Tyrone biked 45 miles at an average speed of 18 miles per hour, without stopping. About how long did the ride take him? Use the formula t equals d over r

The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

\(\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}\)

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

\(\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}\)

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

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Answer:

Step-by-step explanation:

First, put them in order.

5.3x+3.6x+9.8-8.14

Add 5.3x and 3.6x

8.9x

Subtract 8.14 from 9.8

1.66

Answer:

Choice B

Step-by-step explanation:

Even though we have to see the options, I think the answer is B.

Answer:

2x + 4y = 16

4y = 16 - 2x

y = 4 - 1/2x

gradient = -1/2

y - y1 = m(x - x1)

m = gradient, (x1, y1) = (-2,2)

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

y - 2 = -1/2x - 1

y = -1/2x + 1 → ANSWER

Hope it helps!

Answer:

5

4

1

2

8

,.,.,.,.,.,.,.,

The probability that the event will happen is 40/61.

Probability provides a way to reason about uncertain events and helps in making informed decisions based on the likelihood of different outcomes.

To find the probability that an event will not happen, you subtract the probability of the event happening from 1.

For the first question:

Given P(E) = 2/7, the probability of the event not happening is:

P(E') = 1 - P(E) = 1 - 2/7 = 5/7

Therefore, the probability that the event will not happen is 5/7.

For the second question:

Given P(E') = 21/61, the probability of the event happening is:

P(E) = 1 - P(E') = 1 - 21/61 = 40/61

Therefore, the probability that the event will happen is 40/61.

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The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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The value of the given integral is ln|(1 + √(3x² + (x + 1)(x² + 9)))/2x + 11/√10|/16(B + 5).

∫[Bx + 5x + 77]/[√(3x² + (x + 1)(x² + 9)) × 8x × (Bx + 5x + 77) × (x + 1)(x² + 9)]dx can be found out by substituting

(x² + 9) = t.

Since d/dx(x² + 9) = 2xdx,

therefore, dx = dt/2x

Also, substitute 3x² + (x + 1)(x² + 9) = u.

So,

6xdx + 2x²dx = du ...[i]

4x² + 3 = u ...[ii]

Hence, the integral becomes

∫[Bx + 5x + 77]/[√u × 8x × (Bx + 5x + 77) × (t + 1)t] × 2xdt

Since Bx + 5x + 77 = (B + 5)x + 77

Therefore, substitute (B + 5)x = wdw/dx = B + 5dx, therefore,

dx = dw/(B + 5)

Substitute the value of dx and Bx in the integral obtained above

.∫[wdw/(B + 5) + 5x + 77]/[√u × 8(B + 5)w × (w/B + 5 + 5) × (t + 1)t] × 2dt

taking 2 common and cancelling the like terms, the expression becomes

∫[w/(B + 5) + 5]/[√u × 4(B + 5) × (w/B + 5 + 5) × (t + 1)t]dt

Taking (t + 1) = v, so dt = dv

Therefore, the integral becomes

∫[w/(B + 5) + 5]/[√u × 4(B + 5) × (w/B + 5 + 5) × v]dv

= ∫[w/(B + 5) + 5]/[√u × 4(B + 5) × v(w/B + 5 + 5)]dv

Integrating the above expression

∫[w/(B + 5) + 5]/[√u × 4(B + 5) × v(w/B + 5 + 5)]dv

= ln|v(1 + √u/√(3 + u))|/16(B + 5)

Now substituting the values of w, v and u in the above expression

∫[Bx + 5x + 77]/[√(3x² + (x + 1)(x² + 9)) × 8x × (Bx + 5x + 77) × (x + 1)(x² + 9)]dx

= ln|(1 + √(3x² + (x + 1)(x² + 9)))/2x + 11/√10|/16(B + 5)

Therefore, the value of the given integral is ln|(1 + √(3x² + (x + 1)(x² + 9)))/2x + 11/√10|/16(B + 5).

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The given statement "if set of difference scores with df = 8 has a mean of md = 3.5 then sample will produce repeated-measures t statistic of t = 1.75." is false because  it is not possible to determine t statistic.

In a repeated-measures t-test, the t statistic is calculated using the sample mean difference, the standard deviation of the sample mean difference, and the sample size. The formula for calculating the t statistic in a repeated-measures t-test is:

t = (md - μd) / (s / √n)

where md is the mean of the difference scores, μd is the population mean of the difference scores (typically assumed to be zero), s is the standard deviation of the difference scores, and n is the sample size.

In the given statement, we are provided with the mean of the difference scores (md = 3.5) and the variance (s² = 36), but we do not have the sample size (n). Therefore, we cannot calculate the t statistic using the given information.

Hence, it is not possible to determine whether the sample will produce a repeated-measures t statistic of t = 1.75 based on the provided information.

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Answer:

the answer is angle y = 54. ........

Answer:

y = 54

Step-by-step explanation:

Two of the sides are congruent, so the angles that are facing the two sides are also congruent, so:

3(x + 7) = 63

3x + 21 = 63

3x = 42

x = 14

A triangle equals 180 degrees,  and input 14 into the equation, so:

3(14 + 7) + 63 + y = 180

3(21) + 63 + y = 180

63 + 63 + y = 180

126 + y = 180

y = 54

Answer:

the slope is 1

you find two points that are directly on an intersection of the grid. and then count rise/run

rise is going up and down and run is left and right

start at the point you found furthest to the left and count to the next point that's to the right.

if you have to go down to find it or left to find it, the slope is negative

in this case. theres a point at (-1,0) and (0,1)

you have to count up one and right one, making the slope 1/1 or simplified to 1

Step-by-step explanation:

I hope this helps :)

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Which TWO expressions are equivalent to (x - y) 2/3 - 3/4 (y-x)

a) There are 32432400 different layouts possible when 7 chips of different types are placed on the board.

b) There are 6435 different layouts possible when 7 chips of the same type are placed on the board.

c) There are 48385814400 different layouts possible when all of the locations are filled with chips, with 3 of one type, 5 of another type, and all others different.

(a) If 7 chips of different types are to be placed on the board, the number of different layouts can be calculated using permutations.

Since each chip is placed in a different location, the order of placement matters.

The number of different layouts can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of locations (15) and r is the number of chips (7).

P(15, 7) = 15! / (15 - 7)!

= 15! / 8!

= (15 × 14 × 13 × 12 × 11 × 10 × 9) / (7 × 6 × 5 × 4 × 3×2 × 1)

= 32432400

(b) If 7 chips of the same type are to be placed on the board, the order of placement does not matter.

The number of different layouts can be calculated using combinations.

The number of different layouts can be calculated using the formula for combinations:

C(n, r) = n! / (r!×(n - r)!)

Where n is the total number of locations (15) and r is the number of chips (7).

C(15, 7) = 15! / (7! × (15 - 7)!)

= 15! / (7!× 8!)

= (15 × 14× 13 × 12 × 11 × 10×9) / (7 ×6 ×5 × 4× 3 × 2 × 1)

= 6435

(c) The number of different layouts can be calculated using the formula for permutations:

P(n, r₁) × P(n - r₁, r₂) × P(n - r₁- r₂, r₃)

Where n is the total number of locations (15), r₁ is the number of locations for the first type of chip (3), r₂ is the number of locations for the second type of chip (5), and r₃ is the remaining number of locations for the other chips (7 - r₁ - r₂).

P(15, 3) × P(15 - 3, 5) × P(15 - 3 - 5, 7 - 3 - 5)

P(15, 3) × P(12, 5) × P(7, 1)

72730×95040×7

48385814400

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In the layout of a printed circuit board for an electronic product, 15 different locations can accommodate chips.

(a) If 7 chips of different types are to be placed on the board, how many different layouts are possible?

(b) If 7 chips of the same type are to be placed on the board, how many different layouts are possible?

(c) If all of the locations are to be filled with chips, 3 of which are of one type, 5 of which are another type, and all others different, how many different layouts are possible?

Answer:

(-4, ∞)

Step-by-step explanation:

The domain of a function is how far the x goes left and right.

We see the x starts at -4 and goes forever.

So, the Domain of the function is (-4, ∞)

The domain of the function in the given graph of a function represents all the x-values equal to (−4,∞).

The domain of a function is the set of all possible input values for the function.

In other words, it is the set of all x-values for which the function has a defined y-value.

To find the domain of a function from its graph, we need to look for any x-values for which the function is undefined.

The graph in the image you sent shows a function that is defined for all real numbers.

This means that the domain of the function is all real numbers, here in the given graph domain is  (−4,∞).

Another way to think about it is that the graph of the function extends infinitely far to the left and to the right, which means that there are no x-values for which the function is undefined.

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In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.

For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.

Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.

Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.

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Answer:

|7-3|=4 Is true.

|7-3|+4 Not true.

Step-by-step explanation:

7-3 does equal four but |7-3|+4 doesn't really make sense for an answer.

So I believe you were trying to say = 4 you just had your finger on the shift key when you were typing.

The population doubles in approximately 1.51 hours and triples in approximately 2.03 hours.

To find the time it takes for the bacterial population to double in size, we need to solve the equation N = 2N₀, where N₀ represents the initial population size. Substituting the given model N = 220ekt into the equation, we have 2(220) = 220ekt. Cancelling out the common factor of 220, we get 2 = ek(10).

To isolate k, we take the natural logarithm (ln) of both sides: ln(2) = k(10). Solving for k, we find k = ln(2)/10 ≈ 0.06931 (rounded to five decimal places).

Next, we can determine the time it takes for the population to double by substituting the doubled population size (440) into the model and solving for t. Using N = 440 and k = 0.06931 in N = 220ekt, we have 440 = 220e0.06931t. Dividing both sides by 220 and taking the natural logarithm, we get ln(2) = 0.06931t. Solving for t, we find t ≈ 1.51 hours (rounded to two decimal places).

Similarly, to find the time it takes for the population to triple, we substitute the tripled population size (660) into the model and solve for t. Using N = 660 and k = 0.06931 in N = 220ekt, we have 660 = 220e0.06931t. Dividing both sides by 220 and taking the natural logarithm, we get ln(3) = 0.06931t. Solving for t, we find t ≈ 2.03 hours (rounded to two decimal places).

Therefore, the bacterial population takes approximately 1.51 hours to double in size and approximately 2.03 hours to triple in size.

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To find the inverse of the given function f(x) = √(x-9) + 10, we can switch the roles of x and y and solve for y. The inverse function, denoted as f^(-1)(x), is obtained by isolating y. It is f^(-1)(x) = (x - 10)^2 + 9.

The given function is f(x) = √(x-9) + 10.

To find the inverse of this function, we switch the roles of x and y and solve for y.

Let's interchange x and y:

x = √(y - 9) + 10.

To isolate y, we can start by subtracting 10 from both sides:

x - 10 = √(y - 9).

Next, we square both sides of the equation to eliminate the square root:

(x - 10)^2 = y - 9.

Finally, adding 9 to both sides gives us the inverse function:

y = (x - 10)^2 + 9.

Therefore, the inverse function of f(x) = √(x-9) + 10 is f^(-1)(x) = (x - 10)^2 + 9.

The inverse function represents the original function reflected over the line y = x.

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Answer:

B, x=5

Step-by-step explanation:

Both triangles are similar with a ratio of 22.5/9

so using that an equation can be created like this, \(\frac{22.9}{9}\) = \(\frac{23.5}{x+4.4}\)

If simplified, 22.9(x + 4.44) = 23.5(9)

22.5x + 99 = 211.5

22.5x = 112.5

x = 5

Answer:

x = 6

Step-by-step explanation:

You use trig to find the hypotenuse of the first triangle. 4^2 + 3^2 = c^2. Then you get c = 5. SInce 10 is 2 times greater than 5 you multiply 3 by 2 and get 6. Hope that helps.

The equation b(x) = a¹(x) mod(x + 1) is true for the given values of a(x) and b(x)

In AES encryption, the MixColumns and InvMixColumns functions are used to transform the state of the cipher.

During the discussion of these functions, it was mentioned that b(x) is equal to a¹(x) mod(x + 1), where a(x) is a polynomial expression and b(x) is the output polynomial after applying the function.

Using the given values, a(x) = {03)x³ + {01}x² + {01}x + {02) and b(x) = {0B]x³ + {0D]x² + {09}x+ (OE.), we can verify this equation.

First, we need to calculate a¹(x), which is equal to {02}x³ + {03}x² + {01}x + {01}.

Next, we need to calculate (x + 1), which is simply x + 1.

We can then perform the modulo operation of a¹(x) with (x + 1) to get b(x).

After performing the necessary calculations, we can see that a¹(x) mod(x + 1) does indeed equal b(x), as stated in the discussion.

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Based on the analyzed data from more than 5,000 adults, researchers found that the more diet sodas a person drank, the greater the person's weight gain.

But it is not true that drinking diet soda causes weight gain.

The causal link between drinking diet soda and weight gain is not established. People who drink diet soda may be consuming more calories and sugars from other sources or may be leading an unhealthy lifestyle that results in weight gain.

the artificial sweeteners used in diet soda may interfere with the body's natural ability to regulate calorie intake, leading to increased cravings for high-calorie foods and, ultimately, weight gain. However, more research is needed to understand the impact of artificial sweeteners on weight gain fully.

Therefore, it can be concluded that drinking diet soda does not directly cause weight gain. Instead, a healthy lifestyle and balance between calorie intake and energy expenditure is necessary to maintain a healthy weight.

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Answer:

$126

Step-by-step explanation:

The plot of land is worth $18,000 and the tax on the land is $0.70 per $100. You would divide 18000 by 100 which is 180. Then you would multiply 180*0.70 which is $126.

Step-by-step explanation:

Here, given that;

The total value of land us $18000.00

tax per $100.00 is $0.70

now,

$100.00 taxes $0.70

$18000.00 taxes ($18000.00÷100)/$0.70 (as in question given that the tax is charged in each $100)

= $126.

is the required tax amount.

Hope it helps..

The number of gift bags that Taisha will make is 10.

Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator. The denominator is the number below the line. It displays the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.

From the information given, Taisha wants to put 1/2 pound of chocolate in each bag and she has 4 \(\frac{3}{4}\) pounds of chocolate.

The number of bags that she needs will be calculated by dividing the fractions given. This will be:

= Total chocolate / Amount in each bag

= 4 \(\frac{3}{4}\) ÷ 1/2

= 19/4 ÷ 1/2

= 19/4 × 2

= 38/4

= 9 \(\frac{1}{2}\)

Therefore, she will need 10 bags.

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Answer:

Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set.

Step-by-step explanation: