5)

= 31.4 mm³

✔️Volume of rectangular prism = L*W*H

L = 5 mm

W = 4 mm

H = 2 mm

Volume = 5*4*2 = 40 mm³

✅Volume of the figure = 7.85 + 31.4 + 40

= 79.25 mm³

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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Answer:

(12,10.5)

Step-by-step explanation:

the x coordinate is 12

the y coordinate is 10.5

hope this helps you!

The value of ex = e2x + 5 is -5.

The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the term typically refers to the positive-valued function of a real variable. it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Given ,

\(e^x=e^{2 x}+5\)

By simplifying the exponential rule we get

x= -5

Therefore the value of \(e^x=e^{2 x}+5\) is -5

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Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.

The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.

=> P(2) + P(3) + P(4)

=> 1/12 + 2/3 + 1/4

=>  (1 + 8 + 3) / 12

=> 12 / 12 = 1

In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.

In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.

Therefore, a complete probability model cannot be represented by this list.

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The value of x from the diagram below to 3 significant figure is 2.84m

What is a triangle?

A triangle is a polygon with 3 sides and three angles.

Triangles are off different types: equilateral, scalene, isosceles and right-angle.

Common formulae for areas are : 1/2 base x height, 1/2 x side x side x sin theta

Area of this triangle = 1/2 x side1 x side 2 x  sin∅

side1 = (x +2) m, side2 = (2x - 3)m, ∅ = 45°, area of triangle = 4\(\sqrt{2}\)

Substituting into the area of triangle equation, we have

4√2 = 1/2 x (x +2) x (2x - 3) x sin 45

But sin 45 = √2 / 2

4√2 = 1/2 x (x +2) x (2x-3) x √2/2

\(\sqrt{2}\) is a both sides so they cancel out

(x+2)(2x - 3) = 4 x 4

Expanding the terms in bracket we have,

2\(x^{2}\) + 4x -3x -6 = 16

collect like terms and solve the quadratic equation using the general form

2\(x^{2}\) +x -6 -16 = 0

2\(x^{2}\) + x -22 = 0

Using general quadratic formula

\(x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}\)

a= 2, b = 1 c = -22

x = \(\frac{-1 +/-\sqrt{(1)^{2} - 4(2)(-22) } }{2(4)}\)

the simplified form of the numerator is 12.38

x  = 12.34/8 = 1.54m

In conclusion, the value of x is 1.54m

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Answer:

Group the like terms together:

4x²y + 6x²y + 12z² - 2z

Simplify:

10x²y + 12z² - 2z

The simplified expression is 10x²y + 12z² - 2z.

Step-by-step explanation:

Answer:

The simplified expression is 10x²y + 12z² - 2z

Step-by-step explanation:

To simplify the expression, we combine like terms, which are terms that have the same variables raised to the same powers. In this case, we have two terms with the variable 4x²y and two terms with the variable -2z. We can combine these like terms by adding their coefficients:

4x²y + 6x²y = 10x²y

-2z + (-2z) = -4z

So the expression simplifies to:

10x²y + 12z² - 4z

We can further simplify this expression by combining the terms with the variable z:

12z² - 4z = 4z(3z - 1)

Therefore, the final simplified expression is:

10x²y + 4z(3z - 1)

We can also write this expression as:

10x²y + 12z² - 2z

which is the answer provided.

Answer:

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

Parallel lines have identical slopes

As our original line has a slope of 3/4, both lines v and w have slope of -4/3

This means that

C: y = -4/3x + 2

is the only possible option.

Let's check that the given point fits on this line.

10 = -4/3(-6) + 2

10 = 10

So our answer is correct.

Answer:

y = 0.14t + 481

Population in 17 years: 483.38

Step-by-step explanation:

y = (m) (x) + b

y = (slope) (x) + starting value

Answer:

0.8 lbs

Step-by-step explanation:

Ounces are typically used to measure liquid, so I would discourage choosing the top two. And, hopefully you know by now that an orange does not weigh 8 pounds.

9514 1404 393

Answer:

  (a)  0.8 ounces (most precision)

  (b)  8 ounces (best precision for likely weight of an orange)

Step-by-step explanation:

The most precision is obtained by using the smallest unit of measure. On this list, the smallest unit of measure is a tenth of an ounce. That is, the measure 0.8 ounces has the most precision.

__

It is unlikely that the weight of one orange will be 0.8 ounces. The smallest unit used in a measurement likely to correspond to the weight of an orange is 1 ounce, used in the measurement 8 ounces. That measurement has better precision than 0.8 pounds, because 0.1 pounds corresponds to 1.6 ounces.