Answer:
39.2 AU.
Step-by-step explanation:
If my memory serves me right an astronomical unit is 93,000,000 miles.
So the answer is 3647720000/93000000
= 39.2 AU.
write cos2x as sinx
please help with this
Answer:
[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].
Step-by-step explanation:
Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].
Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].
Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].
Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].
[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].
[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].
[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].
Conclusion:
[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]
find the radius of this circle.
Answer:
r = 5 units
Step-by-step explanation:
Given:
Angle subtended at the centre (∅) in radians = 2π/3
Arc length (S) = 10π/3
radius (r) = ?
Required:
Radius (r)
Solution:
Formula for arc length given the central angle in radians is:
S = r∅
Make e the subject of the formula by dividing both sides by ∅
S/∅ = r∅/∅
r = S/∅
Plug in the values
r = (10π/3) / (2π/3)
Change the operation sign to multiplication and turn the fraction by your right upside down
r = 10π/3 × 3/2π
r = (10π × 3)/(3 × 2π)
Cross out terms that can divided each other
r = 5
1.
What is the slope of the line through the points (-2, -1) and (8, -3)?
Answer:
The slope of the line is [tex]-\frac{1}{5}[/tex] in fraction form or -0.2 in decimal form.
Step-by-step explanation:
To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
For finding the slope of this line with the points (-2,-1) and (8,-3), start by writing down the information given from the question.
[tex]y_{2}= -3[/tex]
[tex]y_{1}=-1[/tex]
[tex]x_{2}=8[/tex]
[tex]x_{1}= -2[/tex]
Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(-1)}{8-(-2)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-2}{10}= -\frac{1}{5}[/tex]. The final answer will be [tex]-\frac{1}{5}[/tex] in fraction form or -0.2 in decimal form.
Annabelle is going to see a movie and is taking her 4 kids. Each movie ticket costs $and there are an assortment of snacks available to purchase for $3 each. How much total money would Annabelle have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Annabelle have to pay if she bought x snacks for everybody to share?
Cost for 6 snacks:
Cost for x snacks:
Answer:
(a) $83 for 6 snacks
(b) [tex]y = 65 + 3x[/tex] --- for x snacks
Step-by-step explanation:
Given
Let:
[tex]n \to people[/tex]
[tex]ticket =\$13[/tex] --- per individual
[tex]snacks = \$3[/tex] --- per individual
Solving (a): Amount for 6 snacks
The amount paid (y) is:
[tex]y = ticket * n + snacks * 6[/tex] ---- because she bought 6 snacks
[tex]y = 13 * n + 3 * 6[/tex]
[tex]y = 13n + 18[/tex]
[tex]n = 5[/tex] ---- Annabelle and the 4 kids.
So:
[tex]y =13*5+18[/tex]
[tex]y =65+18[/tex]
[tex]y =83[/tex]
Solving (b): For x snacks
The amount paid (y) is:
[tex]y = ticket * n + snacks * x[/tex] ---- because she bought x snacks
[tex]y = 13* 5 + 3* x[/tex]
[tex]y = 65 + 3x[/tex]
DFGI is a trapezoid with midsegment EH. What is DI?
D
8 cm
F
7 cm
EH = 6.00 cm
FG = 4.00 cm
5 cm
G
6 cm
H
Answer:
a. 8 cm
Step-by-step explanation:
Given:
EH = 6 cm
FG = 4.00 cm
Based on the mid-segment theorem of a trapezoid, we have:
EH = ½(FG + DI)
Plug in the values
6 = ½(4 + DI)
Multiply both sides by 2
6*2 = 4 + DI
12 = 4 + DI
12 - 4 = 4 + DI - 4
8 = DI
DI = 8 cm
Mr. Smith wants to know if he can fit 4 trapezoid tables like the one shown below into a room. What is the total area of 4 trapezoid tables? Answer without units. NUMBER ONLY!
Answer:
(1/2)(2)(5+3)
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
The area of a trapezoid is:
( a + b ) ÷ 2 x h
Where a & b are the bases, and h is the height.
Use formula with the given measurements:
(3 + 5) ÷ 2 x 2
= 8 ÷ 2 x 2
= 4 x 2
= 8
Hope this helps
6. Donna adds 400 ml (milliliters) of water to 100 ml of coffee. What percentage of Donna's drink is coffee?
9514 1404 393
Answer:
20%
Step-by-step explanation:
100 mL of the drink is coffee
The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...
coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%
20% of Donna's drink is coffee.
A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 95% confidence interval for the proportion of employees who prefer plan A: (0253.0553). Identify the point estimate for estimating the true proportion of employees who prefer that plan.
a. 0.403
b. 0.253
c. 0.553
d. 0.15
Answer:
a. 0.403
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
Confidence interval of (0.253,0.553)
The bounds are 0.253 and 0.553, so the point estimate is:
[tex]p = \frac{0.253 + 0.553}{2} = 0.403[/tex]
This means that the correct answer is given by option A.
The coeffcient of determination is the ratio of the explained variation to the total variation. A. The coefficient of determination is the ratio of the unexplained variation to the total variation. B. The coefficient of determination is the ratio of the total variation to the unexplained variation. C. The coefficient of determination is the ratio of the total variation to the explained variation. D. The coefficient of determination is the ratio of the explained variation to the total variation. Choose the correct answer below. A. The coefficient of determination is a measure of how closely two variables vary together. B. The coefficient of determination is the percent of the variation that is unexplained. C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y. D. The coefficient of determination is the percent of the predicted values that equal the actual data values. Choose the correct answer below. A. The value 1r is a measure of how closely two variables vary together. B. The value 1r is the percent of the predicted values that equal the actual data values. C. The value 1r is the percent of the variation that is unexplained. D. The value 1r is the percent of variation of y that is explained by the relationship between x and y.
Answer:
D. The coefficient of determination is the ratio of the explained variation to the total variation.
C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y
Step-by-step explanation:
The Coefficient of determination is the ratio of the explained variation in y to the total variation in y.
Coefficient of determination, r² ;
r² = explained variation / total variation
The coefficient of determination is the proportion of variation in y (predicted value) which is due to the regression line ; Hence, it is the percent of variation of y that is explained by the relationship between x and y.
what percentage of the appies are yellow?
Answer:
20%
Step-by-step explanation:
6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.
Explain how you can use fraction strips or number lines to show that three fourths and six eighths are equivalent. plsssssss
The solution is given below.
What is number line?A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
here, we have,
Refer to the fraction strip to show 3/4 & 6/8 are same.
Also if you reduce 6/8 by dividing 2 to numerator & denominator…
it’s 3/4.
The solution is attached below.
To learn more on number line click:
brainly.com/question/29162579
#SPJ2
For how many minutes did Lynn run at a greater speed
than Kael?
0 12
O 17
O 23
O 28
Answer:
D. ✔ 28
Step-by-step explanation:
E 2021
Expand and simplify (b+6)(b-4)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: {b}^{2} + 2b - 24}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex] \: (b + 6)(b - 4)[/tex]
➼[tex] \: b \: (b - 4) + 6 \: (b - 4)[/tex]
➼[tex] \: {b}^{2} - 4b + 6b - 24[/tex]
Combining like terms, we have
➼[tex] \: {b}^{2} + 2b - 24[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Giving brainliest There are 12 inches in 1 foot. This is equivalent to 60 inches in 5 feet. Which proportions can be used to represent this? Check all that apply.
StartFraction 12 over 1 EndFraction = StartFraction 5 over 60 EndFraction
StartFraction 12 over 1 EndFraction = StartFraction 60 over 5 EndFraction
StartFraction 1 over 12 EndFraction = StartFraction 5 over 60 EndFraction
StartFraction 1 over 12 EndFraction = StartFraction 60 over 5 EndFraction
Answer:
12/1=60/5
1/12=60/5
Answer:
B and C
Step-by-step explanation:
6. Roll a pair of dice. What is the probability that a total of 12 will be face up?
Answer:
The Probability would be 2.78%
Step-by-step explanation: Hope this helps :)
what values of x makes -6x =12 true
Answer:
=> —6x = 12=> —x = 12/6=> —x = 2=> x = —2Step-by-step explanation:
hope it's helpful :-)
Pls Helppppp meeeeee!!
Answer:
G
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals in the expression
[tex]\sqrt{52}[/tex]
= [tex]\sqrt{4(13)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]
= 2[tex]\sqrt{13}[/tex]
------------------
[tex]\sqrt{117}[/tex]
= [tex]\sqrt{9(13)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]
= 3[tex]\sqrt{13}[/tex]
Then
[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]
= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]
= 5[tex]\sqrt{13}[/tex] → G
[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]
[tex]\small\bf{F.} \: \sf{13} [/tex]
[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]
[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]
[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]
Solution:-[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]
[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
Answer:-So, the correct option is D.
=======================#Hope it helps!
(ノ^_^)ノ
Solve each equation.
2p = 2 p = _____
q - 3 = 7 q = _____
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]2p=2[/tex]
[tex]\frac{2p}{2}=\frac{2}{2}[/tex] [tex]\hookleftarrow \mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]=1[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{P=1}}}}}[/tex]
---------------------
[tex]q - 3 = 7[/tex]
[tex]q-3+3=7+3[/tex] [tex]\hookleftarrow \mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]
[tex]=10[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{q=10}}}}}[/tex]
-----------------------
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
The height of the saddle off horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height of the horse's saddle above the base ofthe carousel
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w =\frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]
[tex]T = \frac{2}{\frac{3}{8}}[/tex]
[tex]T = \frac{2*8}{3}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the minimum is:
[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]
And the maximum is:
[tex]\sin(\frac{3\pi}{8}) =1[/tex]
Recall that the height is:
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the maximum and the minimum of are:
[tex]h_{min} =12 * -1 + 42[/tex]
[tex]h_{min} =30[/tex]
and
[tex]h_{max} =12*1+42[/tex]
[tex]h_{max} =54[/tex]
The C Train travels north at a rate of 80 miles per hour. The D Train travels east
at a rate of 150 miles per hour. How far apart will they be after 4 hours?
600
in a triangle the angle with the smallest measure is always the opposite the
Answer:
in a triangle, the angle with the smallest measure is always opposite the shortest side.
Step-by-step explanation:
If Sarah turns 15 on august 27 and her graduation year is 2024 how old will she be when she graduates high school?
Answer:
She will be 17
Step-by-step explanation:
My sister is like that but she's graduating in 22'
It sort of depends where Sarah lives -.-
But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.
So 15 plus 3.
Sarah will be 18 when she graduates high school.
The net of a rectangular prism is shown.
8 in.
2 in.
2 in.
8 in.
2 in.,
1
1
1
6 in.
1
2 in. :
1
is the correct answer lol ez stuff
A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
10h
3
31
34
==============================================
Explanation:
The recursive rule
f(n+1)=f(n)-3
can be rearranged to
f(n) = f(n+1)+3
after adding 3 to both sides
----------------
Now let's say we plug in n = 3
f(n) = f(n+1)+3
f(3) = f(3+1)+3
f(3) = f(4)+3
f(3) = 22+3
f(3) = 25
Repeat for n = 2
f(n) = f(n+1)+3
f(2) = f(2+1)+3
f(2) = f(3)+3
f(2) = 25+3
f(2) = 28
Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).
Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.
Which compound inequality could be represented by the graph?
–4 ≤ x ≤ 4
–2 ≤ x ≤ –1
x ≤ –1 or x ≥ 0
x ≤ 3 or x ≥ –1
Answer:
It is D.
Step-by-step explanation:
x ≤ 3 or x ≥ –1
Answer:
D) X <_ 3 or X _> -1
Whole Unit Test Review Answers:
1) D
2)D
3)B
4)C
5)D
6)A
7)B
8)C
9)A
10)B
11)D
12)D
13)B
14)B
15)D
(I got a 100%, and these were my answers, hope they help!)
(The pic below is a screenshot of the 100%, for reassurance)
In Problem, p is in dollars and q is the number of units.
(a) Find the elasticity of the demand function
p2 + 2p + q = 49 at p = 6.
(b) How will a price increase affect total revenue?
Answer:
-14
Explanation:
Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.
Formula for calculating price elasticity is: change in price/change in quantity =dq/dp
Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:
2p+2+dq/dp=0
dq/dp=-2p-2
Given p =6, we substitute:
dq/dp=-2×6-2
dq/dp=-12-2
dq/dp=-14
With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.
Tom went to bed at 8.30 pm and woke up at 6.15 am the next day . How long did he sleep ?
Answer:
tom sleep 14hour my ans lt might help you
0.7(1.5 + y) = 3.5y - 1.47
Answer:
y = 0.9
Step-by-step explanation:
1.05 + 0.7y = 3.5y - 1.47
-3.5y + 0.7y = -1.47 - 1.05
-2.8y = -2.52
y = 9/10 = 0.9
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]0.7\left(1.5+y\right)=3.5y-1.47[/tex]
[tex]1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}[/tex]
[tex]1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides[/tex]
[tex]0.7y=3.5y-2.52[/tex]
[tex]0.7y-3.5y=3.5y-2.52-3.5y[/tex]
[tex]\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow[/tex]
[tex]-2.8y=-2.52[/tex]
[tex]\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}[/tex]
[tex]\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet[/tex]
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
Use the diagram shown to find 4 ÷ 1/3
Answer:
12
Step-by-step explanation:
Since there is no diagram. I will just tell you the answer. first convert into multiplcation keep everything but the 1/3. Change 1/3 into 3/1 (3). Multiply 4*3=12.
Sorry if I don't have a graph.
Hope this helps!
Help help help help help
Answer:
x2+y2−12x+4y−60=0
The center of the circle is point: C=(6,−2).
The radius of the circle is r=10.