Kathryn asked 156 people to rate colors were purple, blue, and green as she is creating a new logo using one of her original doodle designs. She found the responses in the ratio 5-3-4. How any people chose purple?

A. 13
B. 65
C. Not possible to tell based on the given information
D. 60

Answer:

5y + 2y - 4x + 4x = -7 +14

7y = 7

y = 1

2(1) + 4x = 14

4x = 12

x = 3

Step-by-step explanation:

Using the process of elimination

Add both equations. The 4x will be eliminated since one is positive and one is negative. The equation is left with only the y variable and the constant.

When y is found, input it into the second equation to find x.

Answer:

52 R17

Step-by-step explanation:

52 * 36 = 1872

1889 - 1872 = 17

--> 52 R17

to achieve the same overall speedup, approximately 66.67% (two-thirds) of all dynamically executed instructions should be optimized using enhancement Y.

Let's denote the fraction of dynamically executed instructions optimized using enhancement Y as "p." Since enhancement Y makes the optimized instructions only 75% faster, the remaining fraction of instructions (1-p) will not be optimized and will maintain their original speed.

To achieve the same overall speedup, we need to equate the performance improvement gained from enhancement X and enhancement Y.

For enhancement X, 50% of the instructions are optimized and made three times faster, resulting in an overall speedup of 1.5 (3/2).

For enhancement Y, a fraction "p" of the instructions is optimized and made 75% faster, while the remaining fraction (1-p) remains the same. This results in an overall speedup of (1-p) + 0.75p = 1 - 0.25p + 0.75p = 1 + 0.5p.

To achieve the same overall speedup as enhancement X, we set up the equation:

1.5 = 1 + 0.5p

Solving for "p," we find:

0.5p = 0.5

p = 1/2

Therefore, to achieve the same overall speedup, approximately 66.67% (two-thirds) of all dynamically executed instructions should be optimized using enhancement Y.

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Answer:

d.

Step-by-step explanation:

Answer:

y = 5x - 3

Step-by-step explanation:

equation of a straight line is y = mx + b where m=slope and b=y-intercept

in this case m=5 and b= -3

y = mx + b

y = 5x - 3

answer:

Lin should have about 19 novels in total when you add up all the amounts she gets after 3 months.

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

Step-by-step explanation:

A regular quadrilateral has 4 congruent sides and 4 angles

Conjecture: Every prime number greater than 2 is odd. A positive integer is a whole number greater than zero. In other words, it is a number that does not include fractions, decimals, or negative values. Positive integers include the numbers 1, 2, 3, 4, 5, and so on.

Indirect Proof:

Assume, for the sake of contradiction, that there exists a prime number greater than 2 that is even.

Let's suppose this even prime number is represented as 2n, where n is a positive integer.

By the definition of an even number, 2n can be divided by 2 without leaving a remainder.

Since 2n is a prime number, it can only be divided by 1 and itself.

Considering the assumption, 2n can be divided by 2 without leaving a remainder, contradicting the definition of a prime number.

Therefore, our assumption that there exists an even prime number greater than 2 is false.

Thus, every prime number greater than 2 must be odd.

By proving the assumption false and reaching a contradiction, we have indirectly established the validity of the conjecture that every prime number greater than 2 is odd.

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The table that shows the distribution of q to r illustrates a direct variation

The proportionality constant from q to r is 1/8

From the table, we have the following points

When q = 48, r = 6

The proportionality constant is then calculated as:

k = r/q

Substitute known values

k = 6/48

Divide

k = 1/8

Hence, the proportionality constant from q to r is 1/8

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Given:

The recursive formula is:

For n = 2, 3, 4, ...

If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.

As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.

We are required to determine the characteristic name for the above mentioned events.

And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events,  the events "a" and "b" are be disjoint.

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If x is the number 0.222…, then 10x = 2.222…. Subtracting x from 10x eliminates the fractional part, so that

10x - x = 2.222… - 0.222…

==>   9x = 2

and solving for x gives x = 2/9.

Answer:

The equation of the line through the given points is y = (1/2)x + 1.

Step-by-step explanation:

To find the equation of a line passing through two given points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Given the points (7, 2) and (-1, 0), we have:

m = (0 - 2) / (-1 - 7) = -2 / -8 = 1/4

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) represents one of the given points. Let's choose the point (7, 2):

y - 2 = (1/4)(x - 7)

Expanding and rearranging the equation, we get:

y - 2 = (1/4)x - (7/4)

y = (1/4)x - (7/4) + 2

y = (1/4)x - (7/4) + (8/4)

y = (1/4)x + 1

Therefore, the equation of the line passing through the points (7, 2) and (-1, 0) is y = (1/4)x + 1.

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If Legolas shoots 3 arrows at once from his bow which consist of 177 arrows, then Legolas can shoot 59 times before he needs more-arrows.

We know that, if Legolas shoots 3 arrows at once, so he uses 3 arrows each time he shoots his bow,

To find the number of times he can shoot his bow, we divide the total number of arrows by the number of arrows that can be shoot at once.

The total number of arrows is = 177,

The number of arrows that can be shoot at once is = 3 arrows.

So, Legolas can shoot his bow = (177/3) = 59 times before he needs more arrows.

Therefore, Legolas can shoot his bow 59 times before running out of arrows.

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The given question is incomplete, the complete question is

Legolas shoots 3 arrows at once from his bow. He has 177 arrows. How many times can Legolas shoot his bow before he needs more arrows?

Answer:

8

Step-by-step explanation:

Answer: False

Step-by-step explanation:

If \(y=0.5\), then \(y^2=0.25\), whereas \(y=0.5\).

Therefore, this is a counterexample. Hence, the statement is false.

The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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Answer:

$26.94

.................

Answer:

Describe the middle class of Central America. Mention jobs, homes, and education.ury

Step-by-step explanation:

The correct answer that is the value of  dy/dt = -3.

To evaluate dtdy​, we need to find the derivative of y with respect to t (dy/dt) using implicit differentiation.

The given equation is:

\(3xy - 3x + 4y^3 = -28\)

Differentiating both sides of the equation with respect to t:

(d/dt)(3xy - 3x + 4y^3) = (d/dt)(-28)Using the chain rule, we have:

\(3x(dy/dt) + 3y(dx/dt) - 3(dx/dt) + 12y^2(dy/dt) = 0\)

Now we substitute the given values:

dx/dt = -12

x = 4

y = -1

Plugging in these values, we have:

\(3(4)(dy/dt) + 3(-1)(-12) - 3(-12) + 12(-1)^2(dy/dt) = 0\)

Simplifying further:

12(dy/dt) + 36 + 36 - 12(dy/dt) = 0

24(dy/dt) + 72 = 0

24(dy/dt) = -72

dy/dt = -72/24

dy/dt = -3

Therefore, dy/dt = -3.

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Answer:

605.69 or if you round it 606 but that's the answer

Answer: the length is 23 feet     the width is 14 feet

Step-by-step explanation:

Let  the length is x feet

Hence, the width is (x-9) feet

The perimeter of a rectangular pool is:

P=(2)(x+(x-9))

74=(2)*(2x-9)

74=(2)(2x)-(2)(9)

74=4x-18

74+18=4x-18+18

92=4x

(4)(23)=(4)(x)

Divide both parts of the equation by 4:

23 feet=x

23-9=x-9

14 feet=x-9

Answer:

x

Step-by-step explanation:

Answer:

a rational number

Step-by-step explanation:

The value of x in the given trapezium is 13.

The distance between the bases is referred tο as the trapezium's height οr altitude. In cοntrast tο a parallelοgram, a trapezium's bases and οppοsite sides are nοt always the same angle and length.

Area of trapezium is,

\($A={\frac{A+b}{2}}\times h$\)

In figure given that, a = x - 4, b = x + 5 and h = 2x

Put the values in area of trapezium and find an equation, that is

\($4x^{2}+2x-702=0$\)

Given equation is

\($2x^{2}+x-351=0$\)

Solve both the equation:

the solutions to the two equations are:

\($\begin{array}{c}{{2x^{2}+x-351=0}}\\ {{\qquad\qquad\qquad}}\\ {{x=13 \ \text{or }x=-13/2}}\end{array}$\)

only one set of parallel sides can be found in a quadrilateral. The bases and legs, respectively, of a trapezium are its parallel and non-parallel sides.

Therefore, The value of x is 13.

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

134 students at west middle school walk to school

Step-by-step explanation:

26% of students at West Middle School get to school by walking. The table shows 515 students in total. To find 26% of 515 we first divide 515 by 100 = 5.15 and then multiply 5.15 by 26% which is 134 students.