a coin is altered so that the probability that it lands on heads is less than 1 2 12 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1 6 16. what is the probability that the coin lands on heads?

The rate at which length of shadow of person changing is 3 ft /sec.

H = Height of streetlight; 16 ft

h = Height of man; 6 ft

x = Length of man's shadow.

s = Distance from streetlight to man.

Using the similarities of the triangles.

H/h = (s + x)/x

Hx = h(s + x)

Differentiate with respect to 't' on both sides.

H(dx/dt) = h(ds/dt + dx/dt)

Put the values.

16(dx/dt) = 6(5 + dx/dt)

16(dx/dt) = 30 + 5dx/dt

10dx/dt = 30

dx/dt = 3 ft /sec

Thus, the rate at which length of shadow of person changing is 3 ft /sec.

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Answer:

  -4.697 in/s

Step-by-step explanation:

You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.

The volume of a cone is given by ...

  V = π/3r²h

The rate of change is found by implicit differentiation:

  V' = (π/3)((2rr')h +r²h')

Here, the height is constant, so h' = 0. Solving for r', we find ...

  r' = 3V'/(2πrh)

Using the given values of V', r, and h, we find the rate of change of radius to be ...

  r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s

The radius is decreasing at about -4.697 inches per second.

__

Additional comment

The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.

Answer:  The correct answer is C. The product is greater than 0 but less than 1.

Step-by-step explanation:

X and Y are both fractions

X is greater than 0 but less than 1

X * Y > 0 and < 1

The product of these two fractions will result in a fraction between 0 and 1.

For example:

1/2 x 1/2 =1/4, 1/6 x 2/6 = 1/18, 1/10 x 5/6 = 1/12

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

Explanation:

If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.

Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.

Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.

The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one  blue point.

Answer:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.

The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.

So, the equation we can construct from this information is:

[tex]f(x)=-|2x|[/tex]

The value of k for which the quadratic equation 4s² - 4s + (k - 2) has one real solution is:

k = 16.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

In this problem, the equation is given as follows:

4x² - 4s + (k - 2) = 0.

Hence the coefficients are given as follows:

a = 4, b = -4, c = k - 2.

Hence the discriminant is:

Δ = (-4)² - 4(4)(k - 2)

Δ = 16 - 16k + 32

Δ = 48 - 3k

It has one real solution if Δ = 0, hence:

48 - 3k = 0

3k = 48

k = 48/3

k = 16.

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Solution of the equation 3x-2y = 5 for domain {-3} is (-3,-7).

Given,

Eq => 3x - 2y = 5

Domain = x = -3

Put x = -3 in equation

3(-3) - 2y = 5

   -9 - 2y = 5

     -9 - 5 = 2y

         -14 = 2y

            y = - 14 / 2

               = -7

Hence, solution is (-3,-7).

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The domain of the given function is equal to: {-4, 2, 6, 9}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Generally speaking, the horizontal extent of the graph of a function represents all domain values and they are read and written from the smallest to the largest numerical values, and from the left of a graph to the right.

By critically observing the given function, we can reasonably and logically deduce the following:

Domain = {-4, 2, 6, 9}.

Range = (-3, 1).

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Answer:

For part a you would decompose the fraction into two independent fractions with the following form:

() = ()/( x^2+5)(x ^2+3x−4)  = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)

Combining these fractions we get:

((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)

Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()

You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().

You would follow a similar process for part b as well.

Step-by-step explanation:

Answer:

x-4<12 x<-4

-3x<12

-3x/-3=x

12/-3=-4

x-4+4=x

8+4=12

The total number of cupcakes ordered, using proportions, is of:

5.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.

These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.

In this problem, the amounts are given as follows:

The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:

3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.

The problem is:

I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?

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Answer:

x = 650/7

Step-by-step explanation:

7/26 = 25/x

7*x = 25*26

7x = 650

x = 650/7

Check:

7/26 = 25/(650/7)

7/26 = 25*7/650

7/26 = 175/65

7*650 = 26*175 = 4550

Answer: x= 9

Step-by-step explanation:

I just checked that its right!

Answer:

The correct answer would be 9

Step-by-step explanation:

The third term in the sequence generated by 5n is 15.

According to the question,

We have the following information:

The sequence is given by the formula 5n.

In this case, n represents the number of the term.

(Note that the sequence generated by this formula can not be a geometric sequence because the common ratio of these terms is not the same.)

So, we have to find the 3rd term of this sequence. Then, we will find the value of this sequence by putting the value of n as 3.

So, we have the following expression:

5*3

15

Hence, the third term in the sequence generated by 5n is 15.

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Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

Given that;

A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.

The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]

Sum of  [tex]3\frac{2}{3}[/tex] +  [tex]2\frac{5}{8}[/tex] this is bought by the company.

So, to purchase the remaining  [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]

We use a common denominator of 24 for the fraction parts.

Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]

Similarly, convert;

[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]

[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]

By solving all the above conversions, we get;

[tex]\frac{42-16-15}{24}[/tex] = 11/24

Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

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Step-by-step explanation:

common factor= x and y

remaining factor = x , 2 , 3

L.C.M = 6 x sq. y

The time it takes to paint the whole bookcase is 50 minutes.

From the information, Wilson paints 40% of a bookcase in 20 minutes.

Let the time taken to paint the whole bookcase be x. This will be illustrated as:

20/x = 40/100

Cross multiply

40x = 100 × 20

40x = 2000.

Divide

x = 2000 / 40

x = 50

The time taken is 50 minutes.

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The amount of money paid by each of the 4 persons will be $33.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.

Total cost = $105.73 x 1.06 x 120

Total cost = $134.48

Amount for each person,

A = $134.48 / 4

Amount = $33.62

Therefore, the amount of money paid by each of the 4 persons will be $33.6.

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Step-by-step explanation:

if the solution has "nice" numbers, we can split the expression into 2 factors in the form

(x + a)(x + b) = x² + (a+b)x + ab

as this is equal to x² + 4x - 21.

ab = -21

so, one is positive and one is negative.

and 4 = a + b

we know the typical factors of 21 : 3×7

and then we see easily : 7-3 = 4

so,

we have

(x + 7)(x - 3) >= 0

this has 2 x-intercepts (x-values when y = 0) :

x = -7

x = 3

because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.

that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.

so, the solution are the intervals

x <= -7 and x >= 3

in these areas is the expression x² + 4x - 21 >= 0.

The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.

Given,

Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)

The normal distribution's standard deviation, s = 3000 pounds

95% confidence interval

N = 20 observations were made.

Mean = 30,800

Margin of error :

z₇ × √3000².20

±1.314.8079

Confidence interval

= Mean + Margin of error

= 30,800 ±1.314.8079

= 29,485.192 , 32,114.8

The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).

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Answer:

31

Step-by-step explanation:

x+10+2x+20+2x-5=180

5x+25=180

5x=155

x=31

Answer: The probability is 3 out of 20

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

2(2)*3-14

4*3-14

12-14

-2

We use the Serial Autocorrelation in the classical linear regression model.

In the classical linear regression model the serial autocorrelation is assumed to solve the problem.

Hence, we use the Serial Autocorrelation in the classical linear regression model.

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By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.

We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:

H = 5/9

While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:

J =  7/12

Now we only need to see which one of the fractions is larger.

If we simplify both we will get:

H = 5/9 = 0.556

J = 7/12 = 0.583

So we can see that Jessica's fraction is larger, which means that she will get more rocks.

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The equation of the line in slope intercept form is y = (-4/3)x   .

In the question ,

a line graph is given ,

we need to find the equation of that line .

the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,

the equation of the line passing from the points (x₁ , y₁) with slope m  in the slope intercept form is given by

(y - y₁) = m(x - x₁) .

we first need to find the slope .

So , m = (0 - 4)/(0 + 3)

m = -4/3

The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is

(y - 4) = (-4/3)(x -(-3))

y - 4 = (-4/3)(x + 3)

y - 4 = (-4/3)x - 4

y = (-4/3)x - 4 + 4

y = (-4/3)x

Therefore , The equation of the line in slope intercept form is  y = (-4/3)x  .

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Answer: -1/3

Step-by-step explanation:

The formula for slope =y1-y2/x1-x2. You first subtract the numbers for the y coordinate which is -6-(-5), and thats -1. Then you subtract the x coordinates. -6-(-9)=3. So the slope is -1/3

Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Given:

x - intercept = 4

y - intercept = 5

At x intercept y = 0 and at y intercept x = 0

(4,0) and (0,5)

slope = 5-0/0-4

= 5/-4

m = -5/4

substitute (4,0) and m value,

y = mx+c

0 = -5/4*4 +c

0 = -5 + c

c = 5

y = mx + c

y = -5/4(x) + 5.

Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

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