Answer:
can you please send the images of figure of these angle
A fish tank is three-fourths full.
One-third of the water leaks out.
How full is the fish tank now?
Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
We will subtract the amount of water that leaked out from the amount of water originally in the fish tank.
[tex]\displaystyle \frac{3}{4} - \frac{1}{3} =\frac{3*3}{4*3} -\frac{1*4}{3*4} =\frac{9}{12} -\frac{4}{12}=\frac{5}{12}[/tex]
The fish tank is [tex]\frac{5}{12}[/tex] of the way full.
Find A and B if Cos(A - B) = (sqrt(3))/2 ; Sin(A + B) = 1
a number, n is multiplied by -5/8 the product is -0.4 how would you set this up to solve
The value of n in the mathematical statement is 0.64
How to solve the equation?The statement is given as:
n multiplied by -5/8 equals -0.4
Rewrite properly as:
n * -5/8 = -0.4
Multiply both sides by -1
n * 5/8 = 0.4
Multiply both sides by 8/5
n = 0.64
Hence, the value of n in the mathematical statement is 0.64
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Find the gradient of the curve y =2x³-7x+4when x=-2
By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
How to find the gradient of a functionA gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:
[tex]\nabla f = \frac{df}{dx}[/tex] (1)
Now we proceed to calculate the gradient of the curve:
[tex]\nabla f = 6\cdot x^{2}-7[/tex]
[tex]\nabla f = 6\cdot (-2)^{2}-7[/tex]
[tex]\nabla f = 17[/tex]
By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
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Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).
X -6 -4 -1 3 4
f(x) 15 11
5 -3 -5
g(x) -36 -26 -11 9 14
O (0,9)
O (0, 3)
O (0, -3)
O (0, -9)
The y-intercept of linear function (f- g)(x) is (0,9)
How to determine the y-intercept?The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1[/tex]
So, we have:
[tex]f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15[/tex]
Evaluate
f(x) = -2x + 3
Also, we have:
[tex]g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36[/tex]
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
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Holly is looking up at an angle at a helicopter. The direct distance from Holly to
the helicopter is 16 km. The helicopter is hovering 11 km above the ground.
Calculate the angle of elevation from Holly to the helicopter. Include a labelled
diagram in your solution
Answer:
43.43 degrees
Step-by-step explanation:
This is a right triangle with the opposite LEG = 11 km and the hypotenuse = 16 km
sin (angle) = opposite/hypotenuse
= 11/16
arc sin (11/16) = angle = 43.43 degrees
chandra is constructing a weighted bookend for her shelf. it is a hollow rectangular prism, as shown, and she will fill it with sand to weigh it down
Since it is said to be a hollow rectangular prism, she will fill it with sand to weigh it about (573 + 9/2) cubic inches.
What is the prism about?
Note that the volume is said to be:
V = L x B x H
316 in = 6 √2 x 2 √3
The answer is 573 while the other part of the prison is 9√2 cubic inches.
Therefore, option A is correct.
See full question below
Chandra is constructing a weighted bookend for her shelf. It is a hollow rectangular prism, as shown, and she will fill it with sand to weigh it
down
6 √(2 in
316 in
2 √3 in
What is the volume of the bookend?
(Hint: The volume of a rectangular prism is the product of its length width and height.)
OA (573 + 9/2) cubic inches
B. 36/12 cubic inches
C 108 cubic inches
D. 216 cubic inches
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the atlanta braves are offering bobblehead to every 10th person who enters your fundraiser. the nashville predators are offering a free ticket to every 15th person who enters the fundraiser. how many attendees must come before someone receives both bobblehead and a ticket?
In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.
Which attendees will receive the bobblehead and the ticket?Bobblehead:
Attendee number 10Attendee number 20Attendee number 30Ticket:
Attendee number 15Attendee number 30What can be concluded?It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.
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Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink?
A. 1/3
B. 2/9
C. 2/3
D. 6/9
The probability of randomly selecting a can of pink paint is P = 1/3, so the correct option is A.
What is the chance that he will paint his bedroom pink?Assuming that all the cans of paint have the same probability of being randomly selected, the probability that he will choose a pink can is equal to the quotient between the number of pink cans and the total number of cans.
There are 2 cans of white, 4 cans of green, and 3 cans of pink, so a total of 9 cans.
Then the probability is:
P = 3/9 = 1/3.
The correct option is A.
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Olivia’s power went outa at midnight she knows that during a power outage if is important to leave the freezer and refrigerator doors closed
Based on the fact that there is power outage, it is important to leave the freezer and refrigerator doors closed as when it is open, it may lead to heating off fast.
What is power outage?This is known to be when there is no electrical power due to unforeseen reasons.
Based on the fact that there is power outage, it is important to leave the freezer and refrigerator doors closed as when it is open, it may lead to heating off fast and thus things on it may get bad easily. The right thing to do is to leave it closed.
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If f (x) = 3x²-x, find f (-2).
Answer:
f(-2) = 14
Step-by-step explanation:
put -2 where x is
f(x) = 3x²-x
f(-2) = 3(-2)²-(-2)
f(-2) = 3(4)+2
f(-2) = 12+2
f(-2) = 14
1 euro = $1.09 $1= 62 rupees Change 400 euros into rupees using these exchange rates.
Answer:
27,032 Rupees
Step-by-step explanation:
$1.09 x 400 = $436
$436 x 62 = 27,032
(Hope this helps and that it's not wrong ^-^)
Which trigonometric function requires a domain restriction of [0, pi/2) ∪ (pi/2 , pi]
The ANSWER is f(x) = secx ----- PLEASE EXPLAIN THANK YOU!!!!!
The trigonometric function requires a domain restriction of [0, π/2) ∪ (π/2, pi] is tan x, sec x.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
tan x = (sin x)/(cos x)
sec x = 1/(cos x)
cos x becomes zero at {-π/2,π/2}
Therefore, the both of the function are undefined at {-π/2,π/2}
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Point L is located at (-1,-6). Determine the coordinates of point L’ after a translation 7 units to the left and 6 units up.
Answer:(-8,0)
Step-by-step explanation:
Add (-1,-6) with translation move (-7,6)
-1 , -6
-7 , 6
____
-8 , 0
what is the difference in length between 15 1/8 and 14 5/8
Answer:
4/8
Step-by-step explanation:
15 1/8 - 1/2(4/8) = 14 5/8
The vertices of a triangle are A(2,5), B(1, 2), and C(3, 1). Find the coordinates of the image after a dilation with respect
to the origin using a scale factor of 2 and then a translation 2 units left and 1 unit up.
A" (). B" (). c" ()
The coordinates of the image after a dilation with respect to the origin is A'' (2,10), B" (0,4), C" (4,2) .
How does dilation work?Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.
Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.
Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).
The vertices of a triangle are A(2,5), B(1, 2), and C(3, 1).
A' = 2(2.5) = (4,10)
B' = 2(1,2) = (2,4)
C' = 2(3,1) = (6,2)
Translation of 2 units left means change in x
A'' = (4-2,10) = (2,10)
B" = (2-2,4) = (0,4)
C" = (6-2,2) = (4,2)
Translation of 1 units up means change in y
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Persevere with Problems The table shows the highway fuel economy of various popular vehicles.
The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9
How to find mean absolute deviation?Find the mean of the data set
= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10
= 335 / 10
= 33.5
Mean deviation of each set;
38 - 33.5 = 4.5
48 - 33.5 =14.5
25 - 33.5 = -8.5
35 - 33.5 = 1.5
33 - 33 .5 = -0.5
37 - 33.5 = 3.5
32 - 33.5 = -1.5
34 - 33.5 = 0.5
23 - 33.5 = -10.5
30 - 33.5 = -3.5
Absolute deviation of each value
|4.5| = 4.5
|14.5| = 14.5
|8.5| = 8.5
|1.5| = 1.5
|-0.5| = 0.5
|3.5| = 3.5
|-1.5| = 1.5
|0.5| = 0.5
|-10.5| = 10.5
|-3.5| = 3.5
Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5
= 49
Mean absolute deviation = Total absolute deviation / mean
= 49/10
= 4.9
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which expression is equivalent to 56x - 28y + 42?
A) 8(7x-3y + 6)
B) 7(8x + 4y +6z)
C) 7(8x - 4y + 6)
Answer: c or a
Step-by-step explanation:
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L
The domain of the functionThe equation of the function is given as:
[tex]C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex]
Time can be 0 or greater but cannot be negative.
So, the domain of the function includes t ≥ 0
Set the function to 0 to determine the maximum value of t.
[tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0[/tex]
Cross multiply
[tex]-18t^2 + 54t = 0[/tex]
Factor out -18t
-18t(t - 3) = 0
Divide both sides by -18t
t - 3 = 0
Add 3 to both sides
t = 3
This means that the maximum value of t is 3
Hence, the domain of the function is 0 ≤ t ≤ 3
The greatest concentration of the medicationFrom the graph of the function (see attachment), we have the maximum value to be;
C(t) = 2
Hence, the greatest concentration of the medication is 2mg/L
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Suppose the average age of family members is 34 with a standard deviation of 4. if 100 members of the community decided to have a summer outing bonding and relaxation, find the probability that the average of these members is less than 35?
Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].
The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 34}{0.4}[/tex]
Z = 2.5
Z = 2.5 has a p-value of 0.9938.
0.9938 = 99.38% probability that the average of these members is less than 35.
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David's phone battery level drops 6 percentage points each hour when he is not playing a game on it. When David does play a game on his phone, the phone battery level drops 18 percentage points each hour. On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M. If David did not charge his phone during this time, how many hours did he spend playing the game between 12:00 noon and 6:00 P.M. on that day
The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.
When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.
On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.
If David did not charge his phone during this time.
Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be
Let x be the number of no gaming hours and y be the number of gaming hours.
Then the equation will be
6x + 18y = 100 - 22
6x + 18y = 78
x + 3y = 13 ...1
x + y = 6 ...2
By solving the equations 1 and 2, we have
x = 2.5 hours and y = 3.5 hours
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What is 6x-6x56 =?
Show all work.
Answer:
6x-6x56 =-2016
Step-by-step explanation:
You have to subtract, then multiply by 56 to get -2016, as it shows a negative.
Match the given side or angle to its measure using the parallelogram below.
Answer:
A=108
B=22
C=51
D=28
Step-by-step explanation:
A= AFB is a vertical angle opposite 108
B= congruent angles congruent sides, 11 x 2 sides
C= using angle rules, alternate interior angles of 21 puts 21 in the
triangle with 108, all triangles sum total 180, so (180-21=51)
for the 3rd angle ACD
D=last answer
One week, Genesis earned $367.40 at her job when she worked for 22 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $584.50?
Answer:
Step-by-step explanation:
Givens
time = 22 hourswage = 367.40time2 = ?desired wage2 = 584.50Comment
This is a proportion. A proportion is 2 equal ratios. If you know 3 parts of a proportion, you can solve for the 4th.
Equation
wage/time = wage2/time2 Substitute values.
Solution
367.40 /22 = 584,50 /x Cross multiply
367.40x = 22 *584.50 Simplify the right
367.40x = 12859 Divide both sides by 367.40
x = 12859/367.40
x = 35
Answer
Genesis will have to work 35 hours.
B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam?
A.4 h
B.6 h 40 min
C.6 h 20 min
D.3h 40 min
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
How long does it take to fill the dam?Given that;
Amount of water needed to fill the dam A = 30000 litresPump rate r = 75 litres per minuteTime needed to fill the dam T = ?To determine how long it take to fill the dam, we say;
Time need = Amount of water needed ÷ Pump rate
T = A ÷ r
T = 30000 litres ÷ 75 litres/minute
T = 400 minutes
Note that; 60min = 1hrs
Hence,
T = 6hours 40minutes
Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.
Option B)6h 40min is the correct answer.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
12-².4³ =
Submit
[tex]12^{-2} \times 4^3\\\\=(4 \times 3)^{-2} \times 4^3\\\\=4^{-2} \times 4^3 \times 3^{-2}\\\\=4^{-2+3} \times 3^{-2}\\\\=4^1 \times \dfrac1{3^2}\\\\=\dfrac 49[/tex]
A racehorse weighs 490 kilograms. How much does it weigh in grams?
Answer:
490,000 grams
Step-by-step explanation:
To convert from kilograms to grams - multiply the number of kilograms by 1000. (there are 1000 grams in a kilogram)
[tex]490 * 1000 = 490,000[/tex]
Answer:
490000
Step-by-step explanation:
1 kg : 1000 gram
So,
490 kilograms : 490 ×1000 grams
: 490000 grams
Justin rides his bicycle 2.5 kilometers to school.
Luke walks 1,950 meters to school. How much
farther does Justin ride to school than Luke
walks to school?
Answer:
1 kilometre = 1000 metres
2.5km = 2.5 × 1000m = 2500m
2500 - 1950 = 550m
Therefore Justin rides 550m farther than Luke walks to school.
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Problem 5.2
Here are three lines that intersect at
one point.
Determine the values of x, y, and z
Answer:
z=98 degrees
x=64 degrees
y=18 degrees
Step-by-step explanation:
y is congruent to 18 since theyre opposite of eachother, same with x and 64. find z by using the straight 180 line. (180=64+18+z, so z=98)
A family of 4 gets 505 text messages per month. Which of the following best describes the most even way these texts can be divided?
2 family members get 124 text messages each
2 family members get 125 text messages each
2 family members get 126 text messages each
2 family members get 125 text messages each
3 family members get 126 text messages each
1 family member gets 127 text messages
3 family members get 125 text messages each
1 family member gets 126 text messages
Answer:
3 family members get 126 text messages each
1 family member gets 127 text messages
Step-by-step explanation:
If you were finding the exact division of texts, 505 texts / 4 people, you would end up with 126.25 texts.
However, you can't get 0.25 of a text. If we take back each family member's 0.25 text, they will all be left with 126 texts (with an extra text leftover)
This extra text is considered the "remainder", meaning the amount left over when a number is divided [when it doesn't go into the larger number evenly]. The only importance/relevancy of a remainder is when a value cannot be split, such as a dog or a text.
So, we can give each family member 126 texts, and then we can give one family member an additional text, so that all texts are distributed.
This means that 3 family members get 126 texts, and 1 family member gets 127 texts
hope this helps!!