Twice a day cameron's cat eats 4 ounces of dry cat food and 3 ounces of wet cat food. Dry food comes in a 5-pound bag. Wet food comes in 6-ounce cans. How many cans of wet food should he buy to feed his cat for a week?

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

Answer:

I belive the anwers is a

Step-by-step explanation:

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! ⭐

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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:

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:-93

Step-by-step explanation:4-(-3)-10²

4+3-100

7-100

=-93

Answer:

1,365 divided by 8 is equal to 169.5

the fraction form is 169 1/2

Answer:

-0.83

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

2(4)=8

Yes, 4 is a solution of 2x = 8

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation.

Given,

4 is solution of 2x = 8,

Then, putting x = 4

2(4) = 8

8 = 8

LHS = RHS

Hence, 4 is a solution of 2x = 8.

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Answer:

  $39.80

Step-by-step explanation:

If the price is reduced by 40%, it is 100% -40% = 60% of what it was. If 7% tax is added to that, the result is 100% +7% = 107% of the sale price. The final price is ...

  $62 × 0.60 × 1.07 = $39.80

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]

Answer:

Part 4) [tex]ER=3\ units[/tex]

Part 5) [tex]DF=9\sqrt{10}\ units[/tex]

Part 6) [tex]DE=30\ units[/tex]

Step-by-step explanation:

Part 4) Find ER

we know that

In the right triangle ERF

Applying the Pythagorean Theorem

[tex]EF^2=ER^2+RF^2[/tex]

substitute the given values

[tex](3\sqrt{10})^2=ER^2+9^2[/tex]

solve for ER

[tex]ER^2=(3\sqrt{10})^2-9^2[/tex]

[tex]ER^2=90-81\\ER^2=9\\ER=3\ units[/tex]

Part 5) Find DF

we know that

In the right triangle DRF

Applying the Pythagorean Theorem

[tex]DF^2=DR^2+RF^2[/tex]

substitute the given values

[tex]DF^2=27^2+9^2[/tex]

[tex]DF^2=810\\DF=\sqrt{810}\ units[/tex]

simplify

[tex]DF=9\sqrt{10}\ units[/tex]

Part 6) Find DE

we know that

[tex]DE=DR+RE[/tex] ----> by segment addition postulate

we have

[tex]DR=27\ units\\RE=ER=3\ units[/tex]

substitute

[tex]DE=27+3=30\ units[/tex]

Answer: A.2/5

Step-by-step explanation:

5 divided by 2 equals 2.5

Answer:D

Step-by-step explanation:

2×5=10 meaning each friend can have 2 pieces of pizza because 2 can fit into ten 5 times

You need to isolate/get x by itself in the equation

6 + 3(6x - 2) = -12      Distribute/multiply 3 into (6x - 2)

6 + (3)6x - (3)2 = -12

6 + 18x - 6 = -12       Combine like terms (6 and -6)

18x = -12      Divide 18 on both sides to get x by itself

[tex]x = -\frac{12}{18}[/tex]       Simplify

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

PROOF

[tex]6+3(6(-\frac{2}{3} )-2)=-12[/tex]           Plug in -2/3 into x, then multiply 6 and -2/3

6 + 3(-4 - 2) = -12         Simplify what's in the parentheses

6 + 3(-6) = -12          Multiply 3 and -6

6 - 18 = -12              

-12 = -12

Answer:

A F because it is right i took the test

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:

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:

f(2)=19

Step-by-step explanation:

If *=x, f(2)=2(3^2)+1=2*9+1=18+1=19

Answer:

10,000

Step-by-step explanation:

_ _ _ _

10 options for each position

10×10×10×10 = 10000

Answer:

210 combinations.

Step-by-step explanation:

We have 10 total digits (0-9) and we only use 4 at a time. We can use the permutation formula [tex]\frac{n!}{k!(n-k)!}[/tex], and plug in 10 for n and 4 for k. This is called:

n choose k.

Plug the values in, and we get 210 permutations for the password.

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

Step-by-step explanation:

The given system of linear equations:

x - 2y = 8                        ........ (1)

and 4x + y = 5               ........ (2)

To find, the values of x and y = ?

Multiplying equation (2) by 2, we get

2(4x + y) = 5 × 2  

⇒ 8x + 2y = 10                ........ (3)

Adding equations (1) and (3), we get

x - 2y + (8x + 2y) = 8  + 10  

⇒ x - 2y + 8x + 2y = 8  + 10

⇒ 9x = 18

⇒ x = 2

Put x = 2 in (1), we get

2 - 2y = 8        

⇒ 2y =2 - 8

⇒ 2y = - 6

⇒ y = - 3

∴  x = 2 and y = - 3

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:

About [tex]9,693,180\ liters[/tex]

Step-by-step explanation:

we know that

The volume of the tank is equal to the volume of a cylinder plus the volume of hemisphere

so

[tex]V=\pi r^{2}h+\frac{2}{3}\pi r^{3}[/tex]

where

[tex]r=10.5\ m\\h=21\ m\\\pi=3.14[/tex]

substitute

[tex]V=(3.14)(10.5)^{2}(21)+\frac{2}{3}(3.14)(10.5)^{3}[/tex]

[tex]V=7,269.885+2,423.295=9,693.18\ m^3[/tex]

Convert to liters

[tex]1\ m^3=1,000\ L[/tex]

therefore

The volume is equal to

[tex]9,693.18(1,000)=9,693,180\ liters[/tex]

Answer:

16 ounces

Step-by-step explanation:

The answer is option C. 16 ounces.

The most accurate measurement of 1 pound would be 16 ounces, because, by definition, there are 16 ounces in 1 pound.

Among the options provided:

A. 6 ounces: This is less than 1 pound.

B. 20.099 ounces: This is more than 1 pound.

C. 16 ounces: This is equal to 1 pound.

D. 10 ounces: This is less than 1 pound.

So, the most accurate measurement of 1 pound is 16 ounces.

One pound is most accurately measured as 16 ounces. This is because the imperial system defines one pound as equivalent to 16 ounces.

The question is:

Which is the most accurate measurement of 1 pound? (Remember, there are 16 ounces in a pound.)

A. 6 ounces

B. 20.099 ounces

C. 16 ounces

D. 10 ounces

Answer:$200 per month is spent.

Step-by-step explanation:

$2400 divided by 12 = $200

The amount of debt remaining as Catherine pays off her $2400 loan over 12 months is expressed by the function D(t) = 2400 - 200t, where t is the time in months.

Catherine is paying off a $2400 loan by making equal payments over a 12-month period until the loan is paid. To express the amount of debt remaining as a function of time in months, let's denote the amount of debt remaining as D(t), where t is the time in months.

Since she is making equal payments over 12 months, the total amount she needs to pay each month is $2400 divided by 12 months, which is $200 per month. Therefore, the function that represents the amount of debt remaining at any time t is given by : D(t) = 2400 - 200t

This linear function shows that for each month that passes, $200 is subtracted from the original loan amount of $2400, representing the payments made towards the loan. Thus, after t months, the amount of debt remaining is calculated by subtracting $200 times the number of months from the initial loan amount.

answer:

1/10 as a fraction or if you want it as a decimal it would be 0.1

step-by-step explanation:

-4(x-4)- 3=12+6x after seeing you multiply -4 by x and -4

and you would get

-4x+0-3=12+6x and then you distribute all the way and you would get

1/10 or if you dont want a fraction and want a decimal is would be 0.1

Answer:

x=1/10 or x=0.1

Step-by-step explanation:

Multiply the parenthesis by 4 (-4x+16-3=12+6x)then subtract the numbers (16-3=13) then move the variable to the left side and change its sign (-4-6x+13=12 to -4x-6x=12-13) then add the terms (-4x-6x=12-13 to -10x=12-13) and get the difference (-4x-6x=12-13 to -10x=-1) then divide bothe sides of the equation by -10 then your answer would be x=1/10

Answer:

1.) Ferris wheel

Step-by-step explanation:

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]