a telephone pole support cable attaches to the pole 100 feet high. if the cable is 260 feet long, how far from the bottom of the pole does the cable attach to the ground?

When the problem says "a number", it refers to a variable which we are going to call n.

So, the expression would be

Now, we reduce all like terms

Then, we divide the equation by 8

Answer:

Step-by-step explanation:

\(p(\frac{(1+i)^n-1}{i})\\i=.07/12=.0058333\\\\n=27*12\\96(\frac{(1+.0058333)^{12*27}-1}{.0058333})= 91882.2085266=91882.21\)

Answer:

x = 21

Step-by-step explanation:

As stated in the hint: When angles form a linear pair, their sum is 180° in other words, these are supplementary angles:

3x + 18 + 4x + 15 = 180 add like terms

7x + 33 = 180 subtract 33 from both sides

7x = 147 divide both sides by 7

x = 21

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

Learn more about probability here:

https://brainly.com/question/23417919

#SPJ8

Answer:

Option 1, 3 and 5 are correct

Step-by-step explanation:

Given

Eggplants = $1.79 each

Apples = $0.59 each,

Bags of spinach = $2.55 each

Cartons of orange juice = $3.89 each

Required

Select three true statements

To do this, we'll check the options one after the other

1. 4 eggplants cost about $0.50 less than 3 bags  of spinach

First, we need to calculate the cost of 4 eggplants

4 Eggplants = 4 * 1 Eggplants

4 Eggplants = 4 * $1.79

4 Eggplants = $7.16

Next, we calculate the cost of 3 bags of Spinach

3 bags of Spinach = 3 * 1 bag of Spinach

3 bags of Spinach = 3 * $2.55

3 bags of Spinach = $7.65

Determine the difference

Difference = |Eggplants - Bags of Spinach|

Difference = |$7.16 - $7.65|

Difference = |-$0.49|

Difference = $0.49

This statement is true because $0.49 approximates to $0.50

2. Total cost of 4 apples and 2 eggplants $0.50 is more than $6.00

First, we need to calculate the cost of 4 apples

4 Apples = 4 * 1 Apples

4 Apples = 4 * $0.59

4 Apples = $2.36

Next, we calculate the cost of 2 Eggplants

2 Eggplants = 2 * 1 Eggplant

2 Eggplants = 2 * $1.79

2 Eggplants = $3.58

Add this two results together

Total = 4 Apples + 2 Eggplants

Total = $2.36 + $3.58

Total = $5.94

This statement is false because the sum is less than $6.00

3. Total cost of 4 eggplants, 4 apples and 1 carton of orange juice is $13.41

In (1) & (2) above

4 Eggplants = $7.16

4 Apples = $2.36

1 carton of orange juice = $3.89

Add the above together

Total = $7.16 + $2.36 + $3.89

Total = $13.41

This statement is true because the sum is $13.41

4. Total cost of 5 eggplants is greater than cost of 4 bags of spinach

First, we need to calculate the cost of 5 eggplants

5 Eggplants = 5 * 1 Eggplants

5 Eggplants = 5 * $1.79

5 Eggplants = $8.95

Next, we calculate the cost of 4 bags of Spinach

4 bags of Spinach = 4 * 1 bag of Spinach

4 bags of Spinach = 4 * $2.55

4 bags of Spinach = $10.20

This statement is false because 4 Eggplants costs less than $ bags of spinach

5. Total cost of 2 eggplants, 2 apples and 2 cartons of orange juice is $9.99 more than cost of 1 bag of spinach

From (2) above

2 Eggplants = $3.58

Next, we need to calculate the cost of 2 apples

2 Apples = 2 * 1 Apples

2 Apples = 2 * $0.59

2 Apples = $1.18

Next, we need to calculate the cost of 2 cartons of orange juice

2 Cartons = 2 * 1 Carton

2 Apples = 2 * $3.89

2 Apples = $7.78

Sum these up

Total = $3.58 + $1.18 + $7.78

Total = $12.54

1 Bag of spinach = $2.55 each

Subtract 1 Bag of spinach from the $12.54

Difference = $12.54 - $2.55

Difference = $9.99

This statement is true because the difference is $9.99

The probability that both events B and C will occur is:

P(B and C) = 9/20

Probability is the likelihood of an event to occur. It is expressed as a number in the range from 0 to 1.

The probability of an impossible event is 0, that of an event that is certain to occur is 1.

We have:

The probability that event B will occur, P(B) = 3/4

The probability that event C will occur, P(C) = 3/5

The probability that both events B and C will occur is:

P(B and C) = P(B) × P(C)

P(B and C) = 3/4 × 3/5

P(B and C) = 9/20

Learn more about probability on:

brainly.com/question/251701

#SPJ1

Answer:

(2,-5)

Step-by-step explanation:

To solve this, simply substitute the values for x and y. The only one that works is (2,-5).

-5 = -2(2) -1

-5 = -4 - 1

-5 = -5

Answer:

A shape that can be pushed to make a different shape

Step-by-step explanation:

The equivalent of the expression [-(6/5)t + 3/16] - [-(7/10) + 9/8] will be - (5/10)t - 15/16. Then the correct option is D.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ [-(6/5)t + 3/16] - [-(7/10) + 9/8]

Simplify the equation, then we have

⇒ [-(6/5)t + 3/16] - [-(7/10) + 9/8]

⇒ -(6/5)t + (7/10)t + 3/16 - 9/8

⇒ -(5/10)t - 15/16

The equivalent of the expression [-(6/5)t + 3/16] - [-(7/10) + 9/8] will be - (5/10)t - 15/16. Then the correct option is D.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ1

Answer: y=6

Explanation:

Answer:

Step-by-step explanation:

Answer:

Vertex: (3, 5)

Axis of symmetry: x=3

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

For more such questions on Parameters

https://brainly.com/question/29673432

#SPJ8

Answer:

(2x-1)(x+3)

Step-by-step explanation:

2x(x+3)-1(x+3)

(2x-1)(x+3)

Answer:

(x + 1) (2 x + 3)

Step-by-step explanation:

Write the middle term as + 5 x = 2 x + 3 x

And factor by grouping:

2 x^2 + 2 x + 3 x - 3

2 x (x + 1) + 3 (x + 1)

(x + 1) (2 x + 3)

The other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Given that, find the other side of this equation so it's true for all values of x:

1/2(6x - 10) - x

= 6x/2 - 10/2 -x

= 3x-5-2

= 2x-5

Now for, equation so it's true for no values of x:

1/2(6x - 10) - x =

Distribute the parentheses:

1/2(6x - 10) - x =

= 3x -5 -x

= 2x -5

We need to other side to be of the form 2x - constant where the constant is not equal to 5.

2x-5 = 2x+3

Subtract 2x from each side.

-5 =3

This is not true so there is no solution.

Hence, the other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

Learn more about equations here:

https://brainly.com/question/29657992

#SPJ1

According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

Learn more about yards in: https://brainly.com/question/28062239
#SPJ1

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

For more such question on combination visitr;

https://brainly.com/question/28065038

#SPJ8

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

For more such questions on linear regression line:

https://brainly.com/question/30401933

#SPJ8

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

Learn more about mean on:

https://brainly.com/question/1136789

#SPJ1

Answer:

The answer would be E.

When you solve 25 x 1/5, you get 5.

When you solve 25 ÷ 5, you get 5.

The equivalent expression is 25 ÷ 5.

Option E is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example.

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

25 x 1/5

= 25 x 1/5

= 5 x 5 x 1/5

= 5

Now,

1/25 x 5

= 1/5

1/25 x 1/5

= 1/125

1/25 ÷ 1/5

= 1/25 x 5

= 1/5

5 ÷ 25

= 5/25

= 1/5

25 ÷ 5

= 5

We see that,

25 x 1/5 and 25 ÷ 5 have the same value.

Thus,

The equivalent expression is 25 ÷ 5.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

For similar question on depreciation.

https://brainly.com/question/15998639  

#SPJ8

Answer:

150

Step-by-step explanation:

20 percent of 150 is 30.

To check the answer... 150 times 0.2 is 30.

Answer:

150

20 percent of what number equals 30; Answer: 150.

Step-by-step explanation:

20% of what is 30?

Written using the formula: X = 30 ÷ 20%

Convert the percent to a decimal.

20% ÷ 100 = 0.2.

X = 30 ÷ 0.2.

X = 150.

So 20% of 150 is 30.

Answer:

\(KL = \boxed{31.78}\)

Step-by-step explanation:

\( \boxed {IJ=9, \: JK=11 \: and \: IL \: is \: 26 } \\then \to \\ \boxed{ K = \frac{11}{J} \: and \: L = \frac{26}{I} \: and \: I = \frac{9}{J}} \\ hence \to \\ \boxed{KL = \frac{11(26)}{J(I)} = \frac{286}{J \frac{9}{J} } } = \frac{286}{9} = \boxed{31.78}\)

Answer:

Step-by-step explanation:

the dot would either (1,4) or (4,1)

a squared+ b squared= c squared

the length of the sides are 3

3 squared + 3 squared= c squared

9+9 =c squared

18= c squared

square root of 18 rounded to the nearest tenth is 4.2

Answer:

There isn't anything i can do when there isn't even a graph or a picture showing what it even looks like so I can't help you maybe re-post it with a picture then i can help.

In the given expression, the number of terms is 5, the constants are 8, -5 6, -10 and 2. The fourth term is j and the coefficient of the third term is 6

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols. An expression in math is a statement involving at least two different numbers (known or unknown) and at least one operation.

In the given expression, we have to answer some questions here;

a) The number of terms in the expression is 5

b) The constant of the expression are 8, -5, 6, -10 and 2

c) The fourth term in the expression is j

d) The coefficient of the third term is 6

Learn more on expressions here;

https://brainly.com/question/4344214

#SPJ1

Answer:

a

Step-by-step explanation:

inverse ----> y = x

x = 2y - 7

2y = x + 7

y = (x+7)/2

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation: