What is the equation of the following line written in slope-intercept form?
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Answer:

56% shaded

Step-by-step explanation:

if there are 100 boxes, then every box it 1%

5 rows (50%) + 6 extra boxes (6%) = 56%

The symbol [tex]\ge[/tex] can be thought of a greater than sign over top an equal sign, like this [tex]\stackrel{>}{=}[/tex] though the second horizontal line is erased to keep things relatively more simple (in terms of having to write it out).

Answer:

m^4+(1/m^4)= 123.4641 or 118.6

Step-by-step explanation:

m-(1/m)=3

m² - 1= 3m

m² -3m -1= 0

m = (3-√13)/2 = -0.3

Or

m =( 3+√13)/2= 3.3

m^4+(1/m^4) for m = -0.3

= (-0.3)^4 + (1/(0.3)^4)

= 0.0081 + 123.456

= 123.4641

m^4+(1/m^4) for m = 3.3

= (3.3)^4 + (1/(3.3)^4)

= 118.5921 + 0.008432

= 118.6

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

Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

--------------------------

Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

Together they can mow the lawn in 24 minutes.

Time and efficiency are inversely proportional to each other.

Time and work are directly proportional to each other.

Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.

Assuming total work to be 120 as it is the LCM of 40 and 60.

So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is

(120/40) = 3.

Now together their efficiency is (2 + 3) = 5.

∴ Together they can complete the work in (120/5) = 24 minutes.

learn more about time and work here :

https://brainly.com/question/3854047

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Hey there! :)

Answer:

Choice C: x + 8 = 3x.

Step-by-step explanation:

Solve this question by simplifying each answer choice:

a) 4x = 20

Divide both sides by 4:

4x/4 = 20/4

x = 5. This is incorrect.

b) x/2 = 8

Multiply both sides by 2:

x = 16. This is incorrect.

c) x + 8 = 3x

Subtract x from both sides:

8 = 2x

Divide 2 from both sides:

x = 4. This is correct.

d) x = x+5 /2

Multiply both sides by 2:

2x = x + 5

Subtract x from both sides:

x = 5. This is incorrect.

Therefore, choice C is the correct answer.

Answer:

C . x+8=3x

Step-by-step explanation:

[tex]x +8 = 3x\\Collect-like-terms\\8=3x-x\\8=2x\\\frac{2x}{2} =\frac{8}{2} \\x =4[/tex]

Answer:

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Step-by-step explanation:

Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(50,5)[/tex]  

Where [tex]\mu=50[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Answer:

16x^2 + 8x.

Step-by-step explanation:

To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.

The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.

The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.

So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.

If you want, you can factor that and make it 8x(2x + 1).

Hope this helps!

Answer:

1). sinB × tanC = [tex]\frac{c}{a}[/tex]

2).  sinC × tanB = [tex]\frac{b}{a}[/tex]

Step-by-step explanation:

From the figure attached,

A right triangle has been given with m∠A = 90°, m(AC) = b, m(AB) = c and m(BC) = a

SinB  = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{\text{AC}}{\text{BC}}[/tex]

         = [tex]\frac{b}{a}[/tex]

tanB = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

        = [tex]\frac{\text{AC}}{\text{AB}}[/tex]

        = [tex]\frac{b}{c}[/tex]

SinC = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

        = [tex]\frac{\text{AB}}{\text{BC}}[/tex]

        = [tex]\frac{c}{a}[/tex]

tanC = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

        = [tex]\frac{c}{b}[/tex]

Now sinB × tanC = [tex]\frac{b}{a}\times \frac{c}{b}[/tex]

                            = [tex]\frac{c}{a}[/tex]

And sinC × tanB = [tex]\frac{c}{a}\times \frac{b}{c}[/tex]

                           = [tex]\frac{b}{a}[/tex]

Answer:

7+c or 6

Step-by-step explanation:

Answer:

-89+c

Step-by-step explanation:

I'm assuming

"(7-6)(-1)

-7 +0

-7-

7-6

7+ c"

Is the whole equation.

(7-6)(-1) -7+0 -7- 7-6 7+c=

(1)(-1)-7+0-7-7-67+c=

-1-7+0-7-7-67+c=

-8+0-7-7-67+c=

-8-7-7-67+c=

-15-7-67+c=

-22-67+c=

-89+c

Answer:

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 100, p = 0.42[/tex]

92% confidence level

So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.3336[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.5064[/tex]

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Answer:

The 97% upper confidence limit for the proportion of green items is 0.502.

Step-by-step explanation:

We have to calculate a 97% upper confidence limit for the proportion.

The sample proportion is p=0.294.

[tex]p=X/n=5/17=0.294\\[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.294*0.706}{17}}\\\\\\ \sigma_p=\sqrt{0.01221}=0.11[/tex]

The critical z-value for a 97% upper confidence limit is z=1.881.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208[/tex]

Then, the upper bound is:

[tex]UL=p+z \cdot \sigma_p = 0.294+0.208=0.502[/tex]

The 97% upper confidence limit for the proportion of green items is 0.502.

Answer:

1) 2/9

2)3/9

Step-by-step explanation:

sorry,thats what i know so far

Answer:

-189

Step-by-step explanation:

(63) -3

Calculate the product

-3(63)

Multiply both numbers

-3 × 63

= -189

Answer:

Lower Quartile: 62

Upper Quartile: 81

Interquartile Range: 19

Step-by-step explanation:

To find the lower quartile, you want to find the median from the minimum to the median.

49, 55, 62, 64, 67

The median of this is 62. Therefore, 62 is the lower quartile.

To find the upper quartile, you want to find the median from the median to the maximum.

76, 79, 81, 82, 83

The median of this is 81. Therefore, 81 is the upper quartile.

To find the interquartile range, you subtract the upper and lower quartile.

81-62=19

The difference is 19. Therefore, the interquartile range is 19.

Answer:

A

Step-by-step explanation:

9-2x≤3x+24

-15≤5x

-3≤x

so it's:

[-3,∞)

Answer:

The equation is:

[tex]L=3\,\,d^2\\[/tex]

and a beam with 10 in diagonal will support 300 lb

Step-by-step explanation:

The mathematical expression that represents the statement:

"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "

can be written as:

[tex]L=k\,\,d^2[/tex]

where k is the constant of proportionality

To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":

[tex]L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}[/tex]

Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:

[tex]L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb[/tex]

Answer:

L=3d^2 the beam will support 300 pounds

Step-by-step explanation:

108=k x 6^2

Dividing by 6^2=36 gives k=3, so an equation that relates L and d is

L=3d^2 d=10 yields

3(10)^2=300

So a beam with a 10in diagonal will support a 300lb load.

Answer:

Pr(Three 2's) = 1/27

Step-by-step explanation:

Let's assume the die is a fair die, on the first roll of the die, the child has a 1/6 chance of getting any number, including 6.

Second roll, the child has a 1/36 chance of getting any two numbers, including two 6's.

And on the third roll, the child has a 1/36×1/6=1/216 chance of getting any three numbers, including three 6's. And this is due to the fact that the rolls are independent, so the total possible outcomes multiply each roll with each roll's probability. Since each roll's probability is 1/6.

The probability of the child rolling no more than three twos will be =2/6×2/6×2/6

=1/3×1/3×1/3

=1/27

Therefore, the chances of three twos will be 1/27

Answer:

81

Step-by-step explanation:

Let's do this systematically:

Four numbers: a, b, c, d

Whose mean is 85: [tex]\frac{a + b + c + d}{4} = 85[/tex]

Whose largest number is 97: [tex]\frac{a + b + c + 97}{4} = 85[/tex]

Lets solve for the other numbers:

a+b+c+97 = 85*4 = 340

340 - 97 = 243

a+b+c = 243

at this point it doesn't matter what the numbers are, they just need to add up to 243.

We can do 243÷3=81, which is our answer

Answer: k = 4, k = -4 and k = 0.

Step-by-step explanation:

If we have y = sin(kt)

then:

y' = k*cos(kt)

y'' = -k^2*son(x).

then, if we have the relation:

y'' - y = 0

we can replace it by the things we derivated previously and get:

-k^2*sin(kt) + 16*sin(kt) = 0

we can divide by sin in both sides (for t ≠0 and k ≠0 because we can not divide by zero)

-k^2 + 16 = 0

the solutions are k = 4 and k = -4.

Now, we have another solution, but it is a trivial one that actually does not give any information, but for the diff equation:

-k^2*sin(kt) + 16*sin(kt) = 0

if we take k = 0, we have:

-0 + 0 = 0.

So the solutions are k = 4, k = -4 and k = 0.

Answer:

40 /9 or also can be written as 4 4/9

Step-by-step explanation:

hope this helps

Answer:

x is 64 and y is 16 but if you can't comprehend thats 64/16 = 4

Step-by-step explanation:the power is the number multiplied by it self so 8 to the power if 2 is 8 x 8 and 2 to the power of four is 2 x 2 x 2 x 2= 16

Hey there! :)

Answer:

To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:

X                   Y

-2                  4

-1                    1

0                   -2

1                     -5

2                    -8

Use these points to graph the line (Graphed below)

Answer:

To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

Step-by-step explanation:

We are given the following information:

The sample size is

[tex]n = 235[/tex]

The mean weight is

[tex]\bar{x}= 33.7 \: hg[/tex]

The standard deviation is

[tex]s = 7.3 \: hg[/tex]

Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.

The correct option is (b)

The critical value corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

What is Normal Distribution?

A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

Answer:

[tex]\overrightarrow{AB}=\frac{-9}{-4}[/tex]

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Step-by-step explanation:

A vector quantity is represented by [tex](\frac{y}{x})[/tex]

where y = y-coordinate and x = x-coordinate

Since vector AB represents a vector in 3rd quadrant,

It starts from point A and ends at B,

Therefore, coordinates of B are (-9, -4)

[tex]\overrightarrow{AB}[/tex] = [tex](\frac{-9}{-4})[/tex]

Similarly vector CD starts with C and ends at D in the 2nd quadrant,

Therefore coordinates of D will be (-5, 4)

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Answer:

P(X < 80) = 0.89435.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 60, \sigma = 16[/tex]

P(X < 80)

This is the pvalue of Z when X = 80. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 60}{16}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.89435.

So

P(X < 80) = 0.89435.

Answer:

The breadth is 16m because a square is a quadrilateral (four sided shape) that has all its side to be of equal measure.

Answer:

Correct option: C.

Step-by-step explanation:

(Assuming the correct function is R(x) = 2x^2 + 3x + 5)

To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:

[tex]R(x) = 2x^2 + 3x + 5[/tex]

[tex]19 = 2x^2 + 3x + 5[/tex]

[tex]2x^2 + 3x -14 = 0[/tex]

Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:

[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]

So looking at the options, the input to the function is x = 2

Correct option: C.

Answer:

Step-by-step explanation:

No, it is not an even function.  The graph is not symmetric about the y-axis.

Answer:

Step-by-step explanation: