Answer:
4a^2+4ab+b^2
Step-by-step explanation:
To find the square we multiply the expression with itself
(2a+b)×(2a+b) = 4a^2+4ab+b^2
If tan A=2/3 and tan B= -3/5 what is the exact value of cot(A-B)?
Answer:
cot(A-B) = 3/19
Step-by-step explanation:
The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)
we know that cot A = 1/ Tan A
Given
tan A=2/3
therefore cot A = 1/ tan A = 1/2/3 = 3/2
tan B= -3/5
cot B = 1/ tan B = 1/-3/5 = -5/3
Thus,
(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2
(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2
Thus,
cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2 / -19/2 = 3/19
Thus,
cot(A-B) = 3/19
what is the value of X
Answer: x=48°
Step-by-step explanation:
The 3 angles of the triangle add up to 180°. We can set the angles to 180 and solve.
47+85+x=180 [combine like terms]
132+x=180 [subtract both sides by 132]
x=48
Answer:
x=48
Step-by-step explanation:
Total sum of angles in a triangle =180
47+85+x=180
132+x=180
x=180-132
x=48
Please help I would be very greatful. On a coordinate plane, a solid straight line has a positive slope and goes through (0, 0.2) and (3, 2.2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y > Two-thirdsx – One-fifth y ≥ Three-halvesx + One-fifth y ≤ Two-thirdsx + One-fifth y < Three-halvesx – One-fifth
Answer: C. y ≤ 2/3x + 1/5
Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.
Answer:
C
Step-by-step explanation:
just did the test.
Find the value of the trigonometric and simplify the fraction if needed. Thanks!
Answer:
Tan<C=2.4
Step-by-step explanation:
Opp=36
Adj=15
Tan<C=opp/adj
Tan<C=36/15
Tan<C=2.4
Hope this helps :) ❤
graph the function f(x)=3/8(×-1)(x-9)
During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3 plays. Which method finds the total yards at the end of the first four plays?
A) add –12 to 3 times 5
B) add 12 to 3 times 5
C) add –12, 5, and 3
D) add 12, 5, and 3
They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value. The answer is A.
Answer:
A
Step-by-step explanation:
A state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement. You choose 4 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.Is the experiment binomial?A. Yes, there are a fixed number of trials and the trials are independent of each other.B. No, there are more than two outcomes for each trial.C. Yes, the probability of success is the same for each trial.D. No, because the probability of success is different for each trial.
Answer:
A) Yes, there are a fixed number of trials and the trials are independent of each other.
Sample size 'n' = 37
probability of success p = 0.1081
q = 0.8919
Step-by-step explanation:
Explanation:-
Given data we will observe that
There are a fixed number of trials and the trials are independent of each other.
Given a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Given size 'n' = 37
The probability that a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Proportion
[tex]p = \frac{x}{n} = \frac{4}{37} = 0.1081[/tex]
q = 1 - p = 1 - 0.1081 = 0.8919
Final answer:-
Sample size 'n' = 37
p = 0.1081
q = 0.8919
Please help me answer my question
Answer:
All angles in any quadrilateral adds up to 360°
Step-by-step explanation:
We can prove this by using 180(n - 2)
n = 4 for a quadrilateral
180(4 - 2)
180(2)
360°
So, 360 - (125 + 67 + 80) = 88°
Answer:
See below
Step-by-step explanation:
The interior angles of a quadrilateral (having 4 sides) add up to 360 degrees.
=> So, to find x, we'll simply subtract the rest if the angles from 360
So,
=> x = 360-125-67-80
=> x = 88 degrees
answer of this please
Answer: 205 and 1/7
Step-by-step explanation:
Hope this helped!
<!> Brainliest is appreciated! <!>
Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data met these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers
Answer:
Check the answers to the questions below
Step-by-step explanation:
a) If [tex]\mu_1[/tex] is the average learning rate of the 6th graders without background noise level and [tex]\mu_2[/tex] is the average learning rate of the 6th graders with background noise level
The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.
Null hypothesis, [tex]H_0: \mu_1 = \mu_2[/tex]
b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.
Alternative hypothesis, [tex]H_a: \mu_1 \neq \mu_2[/tex]
c) Assumptions that must be met about the data before she can correctly use independent t-test
There must be random selection of the 6th graders
That the two groups are normally similar in their learning abilities
The division of students into the two groups should be at random
d) She has to make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.
She can still get accurate results if she include some bias in the selection to prove a particular result.
hurry helpppppppppp please guys
Answer: The box with three shaded squares and one non-shaded square
Step-by-step explanation:
You are trying to find the representation of the shaded region.
The scale shows point A at 0.75, and the scale can range from 0 to 1.
0.75 is equal to 3/4 of 1
3 of the 4 squares are shaded
So, the common ratio is 3:4 or 3/4
Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?
This question is incomplete, here is the complete question:
Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?
A) $1388.89
B) $3571.43
C) $5555.56
D) $9500.00
E) $25888.89
number of students = 36,000
Answer: A) $
1388.89
Step-by-step explanation:
the college received additional grant which is $50,000,000
and the number of students is 36,000,
and we also know that expenses and enrollment remained the same.
So if we have more money (grants) and nothing changed (expenses remain the same)
dividing the grant by the number of students will show just how much the average tuition fee would be reduced
therefore R = G/n
R = 50,000,000 / 36000
R = 1,388.888 ≈ $1388.89
Describe el tipo de transformación de la siguiente figura y sus coordenadas.
Answer:
triangle pythagora
Step-by-step explanation:
the pythagora is made by someone special names albert and you ahve to amke three sides a b and c
in triangle ABC shown below, Segment DE is parallel to Segment AC:
Answer:
Selected option is correct
Step-by-step explanation:
Triangle BDE and BAC are similar because of the two pairs of equal angles (AA)
1. angle B
2. angle BDE = angle BAC
A bank loaned out $20,000, part of it at the rate of 6 % per year and the rest at 16 % per year. If the interest received in one year totaled $1500, how much was loaned at 6 %?
Answer:
$1,020
Step-by-step explanation:
0.06x + 0.16(20,000 - x) = 1500
Problem of the Day
The tortoise and the hare were arguing: who's the fastest? The tortoise boasted he
could swim 220 miles in 10 hours. The hare bragged he could hop 90 miles in 2 hours.
But who is faster? How can you tell?
Answer:
hare
Step-by-step explanation:
Their average rates are ...
tortoise: (220 mi)/(10 h) = 22 mi/h
hare: (90 mi)/(2 h) = 45 mi/h
The hare has a faster speed than the tortoise.
Which list orders the sides of triangle abc from longest to shortest length?
Answer:
B
Step-by-step explanation:
the hotpotuse is always the biggest
the rest is pretty easy to determine
The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.
What is a right-angled triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.
If one of the angle is of 90° then the triangle is right angled triangle.
We can see that the Hypotenuse is always the biggest side among all the sides.
Then the perpendicular side BC is the second biggest and then the base of the triangle.
Therefore, the order must be AB > BC > AC.
The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.
Learn more about right angled triangle here:
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Three populations have proportions 0.1, 0.3, and 0.5. We select random samples of the size n from these populations. Only two of the distributions of the sample proportions are normally distributed. Choose all possible values of n.
a. 10
b. 100
c. 50
d. 40
e. 20
Answer:
(1) A Normal approximation to binomial can be applied for population 1, if n = 100.
(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable X following a Binomial distribution with parameters n and p.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
5) BRAINLIEST + 10+ POINTS! A 60 foot tall radio tower r feet from an observer subtends an angle of 3.25°. Use the arc length formula to estimate r (the distance between the observer and the radio tower) to the nearest foot. r≈ ___ feet
Answer:
1057
Step-by-step explanation:
tower is 60 feet high.
angle of 3.25 degrees.
3.25/360 * 2 * pi * r = the arc length of this angle.
that would be equal to 0.0567232007* r
if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60
solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.
that's about how far the tower is from the observer.
since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.
Answer:
≈ 1058 ft
Step-by-step explanation:
Use of arc formula: s=rθ
Given:
s= 60 ftθ= 3.25°= 3.25*π/180°= 0.0567 radr= s/θ= 60/0.0567 ≈ 1058 ft
Tublu buys a cylindrical water tank height 1.4 M and diameter 1.1 M to catch rainwater off his roof.
Complete Question:
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank(not the base). If he uses 250ml to cover 1m2, will he have enough paint to cover the tank with one layer of paint? Take pie as 3.142
Answer:
Yes. It will be enough to cover the tank with 1 layer of paint. The tank requires 1.21 liters of paint.
Step-by-step explanation:
Given:
Height of cylindrical tank (h) = 1.4m
Diameter = 1.1m (radius = ½ of 1.1 = 0.55 m)
Litres of paint available = 2 liters
Rate of usage of paint = 250 ml to 1 m²
π = 3.142
Required:
Determine if the available 2 liters of paint would be enough for the painting
Solution:
Step 1: calculate the curved surface area of the cylindrical tank
Curved surface area (CSA) = 2πrh
= 2*3.142*0.55*1.4
= 4.84 m²
Step 2: Calculate how many liters of paint is required to paint the cylindrical tank having a curved surface area of 4.84 m²
If 1 m² requires 250ml (0.25 liters) of paint,
4.84m² area will require 4.84*0.25 liters
= 1.21 liters of paint.
Since 2 liters of paint is available, it means the paint will be more than enough to cover the tank with 1 layer of paint.
The price of the petrol is increased by 2/3. Originally the price was £1.02 per litre What is the cost of the petrol now? £ ? per litre
Answer:
£1.53 per litre
Step-by-step explanation:
original = 1.02
if it is increased by 2/3 then we do 1.02 / (2/3) =£1.53 per litre
when the sun is ay certain angles in the sky a 50 foot building casts a 20 foot shadow, what is the length of the shadow in feet cast by a flag pole 20 feet at the same time?
[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]
Hope this helps.
The length of the shadow cast by the flag pole is 6.4 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that;
Height of building= 50 foot
Shadow= 20foot
Now,
Let x be the length of the shadow cast by the flag pole. Then we have:
2050=x20
Cross-multiplying, we get:
50x=20×20
Dividing both sides by 50, we get:
x=5020×20
Simplifying, we get:
x=58×4
Multiplying, we get:
x=6.4
Therefore, by the proportion the answer will be 6.4 feet.
More can be learned about proportions at;
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Which product will result in a sum or difference of cubes?
A (x + 7)(x2 – 7x + 14)
B (x + 8)(x2 + 8x + 64)
C (x – 9)(x2 + 9x + 81)
D (x – 10)(x2 – 10x + 100)
Answer:
C. (x - 9)(x^2 + 9x + 81).
Step-by-step explanation:
The cube identities are
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Checking against the list the one that fits is the difference formula:
x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).
a=1, b = 9, ab = 1 *9 = 9.
15 liters of water flow
through a water pipe
and enter a tank
within 4.5 minutes
How much time does
it take to pump 727.5
liters of water into a
water tank using 2
similar water pipes?
Answer:
Step-by-step explanation:
Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters
Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is
(727.5 × 4.5)/30 = 109.125 minutes
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2
Answer:
Option (4)
Step-by-step explanation:
Surface area of a prism = 2B + P×h
where B = Area of the triangular base
P = perimeter of the triangular base
h = height of the prism
B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]
Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]
(20)² = (12)² + (Leg 2)²
Leg 2 = [tex]\sqrt{400-144}[/tex]
= 16 units
Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]
= 96 units²
P = 12 + 16 + 20
P = 48 units
h = 7.5 units
Surface area of the prism = 2(96) + (48×7.5)
= 192 + 360
= 552 units²
Therefore, surface area of the given triangular prism = 552 units²
Option (4) will be the answer.
Please answer this correctly
3(x + 2) = 12 solve for x
Answer:
x = 2.
Step-by-step explanation:
3(x + 2) = 12
3x + 6 = 12
3x = 6
x = 2
Hope this helps!
Answer:
4
Step-by-step explanation:
AHH!! IM STUCK PLEASE HELP! :(
Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -
[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]
Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.
The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -
Solution = Option B
what is -14 squared + 5675843
Answer:
5676039
Step-by-step explanation:
-14² + 5675843
Solve for exponent.
196 + 56758
Add the numbers.
= 5676039
What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months? Calculate the result to the nearest cent.
Given Information:
Annual interest rate = r = 10%
Accumulated amount = A = $6380.00
Semi-annual compounding = n = 2
Number of years = t = 38/12 = 19/6
Required Information
Principle amount= P = ?
Answer:
Principle amount= P = $4,684.05
Step-by-step explanation:
The principal amounts in terms of compound interest is given by
[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]
Where
i = r/n
i = 0.10/2
i = 0.05
N = n*t
N = 2*19/6
N = 19/3
So, the principal amount is
[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]
Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.