9514 1404 393
Answer:
48°
Step-by-step explanation:
The acute angles in a right triangle are complementary, so angle CAD is ...
∠CAD = 90° -60° = 30°
When an angle is divided, the whole is the sum of the parts.
∠DAB +∠CAD = ∠CAB
∠DAB +30° = 78°
∠DAB = 48° . . . . . . . . . . subtract 30°
_____
Alternate solution
The sum of angles in a triangle is 180°, so ...
60° +78° +∠B = 180°
∠B = 180° -138° = 42°
∠DAB = 90° -42° = 48° . . . . . acute angles in a right triangle
Can someone answer this
Answer:
[tex]x=-\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} -4x+\frac{7}{2} =-9x+\frac{5}{6}[/tex]
Adjust Fractions based on the Least Common Multiplier (LCM)
[tex]-4x+\frac{4}{6} +\frac{21}{6} =-9x+\frac{5}{6}[/tex]
Solve the addition then subtract from each side
[tex]-4x+\frac{25}{6} -\frac{25}{6} =-9x+\frac{5}{6} -\frac{25}{6}[/tex]
Simplify & Add
[tex]-4x +9x=-9x-\frac{10}{3}+9x[/tex]
Simplify
[tex]5x=-\frac{10}{3}[/tex]
Divide
[tex]\frac{5x}{5} =\frac{-\frac{10}{3}}{5}[/tex]
Simplify
[tex]x=-\frac{2}{3}[/tex]
1 2/3 times 2 1/4 multiplie
Answer:
15/4
or 3 3/4
i think atleast
LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (-100,0) and (100,0), where unit distance on the coordinate plane is measured in miles
A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 180 miles.
What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the
hyperbola?
Answer:
The differences between the distances from the receiver to the two
transmitters is a constant.
[tex]\mathrm{The \ equation \ of \ the \ hyperbola\ is}\displaystyle \ \underline{\frac{y^2}{90^2} - \frac{x^2}{10\left(\sqrt{19} \right)^2} = 1}[/tex]Reasons:
The location of the transmitters = (-100, 0) and (100, 0)
The difference in the distance from the receiver to the transmitters = 180 miles.
Let the distances from the receiver to the transmitters be d₁ and d₂, we have;
|d₂ - d₁| = 180 = 2·a
[tex]\displaystyle a = \frac{180}{2} = 90[/tex]
c = The x-coordinates of the transmitters = 100
b² = c² - a²
∴ b² = 100² - 90² = 1900
b = √(1900) = 10·√(19)
Therefore;
The general form of the equation of an hyperbola is presented as follows;
[tex]\displaystyle \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1[/tex]
The standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola is; [tex]\displaystyle \underline{\frac{y^2}{90^2} - \frac{x^2}{10\left(\sqrt{19} \right)^2} = 1}[/tex]
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Help help please please
✽ Hello there! ✽
4x+9<21
Move all the constants (numbers) to the right, using the opposite operation:
4x<21-9
4x<12
Divide both sides by 4 to isolate x:
x<3
Therefore, x<3 ✔︎Hope this helps!
~Just a felicitous girlie
#HaveASplendidDay
[tex]SilentNature[/tex]
10x-6x-4-1=7-12+2x+2x
Any value of
x
makes the equation true.
Always true
Interval Notation:
(−∞,∞)
I NEED THIS ANSWERED ASAP
Answer:
X = 3
Bc = 6
AC = 12
Step-by-step explanation:
Hope it helped
If the Mac and cheese is 7.50 for 3 lbs how much can you get for 29 dollars?
Answer:
6lbs
Step-by-step explanation:
7.50 can only go into 20, two times
7.50
× 2
-------
15.00
James took a math quiz in which he earned 1 point for every correct answer and lost 0.5
point for every incorrect answer. James answered 12 out of 18 questions correctly. What
was James quiz score?
A. 6
B.9
C 15
D. 18
Answer:
is the b
Step-by-step explanation:
i did the correct operation oki?
Whoever answers correct gets brainliest
This is Arithmetic sequence explicit formula
d(n)=6−4(n−1)
Find the 5th term in the sequence
Answer:
5th term = - 10
Step-by-step explanation:
5th term
Here,
n = 5
d ( n ) = 6 - 4 ( n - 1 )
d ( 5 ) = 6 - 4 ( 5 - 1 )
= 6 - 4 ( 4 )
= 6 - 16
d ( 5 ) = - 10
Given f(x)=-x+2, find f(-5)
Answer:
7
Step-by-step explanation:
f(-5) means you have to plug -5 in for x.
f(x)=-x+2, so f(-5)=-(-5)+2=5+2=7
f(-5)=7
Answer:
Step-by-step explanation:
Simply plug -5 into the equation where an x is:
f(x) = -x + 2
f(-5) = -(-5) + 2
Two negatives make a positive so:
f(-5) = 5 + 2
f(-5) = 7
Hope this helps!
A company makes a profit of $y (in thousand dollars) when it produces x computers,
where y is given by the formula y = a(x - 100)(x - 200) for x 20 If 120
computers are produced, the profit will be $3,200,000.
a) Find the value of a.
b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?
c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?
The solutions to the questions if y is represented by the formula y = a(x - 100)(x - 200) are:
a) The value of a = -2000
b) The maximum profit the company can make = $5,000,000
To make maximum profit, 150 computers must be produced
c) The company must produce between 140 and 160 computers to make at least $4,800,000
The equation representing the company's profit is:
y = a(x - 100)(x - 200) for x > 20
If 120 computers are produced, the profit will be $3,200,000
That is, y = 3,200,000 if x = 120
a) Find the value of a
3,200,000 = a(120 - 100)(120 - 200)
3200000 = -16000a
a = -3200000/1600
a = -2000
b) Maximum profit the company can make
The equation becomes:
y = -2000(x - 100)(x - 200)
y = -2000(x² - 200x - 100x + 20000)
y = -2000(x² - 300x + 20000)
y = -2000x² + 600000x - 40000000
dy/dx = -4000x + 600000
dy/dx = 0 at maximum value
-4000x + 600000 = 0
4000x = 600000
x = 600000/4000
x = 150
To make maximum profit, 150 computers must be produced
Substitute x = 150 into y = -2000x² + 600000x - 40000000 to find the maximum profit
y = -2000(150²) + 600000(150) - 40000000
y = 5000000
The maximum profit the company can make = $5,000,000
c) Calculate the range of the number of computers to be produced If the company targets to make at least $4,800,000
-2000x² + 600000x - 40000000 ≥ 4800000
-2000x² + 600000x - 40000000 - 4800000 ≥ 0
-2000x² + 600000x - 44800000 ≥ 0
Divide through by -2000
x² - 300x +22400 ≤ 0
(x - 140)(x - 160) ≤ 0
140 ≤ x ≤ 160
The company must produce between 140 and 160 computers to make at least $4,800,000
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Susan spent a total of 45$ at the grocery store I’d this amount she spent $18 on fruit what percentage of the total did she spend on fruit
Answer:
40% of the total was spent on fruit
Step-by-step explanation:
100%=45 x=18
100/x = 45/18 Now take the inverse of both sides
x/100 = 18/45
This leads to 1800 = 45x
1800 divided by 45 is equal to 40
The total percentage spent on fruit was 40%
A continuous random variable X has probability density function X. Show how its
moment generating function can be used to determine the variance of this random
variable.
The moment generating function is defined by
[tex]M_X(t) = \mathbb E[e^{tX}][/tex]
Recall the power series expansion for the exponential function:
[tex]\displaystyle \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}2 + \frac{x^3}6 + \cdots[/tex]
Then by extension, the MGF could be similarly written as
[tex]\displaystyle M_X(t) = \mathbb E \left[1 + Xt + \frac{(Xt)^2}2 + \frac{(Xt)^3}6 + \cdots\right][/tex]
There's a certain theorem (due to Fubini, in case you're interested in learning more about it) that let's us exchange the order of integration (recall the definition of expectation for continuous random variables) and summation, so that
[tex]\displaystyle M_X(t) = \mathbb E[1] + \mathbb E[Xt] + \mathbb E\left[\frac{X^2t^2}2\right] + \mathbb E\left[\frac{X^3t^3}6\right] + \cdots[/tex]
and by the linearity of expectation,
[tex]\displaystyle M_X(t) = 1 + \mathbb E[X] t + \frac12 \mathbb E\left[X^2\right] t^2 + \frac16 \mathbb E\left[X^3\right] t^3 + \cdots[/tex]
and here we see where the name MGF comes from: the coefficient of the n-th order term in the series expansion "generates" the n-th moment, which is defined as E[Xⁿ].
Now, recall the definition of variance:
[tex]\mathrm{Var}(X) = \mathbb E\left[\left(X - \mathbb E[X]\right)^2\right][/tex]
[tex]\mathrm{Var}(X) = \mathbb E\left[X^2\right] - \mathbb E[X]^2[/tex]
and this is exactly the difference between the second moment and the square of the first moment.
So if you know the MGF, then you essentially get the variance for free with little effort. By differentiating the MGF, we get
[tex]\displaystyle M_X''(t) = \mathbb E[X] + \mathbb E\left[X^2\right] t + \frac12 \mathbb E\left[X^3\right] t^2 + \cdots[/tex]
and setting t = 0 lets us recover the first moment, E[X].
Differentiating again gives
[tex]\displaystyle M_X'(t) = \mathbb E\left[X^2\right] + \mathbb E\left[X^3\right] t + \cdots[/tex]
and setting t = 0 once again recovers the second moment.
Then in terms of the MGF, we have
[tex]\boxed{\mathrm{Var}(X) = M_X''(0) - M_X'(0)^2}[/tex]
Mr. Solomon, the art teacher, has 49.6 pounds of clay. If he gives every student 1.6 pounds of clay and has none left, how many students are in his class?
Answer:
He has 31 students
Step-by-step explanation:
You know this because 49.6 ÷ 1.6 = 31
PLEASE HELP WILL GIVE 40 POINTS
Amy is planning the seating arrangement for her wedding reception. Each round table can sit 8 guests. The head table can sit the bride and groom with the 6 wedding attendants. If Amy expects 158 to 174 guests to attend her wedding, including the attendants, what is the range for the number of round tables she will need for her reception?
A. 20 to 22
B. 25 to 27
C. 19 to 21
D. 21 to 23
Answer:
19 to 21
Step-by-step explanation:
Head table is for 6 attendants
158 to 174 - 6 attendants
152 to 168 people for round tables
each round table can sit 8 guests
so, 152/8 168/8
19 to 21
Answer:
D. 21 to 23
Step-by-step explanation:
1. First, you use the biggest number of guests just to be safe. Since there will be about 174 guests attending
2. you divide 174 by the number of seats a round table can hold. Since the number is 8, you 174/8 which is 21.75.
3. You round up to the biggest number of tables that has the number 21 in it.
4. Your answer is D. 21 to 23
The bill for Adrian's brunch at a downtown LA restaurant is $19. He wants to leave 20% tip. How much should the tip be
HELPLPLPLPLPPkkkki need help
Answer:
2 is the variable
Step-by-step explanation:
8(2) = 16
16-27 = -11
Please answer the question in the picture
Answer:
2x² + 2x - 24
Step-by-step explanation:
We can use the FOIL method to multiply the terms together and then find the values in our trinomial. First, the F in FOIL. It stands for first, and we need to multiply the first terms in the two expressions. These terms are 2x and x. Multiplying 2x by x gives us 2x², so that's our first term.
Next, the O in FOIL. It stands for outside, and we need to multiply the terms on the very left and the very right. These are 2x and -3, and multiplying 2x by -3 gives us -6x. That's our second term.
Now, the I in FOIL. It stands for inside, so we need to multiply the terms in the middle of the expressions. Those are 8 and x, and we multiply those together to get 8x. That's our third term.
Finally, the L in FOIL. This stands for last; we need to multiply the last terms of each expression. Those are 8 and -3, and we can multiply those to get -24. Now we can get all our terms added together and simplify as needed.
2x² - 6x + 8x - 24
We can simplify -6x and 8x since they are like terms.
2x² + 2x - 24
And there is our trinomial. Hopefully that's helpful! :)
Which of the following could be the number shown on the number line?
A. V66
B. V60
C. V63
D. V65
Answer:
A
Step-by-step explanation:
v666
Which is a property of an angle?
A-has two sides that each extend forever in both directions
B-has two endpoints
C-has two center points
D-has two rays that share a common endpoint
Which of the following are the correct properties of slope?
Check all that apply.
O A. The slope of a line that moves up from left to right is positive.
a
B. The slope of a line is always positive.
C. Some lines have an undefined slope.
D. A steep line has negative slope.
E. If two lines have the same slope, then they are the same line.
Answer:
I think one of them may be C and B but I'm not sure
If you built a model of the Empire State Building that is proportional to the real building. The height of the Empire State Building is 1,250 feet. If the scale of your model is 1 inch = 50 feet how tall is your model?
A supplier cells wire for $4.30 per pound is the total sale is $120.95 to the nearest hundredth of a pound how much did the customer by
Solve all of them please u get 30 points
Step-by-step explanation:
from which text book please
The difference of a number and six is negative four
Answer:
(2) is the possible missing number substitute for (n)Step-by-step explanation:
Let the number word be (n)And number 6 remain (6)The possible answer will be (-4)Here we go: n-6=(-4)Try to add six and negative four: 6+-4=2Therefore u got two 2+-6=-4
A tin contains 425g baked beans in sauce. The tin itself weighs 60g. How much will a pack of 6 tins weigh in kilograms
Answer:
2.91 Kg
Step-by-step explanation:
Tin weighs 60g, it contains 425g of baked beans, add that together to get a full tin of baked beans
= 485.
Multiply by 6 to get the total amount in grams
= 2910g.
Turn that into Kg.
2.91 kg.
The weight of 6 tins will be 2.19 Kg,
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Tin weighs 60g, it contains 425g of baked beans,
So, the total weight along with tin
= 425 + 60
= 485 g
Now, the weight of 6 tins
= 485 x 6
= 2190 g
= 2190/1000 Kg
= 2.19 Kg
Hence, the weight is 2.19 Kg.
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If you spent 24 weeks working on a project for your job and are rewarded with 3 days of vacation write the ratio of time on vacation to time working as a fraction in lowest terms
3. Round the numbers to the nearest given place
value
a. Round 63 to the nearest ten.
b. Round 56 to the nearest hundred.
Cound 56 to the nearest ten.
Answer:
a) 60
Step-by-step explanation:
sorry I know only of one
If the map distance is 20 cm and the scale is 4 cm = 60 km, what is the actual distance?
Answer:
300
Step-by-step explanation:
1. 60/4=15
2. 15x20=300
What is the equation of the line in slope-intercept form?
6
5
4
3
2
1
-5 -4
1
2
3
4
43 -2 -1
-1
-2
-3
-4
Enter your answer in the boxes.
y = IX +
Answer:
y = 4/3x + 4
Step-by-step explanation:
The y intercept is 4. So if we look the 2 points are (-3,0) and (0,4)
So the run is 3 and rise 4
so 4/3 is the slope