Simplify the following expression:

2x − 6y + 3x2 + 7y − 14x

Answer:

5 millimetres

Step-by-step explanation:

Area of rectangle = lenght x width

35 = 7 x width

Width = 35/7

Width = 5 mm

The width of rectangle is 5 millimeters, whole length is 7 millimeters and area is 35 square millimeters.

A rectangle is a part of a quadrilateral, whose corresponding sides are parallel to each other and equal, and makes right angle to each others.

Given that,

The area of rectangle = 35 square millimeters.

Also,

The length of the rectangle l = 7 millimeters.

Let the width of the rectangle is x millimeters.

To find the width of rectangle,

Use formula,

Area of rectangle = 35

length × width = 35

7 × x = 35

x = 5 millimeters.

The required width of rectangle is 5 millimeters.

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Answer: 9.46 grams

Step-by-step explanation:

Given: Number of muffins made in one batch = 1 dozen =12 ]

[ as 1 dozen = 12]

Also, in one batch the quantity of sugar = [tex]\dfrac14[/tex] pound

As there are 454 grams of sugar in a pound.

So,  in one batch the quantity of sugar = [tex]\dfrac14\times454=113.5\ grams[/tex]

i.e. in 12 muffins , there is 113.5 grams of sugar.

Then, in one muffin the quantity of sugar = (113.5 grams) ÷ 12

≈9.46 grams

Hence, there are 9.46 grams of sugar in 1 muffin.

Answer:

£107,714  > £107,674

Step-by-step explanation:

Given

£107,714  and £107,674

Required

Determine the relationship between them using > or <

From the given parameters, we understand that

£107,714  is greater than £107,674

The keyword greater than is represented mathematically with  >

Hence:

£107,714  is greater than £107,674

becomes

£107,714  > £107,674

Answer:

(a) P-value = 0.044

(b) P-value = 0.0022

(c) P-value = 0.4402

(d) P-value = 0.022

Step-by-step explanation:

The complete question is: An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and t-test statistics. Also, determine if the null hypothesis would be rejected at α = 0.05.

a) HA : μ > μ0, n = 11, T = 1.91

b) HA : μ < μ0, n = 17, T = -3.45  

c) HA : μ [tex]\neq[/tex] μ0, n = 7, T = 0.83  

d) HA : μ > μ0, n = 28, T = 2.13

(a) We are given the right-tailed test with sample size (n) of 11 and the test statistics of 1.91.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 1.91)

                              = P([tex]t_1_0[/tex] > 1.91) = 0.044

Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(b) We are given the left-tailed test with sample size (n) of 17 and the test statistics of -3.45.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] < -3.45)

                              = P([tex]t_1_6[/tex] < -3.45) = 0.0022

Since the P-value of the test statistics is less than the level of significance as 0.0022 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(c) We are given the two-tailed test with sample size (n) of 7 and the test statistics of 0.83.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 0.83)

                              = P([tex]t_6[/tex] > 0.83) = 0.2201

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.2201 = 0.4402.

Since the P-value of the test statistics is less than the level of significance as 0.044 < 0.05, so we have sufficient evidence to reject our null hypothesis.

(d) We are given the right-tailed test with sample size (n) of 28 and the test statistics of 2.13.

Now, the P-value of the test statistics is given by;

                P-value = P([tex]t_n_-_1[/tex] > 2.13)

                              = P([tex]t_2_7[/tex] > 2.13) = 0.022

Since the P-value of the test statistics is less than the level of significance as 0.022 < 0.05, so we have sufficient evidence to reject our null hypothesis.

This question is incomplete, the complete question is;

The Millennium Falcon is chased by the Imperial Forces. The ship is moving at a speed of 0.525 c. Han Solo is shooting at the imperial fighters with his newly installed proton cannon purchased at the MSU Surplus Store for $20.00 plus 6.00% TAX. The cannon emits protons at a speed of 0.741 c with respect to the ship.

What is the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction?  0.911 ANS .

What is the velocity of the protons in the resting frame when the cannon is shot in the backward direction?

(Use positive sign for the forward direction, and negative for the backward direction.)

Answer:

A)

the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c

B)

the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.

The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)

Step-by-step explanation:

Given that;

speed of ship u = 0.525C

speed of proton emission v = 0.741C

Now When Cannon is shot in Forward Direction

Relativistic speed S is Calculated as;

S = (u+v) / ((1 + (uv))/c²)

we substitute (0.525 + 0.741 )C / ((1 + (0.525 × 0.741) C)/c²)

the C² cancel each other

so we have

S = 1.266 / 1.389925

S = 0.9108 ≈ 0.911c

Therefore the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c

When Cannon is shot in Backward  Direction

Relativistic speed S is Calculated as;

S = ( u – v ) / ( 1 – uv / c ²)

S =  (0.525 - 0.741) C / ((1 - (0.525 × 0.741) C)/c²)

the C² cancel each other

so S = -0.216 / 0.610975

S = -0.3535c

The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)

Therefore the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.

Answer:

see below

Step-by-step explanation:

14. We can represent 1 as √1 and 2 as √4 and because 1 < 3 < 4, we know that √3 is in between 1 and 2. However, 3 is closer to 4 than it is to 1 so √3 is about 2.

15. Again, 3 is √9 and 4 is √16. 9 < 10 < 16 so √10 is in between 3 and 4, however, since 10 is closer to 9 as it is to 16, we know that √10 is about 3.

16. -4 = -√16 and -5 = -√25, since 16 < 22 < 25, we know that -√22 is in between -4 and -5 but 22 is closer to 25 so the answer is -5.

17. -10 = -√100 and -11 = -√121 so -√120 is in between -10 and -11. Since 120 is closer to 121, the answer is -11.

Answer:

rotation of 270°

Step-by-step explanation:

Consider the coordinates of of preimage and image of ABC

A(1, 0 ) → A'*0, - 1 )

B(6, - 7 ) → B'(- 7, - 6 )

C(0, - 4 ) C'(- 4, 0 )

What we note is the x- coordinate of the image is the y- coordinate of the preimage and the y- coordinate of the image is the negative of the x- coordinate of the preimage, that is

(x, y ) → (y, - x )

This is equivalent to a counterclockwise rotation about the origin of 270°

Answer:

54

Step-by-step explanation:

4x+7=18

subtracting 7 from both side of the equation

4x+7- 7=18 - 7

4x = 11

to find value of x , we divide both side of the equation by 4

4x/4 = 11/4 = 2.75

x = 2.75

now we plug in the found value of x = 2.75 in place of x in equation 12x+21

12*2.75 + 21 = 33 + 21 = 54

Thus, answer is 54

Answer:

10x.

Step-by-step explanation:

It is given that,

JK = 3x

LM = 12x

JM = 25x

Let as consider the line as shown in the below figure.

From the figure it is clear that,

[tex]JK+KL+LM=JM[/tex]

[tex]3x+KL+12x=25x[/tex]

[tex]KL+15x=25x[/tex]

[tex]KL=25x-15x[/tex]

[tex]KL=10x[/tex]

Therefore, the length of KL is 10x.

Answer:

C) e²+(w-x)²=b²

Step-by-step explanation:

C) e²+(w-x)²=b²

B is the hypotenuse and takes the place of c in the Pythagorean Theorem.  The second answer (x²+e²=b²) is also true, but isn’t what the question is asking for.

Answer:

Histogram

Step-by-step explanation:

A histogram is a representation of approximate numerical data distribution. It was first introduced by Karl Pearson. Constructing a histogram, requires one to "bin" (or "bucket") the range of values, or say, divide the entire range of values into a series of Intervals, thereafter, count how many values fall into each interval. The bins well be specified as consecutive, and or non-overlapping intervals of a variable. The bins (intervals) is best left to be adjacent, and are often (but not required to be) of equal size.

An example of where a histogram would be used, is that of the distribution of grades on a school exam or the sizes of pumpkins, divided by size group, in a pumpkin festival.

Answer:

Bar graph

Step-by-step explanation:

It compares the data

Answer:  the known variable; the to-be-predicted variable

Step-by-step explanation:

In statistics, linear regression is a technique to model the relationship between two variables ( one independent and other dependent).

It requires some previous data to plot a best fit line.

It is used to predict the values for dependent variable for each independent variable.

Here, independent variable = known variable and dependent variable = is to be predicted

Hence, Linear regression describes the extent to which the known variable predicts the to-be-predicted variable.

4y-5x=20

. Just give numbers for x or y . Then, find the x value or y value from the equation.

Remember that y-axis is the vertical and x-axis is the horizontal line.

For example, just give x = 0 . 4y=20 y = will be 5 .

Now, write these on your graph.

As you see, 0 means orijin point , but if y=5 , use vertical line for writing 5.

Then, find the values while x=1 , x=2 ,and also x= -1 , x= -2 .

Finally, find the points from the connection of x and y points.

Then, combine all of connected points as a curve .

Answer: 2 = |x − 47|

Step-by-step explanation:The total weight of the container and the nuts is x ounces. The desired weight of the container and the nuts is (45 + 2), or 47 ounces. The absolute error allowed is 2 ounces.

absolute error = |actual weight − desired weight|

Substituting the values, the equation obtained is 2 = |x − 47|.

Answer:

yes

Step-by-step explanation:

20x10= 200 therefor its 10times as much

Answer:

941

Step-by-step explanation:

= 1, 2, 3...900 is the number of parents that are going to attend the ceremony.

we are given a random number of parents (0 1 2)

each of these random numbers have a probability of 1/3

so we multiply the numbers by their probability

E(X) = 0*1/3 + 1*1/3 +2*1/3

= 1

E(X²) = 0²*1/3 + 1²*1/3 + 2²*1/3

= 5/3

we calculate the variance

= E(X²)-[E(X)²

= 5/3 - 1²

= 2/3( got this by taking the lcm)

∑Xi with n = 900 will have  to be the number of parents attending this ceremony for all seniors

E|S| = 900 * 1

= 900

var |S| = 900*2/3

=600

we are usng normal distribution to solve this

μ = E(S) = 900

σ² = var(S) = 600

for a seating area wth 900 seats now we are to find the probability that all the parents present will have seats

s-μ/√σ

900 -900/√600

= 0

p(z≤0)

= 0.5

for a seating area wth 925 seats we are to fnd probability that all parents will be seated

= s-μ/√σ

= 925-900/√600

= p(z≤1.0208)

= 0.84623

going to the table of standard normal distribution we have

p(z≤1.644845)= 0.95

s-μ/σ≤1.644845 = 0.95

we cross multply

s-μ≤1.644845σ

we make s subject of the formula

s ≤ μ+1.644845σ = 0.95

we now μ = 900 and

σ = √600

900+1.644845*√600

=900 +40.388

=940.388

= 941

we have that the minimum number of seat requred for all parents n attendance to be seat is 941 at a probability of 0.95

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

1, 2, 3, .....900 is the number of parents that are going to attend the ceremony.

A random number of parents (0, 1, 2)

The probability is 1/3.

[tex]\rm E(X) = 0 * \dfrac{1}{3} + 1*\dfrac{1}{3}+2*\dfrac{1}{3} = 1\\\\\\E(X^2) = 0^2*\dfrac{1}{3}+1^2*\dfrac{1}{3}+2^2*\dfrac{1}{3}= \dfrac{5}{3}[/tex]

Then the variance will be

[tex]\rm Var = E(X^2) -[E(X)]^2\\\\Var = \dfrac{5}{3} -1 \\\\Var = \dfrac{2}{3}[/tex]

∑Xi with n = 900 will have to be the number of parents attending this ceremony for all seniors

[tex]\rm E \left| S \right| = 900* 1 \\\\E \left| S \right| = 900[/tex]

And

[tex]\rm Var \left| S \right| = 900 * \dfrac{2}{3} \\\\Var \left| S \right| = 600[/tex]

Then by the normal distribution, we have

[tex]\rm \mu = E(S) = 900\\\\\sigma ^2 = Var (S) = 600[/tex]

For a seating area with 900 seats then the probability of the parents present will have seats.

[tex]\rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{900-900}{\sqrt{600}}\\\\\\\rightarrow 0[/tex]

For a seating area with 925 seats then the probability of the parents present will have seats.

[tex]\rm \rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{925-900}{\sqrt{600}}\\\\\\\rightarrow P(z \leq 1.0208) \\\\\rightarrow 0.84623[/tex]

From the standard normal distribution table, we have

[tex]\rm p(z\leq 1.644845) = 0.95\\\\\dfrac{S-\mu}{\sqrt{\sigma }} \leq 1.644845= 0.95\\\\S \leq \mu + 1.644845 \sqrt{\sigma }= 0.95\\\\S=900 + 1.644845*\sqrt{600}\\\\S= 941[/tex]

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

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Answer:

15 = 9 + 5j

Step-by-step explanation:

When you want to make words become an equation, the word is usually means = and more usually means +.

In this case, we have 15 is 9 more than 5j.

We can rewrite this as 15 = 9 + 5j.

Answer:

9.2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 57 = x/6

6 tan 57 = x

9.239189783 = x

9.2 =x

Answer:

x = 9.2

Step-by-step explanation:

Step 1: Find out what primary trigonometry ratio is needed

The give us the adjacent and the angle.  We need to find the opposite value so we will use tangent

Step 2: Plug in information and solve

[tex]tan(57)=\frac{x}{6} \\x=6tan(57)\\x=9.239[/tex]

Therefore x= 9.2

Answer:

25

Step-by-step explanation:

50:2=25

75:3=25

100:4=25

125:5=25

The rate of change of the given data in the table will be 25.

The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time.

The formula for the rate of change is straightforward: it simply divides the current value of a stock or index by the value from a previous time period.

The rate of change will be calculated by using the following formula:-

rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )

The rate of change will be calculated as below:-

50:2=25

75:3=25

100:4=25

125:5=25

Therefore, the rate of change of the given data in the table will be 25.

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Answer:

A, B, and D

Step-by-step explanation:

Just took the test :)

Answer:

a b d edge

Step-by-step explanation:

1: Add 60 and 15.

2: Divide by 3.

3: Subtract 2.

Answer:

w ≥ 14

Step-by-step explanation:

Step 1: Solve

11 ≤ w - 3

11 + 3 ≤ w

14 ≤ w

Therefore w is bigger or equal to 14

Answer:

Step-by-step explanation:

[tex]11 \leqslant w - 3 \\ 11 + 3 \leqslant w \\ 14 \leqslant w[/tex]

Step 1 : Collect like terms and simplify

Answer =

w≤14

Answer:

3/4, 0.78, 0.8

Step-by-step explanation:

3/4= 0.75.

0.78 is greater and 0.8 is greater again.

Answer:  see image below

Step-by-step explanation:

Draw a line and label it L

Plot three points on the line and label them, M, N, and Q.

I am using o to represent each point.

<---------o-------------o---------------o-----------> L

           M              N                 Q

Just write it in the order it first was in for instance. Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in. Like that.

Answer:

Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in.

When we transform the big quantity to the small one, we always have to multiply something. So micro refers x 10 to the power of 6

55 x 10^6 = 55,000,000 microliters.

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, the correct question is:

If B is between A and C, and AB=3x+1, BC=2x-7, and AC=24, then find the value of x and the value of AB

Answer: The line segment addition postulate states that if a point B is placed between a line segment with end points A and C, then the distance between the points can be expressed by the equation:

AB + BC = AC

But AB=3x+1, BC=2x-7, and AC=24, Hence:

3x + 1 + 2x - 7 = 24

3x + 2x + 1 - 7 = 24

5x - 6 = 24

5x = 24 + 6

5x = 30

x = 6

AB = 3x + 1 = 3(6) + 1 = 18 + 1 = 19

BC = 2x - 7 = 2(6) - 7 = 12 - 7 = 5

Answer:

the answers are below

Step-by-step explanation:

1. the populaton of ths study are the college students that are beng tested on the effect of alcohol on their emotions. college students are the main focus of this experiment.

2. The sample for this study is the 120 students from the University. the sample of a study is actually the number of participants in that study. this queston says that they are 120

3. the null hyothesis:

 h₀ : alcohol has no effect on college students emotions

4. the alternate hypothesis:

 h₁: there is effect of alcohol on college students emotions

5. The researcher would have to use a t test which is an inferential statistical test. A t test is used to test for the existence of statistical difference between two means that may have similar features

By the chain rule,

[tex]\dfrac{\partial w}{\partial r}=\dfrac{\partial w}{\partial x}\dfrac{\partial x}{\partial r}+\dfrac{\partial w}{\partial y}\dfrac{\partial y}{\partial r}+\dfrac{\partial w}{\partial z}\dfrac{\partial z}{\partial r}[/tex]

and similarly, [tex]\frac{\partial w}{\partial\theta}[/tex] is the same with [tex]r[/tex] replaced with [tex]\theta[/tex].

We have

[tex]\dfrac{\partial w}{\partial x}=y+z[/tex]

[tex]\dfrac{\partial w}{\partial y}=x+z[/tex]

[tex]\dfrac{\partial w}{\partial z}=x+y[/tex]

[tex]\dfrac{\partial x}{\partial r}=\cos\theta[/tex]

[tex]\dfrac{\partial y}{\partial r}=\sin\theta[/tex]

[tex]\dfrac{\partial z}{\partial r}=\theta[/tex]

Putting everything together, we get

[tex]\dfrac{\partial w}{\partial r}=(y+z)\cos\theta+(x+z)\sin\theta+(x+y)\theta[/tex]

Replace [tex]x,y,z[/tex] with their equivalent expressions in terms of [tex]r,\theta[/tex]:

[tex]\dfrac{\partial w}{\partial r}=r(\sin\theta+\theta)\cos\theta+r(\cos\theta+\theta)\sin\theta+r(\cos\theta+\sin\theta)\theta[/tex]

[tex]\dfrac{\partial w}{\partial r}=2r\theta\sin\theta+2r\theta\cos\theta+r\sin(2\theta)[/tex]

When [tex]r=4[/tex] and [tex]\theta=\frac\pi2[/tex], the derivative has a value of

[tex]\dfrac{\partial w}{\partial r}\left(4,\dfrac\pi2\right)=\boxed{4\pi}[/tex]

The same process will yield

[tex]\dfrac{\partial w}{\partial\theta}\left(4,\dfrac\pi2\right)=\boxed{-8\pi}[/tex]

The value of partial derivative are,

                    [tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex]     and  [tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]

It is given that,

                  [tex]w = xy + yz + zx, x = r cos(\theta), y = r sin(\theta), z = r\theta[/tex]

We have to find partial derivative.

            [tex]\frac{\partial w }{\partial r}=\frac{\partial w }{\partial x}*\frac{\partial x }{\partial r}+\frac{\partial w }{\partial y}*\frac{\partial y }{\partial r}+\frac{\partial w }{\partial z}*\frac{\partial z }{\partial z}\\\\\frac{\partial w }{\partial r}=(y+z)cos\theta+(x+z)sin\theta+(x+y)\theta\\\\\frac{\partial w }{\partial r}=2r\thetasin\theta+2r\thetacos\theta+rsin(2\theta)[/tex]

When [tex]r=4,\theta=\frac{\pi}{2}[/tex]

      [tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex]

Similarly,

      [tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]

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