Answer:
11/2
Step-by-step explanation:
[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]
= 3/4 + 5/8 = 11/8 (take LCM)
3/4 - 1/2 = 1/4 (take LCM)
11/8 ÷ 1 /4
= 11/8 x 4
= 11/2
Answered by Gauthmath
PLS
Write the equation of the piecewise function that is represented by its graph.
IS IT A, B, C, OR D
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Answer:
a) domain bounds are -1 ≤ x ≤ 1, x > 1
Step-by-step explanation:
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.
The one answer choice that combines these domain descriptions is ...
[tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]
How many counting numbers have three distinct nonzero digits such that the sum of the three digits is 7?
Answer:
6
Step-by-step explanation:
You have 2 conditions.
1. The digits must be different.
2. The digits must add to 7.
There aren't very many
124
142
214
241
412
421
That's it. That's your answer. There are 6 of them
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
Reasoning by induction
Question 1 options:
1)
develops a general conclusion based on observations of cases.
2)
develops a general conclusion based on given information.
3)
starts with assumptions that are known to be valid to draw another new truths.
4)
uses patterns to create logical proofs.
Answer:
1because the occasion of cases
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Solve for x and y…….
The shapes are the same size. Match the sides.
3x -1 = 17
Add 1 to both sides:
3x = 18
Divide both sides by 3:
X = 6
2y = 16
Divide both sides by 2
Y = 8
Answer: x = 6, y = 8
Based on this example, make a
generalization about the acute angles
formed when two parallel lines are
cut by a transversal.
Answer:
Step-by-step explanation:
There are 4 of them (acute angles that is)Those 4 are less than 90 degrees.They have supplementary angles which are greater than 90 degrees.There are 4 of them also.The total number of angles should be 8 if there are 2 parallel lines and 1 transversal.
The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?
Answer:
B. 28, 32, 36 millions
Step-by-step explanation:
Given:
P(t) = 24 + 0.4t
Where,
P(t) = population in millions
t = number of years
✔️Value of the population when t = 10:
Plug in t = 10 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(10)
P(t) = 24 + 4
P(t) = 28 million
✔️Value of the population when t = 20:
Plug in t = 20 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(20)
P(t) = 24 + 8
P(t) = 32 million
✔️Value of the population when t = 30:
Plug in t = 30 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(30)
P(t) = 24 + 12
P(t) = 36 million
REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:
Please explain this! Thank you!
Supplementary angles are those angles which make a sum of 180°.
Complementary angles are those angles which make a sum of 90°.
The supplementary angles are given by the straight lines making angles of 180°.
There are two straight lines CB and DE
The angles DAF and FAE are the two angles making a straight line DE
The angles CAF and FAB are the two angles making a straight line CB
The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.
Angle BAF is formed by angle BAE and angle AEF
Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.
Complementary Angle BAF is formed by angle BAE and angle AEF.
https://brainly.com/question/12919120
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
11 + box equals 19 find box
Answer:
8
Step-by-step explanation:
11 + x = 19
Subtract 11 from each side
11+x -11 = 19-11
x = 8
Answer:
8
Step-by-step explanation:
11 + box = 19
=> box = 19 - 11
.°. box = 8
AABC-AXYZ. What's the scale factor from
AABC to AXYZ?
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Answer:
(d) 1/4
Step-by-step explanation:
The scale factor is the ratio of lengths of corresponding sides:
XZ/AC = 3/12 = 1/4
_____
Additional comment
I find the wording of the question a bit ambiguous. To transform ΔABC to ΔXYZ, every linear dimension of ΔABC is multiplied by 1/4. This is the sense of "ΔABC to ΔXYZ" that is used in the above answer.
On the other hand, one of the ways ratios are written is using the word "to," as in "12 to 3". Using this idea, we might interpret the question to be asking for ...
ΔABC to ΔXYZ = AC to XZ = 12 to 3 = 12/3 = 4
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
Which one is greater 4.5% or 0.045
Answer:
They are equal
Step-by-step explanation:
4.5% is 0.045 in decimal form
Answer: They are equal
Step-by-step explanation:
I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent (move it two spots to the right).
I need help ASAP please no links
Answer: D' = (1, -1)
Step-by-step explanation:
When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).
Is the answer right?
Answer:
one solution.. your answer is correct
Step-by-step explanation:
discriminate = 900 - (4*9*25) = 0
thus only one solution
Describe the system of equations
How many solutions does this system have.
Answer:
Step-by-step explanation:
One solution, at the point of intersection, (3,3)
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Evaluate the given expression for x = 5 and y=5. 6x2 + 7xy + 3y?
Step-by-step explanation:
Given, x = 5
y = 5
= 6(5)^2 +7(5)(5) +3(5)
= 6(25)+7(25) +15
= 150+175 + 15
= 150 + 190
=340
Answer:
x = 12 y = 7
Step-by-step explanation:
6x^2 + 7xy + 3y
6(5)^2+ 7(5) + 7(8)y
6(5+5)+25+35 + 7(8)-7y
60+25+35+ 56-7y
y - 5 = 120 + 35 - 5 (+49y)
sqrt 150 + sqrt 49
x = 12 y = 7
Simplify
x * x^5 / x^2 * x
Function below, choose the correct description of its graph.
vertical
line
horizontal
line
line with a
negative
slope
line with a parabola
positive opening
slope down
O
O
O
O
O
h(x)=0
k(x) = 4x2 +312
f(x) = x-1
O
o
o
O
O
O
Step-by-step explanation:
I think something went wrong with the answer options you provided. and maybe with the problem statement itself.
I see 3 function definitions.
I can tell you what they are and use the provided option phrasing as closely as possible :
h(x) = 0 is a horizontal line (in fact the x-axis)
k(x) = 4x² + 312 is a parabola with the opening upwards
f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)
A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]
Step-by-step explanation:
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value =[tex]t\alpha /2,[/tex] df = 1.771
Margin of error
[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,
[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]
f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
Please helppppppppp!!!!
Terminal point for 4π/3
(cos4π/3 ,sin4π/3)
{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)
or ,(- 1/2, -√3/2)
OPTION C
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=12
Step-by-step explanation:
each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle
ex: 8*4=32 and 17*4=68
so we can assume that 15*4= 4x+12
60=4x+12
48=4x
x=12
Answer:
x = 12
Step-by-step explanation:
The triangles are similar so we can use ratios
4x+12 32
------- = ------------
15 8
Using cross products
(4x+12) *8 = 15 * 32
(4x+12) *8 = 480
Divide each side by 8
(4x+12) *8/8 = 480/8
4x+12 = 60
Subtract 12 from each side
4x+12 -12 = 60-12
4x = 48
Divide by 4
4x/4 = 48/4
x = 12
Please Help!! much appreciated! :D
Find the value of y.
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
