on a map 1 inch equals 7.2 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses?

Answer:

31.41ft

Step-by-step explanation:

the area A of a circle is πr² = 78.5 square feet

3.1416* r² = 78.5

r² =78.5/3.1416 =  24.987

r = √24.987 = 4.999ft

the circumference C of a circle is 2πr

C = 2* 3.1416 * 4.999 = 31.41ft

Answer:

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

From the graph we have the points A(-2, 4) and C(3, -3).

Substitute:

[tex]M_{AC}(x,\ y)\\\\x=\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\y=\dfrac{4+(-3)}{2}=\dfrac{1}{2}=0.5[/tex]

Answer:

0.5 0.5

Step-by-step explanation:

because it is logically correct now deal with it! hehehe have a grate day un like me!;)

Use trigonometry.

cos(18°) = x/25

Multiply both sides by 25.

cos(18°)25 = x

23.7764129074 = x

We round off to the nearest hundredth. This means to round off to two decimal places.

Doing so, we get 23,78 cm = x.

Answer:

The best answer would be B. systematic random sampling

Step-by-step explanation:

The best sampling method for choosing a committee is Cluster Sampling.

Simple random sampling - Simple random sampling is a sort of probability sampling in which a researcher selects a subset of a population at random.

Systematic random sampling  A probability sampling approach in which a random sample of a bigger population is selected with a defined periodic interval.

Stratified random sampling A form of sampling known as stratified random sampling includes dividing a population into smaller sub-groups known as strata.

Cluster Sampling  The population is divided into groups first. Every member of some of the groupings is included in the total sample. The teams are chosen at random.

If we are trying to choose a committee, cluster sampling method would be the best as there should be representatives of every group of the society in that committee and the representative from each group should be chosen completely randomly.

Hence the cluster sampling method is the best way to choose a committee.

Learn more about sampling on:

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D is most likely right. Basically, I would turn them into decimals and divide using a graphing calculator.

Answer:

D

Step-by-step explanation:

Answer:

(x + 1) is a factor of f(x).

Step-by-step explanation:

Please share the answer choices.  Thank you.

If –1 is a root of f(x), which of the following must be true?  

(x + 1) is a factor of f(x).

Answer:

The volume is equal to [tex]98,470.4\ cm^{3}[/tex]

Step-by-step explanation:

step 1

Find the radius of the base of cylinder

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=87.92\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]87.92=2(3.14)r[/tex]

[tex]r=87.92/[2(3.14)]=14\ cm[/tex]

step 2

Find the volume of the water tank (cylinder)

The volume is equal to

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

we have

[tex]r=14\ cm[/tex]

[tex]h=160\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(14)^{2} (160)[/tex]

[tex]V=98,470.4\ cm^{3}[/tex]

Answer:

The answer is 98470.4

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is

[tex]V=\pi r^2h[/tex]

Differentiate both sides with respect to time:

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]

We're given that

[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]

[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]

so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]

[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]

The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.

The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).

According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.

Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.

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Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

In calculating probability, remember that "AND" means "MULTIPLICATION" and "OR" means "ADDITION".

Since we want the probability of red necklace AND yellow bracelet, we calculate individual probabilities and "MULTIPLY" them.

Probability of red necklace:

There are 4 necklaces and 1 of them is red, hence probability of red necklace is 1/4

Probability of Yellow bracelet:

There are 2 bracelet and 1 of them is yellow, hence probability of yellow bracelet is 1/2

Now, we multiply both to get our answer.

1/4 * 1/2 = 1/8

Answer:

1/8

Step-by-step explanation:

Answer:

The area is

[tex]A=254.34\ in^2[/tex]

Step-by-step explanation:

The circumference of a circle is given by a following formula:

[tex]C = 2\pi r[/tex]

Where r is the radius of the circumference.

In this case we know that

[tex]C = 2\pi r=56.52\ in[/tex]

We solve the equation for r

[tex]C = 2\pi r=56.52\ in[/tex]

[tex]2\pi r=56.52\\\\r=\frac{56.52}{2\pi}\\\\r=9\ in[/tex]

The area of a circumference is given by the following formula

[tex]A=\pi r^2[/tex]

Now we substitute the value of r in the equation to find the area

[tex]A=\pi (9)^2[/tex]

[tex]A=3.14* (9)^2[/tex]

[tex]A=254.34\ in^2[/tex]

Answer:

B. 2x + y -8 = 0

Step-by-step explanation:

2x + y -8 = 0

2x - 8 = -y

Divide both sides by negative one

-2x + 8 = y

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope m = -2 and the y-intercept b = 8. Substitute:

[tex]y=-2x+8[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]y=-2x+8[/tex]              add 2x to both sides

[tex]2x+y=8[/tex]              subtract 8 from both sides

[tex]2x+y-8=0[/tex]

For this case we have the following functions:

[tex]f (x) = 2x ^ 2-18\\g (x) = - 3x-7[/tex]

We must find:

[tex](f-g) (2)[/tex]

By definition, we have to:

[tex](f-g) (x) = f (x) -g (x)[/tex]

So:

[tex](f-g) (x) = 2x ^ 2-18 - (- 3x-7)\\(f-g) (x) = 2x ^ 2-18 + 3x + 7\\(f-g) (x) = 2x ^ 2 + 3x-11[/tex]

Then, we evaluate in x = 2:

[tex](f-g) (2) = 2 (2) ^ 2 + 3 (2) -11\\(f-g) (2) = 2 (4) + 6-11\\(f-g) (2) = 8 + 6-11\\(f-g) (2) = 8 + 6-11\\(f-g) (2) = 3[/tex]

ANswer:

[tex](f-g) (2) = 3[/tex]

Answer:

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you.  f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation:  f(x) = 4(2)^x

                                                                                      f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

                                                                                           b - a

                                    change in function value

This is equivalent to  ---------------------------------------

                                            change in x value

For Section A:  x changes from 1 to 2 and the function changes from 4(2)^1 to  4(2)^2:  8 to 16.  Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2.  Thus, in this Section, the a.r.c. is:

                 8

               ------ = 8 units    (Section A)

                  1

Section B:  x changes from 3 to 4, a net change of 1 unit:  f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units.  Thus, the a.r.c. is

        224 units

      ----------------- = 224 units (Section B)

            1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

Answer:

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Step-by-step explanation:

The function is given by .

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is =  8

And in section B, the average rate of change is  =  32

Part B:

Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)

Answer:

106 m²

Step-by-step explanation:

Imagine this shape was a square, it's area would be 120 m².

Now imagine the little rectangle with 7 m as the side, you will have to work out the area of that so

Side = 7

4 + 4 + ? = 10

8 + ? = 10

? = 2

So the area of the little rectangle is 14 m²

Now we minus both of the areas : 120 - 14 = 106

The answer is:

The area of the triangle is:

[tex]Area=13.2cm^{2}[/tex]

We can solve the problem using the Side-Angle-Side (SAS) method, to calculate the area of a triangle given two sides and a single angle.

The SAS method to calculate the area of a triangle is given by the following the equation:

[tex]Area=\frac{abSinC}{2}[/tex]

Where,

a and b are the known sides.

C is the known angle

Now, we are given a triangle with the following dimension:

[tex]Side_{a}=7cm\\Side_{b}=8cm\\\alpha=28\°[/tex]

Then, using the information and solving we have:

[tex]Area=\frac{7cm*8cm*Sin(28\°)}{2}[/tex]

[tex]Area=\frac{56cm^{2}*Sin(28\°)}{2}\\\\Area=\frac{56cm^{2}*0.47}{2}\\\\Area=\frac{26.32cm^{2}}{2}\\\\Area=13.16cm^{2}[/tex]

Hence, the area of the triangle, rounded to the nearest tenth is:

[tex]Area=13.2cm^{2}[/tex]

Have a nice day!

5 1/4 in decimal form is 5.25 because 25 is 1/4 of 100.

The mixed fraction 5 1/4 is equivalent to 5.25 in decimal form. The fraction 1/4 is converted to decimal by dividing 1 by 4 to get 0.25 and then added to the whole number 5.

To convert the mixed fraction 5 1/4 to decimal form, you need to divide the numerator by the denominator for the fractional part and then add that result to the whole number part. In this case, 1 divided by 4 equals 0.25. Adding this result to the whole number 5 gives you 5.25, which is 5 1/4 in decimal form.

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Answer:

1:7 2:9

Step-by-step explanation:

Answer:

Step-by-step explanation:

\frac{27}{40}  in a decimal is 0.675

I’ve attached a picture of my work!!

Answer:

Step-by-step explanation:

[tex]-3(2x-5)<5(2-x)\qquad\text{use the distributive property}\\\\(-3)(2x)+(-3)(-5)<(5)(2)+(5)(-x)\\\\-6x+15<10-5x\qquad\text{subtract 15 from both sides}\\\\-6x<-5-5x\qquad\text{add 5x to both sides}\\\\-x<-5\qquad\text{change the signs}\\\\x>5[/tex]

the translation should make the equation

g(x)= (x+5)2

Answer:

b

Step-by-step explanation:

If Eli has a total of 21 baseball cards, and wants each bag to have 3 cards, you would divide the number of total cards by the amount you want in each group. Dividing is like grouping.

So, the equation he'd use is: 21 / 3 = 7

I hope that helped.

Answer:

21÷3=7

Step-by-step explanation:

Dividing the number of available cards by the quantity in each bag will tell Eli how many bags he can fill.

___

Division can be thought of as "repeated subtraction" with the quotient telling you how many times the divisor can be subtracted from the dividend. One way Eli can do this repeated subtraction is to put the cards into piles of 3:

ccc . ccc . ccc . ccc . ccc . ccc . ccc

He will run out of cards when he has made 7 piles.

Answer:

Actually it does relate to sin, cos and tan.

* tan50° = 16/b

=> b = 16/tan50° ≈ 13.426

* sin50° = 16/c

=> c = 16/sin50° ≈ 20.887

*cos∠B = 16/c = 16/20.887

=> m∠B ≈ 40.002

Answer:

The graph of G is 3 units to the left of graph F

Step-by-step explanation:

I used Desmos graphing calculator to check my answer, but generally you can use this formula.

a(x + or - h) + or - k = y

h is vertical movement and k is horizontal movement.

Answer: Never mind that answer was incorrect it is not B!!

Step-by-step explanation:

Answer:

228.8 meters

Step-by-step explanation:

y = -0.04 x² + 9.1 x + 11.9

When the rocket lands, y = 0:

0 = -0.04 x² + 9.1 x + 11.9

Solving for x, start by multiplying by -1:

0 = 0.04 x² - 9.1 x - 11.9

Multiply by 100:

0 = 4x² - 910 x - 1190

Solve with quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2a

x = [ 910 ± √((-910)² - 4(4)(-1190)) ] / 2(4)

x = [ 910 ± √(847140) ] / 8

x ≈ -1.3, 228.8

Since x can't be negative, x = 228.8 meters.

Answer:

The rocket will land at 208.02 m. Hence, if you are on the same connexus assignment, your answer will be A.

Hope this helps! :D

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

C

Step-by-step explanation:

From the table we see that

[tex]f(-2)=12\\ \\f(-1)=10\\ \\f(0)=8\\ \\f(1)=6\\ \\f(2)=4[/tex]

Thus, the inverse function has the rule

[tex]f^{-1}(12)=-2\\ \\f^{-1}(10)=-1\\ \\f^{-1}(8)=0\\ \\f^{-1}(6)=1\\ \\f^{-1}(4)=2[/tex]

This gives us that ordered pairs

[tex](12,-2),\ (10,-1),\ (8,0),\ (6,1),\ (4,2)[/tex]

are on the graph of the inverse function

Answer:

it is c

Step-by-step explanation:

yep

Answer: 5.18 pounds

Step-by-step explanation:

Given: The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to  the temperature of the gas.

Let 'p' denote the pressure exerted on the walls and 't' denotes  temperature of the gas.

Then the equation is given by :-

[tex]p=ct[/tex], where c is the proportionality constant.

Also, the pressure is 6 pounds per square inch when the temperature is 440° F.

[tex]\Rightarrow\ 6=440c\\\\\Rightarrow\ c=\dfrac{6}{440}=\dfrac{3}{220}[/tex]

Then, the final equation to calculate pressure becomes :-

[tex]p=\dfrac{3}{220}t[/tex]

Now, the pressure exerted when the temperature of the gas is 380°F is given by :-

[tex]p=\dfrac{3}{220}\times380=5.181818\approx5.18\text{ pounds}[/tex]

ANSWER

Option C

EXPLANATION

The given inequality is

[tex]y - 3 \: > \: 2x + 2[/tex]

We add 3 to both sides to get,

[tex]y \: > \: 2x + 2 + 3[/tex]

[tex]y \: > \: 2x +5[/tex]

The corresponding linear equation is

[tex]y = 2x + 5[/tex]

This becomes the dashed boundary line of the inequality.

We test the origin to determine which half plane to shade.

[tex]0\: > \: 2(0)+5[/tex]

[tex]0\: > \: 5[/tex]

This is false.

Hence we shade the upper half plane.

The correct answer is C

Answer:

x = 12z + 1  and y = 10z - 1

Step-by-step explanation:

To solve the system of equations, we can use the substitution method

If we call

3x - 4y + 4z = 7 I

x - y - 2z = 2 II

2x - 3y + 6z = 5 III

Clearing II  x = 2 + y + 2z

Now, replacing II in III

2(2 + y + 2z) - 3y +6z = 5

4 + 2y + 4z - 3y + 6z = 5

10z - y = 1 from here y = 10z - 1

Finally, replacing y in I

3x - 4(10z - 1) + 4z = 7

3x -40z + 4 + 4z = 7

3x - 36z = 3

3x = 36z + 3

x = 12z + 1

Done