david mad e a dot plot of how many miles he biked each day for two weeks. how many miles did he bike in all

By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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Answer:

A horizontal line has a slope of zero

Step-by-step explanation:

Let’s start by some examples!

We’re going to use two points that identify that a horizontal line has a slope of zero

Two points will be: (7, 4) & (7, -6)

Then use the Slope-Formula to identify the slope

Slope = change in y/change in x

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 4)/(7 - 7)

Slope = -10/0

Slope = 0

Therefore, a horizontal line has a slope of zero

Answer:

Step-by-step explanation:

Horizontal lines have no steepness at all because any calculation the slope of line means dividing zero by another number to the answer is always zero

Answer:

2

PLZ MARK BRAINLIEST

Step-by-step explanation:

(-8+4) - (3-9) = (-4) - (-6) = -4 + 6 = 2

For Grace, reduce the number of operations thus his strategy is best. This can be solved using the concept of equation formation.

The relationship between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 6x + 11 = 20 has the two expressions

6x + 11 and 20 that are separated by the 'equal' sign. Equations can be classified as either conditional equations or identities.

Here,

Equation becomes:  1.2 = 6 (4 - 0.4g) - 4.8

For Bode: begins solving by dividing both sides of the equation by 6 and then adding 4. 8 to both sides

Thus,

1.2 = 6 (4 - 0.4g) - 4.8

or, 0.2 = (4 - 0.4g) - 0.8

or, 0.4g = 4 - 0.8 - 0.2

or, 0.4g = 3

or, g = 7.5

For Grace: begins solving by adding 4. 8 to both sides of the equation and then dividing both sides by 6

1.2 = 6 (4 - 0.4g) - 4.8

or, 6 = 6 (4 - 0.4g)

or, 1 = 4 - 0.4g

or, 0.4g = 3

or, g = 7.5

Here, for Grace, reduce the number of operations thus his strategy is best.

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The probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

To find the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

- P(X = k) is the probability of exactly k successes,

- n is the number of trials,

- k is the number of successes,

- p is the probability of success in a single trial, and

- C(n, k) is the combination of n choose k.

In this case, n = 12, k can be 0, 1, or 2, and p = 0.59 (the probability of using smartphones in meetings or classes).

Now we can calculate the probabilities for each value of k and sum them up:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Calculating these probabilities and summing them up will give us the desired probability that fewer than 3 out of 12 users use their smartphones in meetings or classes.

Let's calculate the probabilities.

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

Using the combination formula, C(12, 0) = 1, and simplifying the equation:

P(X = 0) = 1 * 1 * (1 - 0.59)^12 = 0.0003159

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

Using the combination formula, C(12, 1) = 12, and simplifying the equation:

P(X = 1) = 12 * 0.59^1 * (1 - 0.59)^11 = 0.0065294

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Using the combination formula, C(12, 2) = 66, and simplifying the equation:

P(X = 2) = 66 * 0.59^2 * (1 - 0.59)^10 = 0.0470972

Now, let's sum up these probabilities to find P(X < 3):

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0003159 + 0.0065294 + 0.0470972 = 0.0539425

Therefore, the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

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Answer:Roughly Symmetric

Step-by-step explanation:

I'm too lazy

Answer:

m = 4

Step-by-step explanation:

The slope of two given points are:

\(\frac{y_2-y_1}{x_2-x_1}\)

We are given the points of (-11, -2) & (-15, -18).

\(m = \frac{-18+2}{-15+11} = \frac{-16}{-4}=\boxed{4}\)

The slope of the line is 4.

Hope this helps.

Answer:

ANSWER is B. look at the sides and simplified.

Step-by-step explanation:

\(\tt{ 4m-(-3m)-17m-(-m)-(-7m)=12 }\) ⠀

\(\tt{ 4m+3m-17m+m+7m=12 }\) ⠀

\(\tt{ 15m-17m=12 }\) ⠀

\(\tt{ -2m=12 }\) ⠀

\(\tt{ m=\dfrac{12}{-2}}\) ⠀

\(\tt{m=-6 }\) ⠀

Step-by-step explanation:

\(4m−(−3m)−17m−(−m)−(−7m)=12\\\\\\4m+3m−17m+m+7m=12\\\\\\15m−17m=12\\\\\\−2m=12\\\\\\m=\dfrac{12}{-2}\\\\\\\bold{m=-6 }\)

The average of the sample ranges for the weight of packages of Skittles is 0.11. So, the correct answer is (e) 0.11.

To find the average of the sample ranges for the weight of packages of Skittles, we first calculate the range for each sample. The range is the difference between the maximum and minimum values in each sample.

Sample 1: Range\(= 3.62 - 3.58 = 0.04\)

Sample 2: Range\(= 3.65 - 3.49 = 0.16\)

Sample 3: Range \(= 3.65 - 3.45 = 0.20\)

Sample 4: Range \(= 3.64 - 3.54 = 0.10\)

Sample 5: Range\(= 3.62 - 3.49 = 0.13\)

Next, we calculate the average of these sample ranges:

A\(verage = (0.04 + 0.16 + 0.20 + 0.10 + 0.13) / 5 = 0.11\)

Therefore, the average of the sample ranges for the weight of packages of Skittles is \(0.11\). So, the correct answer is (e) \(0.11.\)

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Check the picture below.

\(z+25=(z-27) + (z-11)\implies z+25=2z-38 \\\\\\ 25=z-38\implies \boxed{63=z}\)

Divide number of pens given by percentage:

2/0.25 = 8

She has 8 pens total.

The derivative of the function using the definition of derivative is 3.

The given function is g(t) = 3t.

We have to find the derivative of the function using the definition of derivative.

We know that,

Definition of derivative:-

The derivative of a function is the rate of change of the function's output relative to its input value.

Here,

Input value = t

Output value = g(t)

Given y = g(t), the derivative of g(t), denoted g'(t) (or dg(t)/dt), is defined by the following limit:

\(g'(t)= \lim_{h \to 0} \frac{g(t+h)-g(t)}{h}\)

We have the function:-

g(t) = 3t

Hence, according to the data given in the question, we can write,

g'(t) =

\(\lim_{h \to 0} \frac{g(t+h)-g(t)}{h} \\\\ \lim_{h \to 0} \frac{3(t+h)-3(t)}{h}\\\\ \lim_{h \to 0} \frac{3t+3h-3t}{h}\\\\ \lim_{h \to 0} \frac{3h}{h}\\\\\lim_{h \to 0} 3\)

g'(t) = 3

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The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

2x²-4x-3 = 0

Here, a = 2, b = - 4 and c = -3

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-4)² - 4×2×(-3)

= 16 -8(-3)

= 16 + 24

=40

Since,

D = 40 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer:

The answer is 0.01. We assume you are converting between dollar bill and penny. You can view more details on each measurement unit: Dollar or penny The main non-SI unit for U.S. currency is the dollar. 1 dollar is equal to 100 penny. Note that rounding errors may occur, so always check the results.

Step-by-step explanation:

Answer:

Huh? ---

Yea, there are 100 pennies in a dollar....

The acceleration function is a(t) = 20.

v(t) = 20t (velocity function)

a(t) = 20 (acceleration function)

To find the velocity and acceleration, we need to differentiate the position function with respect to time.

The position function is given by \(s(t) = 10t^2 + 17.\)

To find the velocity function, we differentiate s(t) with respect to t:

v(t) = s'(t) = d/dt (10t^2 + 17).

Using the power rule of differentiation, the derivative of\(t^n is n*t^(n-1),\)where n is a constant, we can differentiate each term:

v(t) = 20t.

Therefore, the velocity function is v(t) = 20t.

To find the acceleration function, we differentiate v(t) with respect to t:

a(t) = v'(t) = d/dt (20t).

Using the power rule of differentiation, the derivative of \(t^n is n*t^(n-1),\)where n is a constant, we can differentiate the term:

a(t) = 20.

Therefore, the acceleration function is a(t) = 20.

v(t) = 20t (velocity function)

a(t) = 20 (acceleration function)

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Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

π is an irrational number. It can't be rewritten as a fraction

Answer:

7.3

Step-by-step explanation:

11.6 - 4.3 = 7.3

Helping in the name of Jesus.

Rolling-circle replication of plasmids proceeds in one direction from a single fixed origin

Explanation:

Rolling-circle replication of plasmids is a replication mechanism in which the replication process moves in one direction from a single fixed origin. Rolling-circle replication is a process that is often seen in circular plasmid DNA. It is a process that begins with an initiator protein, which is responsible for the nicking of a single DNA strand.The initiation point allows the helix to begin unwinding in one direction.

             As the DNA helix unwinds, replication is carried out in a continuous manner, and the helix is wound up behind it. During the replication process, a new strand is synthesized that is attached to the parent strand's 3' end.

                     Rolling-circle replication, on the other hand, is utilized to produce new plasmids that have a single strand, which can then be employed in other cells for the production of proteins or for research purposes.

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Answer:

Point C

Step-by-step explanation:

We want to reflect across the x axis

That means the y coordinate changes sign

Z = ( 5 1/2 , 3)

Z' = ( 5 1/2 , -3)

That is point C

Answer: C

Step-by-step explanation: sorry if im wrong

The equation of the graph of the function g(x) is -√(x-7).

Turns are frequently used to refer to reflection, which is when an object is flipped over a line without affecting its size or shape. The preimage is flipped over a line in a rigorous transition known as a reflection, but its size and shape are left unchanged. Flips is another name for reflections.

A figure can be translated if it is moved in any direction without altering its size, form, or orientation. A hard transformation called a translation alters the preimage's position but not its size, shape, or orientation. Slides are another name for translations.

Given that, f(x)= square root of x, that is:

f(x) = √x

Reflect the graph over x-axis we have:

Reflecting f(x) across the x-axis gives us -f(x) = -√x.

Translating -f(x) = -√x 7 units to the right gives us -f(x-7) = -√(x-7).

Hence, the equation of the graph of the function g(x) is -√(x-7).

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The 21st term of the sequence 3, 8, 13, 18, .. is 103

To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference, and n is the term number.

In this case, we have:

a(1) = 3 (the first term)

d = 5 (the common difference)

To find the 21st term, we substitute n = 21 in the formula:

a(21) = a(1) + (21-1)d

a(21) = 3 + 20(5)

a(21) = 103

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Step 1: Use the slope formula y₂ - y₁/x₂ - x₁ to find the slope.

\(\frac{0 - (-4)}{-3 - 3}\\ \\\frac{4}{-6} = -\frac{2}{3}\)

Step 2: Plug the slope we found and one point into the slope-intercept formula, y = mx + b.

\(y = mx + b\\\\0 = -\frac{2}{3}(6) + b\\\\0 = -4 + b\\\\4 = b\)

Step 3: Put it all together.

\(y = -\frac{2}{3}x + 4\)

Answer:

5.7 hours

Step-by-step explanation:

average speed = distance / time

rewriting gives

time = distance / average speed.

distance = 320 km

average speed = 56 km/hour

so

time = 320 / 56 = 5.7 hours

The number of verbs memorized after two hours (t = 120) is:y = 50 - 15(30/2)^(-1/30)(120)= 45.92. Therefore, the student will memorize about 45 verbs in two hours.

(a) A student studying a foreign language has 50 verbs to memorize. Suppose the rate at which the student can memorize these verbs is proportional to the number of verbs remaining to be memorized, 50 – y, where the student has memorized y verbs. Initially, no verbs have been memorized.

Suppose 20 verbs are memorized in the first 30 minutes.

For part a) we have to find how many verbs will the student memorize in two hours.

It can be seen that y (the number of verbs memorized) and t (the time elapsed) satisfy the differential equation:

dy/dt

= k(50 – y)where k is a constant of proportionality.

Since the time taken to memorize all the verbs is limited to two hours, we set t = 120 in minutes.

At t

= 30, y = 20 (verbs).

Then, 120 – 30

= 90 (minutes) and 50 – 20

= 30 (verbs).

We use separation of variables to solve the equation and integrate both sides:(1/(50 - y))dy

= k dt

Integrating both sides, we get;ln|50 - y|

= kt + C

Using the initial condition, t = 30 and y = 20, we get:

C = ln(50 - 20) - 30k

Solving for k, we get:

k = (1/30)ln(30/2)Using k, we integrate to find y as a function of t:

ln|50 - y|

= (1/30)ln(30/2)t + ln(15)50 - y

= e^(ln(15))e^((1/30)ln(30/2))t50 - y

= 15(30/2)^(-1/30)t

Therefore,

y = 50 - 15(30/2)^(-1/30)t

Hence, the number of verbs memorized after two hours (t = 120) is:y = 50 - 15(30/2)^(-1/30)(120)

= 45.92

Therefore, the student will memorize about 45 verbs in two hours.

(b) Now, we are supposed to determine after how many hours will the student have only one verb left to memorize.

For this part, we want y

= 1, so we solve the differential equation:

dy/dt

= k(50 – y)with y(0)

= 0 and y(t)

= 1

when t = T.

This gives: k

= (1/50)ln(50/49), so that dy/dt

= (1/50)ln(50/49)(50 – y)

Separating variables and integrating both sides, we get:

ln|50 – y|

= (1/50)ln(50/49)t + C

Using the initial condition

y(0) = 0, we get:

C = ln 50ln|50 – y|

= (1/50)ln(50/49)t + ln 50

Taking the exponential of both sides, we get:50 – y

= 50(49/50)^(t/50)y

= 50[1 – (49/50)^(t/50)]

When y = 1, we get:

1 = 50[1 – (49/50)^(t/50)](49/50)^(t/50)

= 49/50^(T/50)

Taking natural logarithms of both sides, we get:

t/50 = ln(49/50^(T/50))ln(49/50)T/50 '

= ln[ln(49/50)/ln(49/50^(T/50))]T

≈ 272.42

Thus, the student will have only one verb left to memorize after about 272.42 minutes, or 4 hours and 32.42 minutes (approximately).

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Answer: 5

Step-by-step explanation:

the y intercept is the "b" value in the form y = mx + b