Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using function notation? f(y)=1/3v+4/3 f(x)=-3x+4 f(x)-1/3x+4/3 f(y)=-3y+4​

If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

Learn more about inflation rate at

https://brainly.com/question/31635911

#SPJ11

Working in certain industries or environments can lead to various injuries, including sprains, muscle pains, severe fatigue, falls, burns, chemical exposure, machinery malfunctions, and even explosions.

In certain industries or work environments, employees may face a higher risk of injuries due to the nature of their tasks and the surrounding conditions.

Severe fatigue is another concern, especially in occupations that involve long hours or physically demanding work. Fatigue can impair judgment and coordination, increasing the likelihood of accidents and injuries

Additional injuries can result from falls, which can happen due to slippery surfaces, uneven ground, or inadequate safety precautions. Burns may occur when working with hot objects, open flames, or chemicals without proper protective measures. Chemical exposure can lead to injuries ranging from skin irritation to more severe health issues.

Machinery malfunctions pose a significant risk, especially if safety features are not in place or not properly maintained. Accidents involving machinery can cause serious injuries, such as fractures, amputations, or even fatalities. In some cases, explosions may occur in work environments where hazardous materials or volatile substances are present.

To know more about workplace injuries, visit:
brainly.com/question/31184578
#SPJ11

The length of the other leg is 12 inches.

What is the Pythagorean theorem?

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

The hypotenuse of a right triangle is the side opposite the right angle, and the legs of a right triangle are the two sides that are adjacent to the right angle.

If we know the length of the hypotenuse and one leg of a right triangle, we can use the Pythagorean theorem to find the length of the other leg.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

We can use this theorem to write the equation:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

In this problem, the hypotenuse is 13 inches and one of the legs is 5 inches. We can substitute these values into the equation to find the length of the other leg:

c² = a² + b²

(13)² = a² + (5)²

169 = a²+ 25

144 = a^2

a = 12

Hence, the length of the other leg is 12 inches.  

To learn more about the Pythagorean theorem visit,

https://brainly.com/question/231802

#SPJ1

Answer:

43/160

Step-by-step explanation:

To find the relative frequency,

We just have to know things:

1. The data for asked event

2. Total number of data.

With these 2 points, we can create a fraction that is formed like this:

Data of event / Total data

In this case it is:

43/160

Hope this helps

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

The problem describes three children riding on the edge of a merry-go-round with given masses. The task is to calculate the angular momentum of the system.

To calculate the angular momentum of the system, we need to consider the angular momentum of both the merry-go-round and the children.

Calculating the moment of inertia of the merry-go-round: \((1/2) × 142 kg × (1.60 m)^2 = 181.76 kg·m^2.\)

The angular momentum of the merry-go-round is then: angular momentum = \(181.76 kg·m^2 × (21.3 rpm × 2π/60) = 766.34 kg·m^2/s.\)

For the children, we calculate their individual angular momenta using the formula: angular momentum = mass × velocity × radius. Since the children are riding on the edge of the merry-go-round, their velocities are equal to the tangential velocity of the merry-go-round.

Calculating the angular momentum for each child:

Child 1: 22.4 kg × \((1.60 m × 21.3 rpm × 2π/60) = 471.95 kg·m^2/s\)

Child 2: 29.5 kg × \((1.60 m × 21.3 rpm × 2π/60) = 622.20 kg·m^2/s\)

Child 3: 40.8 kg × (1.60 m × 21.3 rpm × 2π/60) = 855.01 kg·m^2/s

The total angular momentum of the system is the sum of the angular momenta of the merry-go-round and the children:

Total angular momentum = \(766.34 kg·m^2/s + 471.95 kg·m^2/s + 622.20 kg·m^2/s + 855.01 kg·m^2/s = 2715.50 kg·m^2/s.\)

Therefore, the total angular momentum of the system consisting of the merry-go-round and the three children is \(2715.50 kg·m^2/s.\)

Learn more about angular momentum here:

https://brainly.com/question/30656024

#SPJ11

Answer:

Decimal--x= -1.39

Fraction--x= -139/100

Step-by-step explanation:

You want to get x by itself in this problem

You have to distribute the 3 into the parenthesis first

1.2/8=15x+21

Now you can do 2 of either things....you can either divide 1.2/8 and then subtract 21 from both sides or you can just subtract 21 from both sides without dividing. I will use option 2.

1.2/8-21=15x+21-21

So now you cancel out the 21 on the right side and get...

-20.85=15x

Now divide by 15

-1.39=x in fraction form -139/100=x

Hope this helped!

The possible total amounts can be formed by combining various quantities of 25-dollar and 50-dollar gift certificates in accordance with your needs.

To determine the possible total amounts that can be formed using gift certificates in denominations of $25 and $50, we can use a simple formula. Let x represent the number of $25 gift certificates and y represent the number of $50 gift certificates.

The formula for finding the total amount is:

Total amount = 25x + 50y

To find all possible total amounts, we need to consider all possible combinations of x and y.

For example:

- If we have 1 $25 gift certificate and 0 $50 gift certificates, the total amount is $25.
- If we have 2 $25 gift certificates and 0 $50 gift certificates, the total amount is $50.
- If we have 0 $25 gift certificates and 1 $50 gift certificate, the total amount is $50.
- If we have 1 $25 gift certificate and 1 $50 gift certificate, the total amount is $75.
- If we have 2 $25 gift certificates and 1 $50 gift certificate, the total amount is $100.

In general, any total amount can be formed using a combination of $25 and $50 gift certificates. The possible total amounts are:

$25, $50, $75, $100, $125, $150, $175, $200, $225, $250, and so on.
Hi! I'd be happy to help you with this question. To determine the possible total amounts you can form using gift certificates in denominations of 25 dollars and 50 dollars, follow these steps:

Step 1: Identify the minimum amount.
The minimum amount you can form is with one 25-dollar gift certificate, which gives a total of 25 dollars.

Step 2: Determine the increments.
Since the denominations are 25 dollars and 50 dollars, the possible amounts will increase in increments of 25 dollars.

Step 3: List the possible amounts.
Using the minimum amount (25 dollars) and the increments (25 dollars), the possible total amounts you can form using these gift certificates are:

- 25 dollars (1 x 25-dollar gift certificate)
- 50 dollars (2 x 25-dollar gift certificates or 1 x 50-dollar gift certificate)
- 75 dollars (3 x 25-dollar gift certificates or 1 x 25-dollar + 1 x 50-dollar gift certificates)
- 100 dollars (4 x 25-dollar gift certificates or 2 x 50-dollar gift certificates)
- ... and so on, increasing in 25-dollar increments.

The possible total amounts can be formed by combining various quantities of 25-dollar and 50-dollar gift certificates in accordance with your needs.

Learn more about denominations at: brainly.com/question/7067665

#SPJ11

Answer:

6, but the question makes more sense when asking about 12.5% from 48

Step-by-step explanation:

to get a percentage of something, we just have to remember that \(X\% = \frac{X}{100}\) and that we just need to multiply.

Yes, percentages are just numbers, but the percentage sign lets us signify the purpose of a number.

48 * 12.5% = 48 * 0.125 = 48 / 8 = 6

In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

To learn more about sets visit:

brainly.com/question/30705181

#SPJ11

Answer:

2.5

Step-by-step explanation:

Let the time = X

Distance = Rate times time

Level roads = 18x

Hills = 10x

Total is 98 miles

18x+10x = 98

Add:

28x = 98

Divide both sides by 28:

x = 3.5

She spent 3.5 hours on each part

Total time = 3.5 + 3.5 = 7 hours

Albert used the division and multiplication properties of equality to rewrite the equation.

To understand the properties used by Albert to rewrite the equation, let's analyze the steps taken:

The original equation is: -13x/5 = 286.

Albert's rewritten equation is: x/5 = 286/-13.

To transform the original equation into the rewritten form, Albert applied the following properties:

Division Property of Equality: Albert divided both sides of the original equation by -13/5. This property states that if you divide both sides of an equation by the same non-zero number, the equality remains unchanged.

Multiplication Property of Equality: Albert multiplied both sides of the equation by -13/5. This property states that if you multiply both sides of an equation by the same non-zero number, the equality remains unchanged.

Therefore, Albert used both the division property of equality and the multiplication property of equality to rewrite the equation. The division property was used to isolate the variable term on one side of the equation, and the multiplication property was used to manipulate the coefficients and maintain the equality.

Learn more about properties of equality:

https://brainly.com/question/13130806

#SPJ11

The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .

Here,

a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:

=> The mοnthly payοut =  (P*r) / (1 - (1+r)(-n)).

We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:

=>  \(9900 \times (1 + 0.0429/12)^{(12 \times 4.5)\) = 12,723.97

The οverall debt balance is $12,723.97.

The numbers can then be entered intο the fοrmula as fοllοws:

=>  (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))

is the fοrmula fοr the mοnthly payοut.

Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)

Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.

b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:

=> tοtal interest = (mοnthly payment X n) - P .

There have been a tοtal οf:

=> 120 is equal tο ten years times οne year.

The entire interest paid is thus:

=> ($3,943.80) (tοtal mοnthly installments * n) - P

=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)

Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

To know more about interest visit:

brainly.com/question/28792777

#SPJ1

a.) The type of distribution that is represented by the histogram is a left skewed histogram.

b.) The type of sampling this will represent is a simple random sampling.

A left skewed histogram can be defined as the type of distribution where by the tails is displayed towards the left of the histogram. This is represented in the histogram given in the diagram above.

A simple random sampling is defined as the type of sampling whereby every member of a population is given an equal chance to be selected. Since the information represented is the sample of an entire league, making another bigger league from it gives them all equal chance to be selected.

Learn more about sampling here:

https://brainly.com/question/24466382

#SPJ1

Answer:

G (-2,8)

Step-by-step explanation:

(-8+x)/2 = -5

-8 + x = -10

x = -10 + 8

x = -2

(0+y)/2 = 4

y = 4 · 2

y = 8

Answer:

Add 5 to each side

You get x=15

1. m • m (factors)  =>  m² (exponents)

2. a^a * b³ • a² (factors) =>  a^(a+2) * b³ (exponents)

3. rs³ • 6r²s (factors) =>  6r³s⁴ (exponents)

1. Expression: m • m

  Factors: The expression consists of two factors, both of which are 'm'.

  Exponents: To rewrite it with exponents, we count the number of 'm' factors, which is 2. Therefore, we can write it as m².

2. Expression: aªb³ • a²

  Factors: The expression consists of two factors. The first factor is 'a' raised to the power of 'a', and the second factor is 'b' raised to the power of 3.

  Exponents: To rewrite it with exponents, we simplify the first factor 'aªb³' as a³b³. Then, we multiply it by the second factor 'a²'. The resulting expression is a³b³ • a².

3. Expression: rs³ • 6r2s

  Factors: The expression consists of two factors. The first factor is 'rs' raised to the power of 3, and the second factor is 6r²s.

  Exponents: To rewrite it with exponents, we simplify the first factor 'rs³' as r³s³. Then, we multiply it by the second factor '6r²s'. The resulting expression is r³s³ • 6r²s.

Learn more about exponents at https://brainly.com/question/13669161

#SPJ1

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

Convert 10% to decimal =.10

10/100=.10

Them multiply 754 by .10 and you get $75.40. This is the amount that will be subtracted from the full price to get your sales price.
now you have

$754.00-$75.40=$678.60

$678.60 is the sale price.

Solution

Question 1:

Question 2:

Final Answer

Question 1:

The exponential function to model the scenario is

Question 2:

The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits

The probability of having to try three or more times is = 431/46656.

To find the probability of having to try three or more times to get all three dice to show the same number, we need to consider the probabilities of different outcomes.

On the first roll, all three dice can show any number with equal probability, so the probability of not getting a match on the first roll is 1.

On the second roll, we want to calculate the probability of not getting a match again. There are two cases to consider:

Since we want to calculate the probability of having to try three or more times, we are interested in the event where we do not get a match on the first two rolls.

Therefore, the probability of this event is \((215/216)^2\) = 46225/46656.

Thus, the probability of having to try three or more times is 1 - 46225/46656

= 431/46656.

Learn more about probability

brainly.com/question/31828911

#SPJ11

Which types of triangles can always be used as a counterexample to the statement "all angles in a triangle are acute" they include

Acute angles are those that are smaller than 90 degrees. 90 degrees is the angle at a right angle.

Obtuse angles are those that are more than 90 degrees.

A right triangle can be isosceles or scalene, meaning that each of its three sides is of a different length (having exactly two sides of equal length).

Equilateral triangle always have angel 60 degrees which as an acute angel

Learn more about acute angles at:

https://brainly.com/question/6979153
#SPJ1

Answer:

15,600,000

Step-by-step explanation:

We start with our initial population of 600,000. Then multiply that with the rate of 4% (0.04 in decimal, or 1.04 so that the 0.04 is automatically added to the 600,000.)

Since the safety factor is less than 1.0, the design is unsafe.

A designer selects a 1-in dowel bar size for contraction joints in a 10" concrete slab resting on a subgrade material with a 200psi/ in modulus of subgrade reaction. The design load is a 9,000-lb dual wheel load centered 6" from the slab edge. Assume a 12" dowel spacing.

The slab is divided into two slabs of equal area by the contraction joint, and the outermost dowel is considered in each slab. The 9,000-lb dual wheel load is distributed uniformly across the two slabs.

Thus, the total load per slab equals 4,500 lbs.

Assume that the modulus of elasticity of concrete =4.5×106psi, concrete compressive strength is 2800psi, and Poisson ratio of concrete =0.15.

Determine the maximum bearing stress at the outermost dowel bar and assess the safety of the design. Assume modulus of dowel support (K)=1500ksi/in,

Esteel ​=29,000ksi, and z=0.25in.

The maximum bearing stress occurs at the outermost dowel bar and is determined using the equationσ=WL/2bd

The length of slab L is equal to 12 in (i.e., 1 ft), and the width b is equal to 1 ft.

The subgrade modulus of reaction is given byKs=200psi/in.

The spring constant of the dowel is given byK=1500ksi/in.

The deflection of the dowel bar is given byδ=5WL3Kb3d3

Thus, the maximum deflection occurs at the edge of the slab, where y = 0.25 in.

The deflection at this location is given byδmax=5(4,500)(6)3(1500)(1)3(1)=0.67 in

Therefore, the maximum bearing stress at the outermost dowel bar is given byσmax=WL/2bd+3Kδmax/z2

=4,500/2(1)(1)+(3)(1500)(0.67)/(0.25)2

=29,953 psi,

Assuming that the yield stress of the steel is 36 ksi, the maximum allowable bearing stress is given byσallowable

=Fy/ρ=36,000/1.5

=24,000 psi

Therefore, the safety factor is given by

SF=σallowable/σmax

=24,000/29,953

=0.8

To know more about ratio visit:

https://brainly.com/question/13419413

#SPJ11

Answer:

Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

Step-by-step explanation:

Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.

Since we want to make 30 liters of a 10% solution, we can set up the following equations:

Equation 1: x + y = 30 (total volume equation)

Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)

From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:

(0.06(30 - y) + 0.15y) / 30 = 0.10

Simplifying the equation gives:

(1.8 - 0.06y + 0.15y) / 30 = 0.10

1.8 + 0.09y = 3

0.09y = 1.2

y ≈ 13.33

Substituting y back into Equation 1, we find:

x + 13.33 = 30

x ≈ 16.67

Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

To know more about circular motion refer here:

https://brainly.com/question/19221273

#SPJ11

Answer:

x^2 +2x -15

Step-by-step explanation:

FOIL

(x-3)(x+5)

first x*x = x^2

outer 5x

inner -3x

last -3*5 = -15

Add them together

x^2 +5x-3x-15

Combine like terms

x^2 +2x -15

We have a translation of 2 units to the left, and 6 units dow.

For a function:

y = f(x)

A horizontal translation of N units is written as:

y = f(x + N)

if N > 0, the translation is to the left.

if N < 0, the translation is to the right.

and a vertical translation of N units is written as:

y = f(x) + N

if N > 0, the translation is up

if N < 0, the translation is to the down.

Here we start with y = x²

And the transformation is:

y = 3*(x + 2)² - 6

So we have a translation of 2 units to the left and 6 units down (and a vertical dilation of scale factor 3, but that is not a translation, so we ignore that one).

Learn more about translations at.

https://brainly.com/question/24850937

#SPJ4

Inequality that represents this statement is -90 < -62

Hence, the if on the horizontal number line, -62 is located to the right of

-90. The inequality that represents this statement is -90 < -62

To learn more about inequality, refer to

https://brainly.com/question/25275758

#SPJ1