Which can be represented by the expression 5+3(x-6)
O6 less than 3 times the sum of a number and 5
O the sum of 5 and 3 times the difference of a numbe
Othe cube of the sum of a number and 3 less than 5
the difference between 5 and the cube of the difference of a number and 6

Step-by-step explanation:

x⁴(4x+1)

4x⁵+x⁴

degree is 5

We have the function:

()=−2(−3)^4+1

We need to go from this equation to the parent function x^4. To do that, we first do a vertical translation of 1 unit below. That is:

Vertical translation: f(x) - 1

= −2(−3)^4

Now, we make a horizontal shift of 3 units to the left, replacing x by x + 3:

f(x + 3) + 1 = −2()^4

Horizontal shift: f(x + 3) - 1

= −2x^4

We can make a horizontal expansion if we multiply this function by 1/2:

Horizontal expansion: ( f(x + 3) - 1 ) / 2

= -x^4

Finally, we make a reflection around the x-axis by multiplying this result by -1:

x-axis reflection: -( f(x + 3) - 1 ) / 2

= x^4

Answer:

5:20 to 9:20

Step-by-step explanation:

Velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

According to the quantity equation (MV = PQ), changes in the money supply (M) will lead directly to changes in the price level (P) if velocity (V) and real GDP (Q) remain constant. However, velocity is not necessarily constant over time and can be influenced by various factors.

Velocity represents the rate at which money circulates in the economy, indicating how quickly money is used to facilitate transactions. It is influenced by factors such as changes in consumer and business behavior, technological advancements, financial innovation, and shifts in confidence and trust in the economy.

Changes in velocity can occur due to several reasons. For example:

Changes in Transaction Patterns: Shifts in consumer preferences or business practices can alter the frequency and speed of transactions, affecting how money circulates and influencing velocity.

Financial Innovation: Advancements in payment systems, such as the rise of electronic transactions, online banking, or mobile payments, can potentially impact the velocity of money by facilitating faster and more efficient transactions.

Confidence and Economic Stability: Changes in economic conditions, inflation expectations, or financial stability can influence people's willingness to hold money, affecting velocity.

Monetary and Fiscal Policies: Changes in monetary policy, such as interest rate adjustments or changes in the money supply, can indirectly affect velocity by influencing borrowing and spending behavior.

While changes in velocity can occur independently of changes in the money supply, they can also be related. For instance, if the money supply increases without a corresponding increase in the demand for money (velocity decreases), it can put upward pressure on prices. On the other hand, if velocity increases due to changes in transaction patterns or increased economic activity, it can offset the impact of changes in the money supply on prices.

Overall, velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

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Answer:

y= 3x + 5

Step-by-step explanation:

y

the intecept cross x=3 and y=5

Answer:

ok what is it

Step-by-step explanation:

Answer:

To calculate the average annual percentage gain, we need to use the formula:

Average annual percentage gain = ((Ending value / Beginning value)^(1/n) - 1) x 100%

where:

- Ending value = the value of the investment at the end of the period

- Beginning value = the value of the investment at the beginning of the period

- n = the number of years

In this case, the beginning value of the stocks is not given, so we cannot calculate the exact average annual percentage gain. We only know the profit and the ending value. However, we can make an estimate assuming that the profit is equal to the gain, i.e., there were no transaction costs or other fees.

If the profit was $3,250 and the ending value was $10,500, then the beginning value was:

Beginning value = Ending value - Profit

Beginning value = $10,500 - $3,250

Beginning value = $7,250

The number of years is given as 4.

Using the formula above, we can estimate the average annual percentage gain as:

((10,500 / 7,250)^(1/4) - 1) x 100%

= (1.1267^(0.25) - 1) x 100%

= (1.0266 - 1) x 100%

= 0.0266 x 100%

= 2.66%

Therefore, the estimated average annual percentage gain is 2.66%.

Step-by-step explanation:

The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

The missing side length is 5 cm

Step-by-step explanation:

We see that 4cm is on the top and 9 cm is on the bottom.

All we need to do is subtract 4 from 9

9-4=5

The missing side length is 5 cm

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The correct equation is:  5/6 - 1/6 = 4/6

A number line is a visual representation of numbers, ordered from left to right, where each point on the line corresponds to a number. The number line can be used to represent a wide range of numbers, including integers, fractions, decimals, and even negative numbers.

On a basic number line, 0 is located in the center, with positive numbers to the right and negative numbers to the left. The numbers are usually evenly spaced, with tick marks or dots indicating each value. The distance between any two points on the number line represents the difference between the corresponding numbers.

According to question Option D is correct

This is because starting at 5/6 and ending at 1/6 involves moving in the negative direction on the number line. To find the distance between these two points, we need to subtract the smaller number (1/6) from the larger number (5/6).

So, 5/6 - 1/6 = 4/6, which simplifies to 2/3. This means that the distance between 5/6 and 1/6 on the number line is 2/3.

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Answer:

2

Step-by-step explanation:

2x+2=6 (as given in other figure)

2x= 6-2

x= 4/2 = 2

To check

PERIMETER OF RECTANGLE

2(l+b)

2(6+2)

2×8

16 of both the figures

Answer:

f(3) =-1

Step-by-step explanation:

f(x) = x^2 - 5x + 5

Let x=3

f(3) = 3^2 -5(3) +5

      = 9 -15+5

      = -6+5

      =-1

Answer:

7/5 is greater than 4/5

Answer:

\(\frac{4}{5}\)  <  \(\frac{7}{5}\)

Answer:

75

Step-by-step explanation:

100% - 12% = 88% (% of good thermometers)

88% = 66

100% = 75 (total)

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

the work required is 4.98 J

Step-by-step explanation:

Given;

Energy applied to the spring, E = 3 J

initial length of the spring, x₀ = 32 cm

final length of the spring, x₁ = 43 cm

Extension of the spring, Δx = x₁ - x₀ = 43 cm - 32 cm = 11 cm = 0.11 m

The spring constant is calculated as follows;

E = ¹/₂Δx²

k=2E/(xΔ)^2= 2*3/(0.11)^2=495.87 N/m^2

The extension of the spring when it is stretched from 37 cm + 39 cm:

Δx =  39 cm - 37 cm = 2 cm = 0.02 m

The work required:

W = ¹/₂kΔx²

W = ¹/₂ x (495.87) x (0.02)²

W = 4.98 J

Therefore, the work required is 4.98 J.

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The correct answer is C) Consumers differ in their preference for Android phones and iPhones.

The p-value is a measure of the strength of evidence against the null hypothesis. It is calculated based on the observed data and the alternative hypothesis. The alternative hypothesis is the statement that we are trying to test against the null hypothesis.

In general, the calculation of the p-value does not depend on whether the alternative hypothesis violates the assumption of equal or expected values. However, the choice of the appropriate statistical test and its assumptions may depend on the alternative hypothesis.

In this regard, the p-value can be calculated without bothering about the expectation violation while testing the alternative hypothesis of "consumers differ in their preference for Android phones and iPhones." This hypothesis does not make any assumption about the expected preference of consumers for Android or iPhone, so the calculation of the p-value is not affected by any expectation violation.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

By the remainder theorem, dividing \(f(x)\) by \(x-2\) leaves a remainder of \(f(2)\), which is

\(f(2)=2(2)^4+(2)^3-8(2)-1=\boxed{23}\)

which makes B the correct answer.

The remainder when f(x) = 2x^4 + x^3- 8x - 1 is divided by x - 2 is 23

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.

Polynomial based on degree is linear, quadratic, cubic.

The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial x - a, the remainder of is to f(a)

Given that f(x) = 2x⁴ + x³ - 8x - 1 is divided by x - 2

x - 2 = 0

x = 2

f(2) = 2(2)⁴ + (2)³ - 8(2) - 1 = 23

Hence The remainder when f(x) = 2x^4 + x^3- 8x - 1 is divided by x - 2 is 23

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Answer:

60

Step-by-step explanation:

Notice since you want to find a number, and the 95% of that number is 57:

\((0.95) x = 57\)

Solving for X

\(x=\frac{57}{0.95} =60\)

Answer:

Answer: 60

Step-by-step explanation:

STEP 1 57 = 95% × Y

STEP 2 57 = 95/100 × Y

STEP 3 Y = 57 × 100/95

STEP 4 Y = 57 × 100 ÷ 95

STEP 5 Y = 60

You can easily calculate 57 is 95 percent of what number by using any regular calculator, simply enter 57 × 100 ÷ 95 and you will get your answer which is 60

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Answer:

  1. 14.9 cm

  2. 16.9 cm

  4. 18.7 in

  6. 50 m

Step-by-step explanation:

The Pythagorean theorem relates the legs (a, b) and the hypotenuse (c) of a right triangle:

  c² = a² +b²

If you want to know the hypotenuse, take the square root:

  c = √(a² +b²)

__

In the given rectangular prism, length AC is the hypotenuse of right triangle ABC, which has legs AB=14 and BC=5 in units of centimeters. Then ...

  AC = √(14² +5²) = √(196 +25) = √221 ≈ 14.9 . . . cm

__

Length AD is the hypotenuse of the right triangle with legs AC=√221 and CD=8 in units of cm. Then ...

  AD = √((√221)² +8²) = √(221 +64) = √285 ≈ 16.9 . . . cm

__

The slant height (s) of the cone is the hypotenuse of the right triangle with legs r=5 and h=18 in units of inches. Then ...

  s = √(5² +18²) = √(25 +324) = √349 ≈ 18.7 . . . inches

__

The slant height of the pyramid is the altitude of any of the triangular faces. As such, it is the hypotenuse of the right triangle whose legs are half the base dimension, 40 m, and the given height, 30 m. We recognize these numbers as multiples of the sides of a {3, 4, 5} triangle, so we know immediately the slant height is 50 meters.

  s = √(40² +30²) = √2500 = 50 . . . meters

Answer:

False

Step-by-step explanation:

(3)(5)>15

15>15

False

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Answer:

A= ₱1000 + t( ₱250) ------where t is the time in months

Step-by-step explanation:

The principal amount ,P, is given as : ₱1000----- P=₱1000 ------equation (i)

Additional amounts to be added by grandmother = ₱200 monthly

Amount expected to add monthly =  ₱50

Additional amounts in total added monthly = ₱200 + ₱50=₱250

Monthly amounts ,A, in the fund after the first month, t =1 month will be:

A=P + ₱250= ₱1000 + 1( ₱250) ------where t= 1, amount at end of month 1

A=P +₱250= ₱1000 + 2( ₱250)--------where t=2,  amount at end of month 2

A=P +₱250= ₱1000 + 3( ₱250)---------where t=3, amount at end of month 3

A=P +₱250= ₱1000 + 4( ₱250)--------where t=4, amount at end of month 4

From the breakdown above of 4 months, the general equation of monthly amounts will be;

A= ₱1000 + t( ₱250) ------where t is the time in months

A sequence of the monthly amounts in your college book fund is given by the equation (A = 1000 + 250t) and this can be determined by forming the linear equation with the help of the given data.

Given :

The following steps can be used to determine a sequence of the monthly amounts in your college book fund:

Step 1 - Given that the principal amount is ₱1000 which is given by the grandmother.

Step 2 - Additional amount is given by grandmother is ₱200 and each month ₱50 is added. So, the total additional amount each month is:

= 200 + 50

= ₱250

Step 3 - Let 't' be the number of months. So, the linear equation becomes:

A = 1000 + 250(t)

where A is the total amount and t is the time in months.

A sequence of the monthly amounts in your college book fund is given by the equation (A = 1000 + 250t)

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Answer: Number 1 answer: I agree with Andre. Number 2 answer: The diagram could represent 14.

Step-by-step explanation:

1. I agree with Andre because the squares are all tenths. so the first rectangle has 10 tenths which is 100. The four small squares equal 40 since 4 tenths is 40. If you add them both you get 140.

2. The diagram could represent 14 because you can think of the squares as ones. so ten ones is 10, and four ones is 4. So 10 plus 4 is 14.

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Suppose, Melissa makes deposits for 10 years, the total amount of deposited money in 10 years will be $61,070.14 by using geometric series.

A savings account is a type of bank account that is designed to help people save money. When you deposit money into a savings account, the bank pays you interest on your balance, which means that your money can grow over time.

To find the sum Sn of a geometric series of n terms, we can use the formula:

Sn = a(1 - \(r^{n}\)) / (1 - r)

where a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $1,000, and the common ratio is 1.02 (since each subsequent deposit is 2 percent greater than the previous deposit). So we can use: a = 1000 and r = 1.02

To find the number of terms, we need to know how many years Melissa plans to make deposits. Let's say she plans to make deposits for 10 years. Then we have: n = 10

Now we can use the formula to find the sum Sn:

Sn = 1000(1 - \(1.02^{10}\)) / (1 - 1.02)

Sn = 1000(1 - 1.221402758) / (-0.02)

Sn = 61070.138

Therefore, if Melissa makes deposits for 10 years as supposed, the total amount of deposited money will be $61,070.14.

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