Answer:
(15°, 165°)
Step-by-step explanation:
Given the equation 6 sin2(x) = 3, we are to find the value of x that satisfies the equation in the interval [0, 2π]
Given
6 sin2(x) = 3,
Divide both sides by 6
6 sin2(x)/6 = 3/6
sin2(x) = 1/2
2x = sin^-1(0.5)
2x = 30°
x = 30°/2
x = 15°
Since sin is positive in the second quadrant, x2 = 180-15
x = 165°
Hence the values within the interval are 15 and 165.
(15°, 165°)
Emilie rides her bike x miles before she gets a flat tire. She walks 1/3 mile to a bus stop and then takes a bus for 2 1/2 miles. Which expression shows how many miles Emilie travels in all?
Answer there is no choice, but it is x+1/3+2 1/2.
Step-by-step explanation:
Answer:
The answer is x + 2 5/6.
Step-by-step explanation:
Emilie rides her bike x miles before it gets a flat tire.
She walks 1/3 mile to a bus stop and then goes another 2 1/2 miles or 5/2 miles on a bus.
The equation would be:
x + 1/3 + 2 1/2
But, since that isn't an option, we have to simplify the equation.
x + 1/3 + 5/2
= x + [tex]\frac{2+15}{6}[/tex]
= x + 17/6
= x + 2 5/6
Thus, the answer is x + 2 5/6.
Find the value of P for which the inflows will equal the outflows. Find the effective rate first.
Rate 8% p y c d
Year Outflows Inflows
0 -P
1 -2P
2 -4P
3 -8P
4 -16P
5 $24,000
6 $30,000
7 $36,000
8 $42,000
9 $48,000
10 $54,000
Answer:
The answer is "p= $5,246".
Step-by-step explanation:
Using formula:
Present value of [tex]\frac{in-flow}{out-flow}[/tex] = cash-flow [tex]\times[/tex] present value of discounting factor(rate %, time period)
[tex]\to -p-\frac{2p}{1.08}-\frac{4p}{1.08^2}- \frac{8p}{1.08^3}-\frac{16p}{1.08^4} =\frac{24000}{1.08^5}+ \frac{30000}{1.08^6}+ \frac{36000}{1.08^7} + \frac{42000}{1.08^8}+ \frac{48000}{1.08^9}+ \frac{24000}{1.08^{10}}\\\\[/tex]
[tex]\to -p[1+\frac{2}{1.08}+\frac{4}{1.08^2}+ \frac{8}{1.08^3}+\frac{16}{1.08^4}] = 127960.43169\\\\\to -p[24.3923427] = 127960.43169\\\\\to -p = \frac{127960.43169}{24.3923427}\\\\\to p= 5245.93\\\\\to p= 5246[/tex]
Candice scored 74 on an exam that had a mean of 66 and a standard deviation of 4. Erin scored 58 on an exam with a mean of 42 and a standard deviation of 7. Who scored better?
Answer:
Erin
Step-by-step explanation:
Z score formula:
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
For Candice:
Z score = 74 -66/4
Z score = 2
For Erin
Z score = 58 - 42/7
Z score = 2.28571
Erin z score is larger hence, he did better
this is factoring quadratics with a leading coefficient: 5p to the 2 power - 52p + 20
Answer:
(-5p + 2)(-p + 10)
Step-by-step explanation:
[tex]5p^{2}[/tex]-52p + 20
(-5p + 2)(-p + 10)
You can double check this by using the distributive property..
-5p * -p = -5p^2
2*-p = -2p
10*-5p = -50p
10*2 = 20
-5p^2 + -2p + -50p + 20
Now we combine like terms and simplify
-5p^2 -52p + 20
So, we are correct
Find the critical value z Subscript alpha/2 that corresponds to the given confidence level. 99?% z Subscript alpha/2 = nothing?
Answer:
2.576
Step-by-step explanation:
Given :
Confidence level (α) = 99%
Z(1 - α)/2 = Z(1 - 99%)/2
Z1%/2 = Z1%/ 2
Z0.5% = Z0.005
Z(0.99 + 0.005) = Z0.995
Using the Z distribution table ; locate the z value for the proportion 0.995 ; this corresponds to approximately 2.57
Similarly, using the Invnorm calculator function :
Invnorm(0.995) gives a Zscore of :
2.576
Recall that you algebraically find the intersection point of two lines by setting their equations equal to each other and solving for the x-coordinate of intersection. Then substitute to find the y-coordinate. Algebraically determine the intersection point of y = 6x-27 with y = 2x – 7.
Answer:
[tex]x = 5[/tex]; [tex]y = 3[/tex]
Step-by-step explanation:
Given
[tex]y = 6x - 27[/tex]
[tex]y = 2x - 7[/tex]
Required
Determine the point of intersection
We simply equate both equations; i.e.
[tex]y = y[/tex]
or
[tex]6x - 27 = 2x - 7[/tex]
Collect Like Terms
[tex]6x - 2x = 27 - 7[/tex]
[tex]4x = 20[/tex]
Solve for x
[tex]x = 20/4[/tex]
[tex]x = 5[/tex]
Substitute 5 for x in [tex]y = 2x - 7[/tex]
[tex]y = 2 * 5 - 7[/tex]
[tex]y = 10- 7[/tex]
[tex]y = 3[/tex]
Hence, the point of intersection is:
[tex]x = 5[/tex]; [tex]y = 3[/tex]
work out (10-3 x 2) to the power of 2
Answer:
16
Step-by-step explanation:
parentheses first: 10-6 which is 4^2 or 16.
Hope this helps :D
A rectangle is 1/2 red, 1/5 green and 1/10 blue. The rest is yellow. What ratio of the rectangle is yellow? PLEASE HELP
A rectangular poster is 50 cm long and 25 cm wide. If 1 cm is approximately .4 inches What is the perimeter of the poster
please help me out -4x – 6 – 2x –3
The beginning balance in a person's savings account was 3900 dollars. After making a withdrawal of 300 dollars but earning interest of 14 dollars, what was the new balance in the account?
Balance: _____ Dollars
Answer:
The answer is 3,614. If you have 3900 dollars and withdraw ( take away) 300 you subtract, and you EARN 14, so you add.
Step-by-step explanation:
The reasoning is in the calculator picture attached
PLS AMSWER ASAP I WILL MARK BRAINLIEST DONT ANSWER IF YOUR NOT SURE THIS IS DUE VERY SOON
Answer: point B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Absolute value negates positive or negative values, therefore the larger number wins (e.g |6|=6, |-7|=7)
I hope this helps and good luck!
solve the equation 4x-2(x+3)=8
Answer:
4x-2x-6=8
2x-6=8
2x=8+6
2x=14
x= 14/2
x= 7
Answer:
X=7
Step-by-step explanation:
4x-2(x+3)=8
4x-2x-6=8
2x=8+6
2x=14
X=7
If $620 is invested at 6% per
annum, how long will it be until
it reaches $713?
Answer:
It will take 2 1/2 years
Step-by-step explanation:
Using simple interest, it is found that it will take 2.5 years for the account to reach $713.
The amount of money after t years in simple interest is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount. r is the interest rate, as a decimal.For this problem, the parameters are: [tex]A(t) = 713, A(0) = 620, r = 0.06[/tex].
Then:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]713 = 620(1 + 0.06t)[/tex]
[tex]1 + 0.06t = \frac{713}{620}[/tex]
[tex]0.06t = 1.15 - 1[/tex]
[tex]0.06t = 0.15[/tex]
[tex]t = \frac{0.15}{0.06}[/tex]
[tex]t = 2.5[/tex]
It will take 2.5 years for the account to reach $713.
For more on simple interest, you can check https://brainly.com/question/25781328
Quiz 2: percent and percentage
solve: 24% of 80=
A. 19.2
B. 38.4
C. 192
D. 384
Answer:
Answer: 19.2
Step-by-step explanation:
To calculate percentage, multiply the number 80 by 0.24, and the answer is 19.2.
For each linear function graphed on the coordinate grid, enter the value of m and the value of b. Give your answers as fractions in simplest form. 8 6 5 183 4 3 2 1 3 -3 - 3 -10 -98 lo S 910 f(x), red line: g(x), blue line: m= h(x), green line: m = Check Answer Next Question Question 6 of 8 POWER ? XKNEWTON ! Turn it in Save & Close O E e
Answer:
f(x), Red Line: m = -½; b = 2
g(x), Blue Line: m = ⅓; b = -1
h(x), Green Line: m = 3; b = 0
Step-by-sep explanation:
✍️Note the following:
✔️The slope of a line, m, = [tex] \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
✔️y-intercept, b, = the point on the y-axis where the line intercepts the y-axis, and where x = 0.
f(x), Red Line:
Using 2 points on the red line, (6, -1) and (8, -2)
slope (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 -(-1)}{8 - 6} = \frac{-1}{2} [/tex]
m = -½
The red line intercepts the y-axis at y = 2, therefore:
b = 2
g(x), Blue Line:
Using 2 points on the blue line, (0, -1) and (3, 0)
slope (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 -(-1)}{3 - 0} = \frac{1}{3} [/tex]
m = ⅓
The blue line intercepts the y-axis at y = -1, therefore:
b = -1
h(x), Green Line:
Using 2 points on the green line, (0, 0) and (1, 3)
slope (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{1 - 0} = \frac{3}{1} = 3 [/tex]
m = 3
The green line intercepts the y-axis at y = 0, therefore:
b = 0.
Yvette invests $300 each quarter in a fixed-interest mutual fund paying annual
interest of 7% compounded quarterly. How much will her account have in it at
the end of 11 years?
Answer:
Step-by-step explanation:
The formula for calculating the amount after t years is expressed as;
A = P(1+r/n)*nt
P is the Principal (amount invested) = $300
r is the rate = 7% = 0.07
t is the time used to save = 11 years
n is time of compounding = 1/4 (quarterly)
Substitute;
A = 300 (1+0.07/(1/4))^(1/4)(11)
A = 300(1+4(0.07))^2.75
A = 300(1+0.28)^2.75
A = 300(1.28)^2.75
A = 300(1.9716)
A = 591.49
Hence the amount that will be in her account after 11 years is $591.49
8.
Say that you (or your parents) are purchasing a house for $235,000 and have an excellent credit score. If you pay $1,678.93 at the end of
the first month, how much is applied to the principal balance?
Credit
Excellent
Good
Average
Fair
Poor
Secured
APR (%)
4.75
5.00
5.85
6.40
7.50
Unsecured
APR (%)
5.50
5.90
6.75
7.25
8.40
$616.29
$685.25
$748.72
$721.19
Answer:
The correct answer is 748.72
Step-by-step explanation:
$748.72 is applied to the principal balance if you pay $1,678.93 at the end of the first month.
What is principal amount?The loan amount that the lender gave to the borrower is referred to as the primary amount. Also, it is the factor the lender uses to calculate interest.
Please be aware that the amount you pay toward your loan's principal is without the interest that is charged on that amount. Your lender determines how much interest customers will pay over a specific length of time based on the amount still owing. The principle amount is simply the amount you owe their lender before interest.
principal amount = 4.75% of $1,678.93
= 4.75% × $1,678.93
= $748.72
Therefore, $748.72 is applied to the principal balance if you pay $1,678.93 at the end of the first month.
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What quadrant is the
ordered pair (2,-3) in?
Answer:
quadrant 4
Step-by-step explanation:
How is locating -1.5 on a number line the same as locating 1.5 on a number line How is it different?
Which expression uses the commutative property to make it easier to evaluate 3/5·1/4·25
A.25·4·3/5
B.5/3·25·1/4
C.3\5·25·1\4
D.3/5·1/25·1/4
Answer:
C
Step-by-step explanation:
The expression that uses the commutative property is 3/5 × 25 × 1/4
What is the commutative property?The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
Given is an expression 3/5 × 1/4 × 25
We know that,
The commutative property of multiplication states that:
A × B × C = B × C × A
Using the above equation, we have the result of the commutative property to be:
3/5 × 1/4 × 25 = 3/5 × 25 × 1/4
Hence, the expression that uses the commutative property is 3/5 × 25 × 1/4
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please help! i need this answer i just cant figure it out
I think it's b. Not completely sure though. I hope you get it right though. If i happen to be right i would love to be picked brainliest.
Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?
Answer:
D would be the actual answer.
Step-by-step explanation:
15.4: Ordering Percentages of Different Numbers Order from least to greatest: 65% of 80 36% of 125 82% of 50 170% of 30
Answer:
82% of 50 (41) 36% of 125 (45) 170% of 30 (51) 65% of 80 (52)
Step-by-step explanation:
BRAINLIEST PLS
A car dealership sold 120 cars in April. The dealership wants to increase the number of cars sold by 15% in May. How many cars will the dealership need to sell to reach their goal?
Answer:
138
Step-by-step explanation:
120+15%=138
Answer:
138
Step-by-step explanation:
A cake was cut into 12 equal pieces. Someone ate part of the cake so that 3/4 of the cake remains. How many 1/12 pieces are left?
Answer:
Nine pieces
Step-by-step explanation:
If you multiply the 3/4 pieces until the denominator is equal to twelve the numerator would be nine
Help Me on this palzz
Answer:
That should be 11.99+35.50+6.75+3+ 7.15% of EACH of those items added together minus 11.99+35.50+6.75+3+ 6.35% of EACH of the same items added together
evaluate log2/3 (4/9)
Answer:
2
Step-by-step explanation:
a circle has a radius o 12 inches, what is its diameter
Answer:
24
Step-by-step explanation:
Answer:
113
Step-by-step explanation:
First you need to find the radius, the key term to find the radius is diameter=2⋅radius ; therefore the radius r is 122=6 inches. To find the area of a circle, you need to use the formula A=π⋅r2 ; therefore the area A is π⋅62≈113 square inches.
A submarine is -18 feet below the surface of the ocean. The submarine then dove to a depth of -50 feet below the surface of the ocean. What was the change in depth?
Answer:
-32ft
Step-by-step explanation:
Given parameters:
Original depth of the submarine = -18ft
New depth = -50ft
Unknown:
Change in depth = ?
Solution:
The change in depth will be the difference in depth between the new and original depth.
Change in depth = New depth - original depth
Change in depth = -50ft - (-18ft) = -32ft
The change in depth of the submarine is -32ft.