Answers
Answer:
Step-by-step explanation:
2^2=1.75^2+3^2-2*3*1.75cos x
4=3.0625+9-10.5 cosx
10.5cos x=9-4+3.0625
10.5cosx=8.0625
cos x= 8.0625/10.5≈0.77
x≈40 degrees
Answer: D) 40 degrees
Step-by-step explanation:
Let A = θ
then a = 2 b = 3 c = 1.75
Use the Law of Cosines:
a² = b² + c² - 2bc · cos A
2² = 3² + 1.75² - 2(3)(1.75) · cos θ
4 = 9 + 3.0625 - 10.5 cos θ
4 = 12.0625 - 10.5 cos θ
-8.0625 = -10.5 cos θ
[tex]\dfrac{-8.0625}{-10.5}=\cos \theta\\\\\\\cos^{-1}\bigg(\dfrac{-8.0625}{-10.5}\bigg)=\theta\\\\\\\large\boxed{39.838=\theta}[/tex]
Related Questions
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answers
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32
Answers
Answer:
work is shown and pictured
Answer:
Answer B. (6, 2)
Hope it works!
Step-by-step explanation:
Bob bought some land costing $15,540. Today, that same land is valued at $45,117. How long has Bob owned this land if the price of land has been increasing at 5 percent per year
Answers
Answer:
21.84 years
Step-by-step explanation:
From the compound interest formula;
F = P(1+r)^t .......1
ln(F/P) = tln(1+r)
t = ln(F/P)/ln(1+r) .......2
Where;
F = Final value = $45,117
P = Initial value = $15,540
r = rate = 5% = 0.05
t = time
Substituting the values into equation 2;
t = ln(45117/15540)/ln(1.05)
t = 21.84542292124 years
t = 21.84 years
It will take Bob 21.84 years
Tickets to a baseball game can be ordered online for a set price per ticket plus a $5.59 service fee. The total cost in dollars for ordering 5 tickets is $108.09. Which linear function represents c, the total cost, when x tickets are ordered
Answers
Answer:
c = 20.5x + 5.59
Step-by-step explanation:
c = mx + b
c = mx + 5.59
108.09 = m(5) + 5.59
5m = 102.5
m = 20.5
c = 20.5x + 5.59
You want to put a 2 inch thick layer of topsoil for a new 14 ft by 26 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answers
Answer:
2 1/4
Step-by-step explanation:
The volume of soil needed is ...
(14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³
The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.
You need to order 2 1/4 cubic yards.
___
There are 3 ft or 36 inches to a yard.
Evaluate: .25 (1.2 x 3 - 1.25) + 3.45
Answers
The order to us solve is:
ParenthesesMultiplicationSum and subtractionLet's go:
[tex]25(1.2\times 3 - 1.25) + 3.45\\25(3.6-1.25)+3.45\\25\times 2.35 + 3.45\\58.75+3.45\\62.2[/tex]
Therefore, the result is 62.2.
Answer:
4.0375
Step-by-step explanation:
.25(3.6-1.25)+3.45
.25(2.35)+3.45
.5875+3.45
4.0375
HOPE THIS HELPS:)
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim ||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Answers
Answer:
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
The answer of the above definite integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
Step-by-step explanation:
The given limit interval is
[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]
[tex][a, b] = [-8, 6][/tex]
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
Bonus:
The definite integral may be solved as
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]
Therefore, the answer to the integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
The Demon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three other were sprayed with Action. When the grape ripened, 400 of the vines treated with Pernod 5 and 400 of the vines treated with Action were checked for infestation. The number of infested vines treated with Pernod 5 and Action are 24 and 40 respectively.
At 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answers
Answer:
At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Then, the null and alternative hypothesis are:
H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0
The significance level is 0.05.
The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.
[tex]p_1=X_1/n_1=24/400=0.06[/tex]
The sample 2, of size n2=400 has a proportion of p2=0.1.
[tex]p_2=X_2/n_2=40/400=0.1[/tex]
The difference between proportions is (p1-p2)=-0.04.
[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]
As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
What is the value of x?
10
2x
Answers
Answer:
The only way of getting to 10 using 2x it should mean that x = 5
2 * 5 = 10
A jar of sweet contains 5 yellow sweets, 4 red sweets, 8 green sweets, 4 orange sweets and 3 white sweets. Ola chose a sweet at random, what is the possibility that she will pick either a yellow or orange sweet?
Answers
Answer:
9/24 or 37.5%
hope this helps :)
Hi,
first thing you must do with a probability problem is to count how many thing you have in your universe.
Here we are dealing with sweets. So let's count : 5 +4+8+4+3 = 24
and there is 5 yellow so probability to pick up a yellow is 5/24
and there is 4 orange so probabilitu to pick up a orange is 4/24
To say : Ola will pick orange or yellow mean if she pick either one of the two sort is good. So you add the proba of each : 5/24 +4/24 = 9/24
and then you must reduce if you can : 9/24 = 3*3 /8*3 = 3/8
So the probability that Ola pick a yellow or orange sweet is 3/8 = 0.375
which is bigger 1 or
[tex] \frac{19}{9} [/tex]
Answers
Answer:
19/9 because it equals to 2.111.. Which is greater than 1
Step-by-step explanation:
By the way if it's right can i get brainliest.
Answer:
1 < 19/9
Step-by-step explanation:
1 vs 19/9
Rewriting 19/9 as 9/9 + 9/9+ 1/9
1 vs 1+1 +1/9
1 vs 2 1/9
1 < 19/9
Elliot’s school has 24 classrooms. Each classroom has seats for 26 students. What is the maximum number of students the school can seat? Multiply to find the answer.
Answers
Answer:
24*26= 624 students
hope this helps!
Answer:
624 seats
Step-by-step explanation:
Total classrooms = 24
Each classroom has seats = 26
Total Number of seats = 24*26
=> 624 seats
Think of a number subtract 5 from it and divide your answer by 72 if you get 4 which number did you use?
Answers
Answer:
293
Step-by-step explanation:
4*72+5 = 293
Answer:
293
Step-by-step explanation:
So 293-5 is 288.
288 / 72 = 4.
one more lol then she is done (my friend) lol
Which of the following correctly uses absolute value to show the distance between –60 and 11? |–60 – 11| = |–71| = –71 units |–60 + 11| = |–49| = 49 units |–60 + 11| = |–49| = –49 units |–60 – 11| = |–71| = 71 units
Answers
Answer:
|–60 – 11| = |–71| = 71 units
Step-by-step explanation:
Subtract the two points and take the absolute value
(-60 - 11)
The absolute value
| -60 -11| =
|-71|
71
Answer: D
Step-by-step explanation:
Absolute value turns the -60 into 60
Hope this helps!
9. The basketball team sold t-shirts and hats at a fundraiser. They sold a total of 23 items and made a
profit of $154. They made a profit of $8 from each t-shirt sold and a profit of $10 from each hat sold.
Identify your variables. Then, write and solve a system of equations to find the number of t-shirts and
hats the basketball team sold.
Answers
Answer:
t-shirts = 8, hats= 15
Step-by-step explanation:
let the no of of t-shirt be x
and the no of hats be y
[tex]x+y= 23-----------1[/tex]
[tex]8x+10y= 154---------2[/tex]
solving equations 1 and 2 simultaneously we have
multiplying equation 1 by 8 and subtracting from 2 we have
[tex]8x+8y=184-------------4\\-8x+10y=154------------2[/tex]
[tex]=0x-2y=30[/tex]
[tex]y=\frac{-30}{2} \\y=-15[/tex]
y= 15
substituting y= 15 in equation 1 to find x we have
[tex]x+15=23\\x=23-15\\x= 8[/tex]
x=8
In a circle of radius 5 miles, the length of the arc that subtends a central angle of 4 radians is how many miles?
Answers
Answer:
The length of the arc is 20 miles.
Step-by-step explanation:
We know that an arc formed by an angle of 1 radian in a circle of radius of 1 mile will have a length of 1 mile.
If the radius is 5 miles, an arc of 1 radian will have a length of 5 miles.
Then, if the angle is 4 radians, and the radius is 5 miles, we will have an arc length of:
[tex]\text{arc length}=\text {angle} \cdot \text {radius}=4\cdot 5 =20\;\text{miles}[/tex]
The number of accidents that occur
each day at a certain intersection along
with the corresponding probabilities are
shown.
Answers
Answer: 0.12 accidents.
Step-by-step explanation:
The expected value is:
EV = ∑pₙ*xₙ
where xₙ is the event number n, pₙ is the probability of event xₙ
in this case we have:
x₀ = 0 accidents and p₀ = 0.935
x₁ = 1 accident, and p₁ = 0.03
x₂ = 2 accidents, and p₂ = 0.02
x₃ = 3 accidents, and p₃ = 0.01
x₄ = 4 accidents, and p₄ = 0.005
Then the expected value is:
EV = (0*0.935 + 1*0.03 + 2*0.02 + 3*0.01 + 4*0.05) = 0.12 accidents.
Answer:
0.12
Step-by-step explanation:
What are the composite factor of 20
Answers
Answer:
4×4+4Step-by-step explanation:
hope its helpful
Answer:
4, 10, and 20.
Step-by-step explanation:
20 is a composite number because it has more than 2 factors.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
1 is neither prime nor composite.
2, 5 are prime numbers because they only have 2 factors.
4, 10, 20 are composite numbers because they have more than 2 factors.
The length of a rectangle is 11 yds more than twice the width, and the area of the rectangle is 63 yd ^2, find the dimentions of the rectangle
Answers
Answer:
The length is 18 ydThe width is 3.5 ydStep-by-step explanation:
Area of a rectangle = l × w
where l is the length
w is the width
length of a rectangle is 11 yds more than twice the width is written as
l = 11 + 2w
Area = 63 yd²
(11+2w)w = 63
2w² + 11w - 63 = 0
Solve the quadratic equation
( w + 9) ( 2x - 7) = 0
w = - 9 w = 7/2 or 3.5
Since width is always positive w is 3.5 yd
l = 11 + 2(3.5)
l = 11 + 7
l = 18 yd
The length is 18 yd
The length is 18 ydThe width is 3.5 yd
Hope this helps you
Rationalize the denominator and simplify
Answers
Answer:
sqrt(70)/7
Step-by-step explanation:
sqrt(10/7)
sqrt ( a/b) = sqrt(a)/ sqrt(b)
sqrt(10) / sqrt(7)
But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)
sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)
sqrt(70)/ sqrt(49)
sqrt(70)/7
Consider the following information. SSTR = 6750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8000 Ha: At least one mean is different If n = 5, the mean square due to error (MSE) equals a. 1687.5. b. 400. c. 500. d. 2250.
Answers
Answer:
d. 2250.
Step-by-step explanation:
The calculation of mean square due to error (MSE) is shown below:-
Since there are four treatments i.e H0: μ1 = μ2 = μ3 = μ4
And, the SSTR is 6,750
Based on this, the mean square due to error is
= [tex]\frac{SSTR}{n-1}[/tex]
[tex]= \frac{6,750}{4-1}[/tex]
= [tex]\frac{6,750}{3}[/tex]
= 2,250
Hence, the mean square due to error is 2,250
Therefore the correct option is d.
All the other information is not relevant. Hence ignored it
Domain and range of T
Answers
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
6th grade math help me please :))
Answers
Answer:
b) a coefficientd) a constant1, 2, 4Step-by-step explanation:
Just definitions :)
Hope it helps <3
Malik is buying a guinea pig. The guinea pig comes with a cage and food bowls for $ 125.00 . The expenses for feeding and caring for the guinea pig are $ 18.00 each month. How much will it cost Malik to buy and care for the guinea pig for one year?
Answers
Answer:
$341.00
Step-by-step explanation:
"$ 18.00 each month."
$18.00*$12.00=$216.00
$216.00+$125.00=$341.00
hope this helpes
be sure to give brainliest
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not
replacing it, and then choosing a red marble
Answers
Answer:
1/12
Step-by-step explanation:
Initially there are 4 marbles, 1 of which is green.
After the green marble is removed, there are 3 marbles, 1 of which is red.
The probability is therefore 1/4 × 1/3 = 1/12.
My Answer:
1/12 OR letter B.
My Explanation:
P(G) = 1/4....P(R) = (1/3)
(1/4)(1/3) = 1/12
I hope this makes sense! Glad to help anytime :)
(This is the correct answer on edge 2020/2021 btw)
Please help me it’s due tomorrow and I really need help
Answers
Answer:
5 [tex]\frac{1}{3}[/tex], 10 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex] ÷ 1 [tex]\frac{1}{3}[/tex] = 2
Thus to obtain a term in the sequence multiply the previous term by 2, thus
a₅ = [tex]\frac{8}{3}[/tex] × 2 = [tex]\frac{16}{3}[/tex] = 5 [tex]\frac{1}{3}[/tex]
a₆ = [tex]\frac{16}{3}[/tex] × 2 = [tex]\frac{32}{3}[/tex] = 10 [tex]\frac{2}{3}[/tex]
The function C(x) = 200x + 240 gives the cost for a college to offer x sections of an introductory class in CPR. The function R(x) = 280x gives the amount of revenue the college brings in when offering x sections of CPR. Find the point where the cost equals the revenue by graphing each function on the same coordinate system.
Answers
Answer:
C(3) = R(3) = 840
Step-by-step explanation:
See the attached for a graph.
Express it in slope-Intercept form
Answers
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
Of all vehicles sold by a certain car dealership, 35% are sports cars. From 50 randomly selected vehicle purchases, use the normal distribution to approximate the probability that less than 14 are sports cars.
a) 0.1178
b) 0.1497
c) 0.0911
d) 0.1869
Answers
Answer:
a) 0.1178
Step-by-step explanation:
The calculation is shown below:-
Mean = np
= 50 × 0.35
= 17.5
Standard deviation is
= [tex]\sqrt{n\times p\times q}[/tex]
= [tex]\sqrt{50\times 0.35 \times 0.65}[/tex]
= 3.373
Therefore, as we know that
P which is Less than 14
So,
= P(X < 13.5)
= P(z < (13.5 - 17.5) ÷ 3.373
= P(z < -1.186)
= 0.1178
Hence, the correct option is a. 0.1178
basically we used the above formulas i.e mean and standard deviation
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? Round the answer to the nearest whole number
Answers
Answer:
61,925 miles
Step-by-step explanation:
Given :
The p-value of the tires to outlast the were warranty were given in the the question as = 0.96
Checking the normal distribution table, The probability that corresponds to 0.96
from the Normal distribution table is 1.75.
Mean : 'μ'= 60000 miles
Standard deviation : σ=1100
The formula for z-score is given by
: z= (x-μ)/σ
1.75=(x-60000)/1100
1925=x-60000
x=61925
Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.