Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.

The point on the number line which represents the first tomato Carmen will eat is: B. K.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In Mathematics, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

By critically observing the number line (see attachment) which models the weight of the tomatoes Carmen would eat, we can logically deduce that each of the interval represent 1/8 pound.

First tomato = 2/8

First tomato = 1/8 + 1/8 ≡ 2/8 = point K.

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Complete Question:

Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound. Which point on the number line represents the first tomato Carmen will eat?

A. J

B. K

C. L

D. M

The correct statements regarding sum and subtraction with negative numbers are given as follows:

When two negative numbers are added, the result is negative, as we keep the signal and then add the absolute amounts of each value, for example:

-5 + (-5) = -(5 + 5) = -10.

Hence the fourth statement is correct, while the first and the third are not.

When we subtract two negative numbers, we first transform the second number to positive, meaning that the result can be either positive or negative, as the result will take the signal of the higher value and their absolute amounts are subtracted.

Hence:

Hence the fifth and the sixth statements are correct.

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Answer:

8 and 9

Step-by-step explanation:

consider perfect squares either side of 78

64 < 78 < 81 , then

[tex]\sqrt{64}[/tex] < [tex]\sqrt{78}[/tex] < [tex]\sqrt{81}[/tex] , that is

8 < [tex]\sqrt{78}[/tex] < 9

Explanation

Step 1

et

w represents the cost of gift-wrapping.

then

Jessie spent a total of $14

total= 14

the cost for postage=$2.25

the cost of the gift( itself)=9.50

in words, the total is

the total cost is the cost of the gift plus the cost of the postage plus the cost of gift-wrapping

Now,replace

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

Here's your answer :)

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Answer:

please mark my brain list answer

Answer:

s = ut + 1/2 at²

2.4 = 4.9t²

t = 0.70

distance = speed x time

d = 24 x 0.7

d = 16.8 m

(a)

In order to find the function, let's use the ordered pair (-3, 8) in the given exponential function f(x).

So we have:

So the function is f(x) = (1/2)^x

(b)

The asymptote of this graph is y = 0, that is, the horizontal axis.

(c)

The domain is the values that x can assume, so the domain of this function is all real numbers, that is, (-infinity, infinity)

The range is the values that f(x) can assume, so the range of this function is y>0, that is, all positive numbers: (0, infinity)

Answer:

-10v

Step-by-step explanation:

-3v - 7v

OR

(-3v)+(-7v)

= -10v

Answer:

the answer is -3v-7v= -10

In a single year, factories create a total of 21550 gallons.

In both imperial and US customary units, the gallon is a unit of volume.A gallon is a unit of measurement for liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.

We have been given that

Lemonade = 11,650 gallons

Ice tea = 4,950 fewer than lemonade

Root beer = 3,500 fewer than Ice tea.

After calculating

Ice tea = 11,650 - 4,950

Ice tea = 6700 gallons

Root beer = 6700 - 3,500

Root beer = 3200 gallons

Total  factory produced in one year

= 11,650 + 6700 + 3200

Hence , 21550 gallons are total factory produced in one year.

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Simplification of the given expression to single complex number are as follow :

9. -11 +4i

13. 30 - 10i

17.20

21. (3 + 5i)/2

25.  -1

As given,

To simplify the following expressions to a single complex number,

9) (- 5 + 3 i) - (6 - i)

   = - 5 + 3 i - 6 + i

   = - 5 - 6 +3i + i

   = - 11 + 4 i

13) (6 - 2 i) 5

    = (6 x 5) - (2  x 5) i

    = 30 - 10 i

17) (4 - 2 i) (4 + 2 i)

    = [tex]4^{2} - (2i)^{2}[/tex]

    = 16 - 4 [tex]i^{2}[/tex]

    = 16 - 4 (-1)

    = 16 + 4

    = 20

21) [tex]\frac{-5+3i}{2i} = \frac{i(-5+3i)}{2i^{2}} = \frac{-5i + 3i^{2} }{2(-1)}[/tex]

    = [tex]\frac{-5i+3(-1)}{-2} = \frac{3+5i}{2}[/tex]

25) [tex]i^{6} = (i^{2})^{3} = (-1)^{3} = -1[/tex]

Note: To simplify a fraction where denominator has complex component (i) as coefficient, multiply both numerator and denominator by i to eliminate i from denominator (by converting it to real number)

Therefore, simplification of  the given expression to single complex number are as follow :

9. -11 +4i

13. 30 - 10i

17.20

21. (3 + 5i)/2

25.  -1

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Answer: u≤29

Hope this helps! :)

The differential equation used to solve an equation of the amount (mass) of salt within the tank at any given time t is [tex]\frac{ds}{0.04s-0.1} = dt[/tex].

Let the amount of salt any time t is given by s kg then the rate of change of s with respect to t is given by,

[tex]\frac{ds}{dt}[/tex] = (rate of salt out) - (rate of salt in)

Rate of salt in = 0.01 kg/litre × 10 litre/min = 0.1 kg/min

Rate of salt out = s/500 kg/litre × 20 litre/min = (20s/500) kg/min

A differential equation can be made on the concept that the rate of change of salt is the difference between the rate of in and the rate of out.

That gives us when combined,

[tex]\frac{ds}{dt} = 0.04s -0.1[/tex]

Now solving this differential equation,

[tex]\frac{ds}{0.04s-0.1} = dt[/tex]

Integrating both sides,

[tex]\int\ {\frac{ds}{0.04s-0.1} } \, = \int dt[/tex]

[tex]\frac{ln(0.04s -0.1)}{0.04} = t+C_{1}[/tex]

[tex]ln(0.04s - 0.1) = 0.04t +0.04C = 0.04t +C_{2}[/tex]

[tex]0.04s - 0.1 =e^{0.04t + C_{2} } =Ae^{0.04t}[/tex]

Now at t = 0, s = 10 kg

0.04(10) - 0.1 = A

A = 0.3

So the differential equation can be written as,

[tex]0.04s - 0.1 = 0.3e^{0.04t}[/tex]

Now time at which no salt is left which means s = 0 at some time t

[tex]0.1 - 0.04(0) = -0.3e^{-20t}[/tex]

The equation is not further solvable as we can see.

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One angle's measurement is 11 times that of another. if the two angles supplementary one another. The measure of the angles area one is 165° and other angle is 15°.

Given that,

One angle's measurement is 11 times that of another. if the two angles supplementary one another.

We have to determine the angles' measurements.

The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another

It has an acute angle on one side and an obtuse angle on the other.

The angles are both right angles.

So, It follows that A + B = 180°.

Angle A is 11 times angle B means

A=11B

We get,

11B+B=180

12B=180

B=180/12

B=15°

Then angle A is

A=11×15

A=165°

Therefore, The measure of the angles area one is 165° and other angle is 15°.

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The circumference of a circle with diameter 2.76 m is 8.66 m.

What is Circumference?

Circumference of a circle is perimeter of circle.

Given that;

Diameter of a circle = 2.76 m

Since, Circumference of  a circle = 2πr

Where, r is radius of circle.

Now, Diameter of a circle = 2.76 m

Then, Radius of a circle = 2.76/2 = 1.38 m

Hence, Circumference of  a circle = 2πr

Substitute all the values;

Circumference of  a circle = 2 x 3.14 x 1.38

                                        = 8.66 m

Thus, The circumference of a circle with diameter 2.76 m is 8.66 m.

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If the original price =$50

If we take $20 off, we have: $50-20 =$30

Next, taking 25% off of $30, we have:

Final Price = (100%-25%) of $30

=0.75 x 30

Final Price Final 0Price=$22.5

9

If we take $20 off, we have: $90-20 =$70

Next, taking 25% off of $70, we have:

Final Price = (100%-25%) of $70

=0.75 x 70

Final Price =$52.50

Answer: 55 cm

Step-by-step explanation:

a^2 + b^2 = c^2

X^2 + 48^2 = 73^2

X^2 + 2,304 = 5,329

X^2 = 3,025

X = 55

[tex]8x + 6 + 118 = 180 \\ 8x + 124 = 180 \\ 8x = 180 - 124 \\ 8x = 56 \\ \frac{8x}{8} = \frac{56}{8} \\ x = 7[/tex]

NOTE THAT DUE TO LACK OF LABELLING OF ANGLES IN THE DIAGRAM I COULDN'T GIVE YOU BRIEF EXPLANATION BUT I HOPE YOU UNDERSTAND.

B

1) To solve this question, we can write out two equations within this expression:

So we can do it with 10L of that 30% solution.

2)Let's find the other volume, plugging into that x=10, since the whole volume of this new solution is 30L we can subtract from that 30L that 10L we have just found:

3) So we found 20l of the 15% solution.

Thus the answer is B

The most appropriate choice for exponent will be given by-

-31 is the required answer. The second option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2\times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\frac{a^m}{a^n} = a^{m - n}\\a^ 0 =1\\(a^m)^n = a^{mn}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\a^{-m} = \frac{1}{a^m}[/tex]

Here,

[tex]5s \times 2^3 + (h-1)^2\\h = 4, s = -1\\5(-1) \times 8 + (4 - 1)^2\\-40 + 9\\-31[/tex]

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Hey you man what are you doing here go to there

Answer:

C. the dilate with scale of 2

Step-by-step explanation:

when you dilate, a scale bigger than 1 means you enlarge the figure A

no other choices make figure a bigger to 'fit into' or be the same as figure B

so thus, the answer is C.

Answer:

C.

Step-by-step explanation:

as we can clearly see, when going from figure A to figure B every length and coordinate is doubled. that means a constant scale factor of 2 for all of that. but the angles and the general structure of the object remained the same (so, both are similar).

The subset's components can be listed in any order when combined.

The former two are both 15/16.

P(at least one boy) and then P(at least one Girl)

P(at least one boy and one girl)

If we assume P(girl) = P(boy) = 50%

The latter results from the 16 possible combinations.

noting only two of which are single sex.

So 14/16 = 7/8.

Therefore, the former two are both 15/16.

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By finding coterminal angles, we conclude that another way of writing the angle 530° is 170°.

For any angle A, we define the family of coterminal angles B as:

B = A + n*360°.

Where n is an integer different than zero.

In this case we have A = 530°

Then the coterminal angles are:

B = 530° + n*360°

If we define n = -1, then:

B = 530° - 360° = 170°

So 170° is another way of writing 530°.

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Let

[tex]\displaystyle f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2(n^2-1) \binom{2n}n}[/tex]

Differentiate and multiply by [tex]x[/tex].

[tex]\displaystyle xf'(x) = \sum_{n=2}^\infty \frac{x^n}{n(n^2-1) \binom{2n}n}[/tex]

Now differentiate twice.

[tex]\displaystyle x f''(x) + f'(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{(n^2-1)\binom{2n}n}[/tex]

[tex]\displaystyle xf'''(x) + 2f''(x) = \sum_{n=2}^\infty \frac{x^{n-2}}{(n+1)\binom{2n}n}[/tex]

Multiply by [tex]x^3[/tex].

[tex]\displaystyle x^4 f'''(x) + 2x^3 f''(x) = \sum_{n=2}^\infty \frac{x^{n+1}}{(n+1)\binom{2n}n}[/tex]

Differentiate one last time and multiply by [tex]\frac1x[/tex].

[tex]\displaystyle x^3 f^{(4)}(x) + 6x^2 f'''(x) + 6x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{\binom{2n}n}[/tex]

Now integrate with the fundamental theorem of calculus, noting that [tex]f(0)=f'(0)=0[/tex] follows from our series definition. We do this twice and make use of the recurrence

[tex]I_n = \displaystyle \int_0^x y^n f^{(n+1)}(y) \, dy = x^n f^{(n)}(x) - n I_{n-1}[/tex]

Integrating once yields

[tex]\displaystyle x^3 f'''(x) + 3x^2 f''(x) = \sum_{n=2}^\infty \frac{x^n}{n \binom{2n}n}[/tex]

Multiply by [tex]\frac1x[/tex].

[tex]\displaystyle x^2 f'''(x) + 3x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{n \binom{2n}n}[/tex]

Integrating once more yields the ordinary differential equation

[tex]\displaystyle x^2 f''(x) + x f'(x) - f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n}[/tex]

and we recognize the right side as the series

[tex]\displaystyle \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n} = 2\arcsin^2\left(\frac{\sqrt x}2\right) - \frac x2[/tex]

Solving the differential equation is quite doable with the variation of parameters method; we ultimately find

[tex]\displaystyle f(x) = \frac12 + \frac{7x}8 - \left(\frac1x+\frac12\right) \sqrt x \sqrt{4-x} \, \arcsin\left(\frac{\sqrt x}2\right) + 2 \left(\frac1x-1\right) \arcsin^2\left(\frac{\sqrt x}2\right)[/tex]

Recover the sum we want by letting [tex]x=-1[/tex]. Recall that

[tex]\arcsin(iz) = i \,\mathrm{arsinh}(z) = i\ln(z + \sqrt{1+z^2})[/tex]

Then we have the following equivalent results involving our old friend [tex]\phi[/tex].

[tex]\displaystyle f(-1) = -\frac38 - \frac{\sqrt5}2\, \mathrm{arsinh}\left(\frac12\right) + 4 \,\mathrm{arsinh}^2\left(\frac12\right) \\\\ f(-1) = -\frac38 - \frac{\sqrt5}2 \ln\left(\frac{1+\sqrt5}2\right) + 4 \ln^2\left(\frac{1+\sqrt5}2\right) \\\\ f(-1) = \boxed{-\frac38 - \left(\frac12 - \phi\right) \ln(\phi) + 4 \ln^2(\phi)}[/tex]

It takes 1.5 years for Evelyn to reach $5,750.

In this question, it is clear that principal amount that Evelyn deposited is $5,000. The annual interest rate as per the question is 0.1%. The final amount that Evelyn gets is $5,750.

Lets assume that it will take t years for Evelyn to get a final amount of $5,750.

So,

Principal amount, P = $5,000

annual rate, r = 0.1%

Final amount, A = $5,750

From the formula for simple interest, we have,

A = P( 1 + rt)

Hence, t = (1/r)  x  { (A/P) -1 }

              = 1/0.1 x { (5750/5000) - 1}

               = 10 x { 1.15 - 1 }

               = 10 x  0.15

               =1.5

Therefore it will take 1.5 years for Evelyn to get a total amount of $5,750 provided she deposited an amount of $5,000 at an annual simple interest rate of 0.1%

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Answer:

y=-3/2x+4

Step-by-step explanation:

The expression 6⁻² can be written as -

6⁻² = 1/6²

6⁻² = 1/36

6⁻² = (1/6 x 1/6)

A mathematical expression is a combination of terms separated by mathematical operators. For example : 2x + 3y + 6. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following expression -

6⁻²

We can write the expression 6⁻² in the following possible ways -

6⁻² = 1/6²

6⁻² = 1/36

6⁻² = (1/6 x 1/6)

Therefore, the expression 6⁻² can be written as -

6⁻² = 1/6²

6⁻² = 1/36

6⁻² = (1/6 x 1/6)

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Step-by-step explanation:

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