If 4 cans of cat food costs $17.20, how many cans of cat food can be purchased
with $38.70

Formula for the volume of a cone: V = 1/3 x pi x r^2 x h

Since this is a right cone, the height is given as 8.5 and the radius is 4.

V = 1/3 x pi x 4^2 x 8.5

V = 1/3 x pi x 16 x 8.5

V = 1/3 x pi x 136

V = 45 1/3 pi

V = 142.4 cubic units

Hope this helps!

Answer:

142.4 units^3

Step-by-step explanation:

We use the same formula for volume as for a cone

V = 1/3 pi r^2 h

V = 1/3 pi (4)^2 ( 8.5)

  = 1/3 pi (16)(8.5)

Letting pi = 3.14

 =142.34666667

Rounding to the nearest tenth

  = 142.4

Answer:

B

Step-by-step explanation:

Given:

The population, P, of six towns with time t in years are given by the following exponential equations:

(i) [tex]P=1000(1.08)^t[/tex]

(ii) [tex]P = 600 (1.12)^2[/tex]

(iii) [tex]P =2500 (0.9)^t[/tex]

(iv) [tex]P=1200 (1.185)^t[/tex]

(v) [tex]P=800 (0.78)^t[/tex]

(vi) [tex]P=2000 (0.99)^t[/tex]

To find:

The town whose population is decreasing the fastest.

Solution:

The general form of an exponential function is:

[tex]P(t)=ab^t[/tex]

Where, a is the initial value, b is the growth or decay factor.

If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.

The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town  [tex]P=800 (0.78)^t[/tex] is decreasing the fastest.

Therefore, the correct option is b.

The total distance the particle travels from t=0 seconds to t=4 seconds would be 11.33 meters.

Used the concept of integration that states,

In Maths, integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given that,

A particle moves along a line with a velocity v(t) = t² - t - 6, measured in meters per second.

Now the total distance the particle travels from t=0 seconds to t=4 seconds is,

D = ∫₀⁴ |(t² - t - 6)| dt

D =  ∫₀⁴ (t²) dt - ∫₀⁴ (t) dt -  ∫₀⁴ (6) dt

D = (t³/3)₀⁴ - (t²/2)₀⁴ - 6 (t)₀⁴

D =| (64/3) - (16/2) - 6 (4)|

D = | (64/3) - 8 - 24 |

D = | (64/3) - 32|

D = 11.33 meters

Therefore, the total distance is 11.33 meters.

To learn more about integration visit:

brainly.com/question/18125359

#SPJ4

Answer:

[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]

Step-by-step explanation:

we would like to solve the following using double-angle formula:

[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]

there're 4 double Angle formulas of cos function which are given by:

[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]

since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore

step-1: assign variables

to do so rewrite the given function:

[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]

so,

Step-2: substitute:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]

recall unit circle thus cos300 is ½:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]

simplify square:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]

reduce fraction:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]

simplify substraction and hence,

[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]

Step-by-step explanation:

Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced

Answer:

x=110.6

Step-by-step explanation:

sin(19)=36/x. x=36/sin(19)=110.6

Answer:

Step-by-step explanation:

Total frequencies:

Median group is the containing the middle - 25th and 26th frequencies. This is the 11-15 interval.

Estimated median formula:

Substitute values and work out the number:

The area of one side of the coin is 41.605 mm².

Given that, the diameter of a $1 coin is 26.5 mm.

We need to find the area of one side of the coin.

The area of a circle formula is A=πr².

Now, radius=26.5/2=13.25 mm.

Area of a coin=3.14×13.25=41.605 mm².

Therefore, the area of one side of the coin is 41.605 mm².

To learn more about the area of the circle visit:

https://brainly.com/question/11952845.

#SPJ2

Answers:

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

Work Shown:

AP = arithmetic progression, which is the same as arithmetic sequence

d = common difference

Notice how we scale up the d terms d, 2d, 3d, counting up by 1 each time.

So that must mean 25 is the same as 20+4d

20+4d = 25

4d = 25-20

4d = 5

d = 5/4

d = 1.25

and therefore,

We could convert these to fraction form, but I find decimal form is easier in this case.

Answer:

y = 2 - [tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex] results in a parabola (U-shape). Adding a negative in front of it flips the parabola to look like an upside-down U.

The 2 makes it shift up two decimal spots to (0,2).

Answer:

[tex]ST = 6cm[/tex]

Step-by-step explanation:

Given

[tex]RS =2x[/tex]

[tex]ST = 3x[/tex]

[tex]RT = 10[/tex]

Required

Find ST

From the question, we understand that S is between R and T.

So:

[tex]RS + ST = RT[/tex]

Substitute known values

[tex]2x + 3x = 10[/tex]

[tex]5x =10[/tex]

Divide both sides by 5

[tex]x =2[/tex]

Given that:

[tex]ST = 3x[/tex]

[tex]ST = 3 * 2[/tex]

[tex]ST = 6cm[/tex]

Answer:

C or 6 centimeters

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

The question is asking for the net area from x=3 to x=10.

It gives you the net area from x=3 to x=5 being -18.

It gives you the net area from x=5 to x=10, being 42.

Together those intervals make up the interval we want to find the net area for.

-18+42=42-18=24

Answer:

[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^{5}_3 {f(t)} \, dt = -18[/tex]

[tex]\displaystyle \int\limits^{10}_5 {f(t)} \, dt = 42[/tex]

[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Step-by-step explanation:

gxhkmnjggggffffffcccccccccccc

The statement that is true about the quadratic equation is (b) There are two complex solutions.

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

y = 12 – 11x + 7

Express properly

So, we have

y = 12x² – 11x + 7

Next, we calculate the discriminant using

d = b² - 4ac

Where

a = 12

b = -11

c = 7

Substitute the known values in the above equation, so, we have the following representation

d = (-11)² - 4 * 12 * 7

Evaluate

d = -215

This value is less than 0

This means that it has complex solutions

Read more about quadratic functions at

https://brainly.com/question/25841119

#SPJ1

Answer: y = -3x + 5

Step-by-step explanation:

slope = m

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-4)}{1-3}=\frac{6}{-2}=-3[/tex]

y = mx + b, (3,-4), (1,2), m = -3

(both points work for the y = mx + b equation)

[tex]y=mx+b\\2=-3(1)+b\\2=-3+b\\b=5\\y=-3x+5[/tex]

Answer:

+or- sqrt(3/4)

Step-by-step explanation:

If x + m is a factor, that means that when x = -m the equation equals 0. Sub -m into x

0 = (-m)^2 - 5m(-m) + 3

0 = m^2 - 5m^2 + 3

0 = -4m^2 + 3

Factorise

0 = -4(m^2 - 3/4)

0 = -4(m + sqrt(3/4))(m - sqrt(3/4))

:. m = +or- sqrt(3/4)

Answer:

[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]

Step-by-step explanation:

Given

[tex]0 = x^2 - 2x -3[/tex]

Required

The correct quadratic formula for the above

A quadratic equation is represented as:

[tex]ax^2 + bx + c = 0[/tex]

And the formula is:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

So, we have:

[tex]0 = x^2 - 2x -3[/tex]

Rewrite as:

[tex]x^2 - 2x - 3 = 0[/tex]

By comparison:

[tex]a= 1; b = -2; c = -3[/tex]

So, we have:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]

Answer:

115 in.^2

Step-by-step explanation:

The total surface area is the sum of the areas of the square base and the 4 congruent triangular faces.

SA = b^2 + 4 * bh/2

SA = (5 in.)^2 + 4 * (5 in.)(9 in.)/2

SA = 25 in.^2 + 2 * 45 in.^2

SA = 115 in.^2

here it is :)

do check properly, I have given step by step instructions:)

do give feedback on my answer, would appreciate it!

Answer:

900000

Step-by-step explanation:

[tex]30*10^{4}[/tex]

=3*10000

=30000

=30*30000

=900000

Answer:

d may cause f.

Step-by-step explanation:

Here are the options

d must not cause f.

f must cause d.

d must cause f.

d may cause f.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

1. Positive correlation : it mean that the two variables move in the same direction. If one variable increases, the other variable also increases.

For example, there should be a positive correlation between quantity supplied and price

When there is a positive correlation, the graph of the variables is upward sloping

2. Negative correlation :  it mean that the two variables move in different direction. If one variable increases, the other variable decreases.

For example, there should be a negative correlation between quantity demanded and price

When there is a negative correlation, the graph of the variables is downward sloping

3. Zero correlation : there is no relationship between the variables

the measure of m is24 according to the questions

Answer:

I think this is right for the 2nd problem

Step-by-step explanation:

a1=7+(3)(1)

Step 1: Simplify both sides of the equation.

a1=7+(3)(1)

a=7+3

a=(7+3)(Combine Like Terms)

a=10

a=10

Answer:

a=10

Step-by-step explanationIf you are reading this say

thank u