Michael bought a $12.99 CD and 3 packs of gum. Andie bought a different CD for $8.99 and 6 packs of
gum. Each of them spent the exact same amount. Which equation below could be used to find g, the
cost of one pack of gum?
A 12.99+ g = 8.99 + 9
B 12.99 + 3g = 8.99 + 69
C 12.99 + 8.99 = 3g + 69
D 12.99 + 69 F 8.99 +39

Answer:

A Discrete.

Step-by-step explanation:

Answer:

C. Graphs are used to demonstrate numerical concepts visually

Step-by-step explanation:

Answer:

the answer for this question is 1

Answer:

4/5

Step-by-step explanation:

divide brownies by friends

Answer:

48 beats per minute

Step-by-step explanation:

I learned this is gym today he told us if you only count 10 seconds multiply the heart beat by 6 so the answer is 48 Noah's resting heart rate is lower than average so he's probably an athlete.

The rock will hit the water after approximately 4.75 seconds.

To find the time it takes for the rock to hit the water, we need to determine the value of t when the height h is equal to zero. We can set the equation h = -16t^2 + 76t + 120 to zero and solve for t.

-16t^2 + 76t + 120 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values a = -16, b = 76, and c = 120 into the formula, we get:

t = (-76 ± √(76^2 - 4(-16)(120))) / (2(-16))

Simplifying the equation further, we have:

t = (-76 ± √(5776 + 7680)) / (-32)

t = (-76 ± √(13456)) / (-32)

Since we are interested in the time it takes for the rock to hit the water, we discard the negative value:

t ≈ (-76 + √(13456)) / (-32)

Evaluating this expression, we find t ≈ 4.75 seconds. Therefore, it will take approximately 4.75 seconds for the rock to hit the water.


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Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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The concept of marginal thinking suggests that you should only consider the marginal benefit and marginal cost of accepting the piece of chocolate.

Marginal benefit refers to the additional pleasure or satisfaction that you will receive from consuming the chocolate, while marginal cost refers to any negative consequences, such as calories or sugar intake, or potential discomfort if you have an allergy. It's important to consider the trade-off between these two factors and decide whether the marginal benefit outweighs the marginal cost. If it does, then accepting the piece of chocolate may be a good decision. However, if the marginal cost is too high, then it may be better to decline the offer and seek alternative sources of pleasure or satisfaction. In this way, the concept of marginal thinking helps you make rational and informed decisions that optimize your well-being and resources.

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Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Answer:

the amount of cupcakes

Step-by-step explanation:

you said the amount of cupcakes can be represented by

The equation that represents the exponential function passing through the points (-2, 1) and (2, 16) is: y = 4(2)^x

To write the exponential equation that passes through the points (-2, 1) and (2, 16), we can use the general form of an exponential function:

y = ab^x

Where y is the dependent variable, x is the independent variable, a is the initial value or y-intercept, and b is the base of the exponential function.

Step 1: Determine the value of a.

To find the value of a, substitute the coordinates of one of the given points into the equation. Let's use (-2, 1):

1 = ab^(-2)

Step 2: Determine the value of b.

To find the value of b, substitute the coordinates of the other given point into the equation. Let's use (2, 16):

16 = ab^2

Step 3: Solve the system of equations.

We now have a system of two equations with two unknowns (a and b):

1 = ab^(-2)

16 = ab^2

We can solve this system of equations to find the values of a and b. To do this, divide the second equation by the first equation:

16 / 1 = (ab^2) / (ab^(-2))

16 = b^4

Taking the fourth root of both sides, we get:

b = ±2

Step 4: Substitute the value of b back into one of the original equations to solve for a.

Let's substitute b = 2 into the first equation:

1 = a(2)^(-2)

1 = a / 4

a = 4

Alternatively, if we had chosen b = -2, we would have obtained a = -4, and the equation would be:

y = -4(-2)^x

Both equations represent exponential functions that pass through the given points.

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Repeated-measures design would require the smallest number of subject

Repeated-measures design: Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods. For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed

given that, a researcher conducts an experiment comparing two treatment conditions and obtains 20 scores in each treatment

Repeated-measures design would require the smallest number of subjects

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The standard deviation of a probability distribution must be a non-negative value. It represents the measure of the dispersion or spread of the data in the distribution. The standard deviation quantifies how much the values in the distribution deviate from the mean.

Mathematically, the standard deviation (σ) is calculated as the square root of the variance (σ^2) of the probability distribution. The variance is obtained by calculating the average of the squared differences between each data point and the mean, weighted by their respective probabilities.

The standard deviation provides important information about the shape and characteristics of the distribution. A smaller standard deviation indicates that the data points are closer to the mean, resulting in a more concentrated or less dispersed distribution. Conversely, a larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider or more dispersed distribution.

The standard deviation of a probability distribution must be a non-negative value and is a measure of the dispersion or spread of the data in the distribution.

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Answer:

82%

Step-by-step explanation:

Statement 1 is a false statement.

What are supplementary angle?

Supplementary angles are two angles whose measures add up to 180° . ex 150° and 30°

What are complementary angles?

When the sum of two angles is equal to 90° degrees, they are called complementary angles. For example, 30° and 60° are complementary angles.

What are vertical angles?

What are congruent angles?

Two or more angles that are identical to each other.

Thus we can conclude that all vertical angles are congruent but not all congruent angles are considered vertical angles

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Answer:

12+x=

Step-by-step explanation:

Answer:

Step-by-step explanation:

The x represents the money he earned on sunday

Answer:

The line graph because it shows how the number of miles increases over the number of minutes.

Step-by-step explanation:

ake it or leave it

The best explanation graph is a better representation of the data below: "The line graph because it shows how the number of miles increases over the number of minutes."

A graph can be defined as a visual representation or a diagram that represents data or values.

The distance in miles a car travels over time in minutes is shown in the table.

Distance (miles)    Time (minutes)

    10                                 15

   20                                 30

   30                                 45

   40                                 60

A line graph is a good choice for representing data that show a change in value over time. In this case, the value being measured is the distance in miles traveled, and the time is being used as the variable. A line graph is a good choice because it can show the change in distance over time, which is what the data represents.

Hence, the correct answer would be an option (A).

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Answer: 4

Step-by-step explanation: To solve the equation (x/(x-2)) + (1/5) = (2/(x-2)), we can follow these steps:

Step 1: Find a common denominator for the fractions on the left-hand side of the equation. The common denominator will be (5(x-2)).

Step 2: Rewrite the equation using the common denominator:

[(5(x)/(x-2)) + (1(x-2))/(5(x-2))] = (2/(x-2))

Step 3: Simplify the equation:

(5x + (x - 2))/(5(x-2)) = (2/(x-2))

Step 4: Combine like terms:

(6x - 2)/(5(x-2)) = (2/(x-2))

Step 5: Cross-multiply to eliminate the denominators:

(6x - 2)(x-2) = 2 * 5(x-2)

Step 6: Expand and simplify both sides of the equation:

6x^2 - 20x + 4 = 10x - 20

Step 7: Rearrange the equation to one side:

6x^2 - 30x + 24 = 0

Step 8: Divide the equation by 6 to simplify:

x^2 - 5x + 4 = 0

Step 9: Factor the quadratic equation:

(x - 4)(x - 1) = 0

Step 10: Solve for x:

x - 4 = 0 or x - 1 = 0

x = 4 or x = 1

Therefore, the solutions for x are 4 and 1.

Answer:

yes that is

Step-by-step explanation:

Answer:

(a) 6

(b) 14

Step-by-step explanation:

Answer:  (a) 6

               (b) 14

Step-by-step explanation:

Let a represent the unknown digit for Chinese --> 70 + a

Let b represent the unknown digit for Mathematics --> 80 + b

Total scores ÷ Total number of tests = Average

\(\dfrac{78 + (70 + a) + (80 + b) + 62}{4}=76\\\\\\\dfrac{290 + a + b}{4}=76\\\\\\290 + a + b=304\\\\\\a+b=14\)

The two digits must add up to 14.

The only options are: (9,5), (8,6), (7,7), (6,8), and (5,9),

            Mathematics   -   Chinese  

(9, 5)          89              -         75       =      14       LARGEST Difference

(8, 6)          88              -         76       =      12

(7, 7)          87              -          77       =      10

(6, 8)          86              -         78       =       8

(5, 9)          85              -         79       =       6      SMALLEST Difference

The actual value of the bill can either be $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bill.

A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.

The bill of customer was mistakenly interchanged by $45.

The sum of the two digits of the bill is 9.

Now,

9 = 9 + 0 or,

9 = 8 + 1 or,

9 = 1 + 8 or,

9 = 5 + 4 or,

9 = 2 + 7 or,

9 = 7 + 2 or,

9 = 3 + 6 or,

9 = 6 + 3

Therefore, $45 bill can be mistakenly interchanged by $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bills.

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If a shopkeeper undercharges a customer by interchanging the digits of the bill by $45 and the sum of the digits is 9, then the actual value of the bill is 72 dollars.

Therefore the answer is $72.

Let the tenth and once place value digits of the actual value of bill be x and y. Then actual value of bill in dollars is expressed by

10x + y

The value of bill obtained by interchanging the two digits in dollars is

10y + x

It is said that by interchanging digits the shopkeeper undercharged him by $45.0, that is

(10x + y) - (10y + x) = 45

9x - 9y = 45

Dividing by 9

\(\frac{9x + 9y}{9} = \frac{45}{9}\)

x - y = 5

He remembers that the sum of the digits is 9, that is

x + y = 9

Solving the system of equations

x + y = 9

x - y = 5

Adding the equations

(x + y) + (x - y) = 9 + 5

2x = 14

Dividing by 2

x = 7

Substituting x = 7 in first equation

7 + y = 9

y = 2

The actual value of the bill is

10x + y = 10×7 + 2 = 72

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

SOLUTIONS

Find the square root of 36/49

Simplify radical

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

Therefore the simplify radical is

Decimal Form:

0.857142

The conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

Let E be the case where you choose the bogus coin and F be the case where you got heads twice. We wish to calculate P(E|F), which is the likelihood that you chose the fake coin given that you received heads twice.

By Bayes' theorem, we have:

P(E|F) = P(F|E)P(E) / P(F)

We can calculate each term on the right-hand side as follows:

P(F|E) = 1, Because the fake coin contains heads on both sides and always results in two heads when flipped.

P(E) = 1/n, since there is only one fake coin among n coins.

P(F) = P(F|E)P(E) + P(F|not E)P(not E), where not E is the event that you picked a normal coin. We can calculate:

P(F|not E) = (n-1) * (1/2)^2 = (n-1)/4, Because each normal coin has a 50% chance of revealing heads on each given flip and there are n-1 normal coins

P(not E) = (n-1)/n, since there are n-1 normal coins among n coins.

Therefore, we have:

P(F) = 1 * (1/n) + (n-1)/4 * (n-1)/n = (3n-1)/(4n)

Substituting these values into Bayes' theorem, we get:

P(E|F) = 1 * (1/n) / ((3n-1)/(4n)) = 4/(3n-1)

Thus, the conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

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Answer:

have a great day

god bless you

The steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Given the equation;

8x² + 16x + 3 = 0

Collect like terms

8x² + 16x = -3

Take the common factors, we have

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation in the right side

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square

\(8(x + 1)^2} = 5\)

Make 'x' subject

\((x + 1)^2= \frac{5}{8}\)

\((x + 1) =\) ±\(\sqrt{\frac{5}{8} }\)

\(x =\) -1 ±\(\sqrt{\frac{5}{8} } }\)

Thus, we can clearly see the steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Step-by-step explanation:

The required problem can be stated as the sum of a number and 4 is 10.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
To write a word a problem can be translated into the equation x + 4 = 10. So, the problem can be given as " the required problem can be stated as the sum of a number, and 4 is 10."

Thus, the required problem can be stated as the sum of a number, and 4 is 10.

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The amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)

The volume of a tennis ball:

The circumference of the tennis ball is 8 inches.

The tennis ball is the form of sphere whose circumference is given by formula \(2\pi r\) , where r is the radius.

Thus, if r is the radius then according to condition,

\(2\pi r\)  = 8 or

r = 8/2\(\pi\) inches.

Now, the volume of the sphere of radius r is \(\frac{4}{3}\pi r^3\) hence, find the volume of the given tennis ball by substituting r  = 8/2\(\pi\) inches in \(\frac{4}{3}\pi r^3\) and simplify:

Volume = \(\frac{4}{3} \pi\) × \((\frac{8}{2\pi } )^3\)

Volume = 8.65 \(inches^3\)

Hence the required volume of the tennis ball is 8.65 \(inches^3\)

The volume of three tennis balls is (3 × 8.65) \(inches^3\)  = 25.96 \(inches^3\)

Find the volume of the cylinder:

The volume of the cylinder with radius r units and height h units is given by  \(\pi r^2h\) Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:

\(\pi (1.32)^2\) × 8.2

= 3.14 × \((1.32)^2\) × 8.2

= 44.86 \(inches^3\)

Hence the volume of the cylinder is 44.86 \(inches^3\)

Find the amount of space within the cylinder not taken up by the tennis balls.

The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:

Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 \(inches^3\)

Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\).

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