The solution of (15 feet, 51.5 feet) represents the perimeter of a shape with a longest side of 15 feet.
What is Equation?Equation is a mathematical statement that express the equality of two expression use in equal sign.
The equation for this perimeter can be written as y = 2.5x + 14, where y is the perimeter of the shape and x is the longest side of the shape.
Thus, when x is 15 feet, the perimeter of the shape is 51.5 feet, as represented by the solution (15 feet, 51.5 feet).
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The dot plots show the number of minutes that each of two sisters practiced the piano each day for 14 days.
ana
+++++
0 10
+
20
30
40
80
90
100
110
120
50 60 70
minutes practiced
tara
:
:
.
+++++ +
0 10 20
+
+
40
.
+ +
50 60 70 80
minutes practiced
++++
100 110 120
30
90
which sister showed more consistency in the amount of time she practiced? move a word to each blank to complete the sentence.
showed more consistency because the
of her data was less than that of her sister's data.
ana
tara
median
range
Averagely, Ana practiced for a greater amount of time each day.
What is the Mean and Median of a Data Set?Mean = sum of data points / number of data points.Median = center/middle of the data distribution.Mean for ana= (20 + 20 + 30 + 60 + 60 + 60 + 70 + 70 + 100 + 100 + 100 + 115 + 115 + 115)/14 = 69.6
Mean for tara= (20 + 20 + 30 + 30 + 45 + 45 + 45 + 70 + 70 + 70 + 75 + 90 + 90 + 120)/14 = 58.6
Median for ana= 70
Median for tara= (45 + 70)/2 = 57.5
Ana has the greater median and also has the greater mean.
Averagely, we can conclude that ana practiced for a greater amount of time each day.
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Sin(4x) in the term of just x
Please help!!
I think you mean in terms of [tex]\sin(x)[/tex]?
Recall Euler's identity
[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]
and de Moivre's theorem
[tex]\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}[/tex]
where [tex]i=\sqrt{-1}[/tex].
It follows that
[tex]\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4[/tex]
By the binomial theorem, expanding the right side gives
[tex]\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)[/tex]
and so
[tex]\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)[/tex]
We can factorize this as
[tex]\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)[/tex]
and using the Pythagorean identity
[tex]\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}[/tex]
this reduces to
[tex]\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))[/tex]
Using the net below, find the surface area
of the triangular prism.
7 cm
5 cm
15 cm
4 cm
Surface Area =
5 cm
7 cm
[?] cm²
Enter
The Surface area of the triangular prism with the net shown below is 106 cm²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²
The Surface area of the triangular prism with the net shown below is 106 cm²
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Marge conducted a survey by asking 350 citizens whether they frequent the city public parks. of the citizens surveyed, 240 responded favorably. what is the approximate margin of error for each confidence level in this situation?
Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate are given by:
[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]
Hence the margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]
M = 0.0486 = 4.86%.
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Answer:
99% - 0.06
95% - 0.05
90% - 0.04
Step-by-step explanation: i got it right
A man leaves home at 22:15 hours and reaches his destination at 04:00 hours on the following day. how many hours did the journey take?
Answer,
Leaves from home=22:15hour
get to destination=4:00hour
time taken on a journey,
from time 22:15hour to 24:00hour=2:45hour and,
time is taken form 22:00hour to 4:00hour=4:00hour
So, the total time taken to reach the destination is 2:45+4:00=6:45hour
Suppose the expression a(b)n models the approximate number of people who registered for a dance program every day since the registration started, where a is the initial number of people who registered, b is the rate of increase in the number of people who registered every day, and n is the number of days since the registration started.
If the expression below models the registration for a particular dance program, what is the correct interpretation of the second factor?
There were 2.07 times as much people that applied in the fourth month than in the first month.
What is an exponential function?An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.
Thus we have;
f(x) = 27(1.2)^4
This shows us that the time elapsed is four months and f(x) = 2.07.
Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.
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A man left savings of the 2 50,000 to his wife, 2 daughters and a son. find the value of the shares that each received.q
Answer:
62,500
Step-by-step explanation:
250,000 ÷ 4 = 62,500
∴ Each member would receive 62,500.
24 people go out for a meal.
13 have a starter, 15 have a pudding and 7 have both a starter and a pudding.
Show this information on a Venn diagram.
Answer:
see image
Step-by-step explanation:
The two circles will represent "starter" or "pudding" people and the overlap are both, but also don't forget people who chose neither. There must be 3-neither people. Because 6+7+8 only add to 21 and the question said there were 24 people.
Alice and Bob each arrive at a party at a random time between $1:00$ and $2:00$. If Alice arrives after Bob, what is the probability that Bob arrived before $1:30$
The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
According to the question,
Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.
In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.
Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.
s = {(x, y) /1≤x≤2 and 1≤y≤2}
In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.
Formula for Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]
= 1/2
Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
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What is the perimeter of the contest area on the judo mat?
(please be quick)
It cost Josiah $9.75 to send 65 text messages. How many text messages did he send if
he spent $28.20?
According to my calculation the answer is 188.
3x^2 - 5x -1 =0
Quadratic Equation
please explain step by step
Answer:
Step-by-step explanation:
Solving 3x2-5x-1 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C number, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -5
C = -1
B2 - 4AC =
25 - (-12) =
37
Applying the quadratic formula :
5 ± √ 37
x = —————
6
√ 37, rounded to 4 decimal digits, is 6.0828
So now we are looking at:
x = ( 5 ± 6.083 ) / 6
Two solutions:
x =(5+√37)/6= 1.847
x =(5-√37)/6=-0.180
what is the slope is the line that passes through the points (-1,6) and (14,3)? Write your answer in simplest form.
Answer:
m= -1/5
Step-by-step explanation:
slope formula to find it ^^
Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer
The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively
What is a kite?A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
The given figure is a kite with two intersecting lines that are perpendicular to each other.
Since the lines are perpendicular to each other, hence;
m<1 = 90 degrees
For the measure of m<2
m<2 + 90 + 27 =180
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63degrees
Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees
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If 5/6 is 180, what is 1/6?
(please answer and explain pls)
[tex] \frac{5}{6} \: of \: a \: number \: is \: 180[/tex]
[tex] \frac{1}{6} \: is \: 5 \: times \: less \: than \: \frac{5}{6} \\ \frac{1}{6} = \frac{180}{5} = 36[/tex]
I NEED IT NOW
Owen made 60% of the shots he attempted during his hockey practice. He made 18 shots. How many shots did Owen attempt during his hockey practice?
There are 25 students in a class. How many ways can the teacher (randomly) pick two students for the lead roles in the class play?
Answer:
300
Step-by-step explanation:
25 choose 2 (exactly how it sounds like)
= (25*24)/(2*1)=600/2=300
Can someone help? ASAP
[tex]\tan 45^{\circ}=\frac{x}{2\sqrt{10}}\\\\1=\frac{x}{2\sqrt{10}}\\\\\boxed{x=2\sqrt{10}}\\\\\\\\\sin 45^{\circ}=\frac{2\sqrt{10}}{y}\\\\\frac{1}{\sqrt{2}}=\frac{2\sqrt{10}}{y}\\\\y=2\sqrt[20}\\\\\boxed{y=4\sqrt{5}}[/tex]
This graph represents a quadratic function. An upward parabola on a coordinate plane vertex at (minus 2, 2) and passes through (minus 3, 5) and (minus 1, 5). What is the value of a in the function’s equation? A. 3 B. 2 C. -3 D. -2
The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:
y = ax² + bx + c
The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.
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Answer:
The correct answer is A:3
Step-by-step explanation:
Lukas paid for a pair of shoes with a $50 bill. After the clerk added 9% tax to the purchase, Lukas received $17.30 in change. What was the price of the shoes, not including the tax?
Answer:
$29.75
Step-by-step explanation:
If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757
Six numbers from a list of nine integers are $7$, $8$, $3$, $5$, $9$, and $5$. What is the largest possible value of the median of all nine numbers in this list
8 is the largest possible value of the median of all nine numbers in this list.
Lets simplify it,
⇒ The given six numbers are 7,8,3,5,9 and 5.
⇒ Arrange the six numbers in order 3,5,5,7,8,9.
⇒ We have three more numbers to insert into the list, and the median will be the highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.
∴ The median is the 5th item of data which is 8.
∴ Median=8
Hence 8 is the largest possible value of the median of all nine numbers in this list.
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Roselyn is driving to visit her family, who live 150150150 kilometers away. Her average speed is 606060 kilometers per hour. The car's tank has 202020 liters of fuel at the beginning of the drive, and its fuel efficiency is 666 kilometers per liter. Fuel costs 0.600.600, point, 60 dollars per liter.
What is the price for the amount of fuel that Roselyn will use for the entire drive?
Answer:
Step-by-step explanation:
150 kilometers
60 kph
tank is 20 liters
6 km/l
150/6 = 25 liters needed
$60/l
5 more liters of fuel
total cost 25 x .60 = $15
Which of the following numbers is a factor of 78?
.7
.4
.6
.9
PLEASE ANSWER AS SOON AS POSSIBLE!
Answer:
6
Step-by-step explanation:
If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.
I hope this helps!
hurry
help me please !!!!
Answer:
Step-by-step explanation:
(a)
1 - Simplify 4 - 9 to -5.
⇒ | - 5 |
2 - Simplify.
⇒ 5
(b)
1 - Simplify
⇒ -5
The domain of this function is {-12, -6, 3, 15}. y=-2/3x+7 complete the table based on the given domain.
If the domain of the function y=-2/3 x+7 is {-12,-6,3,15} then the range of the function is {15,11,5,-3}.
Given that the domain of the sunction y=-2/3 x+7 is {-12,-6,3,15}.
We have to find the range of the function and complete the table.
Function is relationship between two or more variables expressed in equalto form. In a function each value of x has some value of y.
To complete the table we need to find the value of the function at different values of x.Domain is basically value of x which satisfies the function.
We have to first put the value of x=-12 in y=-2/3+7
y--2/3*-12+7
=15
Now put x=-6 in the function.
y=-2/3 *-6+7
=3
Put the value of x=3 in the function.
y=-2/3*3+7
=5
Put the value of x=15.
y=-2/3*15+7
=-41/3.
Hence the range of function is {15,11,-41/2,5}.
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ASAP help me 30 points
Answer:
large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la
or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues
Identify the root tissues. Record your answer under "Slide 5" on your lab report.
Sheila has a plan to save $45 a month for 18 months so that she has $810 to remodel her bathroom. After 13 months Sheila has saved $510. If the most Sheila can possibly save is $70 per month, which of the following statements is true?
a.
Sheila will meet her goal and does not need to adjust her plan.
b.
Sheila must save $50 per month to achieve her goal.
c.
Sheila must save $60 per month to achieve her goal.
d.
Sheila will not be able to achieve her goal.
The statement that is true about Sheila's savings plan is that; C.
Sheila must save $60 per month to achieve her goal.
What is true about the savings plan?
The price of bathroom remodeling is $ 810.
After 13 months , she has saved $ 510
This means that she has a $300 shortage to cover in 5 months.
This means that she need to save :
$300/5 = $60 / month in order to achieve her goal
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Answer: C
Step-by-step explanation: edge
n a chemical plant, 24 holding tanks are used for final product storage. Four tanks areselected at random and without replacement. Suppose that six of the tanks contain material inwhich the viscosity exceeds the customer requirements.(a) What is the probability that exactly one tank in the sample contains high-viscosity material
The probability that exactly one tank in the sample contains high-viscosity material is P(A) = 0,4607 or P(A) = 46,07 %
The probability of an event (A) is for definition:-The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring. In the very simplest cases, the probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes.P(A) = Number of favorable events/ Total number of events FE/TE
If A and B are complementary events ( the sum of them is equal to 1) then:
P(A) = 1 - P(B)
The total number of events is:
C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!
C ( 24,4) = 24*23*22*21*20! / 4! * 20!
C ( 24,4) = 24*23*22*21/4*3*2C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626
TE = 10626
Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v
we get that total number of favorable events is the product of:
FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!
FE = 4896
Then P(A) ( 1 tank in the sample contains h-v material is:
P(A) = 4896/10626
P(A) = 0,4607 or P(A) = 46,07 %
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pls help me on 109 I got it wrong :c
Answer:
30
Step-by-step explanation:
Let's start by multiplying the equation through bt the least common denominator so that we can clear the denominator:
[tex]\frac{2}{5}x+\frac{1}{3}y=1[/tex]
The least common of 3 and 5 is 15, so we can multiply through by 15:
[tex]15(\frac{2}{5}x+\frac{1}{3}y)=15(1)\\6x+5y=15[/tex]
We want the left side of the equation to be 12x + 10y. We can get this if we multiply the expression we currently have (6x + 5y) by 2. However, if we multiply the left side by 2, we must also multiply the right side by 2 to balance out the equation. If we do this, we will get our answer:
[tex]2(6x+5y)=2(15)\\12x+10y=30[/tex]
On the right side, we get 30. Therefore, the answer is 30
Xy has 10 pets: 4 dogs, 3 cats, 2 alpacas and 1 bunny. If he wants to arrange them in a row and make sure the pets are always grouped according to species, how many ways can he arrange the pets?
The number of ways pets can be arranged in group according to the species is in a row 288 ways.
Pets can be grouped by permutation concept as follows.
Total number of pets = 10
Number of dogs = 4
Number of cats = 3
Number of alpacas = 2
Number of bunny = 1
The number of ways pets can be arranged in group according to the species in a row as,
⇒ (4!)(3!)(2!)(1!)
⇒ (24)(6)(2)(1)
⇒ 288
Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.
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