Heather, Eric, and Chang sent a total of 116 text messages over their cell phones during the weekend. Chang sent 3 times as many messages as Eric. Eric sent 9 more messages than Heather. How many messages did they each send?

ye answer's here  

If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.

Given sample size is 40, sample mean is 20, sample standard deviation is 5.

We have to find whether the distribution is normally distributed or not.

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.

Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.

Signs of normal distribution are:

Hence the sampling distribution is normally distributed.

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Answer:

27 < AB < 81

Step-by-step explanation:

By the triangle inequality theorem,

If CB is the longest, AB + 27 > 54, meaning AB > 27.

If AB is the longest, 27 + 54 < AB, meaning 81 < AB.

Thus, 27 < AB < 81

Answer:

your slow

Step-by-step explanation:

Step-by-step explanation:

good study habits will help! study before you plan on sleeping and designate times to do your work

Answer:

The answer would be 8.3*10^7.

Step-by-step explanation:

This is because the beginning factor in scientific notation (in this case it is 8.3) must be no less than one, and no more than ten. Once we figured that out, we simply count the number of decimal points from 3 to the final 0. Try it yourself. You will discover that the resulting answer is 7 decimal movements. Now, since we are using scientific notation, we will want to multiply by ten to the power of the number of decimal movements (in this case it is 7.) And that's all! The answer is 8.3*10^7. I hope this helped (:

The expression x³ - 64 can be rewritten using difference of cubes is; (x - 4)(x² + 4x + 16)

Difference of cubes can be rewritten in the form of;

a³ – b³ = (a – b)(a² + ab + b²)

So in this question, we are given;

x³ - 64 = x³ - (4)³

where a = x and b = 4

This gives us;

(x - 4)(x² + 4x + 4²)

⇒ (x - 4)(x² + 4x + 16)

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The probability of getting a tail on the coin and an even number on the number cube is 1/4.

option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The sample space for flipping a coin and rolling a cube dice.

S = (H, T) x (1, 2, 3, 4, 5, 6)

S = { (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5),

(T, 6) }

n(S) = 12

The number of outcomes of getting a tail and a number even number on the number cube.

= { (T, 2), (T, 4), (T, 6) }

= 3

The probability of getting tails on the coin and an even number on the number cube.

= 3/ 12

= 1/4

Thus,

The probability of getting a tail and an even number is 1/4.

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Answer:

y=3x+3

Step-by-step explanation:

So generally you'll have a linear equation in the form of slope-intercept which looks like: y=mx+b, where m is the slope, and b is the y-intercept. the y-intercept, is the value of y, when x=0, which is going to be the constant b, because mx will be 0, because m * 0 = 0. m is the slope because as x increases by 1, the y-value increases by m, which in definition is the slope, how much a function increases as x increases by 1. So if you look at the table when x goes from -1 to 0, the y value goes from 0 to 3 or an increase in 3, and the same happens when x goes from 0 to 1. So the slope is 3, and the y-intercept as mentioned before is the value of y when x=0, which in this case is 3, which can be determined by looking at the table (look at y when x=0, it's 3). So this gives you the formula y=3x+3

The statement about the system of of equations that are true are as follows:

The system of equation can be solved as follows;

2x - 7y = - 13

2x + 11y = 1

18y = 14

y = 14 / 18

y = 7 / 9

2x  = 1 - 11(7 / 9)

2x = 1 - 77 / 9

2x = 9 - 77 / 9

2x = -68 / 9

cross multiply

18x = -68

x = -68 / 18

x = -34 / 9

Hence, the statement about the system of of equations that are true are as follows:

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Answer:

x<40

Step-by-step explanation:

x+10<50

x+10-10<50-10

x<40

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain from the first point,

[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]

The height of the mountain from the second point,

[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]

Equating the height,

H = H

(1000+x) × tan(29°) = x tan( 34°)

x = 4611.5767 feet

Now, the height of the mountain is,

H = x tan(34°)

H = 3110.54776 feet

Hence, the height of the mountain is 3110.5767 feet.

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The missing segment in the image below is 78 units.

An equation is an expression that shows the relationship between two or more variables and numbers.

The ratio or two corresponding sides of similar shapes are in the same proportion.

Let x represent the missing side, hence:

(x + 26)/26 = 48/12

x =78

The missing segment in the image below is 78 units.

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Answer:

a. What is the measure of ∠CAT?   Answer:  70°

b. What is the measure of ∠BAR?  Answer:  50°

c. What is the measure of ∠RAT?  Answer:   110°

d. What is the measure of ∠CAB? Answer:   130°

e. What is the measure of ∠BAT? Answer:    60°

Step-by-step explanation:

I just looked at the degrees of the protractor.

Hope this helps!

If not, I am sorry.

Answer:

159.3

Step-by-step explanation:

456 - 121.3 = 334.7

333.7 - 175.4 = 159.3

Hope this helped

Answer:

152

Step-by-step explanation:

You actually don't need to find the thirds number. Just by taking 456 and dividing it by three, you will get your answer and the average of the three numbers.

Answer:

a and c

Step-by-step explanation:

y - 1 = 1/3(x - 2)

y = 1/3x - 4/3

Only the slope matters in this problem. If the original equation has a slope of 1/3, you need to use the reciprocal and negate it. So the perpendicular slope would be -3.

 a. y 2 = –3(x – 4)

b. y − 5 = 3(x 11)

c. y = -3x – five-thirds

d. y = one-thirdx – 2 3x y = 7

So a and c are perpendicular to y - 1 = 1/3(x - 2)

Answer:

<3 and <4

Step-by-step explanation:

From the diagram above,

Exterior angles are angles formed outside the triangle.

The angles are: <3 and <4

Pn(Z>zp)=1−p%

Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a

is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.

The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.

Pn(Z>zp)=1−p%

Here Pn is the probability for the standard normal variable.

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Answer:

Step-by-step explanation:

[tex]1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta[/tex]

[tex]\angle PYZ=116^{\circ}[/tex] (angles on a line add to 180 degrees)

[tex]\angle ZYQ=58^{\circ}[/tex] (angle bisector)

[tex]\angle XYQ=122^{\circ}[/tex] (angle addition postulate)

[tex]\angle QYP=58^{\circ}[/tex] (angle bisector)

Reflex [tex]\angle QYP=302^{\circ}[/tex] (an angle and its reflex angle add to 360 degrees)

Answer:

Step-by-step explanation:

Let [tex]a,b,c[/tex] be the randomly selected lengths. Without loss of generality, suppose [tex]a

[tex]P(A + B \ge C) = P(A + B - C \ge 0)[/tex]

where [tex]A,B,C[/tex] are independent random variables with the same uniform distribution on [0, 1].

By their mutual independence, we have

[tex]P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)[/tex]

so that the joint density function is

[tex]P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}[/tex]

where [tex][0,1]^3=[0,1]\times[0,1]\times[0,1][/tex] is the cube with vertices at (0, 0, 0) and (1, 1, 1).

Consider the plane

[tex]a + b - c = 0[/tex]

with [tex](a,b,c)\in\Bbb R^3[/tex]. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)

The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region [tex]a+b-c\ge0[/tex], since [tex]0+0-1=-1<0[/tex]. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.

Then we have

[tex]\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}[/tex]

Answer:

848.23 mm²

Step-by-step explanation:

LA = πdh

LA = 3.14159 × 18 mm × 15 mm

LA = 848.23 mm²

Answer:

30°

Step-by-step explanation:

x + 90 = 2 × 60 ( angle at center = 2 × angle at circumference.)

x +90 = 120

x = 120-90

x = 30°

[tex]\frac{1820728291}{14285714286}[/tex]

Answer:

  z = 110°

Step-by-step explanation:

Angles z and the one marked 70° form an linear pair, hence are supplementary.

  z = 180° -70° = 110°

The angle made by two chords is half the sum of the arcs intercepted by those chords. Here, that means ...

  70° = 1/2(60° +x)   ⇒   x = 140° -60° = 80°

The arc w completes the circle of 360°, so we have ...

  w +x +79° +60° = 360°   ⇒   w = 360° -219° = 141°

Finally, z is the average of w and 79°:

  z = (w +79°)/2 = (141° +79°)/2 = 110° . . . as above

1. R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2. Domain = {1, 2, 3, 4}

3.  Range = {2, 3, 4, 5, 10, 17}

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Given:

R = { ( 1 + x , 1 + x^2 ) ∶ x≤ 4, ∈ }

1) R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2) Domain = {1, 2, 3, 4}

3) Range = {2, 3, 4, 5, 10, 17}

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Based on the data, table that shows a proportional relationship is the first table.

Data is said to be proportional if it increases or decreases at a constant rate.

The first table has proportional data because the height increases by 5 centimeters everyweek, which shows a constant rate.

Note: This question is incomplete; below I attach the missing section:

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Answer:

33x - 13 = 13x + 7

Step-by-step explanation:

If "G" is the midpoint of line FH, then both segments (lines FG and GH) must be the same length. Therefore, to find "x", you can set both segments equal to each other. After doing this, you can simplify and isolate to find "x".

FG = 33x - 13

GH = 13x + 7

FG = GH

33x - 13 = 13x + 7

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming that your equation should}\\\huge\textbf{look like that: }[/tex]

[tex]\mathbf{33x - 13 = 13x + 7}[/tex]

[tex]\huge\textbf{If so:}[/tex]

[tex]\mathbf{33x - 13 = 13x + 7}[/tex]

[tex]\huge\textbf{SUBTRACT 13x to BOTH SIDES}[/tex]

[tex]\mathbf{33x - 13 - 13x = 13x + 7 - 13x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{20x - 13 = 7}[/tex]

[tex]\huge\textbf{ADD 13 to BOTH SIDES}[/tex]

[tex]\mathbf{20x - 13 + 12 = 7 + 13}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{20x = 20}[/tex]

[tex]\huge\textbf{DIVIDE 20 to BOTH SIDES}[/tex]

[tex]\mathbf{\dfrac{20x}{20} = \dfrac{20}{20}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = \dfrac{20}{{20}}}[/tex]

[tex]\mathbf{x = 1}[/tex]

[tex]\huge\text{Answer: \boxed{\mathsf{33x - 13 = 13x + 7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Trigonometric substitution may useful when integrating the integrals root of a sum or difference of two squares.

In arithmetic, trigonometric substitution is the substitution of trigonometric features for other expressions. In calculus, trigonometric substitution is a way of comparing integrals.

Moreover, one can also use trigonometric identities to simplify sure integrals containing radical expressions.

You can use trig substitution even when you do not have square roots. particularly, if you have an integrand that looks like an expression in the square roots proven inside the above table, then you can use trig substitution.

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