===========================================================
Explanation:
Each component has 1/3 as the probability of failure.
1 - 1/3 = 2/3 is the probability a particular component works.
Each component is independent of one another, allowing us to multiply the probabilities: (2/3)*(2/3)*(2/3) = 8/27
8/27 is the probability that all three components work simultaneously, and it's the probability that the machine works.
1 - 8/27 = 19/27 represents the probability that at least one component fails, and hence causes the entire machine to fail also.
19/27 = 0.7037 = 70.37% approximately. It appears this machine fails pretty often.
If the line in a linear-quadratic system of equations is a vertical line, how many solutions are there?
The number of solutions in the system is 1
How to determine the count of the solutions?From the question, the system of equations is given as
A linear equationA quadratic equationAlso, we understand that the linear equation is a vertical straight line.
So, we have the system to be
A vertical-line linear equationA quadratic equationA vertical line can only intersect with a quadratic line at one point
Hence, there is only one solution in the system
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Divide usando un modelo de área
6426 ÷ 9
Write the equation of a line that has a slope of -3/5 and passes through the point (10,4) in slope intercept form.
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{3}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-4=- \cfrac{3}{5}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{5}x+10 \end{array}}[/tex]
A scale drawing of a rectangular blacktop
is 21 inches by 12 inches. If the actual
blacktop is 126 feet by 72 feet, which is
the scale used for the drawing?
Answer:The area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. The length of the rectangle is 5.
Write an equation that makes it easy to find the width of the rectangle if we know the area and the length.
Step-by-step explanation:
Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins. How many pounds of chocolate chips were left?
three-twelfths pounds
eleven-twelfths pounds
one and two-twelfths pounds
one and seven-twelfths pounds
The amount of chocolate left is three and seven-twelfths pounds
How to find the amount of chocolate leftThe amount of chocolate left is found by addition and subtraction of fraction
The fraction required are:
Eva bought seven and one-half pounds of chocolate chips = 7 1/2
She used three and three-fourths pounds = 3 3/4
two and five-sixths pounds in some muffins = 2 5/6
total amount used = addition of amount used
3 3/4 + 2 5/6
= 3 11/12
the amount left is gotten by subtraction of amount used from amount Eva bought
= 7 1/2 - 3 11/12
= 3 7/12
this is three seven-twelfths
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-3+-u=-4 Please help!!!!!
Determine the convergence of divergence of the sequence. If the sequence converges, find its limit.
The sequence converges and its limit is zero
What is a sequence?A sequence is an ordered set of numbers governed by a rule.
What is the limit of a sequence?The limit of a sequence is the value the sequence approaches
What is convergence of a sequence?The convergence of a sequence is when the sequence approached a definite value
What is divergence of a sequence?The divergence of a sequence is when the sequence does not approach a definite value.
How to determine the convergence of divergence of the sequence?Since we have the sequence (√3 - √1), (√4 - √2), (√5 - √3), (√6 - √2), We need to find the general term of the sequence.
Observing this, we find that the general term Uₙ = √(n + 2) - √n
To determine if the limit converges or diverges, we take the limit of the sequence as n → ∞.
So,
[tex]\lim_{n \to \infty} U_n = \lim_{n \to \infty} \sqrt{n + 2} - \sqrt{n} \\= \lim_{n \to \infty} \sqrt{n + 2} - \lim_{n \to \infty} \sqrt{n} \\= \sqrt{\infty - 2} - \sqrt{\infty} \\= \sqrt{\infty} - \sqrt{\infty} \\= \infty -\infty[/tex]
Since this is an indeterminate form, we use L'hopital's rule to find the limit.
Uₙ = √(n + 2) - √n
= √n{√[(n + 2)/n] - 1}
= √n÷ 1/{√[(1 + 2/n] - 1}
Differentiating, we have
lim n → ∞ Uₙ = lim n → ∞ d√n/dn ÷ d(1/{√[(1 + 2/n] - 1})/dn
= 1/(2√n)/-√[(1 + 2/n] - 1})⁻² × 1/2√(1 + 2/n] × (-2/n²)
= n²[√(1 + 2/n] - 1})²/(2√n)√(1 + 2/n]
= n²[√(1 + 2/n] - 1})²/(2√n)√(1 + 2/n)]
Dividing through by n², we have
= n²[√(1 + 2/n] - 1})²/n² ÷ (2√n)√(1 + 2/n)]/n²
= [√(1 + 2/n] - 1})² ÷ (2(√n)³√(1 + 2/n³)]
Dividing both the numerator and denominator by (√n)³, we have
= [√(1 + 2/n] - 1})²/(√n)³ ÷ (2(√n)³√(1 + 2/n³)]/(√n)³
= (1 + 2/n] - √(1 + 2/n] + 1)/(√n)³ ÷ [2√(1 + 2/n³)]
= (1(√n)³ + 2/n²] - √{(1 + 2/n]/n)³} + 1/(√n)³) ÷ [2√(1 + 2/n³)]
= (1(√n)³ + 2/n²] - √{(1/n³ + 2/n⁴} + 1/√n)³) ÷ [2√(1 + 2/n³)]
So, lim n → ∞ Uₙ = lim n → ∞ (1(√n)³ + 2/n²] - √{(1/n³ + 2/n⁴} + 1/√n)³) ÷ [2√(1 + 2/n³)]
= (1(√∞)³ + 2/∞²] - √{(1/∞³ + 2/∞⁴} + 1/√∞)³) ÷ [2√(1 + 2/∞³)]
= (0 + 0] - √{(0 + 0} + 0) ÷ [2√(1 + 0)]
= (0 - 0 + 0)/2
= 0/2
= 0
The sequence converges and its limit is zero
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The three angles of a quadrilateral are 60 degrees, 90 degrees and 110 degrees. Determine the fourth angle
Answer:
100°
Step-by-step explanation:
The sum of any polygon angles add to ( n-2)(180) where n is the number of sides ......for a quadrlateral ( 4-2)(180 ) = 360
60 + 90 + 110 + x = 360 shows x = 100 °
Answer:
sin75^°-sin15^°=1/√2
What is the y-intercept, b, of the following linear equation? y = 2x+4 b=
Answer:
4
Step-by-step explanation:
you can use the formula y=mx+b where b is 4
Please help please please
Answer: 44
Step-by-step explanation:
since OPN and RPQ are similar triangles, you can use ratios to find their sides
[tex]\frac{24}{15} =\frac{x}{15+12.5}[/tex] or [tex]\frac{24}{15} =\frac{x}{27.5}[/tex]
cross multiply to get: 24*27.5 = 15x
660/15 = x
x = 44
construct triangle abc if ac=10cm angle bac=50 degrees and angle bca=50 degrees what type of triangle does this create
Answer:
Angle BAC =50
Step-by-step explanation:
Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC
Write a recursive formula: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21
Answer:
[tex]a_1=3[/tex]
[tex]a_n=a_n_-_1+2[/tex]
Step-by-step explanation:
Recursive formula : an = a(n-1) + d
where d = common difference , an = nth term, and n = number of terms
Because we are just writing the recursive formula rather than the explicit formula, the only defined term will be "d" or the common difference.
Here, the common difference is +2. This is evident as you must add 2 to get to 5 and then add 2 to get to 7 etc.
So d = 2
Plugging this into the recursive formula we get an = a(n-1) + 2
Also it's very important to state the first term which is 3 so a1 = 3
What is the equation of the line that passes through the point (5, 3) and has a slope of 3/5?
Answer:
y -3 = 3/5(x -5) . . . . point-slope formy = 3/5x . . . . . . slope-intercept formStep-by-step explanation:
You want the equation of the line with slope 3/5 that passes through point (5, 3).
Point-slope formThe point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=3/5, (h, k) = (5, 3), so your equation is ...
y -3 = 3/5(x -5) . . . . point-slope form of desired equation
Slope-intercept formThis can be simplified to ...
y -3 = 3/5x -3
y = 3/5x . . . . . . . add 3
Which of the equations below represent a proportional relationship? Choose all that apply.
Answer:
1
3
6
are all the correct answers because they made the most sense and looked the most proportional
polynomial function
Answer:
[tex]f(x) = (x+1)(x-2)(x+4)[/tex]
[tex]= (x^{2} +x-2x-2)(x+4)\\\\= (x^{2} -x-2)(x+4)\\\\= x^{3}-x^{2}-2x+4x^{2} -4x-8\\\\= x^{3} +3x^{2} -6x-8[/tex]
The equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds
of apples. What does the number 4.3 represent in the equation?
the 4.3 represents The number of apples in 1 pound
The 4.3 in the equation represents the number of apples in 1 pound
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds of apples.
Here we can see that y = 4.3x
4.3 = y/x
then we can say that 4.3 is slope of striaght line in term os linear equation.
4.3 in the equation represents the number of apples y, in dollars, of x pounds.
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Determine the range of the following graph:
The range of the given function is represented as {y | -5 ≤ y ≤ 5 , y ∈ R} .
Range of a function is defined as the possible values of y or the dependent variable in relation to the values of x.
Here from the graph we can see that the greatest value y achieves is 5.
The lowest value of y from the graph is -5 for all the values of x.
Hence the range will be {-5 ≤ y ≤ 5}
Now the graph is continuous, so we accept all values of y, hence y ∈ R .
Therefore the range will be: {y | -5 ≤ y ≤ 5 , y ∈ R} .
The set of all possible values for the results of the dependent variable, or the entire set of all possible values when the domain is substituted, is the range of a function.
The steps to find the range is:
The range of a function or similar object is the range of all y values, from least to greatest.We determine whether the provided expression of y is positive, negative, or equal to other values by substituting all possible values of x into it.We find the minimum and greatest values of y.To learn more about range visit:
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(x-3)45° find the value of x
Answer:
the value of x is 135 i believe
Step-by-step explanation:
sorry if im wrong
Graph the polygon with vertices A(-3,-1), B(2, 2), C(3,-3) and its image after a rotation 90° about the origin
What are the points???
Geometry chapter 4 review
The image of the polygon after rotation of 90° about the origin is A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) , the graph of the polygon and its image is shown below .
In the question ,
it is given that ,
the vertices of the polygon is A(-3,-1), B(2, 2), C(3,-3) .
the graph of the polygon ABC is shown below .
We know when the point (x , y) is rotated 90° in clockwise direction , it s coordinate change to (y , -x) .
So , image of coordinate A(-3,-1) is
A'(-1,-(-3)) = A'(-1, 3)
image of coordinate B(2, 2) is
B'(2 , -2)
image of coordinate C(3,-3) is
C'(-3 , -3)
So , the graph of the image with coordinates A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) is shown below .
Therefore , The image of the polygon after rotation of 90° about the origin is A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) , the graph of the polygon and its image is shown below .
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Nadia is a stockbroker. She earns 13% commission each week. Last week, she sold $7500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she
make in commission in 2011?
Answer:6400 multiplied by 13% (0.13) then multiply that answer by 52 , for weeks in the year.
Step-by-step explanation:
6400*.013= $832.00
832*52= $43264.00
Can I pls get sum help
The values of the variables "a", "b", and "c" are 3.06, 169.74, and 0, respectively. The total amount Gary will pay is $769.74.
Gary purchased a S750 TV on a credit card with a 22% annual percentage rate, and he wants to pay it off in payments of $200 per month. The table shows the information for the first four months after Gary used his credit card. We need to calculate the values of the missing variables and the total amount he will pay.
The variable "a" is the interest charged on the left amount in the third month.
a = (366.68 - 200)*0.018333 = 3.06
The variable "b" is the monthly amount paid by Gary. It is less than or equal to $200, depending on the payment amount. Since the amount to be paid is $169.74, which is less than $200, he will pay the whole amount in one go.
b = 169.74
The variable "c" is the interest charged on the left amount in the fourth month. Since then, the entire amount has been paid.
c = 0
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a survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. for a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. which of the following best describes a conclusion that can be drawn from this study?
Answer: based on the information that you gave me, I think the answer is :
A. sex is an explanatory variable; starting salary is the response variable ;area of specialization is a possible confounding variable
hope this helps
Step-by-step explanation:
Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes. How much longer does it take Carlos to sing the song? Estimate by rounding to the nearest whole number.
HELP
Approximately Carlo takes 2 minutes time to sing the song.
Given that, Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
Now,
Difference of singing time = 7.73-5.92
= 1.81 minutes
≈ 2 minutes
Hence, approximately Carlo takes 2 minutes time to sing the song.
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what is the volume of a trunk of a regular quadrangular pyramid where the side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm
The volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.
According to the question,
We have the following information:
The side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm.
Now, we know that the trunk of a regular quadrangular pyramid is in the shape of a cuboid.
And the following formula is used to find the volume of cuboid:
Length*breadth*height
Volume of a trunk of a regular quadrangular pyramid = 7.5*18*20.4
Volume of a trunk of a regular quadrangular pyramid = 2754 cubic centimeters
Hence, the volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.
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Use the Law of Cosines. Find x to the nearest tenth.
B
15
24
16
Using the Law of Cosines, the value of x is 40.9°.
Cosine formula, cos A [tex]=\frac{b^{2}+c^{2}-a^{2} }{2bc}[/tex].
Here, A = x
a = 16
b = 15
c = 24
cos x [tex]=\frac{15^{2}+24^{2}-16^{2}}{2*15*24}[/tex]
[tex]=\frac{225+576-256}{720}[/tex]
[tex]=\frac{801-256}{720}[/tex]
[tex]=\frac{545}{720}[/tex]
= 0.756
x [tex]= cos^{-1}0.756[/tex]
= 40.9
Hence, value of x is 40.9°.
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Write the slope-intercept form equation of a line that passes through the points (-1,2) and (4,-8).
Answer: y=-2x
Step-by-step explanation: Use the slope formula
-8-2/4-(-1)
-10/5=-2
y=-2
Answer:
y = - 2x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (4, - 8 )
m = [tex]\frac{-8-2}{4-(-1)}[/tex] = [tex]\frac{-10}{4+1}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = 2 + c ⇒ c = 2 - 2 = 0
y = - 2x + 0 , that is
y = - 2x ← equation of line
waste management company wants to construct a dumpster in the shape of a rectangular solid with no top whose length is four times its width. its volume is fixed at 25.6 yd3. find the dimensions of the dumpster that will minimize its surface area.
the dimensions of the dumpster that will minimize its surface area
length l = 6.32
width w = 1.58
height h = 0.39
Length = l
width = w
height = h
given that length is four times its width
l = 4w
Now, the formula for the surface area of a cube is;
S = 2lh + 2lw + 2wh
substitute l = 4w in the above equation
S = 2(4w)h+2(4w)w+2wh
S = 8wh+8[tex]w^{2}[/tex]+2wh
S = 10wh + 8[tex]w^{2}[/tex]
formula for the volume of a cube is;
V = lwh
now substitute l=4w in the above equation
V = (4w)wh
V = 4[tex]w^{2}[/tex]h
h = 4[tex]w^{2}[/tex]/V
Put V/2w² for h in the surface area equation to get;
S= 8w² + 10w(V/4w²)
= 8w² + 5V/2w
given that volume V = 25.6 substitute that in the above equation
S = 8w² + 5(25.6)/2w
= 8w² + 128/2w
Since we want to minimize the surface area, let us find the first derivative of S to get;
S' = 16w - 128/2w²
At S' = 0
0 = 16w- 128/2w²
16w = 128/2w²
32w³ = 128
w³ = 128/32
w³ = 4
w = [tex]\sqrt[3]{4}[/tex]
w = 1.58 yds
since l = 4w substitute the value of w in that
l = 4(1.58) = 6.32
h = 4[tex]w^{2}[/tex]/V = 4([tex]1.58^{2}[/tex])/25.6
h = 0.39
the dimensions are
length l = 6.32
width w = 1.58
height h = 0.39
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A scale drawing of a rectangular park had a scale of 1 cm = 90 m. 7.6 cm 9.1 cm- What is the actual area of the park in meters squared?
please answer this quickly this is due by 8pm ;((
Step-by-step explanation:
The drawing has the side dimension of 7.6 cm
since each cm represents 90 m the ACTUAL park is
7.6 x 90 = 684 meters
similarly, the bottom of the drawing has the dimension 9.1 cm which represents 9.1 x 90 = 819 m
the area of the park is then
Area = height x width = 684 m x 819 m = 560 196 m^2
OR in one step:
Area of the actual park is then
(7.6 cm * 90 m / cm ) X ( 9.1 cm * 90 m/cm ) = 560 196 m^2
What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
PLS RN!!
The equation of the trend line in the scatter plot is y = - 4x + 24
What is the slope-intercept form?
Writing the equation of a line in the slope-intercept form simply makes the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) obvious.
Here, we have
The yellow points are located at points (6, 0) and (4, 8)
For a linear equation that passes through the points (x₁, y₁) and (x₂, y₂), the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
Then, for the equation, the slope is
s = (8-0)/(4-6) = -4
Then the linear equation become
y = -4x + b
where b is the y-axis intercept.
To find b, we use that when x = 6, y = 0
0 = 6×(-4) + b
b = 24
Then equation become y = - 4x + 24
Hence, the equation of the trend line in the scatter plot is y = - 4x + 24
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The product of 9 and the sum of a number x and 4 is 6
Answer:
9(x+4)= 6
Step-by-step explanation:
I could be wrong but im not sure