Question 9 OT 10
The lines shown below are perpendicular. If the green line has a slope of -2/3
. what is the slope of the red line?

Answer:

m > -7 OR m < -10

Step-by-step explanation:

5 + m > -2

5 + m + 2 > 0

5 + 2 > - m

7 > -m

-7 > m

2m < -20

m < -20 / 2

m < -10

As per the given Ratio difference between the amount of money spent and the amount of money saved in a week is $2.

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.

The ratio formula can be used to represent a ratio as a fraction. For any two quantities, say a and b, the ratio formula is a:b = a/b. Because a and b are separate amounts for two portions, the total quantity is given as (a + b).

et 5x be the money he spends and 4x be the amount he saves

therefore, 5x+4x= 18

9x= 18

x= 18/9= 2

Tom spends, 5×2 = $10

and he saves, 4×2= $8

Difference, = $10-$8= $2

Therefore, as per the given ratio in the question difference between the amount of money spent and the amount of money saved in a week is $2.

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Tom receives $18 from his father in a week. The ratio of the amount of

the money he spends to the amount of money he saves in a week is 5:4

What is the difference between the amount of money spent and

amount of money saved in a week?

To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)

This is:

The nurse will have to administer 3 milliliters with each dose.

When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:

medication f 0.05 mg/ml.

Milliliters will the nurse administer with each dose :

The conversion factor from mcg to mg is 1/1000.

Therefore, 150 mcg = 150/1000 = 0.15 mg.

The nurse has to administer 0.15 mg of medication f per dose.

The medication f available with the pharmacy is 0.05 mg/ml.

So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).

Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.

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The algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

The statement is given as:

the difference of 27 and 5​

Difference means minus.

The minus sign is represented as -

This means that the statement given as: the difference of 27 and 5​

Can be represented as

27 minus 5

So, have

27 - 5

Hence, the algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

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The y-coordinate of the point that divides the directed line segment from J to K into a ratio of is 5.

The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,

Coordinates of point = \((\frac{mx_{2}+ nx_{1} }{m+n} \frac{my_{2}+ ny_{1}}{m+n} )\)

The coordinate of point J is (-3,1)

The coordinate of point K is (-8,11)

Consider the point that divides the line segment into 2:3 ratio as P(x,y).

The coordinates of point that divides the line segment into 2:3 ratio can be calculated as follows,

\(Coordinates of P = (\frac{3(-3)+2(-8)}{2+3}, \frac{3(1)+2(11)}{2+3} )\)

\(= (\frac{-9-16}{5}, \frac{3+22}{5} )\\\\= (\frac{-25}{5} \frac{25}{5} )\)

= (-5,5)

Hence the answer is The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.

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Answer:

1.-dh/dt  =  5.31*10⁻⁵ m/seg

2.-dh/dt =   1.99*10⁻⁵  m/seg

3.-dh/dt  =  1.59*10⁻⁴  m/seg

Step-by-step explanation:PREGUNTA INCOMPLETA NO SE INDICAN LAS FORMAS DE LOS TANQUES.

Asumiremos que los tres tanques son:

el primero cilindro recto     de  Vc = π*r²*h      ( r es radio de la base y h la altura)

el segundo asumiremos que es eliptico recto de Ve = π*a*b*h aqui a y b son los ejes de la elipse y h la altura

El tercero es un cono invertido Vco  = 1/3 *π*r²*h  ( r es el radio de la base.

1.-Caso del cilindro

Vc = π*r²*h

Derivando en ambos miembros de la expresión tenemos:

dV(c) / dt  = π*r²*dh/dt

Sustituyendo

1.5 Lts/seg =  3.14 * (3)²*dh/dt  

1.5/1000 m³/seg  =  28.26 m² dh/dt

1.5/ 28260 m  =  dh/dt

Despejando dh/dt

dh/dt  =  1.5 / 28260    =  5.31*10⁻⁵ m/seg

dh/dt  =  5.31*10⁻⁵ m/seg

2.-La elipse

Ve  = π*a*b*h  

Aplicando el mismo procedimiento tenemos:

DVe/dt  =  1.5 Lts/seg  =  π* 6*4* dh/dt

1.5 /1000   =  75.36 *dh/dt

dh/dt =  1.5 / 75360  m/seg

dh/dt =   1.99*10⁻⁵  m/seg

3. El cono invertido

Vco = (1/3)*π*r²*h

DVco/dt =  (1/3)*π*r²*dh/dt

1.5/1000  =  9.42 *dh/dt

dh/dt  =  1.5/9420

dh/dt  =  1.59*10⁻⁴  m/seg

Answer:

8

Step-by-step explanation:

8 njdjijfvffjbjghbggfbgkljhbhgf9igripogr9fkhj siad said had to n be 20 things long sorry

Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

one reflection would be (-2, -2) (-2,-4) and (-6, -2)

Step-by-step explanation:

Hope this helps

The probability of the binomial distribution:

R

Copy code

sum(dbinom(0:15, size = 60, prob = 1/6))

To estimate the probability of rolling 15 or fewer sixes when rolling a die 60 times, we can use a normal approximation.

In this case, we can assume that rolling a six follows a binomial distribution with parameters n = 60 (number of trials) and p = 1/6 (probability of success, which is rolling a six).

To estimate the probability using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use these values to approximate the probability using a normal distribution.

The mean of a binomial distribution is given by μ = n * p, and the standard deviation is given by σ = √(n * p * (1 - p)).

For this problem, we have n = 60 and p = 1/6. Therefore, μ = 60 * (1/6) = 10 and σ = √(60 * (1/6) * (1 - 1/6)) ≈ 2.5819.

To estimate the probability using the normal approximation, we can use the cumulative distribution function (CDF) of the normal distribution. We want to find P(X ≤ 15), where X is the number of sixes rolled.

Using R, we can calculate this probability using the pnorm() function with the parameters mean = μ and sd = σ:

pnorm(15, mean = 10, sd = 2.5819)

The true probability can be found by using the dbinom() function, which directly calculates the probability of the binomial distribution:

R

Copy code

sum(dbinom(0:15, size = 60, prob = 1/6))

By comparing the estimated probability using the normal approximation with the true probability calculated using the binomial distribution, we can assess the accuracy of the approximation.

Please note that the values obtained will depend on the specific version of R and its packages used, as well as the specific implementation details.

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Russ Krieger, Don Hicks, Pamela Drake, and Stephanie Braun are the four friends who received sports scholarships. Krieger has a full ride as a star in two different sports.

Based on the given clues, we can deduce the full names of the four friends who received sports scholarships.

From clue 1, we know that Hicks and Russ play on the same men's volleyball team. Therefore, one of the friends must be Don Hicks.

From clue 2, we learn that Drake and Braun have both set women's records in swimming. Therefore, one of the friends must be Stephanie Braun.

From clue 3, it is stated that Stephanie and Drake went to the same high school. Combining this information with clue 2, we can conclude that Pamela Drake is the full name of one of the friends.

Lastly, we know that Krieger has a full ride because he is a star in two different sports. Since the other three friends have been assigned their full names, it follows that Russ Krieger is the remaining friend.

In summary, the four friends who received sports scholarships and their full names are: Russ Krieger, Don Hicks, Pamela Drake, and Stephanie Braun.

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The full names of the friends based on the provided clues are Russ Hicks, Pamela Drake, Stephanie Braun, and Don Krieger.

The question involves a puzzle which requires using deduction and logical thinking skills to solve, typically found in mathematics problems.

Based on the clues provided:

Thus, the full names of the friends are Russ Hicks, Pamela Drake, Stephanie Braun, and Don Krieger.

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Answer:

k = 2

Step-by-step explanation:

f(2) = 1
g(2) = 2

g(x) is double of f(x)

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

x = -13 1/4

Step-by-step explanation:

Use cross multiplication here.

-3 x 11 = 4(x + 5)

-33 = 4x + 20

-53 = 4x

x = -53/4, or -13 1/4

Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624

Answer:

0.001

Step-by-step explanation:

Answer:

\(\frac{1}{1000}\)

Step-by-step explanation:

\(10^{-3}\)

\(= \frac{1}{10^{3}}\)

\(= \frac{1}{1000}\)

The trigonometric identity sin 2x/ 1 - cos 2x = cot x is proved using the trigonometric formulas

To prove the trigonometric identity, sin 2x / 1 - cos 2x = cot x

Let's write the left-hand side of the equation, sin 2x / 1 - cos 2x

Multiply the numerator and the denominator by 1 + cos 2x, (sin 2x * (1 + cos 2x))/ (1 - cos^2 2x)

Now, we know that sin 2x = 2 sin x cos x and cos^2 x + sin^2 x = 1,

Therefore, cos 2x = 2 cos^2 x - 1 and 1 - cos^2 x = sin^2 x

Hence, we can substitute cos 2x with 2 cos^2 x - 1 and 1 - cos^2 x with sin^2 x,  

(2sin x cos x * (1 + 2cos^2 x - 1))/sin^2 x

Simplifying, we get, 2sin x cos x * 2cos^2 x / sin^2 x  = 4cos^3 x / sin x cos x

Now, we know that cot x = cos x / sin x

Dividing both sides by cos x / sin x, we get, 4cos^3 x / sin x cos x = 4 cos x / sin x = 4 cot x

Therefore, we have proved that sin 2x / 1 - cos 2x = cot x.

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Answer:

Step-by-step explanation:

Given,

Length of the room = 12m

Width of the room = 5m

Therefore,

Area of the room = l × w

= 12m × 5m

= 60 sq.m (Ans)

Answer: 378,885

Step-by-step explanation:

We could just add it all up but there is a simple easy formula :D

n(n + 1)/2 = Sum of Integers

We make n be the biggest number in the sequence. n=870 then

870(870 + 1)/2 = 378,885

Just by using a simple formula, we were able to calculate the sum very quickly.

I hope this helps!

The probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321. The expected amount of time until the first bulb goes out is 10 minutes. The probability density function (pdf) of the random variable T, representing the time when you leave the room after the last light bulb goes out, is given by \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\).

To find the probability that a single bulb will burn out within the next 10 minutes, we can use the exponential distribution. The exponential distribution with a mean of 10 minutes has a rate parameter λ = 1/10.

The probability density function (pdf) for an exponential distribution is given by \(f(x) = λ * e^{(-λx)}\)

In this case, we want to find the probability that a bulb burns out within the next 10 minutes, which corresponds to the cumulative distribution function (CDF) at x = 10. The CDF is given by \(F(x) = 1 - e^{(-λx)\)

So, substituting the values, we have:

\(F(10) = 1 - e^{(-(1/10)*10)\)

\(= 1 - e^{(-1)\)

= 1 - 0.3678794412

≈ 0.6321

Therefore, the probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321.

The amount of time until the first bulb goes out follows an exponential distribution with a rate parameter of λ = 1/10 (since it has a mean of 10 minutes).

The probability density function (pdf) for the time until the first bulb goes out is given by\(f(t) = λ * e^{(-λt).\)

To find the expected amount of time until the first bulb goes out, we need to calculate the mean (or expected value) of this distribution.

The expected value of an exponential distribution with rate parameter λ is equal to 1/λ. In this case, the expected value is 1/(1/10) = 10 minutes.

Therefore, the expected amount of time until the first bulb goes out is 10 minutes.

To find the probability density function (pdf) of the random variable T, which represents the time when you leave the room (after the last light bulb goes out), we need to consider the distribution of the maximum of the exponential random variables.

Since there are 20 light bulbs in the room, and each follows an exponential distribution with a rate parameter λ = 1/10, the time until the last bulb goes out can be modeled as the maximum of 20 exponential random variables.

The pdf of the maximum of independent exponential random variables with the same rate parameter λ is given by \(g(t) = n * λ * e^{(-λt)} * (1 - e^{(-λt))^(n-1)}\), where n is the number of random variables.

In this case, n = 20, and λ = 1/10. Thus, the pdf of T is \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\)

This expression represents the pdf of the random variable T, which denotes the time when you leave the room after the last light bulb goes out.

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The ratio of a to b to c is written as a:b:c

Then, the ratio of starts to hearts to circles is:

Answer: Itll always be a rational number and never zero

Step-by-step explanation:

Answer:

A rational number (The third option).

Step-by-step explanation:

1. By definition, rational numbers have the following form, where and are integers and \(b\neq 0\).

2. Therefore, when you add two rational numbers, the result will be a rational number.

3. An example is shown below:

\(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}\)

The result is a fraction whose numerator and denominator are integers.

A relation may or may not represent a function.

The given relation is a function

For a relation to be a function, each x-value must have one unique corresponding y-value

The relation can be interpreted as:

\(x \to y\)

\(-2 \to 3\)

\(0 \to -1\)

\(5 \to 8\)

\(7 \to 5\)

Notice that, each value of x have distinct corresponding y-value.

This means that, the relation satisfies the condition to be a function.

Hence, the relation is a function

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As AD = DB, CD bisects ∠ACD

In Δ ACD and ΔBCD

We need to prove that  CD bisects ACB

∠A = ∠B

side AC = CB (as angle A and angle B are same)

CD is ⊥ AB

So, ∠ADC = ∠BDC

By SAS  Δ ACD and ΔBCD are congurent

In congurent triangles, corresponding angles and sides are equal

So, in  Δ ACD and ΔBCD

ACD = DCB

Therefore, as AD = DB, CD bisects ∠ACD

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Answer:

two points

Step-by-step explanation:

Complete the sentence. The intersection of three line segments can be two points.​

Answer:

x = \(\frac{c+b}{a}\)

Step-by-step explanation:

Given

ax - b = c ( add b to both sides )

ax = c + b ( divide both sides by a )

x = \(\frac{c+b}{a}\)

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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The poem For Want of a Nail is a warning about how small things can have large and unforeseen consequences. The lack of a horseshoe could lead to the loss of a horse, which could result in the loss of a rider, which could lead to the loss of a battle.

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