Answer:
the answer is going to be 2/4
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. Which of the following statements is not true?
a.The exact mass of the cup of flour must be between 121.7 and 121.9 grams.
b.The cup of flour has a mass of exactly 121.8 grams.
c.Given the limitations of the scale, the measurement has an appropriate level of accuracy.
d.To the nearest gram, the cup of flour has a mass of 122 grams.
Answer
Is it C I may have done my math wrong lol
Step-by-step explanation:
Suppose you have a bag with the following in it: 5 one dollar bills, 4 fives, 3 tens, 5 twenties, and 3 fifties. Assuming the experiment requires drawing one bill from the bag at random, complete the probability distribution for this experiment.
Required:
What is the probability of drawing 9 dollars or less in a single draw?
Answer:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
(b) P($9 or less) = 3/5
Step-by-step explanation:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
Any other denomination
0
(b)
ways to draw $9 or less in a single draw
P($1) = 1/3
P($5) = 4/15
P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5
Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx
Answer:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(−6,0)
y-intercept(s):
(0,3)
So I would say -6 and 0 and 2 are in domain
Answer:
-6, 0 ,2 are in the domain
Step-by-step explanation:
The domain is what values that x can take
There are no restrictions on the values that x can take
All real numbers are in the domain
-6, 0 ,2 are in the domain
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children ages 5 to 15 years. Based on this data, the authors conclude that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.5 mm and a standard deviation of 4.8 mm.
Required:
a. Approximately what proportion of healthy children has left atrial diameters less than 24 mm?
b. Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?
c. Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?
d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
a) P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b) P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) z(s) = 0,84
Step-by-step explanation:
Normal Distribution N ( μ₀ ; σ ) is N ( 26,5 ; 4,8 )
a) P [ X < 24 mm ] = ( X - μ₀ ) / σ
P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52
P [ X < 24 mm ] = - 0,52
And from z-table we find area for z score
P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b)P [ X > 32 mm ] = 1 - P [ X < 32 mm ]
P [ X < 32 mm ] = ( 32 - 26,5 ) / 4,8
P [ X < 32 mm ] = 5,5/4,8 = 1,1458 ≈ 1,15
P [ X < 32 mm ] = 1,15
And from z-table we get
P [ X < 32 mm ] = 0,8749
Then:
P [ X > 32 mm ] = 1 - 0,8749
P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]
P [ X < 30 ] = 30 - 26,5 / 4,8 = 0,73
From z-table P [ X < 30 ] = 0,7673
P [ X < 25 ] = 25 - 26,5 / 4,8 = - 0,3125 ≈ - 0,31
From z-table P [ X < 25 ] = 0,2709
Then
P [ 25 < X < 30 ] = 0,7673 - 0,2709
P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) If 20 %
z- score for 20% is from z-table
z(s) = 0,84
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places. 800 grams = ______ pounds 700 grams = _____ pounds
Answer:
800= about 1.76 lbs
700= about 1.54 lbs
(there are about 453.5 grams in a pound
Step-by-step explanation:
Answer:
800 grams = 1.76 pounds
700 grams = 1.54 pounds
Step-by-step explanation:
i googled it
is this a function {(-2, 6), (-3, 7), (-4, 8), (-3, 10)}
No, that is not a function.
To be a function, each different input (x) needs a different output (y)
In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.
Answer: no
Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.
Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.
Ask yourself, do any of the ordered pairs
in this relation have the same x-coordinate?
Well by looking at this relation, we can see that two
of the ordered pairs have the same x-coordinate.
In this case, the x-coordinate of 3 appears twice.
So no, this relation is not a function.
The value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2, find the value of y when x = 3 and z = 336. I will rate you brainliest
Answer:
18
Step-by-step explanation:
Given that:
y∞ xz
y=kxz. Where k is constant
When z=196 and x= 2 then y= 7
7=(196)(2)k
7=392k
k=1/56
There fore y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Value of y varies jointly with x and z.
y ∞ xz
y=kxz.
Where k is constant
When z=196 and x= 2 then y= 7
Let us find the value of k
7=(196)(2)k
7=392k
Divide both sides by 7
k=1/56
y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
Hence, the value of y when x = 3 and z = 336 is 18.
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ2
Policeman A and Policeman B hand out 70 speeding tickets in a month.
Policeman A hands out 4 times as many speeding tickets as Policeman B.
Policeman A handed out ? Speeding tickets.
Answer:
Policeman A = 56 tickets
Step-by-step explanation:
Policemen A + B = 70
If Policeman B hands out x no of tickets...
Then Policeman A hands out 4x no of tickets
meaning...
x + 4x = 70
5x = 70
x = 70/5
x = 14
Therefore Policeman A hands out..
4x = 4 × 14 = 56 tickets
A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with a mean 0.499 in. and standard deviation 0.002 in. What percentage of bearings will now not be acceptable
Answer:
the percentage of bearings that will not be acceptable = 7.3%
Step-by-step explanation:
Given that:
Mean = 0.499
standard deviation = 0.002
if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.
Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )
= ( 0.496 , 0.504)
If x represents the diameter of the bearing , then the probability for the z value for the random variable x with a mean and standard deviation can be computed as follows:
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]
From the standard normal tables
[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]
[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]
By applying the concept of probability of a complement , the percentage of bearings will now not be acceptable
P(not be acceptable) = 1 - P(acceptable)
P(not be acceptable) = 1 - 0.927
P(not be acceptable) = 0.073
Thus, the percentage of bearings that will not be acceptable = 7.3%
Which of the following is a correct interpretation of the expression -4 - (-7)?
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex]-4-(-7)[/tex]
First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:
[tex]-4-(-7)\\=-4+7[/tex]
When adding on the number line, we move to the right.
Therefore, the correct interpretation is the value 7 digits to the right of -4.
D is the correct answer.
Answer:
D. the number that is 7 to the right of -4 on the number line
Step-by-step explanation:
interpret -4 - (-7)
= -4 +7
therefore
the number that is 7 to the right of -4 on the number line
so its D.
You meet with the financial aid office to discuss your costs for attending LSU next semester.Tuition is $113.67 per credit hour, and fees are a flat rate of $660. You have a grant of $350 and a scholarship of $400. If you are taking 15 credit hours what amount will you need go pay for your classes next semester?
Show you work
Answer:
$1615.05Step-by-step explanation:
Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.
Revenue generated = Grant + Scholarship amount
Revenue generated = $350 + $400
Revenue generated= $750
Total money needed to be spent in school = Tuition + fees
If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 = $1705.05
Total fees = $660
Total money needed to be spent in school = $1705.05 + $660
Total money needed to be spent in school = $2365.05
Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)
= $2365.05 - $750
= $1615.05
Hence, the amount I will need to pay for classes next semester is $1615.05
True or false? induction is a kind of thinking you use to form general ideas and rules based on mathematical formuals
Answer:
Hey there!
True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.
Let me know if this helps :)
Compute the flux of the vector field LaTeX: \vec{F}=F → =< y + z , x + z , x + y > though the unit cubed centered at origin.
Assuming the cube is closed, you can use the divergence theorem:
[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]
where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].
We have
[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]
so the flux is 0.
The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?
A. Fail to reject the null hypothesis and conclude the mean is 6.6 lb.
B. Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
C. Reject the null hypothesis and conclude the mean is greater than 6.6 lb.
D. Cannot calculate because the population standard deviation is unknown
Answer:
The correct option is A
Step-by-step explanation:
From the question we are told that
The population is [tex]\mu = 6.6[/tex]
The level of significance is [tex]\alpha = 5\% = 0.05[/tex]
The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds
The Null hypothesis is [tex]H_o : \mu = 6.6[/tex]
The Alternative hypothesis is [tex]H_a : \mu > 6.6[/tex]
The critical value of the level of significance obtained from the normal distribution table is
[tex]Z_{\alpha } = Z_{0.05 } = 1.645[/tex]
Generally the sample mean is mathematically evaluated as
[tex]\=x = \frac{\sum x_i }{n}[/tex]
substituting values
[tex]\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}[/tex]
[tex]\=x = 7.5571[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }[/tex][tex]\sigma = 1.1774[/tex]
Generally the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }[/tex]
[tex]t = 1.4274[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate
The conclusion is that the mean is [tex]\mu = 6.6 \ lb[/tex]
1/9, -0.1, -2/12 in order
Answer:
-2/12, -0.1, 1/9
Step-by-step explanation:
Answer:
Least to greatest: -2/12 , -0.1 , 1/9
Greatest to least: 1/9, -0.1, -2/12
Step-by-step explanation:
Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.
Divide:
1/9 = ~0.111 (rounded)
-0.1 = -0.1
-2/12 = - ~0.167 (rounded)
Put the numbers in number order:
-~0.167 , -0.1 , ~0.111
-2/12 , -0.1 , 1/9
~
Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.
Answer:
the equation is not correct, u have to write like
ax'3+bx'2+cx+d
Answer:
x=-2 and x=0
Step-by-step explanation:
So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.
First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x
Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in
So, in conclusion I believe the answer to be x=-2 and x=0
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
Techwiz electronics makes a profit of $35 for each mp3 and $18 for each DVD last week techwiz sold a combined total of 118 mp3 and DVD players. Let x be the number of mp3 sold last week write an expression for the combined total profit (in dollars) made last week
Answer:
The total profit is [tex]p = 17x + 2124[/tex]
Step-by-step explanation:
From the question we are told that
The profit made on each mp3 is k = $35
The profit made on each mp3 is y = $18
The total amount sold is n = 118
Now given that the amount of mp3 sold is x then the amount of DVD sold is mathematically evaluated as
[tex]n - x[/tex]
Now the profit made on the x number of mp3 sold is
[tex]x * 35 = 3x[/tex]
And the the profit made from the n-x number of DVD sold is 18 (n-x ) = 18 - 18x
So the total profit made last week from the sales of both mp3 and DVD is
[tex]p = 35x + 18n - 18x[/tex]
[tex]p = 17x + 18(118)[/tex]
[tex]p = 17x + 2124[/tex]
A sports club was formed in the month of May last year. The function below, M(t), models the number of club members for the first 10 months, where t represents the number of months since the club was formed in May. m(t)=t^2-6t+28 What was the minimum number of members during the first 10 months the club was open? A. 19 B. 28 C. 25 D. 30
Answer:
A: 19
Step-by-step explanation:
For this, we can complete the square. We first look at the first 2 terms,
t^2 and -6t.
We know that [tex](t-3)^2[/tex] will include terms.
[tex](t-3)^2 = t^2 - 6t + 9[/tex]
But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:
[tex]m(t) = (t-3)^2 - 9 +28[/tex]
[tex]m(t) = (t-3)^2 +19[/tex]
Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.
Simplify the following expression. (4x − 8)(4x + 8)
Answer:
16x^2 - 64
Step-by-step explanation:
(4x − 8)(4x + 8)
We recognize that this is the difference of squares
(a-b) (a+b) = a^2 - b^2
=(4x)^2 - 8^2
=16x^2 - 64
Average of 44.64, 43.45, 42.79, 42.28
Answer:
43.29Step-by-step explanation:
[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]
The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Question options :
A. There is sufficient evidence to reject the claim
u < 99.
B. There is sufficient evidence to support the claim
u < 99.
C. There is not sufficient evidence to reject the claim
u < 99.
D. There is not sufficient evidence to support the claim
u< 99.
Answer:
B. There is sufficient evidence to support the claim
u < 99.
Step-by-step explanation:
We construct the n*ll and alternative hypotheses to support our claim
The n*ll hypothesis :H0
The alternative hypothesis : Ha
N*ll hypothesis =H0: u=99
Alternative hypothesis =Ha: u<99
So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99
we can therefore have sufficient evidence to support our claim that u<99
Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score? % (b) What percentage were above?
Answer:
Step-by-step explanation:
From the given information;
Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting.
What percentage of the scores were at or below her score?
The percentage of scores that were at or below her score is
Percentage P = 90%
This benchmark is more than average, so we can typically say more of the scores were at or below her score
What percentage were above?
Since The percentage of scores that were at or below her score is
Percentage P = 90%
Then the percentage of the scores that were above will be : (100 -90)%
= 10 %
We can see here that less percentage of score were above Angela's Score.
A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings
Answer:
144 ways
Step-by-step explanation:
Number of paintings = 7
Renaissance = 4
Baroque = 3
We are hanging from left to right and we will first hang Renaissance painting before baroque painting.
For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24
For baroque we have 3! Ways of doing so. 3x2x1 = 6
We have 4!ways x 3!ways
= (4x3x2x1) * (3x2x1) ways
= 144 ways
Therefore we have 144 ways to hang the painting.
What is the solution to 5x - 15 = 5(-4x - 3) ? Group of answer choices -12 6 0 -16
Answer:
x = 0Step-by-step explanation:
5x - 15 = 5(-4x - 3)
Multiply the terms in the bracket
5x - 15 = - 20x - 15
Group like terms
Send the constants to the right side of the line and those with variables to the left side
That's
5x + 20x = - 15 + 15
Simplify
25x = 0
Divide both sides by 25
We have the final answer as
x = 0Hope this helps you
Answer:
x=0
Step-by-step explanation:
5x - 15 = 5(-4x - 3)
To find the solution to this equation, we have to get x by itself on one side of the equation.
First, distribute the 5 on the right side. Multiply each term by 5.
5x - 15= (5*-4x) + (5*-3)
5x-15 = -20x + (5*-3)
5x-15= -20x -15
Next, add 20x to both sides of the equation.
(5x+20x) -15 = (-20x+20x) -15
(5+20x) -15 = -15
25x -15=-15
Next, add 15 to both sides of the equation.
25x -15 +15 = -15+15
25x= -15+15
25x=0
Finally, divide both sides of the equation by 25.
25x/25=0/25
x= 0/25
x= 0
The solution to this equation is x=0
a department store regularly sells a pair of pants for $49.95. they are having a sale where clothing 30% off.
after including an 8% sales tax, how much do the pants cost on sale?
A. $30.97
B. $38.96
C. $37.76
D. $32.17
Answer:
C. $37.76
Step-by-step explanation:
30% of $49.95
=30/100×49.95
=$14.99
selling price = 49.95 -14.99
= $34.96
8% sales tax included
=8/100×34.96
=$2.80
new price= 34.96+2.80
=$37.76
Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth table
It is.........................................................
One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q
Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.
Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.
Help please, i really need the answer asap.
The larger metallic object is initially at rest, so the velocity is 0 when t = 0. The speed changes after t = 3 seconds.
Answer:
It would be the last one.
Step-by-step explanation:
It says the object is initially at rest, so you look for a table with 0 m/s and you find the last table had been at rest for 0 -2 seconds. The small rocky object initially had a speed of 90 m/s and then decreased to 36 m/s as its energy transferred to the metallic object. The metallic object's speed from time 4-6s with the small rocky object equals the small rocky initial speed.
Rocky Object initial speed = 90 m/s
Rocky Object new speed = 36 m/s
Large metallic object speed after collision = 64 m/s.
64 m/s + 36 m/s = 90 m/s
Large metallic object speed after collision + Rocky Object new speed
= Rocky Object initial speed
You can also test this for kinetic energy.
The entire graph of the function h is shown below write the domain and range of h using interval notation.
you can only see values of [tex] x[/tex] Ranging from $-3$ to $3$ and they're included, so domain is $[-3,3]$
and $y$ values ranging from $-2$ to $4$ but $-2$ is not included so range is $(-2,4]$
