two friends are playing with water balloons. they each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. joy walked 12 steps forward, and shaunte walked 8 steps backwards. which expression correctly represents the distance between the friends?

Answer:

To solve this problem, we can set up a system of equations using the information given. Let x be the number of quarters, y be the number of dimes, and z be the number of nickles.

From the problem, we know that:

x:y = 8:5 (the ratio of the number of quarters to the number of dimes)

y:z = 6:11 (the ratio of the number of dimes to the number of nickles)

x+y+z = between 500 and 600 (the total number of coins)

We can start by using the first ratio to find the value of y in terms of x:

x:y = 8:5

y = (5/8)x

We can use the second ratio to find the value of z in terms of y:

y:z = 6:11

z = (11/6)y

We can substitute the value of y into the expression for z to get an expression for z in terms of x:

z = (11/6)(5/8)x

Now we can use the equation x + y + z = between 500 and 600 to find the value of x:

x + (5/8)x + (11/6)(5/8)x = between 500 and 600

Combining like terms:

(63/40)x = between 500 and 600

x = between 800 and 1000

So, x represents the number of quarters, which is between 800 and 1000.

We know that the value of a quarter is $0.25. So the total value of the quarters is between $200 and $250.

Similarly, we know that the value of a dime is $0.1 and a nickel is $0.05.

so,

y = (5/8)x

z = (11/6)(5/8)x

y = (5/8)x * $0.1 = $0.125x

z = (11/6)(5/8)x * $0.05 = $0.04166x

So, the total value of the money in the jar is $200 <= $0.25x + $0.125x + $0.04166x <= $250

If the value of 'a' changed from -a  to +a , the equation of the directrix of the parabola is x= a

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

If parabola is y² = 4ax and the equation of the directrix of the parabola is x= -a

when parabola becomes y² = - 4ax and the equation of the directrix of the parabola is x= a

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The inequality that models the situation is:

x + 2y ≥ 12

We know that a Mecnahinc named Zeke plans to work a maximum of 12 hours (12 hours is an allowed value) tomorrow.

And we know that he works doing tune-ups and oil changes.

Let's define the variables:

We know that It takes 1 hour to perform a tune-up and 2 hours to perform an oil change.

Then the total number of hours worked by Zeke is given by the expression:

x*1 + y*2

And that must be equal to or smaller than 12, so we will get the inequality:

x + 2y ≥ 12

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The standard deviation of the mean was 1.256.

Now, in response to the question: We have given that, some stores print many coupons and advertisements on business receipts, resulting in exceptionally long receipts.

A curious customer makes the identical purchase at ten different stores and counts the length of the each receipt (in inches).

Here are the results,

8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18.

Therefore, The value of the standard error of the mean is 1.256.

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The number of cards sold by Samantha on mother's day is 70.

Total number of cards sold on mother's day = 700

Percentage of cards Samantha sold = 10 %

Fraction of cards Samantha sold  = 700 × 10/100

                                                        = 70

The number of cards Samantha did not sold, or sold by other salesman = Total cards sold - number of cards Samantha sold

                           700 - 70 = 630

Or else we can calculate by using percentages.

Percentage of the cards sold by other salespersons = 100- 10

                                                                                         = 90

90 % of 700 = 90/100 × 700

                     = 630

We can also use proportions.

    10 : 90 :: 70 : x

    10/90 = 70/x

          x = (70× 90)/ 10

              = 630.

So the number of cards Samantha sold = 70

     Number of cards others sold = 630

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Answer:

The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.

For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.

There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.

So your expected gain/loss per roll is:

(3/9) * $3 + (3/9) * (-$6) = -$1

Therefore, on average, you will lose $1 per each throwing.

Yes , it is possible to divide the line segment in the ratio of [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] because after simplifying the ratio becomes of integers .

For a line segment to be divided in the ratio "a:b" , both the numbers "a" and "b" should be integers ,

the ratio to divide line segment is given as : [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] ;

multiplying each term of the ratio by [tex]\sqrt{3}[/tex] , we get ,

the ratio as ⇒[tex]3 :1[/tex] , where both the numbers "3" and "1" are integers .

So ,we get that ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] can be written in simplified ratio form as 3:1    .

Therefore , a line segment can be divided in the ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] .

The given question is incomplete , the complete question is

Is it possible to divide a line segment in the ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex]   ?

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Answer:

log10 195 = 2.29

Answer:

I found this

To solve for the value of log10 19.5, we can use the property of logarithms that states:

loga(b^c) = c * loga(b)

In this case, we can express 19.5 as 10^2.29:

19.5 = 10^2.29

So, we can find the logarithm of 19.5 by solving for c:

log10(19.5) = log10(10^2.29)

By using the property of logarithms mentioned above, we can simplify the equation to:

log10(19.5) = 2.29 * log10(10)

Since log10(10) = 1, we can further simplify the equation to:

log10(19.5) = 2.29

Therefore, the value of log10 19.5 is 2.29.

Two common types of ratios we'll see are part to part and part to whole.

The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.

30 numbers complete the ratio table to make an equivalent ratio.

What is equivalent ratio?

When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.

Here in this case,

for trees: 2: 12    [ 2 to 12, 6 times more ]

for plants: 5: 30  [ 5 to 30, it is also 6 times more]

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Answer:

88% of the coins are quarters.

To find out, you can convert the fraction 44/50 to a percentage by multiplying it by 100.

(44/50) * 100 = 88%.

The slope intercept from of equation exists y = -0.25x -19.5.

The relationship between how a line's y coordinate and x coordinate change determines the slope of that line. The net modifications to the y and x coordinates, respectively, are denoted by y and x. In light of this, it is possible to express the change in y coordinate in relation to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given: A line that passes through points  (8, 13) and(-12, 18)

substituting the values, we get

m = ( 18 - 13)/ ( -12 - 8)

simplifying the above equation, we get

m = -0.25

Now, using slope intercept form

y - a = -0.25( x- b)

substitute the values in the above equation, we get

y - (13)= -0.25(x-(18))

y - 15= -0.25x-(-0.25 × 18))

simplifying the equation, we get

y = -0.25x - 4.5 -15

y = -0.25x -19.5

Therefore, the slope intercept from of equation exists y = -0.25x -19.5.

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   When we say two values are equivalent, we mean that their numerical values are the same. In mathematics, transforming one value into another that is more useful in a specific context is one technique to demonstrate that two values are comparable.

  In this instance, the values of the fraction 3/4 and the decimal 0.75 are the same. This can be demonstrated by dividing the numerator (3) by the denominator (4) using long division or a calculator to represent the fraction 3/4 in decimal form.

 The following steps can be used to breakdown the conversion of a fraction to a decimal:

           Therefore, In mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value.

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Pat left the office at 10:50 am.

What is the relation between speed, distance, and time?

The relation between speed, distance, and time would be

distance = speed x time

We know that Pat had a 12:30 pm appointment 72 miles from his office, arrived ten minutes late, and averaged 48 mph for the trip. So we can set up the equation as:

distance = speed x time

72 = 48 x time

To solve for time, we divide both sides of the equation by 48:

time = distance / speed

time = 72 / 48

time = 1.5 hours

Since Pat arrived 10 minutes late, we need to subtract that 10 minutes from the time it took him to get to the appointment

12:30pm - 00:10 = 12:20 pm

Now, we have to subtract the time it took Pat to get to the appointment from the time he left the office

12:20 pm - 1.5 hours = 10:50 am

So Pat left the office at 10:50 am.

Hence, Pat left the office at 10:50 am.

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The largest possible solution is x + y =w = 4

Now, According to the question:

Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of the cubes is 10.

Now, One way to solve this problem is by substitution. We have

[tex]x^{2} +y^2 = (x+y)^2+2xy=7[/tex]

and,

[tex]x^3+y^3=(x+y)(x^2-xy+y^2)=(7-xy)(x +y)=10[/tex]

Hence observe that we can write :

x +y = w and xy = z

This reduces the equations to [tex]w^2-2z =7[/tex] and w(7 - z) =10

Because we want the largest possible w, let's find an expression for z in terms of w.

[tex]w^2-7 =2z[/tex] => [tex]z = \frac{w^2-7}{2}[/tex]

Substituting, [tex]w^3-21w+20=0[/tex]

which factorizes as (w-1) (w+5) (w-4) = 0

Hence, The largest possible solution is x + y =w = 4

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The rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

This can be interpreted as follows:

In each stage, the number of black triangles is determined by the number of triangles that were present in the previous stage. This suggests that the sequence may be formed by repeatedly adding a certain number of triangles to the previous stage, with the number of added triangles equal to the number of triangles present in that stage.

Therefore, the rule can be described as The number of black triangles in each stage is the number of triangles in the previous stage multiplied by 2.

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Answer: 3 times

Step-by-step explanation:

edge 2023

Answer:First we need to simplify the left side of the equation:

12,5(3x-1)+132,4 = 12,5*3x - 12,5 + 132,4 = 37,5x + 120,9

Now we need to simplify the right side of the equation:

2,8-4x = 2,8 - 4x

Now we have to set the two sides equal:

37,5x + 120,9 = 2,8 - 4x

Now we have to move all the x terms to one side of the equation:

37,5x - 4x + 120,9 = 2,8

Next step is to combine like terms:

33,5x + 120,9 = 2,8

Subtracting 120.9 from both sides of the equation:

33,5x = -118.1

Dividing both sides by 33,5

x = -3,54

So the solution of the equation is x = -3,54

Step-by-step explanation:

D) In my opinion Answer is D because 0.01 is the maximum safe value for some naturally occurring human consumption. So, value cannot be maximize for the significance and alpha.

Null Hypothesis:

The null hypothesis (often called H0) is the assertion that there is no difference or relationship between the two data sets or variables being analyzed. The null hypothesis states that all experimentally observed differences are due to chance and that there is no underlying causal relationship, hence the term "null". In addition to the null hypothesis, alternative hypotheses are also developed. This claims that there is an association between the two variables.

Alternative Hypothesis:

In statistical hypothesis testing, the alternative hypothesis is one of the statements proposed in the hypothesis test. In general, the purpose of hypothesis testing is to show that, given the conditions, there is sufficient evidence to support the reliability of the alternative hypothesis rather than the sole assertion in the test (the null hypothesis). They are usually consistent with research hypotheses, as they are generated from literature reviews, previous studies, etc. However, in some cases the research hypothesis is consistent with the null hypothesis. In statistics, the alternative hypothesis is often denoted by Ha or H1. Hypotheses are formulated to compare them in statistical hypothesis testing. In the field of inferential statistics, two competing hypotheses can be compared for their explanatory and predictive power.

According to The Question:

H subscript o : mu less or equal than 0.01

H subscript alpha : mu greater than 0.01

From the given statement we think we should have to maximize the power of test because maximize the significance alpha is not true because alphas value is given according to the table that is mentioned.

Complete Option:

A. maximize the power of the test

B. maximize beta

C. minimize mu

D. maximize the significance, alpha

E. maximize 1 minus alpha

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The value of c can be found by solving the equation yc^2 = -x^2 + 5x.

Square is a two-dimensional shape with four equal sides and four equal angles of 90 degrees each. It is a regular polygon and is one of the most common shapes in mathematics. Squares can be found in nature, architecture, and art. They are used to divide and organize space, and are often used as a form of measurement in areas such as geometry, construction, and engineering.

After rearranging the equation, we can solve for c by using the quadratic formula. c = (x^2 - 5x)/(x^2). Therefore, the value of c is (x^2 - 5x)/(x^2).

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Answer:

(x + 8)^2 + (y - 3)^2 = 64

Step-by-step explanation:

The equation of a circle with a center of (-8,3) and radius of 8 is:

(x + 8)^2 + (y - 3)^2 = 64

You can see that the center of the circle is represented by the point (-8,3) in the equation, and the radius is represented by the value on the right side of the equation (64) which is derived from 8^2

If a study concluded that among people with a certain​ virus, 99.2​% of tests conducted were​ (correctly) positive, while for people without the​ virus, 98.1​% of the tests were​ (correctly) negative.  the probability that a patient testing negative is truly free of the​ virus is 0.9967.

Probability (testing negative is truly free of the​ virus) =  (1- 0.29) (0.981) / (0.29) (1- 0.992) + (1- 0.29) (0.981)

Probability (testing negative is truly free of the​ virus) =  (0.71) (0.981) / (0.29) (0.008) + (0.71) (0.981)

Probability (testing negative is truly free of the​ virus) = 0.69651 / 0.00232 + 0.69651

Probability (testing negative is truly free of the​ virus) = 0.69651/ 0.69883

Probability (testing negative is truly free of the​ virus) =0.9967

Therefore we can conclude that the probability (testing negative is truly free of the​ virus) is 0.9967.

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Yes, it is possible to draw a right angled triangle with sides 1.5cm , 2cm , and 2.5cm.

As given in the question,

In the given triangle,

Measure of the side length of the given triangle are :

1.5cm , 2cm , and 2.5cm

In this triangle longest side is equal to 2.5cm.

Given triangle is right angled triangle check whether Pythagoras theorem satisfied the measure of the sides of the triangle.

Hypotenuse represents the longest side.

( Hypotenuse)² = ( Side 1 )² + ( Side 2)²

Right hand side

= ( 1.5 )² + ( 2 )²

= 2.25 + 4

= 6.25

= ( 2.5 )²

= Hypotenuse²

It satisfied the Pythagoras theorem.

Therefore, the given sides of the triangle represents it is a right angled triangle.

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Answer:

(4,2)

Step-by-step explanation:

the solution to the system of equations is the point where the 2 lines intersect:  (4,2)

As per the given divisor and product, the value of e is 5.

The term divisor in math is defined as a number which divides another number and it is a part of the division process.

Here we have given that let us consider that s denote the set of all positive divisors of 60⁵

Here we also know that the product of all the numbers in s equals 60ⁿ for some integer n.

As per the given condition, the terms are written as,

=> s =  60⁵

=> s = 60ⁿ

Here we have to compare the given values then we the expression like the following,

=> 60⁵ = 60ⁿ

As per the rule of exponent, the value of e = 5.

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The frequency shown in the given sinusoidal graph is:

f = 1/T (s⁻¹).

Frequency means the rate at which something occurs or is repeated over a particular period of time or in a given sample.

A sinusoidal function is a periodic function because the basic shape repeats indefinitely in both the positive and negative directions. The frequency of a sine wave is defined as the number of cycles it completes in a given interval and is the reciprocal of the period.

In a mathematical language, this is written as:

f = 1/T

Where,

f = frequency,

T = Period

To get the period, just subtract the x-coordinates of two consecutive peaks, so:

T = п - 0

T = п (s)

Therefore, the frequency is:

f = 1/T (s⁻¹).

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Answer:2

Step-by-step explanation:

The inequality that correctly compares the elevations is given as follows:

-7 and 7/10 > -10 and 9/10.

The four inequality symbols are given as follows:

The elevations are given as follows:

Those two elevations are given by mixed numbers, which are composed by both an integer part and a fractional part.

To compare which elevation is greater, we look at which one has the greater integer part. An integer part of -7 is greater than an integer part of -10, hence the inequality is given as follows:

-7 and 7/10 > -10 and 9/10.

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According to the vector rule, the values of the 2u, -3v, u + v, and 3u + 4v are (-4, 18), (-18, 6), (4, 7) and (18, 19) respectively.

Here we have given the following two vector such as

u = (-2, 9)

v = (6, -2)

Then as per the following vector rule, t

=> ku = (ka , kb)

where k refers the constant in vector.

Then the value of 2u is calculated as,

=> 2u = ((-2 x 2), (9 x 2)) = (-4, 18)

And the value of -3v is calculated as ,

=> -3v = ((-3 x 6), (-3 x- 2)) = (-18, 6)

Here we have to use the following rule, that is written as,

=>  (u ± v) = (a ± c, b ± d)

Then the value of u + v is calculated as,

=> (u + v) = ((-2 + 6),  (9 + (-2)) = (4, 7)

Then the value of 3u + 4v is calculated as,

=> 3u = ((3 x -2), (3 x 9)) = (-6, 27)

And the value of

=> 4v = ((4 x 6), (4 x- 2)) = (24, -8)

Then the value of

=> 3u + 4v = (-6, 27) + (24, -8)

=>  3u + 4v = ((-6+24) , (27 + (-8))

Therefore, the resulting value is (18, 19).

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After finding the LCM, the sum of 8/9 and 3/4 is 59/36

In the given question, we have to find the sum of 8/9 and 3/4.

The given numbers are 8/9 and 3/4

Sum = 8/9 + 3/4

The denominator of the both number are different. So to find the sum we find the LCM of the both number 9 and 4.

So the LCM of 9 and 4 is 36.

Multiply 4 on the number 8/9 and 9 on the number 3/4. So

Sum = [tex]\frac{8}{9}\times\frac{4}{4}+\frac{3}{4}\times\frac{9}{9}[/tex]

Sum = 32/36 + 27/36

Now the denominator is same. So now we add them.

Sum = (32+27)/36

Sum = 59/36

Hence, the sum of 8/9 and 3/4 is 59/36.

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Answer:

Chebyshev's Theorem states that for any dataset with a mean and standard deviation, at least 1 - (1/k^2) of the data will lie within k standard deviations of the mean.

In this case, we're looking for households that have between 0 and 4 televisions, which is 4 - 0 = 4 - 2 = 2 standard deviations from the mean of 2 televisions.

So, using Chebyshev's Theorem, we can calculate that at least 1 - (1/2^2) = 1 - (1/4) = 3/4 or 75% of the households have between 0 and 4 televisions.

At least 75% of the households have between 0 and 4 televisions.