A park is 5 miles east of Roxana's home. A library is 4 miles north of the park. How far is Roxana's home from the library? ​

Answer:

7.3

Step-by-step explanation:

y=2.5x+5.8

=2.5×0.6+5.8

= 1.5+.8

=7.3

Answer:

Range → {y| y ≥ -11}

Step-by-step explanation:

Range of a function is the set of of y-values.

Given function is,

f(x) = 2x² + 6x - 8

By converting this equation into vertex form,

f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]

     = [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]

     = [tex]3[(x+1)^2-\frac{11}{3}][/tex]

     = [tex]3(x+1)^2-11[/tex]

Vertex of the parabola → (-1, -11)

Therefore, range of the function will be → y ≥ -11

The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

The range of a function is the set of output values of the function

Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.

So, df(x)/dx = d(3x² + 6x - 8)/dx

= d(3x²)/dx + d6x/dx - d8/dx

= 6x + 6 + 0

= 6x + 6

Equating the experssion to zero, we have

df(x)/dx = 0

6x + 6 = 0

6x = -6

x = -6/6

x = -1

From the graph, we see that this is a minimum point.

So, the value of y = f(x) at the minimum point is that is a t x = - 1 is

y = f(x) = 3x² + 6x - 8

y = f(-1) = 3(-1)² + 6(-1) - 8

y = 3 - 6 - 8

y = -3 - 8

y = -11

Since this is a minimum point for the graph, we have that y ≥ -11.

So, the range of the function is {y|y ≥ -11}

So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

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9514 1404 393

Answer:

  120 days

Step-by-step explanation:

Using the formula for simple interest, we can solve for t:

  I = Prt

  t = I/(Pr) = 608/(22800×.08) = 608/1824 = 1/3 . . . . year

For "ordinary interest", a year is considered to be 360 days, so 1/3 year is ...

  (1/3)(360 days) = 120 days

It will take 120 days for the loan to earn 608 in interest.

Answer:

1.5 cubic metres

Step-by-step explanation:

Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.

The total number of parts = 1 + 2 + 3 = 6 parts.

The amount of marvel present the concrete mix = amount of marvel / total mix

= 3 parts / 6 parts = 1/2

Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:

Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres

Answer: He can make 36 different salds

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

hope it is well understood?

The slope is 4 and y- intercept is 13

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

Given

Slope

y = 4x-3

dy/dx = 4

slope =  4

intercepts y = 4(4) 3

y = 16-3

y = 13

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9514 1404 393

Answer:

  [tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  [tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]

Answer:

A. Increase speed to approximately 7.1 mph so that you cover the field more.

Step-by-step explanation:

The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.

Answer:

a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches

The sampling distribution of the sample means annual rainfall for California is 1.278.

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

The sampling distribution of the sample means annual rainfall for New York is 1.0435.

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Step-by-step explanation:

California:

[tex]\mu_{1} = 22[/tex] inches.

[tex]\sigma_{1}[/tex] = 7 inches.

[tex]n_{1}[/tex] = 30 years.

New York:

[tex]\mu_{2} = 42[/tex] inches.

[tex]\sigma_{2}[/tex] = 7 inches.

[tex]n_{2}[/tex] = 45 years.

a)

[tex]E(\bar x) = \mu_{1} = 22[/tex] inches

[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Answer:

Point estimate = 76.4

Margin of Error = 2.680

Step-by-step explanation:

Given that distribution is approximately normal;

The point estimate = sample mean, xbar = 76.4

The margin of error = Zcritical * s/√n

Tcritical at 95%, df = 42 - 1 = 41

Tcritical(0.05, 41) = 2.0195

Margin of Error = 2.0195 * (8.6/√42)

Margin of Error = 2.0195 * 1.327

Margin of Error = 2.67989

Margin of Error = 2.680

Answer:

1197 miles.

Speed(s) = 63 mph

Time(t) = 19 hours

Distance(d) = ?

We know,

D = S × T

= 63 × 19

= 1197 miles

Answer:

see explanation

Step-by-step explanation:

Using the identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x

sin2x = 2sinxcosx

Consider left side

cosθ × sin2θ

= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )

= 2sin²θ

= 2(1 - cos²θ)

= 2 - 2cos²θ

= right side , then established

Answer:

3/5 so A.

Step-by-step explanation:

Answer:

slope = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)

m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

5

Step-by-step explanation:

the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.

and that is automatically the result. there is not anything else to it.

9514 1404 393

Answer:

Step-by-step explanation:

We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.

"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."

1. Move terms to the left side

2.Subtract the numbers

3.Use the quadratic formula

4.Simplify

5.Separate the equations

6.Solve

Rearrange and isolate the variable to find each solution.

Solution,

Solution

x=5±√39

Given:

The cost function is:

[tex]C(x)=0.28x^2-0.7x+1[/tex]

where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.

To find:

The minimum production cost.

Solution:

We have,

[tex]C(x)=0.28x^2-0.7x+1[/tex]

It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:

[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,

[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]

[tex]-\dfrac{b}{2a}=1.25[/tex]

Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.

[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]

[tex]C(x)=0.28(1.5625)-0.875+1[/tex]

[tex]C(x)=0.4375+0.125[/tex]

[tex]C(x)=0.5625[/tex]

Therefore, the minimum production cost is 0.5625 million dollars.

Answer:

The minimum cost is 0.5625.

Step-by-step explanation:

The cost function is

C(x) = 0.28x^2 - 0.7 x + 1

Differentiate with respect to x.

[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]

The minimum value is

c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1

C = 0.4375 - 0.875 + 1

C = 0.5625

Answer:

ON = KJ

Step-by-step explanation:

JKL = NOP

We know the angles match

<J = <N

<K = <O

< L = <P

And we know

JK = NO

KL =  OP

JL = NP

We are looking for ON = KJ

9514 1404 393

Answer:

  (d)  KJ

Step-by-step explanation:

The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.

The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.

9514 1404 393

Answer:

  y = 16

Step-by-step explanation:

Perhaps you want to solve ...

  10 +√y = 14

  √y = 4 . . . . . . subtract 10

  y = 4² = 16 . . . square both sides

Answer:

How should we proceed with this question

Answer:

Step-by-step explanation:

This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.

We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is

[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:

The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];

the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];

and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:

[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and

[tex]\frac{dA}{dt}=72+56[/tex] so

[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]

Answer:

Statement A is correct

Step-by-step explanation:

Statement A is correct:  Model A1 (0.25) is more prefered than Model C3 (0.15)

Answer:

Here is your answer.....

Hope it helps you....

Answer:

Step-by-step explanation:

You need to put parentheses around the radicands.

√z · √(30z²) · √(35z³) = √(z·30z²·35z³)

= √(1050z⁶)

= √(5²·42z⁶)

= √5²√z⁶√42

= 25z³√42

The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been the expression as:

⇒ √z · √(30z²) · √(35z³)

Multiply and remove all perfect squares from inside the square roots

⇒ √(z·30z²·35z³)

⇒ √(1050z⁶)

⇒ √(5²·42z⁶)

Assume z is positive.

⇒ √5²√z⁶√42

⇒ 25z³√42

Therefore, the obtained expression would be 25z³√42.

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f(x) = 2x³ - 3x² + 7

f(-1) = 2(-1)³ - 3(-1)² + 7

=> f(-1) = 2(-1) - 3(1) + 7

=> f(-1) = -2 -3 + 7

=> f(-1) = 2

f(1) = 2(1)³ - 3(1)² + 7

=> f(1) = 2(1) - 3(1) + 7

=> f(1) = 2 -3 + 7

=> f(1) = 6

f(2) = 2(2)³ - 3(2)² + 7

=> f(2) = 2(8) - 3(4) + 7

=> f(2) = 16 - 12 + 7

=> f(2) = 11

Answer:

3.51%

Step-by-step explanation:

From the given information:

For the first stream, the present value can be computed as:

[tex]= 100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}}[/tex]

Present value for the second stream is:

[tex]=\dfrac{600}{(1+i)^{10}}[/tex]

Relating the above two equations together;

[tex]100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}} =\dfrac{600}{(1+i)^{10}}[/tex]

consider [tex]v = \dfrac{1}{1+i}[/tex], Then:

[tex]\implies 100+200v^n + 300v^{2n} = 600 v^{10}[/tex]

where:

[tex]v^n = 0.75941[/tex]

Now;

[tex]\implies 100+200(0.75941) + 300(0.75941))^2 = 600 (v)^{10}[/tex]

[tex](v)^{10} = \dfrac{100+200(0.75941) + 300(0.75941))^2 }{600}[/tex]

[tex](v)^{10} = 0.7082[/tex]

[tex](v) = \sqrt[10]{0.7082}[/tex]

v = 0.9661

Recall that:

[tex]v = \dfrac{1}{1+i}[/tex]

We can say that:

[tex]\dfrac{1}{1+i} = 0.9661[/tex]

[tex]1 = 0.9661(1+i) \\ \\ 0.9661 + 0.9661 i = 1 \\ \\ 0.9661 i = 1 - 0.9661 \\ \\ 0.9661 i = 0.0339 \\ \\ i = \dfrac{0.0339}{0.9661} \\ \\ i = 0.0351 \\ \\ \mathbf{i = 3.51\%}[/tex]

Answer:

b. 01285 esa es, espero este buena y que te ayude

Step-by-step explanation:

use the equation of the straight line

y-y1=m (x-x1)

y-2=-2(x+4)

y-2= -2x-8

y= -2x-8+2

y= -2x-6

I hope this helps

Step-by-step explanation:

6 carpets=1month

10 carpets=?

1month=31 days

10 /6*31

51

Step-by-step explanatio

Answer: Volume of Cylinder A is                          pi times the area of the base times the height

                                                             π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3

Volume of Cylinder B is likewise             pi times the area of the base times the height

                                                             π r2 h = (3.1416)(6)(6)(7)   = 791.68 ft3

After pumping all of Cyl A into Cyl B

there will remain empty space in B         791.68 – 753.98 = 37.7 ft3  

The percentage this empty space is

of the entire volume is                            37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth  

.

Step-by-step explanation: I hope that help you.

Note: you may not need to type in the percent sign.

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

Explanation:

Let's find the volume of water in container A.

Use the cylinder volume formula to get

V = pi*r^2*h

V = pi*5^2*8

V = 200pi

The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.

We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.

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

Now find the volume of cylinder B

V = pi*r^2*h

V = pi*6^2*6

V = 216pi

Despite being shorter, tank B can hold more water (since it's more wider).

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

Now divide the results of each section

(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%

This shows us that 92.59% of tank B is 200pi cubic feet of water.

In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.

This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%

Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.