A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represents the length then the length can be found by solving the equation:
If x represents the length, then the length can be found by solving the equation: x(x-4)=140

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Explanation:

Here's our sample space

{1,2,3,4,5,6,7,8,9,10}

This is the set of all possible outcomes.

We see that {1,3,5,7,9} are odd. We have 5 odd numbers out of 10 total. The probability of getting an odd number is therefore 5/10 = 1/2. Let A = 1/2 as we'll use it later.

After we select the first card and put it back (or replace it with a copy), the stack of cards is the same as before we made that first selection. So the sample space hasn't changed. The set of values greater than 7 is {8,9,10}. We have 3 items in here out of 10 total. The probability of getting a value larger than 7 is 3/10. Let B = 3/10.

Multiply the values of A and B to get the answer

A*B = (1/2)*(3/10) = 3/20

This represents the probability of getting an odd number on the first selection, and a second card that is larger than 7. This only applies if a replacement is made on the first card. Otherwise, 3/10 would be different.

Answer:

Step-by-step explanation:

We can solve each inequality apart and then see the possible solution sets.

Consider the inequality 4x+8 < -16. If we divide by 4 on both sides, we get

x+2 < -4. If we substract 2 on both sides we get x<-6. So the solution set for this inequality is the set of real numbers that are less than -6 (lie to the left of the point -6).

Consider 4x+8>4. If we divide by 4 on both sides we get x+2>1. If we substract 2 on both sides we get x>-1. So the solution set for this inequality is the set of real numbers that are bigger than -1 (lie to the right of the point -1).

So, for us to have 4x+8<-16 or 4x+8>4 we must have that either x <-6 or x>-1. So the solution set for the set of inequalities is the union of both sets, that is

[tex](\-infty, -6) \cup (-1,\infty)[/tex]

Answer:

D. Y= -2x - 3

Step-by-step explanation:

The reason the answer is D is because it is the reverse form of standard. D shows that the form of slope-intercept for is y=mx + b.

Answer:

C. Y=X - 3

Step-by-step explanation:

[tex]2X - 2Y - 6 = 0\\\mathbf{y=mx+b}\:\mathrm{is\:the\:slope\:intercept\:form\:of\:a\:line\:where}\: \mathbf{m}\:\mathrm{is\:the\:slope\:and}\:\mathbf{b}\:\mathrm{is\:the}\:\mathbf{y}\:\mathrm{intercept}\\\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\Y=X-3[/tex]

Answer:

[tex] y = 15.621x +8.83[/tex]

We assume that y represent the number of pages predicted and x the number of chapters.

And we want to find the predicted value for a book of x =8 chapters. S replacing we got:

[tex] y = 15.621*8 + 8.83= 133.798[/tex]

And we can conclude that approximately we would have between 133 and 134 pages for a book of 8 chapters

Step-by-step explanation:

For this case we have the following model given:

[tex] y = 15.621x +8.83[/tex]

We assume that y represent the number of pages predicted and x the number of chapters.

And we want to find the predicted value for a book of x =8 chapters. S replacing we got:

[tex] y = 15.621*8 + 8.83= 133.798[/tex]

And we can conclude that approximately we would have between 133 and 134 pages for a book of 8 chapters

Answer:

.

Step-by-step explanation:

Answer:

-2.95

Step-by-step explanation:

Given the functions w=y^3-4x^2y where x=e^s and y=e^t, to get dw/ds, we will use the chain rule for composite functions as shown;

dw/ds = dw/dx*dx/ds + dw/dy*dy/ds

dw/dx = -8xy

dx/ds = e^s

dw/dy = 3y²-4x²

dy/ds = 0 (since there are no s variable in the function)

Substituting the differentials into the formula above;

dw/ds = -8xy(e^s) + 3y²-4x²(0)

dw/ds = -8xy(e^s)

Substituting s = -3 and t = 5 into the resulting function;

dw/ds = -8(e^s)(e^t)(e^s)

dw/ds = -8(e^2s)(e^t)

dw/ds =  -8(e^-6)(e^5)

dw/ds = -8*0.00248*148.413

dw/ds = -2.945 ≈ --2.95 (to 2 dp)

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

Answer:

Option (2)

Step-by-step explanation:

If a point having coordinates (x, y) is translated by 'h' units right and 'k' units down,

New coordinates of the point will be,

(x, y) → [(x + h), (y - k)]

Coordinates of the vertices of the given triangle ABC are,

A(-1, 0), B(-5, 0) and C(-1, 2)

If this triangle is shifted 5 units right and 2 units down then the coordinates of point B will be,

B(-5, 0) → B'[(-5 + 5), (0 -2)]

             → B'(0, -2)

Therefore, coordinates of vertex B' will be (0, -2).

Option (2) will be the answer.

Answer:

(0,-2) is Correct

Have a Blessed day!

Answer:

5 ≥ c

Step-by-step explanation:

-15≤-3c

Divide each side by -3, remembering to flip the inequality

-15/-3 ≤ -3c/-3

5 ≥ c

Answer:

c ≤ 5

Step-by-step explanation:

Since you have to divide both sides of the equation by a negative number, you have to flip the equality sign.

-15 ≤ -3c

(-15)/(-3) ≤ (-3c)/-3

5 ≥ c

c ≤ 5

Answer:

6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.

Step-by-step explanation:

Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.

Answer:

[tex] y = 3 [/tex]

Step-by-step explanation:

Given the above right angled triangle, we would use a trigonometric ratio formula to find y.

Given angle = 30°

Hypotenuse = 6

Opposite side = y

Solve for y using the trigonometric ratio formula as follows:

[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]

[tex] sin(30) = \frac{y}{6} [/tex]

Multiply both sides by 6

[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]

[tex] 0.5*6 = y [/tex]

[tex] 3 = y [/tex]

[tex] y = 3 [/tex]

Answer as a fraction = 1/5040

Answer in decimal form (approximate) = 0.000198

Answer in percentage form (approximate) = 0.0198%

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Explanation:

There is only one ordering of the letters to get DESIGN out of 5040 different permutations. The 5040 comes from the fact that 7*6*5*4*3*2*1 = 5040. In shorthand notation, use factorials to say 7! = 5040. Notice how we started with 7 and counted down until reaching 1, multiplying all along the way. You could use the nPr permutation formula to get the same result of 5040 (use n = 7 and r = 7).

So because we have 1 way to order the letters (getting DESIGN) out of 5040 ways total, this means the probability is the fraction 1/5040. Use your calculator to find that 1/5040 = 0.000198 approximately. Move the decimal over 2 spots to the right to convert 0.000198 to 0.0198%

Answer:

Yes, the confidence interval contradict this statement.

Step-by-step explanation:

The complete question is attached below.

The data provided is:

[tex]n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8[/tex]

Since the population standard deviations are not provided, we will use the t-confidence interval,

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

Compute the pooled standard deviation as follows:

[tex]s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723[/tex]

The critical value is:

[tex]t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962[/tex]

*Use a t-table.

The 95% confidence interval is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

     [tex]=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)[/tex]

The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).

To test the magazine's claim the hypothesis can be defined as follows:

H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}=0[/tex].

Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}\neq 0[/tex].

Decision rule:

If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the mean weights does not consists the value 0.

Thus, the null hypothesis will be rejected.

Conclusion:

There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.

Answer:

23/90

Step-by-step explanation:

23/90 balls are green or white

i hope this helps!

Answer:

A) it is not an experiment it is an observational study/analysis

B) i)Foods high in fats and sugar affects IQ  (ii)Foods that contain the required classes of food affects IQ positively

Step-by-step explanation:

A) An analysis carried out on 400 children using the data derived from the long term investigation can not be said to be an experiment but an observational analysis this is because the complete data has been provided already from the long term investigation already. hence it can only be observed

B ) i) foods high in fats and sugar affects The IQ of children later in life as seen from the results of the observational study that children whom had processed foods had a significant negative difference in IQ when compared with children who had health-conscious diets

ii) following health conscious diets early in childhood will have a positive effect on one's IQ later in life .

Answer:

500

Step-by-step explanation:

350/70%=500

Answer:

4! * 2!  = 48

Step-by-step explanation:

In general you have 6 elements so there are 6! = 6*5*4*3*2*1  lists in total, now, you have to think about the second condition, an odd integer has to appear before any even integer. Therefore odd integers go first, and since there are 4 odd integers, there are 4! possible lists, and  since there are two even integers there are 2! lists, so in total you have 4! * 2! lists

Answer:

Option A

Step-by-step explanation:

With the following data, H0:p=0.35 ; Ha:p>0.35 The p-value for this hypothesis test is 0.03. The level of significance is α=0.05.

Since the p value (0.03) is less than alpha (0.05), we will reject the null hypothesis and conclude that there is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.

Answer:

x=8 i got it right on my homework on khan academy

Step-by-step explanation:

Answer: Using logarithms to solve you will get x = 8

Answer:

Step-by-step explanation:

Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.

  Linda has $15

  Reuben has $25 . . . . . . $10 more than Linda

  Manuel has $30 . . . . . . twice what Linda has

Answer:

D

Step-by-step explanation:

Sam's weight to the nearest stone is equal to 8.0 stone.

Given the following data:

To determine Sam's weight to the nearest stone:

In this exercise, you're required to determine Sam's weight to the nearest stone. Thus, we would convert his weight in kilograms to pounds and lastly to stone as follows:

Conversion:

1 kg = 2.2 pounds.

51 kg = [tex]51 \times 2.2[/tex] = 112.2 pounds.

Next, we would convert the value in pounds to stone:

14 pounds = 1 stone.

112.2 pounds = X stone.

Cross-multiplying, we have:

[tex]14X = 112.2\\\\X=\frac{112.2}{14}[/tex]

X = 8.01 ≈ 8.0 stone.

Read more on weight here: brainly.com/question/13833323

Answer:

CIM

Step-by-step explanation:

C is the 3rd letter of the alphabet, A is the 1st, and B is the 2nd.

CAB = 3,1,2

Repeating for DEK:

DEK = 4,5,11

Comparing:

4−3 = 1

5−1 = 4

11−2 = 9

BED = 2,5,4, so adding the corresponding numbers:

2+1 = 3

5+4 = 9

4+9 = 13

So the code is CIM.

The code for BED is CIM. A further explanation is below.

As we know that,

then,

→ CIB = 3, 1, 2

Same as above,

→ DEK = 4, 5, 11

By comparing the values, we get

Same as above,

→ BED = 2, 5, 4

then,

Thus the above approach is appropriate.

Learn more:

https://brainly.com/question/18804431

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer:

Step-by-step explanation:

The null hypothesis is usually the default statement. The alternative is the opposite of the null and usually tested against the null hypothesis

In this case study,

The null hypothesis in would be that the mean time between clicks of the second hand on a particular clock is 1 second. In symbolic form it would be u = 1

The alternative hypothesis would be that the mean time between clicks of the second hand on a particular clock is 1 not second. In symbolic form, it would be: u =/ 1

Answer:

Let the number be x

The statement

A number is increased by five is written as

x + 5

Then it's squared

So we the final answer as

Hope this helps

Answer:

Y = 6*y

Step-by-step explanation:

We have Y = b * y by a factor of 6.

That is, b = 6.

now, to find what results only in a horizontal compression of y = b * y by a factor of 6.

By transformation rule, the function would be a horizontal compression f (a * x) if a> 1.

Therefore, knowing the above, the answer would be:

Y = 6 * y

Answer:

x = 3

y = -2

Step-by-step explanation:

Given:

8x - 3y = 30 ..................(1)

3x + y = 7 .......................(2)

Eliminate y by adding (1)+3*(2)

8x-3y + 3*( 3x+y) = 30 + 3*7

8x + 9x -3y + 3y = 51

17x = 51

x = 3  .....................(3)

substitute (3) in (2)

3(3) + y = 7

y = 7-9 = -2

y = -2 ....................(4)

Answer:

Step-by-step explanation:

[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]

Answer:

1360cm²

Step-by-step explanation:

Since the shape of the cake is in L shape, we can divide the cake in to rectangles..

The amount of space covered by the frosting = The sum of the areas of the sides that we can find in this L shaped cake diagram.

The sides of this cake, are shaped like a rectangle.

Hence, Area of a Rectangle = Length × Width

a) Side 1 = Rectangle on the left

Area of a Rectangle = Length × Breadth

Length = 30cm

Breadth =10cm

Area = 30 × 10 = 300cm²

Since we have another side with this measurement/ dimensions also,

Side 2 = 300cm²

Side 3 = The front face of the cube by the right

Area of a Rectangle = Length × Breadth

Length = 22cm - 10cm = 12cm

Breadth =10cm

Area = 12 × 10 = 120cm²

Likewise, we have the another side with the same dimensions as well

Hence, Side 4 = 120cm²

Side 5

30 × 5 = 150cm²

Side 6

10 × 5 = 50cm²

Side 7

20 × 5 = 100cm²

Side 8

22cm × 5 cm = 110cm²

Side 9

10cm × 5cm = 50cm²

Side 10

12cm × 5cm = 60cm²

The amount of space covered by the frosting = Area of Sides( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)

= (300 + 300 + 120 + 120 + 150 + 50 + 100 + 110 + 50 + 60) cm²

= 1360cm²

Answer:

The correct answer that corresponds with that graph is B: y ≤-3x+2.

Step-by-step explanation:

1) First we need to figure out what kind of symbol the line is, greater or less than equations (< , >) then the line are dotted,and if its greater than or equal to or less than or equal to equations ( ≤, ≥) since the line are solid.

2) Now we need to figure out which side should be shaded, if the symbol is a less than or a less than or equal to then the shaded side should be on the left, if the symbol is a greater than or a greater than or equal then the shaded side should be on the right.

In this case we have a solid line and a shaded left side which mean the symbol that been used here is a less than or equal to symbol ( ≤ ).

So our answer is B: y ≤-3x+2.

Remember:

- greater or less than equations (< , >) = dotted line

- greater than or equal to or less than or equal to equations ( ≤, ≥) = solid line

- less than or a less than or equal to = shaded left side

- greater than or greater than or equal to = shaded right side