Mara spent 3/5 of her vacation in British Columbia. While in that province, she spent 1/2 of her time in Vancouver. What fraction of her vacation did Michaela spend in Vancouver? If her vacation lasted 20 days, how many days did she spend in Vancouver?

Problem 1

S = sample space = set of all possible outcomes

S = set of positive factors of 72

S = {1,2,3,4,6,8,9,12,18,24,36,72}

n(S) = number of items in sample space

n(S) = 12

E = event space = set of outcomes we want to happen

E = set of factors of 72 such that they are less than 10

E = {1,2,3,4,6,8,9}

n(S) = number of items in event space

n(S) = 7

P(E) = probability get a value in set E (that is also in set S as well)

P(E) = probability we get a positive factor of 72 that is less than 10

P(E) = n(E)/n(S)

P(E) = 7/12

============================================

Problem 2

[tex]\begin{array}{ccl}S & = & \text{Sample Space}\\\\S & = & \{\\ & & ~~DAB, DAC, DAE, DAF, DAG, DAH\\ & & ~~DBA, DCA, DEA, DFA, DGA, DHA\\ & & \}\end{array}[/tex]

n(S) = 12

E = event space

E = {DCA}

n(E) = 1

P(E) = probability we get an item in set S that is in set E also

P(E) = probability we get DCA from set S listed above

P(E) = n(E)/n(S)

P(E) = 1/12

[tex]y = 48.28(1.06)^t[/tex] is the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Solution:

Given that,

In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28

During the next 20 years, the price increased an average of 6% each year

The increasing function is given by:

[tex]y = a(1+r)^t[/tex]

Where,

y is the value after t years

t is the number of years

a is the initial value

r is rate of increase in decimal

From given,

a = 48.28

[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]

Substituting the values we get,

[tex]y = 48.28(1+0.06)^t\\\\y = 48.28(1.06)^t[/tex]

Thus the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Answer:

4/7

Step-by-step explanation:

1/6-8/6=-7/6

-[1/6-8/6]=7/6

---------------------

(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7

Answer:

1/3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

1. Expand.

−3x − 12 + 15 = 6 − 4x

2. Simplify  −3x − 12 + 15 to −3x + 3.

−3x + 3 = 6 − 4x

3. Subtract 3 from both sides.

−3x = 6 − 4x − 3

4. Simplify 6 − 4x − 3 to −4x + 3.

−3x=−4x+3

5. Add 4x to both sides.

−3x + 4x = 3

6. Simplify -3x + 4x to x.

x = 3

Answer:

  No

Step-by-step explanation:

The distance from Nick's current spot to the town ahead and back to this spot is 2·8 = 16 miles. Additionally, it is 19 miles back to the gas station, so a total of 35 miles to the gas station via the town ahead. Nick does not have enough gas for that.

If there is no gas in the town ahead, there will need to be a station within 18 miles further on, or Nick will be walking 9 miles to the station he just passed.

Answer:

2108

Step-by-step explanation:

Divide 67,456 by 32, using long division.

1) How many times 32 go into 67? (2 times, with a remainder of 3)

2) Bring down the 4.

3) How many times does 32 go into 34? (1 time, with a remainder of 2)

4) Bring down the 5

5) How many times does 32 go into 25? (0 times, so write 0)

6) Bring down the 6.

7) How many times does 32 go into 256? ( 8 times, no remainder)

8) Your answer is 2108

Answer:

Step-by-step explanation:

10 + 6(-9 - 4x) = 10(x - 12) + 8

10 - 54 - 24x = 10x - 120 + 8

-44 - 24x = 10x - 112

-24x - 10x = -112 + 44

-34x = -68

x = -68/-34

x = 2 <====

Answer:

She spend $32,640 on cruises.

Step-by-step explanation:

Given:

Shane spends 48% of her income on cruises.

If she makes $68,000 per year.

Now, to find the money she spend on cruises.

Shane makes income per year = $68,000.

Percent Shane spends of her income on cruises = 48%.

Now, to get the income she spends on cruises:

48% of $68,000.

[tex]=\frac{48}{100} \times 68000[/tex]

[tex]=0.48\times 68000[/tex]

[tex]=\$32,640.[/tex]

Therefore, she spend $32,640 on cruises.

Answer: For the figure on the left {c}, the Area is 30m (squared) and the Perimeter is 46m.

For the figure on the right {d}, the Area is 32cm (squared) and the Perimeter is 34cm

Step-by-step explanation: (Please refers to the attached diagram)

We shall start with the diagram on the left. The first thing is to break it down into regular shapes, such as rectangles, squares, etc. The dotted line that runs from point C to point G divides the figure into two rectangles which are ABCG {or X} and GDEF {or Y}. Line AG measures 10m since it’s the same length as line BC. Similarly line GF measures 2m since it’s the same length as line DE. So rectangle “X” has dimensions;

L = 10, W = 1

Area of a rectangle = L x W

Area = 10 x 1

Area = 10m

Similarly rectangle Y has dimensions L= 10m and W = 2m

Hence area of rectangle “Y” is computed as

Area = L x W

Area = 10 x 2

Area = 20m

Area of the entire figure is derived as

Area of rectangle X + Area of rectangle Y, which is

10m + 20m = 30m {squared)

The perimeter of rectangle X is given as Perimeter = 2(L + W)

Perimeter = 2(10 + 1)

Perimeter = 2(11)

Perimeter = 22m

Also, perimeter of rectangle Y is derived as

Perimeter = 2(L + W)

Perimeter = 2(10+ 2)

Perimeter = 2(12)

Perimeter = 24m

Therefore the perimeter of the entire figure is derived as

Perimeter of rectangle X + perimeter of rectangle Y, which is

22m + 24m and that equals 46m

For the second figure on the right side of the page, we shall also break it down with the dotted lines that runs from point E to point G. That leaves us with rectangle ABGF {or P} and rectangle EGCD {or Q}.

Rectangle “P” has dimensions L= 4 and W = 2

Area of rectangle P = 4 x 2

Area of rectangle P = 8cm

Similarly area of rectangle Q is given as Area of Q = 8 x 3

Area of Q = 24cm

Area of the entire figure is derived as

Area of P + Area of Q,

8cm + 24cm

= 32cm {squared}

To compute the perimeter of rectangle P

Perimeter of a rectangle = 2(L + W)

Perimeter of rectangle P = 2(4 + 2)

Perimeter of rectangle P = 2(6)

Perimeter of rectangle P= 12cm

Similarly Perimeter of rectangle Q = 2(L + W)

Perimeter of rectangle Q = 2(8 + 3)

Perimeter of rectangle Q = 2(11)

Perimeter of rectangle Q = 22cm

Hence, perimeter of the entire figure is derived as perimeter of rectangle P + perimeter of rectangle Q which equals

12cm + 22cm and that equals

34cm.

a) [tex]\frac{dy}{dx} = \frac{1-3lnx}{x^4}[/tex]

b) [tex]\frac{dy}{dx} = \frac{-2}{3\sqrt[3]{1-x} }[/tex]

Explanation:

a) [tex]y=\frac{lnx}{x^3}[/tex]

[tex]y = \frac{lnx}{\sqrt[3]{x} }[/tex]

[tex]y = lnx. x^-3[/tex]

Differentiating the above equation in terms of x

[tex]\frac{dy}{dx} = \frac{1}{x} \times x^-3 - 3lnx\times x^-^4\\\frac{dy}{dx} = \frac{1}{x^4} - \frac{3lnx}{x^4} \\\frac{dy}{dx} = \frac{1-3lnx}{x^4} \\[/tex]

b) [tex]y = \sqrt[3]{1-x^{2} }[/tex]

Differentiating the above equation in terms of x

[tex]y = \sqrt[3]{(1-x)^{2} } \\\frac{dy}{dx} = (1-x)^\frac{2}{3} \\\frac{dy}{dx} = \frac{2}{3}\times (1-x)^\frac{-1}{3} \times -1\\\frac{dy}{dx} = \frac{-2}{3\sqrt[3]{1-x} }[/tex]

Thus,

a) [tex]\frac{dy}{dx} = \frac{1-3lnx}{x^4}[/tex]

b) [tex]\frac{dy}{dx} = \frac{-2}{3\sqrt[3]{1-x} }[/tex]

Answer:

15(3+2x)

Step-by-step explanation:

Factor out the 15.

Step-by-step explanation:

Let the radius of a circle be r

The circumference of a circle is(C) [tex]=2\pi r[/tex]

                                                          [tex]=\pi d[/tex]      [∵2r =d= diameter]

Therefore [tex]C = \pi d[/tex]

Since the value of [tex]\pi[/tex] is always constant. Here the diameter and the circumference are the variables.

So, [tex]C \propto d[/tex]

Therefore the constant of proportionality is [tex]\pi[/tex]

Step-by-step explanation:

[tex] \frac{50}{400} = \frac{5}{40} = \frac{1}{8} = 0.125[/tex]

Without knowing the function itself, it's impossible to definitively say which of the values (-6,-2,4,7) is an output. Any of these numbers could potentially be an output depending on the function.

In the context of this question, an output of a function refers to the result you get after substituting an input (or value from the domain) into the function. For example, if we have a function f(x) = x+2, and we input the value 3 (from our domain), our output (or range) will be 5. Unless we know the actual function, it's difficult to determine which of the listed values (-6,-2,4,7) is an output because any of these could potentially be an output depending on the function. Thus, without additional context, the statement 'Which value is an output of the function?' cannot be definitively answered.

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The output of a function is -6.

The output of a function is the value that the function produces when a certain input is given. In the table above, the function is f(x). We are given that x can be any of the values -6, -2, 4, or 7. We want to know which of the values -6, -2, 4, 7, or 12 is an output of the function.

To find out, we can look at the table. We see that the only value in the table that is an output of the function is -6. This is because when we plug in x = -6 into the function, we get f(x) = -6.

Therefore, the answer is -6.

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Answer:

2

Step-by-step explanation:

do like terms

1/4 x 8 = 2

divide un-like terms

4x ÷ 8 = 2

Answer:

8.212°

Step-by-step explanation:

Hypotenuse^2=base^2+perp^2

(8)^2=(7)^2+(perp)^2

64=49+(perp)^2

64/49=perp^2

1.306=perp^2

Now taking sq root on both sides

Perp=√1.306

Perp=1.142

Sin C=opposite/hypotenuse

Sin C=1.142/8

Sin C=0.14285

C=Sin^-1 0.14285

C=8.212°

Answer:

correct answer is B

Step-by-step explanation:

usatestprep

Answer:

So, we divide  

1

by  

5

6

→

1

÷

5

6

→

1

⋅

6

5

→

6

5

⇒

1

1

5

=

1.2

So, there are  

1

1

5

number of  

5

6

's in  

1

Step-by-step explanation:

the function that gives the deer population \( P(t) \) on the reservation t years from now is:

[tex]\[ \boxed{P(t) = 170 \times (1.30)^t} \][/tex]

To write a function that gives the deer population [tex]\( P(t) \)[/tex] on the reservation t years from now, where the population is increasing at a rate of 30% per year, we'll use the formula for exponential growth:

[tex]\[ P(t) = P_0 \times (1 + r)^t \][/tex]

Where:

- [tex]\( P(t) \)[/tex] is the population after t years,

- [tex]\( P_0 \)[/tex] is the initial population (in this case, 170),

- r is the annual growth rate (in decimal form), and

- t is the number of years.

Given that the population is increasing at a rate of 30% per year, we have [tex]\( r = 0.30 \)[/tex].

Substituting the given values into the formula, we get:

[tex]\[ P(t) = 170 \times (1 + 0.30)^t \][/tex]

Simplifying further:

[tex]\[ P(t) = 170 \times (1.30)^t \][/tex]

Therefore, the function that gives the deer population \( P(t) \) on the reservation t years from now is:

[tex]\[ \boxed{P(t) = 170 \times (1.30)^t} \][/tex]

The complete Question is given below:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

Answer:-93

Step-by-step explanation:4-(-3)-10²

4+3-100

7-100

=-93

The probability defined as P(A and C) is the probability of P(A) × P(B) = (0.6 × 0.3) = 0.18

The probability of A ; P(A) from the tree diagram is 0.6

The probability of B ; P(B) from the tree diagram is 0.3

The probability, P(A and B) equals ;

P(A) × P(B) = 0.6 × 0.3 = 0.18

Therefore, probability of A and B is 0.18

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The probability of P(A and C) would be 0.18. To understand, check the calculations below.

The probability is recounted as the proportion of outcomes favorable upon the total possibilities.

What information do we have from the tree diagram:

P(A) = 0.6

P(B) = 0.3

so,

we know that,

P(A and C) = P(A) × P(B)

= 0.6 × 0.3

= 0.18

Therefore, the probability of A and C is 0.18.

Learn more about "Probability" here:

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Answer:

59

Step-by-step explanation:

77+(-18)=59

Check:

59-77=(-18)

Hoped this helped !

Cheers, Z.

Answer:

59

Step-by-step explanation:

59-77=-18

77+-18=59

Answer:

A F because it is right i took the test

Hey there!

First off, I’m going to assume that the 2 in the second term is an exponent. If it isn’t, let me know and I’ll fix the answer.

Anyways, let’s start by plugging the values for the variables into the equation.

36(3)-8(-6)^2

Square -6

108-8(36)

Multiply.

108-288

Subtract.

-180

Your answer is -180.

Hope this helps!

The terms in the expression 2 + 6 + 10b - 8a are 2, 6, 10b, and -8a, where 2 and 6 are constants, and 10b and -8a are variable terms.

The terms in the expression 2 + 6 + 10b – 8a are 2, 6, 10b, and –8a. A term is a single mathematical expression which can be a number, a variable, or numbers and variables multiplied together. Here, the numbers 2 and 6 are called constant terms because they don’t change, 10b is a variable term which means it has a number (coefficient) and a variable (b), and similarly, –8a is a variable term with a negative coefficient and the variable a.

Work from the inside set of parentheses to the outside at:

(()10-9)+2)-3)

10-9 = 1

1+ 2 = 3

3-3 = 0

The answer is 0

(((10 - 9)+2)-3)

((1+2)-3)

(3-3)

The answer is 0.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

The variable that has the highest power is considered to be the degree of polynomials in an algebraic equation.

A column:

1) [tex]4x^3[/tex] .

The degree is 3.

2)[tex]x^2+4[/tex].

The degree is 2.

3) [tex]x-2[/tex]

The degree is 1.

B column:

1) [tex]2x^2+1[/tex]

The degree is 2.

2) [tex]x^2-x[/tex]

The degree is 2.

3) [tex]x^3-5x^2+1[/tex]

The degree is 3.

A×B columns:

While Multiplying two terms in a equation, if the variables are same then multiply the constant value and sum the exponent value.

1) [tex](4x^3)(2x^2+1)[/tex].

=[tex]8x^5+4x^3.[/tex]

The degree is 5.

2) [tex](x^2+4)(x^2-x)[/tex].

=[tex]x^4-x^3+4x^2-4x[/tex].

The degree is 4.

3) [tex](x-2)(x^3-5x^2+1)[/tex].

[tex]=x^4-5x^3+x-2x^3+15x^2-3.\\=x^4-7x^3+15x^2+x-3.[/tex]

The degree is 4.

Answer:

c

Step-by-step explanation:

-6m + 9

-3(2m - 3)

Answer:

I think it's c sorry if I am wrong.

Step-by-step explanation:

Answer:

Step-by-step explanation:5×6=30 and 5+7=12

Then is 30+12=42

The answer is 42

I believe the answer is 42.

Answer:

[tex]\large \boxed{\text{129 g}}[/tex]

Step-by-step explanation:

We can use ratio and proportion to solve this problem.

Let x = the mass of Zn

[tex]\begin{array}{cccl}\dfrac{\text{Zn}}{\text{Cu}} & = & \dfrac{3}{11} & \\\\\dfrac{x}{473} & = & \dfrac{3}{11} & \text{Substituted the mass of Cu}\\\\x & = & \dfrac{3\times473}{11} &\text{Multiplied each side by 473} \\\\ & = &\mathbf{129} & \text{Simplified}\\\end{array}\\\text{The mass of Zn is $\large \boxed{\textbf{129 g}}$}[/tex]

Check:

[tex]\begin{array}{rcl}\dfrac{129}{473} & = &\dfrac{3}{11} \\\\\dfrac{3}{11} & = & \dfrac{3}{11} \\\end{array}[/tex]

OK

Answer:

0.4

Step-by-step explanation:

Vicki has a computer randomly select 0 or 1 three times, with 0 representing heads and 1 representing tails. The results of 15 trials are shown in the table.

110    111   000    011   000

010   101   100   000   000

111     101    110     101    111

Vicki would like to estimate the probability of tails (1) coming up fewer than 2 times (must be 0 or 1 digit 1 in record). All such seuences are marked in bold int the above table. There are 6 such trails. Hence, Vicki's estimated probability, based on this simulation is

[tex]\dfrac{6}{15}=\dfrac{2}{5}=0.4[/tex]

♡ The Question ♡

-What is Vicki's estimated probability, based on this simulation?

* ୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Answer ♡

-The answer would be 0.4, but if you're looking for it in fraction-form it would be 2/5! So your answer is 2/5!

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

-No Explanation/Step-By-Step provided!

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♡ Tips ♡

-No Tips provided!

Answer:

[tex]y=3x[/tex]

Step-by-step explanation:

Let

x ----> the number of kids in a group

y ----> the total number of caramel chews Erica gives to that group

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Find the value of the constant of proportionality k

take a ordered pair from the data in the table and determine the value of k

For x=2, y=6 ----> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3\ caramels/kid[/tex]

therefore

[tex]y=3x[/tex]