which of the following statements are true​

Answer:

Step-by-step explanation:

[tex]\dfrac{8^2}{2^{10}}\\=\dfrac{(2^3)^2}{2^{10}}\quad (8=2^3)\\\\=\dfrac{2^6}{2^{10}}\\\\=\dfrac{1}{2^{4}}=\dfrac{1}{16} \\\\or \quad 2^{-4} .[/tex]

Answer:

C

Step-by-step explanation:

negative exponent flips the fraction

4^2=16

x^2 becomes x^4

y becomes y^2

The statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

If we have two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = a, this implies that the values of the functions a(x) and b(x) are equal at x = a.

Then the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

So, the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

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You define complex numbers as the reals, i, as usually defined, and their linear combinations using real coefficients, then,

The reals are complex numbers, even if you haven’t fully defined their properties.

If you define complex numbers as the form (a,b) with and a, b are real numbers, then you can say that each real number a is isomorphic with that complex number,

if b=0 once you define their properties.

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Of course, (0,1) will be i. You’ll have to define the multiplication rule, etc.

In actual usage, we gloss over the distinction, and real numbers are complex numbers with no imaginary part.

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BC = EF

the side has to lie between the two angles

Answer:

-x^3-5x^2+10x-4

Step-by-step explanation:

(−x + 1) (x ^ 2 + 6x − 4) = (-x)(x ^ 2 + 6x − 4) + 1(x ^ 2 + 6x − 4)

= -x^3-6x^2+4x+x^2+6x-4 = -x^3-5x^2+10x-4

Answer:

(4,6)

Step-by-step explanation:

To calculate the midpoint of two points, just calculate the arithmetic mean (average) of the x and y values of the two points given. For example, it is easy to see visually that the midpoint of (2, 0) and (4, 0) is (3, 0), since (3,0) falls right in the middle of the two points. However, the way to calculate this would be to take the average of 2 and 4 (3), along with the average of 0 and 0 (0). This process gives us our new point (3, 0). In case this doesn't make sense, here is the formula for the midpoint of two points - (x1,y1) and (x2,y2):

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

For this problem, E is (2,4) and F is (6,8). So, the midpoint would be:

[tex](\frac{2+6}{2},\frac{4+8}{2})=(\frac{8}{2},\frac{12}{2})=(4,6)[/tex]

Therefore, the midpoint is (4,6)

Answer:

Invalid statement: There is exactly 1 yellow marble in the box

Step-by-step explanation:

The probability of finding a yellow marble is Py = 1/30, according to the sample. Then, the number of yellow marbles expected to find in the box is:

N x Py > 1 ,

where N = 250 (number of marbles in the box).

Thus, we expect to find more than one yellow marble in the box and the Invalid statement is: "There is exactly 1 yellow marble in the box".

Answer:

1/5

Step-by-step explanation:

P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.

P = 3/15 = 1/5

The decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

From the given graph, the function value decrease at the following x values

This can be properly represented as:

x ≤ -6, 1 < x ≤ 5 and x > 6

Hence, the decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

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The verbal description matches option D; Gene earns 2% interest after depositing $150 into his account.

The function is a type of relation, or rule, that maps one input to specific single output.

The function given;

f(x) = 0.02 x +150

Gene earns 2% interest after depositing $150 into his account.

Thus, this verbal description matches the function given as it represents, the total account balance Gene.

Hence, Option D is the correct answer.

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Answer:

x= -2, -11

Step-by-step explanation:

The slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

Given that;

y ≥ -x + 4

First, we use the slope intercept form y = mx + b to determine the slope and y-intercept.

y ≥ -x + 4

y = mx + b

We can see that;

m = -1

b = 4

Hence, the slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

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The test statistic z will be equal to -0.946 and it shows that there is no significant difference in the proportion of rehires between full time and part time.

Given sample sizes of 833 and 386 and result of samples 434 and 189.

[tex]n_{1} =833, n_{2}=386[/tex]

Proportion  of full time=434/833=0.52

Proportion of part time=189/386=0.49.

Difference in proportion =0.52-0.49

[tex]H_{0}:[/tex]TTF- i∈ rho=0

[tex]H_{1}:[/tex] TTF+i∈ rho≠0.

Mean of difference=0.03

Z=(X-μ)/σ

σ=[tex]\sqrt{0.4517/447}[/tex]

=0.0317

σ=0.0317

z=(0-0.03)/0.0317

=-0.03/0.0317

=-0.317

p value will be =0.1736.

Because p value is greater than 0.01 so we will accept the null hypothesis which shows that there is no significant difference in the proportions.

Hence there is no significant difference in the proportion of rehires between full time and part time.

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Answer:

[tex] \tt \: x.( - 1).( - x).(1)[/tex]

[tex] \longrightarrow \tt ( - x). (- x)[/tex]

[tex] \longrightarrow \boxed{\tt{x}^{2} }[/tex]

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The probability that the company will be fined is 0.1587.

From the information given, it was assumed that μ = 500 ml and σ = 10 ml.

Also, the random sample of 5 bottles has a sample mean under 490 ml.

Here, the probability will be:

= P(x < 490)

= P[(z < (490 - 500)/10]

= P (z < -10/10)

= P(z < -1)

Looking at this under the z table, the probability will be 0.1587

The probability is 0.1587.

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Answer:

4 ounces

Step-by-step explanation:

I'm assuming when it says: [tex]33\frac{1}{3}%[/tex]% it means 33.3333333333 instead of 33/3.

Anyways under that assumption, we currently have 20 ounces in the grape juice, since 4 ounces is grape juice concentrate and 16 ounces is water. So currently let's just say that the total amount of grape juice concentrate is going to be: [tex](4+x)[/tex] where x is the amount of grape juice concentrate you need to add to make it 33.33%. The next thing to know is how to calculate how much percent a is of b. This can be calculated using the equation: [tex]\frac{a}{b}*100[/tex]. So in this case the a is going to be the grape juice concentrate, and the b is going to be the entire mixture (water and grape juice). Since the concentrate is having x added to it, that means the entire thing is also having x added to it. This means we have the equation: [tex]\frac{4+x}{20+x} * 100[/tex], since we already have 4 ounces of grape juice concentrate, and we already have 20 ounces in total (16 ounces of water + 4 ounces of grape juice). This is going to be equal to 33.33%, or in other words 33 1/3. So to make this a bit easier, I'm going to convert this mixed fraction into one fraction, this gives you the fraction: [tex]\frac{100}{3}[/tex]. So now that's all left to do is set these two expressions equal to each other and solve for x

Original equation

[tex]\frac{4+x}{20+x}*100=\frac{100}{3}[/tex]

Divide both sides by 100

[tex]\frac{4+x}{20+x}=\frac{100}{3}\div 100[/tex]

Keep fraction, change division to multiplication, flip 100

[tex]\frac{4+x}{20+x}=\frac{100}{3}* \frac{1}{100}[/tex]

The 100 in the numerator will cancel out the one in the denominator

[tex]\frac{4+x}{20+x}=\frac{1}{3}[/tex]

Multiply both sides by 20+x

[tex]4+x=\frac{20+x}{3}[/tex]

Multiply both sides by 3

[tex]3(4+x)=20+x[/tex]

Distribute the 3

[tex]12+3x=20+x[/tex]

Subtract x from both sides

[tex]12+2x=20[/tex]

Subtract 12 from both sides

[tex]2x=8[/tex]

Divide both sides by 2

[tex]x=4[/tex]

So Kahn needs to pour 4 more ounces of grape juice, to double check this, since the mixture already has 4 ounces of grape juice, this means the final mixture will have a total of 8 ounces of grape juice concentrate, and a total of 24 ounces, since it already had 16 ounces of water, and 4 ounces of grape juice and now there is 4 more ounces of grape juice being added, so a total of 24 ounces. this means that 8/24 will be grape juice concentrate or in other words: [tex]\frac{1}{3}[/tex] and when you multiply this by 100 (to convert to percent), you get 100/3 or 33 1/3%

Using the ASA congruence theorem, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

Two triangles are congruent by the ASA congruence theorem if they have two pairs of corresponding congruent angles and a pair of included congruent sides.

In the proof given in the diagram, using the ASA congruence theorem, Rowena has been able to prove that ΔACD and ΔECB have two pairs of corresponding congruent angles and a pair of included congruent sides.

Therefore, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

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Answer:

A   see picture

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

       The ratio of the side of 30-60-90 triangle is x : x√3 : 2x

 The angle opposite to 90° = 2x

            2x = 10

              x = 10÷2

               x = 5

The side opposite to 30° is x which is 5.

The side opposite to  60° is x√3 = 5√3

The ratio of sides of 30-60-90 triangle:

        5 : 5√3 : 10

Answer:

The first one is correct

Step-by-step explanation:

I got a 100 on the test, hope this helps

Using translation concepts, the transformation is given as follows:

a) Polygon A has been translated down then right.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the orientation of the polygon is the same, hence there was no rotation nor reflection, which means that option A is correct.

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Answer:

B) Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

I'm pretty sure :P

Answer:

Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

Answer: y=[tex]\sqrt[3]{x}[/tex]-4

Step-by-step explanation:

The statement that apply is that the volume of the cone is One-third the volume of the cylinder

volume of a cone = 1 / 3 πr²h

where

Volume of a cylinder = πr²h

where

The cone and the cylinder has the same base and height. Therefore, the radius and height are the same .

volume of the cylinder = 84π

Therefore, the volume of the cone is One-third the volume of the cylinder.

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Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

[tex]f(x)=a(x-2)(x-6)[/tex]

Substituting in the coordinates of the vertex,

[tex]-4=a(4-2)(4-6)\\\\-4=-4a\\\\a=1[/tex]

So, the equation is [tex]f(x)=(x-2)(x-6)[/tex]

On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]

Answer:

(2, -32)

Step-by-step explanation:

1) Expand them.

y = 2(x² - 6x + 2x - 12)

y = 2(x² - 4x - 12)

y = 2x² - 8x - 24.

2) Complete the square to find the vertex.

y = 2([x² - 4x)] - 24

y = 2[(x - 2)² - 4] - 24

y = 2(x - 2)² - 8 - 24

y = 2(x - 2)² - 32

The vertex: (2, -32)

or you can use this: x = -b/2a

x = -(-8)/2(2)

x = 8/4

x = 2

Substitute the value into the original equation for y.

y = 2(2)² - 8(2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

Vertex: (2, -32)

Answer:

  (2, -32)

Step-by-step explanation:

The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.

The given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x -6) = 0   ⇒   x = 6

The midpoint between these values of x is their average:

  x = (-2 +6)/2 = 4/2

Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...

  x = 2

Using this value of x in the quadratic relation, we find the y-value at the vertex to be ...

  y = 2(2 +2)(2 -6) = 2(4)(-4)

  y = -32

The coordinates of the vertex are (x, y) = (2, -32).

The number of different meals possible is 96, computed using combinations.

The combination is a method of choosing a number of articles from a larger set of articles in no particular order.

In the question, we are asked about the different dinner meals possible when a dinner meal is made up of an appetizer, a main course, a dessert, and a drink.

The choices for the appetizer are soup or salad, so the number of ways of choosing an appetizer = 2C1 = 2.

The choices for the main course are chicken, fish, steak, or lobster, so the number of ways of choosing a main course = 4C1 = 4.

The choices for the dessert are ice cream, pie, sorbet, or pastry, so the number of ways of choosing a dessert = 4C1 = 4.

The choices for the drink are coffee, tea, or milk, so the number of ways of choosing a drink = 3C1 = 3.

The total number of ways is the product of all of them.

Therefore, the total number of ways = 2*4*4*3 = 96.

The number of different meals possible is 96, computed using combinations.

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Answer:

Step-by-step explanation:

4x + 2(-2X +1) = -2

Order of operations -

4x + -4x +2 = -2

Combine terms

4x-4x=0x

2 = -2

Answer:

no solution

Step-by-step explanation:

y = - 2x + 1 → (1)

4x + 2y = - 2 → (2)

substitute y = - 2x + 1 into (2)

4x + 2(- 2x + 1) = - 2 ← distribute parenthesis and simplify left side

4x - 4x + 2 = - 2 ( subtract 2 from both sides )

0 = - 4 ← not possible

this indicates the system of equations has no solution

Answer:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

Step-by-step explanation:

Given functions:

  [tex]p(x)=2x-4[/tex]

  [tex]r(x)=\dfrac{6x-1}{9x+1}[/tex]

Solve for p(x) = r(x):

[tex]\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}[/tex]

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=18, \quad b=-40, \quad c=-3[/tex]

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}[/tex]

Therefore, the solutions are:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

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Answer: Algebraic expression

Step-by-step explanation: