5. Yolanda has five times as many rubber bands as Jim. She has 365 rubber bands. How many rubber bands do Yolanda and Jim have together?​

{-15}

1) Let's solve this expression:

Note that we multiplied by 2 and then by (x+5) so that we could get rid of the denominators.

2) Examining the options, we can state that:

The solution set is S={-15}

Since there's one solution for that.

Answer:

4

Step-by-step explanation:

Q*1/5-t

Q=k/5-t

8=k/5-3

8=k/2

8x2=16

k=16

Q=16/5-t

16=16/5-t

16(5-t)=16

80-16t=16

80-16=16t

64/16=t

t=4

The value of t when Q = 16 is, 5

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

⇒ Q varies inversely with (5 - t).

Here, We have;

⇒ Q varies inversely with (5 - t ).

So, We can formulate;

⇒ Q = k / (5 - t)

Where, k is constant of proportionality.

Now, If Q = 8 when t = 3,

So, We get;

⇒ Q = k / (5 - t)

⇒ 8 = k / (5 - 3)

⇒ 8 = k / 2

⇒ k = 16

So, When Q = 16 and k = 16, the value of t is,

⇒ Q = k / (5 - t)

⇒ 16 = 16 / (5 - t)

⇒ (5 - t)  = 1

⇒ 5 = t

⇒ t = 5

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The two equations for this system are C = 0.60f + 15 and C = 0.80f + 13.

The number of fish for which the cost is the same is 10 fishes.

The cost of this fish is equal to $21.

In order to write a system of linear equations to model and describe this situation, we would assign variables to the number of fish and the cost of fish respectively, and then translate the word problem into algebraic equation as follows:

Note: 1 dollar is equal to 100 cents.

Since the starter aquarium kit costs $15 plus 60 cents per fish at wet pets, we have:

C = 0.60f + 15     ........equation 1.

Since the starter aquarium kit costs $13 plus 80 cents per fish at gills and frills, we have:

C = 0.80f + 13          ........equation 2.

Next, we would solve the system of equations as follows:

0.80f + 13 = 0.60f + 15

0.80f -0.60f = 15 - 13

0.20f = 2

Number of fish, f = 2/0.20

Number of fish, f = 10 fishes.

From equation 1, we have:

Cost of fish, C = 0.60f + 15

Cost of fish, C = 0.60(10) + 15

Cost of fish, C = 6 + 15

Cost of fish, C = 21 dollars.

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Answer:

Step-by-step explanation:


∣∣2. 8−(−9. 4)∣∣

∣∣2. 8+(−9. 4)∣∣

Let's call the average speed for the last three hours "S".

First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.

Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.

Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:

S = 170 miles / 2 hours = 85 miles per hour

So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.

Answer:

68 mph

Step-by-step explanation:

Let's call the average speed for the last three hours "S".

The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.

So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.

The time it took him to cover that distance is 3 hours.

We can use the formula distance = speed * time to find S:

204 = S * 3

Solving for S:

S = 68 mph

So the average speed for the last three hours was 68 mph.

a) Situations when an observer needs to be introduced and the role of each matrix: In order to observe the state of a system in practice, an observer must be introduced. The observer's role is to assess the system's state variables based on the system's input and output values, as well as the system's dynamics. The observer consists of three matrices:L: State feedback gain matrix M: Determines the observer's internal dynamics N: Maps the output signal to the observer's inputThe purpose of the observer is to estimate the system's states so that they can be fed back into the control loop.

b) Det[s1 - L] discussion: When designing an observer, the choice of observer poles has a significant impact on the system's efficiency. If the observer poles are placed far too close to the system poles, the observer may become unstable and diverge from the true state values. Alternatively, if the observer poles are placed far too far from the system poles, the observer may not be sensitive enough to changes in the system's states.In this context, det[s1 - L] refers to the determinant of the system's matrix minus the state feedback gain matrix. To ensure that the observer's poles are not too close or too far from the system's poles, this determinant must be non-zero.

c) Designing state observer: The observer's gain matrix L can be determined using the Ackerman formula.

By using Ackerman formula, the observer gain matrix is:L = acker(A', C', [s1, s2])L = [21 12]s1 = -4; s2 = -5 The observer's matrix M is given by:M = A - LC = [0 1;-1 -2] - [21; 12][1 0]M = [-21 -12;-21 -8]

The observer's matrix N is given by:N = B - LD = [0] - [21; 12][0]N = [0]d) Observer block diagram with matrices:Based on the information given above, the observer's block diagram with matrices L, M, and N can be presented in the following diagram:state observer block diagram

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Answer:

What is the numerical sum of the degree measures of ∠DEA and ∠AEB?

180

What are the numerical measures of the angles?

x = 14.5

m∠DEA = 39.5°

m∠AEB =  140.5°

Step-by-step explanation:

x + 25 + 9x + 10 = 180

Subtract 35 from both sides and you get,

10x = 145

The divide both sides by 10 and you get,

x = 14.5

To get the angle measurements you plug x back into the angle equations which in this case is 14.5.

It would look like,

m∠DEA = (14.5 + 25) = 39.5

and,

m∠AEB = (9 (14.5) + 10) = 140.5

The numerical sum of ∠DEA and ∠AEB  is 180°.

Numerical value of x is 14.5°.

Measure of ∠DEA is 39.5°.

Measure of ∠AEB is 140.5°.

Given: Two lines intersect.

Points D, E and B lie on a horizontal line and point E is intersected by line AC.

∠DEA = x + 25

∠AEB = 9x + 10

Now, from the given information we can deduce that to obtain the angles ∠AED and ∠AEB, point E should lie in between points D and B.

Since, points D, E and B lie on the horizontal line, then the ∠DEA and ∠AEB should form the supplementary angles (Figure 1).

⇒ ∠DEA + ∠AEB = 180°

⇒ (x + 25) + (9x + 10) = 180°

⇒ 10x + 35° = 180°

⇒ 10x = 145°

⇒ x = 14.5°

Now, we will substitute the value of x = 14.5° in the ∠DEA and ∠AEB, hence we get:

⇒ ∠DEA = x + 25°

⇒ ∠DEA = 14.5° + 25°

⇒ ∠DEA = 39.5°

Also,

⇒ ∠AEB = 9x + 10°

⇒ ∠AEB = 9 × 14.5° + 10°

⇒ ∠AEB = 130.5° + 10°

⇒ ∠AEB = 140.5°

Therefore, the numerical sum of the degree measures of ∠DEA and ∠AEB is 180°; The numerical measures of the angles is, x = 14.5°, m∠DEA = 39.5° and m∠AEB = 140.5°.

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Answer:

425

Step-by-step explanation:

To find the approximate direction angle of vector v = ⟨8, -1⟩, we can use trigonometry and the inverse tangent function (arctan). Therefore, the approximate direction angle of vector v is approximately -0.1244 radians or -7.12 degrees.

The direction angle (θ) of a vector can be calculated using the formula:

θ = arctan(y/x)

where (x, y) are the components of the vector.

For the given vector v = ⟨8, -1⟩, we have x = 8 and y = -1.

θ = arctan((-1)/8)

Using a calculator or a mathematical software, we can evaluate this expression to find the approximate direction angle:

θ ≈ -0.1244 radians or approximately -7.12 degrees.

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The mean and standard deviation of the number of people with blood type a-positive in 100 randomly selected is μ=85, σ=3.5707

The standard deviation is a statistic that measures the amount of variation or dispersion of a group of values.

Standard deviation is usually abbreviated SD and is most commonly represented in mathematical texts and equations by the lower case Greek letter (sigma) for population standard deviation or the Latin letter s for sample standard deviation.

A low standard deviation indicates that the values are close to the mean of the set (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a broader range.

Given, The population proportion of success is p=0.85

And also given that the sample size is n=100

b) The population mean is:

μ=np

μ=100(0.85)

μ=85

Therefore, mean=85

And the population standard deviation is:

σ=√np(1-p)

σ=√100(0.85)(1-0.85)

σ=3.5707

Therefore, standard deviation=3.5707

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The complete question is:

" Rh - positive blood appears in 85% of the population in the USA. a) Verify that it's possible to use the normal approximation to binomial distribution if a sample size is 100 randomly selected people. b) Find the mean and standard deviation of the normal distribution."

Answer:

1.4

Step-by-step explanation:

when you divide you get

1.41129032

but you need it rounded to the nearest tenth which would make it

1.4

Answer:

x<9

Step-by-step explanation:

x-6<x/3

3(x-6)<x

3x-18<x

3x-x<18

2x<18

X<18/2

X<9

In the 2018 qualifiers, Daniel Ricciardo set a new record for one lap in 1 minute, 11.841 seconds. To calculate his average speed for that lap, we can use the formula: average speed = distance / time.

However, since we are not given the distance of the lap, we cannot calculate the average speed accurately. Therefore, we cannot determine Daniel Ricciardo's average speed for that lap based on the information provided.

The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.

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We can be concluded that each of the proposals can be represented by linear functions.

The class has money in the accounts because the linear function of each proposal has an initial value (b).

What is a Linear Function?

The graph represents Sarah's Proposal as a straight-line graph, therefore Sarah's proposal can be represented by a linear function.

The table representing Gene's Proposal denotes the unit rate = change in y / change in x = 7. Therefore, it can be represented by a linear function.

So, we conclude that each of the proposals can be represented by linear functions.

The class has money in the accounts because the linear function of each proposal has an initial value (b).

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The funds collected by Sarah are between 127

From Sarah’s proposal graph, we can say that it can be represented by linear representation.

The slope of equation(m)= (90-30)/ (7-2)= 60/5= 12

The equation is given as y=12x+7

From Gene’s table, it is observed that it x and y values can be represented by the function: y=5x+7.

Paul’s proposal is already represented by a linear function.

Let us consider 10 hours of work. We calculate the funds collected for this.

From the graph, it is evident that the funds collected by Sarah are between 127.

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Answer:

x=y

Step-by-step explanation:

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

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Answer:

2/5

Step-by-step explanation:

Answer:2/5

Step-by-step explanation:

right on edge

The transfer function of the system is:

G(s) = X(s)/U(s) = 1/(s+2)

To find the transfer function G(s) = X(s)/U(s) of the system described by the differential equation x(t) + 2x(t) - u(t), we can take the Laplace transform of both sides of the equation, assuming zero initial conditions:

L{x(t) + 2x(t) - u(t)} = L{0}

Applying the linearity property of the Laplace transform, we get:

L{x(t)} + 2L{x(t)} - L{u(t)} = 0

Substituting X(s) for L{x(t)} and U(s) for L{u(t)}, we get:

X(s) + 2X(s) - U(s) = 0

Solving for X(s)/U(s), we get:

X(s)/U(s) = 1/(s+2)

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Answer:

  about 3.08 L

Step-by-step explanation:

You want the number of litres in the volume of a cylindrical can 14 cm in diameter and 20 cm high.

A litre is a cubic decimeter, 1000 cubic centimeters. As such, it is convenient to perform the volume calculation using the dimensions in decimeters:

The volume of the cylinder is given by the formula ...

  V = (π/4)d²h . . . . . . . where d is the diameter and h is the height

  V = (π/4)(1.4 dm)²(2.0 dm) ≈ 3.079 dm³ ≈ 3.08 L

The cylindrical can will hold about 3.08 litres.

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Answer:

y=2/x=1    y=4/x=4

Step-by-step explanation:

Answer:

For every 3 tablespoons of cocoa Nate uses 1 tablespoon of sugar

Answer:

i got b and h{i hope this helps}

Step-by-step explanation:

The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Answer:

37

Step-by-step explanation:

Answer:

The formula of (a+b)² and (a-b)² are as follows:

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(a-b)²=a²-2ab+b²

Step-by-step explanation:

These are identities .

\(:\implies \) ( a + b)²

\(:\implies \) ( a + b) ( a + b)

\(:\implies \) a ( a + b ) + b ( a + b)

\(:\implies \) a² + ab + ab + b²

\(:\implies \) a² + 2ab + b²

\(:\implies \) ( a - b)²

\(:\implies \) ( a - b) ( a - b)

\(:\implies \) a ( a - b ) - b ( a - b)

\(:\implies \) a² - ab - ab + b²

\(:\implies \) a² - 2ab + b²

Given function:

a = 3

As a is positive the parabola opens upward. It has a minimum value.

To find the minimum:

1. Find the value of x where the parabola has the minimum value, use the next formula:

2. Use the value of x where the function has minimum value (step 1) to find the value of the function: