In art class students are mixing black and white paint to make gray paint. Julian mixes 9 cups of black paint and 8 cups of white paint. Harper mixes 7 cups of black paint and 5 cups of white paint. Use Julian and Harper's percent of black paint to determine whose gray paint will be darker.

The measure of the acute angles are 62° and 28° .

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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The term for breaking a number into smaller sections and multiplying these numbers is factorization.

This is a common method used in math that implies breaking a big number into smaller ones and then multiplying the numbers. This multiplication should lead you to the original number.

120 can be broken as 12 and 10, then 12 × 10 = 120

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The probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].

To find the probability of getting two numbers whose sum is greater than 9:

The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Set of numbers greater than 9:

{(5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

Formula:

Favorable event / Total number of events = [tex]\frac{5}{36}[/tex]

Therefore, the probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].

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Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

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

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]

[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]

[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]

In one decimal point:

[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]

This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

[tex]x^2+3x-40=0[/tex]

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

[tex](x+8)(x-5)=0[/tex]

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

[tex]x+8=0\\x=-8[/tex]    [tex]x-5=0\\x=5[/tex]

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

3a) The coordinate of R after dilation is; R' = (-6, 21)

3b) The coordinate of T after dilation is; T' = (1, 3)

5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.

3a) We are given the coordinates of the rectangle as;

Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)

Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;

R' = (-2 *3), (3 * 7)

R' = (-6, 21)

3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;

Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))

Coordinate of T' = (-2, 7) + ¹/₂(6, -8)

Coordinate of T' = (-2, 7) + (3, -4)

Coordinate of T' =  (1, 3)

5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.

Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)

Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.

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The probability that the number chosen is divisible by 5 is; 1/5.

It follows from the task content that the number of possible outcomes in the probability event is; 100. Additionally, the number of required outcomes is 20 as only 20 numbers are divisible by 5.

Ultimately, the required probability is; 20/100 = 1/5.

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Answer:

4

Step-by-step explanation:

If the probability of drawing a yellow jelly beans is 1/4, the box is has 1/4 yellow jellybeans.

1/4b=6

b=24

14+6+x=24

20+x=24

x=4

Answer:

36 blue jelly beans

Step-by-step explanation:

We can find the total number of jelly beans by adding all red, yellow, and blue jelly beans together.

14+6+x

This simplifies to 20+x

For probability, it is (the number of things you want)/(the total number of things there are).

If the probably of drawing a yellow jelly bean is 1/4, we can set up this equation:

[tex]\frac{14}{20+x}=\frac{1}{4}[/tex]

We can cross multiply:

[tex]20+x=14(4)\\x+20+56\\x=36[/tex]

There are 36 blue jelly beans.

Answer:

20 hrs

Step-by-step explanation:

growth per hour=5%

no of hrs to double=100/5=20

(it may be wrong)<3

Answer: Joe's number is a negative number.

Since the number's opposite is greater in value, the number's value is in the negatives.

The equation which has the values as given in the task content is; y= x² -3x -5.

By convention, the general form representation of a quadratic equations is;

y = ax² + bx +c.

Hence, it follows that when the equation has an a-value of 1 a b-value of -3 and a c-value of -5, the equation is; y= x² -3x -5.

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Answer:

This would be true for a rectangle and a square.

Step-by-step explanation:

Rectangles and square have 90 angles.  The exterior angles would also equal 90 because 90 + 90 is 180.  An interior angle and the exterior angle are supplements (add together to 180).

Answer:

A) 1/9, 3, 27

Step-by-step explanation:

i think you mean 3^x (and not 3x).

because otherwise none of the answer options withdraw makes any sense.

3^-2 = 1/(3²) = 1/9

3¹ = 3

3³ = 27

The polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

The GCF is given as:

GCF = 5z

This means that the polynomial can be represented as:

P(z) = GCF * Another factor

We can make use of the following function

P(z) = 5z * (z - 1)

Expand

P(z) = 5z^2 - 5z

Rewrite as:

P(z) = -5z + 5z^2

Hence, the polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

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we conclude that the system of inequalities has more solutions than the system of equations.

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

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The sum of two terms are:

The sum of two numbers is one that tells you to find the sum of two or more numbers, and as such, you have to add the numbers altogether.

t₅, ₃ =  5 + 3

= 8

t₁₁, ₂ = 11 + 2

= 13

t₁₅,₁₃ =  15 + 13

= 28.

Hence the correct sum of two terms are:

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"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.

A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.

Some characteristics of meta analysis are-

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Answer:

the 4th answer option. W = 153°, P = 71°

Step-by-step explanation:

PQRS ~ TUVW

that means both figures are similar.

and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.

we see due to the proportions of the different parts of the shapes

U corresponds to Q.

T corresponds to P.

W corresponds to S.

V corresponds to R.

therefore, as the angle at S = 153°, so is W.

and as the angle at T = 71°, so is P.

The inflation rate between 2017 and 2018 is 2.86%.

Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.

The inflation rate = (2018 CPI / 2017 CPI) - 1

(180 / 175) - 1 = 0.0286 = 2.86%

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Answer:

Step-by-step explanation:

The correct answer would be C (-6,3).  The y axis is the bold line going up and down on the middle of the page.   If you were able to pick up triangle and flip it over the y axis.  Point C would land at (-6,3).

Also, you can see that point C is six spaces to the right of the y axis.  That means when we flipped it over the axis, it will now be six paces to the right of the y axis.  Since the point did not go up or down when you flipped it.  It is still 3 spaces above the x axis.

Answer:

D (-6, 3)

Step-by-step explanation:

the point C is originally (6, 3).

that means the x coordinate is 6, the y coordinate is 3.

now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.

the y axis is the vertical coordinate axis in the middle of the graph.

so, what is going to happen to the point ?

will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.

so, it will keep the same y coordinate : 3.

will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.

so, +6 turns into -6 (as the y axis represents x=0).

Answer:

Step-by-step explanation:

I got you  first you want to get some little ceasers

Answer:

4. b) an angle

5. b) the angles of a triangle

6. b) opposite, hypotenuse and adjacent

Step-by-step explanation:

4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.

If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.

Answer: b) angle

5. angles of a triangle

6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.

Answer: opposite, hypotenuse and adjacent

The data should be displayed using a line graph, as shown in the attached figure.

Definition of a Line Graph

In a line graph, also known as a line plot or a line chart, each data point is connected by its own line. A line graph displays numerical values across a chosen time span.

Why is a line graph the best choice in this situation?

A line graph would be the best option for showing the data for David's family's grocery spending over the previous 10 weeks because it would show us the trend in the data. This graph tells us of how we can recognize instances where there were significant expenses by analyzing the trend from the line graph.

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Step-by-step explanation:

[tex] {2}^{4n} \times {2}^{2n} = 512[/tex]

[tex] {2}^{4n} \times {2}^{2n} = {2}^{9} [/tex]

[tex] {2}^{4n + 2n} = {2}^{9} [/tex]

[tex]6n = 9[/tex]

[tex]n = \frac{3}{2} [/tex]

Step-by-step explanation:

hello : here is an solution

Answer:

The answer is X=3/4 or -1/2

Answer:

D.10

Step-by-step explanation:

Mode is the number that is repeated the most as we can see the number 10 is there 3 times in the data. 13 isn't there, 14 is only there once and 16 is also not there

In a(n) reversal design, two or more treatments are alternated relatively quickly on a regular schedule.

Reversal designs are used to observe the impact of a remedy on the conduct of a single player. The participant is observed time and again previous to remedy to establish a baseline stage of behavior.

One ought to not use a reversal layout with behaviors that aren't reversible. For instance, if you train a person to fish, that man or woman is not probable to forget about how to fish, making a reversal design a negative preference for evaluating your fishing intervention.

Reversal layout: reversing among remedies (e.g., baseline, treatment, NCR, treatment, NCR, remedy, and many others.) Withdrawal design: reversing among treatment and no treatment (e.g., baseline, remedy, baseline, treatment, etc.)

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It takes 165 minutes per week if 10% increase in volume for an exercising client.

A client is exercising for 150 minutes per week. I.e., 30 minutes, 5 days per week.

So, 10% increase results,

30 minutes × 10% = 3

So, the increased minutes per day = 30 + 3 = 33 minutes/day.

After the 10% increase, the minutes per day = 33 minutes

Since 5 days a week, he does exercise, the total minutes per week

= 33 × 5 = 165 minutes.

So, a 10% increase in volume would result in 165 minutes total per week.

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