Pressure is force per unit area. If the block is sitting at rest on the surface, it applies a pressure of mg/A, where mg is the block's weight and A is the area of the face that makes contact with the surface.
The smaller the value of A, the larger the pressure. So the highest pressure the block can exert is achieved when it's resting on the face with the smallest dimensions.
If the block is a cube with side length 95 cm, then the pressure exerted by each face is the same.
Which ordered pair would form a proportional
relationship with the points in the graph?
O (44)
O (69)
O (9,6)
O (8,5)
A population is equally divided into three class of drivers. The number of accidents per individual driver is Poisson for all drivers. For a driver of Class I, the expected number of accidents is uniformly distributed over [0.2, 1.0]. For a driver of Class II, the expected number of accidents is uniformly distributed over [0.4, 2.0]. For a driver of Class III, the expected number of accidents is uniformly distributed over [0.6, 3.0]. For driver randomly selected from this population, determine the probability of zero accidents.
Answer:
Following are the solution to the given points:
Step-by-step explanation:
As a result, Poisson for each driver seems to be the number of accidents.
Let X be the random vector indicating accident frequency.
Let, [tex]\lambda=[/tex]Expected accident frequency
[tex]P(X=0) = e^{-\lambda}[/tex]
For class 1:
[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]
For class 2:
[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]
For class 3:
[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]
The population is equally divided into three classes of drivers.
Hence, the Probability
[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]
Find the solutions of the quadratic equation x2 + 7x + 10 = 0.
Question 13 options:
A)
x = 2, 5
B)
x = –2, –5
C)
x = –7, –3
D)
x = 7, 3
Answer:
Step-by-step explanation:
x² + 7x + 10 = 0
x = [-7 ± √(7² - 4·1·10)]/(2·1) = [-7 ± √9[/2 = [-7 ± 3]/2 = -2, -5
The length of a rectangle is five times its width. If the perimeter of the rectangle is 108 in, find its area.
Answer:
Step-by-step explanation:multiple 5 times 108 and that gives you your answer..
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
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I want to know how to solve this equation
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
Which percent is eguivalent to 2.5?
1)2.5%
2)25%
3)250%
4)2,500%
Answer: 250%
since, 100% = 100/100
250% = 250/100
Step-by-step explanation:
Which points lie on the graph of f(x) = loggx?
Check all that apply.
Step-by-step explanation:
f(x)=log(x)
=d(log(x)/dx)
=>y=1/x
Please show your steps
Answer:
M of aftershock = 4.90
Step-by-step explanation:
5.6 = log(x/1)
[tex]10^{5.6} = 398107.1 \\[/tex]
1/5 * 398,107.1 = 79,621.4
[tex]10^{m} =[/tex] 79,621.4
m = log (79,621.4) = 4.90
When is the Declaration of Independence?
Answer:
July 4th, 1776.
Step-by-step explanation:
By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.
Which is a direct proportion
y = -4
y = 2x + 1
y = 6
y = 2/3x
Answer:
y=2x+1
Step-by-step explanation:
y is directly proportional to x if it increases as x increases
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
Answer:
Area of rectangle = 2H² - 5H
Step-by-step explanation:
Let the length be L.Let the height be H.Translating the word problem into an algebraic expression, we have;
Length =2H - 5
To write the algebraic expression to model the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = L * H
Where;
L is the Length.H is the Height.Substituting the values into the formula, we have;
Area of rectangle = (2H - 5)*H
Area of rectangle = 2H² - 5H
HELP PLS I DONT KNOW THIS ONE
Answer:
1
-------------
(x+2)(x-4)
Step-by-step explanation:
x+4 x+3
------------- * --------------
x^2+5x+6 x^2 -16
Factor
x+4 x+3
------------- * --------------
(x+3)(x+2) (x+4)(x-4)
Cancel like terms
1 1
------------- * --------------
(1)(x+2) (1)(x-4)
1
------------- x cannot equal -3, -4, -2, 4
(x+2)(x-4)
A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
Answer:
dv = surface area * dh
so
dv/dt = surface area * dh/dt
width at surface = 40 + (80-40)(30/40)
= 40 + 30 = 70 cm = 0.70 m
so
surface area = 9 * .7 = 6.3 m^2
so
.3 m^3/min = 6.3 m^2 * dh/dt
and
dh/dt = .047 meters/min or 4.7 cm/min
Step-by-step explanation:
Find the missing side lengths leave your answer as a racials simplest form
Answer:
m=[tex]7\sqrt3[/tex]
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]
In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7
And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]
Hope this helps!
Find the missing side length image below
Answer:
40
Step-by-step explanation:
Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.
Therefore, we would have the following ratio:
28/35 = ?/50
Cross multiply
35*? = 50*28
35*? = 1,400
Divide both sides by 35
? = 1400/35
? = 40
A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario? Question 23 options: |x + 18| ≤ 4 |x – 18| ≤ 4 |x – 4| > 18 |x + 18| > 4
Answer:
the correct answer is |x – 18| ≤ 4
just took the test
Step-by-step explanation:
HELP. Use the grouping method to factor the polynomial below completely.
x^3 – 5x^2 + 3x - 15
A. (x^2 + 5)(x-3)
B. (x^2 - 3)(x+5)
C. (x^2 - 5)(x+3)
D. (x^2 + 3)(x - 5)
Answer:
D
Step-by-step explanation:
(x^2+3)(x-5)
That's the answer
for the binomial distribution with n=4 and p=0.25
a)find the probability of three success
b)at the most three success
c)two or more failures
Answer:
a.) .0469
b.) .9961
c.) .9492
Rounded these check below for full answers
Step-by-step explanation:
a.)
[tex]{4\choose3}*.25^3*(1-.25)=.046875[/tex]
b.)
Porbability of at most 3 successes is equal to 1-p(4)
p(4)=
[tex]{4\choose4}*.25^4=.003690625[/tex]
1-.003690625=.99609375
c.)
two or more failures is equa lto
p(0)+p(1)+p(2)=
[tex]{4\choose0}*.25^0*(1-.25)^4+{4\choose1}*.25^1(1-.25)^3+{4\choose2}*.25^2*(1-.25)^2=.94921875[/tex]
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!!!. Please help me with these math questions. Chapter 10 part 2
3. How do solving for solving to a rational function differ from solving for solutions to a rational inequality? How they are similar?
4. How is the difference quotient of a function determined? And how is the difference quotient related to the secant line? Is there a pattern for the difference quotient of linear functions?
9514 1404 393
Answer:
3. sign changes in the denominator need to be taken into account
4. difference quotient: (f(x+h) -f(x))/h; It is the slope of the secant line. For linear functions, the slope is constant, as is the difference quotient.
Step-by-step explanation:
3. When solving the equation f(x) = 0, where f(x) is a rational function, only the numerator zeros need to be considered.
When solving the inequality f(x) ≤ 0, or f(x) < 0, both numerator and denominator zeros need to be considered. As with solving any inequality, multiplying or dividing by a negative number changes the sense of the comparison.
Example
f(x) = x/(x-2) changes sign at both x=0 and x=2. Then three regions need to be considered when solving f(x) < 0. Those are x < 0, 0 < x < 2, and 2 < x.
__
4. The difference quotient is defined as ...
dq = (f(x +h) -f(x))/h
The difference quotient is essentially the average slope between (x, f(x)) and (x+h, f(x+h)). That is, it is the slope of the secant line between those two points.
For linear functions, the slope is a constant. The difference quotient is a constant equal to the slope of the line.
Example
f(x) = ax +b . . . . . a linear function with a slope of 'a'
The difference quotient is ...
(f(x+h) -f(x))/h = ((a(x+h)+b) -(ax+b))/h = (ax+ah+b -ax -b)/h = ah/h = a
The difference quotient is the slope of the line.
HELP PLS ! ! !
What is |1 − 8i|?
A) √-65
B) 65
C) √65
D) √13
Answer:
C) SQRT(65)
Step-by-step explanation:
the magnitude of 1-8i is given by the following:
sqrt(a^2+b^2)
sqrt(1^2+8^2)
=sqrt(1+64)
=sqrt(65)
It is to be noted that the magnitude of |1 − 8i| is √(65) (Option C)
What is the computation of the above?To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.
Using the formula, we have -
|1 - 8i| = √(1² + (-8)²)
= √(1 + 64)
= √65
Hence, the magnitude of 1 - 8i is √65.
So the correct answer is C) √65.
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A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answer:
28 seconds ..............
Find the derivative on the value of x=-4
[tex]y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]
[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]
[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]
[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]
[tex]\\ \sf\longmapsto y=-1015i[/tex]
Determine the dimension of the vector space. M4,2
STEP 1: Determine the number of linearly independent vectors needed to span M4,2. The basis for M4,2 has linearly independent vectors.
STEP 2: Using the result from Step 1, determine the dimension of M4,2.
Answer:
STEP 1
M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.
Hence its basis has 8 linearly independent vectors.
STEP 2
Dimension= cardinality of basis = 8.
The word "theory" is composed of the letters of the split alphabet. Three cards are taken out at random and stacked in a row one after another in order of appearance. How many possible compounds can be made up of the letters of this word?
Answer:
There would be [tex]120[/tex] of them.
Step-by-step explanation:
There are [tex]6[/tex] distinct letters in the word "[tex]\verb!theory![/tex]".
Hence, there would [tex]6[/tex] possible choices for the first letter that was selected.
Since the chosen card won't be placed back in the pool, there would be only [tex](6 - 1) = 5[/tex] possible choices for the second letter.
Likewise, there would be [tex](6 - 2) = 4[/tex] choices for the third letter.
[tex]6 \times 5 \times 4 = 120[/tex]. In other words, there are [tex]120[/tex] possible ways to draw three cards out of [tex]6[/tex] one after another.
Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "[tex]\verb!the![/tex]" and "[tex]\verb!het![/tex]" from the number of combinations.
VG¯¯¯¯¯¯¯¯=12.2 in. PG¯¯¯¯¯¯¯¯=13.1 in. Find the radius of the circle.
Answer:iiii
Step-by-step explanation:iiiii
Answer:
17.9
Step-by-step explanation:
You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
