Rationalize the denominator of square root of negative 16 over open parentheses 1 plus i close parentheses plus open parentheses 6 plus 3 i.

By dividing Tanya's swimming goal of 30 miles by her daily swimming rate of 3/4 mile, we find that it will take her 40 days to reach her goal.

To calculate how many days it will take Tanya to reach her goal of swimming 30 miles by swimming 3/4 mile per day, we need to divide the total goal distance by the daily swimming distance. Therefore, the calculation is as follows:

Divide 30 miles by 3/4 mile.

Since dividing by a fraction is equivalent to multiplying by its reciprocal, we multiply 30 miles by 4/3.

30 miles  * 4/3 = 120/3 = 40 days.

Hence, it will take Tanya 40 days to reach her goal of swimming 30 miles if she swims 3/4 mile each day

Answer:

[tex]x+y\geq 36[/tex]

[tex]2x+0.6y<40[/tex]

Step-by-step explanation:

The magnets are on sale for 60 cents each.

The key chains cost $2 each.

Katie must purchase at least 36 gifts but has to spend less than $40.

Now let x represent the amount of key chains.

Let y represent the amount of magnets.

So, the system of inequalities that form are:

[tex]x+y\geq 36[/tex]

And

[tex]2x+0.6y<40[/tex]

Answer:

m=15

Step-by-step explanation:

cube root of 3375 =m

We need to solve the equation for m

[tex]\sqrt[3]{3375} = m[/tex]

In order to solve for m we need to find the cube root of 3375

3375 can be written as 3 times 3 times 3 times 5 times 5 times 5

[tex]\sqrt[3]{3375} = m[/tex]

[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]

For same three factors inside the cube root we pull out one factor outside the cube root

[tex]\sqrt[3]{3 \cdot 3 \cdot 3} = 3[/tex]

[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]

[tex]3 \cdot 5 = m[/tex]

m= 15

The value of the variable that makes the statement true is

m = 15

The given equation is:

[tex]\sqrt[3]{3375} = m[/tex]

We are looking for a number that we can multiply by itself 3 times to get 3375

Note that the given equation can be re-written as:

[tex]m =3375^{\frac{1}{3}[/tex]

This can be further simplified as:

[tex]m=15^{3(\frac{1}{3} )}\\\\m=15[/tex]

Therefore, the value of the variable that makes the statement true is m = 15

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By defining the shorter leg of the triangle as 'x' and applying the Pythagorean Theorem to solve the given equations, we find that the shorter leg is 3cm, the longer leg is 12cm, and the hypotenuse is 15cm.

Let's define the shorter leg of the triangle as 'x'. As given, the longer leg would be '2x + 6' and the hypotenuse would be '2x + 9'.

To solve for the lengths of the sides, let's use the Pythagorean Theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the equation would be (2x + 6)^2 + x^2 = (2x + 9)^2.

Solve this equation by expanding, collecting similar terms, and factoring. You'll end up with x = 3. Therefore, the shorter leg of the triangle is 3cm, the longer leg is 2x + 6 = 2*3 + 6 = 12cm, and the hypotenuse is 2x + 9 = 2*3 + 9 = 15cm.

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The value of [tex]\( y \)[/tex] when x = 6 is 16.

Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:

[tex]\[ y = \frac{k}{x} \][/tex]

where [tex]\( k \)[/tex] is the constant of proportionality.

First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].

[tex]\[ 24 = \frac{k}{4} \][/tex]

Solving for k:

[tex]\[ k = 24 \times 4 = 96 \][/tex]

Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:

[tex]\[ y = \frac{96}{6} \][/tex]

[tex]\[ y = 16 \][/tex]

Answer:

Which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?

Step-by-step explanation:

1200*0.15 = 180

1200-180 = $1020

$1020 after the rebate

Answer:

[tex]12\frac{3}{16} \text{inches}[/tex]

Step-by-step explanation:

Given : The city is [tex]2 \frac{7}{16}[/tex] inches across on the map

To Find:On the map, what is the distance across the actual city?

Solution:

Distance on map = [tex]2 \frac{7}{16}=\frac{39}{16} inches[/tex]

Scale: 1 inch = 5 miles

So, [tex]\frac{39}{16} inches=\frac{39}{16} \times 5[/tex]

[tex]\frac{39}{16} inches=\frac{195}{16} =12\frac{3}{16} [/tex]

Thus ,the distance across the actual city is [tex]12\frac{3}{16} inches[/tex]

So, option C is correct.

Answer:  a. [tex]\dfrac{43}{87}[/tex]

Step-by-step explanation:

From the given table , it can be seen that the total number of flights are given : 43+33+6+5=87

Also, the the number of  Upstate Airlines flights on time = 43

Now if one of the 87 flights is randomly selected, the probability that the flight selected is an Upstate Airlines flight which was on time will be :-

[tex]\dfrac{\text{Number of Upstate Airlines flight on time}}{\text{Total flight}}\\\\=\dfrac{43}{87}[/tex]

Hence, the probability that the flight selected is an Upstate Airlines flight which was on time [tex]=\dfrac{43}{87}[/tex]

x=heavy equipment

y= general labor

x+y=38

x=38-y

134x + 92y=4756

134(38-y)+92y =4756

5092-134y+92y=4756

-42y = -336

y = -336/-42 = 8

x=38-8=30

check 30*134 =4020

8*92 = 736

4020+736 = 4756

 8 general laborers

30 heavy equipment operators

This question has following choices to choose the answer from:

The larger sample would have a center closer to the true population parameter.

The larger sample would have less sampling variability.

The smaller sample would have less sampling variability.

The statistics of the smaller sample have more chance for bias than those of the larger sample.

I believe that the correct answer from the 4 choices would be the last one:

"The statistics of the smaller sample have more chance for bias than those of the larger sample."

This is because in a smaller sample, there is a high probability that not all parts or portion of the sample population is represented hence resulting in bias. This is especially true for distribution types of data wherein extreme values exist. Following that bias would already be effect on the center and the sampling variability. So bias always comes first.

The cube root of -27 is -3, which cannot be graphed in the first quadrant of the complex plane. When considering complex roots, the angles of these roots do not lie in the first quadrant either, contradicting the given requirement.

The cube root of -27 that graphs in the first quadrant in complex form can be represented as 3(cos Θ + i sin Θ), where Θ is the angle in degrees. To find a cube root that lies in the first quadrant, we look for an angle Θ whose cosine is positive and sine is positive, which corresponds to angles between 0° and 90°. However, the cube root of -27 is actually a negative real number, which is -3.

Since we cannot graph a negative real number (-3) in the first quadrant of the complex plane, which only contains positive real and imaginary numbers, the question seems to be a bit contradictory. Nonetheless, if we interpret the cube root in terms of complex numbers, we find that the complex roots of -27 are -3, 3ε², and 3ε⁴, where ε² = e²πi/3 and ε⁴ = e⁴πi/3, correspond to angles of 120° and 240° respectively, which do not lie in the first quadrant.

Answer:

The mean is  

✔ 89

The median is  

✔ 92

The mean of Miriam's test scores is 89 and the median is 92.

"It is the average of a data set. "

"It is the middle value in a list ordered from smallest to largest."

For given question,

Total number of test scores = 9

The sum of all the test scores would be,

96 + 81 + 82 + 99 + 94 + 92 + 95 + 82 + 80 = 801

So, the mean would be,

[tex]\bar{X}=\frac{801}{9} \\\\\bar{X}=89[/tex]

So, the mean of Miriam's test scores is 89.

If we arrange the test scores in ascending order then it would be,

80, 81, 82, 82, 92, 94, 95, 96, 99

The middle value is 92

So, the median is 92.

Therefore, the mean of Miriam's test scores is 89 and the median is 92.

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At (1,1) and (-1,-1) there is minimum value and at (0,0) is the saddle point.

Given-

Given function is-

[tex]f(x,y)=x^4+y^4-4xy+1[/tex]

Locate the critical points,(use the derivation with respect to x and y)

[tex]f'(x)=4x^3-4y\\\\f'(y)=4y^3-4x[/tex]

Equate the above partial derivatives to the zero, we get.]

[tex]4x^3-4y=0\\\\x^3=y[/tex]

The value of x is obtained. Solve the equation two and put this value of x in that equation, we get,

[tex]4y^3-4x=0\\y^3-x=0[/tex]

Put the value of x, we get,

[tex]x^9-x=0[/tex]

[tex]x(x^8-1)=0[/tex]

from above equation we get one value of [tex]x[/tex] is zero.

[tex]x^8-1=0[/tex]

To the above equation we can rewrite,

[tex]x^2-1=0[/tex]

[tex](x-1)(x+1)=0[/tex]

hence we get three values of the [tex]x[/tex] (0,1,-1)

From the equation of partial derivative equation, we get that

[tex]x=0; y=0[/tex]

[tex]x=1;y=1[/tex]

[tex]x=-1;y=-1[/tex]

Thus three critical points are (0,0),(1,1) nd(-1,-1). Now calculate second partial derivative and D(x,y).

[tex]f"(x)=12x^2-0[/tex]

[tex]f'(xy)=-4[/tex]

[tex]f"(y)=12y^2-1[/tex]

[tex]D(x,y)=f"(x)f"(y)-f'(xy)^2[/tex]

[tex]D(x,y)=144x^2y^2-16[/tex]

Check at critical points,

[tex]D(0,0)=-16<0[/tex]

thus no local minima or maxima at point (0,0). this is the saddle point.

[tex]D(1,1)=12>0[/tex]

so (1, 1) is a local minimum.

[tex]D(-1,-1)=12>0[/tex]

so (-1, -1) is a local minimum.

Hence at (1,1) and (-1,-1) there is minimum value and at (0,0) is the saddle point.

For more about the maxima and minima follow the link given below-

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Answer:

12

Step-by-step explanation:

Given that a two pound box of fruit snacks contains 24 packets

We have to find the unit rate per pound

This is a question of direct variation.

[tex]2 pounds = 24 packets\\1 pount= 12 packet[/tex]

i.e. unit rate is 12 packets per pound

The standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.

As we know that,

So, it should be presented below.

Trillion   Billion     Million    Thousand     Hundred    Tens   Ones

 407   ,   000   ,     006   ,       105      ,       0                 2         8

Therefore we can conclude that the standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.

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volume = (4/3) x pi x r^3

diameter = 9 so radius = 9/2 = 4.5

V =(4/3) x 3.14 x 4.5^3 = 381.51 cubic inches

y = cost = $25

25 = 0.75 +10

 subtract 10 from each side

15=0.75x

x = 15/0.75 = 20

 there were 20 words in the ad

The binomial distribution of the number of women (out of six) who could be an interest in baseball is found by using the binomial probability formula. Probabilities range from 0.027 for zero women interested, to 0.002 for all six women interested.

In this problem, we are constructing a binomial distribution for the number of women (out of six) who might consider themselves fans of professional baseball. This involves using the formula for a binomial probability, which is: P(x) = nCx * [tex](p^x) * ((1-p)^(^n^-^x^)[/tex]). Here, n represents the number of trials (in this case, 6 women), p represents the probability of success (here, a woman being a baseball fan, which is 0.36 or 36%), and x represents the number of successful outcomes we're interested in.

Each of these values rounds to the thousandth place

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To construct a binomial distribution, we use the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the combination formula.

To construct a binomial distribution, we use the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the combination formula.

The random variables X and P' represent the number of women who consider themselves fans of professional baseball and the probability of a woman considering herself a fan, respectively.

We should use the binomial distribution for this problem.

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