What is the 27th term in the arithmetic sequence 43,38,33,28,23,

a27 =


(a) 87

(b) -87

(c) -78​

0700 military time is 7:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.

The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0700 military time is equivalent to 7:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.

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Answer:

I think the 3rd one

Step-by-step explanation:

Hope its right

(a) On the basis of eigenvectors for T, it is diagonalizable.

(b) C is diagonalizable.

To determine whether the given linear operator/matrix is diagonalizable, we need to check if it has a complete set of linearly independent eigenvectors. Let's analyze both parts of the question:

(a) T: R³ → R³ with T(1, 1, 1) = (2, 2, 2), T(0, 1, 1) = (0, -3, -3), and T(1, 2, 3) = (-1, -2, -3).

To check if T is diagonalizable, we need to find the eigenvalues and eigenvectors.

First, let's find the eigenvalues:

We solve the equation T(v) = λv, where v is a vector and λ is a scalar.

From the given information:

T(1, 1, 1) = (2, 2, 2) --> T - 2I = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

T(0, 1, 1) = (0, -3, -3) --> T - λI = [[-λ, 0, 0], [0, -λ, 0], [0, 0, -λ]]

T(1, 2, 3) = (-1, -2, -3) --> T - λI = [[-1-λ, 0, 0], [0, -2-λ, 0], [0, 0, -3-λ]]

To find the eigenvalues, we need to solve the equation det(T - λI) = 0:

det([[-λ, 0, 0], [0, -λ, 0], [0, 0, -λ]]) = (-λ)(-λ)(-λ) = -λ³

Setting -λ³ = 0 gives λ = 0 as a possible eigenvalue.

To find the eigenvectors, we solve the equation (T - λI)v = 0 for each eigenvalue:

For λ = 0, we have (T - 0I)v = 0:

[[-2, 0, 0], [0, -2, 0], [0, 0, -2]]v = 0

Row reducing the augmented matrix [[-2, 0, 0, 0], [0, -2, 0, 0], [0, 0, -2, 0]], we get:

[1, 0, 0, 0]

[0, 1, 0, 0]

[0, 0, 1, 0]

This shows that the null space of (T - 0I) is spanned by the vectors [1, 0, 0], [0, 1, 0], and [0, 0, 1]. These vectors form a basis for R³.

Since we have a basis of eigenvectors for T, it is diagonalizable.

(b) C = [[-2², 3], [1, -2]]

To check if C is diagonalizable, we need to find the eigenvalues and eigenvectors.

The eigenvalues of C are the solutions to the equation det(C - λI) = 0:

det([[-2² - λ, 3], [1, -2 - λ]]) = (-2² - λ)(-2 - λ) - 3 = λ² + 4λ + 1

Therefore, C is diagonalizable.

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Answer:

56.25 laps

Step-by-step explanation:

5/4 = 1.25  

y = 1.25 x

number of laps = 1.25 (minutes)

y = 1.25 (45)

y = 56.25

Answer:

$5 per hour

Step-by-step explanation:

60/12= 5

If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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An equivalent expression by combining like terms, we need to group the terms with the same variable exponent, add or subtract them as appropriate, and simplify the resulting expression

Combining like terms refers to the process of adding or subtracting variables with the same exponent and any constants present. The method of combining like terms is similar to how you add or subtract similar items. The key is to simplify the expression by making it as short as possible. Here is an example to demonstrate how to write an equivalent expression by combining like terms:

W 10 w - 4

To combine like terms, we first group all the like terms together, that is, the terms with the same variable exponent. Here, we can see that both terms have the variable w, so we can add them together.

However, the first term has a coefficient of 10, which means it has ten times the value of the second term. Therefore, we can rewrite the expression as follows:

W(10w - 4)

We have now combined like terms, but we can further simplify this expression. The term inside the parenthesis can be simplified by factoring out the common factor 2 from the two terms. This results in:

W(2 * 5w - 2)W(2(5w - 1))

The expression is now in its simplest form, and we have written an equivalent expression by combining like terms.

To summarize, to write an equivalent expression by combining like terms, we need to group the terms with the same variable exponent, add or subtract them as appropriate, and simplify the resulting expression as much as possible by factoring out common factors.

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Options :

A.) On average, the height of a child is 80% of the age of the child.

B.) The least-squares regression line of height versus age will have a slope of 0.8.

C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

D.) The least-squares regression line will correctly predict height based on age 80% of the time.

E.) The least-squares regression line will correctly predict height based on age 64% of the time.

Answer:

C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

Step-by-step explanation: from the scenario stated above, The correlation Coefficient R = 0.8, which shows the strength of relationship between age and height of children. From the value of correlation Coefficient Given, we can obtain the Coefficient of determination (R²) which gives the percentage of Variation which can be explained by the regression model.

Hence the Coefficient of determination (R²) = 0.8² = 0.64. Hence, the proportion of variation in height of children which can he due to age is 0.64 while 0.36 can be based on other factors.

Based on the line created from the data to the height of a child based on age the correct statement is given by: Option C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

For that, we can use the coefficient of determination.

The coefficient of determination is square of correlation coefficient and thus, ranges from 0 to 1.

The coefficient of determination tells for unit variation in one variable will lead to how much variation in other variable and vice versa.

Let we take:

X = age of children of the sample considered

Y = height of children of the sample considered

Then, as it is given that:

\(r(X, Y) = 0.8\)

Thus, the coefficient of determination is: \(r^2 = 0.8^2 = 0.64\)

Thus, we get that 0.64 of the variation in the height is explained by the age of the children.

Thus, the true statement is:

Option C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

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Answer:

If this is true or false, I think true. Hope I helped! If not, please make sure to correct me.

Step-by-step explanation:

Answer:

answer choice C.

Step-by-step explanation:

complementary angles are 2 angles that add up to 90 degrees

90=58+x

90-58=x

x=32

Answer:

Step-by-step explanation:

x          -  age of a son three years ago

3x        -  age of a father three years ago

x + 3      -  age of the son now

3x + 3       -  age of the father now

x + 3 + 5       -  age of the son in five years time

3x + 3 + 5       -  age of the father in five years time

in five years time, the father will be twice as old as his son, so:

3x + 3 + 5 = 2(x + 3 + 5)

3x + 8 = 2x + 16

3x - 2x = 16 - 8

  x = 8

x + 3 + 4       -  age of the son in four years time

8 + 3 + 4 = 15

3x + 3 + 4       -  age of the father in four years time

3×8 + 3 + 4 = 31    

the sum of their ages in four years time:

15 + 31 = 46

Answer:

b

Step-by-step explanation:

Answer:

8 feet

12 inches equals 1 foot, so 8 inches is a lot smaller than 8 feet.

Answer:

8 feet is equal to 96 inches.

Step-by-step explanation:

There are 12 inches in one foot

An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216

Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.

Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.

a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.

b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.

c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.

d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.

Expression = 1 × 2²⁴ = 16,777,216

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Answer:

this is easy get a protractor

Step-by-step explanation:

The solution is: The General Solution of the expression is: Cos x = 2/3

Here, we have,

Explanation:

Given expression:

3sinx = 2tanx​

Find:

Simplify expression......

Computation:

By taking given trigonometric equation

⇒ 3sinx = 2tanx​

Using substitution method...

⇒ sinx = [2/3]tax

⇒ sinx / tanx = 2/3

⇒ sinx / [sinx / cosx] = 2/3

⇒ [sinx × cosx] / sinx = 2/3

⇒ cosx = 2/3

Simplify expression

Cos x = 2/3

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complete question:

Determine the general solution of 3sin x=2tan x​

Answer:

h = 3V/πr^2

Step-by-step explanation:

\(IF ;\\V = \frac{1}{3} \pi r^2 h\\Make ; h , subject-of-the-formula\\3V = \pi r^2 h\\Divide-both-sides-of-the-equation -by \pi r^2\\\frac{3V}{ \pi r^2} = \frac{ \pi r^2 h}{ \pi r^2 } \\\frac{3V}{ \pi r^2} = h\)

Answer:

Step-by-step explanation:

the answer is

If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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The maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

Function is an operation that takes one or more inputs and produces an output, or a set of outputs, depending on the type of function. Functions are commonly used in mathematics and computer science, and are essential for solving a wide range of problems.

We are given a function f(x, y, z) = xyz and the constraint x2 + 2y2 + 3z2 = 96. To find the maximum and minimum values of f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Let λ be the Lagrange multiplier. Then, the Lagrange function is given by:

L(x, y, z, λ) = xyz + λ (x2 + 2y2 + 3z2 - 96)

We will now calculate the partial derivatives of L with respect to x, y, z and λ.

∂L/∂x = yz + 2xλ = 0
∂L/∂y = xz + 4yλ = 0
∂L/∂z = xy + 6zλ = 0
∂L/∂λ = x2 + 2y2 + 3z2 - 96 = 0

Solving the above equations, we get:
2xλ = -yz
4yλ = -xz
6zλ = -xy
x2 + 2y2 + 3z2 = 96

Substituting the values of λ in the first three equations, we get:
2x(-xz/4y) = -yz
2x2z/4y = -yz
x2z/2y = -yz

From the fourth equation, we get:
x2 + 2y2 + 3z2 = 96

Substituting the values of x2, y2 and z2 from the above equation in the fifth equation, we get:
(96 - 2y2 - 3z2)z/2y = -yz
96z/2y - yz - 3z3/2y = 0

Solving for z, we get:
z = (96/4y) ± √(962/16y2 - 3y2)

Substituting the values of z from the above equation in the fourth equation, we get:
x2 + 2y2 + 3 (96/4y)2 ± √(962/16y2 - 3y2)2 = 96

Solving for y, we get:
y = ±√(96/14 - 3z2/2)

Substituting the values of y from the above equation in the third equation, we get:
x = ± 2z √(14z2/96 - 1/3)

Hence, the maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

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Where is the graph I need to see the graph for the answer

Answer:

"23,520"

Step-by-step explanation:

one trip: 14 passengers

one day: 3 trips

passengers: 80

80x14= 1,120

1,120x3= 3,360

3,360x7= 23,520

An aggregation of parts is also called a A. Subsystem.

In computing, a subsystem is an aggregation or a compilation of parts that then form a system that is able to carry out certain types of purposes.

For instance, a central processing unit on a computer is a subsystem that has things such as the processor and the ram.

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To calculate depletion expense, you need to determine the depletion per unit. The depletion per unit can be calculated by taking (cost of the resource) / total units of capacity.

Depletion is an accounting method used to allocate the cost of natural resources over their useful life. It is commonly used in industries such as mining, oil and gas extraction, and timber harvesting, where companies extract and deplete natural resources as part of their operations.

The first step in calculating depletion expense is to determine the cost of the resource. This includes all costs incurred to acquire and develop the resource, such as exploration costs, development costs, and acquisition costs. These costs are typically capitalized and then allocated over the estimated recoverable units of the resource.

Once you have determined the cost of the resource, you need to calculate the total units of capacity. This refers to the estimated amount of resource that can be extracted or harvested from the reserve. For example, in mining, it could be measured in tons of ore, while in oil and gas extraction, it could be measured in barrels or cubic feet.

To calculate the depletion per unit, divide the cost of the resource by the total units of capacity. This will give you the amount of depletion expense that should be recognized for each unit extracted or harvested.

It's important to note that there are different methods for calculating depletion expense, such as units-of-production method and percentage depletion method. The units-of-production method calculates depletion based on actual production or extraction during a given period. On the other hand, the percentage depletion method allows for a fixed percentage deduction from gross income based on statutory rates.

In conclusion, to calculate depletion expense, you need to determine the depletion per unit by dividing the cost of the resource by the total units of capacity. This allows for an appropriate allocation of costs over the useful life of natural resources.

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Answer:

that means it would get bigger

Step-by-step explanation:

Answer:

\(\frac{30x+30}{x+7}\) is the simplified radical expression.

Step-by-step explanation:

For this one, we have fractions in the bottom of a fraction (denominator).

So, we would multiply by \(\frac{1}{x+1}\).

\(\frac{5x+5}{\frac{1}{6}x+\frac{7}{6} }\)

Then Multiply by 6.

\(\frac{30x+30}{x+7}\) is the simplified radical expression.

Answer: There would be 20 boys!

Step-by-step explanation:

You can just scale up the ratio until it makes 28!

2 girls: 5 boys

4:10

6:15

8:20

Answer:

?

Step-by-step explanation:

Given that Dimitri's car has a fuel efficiency of 21 miles per gallon, and his tank is full with 12 gallons of gas. We need to determine if he has enough gas to drive from Cincinnati to Toledo, a distance of 202.4 miles.

We can use the formula of fuel efficiency to calculate the number of gallons of gas Dimitri will use.

Distance traveled = Fuel Efficiency x Number of gallons of gas used.

Dimitri has 12 gallons of gas.

To start with, let's first identify the conversion factors that we require in this problem:

The car has fuel efficiency of 21 miles per gallon (mpg) 202.4 miles is the distance from Cincinnati to Toledo.

Using the given conversion factors above, we can carry out the following dimensional analysis:

\(12 \ \text{gal} \times \dfrac{21 \ \text{miles}}{1 \ \text{gal}} = 252 \ \text{miles}\)

Therefore, the number of miles Dimitri's car can cover with 12 gallons of gas is 252 miles. Since the distance from Cincinnati to Toledo, a distance of 202.4 miles is less than the 252 miles

Dimitri can travel on a full tank, he has enough gas to drive from Cincinnati to Toledo.

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