melissa ran "m" meters per second, and jasmine ran "j" meters per second. They ran for "t" seconds. The expression t(m-j) describes how many more meters melissa ran than jasmine ran during that time. We can also use the expression tm-tj to represent the same quantity. explain how the expression t(m-j) and tm-tj are equivalent.​

Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

Probability of receiving a hand with exactly three suits \(= (4 * (13^3)) / 2,598,960\)

What is Combinatorics?

Combinatorics is a branch of mathematics that deals with counting, arranging, and organizing objects or elements. It involves the study of combinations, permutations, and other related concepts. Combinatorics is used to solve problems related to counting the number of possible outcomes or arrangements in various scenarios, such as selecting items from a set, arranging objects in a specific order, or forming groups with specific properties. It has applications in various fields, including probability, statistics, computer science, and optimization.

To calculate the probability of receiving a hand with exactly three suits when dealt 5 cards from a well-shuffled deck of cards, we can use combinatorial principles.

There are a total of 4 suits in a standard deck of cards: hearts, diamonds, clubs, and spades. We need to calculate the probability of having exactly three of these suits in a 5-card hand.

First, let's calculate the number of favorable outcomes, which is the number of ways to choose 3 out of 4 suits and then select one card from each of these suits.

Number of ways to choose 3 suits out of 4: C(4, 3) = 4

Number of ways to choose 1 card from each of the 3 suits\(: C(13, 1) * C(13, 1) * C(13, 1) = 13^3\)

Therefore, the number of favorable outcomes is \(4 * (13^3).\)

Next, let's calculate the number of possible outcomes, which is the total number of 5-card hands that can be dealt from the deck of 52 cards:

Number of possible outcomes: C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960

Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:

Probability of receiving a hand with exactly three suits =\((4 * (13^3)) / 2,598,960\)

This value can be simplified and expressed as a decimal or a percentage depending on the desired format.

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Answer:

770

Step-by-step explanation:

280 divided by 4 = 70 so every year is 70 year increase

770 but it asked to round so by 2001 it increased to 770

Answer:

c

Step-by-step explanation:

xxxxx

Answer:

25

Step-by-step explanation:

Answer:

Original volume: 6^3 = 216 cubic cm

New volume: 3^3 = 27 cubic cm

The volume of this cube would decrease by 189 cubic centimeters if the length of each side was reduced from 6 cm to 3 cm.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.

Here,

A quadratic function is one where an equation has two roots.

A quadratic function's two roots are equal if D=0.

D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.

As a result, if an equation has two roots, a quadratic function is what it is.

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Answer:

Let P(h,k) be the point which is equidistant from the point (2,4) and the y-axis. The distance of point P(h,k) from the y-axis is h. ∴h=√(h−2)2+(k−4)2⇒h2−4h−4+k2−8k+16=h2⇒k2−4h−8k+20=0.

Hence,the locus of (h,k)is y2−4x−8y+20=0.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Draw a vertical line anywhere on the graph. If it hits 2 points, then it's not.

I also attached an example when a graph is not a function

See how it hits two point on the graph?

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

The probability that one of the events Franco worked last year, selected at random, was a wedding is equals to the \( \frac{4}{17} \).

Franco is a professional DJ and he was very busy in work during Last year. Number of events where he worked = 26

Number of wedding where he worked

= 8

So, total events where he played his DJ

= 26 + 8 = 34

We have to determine probability that one of the events Franco worked last year, selected at random, was a wedding.

Now, one of event is Randomly selected from all of above events. Number of favourable outcomes for worked on wedding events = 8

So, probability of selected a wedding event \( = \frac{8}{34} \)

\( = \frac{4}{17} \). Hence the required probability value is \( \frac{4}{17} \).

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Answer:

Step-by-step explanation:

Let's open the brackets,

12z - 21 = -21 + 12z (distributive property)

12z - 12z = -21 + 21

0z = 0

z = 0

Let x represent Alex's number.

Then Grogg wrote down 1/10 · x = x/10 = 0.1x.

Winne write down 1/100 · x = x/100 = 0.01x

The product of all three is:

    (x)(0.1x)(0.01x) = 0.001x^3

     0.001x^3 = 0.000008

Multiplying by 1000 on both sides we have:

              x^3 = 0.008

                 x = cuberoot(0.008)

                 x = 0.2

Alex's number is 0.2, Grogg's is 0.02, and Winnie's is 0.002.

So the triangle has three equal angles of 60 degrees.

To find the measures of the angles of the triangle with vertices at (-2,0), (2,1), and (1,-2), we can use trigonometry.

Let's use the following notation:

a = (-2,0)

b = (2,1)

c = (1,-2)

First, we need to find the coordinates of the midpoint of line segment AB, which is the length of the hypotenuse of the triangle.

Using the Pythagorean theorem, we have:

\(c^2 = a^2 + b^2\\1^2 + (-2)^2 = 2^2 + 1^2\)

25 = 4 + 1

23 = 3

So the length of the hypotenuse is 3 units.

Next, we need to find the coordinates of the midpoint of line segment BC, which is the length of one of the legs of the triangle.

Again, using the Pythagorean theorem, we have:

\(b^2 = a^2 + c^2\\1^2 + (-2)^2 = 2^2 + 1^2\)

25 = 4 + 1

23 = 3

So the length of the leg of the triangle is 3 units.

Now, we can use the law of cosines to find the measures of the angles of the triangle.

Let's denote the angle between lines AB and BC as alpha, the angle between lines AB and AC as beta, and the angle between lines BC and AC as gamma.

Using the law of cosines, we have:

\(cos(alpha) = (b^2 + c^2 - a^2) / (2bc)\\cos(beta) = (a^2 + c^2 - b^2) / (2ac)\\cos(gamma) = (a^2 + b^2 - c^2) / (2ab)\)

We know that:

a = (-2,0)

b = (2,1)

c = (1,-2)

So we can substitute these values into the above equations:

\(cos(alpha) = (2^2 + (-2)^2 - (-2)^2) / (2(-2)1) = (2 + (-2) + 2) / (2(-2)1) = 4 / 3\\cos(beta) = ((-2)^2 + 2^2 - (-2)^2) / (2(-2)2) = (-2 + 4 + 2) / (2(-2)2) = -1\\cos(gamma) = (2^2 + 1^2 - 1^2) / (2(1)(-2)) = 2 + (-1) + (-1) / (2(1)(-2)) = 1\)

Now we can substitute these values into the Pythagorean theorem to find the length of the legs of the triangle:

sin(alpha) = length of leg 1 / (2bc)

sin(beta) = length of leg 2 / (2ac)

sin(gamma) = length of leg 2 / (2ab)

We know that:

a = (-2,0)

b = (2,1)

c = (1,-2)

So we can substitute these values into the above equations:

sin(alpha) = √(8) / (2(-2)1)

= √(8) / √(3)

= √(2)

sin(beta) = √(5) / (2(1)2)

= √(5) / √(3)

= √(2)

sin(gamma) = √(5) / (2(1)(-2))

= √(5) / 1

= √(5)

Therefore, the measures of the angles of the triangle are:

alpha = 60 degrees

beta = 60 degrees

gamma = 60 degrees

So the triangle has three equal angles of 60 degrees.  

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Answer:

870 X 40% = $338.00

The original price was $1208.00

The price was marked with the discount already

40%

Step-by-step explanation:

Answer:

x/> -y/2 + 1/2

Answer: 60

Step-by-step explanation:

Answer:

-800/100 and 80 ÷ (–10)

Step-by-step explanation:

I did the test and I got 100%

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

A

Step-by-step explanation:

Answer:

I beleive it is A and C i just took the test!

Step-by-step explanation:

yourwelcome! :)

We're given

(0, 144)

(1, 48)

(2, 16)

(3, 16/3)

\(f(x) = a*b^x\\144 = a*b^0\\144 = a\\\)

now that we know a, we can find b

\(f(x) = 144*b^x\\48 = 144*b\\b = \frac{48}{144}\\b = \frac{1}{3}\)

\(f(x) = 144*(\frac{1}{3})^x\)

Answer:

Step-by-step explanation:

By process of elimination we see that only D or E could be correct. Now to find the angle o, we must subtract

360- 150 - 150 = 60

Now we divide that between angle o and m and... we get 30!

The answer is... angle j is 150 and angle o is 30

Answer:

x = 6 rides

Step-by-step explanation:

4x + 5 = 29

4x = 29-5

4x = 24

x = 24/4

Answer:

Hope this helps :D

Step-by-step explanation:

Explanation on picture

Answer:

Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4.

Step-by-step explanation:

Given

Minutes: 10 || 16 || ?  || 48

-----Miles: 2.5 || 4 || 7.5 || 12

Required

Which statements solve for the missing value?

First, we need to calculate the ratio of minutes to mile

\(Ratio = \frac{Minutes}{Mile}\)

When minutes = 16; mile = 4

So, we have:

\(Ratio = \frac{16}{4}\)

\(Ratio = 4\)

Next, we multiply the ratio by 7.5

\(Minutes = Ratio * 7.5\)

\(Minutes =4 * 7.5\)

\(Minutes = 30\)

Hence, option B answers the question.

The ordered pair (6,8) represents the number of calls made after the customer service center opened for 6 hours.

Given that the volume of calls, V( h), at a particular customer service center can be written as a function of the number of hours after opening each day, h. So, (6,8) means that the center has been opened for 6 hours and that there have been 8 calls during this period. It represents the value of the volume of calls V(6) which is 8. Therefore, after opening the customer service center for 6 hours, 8 calls were made.

This function has a direct relationship between the number of hours after opening the center and the number of calls made. Therefore, the longer the center is open, the more calls are expected to be received, and vice versa.

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The equivalent equation is 3x − 2y + 5.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given that equation as:

⇒ 8 + 3x − 2y − 3

Rearrange the terms and apply arithmetic operations

⇒ 3x − 2y + 8 − 3

⇒ 3x − 2y + 5

Hence, the equivalent equation is 3x − 2y + 5.

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Answer:

C

Step-by-step explanation:

Plug the values into the function

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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