In the accompanying diagram, ΔA′B′C′ is the image of ΔABC. Which type of transformation is shown in the illustration?

A. rotation
B. translation
C. reflection
D. dilation

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:

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:

3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]

Step-by-step explanation:

You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.

If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.

What do we know?

We know that there are 15 billiard balls.

We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.

And the other 7 balls are striped.

Now we want to find the probability for a randomly selected ball to be a striped ball.

Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).

Then we have:

P = 7/15 = 0.467

That quotient is also what is called the "odds"

So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.

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A line of symmetry would separate a shape to make multiple shapes that are exactly the same.

The answer is C.2

Answer:

7.3

Step-by-step explanation:

y=2.5x+5.8

=2.5×0.6+5.8

= 1.5+.8

=7.3

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Answer:

  12

Step-by-step explanation:

Apparently, you want the sum a+b when ...

  [tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]

A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...

  a+b = 9+3 = 12

Answer:

12

Step-by-step explanation:

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:

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:

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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#SPJ2

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:

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.

9514 1404 393

Answer:

  120

Step-by-step explanation:

I find it pretty easy to obtain the solution by graphing ...

  c(x) -13865 = 0

The positive value of x that makes this so is x = 120.

120 units will have a cost of 13,865 to manufacture.

__

If you like to solve this algebraically, you can probably do it most easily by completing the square.

  x^2 -5x = -65 +13865

  x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)

  (x -2.5)² = 13806.25

  x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting

  x = 117.5 +2.5 = 120

Answer: He can make 36 different salds

Step-by-step explanation:

Answer:

Each triangle is a right triangle.

Step-by-step explanation:

You can see each one has one 90 degree corner.

Answer:

13. True

14. True

15. False

Step-by-step explanation:

By using the Pythagorean Theorem a^2+b^2=c^2, you can evaluate whether or not the triangles are right triangles.

13. 8^2+15^2=17^2   ->  64+225=289  -> TRUE

14. 50^2+120^2=130^2  -> 2500+14400=16900  -> TRUE

15. 12^2+35^2=36^2  -> 144+1225 =/=1296 -> FALSE

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:

7 1/2

Step-by-step explanation:

2 1/2 ÷ 1/3

Change to an improper fraction

(2*1+2)/2 ÷ 1/3

5/2 ÷1/3

Copy dot flip

5/2 * 3/1

15/2

Change to a mixed number

7 1/2

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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Answer:

24

Step-by-step explanation:

The number of rows (x) should b equal to the number of columns (x).

x²=576

x=√576 taking the square root of the product

x=24

Answer:

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

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.

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

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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."

Answer:

Four places to the left.

Step-by-step explanation:

14.6/10000

=> 1.46/1000 [Shifted 1 decimal place after dividing by 10]

=> 0.146/100 [Shifted 1 decimal place after dividing by 10]

=> 0.0146/10 [Shifted 1 decimal place after dividing by 10]

=> 0.00146   [Shifted 1 decimal place after dividing by 10]

Number of decimal places = 1+1+1+1=4

Four places to the left.

Answer:

0.19

Step-by-step explanation:

Jane bought a shoe for 54.82 euros

She gave the store owner 55 euros

= 55-54.82

= 0.18 euros to franc

= 0.18× 1.08222

= 0.19 franc

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:

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:

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

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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.

Answer:

3.418

Step-by-step explanation:

3.4175

3.4178

u round if the number behind it is higher than 5