To cheer up your friend who is safely social distancing at home, you decide to put together and send them a box of chocolates! Let j,k,l,m be natural numbers such that 1 < = k <= j and 1 <= 2l < =m. You have a total of j dark chocolates and m milk chocolates for you to choose from. All of the chocolates (even the same type) have different fillings and are therefore all distinguishable. However, you remember that l of the milk chocolates have nuts inside of them and that your friend isn't the biggest fan of nuts with milk chocolate. Thus, you decide to include one of these l milk chocolates with nuts (yes, you can include none).

Required:
How many different chocolate boxes can you form consisting of exactly k dark chocolates and l milk chocolates?

The reflection of the graph in the x-axis gives the function

g(x) = -x² - 3x - 2

The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.

The vertex of the function is at (-3/2 , -1/4)

The focus is at ( 3/2 , 0 )

The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0

Now when the parabola is reflected along the x-axis we get

the focus at ( -3/2 , 0 )

the vertex is at  (-3/2 , 1/4)

Axis of symmetry remains the same

The directrix becomes 2y-1 =0

The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.

Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2

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The number of ways of selecting a committee of 4 women and 3 men from  8 women and 5 men is 700 ways

First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(8, 4) = 8! / [4!(8 - 4)!]

C(8, 4) = 70 ways

Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(5, 3) = 5! / [3!(5 - 3)!]

C(5, 3) = 10 ways

Finally, we shall determine the Total ways of selecting the committee. Details below:

Total ways of selecting = [C(8, 4)] × C(5, 3)]

Total ways of selecting = 70 × 10

Total ways of selecting = 700 ways

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The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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The solution to the inequality is -3 ≤ x ≤ -1/3

Given the inequality:

4|3x+5| ≤ 16

Let us simplify it by dividing both sides by 4 to get:

|3x+5| ≤ 4

Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:

First: 3x+5 ≥ 0

In this case, the inequality simplifies to:

3x+5 ≤ 4

Subtracting 5 from both sides, we get:

3x ≤ -1

Dividing by 3 (which is positive) gives:

x ≤ -1/3

Second: 3x+5 < 0

In this case, the inequality simplifies to:

-3x-5 ≤ 4

Adding 5 to both sides, we get:

-3x ≤ 9

Dividing by -3 (which is negative and requires us to flip the inequality), gives:

x ≥ -3

Therefore, the solution to the inequality is:

-3 ≤ x ≤ -1/3

The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.

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Answer:

1) 152

Step-by-step explanation:

(Length)l = 10cm

(width) w = 4cm

(height) h = 8 cm

SA= lw+wh+lh

= 10×4+4×8+10×8

=40+32+80

=152

the only criteria, really, to be a function is to assign exactly 1 y-value to every valid x-value. not 2 or 0 y-values.

we see here, x = 2 has one assigned y-value : y = 3.

x = 4 has y = 9.

x = 6 has y = 10.

x = 9 has y = 5.

there is no indication that there are more valid x-values.

each x-value used has exactly 1 y-value.

so, the criteria is fulfilled. it is a function.

Answer:

its 2 the negative cancles out

Step-by-step explanation:

Answer:

The answer would be $83.93

because there's no added information stating a surplus in money growth or decrease in the word p

Step-by-step explanation:

Because there's no added information stating a surplus in money growth or decrease from the account.

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer:

Okay so z is 3.

We are going to put taht into our equation

2(L + 8(3)) + L

2(L + 24) + L

Now we do the 2

2L + 48 + L

Okay now L is 4.2

SO

2(4.2) + 48 + (4.2)

8.4 + 48 + 4.2 = 60.6

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{2(l + 8z) + l}\\\mathsf{= 2(4.2 + 2(8)(3)) + 4.2}\\\mathsf{= 2(4.2) + 2(8)(3) + 4.2}\\\mathsf{= 8.4 + 16(3) +4.2}\\\mathsf{= \mathsf{8.4 + 48 + 4.2}}\\\mathsf{= 56.4 + 4.2}\\\mathsf{= 60.6}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\mathsf{60.6}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

x = ± √((y + 2)/4)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y.

Steps to find the inverse of y = 4x^2 - 2:

Replace y with x and x with y:

x = 4y^2 - 2

Solve for y:

x + 2 = 4y^2

(x + 2)/4 = y^2

± √((x + 2)/4) = y

Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.

Therefore, the inverse of y = 4x^2 - 2 is:

x = ± √((y + 2)/4)

Answer:

y=±(\(\sqrt{x+2}/2\))

Step-by-step explanation:

an expression is:

y = 71 - p

Answer:

23 / 400 = 0.0575

Step-by-step explanation:

Given the distribution :

_____shops__ free park. food _: location total

male 88 24 40 21 173

female 110 38 56 23 227

total 198 62 96 44 400​

From the table of the distribution Given, we obtain :

n(Female n location) = 23

n(Total) = 400

Hence, the probability that a female who chose location gets the prize will be ;

n(Female n location) / n(Total) = 23 / 400 = 0.0575

Answer:

Step-by-step explanation:

Area = (3√3 s2)/

A≈259.81

Answer:

259.8

Step-by-step explanation:

259.81 rounded to the nearest tenth is 259.8

Answer:

1. x is the amount of hours it took to repair the computer

2. 44+45x=$179

3. Around 3 hours

Step-by-step explanation:

44+45x=$179

Subtract 44 on both sides:

44-44+45x=179-42

45x=137

Divide 45 on both sides:

45x/45=137/45

x=3.044444444

Around 3 hours.

Step-by-step explanation:

so, the area of an original patio is

16×16 = 256 ft²

now, when a side is increased to 125% of its original length, it means the original length is multiplied by 1.25

because the area calculation multiplies 2 sides, that increase factor is introduced twice into this multiplication.

so, it squares regarding the total area.

in other words

area new = 16×1.25 × 16×1.25 = 16² × 1.25² =

= area old × 1.25² = area old × 1.5625 =

= 400 ft²

the new patio area is therefore 400-256 = 144 ft² larger.

Answer:

  144 square feet

Step-by-step explanation:

The new dimension of the patio is the product of the original dimension and the scale factor. The builder's plans say the new dimension is 125% of the current dimension, so the new side length is ...

  125% × 16 ft = 1.25 × 16 ft = 20 ft

The new patio area is (20 ft)² = 400 ft².

The original patio area is (16 ft)² = 256 ft².

The new patio is 400 -256 = 144 square feet larger than the current patio.

__

Additional comment

Words like "increase", "larger", "more" and similar can suggest either addition of an amount, or multiplication by a factor. The problem statement must be parsed carefully in order to determine exactly what is meant. There can be some ambiguity when "larger" and "times larger" are used with percentages. (That is not the case here.)

The word "of" almost always means "times" in this context. So "125% of its current measure" means "125% times the current measure." Multiplication by the factor 1.25 is rightly described as an increase.

The solutions to the nearest tenth are x = -0.1 and x = 1.3

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

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

Answer:

60-12=48min

Step-by-step explanation:

Kimberly takes 12 min, 1/5 of 60 min.

Answer:

3/4, 6/8

Step-by-step explanation:

12/4 is 3. 16/4 is 4, repeat for the other one with the number 3

Answer: 5/3

Step-by-step explanation:

When dividing a fraction by another fraction, you multiply it by the reciprocal

5/2 x 4/6 =20/12 which when simplified is 5/3

Answer:

y=2.2

Step-by-step explanation:

5(2.2)=11

9+11=20

Using simple interest, it is found that:

12. The loan matured after 6 years.

13. The actual interest rate was of 12%.

Simple interest is used when there is a single compounding per time period.

The amount of interest after t years in is modeled by:

\(I(t) = Prt\)

In which:

Question 12:

The parameters are: P = 2000, r = 0.06, I = 720, hence:

\(I(t) = Prt\)

\(720 = 2000(0.06)t\)

\(t = \frac{720}{2000 \times 0.06}\)

\(t = 6\)

The loan matured after 6 years.

Question 13:

The parameters are: t = 5, P = 4000, r = 0.11.

Hence:

I = 4000 x 0.11 x 5 = 2200.

$200 more was charged in interest, hence I(5) = 2400, and:

\(I(t) = Prt\)

\(2400 = 4000(5)r\)

\(r = \frac{2400}{20000}\)

\(r = 0.12\)

The actual interest rate was of 12%.

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Answer:

  a)  D. y = 3 ±√x

  b)  parabola opening to the right

Step-by-step explanation:

(a) Solving for t in the equation for y:

  y = t+8

  t = y -8 . . . . subtract 8

Substituting into the equation for x, we have ...

  x = ((y -8) +5)^2 = (y -3)^2

Solving for y, we get

  ±√x = y -3 . . . . . take the square root

  y = 3 ±√x

__

(b) The equation describes a parabola that opens to the right.

Answer:

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

3    12

8    

96 = 3x

x=32. the perimeter is 32

The perimeter of the larger triangle is 32 inches.

What are Similar Triangles?

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Let the perimeter of the larger triangle would be x.

We know that the ratio of the corresponding sides is 3/8.

The perimeter of the smaller triangle is 12 inches

We can use the ratio of corresponding sides to find the length of the sides of the larger triangle.

So 3/8 = 12/x

3x = 96

x = 96/3

x = 32

Thus, the perimeter of the larger triangle would be 32 inches.

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Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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