Answer:
Step-by-step explanation:
Declaration
Let Heather's number of messages = x
Let Eric's number of messages = x + 9
Let Chang's number of messages = 3(x +9)
Equation
x + x + 9 + 3(x + 9) = 116
Solution
x + x + 9 + 3(x + 9) = 116 Remove the brackets
x + x + 9 + 3x + 27 = 116 Combine like terms
x + x + 3x + 9 + 27 = 116
5x + 36 = 116 Subtract 36 from both sides
5x + 36 - 36 = 116 - 36 Combine
5x = 80 Divide both sides by 5
5x/5 = 80/5
x = 16
Answer
Heather = 16
Eric = 16 + 9 = 25
Chang = 3*25 = 75
Find the value of z.
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°
Angles where chords crossThe 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
how would the expression x^3-64 be written using difference of cubes
The expression x³ - 64 can be rewritten using difference of cubes is; (x - 4)(x² + 4x + 16)
How to write an expression as difference of cubes?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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Prove that
1/(sec x - 1) + 1/(sec x + 1) is equal to
2cos x × cosec^2 x
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]
Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area
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]
A coin is flipped, and a number cube is rolled. What is the probability of getting tails on the coin and an even number on the number cube?
A= 1/12
B= 1/8
C=1/4
D= 1/2
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.
What is probability?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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In the following exercises, simplify each expression.
779. Convert 83,000,000 scientific notation.
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 (:
Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
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
Use the quadratic formula to determine the exact solutions to the equation.
6x2+4x−3=0
ye answer's here
g Trigonometric substitution may useful when integrating the _____________ root of a sum or difference of two squares.
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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Which lines are perpendicular to the line y – 1 = one-third(x 2)? check all that apply. y 2 = –3(x – 4) y − 5 = 3(x 11) y = -3x – five-thirds y = one-thirdx – 2 3x y = 7
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)
PLEASE HELPPP
Which statements about this system of equations are true? Select three options.
Options in picture:
The statement about the system of of equations that are true are as follows:
x = -34 / 9y = 7 / 9How to solve system of equation?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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Let R be a relation in N defined by R = { ( 1 + x , 1 +^2 ) ∶ ≤ 4, ∈ } Find
i) R ii) domain of R iii) range of R
1. R= {(2, 2), (3, 5), (4, 10), (4, 17)}
2. Domain = {1, 2, 3, 4}
3. Range = {2, 3, 4, 5, 10, 17}
What is Domain and range?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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A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29° From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 34° How high (in feet) is the mountain?
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.
What is Tangent (Tanθ)?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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Please help me with this question.....
[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)
PLEASE ME HELP ASAP THANK YOUUU
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
Instructions: Find the missing segment in the image below. HELP PLEASEE !!
The missing segment in the image below is 78 units.
What is an equation?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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How would you set this problem up to find x?
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]
help meeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
Find the lateral area of a cylinder that has a diameter of 18 mm and a height of 15 mm.
Answer:
848.23 mm²
Step-by-step explanation:
LA = πdh
LA = 3.14159 × 18 mm × 15 mm
LA = 848.23 mm²
I need help finding the measurements I’m not good at using protractors
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.
very confused with this
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
In the diagram below, all angles are given in
degrees (°).
Find the value of x.
60
x +90
X
3x
Not drawn accurately
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°
The population of weights of a particular fruit is normally distributed, with a mean of 535 grams and a standard deviation of 13 grams. If 8 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.
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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why i`m very weak in maths
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
I need help with this question. thanks.
Answer:
x<40
Step-by-step explanation:
x+10<50
x+10-10<50-10
x<40
Help 20 points please
Based on the data, which table shows a proportional relationship?
Based on the data, table that shows a proportional relationship is the first table.
What is proportional?Data is said to be proportional if it increases or decreases at a constant rate.
What table has proportional data?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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If the sum of three numbers is 456 and the first two numbers are 121.3 and 175.4, what
is the average of the three numbers?
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.
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?
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:
Symmetric bell shapemean and median are equal both located at the center of the distribution68% approximately equals 68% falls within 1 standard deviation of the mean.Hence the sampling distribution is normally distributed.
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0.127450980392 as fraction
[tex]\frac{1820728291}{14285714286}[/tex]