Knowledge Check Simplify. (b^(2))/(b^(-7)) Write your answer with a positive exponent only.

The the distance between the two stations is 300km, then the speed of first motorcyclist is 63 km/h and speed of second-motorcyclist is 70 km/h.

The distance between the "two-stations" is given to be 300 km;

Let the speed of first-motorcyclists be x km/h

and let the speed of second-motorcyclists be (x + 7) km/h,

So, the Distance covered by first motorcyclist after 2 hours is = 2x km

and distance covered by second motorcyclist after 2 hours is = 2(x+7) km

⇒ 2x + 14 km,

So, the distance not covered by them after 2 hours is = 300 - (2x+2x+14) km.

The distance between the motorcyclist after 2 hours is 34 km,

Which means ,

⇒ 300-(4x+14) = 34

⇒ 300 - 4x - 14 = 34

⇒ 4x = 300 - 48

⇒ x = 63,

So, Speed of first-motorcyclists is 63 km/h, and

Speed of second-motorcyclist is = (63 + 7) = 70 km/h.

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The given question is incomplete, the complete question is

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist.

The given histogram is right skewed type.

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.

They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.

Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

Histogram :-

It is a collection of rectangles next to one another, where each bar represents a different type of data.

In this context, frequency refers to the number of times a number appears in statistical data.

It is known as a frequency distribution when shown in a table.

Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

Hence, the given histogram is right skewed type.

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The location of B' after the rotation on the coordinate plane of 90 degrees clockwise about the origin is

90 degree clockwise rotation refers to the rotation of a figure on a coordinate plane about a fixed point in the clockwise direction. Every point (x, y) will rotate to in order to rotate the figure 90 degrees clockwise around a point (y, -x).

This then means that the B will go from B ( 7, 3 ) to B' ( 3, - 7 ) after a clockwise rotation about the origin.

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¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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Answer:

The answer is c 180 miles

Step-by-step explanation:

the exact is 179.8 miles rounded up is 180 mark brainliest pls and your welcome

x = 18 ...... y = 20/3

x = 30 ..... y = ?

____________

[tex]y = \dfrac{30 \cdot 20}{3 \cdot 18} = \dfrac{100}{9}[/tex]

The two functions are not equivalent.

The given functions f(x,y) = x^2 + 3y^2 and f′(x,y) = x^2 + 4xy + 7y^2 are not equivalent.

To determine if two functions are equivalent, we can compare their equations and see if they are the same. In this case, the equations of the two functions are different. The first function, f(x,y), has a term of 3y^2, while the second function, f′(x,y), has a term of 4xy and a term of 7y^2.

Therefore, the two functions are not equivalent.

It is important to note that two functions can have different equations but still be equivalent if they produce the same output for any given input. However, in this case, the two functions will produce different outputs for the same input, so they are not equivalent.

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The value of x is 20 and the given two angles are adjacent .

What are parallel lines ?

Parallel lines are lines that are always the same distance apart and never intersect. They have the same slope but different y-intercepts. In other words, they have the same rate of change but different starting points. Parallel lines can be described by linear equations of the form y = mx + b, where m is the slope and b is the y-intercept.

From the given figure

we can say that,

the two angles 7x and x+20 are adjacent

and sum of two angles is 180 degrees.

SO,

7x+x+20 = 180

8x + 20 = 180

8x = 160

x = 160 / 8

x = 20

Therefore, The value of x is 20 and the given two angles are adjacent .

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A box and whisker plot is the appropriate display for the data, as it shows the minimum and the maximum value of the data-set, while the range is the difference of the maximum value by the minimum value.

From left to right, the five features of the box and whisker plot are listed as follows

The range of a data-set is given as follows:

Range = Maximum value - Minimum value.

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The period of the function is 10 and the amplitude is 4.

The period and amplitude of the function \[ y=-4 \sin \left(\frac{\pi x}{5}\right) \] can be found by examining the coefficients in the equation.

The amplitude is the absolute value of the coefficient in front of the sine function, which in this case is |-4| = 4. Therefore, the amplitude of the function is 4.

The period is found by dividing 2π by the coefficient in front of the x variable inside the sine function. In this case, the coefficient is \[\frac{\pi}{5}\]. So, the period is \[\frac{2\pi}{\frac{\pi}{5}} = 10\].

Therefore, the period of the function is 10 and the amplitude is 4.

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Synthetic Division of the polynomials (x^(4)-5x^(3)+4x-17) and (x-5) gives answer "x^(3)+4+3/(x-5)."

Step 1: Write the coefficients of the polynomial in descending order. In this case, the coefficients are 1, -5, 0, 4, -17.

Step 2: Write the value of x from the divisor (x-5) in the left column. In this case, the value of x is 5.

Step 3: Bring down the first coefficient to the bottom row.

Step 4: Multiply the value of x by the number in the bottom row and write the result in the next column.

Step 5: Add the numbers in the second column and write the result in the bottom row.

Step 6: Repeat steps 4 and 5 until you have completed all the columns.

Step 7: The numbers in the bottom row are the coefficients of the quotient, and the last number is the remainder.

The synthetic division will look like this:

5 | 1 -5 0 4 -17
 |   5 0 0 20
 ----------------
   1  0 0 4   3

So, the quotient is x^(3)+0x^(2)+0x+4, or simply x^(3)+4, and the remainder is 3.

Therefore, the answer is (x^(4)-5x^(3)+4x-17)÷(x-5) = x^(3)+4+3/(x-5).

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Answer:

y = 3.3x + 34.9

Step-by-step explanation:

the slope-intercept form is y = mx + b.

y = total pounds of cans accumulated

m (slope) = pounds of cans collected each week (3.3)

x = # of weeks after sally starts collecting

b (y-intercept) = initial pounds of cans collected (34.9)

so:

y = (pounds per week)(# of weeks) + initial weight

y = 3.3x + 34.9

12cm 6 cm 10cm 8cm tienes que medir 12 ×6 cm

Answer:

277 milliliters

Step-by-step explanation:

945 - 668 = 277

hope this helpz ya

Answer:

277 milliliters

Step-by-step explanation:

Initial volume of ice tea = 945 milliliters

Final volume of ice tea = 668 milliliters

∴Difference in the volume of ice tea = How much tea Jeffrey drank

                                                              = Final volume - Initial volume

                                                            = [tex](945 - 668)[/tex] milliliters

                                                            = [tex]277[/tex] milliliters

[tex]\stackrel{a}{-117}+\stackrel{b}{44}i \\\\[-0.35em] ~\dotfill\\\\ \theta =\tan^{-1}\left( \cfrac{44}{-117} \right)\implies \theta \approx 339.39^o~\hfill r=\sqrt{(-117)^2 + 44^2}\implies r=125 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o }{3} \right) +i \sin\left( \cfrac{ 339.39^o }{3} \right)\right][/tex]

[tex]5[ \cos(113.13^o) +i \sin(113.13^o)]\approx \boxed{-1.96~~ + ~~4.60i} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 699.39^o }{3} \right) +i \sin\left( \cfrac{ 699.39^o }{3} \right)\right] \\\\\\ 5[\cos(233.13^o)+i\sin(233.13^o)]\approx \boxed{-3.00~~ - ~~4.00i} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 1059.39^o }{3} \right) +i \sin\left( \cfrac{ 1059.39^o }{3} \right)\right] \\\\\\ 5[\cos(353.13^o)+i\sin(353.13^o)]\approx \boxed{4.96~~ - ~~0.60i}[/tex]

Cube roots of complex number - 117 + 14i are,

- 1.96 + 4.60i

- 3.00 - 4.00i

4.96 - 0.60i

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Complex number is,

⇒ - 117 + 14i

Let a = - 117

b = 44

Then, tan ⁻¹ (44/117) = 339.39°

⇒ θ = 339.39°

And, r = √117² + 44² = 125

Hence, We have;

[tex]\sqrt[n]{z} = \sqrt[n]{r} [cos (x + 2\pi k/n) + i sin (x + 2\pi k/n)][/tex]

Where, k = 0,1,2, 3, ..

Now, At k = 0

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 0/3) + i sin (339.39 + 0/n)][/tex]

    = - 1.96 + 4.60i

At k = 1;

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360/3) + i sin (339.39 + 360/n)][/tex]

     = - 3.00 - 4.00i

At k = 2;

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360*2/3) + i sin (339.39 + 360*2/3)][/tex]

     = 4.96 - 0.60i

Thus, All Cube roots of complex number - 117 + 14i are,

- 1.96 + 4.60i

- 3.00 - 4.00i

4.96 - 0.60i

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Answer:

  1/3

Step-by-step explanation:

You want the difference in medians in terms of the IQR.

The IQR is the difference of the numbers at the ends of the box.

  top distribution: IQR = 12 -6 = 6

  bottom distribution: IQR = 14 -8 = 6

The median of each distribution is the location of the line in the box.

  top distribution: median = 11

  bottom distribution: median = 9

The difference in medians is 11 -9 = 2. The ratio of that to the IQR is ...

  2/6 = 1/3

The difference in medians is 1/3 times the IQR.

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The IikeIihood that the hawk wiII first take a songbird and subsequentIy a rabbit is therefore (2/9) x (8/11) = 16/99, or roughIy 0.1616.

In mathematics, a percentage is a number or ratio that may be stated as a fraction of 100. Divide a number by the whole and multiply the result by 100 to calculate its percentage. As a result, the percentage represents a part per hundred. 100% is meant by the phrase %. The symbol "%" is used to indicate it.

The probability that a hawk will eat a songbird before a rabbit is calculated as the product of those probabilities.

Given that there are four songbirds with eight rabbits, the IikeIihood that a songbird wiII be consumed by a hawk is 4/(4+6+8) = 4/18 = 2/9.

Three songbirds & eight rabbits remain after the hawk consumes a songbird, hence the IikeIihood that the hawk wiII eat a rabbit next is 8/(3+8) = 8/11.

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The lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years is $25,447.09.

To find the lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years, we can use the formula for compound interest;

A = P(1 + r/n)^(nt)

Where:
- A is the final amount
- P is the initial principal amount
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years

Plugging in the given values, we get:

61,000 = P(1 + 0.07/12)^(12*13)

Solving for P, we get:

P = 61,000 / (1 + 0.07/12)^(12*13)

P = 61,000 / (1.00583)^156

P = 61,000 / 2.39717

P = 25,447.09

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∠T has a cosine ratio of 15/17.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

PQR and STU are the similar triangles.

With the help of cosine function we can find the measure of T.

Cosine = Adjacent side/ hypotenuse

The adjacent side is thirty and hypotenuse is thirty four.

Plug in these values in the above formula.

∠T=30/34

Divide numerator and denominator by 2

∠T=15/17

Hence, ∠T has a cosine ratio of 15/17.

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If the cash register can be off by a maximum of $15, it means that there is an acceptable range of error in the register's calculations. This could be due to various factors such as human error, technical malfunctions, or other issues.

For example, if a customer gives $50 for a purchase and the cash register calculates the total as $45, then the register is short by $5. If the register calculates the total as $65, then it is over by $15. As long as the error falls within the acceptable range of $15, it would not be considered a serious issue.

However, if the error is outside of this range, it may indicate a problem with the register that needs to be addressed. Inaccurate calculations can lead to financial losses for a business, so it is important to ensure that the cash register is functioning correctly and that any errors are promptly corrected.

P.S: An overview was given based on your incomplete information.

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The number of bacteria in the refrigerated food product at T = 3 is -100.5.

The number of bacteria in a refrigerated food product is given by the equation N(T) = 27T^2 - 148T + 100.5. This equation can be used to determine the number of bacteria in the product at any given time, T.

To find the number of bacteria at a specific time, simply plug in the value of T into the equation and solve for N(T). For example, if we want to find the number of bacteria at T = 3, we would plug in 3 for T and solve:

N(3) = 27(3)^2 - 148(3) + 100.5
N(3) = 27(9) - 444 + 100.5
N(3) = 243 - 444 + 100.5
N(3) = -100.5

Therefore, the number of bacteria in the refrigerated food product at T = 3 is -100.5. It is important to note that the number of bacteria cannot be negative, so this equation may not be valid for all values of T. It is important to check the validity of the equation for the specific time period in question.

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The compound interest on N2,000 for 2 years at the rate of 10% per annum is N441.00.

Compound interest is the interest earned not only on the principal amount but also on the accumulated interest. To calculate the compound interest, we use the formula:

where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, P = N2,000, r = 0.1 (10%), n = 1 (compounded annually), and t = 2 years.

So, A = 2000[tex](1 + 0.1/1)^{(1*2)[/tex] = N2,441.00

Therefore, the compound interest is N2,441.00 - N2,000.00 = N441.00.

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Answer:

y = -43x - 175

Step-by-step explanation:

Slope-intercept form is y = mx + b

m = -43

x = -4

y = -3

-3 = -43(-4) + b

b + 172 = -3

b = -3 - 172 = -175

=> y = -43x - 175

The simple interest due on a 67-day loan of $2600 at a rate of 5% is $23.86.

To calculate this, we can use the following formula: I = Prt, where I is the interest due, P is the principal (or initial loan amount), r is the interest rate, and t is the time in years. We can calculate the time in years by taking the number of days (67) divided by the number of days in a year (365). Therefore, t = 0.1831. We can now plug this into our formula to get I = 2600 * 0.05 * 0.1831, which simplifies to I = 21.50. Therefore, the simple interest due is $21.50.

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The artist sold 32 smaller candles and 20 larger candles.

An equation is a mathematical statement that shows the equality of two expressions. It contains an equals sign (=) and at least one variable. An equation can be true or false depending on the values of the variables. Solving an equation involves finding the value or values of the variable that make the equation true. Equations are used to model relationships between different quantities in a wide range of fields, including mathematics, physics, chemistry, economics, and engineering.

A. Let's represent the number of smaller candles sold as x and the number of larger candles sold as y. We know that x + y = 52 (since a total of 52 candles were sold) and 4x + 7y = 269 (since the total sales was $269 and smaller candles sell for $4 and larger candles sell for $7). We can use these two equations to solve for x and y.

Multiplying the first equation by 4, we get 4x + 4y = 208. Subtracting this from the second equation, we get:

4x + 7y - (4x + 4y) = 269 - 208

3y = 61

y = 20.33

This means that the artist sold 20.33 larger candles. However, since we cannot sell a fractional part of a candle, we need to round this down to 20. Similarly, we can find x by subtracting y from 52:

x = 52 - y = 52 - 20 = 32

So the artist sold 32 smaller candles and 20 larger candles.

B. The answer is reasonable since the number of smaller candles sold is larger than the number of larger candles sold, and the total sales amount is closer to the price of the smaller candle than the larger candle. This implies that the artist's records are likely accurate.

Therefore, the artist sold 32 smaller candles and 20 larger candles.

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Lucky duck probabilities include:

A duck with a number:

Every duck has a number, so the probability of choosing a duck with a number is certain (1/1 or 100%).

A duck with a number greater than 10:

is 2/12 or 1/6, since there are 2 ducks with numbers greater than 10 out of a total of 12 ducks.

Duck number 4:

There is only one duck with the number 4, so the probability of choosing this duck is 1/12.

A duck with sunglasses:

There are no ducks with sunglasses so the probability is impossible.

A duck with a hat:

We don't know how many ducks wear hats, so we cannot determine the probability.

An even-numbered duck:

There are 6 even-numbered ducks (2, 4, 6, 8, 10, 12) out of 12 ducks in total, so the probability of choosing an even-numbered duck is 6/12, which simplifies to 1/2.

A duck with a number less than 7:

There are 6 ducks with a number less than 7 (1, 2, 3, 4, 5, 6) out of 12 ducks in total, so the probability of choosing a duck with a number less than 7 is 6/12, which simplifies to 1/2.

A duck with a mustache:

There are no ducks with mustaches, so the probability of getting a duck with a mustache is impossible, 0.

A duck with a bow tie:

Ducks with bowties are 8, so the probability of choosing a duck with bowtie is likely 8/12, 2/3

A duck with a number lower than 25:

All ducks have a number lower than 25, so the probability of choosing a duck with a number lower than 25 is certain (1).

A duck with a number greater than 5:

There are 7 ducks with a number greater than 5 (6, 7, 8, 9, 10, 11, 12) out of 12 ducks in total, so the probability of choosing a duck with a number greater than 5 is 7/12.

A duck with number that's a multiple of 3:

There are 4 ducks with a number that's a multiple of 3 (3, 6, 9, 12) out of 12 ducks in total, so the probability of choosing a duck with a number that's a multiple of 3 is 4/12, which simplifies to 1/3.

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Graph is the collection of all points whose coordinates satisfy a given relation (such as a function).

Coordinates of a point in a 2D plane, also known as cartesian coordinates, are two numbers or sometimes a combination of a letter and a number that tell us the exact location of a specific point on a grid. Here, the grid is known as a coordinate plane.

Let tosses be x and and dollars be y

Then we have, (x, y) as (63, 6)

So if in 6 dollars you get 63 tosses then 1 dollar you get = 63/6 = 10.5 tosses.

Then in 2 dollars we have = 10.5 × 2 = 21 tosses

As 21 tosses = 2 dollars

Then 42 tosses = 2 × 2 = 4 dollars

Thus, we have the table:

[tex]\boxed{\begin{array}{cc}\underline{\text{Tosses}}&\underline{\text{dollars}}&\\ \boxed{10.5}&2&\\42&\boxed4&\\63&6&\end{array}}[/tex]

To graph the given points, just correspond x as tosses and y as dollars.

Graph given in attachment

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Answer:

Step-by-step explanation:

[tex]f(9)[/tex] means we need to find the value of [tex]f(x)[/tex] when [tex]x=9[/tex], so

[tex]f(9)=2[/tex]×[tex]9=18[/tex]

The shortest distance Jose can ride to park is 5 miles.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, Jose can follow the roads getting to the park- first heading south 3 miles, then heading west 4 miles.

Let the shortest root Jose can choose be x miles.

By using Pythagoras theorem, we get

x²=3²+4²

x²=9+16

x²=25

x= 5 miles

Therefore, the shortest distance is 5 miles.

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The dimensions of the rectangle are: length: 20 units and width: 3 units.

To solve the problem, we can set up an algebraic equation using the formula for the area of a rectangle, which is A = length × width.

Let x be the length of the rectangle, and x - 17 be the width.

Then we can set up the equation:

60 = x(x - 17)

Simplifying the equation gives us:

x² - 17x - 60 = 0

Now we can factor the equation:

(x - 20)(x + 3) = 0

This gives us two possible solutions for x:

x = 20 or x = -3

However, since the length of a rectangle cannot be negative, we can disregard the second solution.

Therefore, the length of the rectangle is 20 units, and the width is 20 - 17 = 3 units.

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