Evaluate the expression for x = 6.
12 + 2x - 5
A. 19
B. 79
C. 14
D. 54

Using a linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

Since there are currently 368 glasses(y-intercept), and each set on sale comes with 10 glasses(slope), the number of glasses after x sales is given by:

y = 368 + 10x.

She needs at least 673 glasses, hence the inequality is:

[tex]y \geq 673[/tex]

[tex]368 + 10x \geq 673[/tex].

Now we solve the inequality to find the number of sets needed:

[tex]10x \geq 305[/tex]

[tex]x \geq 30.5[/tex]

As the number of sets is an integer number, the solution is:

[tex]x \geq 31[/tex].

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[tex]not \: penny \: or \: dime = quarter \: or \: nickle[/tex]

[tex]p(x) = \frac{13 + 18}{86} = \frac{31}{86} = 0.36[/tex]

[tex]gallons \: for \: car \: 1 = \frac{450}{18} = 25 \: gal[/tex]

[tex]gallons \: for \: car \: 2 = \frac{450}{25} = 18 \: gal[/tex]

[tex]we \: need \: 25 + 18 = 43 \: gallons[/tex]

[tex]43 \times 2.49 = 107.07 \: dollars[/tex]

Using the binomial distribution, it is found that there is a 0.3125 = 31.25% probability of getting 2 goals out of 5.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

n = 5, x = 2, p = 0.5.

Hence the probability is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

0.3125 = 31.25% probability of getting 2 goals out of 5.

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Answer:

9/19

Step-by-step explanation:

To write the probability as a fraction, put the total number on the bottom and put the number of ways the event can happen, put that on top.

They said there are 38 slots. That's the total, it goes on the bottom.

Landing on an Odd Number is the event we're looking at. There are 18 ways that can happen: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

That number 18 (bc 18 ways to get an odd number) goes on top.

P(Odd) = 18/38

Always simplify when possible.

18/38

= 9/19

Answer:

[tex]14\sqrt{2}[/tex]

Step-by-step explanation:

In a 45°-45°-90° triangle, the legs = x and the hypotenuse = [tex]x\sqrt2}[/tex]

x = 14

[tex]x\sqrt{2} =14\sqrt{2}[/tex]

Answer:

d

Step-by-step explanation:

14 startroot 2 endroot cm

Answer:

$36

Step-by-step explanation:

14.40 is 40% of 36.

Answer:

$36

Step-by-step explanation

40/100 = 14.4/?

100 * 14.4 = 1440

1440 / 40 = 36

The correct hypothesis that can be set up for this test is given as

H0: mu = 5.8

Ha: mu ≠ 5.8

This is the method of inference that is made in a statistical testing in order to know if the dat available is able to support the claims that have been made.

What the manufacturer wants to know is the average filling of the machine. If it is within 5.8 or not.

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Answer: x=0 x=2i x=-2i

if your factoring: x(x^2+4)

Step-by-step explanation:

(if your solving for x)

[tex]x^{3} +4x\\x(x^{2} +4)\\\\x=0\\\\x=\frac{-b}{2a}\frac{+}{-} \frac{\sqrt{b^2-4ac}}{2a} \\\\x=\frac{0}{2}\frac{+}{-} \frac{\sqrt{0^2-16}}{2} \\x={0}}\frac{+}{-} \frac{\sqrt{-16}}{2} \\[/tex]

[tex]x={0}}\frac{+}{-} \frac{4i}{2} \\\\\\x=\frac{+}{-}2i[/tex]

Answer:

6.93

Step-by-step explanation:

formula to find height of equilateral triangle is [tex]\frac{\sqrt{3} }{2} *A[/tex] A is the side of the equilateral triangle

Answer:

6.93 inches

(first option listed)

Step-by-step explanation:

we can find the height of this triangle by turning it into a right triangle, and then using the Pythagorean Theorem

(process shown in photo)

hope this helps!! have a lovely day :)

The solution to the equations is; +1/2, -1/2, +√2, and -√2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

[tex]4x^4 + 7x^2 - 2 = 0\\\\[/tex]

The factored form of the polynomial regression

[tex](4x^2 -1)(x^{2} + 2)[/tex]

So,

[tex](4x^2 -1) = 0\\\\4x^2 = 1\\\\x = \pm \dfrac{1}{2}[/tex]

Also,

[tex](x^{2} + 2) = 0\\\\x^{2} = - 2\\\\x = \pm \sqrt{2}[/tex]

Hence, the solution to the equations are;

+1/2, -1/2, +√2, and -√2.

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Answer:

ABCF

Step-by-step explanation:

Answer:

81pi

Step-by-step explanation:

You are asking yourself the area of pi*r^2 could with r as 9. pi*9^2. solve and you get 81pi :D

The true statement about functions is D. If f and g are functions, then (f + g)(-2) = (g + f)(-2).

It should be noted that a function is used to define the relationship that's exist between rte variables.

In this case, when f and g are functions, then (f + g)(-2) = (g + f)(-2).

Therefore, the correct option is D.

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A graph is a way to represent a lot of data in such a visual format. The correct statements are A, B, and D.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The statement that is correct about the given table is,

A.) The largest total number of electronic devices sold was on Wednesday.

B.) The smallest number of TVs sold was on Monday.

D.) On Tuesday, more tablets were sold than any other type of electronic device

hence, the correct statements are A, B, and D.

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Two common tangents occur when two circles intersect each other at two points.

It should be noted that two common tangents are also referred to as transverse common tangents.

In this case, two common tangents occur when two circles intersect each other at two points.

The diagram is attached.

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Answer: undefined

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-13-12}{5-5}[/tex]

[tex]\frac{-25}{0}[/tex]

= undefined

The congruency statement is true TS ≅ HG. so option C is correct.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given information;

Triangle G H J is rotated 90 degrees about point X to form triangle S T R.

Triangle GHJ is rotated 90° about point X, resulting in triangle STR.

Now, if any triangle is rotated 90 degrees about a point the two sides will be ≅ to each other.

So, ST = GH

RT= HJ

SR= GJ

<S= <G

<T = <H

<R=<J

The side TS ≅ HG.

Hence, option (c) is correct.

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Answer:

C

Step-by-step explanation:

Trust me bro

Answer:

Answer A is correct

Step-by-step explanation:

4 (-15 - 3p ) - 4 (-p + 5 )

First, solve the brackets.

-60 - 12p + 4p - 20

Combine like terms.

- 80 - 8p

∴ - 8p - 80

Answer:

The red is the pre-image. The blue is after the 1st transformation. The green is after the 2nd transformation.

Step-by-step explanation:

This is because; you can see the tiny marks. 1 mark next to the letter represents 1 transformation while 2 marks next to letter symbolize the 2nd transformation! I hope this helped you :D

If [tex]1-4x\ge0[/tex], then by definition of absolute value

[tex]|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32[/tex]

On the other hand, if [tex]1-4x<0[/tex], then

[tex]|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2[/tex]

So, the overall solution to the inequality is interval union

[tex]\left(x < -\dfrac32\right) \cup (x > 2)[/tex]

the answer for the question above is 9/5

5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.

We need to determine the equation, in vertex form, for the following parabolas.

We can find the parabola's equation in vertex form following two steps:

Step 1: Use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)²+k.

Step 2: Find the value of the coefficient a by substituting the coordinates of the point into the equation written in step 1 and solving for a.

Now, substitute (−2, 5) in y=a(x−h)²+k

⇒y=a(x−(-2))²+5

Now, substitute (2, 0) in y=a(x−(-2))²+5.

0=a(2+2)²+5

⇒a=-5/16

So, y=-5/16(x+2)²+5

⇒16y=-5(x²+4x+4)+5

⇒16y=-5x²-20x-20+5

⇒5x²+20x+16y-15=0.

Therefore, 5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.

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Question : Prism A and Prism B have the same volume. Which could be the dimensions of prism B?

Prism A :

Length = 8 feet

Width = 4 feet

Height = 5 feet

Prism B:

Length = ? feet

Width = ? feet

Height = ? feet

Option 1:

Length = 6 feet

Width = 10 feet

Height = 2 feet

Option 2:

Length = 4 feet

Width = 4 feet

Height = 10 feet

Option 3:

Length = 5 feet

Width = 4 feet

Height = 7 feet

Option 4:

Length = 8 feet

Width = 4 feet

Height = 6 feet

Here, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet.

We know that if the a and b be the length and width of the base respectively and c be the height of a prism, then the volume of the prism is abc.

Given that

length of 1st prism = 8 feet

width of 1st prism = 4 feet

height of 1st prism = 5 feet

So volume of 1st prism = 8 * 4 * 5 = 160 feet³

Now the volume of 1st and 2nd prisms are the same.

So, we have to check the options for length, width, and height of the 2nd prism.

1st option:

Height = 6 feet

Width = 10 feet

Length = 2 feet

So, volume = 6 * 10 * 2 = 120 feet³

Then the 1st option is incorrect.

2nd option:

Height = 4 feet

Width = 4 feet

Length = 10 feet

So, volume = 4 * 4 * 10 = 160 feet³

Then the 2nd option is correct.

Therefore, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet. The 2nd option is correct.

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Answer: Each owner gets $300000

Step-by-step explanation:

one and a half million is 1500000

then divide by 5

you get $300000

Answer:

There are two sets of numbers that meet the criteria:

1)  8 and 16, or

2) -8 and -16

Step-by-step explanation:

Let's call the two numbers A and B.

We are told:

1) A-B=8, and

2) A^2 + B^2 = 320

Rearrange 1) to solve for A:

A=8+B

Use this value of A in the second equation:

A^2 + B^2 = 320

(8+B)^2 + B^2 = 320

(64+ 16B + B^2) + B^2 = 320

2B^2 + 16B + 64 = 320

B^2 + 8B + 32 = 160

B^2 + 8B + 32 = 160

B^2 + 8B - 128 = 0

(B+16)(B-8)=0

B is either -16 or +8

Assuming B = 8

Then from A-B=8 we find that A = B+8 and A = 16

Does A^2 + B^2 = 320?

  (16)^2 + (8)^2 = 320?

  256 + 64 = 320?  YES

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

Assuming B=-16

If B=-16, then from A-B=8 we find that A = 8+(-16) and A = -8

Does A-B=8?

 -8 - (-16) = 8?  YES

Does A^2 + B^2 = 320?

 (-8)^2 + (-16)^2 = 320?

 64  + 256 = 320?  YES

Using a geometric sequence, the formula for the number of kilograms of fruit sold on the nth day is:

[tex]f(n) = 5(3)^{n - 1}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For this problem, the first term and common ratio are given as follows:

[tex]a_1 = 5, q = 3[/tex]

Hence the function can be written as:

[tex]f(n) = 5(3)^{n - 1}[/tex]

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Answer:

6

Step-by-step explanation:

The inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.

In the question, we are given that George bought socks for $300.

Therefore, George's total cost = $300.

We assume the number of pairs of socks George sells to be s.

The unit price per pair quoted by George = $6

Therefore, George's total sales = $6s.

We know that the profit over a transaction is given as the difference between sales and costs, that is,

The profit = The total sales - the total costs,

or, profit = 6s - 300.

In the question, we are required to make a profit of more than 210.

This can be shown by the inequality,

6s - 300 > 210.

Thus, the inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.

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Using proportions, it is found that the farmer has planted 258 acres.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

He plants 413 acres during the entire year, hence, considering he plants an equal amount daily, and the year is 5/8 over, the amount he has planted is:

A = (5/8) x 413 = 258 acres.

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