Let A be the point (7,4) and D be (-5, -3). What is the length of the shortest path ABCD, where B is a point (x, 2) and C is a point (x,0)? This path consists of three connected segments, with the middle one vertical.

Answer:

  w ≥ 14.25

Step-by-step explanation:

You want to solve the inequality 34 +12w ≥ 205 for the number of weeks (w) Anna will take to save for a new bike.

This is a 2-step inequality.

Step 1: subtract the constant from both sides:

  34 -34 +12w ≥ 205 -34

  12w ≥ 171

Step 2: divide by the coefficient of the variable

  12w/12 ≥ 171/12

  w ≥ 14.25

It will take Anna a minimum of 14.25 weeks to save the money to purchase the bike.

__

Additional comment

Often, income does not come as a continuous stream, so 14.25 weeks would mean 15 weeks at a minimum.

If Anna earns the last $3 she needs in 1/4 week, then 14 1/4 weeks is the right answer.

This has to do with the practical domain of w in this problem. If w is restricted to integers, then w ≥ 15. Regardless, the answer needs to be given in a way that will satisfy your answer checker.

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Answer:

w>14.25

Step-by-step explanation:

Answer:

It's false

Step-by-step explanation:

1.25*200=250 not 300.

Answer:

730.055m

Step-by-step explanation:

(sorry if wrong)

Answer:

y = \(\frac{4}{5}\) x + \(\frac{6}{5}\)

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 ) = (- 4, - 2) and (x₂, y₂ ) = (6, 6) ← 2 points on the line

m = \(\frac{6-(-2)}{6-(-4)}\) = \(\frac{6+2}{6+4}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\) , then

y = \(\frac{4}{5}\) x + c ← is the partial equation

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

using (6, 6 ) , then

6 = \(\frac{24}{5}\) + c ⇒ c = \(\frac{30}{5}\) - \(\frac{24}{5}\) = \(\frac{6}{5}\)

y = \(\frac{4}{5}\) x + \(\frac{6}{5}\) ← equation of line

Answer:

9

Step-by-step explanation:

E(X) = np

E(X) = (15) (0.6)

E(X) = 9

The mean of the X is 9.

The mean of a binomial distribution is the expected value (long-run average) of the number of successes in the given number of trials.

\(\mu_{x} = n.p\)

where,

\(\mu_{x}\) is the mean of the binomial distribution

n is the number of trials

and, p is the probability of success

According to the given question.

We have

Number of trials, n = 15

Probability of success, p = 0.6

Therefore, the mean of X is given by

\(E(X) = 15(0.6)\)

⇒ \(E(X) = 9\)

Hence, the mean of the X is 9.

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The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. 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.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

answer would most likely be C

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

Step-by-step explanation:

Answer:

C  =  2 +

7c

15

Step-by-step explanation:

Answer:

156

Step-by-step explanation:

Given the data:

Age (X) :

38

41

45

48

51

53

57

61

65

Pressure(Y) :

116

120

123

131

142

145

148

150

152

From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :

The regression equation obtained is :

y = 1.48769X + 60.46103

Using the model, the predicted blood pressure for a person aged 64 will be :

y = 1.48769(64) + 60.46103

y = 95.21216 + 60.46103

y = 155.67319

y = 156 (nearest whole number)

Answer:

\(x > 1\)

if you graph

\(f(x) = x + 1\)

you'll see that it's that part of graph from x=1 to right and x=1 on this graph is not ncluded so it's x>1

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:110 degrees

Step-by-step explanation:

We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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Answer:y=2x+7

Step-by-step explanation:

so for the new equation, we know the slope is going to be the same (because its parallel) so for starters we have y=2x+b so now in order to find b (the y-intercept) we have to plug the point into the equation. So it would look like -1=2(-4)+b and then you solve for b and get 7 for b. SO the final answer is y=2x+7.

Answer:

Step-by-step explanation:

It's a proportion rather than an equation that you might be more accustomed to.

2/0.05 = x/ 0.95       Cross multiply

2 * 0.95 = x * 0.05    Divide by 0.05

2 * 0.95/0.05 = x

x = 38 grams of sugar should be added to the 2 grams of cinnamon.

There's another way to do it.

2/0.05 = (x + 2)/1      Cross multiply

2*1 = 0.05x + 0.1       Subtract 0.1 from both sides

1.9 = 0.05x

1.9/0.05 = x

x = 38

Which ever way you understand better is the answer. 100 / 100% is 1

If I paid $625 interest on $5000 that I borrowed at 5%, 2.5 years did I borrow it.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Here, we have,

formula: I = Prt.

given that,

I paid $625 interest on $5000 that I borrowed at 5%

let,  I borrow it for t yrs.

so, we get,

625= 5000*5%*t

solving we get,

t=2.5

Hence, If I paid $625 interest on $5000 that I borrowed at 5%, 2.5 years did I borrow it.

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The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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I think the answer is:

x ≥ 2.5

Inability to sleep properly for weeks  is a warning sign that someone needs the help of a mental health professional. Correct option is C.

Difficulty sleeping, or insomnia, can be a warning sign that someone needs the help of a mental health professional. Insomnia can be caused by a number of mental health conditions, such as anxiety, depression, or post-traumatic stress disorder (PTSD), as well as other factors such as stress, poor sleep habits, or physical health problems.

Feeling shy when asked to walk onstage and overeating to increase bodily strength may be signs of anxiety or other emotional or psychological issues, but they are not necessarily warning signs that someone needs the help of a mental health professional.

However, if these behaviors are causing significant distress or interfering with daily life, it may be a good idea to seek the help of a mental health professional.

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Hi!

\( \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = \frac{3}{2} = 1 \frac{1}{2} \)

The required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

Given that,
To determine how much each number needs to change for a ten for 1 hundred.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
According to the question,
The number from ten to 1 hundred,
10, 11, ......,99, 100.
From the above series, it can be concluded that each number is greater than by unity from the previous number.

Thus, hte required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

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Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

17

Step-by-step explanation: