7.
Give an example to show that each statement below is not true.
a) "The product of two different primes is never even."
b) "The sum of two different primes is never prime."
ection One - Number

The constant of proportionality between the number of bolts and the number of hours is 2025.

Option B is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Using a ∝ b then a = kb

Where k is the proportionality constant.

Given that;

We substitute into our equation.

a = kb

16200 = k × 8

k = 16200 / 8

k = 2025

The constant of proportionality between the number of bolts and the number of hours is 2025.

Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

Answer: 4, 2, 8

Step-by-step explanation:

4 + 2 + 8 = 14

14 = 14

2(4) + 4(2) + 5(8) = 56

8 + 8 + 40 = 56

56 =56

| 4(4) - 2 | = 14

|16-2| = 14

14 = 14

Answer:2

Step-by-step explanation:

(2x+5)/3 = 3/2

Multiply both sides by 3:

2x + 5 = 9/2

Subtract 5 from both sides:

2x = 9/2 - 5 = 9/2 - 10/2 = 3/2

Divide both sides by :

x = 3/4

Answer:

-1/3

Step-by-step explanation:

A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.

Or, as an equation:

[tex] \frac{2x + 3}{x + 5} = \frac{3}{2} [/tex]

Let's cross multiply:

[tex]4(2x + 3) = 2(x + 5)[/tex]

Expand:

[tex]8x + 12 = 2x + 10[/tex]

Now solve:

[tex]6x + 12 = 10[/tex]

[tex]6x = -2[/tex]

[tex]x = \frac{-1}{3} [/tex]

So the answer is -1/3

Using scientific notation, the length of the hydrogen atom is given as follows:

[tex]1.9 \times 10^{-10}[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

The diameter of a proton is given by:

[tex]1.9 \times 10^{-15}[/tex].

The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:

[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]

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Answer:

801.5625

Step-by-step explanation:

25.65×100/1.6×2=801.5625

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

Simple interest is a method of calculating the interest charge.

Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.

Simple Interest = (Principal × Rate × Time) / 100

25.65 × 100/(1.6 × 2 )

= 801.5625

Therefore, the  principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

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The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n

When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:

[tex]\frac{r}{s}[/tex] x 100%

Therefore in the given question, the required expression is;

m% = [tex]\frac{m}{100}[/tex]

So that;

m% of n can be expressed as;

[tex]\frac{m}{100}[/tex] x n

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An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

Herein we have an application of unit conversions between weight units, from kilograms to pounds. Unit conversions follow this direct proportional formula:

y = k · x

Where:

x - Weight in kilograms

y - Weight in pounds

k - Conversion ratio

If we know that x = 75 kg and k = 2.208 lb/kg, then the weight of the adult in pounds is:

y = (2.208 lb/kg) · (75 kg)

y = 165.6 lb

An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

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The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.

A statement, principle, or policy that creates the link between two variables is known as a function.

A cylinder (round can) has a circular base and a circular top with vertical sides in between.

Let r be the radius of the top of the can and let h be the height.

The surface area of the cylinder (A) is given as

A=2πr² + 2πrh

Part A: Assume that the height of your cylinder is 6 inches.

Consider A as a function of r, so we can write that as

A(r) = 2πr² + 12πr

Then the domain of A(r) will be (0, ∞).

Part B: Continue to assume that the height of your cylinder is 6 inches.

Then the inverse function to A(r) will be

r = 2π[A(r)]² + 12πA(r)

Part C: If the surface area is 175 square inches.

Then the radius will be

                    175 = 2πr² + 12πr

r² + 6r – 27.866 = 0

                        r = 3.07, -9.07

Then the radius will be 3.07 inches.

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The probability that the students gets all the questions correctly is (1/6)^15 .

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability = (number of correct options/ total number of options)^number of questions

(1/6)^15

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The object compresses the spring up to 0.8577m.

Potential Energy is the energy possessed by an object at rest.

The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.

The total amount of potential energy at the top of the ramp is given by

Ep=mgh

Ep=3 * 9.81 *5

Ep=147.15 Joules

This is equal to kinetic energy.

From the formula for elastic potential energy

The distance up to which the spring is compressed is determined

The force constant = 400N/m

147.15 =(1/2)k(x²)

294.3=(400)(x²)

0.73575=x²

x=0.8577 m

So, the object compresses the spring up to 0.8577m.

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Answer:

x = 6

Step-by-step explanation:

We want to find x,

[tex]\frac{3}{5} = \frac{x}{10}[/tex]

to get x alone, we multiple both side by 10

[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]

[tex]\frac{30}{5} = x[/tex]

30 divided by 5 is 6

Check:

We can see that 5 x ____ = 10 where ____ is 2

5 x 2 = 10

so 3 x 2 = 6

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The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.

Mathematically, annuity can be calculated by using this formula:

[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]

P = 13000/53.6932898522

P = $242.12.

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Complete Question:

The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?

Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft

The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.

The length of the ladder is y.

Using Pythagoras theorem:

[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]

When the ladder is  pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:

[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]

The top of the ladder will slide 6 - 4.36 ft = 1.64 ft

In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.

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The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°

We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.

Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.

Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.

Thus;

Angle of rotation = 360/5

Angle of rotation = 72°

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The work done in pushing the box is 64000 lb-ft²/s²

Since person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long, the work done, W is

W = mgh where

So, W = mgh

W = mgLsinФ

So, substituting the values of the variables into the equation, we have

W = mgLsinФ

W = 40 lb × 32 ft/s² × 100 ftsin30°

W = 1280 lb-ft/s² × 100 ft × 0.5

W = 1280 lb-ft/s² × 50 ft

W = 64000 lb-ft²/s²

So, the work done in pushing the box is 64000 lb-ft²/s²

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The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by:

y - y₁ = m(x - x₁)

Where:

In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.

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Answer:

b

Step-by-step explanation:

Hello !

[tex]F(x) = 5 \times ( \frac{1}{3} ) {}^{x} [/tex]

[tex]F(4) = 5 \times ( \frac{1}{3}) {}^{4} = 5 \times \frac{1 {}^{4} }{3 {}^{4} } = 5 \times \frac{1}{81} = \frac{5}{81} [/tex]

Answer:

y > 2/3x + 3

Step-by-step explanation:

It is first option because > because shaded above the line and 2/3x is rise/run so 2/3.

+3 is because y-intercept is 3

The system of linear inequalities represented by the graph is the option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

The system of linear inequalities are given by the in the question, that

describes the inequalities.

The points on the given graph are;

(3, 4), and (-3, 2)

The slope is; (2 - 4)÷((-3) - 3) = 1/3

The equation is;

y - 4 = (1/3)·(x - 3)

y = (1/3)·x - 1 + 4 = (1/3)·x + 3

Therefore;

The graph is y ≥  (1/3)·x + 3

Point on the second graph are;

(0, -2) and (2, 4)

The slope is; (4 - (-2)) ÷ (2 - 0) = 3

The equation is; y - (-2) = 3·(x - 0)

y = 3·x - 2

The inequality is; y < 3·x -2

Which gives;

2 < 3·x - y

Therefore;

3·x - y > 2

The correct option is the first option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

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Answer:

7

Step-by-step explanation:

2 = 2

4 = 2²

6 = 2 * 3

8 = 2³

adding the exponents of 2, we get 1+2+1+3 = 7

Answer:

{(3,-2), (4,-2),(5,-2), (6,-2)}  this relation is not a function.

Answer: First step is to determine the total cost

Total cost at 2,800

=$0.80 ×2,800

=$2,240

Total cost at 5,600

=$0.75 × 5,600

=$4,200

Second step is to determine the Variable cost per unit

Variable cost per unit=$4,200-$2,240

Variable cost per unit=$1,960

Variable cost per unit=5,600-2,800

Variable cost per unit=2,800

Variable cost per unit=$1,960/2,800

Variable cost per unit=$0.70

Now let determine the average cost

Average cost=$0.70×4,800+[($0.80×2800)-(2,800 ×$0.70)]

Average cost=$3,360+($2,240-$1,960)

Average cost=$3,360+$280

Average cost=$3,640

Average cost =$3,640/4,800

Average cost=$0.76

In conclusion What will be the average cost to bake 4,800 is $0.76

Step-by-step explanation:

The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2

The formula for equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.

Let us find the slope using the first two points;

m = (2 - 0)/(0 - (-15))

m = 2/15

Thus, the equation is;

y = ²/₁₅x + 2

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Josiah and Chana travel at constant and different speeds.

Josiah's head start = 10 meters from the start

Josiah's speed = 2 m/s

Chana's speed = 3 m/s

Expressing the distance traveled as an equation, we have;

D = d + s × t

Where;

D = The distance covered

d = The distance from the starting line the runner starts

s = The speed of the runner

t = The time spent running

For Josiah, we have;

D = 10 + 2•t (line a)

For Chana, we have;

D = 0 + 3•t = 3•t (line b)

The above equations are straight line equations.

The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.

Therefore;

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Answer:

Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah

Step-by-step explanation:

I got it right on khan.

It is false that the midpoint is in quadrant IV

The endpoints are given as:

S (1,4) and T (5,2

The midpoint is

(x, y) = 0.5 *(x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 *(1 + 5, 4 + 2)

Evaluate the expression

(x, y) = (3, 3)

The point (3, 3) is located in the first quadrant

Hence, it is false that the midpoint is in quadrant IV

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Answer:

Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Step-by-step explanation:

we have

[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]

we know that

[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]

[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]

substitute in the expression

[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Answer:

I think so, but maybe if the schools are different they change.

The prime factorization of 18 is 2 x 3 x 3.

A prime number is a number that is only divisible by 1 and itself. An example is 11. The factors of a number are numbers that divide another number without leaving any remainder. For example, a factor of 10 is 2. The prime factor of a number is the factors of a number that are prime numbers.

The factors of 18 = 1, 2, 3, 6, 9, 18

Prime factors = 1, 2, 3

Prime factorisation = 2 x 2 x 3

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The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9

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Answer:

A turning point is the highest or lowest point on a quadratic graph.

Step-by-step explanation:

A quadratic graph looks something like the graph below.

The equation of a quadratic graph would normally look like

+/- ax^2 + bx + c

An example might be -16x^2 + 5x + 4

Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.

Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.

Given the radius of 50 miles and the line joining the cities at (0, 56) and (58, 0), the transmitter signal can be picked during 59.24 miles of the drive.

Radius of broadcast of the transmitter = 50 miles

Location of starting point = 56 miles north of the transmitter

Location of destination city = 58 miles east of the transmitter

Therefore we have;

Slope of the line joining the two cities

= 56 ÷ (-58) = -0.966

Which gives the equation of the line as follows;

y = -0.966•x + 56

The equation of the circle is;

[tex] {x}^{2} + {y}^{2} = {50}^{2} [/tex]

[tex] {x}^{2} + { ( - 0.966x + 56)}^{2} = {50}^{2} [/tex]

1.933156•x^2 - 108.192•x + 636 = 0

Which gives;

Therefore;

When x = 6.67, we have;

When x = 49.29, we have;

The length of the drive, during which the driver can pick the signal, l, is therefore;

l = √((49.56-8.4)^2 + (49.29-6.67)^2) = 59.24 miles

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