How many solutions?
4x - y = 18 and -4x + y = -18

a. one
b. infinitely many
c. no solutions

Answer:

x > 12

Step-by-step explanation:

9x>108

x> 108/9

x > 12

Answer:

\( \boxed{ \tt{x > 12}}\)

Step-by-step explanation:

\(9x > 108 \\ x > \frac{108}{9} \\ x > 12\)

Work Shown:

Use the circumference to determine the radius.

C = 2pi*r

12pi = 2pi*r

12 = 2r

r = 12/2

r = 6

Then find the area.

A = pi*r^2

A = pi*6^2

A = 36pi

The units for the area will be "square feet" which can be abbreviated to "sq ft",  ft^2 or \(\text{ft}^2\)

The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.

your answer luv- y-1/2x-7

The injury probability p that makes the decision maker indifferent between entering now and waiting until next year is approximately 0.26.

To calculate this probability, we need to set the expected values of entering now and waiting until next year equal to each other and solve for p. Let EMV₁ be the expected value of entering now and EMV₂ be the expected value of waiting until next year. Then we have:

EMV₁ = -1000p + 5000(1-p)

EMV₂ = 0.9(-1000p) + 0.1(5000)

Setting EMV₁ equal to EMV₂, we get:

-1000p + 5000(1-p) = 0.9(-1000p) + 0.1(5000)

Solving for p, we get:

p ≈ 0.26

Therefore, if the probability of injury is greater than 0.26, the decision maker should wait until next year to enter the market, and if the probability of injury is less than 0.26, the decision maker should enter the market now.

To know more about probability, refer here:

https://brainly.com/question/12629667#

#SPJ11

Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

Learn more on length of an arc here: https://brainly.com/question/2005046

Answer:

1/3

Step-by-step explanation:

There are 6 possible outcomes when you roll this die: 1,2,3,4,5 and 6. Of these, only 5 and 6 are greater than 4, which is 2 successful outcomes. Probability is successful outcomes/total outcomes = 2/6 = 1/3. Hope this helps!

The polygon has an area of 80 square units.

We need to find the scale factor to dilate it to 5 square units.

We need to that "The ratio of the area of one figure to the area of another, similar figure is equal to the square of the scale factor between the two figures"

Then:

Databases of variants are crucial in helping to identify disease gene candidates. Here's how they are used:

1. Collect and store genetic variants: Databases collect and store genetic variants from various individuals, including those with specific diseases and those without.

2. Compare variants between groups: By comparing the variants in affected individuals to those in unaffected individuals, researchers can identify variants that are more common in the disease group. This helps to narrow down the list of potential disease-causing genes.

3. Calculate probability: Databases can be used to calculate the probability of certain variants appearing in the general population. If a variant is rare in the general population but more common in individuals with a specific disease, it may be more likely to be a disease-causing variant.

4. Filter out common variants: As you mentioned, variants that are common in the general population or present in individuals without the disease are less likely to cause a rare genetic disease. By filtering out these common variants, researchers can focus on rare variants that may have a stronger association with the disease.

5. Identify disease gene candidates: Through this process of comparing and filtering genetic variants, researchers can identify potential disease gene candidates that warrant further investigation.

In summary, databases of variants help researchers identify disease gene candidates by storing genetic information, enabling comparison between affected and unaffected individuals, calculating variant probabilities, filtering out common variants, and ultimately pinpointing rare variants that may be associated with specific genetic diseases.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Answer:

11.2

Step-by-step explanation:

15x + 32 = 200       Subtract 32 from both sides

15x + 32 - 32 = 200 - 32

15x = 168  Divide both sides by 15

\(\frac{15x}{15}\) = \(\frac{168}{15}\)

x = 11.2

Answer:

i think the answer is x= 11.2

Step-by-step explanation:

15x= 200-32

15x=168

x=168/15

x=11.2

Answer:

21.5

Step-by-step explanation:

Answer:

This is what I got, but I think if you switch the IQR and Number of Data points, then you'll get it correct.

Step-by-step explanation:

Based on the box plots given:

The median in a box plot is the value indicated by the vertical line that divides the box.

Range = Max - min

Interquartile range = difference of the rectangular box = Q3 - Q1.

Therefore, based on the box plots given, we would conclude that:

Learn more about box plot on:

https://brainly.com/question/24335827

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

Learn more about Kristine from

https://brainly.com/question/27244350

#SPJ11

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer: 181

Step-by-step explanation: hi

The amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)

The volume of a tennis ball:

The circumference of the tennis ball is 8 inches.

The tennis ball is the form of sphere whose circumference is given by formula \(2\pi r\), where r is the radius.

Thus, if r is the radius then according to condition,

\(2\pi r\) = 8 or

r = 8/2\(\pi\) inches.

Now, the volume of the sphere of radius r is \(\frac{4}{3}\pi r^3\) hence, find the volume of the given tennis ball by substituting r  = 8/2\(\pi\) inches in  \(\frac{4}{3}\pi r^3\) and simplify:

Volume = \(\frac{4}{3}\pi\) × \((\frac{8}{2\pi } )^3\)

Volume = 8.65\(inches^3\)

Hence the required volume of the tennis ball is 8.65\(inches^3\)

The volume of three tennis balls is (3 × 8.65) \(inches^3\) = 25.96 \(inches^3\)

Find the volume of the cylinder:

The volume of the cylinder with radius r units and height h units is given by \(\pi r^2h\) Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:

\(\pi (1.32)^2\) × 8.2

= 3.14 × \((1.32)^2\) × 8.2

= 44.86 \(inches^3\)

Hence the volume of the cylinder is 44.86 \(inches^3\)

Find the amount of space within the cylinder not taken up by the tennis balls.

The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:

Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 \(inches^3\)

Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)

Learn more about Volume of Cylindrical at:

https://brainly.com/question/25562559

#SPJ1

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The perimeter of the rectangle is 2(5x – 2) + 2(3x + 1). If x = 4 centimeters, The correct option is c. 2(5x - 2) 2(3x + 1); 62 centimeters.

The distance between two points d = (x 2 – x 1) 2 + (y 2 – y 1) 2, this is the Distance Formula.

Displacement is the shortest distance between two points.

It is a vector quantity because it incorporates both movements, magnitude and direction.

If an object is traveling in one direction (e.g. along the x-axis), without reversing or changing course, then total distance

is the same as total displacement.

The given length of the rectangle is (5x – 2) and the width of the rectangle is (3x + 1).

So, the perimeter of the rectangle is:

Perimeter = 2(5x – 2) + 2(3x + 1)= 10x - 4 + 6x + 2= 16x - 2

Now, the total distance Zohar needs to cut with the scissors can be determined by putting the value of x = 4 centimeters.

Total distance = Perimeter= 16x - 2= 16(4) - 2= 64 - 2= 62

Therefore, the correct option is c. 2(5x - 2) 2(3x + 1); 62 centimeters.

for such more question on perimeter

https://brainly.com/question/25092270

#SPJ11

Answer:

$7.38

Step-by-step explanation:

Let's start out with variable x, representing his original $286

y will represent his balance after his order ($182.06)

a is our variable for our one-time $8 shipping fee

b will represent the cost of one card

our equation is => ((x - a) - y) ÷ 13 = b

Substitute => ((286 - 8) - 182.06) ÷ 13 = b

Solve => (278 - 182.06) ÷ 13 = b

95.94 ÷ 13 = b

b = 7.38

Thus, our answer is $7.38 per card

Answer:

FOIL

Step-by-step explanation:

" is just a mnemonic. It helps some people to remember all the steps needed to multiply two binomials. It "makes sense" because it's methodical and gives the right answer.

Answer:

69.444% is percentage of 25:36

The probability that the mean loss from f-i-re is larger than $300 for an S-R-S of 1000 home owners is 0.3085.

This problem can be solved using the Central Limit Theorem, which states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough (typically if n > 30).

Since the population is strongly right-skewed and the sample size is large (n = 1000), we can assume that the sampling distribution of the mean loss from fi-re will be approximately normal.

The mean of the sampling distribution is equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:

Populatio mean (μ) = $250

Population standard deviation (σ) = $5000

Sample size (n) = 1000

Sample mean = $300

Probability of sample mean > $300 = ?

Now, standard deviation of sample mean = σ / sqrt(n) = $5000 / sqrt(1000) = $158.11

Now, we need to standardize the sample mean using the z-score formula:

z = (sample mean- population mean) / (σ / sqrt(n)) = (300 - 250) / 158.11 = 0.316

Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than 0.316 to be approximately 0.3765 or about 37.65%.

You can learn more about population mean at

https://brainly.com/question/29441200

#SPJ4

The value of the test statistic is approximately 2.065.

To determine the value of the test statistic, we need to calculate the sample mean and standard deviation of the given data and then perform a hypothesis test.

Bag weights: 5.4, 5.3, 4.9, 5.3, 4.9, 5.4

To calculate the sample mean (\(\bar{x}\)) and standard deviation (s), we use the following formulas:

\(\bar{x}\) = (sum of all observations) / (number of observations)

\(s = \sqrt{(\sum (observation - mean)^2) / (number\ of\ observations - 1)}\)

Using these formulas, we calculate:

\(\bar{x}\) = (5.4 + 5.3 + 4.9 + 5.3 + 4.9 + 5.4) / 6 ≈ 5.2167

\(s = \sqrt((5.4 - 5.2167)^2 + (5.3 - 5.2167)^2 + (4.9 - 5.2167)^2 +\)\((5.3 - 5.2167)^2 + (4.9 - 5.2167)^2 + (5.4 - 5.2167)^2) / (6 - 1))\)≈ 0.219

Next, we perform a hypothesis test to determine if the machine is out of control. Since the population standard deviation is unknown, we use a t-test. The test statistic is given by:

test statistic = (\(\bar{x}\) - μ) / (s / \(\sqrt{n}\))

In this case, since the mean amount of sugar filled in a bag under control is 5 pounds, we have:

test statistic = (\(\bar{x}\) - 5) / (s / \(\sqrt{n}\)) = (5.2167 - 5) / (0.219 / \(\sqrt{6}\)) ≈ 2.065

Therefore, the value of the test statistic is approximately 2.065.

To know more about test statistic, refer here:

https://brainly.com/question/33944440

#SPJ4

The equation that expresses the law of refraction is known as Snell’s law or the law of refraction.

The law of refraction is used to determine the direction in which light bends when it enters a new medium.

What is the law of refraction?

The law of refraction (also known as Snell's law) is a principle of optics used to explain how light behaves at the boundary between two media with different refractive indexes.

The law of refraction states that when light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.

The equation for the law of refraction is as follows:

$$\frac{\sin \theta_1}{\sin \theta_2}= \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}$$

Where:θ1 = Angle of incidence

           θ2 = Angle of refraction

           v1 = Velocity of light in medium 1

           v2 = Velocity of light in medium 2

           λ1 = Wavelength of light in medium 1

           λ2 = Wavelength of light in medium 2

           n1 = Refractive index of medium 1

           n2 = Refractive index of medium 2

To know more about law of refraction visit

https://brainly.com/question/28747393

#SPJ11

Answer:

Google mid point formula and plug in your variables

Step-by-step explanation:

hope this helps :)

Since He Sells 15 Iteam The He Meet His Goal Of L + S >= 12

As Far As The Other Inequlty

425*9 + 125*6 = $4575 (Goal Acheived)

The Answer Is Yes He Meets Both Of His Goals

The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.

To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.

Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

For more questions like Critical value click the link below:

https://brainly.com/question/32607910

#SPJ11

The point on the segment AB that is 6/7 of the way from A to B is given as follows:

D. (-7 and 4/7, 17).

The coordinates of the point are obtained applying the proportions in the context of the problem.

The point is 6/7 of the way from A to B, hence the equation is given as follows:

P - A = 6/7(B - A)

The x-coordinate of the point is given as follows:

x - 1 = 6/7(-9 - 1)

x - 1 = -8.57

x = -7.57

x = -7 and 4/7.

The y-coordinate of the point is given as follows:

y - 5 = 6/7(19 - 5)

y - 5 = 12

y = 17.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

\( {10}^{ - 14} \)

Step-by-step explanation:

\( \huge\frac{ {10}^{ - 9} }{ {10}^{5} } \\ \\ \huge = {10}^{ - 9} \times {10}^{ - 5} \\ \\ \huge = {10}^{ - 9 + ( - 5)} \\ \\ \huge = {10}^{ - 9 - 5} \\ \\ \huge \orange {= {10}^{ - 14}} \)