22 mice were introduced to a new environment. Their population triples every year. Using m(t) as the function name and t for time, write this equation.​

Answer:

Cylinder height = 10

Semi-circle height = 3

Cone height = 4

Step-by-step explanation:

The height of the cylinder is always going to be the long side. 6 is the diameter of its circle. Here is a list of variables:

Diameter, D = 6

Radius, r = 3

Slant height of cone, c = 5

To find the height of the cylinder, we will need to find the height's of the cone and semi-circle:

CONE (see image attached)

a² + b² = c²

3² + h² = 5²

h² = 25 - 9

h = √16

h = 4

SEMI-CIRCLE

h = radius

h = 3

CYLINDER

Cylinder height = total h - semi-circle h - cone h

h = 17 - 3 - 4

h = 10

I'm not sure if you're trying to solve for volume, so I'll end it here LOL. Hope this helps and have a great evening!

Answer:

50, 30 and 20

Step-by-step explanation:

Check out the attached photo

Answer:

coke red

Step-by-step explanation:

correct me if im wrong

Answer:

18.85 years

Step-by-step explanation:

Using the [tex]A=P(1+\frac{r}{n} )^{nt}[/tex] we can manipulate it to give us time.

However, let's identify our variables:

A is our final amount which is given to us, $1400.

P is our principle which is $500.

r is our rate which is 5.5% which can be traducted into 0.055.

n is the # of time our money get compounded per year, in this case quarterly means 4 times a year therefore n = 4.

t is time and is what we are trying to solve for.

Now let's manipulate our equation to find t:

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

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

[tex]\frac{1400}{500} =(1+\frac{0.055}{4} )^{4t}[/tex]

[tex]2.8=1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=log_{1.01375}1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=4t[/tex]

[tex]\frac{log_{1.01375}(2.8)}{4} =t[/tex]

[tex]18.84876253=t[/tex]

It would take about 18.85 years in order for you to accumulate at least $1400.

Answer:

not sure if the 4 is seperate but if it is then (30+26)+(6-33)

Step-by-step explanation:

The answer is 1/3.

If you're still not sure (and math teachers will appreciate you doing this), you can check. Divide 1 by 3 and you will get 0.333333333333...

I hope this answers your question.

Although Alex and Lauren will both step into position 4,6, they will not do it at the same time, so they will not meet.

Lauren:

Alex:

Both will step in the position 4,6, However, Lauren will be in this positon in the second 4, while Alek will do it on the second 3.

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Answer:

0

Step-by-step explanation:

7-11=-4

-4+4=0

In order to solve a proportion, you should cross-multiply:-

[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]

Multiply 3x times 2 and 10 times 3:-

[tex]\bf{6x=30}[/tex]

Divide both sides by 6:-

[tex]\boxed{\bf{x=5}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer: Angle 3 and Angle 2

Step-by-step explanation:

The angles form a linear pair, which means they are supplementary.

Answer:

option A

Step-by-step explanation:

Answer os option a

Answer:

Step-by-step explanation:

1 pound = 16 ounces

16 ounces = $7.99

1 ounce = $0.50 (about)

Answer
[tex]\sqrt29[/tex]

Step-by-step explanation:

1. Write the distance formula:

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

2. Substitute

Substitue (6, -4) and (1, -6) into

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

3. Calculate

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

[tex]\sqrt(-5) ^{2} + (-2)^{2}[/tex]

[tex]\sqrt5 ^{2} + 2^{2}[/tex]

[tex]\sqrt25 + 4[/tex]

[tex]\sqrt29[/tex]

Answer:

tan 70 times thirty gives you -1.70

Lets see

Left:-

Not left anything

Answer:

16

Step-by-step explanation:

equal both using corresponding law

Answer:

multiple tasking them right

Answer:

results-driven

Step-by-step explanation:

Using the arrangements formula, it is found that 6 different orders of top-three finishers are possible.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the possible orders are arrangements of 3 elements, hence, the number of orders is given by:

[tex]A_3 = 3! = 6[/tex]

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Answer:

Step-by-step explanation:

Owing represent a negative balance.

So the inequality for this case is:

The word owing is given which simply denotes to negative transaction

So here the inequality is

Or

The average velocity is the rate of the distance function over time

The average velocity over the interval [1, 3] is 8 kilometers per hour

The distance function is given as:

d(t) = 8(t³ - 6t² + 12t)

The interval is given as: [1,3]

Calculate d(1) and d(3)

d(3) = 8(3³ - 6 * 3² + 12 * 3)

Evaluate

d(3) = 72

d(1) = 8(1³ - 6 * 1² + 12 * 1)

Evaluate

d(1) = 56

The average velocity (v) is the calculated as:

v = (d(3) - d(1))/(3 - 1)

Substitute known values

v = (72 - 56)/(3 - 1)

Evaluate

v = 8

Hence, the average velocity over [1, 3] is 8 kilometers per hour

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Answer:

81 [ft].

Step-by-step explanation:

1) the basic formula is: h=gt²/2, where g - acceleration due to gravity, t - elapsed time;

2) if the final velocity is 72, g=32, then it is possible to calculate elapsed time:

[tex]t=\frac{V}{g}=\frac{72}{32}=\frac{9}{4} [sec].[/tex]

3) if g=32, t=9/4, then the required height is:

[tex]h=\frac{32*(\frac{9}{4} )^{2} }{2}=\frac{16*81}{16}=81[ft].[/tex]

The height of the building comes to be 81 feet.

Initial velocity u= 0 feet/sec

Final velocity v= 72 feet/sec

The acceleration due to gravity g =32ft /sec²

Height of the building h= suppose h

The equation of a motion is:

[tex]v^{2} =u^{2} +2gh[/tex]

Where u and v are the initial and final velocities.

[tex]72^{2} =0+2*32*h\\144 = 64h\\h=81[/tex]

So, the height of the building = 81 feet.

Therefore, the height of the building comes to be 81 feet.

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Answer:

-5 and 9

Step-by-step explanation:

To find the solutions we will factor the equation.

First we take out a 2:

[tex]2(x^2-4x-45)[/tex]

Then we can factor again:

[tex]2(x+5)(x-9)[/tex]

This provides us with the answer of:

[tex]x+5=0[/tex]

and

[tex]x-9=0[/tex]

Hence the solutions of -5 and 9.

Step-by-step explanation: please see attached to PDF document.

Answer:

a) 6

b) 1/3

c) 2

Step-by-step explanation:

a) 3 ( x + 1 ) - x = 15. expand the bracket

3x + 3 - x = 15

2x + 3 = 15. collect the like terms

2x = 15 - 3.

2x = 12.

x = 12/2 = 6

b) 5 ( x + 2 ) - 2x = 11. expand the bracket

5x + 10 - 2x = 11

3x + 10 = 11. collect the like terms

3x = 11 - 10

3x = 1

x = 1/3

c) 6 ( 1 - 2x ) = - 4 - 7x. expand the bracket

6 - 12x = -4 -7x. collect the like terms

6 + 4 = -7x + 12x

10 = 5x

or

5x =. 10

x = 10/5 = 2

PLEASE MARK ME BRAINLIEST

Answer:

True

Step-by-step explanation:

like pirates, the stars were their navagation

Answer:

Your answers: -5, 0, 1

Step-by-step explanation:

–8 < 3x + 7 ≤ 10 That is the original compount inequality given.

We need to solve it in order to get an easy option.

-15, -5, -3, 0, 1 are the options.

_________________________________________________

Steps to solve:

–8 < 3x + 7 ≤ 10

Subtract 7 from both sides

–8 < 3x ≤ 10 - 7

Now do 10-7

–8 < 3x ≤ 3

Do 3x divided by 3

–8 < x ≤ 1

________________________________________________________

Evaluation and Answer Explanation:

–8 < x ≤ 1

That is your inequality statement.

The inequality statement states that "x" is greater than -8 but less than or equal to 1.

We can automatically choose 0 and 1 because 0 is greater than -8 and less than or equal to 1.

1 is correct because it is greater than -8 and less than or equal to 1

Now, there are two answers remaining: -15; -5.

Let's try -15.

-15 isn't greater than -8 but is less than 1. This is incorrect because it follows one inequality but doesn't follow both.

**Rule: the bigger you go on the negatives like -20 or -99 your numbers get smaller. If you go more towards the 0 like -1, -5, -3 your numbers get bigger.

-5 works because it is greater than -8 and less than or equal to 1.

Your answers: -5, 0, 1

1) The net area between the two functions is 2.

2) The net area between the two functions is 4/3.

3) The net area between the two functions is 17/6.

4) The net area between the two functions is approximately 1.218.

5) The net area between the two functions is 1/2.

The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:

[tex]A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx[/tex]   (1)

Where:

Now we proceed to solve each integral:

The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:

[tex]A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx[/tex]

[tex]A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})[/tex]

[tex]A = 2[/tex]

The net area between the two functions is 2. [tex]\blacksquare[/tex]

The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:

[tex]A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx[/tex]

[tex]A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)][/tex]

[tex]A = \frac{4}{3}[/tex]

The net area between the two functions is 4/3. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx[/tex]

[tex]A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})[/tex]

[tex]A = \frac{17}{6}[/tex]

The net area between the two functions is 17/6. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx[/tex]

[tex]A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}][/tex]

[tex]A \approx 1.218[/tex]

The net area between the two functions is approximately 1.218. [tex]\blacksquare[/tex]

This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:

[tex]A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx[/tex]

[tex]A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )[/tex]

[tex]A = \frac{1}{2}[/tex]

The net area between the two functions is 1/2. [tex]\blacksquare[/tex]

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Answer:

144 sq cm

Step-by-step explanation:

The base is a triangle. Area of a triangle is:

A = 1/2 b • h

A = 1/2(4)•3

A = 6

There are 2 of these bases.

Area of 2 bases= 12.

There are three rectangular sides. Area of a rectangle is:

A = l × w (or b•h)

A = 5 × 11 = 55

A = 3 × 11 = 33

A = 4 × 11 = 44

Add up three rectangular faces and two bases for Total Surface Area:

12 + 55 + 33 + 44

= 144 sq cm

Answer:

144 cm ²

Step-by-step explanation:

The surface area of a right triangular prism is made up of 2 congruent triangles (these are called the "bases") and 3 rectangles.

Surface area of a right triangular prism formula

Surface area = (S₁ + S₂ + S₃)L + bh

where:

⇒ Surface area = (3 + 4 + 5)11 + 4 × 3

                          = (12)11 + 12

                          = 132 + 12

                          = 144 cm²

Answer:

9d^2(5d−2)

Step-by-step explanation:

The probability that the selected number is even, multiple of 4 and prime are 7/15, 1/5 and 2/5 respectively

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Given the following set

S=​{1, ​2, 3,​ 4,..., 15}

n(S) = 15

If the selected number is even

E = {2, 4, 6, 8, 10, 12, 14}

n(E) = 7

Pr(selecting even number) = n(E)/n(S)

Pr(selecting even number) = 7/15

If the selected number is a multiple of 4

E = {4, 8, 12}

n(E) = 3

Pr(multiple of 4) = n(E)/n(S)

Pr(multiple of 4) = 3/15 = 1/5

If the selected number is a prime number

E = {2, 3, 5, 7, 11, 13}

n(E) = 6

Pr(prime number) = n(E)/n(S)

Pr(prime number) = 6/15 = 2/5

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Answer:

Step-by-step explanation:

Given points P and Q have same x-coordinate but different y- coordinates.

The distance between P and Q is the difference of y- coordinates:

The area is 64 cm², it means the adjacent sides are

a)

If the points R and S are to the left, their coordinates are

b)

If the points R and S are to the right, their coordinates are

Answer:

Points R and S are to the left of Points P and Q

R = (-9, 4)

S = (-9, -4)

Points R and S are to the right of Points P and Q

R = (7, 4)

S = (7, -4)

Step-by-step explanation:

Given coordinates:

Points P and Q have the same x-value.

The vertical distance between these two points is:

[tex]\begin{aligned}\implies \sf y_P-y_Q & =\sf 4-(-4)\\ & =\sf 4+4\\ & =\sf 8\:units \\ & =\sf 8\:cm\end{aligned}[/tex]

Area of a rectangle = width × length

If the area of the rectangle PQRS is 64 cm² then:

[tex]\begin{aligned} \implies \sf 64 & = \sf width \times 8\\\implies \sf width & = \sf \dfrac{64}{8}\\\implies \sf width& = \sf 8 \: cm \end{aligned}[/tex]

This means that the y-values of points R and S will be the same as points P and Q, but the x-values will either be 8 less or 8 more.

Points R and S are to the left of Points P and Q

R = (-1 - 8, 4) = (-9, 4)

S = (-1 - 8, -4) = (-9, -4)

Points R and S are to the right of Points P and Q

R = (-1 + 8, 4) = (7, 4)

S = (-1 + 8, -4) = (7, -4)