Answer
Step-by-step explanation:
Answer:
See the argument below
Step-by-step explanation:
I will give the argument in symbolic form, using rules of inference.
First, let's conclude c.
(1)⇒a by simplification of conjunction
a⇒¬(¬a) by double negation
¬(¬a)∧(2)⇒¬(¬c) by Modus tollens
¬(¬c)⇒c by double negation
Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.
An alternative approach to De Morgan's law is the following:
By contradiction proof, assume h is true.
h⇒d∨h by addition
(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.
You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman
Answer:
0.40
Step-by-step explanation:
The computation of the probability for the second student be sophomore and the first is a freshman is shown below:
Let us assume
Sophomore = S
Freshman = F
Based on this assumption, the probability is as follows
So,
[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]
= 0.40
Hence, the probability for the second student be sophomore and the first student be freshman is 0.40
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $
Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be y;
Let the tip be t
From the question;
15% of y is the tip charge (t). i.e
t = 15%y
=> t = 0.15y --------(i)
The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = [tex]\frac{20.70}{1.15}[/tex]
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
assume the carrying capacity of the earth is 21 billion. use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2% per year?
Answer:
current population growth rate would be -3.1%
Step-by-step explanation:
We have to:
Growth rate = r * (1 - population / carrying capacity)
for 1960,
we have carrying capacity = 21 billion
population = 3 billion
r = Growth rate 1960 / (1 - population / carrying capacity)
replacing:
r = 0.021 / (1 - 3/21)
r = 0.0245
that is to say r = 2.45%
Now the current population would be:
= 0.0245 * (1 - carrying population / carrying capacity)
we replace:
= 0.0245 * (1 - 6.8 / 3)
= -0.031
current population growth rate would be -3.1%
The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.
Given :
Assume the carrying capacity of the earth is 21 billion. Use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion.The growth rate is given by the formula:
[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]
Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).
[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]
[tex]0.021=r\times \dfrac{18}{21}[/tex]
0.0245 = r
So, r = 2.45%.
Now, the growth rate of the current population is:
[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]
[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]
0.031 = Growth Rate
So, the growth rate is -3.1%.
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Given the center of a circle is (0, -4) and the radius is 5, which of the following would be the correct equation?
Answer:
x^2+(y+4)^2=25
If you would like additional help in math or another subject for FREE, check out growthinyouth.org!
Step-by-step explanation:
the exact derivative of f(x)=x^3 at x=5
Answer:
[tex]75[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx}\left(x^3\right)[/tex]
[tex]=3x^{3-1}[/tex]
[tex]=3x^2[/tex]
[tex]3\left(5\right)^2[/tex]
[tex]=3\cdot \:25[/tex]
[tex]=75[/tex]
Which question is best modeled with a division expression? What is the sum of 3 and StartFraction 8 Over 11 EndFraction? What is the quotient of 3 and StartFraction 8 Over 11 EndFraction? What is the product of 3 and StartFraction 8 Over 11 EndFraction? What is the difference of 3 and StartFraction 8 Over 11 EndFraction?
Answer: B
Step-by-step explanation:
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The numbers are given below.
3 and 8/11
The sum of the numbers is calculated as,
⇒ 3 + 8/11
⇒ (33 + 8) / 11
⇒ 41 / 11
⇒ 3.7272
The quotient of the numbers is calculated as,
⇒ 3 / (8/11)
⇒ 3 x 11 / 8
⇒ 4.125
The product of the numbers is calculated as,
⇒ (3) x (8 / 11)
⇒ 24 / 11
⇒ 2.1818
The difference between the numbers is calculated as,
⇒ 3 - 8/11
⇒ (33 - 8) / 11
⇒ 25 / 11
⇒ 2.2727
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
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What is the measure of A? (solve to the nearest WHOLE DEGREE)
Answer:
A = 0.507 or 29 degrees
Step-by-step explanation:
5 = tanA * 9
inv tan = 5/9
angle A = 0.507
angle A = 29 degrees
Can you help me solve this question? (Also explain me how is it possible)
Answer:
Answer B) (2 times )
Step-by-step explanation:
Let's start with the person that shook hands more (Dora), so we already know how four of this connections took place See attached image.
step 1:
D is connected to A, B, C, and E
Step 2:
Now proceed with the connections for the second greatest (C who shook hands with 3 people). Notice that C is already connected with D, and can connect with B and with E, but NOT with A (since this person shook hands only once - with D. So C is connected to B, D, and E completing the three handshakes.
step 3: Now just corroborate that B is already connected to two people (C and D). So just count the number of connections that E is left with: 2 handshakes.
Answer:
( E ) 0
Step-by-step explanation:
Solution:-
- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.
- We will use an intuitive way of tackling this problem.
- We have a total of 5 people who greeted each other at the party.
- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".
- We will define our event as shaking hands. It takes 2 people to shake hands.
- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.
- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:
5C2 = 10 possible ways.
- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.
- We are already given the data for how many handshakes were made by each person as follows:
Name Number of handshakes
Alan 1
Bella 2
Claire 3
Dora 4
=======================================
Total 10
=======================================
- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.
Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.
A dress regularly sells for $137. The sale price is $102.75. Find the discount & the percent of the discount
Answer:
Discount : $34.25 off. Percent of the discount : 25%
Step-by-step explanation:
137 - 102.75 = 34.25.
34.25/137 x 100 = 25%
Need help ASAP! What Is the measure of an angle If It Is 240 less then 6 times It’s own supplement?
Answer:
120°
Step-by-step explanation:
Given that an angle = 240 less than 6 × its own supplement,
Let x = be the angle
Its supplement = (180 - x)
If the angle (x) is 240 less than 6 times its own supplement, (180 - x), we will have the following expression:
[tex] x = 6*(180 - x) - 240 [/tex]
Simplify the expression to solve for x
[tex] x = 1080 - 6x - 240 [/tex]
[tex] x = 1080 - 240 - 6x [/tex]
[tex] x = 840 - 6x [/tex]
Add 6x to both sides
[tex] x + 6x = 840 - 6x + 6x [/tex]
[tex] 7x = 840 [/tex]
Divide both sides by 7 to solve for x
[tex] \frac{7x}{7} = \frac{840}{7} [/tex]
[tex] x = 120 [/tex]
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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Which could be used to evaluate the expression
43)
O (-6)(4)+(-01
0 (-6)(4) «(-6) (
3
O (-6+4)+ -6
G
0 (-6+4)*|-6-
Answer:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
Step-by-step explanation:
The expression, [tex] -6(4\frac{2}{3}) [/tex] , can be understood or interpreted as negative six multiplied by four and two-third.
Thus, it could be evaluated using distributive property of multiplication, as shown below:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
[tex](-6)(4) + (-6)(\frac{2}{3}) \\(-24) + (-2)(2)\\-24 + (-4)\\-24 - 4\\= -28[/tex]
Multiply the rational expressions: Divide the rational expressions:
Answer:
1). [tex]\frac{2}{(x+1)}[/tex]
2). [tex]\frac{x^2}{2(x+1)}[/tex]
Step-by-step explanation:
For multiplication of the rational expressions,
[tex]\frac{x}{(x+1)}\times \frac{2}{x}[/tex]
= [tex]\frac{2x}{x(x+1)}[/tex]
= [tex]\frac{2}{(x+1)}[/tex]
For division of the rational expressions,
[tex]\frac{x}{(x+1)}\div \frac{2}{x}[/tex]
= [tex]\frac{x}{(x+1)}\times \frac{x}{2}[/tex]
= [tex]\frac{x^2}{2(x+1)}[/tex]
[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.
This is applicable for division of the rational expressions only].
The volume of a spherical cancerous tumor is given by the following equation. V(r) =(4/3)pi r^3 If the radius of a tumor is estimated at 1.4 cm, with a maximum error in measurement of 0.005 cm, determine the error that might occur when the volume of the tumor is calculated:___________.
Answer:
The error that might occur is [tex]\±0.123cm^3[/tex]
Step-by-step explanation:
Given
[tex]V = \frac{4}{3}\pi r^3[/tex]
[tex]Radius,\ r = 1.4cm[/tex]
[tex]Error = 0.005cm[/tex]
Required
Determine the error that might occur in the volume of the tumor
Given that there's an error in measurement, this question will be solved using the concept of differentiation;
First, we'll rewrite the given parameters in differentiation notations;
[tex]r = 1.4[/tex] --- Radius
[tex]dV = \±0.005[/tex] --- Change in measurement
[tex]V(r) = \frac{4}{3}\pi r^3[/tex] --- Volume as a function of radius
The relationship between the above parameters is as follows;
[tex]\frac{dV}{dr} = V'(r)[/tex]
This can be rewritten as
[tex]\frac{dV}{dr} = (V(r))'[/tex]
Substitute [tex]\frac{4}{3}\pi r^3[/tex] for [tex]V(r)[/tex]
[tex]\frac{dV}{dr} = (\frac{4}{3}\pi r^3)'[/tex]
Multiply both sides by dr
[tex]dr * \frac{dV}{dr} = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
Differentiate
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
[tex]dV = \frac{4}{3}\pi* 3r^2\ dr[/tex]
[tex]dV = 4\pi* r^2\ dr[/tex]
Substitute the values of r, dr and take [tex]\pi[/tex] as 3.142
[tex]dV = 4 * 3.142* 1.4^2 * \±0.005[/tex]
[tex]dV = \±0.1231664[/tex]
[tex]dV = \±0.123[/tex] (Approximated)
Hence, the error that might occur is ±0.123
A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 14 respectively. The standard error of the mean is
Answer:
1.4Step-by-step explanation:
The formula for calculating the standard error of the mean is expressed as shown below;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma[/tex] is the standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 14 and n = 100
Substituting this values into the formula fr calculating the standard error of the mean;
[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]
Hence, standard error of the mean is 1.4
The rule r_y-axis ° R_0,90 (x,y) is applied to ABC. Which triangle shows the final image?
a. 1
b. 2
c. 3
d. 4
Answer: 4
Step-by-step explanation:
Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.
The attachment shows the graph rotated 1-turn to the left (90°).
Notice it is in the exact same position as #4.
Quadrilateral RSTQ is a parallelogram.
R
Which of the following relationships must be true?
O RS = RO
O TQ QR
O ZT ZR
O ZSRR
Answer:
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
Step-by-step explanation:
According to the Parallelogram definition, every Parallelogram have a pair of congruent sides. In this case, Namely [tex]\overline{RS} \cong \overline{TQ}[/tex] and [tex]\overline{QR} \cong \overline{TS}[/tex]
(not listed as an option)
And the opposite angles are congruent too.
So
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
∠R≅∠T relationship is true for the RSTQ parallelogram
What is Quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices.
A parallelogram is a quadrilateral with four sides.
a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In parallelogram the opposite sides have equal length.
The opposite sides are congruent and the opposite angles are also congruent.
SR=TQ
ST=RQ
These sides are equal and
∠R≅∠T
∠S≅∠Q
In the given options only ∠R≅∠T is given, so we can consider this.
Hence ∠R≅∠T relationship is true for the RSTQ parallelogram
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Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 6 0.10 12 0.35 18 0.25 24 0.30
Answer:
Mean = 16.5
Variance = 35.55
Step-by-step explanation:
x P(x) x. P(x) x² x². P(x)
6 0.10 0.6 36 3.6
12 0.35 4.2 144 50.4
18 0.25 4.5 324 81
24 0.30 7.2 576 172.8
∑x P (x) 16.5 ∑x² P (x) 307.8
The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.
Mean is given by E(X)= ∑x P (x) = 16.5
Similarly the variance is also calculated using the expected value of X and X².
Variance is given= E(X)²- [E(X)]²= 307.8- (16.5)²= 307.8-272.25 = 35.55
which graph represents a function?
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
g Find the mean and the variance of the random variable X with probability function or density f(x) of a uniform distribution on [0, 8].
Answer: E(X) = 4
V(X) = [tex]\frac{16}{3}[/tex]
Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:
f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]
The mean or expectation of an unifrom distribution is:
E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]
For the density function in interval [0,8], expectation value is:
E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]
E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]
E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]
E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]
E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]
E(X) = 4
Variance of a probability distribution can be written as:
V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]
For uniform distribution in interval [0,8]:
V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]
V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]
V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{64}{3}[/tex] - 16
V(X) = [tex]\frac{16}{3}[/tex]
The mean and variance are 4 and 16/3, respectively
In order to estimate the average time spent on the computer terminals per student at a university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours. With a 0.95 probability, the margin of error is approximately
Answer:
The margin of error is approximately 0.39.
Step-by-step explanation:
Formular for the margin of error is
Margin of error = z* (sd/√n)
Where z* is 95% confidence level = 1.96, sd is 1.8 and n is 81
Margin of error = 1.96 (1.8/√81)
= 1.96(1.8/9)
= 1.96*0.2
= 0.392
The lines shown below are parallel.if the green line has a slope of -1,what is the slope of the red line?
Answer:
-1
Step-by-step explanation:
If a line is parallel on a graph, then that means that they will descend/climb at the same rate. Therefore, the slope of this line is also -1.
Hope this helped!
Answer:If they are parallel,
Then their slope will be same...
Step-by-step explanation:
Solve the inequality. –10d ≥ –70
Answer:
d≤7
Step-by-step explanation:
-10d≥-70
d≤7
???????????????????
?
?
?
?
Answer:
It should be 10 for the first box, 1000 for the second box and 100 for the third box.
Step-by-step explanation:
Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t−3.6−1.9t+1.2+5.1t
Question
Combine like terms to create an equivalent expression.
-3.6-1.9t+1.2+5.1t
Answer:
3.2t - 2.4
Step-by-step explanation:
Given;
-3.6 - 1.9t + 1.2 + 5.1t
Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e
=> − 1.9t + 5.1t - 3.6 + 1.2
=> 3.2t - 2.4
Therefore, the equivalent expression is;
3.2t - 2.4
Answer:
3.2t - 2.4
Step-by-step explanation:
right on khan
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\[/tex]
a) For x < 33.2 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]
For x = 42.8 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]
75% of all students finish the activity in less than 37.3 seconds
The formula for the volume of a right circular cylinder is
V = 72h. If r = 26 and h = 5b + 3, what is the
volume of the cylinder in terms of b?
Answer:
20b^3+12b^2
Step-by-step explanation:
v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2
Problem 2
In the above diagram, circles O and O' are tangent at X, and PQ is tangent to both circles. Given that
OX= 3 and O'X = 8. find PQ.
Answer:
√96
Step-by-step explanation:
PQ is tangent to both lines, so PQ is perpendicular to PO and QO'.
The radius of the smaller circle is 3, and the radius of the larger circle is 8.
If we draw a line from O to O', and another line from point O to line QO' that is parallel to PQ, we get a right triangle where OO' is the hypotenuse, the short leg is 8−3=5, and the long leg is the same length as PQ.
Using Pythagorean theorem:
x² + 5² = 11²
x = √96
A rhombus has interior angle measures of 104∘, 104∘, 76∘ and X degrees. Find the measure of angle X in the rhombus. Enter only the number of degrees in the answer box. Angle X measures degrees.
Answer:
76°
Interior angle of a rhombus =360
104° +104° +76° +X =360
X= 360 - 284
X= 76°
We know that the value of ∠x in the given rhombus is 76°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal. A rhombus' internal angles add up to 360 degrees, just like in other quadrilaterals, and, like in a parallelogram, the angles of opposite pairs of vertices are identical. The total of the angles of two neighboring vertices is 180 degrees.So, get the ∠x as follows:
We now know that sum of all angles in a rhombus is 360°.Then,
104 + 104 + 76 + x = 360284 + x = 360x = 360 - 284x = 76°Therefore, we know that the value of ∠x in the given rhombus is 76°.
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