5. James had 1 2/3 liters of soda left on Sunday. He drank 4/5 of one of the point
liters on Monday. How much soda does he have left? *
O 12/15
13/15
3/5
O 113/15

A linear transformation t defined by a square matrix a is an isomorphism if and only if a is nonsingular.

To prove this statement, we first recall that an isomorphism is a linear transformation that is both injective (one-to-one) and surjective (onto). If t is an isomorphism, then it is invertible, which means that there exists another linear transformation t^-1 such that t(t^-1(x)) = x and t^-1(t(x)) = x for all vectors x in the domain of t. In matrix notation, this means that aa^-1 = a^-1a = I, where I is the identity matrix.

Now suppose that a is nonsingular, which means that its determinant det(a) is nonzero. This implies that a^-1 exists and is also a square matrix. If we can show that t is injective and surjective, then we can conclude that t is an isomorphism. To prove injectivity, suppose that t(x) = t(y) for some vectors x and y. Then ax = ay, which implies that a(x - y) = 0. Since det(a) is nonzero, it follows that x - y = 0, which means that x = y. Thus, t is injective. To prove surjectivity, let z be an arbitrary vector in the range of t. Then there exists a vector y such that t(y) = z.

This implies that ay = z, which means that y = a^-1z. Thus, every vector in the range of t can be written as t(a^-1z), which shows that t is surjective. Therefore, we can conclude that t is an isomorphism if a is nonsingular. Conversely, if t is an isomorphism, then it must be invertible, which implies that a must be nonsingular, as we showed earlier. Thus, t is an isomorphism if and only if a is nonsingular.

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Answer:

divide -10 both sides.

Step-by-step explanation:

The negatives are counciled

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

8

Step-by-step explanation:

The product of \(x\) and \(y\) is constant, and this constant product is \((24)(6)=144\).

So, when \(x=18\), \(y=144/18=8\).

Answer: The cost of dress is $20 and belt is $3

Equation's created:

      1) 5d + 4b = 112

      2) 3d + 2b = 66

Here 'd' is dress and 'b' is belt

Make 'd' subject:

  In equation 1:

⇒  5d + 4b = 112

⇒  5d = 112 - 4b

⇒  d = (112 - 4b)/5

  In equation 2:

  ⇒ 3d + 2b = 66

  ⇒ 3d = 66 - 2b

  ⇒ d = (66 - 2b)/3

Solve them simultaneously:

 (66 - 2b)/3 = (112 - 4b)/5

 5(66 - 2b) = 3(112 - 4b)

  330 - 10b = 336 - 12b

   -10b + 12b = 336 - 330

          2b = 6

           b = 3

Now find the value of dress:

d = (66 - 2b)/3

  = (66 - 2(3))/3

  = 20

The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.

The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.

This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.

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There are 3 pairs of earrings that you bought in addition to the jeans. Forming an equation with the given values helps to find the required value.

It is given that,

A pair of jeans cost = $44

A pair of earrings cost = $12

you spent a total of $80 before taxes.

So, the equation for the given data is,

$80 = $44 + $12x

Where x is the number of pairs of earrings.

Simplifying the obtained equation:

$80 = $44 + $12x

⇒ 12x = 80 - 44

⇒ 12x = 36

⇒ x = 36/12

∴ x = 3

Thus, you can buy three pairs of earrings at the mall in addition to the jeans.

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Answer:

Decimal

Step-by-step explanation:

Im going to assume you double pasted, happens sometimes. so the answer would be decimal.

The base and exponent of −2^4 are

Base: -2

Exponent: 4

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

-2^4

In the expression -2^4, -2 is the base and 4 is the exponent.

The base is the number that is being multiplied by itself and the exponent is the number of times the base is being multiplied by itself.

In this case the base is -2 and the exponent is 4.

So the expression -2^4 means -2 multiplied by itself 4 times.

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Answer: yes correct . hernando 6 by 6

Step-by-step explanation:

Answer:

yes they are correct. Hernando divided 6 by 6

Step-by-step explanation:

Hernando ate 2/8 of a pizza for a dinner.

he gave his 6 friends the rest of the pizza, and told them to share equally.

Rest pizza portion=1-2/8

=6/8

6/8 pizza divided into 6 person

6/8÷6

1/8

So 1/8 portion get each person

So the option a is correct

yes they are correct. Hernando divided 6 by 6

Answer: (I hope this helps) The Answer is “No”

Step-by-step explanation:

Answer:

roughly 3%

Step-by-step explanation:

Answer:

about 34.9%

Step-by-step explanation:

I could be wrong on this, but by multiplying his profit per month by 12, and his electricity cost by 12, then you get his yearly profit and cost of electricity. Then, you divide the profit by electricity and wa la you get 34.9%.

PLZ mark me brainliest!!!! :)))))

Answer:

20,30,40,50,60

Step-by-step explanation:

The sequence is given by the relation as follows :

\(a_n=10n+10\)

First term, n = 1

\(a_1=10(1)+10=20\)

Second term, n = 2

\(a_2=10(2)+10=30\)

Third term, n =3

\(a_3=10(3)+10=40\)

Fourth term, n = 4

\(a_4=10(4)+10=50\)

Fifth term, n = 5

\(a_5=10(5)+10=60\)

So, the first five terms of the sequence are 20,30,40,50,60

The group who has the largest percentage of people who prefer to travel by automobile is given as follows:

Adult.

A bar graph, also known as a bar chart, is a type of graph used to represent and compare data. It consists of rectangular bars of equal width and varying heights, where the height of each bar represents the value of the data being graphed.

Automobiles are represented by the green bars, hence we must observe the input for which the green bar has the largest value, which is for adults, hence adults compose the largest percentage of people who prefer to travel by automobile.

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The reason for each step to justify it is:

Division Property of Equality: This step involves dividing both sides of the equation by 4 to isolate the variable term on one side of the equation.

The step involved here is: (w+25)/4

Multiplication Property of Equality: This step involves multiplying both sides of the equation by 4 to simplify the equation and cancel out the denominator.
The step involved here is: 4*(w+25)

Addition Property of Equality: This step involves subtracting 25 from both sides of the equation to isolate the variable term on one side of the equation.

The step involved here is: w+25

Simplifying: This step involves simplifying the expression by combining like terms and performing arithmetic operations to simplify the equation.

The step involved here is: w+25-25=12-25

Subtraction Property of Equality: This step involves subtracting 25 from both sides of the equation to isolate the variable term and solve for the variable.

The step involved here is: w=-13

What is meant by division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is represented by the symbol ÷ or / and is the inverse operation of multiplication. Division can be used to solve problems related to sharing, fractions, and ratios.

What is meant by multiplication?

Multiplication is a mathematical operation that involves adding a number to itself a certain number of times. It is represented by the symbol × or * and is the inverse operation of division. Multiplication can be used to solve problems related to scaling, area, volume, and rates.

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By using a trigonometric relation, we will see that the value of x is 60.57°

On the image, we can see a right triangle where x represents one of the angles.

We can see that the length of the two catheti are shown, such that the adjacent cathetus is 2.2, and the opposite cathetus is 3.9, then we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Then we can write:

tan(x) = 3.9/2.2

Using the inverse tangent function in both sides, we will get:

Atan( tan(x)) = Atan(3.9/2.2)

x = Atan(3.9/2.2) = 60.57°

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Answer: 6 feet and 10 inches

Step-by-step explanation:

Each foot has 12 inches in it

You can either divide 82 by 12 or

1 foot: 12 inches

2 foot: 24 inches

3 foot: 36 inches

4 foot: 48 inches

5 foot: 60 inches

6 foot: 72 inches

7 foot: 84 inches

Since 7 foot is too much you can now take 6 feet (72 inches) and subtract it from 82

82-72=10

10 meaning 10 inches

6 feet and 10 inches

You may also divide but you will get a decimal like this:

6.83333333

Unit conversion is a way of converting some common units into another without changing their real value. The length of the table cloth is 6 ft 10 inches.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

In terms of measurement, one foot is 12 inches.

1 ft = 12 inches

Given that the table cloth is 82 inches long. Therefore, the length in feet and inches are,

Length = 82 inches

            = 82 / 12 foot

            = 6 10/12 foot

            = 6 ft 10 inches

Hence, the length of the table cloth is 6 ft 10 inches.

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Answer:

A) 12/8, 15/10, and 9/6

or 3/2, 3/2, and 3/2

B) PQR = PQ'R' or PQR is congruent with PQ'R'

C) You can tell the corresponding angles of PQR and PQ'R' are congruent because they have the same angle degree and have a proportionate ratio.

Step-by-step explanation:

A) PQ' = 12 and PQ = 8, Q'R" = 15 and QR = 10, PR' = 9 and PR = 6

GCF (12, 8) = 4, GCF (15, 10) = 5, GCF (9, 6) = 3

Answer:

  35

Step-by-step explanation:

The law of sines tells us ...

  sin(C)/c = sin(A)/a

  a·sin(3A) = c·sin(A)

Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...

  sin(A)(4cos(A)^2 -1) = (c/a)sin(A)

  4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9

  cos(A)^2 = 25/36

  cos(A) = 5/6

__

Now, the angle B will be the difference between 180° and the sum of the other two angles:

  B = 180° -A -3A = 180° -4A

Using appropriate trig identities, we can write ...

  sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)

  = 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)

  = 4sin(A)cos(A)(2cos(A)^2 -1)

Filling in our value for cos(A), this becomes ...

  sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)

__

The law of sines tells us ...

  b/sin(B) = a/sin(A)

  b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35

The length of side b is 35 units.

The two such x-values are 2 and 8.

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I can help you with that problem i just did that on my own.

The open sentence involving the absolute value for the problem is |x - 105| ≤ 10.

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

Mary's bowling score was within 10 pins of her average score of 105.

Let x represents the bowling score

So, the absolute difference can be represented as

|x - 105|

This value is within 10 pins of the average score of 105.

So, we have

|x - 105| ≤ 10.

Hence, the open sentence is |x - 105| ≤ 10.

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Answer:

Volume of prism = 3,240 cm³

Step-by-step explanation:

GIven.

Hexagonal prism.

Side of base(b) = 12cm

Height of prism = 9cm

Height of base (h)= 10cm

Find:

The volume of the prism.

Computation:

Area of base of hexagonal prism = n/2[bh]

Area of base of hexagonal prism = 6/2[(12)(10)]

Area of base of hexagonal prism = 360 cm²

The volume of prism = Area of base of hexagonal prism × Height of prism

The volume of prism = 360 × 9

Volume of prism = 3,240 cm³

Answer:

second one

Step-by-step explanation:

The probability of selecting 2 males or 2 females seperately out of the group is 1/7.

The probability of selection is calculated by the formula -

Probability = number of events/total number of samples

Number of events is the number of chosen individuals and total number of samples is the total number of people

Total number of people = 8 + 6

Total number of people = 14

Probability of 2 females = 2/14

Dividing the reaction by 2

Probability of 2 females = 1/7

Probability of 2 males will be the same a probability of females, considering the probability is asked from total number of individuals.

Hence, the probability is 1/7.

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Answer:

3/2

Step-by-step explanation:

Since the lines goes through the point (0,0)

We have a point (2,3)

The slope is y/x = 3/2

\(\textsf {Simplifying the exponents :}\)

\(\mathsf {\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}}\)

\(\mathsf {\frac{1}{5x^{(2+6)}y^{(10+3)}}}\)

\(\mathsf {\frac{1}{5x^{8}y^{13}}}\)

Answer:

pog

Step-by-step explanation:

Poggers

The value of x for the given quadratic expression is x = 5 ± √11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 3(x-5)²=33. The value of x will be calculated as,

3(x-5)²=33

(x - 5 )² = 11

(x - 5 )  = ±√11

x = 5 ± √11

Therefore, the value of x for the given quadratic expression is x = 5 ± √11.

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The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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