The zero product property indicates that if “ab = 0,” then ___?___ = 0 or ___?___ = 0. Substitute the correct variable for the question mark.

Select one:

a

b

a ; b

none of the above

Answer:

x = 12

Step-by-step explanation:

<1 and the 142-deg angle are vertical, so m<1 = 142 deg

The angle measuring 3x + 2 and <1 are same-side interior angles. If the lines are parallel, then those two angles are supplementary.

3x + 2 + 142 = 180

3x + 144 = 180

3x = 36

x = 12

Answer:

To solve this question, we first have to know that we are trying to assemble

and solve equations with two variables: x

and y.

Assuming x

is the number of dimes and y

is the number of quarters, we

can assemble the equations.

since the number of dimes is 3 more than three times the number of quarters,

we get x=3y+3.

Additionally, multiplying the number of dimes by 0.1 and the number of

quarters by 0.25,

we get the total value of x

and y

which appears by this

equation 0.1x+0.25y=11.30

.

Substituting the value of x

in the second equation, we get 0.1(3y+3)+

0.25y=11.30

.

Solving this equation, we get that the value of x,

we get x=3×20+3=

Using the first equation to get the value of x,

we get x=3×20+3=

60+3=63

dimes.

Chapter 9

Math Models and Geometry

Section 2

Solve Money Applications

Prealgebra

Step-by-step explanation:

We can relate the radius (r) with the length of the arc (S) and the arc measure (θ) as:

Then, if r=6.33 cm and θ=5.3 rad, we can find S as:

Answer: S = 33.5 cm

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

1330 rounds of meetings

Step-by-step explanation:

You have a total of 21 people, and  they all want to meet with each other in groups of 3. This means we are dealing with a combination problem, where combination is the selection of items in which order does not matter.

Formula for combination:

ₙCᵣ = \(\frac{n!}{r!(n-r)!}\)

where n is the total number of objects (in this case, total number of people: 21), and r is the sample set (in this case, groups: 3).

We plug in and get:

-> \(\frac{21!}{3!(21-3)!}\)

-> 1330 different meetings for everyone to meet with each other in groups of 3.

Answer:

\(\fbox {5 times}\)

Step-by-step explanation:

Days where both will be done :

⇒ 2nd day × 3rd day

⇒ 6th day

Number of times in September :

⇒ The month has 30 days

⇒ Number of times = 30/6

⇒ Number of times = 5

Answer:

5 times

Step-by-step explanation:

• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:

LCM (2 and 3) = 2 x 3

                       = 6

This means, she will do both every 6th day.

• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:

⇒ 30 ÷ 6

= 5 times

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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The cardinality of the set (A − C) n B is 35 .

We have given three sets A = {x | x ≤ N} where N is a natural number .

Then , set A will get values \(A= \{1,2,3,4,5......\}\)

B = {x-5 < x < 105, x ≤ R} where R is a real number whose values is in domain of (- ∞ ,∞)

Then , set B will get values \(B=(-5,105)\)

C = {x|x is a rational number, 10 < x < 80} rational number which can expressed in \(\frac{p}{q}\) where \(q\neq 0\) .

Then , set C will get values \(=(10,80]\)

According to the question

(A − C) n B \(=(\{1,2,3,4,5 ........\}-(10,80] \sqcap (-5,105)\)

                  \(=\{1,2,3,4,5,6,7,8,9,10,81,82,83 .......\} \sqcap (-5,105)\\\)

                ={1,2,3,4,5,6,7,8,9,10,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103, 104 ,105}

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Answer:

Simplifying

5(6.2a + 9.8) = 18

Reorder the terms:

5(9.8 + 6.2a) = 18

(9.8 * 5 + 6.2a * 5) = 18

(49 + 31a) = 18

Solving

49 + 31a = 18

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-49' to each side of the equation.

49 + -49 + 31a = 18 + -49

Combine like terms: 49 + -49 = 0

0 + 31a = 18 + -49

31a = 18 + -49

Combine like terms: 18 + -49 = -31

31a = -31

Divide each side by '31'.

a = -1

Simplifying

a = -1

Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

Answer:

This is not a function

Step-by-step explanation:

Assuming that the line in question is parallel with the y axis, by using the line test we can see that the line is not a function. The line test is where you draw straight lines going vertically over the graph and if the lines touch the figure in question more than once that means it's not a function.

This can also be proved by imagining there are 2 different points on the line in question. Since the line is straight vertically that means that the points will share the same x value for different y values, which makes it not a function

Answer:

This is not a function.

Step-by-step explanation:

The questioned parallel line within the y-axis does not meet the requirements to be a function. The line test, as the other person stated, is a test where lines are drawn over the points to determine if the graph / model is, or is not a function. Doing so in this process, if the lines touch the same point more than once, that means the graph is not a function.

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

x < 3

Step-by-step explanation:

5x+7x<36

12x<36

Divide both sides by 12

x<3

Answer:

1.6

Step-by-step explanation:

i used calculator

Answer:  1.6

Step-by-step explanation:

Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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The equation that can be used to represent the cost of 4 markers is y = k × 4

5 markers = $6.5

Unit cost of each marker = $6.5 / 5

= $1.3 per marker.

If

y = kx

Where,

y = total cost of markers

k = unit cost of marker

x = number of markers

The equation for the cost of 4 markers:

y = kx

y = 1.3 × 4

y = $5.2

Ultimately, y = k × 4 represents the equation for total cost of 4 markers.

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The number of days took to get the video of Felipe 1024 views is 4.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The relationship between the elapsed time in days, d, since the video was uploaded and the total number of views, v, that the video received is modeled by the equation,

v = 4^(1.25d)

We have to find d when v = 1024

1024 = 4^(1.25d)

We have the rule for exponents aᵇⁿ = (aᵇ)ⁿ

1024 = \((4^{1.25} )^d\)

1024 = (5.6569)^d

Taking logarithms on both sides,

㏒ (1024) = ㏒ [(5.6569)^d]

We have the exponent rule for logarithm, ㏒ (aᵇ) = b ㏒ (a)

㏒ (1024) = d ㏒ (5.6569)

d = ㏒ (1024) / ㏒ (5.6569)

d = 4

Hence it took 4 days to for Felipe's video to get 1024 views.

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Answer:

The correct option is d

Step-by-step explanation:

From the question we are told that

    The sample size is  n = 64

    The mean is  \(\= x = 320\)

    The standard deviation is \(\sigma = 120\)

Generally the standard error of the mean is mathematically represented as  

       \(\sigma_x = \frac{\sigma}{ \sqrt{n} }\)

=>    \(\sigma_x = \frac{120}{ \sqrt{64} }\)

=>    \(\sigma_x =15\)

Answer:

a

The 95% confidence interval is \(1003 < \mu <1023\)

b

Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 1000\)

   The sample size is  \(n = 453\)

   The sample mean is  \(\= x = 1013\)

    The standard deviation is \(s = 108\)

Given that the confidence level is  95% then the level of significance is mathematically represented as

            \(\alpha = 100 - 95\)

=>         \(\alpha = 5\%\)

=>          \(\alpha = 0.05\)

The critical value  for \(\frac{\alpha }{2}\) obtained from the normal distribution table is          

          \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

         \(E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }\)

=>     \(E = 1.96 * \frac{108}{\sqrt{453} }\)

=>      \(E = 9.946\)

Generally the 95% confidence interval is mathematically represented as

           \(\= x - E < \mu < \= x + E\)

=>         \(1013 - 9.946 < \mu < 1013 + 9.946\)

=>         \(1003 < \mu <1023\)

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

Answer:

170.52

Step-by-step explanation:

Let x be the original price

Then,

129.60 = 76% of x

129.60 = 76/100 * x

12960/76 = x

x = 170.52

Answer:

1) yes 2) no 3) yes 4) no 5) no 6) no

Step-by-step explanation:

Horizontal line test

Answer:

10 gallons per hour

Step-by-step explanation:

1/4x4=1. 2 1/2x4=10. Hope it helps!

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Answer:

The cost of the bottle of drink is P4.85. The refund for an empty bottle is 25 thebe.

To express the refund as a percentage of the cost of the drink, we need to convert the refund to the same unit as the cost of the drink.

1 thebe = 0.038 Philippine pesos (as of June 2023)

25 thebe = 0.95 Philippine pesos

Therefore, the refund for an empty bottle is 0.95/4.85 x 100% = 19.59%

So the refund for an empty bottle is 19.59% of the cost of the bottle of drink.

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Answer:

Step-by-step explanation:

Formula for transformation for parent function f(x) = |x|  is

g(x) = a |x -h| + k                    

Where a is your stretch/compression

(h, k) is your vertex or shift (x, y) directions

If the function is shifted down 3 that's  -3 in y direction

g(x) = |x| - 3

Answer:

0

Step-by-step explanation:

=> m = 3 -3/7+5

=> m = 0/12

=> m = 0

Based on the information we can infer that 5/8 between 6 people is equal to 15/24.

To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.

5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder

So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:

(5/4) x 6 = 30/4 = 15/2 = 15/24

So each person would receive 15/24 of the original amount.

Note: Here is the question in English:

5/8 divided in 6 people

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I believe its D. because you put the numbers from smallest to biggest

then find the median (middle number)

and mode is what number you see most often.