REVIEW & REFRESH
42. Tell whether x and y are proportional.
43. What number is 60% of 35?
44. 27 is what percent of 75?

Just do 42 and 44

Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in  6.34 days.

The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:

2 x 4 days = 8 days.

In general, we can use the growth formula:

P(t) = Po . 2^(t/Td)

Where:

P(t) = population at time t

Po = initial population

Td = doubling time

Parameters given:

Td = 4 days

P(t) = 3Po

Plug those parameters into the formula:

3 Po = Po . 2^(t/4)

3 = 2^(t/4)

log 3 = (t/4) log 2

t = 4 . log 3 / log 2 = 6.34 days.

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Answer:

x = 11.2 cms.

Step-by-step explanation:

I infer that the units are in centimeters.

8-3 = 5

One side = 5 cm

Other side = 10 cm

By the Pythagorean Theorem:

x² = 5² + 10²

x² = 25 + 100

x² = 125

√x² = √125

x = 11.18 cms

To the nearest tenth:

x = 11.2 cms

Answer: [tex]-10 < x < 0, x > 12[/tex]

Step-by-step explanation:

[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].

We will solve as follows:

Answer:

4 * ( 2 + 3 * 2) = 32

Step-by-step explanation:

The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.

The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

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Answer:

-44.09

Step-by-step explanation:

Trust bro i am passing collage math at 15

The average before training with new trainer is 20 mph.

Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer

Keep the values in formula to find the average speed with old trainer.

21 = 5/100x + x

Multiplying the equation with 100

2100 = 5x + 100x

Performing addition

105x = 2100

Shifting 105 to Right Hand Side of the equation

x = 2100 ÷ 105

Performing division on Right Hand Side of the equation

x = 20

Thus, average speed with old trainer was 20 mph.

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9x + 6 - 4x - 2x + 1 - 15

9x - 4 x- 2x = (9-4-4)x = 3x

6 +1 -15 = -8

____________

Answer

3x -8

______________

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The statement p is: Saturn is a planet.

The statement q is: Hong Kong is a city.

Now the first part of our composite proposition is:

This means that we have to negate the statement q, this would be: Hong Kong is not a city.

Now we make the disjunction between the statement p and the negation of q, then we have:

The second part of our composite porposition is:

This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:

Finally we make the disjunction between the statements discussed so far, hence the statament

means:

Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.

Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.

The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.

The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.

Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.

Based on the package of boondins and the package of rews, the package of rews will have a weight in relation to the package of boondins that is 3.77 ounces

To find how much more that the package of rews weighs over the boondins, deduct the weight of the package of boondins from the weight of a package of rews.

Weight of package of rews = 9.97 ounces

Weight of package of boondins = 6.2 ounces

The difference in the weight of the packages is:

= 9.97 - 6.2

= 3.77 ounces

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The required difference in the package of the bodies and rews is 3.77 ounces.

As per the given in the question,
boudin is 6.2 ounces in weight and rews are 9.97 ounces in weight.

here,
As per observation, rews weighs more than bodies, and the difference between their weights is simply evaluated from the subtraction between the weight. So,
Weigh difference = weigh of rews  - weigh of boodins
Substitute the value in the above equation,
Weigh difference = 9.97 - 6.2 = 3.77.

Thus, the required difference in the package of the bodies and rews is 3.77 ounces.

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sSlope means the inclination of the line

Intercept is the point where the line touches the Y axis.

The line that is perpendicular to the equation of a line given is y = -2x + 3

The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.

For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).

To find an equation of a line;

The equation of the line can be modified into y - y₁ = m(x - x₁)

substituting the values into the equation above gives y = -2x + 3

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By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.

Combination is the arrangement of objects in which order is not taken into account.

The applicable formula is:

n combination r = n!/[(n - r)!r!]

where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).

Hence;

10 combination 4 = 10!/[(10 - 4)!4!] ways

10 combination 4 = 10!/(6! × 4!) ways

10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways

10 combination 4 = 10 × 3 × 7 ways

10 combination 4 = 210 ways

Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.

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An inscribed circle is the largest circle contained in the polygon (triangle):

• Bisects two angles of the triangle.

• The angle bisector will intersect at the intercenter.

Procedure

To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.

Answer:

y=x+1

Step-by-step explanation:

y-y1=m(x-x1)

y-2=1(x+3)

y-2=x+3

y=x+1

Answer:

The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0

Step-by-step explanation:

Hope this helps! :))

If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

Consider the first odd integer as x

Then the next consecutive odd integer = x+2

The 6 times the second integer=  6(x+2)

= 6x+12

Sum of an integer and 6 times the next consecutive odd integer is 61

Then the equation will be

x + 6x+12 = 61

Add the like terms in the equation

(1+6)x + 12 = 61

7x +12 = 61

Move 12 to the right hand side of the equation

7x = 61-12

7x = 49

x = 49/7

x = 7

The second number is

x+2 = 7+2

= 9

Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

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Given:

There are given that the number of people who said yes is 191 and who said no is 485.

Explanation:

According to the given question:

The total number of people is:

That means the total outcome is 676.

Now,

The probability that the person is chosen own dog is:

So,

Final answer:

Hence, the correct option is C.

Answer:

191/676.

Step-by-step explanation:

The total number of people asked is 191 + 485

= 676.

So. the required probability

= number of people owning a dog/ total number of people

= 191/676.

The money which is expected to spend on new word processors during this year is

The probability distribution is

x:          0            1             2            3

f(x)         [tex]\frac{1}{10}[/tex]           [tex]\frac{3}{10}[/tex]           [tex]\frac{2}{5}[/tex]              [tex]\frac{1}{5}[/tex]

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is [tex]1200x-50x^2[/tex]          

Then the equation of expenses will be

[tex]\text{Expenses}=E(1200x-50x^2)[/tex]

We can rewrite it as

[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]  

  [tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]   -----------------(1)

Now the mean of the probability distribution is ,

[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]      

The variance of the function is

[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]

        [tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]

        [tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]

        [tex]=\frac{37}{10}[/tex]

        [tex]=3.7[/tex]

On substituting the values in equation (1)

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]

              [tex]=1200(1.7)-50(3.7)^2[/tex]

              [tex]=2040-684[/tex]

              [tex]=1855[/tex]

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The measure of the angles are 56.25° and 33.75°.

The value in a complementary angle is equal to 90°.

Let the first angle = x

The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x

Therefore, they'll be added together as follows:

x + 0.6x = 90°

1.6x = 90°

Divide

x = 90/1.6

x = 56.25

The second angle will be:

= 0.6x

Since x = 56.25, this will be used in the illustration below.

= 0.6x

= 0.6 × 56.25

x = 33.75

Therefore, the second angle is 33.75.

This illustrates the concept of complimentary angles.

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Answer:B

Step-by-step explanation:

Answer:

(C) I and III only.

Step-by-step explanation:

Hello! It's me again! Let's help you with this question too!

Now, let's start understanding what information is given to us.

[tex]a < b < 0[/tex]

This means that, some integer a is lower than some integer b and b is lower than 0. So right out of the gate, both integer a and b are both negative numbers. Here, we can evaluate all 3 possibilities like so:

I. [tex]\frac{a}{b} > 0[/tex]

To start, let's see if this is true. The simplest way is to substitute values into integer a and b to where [tex]a < b < 0[/tex] holds true as well. For this example, we can say [tex]a=-2[/tex] and [tex]b=-1[/tex]. If we evaluate as such, it would be:

[tex]\frac{-2}{-1} > 0[/tex]

[tex]2 > 0[/tex]

From this example, 2 is higher than 0. Meaning this is true. Now, it'll be true for every value due to something called the fraction rule. Fraction rule is simply just stating that, if the numerator and denominator both have a negative sign, they cancel each other out and become a positive fraction. So, we can say I. is true.

II. [tex]-b > -a[/tex]

This is simple to prove, all it's saying is that negative integer b is always going to be higher than negative integer a. Using our same example from I. we can substitute as such and evaluate:

[tex]-(-1) > -(-2)[/tex]

[tex]1 > 2[/tex]

Here, we can see that 1 is not greater than 2 and no matter what numbers you substitute, that will always be the case because you're essentially putting the lowest number first and seeing if it's greater than the lower number. So II. is false.

III. [tex]0 < \frac{b}{a} < 1[/tex]

Now this one is a bit more difficult. However, there isn't much we need to do here. This is saying that 0 is lower than [tex]\frac{b}{a}[/tex] but [tex]\frac{b}{a}[/tex] is lower than 1.  Let's split this into 2 parts.

Part 1: [tex]0 < \frac{b}{a}[/tex]

This isn't the same as I. as the numerator and denominators have switched. Let's use the values we've set back in I. to see if this holds true:

[tex]0 < \frac{-1}{-2}[/tex]

[tex]0 < \frac{1}{2}[/tex]

From here, we find that it is true. And it also holds true that it is less than 1. We can use another set of values to see if this still holds. Let's try [tex]a=-7[/tex] and [tex]b=-3[/tex]:

[tex]0 < \frac{-3}{-7}[/tex]

[tex]0 < \frac{3}{7}[/tex]

As you can see here, using the fraction rule. So long as there is an integer a and b are different (they always will be because of [tex]a < b < 0[/tex]), regardless of what they will be, it will always give us a fraction answer. And a fraction answer will always be lower than 1. Therefore, III. is also true.

So, the answer to this question is C. I and III only

The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.

Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.

The sum of all the three sides of a triangle is equal to the perimeter of the triangle.

Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.

Therefore:

Side AB = side XY = 12 cm [corresponding congruent sides]

Side AC = side XZ = 14 cm [corresponding congruent sides]

Side BC = side YZ = 10 cm [corresponding congruent sides]

Find the perimeter of triangle ABC by adding all three triangles together.

Perimeter of triangle ABC = side AB + side AC + side BC

Perimeter of triangle ABC = 12 + 14 + 10

Perimeter of triangle ABC = 36 cm

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A

1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle

2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.

We can finally write

x+88 +50 +50 = 180

x +188 =180 subtract 188 from both sides

x= 180-188

x= -8

3) So x=-8 is the answer.

Step-by-step explanation:

A./11.7/,/22.6/,10.3/

11.7<22.6>10.3

B./-10.3/,/-10.7/,/7.3/

10.3<10.7>7.3

C./-2.5/,/1.42/,/1.25/

2.5>1.42>1.25

D./-9.3/,/-9/,/7.43/

9.3>9>7.43

therefore the answer is C and D

The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

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Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.

Combination formula:

Cn,x is the number of different combinations of x objects from a set of n elements, given by:

Cnₓ= n!÷ x! (n-x!)

In this problem:

2 sophomores from a set of 18.

2 juniors from a set of 12.

3 seniors from a set of 10.

They are independent, so we can just multiply them, thus:

T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760

The committee can be selected in 1,211,760 ways.

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Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620

Law of Cosines

Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:

We have a = 14, b = 9, θ = 71°. Substituting:

The length of CD is 13.96