-x + 12y = -27 and -5x + 3y = -21

Mr. Phillips can fill 10 bottles of paint with the 64 ounces of blue paint and five bottles of paint with the 12 ounces of yellow paint, for a total of fifteen 6-ounce bottles.

He has 64 ounces of blue paint and 12 ounces of yellow paint. In order to figure out how many 6-ounce bottles of paint he can fill with the quantities of pain, he must divide the amount of paint by the size of the bottles. For the blue paint, he needs to divide 64 ounces by 6 ounces, which will equal 10.6 (rounded down to 10). For the yellow paint, he needs to divide 12 ounces by 6 ounces, which will equal 2 (rounded up to 3). This means that he can fill 10 bottles of paint with the 64 ounces of blue paint and three bottles of paint with the 12 ounces of yellow paint, for a total of thirteen 6-ounce bottles. The process of figuring out how many bottles of paint can be filled with the given amounts of paint is a simple one. It requires the painter to divide the amount of paint by the size of the bottles. Once the painter knows the answer, they can use it to accurately fill the appropriate number of bottles for their project. This is an important skill for a painter to have as it helps them plan for the necessary supplies and create a successful project.

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Answer:

To solve the problem, we need to find the maximum height reached by the ball after the 7th bounce, given that each bounce has a rebound height of 20% less than the previous maximum height.

Let's start by finding the maximum height reached by the ball on the first bounce. The ball is dropped from a height of 120.00 inches, so the maximum height reached on the first bounce is:

120.00 inches

For each subsequent bounce, the maximum height reached is 20% less than the previous maximum height. We can express this mathematically as:

maximum height = 0.8 * previous maximum height

Using this formula, we can calculate the maximum height reached on the second bounce as:

maximum height on 2nd bounce = 0.8 * 120.00 inches = 96.00 inches

On the third bounce, the maximum height reached is 20% less than 96.00 inches:

maximum height on 3rd bounce = 0.8 * 96.00 inches = 76.80 inches

We can continue this pattern for each subsequent bounce. The maximum height reached on the fourth bounce is:

maximum height on 4th bounce = 0.8 * 76.80 inches = 61.44 inches

The maximum height reached on the fifth bounce is:

maximum height on 5th bounce = 0.8 * 61.44 inches = 49.15 inches

The maximum height reached on the sixth bounce is:

maximum height on 6th bounce = 0.8 * 49.15 inches = 39.32 inches

Finally, the maximum height reached on the seventh bounce is:

maximum height on 7th bounce = 0.8 * 39.32 inches = 31.46 inches

Therefore, the maximum height reached by the ball after the 7th bounce is approximately 31.46 inches. Rounded to the nearest hundredth, this is 31.45 inches.

Answer:

The answer will be B. y= -3x +6

The exponential function that passes through (0,3) and (1,6) is [tex]f(x) = 3(2^{x})[/tex]

An exponential function is a mathematical function in which an independent variable appears in the exponent. In other words, the function has the form f(x) = [tex]a^{x}[/tex], where 'a' is a constant greater than 0 and not equal to 1, and 'x' is the independent variable.

To find the exponential function that passes through (0,3) and (1,6), we need to determine the values of 'a' and 'b' in the function [tex]f(x)=a(b^{x})[/tex].

First, we can use the point (0,3) to find the value of 'a'. Plugging in x=0 and y=3, we get:

3 = [tex]ab^0[/tex]

3 = a

Next, we can use the point (1,6) to find the value of 'b'. Plugging in x=1 and y=6, we get:

6 = [tex]ab^1[/tex]

6 = 3b

b = 2

Now that we have the values of 'a' and 'b', we can write the exponential function in the form [tex]f(x)=a(b^{x})[/tex]. Substituting 'a' and 'b' into the equation, we get: [tex]f(x) = 3(2^{x})[/tex]

Therefore, the exponential function that passes through (0,3) and (1,6) is [tex]f(x) = 3(2^{x})[/tex]

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Answer:

length = 3x - 1

Step-by-step explanation:

Area of a rectangle = length x width

or using l = length, w = width and A = area

A = l x w

or

l = A/w

Given
A = 18x² - 6x
w = 6x

l = 18x²- 6x/6x

= 18x²/6x - 6x/6x

= 3x - 1

Answer:

3x - 1

Step-by-step explanation:

Area of the Rectangle:

18x^2 - 6x

6x (3x - 1)

Width = 6x

Length =?

Area of Rectangle = Length *  Width

Length = Area/breadth

6x (3x -1) / 6x cross out 6x

Thus, Length of Rectangle = 3x - 1

As X is a discrete uniformly distributed random variable with a mean of 5, a variance of 4, and a range of values from 1, 2, 3, 5, 6, 7, 8, and 10, we know that X can have any one of these values with an equal probability of 1/10.

Calculating the likelihood that X will have a number equal to or greater to 6 is necessary to get [tex]P(X > =6)[/tex]. Due to the fact that X is a continuous uniformly distributed random variable.

We may calculate this probability simply counting all number of potential values for X that are greater or equal to to 6, dividing by the entirety of the potential values for X, and then adding the results together.

The probability of X is more than or equivalent to 6 is given by the fact there are a total of 5 variables of X that are at least equal to 6, namely: 6, 7, 8, 9, and 10.

[tex]P(X > =6) = 5/10 = 1/2[/tex]

Thus, (b) 1/2 is the right response.

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Answer:

El espacio recorrido en el tercer segundo será de 9 m.

Step-by-step explanation:

Answer:

The length of x is (10√3)/3.

Step-by-step explanation:

Using the trigonometric ratios of a 30-60-90 triangle, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, we have:

x/2 = (5/√3)

Multiplying both sides by 2, we get:

x = 10/√3, which can be simplified to:

x = (10√3)/3

So the length of x is (10√3)/3.

Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]

Answer: The total number of possible outcomes in the lottery can be calculated by finding the number of ways to choose 5 distinct numbers out of 70, and then multiply that by the number of possible choices for the gold ball (1 out of 25). So:

Total number of outcomes = (70 choose 5) * 25 = 25,989,600

To win the jackpot, the player must match all 5 white ball numbers and the gold ball number. The number of ways to do this is simply 1, since there is only one winning combination.

Therefore, the probability of winning the jackpot with a single ticket is:

Probability of winning = (number of winning outcomes) / (total number of outcomes) = 1 / 25,989,600

So the probability of winning the jackpot with a single ticket is approximately 0.00000003846, or 1 in 25,989,600.

Step-by-step explanation:

The sοlutiοn οf the given prοblem οf cubοid cοmes οut tο be the cubοid has a density οf abοut 6.0 g/cm³.

In geοmetry, a hypercube is a cοncrete οr muti shape. A hypercube is a cοnvex pοlygοns with 12 sides, 6 rectangular faces, and 8 edges. A cubοid is anοther term fοr the creature. An οbject with six square sides is called a cube. Bricks and literature are amοng the items fοund in bοxes. The main differences between cubic but alsο cubic are as fοllοws.

Here,

This equatiοn can be changed tο read density = mass/vοlume. Since we already knοw the mass (534 g), we can use the rearranged methοd tο determine the vοlume.

=> Vοlume = L, W, and H, and mass = 534 g.

=>  density equals mass/vοlume

=>  weight = 534/ (L x W x H)

The CRC Encyclοpedia οf Chemistry and Physics states that nickel has a density οf 8.908 g/cm³.

Thus, we can enter this number as a substitute in οur fοrmula tο οbtain:

=>  density =  534/(L, W, H)

=> 8.908 g/cm³.

Tο sοlve fοr density, we can rewrite this equatiοn as fοllοws:

=>  density =  534/(L, W, H)

=>  6.0 g/cm³ (tο 1 decimal place)

Cοnsequently, the cubοid has a density οf abοut 6.0 g/cm³.

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To decrease the probability of type I error in order to avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

The researchers should decrease the significance level to decrease the probability of type I error. This is because a type I error occurs when the null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that the diagnostic tool is not effective in detecting the condition.

If the researchers decrease the significance level, they are decreasing the probability of making a type I error, which means they are less likely to conclude that the diagnostic tool is effective when it is actually not. This will help the researchers avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

In general, the significance level (also known as the alpha level) is the probability of making a type I error. By decreasing the significance level, the researchers are making the criteria for rejecting the null hypothesis more stringent, which reduces the likelihood of making a type I error.

It is important to note that decreasing the significance level will also decrease the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false.

However, in this case, the researchers are more concerned with avoiding the more consequential error of falsely concluding that the diagnostic tool is effective, so decreasing the significance level is the appropriate action to take.

In conclusion, the researchers should decrease the significance level to decrease the probability of type I error in order to avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

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The radius is equal to the length of the given line segment GH, which is 20 units. In this case, r = 20, and θ = 90° = π/2 radians.

Arc GJ is the portion of the circumference of circle H that lies between points G and J. Arc GJ can be calculated using the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = GH = 20 and θ = 90° = π/2 radians. Therefore, l = 20π/2 = 10π. Therefore, the length of arc GJ is 10π units.For example, if the radius of circle H is 10 units, l = 10π/2 = 5π. Thus, the length of arc GJ would be 5π units.To calculate arc GJ, we must first determine the radius of circle H. The radius is equal to the length of the given line segment GH, which is 20 units. We then use the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = 20, and θ = 90° = π/2 radians.

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The correlation coefficient between X and Y is approximately -0.483.

We must first determine the mean and standard deviation for both X and Y in order to calculate the correlation coefficient between X and Y.

X has a mean of:

(-5 + 1 + 2 + 11)/4 = 2.25 is the mean of X.

Y has a mean of:

average of Y = (5 + 3 - 3 + 0)/4 = 1.

The value of X's standard deviation is

s_X = sqrt([(-5 - 2.25)^2 + (1 - 2.25)^2 + (2 - 2.25)^2 + (11 - 2.25)^2]/3) = 5.1478

The value of Y's standard deviation is

s_Y = sqrt([(5 - 1)^2 + (3 - 1)^2 + (-3 - 1)^2 + (0 - 1)^2]/3) = 3.7712

After that, we can figure out the correlation between X and Y:

cov(X, Y) = [(-5 - 2.25) × (5 - 1) + (1 - 2.25) × (3 - 1) + (2 - 2.25) × (-3 - 1) + (11 - 2.25) × (0 - 1)]/3 = -7.25

We can finally determine the correlation coefficient:

r = cov(X, Y)/(s X, s Y)=-7.25/(5.1478 3.7712)=-0.483

Thus, roughly -0.483 is the correlation coefficient between X and Y.

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The length of JG is 5 units if ∠EDH ≅ ∠EDG. Thus option b is the correct answer as per the given relation.

The Given data is as follows:

∠EDH ≅ ∠EDG

Here in the question it is given that, ∠EDH is similar to ∠EDG

The corresponding sides of two triangles are congruent are similar to each other.

EH=9, EJ=4.

EH = EG

EG = 9 -------equation(1)

EG = EJ+JG

EG = 4+JG -------equation(2)

From equations 1 and 2, we get

9 = 4 + JG

9 - 4 = JG

JG = 5 units

Therefore, we can conclude that the length of JG is 5 units.

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The complete question is-

In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?

a. 4 units

b. 5 units

c. 6 units

d. 9 units

Answer: 5

Step-by-step explanation:

∠EDH ≅ ∠EDG, EH=9, EJ=4.Corresponding sides of two triangles are congruent.                         (CPCTC)              .... (1)From the given figure it is clear that        ... (2)Using (1) and (2), we getSubtract 4 from both the sides.

Answer:

34 m x 18 m

Step-by-step explanation:

No picture shown, but we can do it anyway. If one inch on the drawing is actually 4 meters, multiply each dimension by 4.
The actual length is (8.5 * 4) = 34 meters.
The actual width is (4.5 * 4) = 18 meters.

The actual dimensions of the pool are 34 meters long and 18 meters wide.

The probability that there will be at least 81 cartoons on a coming Saturday is given as follows:

0.011 = 1.1%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 65, \sigma = 7[/tex]

The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:

Z = (81 - 65)/7

Z = 2.29

Z = 2.29 has a p-value of 0.989.

Hence:

1 - 0.989 = 0.011 = 1.1%.

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Answer: y=3x-2

Step-by-step explanation

(-8)-(7)/ (-2)- (3) = -15/ -5= 3

y=3x+b

f(-2)= -8

y= 3x+ b

-8= 3(-2)+b

-8=-6+b

add 6 on both sides

b=-2

y=3x-2

From the given expression, 3/4(8x+12)+x-5, the simplified expression is 7x + 4.

From the question, we are to simplify the given expression.

To simplify the expression 3/4(8x+12)+x-5, we can follow the order of operations, which is commonly remembered using the acronym PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Using PEMDAS, we can simplify the expression as

3/4(8x+12)+x-5

Distributing 3/4 to the terms inside the parentheses

= 3/4 * 8x + 3/4 * 12 + x - 5

Simplifying the multiplication

= 6x + 9 + x - 5

Combining like terms

= 7x + 4

Hence, the simplified expression is 7x + 4.

Here is the complete question:

Simplify 3/4(8x+12)+x-5

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Since the point (2, 3) lies on the line 2x + ky = 19, the value of k is equal to 5.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making k the subject of formula, we have the following:

k = (19 - 2x)/y

Since the point (2, 3) lies on the line, we have:

k = (19 - 2(2))/3

k = (19 - 4)/3

k = 15/3

k = 5.

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Answer:

2 kph

Step-by-step explanation:

10 kilometers in 5 hours.

1 hour = ?

10/5 = 2 Kilometers

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a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

The definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.

a) The two formulae for cooking times are:

(66 x weight in kg) + (35 x time in an electric oven

Microwave oven time = (26 x weight in kg) + 15

We can compare the two formulae by looking at their coefficients and constants.  This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b) (66 x weight in kg) + (35 x time in an electric oven

2 x 60 = (66 x weight in kg) + 35

120 - 35 = 66 x weight in kg

85 = 66 x weight in kg

weight in kg = 85 / 66

weight in kg ≈ 1.29

So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

Microwave oven time = (26 x weight in kg) + 15

Microwave oven time = (26 x 1.29) + 15

Microwave oven time ≈ 48.34 minutes

Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

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44. cos(x+1x​)

46. sec(x+1x​)

47. tan−1(2x+1​x​)

16.cscxcosx+cotx

17.1+sinx

18.1+cosx

19. cotx−1

29. True

30 True

31. True

32. True

33. True

40. False. The equivalent expression is sin2θ−1+tan2θcos2θ​

41.  False. The equivalent expression is 3sin2θ+4cos2θ−3

42.  False. The equivalent expression is cotθ+cosθsecθ+tanθ​−sec2θ

For the following exercises, find the function if sint=x+1x​:

For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression:

For the following exercises, verify the identity:

For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression:

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Answer:

The answer would be the second one.

Step-by-step explanation:

The answer is this because 65% as a decimal is .65 and the second equation is the only one with a .65 in it. It is also the only equation with 24 in it as well.

The equation for the line with a slope of 5/6 and passing through the point (22,12) is y=5/6x - 16.

The equation for the line with a slope of 5/6 and passing through the point (22,12) can be expressed as y=5/6x + b. To calculate the value of b, we can plug in the given point's coordinates, (22,12), into the equation. This will result in the equation 12=5/6(22)+b. Solving for b, we get b=-16. Therefore, the equation for the line is y=5/6x-16.

In summary, we can express the equation for the line with a slope of 5/6 and passing through the point (22,12) as y=5/6x - 16. To calculate the value of b, we plugged the point's coordinates, (22,12), into the equation, resulting in the equation 12=5/6(22)+b. Solving for b, we got b=-16. Thus, the equation for the line is y=5/6x - 16.

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The Quadratic formula in standard form for points (2.5, 1.5), (2,0) and (3,0) are x²-4x + 3.75 = 0 and x² -2x = 0

The standard form of a quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number

The given parameters that will help us to find the equations are

x = 2.5, and x =  1.5

(x-2.5) (x- 1.5)

Opening the brackets we have

x²-1.5x -2.5x + 3.75 = 0

x²-4x + 3.75 = 0

and the second is given as 2,0

x=2 and x=0

(x-2)(x-0)

Opening the brackets we have

x² -0 -2x+0 = 0

x² -2x = 0

Therefore the standard forms for the quadratic equations are x²-4x + 3.75 = 0 and x² -2x = 0

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Answer:

x ≈ 17

Step-by-step explanation:

using the cosine ratio in the right triangle

cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] ( multiply both sides by x )

x × cos62° = 8 ( divide both sides by cos62° )

x = [tex]\frac{8}{cos62}[/tex] ≈ 17 ( to the nearest whole number )

well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4  and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).

To get the equation of any straight line, we simply need two points off of it, let's use those two above.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}[/tex]

Check the picture below.

Refer to the attached images.

The values of f and g that has been worked out is given as 6 and 8

This is a question that would examine the combination of two shapes into one.

We have area of a triangle = base * height / 2

this would give

f * 4 / 2 = 60 - 48

2f = 12

divide through by 2

f = 12 / 2

f = 6

we have f * g = 48

given that the value of f = 6

g * 6 = 48

6g = 48

Divide through by 6 to get the value of f

6 g / 6 = 48 / 6

g = 8

Hence the value of f is given as 6 and the value of g is given as 8

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 11 &\implies x -11=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -11 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{3em}1( x +2 )( x -11 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-9x-22=f(x) \end{array}} ~\hfill[/tex]

From the graph and the given information, the value of the given function, fg(-3), is 9

From the question, we are to determine the value of the function, fg(-3).

First , we will determine the value of g(-3)

From the given information,

g(x) = 1/(2 + x)

Substitute x = -3 in the function to determine the value of g(-3)

g(-3) = 1/(2 + (-3))

g(-3) = 1/(2 - 3)

g(-3) = 1/-1

g(-3) = -1

Now,

fg(-3) = f(g(-3))

Thus,

fg(-3) = f(-1)

Now, we will determine the value of f(-1) from the given graph.

From the graph, we can read that the value of f(-1) is 9

Hence,

The value of fg(-3) is 9

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