Bradley went on a bike ride to the store 6 miles away. If it took Bradley 38 of an hour to get there and 14 of an hour to get back, what was his average rate of speed (miles per hour) for the entire trip? (Hint: To find the average, divide the total distance by the total duration.)

The expressions when simplified are -9 - 2i and x = ±8i

From the question, we have the following parameters that can be used in our computation:

(6 -7i) - (8 - 5i) - 7

When evaluated, we have

(6 -7i) - (8 - 5i) - 7 = -9 - 2i

Here, we have

6x² = -384

Divide by 6

x² = -64

Take the square roots

x = ±8i

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Answer:

The denominator is 162 in the next term. (1/162)

Step-by-step explanation:

The denominator is the bottom number of the fraction.

In the pattern, the top number (numerator) just stays 1 every time.

But the bottom number (denominator) goes:

2, 6, 18, 54...

The pattern is "times 3"

2 × 3 is 6, which is the next number.

6 × 3 is 18.

18 × 3 is 54.

So to find out what comes next, we can times by 3.

54 × 3 is 162.

So 162 is the next denominator of 1/162, the next term in the geometric sequence.

Answer: 1/162

Step-by-step explanation:

Since you multiply by 3 for each denominator, then that means 54 x 3= 162. so the answer would be 1 /162

Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer:

MAY BE 120 ...IS IT CORRECT

Answer: 1 4/5 feet

Step-by-step explanation:

Here's the complete question:

Taylor is decorating for a party. She cuts 5 equal-length streamers from a strip of yellow paper that is 9 feet long. How long is each streamer in fraction form?

The length of each streamer will be gotten by dividing the length of the strip of yellow paper by the number of streamers. This will be:

= 9 feet / 5

= 1 4/5 feet

Therefore, the length of each streamer is 1 4/5 feet.

So y = 2x + 2 is the equation of a line parallel to line ef and includes point (0, 2).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Since line ef has a slope of 2, any line parallel to it will also have a slope of 2. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line parallel to line ef that contains point (0, 2), we need to find its y-intercept.

We can use the point-slope form of a line to find the equation of the line: y - y1 = m(x - x1)

Plugging in the point (0, 2) and the slope of 2, we get:

y - 2 = 2(x - 0)

y - 2 = 2x

y = 2x + 2

So, the equation of a line parallel to line ef and containing point (0, 2) is y = 2x + 2.

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The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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Answer:

Letter B.

Step-by-step explanation:

Look for where the line corsses the Y axis. that will tell you the most about this line and it corsses at 8 so that can be the only one correct.

After the simplification, five 4th times one fourth is 5. So the option 3 is correct.

Ordinal numbers are a generalization of the idea of a natural number, and they are frequently used to describe how to organize a group of things sequentially.

They are those numbers that can be used to locate and locate persons or objects. If a list of individuals or items is given, ordinal numbers can be used to identify the order in which each individual is listed. First, second, third, fourth, fifth, sixth, and so on are examples of prefixes and suffixes that can be used to write ordinal numbers.

The statement for the expression is:

Five 4th times one fourth

Five = 5

Five 4th times = 5 × 4

Five 4th times one fourth = 5 × 4 × 1/4

Now simplify the expression;

= 5 × 4 × 1/4

= 5

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The complete question is:

What is five 4th times one fourth?

1. Twentieth

2. Tenth

3. Five

4. Twenty-fourth

5. One fifth

Step-by-step explanation:

y = x-3

So, y + 3 = x

x = y + 3

if x = 7

y = 7 - 3 = 4

if y = 1

x = 1 + 3 = 4

......

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

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Answer: 7 seats in each row.

Step-by-step explanation:

14 / 2 = 7 seats in each row.

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

       32*t = 32

            t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

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Hence proved that 3 can divides (4n + 5) for all natural numbers n.

To show that 3 divides (4n + 5) for all natural numbers n, we need to show that there exists some integer k such that:

4n + 5 = 3k

We can rearrange this equation as:

4n = 3k - 5

Since 3k - 5 is an odd number (the difference of an odd multiple of 3 and an odd number), 4n must be an even number. This means that n is an even number, since the product of an even number and an odd number is always even.

We can then write n as:

n = 2m

Substituting this into the original equation, we get:

4(2m) + 5 = 8m + 5 = 3(2m + 1)

So we can take k = 8m + 5/3 as an integer solution for all natural numbers n.

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Hence proved that 3 can divides (4n + 5) for all natural numbers n.

To show that 3 divides (4n + 5) for all natural numbers n, we need to show that there exists some integer k such that:

4n + 5 = 3k

We can rearrange this equation as:

4n = 3k - 5

Since 3k - 5 is an odd number (the difference of an odd multiple of 3 and an odd number), 4n must be an even number. This means that n is an even number, since the product of an even number and an odd number is always even.

We can then write n as:

n = 2m

Substituting this into the original equation, we get:

4(2m) + 5 = 8m + 5 = 3(2m + 1)

So we can take k = 8m + 5/3 as an integer solution for all natural numbers n.

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The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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The number of the books owed by Tara which she has not read would be = 152 books.

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..

The number of books owned by Tara = 160 books

The percentage of books read by Tara = 95%

Therefore, 95% of her books = 95/100 × 160

= 15200/100

= 152 books.

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is this multiple choice? it seems some of it is cut off.

(a) dw/dt = (3e^(3t) - 4t³)e^(3t) (Chain Rule is applied).

(b) dw/dt = e^(3t) - 4t³e^(3t) (w is expressed as a function of t before differentiating).

(a) To find dw/dt using the Chain Rule, we substitute the given expressions for x and y into the equation for w. Then, we differentiate with respect to t, taking into account the chain rule for differentiating composite functions. By applying the Chain Rule, we obtain dw/dt = (d/dt)(x - x^(-1)) = (dx/dt - dx^(-1)/dt) = (3e^(3t) - 4t³)e^(3t).

(b) To find dw/dt by converting w to a function of t, we rewrite w in terms of t using the given expressions for x and y. Substituting x = e^(3t) and y = t^4 into the equation for w, we have w = e^(3t) - (e^(3t - 1)). Differentiating w with respect to t, we find dw/dt = d/dt(e^(3t) - e^(3t - 1)) = e^(3t) - 4t³e^(3t).

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

x= 11

Step-by-step explanation:

\( \frac{2(x + 5)}{4} = 8\)

Simplifying the fraction:

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

Multiply both sides by 2:

x+ 5= 8(2)

x+ 5= 16

Subtract both sides by 5:

x= 16 -5

x= 11

The answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:

3 cupcakes + 1 tea = £9

3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5

1 cupcake = £7.5 ÷ 3 = £2.5

So 2 cupcakes would cost:

2 cupcakes = 2 × £2.5 = £5

Therefore, the answers are:

a) 2 cakes cost £5

b) 1 cake costs £2.5.

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Answer:

q = 3/4

Step-by-step explanation:

7+5(3q-4)=(q-1)

(5×3q)=15q (5×4)=20

7+15q-20=7

(7-20)= -13

-13+15q=7

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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The experiment type of research study is being used.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

As opposed to option A, where the participants are being observed in their natural context, this is not a naturalistic observation example.

The lack of a relationship means that it is neither a correlation research, as in option C, nor a survey, as in option D.

Option B is the appropriate response, thus.

So, the experiment  type of research study is being used.

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Ploidy level shifts between a pair of species (one diploid, one tetraploid) fit the "allopolyploid hybridization model" very well because it explains the origin of the diploid and tetraploid forms.

The allopolyploid hybridization model proposes that the tetraploid species originated from the hybridization between two different diploid species.

Specifically, the hybridization event resulted in a doubling of the chromosome number, creating a tetraploid individual with four copies of each chromosome.

This event is known as allopolyploidization.

The diploid species that served as the parents of the tetraploid species are not identical to either of the two tetraploid species.

Rather, they are thought to be extinct or still-existing diploid species that hybridized to produce the tetraploid offspring.

The allopolyploid hybridization model explains why the diploid and tetraploid species often have similar morphology and DNA sequences. The diploid parent of the tetraploid species contributes half of the genome, while the other half comes from the other diploid parent.

This hybridization event leads to a mix of the two parent genomes, resulting in a unique genome that can contribute to the formation of a new species.

Overall, the allopolyploid hybridization model provides a plausible explanation for the origin of tetraploid species, and it is supported by extensive genetic and morphological evidence.

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Answer:

6

Step-by-step explanation:

First, we can calculate the total number of cards:

total cards = (cards with letters) + (cards with numbers)

total cards = 12 + 16

total cards = 28

Using the total number of cards, we can define the probability of pulling a card with a letter one time (or many times with replacement) as:

\(P(\text{card with letter}) = \dfrac{\text{cards with letters}}{\text{total cards}}\)

\(P(\text{card with letter}) = \dfrac{12}{28}\)

\(P(\text{card with letter}) = \dfrac{3}{7}\)

Finally, we can create a prediction for the number of times a card with letters will be pulled by multiplying the probability of pulling a card with a letter by the number of times we are pulling a card with replacement.

\(\text{prediction} = \text{pulls} \cdot P(\text{card with letter})\)

\(\text{prediction} = 14 \cdot \dfrac{3}{7}\)

\(\boxed{\text{prediction} = 6}\)

From this proportion of days he does the activities, sometimes they will meet in one day.

He will do both in the same day when the day is a common factor of 3 and 4.

Since today he did both, the next time he will do so will be in the least common factor of 3 and 4.

To get the least common factor of these, we can identify the divisors of each and makes the divisions until both get to 1. If one of the divisiors is divisior for both, we don't repeat it.

So, from 3 and 4, we can start by the divisior of 2. 2 Is a divisior of 4, but not of 3, so we divide only the number for:

3, 4 | 2

3, 2 |

Now, we have 3 and 2, so we can divide for 2 again:

3, 4 | 2

3, 2 | 2

3, 1 |

Now, we have 3 and 1, so we can only divide by 3 now:

3, 4 | 2

3, 2 | 2

3, 1 | 3

1 , 1 |

So, in the end we have 2, 2 and 3, so the least common factor is 2*2*3 = 12.

Since the common factor of 3 and 4 is 12, Tyler will lift and jog on the same day 12 days after today.

The table using this function rule y = 3x+2 is as follows:

x      y

1       5

2      8

7      23

8      26

What is function rule?

The relationship between the input or domain and the output or range is represented by the function rule. A relation is a function if and only if each domain value has one value in the range.

An output is produced by a function machine using an input and a set of rules. Connecting a function described by a verbal rule with corresponding values in a table is the goal of this task (one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression).

Although this broad application is not meant to be evaluated, it encourages students to think more broadly about functions as relating objects other than numbers.

Given that, y = 3x+2

Below is the completed table,

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