1. Ralf and Susie share $57 in the ratio 2:1.
(a) Calculate the amount Ralf receives.
(b) Ralf gives $2 to Susie.
Calculate the new ratio Ralf's money: Susie's money.
Give your answer in its simplest form

No, f is not continuous at x=-3. To show this, let's take the limit from both sides.

From the left side, the limit of f(x) as x approaches -3 is 5. From the right side, the limit of f(x) as x approaches -3 is 3. Since the two limits are not equal (5≠3), then f is not continuous at x=-3.No, f is not continuous at x=-3. This is because the limit of f(x) as x approaches -3 does not equal f(-3). The limit of f(x) can be calculated using the formula lim x->-3 f(x) = lim x->-3 (x^2 + 9). Calculating this limit, we get lim x->-3 f(x) = lim x->-3 (x^2 + 9) = 9. However, f(-3) = (-3)^2 + 9 = 0, which does not match the limit.

Mathematically, this can be shown using the following:

limx→−3 f(x) = 5 ≠ 3 = limx→−3+ f(x)

Since the two limits are not equal, then f is not continuous at x=-3.

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The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.

The formula for angular velocity is given by;`ω = (2π / T)`.Where;ω = angular velocity of the object. T = time period (in seconds).`I = 185.0 kg m2` represents the moment of inertia of the flywheel.`ω = 350.0 rev/min = (350.0 * 2π) / 60 = 36.61 rad/s` represents the initial angular velocity of the flywheel.

The flywheel is brought to rest by friction in `5.0 min = 5.0 * 60 = 300 seconds`.

The formula for the angular acceleration is given by;`α = (ωf - ωi) / t`. Where;`α` = angular acceleration of the object.`ωi` = initial angular velocity.`ωf` = final angular velocity of the object.`t` = time taken (in seconds).

At rest, the final angular velocity of the flywheel is zero.

Therefore;`α = (- ωi) / t`.The formula for torque is given by;`τ = I * α`.Where;τ = torque exerted on the object.I = moment of inertia of the object.α = angular acceleration of the object.

Substituting the values;`τ = I * α = 185.0 * (-36.61) / 300 = -22.58 N.m`.

Therefore, the frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.

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D) y = 2x + 8

Parallel lines are coplanar lines that never intersect.

Parallel Slopes

All parallel lines have the same relationship between their slopes. For 2 lines to be parallel, their slopes must be equal. The question tells us that the slope of the first line is 2. This means that only answer choices B and D are viable.

The slopes of answer choices A and C are perpendicular to the line given.

Testing the Answers

Both B and D could be parallel to the line given; however, we are also told that the line must pass through (-2, 4). To see which answer is correct, we can plug in the x and y-values and solve. If a line passes through a point, then the equation will be true when the values are plugged in.

Let's start with answer B.

Since this statement is not true, we know that y = 2x + 4 does not pass through the point (-2, 4).

Next, we need to test answer choice D.

This is true, so y = 2x + 8 must pass through the point (-2, 4). Since answer choice D has a parallel slope and passes through (-2, 4), it must be the correct answer.

Answer:

4:2:3

Step-by-step explanation:

First you need to divide each number by a common factor like 2.

1. 16:8:12

Divide all numbers by two

8:4:6

Divide by two again

4:2:3

Since, you cannot simplify all of them again, the asnwer is

4:2:3

Answer:

4:2:3

Step-by-step explanation:

Blue : Green : Red

 16   :      8    :  12

  4   :       2   :    3

Answer:

False.

Step-by-step explanation:

In a normal distribution, 95% of the data falls within 2 standard deviations of the mean.

False, In a normal distribution, 95% of the data do not falls within 1 standard deviation of the mean.

The empirical rule or 68-95-99.7% rule can give us a good info about normal distribution.

This rule tells us that around 68% of the data will fall within one standard deviation of the mean, whereas around 95% will fall within two standard deviations of the mean and 99.7% will fall within three standard deviations of the mean.

Here given that, in a normal distribution, 95% of the data falls within 1 standard deviations of the mean, which is wrong because in the above description we states that, 95% will fall within two standard deviations of the mean.

So, the given statement is false.

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The missing side lengths are (m = 4\(\sqrt{6}\) , n =  6\(\sqrt{2}\)).

According to given triangle, Using triangular formula;

tan 30 = \(\frac{2\sqrt{6} }{n}\)

⇒\(\frac{1}{\sqrt{3} }\)  = \(\frac{2\sqrt{6} }{n}\)

⇒ n = \(6\sqrt{2}\)

  n = \(6\sqrt{2}\)

Similarly,

sin 30 = \(\frac{2\sqrt{6} }{m}\)

⇒ \(\frac{1}{2}\) = \(\frac{2\sqrt{6} }{m}\)

⇒ m = \(4\sqrt{6}\)

   m = \(4\sqrt{6}\)

so,

    m = \(4\sqrt{6}\) and n = \(6\sqrt{2}\)

So, the correct option is D.

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Answer:

A. A reflection over the y-axis and then a rotation 90 degree clockwise about the origin.

Step-by-step explanation:

Given information: Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.

A sequence of transformations to produce the same results could be the opposite of this, wherein Figure H undergoes a series of transformations to form Figure G.

Answer:

7 17/99

Step-by-step explanation:

Answer:

1134.1 [cm²]

Step-by-step explanation:

A=πr2

Circle area = π * r² = π * 361 [cm²] ≈ 1134.1 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 19 [cm] * 2 = 38 [cm]

Answer:

y=4x+5

Step-by-step explanation:

so like the b in y= mx +b is the starting point well in that graph it is also is where the line touches the y-axis and the slope is rise/run so start at 5 move over 1 then go up 4 that 4/1 = 4 so m=4 so if y= 4x+b and b being 5 then y=4x+5

Answer:

i'll post this answer since the question was already answered, thank you so much for the points! :) <3

Answer:

$ 4,740.76

Step-by-step explanation:

The general formula for compound interest computation is
\(A = P(1 + r)^t\)

where
A = amount accrued

r = annual interest rate as a decimal

t = number of years

Given
P = 40,000
r = 6% = 6/100 = 0.06
n = 6 years

A = 40000(1 + 0.06)⁶
= 40000 (1.06)⁶
= 40,000 X 1.418519112256
= $56,740.76

Interest obtained
= A - P
= $56,740.76 - 40,000.00

= $16,740.76

For simple interest the formula for interest is
I = Prt
where once again

P = amount invested
I = interest earned
r = annual interest rate in decimal
t = number of years

Plugging in values for P, r, t we get
I = 40000 x 0.06 x 5 = $ 12,000.00

So the amount of interest earned if 40,000 is compounded annually at 6% for 5 years
= $16,740.76 - $12,000
= $4,740.76

Answer:

D. linear; y = –x – 1

Step-by-step explanation:

Linear; y=-x - 1

The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x

...............................................................................................................................................

Answer:

The correct answer is D) linear; y = –x – 1

Step-by-step explanation:

To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.

(4, 5)

y = -x - 1

-5 = -4 - 1

- 5 = -5 (TRUE)

(0, -1)

y = -x - 1

-1 = 0 - 1

-1 = -1 (TRUE)

Answer:

- 40/90 or -4/9

Step-by-step explanation:

the answer will be negitive b/c  positive * negitive = negitive

5*8

= 40

that is the numerator

6*15

=90

that is the denominator

then add the - and the answer will be

-40/90

simplify and it is -4/9

ur welcome

Evaluating all possible values of a variable in a model is called a sensitivity analysis.

A sensitivity analysis is a technique used to assess the impact of changes in the values of input variables on the output or outcome of a model or system. It involves systematically varying the values of the variables within a defined range and observing the corresponding changes in the model's output.

The purpose of a sensitivity analysis is to understand how sensitive the model is to changes in the input variables and to identify which variables have the most significant influence on the model's results.

During a sensitivity analysis, different scenarios are created by varying one or more input variables while keeping others constant. By examining the resulting changes in the model's output, analysts can gain insights into the relationships and dependencies between the variables and assess the robustness of the model's predictions or decisions.

Sensitivity analysis helps in understanding the potential risks, uncertainties, and limitations associated with the model, and can aid in decision-making and improving the model's performance by identifying critical variables that need to be carefully monitored or controlled.

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There are 11,440 ways to distribute 7 identical flyers into 10 different mailboxes, where each mailbox receives at most one flyer.

If we are allowed to put at most one flyer per mailbox and the flyers are identical, this problem involves distributing identical objects into distinct containers. The solution can be obtained using the stars and bars method.

We can represent the distribution of flyers as 7 stars (representing the flyers) and 9 bars (representing the dividers between the mailboxes). The number of ways to distribute the flyers is equal to the number of ways to arrange the 7 stars and 9 bars, which is given by the binomial coefficient:

${{7 + 9}\choose{9}} = {{16}\choose{9}} = \frac{16!}{9!7!} = 11440$

Therefore, there are 11,440 ways to distribute 7 identical flyers into 10 different mailboxes, where each mailbox receives at most one flyer.

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The question is incomplete but probably the full question is:

We want to distribute 7 flyers to 10 different mailboxes. How many ways can we do that if (a) We put at most one flyer per mailbox and the flyers are identical?

Applying the distributive property, it is found that the equivalent expression is:

The expression given in this problem is:

\(\frac{1}{4}(16a + 8b + c)\)

Applying the distributive property, each term of the expression is multiplied by the term in front, which is \(\frac{1}{4}\), hence:

\(\frac{1}{4}(16a + 8b + c) = \frac{16a}{4} + \frac{8b}{4} + \frac{c}{4} = 4a + 2b + \frac{c}{4}\)

Hence, option D is correct.

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Answer:

answer is -103

The person who is an american author, anthropologist, and filmmaker who portrayed racial struggles in the early 1900 american south and published research on hoodoo is Zora Neale Hurston.

She is known for portraying racial struggles in the early 1900s American South and published research on hoodoo. Her most popular novel, "Their Eyes Were Watching God," was published in 1937. She also wrote over 50 short stories, plays, and essays.

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According to the given statement  the value of sin x = 8/10

A mathematical field called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of  geometry.

To roof a home, to make the roof slant (in the case of single-family bungalows), to determine the height of a roof in buildings, etc., use trigonometry. The naval and aviation industries use it. It's applied to cartography (creation of maps). Trigonometry is also used in satellite navigation systems.

sin x = 4/5

We know that:

Sin x = opposite/Hypotenuse.

So,

When the triangle is enlarged, the opposite side will increase to an angle of 8, and the hypotenuse will increase to an angle of 10.

= 4/5 we multiply by 2 with 4 and 5 we get:

= 8/10

4/5 will result from simplifying 8/10. Thus, nothing has changed.

So the value of sin x = 8/10.

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Answer:

Step-by-step explanation:

Use this formula:

y - y1 = m ( x - x1 )

We are told m = -3 and given the point (12 , 5) ---- > so x1 = 12 and y1= 5

Put these values into the formula above and you get:

y - y1 = m ( x - x1 )

y - 5 = -3 ( x - 12 )

y - 5 = -3x + 36

y = -3x + 36 + 5

y = -3x + 41

Answer:

AB slope is 1/2

CD slope is 1/3

Since the slopes of the lines aren't the same, the lines aren't parallel.

Step-by-step explanation:

Answer:

2p - 5 ≤ 124.

Step-by-step explanation:

If Chis's pay is p then it is:

2p - 5 ≤ 124.

Therefore, the infinite geometric series representing the decimal 0.44444... converges to the fraction 4/9.

To represent the decimal 0.44444... as an infinite geometric series, we can start by noticing that this decimal can be written as 4/10 + 4/100 + 4/1000 + ...

The pattern here is that each term is 4 divided by a power of 10, with the exponent increasing by 1 for each subsequent term.

So, we can express this as an infinite geometric series with the first term (a) equal to 4/10 and the common ratio (r) equal to 1/10.

The infinite geometric series can be written as:

0.44444... = (4/10) + (4/10)(1/10) + (4/10)(1/10)^2 + ...

To find the fraction to which this series converges, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Plugging in the values, we have:

S = (4/10) / (1 - 1/10)

= (4/10) / (9/10)

= (4/10) * (10/9)

= 4/9

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