Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution

The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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0 = 0 indicates that (d) there are infinitely many solutions to the system.

Equations can have one, zero, multiple or infinitely many solutions.

The end result of the given equation is given as:

\(0 = 0\)

The above equation means that:

The equation has infinitely many solutions.

Hence, the true statement is (d)

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Answer:

There are infinitely many solutions to the system. (D)

Step-by-step explanation:

edge 2022

Answer:

2(2.5) + 2(4.5) + 2(1.75) + 3.25

= 5 + 9 + 3.5 + 3.25 = 14 + 6.75 = 20.75

= 20 3/4 feet

The length of the wall is 20 3/4 feet.

The value of c is -3.

The factorization of the polynomial is \((x+3)(x^3-3x+2)\).

Given that:-

Polynomial P(x) = x⁴ + 3x³ + cx² - 7x + 6 is divisible by (x + 3).

We have to determine the value of c and factorize the polynomial.

Using remainder theorem, putting x = -3 in the given polynomial, we get

\(P(-3)= (-3)^4+3(-3)^3+c(-3)^2-7(-3)+6=0\)

P(-3) = 81 -81 +9c +21 +6 = 0

9c + 27 = 0

9c = -27

c = -27/9 = -3

Dividing the given polynomial  x⁴ + 3x³ -3x² - 7x + 6  by (x + 3), we get,

\(x^3-3x+2\)

Hence, the factorization of the polynomial is given by:-

\((x+3)(x^3-3x+2)\)

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Answer:

15 students on each bus!

Step-by-step explanation:

100-10(with parents)

90÷6(how many busses)

15 students on each

The students travelling on each bus are 15.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

Total number of students is given as 100.

The students to travel on car are 10.

Then, the students to travel on bus are given by following operation as,

Total students - Students to travel on car

⇒ 100 - 10 = 90

Now, the students on each bus can be obtained by using the division operation as below,

Students to travel on bus ÷ Total number of bus

⇒ 90 ÷ 6 = 15

Hence, the number of students on each bus is obtained as 15.

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Answer:

the graph of w passe through point (8,-6)

Step-by-step explanation:

When you draw a line through points (-5, 7) and (3, -1) points (8,-6) also meets the line segment at the very bottom.

Answer:

The graph of w passes through (8,-6)  (FIRST ANSWER)

Step-by-step explanation:

The equation of the graph is -1x+2, therefore no other answer works

The slope is -1, not 2

The Y-intercept is (0,2), NOT the X-intercept

The zero is 2, not -1

Therefore, the only correct answer is The graph of w passes through (8,-6)

I hope this helps and good luck!

Answer:

The correct option is;

C. Marginal frequency

Step-by-step explanation:

The objective of comparison of two distributions is to check the significant difference from each other

The general measures used to compare the difference between distributions are the measures of centers such as the mean, the measures of spread such as the standard deviation and the shape of the compared distribution curves

Marginal frequencies are the values found in the total row and total column portion of a two way frequency distribution table

The marginal frequency is used to calculate the marginal relative frequency

The values of the marginal frequency, which is a sum, does not characterize the details of a distribution to a large extent.

Answer:

C. Marginal frequency

Step-by-step explanation:

The value of the variable x is  125 degrees

It is important to note that alternate angles are equal.

Also, angles at a point is 360 degrees

From the information given in the diagram, we have that;

70 degrees and and the angle tangent to C are equal, so we have;

70 degrees + x degrees + x degrees + 40 degrees = 360 degrees

Let's represent mathematically;

70 + x + x + 40 = 360

collect the like terms

70 + 2x + 40 + 360

2x = 360 - 110

Subtract the values

2x = 250

make 'x' the subject of formula

x = 250/2

divide the values

x = 125 degrees

Hence, the value is 125 degrees

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Answer:

No this is not right

Step-by-step explanation:

The correct answer is 32

Answer:

I think the actual answer is 32, so its incorrect

Step-by-step explanation:

Answer:

  $24,000

Step-by-step explanation:

The difference for principal amount P is ...

  (8% × P) - (7 3/4% × P) = $60

  0.0025P = $60

  P = $24,000 . . . . . multiply by 400

His principal was $24,000.

Answer:

Parallel: Y= -7/3x - 37/3

Perpendicular: Y=3/7x + 7

Step-by-step explanation:

Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.

Remember when the slope is parallel it's always the same slope in this case -7/3

When perpendicular flip it and change the sign 3/7

Answer:

Commutative.

Associative property works on symbols instead of signs!

Answer:

associative property

Step-by-step explanation:

[a+b]+(c)=(a)+[b+c]

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

Answer:

Correct choice: C. \(x=\pm\sqrt{10}\mathbf{i}\)

Step-by-step explanation:

The quadratic equation to solve is:

\(x^2+10=0\)

Since this equation is incomplete, we can solve it without using the quadratic solver formula.

Subtracting 10:

\(x^2=-10\)

Taking square root:

\(x=\pm\sqrt{-10}\)

Recall the square root of a negative number leads to imaginary solutions where the Unit Imaginary Number (i) is used, where:

\(\mathbf{i}=\sqrt{-1}\)

The solutions to the equation are:

\(x=\pm\sqrt{10}\mathbf{i}\)

Correct choice: C. \(x=\pm\sqrt{10}\mathbf{i}\)

Answer:

Look at the step by step explanation

Step-by-step explanation:

The utility function u(x) = 0.25**(x/200) is consistent with Pablo's preferences.

To determine which utility function, represented by u(x), is consistent with Pablo's preferences, we need to compare the utility values for different prospects.

Pablo's certain equivalent for a deal with a 0.8 chance at $500 and a 0.2 chance at $100 is $300. We can calculate the expected value of this prospect:

Expected value = (0.8 * $500) + (0.2 * $100) = $400 + $20 = $420

Now let's evaluate the utility values for the given utility functions and compare them to $300 and $420.

a) u(x) = 10 - 10x^4 - x/200

If we substitute x = $420 into this utility function, we get:

u($420) = 10 - 10($420)^4 - $420/200 ≈ -1.06 x 10^18

b) u(x) = 1 - 0.25 - x/200

If we substitute x = $420 into this utility function, we get:

u($420) = 1 - 0.25 - $420/200 = 1 - 0.25 - 2.1 ≈ -1.35

c) u(x) = 5 - 2x^4 + x/300

If we substitute x = $420 into this utility function, e get:

u($420) = 5 - 2($420)^4 + $420/300 ≈ -1.59 x 10^16

d) u(x) = 0.25**(x/200)

If we substitute x = $420 into this utility function, we get:

u($420) = 0.25**(420/200) ≈ 0.063

Comparing the utility values to Pablo's certain equivalent ($300) and the expected value ($420), we find that option d) u(x) = 0.25**(x/200) is consistent with Pablo's preferences, as it yields a utility value (0.063) closer to the expected value than the others.

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Answer: 160

Step-by-step explanation:

12+37+78

The recursive definition is a formula that gives the nth term of the sequence as a function of one or more of the preceding terms of the sequence. Recursive definitions are used in mathematics to define sequences of numbers, where each term of the sequence is a function of one or more of the preceding terms of the sequence.

A recursive definition of the sequence {4,8,16,32,64,....} is given by the formula T(n) = 2T(n-1) with T(1) = 4. This formula states that each term in the sequence is double the preceding term. That is, to find the nth term of the sequence, we find the (n-1)st term of the sequence and multiply it by 2.

The recursive definition of a sequence is a formula that gives the nth term of the sequence as a function of one or more of the preceding terms of the sequence. Recursive definitions typically consist of two parts: a formula for the first term (or first few terms) of the sequence and a formula for each subsequent term that depends on one or more preceding terms.

A recursive definition of the sequence {4,8,16,32,64,....} can be obtained using the formula T(n) = 2T(n-1) with T(1) = 4. To find the nth term of the sequence, we find the (n-1)st term of the sequence and multiply it by 2. For example, T(2) = 2T(1) = 2(4) = 8, T(3) = 2T(2) = 2(8) = 16, and so on. Hence, the recursive definition of the sequence {4,8,16,32,64,....} is given by T(n) = 2T(n-1) with T(1) = 4.

:The recursive definition is a formula that gives the nth term of the sequence as a function of one or more of the preceding terms of the sequence. Recursive definitions are used in mathematics to define sequences of numbers, where each term of the sequence is a function of one or more of the preceding terms of the sequence.

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Answer:

Here’s the answer! Best of luck.

Step-by-step explanation:

Answer:

Similar Triangles must have matching angles, so you need to prove the angles all match.

Step-by-step explanation:

1.

Angle RTW = Angle STV becasue it's the same angle.

2.

Because ST is parallel to RW and RT cuts through those two parallel lines, you have

Angle TSV = Angle TRW because they are corresponding angles.

3.

Because ST is parallel to RW and TW cuts through those two parallel lines, you have

Angle TVS = Angle TWR because they are corresponding angles.

So now you know the three angles in each triangle match the three angles in the other triangle.  They're similar triangles.

The probability that Anna picks out two red sweets and eat them is equal to (x² - x)/870 in terms of x.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 30

number of red sweets = x

number of blue sweets = 30 - x

probability of Anna picks out 2 red sweets = x/30 × (x -1)/29

probability of Anna picks out 2 red sweets = (x² - x)/870

Therefore, the probability that Anna picks out two red sweets and eat them is equal to (x² - x)/870 in terms of x.

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Answer:

2.1

Step-by-step explanation:

using cosine theorem or substraction of two vector

b = AC = 5

c = AB = 6

a² = b² + c² - 2bc cos A

a² = 5² + 6² - 2*5*6 cos 20°

a² = 4.62

a = √4.62

a = 2.149

a ≈ 2.1

Answer: x = 15.035677095729 approximately

Round this however you need to.

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

Explanation:

I'm assuming you want to find the value of x, which your diagram is showing to be the length of segment QR.

If so, then we'll need to find the measure of angle Q first. Using the law of sines, we get the following:

sin(Q)/q = sin(R)/r

sin(Q)/PR = sin(R)/PQ

sin(Q)/13 = sin(85)/19

sin(Q) = 13*sin(85)/19

sin(Q) = 0.6816068987

Q = arcsin(0.6816068987) ... or ... Q = 180-arcsin(0.6816068987)

Q = 42.9693397461 ... or ... Q = 137.0306602539

These values are approximate.

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

Now if Q = 42.9693397461 approximately, then angle P is

P = 180-Q-R

P = 180-42.9693397461-85

P = 52.0306602539

Similarly, if Q = 137.0306602539 approximately, then,

P = 180-Q-R

P = 180-137.0306602539-85

P = -42.0306602539

A negative angle is not possible, so we'll ignore Q = 137.0306602539

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

The only possible value of angle P is approximately P = 52.0306602539

Let's apply the law of sines again to find side p, aka segment QR

sin(P)/p = sin(R)/r

sin(P)/QR = sin(R)/PQ

sin(52.0306602539)/x = sin(85)/19

19*sin(52.0306602539) = x*sin(85)

19*sin(52.0306602539)/sin(85) = x

x = 15.035677095729

This value is approximate.

Round this value however you need to.

Answer:

Call x is childrens

Call y is adults

x + y = 386 (1)

1,75x + 2,5y = 807,5 (2)

(1) => x = 386 - y => (2) 1,75 ( 386-y )+2,5y = 807,5

0,75y=132 => y = 176 and x = 210

Step-by-step explanation:

Answer:78.5

Step-by-step explanation:

the median is the middle digit so with 10 different numbers it would be the 5th or sixth number  

but you have to first have them in least to greatest order

53,59,68,70,75,82,82,87,94,95

5th+6th/2

75+82= 157

157/2

78.5  

hope its helpful

Answer:

3,-2,-7,-12,-17,-22

when going up add, when going down subtract.

Example: -2+5=3

-17-5=-22

Answer:

21 Pounds =

9.5254398 Kilograms

(rounded to 8 digits)

Step-by-step explanation:

K, x<18 is the inequality.

Step-by-step explanation:

Calculate the term