Find all the pairs of numbers that make each statement an equation. How do you know you have found all the pairs?

Step-by-step explanation:

please make sure that fractions are still in the problem text after scanning it.

because they are missing here, and I have to guess around.

Basically the problem is

x + 1/a × x = 15

that means

ax + x = 15a

(a+1)x = 15a

x = 15a/(a+1)

for a = 2 (so, 1/2 x is added to x), we get

x = 15×2/3 = 30/3 = 10

for a = 4 (1/4 of x is added to x), we get

x = 15×4/5 = 60/5 = 12

these are also the first 2 answer options. so, please pick the one that fits the complete problem definition.

the 3rd and 4th answer options are nonsense anyway, as when you add something greater than 0 to x and get 15, then the initial x cannot be already 15 or even bigger.

Answer:

Area of a rectangle is w • L

w = 5 while L = (b + 3)

Area is

5 • (b + 3) = 5b + 15

So answer is 2. 3. and 4. which are all similar forms of the same expression.

Step-by-step explanation:

The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

To know more about combination formulas visit:

brainly.com/question/14685054

#SPJ11

The probability of either event E or event F occurring, when E and F are mutually exclusive, is 0.85.

If E and F are mutually exclusive events, it means that they cannot occur simultaneously. In such cases, the probability of either event E or event F occurring is the sum of their individual probabilities.

Given that P(E) = 0.34 and P(F) = 0.51, we can calculate the probability of E or F, denoted as P(E or F), as:

P(E or F) = P(E) + P(F)

Substituting the given values, we have:

P(E or F) = 0.34 + 0.51

Calculating the sum, we find:

P(E or F) = 0.85

Know more about probability here:

https://brainly.com/question/32004014

#SPJ11

22/35+35x3

Division comes first.

22/35=0.62857142857 or just 0.629, or 0.63

0.63+35x3

Now we multiply.

35x3=105

So now we have 0.63+105.

Lastly, we add.

0.63+105=105.63

The answer is 105.63.

---

hope it helps

(a) The average velocity over the interval [1,9] is 16 ft/s. (b) The average velocity over the interval [1,8] is 16 ft/s. (c) The average velocity over the interval [1,7] is 16 ft/s. (d) The average velocity over the interval [1,1+h] is -16h ft/s.

To find the average velocity of an object over a given interval, we need to calculate the displacement of the object during that interval and divide it by the duration of the interval.

The position function of the object is given by s(t) = -16t^2 + 48t.

(a) For the interval [1,9], the displacement is s(9) - s(1):

Displacement = [ -16(9)^2 + 48(9) ] - [ -16(1)^2 + 48(1) ] = 144 ft

Duration of interval = 9 - 1 = 8 s

Average velocity = Displacement / Duration = 144 ft / 8 s = 16 ft/s

(b) Similarly, for the interval [1,8]:

Displacement = [ -16(8)^2 + 48(8) ] - [ -16(1)^2 + 48(1) ] = 112 ft

Duration of interval = 8 - 1 = 7 s

Average velocity = Displacement / Duration = 112 ft / 7 s = 16 ft/s

(c) For the interval [1,7]:

Displacement = [ -16(7)^2 + 48(7) ] - [ -16(1)^2 + 48(1) ] = 96 ft

Duration of interval = 7 - 1 = 6 s

Average velocity = Displacement / Duration = 96 ft / 6 s = 16 ft/s

(d) In general, for the interval [1, 1+h]:

Displacement = [ -16(1+h)^2 + 48(1+h) ] - [ -16(1)^2 + 48(1) ] = -16h ft

Duration of interval = 1+h - 1 = h s

Average velocity = Displacement / Duration = -16h ft / h s = -16 ft/s

Therefore, the average velocity of the object over the given intervals is 16 ft/s, except for the interval [1, 1+h], where it is -16 ft/s.

learn more about interval here:

https://brainly.com/question/11051767

#SPJ11

The length of side DE is 3cm

Since the line AC is equivalent to DE, hence AC = DE

To get the length of DE, we will need to get the length oF AC using the Pythagoras theorem:

Given the following parameters

Hypotenuse = 5

Opposite = 4

Required

Adjacent side

Substitute the given parameters into the formula of Pythagoras theorem.

AC² = 5² - 4²

AC² = 25 - 16

AC² = 9

AC = 3

Hence the length of side DE is 3cm

Learn more on Pythagoras theorem here: https://brainly.com/question/12306722

Since the points on this graph represent a relationship between x- and y-values, the statement which is true about the relationship is that: 4. It cannot be proportional because a straight line through the points does not go through the origin.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in this graph is not proportional.

Read more on graphs here: brainly.com/question/4546414

#SPJ1

Complete Question:

The points on this graph represent a relationship between x- and y-values. Which statement about the relationship is true?

1. It must be proportional because the points lie on the same line.

2. It must be proportional because each time x increases by 2, y stays the same.

3. It cannot be proportional because the y-values are not whole numbers.

4. It cannot be proportional because a straight line through the points does not go through the origin.

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

In Listening 1.2, Miley Cyrus’ Wrecking Ball, identifying the difference in Verse, Chorus, and Bridge is quite easy.

The verse part of the song is the section that is generally sung in a lower key and can be regarded as the storytelling aspect of the song. The musical form or structure of the song, “Wrecking Ball” impacts the song's repeatability as it is designed to create a catchy, repeating theme that sticks in the listener's head.

Additionally, the predictability of the song's structure makes it easier for DJs to mix songs in clubs or at parties. My aesthetic response to the song is a bit mixed. This structure makes the song more engaging, and it is easy to get lost in the emotion of the song. Additionally, the repeating theme of the chorus makes it easier for the listener to sing along.

To know more about difference visit:

https://brainly.com/question/30241588

#SPJ11

Answer:

x = 6, y =3

Step-by-step explanation:

4x-7y=3

x-7y=-15

Multiply the first equation by -1

-4x+7y=-3

Then add this to the second equation to eliminate y

-4x+7y=-3

x-7y=-15

------------------

-3x +0y = -18

-3x = -18

Divide by -3

-3x/-3 = -18/-3

x = 6

Now find y

x -7y = -15

6 -7y = -15

Subtract 6 from each side

6-7y-6 = -15-6

-7y = -21

Divide by -7

-7y/-7 = -21/-7

y =3

We cannot conclude that listening to Mozart will lead to much higher scores on an IQ test based on the given information.

While the mean IQ scores were 1.2 points higher after listening to Mozart, the statistical significance of this difference depends on the chosen level of significance (alpha level) and the sample size. The p-value of 0.0004 indicates that if there is no difference in IQ scores between the Mozart and silent background conditions in the population, there is only a 0.04% chance of observing a sample mean difference of 1.2 points or larger. However, we would need to know the alpha level and sample size used in the study to determine if this is statistically significant at a practical level. Additionally, this experiment only shows a correlation between listening to Mozart and higher IQ scores, and cannot prove causation.

To know more about higher scores,

https://brainly.com/question/16278100

#SPJ11

The sample space of rolling a 6 sided number cube is the set of all possible outcomes of rolling the number cube. The sample space for a 6 sided number cube is the set of numbers 1,2,3,4,5, and 6.

When rolling a 6 sided number cube, the sample space is the set of all possible outcomes, which are the numbers from 1 to 6. This means that the sample space includes each of the six numbers, with no bias towards any particular number. Each of the six numbers has an equal chance of being obtained when rolling the number cube.

The sample space of a 6 sided number cube is also known as a discrete sample space, since all of the possible outcomes are predetermined and known. The sample space of a 6 sided number cube is finite and can be easily calculated by listing all the possible outcomes. Since there are 6 possible outcomes, the sample space consists of 6 elements.

The sample space of a 6 sided number cube can be easily visualized by imagining a six-sided die being rolled and each side being labeled with a number from 1 to 6. This demonstrates that the sample space of a 6 sided number cube is a discrete sample space, and each of the six numbers has an equal chance of being obtained.

Learn more about six-sided die at : https://brainly.com/question/21563697

#SPJ4

a) The central 95% of all copper contents would be bounded by the values of 26.02 and 35.58.

b) The distribution of the sample mean copper content follows an approximately normal distribution with a mean of 30.8 and a standard error of \($\frac{2.45}{\sqrt{16}}\) =0.6125.

c) If we were to randomly sample 16 brake pads from this distribution, the bounding values for the central 95% of possible means would be (29.6, 32)

a) Since the copper content in sintered brake pads follows an approximately normal distribution with a mean of 30.8 and a standard deviation of 2.45, we can use the standard normal distribution to find the values that bound the central 95% of all copper contents. The 95% confidence interval corresponds to z=1.96 in the standard normal distribution. Thus, the values that bound the central 95% of all copper contents are given by:

30.8−1.96×2.45=26.02,30.8+1.96×2.45=35.58

b) The sample mean of copper content for a sample of 16 pads is also normally distributed with a mean of 30.8 and a standard deviation of \($\frac{2.45}{\sqrt{16}}=0.6125$\), which is called the standard error. The distribution of the sample mean is given by:

c) The bounding values for the central 95% of possible means can be found by using the formula:

where \($\sigma$\) is the population standard deviation, n is the sample size and \($z^*$\)is the critical value of the standard normal distribution that corresponds to a 95% confidence interval. Substituting the values, we get:

Therefore, the bounding values for the central 95% of possible means are given by:

Learn more about Normal Distribution:

https://brainly.com/question/4079902
#SPJ4

Answer:

C

Step-by-step explanation:

the first person's grows in a line/ with a slope and the second persons grows with a growth rate (the percent).

Answer:

C

Step-by-step explanation:

and forvthe explination the other person explained pretty well

Question:

13 + b > 34

Step 1: Keep variable on one side, and subtract 13 on both sides.

b > 21

Step 2: Now that you have the value of b, create a number line that includes the number "21"

Step 3: Since it is not "or equal too" we will use an open dot, since we do not contain that point. Put dot over 21.

Step 4: The sign is ( > ) meaning greater than. Therefore all points greater than 21 is true. See graph.

Answer:

ue mom

Step-by-step explanation:

Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.

Remember the relation:

Speed*time = distance.

Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.

Here we know that:

Kadeem drives at a constant speed of 50mi/h

Quinn drives at a constant speed of 75 mi/h.

Replacing that in the equation:

Kadeem's case:

(50 mi/h)*t = 25mi

t = (25 mi)/(50 mi/h) = 0.5 hours.

Quinn's case:

t = (25mi)/(75 mi/h) = 0.33 hours.

So Kadeem takes longer.

Learn more about speed:

https://brainly.com/question/4931057

#SPJ1

The maximum profit is $288, and you should charge $6 per dozen.

Let's assume that demand depends linearly on price, such that we can write:

q = a*p + b

where q is the demand and p is the price.

We have 3 points of that line:

The slope of the line is given by:

\(a = \frac{q_2 - q_1}{p_2 - p_1}\)

Where these are values of demand and prize for two different points, if we use the first two points we get:

\(a = \frac{72 - 80}{3 - 2} = -8\)

Then the line is something like:

q = -8*p + b

Remember that when p = 2, the demand is equal to 80, replacing that we get:

80 = -8*2 + b

80 + 16 = b = 96.

So the line is:

q = -8*p + b

Profit is given by the product between the demand and the price, so we have.

Profit = p*q = p*(-8*p + 96) = -8p^2 + 96p

We want to maximize that, notice that is a quadratic equation of negative leading coefficient, so the maximum is at the vertex, using the equation for the vertex of a quadratic equation we will see that the maximum is at:

p = -96/(2*-8) = 6

Then the maximum profit is:

profit = -8*(6)^2 + 96*6 = 288

The maximum profit is $288, and you should charge $6 per dozen.

If you want to learn more about linear relations, you can read:

https://brainly.com/question/1884491

Answer:

4 cm

Step-by-step explanation:

x = the side of a cubical box

x^3 = 64

But 4^3 also = 64

=> x = 4

Answer:

Volume of a cube = a³

64 = a³

3 root 64 = a

4 cm = a

Answer:

\(area = 2 \times 6 \times \pi = 12\pi\)

Answer:

4

Step-by-step explanation:

Hope this helps!

The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs. The distance traveled in one year of normal commuting could be more suitable in this case.

A. The functional unit, which is defined as the quantified performance of a product system or service that will be used as a reference for conducting the life cycle assessment, is important for evaluating the impacts of products or systems on the environment.

The following are the different functional units that are acceptable or not acceptable to assess the environmental impacts of the product or system.

The first functional unit, one vehicle, is not appropriate as it doesn't represent the amount of driving a person could expect to do if they bought a new car and drove it until the end of its life.

The second functional unit, distance traveled in one full gas tank or battery charge, would not be appropriate for our purpose as it is not clear what type of vehicle it will be used for.

The third functional unit, one year of normal commuting, would not be appropriate as it does not consider all the environmental impacts over the lifetime of the vehicle.

The fourth functional unit, 1 kg of vehicle, would not be appropriate as it is too small of a functional unit to evaluate the environmental impacts of the vehicle.

B. If we also wanted to consider riding the public bus as a personal transportation option, 200,000 miles driven would not be an appropriate choice of functional unit. This is because buses are used for transportation purposes, and they will have different environmental impacts than cars.

Therefore, the distance traveled in one year of normal commuting could be more suitable in this case.

C. One other impact category we could consider is the acidification potential. The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs.

Learn more about distance  here:

https://brainly.com/question/15256256

#SPJ11

The rectangle can have P = 20 and L = 6 because P = 2(6) + 2(4) would equal 20.

Here, we have,

given that,

L=6 and A=24

so, we get,

W = 24/6 = 4

The formula for the perimeter of a rectangle is P=2L + 2W.

If the width is W = 4 and the length is L=6, then the perimeter becomes:

P = 2(6) + 2(4)

so, we get,

P = 20

Therefore the answer is 20

The rectangle can have P = 20 and L = 6 because P = 2(6) + 2(4) would equal 20,

Learn more about perimeter here:

brainly.com/question/397857

#SPJ2

Answer:

See attachment for number line

Step-by-step explanation:

Given

\(Ian = \frac{6}{8}\)

\(Anna = \frac{3}{4}\)

Required

Number line to represent both amounts

The interval on the number line is 16.

So, we need to calculate the position of both as thus.

\(Ian = \frac{6}{8} * 16 = \frac{96}{8} = 12\)

\(Anna = \frac{3}{4} * 16 = \frac{48}{4} = 12\)

So, both will be positioned on the 12th position.

The yellow dot represents Anna while the blue dot represents Ian

See attachment for their position on the number line

Answer:

50 children tickets; 60 adult tickets

Step-by-step explanation:

Let a = number of adult tickets.

Let c = number of children tickets.

a + c = 110

5a + 3c = 450

  -3a - 3c = -330

  5a + 3c = 450

------------------------

   2a        = 120

a = 60

a + c = 110

c = 50

Answer: 50 children tickets; 60 adult tickets

Answer:

Given,

ABC is triangle with vertices A(-2,1), B(2,2) and C(6, -2)

Slope of BC(m_1) =\(\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{-2-2}\)

\(=\frac{4}{-4}=-1\)

Since AD is perpendicular to BC

let slope of BC be (\(m_2\)).

We have for perpendicular

\(m_1*m_2=-1\)

\(-1*m_2=-1\)

\(m_2=1\)

Now equation of line passing through point A(-2,1) is

\(y-y_1=m_2(x-x_1)\)

y-1=1(x-(-2))

y-1=x+2

y=x+2+1

y=x+3 which is a required equation of the altitude of AD drawn from A to BC.

The required equation of the altitude of AD drawn from A to BC is y=x+3

Given that ABC is triangle with vertices

Given the slope of BC(m_1)

= y2-y1/x2-x1

= -1.

For perpendicular,

m1 * m2= -1

m2= 1.

Now equation of line passing through point A(-2,1) is

Read more about vertices of triangle here:

https://brainly.com/question/15146806

Answer:

20 square yards

Step-by-step explanation:

Area of workshop

= length * width

= 5 * 4

= 20 square yards

The expression why represents the amount of money he has saved after 8 weeks is y = 304 - 8g

Given:

The expression which represents the amount of money he has saved after 8 weeks = (Amount Mike earns per week × Number of weeks) - (Amount spent on gas each week × Number of weeks)

y = (38 × 8) - (g × 8)

y = 304 - 8g

Learn more about algebraic expression:

https://brainly.com/question/4344214