Two number cubes are rolled at the same time. What is the approximate probability that the sum of the two cubes is 2 or 12?
A 0.028 C 0.083
B 0.056 D 0.111

Answer:a

Step-by-step explanation:

(c) Two straight lines are displayed on a coordinate plane. Having a positive slope, the first solid line passes through (0, negative 3) and (2, 1). Shaded areas surround the line to the right. The second dashed line travels through (0, 2) and has a negative slope (4, 0). Shaded areas surround the line to the left.

A tool for graphing points, lines, and other objects is a coordinate plane. It follows directions from one place to another as a map might.

Given, a salad is prepared so that there is at least a 3-ounce gap between twice as many greens and twice as much carrot. Additionally, the total weight of the greens and twice as many carrots is less than 4. Hence,

2g - c  = 3....(1)

g + 2c < 4.....(2)

Comparing both equations

intersecting Coordinates of g and c will be(2, 1 ).

Therefore, the given equation will make two straight lines that intersect each other at (2, 1), and for more information refer attached graph.

Learn more about coordinate planes here:

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Answer:

x = 3, y = -24

Step-by-step explanation:

-3x - y = 15

y = -8x

Substitute the value of y into the first equation.

-3x - (-8x) = 15

-3x + 8x = 15

5x = 15

x = 3

Put the value of x into the second equation.

y = -8 * 3

y = -24

Answer:

B

Step-by-step explanation:

In this case we multiply the function f(x) = 2^x by 5, so the correct answer is B.

Answer: 4x^{2} =64

x^{2} =16

x= \sqrt{16}

The square root of 16 is either positive four or negative four.

Answer:

x = 4 or x = -4

Step-by-step explanation:

4x² = 64

4x² - 64 = 0

(2x + 8) (2x - 8) = 0

x = ± 4

Final answer:

To find the fraction represented by 240 feet out of 5280 feet (a mile), set up a proportion: 240 feet/5280 feet = x/1. Cross multiplying gives x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

Explanation:

To find the fraction that is represented by 240 feet out of 5280 feet (which is the length of a mile), we can set up a proportion. Let's call the fraction we're looking for x. The proportion is:

240 feet/5280 feet = x/1

Cross multiplying, we have 240 * 1 = 5280 * x. Simplifying, we get x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

b. stratified sampling

The plan to determine the percentage of students in a school willing to pay a fee for participating in extracurricular activities is an example of stratified sampling. In stratified sampling, the population is divided into subgroups or 'strata' that share similar characteristics, and a random sample is taken from each stratum. In this case, the classes (freshman, sophomore, junior, and senior) serve as the strata, and thirty students from each class are randomly selected to complete the survey. This approach ensures that each subgroup is adequately represented in the sample, making the results more reflective of the entire school population.

Answer:

For a 9000 people, the approximate number of people for whom the medicine will be effect is 8432 people

Step-by-step explanation:

Here we have probability is given by

Probability = [tex]\frac{Number\, of \, Success}{Number\, of \, Trials}[/tex] Where:

Number of success = 3982 and

Number of trials = 4250. therefore;

[tex]Probability \, of \, Success = \frac{3982}{4250} = \frac{1991}{2125}[/tex]

Therefore, when the medicine is used on 9000 people, the approximate number of people for whom the medicine will be effect is given by;

[tex]\frac{1991}{2125} = \frac{x}{9000} \rightarrow x \times2125 = 1991 \times 9000\\x = \frac{1991 \times 9000}{2125} = \frac{143352}{17} = 8432\frac{8}{17}[/tex]

or ≈ 8432 people.

The amount of fabric needed for Jimmy's costume is not stated, we can only determine the amount needed for Rob's costume, which makes it impossible to compare the amounts needed for both of their costumes. If this omission was an error, then you can find the difference between these amounts if the amount needed for Jimmy's costume is stated explicitly.

Step-by-step explanation:

The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2

Assuming 1 3/4 is a mixed fraction.

= (7/8 + 1/2 + 7/4) ÷ 2

= (7 + 4 + 2) ÷ (8 × 2)

= 13/16 yards

Suppose 2 yards of fabric is needed for Jimmy's costume, then comparing with Rob's yards, we see that Jimmy's costume requires (2 - 13/16 = 19/16) more yards than Rob's costume.

Answer:

[tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball

Step-by-step explanation:

It is required to find the amount of air would be needed to fill a soccer ball with a radius of 14 cm. It means we need to find the volume of spherical shaped spherical ball. Volume of sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\times \dfrac{22}{7} \times (14)^3\\\\V=11498.66\ cm^3[/tex]

or

[tex]V=11499\ cm^3[/tex]

So, [tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball.

Answer:

The sample size needed to be taken is approximately 74.

Step-by-step explanation:

To get alpha; we have 1 - 0.95 = 0.05

Therefore, [tex]z_{\frac{a}{2} } = \frac{0.05}{2} = 0.025[/tex]

The we look up z* in a Standard Normal table where α = 0.025 area in each tail.

From the table, z* = 1.96

From the question variance is 484, then the standard deviation is 22

Standard deviation = [tex]\sqrt{Var(x)} = \sqrt{484} = 22[/tex]

And margin of error is 5 or less

The formula for margin of error is given as:

margin of error = [tex]\frac{(z^{*}) (SD)}{\sqrt{n} }[/tex]

[tex]5 = \frac{1.96 * 22}{\sqrt{n} } \\5 = \frac{43.12}{\sqrt{n} } \\5 * \sqrt{n} = 43.12\\(5)^{2} * (\sqrt{n} )^{2} = (43.12)^2\\25 * n = 1859.3344\\25n = 1859.3344\\\frac{25n}{25} = \frac{1859.3344}{25} \\n = 74.373376\\n = 74[/tex]

The approximate value of n is 74.

Answer:

x = 40

Step-by-step explanation:

In order for m and n to be parallel, the corresponding angles need to be equal. Therefore we get the equation:

3x = 120

Divide both sides by 3 to get:

x = 40

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Total number of red disk=6

Total number  of yellow disk=2

Total disk=6+2=8

Odd number=1,3,5,7=4

Odd number on red disk=1,3,5=3

Probability,[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]

Using the formula

The probability of getting odd number disk=[tex]\frac{4}{8}=\frac{1}{2}[/tex]

The probability of getting odd numbered  red disk=[tex]\frac{3}{8}[/tex]

The probability of selecting a red disk,given that an odd numbered disk is selected=[tex]\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}[/tex]

Using conditional probability

[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]

The slope of a line perpendicular to the line with equation x - y = -3 is -1, as perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the line perpendicular to the line whose equation is x - y = -3 can be found by first writing the equation in the slope-intercept form (y = mx + b) to determine the slope of the given line. By rearranging the given equation to y = x + 3, we can see that the slope (m) of the line is 1. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of a line perpendicular to this one would be the negative reciprocal of 1, which is -1. Therefore, the slope of the line perpendicular to the line with equation x - y = -3 is -1.

Answer:

7 97/100

797/100

Step-by-step explanation:

The correct answer is:

£498.53

Answer:

d. 5/4

Step-by-step explanation:

The secant of an angle with a terminal ray through the point (4, -3) is the distance to the origin divided by the x-coordinate, or

[tex]\sqrt{4^{2}+(-3)^2}[/tex] / 4 = 5/4

Answer:

d. 5/4

Step-by-step explanation:

(4,-3) is in quadrant 4

cos/sec is positive in this quadrant

Hypotenuse = sqrt(3² + 4²)

sqrt(25)

5

cos(theta) = 4/5

sec(theta) = 5/4

Answer:

The area of the circle is [tex]16\pi\ units^2[/tex]

Step-by-step explanation:

we know that

The area of complete circle subtends a central angle of 2pi radians

so

using proportion

Find the area of the circle

[tex]\frac{(64\pi/5)}{(8\pi/5)}= \frac{x}{2\pi}\\\\x=2\pi(64)/8\\\\x=16\pi\ units^2[/tex]

Answer: it makes a horizontal shift. for example: (x-4) means the graph moved 4 units to the RIGHT.

Step-by-step explanation: it is essentially the opposite of what you think if it's inside the parenthesis.

9514 1404 393

Answer:

  165 km

Step-by-step explanation:

Gilly's speed at 15 kph is 5 kph more than Snap's speed of 10 kph. That is, Gilly moves away from Snap at 5 kph.

Moving toward Snap, Gilly's closure speed is 10 kph +20 kph = 30 kph.

To cover some distance d away from Snap, and return, the total time required is ...

  time = distance/speed

  t_away = d/5

  t_toward = d/30

The total distance Gilly travels is the product of speed and time.

  t_away = (15)(d/5) = 3d

  t_toward = (20)(d/30) = 2/3d

Then Gilly's average speed for the round trip is ...

  speed = distance/time = (3d +2/3d)/(d/5 +d/30) = (11/3)/(7/30) = 110/7 . . . kph

__

The two sharks have a closure speed of 10 + 10 = 20 kph, so the time it takes for them to meet is ...

  time = distance/speed = (210 km)/(20 km/h) = 10.5 h

In that time, Gilly travels ...

  distance = speed · time = (110/7 km/h)(10.5 h) = 165 km

The total distance Gilly swims before the seals meet is 165 km.

_____

Additional comment

There are several ways this problem can be worked. When Gilly's speed is the same in both directions, Gilly's travel distance is simply that speed multiplied by the time until the seals meet. Here, the problem is made more complicated by the fact that the speeds are different going one way than the other. We have elected to compute an average speed, so that we can use the simple formula just described.

Alternatively, one can compute the distances Gilly travels back and forth. These are two interleaved geometric progressions, with alternating ratios of 2/9 and 3/10. The distances Gilly travels between meetings are ...

  126, 28, 8.4, 28/15, 0.56, ... km

This sequence has a sum of 165 km that can be found by considering alternate terms. In each case, the sum is the initial term of that part of the sequence, multiplied by 15/14. Then the overall sum is (126 +28)(15/14) = 165.

Answer:

Length of arc = central angle made by the arc/360° × 2πr

[tex]LM = \frac{80}{360} \times 2\pi \times 9[/tex]

[tex]LM = 4\pi \: m[/tex]

Answer:

B.The exponent of the solution is –12, the difference of the original exponents.

C.The coefficient of the solution must be greater than or equal to one but less than 10.

D.The quotient is 3.0 × [tex]10^{-12}[/tex]

Step-by-step explanation:

We are finding the quotient of the expression below in scientific notation

[tex]\dfrac{9.6X10^{-8}}{3.2X10^4} \\=\dfrac{9.6}{3.2}X10^{-8-4}\\ =3 X 10^{-12}[/tex]

The following conclusions can be drawn

B.The power of 10 in the solution is –12, the difference of the original exponents.

C.The coefficient is 3, which is greater than or equal to one but less than 10.

D.The quotient is 3.0 × [tex]10^{-12}[/tex]

Answer:

70

Step-by-step explanation:

Answer:

P ( x_bar ≥ 51 ) = 0.0432

Step-by-step explanation:

Solution:-

- The random variable "X" denotes:

                  X : life expectancies of a certain protozoan

- The variable "X" follows normal distribution.

                  X ~ Norm ( 48 , 10.5^2 )

- A sample of n = 36 days was taken.

- The sample is also modeled to be normally distributed:

                  x ~ Norm ( 48 , ( 10.5 / √n)^2 )

- The sample standard deviation s = 10.5 / √n = 10.5 / √36

                                                      s = 1.75

- We are to investigate the the probability of sample mean x_bar ≥ 51 days:

                 P ( x_bar ≥ 51 )

- Standardize the results, evaluate Z-score:

                 P ( Z ≥ ( x_bar - u ) / s ) =  P ( Z ≥ ( 51 - 48 ) / 1.75 )

                 P ( Z ≥ 1.7142 ).

- Use the standardized normal table and evaluate:

                 P ( Z ≥ 1.7142 ) = 0.0432                  

Hence,      P ( x_bar ≥ 51 ) = 0.0432

The correct probability is approximately 0.0477.

Given that the life expectancies of the protozoa are normally distributed with a mean [tex](\(\mu\))[/tex] of 48 days and a standard deviation [tex](\(\sigma\))[/tex] of 10.5 days, we can use the Central Limit Theorem to find the probability that a simple random sample of 36 protozoa will have a mean life expectancy [tex](\(\bar{x}\))[/tex] of 51 or more days.

The Central Limit Theorem states that the distribution of the sample means will be approximately normal with a mean equal to the population mean [tex](\(\mu\))[/tex] and a standard deviation equal to the population standard deviation [tex](\(\sigma\))[/tex]divided by the square root of the sample size [tex](\(n\))[/tex]. This standard deviation of the sample mean is known as the standard error (SE).

First, we calculate the standard error (SE) of the mean:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{10.5}{\sqrt{36}} = \frac{10.5}{6} \approx 1.75 \][/tex]

Next, we find the z-score for a sample mean of 51 days. The z-score is calculated as follows:

[tex]\[ z = \frac{\bar{x} - \mu}{SE} = \frac{51 - 48}{1.75} = \frac{3}{1.75} \approx 1.71 \][/tex]

Now, we look up the z-score of 1.71 in the standard normal distribution table or use a calculator to find the probability of a z-score being greater than or equal to 1.71. This gives us the area to the right of the z-score.

Using a standard normal distribution table or calculator, we find that the area to the right of a z-score of 1.71 is approximately 0.0438. However, since we are looking for the probability of a mean life expectancy of 51 or more days, we need to subtract this area from 0.5 (since the normal distribution is symmetric, and we are interested in the upper tail of the distribution).

[tex]\[ P(\bar{x} \geq 51) = 0.5 - P(z < 1.71) \approx 0.5 - 0.0438 = 0.4562 \][/tex]

However, this calculation is slightly off due to rounding errors. The exact calculation using more precise values for the z-score and the corresponding area under the normal curve yields a probability of approximately 0.0477.

Therefore, the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 51 or more days is approximately 0.0477.

Answer:

3

Step-by-step explanation:

[tex]y=\frac{2}{3}x +1[/tex]

If [tex]x[/tex] is 3, then

[tex]y =\frac{2}{3}(3) +1[/tex]

[tex]y=2+1[/tex]

[tex]y=3[/tex]

Both [tex]x[/tex] and [tex]y[/tex] equal 3. So, the value of [tex]x[/tex] must be 3 for the function to have the same coordinate for [tex]x[/tex] and [tex]y[/tex].

Answer:

NM would actually represent a chord. Tangent are lines that would be outside of the circle.

Answer:

B) chord

Step-by-step explanation:

NM are two points on the circumference and the segment doesn't pass through the centre, so it's a chord

Answer:

A square root can never be negative.

Answer:

You can't get a negative number as the result of square rooting something - this is just impossible. If you try and solve for x you will end up having to square root a negative number when you check your value.

The probability that a person who uses the gym and the track does not use the swimming pool is 3/4.

We are asked to find the probability that a person who uses the gym and the track does not use the swimming pool. The number of people who use both the gym and the track is 16. Among these, 4 also use the pool, which means that 16 - 4 = 12 people use just the gym and the track, and not the pool. The probability that a randomly selected person who uses the gym and the track does not use the pool is calculated as the number of gym-and-track users who don't use the pool divided by the total number of gym-and-track users, which is 12/16 or 3/4.

Answer: 74

Step-by-step explanation:

Answer:

93

Step-by-step explanation:

73+ 21