Sidney made $35 less than four times Casey’s weekly salary. If x represents Casey’s weekly salary, write an expression for Sidney’s weekly salary.

The normal distribution has the following behavior:

First question

Answer:

20 miles/hour

Step-by-step explanation:

40 miles in 2 hours,

thus,

         40/2 miles  in 2/2 hours = 20 miles in 1 hour.

Therefore, Tim bikes 20 miles per hour.  

The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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Answer:

B 2/1

Step-by-step explanation:

2/2=1

3/3=1

4/4=1

and 2/1=2

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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The possible values of x, given the number of bets are $54,999, $14,999, and -$1.

The expected winnings would be -$0.97.

The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.

The possible values would therefore be:
$54,999, $14,999, and -$1.

These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.

The expected winnings would be:

= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )

= - $ 0.97

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The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).

In the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.

To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).

If we subtract each value in column 1 from the corresponding value in column 2, we find that:

11 - 1 = 10

22 - 2 = 20

33 - 3 = 30

44 - 4 = 40

By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

9514 1404 393

Answer:

  3

Step-by-step explanation:

The x-values in the table are evenly-spaced, so we can determine the degree of the function by looking at successive differences of the f(x) terms.

f(x): -23, -4, 3, 4, 5, 12, 31

first differences: 19, 7, 1, 1, 7, 19

second differences: -12, -6, 0, 6, 12

third differences: 6, 6, 6, 6

The third differences are constant, so the function values can be matched by a third degree polynomial.

_____

Additional comment

The first differences are found by subtracting the function value from the next one. Likewise, the second differences are found by subtracting each first-difference value from the next one. An so on for the third differences.

The level at which the differences are constant is the degree of the polynomial that will match the function values. (Compare this to what you know about an arithmetic sequence, where first differences are constant and the sequence is described by a linear (degree 1) equation.)

Answer:

Step-by-step explanation:

To solve the initial-value problem y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2, we first find the characteristic equation by assuming that y = e^(rt):

r^3 - 2r^2 + r = 0

r(r^2 - 2r + 1) = 0

r(r-1)^2 = 0

r = 0, 1, 1

Therefore, the general solution to the homogeneous equation y''' − 2y'' + y' = 0 is:

y_h = c1 + c2e^x + c3xe^x

To find the particular solution to the non-homogeneous equation y''' − 2y'' + y' = 2 − 24ex + 40e5x, we guess a particular solution of the form:

y_p = Ax^2e^5x + Be^x

y_p' = (2Ax + 5Ax^2)e^5x + Be^x

y_p'' = (10Ax^2 + 4Ax + 25Ax^2)e^5x + Be^x

y_p''' = (70Ax^2 + 60Ax + 10A + 25Ax^2)e^5x + Be^x

Substituting these expressions into the original equation, we get:

(70Ax^2 + 60Ax + 10A + 25Ax^2)e^5x + Be^x − 2[(10Ax^2 + 4Ax + 25Ax^2)e^5x + Be^x] + [(2Ax + 5Ax^2)e^5x + Be^x] = 2 − 24ex + 40e5x

Simplifying, we get:

(45Ax^2 + 2Ax − 2)e^5x + Be^x = 2 − 24ex + 40e5x

Equating the coefficients of the like terms on both sides, we get:

45A = 40

2A − 2 = 0

B = 2

Therefore, the particular solution is:

y_p = 8/9 x^2e^5x + 2e^x

The general solution to the non-homogeneous equation is therefore:

y = c1 + c2e^x + c3xe^x + 8/9 x^2e^5x + 2e^x

Using the initial conditions y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2, we get:

c1 + c2 + 2 = 1/2

c2 + 2c3 + 5/2 = 5/2

2c2 + 10/9 + 10 = -11/2

Solving this system of equations, we get:

c1 = 1/9

c2 = -25/18

c3 = 0

Therefore, the solution to the initial-value problem y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2 is:

y = 1/9 - 25/18e^x + 8/9

Answer:

slip/ do/ flapYvessshtvdBmto

Answer:

que sesupone que hay que hacer

The value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

The limit of a function is the limit of a function as x tends to a value.

From the given graph, you can see that the function g(x) goes large at the point where the arrows orange and purple point down from the x-coordinates -1 and 1.

Hence the value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

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Answer:

10%

Step-by-step explanation:

495-450=45

45x100/450=10

Answer:

Profit made by reselling = 495 - 450 = ₹45

So, percentage =

\( \frac{45}{450} \times 100 = 10\%\)

So, gain percentage is 10%

Answer:

3

Step-by-step explanation:

(six times a number) is (equal) to (the number increased by 15)

            6x                          =                            x + 15

6x = x + 15

Subtract x from both sides

5x = 15

Divide both sides by 5

x = 3

Answer: B   =\(x^{\frac{4}{5} }\)

Step-by-step explanation:

Rules needed:

When you have a root, you can write it in exponented form.  It becomes a fraction.

             EX.

                          \(\sqrt[5]{x} =x^{\frac{1}{5} }\)

When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents

            EX.

                       \(x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }\)

Your problem:

\(\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}\)              >convert to exponent form

=\(x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }\)                >add all exponents \((\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})\)

=\(x^{\frac{4}{5} }\)

B

Answer:

73.72 units²

Step-by-step explanation:

Area of the shaded region = Area if the rectangle - area of the semicircle

Area of the rectangle = length*width

Length = 10 units

Width = 8 units

Area of rectangle = 10*8 = 80 units²

Area of semicircle = ½(πr²)

radius (r) = 8/2 = 4 units

π = 3.14

Area of semicircle = ½(3.14*4) = 3.14*2 = 6.28 units²

Area of the shaded region = 80 - 6.28 = 73.72 units²

Answer: 54.88

Step-by-step explanation:​

The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 10. The width of the rectangle is the diameter of the circle, 8. First, find the area of the rectangle:

AAA=length×width=10⋅8=80

To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=4. Use the value of r to solve for the area:

AAA=πr2=3.14⋅(42)=50.24

Now we can subtract half the area of the circle from the area of the rectangle:

Area of rectangle−Area of half circle=Area shaded region

80−50.242

A=54.88

So the area of the shaded region is 54.88.

Answer:

224

Step-by-step explanation:

360.-136.

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Answer:

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

Step-by-step explanation:

What is probability?

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.

To find which 2 books describe a pair of dependent events:

A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.

Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.

Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.

Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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Answer:

85 cm

I have to use 20 characters to answer so extra space here :/

Answer:

5a - 8b

Step-by-step explanation:

Mr Davis buys 5 package of a glue stick

= 5a

Mr. Wilson buys 8 packages of b glue sticks

= 8b

Therefore the difference in the total is

5a-8b

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

What is additive inverse?

The Property of Additive Inverse states that the summation of a number and it's Additive inverse is zero.

The expressions are;

3 - 5 and 5 - 3

Now, The Property of Additive Inverse states that the summation of a number and it's Additive inverse = 0

And, An Additive inverse of a positive integer is a negative integer and vice versa.

For example: 7 - 7 = 0

Here, The additive inverse of 7 = -7

Since, For the question above, we are asked to use the additive inverses and their properties to find the equivalent expressions.

a) 3 - 5

Hence, Additive inverse = - 3 - (-5)

                                      = -3 + 5

                                      = 2

b) 5 - 3

Hence, Additive inverse = - 5 - (-3)

                                      = - 5 + 3

                                      = - 2

So, The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

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Answer:

3-5:

3+(-5)

-5+3

5-3:

-3+5

5+(-3)

Step-by-step explanation:

hope this helps ya (⁠☆⁠▽⁠☆⁠)

The volume of the rectangular prism is

Where:

L is its length

W is its width

H is its height

From the given figure

L = 15.2 cm

W = 8 cm

H = 5.8 cm

Substitute them in the rule above

Round it to the nearest tenth

Answer D

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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