Answer:
v
Step-by-step explanation:
An angle whose measure is - 102° is in standard position in which quadrant does the terminal side of the angle fall?
O Quadrant
O Quadrant il
Quadrant III
O Quadrant IV
According to a NY Times article on December 13, 2009, The average selling price of a 32-inch LCD TV was $600. Use the annual CPI values from your text to compute the cost of that same TV in 2010 dollars. Express your answer rounded to the nearest cent.
Answer:
Your answer should be 647.51
Explanation : the price was 215.949 in December, 2009.
the price was 233.049 in December, 2013.
divide 233.049 by 235.949 and got 1.079185363.
multiply that by 600 and got 647.5112179.
The cost of the TV in 2010 is $647.5
Calculations and ParametersGiven that the complete information contains the Consumer Price Index values:
To find the CPI,
CPI= [tex]\frac{C_t}{C_0}[/tex]
Where C_t= cost of the market basket in the current period
C_0 = cost of the market basket in the base period
In December 2009, the price was 215. 949
In December 2013, the price was 233.049
Hence,
215. 949/233.049
= 1.079185363.
Then we would multiply by the base selling price
[tex]1.079185363 * 600 = 647.5112179.[/tex].
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Which expression is equivalent to Cube root of 343 x Superscript 9 Baseline y Superscript 12 Baseline z Superscript 6?
7x3y4z2
7x3y6z2
49x3y6z2
49x3y4z2
9514 1404 393
Answer:
7x^3y^4z^2
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{343x^9y^12z^6}=\sqrt[3]{(7x^3y^4z^2)^3}=\boxed{7x^3y^4z^2}[/tex]
Answer:
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
Step-by-step explanation:
[tex] \small \sf \leadsto \: \sqrt[3]{343 \: x {}^{9} \: y{}^{12} \: z {}^{6} }[/tex]
[tex] \small \sf \leadsto \: \sqrt[3]{7x {}^{3}y {}^{6}z {}^{2} } [/tex]
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
help? (the last part of it “what is rhe shortest name lengths” is what i need help) :) (i mark brainlist)
Answer:
8
Step-by-step explanation:
eight letters
there is only one who has 8 letters in the name
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum.
[infinity]
Σ 8/n^2-1
n=3
Answer:
The sum converges at: [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sum\limits^{\infty}_{n =2} \frac{8}{n^2 - 1}[/tex]
Express the denominator as difference of two squares
[tex]\sum\limits^{\infty}_{n =2} \frac{8}{(n - 1)(n+1)}[/tex]
Express 8 as 4 * 2
[tex]\sum\limits^{\infty}_{n =2} \frac{4 * 2}{(n - 1)(n+1)}[/tex]
Rewrite as:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{2}{(n - 1)(n+1)}[/tex]
Express 2 as 1 + 1 + 0
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+0}{(n - 1)(n+1)}[/tex]
Express 0 as n - n
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+n - n}{(n - 1)(n+1)}[/tex]
Rewrite as:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)-(n - 1)}{(n - 1)(n+1)}[/tex]
Split
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)}{(n - 1)(n+1)}-\frac{(n - 1)}{(n - 1)(n+1)}[/tex]
Cancel out like terms
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]
In the above statement, we have:
[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{6})][/tex]
[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{6})][/tex]
Add [tex]a_7[/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{7 - 1} - \frac{1}{7+1})][/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{8})][/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{8})][/tex]
Notice that the pattern follows:
[tex]a_3 + a_5 + a_7 + ...... + a_{k}= 4[(\frac{1}{2} - \frac{1}{k+1})][/tex]
The above represent the odd sums (say S1)
For the even sums, we have:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]
In the above statement, we have:
[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{7})][/tex]
[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{7})][/tex]
Add [tex]a_8[/tex] to both sides
[tex]a_4 + a_6 +a_8 = 4[(\frac{1}{3} - \frac{1}{7}) + \frac{1}{7} - \frac{1}{9}][/tex]
[tex]a_4 + a_6 +a_8 = 4[\frac{1}{3} - \frac{1}{9}][/tex]
Notice that the pattern follows:
[tex]a_4 + a_6 + a_8 + ...... + a_{k}= 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]
The above represent the even sums (say S2)
The total sum (S) is:
[tex]S = S_1 + S_2[/tex]
[tex]S =4[(\frac{1}{2} - \frac{1}{k+1})] + 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]
Remove all k terms
[tex]S =4[(\frac{1}{2}] + 4[(\frac{1}{3}][/tex]
Open bracket
[tex]S =\frac{4}{2} + \frac{4}{3}[/tex]
[tex]S =\frac{12 + 8}{6}[/tex]
[tex]S =\frac{20}{6}[/tex]
[tex]S =\frac{10}{3}[/tex]
The sum converges at: [tex]\frac{10}{3}[/tex]
Joseph leans a 20-foot ladder against a wall so that it forms an angle of 69° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest hundredth of a foot if necessary.
Answer:
18.67 ft
Step-by-step explanation:
|\
| \
| \
h | \ 20 ft
| \
| \
|-- 69° \
---|----------------
For the 69° angle, h is the opposite leg, and 20 ft is the hypotenuse.
sin A = opp/hyp
sin 69° = h/20
h = 20 * sin 69°
h = 18.67
Answer: 18.67 ft
Solve the linear equations
1/4(x-5)+4=1/3(2x+7)-5/6
Answer:
x = 3
Step-by-step explanation:
Given the linear equation :
1/4(x-5)+4=1/3(2x+7)-5/6
(x-5)/4 + 4 = (2x+7)/3 - 5/6
Take the lcm and sum
(x-5+16)/4 = (4x+14-5)/6
(x+11)/4 = (4x+9)/6
Cross multiply
6(x+11) = 4(4x+9)
6x + 66 = 16x + 36
Collect like terms
6x - 16x = 36 - 66
-10x = - 30
x = 30/10
x = 3
PLEASE HELP!! WILL MARK BRAINLIEST TO WHOEVER GET IT RIGHT
Answer:
neither, since the gradients are not the same, as well as the c value
Step-by-step explanation:
First line : y = -4x + 7
Second line : y = -4x + 3
We know that the standard form of equation of a line is y = mx + c
where :
m is the slope
c is the y intercept
Comparing both line equations with the standard form, we can notice that :
⊕ Slope of the first line = -4
⊕ Slope of the second line = -4
We know that Slopes of parallel lines are same
So, We can conclude that the given two lines are parallel to each other
Answer : Parallel because the slopes are the same
Question 2
Find the volume.
Answer:
It is D...........nnnnnnn
Can someone please help me with this problem?
Answer:
C 6
Step-by-step explanation:
Pythagoras
c² = a² + b²
117 = x² + (x+3)² = x² + x² + 6x + 9 = 2x² + 6x + 9
=>
108 = 2x² + 6x
54 = x² + 3x
0 = x² + 3x - 54 = (x-6)(x+9)
just think by what numbers can we divide 54 without any remainder (so that when multiplying we get 54) ? and which pair of these have a difference of 3 (so that with +/- combination we get "3x" in the multiplication)?
the solutions for x are the 2 numbers that would make one of the bracket expressions 0, as this turns the whole expression to 0.
x = 6 and x = -9
a negative number does not make any sense for a side length.
so, the only possible solution is x = 6
George buys a pizza. He eats 3/8 of the pizza for lunch and 1/4 of the pizza for dinner. What fraction of the pizza has George eaten?
Answer:
5/8
Step-by-step explanation:
Make denominators equal
1/4 = 2/8 (Multiply both sides by 2 to get a common denominator)
2/8 + 3/8 = 5/8
Flora is baking a pie and a cake for her restaurant. She needs 1/6 cup flour for the pie crust and 3/5 cup flour for the cake's frosting. How much flour will she use to make both?
(Type a whole number, fraction, or mixed number)
I need help with #3. Please help. I have to show all work so please explain
Answer:
a = 2
Step-by-step explanation:
Use Pythagorean Theorem:
[tex]a^2+b^2=c^2\\a^2+2.1^2=2.9^2\\a^2+4.41=8.41\\a^2=4\\\sqrt{a^2}=\sqrt{4}\\a=2[/tex]
Therefore, a is 2 meters.
please answer correctly thanks
What is the domain of function p?
p(x) = /x-1+2
Answer:
A.
Step-by-step explanation:
a strange question, as 2 answer options are actually possible, as they define valid domains for this function.
and if the range of the function would include imaginary numbers ("i"), all 4 would be correct.
the problem statement has to be much more precise. you can tell your teacher that.
but I assume, we base just on real numbers and want the biggest domain range. and that is A.
A. for x=1 we get sqrt(0) + 2, which is absolutely valid.
B. a square root of a negative number is undefined in the works of real numbers. we would need "i", the imaginary numbers, to make this a valid function.
C. is also valid. no bad values and expressions involved. it is just a snake range than A.
D. the same a for B.
The domain of the function [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]
How to determine the domain?The function is given as:
[tex]f(x) = \sqrt{x - 1} + 2[/tex]
Set the radicand greater than or equal to 0
[tex]\sqrt{x - 1} \ge 0[/tex]
Take the square of both sides
[tex]x - 1 \ge 0[/tex]
Add 1 to both sides
[tex]x \ge 1[/tex]
This means the possible values of x starts from 1 till infinity
Hence, the domain of [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]
Read more about domain at:
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Sung Lee invests $3,000 at age 18. He hopes the investment will be worth $9,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
.169
Step-by-step explanation:
I hoped I helped you solve sorry if I'm wrong
In ΔDEF, d = 440 inches, f = 410 inches and ∠F=120°. Find all possible values of ∠D, to the nearest 10th of a degree.
There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.
How to find all possible values of a triangle by law of sinesIn this question we have a triangle with two known sides and a known angle. By the law of sines we find the possible values of the angle D:
410/sin 120° = 440/sin D
Please notice that the sum of the internal angles of triangles equals 180°. Then,
sin D = (440/410) · sin 120°
sin D ≈ 0.929
There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.
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Find the area of the triangle.No links
please help! (listing BRAINLIST and giving points) :D
What is the equation of the line that is parallel to the line defined by the equation y = 3x + 6 and goes through the point (3, 2)?
options:
y = 2x – 1
y = 3x – 7
y = 2x + 4
y = 4x + 3
y = -2x + 9
Answer:
Step-by-step explanation:
Parallel lines have the same slope. The slope of the given line is 3. The easy way to do this, the one that uses our logical brains as opposed to our mathematical brain, tells us that since there is only one choice that has a given slope of 3, that is the one that we want. The second choice down is the only one that has a slope of 3.
Mathematically,
[tex]y-2=3(x-3)[/tex] and
[tex]y-2=3x=9[/tex] and
[tex]y=3x-9+2[/tex] so
y = 3x - 7 (the second choice)
ebsites
John has a bag of red and blue marbles. John chooses 2 marbles without replacing the first. Let A be the event where the first marble chosen
is red. Let B be the event where the second marble chosen is blue.
Which statement explains what the equation P (BA) = 0.6 means for these events?
A. The probability of choosing a blue marble after any marble has been removed is 0.6.
OB. The probability of choosing a red marble after a blue marble has been removed is 0.6.
O O O
C. The probability of choosing a blue marble after a red marble has been removed is 0.6.
OD. The probability of choosing a blue marble is 0.6, regardless of what else has been chosen.
Answer:
C. The probability of choosing a blue marble after a red marble has been removed is 0.6.
Step-by-step explanation:
P(B|A)
P(B|A) states the probability of event B happening, given that event A has happened.
In this question:
Event A: First marble is red.
Event B: Second marble is blue.
P(B|A) = 0.6
This means that the probability that the second marble is blue, considering that the first marble was red, is of 0.6, and thus, the correct answer is given by option C.
Solve x2 + 13x + 22 = 0 using the quadratic formula.
x^2 + 13x + 22 = 0
( x + 11 )( x + 2 ) = 0
x = - 11 Or x = - 2
3 consecutive integers have a sum of 27. What are the integers?
Three consecutive integers that add up to 27 are 8, 9, and 10
Hope this helps =)
First represent your 3 consecutive integers as x, x + 1, and x + 2.
Since their sum is 27, our equation reads x + (x + 1) + (x + 2) = 27.
Now simplifying on the left side we get 3x + 3 = 27.
You should be able to easily solve for x and find that x = 8.
Make sure you list all your answers.
If x is 8, then x + 1 is 9 and x + 2 is 10.
X – 10x = 100
Use a trial and improvement method to find this solution.
Give
your answer correct to 1 decimal place.
You must show all your working.
On the same line as your final answer you must write “to 1 decimal place"
Answer:
x-10x=100
-9x=100
-9x÷-9=100÷-9
x=-11,1
The points (-18, 15) and (-20, 15) lie on a circle with a radius of 1.
Find the coordinates of the center of the circle.
Answer:
Step-by-step explanation:
eq. of any circle with center (h,k) and r=1 is
(x-h)²+(y-k)²=1²
points (-18,15) and (-20,15) lie on it.
(-18-h)²+(15-k)²=1
(15-k)²=1-(-18-h)²
and (-20-h)²+(15-k)²=1
(15-k)²=1-(-20-h)²
so 1-(-18-h)²=1-(-20-h)²
-(18+h)²=-(20+h)²
324+36h+h²=400+40h+h²
40h-36h=324-400
4h=-76
h=-19
(15-k)²=1-(-18-(-19))²=1-1=0
k=15
so center is (-19,15)
What is the area and perimeter of the triangle
Answer:
Area = 20yd
Perimeter = 23 yd
Step-by-step explanation:
Area = 1/2 ×bh
b, which I the base = 10yd
h, which is the height = 4yd
Note: 5yd is the base because when you turn the triangle you will see that 10yd is the base and 5yd is the height not 8yd because 8 yd is not a straight line at a right angle
Therefore;
Area = 1/2× 10 × 4
= 1× 5 × 4
= 20yd
Perimeter = 8yd +5yd +10yd
= 13yd + 10yd
= 23yd
Kevin was asked to determine the length of side XZ. His work is shown.
Which error did Kevin make?
Answer:
A.// He has the side lengths in the wrong place in the cosine ratio.
Step-by-step explanation:
What is the area of this???
osha stacked 65 quarter. nicky has 5 times as many. how many more quarters does Nicky have
.An ice cream vendor serves 4 flavors: vanilla, chocolate, strawberry, and mint. If the
vendor selects two flavors at random, what is the probability that vanilla and strawberry
are chosen?
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
This question may be relatively tricky. Since no specific order is stated or implied, it does not matter whether the vendor chooses vanilla or strawberry first, as long as the vendor chooses both.
Therefore, for the first flavor the vendor can either choose vanilla or strawberry. There is a [tex]\frac{2}{4}=\frac{1}{2}[/tex] chance of this happening.
For the second flavor, the vendor must choose the one they didn't pick for the first flavor (either strawberry or vanilla). There is a [tex]\frac{1}{4}[/tex] chance they do so.
Therefore, there is a [tex]\frac{1}{2}\cdot \frac{1}{4}=\boxed{\frac{1}{8}}[/tex] chance that vanilla and strawberry are chosen.