Answer:
Combination 25 to 12
Step-by-step explanation:
[tex]C^{12} _{25}[/tex]
The expression 25! / [(25 - 12)! x 12!] represents the combination.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Let a be the number of items selected from the group of n.
We know that the combination is given by,
ⁿCₐ = n! / [(n - a)! x a!]
The expression is given below.
⇒ 25! / [(25 - 12)! x 12!]
Then the expression can be written as,
⇒ ²⁵C₁₂
Then the expression 25! / [(25 - 12)! x 12!] represents the combination.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ2
Based on the family the graph below belongs to, which equation could represent the graph? image below.
Answer:
y = 1/x+2 + 3
Step-by-step explanation:
x = -2
y = 3
Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
[tex]A=1500-1450e^{-\dfrac{t}{250}}[/tex]
Step-by-step explanation:
The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.
Volume = 500 gallons
Initial Amount of Salt, A(0)=50 pounds
Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min
[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}[/tex]
When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
Concentration c(t) of the salt in the tank at time t
Concentration, [tex]C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}[/tex]
[tex]R_{out}[/tex]=(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}[/tex]
Now, the rate of change of the amount of salt in the tank
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]
[tex]\dfrac{dA}{dt}=6-\dfrac{A}{250}[/tex]
We solve the resulting differential equation by separation of variables.
[tex]\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}[/tex]
Taking the integral of both sides
[tex]\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}[/tex]
Recall that when t=0, A(t)=50 (our initial condition)
[tex]50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}[/tex]
A fair die has just been rolled five times – giving scores of 1, 2, 3, 4, 5 in that order. How likely is it that the score on the next roll will be a 6?
A. no chance B. less than evens C. evens D. better than evens E. certain
Answer:
b. less than evens
Step-by-step explanation:
the probability that the next roll is 6 is
[tex] \frac{1}{6} [/tex]
B. less than evens should be the answer
A farmer plants corn in of his field. He plants white corn in of the corn
section of his field. This situation is shown in the model. What fraction of the
whole field is planted with white corn?
Answer:
3/20
Question:
A farmer plants corn in 1/4 of his field. He plants white corn in 3/5 of the corn
section of his field. This situation is shown in the model. What fraction of the whole field is planted with white corn
Step-by-step explanation:
Portion of the field planted with corn = 1/4
Total corn planted = 1/4 of field
Portion of the corn section planted with white corn = 3/5
Total white corn planted = 3/5 of corn section
We need to find the portion of the total field planted with white corn
The fraction of the whole field planted with white corn would be the product of the fraction of Total corn planted and fraction of Total white corn planted
= 1/4 × 3/5
= 3/20
The fraction of the whole field planted with white corn = 3/20
Need help ASAP thanks!!
Answer:
43.96
Step-by-step explanation:
you do 6 divided by 2 to find the radius
then u find the volume
v= [tex]\pi[/tex]r^2h/3
v=3.14(3 to the power of 2)7/3
hope this helps
correct me if this is wrong
If SinP + SinQ = 7/5 and angle P + angle Q = 90 degrees, without the use of a calculator, determine the value of Sin2P
Answer:
sin2P ≈ 1Step-by-step explanation:
Given SinP + SinQ = 7/5...1 and
∠P + ∠Q = 90°... 2
From compound angle; SinP +SinQ = [tex]2sin(\frac{P+Q}{2} )cos(\frac{P-Q}{2} )[/tex]... 3
Substituting equation 2 into 3 we will have;
SinP +SinQ = [tex]2sin(\frac{90}{2} )cos(\frac{P-Q}{2} )[/tex] = 7/5
[tex]2sin45^{0} cos\frac{P-Q}{2}=7/5[/tex]
since P = 90-Q from equation 1, then;
[tex]2sin45^{0} cos\frac{90-Q-Q}{2}=7/5\\2sin45^{0} cos\frac{90-2Q}{2}=7/5\\2(\frac{1}{\sqrt{2} } ) cos\frac{90-2Q}{2}=7/5\\cos\frac{90-2Q}{2} = 7/5* \frac{\sqrt{2} }{2} \\cos\frac{90-2Q}{2} = \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = cos^{-1} \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = 8.15\\90-2Q = 16.30\\2Q = 90-16.3\\2Q = 73.7\\Q = 36.85^{0} \\\\P = 90-36.85\\P = 53.15^{0}[/tex]
To get sin2P; Accoding to the trig identity;
Sin2P = 2SinPCosP
Sin2P = 2Sin53.15cos53.15
sin2P = 0.9598
sin2P ≈ 1
Can someone solve this??
Answer:
see below
Step-by-step explanation:
There are a few relevant relations involved:
an inscribed angle is half the measure of the arc it interceptsan arc has the same measure as the central angle that intercepts itthe angle exterior to a circle where secants meet is half the difference of the intercepted arcs (near and far)the angle interior to a circle where secants meet is half the sum of the intercepted arcsthe angle where tangents meet is the supplement of the (near) arc interceptedan exterior angle of a triangle is equal to the sum of the remote interior anglesthe angle between a tangent and a radius is 90°the angle sum theoremAB is a diameter, so arcs AB are 180°.
a) BC is the supplement to arc AC: 180° -140° = 40°
b) BG is the supplement to AG: 180° -64° -38° = 78°
c) ∠1 has the measure of BC: 40°
d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°
e) ∠3 is half the measure of arc AE: 64°/2 = 32°
f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°
g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°
h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°
i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°
j) ∠8 is the measure of arc AC: 140°
k) ∠9 is the supplement to arc AC: 180° -140° = 40°
l) ∠10 is the complement of angle 7: 90° -31° = 59°
Given Line segment E D is-congruent-to Line segment D B , which statements about the figure are true? Check all that apply.
Line segment E B is bisected by Line segment D F .
A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
Line segment E B is a segment bisector.
FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Answer:
A, B, D and E.
Step-by-step explanation:
From the diagram
[tex]ED \cong DB\\FA \cong AC[/tex]
Since D is the midpoint of EB, Line segment EB is bisected by Line segment DF.Since [tex]FA \cong AC[/tex], A is the midpoint of Line segment FC.EB bisects FC at point A, therefore, Line segment E B is a segment bisector.Point A divides FC into two equal parts, FA and AC, therefore [tex]FA=\frac{1}{2}FC[/tex]The correct options are A, B, D and E.
Answer:
1, 2, 4, 5
Step-by-step explanation:
Line segment E B is bisected by Line segment D F .
A is the midpoint of Line segment F C .
Line segment E B is a segment bisector.
FA = One-halfFC.
A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time t=0 is v(0)=13. What is its position at time t=5?
Answer:
It's position at time t = 5 is 593.
Step-by-step explanation:
The velocity v(t) is the integral of the acceleration a(t)
The position s(t) is the integral of the velocity v(t)
We have that:
The acceleration is:
[tex]a(t) = 24t + 2[/tex]
Velocity:
[tex]v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K[/tex]
K is the initial velocity, that is v(0). Since V(0) = 13, K = 13
Then
[tex]v(t) = 12t^{2} + 2t + 13[/tex]
Position:
[tex]s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K[/tex]
Since s(0) = 3
[tex]s(t) = 4t^{3} + t^{2} + 13t + 3[/tex]
What is its position at time t=5?
This is s(5).
[tex]s(t) = 4t^{3} + t^{2} + 13t + 3[/tex]
[tex]s(5) = 4*5^{3} + 5^{2} + 13*5 + 3[/tex]
[tex]s(5) = 593[/tex]
It's position at time t = 5 is 593.
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters, and a standard deviation of 7. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would be greater than 141.4 millimeters
Answer:
Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.
Step-by-step explanation:
We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.
A random sample of 39 steel bolts is selected.
Let [tex]\bar X[/tex] = sample mean diameter
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean diameter = 141 millimetres
[tex]\sigma[/tex] = standard deviation = 7 millimetres
n = sample of steel bolts = 39
Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P([tex]\bar X[/tex] > 141.4 millimetres)
P([tex]\bar X[/tex] > 141.4) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex] > [tex]\frac{141.4-141}{\frac{7}{\sqrt{39} } } }[/tex] ) = P(Z > 0.36) = 1 - P(Z [tex]\leq[/tex] 0.36)
= 1 - 0.6406 = 0.3594
The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.
what do you think 40x40 is And tell me how you got your answer
Answer:
40*40 =1600
Step-by-step explanation:
Evaluate: 2a + 4b when a = 10 & b = 6
A: 20
B: 4
C: 44
D:24
Answer: Option C: 44
Step-by-step explanation:
so, here we have the equation:
H(a,b) = 2a + 4b
"evaluate" means change the values of the variables for specific values, here we must replace the "a" for 10, and the "b" for a 6.
So we have:
H(10, 6) = 2*10 + 4*6 = 20 + 24 = 44
Is
1x7x6x7x89x7x33x188+4444-82x77x9999= 1073207806
Answer:
Yes
Step-by-step explanation:
Simplify the following:
1×7×6×7×89×7×33×188 + 4444 - 82×77×9999
1×7 = 7:
7×6×7×89×7×33×188 + 4444 - 82×77×9999
7×6 = 42:
42×7×89×7×33×188 + 4444 - 82×77×9999
42×7 = 294:
294×89×7×33×188 + 4444 - 82×77×9999
| | 2 | 9 | 4
× | | | 8 | 9
| 2 | 6 | 4 | 6
2 | 3 | 5 | 2 | 0
2 | 6 | 1 | 6 | 6:
26166×7×33×188 + 4444 - 82×77×9999
26166×7 = 183162:
183162×33×188 + 4444 - 82×77×9999
| 1 | 8 | 3 | 1 | 6 | 2
× | | | | | 3 | 3
| 5 | 4 | 9 | 4 | 8 | 6
5 | 4 | 9 | 4 | 8 | 6 | 0
6 | 0 | 4 | 4 | 3 | 4 | 6:
6044346×188 + 4444 - 82×77×9999
| | | 6 | 0 | 4 | 4 | 3 | 4 | 6
× | | | | | | | 1 | 8 | 8
| | 4 | 8 | 3 | 5 | 4 | 7 | 6 | 8
| 4 | 8 | 3 | 5 | 4 | 7 | 6 | 8 | 0
| 6 | 0 | 4 | 4 | 3 | 4 | 6 | 0 | 0
1 | 1 | 3 | 6 | 3 | 3 | 7 | 0 | 4 | 8:
1136337048 + 4444 - 82×77×9999
| | 8 | 2
× | | 7 | 7
| 5 | 7 | 4
5 | 7 | 4 | 0
6 | 3 | 1 | 4:
1136337048 + 4444 + -6314×9999
| | | | 9 | 9 | 9 | 9
× | | | | 6 | 3 | 1 | 4
| | | 3 | 9 | 9 | 9 | 6
| | | 9 | 9 | 9 | 9 | 0
| 2 | 9 | 9 | 9 | 7 | 0 | 0
5 | 9 | 9 | 9 | 4 | 0 | 0 | 0
6 | 3 | 1 | 3 | 3 | 6 | 8 | 6:
1136337048 + 4444 + -63133686
| | | | | | 1 | | | 1 |
| 1 | 1 | 3 | 6 | 3 | 3 | 7 | 0 | 4 | 8
+ | | | | | | | 4 | 4 | 4 | 4
| 1 | 1 | 3 | 6 | 3 | 4 | 1 | 4 | 9 | 2:
1136341492 - 63133686
| | | | | | | 10 | | |
| | 0 | 13 | | | 3 | 0 | 14 | 8 | 12
| 1 | 1 | 3 | 6 | 3 | 4 | 1 | 4 | 9 | 2
- | | | 6 | 3 | 1 | 3 | 3 | 6 | 8 | 6
| 1 | 0 | 7 | 3 | 2 | 0 | 7 | 8 | 0 | 6:
Answer: 1,073,207,806
Answer:
4.6570394e+12
Step-by-step explanation:
1. 1x7=7
2. 7x6=42
3. 42x7=294
4. 294x89=26166
5. 26166x7=183162
6. 183162x33=6044346
7. 6044346+4444=6048790
8. 6048790-82=6048708
9. 6048708x77=465750516
10. 465750516x9999=4.6570394e+12
A pile of 23 coins consists of nickels and dimes. The total value
of the coins is $1.40. Find the number of each type of coin.
Answer:
5 dimes and 18 nickels
Step-by-step explanation:
5D + 18 N =
5 x 10 + 18 x 5 =
5 x.10 + 18 x 0.05=
.50 + .90=
$1.40
g(x) = -4x + 5, find g(5).
Answer:
-15
Step-by-step explanation:
g(x) = -4x + 5, find g(5)
Let x = 5
g(5) = -4*5 +5
= -20 +5
= -15
The answer ? What is it i want to kbow it get better in maths and studying so please give me the answer and thank you .
Answer:
6/8
Step-by-step explanation:
6/8
Please help! Correct answr only, please! The following information matrices show the number of breakfasts & lunches sold at a little creek middle school on Monday and the prices of breakfast and lunch Which of the following best describes the element? A. Sixth graders paid a total of $60.50 for their breakfast meals on Monday. B. There are 22 sixth graders eating breakfast on Monday. C. Sixth graders paid a total of $508.50 for all their meals on Monday. D. Breakfast costs $2.75
Answer:
Hello There Again. The correct answer is D.
Explanation: Because it shows that you need to subtract 2.75 - 3.50 which that will be 75. So the correct answer will be D.
Hope It Helps! :)
Sixth graders paid a total of $508.50 for all their meals on Monday.
Solve the equation.
6.35 + b = 9.89
Answer:
b=3.54
Step-by-step explanation:
9.89-6.35=3.54
Answer: b=3.54
Step-by-step explanation:
Subtract 6.35 from both sides and you will get that b=9.89-6.35 solve that and you will get that b= 3.54.
The number of houses being built each year is modeled by the growth equation, H(=350 20.12. How long will it take for the
number of new houses to reach 70,000? Round to the nearest whole number.
Answer:
H(24) = 70,000
Step-by-step explanation:
If the growth equation is
H(35020) = 12
Then we are told to find H(70,000)
35020 = 12
70,000 = x
35020x = 12 × 70,000
x = 12 × 70,000/35020
= 23.99
≈ 24.
H(24) = 70,000
The department of public safety has an old memo stating that the number of accidents per week at a hazardous intersection varies according to a Normal distribution, with a mean of 2.2 and a standard deviation of 1.4. Department officials implemented a new safety plan, heavier police patrols and new signs, to see if they could reduce the average number of accidents at this intersection. They recorded the number of accidents per week for 52 weeks. They find that the average over that period was two accidents per week.
What is the PP‑value for the test of H0:????=2.2 against H????:????<2.2H0:μ=2.2 against Ha:μ<2.2 ?
A. 0.8485
B. 0.4443
C. 0.1515
Answer:
C. 0.1515
Step-by-step explanation:
The main objective here is to find the P-value for the test of [tex]H_0[/tex]
Given that ;
the mean value = 2.2
the standard deviation = 1.4
number of recorded accident per week = 52
The null hypothesis is : [tex]H_o: \mu =2[/tex]
The alternative hypothesis is : [tex]H_A = \mu < 2[/tex]
The Z- value can be calculated as:
[tex]z = \dfrac{x- \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]z = \dfrac{2- 2.2}{\dfrac{1.4 }{\sqrt{52}}}[/tex]
[tex]z = \dfrac{- 0.2}{\dfrac{1.4 }{7.211}}[/tex]
z = -1.03
From the normal distribution table for probability;
P(z< -1.03 ) = 0.1515
A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, TechnicsA switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules to answer the following questions:
a. In how many ways can one component of each type be selected?
b. In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?
c. In how many ways can components be selected if none is to be Sony?
d. In how many ways can a selection be made if at least one Sony component is to be included?
e. If someone flips switches on the selection in a completely random fashion, what is the probability that the
system selected contains at least one Sony component?Exactly one Sony component?
Answer:
a) 240 ways
b) 12 ways
c) 108 ways
d) 132 ways
e) i) 0.55
ii) 0.4125
Step-by-step explanation:
Given the components:
Receiver, compound disk player, speakers, turntable.
Then a purcahser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers
Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers
Speakers: Boston, Infinity, Polk => 3 offers
Turntable: Onkyo, Sony, Teac, Technics => 4 offers
a) The number of ways one component of each type can be selected =
[tex] \left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 5 * 4 * 3 * 4 = 240 ways [/tex]
b) If both the receiver and compact disk are to be sony.
In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.
Thus, the number of ways components can be selected if both receiver and player are to be Sony is:
[tex] \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 1 * 1 * 3 * 4 = 12 ways [/tex]
c) If none is to be Sony.
Let's exclude Sony from each component.
Receiver has 1 sony = 5 - 1 = 4
CD player has 1 Sony = 4 - 1 = 3
Speakers had 0 sony = 3 - 0 = 3
Turntable has 1 sony = 4 - 1 = 3
Therefore, the number of ways can be selected if none is to be sony:
[tex] \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) [/tex]
[tex] = 4 * 3 * 3 * 3 = 108 ways [/tex]
d) If at least one sony is to be included.
Number of ways can a selection be made if at least one Sony component is to be included =
Total possible selections - possible selections without Sony
= 240 - 108
= 132 ways
e) If someone flips switches on the selection in a completely random fashion.
i) Probability of selecting at least one Sony component=
Possible selections with at least one sony / Total number of possible selections
[tex] \frac{132}{240} = 0.55 [/tex]
ii) Probability of selecting exactly one sony component =
Possible selections with exactly one sony / Total number of possible selections.
[tex] \frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240} [/tex]
[tex] = \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240} [/tex]
[tex] \frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125 [/tex]
if 4 sec a _ 5 = 0, evaluate 2 cos a + 5 sin a ÷ 2 sin a + 5 cos a
Answer:
23/26 = 0.8846=0.88 [ to the nearest hundredth]
Step-by-step explanation:
4 sec a-5 = 0; seca=1/cos a
Therefore;
4 sec a-5 = 0=>4/cos a - 5 = 0
Multiplying through by cos a, we have;
4-5cosa= 0=>4= 5cosa
4/5 = cosa
a = cos^{-1}0.8
=36.88
Alternatively Cos a =4/5
Sina = 3/5; {note Cos a = adjacent / hypothesis and from Pythagoras rule we can derive the value of the opposite side which is;
5^2 -4^2 = 25-16 = 9; hence the opposite side is √9 = 3;sin a = opposite/ hypothenus = 3/5}
Substituting the value of Cosa and Sina into the expression below;
2 cos a + 5 sin a ÷ 2 sin a + 5 cos a
We have ;
[2×4/5 + 5× 3/5 ]/ [2 × 3/5 + 5× 4/5]
[8/5 + 15/5 ]/ [6/5 + 20/5]
[23/5]/[26/5] = 23/5 × 5/26 = 23/26
=
Find the value of x round to the nearest tenth
Answer:
4.1 cm
Step-by-step explanation:
The segment marked x bisects the chord, so the triangle shown has legs x and 7.8, and hypotenuse 8.8.
The Pythagorean theorem can be used to find x:
8.8² = x² +7.8²
x² = 8.8² -7.8² = 77.44 -60.84 = 16.60
x = √16.6
x ≈ 4.1 . . . cm
WILL GIVE BRAINLIST.Which of the following multiplication expressions can be modeled by the tiles shown?Check all that apply 8(3)=24 6(4)=24 (3)(12)=36 24(3)=72 3(8)=24 2(12)=24
Answer:
8(3)=24
3(8) =24
Step-by-step explanation:
Step-by-step explanation:
i want brainliest please
Answer:
8 sets of 3 positive tiles.
Which of the following multiplication expressions can be modeled by the tiles shown? Check all that apply.
yes 8(3) = 24
no 6(4) = 24
no (3)(12) = 36
no 24(3) = 72
yes 3(8) = 24
no 2(12) = 24
yah welcome
Select the most important variables and expressions the park owners should consider as they decide whether to add another roller coaster
Answer:
The park owners should take into account the population of children in the community, if there are a good number of kids living in that area and the towns nearby - there would be a great demand for another roller coaster. They should consider the safety measures on the particular roller coaster they intend to add and check for the available space where they plan to fit the ride in the park.
Hope that answers the question, have a great day!
2
Select the correct answer.
Some persuasive texts rely on common but faulty forms of reasoning. Which term refers to these faulty ways of reasoning?
ОА.
emotional appeals
OB. blased arguments
OC. rhetorical techniques
OD. logical fallacles
O E
endorsements
Reset
Next
Answer:
D. Logical Fallacies
Step-by-step explanation:
Let's break this down:
fallacy: A false or mistaken idea.
By this definition, we can see that "false" would go with the word "faulty". A logical Fallacy is is a false or mistaken idea that's intended to sound logical. I hope this helps you!!
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 17 in-state applicants results in a SAT scoring mean of 1046 with a standard deviation of 37. A random sample of 10 out-of-state applicants results in a SAT scoring mean of 1118 with a standard deviation of 50. Using this data, find the 90% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score of in-state applicants
x2 = sample mean score of out -of-state applicants
s1 = sample standard deviation for in-state applicants
s2 = sample standard deviation for out-of-state applicants
n1 = number of in-state applicants
n1 = number of out-of-state applicants
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (17 - 1) + (10 - 1) = 25
z = 1.708
x1 - x2 = 1046 - 1118 = - 72
Margin of error = z√(s1²/n1 + s2²/n2) = 1.708√(37²/17 + 50²/10) = 31.052239
Confidence interval is - 72 ± 31.052239
the sum of three consecutive odd numbers is 51
Answer:
the answer for the question is 25 and 26
What is the solution to the system of equations below?
x + 3y = 1
-3x - 3y = -15
Answer:
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
-2x = -14
x = 7
7 + 3y = 1
3y = -6
y = -2
(7, -2)
Answer:
x =7 , y= -2
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
Add the equations together to eliminate y
x + 3y = 1
-3x - 3y = -15
-------------------------
-2x = -14
Divide by -2
-2x/-2 = -14/-2
x = 7
Now we can find y
x+3y = 1
7 + 3y = 1
Subtract 7 from each side
7+3y-7 = 1-7
3y = -6
Divide by 3
3y/3 = -6/3
y = -2
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200students in group 1 had a mean score of 24.5 with a standard deviation of 4.3, while the 200 students in group 2 had a mean score of 16.3 with a standard deviation of 3.1.Complete parts (a) and (b) below.(a) Determine the 90% confidence interval for the difference in scores, mu 1 minus mu 2.Interpret the interval. ( , ) (Round to three decimal places asneeded.)Interpret the interval. Choose the correct answer below.A.There is a 90% probability that the difference of the means is in the interval.B.The researchers are 90% confident that the difference of the means is in the interval.C.The researchers are 90% confident that the difference between randomly selected individuals will be in the interval.D.There is a 90% probability that the difference between randomly selected individuals will be in the interval.(b) What does this say about priming?A.Since the 90% confidence interval does not contain zero, the results suggest that priming does not have an effect on scores.B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.C.Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores.D.Since the 90% confidence interval contains zero, the results suggest that priming does not have an effect on scores.
Answer:
Step-by-step explanation:
a) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of group 1
x2 = sample mean of group 2
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 24.5
s1 = 4.3
n1 = 200
x2 = 16.3
s2 = 3.1
n2 = 200
x1 - x2 = 24.5 - 16.3 = 8.2
z√(s1²/n1 + s2²/n2) = 1.645√(4.3²/200 + 3.1²/200) = 1.645√0.1405
z = 0.62
Therefore, the 90% confidence interval is 8.2 ± 0.62
Interpretation:
B.The researchers are 90% confident that the difference of the means is in the interval.
b) B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
