f(x) = − ³/2 x and g(x) = (½)² – 1
-
Graph the functions on the same coordinate plane.
Let
What are the solutions to the equation
?
f(x) = g(x) ₂

Answer: 28, 30, 32

Step-by-step explanation: The first integer is 28, the second is 30, and the third is 32. The difference from the first integer and the last integer should be 4. x is the first integer, so the equation is:

x+x+2+x+4=90

The first integer plus the second integer(x+2) plus the third integer(x+4) equals 90. Now solve.

x+x+2+x+4=90

3x+6=90

    -6  -6

3x=84

/3   /3

x=28

So the first integer is 28, second is 30, third is 32.

Hope this helps!

Answer: You will walk 2.795 miles

Step-by-step explanation:

You can solve this using the Pythagorean theorem which is a^2 + b^2 = c^2

Plug in your numbers so you have 2.5^2 + 1.25^2 = c^2

Simplify that down to 6.25 + 1.5625 = c^2

Add   7.8125 = c^2

Find the square root of each of them.   2.795 = c

I don't know how you want me to round the answer so I just did it to the nearest thousandths.

The time it takes is 2 seconds

To find the time that the balloons collided at the highest point, we need to find the vertex of the resulting quadratic function.

First, we can set the two functions equal to each other, since they represent the height of the two balloons at any given time:

-7x^2 + 26x + 3 = -6x^2 + 23x + 5

Simplifying and rearranging terms, we get:

-x^2 + 3x + 2 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -1, b = 3, and c = 2.

Plugging in these values, we get:

x = (-3 ± sqrt(3^2 - 4(-1)(2))) / 2(-1)

x = (-3 ± sqrt(1)) / (-2)

Simplifying further, we get:

x = (-3 ± 1) / (-2)

So, x can be either 1 or 2. However, we're only interested in the positive value for x since time cannot be negative.

Therefore, the time that the balloons collided at the highest point is:

x = 2 second

So, the correct answer is: 2.0 seconds

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Answer:

52.40

Step-by-step explanation:

Given that,

Keith's bookshelf has 5 shelves.

He has 262 books.

To find the number of books he can put on each shelf.

 [tex]required \\ number = \frac{Total Books}{Total Shelves}\\\\= \frac{262}{5} = 52.40[/tex]

Hence 52.40 is the right answer.

Answer:

you in BBC FDA's in BBC FDA's in just had not had not had not had on under end

Step-by-step explanation:

no exception

The probability that Justen wins is 4/9.

The probability that Justen wins is determined by the likelihood that the highest number rolled on the two dice is a 1, 2, 3, or 4. To find this probability, we can first calculate the probability that the highest number rolled is a 5 or 6, which is what would cause Gaberil to win.

The probability of rolling a 5 or 6 on one die is 2/6, or 1/3. The probability of rolling a 5 or 6 on both dice is (1/3) * (1/3) = 1/9.

However, we also need to account for the possibility that one die rolls a 5 or 6 and the other does not.

This can happen in two ways: either the first die rolls a 5 or 6 and the second does not, or the first die does not roll a 5 or 6 and the second does.

The probability of each of these scenarios is (1/3) * (2/3) = 2/9.

So the total probability of Gaberil winning is 1/9 + 2/9 + 2/9 = 5/9.

Since there are only two possible outcomes (either Gaberil wins or Justen wins), the probability of Justen winning is 1 - the probability of Gaberil winning. So the probability of Justen winning is 1 - 5/9 = 4/9.

Therefore, the probability that Justen wins is 4/9.

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Answer:

No

Step-by-step explanation:

[tex]\frac{p}{13}[/tex] = 3 ( multiply both sides by 13 to clear the fraction )

p = 13 × 3 = 39

then p = 39 is the solution not p = - 39

[tex] \frac{p}{13} = 3[/tex]

[tex]p = 13 \times 3[/tex]

[tex] = 39[/tex]

[tex] \frac{p}{13} = 3[/tex]

[tex] \frac{p}{13} \times 3 = 3 \times 13[/tex]

[tex] \frac{p}{39} = 3[/tex]

[tex]p = 13 \times 3 \\ = 39[/tex]

[tex]\textbf{\textcolor{red}{Thank you!}}[/tex]

The intermediate step in the form (x+a)2 = b is (x - 8)^2 = 72

From the question, we have the following parameters that can be used in our computation:

x^2 = 16x + 8

Rewrite as

x^2 - 16x = 8

Take the coefficient of x

k = 16

Divide by 2

= 8

Square the quotient

= 64

So, we add 64 to both sides of the equation

So, we have

x^2 - 16x + 64 = 8 + 64

Express as squares and evaluate

(x - 8)^2 = 72

Hence, the intermediate step is (x - 8)^2 = 72

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The expected number of cars that are a color other than silver is 42 cars.

Option D is the correct answer.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

If 16% of the cars passing by are silver, then the percentage of cars that are not silver.

= 100% - 16%

= 84%.

If 50 cars are selected at random on one day, the expected number of cars that are a color other than silver is equal to the total number of cars (50) multiplied by the percentage of cars that are not silver (84%).

= 50 x 84%

= 50 x 0.84

= 42 cars

Therefore,

The expected number of cars that are a color other than silver is 42 cars.

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Answer:

The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.

Step-by-step explanation:

I hope this helped

Answer:2y32 is the answer u the graph line and some o f the sqaures to count it

Step-by-step explanation:

Answer: D.) 14

Step-by-step explanation:

First, you first calculate the square root of 64 , this gives you 8

Next, you calculate the square root of 36, which gives you 6

Then, since you are asked to add the two, you add 8 + 6 since this is the simplified version of the original equation.

8 + 6 = 14

Therefore, your answer is D.) 14

Answer:

$1770.87

Step-by-step explanation:

Formula;    Simple Interest(I) =  P × R × T/100

= $1770.87

The number of moles is given by the equation n = 0.611 moles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

PV = nRT   be equation (1)

Divide by RT on both sides of the equation , we get

n = PV / RT

Now , when temperature T = 299 K

The value of pressure P = 3 atm

The value of volume V = 5 Liters

The universal gas constant R = 0.0821

Substituting the values in the equation , we get

n = ( 3 x 5 ) / ( 0.0821 x 299 )

On simplifying the equation , we get

n = 15 / 24.5479

n = 0.611 moles

Therefore , the number of moles is 0.611 moles

Hence , the equation is n = 0.611 moles

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A unit of measurement equal to one thousand meters is called a kilometer.

A kilometre is a length measurement in the metric system that is equivalent to 1000 metres because the word "kilo" implies "one thousand". Longer distances, such those between cities or nations or the duration of a marathon, are frequently measured in kilometers. The lower length units of the metric system, such as meter's, centimeters, and millimeters, can be used to measure shorter distances.

A length measurement in the metric system that is 1,760 yards or 5,280 feet long. A metric capacity unit is one thousandth of a liter. a length expressed as a thousandth of a meter in meters. a common measure of time that is equal to 60 seconds and 1/60 of an hour.

Therefore, the kilometer is equal to one thousand meter's.

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The expressions are evaluated below

Expression 1: 4 < 7

Multiplying both sides by 3, 2, 4, and 9 respectively:

3 * 2 * 4 * 9 * (4 < 7)

864 < 1515

Expression 2: 11 > -2

Adding 3 to both sides, then adding 3, then adding (-4) respectively:

3 + 3 - 4 + (11 > -2)

13 > 0

Expression 3: -2 = -2

Subtracting 6 from both sides, then adding 8, then adding 2 respectively:

-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2

14 = 14

Expression 4: -4 < 8

Dividing both sides by -4, then by -2 respectively:

-4/(-4 * -2) < 8/(-4 * -2)

-1/2 < 1

The operations performed on the inequalities in each question did not affect the inequality sig.

The truth of the inequality was also not affected by the operations in all cases.

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The value of 30000 south korean currency is $25.50.

To convert 30000 South Korean Won to US Dollars, we can use the current exchange rate between the two currencies.

1. First, we need to find the current exchange rate between South Korean Won and US Dollars. As of September 9th, 2021, the exchange rate is 0.00085 USD per 1 South Korean Won.

2. Next, we can multiply the amount of South Korean Won we have by the exchange rate to find the equivalent amount in US Dollars.

30000 South Korean Won * 0.00085 USD/South Korean Won = 25.50 USD

3. Therefore, 30000 South Korean Won is equivalent to 25.50 US Dollars.

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Answer:

Step-by-step explanation:

A binomial distribution table is a table that lists the probabilities of obtaining a specific number of success outcomes in a fixed number of independent trials, given a constant probability of success in each trial. The binomial distribution is a discrete probability distribution that describes the number of success outcomes in a fixed number of independent trials with a binary outcome (success or failure).

The table lists the probabilities of obtaining k successes in n trials, where k is a non-negative integer and n is a positive integer. The probabilities are calculated using the binomial formula, which is given by:

P(k successes in n trials) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the number of ways to choose k success outcomes from n trials, p is the probability of success in each trial, and (1 - p) is the probability of failure in each trial.

Binomial distribution tables are useful for solving problems related to counting and probability, especially in situations where the number of trials is fixed and the probability of success is constant. They can also be used for hypothesis testing, calculating confidence intervals, and estimating population proportions in statistical applications.

Answer:The answer to your question “the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False” Is FALSE.

The second graph given in the figure attached below is a correct representation of the given points.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, few points on cartesian plane A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)

The xy pairs of a cartesian point are written in parenthesis as follows: (x, y).

To graph a point, first determine where it lies on the x-axis, then determine where it lies on the y-axis, and lastly plot the intersection of these two axes.

Due to its location at the intersection of the x- and y-axes, the origin of the graph, also known as the point (0, 0), is the center of the diagram.

For point A(-2, -3)

Find the negative 2 on the x-axis and the negative 3 on the y-axis, for instance, to draw the point (-2, -3).

The same will go for the remaining three points.

Therefore, The second graph given in the figure attached below is a correct representation of the given points.

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The graph representing the association will be a negative linear association. Then the correct option is C.

The form, direction, confidence, and outliers of an association (relationship) between two quantitative variables can be used to describe it. • A positive association exists when one variable increases as the other dependent variable.

There is no boundary and all the dots are widely dispersed if there is no association. Variational individuals who are part that the dots are close together but not in a straight line.

From the graph, the slope of the best line will be negative.

The graph representing the association will be a negative linear association. Then the correct option is C.

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Answer: A monomial representation is a way to express a polynomial as a product of powers of its variables, where each power is a non-negative integer. For example, the polynomial 2x^3 + 4x^2 - 6x + 8 can be represented as a monomial representation of (2x^3)(x^2)(-6x)(8).

Symmetric polynomials are polynomials that are invariant under permutation of their variables. A symmetric presentation is a way of expressing a symmetric polynomial as a sum of elementary symmetric polynomials, which are defined as the sum of all possible products of variables taken i at a time, where i ranges from 1 to the number of variables. For example, the symmetric polynomial x^3 + y^3 + z^3 can be expressed as a symmetric presentation of x + y + z.

Step-by-step explanation:

Since, 1 JPY = 0.0077 USD in Jan 27, 2023 08:45 UTC

Therefore, based on above information :

800 Japanese Yen 5.93 US Dollar.

The yen is the official currency of Japan. It is the third most traded currency on the foreign exchange market, after the US dollar (USD) and the euro. It is also widely used as the third key currency after the US dollar and the euro.

After World War II, the yen lost much of its pre-war value. To stabilize the Japanese economy, the yen exchange rate was fixed at 360 yen per US dollar under the Bretton Woods system. When this system was abolished in 1971, the yen was devalued and became liquid. After peaking at 271 yen per dollar in 1973, the yen appreciated to 271 yen per dollar due to the oil crisis in 1973, reaching 227 yen per dollar in 1980.

Another option is to do the calculations manually using simple mathematical formulas. However, for this you need to know the current exchange rate. As of this writing, one yen is worth $0.007.

Once you know this information, multiply the amount in JPY by the current exchange rate.

The resulting number shows how much you need to spend on your trip in US dollars.

Manual Currency Conversion Example

Suppose you have 100,000 yen and want to calculate how much money you will need to travel to the United States. Using the current exchange rate, the conversion formula would be

100,000 yen x 0.007 = $700

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The amount of white paint did she use to paint her bedroom walls is 6 21/40 or 6.525 pints.

To find the amount of white paint used, we first need to find the amount of blue paint used. Since 1/4 of the total amount of paint is blue, we can multiply the total amount of paint by its fraction, 1/4, to find the amount of blue paint:
Blue paint = 8.7 pints × 1/4 = 87/40 = 2.175 pints

Now, to find the amount of white paint used, we can subtract the amount of blue paint from the total amount of paint:
White paint = 8.7 pints - 2.175 pints = 261/40 = 6.525 pints

So, Araceli used 6.525 pints of white paint to paint her bedroom walls.

In fraction form, this can be written as 6525/1000 pints, or 6 21/40 pints.

In decimal form, it is simply 6.525 pints.

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The final payment and amount saved based on the given interest are respectively;

a)  $17697.5 and $1215.12

b) $12377.80 and $562.40

The equation for the interest  is mathematically expressed as:

I = balance*percentage/12

Therefore:

I = 17565.74 * 0.09/12

I = 131.7

The final payment is; F = I + B

F = 131.7 + 17,565.74

F = 17697.5

Amount saved

A.S = (19 * 995.40) - 17697.5

A.S = 1215.12

b) For the loan is paid off with payment 36 with a loan balance of $12,285. 66

I= balance*percentage/12

Therefore:

I = (12,285.66 * 0.09)/12I92.142

I = 92.142

Final payment

F = I + B

F = 92.142 + 12377.80

F = 12377.80

Amount saved

A.S = (13 * 995.40) - 12377.80

A.S = $562.40

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The complete question is;

Doreen Short was looking over the repayment schedule for a loan of $40,000. 00 at 9% for 4 years with a monthly payment of $995. 40.

Find the final payment and amount saved if :

A. ) The loan is paid off with payment 30 with a previous balance of $17,565. 74

B. ) The loan is paid off with payment 36 with a loan balance of $12,285. 66

Answer:

43%

Step-by-step explanation:

Something to do with msth not sure js smart wnough to guess it but trust me thats the answer

In the triangle that we have here cos 42 degrees is equal to sin 48

This was simply solved using the calculator

cos 42 = 0.7431

sin 42 = 0.6691

cos 48 = 0.6691

sin 48 = 0.7431

From the above we can see that the value of cos 42 and sin 48 returned the same digits at 0.7431

Hence the value of cos 42 is sin 48 degrees

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