Shari bought 3 breath mints and received $2. 76 change. Jamal bought 5 breath mints


and received $1. 20 change. If Shari and Jamal had the same amount of money, how


much does one breath mint cost?



A. Each breath mint costs $0. 28.



B. Each breath mint costs $0. 49.



c. Each breath mint costs $0. 78.



D. Each breath mint costs $1. 98.

If e is a nonempty compact subset of x and a is a closed subset of x, and e ∩ a = ∅, then there is a positive "gap" between e and a. This can be proven by showing that the infimum of the distances between points in e and a is greater than zero.


1. Let e be a nonempty compact subset of x and a be a closed subset of x. Since e is compact and a is closed, both sets are bounded and closed, which implies that they are disjoint (e ∩ a = ∅).

2. Consider the set S = {d(x, a) : x ∈ e, a ∈ a}. This set consists of the distances between each point in e and each point in a.

3. Since e and a are disjoint, S contains only positive distances. Moreover, since both e and a are compact and closed, the distance function d(x, a) is continuous. Therefore, S is a nonempty set of positive real numbers.

4. By the properties of real numbers, S has a minimum element, which we denote as inf{d(x, a) : x ∈ e, a ∈ a}. Since S contains only positive distances, this minimum element must be greater than zero. Hence, there is a positive "gap" between e and a.

Therefore, if e is a nonempty compact subset of x and a is a closed subset of x, and e ∩ a = ∅, then there is a positive "gap" between e and a. This can be proven by showing that the infimum of the distances between points in e and a is greater than zero.

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Answer:To determine the measurement of KL, we can use the concept of similar triangles and the corresponding sides.

In triangle XYZ, the ratio of the lengths of corresponding sides is:

XY/XJ = XZ/JK = YZ/KL

Plugging in the given values:

8.7/10.44 = 8.2/JK = 7.8/KL

From this, we can solve for JK:

JK = (8.2 * 10.44) / 8.7 ≈ 9.84

Therefore, the measurement of KL is approximately 9.84.

~hope this helps you guys~

~if you need any other help i will answer~

=D

An equivalent function can be written as \(G(t) = 1920 \times 2^t\)

What is equivalent fraction?

Fractions that represent the same amount or portion of a whole, but have different denominators and numerators is called Equivalent fractions.

They are equal in value, but may have different forms.

We can multiply or divide both the numerator and the denominator of a fraction by the same number for find equivalent fractions.

Some examples are 2/4 is equivalent to 1/2 because if you divide both the numerator and the denominator of 2/4 by 2, you get 1/2.

Starting from the given function, we can simplify it as

\(G(t) = 960(2^t + 1) \\ G(t) = 960 \times 2^t \times 2^1 \\ G(t) = 1920 \times 2^t\)

We can see that this function is of the form

\(G(t) = ab^t\)

where a = 1920 and b = 2.

Therefore, an equivalent function can be written as \(G(t) = 1920 \times 2^t\)

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Answer:

so what are you trying to figure out

Step-by-step explanation:

Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

Explanation:

Cam saved $270 per month for three years while working. Considering that money is worth 4.8% compounded monthly, we can calculate the total amount he will have in his savings account when he finishes his studies.

To find the future value, we can use the formula for compound interest:

FV = PV * (1 + r)^n

Where:

FV is the future value

PV is the present value

r is the interest rate per compounding period

n is the number of compounding periods

In this case, Cam saved $270 per month for three years, which gives us a present value (PV) of $9,720. The interest rate (r) is 4.8% divided by 12 to get the monthly interest rate of 0.4%, and the number of compounding periods (n) is 5 years multiplied by 12 months, which equals 60.

Plugging these values into the formula, we get:

FV = $9,720 * (1 + 0.004)^60

≈ $18,034.48

Therefore, Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

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Answer:

0.5 :)

Step-by-step explanation:

On solving the question we have that Therefore, the center of the circle equation is (3/10, -7/10) and the radius is √(1/5).

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

The given equation is that of a circle in standard form:

\((x - h)^2 + (y - k)^2 = r^2\)

where the center of the circle is (h, k) and the radius is r.

To convert the given equation to this form, we need to complete the square for both x and y terms. Let's start with the x terms:

\(5x^2 - 3x = 5(x^2 - (3/5)x)\\5(x^2 - (3/5)x + (3/10)^2 - (3/10)^2)\\5((x - 3/10)^2 - 9/100)\\5y^2 + 7y = 5(y^2 + (7/5)y)\\5(y^2 + (7/5)y + (7/10)^2 - (7/10)^2)\\5((y + 7/10)^2 - 49/100)\\5((x - 3/10)^2 - 9/100 + (y + 7/10)^2 - 49/100) - 1 = 0\\5(x - 3/10)^2 + 5(y + 7/10)^2 = 1\\\)

Therefore, the center of the circle is (3/10, -7/10) and the radius is √(1/5).

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Answer: A its B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

if y = 0

0 = -2x + 4 _ eq 1

0 - 4 = -2x

-4 = -2x

divide through by 2

x = -4 ÷ -2

x = 2

if x = 0

y = -2(0) + 4_ eq 2

y = 0 + 4

y = 4

:.(x,y) = (2,4)

Answer:

Answers: (to the nearest hundredth)

Between two cars,

Central angle = 0.39 radians (or 71.4°)

Arc length = 7.85 ft

Area of a sector = 78.54 ft²

Step-by-step explanation:

Answer:

117 cups

Step-by-step explanation:

two dozen cookies calls for 234cups of sugar

2 dozen cookies = 234 cups of sugar

How much sugar is needed to make one dozen cookies?

Let x = cups of sugar needed

1 dozen cookies = x cups of sugar

2 dozen cookies : 234 cups of sugar = 1 dozen cookies : x cups of sugar

2 : 234 = 1 : x

2 / 234 = 1 / x

Cross product

2*x = 234 * 1

2x = 234

x = 234 / 2

= 117 cups

Your options are wrong because none corresponds with the answer

Answer: 5

Step-by-step explanation:

-4x/4x = x

-20/-4 = 5

therefore x = 5

Answer:

-11/16

Step-by-step explanation:

1) Find the Least Common Denominator (LCD) of \(\frac{15}{32} ,\frac{7}{31}\) In other words, find the Least Common Multiple (LCM) of 32,31.

Method 1: By Listing Multiples

1. List the multiples of each number.

Multiples of 32: 31,64,96,... 928, 960 ,992,...

Multiples of 31: 31, 62, 93 , ... , 930, 961 , 992, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 992

Method 2: By Prime Factors

1. List the prime factors of each number.

Prime Factors of 32: 2,2,2,2,2

Prime Factors of 31: 31

2.  Find the union of these primes.

2,2,2,2,2,31

3. Multiply these numbers: 2 * 2 * 2 * 2 * 2 * 31 = 992. This is the LCM.

LCM = 992

2) Make the denominators the same as the LCD.

\(-\frac{15*31}{32*31} +\frac{7*32}{31*32}\)

3) Simplify. Denominators are now the same.

\(-\frac{465}{992} +\frac{224}{992}\)

4) Join the denominators.

\(\frac{-465+224}{992}\)

5) Simplify

\(-\frac{241}{992}\)

Decimal Form: -0.242944

The strength factor of the evidence you just got that you picked the special box is 4.

Given:

There are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue.

Hypothesis =  The box the blue marble was picked from is the special box.

Prior confidence = 1:3 (ratio of special boxes to non special boxes )

Now P(B | S) = 1/2 (given that a box is selected from the special box, there is 1/2 chance that it is blue)

And P(B | NS) = 1/8 (given that a box is selected from a non-special box, there is 1/8 chance that it is blue)

According to  bayes factor ,we get:

P(B | S)/P(B | NS) = (1/2)/(1/8) = 4

Thus, 4.

Therefore the strength factor of the evidence you just got that you picked the special box is 4.

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Answer:

The proposition is true.

Step-by-step explanation:

Now we proceed to demostrate that expression given is true by algebraic means:

1) \(\frac{x^{-1}+y^{-1}}{x^{-1}}+\frac{x^{-1}-y^{-1} }{y^{-1}}\) Given

2) \(\frac{y^{-1}\cdot (x^{-1}+y^{-1})+x^{-1}\cdot (x^{-1}-y^{-1})}{x^{-1}\cdot y^{-1}}\)   \(\frac{a}{b} + \frac{c}{d} = \frac{a\cdot d+b\cdot c}{b\cdot d}\)

3) \(\frac{x^{-1}\cdot y^{-1}+y^{-2}+x^{-2}-x^{-1}\cdot y^{-1}}{x^{-1}\cdot y^{-1}}\) Distributive property/\(a^{b}\cdot a^{c} = a^{b+c}\)

4) \(\frac{x^{-2}+y^{-2}}{(x\cdot y)^{-1}}\) Commutative, associative and modulative properties/Existence of additive inverse/\(a^{b}\cdot c^{b} = (a\cdot c)^{b}\)

5) \([(x\cdot y)^{-1}]^{-1}\cdot (x^{-2}+y^{-2})\) Commutative property/Definition of division

6) \((x\cdot y)\cdot (x^{-2}+y^{-2})\)         \((x^{-1})^{-1}\)

7) \(x^{-1}\cdot y + x\cdot y^{-1}\) Distributive property/Associative property/\(a^{b}\cdot a^{c} = a^{b+c}\)

8) \((x^{-1}\cdot y^{-1})\cdot y^{2} + (x^{-1}\cdot y^{-1})\cdot x^{2}\)  Modulative property/Existence of additive inverse/\(a^{b}\cdot a^{c} = a^{b+c}\)

9) \((x^{-1}\cdot y^{-1})\cdot (x^{2}+y^{2})\) Distributive property

10) \((x\cdot y)^{-1}\cdot (x^{2}+y^{2})\) \(a^{b}\cdot c^{b} = (a\cdot c)^{b}\)

11) \(\frac{x^{2}+y^{2}}{x\cdot y}\) Commutative property/Definition of division/Result

Answer:

67.5

Step-by-step explanation:

what i did is i subtracted

180-45=135

so both sides is equal to 135

both sides are = so divide

135 divided by 2 = 67.5

hope this helps

Answer:

8 or -8

Step-by-step explanation:

Lets just say their net results equals x so -10+2=x

-10+2=-8 which i think you would take off the negitave and it would be an 8 I'm not sure sorry:(

Sorry I couldn't help

Answer:

2

Step-by-step explanation:

opposite of -2 is 2 because it is like 2 is opposite of -2

Answer:

2.

Step-by-step explanation:

The opposite of a number is the number which when added to it gives a result of zero.

-2 + 2 = 0 so the required  number is  2.

Answer:

16

Step-by-step explanation:

Using PEMDAS:

3 + 9 x 2 - 5

= 3 + 18 - 5

= 21 - 5

= 16

Comparison of y-intercept and rate of change , the answer is  A) The y-intercept is same , but rate of changes are different.

What is rate of change?

The relationship between two quantities is described by their rate of change. Either a positive or negative rate of change is possible. The ratio of the vertical and horizontal change between two points on a plane or a line, which is the definition of a line's slope, means that the slope is the ratio of rise to run.

Here the y-intercept is y=3.

Here the line equation is y=mx+c.

Comparing with equation, rate of change is 0.

The given two points are \((x_1.y_1)=(3,6) , (x_2,y_2)=(4,7)\).

Now using slope formula, m=\(\frac{y_2-y_1}{x_2-x_1}\)

=> Slope m = \(\frac{7-6}{4-3}\) = 1

Then rate of change is 1.

Now the equation is , y-6=1(x-3)

=> y-6=x-3

=> y=x-3+6=x+3

Hence the y-intercept is 3.

Hence the correct option is A) The y-intercept is same , but rate of changes are different.

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The probability that the jury makes the correct decision that the defendant is guilty is 0.7063.

In order to resolve this issue, we must determine the likelihood that the jury would find the defendant guilty. Let's divide the issue into more manageable components.

We are aware that there is a 0.80 chance that a single juror would choose correctly. If the defendant is found guilty, there is still an 80 percent chance that the jury will reach the right verdict. Consequently, if the defendant is found guilty, there is an 80 percent chance that one jury will reach the right verdict.

The likelihood that at least 10 out of 12 jurors will choose the right course of action may be calculated using the binomial distribution formula. The equation is:

\(P(X \geq k) = 1 - \sum (i=0, k-1) [\frac{i!}{(i!(n-i)!)} ]p^i*(1-p)^(^n^-^i^)\)

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Using a calculator or software, we can calculate this to be approximately 0.7063.

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The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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The statement "The average boy plays 6 hours more per week than the average girl" is true based on the given data sets.

What is a true statement about the data sets of hours of video game time per week for teen boys and girls based on Raj's survey results?

The answer states that "The average boy plays 6 hours more per week than the average girl" based on the given data sets.

This implies that, on average, teen boys spend more time playing video games each week compared to teen girls.

The statement is derived from comparing the averages of the two data sets and finding a difference of 6 hours.

It suggests that, overall, boys in Raj's class are spending more time on video games than girls.

It's important to note that this statement doesn't provide information about individual cases or the distribution of video game time within each group.

The difference in average hours could be influenced by various factors such as personal preferences, gaming habits, or other external variables.

It is crucial to consider the limitations of this statement and analyze the data more comprehensively to gain a complete understanding of the patterns in video game time for teen boys and girls.

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Answer:

46in²

Step-by-step explanation:

1/2 1 +5+3+1+3+14

46in²

Answer:

1)

Y decreases because when x is 9, y is really close to zero.

2)

The same/equal, function is a quadratic or a reciprocal

3)the function value y= greater or less than 0.

Y-intercept is 8 or y=8

4)

When x=1,y=5

Answer:

145°

Step-by-step explanation:

because opposite angles r equal

(a) The expression for Raul's monthly data costs is 29.99 + 10 (n - 5).

(b) The minimum number is 9 GB to make the unlimited plan cheaper.

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The weakest correlation is represented by the value of c. 0.11.

The weakest correlation is represented by the value that is closest to zero, as it indicates a weaker relationship between the variables. In this case, the answer is: c. 0.11

A correlation coefficient of 0.11 is closer to zero than the other options provided, indicating a weaker correlation compared to the rest. The negative values (-0.75 and -0.27) represent negative correlations, but their magnitudes are larger than 0.11, making them stronger correlations (although still considered weak in general). The positive value of 0.54 represents a moderate positive correlation.

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