Explain Linear Equations in One Variable. ​

Answer: x=90 y=48 z=60

Step-by-step explanation: z=y+12 because they are parallel lines and must be equal alternate interior angles theorem. And y-18+z=90, because they are a right angle. x is 90 degrees because it is also a right angle

a) Radicand is 1/4

b) x= 4.5 or -2.5

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given equation is:

16x²-8x+1=0

Now,

(4x)²-2*4x*1 + (1)²=0

Using

(a+b)²= a² + 2ab + b²

So,

(4x)²-2*4x*1 + (1)² = (4x+1)²

x=1/4

b) 4x² - 8x - 45 = 0

Using discriminant method

D = √[(-8)² - 4(4)(-45)]

   = √784

   = 28

Now, x = (1/8)[8 +/- 28]

  = (1/8)(36) = 4.5

or, x = (1/8)(-20)

 = -2.5

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Answer:

tan(57°) = 12/x

x tan(57°) = 12

x = 12/tan(57°) = 7.793

Answer:

x ≈ 7.8

Step-by-step explanation:

using the tangent ratio in the right triangle

tan57° = \(\frac{opposite}{adjacent}\) = \(\frac{12}{x}\) ( multiply both sides by x )

x × tan57° = 12 ( divide both sides by tan57° )

x = \(\frac{12}{tan57}\) ≈ 7.8 ( to the nearest tenth )

Answer:

4x²y² + 20xy² + 25y²

Step-by-step explanation:

(a + b)² =  a² + 2ab + b²

a = 2xy   ; b = 5y

(2xy +5y)² = (2xy)² + 2*(2xy) * (5y)  +(5y)²

                 = 2²x²y² + 2* 2* 5 * x*y*y + 5²*y²

                =4x²y² + 20xy² + 25y²

Answer:

false

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rhombus is an isosceles trapezoid.

The probability that at least one household in the sample of 25 has an annual property tax bill of at least $17,000 is 97.36%.

The above scenario describes a normal distribution with a mean of $15,000 and a standard deviation of $4,000. A simple random sample (SRS) of 25 households has been taken from this distribution.

A normal distribution with a specified mean and standard deviation can be used to find the probability of any value. In this case, we can use the normal distribution to find the probability that a randomly selected household will have an annual property tax bill of a certain value.

For example, the probability that a randomly selected household has an annual property tax bill of at least $17,000 can be calculated as follows:

First, we need to calculate the z-score of this value. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation:

z-score = ($17,000 - $15,000) / $4,000 = 0.5

Then, we use a normal distribution table to calculate the probability that the randomly selected household has an annual property tax bill of at least $17,000.

Using the table, the probability that a randomly selected household has an annual property tax bill of at least $17,000 is 0.6915.

Since a simple random sample of 25 households were selected, the probability that at least one household in the sample has an annual property tax bill of at least $17,000 is 1 - (1 - 0.6915)^25, which is 0.9736.

Therefore, the probability that at least one household in the sample of 25 has an annual property tax bill of at least $17,000 is 97.36%.

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Answer:

1/8 is half of 1/4 so, you need to measure half cup

A confidence interval can be used to define a range of plausible values for an unknown parameter, like the variance ratio.

variances of two portfolios with sample variances of s1^2 and s2^2. Let's calculate the confidence interval for the ratio of population variances 05 using the given information.

\((s1^2 / s2^2) * (Fα/2),v2, v1 ≤ (s1^2 / s2^2) * (F1-α/2),v1,v2\)

\((s1^2 / s2^2) * (Fα/2),v2, v1 ≤ (s1^2 / s2^2) * (F1-α/2),v1,v2= (0.0049 / 0.0064) * (2.377) ≤ (0.0049 / 0.0064) * (0.414)= 1.8375 ≤ 1.2156\)

To find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg), the following steps should be taken:Null hypothesis, : ρ = 0Alternative hypothesis, Ha: ρ ≠ 0where ρ is the

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The number of tomato slices, t and the number of hamburgers, h is t=2h

A ratio is a mathematical relationship between two or more numbers that shows how much one value is proportional to another. It is expressed in the form of a fraction or as a colon between the two values.

Since each hamburger gets the same number of slices of tomatoes, we can assume that the relationship between the number of tomato slices, t, and the number of hamburgers, h, is a proportional relationship.

To find the constant of proportionality, we can choose any two sets of data from the table and calculate the ratio of tomato slices to the number of hamburgers:

For the first two days: 72/36 = 2, or 100/50 = 2

For the last two days: 150/75 = 2, or 200/100 = 2

Since the ratios are all equal, we can conclude that the equation representing the relationship between t and h is:

Ht = 2h

Therefore, the answer is (G) t=2h.

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Answer:

50.2

Step-by-step explanation:

Answer:

50.24 should be correct, (2 * pi) * r.  With pi = 3.14 and radius = 8, we get 50.24.

Answer:

3/70

Step-by-step explanation:

3 orange,6 pink , 1 yellow , and 5 red = 15

P(pink) = number of pink/ total = 6/15 = 3/5

Then without putting it back

3 orange,5 pink , 1 yellow , and 5 red = 14

P(yellow) = number of yellow/ total = 1/14

P(pink, no replacement, yellow) = 3/5*1/14 = 3/70

Answer:

This is most definately an impulse purchase because Ronnie had not planned to buy the stereo speaker, but had a impulse to buy it even when he didn't have the money. Had he already decided he wanted the stereo and went to the store to buy it that would not be an impulse purchase it would be a planned purchase.

Most data is likely to be skewed following a particular trait because when considering real life data, it is likely that it may concentrate on one end of the values on the real line as there is high uncertainty that exists with real life.

There is very little confidence that the population would behave in expected ways.

The skewed distribution implies the distribution that is not symmetrical. If a distribution is skewed it can be skewed to the left i.e. mean lies to the left of the center or skewed to the right i.e. mean lies to the right of the center of the distribution.

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Answer:

.....

..................

Answer:

-8

Step-by-step explanation:

3=w+11

-11    -11

-8=w

Answer:

To calculate the total amount, first find out how much you contribute and then add the amount your employer contributes.

Your contribution: 10% of $50,000

= ($50,000 * 10) / 100

= $5,000

Employer's contribution: 3% of $50,000

= ($50,000 * 3) / 100

= $1,500

Total contribution:

= Your contribution + Employer's contribution

= $5,000 + $1,500

= $6,500

So, the total amount being put away in your account each year is $6,500.

Step-by-step explanation:

Answer:

86.1 I believe because I'm assuming you meant 2.87

Answer:

C = g x 5.72

Hope this helps.

This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.

For the first five digits you can choose from the numbers 0,1,2...,9 or 10 choices.

A we cannot repeat the digits, so, first five digits will be:

10 × 9 × 8 × 7 × 6

Now the next 1 digit will all be letter all being different

There are 26 letters in the alphabet.. for our second digit we have 26 choices,

Here is the whole calculation:

= 10 × 9 × 8 × 7 × 6 × 26

= 786240

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Hence, the students voted in favour of both issues is \(99\).

What is the inclusion exclusion?

Principle of Inclusion and Exclusion is an approach which derives the method of finding the number of elements in the union of two finite sets.

This is used for solving combinations and probability problems when it is necessary to find a counting method, which makes sure that an object is not counted twice.

Here given that,

Euler middle school, \(198\) students voted on two issues in a school referendum with the following results: \(149\) voted in favor of the first issue and \(119\) voted in favor of the second issue.

If there were exactly \(29\) students who voted against both issues

Using the Principles of Inclusion Exclusion then,

\(149+119+29-198=99\)

Hence, the students voted in favour of both issues is \(99\).

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Answer:

subject tooo

Step-by-step explanation:

sorry

Answer:

$450.50

Step-by-step explanation:

Answer:

$80.59

Step-by-step explanation:

You add the price of the raincoat and shoes to get 152.75, you then subtract the price of the 4 shirts you returned to get 76.75. The 5% tax for this is 3.84 so you add the two together and you get $80.59.

The three-digit numbers that are not divisible by 5 are 60.

Numbers to be divisible = Three digits = abc

Numbers are not divisible by = 0 and 5

Thus,

Now x ≠ 0 and x ≠ 5, whereas

x = 0 does not yield a three-digit integer and x = 5 yields a number divisible by 5.

Now, since sum should be less than 20, thus -

2x + y ≤ 20

where x can be 1, 2,3 or 4 and y can be 0-9. Hence

2x ≤ 10. Thus 10(4) = 40

Finding out the combinations -

When x = 6

12 + y ≤ 20, y ≤ 8 = Calculates 8 more numbers.

When x = 7

14 + y ≤ 20, y ≤ 6 = Calculates 6 more numbers.

When x = 8

16 + y ≤ 20, y ≤ 4 = Calculates 4 more numbers.

When x = 9

18 + y ≤ 20, y ≤ 2 = Calculates 2 more numbers.

Total numbers -

= 40 + 8 + 6 + 4 + 2

= 60

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Answer: they are equal

Step-by-step explanation:

Since they are on opposite sides you just have to measure one and you got the answer to question b

Answer:

they are eqaul

Step-by-step explanation:

Answer:

more than 55 days

Step-by-step explanation:

440 a year

6+5=11 per class

minimum number of classes to avail full benefit440/11=40

440+3x= > (6+5)x

8x=440

x=440/8=55

Step-by-step explanation:

Amount borrowed=400

interest rate=4%

Amount of interest after x years =0.04XxX400=$16x

Total to be paid back=400+0.04XxX400=400+16(1)

1) the amount of interest.if Franco pays back the loan in x=1 years is

16x1=$16

2) the amount of interest,if Franco pay back the loan in x=2 years is,

16x2=$32

3) the amount of franco will pay the lender after 2 years will be

400+(16x2)=400+32=$432

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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