The probability that at least one of the births requires a cesarean delivery is 0.897.
To calculate prob(x >= 1):
prob(x>=1) = 1 - prob(x = 0)
= 1 - (1-0.248)^8
= 0.897
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Find the volume of the solid of revolution formed by rotating
about the x-axis each region bounded by the given curves.
f(x) =(1/3)x + 2, y = 0, x = 1, x = 3
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
Let us think of any region that is enclosed by a function g(x) and the x-axis between x=a and x=b. If this region is rotated about the x-axis, the solid of rotation that results can be thought of as consisting of thin cylindrical discs with a width of dx and a radius of g (x). Therefore, by integrating the volume of this disc, the whole volume of the solid will be revealed.
Volume=[tex]\int^{a}_{b}\pi [g(x)]^2dx[/tex]
The given function is g(x)=(1/3)x+2 ranging from x=1 to x=3
Therefore volume of the solid formed is:
[tex]\int^{3}_{1}\pi [\frac{1}{3}x]^2dx\\=\int^{3}_{1}\pi [\frac{1}{9}x^2]dx\\=\pi \int^{3}_{1} [\frac{1}{9}x^2]dx\\\\=\pi [\frac{1}{27}x^3 ]^3_1\\= \frac{26}{27} \pi[/tex]
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
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Solve for y.
5. x = 1/3y +2
Answer: y=3x-6
Step-by-step explanation:
ANSWER:y=1/(3x-6)
Step-by-step explanation:
i think you are asking for the change of subject of formula(Transposition of subjects).
x=1/3y+2
multiply both sides by 3y
x × 3y=1/3y × 3y + 2 × 3y
3xy=1+6y
collect like terms
3xy-6y=1
fractionalize
y(3x-6)=1
divide both sides by (3x-6)
y=1/(3x-6)
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Which measurement is closest to the circumference of the circle in square centimeters
Answer:
the measurement of the circumference of a circle is 21
Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 11 inches of wire cost?
Answer:
11 inches of wire will cost 66 cents
Step-by-step explanation:
14 inches - 84 cents
find unit rate by dividing 84 by 14
84/14=6
so is is 6 cents per inch
so multiply 6 by 11
11 inches of wire will cost 66 cents
Find the x- and y-intercepts of the graph of the equation. (If an
(a)
X^2-xy+4y=49
Answer:
x=±7; y=12.25.
Step-by-step explanation:
1) x-interception:
(y=0): x²=49, ⇒ x=±7;
2) y-interception:
(x=0): 4y=49; ⇒ y=12.25.
please help me with this math homework
Answer:
Step-by-step explanation:
(2*9/5d*9)-(1*5/9d*5)
18/45d-5/45d
13/45d
Help please Im confused becuz i got 19.4 but its wronggg
Answer:
20.75
Step-by-step explanation:
1cm=10mm
so:1mm=0.1cm
0.1/2=0.05
if it asks lower bound:
5.2-0.05=5.15 +
6.3-0.05=6.25 +
9.4-0.05=9.35
Create and solve a proportion: to find the cost of 4 hamburgers if 5 hamburgers cost $21.98.
Answer:
4/x = 5/21.98 ; x=17.584
Step-by-step explanation:
subes la x al otro lado , multiplicas el 21.98 con el 4 y luego lo divides entre 5, así resulta q x es igual a 17.584
Answer:
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Calculator is showing a result of 78.987625. What is this to 2 decimal places
Answer:
78.99
Step-by-step explanation:
Rounding to the 2nd decimal place the number 78.987625
Write down everything upto and including the 2nd decimal: 78.98
Check out the next digit. If >= 5, then increase the 2nd decimal digit above by 1, if not leave it as is.
For 78.987625 the digit next to the 2 decimal digit is 7 so we increase 78.98 to 78.99
A rectangular field is eleven times as long as it is wide. If the perimeter of the field is 1680 feet, what are the dimensions of the field? A) Write an equation you can use to answer the given question. Let w be the width of the field.
Answer:
2(w+11w)=1680
Step-by-step explanation:
If the width is w, then the length is 11w.
Using the formula for the perimeter of the rectangle, the equation is 2(w+11w)=1680
Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.
Answer:
The length of AC is 15 units
Step-by-step explanation:
Find the future value (in dollars) of an 18-month investment of $4,300 into a simple interest rate account that has an annual simple interest rate of 5.1%.
keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4300\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ A=4300[1+(0.051)(\frac{3}{2})] \implies A=4628.95[/tex]
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
A.1
B.3
C.4
D.12
Using a proportional relationship, the fewest number of vegetables that can be used to make this salad is:
C. 4
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, looming at the table, we have that the number of Broccoli is triple the number of carrots, hence the proportional function is:
B = 3C.
When there is one carrot, the number of broccoli is given by:
B = 3 x 1 = 3.
Hence the fewest number of vegetables is of 4, as 1 carrot + 3 broccoli = 4 vegetables, hence option C is correct.
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6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
The steel is more dense than lake water
Answer:
true
Step-by-step explanation:
That is a true statement.
The density of steel is approx. 7.85 g/cm³.
The density of water is approximately 1 g/cm³.
Use the given domain to find the range of each function. F(x)=|x|, D={-4,0,-3}
Answer:
[tex]R=\{0,3,4\}[/tex]
Step-by-step explanation:
We can find the range by finding the set of values the function takes for each element in the domain.
[tex]F(-4)=|-4|=4 \\ \\ F(0)=|0|=0 \\ \\ F(3)=|3|=3 \\ \\ \therefore R=\{0,3,4\}[/tex]
The domain and the range of the function are
Domain, D = {-4,0,-3}Range, R = {4,0,3}Calculating the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = |x|
The rule of a function is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain, D = {-4,0,-3}
Range, R = {4,0,3}
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5(x+11)>-4(-x-12)
someone pls help this is due tmrw!
Answer:
work is shown and pictured
Question 3
1 pts
A survey was conducted by visiting a student parking lot to estimate the proportion of
cars that were red. Which of the following is NOT correct?
A. If another sample of cars was chosen, it is likely that a different proportion of cars that are red
would be obtained.
B. The sample would be representative of the population if 100 cars were chosen regardless if
randomization was used or not.
C. Even though a random sample was taken from cars in the parking lot, the sample may not be
representative of the cars driven by students because the decision to park in that particular lot is
self-selected.
D. If the sampled stall was empty, we can simply choose another stall, at random, to take its place
because it is not likely that the stall being vacant is related to a car being red.
The sample would be representative of the population if 100 cars were chosen regardless if randomization was used or not; this statement is not correct;
A survey was carried out by visiting a student parking lot to estimate the number of red cars.
If a different sample of cars was picked, the proportion of red cars would most likely be different. This statement is correct.
The sample would be representative of the population if 100 cars were chosen regardless if randomization was used or not. This statement is not correct because you select only 100 cars to represent whole population that too without randomization;
Despite the fact that a random sample was obtained from cars in the parking lot, the sample may not be representative.
because the decision to park in that particular lot is typical of the cars driven by students self-selected.
If the sampled stall was empty, we can simply choose another stall at random to take its place because the stall being unoccupied is unlikely to be associated to a red car.
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What is the equation of the tangent of f(x) 3 X at (1, 3)?
The Equation of the tangent line is y = 4x - 1.
According to the statement
We have to find that the equation of the tangent of the line.
So, For this purpose, we know that the
Equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.
From the given information:
f(x) = 3 X at (1, 3)
Then
The tangent line of a curve y = f(x) is a line that touches the curve at a point (x0, y0). Its slope (m) is found by substituting the point where it is drawn in the derivative f'(x) and its equation is found by using y - y0 = m (x - x0).
From the given it is clear that the slope of the equation is a 3.
Then m = 3
then
y – y1 = m (x – x1)
Substitute the points here
y - 3 = 4(x - 1)
Then
y = 4x - 4 +3
y = 4x - 1.
So, The Equation of the tangent line is y = 4x - 1.
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Which diagram shows two figures intersecting at exactly four points?
Answer:
The rightmost figure
Step-by-step explanation:
That is the only figure where there are 4 points of intersection. It is a rhombus inscribed in a square
Erin watches the price of an item advertised on the internet. The ad says the price will go down $3 each hour. Erin wants to know how much the
price will change in 6 hours. She writes this number sentence.
(-3) x 6=-18
What does the number sentence mean?
O The price will rise $6 in 18 hours.
O The price will rise $18 in 6 hours.
O The price will drop $6 in 18 hours.
O The price will drop $18 in 6 hours.
if x=2 then solve |-3x - 5| + |-1 - x^2| + 2x^3
Answer:
32
_____
Work[tex]\left|-3\left(2\right)-5\right|+\left|-1-2^2\right|+2\cdot \:2^3\\\left|-3\cdot \:2-5\right|+\left|-1-2^2\right|+2\cdot \:2^3\\-3 \cdot 2 - 5 = -11\\\left|-11\right|+\left|-1-2^2\right|+2\cdot \:2^3\\-1 - 2^2 = -1 - 4 = -5\\\left|-11\right|+\left|-5\right|+2\cdot \:2^3\\|-11| = 11\\|-5| = 5\\2 \cdot 2^3 = 2 \cdot 8 = 16\\11+5+16\\=32[/tex]
_____
Identify the errors made in finding the inverse of
y = x- + 12x.
x = y2+ 12x
y?=x-12x
y2=-11x
y=V-11x, for x 2 0
Describe the three errors.
The following mistakes were made in the solution of the inverse function:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.What are inverse functions?The original value for which the function's output was provided is returned by the inverse function.F and G are inverse in terms of functions, with f(g(x)) = g(f(x)) = x.The initial value is returned by a function that is its inverse. The inverse of f is then g(y) = (y-5)/2 = x. (x).Therefore, the first error is caused by the incorrect variable swap.
The correct expression is:
x = y² + 12yThe following error is:
y = √-11xThe correct expression:
y = ± √-11xFinally, the domain is incorrect.
Because if x is 0 or positive, y = -11x has no true value.As a result, the following errors were made in the inverse function solution:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.Know more about inverse functions here:
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The correct question is given below:
Identify the errors made in finding the inverse of y = x2 + 12x.
Describe the three errors.
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was
then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (a) through (f).
a. What was the most frequent outcome of the experiment?
b. What was the least frequent?
c. How many times did we observe a 5?
d. How many more 8's were observed than 11's?
e. Determine the percentage of time a 5 was observed.
f. Describe the shape of the distribution.
The answers to the questions are:
The most frequent outcome of the distribution that we have here is 7.The least frequent outcome is 12The number of times that we observed a 5 is 10 timesThe 8ths that were observed than 11 is 16 - 4 = 12 timesA 5 was attempted at 10 percent of the timeThe shape of the distribution is the bell shaped distribution.What is a frequency histogram?This is the term that is used to refer to the graphical representation of a frequency distribution. It helps to show us the frequency that the details in the class would have to fall under.
For example, the most frequent outcome can be seen as the one that has the highest point on the graph. We can see the highest point as 7 and its frequency is 20.
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Answer:
A. 7
B. 12
C. 15
D. 16
E. 15%
F. Bell-shaped
Find the area of the triangle. Show your reasoning. If you get stuck, carefully consider which side of the triangle to use as the base.
The area of the triangle is found as 12 unit².
What is defined as the triangle?A triangle is a three-sided polygon with three sides that closes a space.
The three sides are formed by lines, line segments, or rays (in just about any combination). Three vertices, or corners, are formed if three sides form or meet.A triangle's height or altitude is calculated by drawing a perpendicular line through one side to the opposite angle.The base is the side with which the altitude intersects wherever it is built.The formula for the area of the triangle is;
Area of triangle= ½ × base × height
The base is given as 6 units and the height is 4 units. (count 1 column of graph as 1 unit).
Put the values in formula.
Area of triangle = ½(6)(4)
Area of triangle = 12 unit.²
Therefore, the area of the triangle is found as 12 unit.²
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Drag the decimal values to match the corresponding fraction values.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1/3 =
1/2 =
1/4 =
3/4 =
2/3 =
to choose from: 0.50 0.75 0.25 0.66 0.33
please help
[tex]1/3 \longrightarrow 0.33 \\ \\ 1/2 \longrightarrow 0.50 \\ \\ 1/4 \longrightarrow 0.25 \\ \\ 3/4 \longrightarrow 0.75 \\ \\ 2/3 \longrightarrow 0.66[/tex]
Which polynomial represents the sum below?
+
2x² + 5x+4
5x2+
Answer:
????
Step-by-step explanation:
I don't get this
at all
5 is 1/2% of what number
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
Answer:
each takes 3 together 3x3=9
Solve the literal equation for x. State any
necessary restrictions on the letters
representing constants in the equation.
a (bx + c) = 0
