What's the slope of the line

Answer:

x = 7.55

Step-by-step explanation:

Pythagorean Formula:

a² + b² = c²

Given:

a = x

b = 8

c = 11

Work:

a² + b² = c²

x² + 8² = 11²

x² + 64 = 121

x² = 121-64

x² = 57

\(\sqrt{x^2} =\sqrt{57}\)

x = 7.55

Answer:

y=\(\frac{3}{5}x\)-6

Step-by-step explanation:

Remember the slope-intercerpt form

y=mx+b

There are total 8000000 phone numbers which don't start with 0 or 1.

The first can’t be 0 or 1 so that means that it can be 2,3,4,5,6,7,8,9 which is 8 numbers

Now we have settle what the first digit can or can’t be, there are 6 numbers left.

Because there are no more restrictions for phone numbers that don’t work (first digit can’t be one or zero was the only restriction) . when you are counting the amount of numbers between let’s say a and b inclusive, the amount of numbers between them inclusive is |a-b| +1. Example : The amount of numbers between 2 and 13 inclusive is just |2–13|+1 which is 12. 2,3,4,5,6,7,8,9,10,11,12,13 is 12 numbers so |a-b|+1 works for the amount of numbers between a and b inclusive.

There are, 999999–000000+1 means there are 1000000 or 1 million possible 6 digit numbers. But that’s not the answer to the problem because each 1 of those 1 million 6 digit numbers needs a 7th digit which and be any number from 2–8 . This means that you need to multiply 1000000 by 8 to get 8 million possible phone numbers. If your wondering why I multiplied by 8, let’s say the number abcdef is one of the possible 6 digit numbers. If you add a 7th digit 2–9 to our number abcdef, then our number abcdef can be 2abcdef, 3abcdef, 4abcdef, 5abcdef, 6abcdef, 7abcdef, 8abcdef, 9abcdef.

Just a quick side note for any misconceptions, when I say the number abcdef, I don’t mean a times b times c times d times e times f, I mean a is the number in the hundred thousands place, b is the number in the 10 thousands place, c is the number in the thousands place, d is the number in the hundreds place, e is the number in the tens place, f is the number in the ones place.

Back to the problem, because there are 8 possible numbers for the 7th digit  you need to multiply the 1000000 different 6 numbers by 8 because each of those numbers has 8 variations.

Therefore, there are 8*1000000 or 8 million different phone numbers whose digits aren’t 0 or 1.

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The analysis of variance is a valuable tool for examining potential differences among three or more groups, helping to make informed decisions based on data. It enables researchers to determine if there is a significant factor affecting the outcome or if the observed variations are simply due to chance.

The analysis of variance (ANOVA) procedure is a statistical technique used to test hypotheses about the means of three or more groups. ANOVA compares the variance within each group to the variance between the groups to determine if there is a significant difference in means. This test is commonly used in research studies to determine if a particular treatment or intervention has an effect on the outcome of interest.

In an ANOVA, the null hypothesis assumes that all group means are equal, while the alternative hypothesis suggests that at least one group mean is different from the others. By calculating the F-statistic and comparing it to a critical value, we can determine whether to reject or fail to reject the null hypothesis.

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ANSWER

EXPLANATION

There are six students in the class.

There are 7 days in a week. There are 2 days in the weekend. There are 5 weekdays.

The probability that any student is born on the weekend is given as:

P(weekend) = 2/7

The probability of being born on a weekday is:

P(weekday) = 5/7

Now the probability that 4 out of the six students is born on a weekend will be given as the products of four of them born on a weekend and the remaining two born on a week day:

That is the probability that 4 out of 6 of them are born on a weekend.

Answer:

142.5

Step-by-step explanation:

150/x=100/95

95*150/100=

142.5

Step-by-step explanation:

ok multiply the denominator by the whole number to get 8 and add it to the numerator to get 11. the denominator stays the same so you get 11/4

Answer:

=================

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

We know that

• You have 2 1/2 yards of fabric.

• You want to make 3 pillows.

To find the number of yards of fabric you can use for each pillow, we just have to divide. We know that 2 1/2 is equivalent to 5/2 yards.

The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.

The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).

The slope of the graph gives the unit rate, which is calculated as m = y/x.

Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.

Therefore:

Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.

Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.

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Answer:

x < -12

Step-by-step explanation:

Given the inequality

-2(x + 3) < 6 - x

Expand

-2x - 6 < 6 - x

Collect the like terms;

-2x + x < 6 + 6

-x < 12

Multiply through by -1

-1(-x) < -1(12)

x < -12

The p-value (0.0251) is greater than the significance level (0.02), we fail to reject the null hypothesis. There is not sufficient evidence at the 0.02 level to dispute the company's claim.

To determine if there is sufficient evidence to dispute the company's claim, we can set up the following hypotheses:

Null hypothesis (H₀): The proportion of chips that fail in the first 1000 hours is equal to 49%.

Alternative hypothesis (H₁): The proportion of chips that fail in the first 1000 hours is not equal to 49%.

In symbols:

H₀: p = 0.49

H₁: p ≠ 0.49

Where:

p represents the true proportion of chips that fail in the first 1000 hours.

The significance level is given as 0.02, which means we want to test the hypotheses at a 2% level of significance.

Now, let's perform a hypothesis test using the provided sample data.

Given that the sample size is 1300 and the proportion of chips that fail in the first 1000 hours is found to be 46%, we can calculate the test statistic and p-value using the binomial distribution.

The test statistic follows an approximate standard normal distribution when the sample size is large. To calculate the test statistic, we need to compute the standard error (SE) of the sample proportion:

SE = √((p * (1 - p)) / n)

where n is the sample size.

SE = √((0.49 * (1 - 0.49)) / 1300)

≈ 0.0134

We can now calculate the test statistic (Z-score):

Z = (p sample - p) / SE

where p sample is the sample proportion and p is the proportion specified in the null hypothesis.

Z = (0.46 - 0.49) / 0.0134

≈ -2.2388

Using the standard normal distribution table or a statistical calculator, we find that the p-value corresponding to Z = -2.2388 is approximately 0.0251 (two-tailed test).

Since the p-value (0.0251) is greater than the significance level (0.02), we fail to reject the null hypothesis. There is not sufficient evidence at the 0.02 level to dispute the company's claim.

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The complete question is:

A sample of 1300 computer chips revealed that 46% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 49% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

Answer:

Step-by-step explanation:

5-2(2x - 3) = 12

Expanda los términos en el corchete

Eso es

5 - 4x + 6 = 12

Agrupar términos similares

Envíe las constantes al lado derecho de la ecuación y aquellas con variables al lado izquierdo

Tenemos

- 4x = 12 - 5 - 6

- 4x = 1

Divide ambos lados entre - 4

Tenemos la respuesta final como

Espero que esto te ayude

Step-by-step explanation:

to cross the y-axis x must be 0.

so,

y - 4×0 = 1

y = 1.

so, the point is

(0, 1)

Answer:

Interest = $60.75

Amount = $510.75

Step-by-step explanation:

The formula for finding interest is;

Interest = Principal * Rate * Time

And here;

Principal = $450

Rate = 41/2% or 4.5%

Time = 3 years

Interest = \(\frac{450 * 45 * 3}{1000}\)

Divided by 100 because of the percentage of the rate but here I made it 1000 because I moved the decimal point in the 4.5 forward once which means I have to add 0 to the denominator.

              = \(\frac{45*45*3}{100}\)

             = \(\frac{6075}{100}\)

            = $60.75

Now the amount is simply the Principal + Interest which will be;

= $450 + $60.75

= $510.75

Answer:

36 &49

Step-by-step explanation:

6²=36

7²=49

Answer:

36 ,49

Step-by-step explanation:

36 = 6 * 6 = 6²

49 = 7 * 7 = 7²

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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When a range of values is used to estimate a population parameter, it is called an interval estimate. The correct answer is option D.

An interval estimation is the evaluation of a parameter of a population by computing an interval, or range of values, within which the parameter is most likely to be located. An interval estimate gives you a range of values where the parameter is expected to lie. In other words, an interval estimate is a range in which the population parameter probably falls for a given level of confidence. We have to establish a level of confidence because we can never be 100 percent sure that the population mean falls within our confidence interval. A confidence interval is the most common type of interval estimate.

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The sample type used in this scenario is a census sample, not one of the options provided is correct.

A census collects data from all members of a population. In this scenario, Christopher collected data from all athletes in his school.

Of the options provided, the "cluster sample" that most closely resembles a census is dividing the population into clusters and randomly selecting a number of clusters to include in the sample.

 However, Christopher collected data from all members of the population, so cluster sampling is not the appropriate term for this situation.

So the answer is none of the options offered. 

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Answer:

(-12,2)

Step-by-step explanation:

x^2 + 10x = 24

x^2 + 10x + (10/2)^2 = 24 + (10/2)^2

10/2 = 5

5^2 = 25

x^2 + 10x + 25 = 24 + 25

x^2 + 10x + 25 = 49

(x + 5)^2 = 49                 Take the square root of both sides

(x + 5) = sqrt(49)

x + 5 = +/- 7

x = +/- 7 - 5

x = +7 - 5 = 2

x = -7 - 5 = -12

Answer:

{ -12 , 2}

Step-by-step explanation:

x² + 10x = 24

In order to complete the square, the equation must first be in the form x² + bx =c.

Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

expand exponents.

Add 24 and 25

Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².

Take the square root of both sides of the equation.

\( \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} \)

simplify

Subtract 5 from both sides.

x + 5 - 5 = 7 - 5

x + 5 - 5 = +/- 7 -5

Answer:

2. 137°

3. 24.7°

Step-by-step explanation:

Using cosine law:

2. 28² = 12² + 18² - 2(12)(18)cosA

cosA = -79/108

A = 137.0107361°

3. 15² = 19² + 30² - 2(19)(30)cosC

cosC =259/285

C = 24.66381079°

The measure of the angle is:

m∠A = 66.8°

m∠C = 30°

We have,

2.

Using tan trigonometric identities.

tan A = 28/12

Simplify the fraction

tan A = 7/3

Take inverse trigonometry

A = \(tan^{-1}(7/3)\)

A = 66.8°

3.

Using sin trigonometric identities.

sin C = 15/30

Simplify the fraction

sin C = 1/2

Take inverse trigonometry

C = \(sin^{-1}(1/2)\)

C = \(sin^{-1} sin ~30\)

C = 30°

Thus,

The measure of the angle is:

m∠A = 66.8°

m∠C = 30°

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Answer:

$18.90

Step-by-step explanation:

$15 with a 40% markup is $21

$21 with a 10% off is

$18.90

Answer:

Option 2

Step-by-step explanation:

You can find the answer by just counting to the left and down

For a normal distribution of the money spent on food per visitor at the san diego zoo, probability that a randomly selected par visitor will spend less than 20 is equals to 0.3488.

There is the money spent on food per visitor at the san diego zoo.

Mean of money = $27.50

Standard deviations= 8

We have to determine the probability that a randomly selected par visitor will spend less than 20, P( X < 20), where X is random variable for spending money. Using the Z-Score formula for normal distribution, \(Z = \frac{X - \mu}{\sigma } \)

where, X --> observed value

μ --> mean

σ --> standard deviations

Substitutes the known values in above formula, \(Z = \frac{20 - 27.50}{8 } \)

\(= \frac{7.50 }{8 } \)

= 0.937

The probability that a randomly selected par visitor will spend less than 20, P( X < 20) = \(P ( \frac{ X - \mu }{\sigma} < \frac {20 - 27.50}{8})\)

= P ( z < 0.937)

Using the Z-distribution table the value of P( z< 0.937) is equals to the 0.3488. So, P( X < 20) = P( z< 0.937) = 0.3488.

Hence, required probability value is 0.3488.

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Answer:

Step-by-step explanation:

the degree of a polynomial is determined by the biggest exponent. For example, in this equation: 6x^4+3x^3+3x^2+2x+1, you can see that the biggest exponent is the 4, so it would be a polynomial of the 4th degree.

let's pry open the triangles a bit and plug their values for the pythagorean theorem to get the hypotenuse, Check the picture below, those are only the first 4 triangles, notice the hypotenuse.

now let's move like the crab, backwards, let's do D first and then C

D)

well, since for the 1st triangle the root has a "2", that means "1+1", and it's pretty much the same for any subsequent triangle, so the rule must be

\({\Large \begin{array}{llll} P_{n}=\sqrt{n+1} \end{array}}\hspace{5em}\textit{rule for the }n^{th}~triangle\)

C)

what does that make the 9th one?

\({\Large \begin{array}{llll} P_{9}=\sqrt{9+1}\implies P_9=\sqrt{10} \end{array}}\)

Answer:

x = {-5, -⅓}

Step-by-step explanation:

\(3 {x}^{2} + 16x + 5 = 0\)

\(3 {x}^{2} + 15x + x + 5 = 0\)

\(3x(x + 5) + 1(x + 5) = 0\)

\((x + 5)(3x + 1) = 0\)

\(x = - 5 \: or \: - \frac{1}{3} \)

\(x = \{ - 5 \: , - \frac{1}{3} \}\)

Answer:

$1417.50+$4500= 5917.50

The required manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.

Let x be the number of $20 increases in the price of a one-bedroom unit, and y be the number of $60 increases in the price of a two-bedroom unit. Then the rental prices for one-bedroom and two-bedroom units can be expressed as:

One-bedroom price = $1200 + $20x

Two-bedroom price = $1800 + $60y

The total number of customers for one-bedroom units is 90 minus the number of customers lost due to the price increase, which is x. Similarly, the total number of customers for two-bedroom units is 100 minus the number of customers lost due to the price increase, which is 2y. Therefore, the total revenue can be expressed as:

Revenue = (90 - x) * ($1200 + $20x) + (100 - 2y) * ($1800 + $60y)

Expanding and simplifying this expression, we get:

Revenue = 216000 + 9600x - 240x² + 180000 + 108000y - 7200y²

Collecting like terms, we get:

Revenue = -240x² - 7200y² + 9600x + 108000y + 396000

To find the rental price that maximizes revenue, we need to find the values of x and y that maximize the revenue. We can do this by taking partial derivatives of the revenue function with respect to x and y and setting them equal to zero:

dRevenue/dx = -480x + 9600 = 0

dRevenue/dy = -14400y + 108000 = 0

Solving for x and y, we get:

x = 20

y = 7.5

Therefore, the rental prices that maximize revenue are:

One-bedroom price = $1200 + $20x = $1600

Two-bedroom price = $1800 + $60y = $2250

So the manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.

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