factorise completely:
1. 3xy - x
2. 4a² - 9​

Answer:

The number of gallons in the tank after one hour.

Step-by-step explanation:

g=6.5-0.4(1)=6.1

Answer:

Integers are 48, 49, 50

Step-by-step explanation:

x+(x+1)+(x+2) = 147

3x + 3 = 147

3x = 147-3

x = 144 / 3 = 48

Answer:

86 / 6 = 14.33

14.33 * 4 = 57.33

(round to 58)

The integer that can be  inserted on the blank line in the list is: -2

The number line is given as:

-15, -3, ____, -1.5, 2, 3, 5

Now, a number line is defined as a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

In this case, we see that the interval of the number line is from -15 to 5.

Thus, the range of values for the blank space will fall in between those two numbers.

Now, since we have positive 2 on the number line, then we must likely also have the negative one to balance it as the blank number.

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Answer:

3.70 < 3.702 < 3 10/11 < 79/20

Step-by-step explanation:

Answer:

4 in.

Step-by-step explanation:

The surface area of a cube is the area of one of the faces times 6 for each face.

96/6=16

16 is the area of one face of the cube.

The side of the face is the square root of the area of the face.

√16=4

Answer:

4in

Step-by-step explanation:

I had the same problem but revirsed

Answer:

m = 3+y/y-4

Step-by-step explanation:

Answer:

im sorry this makes absolutely no sense

Step-by-step explanation:

To evaluate the probabilities of type I and type II errors in this scenario, we need to use the binomial distribution and consider the given hypotheses.

a) Type I Error:In this case, the null hypothesis is that the new stain remover product removes no more than 70% of stains, which means p = 0.7. If we reject the null hypothesis when it is actually true, it would be a type I error. We are testing if fewer than 11 out of 12 stains are removed. The probability of making a type I error can be calculated by summing up the probabilities of observing 0 to 10 successful outcomes (spots removed) in 12 trials, given a success probability of p = 0.7. Using a binomial distribution:P(Type I Error) = P(X ≤ 10), where X follows a binomial distribution with n = 12 and p = 0.7. Calculating this probability depends on the specific software or calculator used. However, you can use binomial probability tables, Excel, or statistical software to find the cumulative probability for X ≤ 10 with n = 12 and p = 0.7. This cumulative probability represents the probability of observing 10 or fewer successful outcomes (spots removed) in 12 trials. Subtracting this value from 1 will give you the probability of making a type I error.b) Type II Error:

In this case, the alternative hypothesis is that the new stain remover product removes more than 70% of stains, meaning p = 0.9. If we fail to reject the null hypothesis (claiming p ≤ 0.7) when the alternative hypothesis is true (p > 0.7), it would be a type II error.We want to calculate the probability of committing a type II error when p = 0.9. This probability is given by: P(Type II Error) = P(X ≥ 11), where X follows a binomial distribution with n = 12 and p = 0.9. Similar to the previous case, you can calculate this probability using binomial probability tables, Excel, or statistical software. The cumulative probability for X ≥ 11 represents the probability of observing 11 or more successful outcomes (spots removed) in 12 trials when p = 0.9.

Please note that the exact calculations depend on the specific software or calculator you are using, but the general approach is as described above.

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Step-by-step explanation:

1/3*12=1/4

1/4=1/4

=1/4÷1/4

=0 answer

Answer:

  x = 5

Step-by-step explanation:

It can help a lot to draw a diagram, if one is not provided. There is no requirement that it be drawn to scale. It just needs to be able to show the given information.

Given angle QRS is exterior to the triangle. Its measure is the sum of the two given remote interior angles:

  8x -9 = (3x -11) +(3x +12)

  2x = 10 . . . . . . . add 9-6x and simplify

  x = 5 . . . . . . divide by 2

|x-3|+|x+2|-|x-5| can be broken down into three separate cases based on the value of x:

(x-3) + (x+2) - (x-5) = 2x + 4

(x-3) + (x+2) - (5-x) = 2x - 6

-(x-3) - (x+2) - (5-x) = -3x - 4

We break down the expression into three separate cases based on the value of x. This is because the absolute value function creates "turning points" at which the behavior of the expression changes. We analyze the expression for each case and simplify it to obtain the final answer. The answer depends on the value of x, and we must consider the expression separately for each case.

If x ≥ 5, then the expression becomes:

(x-3) + (x+2) - (x-5) = 2x + 4

If -2 ≤ x < 3, then the expression becomes:

(x-3) + (x+2) - (5-x) = 2x - 6

If x < -2, then the expression becomes:

-(x-3) - (x+2) - (5-x) = -3x - 4

Therefore, the final answer depends on the value of x. If x is greater than or equal to 5, then the answer is 2x + 4. If x is between -2 and 3, then the answer is 2x - 6. And if x is less than -2, then the answer is -3x - 4.

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a) The probability that an apple from the tree has a weight greater than 90 grams is of: 0.2514 = 25.14%.

b) i) The p-value of the test is of: 0.0045.

b) ii) The conclusion of the test is given as follows: There is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B, as the p-value of the test is less than the significance level.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation of the weight of the apples are given as follows:

\(\mu = 85, \sigma = 7.5\)

The probability that an apple from the tree has a weight greater than 90 grams is one subtracted by the p-value of Z when X = 90, hence:

Z = (90 - 85)/7.5

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514 = 25.14%.

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = 4.2/1.61 = 2.61.

Using the z-table, with z = 2.61, the p-value is of:

0.0045.

As the p-value is less than the significance level, there is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B.

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To minimize the cost of the fence, we need to find the dimensions of the rectangular field that will result in the smallest perimeter. Let's assume the length of the rectangle is x feet.

Since we want to divide the field in half with a fence parallel to one of the sides, the width of the rectangle will also be x feet.

The area of the rectangular field is given as 37.5 million square feet, so we have the equation x * x = 37.5 million.

Simplifying, we find x² = 37.5 million.

To minimize the cost, we need to minimize the perimeter of the rectangular field. The perimeter is given by P = 2x + 2x = 4x.

Using the equation x² = 37.5 million, we can solve for x by taking the square root of both sides. This gives us x = √(37.5 million).

Substituting this value of x into the perimeter equation, we get P = 4 * √(37.5 million).

Therefore, the lengths of the sides of the rectangular field that will minimize the cost of the fence are √(37.5 million) feet and √(37.5 million) feet.

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The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

$8190

Step-by-step explanation:

So we know that were putting away $2 each month from  our allowance.

Jan-$2

Feb-$4

March-$8

April-$16

Ok so we already put away 4 months of our allowance from 12. So we need 8 more months to count how much.

So lets add: 2 + 4 + 8 + 16=30

Now we need to figure out how much in May and so on.

May- 16x2=32

June-32x2=64

July-64x2=128

August-128 x 2=256

September-256 x 2=512

October-512 x 2=1024

November-1024 x 2=2048

December-2048 x 2=4096

In total to add:

2 + 4 + 8 + 16 + 32 +64 + 128 + 256 + 512 + 1024 + 2048 + 4096 = 8190

Hope this helps :)

Answer:

Step-by-step explanation:

Perimerter is 9.6ft

Answer:

d=69, e=32, f=79

Step-by-step explanation:

e=32

d=69

f=180-69-32=79

The measure of each of the missing angles include the following:

d = 69.

e = 32.

f = 79.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following:

m∠e = 32°

m∠d = 69°

From the linear postulate theorem, we have:

m∠e + m∠d + m∠f = 180°

32° + 69° + m∠f = 180°

m∠f = 180° - (32° + 69°)

m∠f = 79°

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Answer:

op 1

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

16x5=80

80/4=20

Answer:

2 degrees celsius

The final temperature in Ottawa is 2°C.

We have,

Given:

Initial temperature = -4°C

Temperature rise = 14°C

Temperature fall = -8°C

The formula to calculate the final temperature.

Final temperature = Initial temperature + Temperature rise + Temperature fall

Final temperature = -4°C + 14°C + (-8°C)

Simplify

Final temperature = -4°C + 14°C - 8°C

Final temperature = 2°C

Therefore,

The final temperature in Ottawa is 2°C.

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Answer: \((6\sqrt{5})i\)

This is the same as saying \(6i\sqrt{5}\)

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

Work Shown:

\(\sqrt{-180} = \sqrt{-1*36*5}\\\\\sqrt{-180} = \sqrt{-1}*\sqrt{36}*\sqrt{5}\\\\\sqrt{-180} = i*6*\sqrt{5}\\\\\sqrt{-180} = 6i\sqrt{5}\\\\\sqrt{-180} = (6\sqrt{5})i\\\\\)

where \(i = \sqrt{-1}\)

As the steps show above, the idea is to factor the radicand into smaller pieces where one of those pieces is the largest perfect square possible. In this case, 36 is the largest factor of 180 that's a perfect square. Then I used the rule \(\sqrt{A*B} = \sqrt{A}*\sqrt{B}\) to break up the root.

The parenthesis used at the very end is to help separate the \(6\sqrt{5}\) from the \(i\) term. The "i" is not under the square root.

Answer:

13

Step-by-step explanation:

Substitute the variables given

w=7 &x=2

3(7)-4(2)

21-8

=13

Answer:

\(13\)

Step-by-step explanation:

\(w = 7 \: \: \: \: \: \: x = 2 \\ 3w - 4x \\ 3 \times 7 - 4 \times2 \\ 21 - 8 \\ =1 3\)

(1) Marginal PDFs, fX(x) and fY(y):

To find the marginal PDF fX(x), we integrate the joint PDF f(x, y) over the range of y, from 0 to infinity:

fX(x) = ∫[0,∞] f(x, y) dy

      = ∫[0,∞] (1/2)(x+y)e^(-(x+y)) dy

Applying the integral, we get:

fX(x) = (1/2)x ∫[0,∞] e^(-x-y) dy + ∫[0,∞] ye^(-x-y) dy

Using the integral properties, we can simplify it as follows:

fX(x) = (1/2)x * e^(-x) + 1

Similarly, to find the marginal PDF fY(y), we integrate the joint PDF f(x, y) over the range of x, from 0 to infinity:

fY(y) = ∫[0,∞] f(x, y) dx

      = ∫[0,∞] (1/2)(x+y)e^(-(x+y)) dx

Simplifying the integral, we obtain:

fY(y) = (1/2)y * e^(-y) + 1

(2) Independence of X and Y:

To determine if X and Y are independent, we need to check if the joint PDF can be expressed as the product of the marginal PDFs:

f(x, y) = fX(x) * fY(y)

Substituting the derived expressions for fX(x) and fY(y), we have:

(1/2)(x+y)e^(-(x+y)) ≠ [(1/2)x * e^(-x) + 1] * [(1/2)y * e^(-y) + 1]

Since the joint PDF cannot be expressed as the product of the marginal PDFs, X and Y are not independent random variables.

(3) Density function of Z = X + Y:

To find the density function of Z, we need to consider the probability distribution of the sum of two random variables. We can obtain it by convolving the marginal PDFs:

fZ(z) = ∫[-∞,∞] fX(x) * fY(z - x) dx

Substituting the expressions for fX(x) and fY(z - x) obtained earlier, we have:

fZ(z) = ∫[0,z] [(1/2)x * e^(-x) + 1] * [(1/2)(z - x) * e^(-(z - x)) + 1] dx

By evaluating the integral, we can obtain the density function of Z.

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Answer:

1)40

17+23-->20+20=40

2)80

42+37=40+40=80

3)80

9+73=10+70=80

4)90

68+21=70+20=90

5)90

12+81=10+80=90

The variable which the scientist willfully modifies is referred to as the independent variable. Every variable observed throughout the experiment seems to be the dependent variable.

A symbol (often a letter) used in mathematics to represent an unknowable quantitative score in such an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed.

Examples of variables include age, gender, company revenue and costs, the country of birth, expenditures, class grades, eye color, and vehicle kind. Because the amount may differ between data units within a population and may change over time, it is referred to as a variable.

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The chord of the sphere is represented by OT.

The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.

So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.

Hence, the chord of the sphere is represented by OT.

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The correct option is (a). The man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.

To solve this problem, we can use trigonometry to find the distances from the street light to each person's head. Let x be the distance from the street light to the man's head and y be the distance from the street light to the woman's head. Then, we can set up two equations using the tangent function:

tan(42) = x / d and tan(50) = y / d

where d is the distance between the two people (60 ft). Solving for x and y, we get:

x = d * tan(42) = 78.3 ft

y = d * tan(50) = 89.6 ft

Therefore, the man’s head is 78.3 ft away from the street light and the woman’s head is 89.6 ft away from the street light.

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