Answer:
A 98% confidence interval for the population mean of printouts per ink cartridge is [430.5, 489.5].
Step-by-step explanation:
We are given that a consumer advocate group selects a random sample of 20 ink cartridges and finds that the average number of printouts per ink cartridge is 460 with a standard deviation of 52.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average number of printouts per ink cartridge = 460
s = sample standard deviation = 52
n = sample of ink cartridges = 20
[tex]\mu[/tex] = population mean printouts per ink cartridge
Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 98% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.54 < [tex]t_1_9[/tex] < 2.54) = 0.98 {As the critical value of t at 19 degrees of
freedom are -2.54 & 2.54 with P = 1%}
P(-2.54 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.54) = 0.98
P( [tex]-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.98
P( [tex]\bar X-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.98
98% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]460-2.54 \times {\frac{52}{\sqrt{20} } }[/tex] , [tex]460+2.54 \times {\frac{52}{\sqrt{20} } }[/tex] ]
= [430.5, 489.5]
Therefore, a 98% confidence interval for the population mean of printouts per ink cartridge is [430.5, 489.5].
Multiply.
(2x2 – 3x + 1)(x2 - 4x – 3)
Answer:
2x^4−11x^3+7x^2+5x−3
Step-by-step explanation:
The ^ means exponent
What number is 408% of 568?
Answer:
2317.44
Step-by-step explanation:
Solution for What is 408 percent of 568:
408 percent *568 =
(408:100)*568 =
(408*568):100 =
231744:100 = 2317.44
Answer:
2317.44
Step-by-step explanation:
Find the product of 4 2/7 x 3 1/2
Answer:
Hey there!
The product of these two fractions would equal 15.
Hope this helps :)
Answer:
Hi! The answer to your question is 7 11/14 or rounded will be 15
Step-by-step explanation:
So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.
Now we do LCD (least common denominator)
4/14+7/14=11/14
So the answer is 7 11/14 or 15
(In mixed number the answer is 7 11/14 and in whole the answer is 15)
Hope this helps! :)
Write the equations of the line with the slope=6 that passes through (4,-6)
Answer:
y=6x+18
Step-by-step explanation:
Answer:
y = 6x - 30
Step-by-step explanation:
The slope is 6.
Use the formula for the equation of a line.
y = mx + b
Where m is the slope, and b is the y-intercept.
y = 6x + b
The point is given (4, -6)
(x , y)
Put x as 4, y as -6.
-6 = 6(4) + b
-6 = 24 + b
-6 - 24 = b
-30 = b
The y-intercept is -30.
The equation of the line is y = 6x - 30.
What are the quadratic factors of the function represented by this graph?
Answer:
B. (x + 5)(x + 1)
Step-by-step explanation:
Since our roots are x = -5 and x = -1, we have:
x + 5 = 0
x + 1 = 0
Put that into quadratic binomials:
(x + 5)(x + 1)
Connie is packing for a trip. She has 18 pairs of shoes. If she has room to pack 5 pairs, how many ways can she choose which shoes to take?
Answer:
There are 8568 ways to combine the shoes.
Step-by-step explanation:
In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:
[tex]C_{(n,r)} = \frac{n!}{r!*(n - r)!}[/tex]
In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.
[tex]C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568[/tex]
There are 8568 ways to combine the shoes.
The number of ways can she choose which shoes to take is 8,568.
Given that,
Connie is packing for a trip. She has 18 pairs of shoes and she has room to pack 5 pairs.Based on the above information, the calculation is as follows:
[tex]= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}[/tex]
= 8,568
Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.
Learn more: brainly.com/question/17429689
An article gave the accompanying data on ultimate load (kN) for two different types of beams. Assuming the underlying distributions are Normal, calculate and interpret a 99% Cl for the difference between the true average load for the fiberglass beams and that for the carbon beams.
Type Sample size Sample Mean Sample SD
Fiberglass grid 26 33.4 2.2
Commercial carbon 26 42.8 4.3
grid
1. Calculate and interpret a 99% Cl for true average stance duration among elderly individuals.
2. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than younger individuals.
Answer:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.
The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.
The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.
The difference between sample means is Md=-9.4.
[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]
The critical t-value for a 99% confidence interval is t=2.678.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.
[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]
The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:
[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
See more about statistics at brainly.com/question/2289255
For every touchdown scored by the Timberwolves, the mascot does 333 back flips and the cheerleaders set off 666 confetti cannons.
How many touchdowns did the Timberwolves score if the cheerleaders set off 181818 confetti cannons?
Answer:
273 Touchdowns
Step-by-step explanation:
You divide the amount of confetti cannons set off by the amount of confetti cannons set off every time there is a touchdown scored. So in this case 181818 ÷ 666
factorise 12x² + x - 20
━━━━━━━☆☆━━━━━━━
▹ Answer
(3x + 4) * (4x - 5)
▹ Step-by-Step Explanation
12x² + x - 20
Rewrite
12x² + 16x - 15x - 20
Factor out
4x(3x + 4) - 15x - 20
4x(3x + 4) - 5(3x + 4)
Factor
(3x + 4) * (4x - 5)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Find
dy/dx and d2y/dx2,
and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)
Parametric Equations Point
x = 5t, y = 6t − 1
t = 2
Answer:
dy/dx = slope = 6/5d²y/dx² = concavity = 0.Step-by-step explanation:
Given the parametric equation points x = 5t, y = 6t − 1 when t = 2
From x = 5t, t = x/5. Substituting t = x/5 into the second equation y = 6t − 1 we will have;
y = 6(x/5) - 1
y = 6/5 x - 1
The derivative of y with respect to x i.e dy/dx = 6/5 - 0. (Note that differential of any constant is zero).
dy/dx = 6/5
d²y/dx² = d/dx(dy/dx)
d²y/dx² = d/dx(6/5)
Since 6/5 is a constant, the derivative of 6/5 with respect to x will be zero.
d²y/dx² = 0.
Since the first derivative and the second derivative are both constant then, the slope m at the given parameter will be 6/5.
m = dy/dx = 6/5
The concavity is the value of the second derivative at the given value of the parameter.
The concavity d²y/dx² = 0.
A researcher wants to study the average miles run per day for marathon runners. In testing the hypotheses: H0: μ = 25 miles vs. H1: μ ≠ 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. What is the rejection region associated with 3% significance level?
Answer:
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
A researcher wants to study the average miles run per day for marathon runners is 25
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 36
Given mean of the sample x⁻ = 22.8 miles
Given mean of the Population 'μ' = 25
Given standard deviation of the Population 'σ' = 10
Null hypothesis:-H₀: μ = 25
Alternative Hypothesis:H₁:μ ≠ 25
Level of significance = 3 % or 97%
The critical value Z₀.₉₇ = 1.881
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }[/tex]
Z = -1.325
|Z| = |-1.325| = 1.325
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
conclusion:-
A researcher wants to study the average miles run per day for marathon runners is 25
Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.
Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
Answer:
a) 26.33 kg/d and 29.67 kg/d
b) 94.5%
Step-by-step explanation:
a. Find a 99% confidence interval for the true mean milk production.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d
The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d
The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
We need to find z initially, when M = 1.25.
[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]2.25z = 1.25\sqrt{12}[/tex]
[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]
[tex]z = 1.92[/tex]
When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.
1 - 2*(1 - 0.9725) = 0.945
So we should use a confidence level of 94.5%.
In how many different ways can each of the letters in the following words be arranged? Show your work and solutions. 25. LEARN
Answer:
120 waysStep-by-step explanation:
This problem bothers on permutation
Given the letters LEARN
The total alphabets are 5 in numbers
Since there are no repeating letters, and there are 5 total letters, there are 5!=5*4*3*2*1= 120 ways to arrange them
The form of the alternative hypothesis can be: A. neither one nor two-tailed B. two-tailed C. one or two-tailed D. one-tailed
Answer:
The answer is "Option C"
Step-by-step explanation:
It is the hypothesis which would be opposed to just the null hypothesis, that is used in its testing. In this, we generally believed that the results derive from a particular effect with some superimposed variance of chance. It is nothing but an option in contrast to the null and its original test starts by considering its two hypotheses, that's why the only option C is correct.Verify the identity.
sin 2 t / cos t = t - cost
Answer:
Step-by-step explanation:
The question is incorrect. Here is the correct question.
Verify the identity sin²t / cos t = sect - cost
Given the identity sin²t / cos t = sect - cost, to verify means we are to check if both sides are equivalent. To do that we are going to start the proof from any sides of the equation and solve until we get to the function at the opposite side.
Starting with the left hand equation (LHS)
sin²t / cos t ...1
From trigonometry identity, sin²t+ cos²t = 1
sin²t = 1- cos²t ... 2
Substituting eqn 2 into 1 we have:
= 1- cos²t/cost
= 1/cost - cos²t/cost
= 1/cost - cost
Also from trig. identity, 1/cost = sect
On replacing this identity in the resulting equation we will have;
= sect - cost (which is equivalent to the RHS)
This shows that sin²t / cos t = sect - cost (Identity Proved!)
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as significant if its probability is less than or equal to 0.05. Select one: a. Significant at .055 b. Not significant at .945 c. Not significant at .055 d. Significant at .028
Answer:
c. Not significant at .055
Step-by-step explanation:
When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:
When the first dice is 5 and the second is 6.When the first dice is 6 and the second is 5.Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.
Then, the probability of getting 11 is:
[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]
This probability is not equal or less than 0.05, so it is not significant at 0.055.
Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2
Answer:
48.3 cm²
Step-by-step explanation:
Let A be the area of the yellow region
A= the area of the square - the area of the quarter square
A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²
9. A water glass can hold 2/9 of a litre of water. How many glasses of water can be filled with a 3 litre bottle?
Solve the problem
Answer:
13 1/2 glasses of water.Step-by-step explanation:
From the question, a water glass can hold 2/9 of a litre of water, to know the number of glasses of water that can be filled with a 3-litres bottle, the following steps are crucial;
1 water of glass = 2/9 litre of water
x = 3 litre of water
cross multiplying;
2/9 * x = 3*1
2x/9 = 3
2x = 27
Dividing both sides by 2;
2x/2 = 27/2
x = 13 1/2
This means 13 1/2 glasses of water can be filled with a 3-litre bottle.
In the given the figure above, m∠BAC = 64° and m∠CBA = 56°. Part I: Find the m∠DEC. Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
Answer:
56, see step-by-step.
Step-by-step explanation:
1. AB is parallel to CD. 1. Given
BC is parallel to DE.
m<BAC=64 and m<CBA =56
2. m<BAC + m<CBA + m<BCA =180 2. The angles in a triangle add up to 180
3. 64+ 56+ m<BCA=180 3. Substitution property of equality.
4. 120 + m<BCA=180 4. Addition property of equality.
5. m<BCA=60 5. Subtraction property of equality.
6. BC is a transversal that cuts through parallel lines AB and CD.
6. Def. of transversal.
7. m<CBA = m<BCD 7. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
8. m<BCA+m>BCD+m<DCE= 180. 8. Angle addition postulate
9. 60+56+m<DCE=180. 9.substitution.
10. 116 + m<DCE =180 10. Addition property of equality.
11. M<DCE =64 11. Subtraction property of equality.
12. DC is a transversal that cuts through parallel line BC and DE.
12. Def of transversal.
13. m<EDC= m<BCD 13. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
14. m<EDC= 60. 14. Substitution property of equality.
15. m<EDC+m<DCE+m<Dec=180. 15. Angle addition postulate
16. 56+64+m<dec = 180.16 Substitution property of equality.
17. 120+ m<dec = 180. Addition property of equality.
18. m<dec = 60 18. Subtraction property of equality.
Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alphaequals0.05.Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines g
Answer:
Step-by-step explanation:
Hello!
Full text:
Listed below are amounts of court income and salaries paid to the town justice. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P value using α = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines?
Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0
Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18
a. What are the null and alternative hypotheses?
To test if there is a linear correlation between the court income and the justice salary, you have to use the following hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
b. Construct a scatterplot. See attachment.
c. The linear correlation coefficient r is: _____.
[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]} }[/tex]
n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123
r= 0.86
d. The P value is: _____.
This test is two-tailed and so is its p-value. I've calculated it using a statistics software:
p-value: 0.0027
e. Based on the results, does it appear that justices might profit by levying larger fines?
Using the p-value approach, the decision rule is:
If the p-value ≤ α, reject the null hypothesis.
If the p-value > α, do not reject the null hypothesis.
The calculated p-value is less than the significance level, then the decision is to reject the null hypothesis.
At a 5% significance level you can conclude that there is a linear correlation between the "court income" and the "Justice salary"
I hope this helps!
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation:
In the absence of answer choices, let's find the expression for the volume.
Given: Volume = length×width×height
V = lwh
length =(2a + 11)
width =(5a – 12)
height= (a + 6)
V = (2a + 11)(5a – 12) (a + 6)
Expand the first two brackets using distributive property
V = (10a² -24a +55a - 132)(a + 6)
Collect like terms
V = (10a² + 31a -132)(a + 6)
Expand the two brackets using distributive property
V = 10a³ + 31a² - 132a + 60a² + 186a - 792
Collect like terms
V = 10a³ + 91a² + 54a - 792
The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation:
Solve 0=4x^2+12x+9
Simplify the expression to solve the equation
Answer:
x = -3/2
Step-by-step explanation:
0 = 4x² + 12x + 9
4x² + 12x + 9 = 0
(2x + 3)² = 0
2x + 3 = 0
2x = -3
x = -3/2
Hope this helps! :)
Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =
For the ODE
[tex]ty'+2y=\sin t[/tex]
multiply both sides by t so that the left side can be condensed into the derivative of a product:
[tex]t^2y'+2ty=t\sin t[/tex]
[tex]\implies(t^2y)'=t\sin t[/tex]
Integrate both sides with respect to t :
[tex]t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C[/tex]
Divide both sides by [tex]t^2[/tex] to solve for y :
[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}[/tex]
Now use the initial condition to solve for C :
[tex]y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}[/tex]
[tex]\implies9=\dfrac4{\pi^2}(1+C)[/tex]
[tex]\implies C=\dfrac{9\pi^2}4-1[/tex]
So the particular solution to the IVP is
[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}[/tex]
or
[tex]y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}[/tex]
Which linear inequality is represented by the graph?
Oy>2/3x-2
O y<2/3x+2
Oy> 2/3x+1
Oy<2/3x1
Answer:
Option (4)
Step-by-step explanation:
From the graph attached,
A dotted line passes through two points (3, 1) and (-3, -3)
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept
Slope of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For the given points,
m = [tex]\frac{1+3}{3+3}[/tex]
m = [tex]\frac{2}{3}[/tex]
y-intercept 'b' = -1
Therefore, equation of the given line will be,
[tex]y=\frac{2}{3}x-1[/tex]
Since graphed line is a dotted line so it's representing an inequality(having < or > sign)
And the shaded part is below the dotted line,
Inequality will be,
y < [tex]\frac{2}{3}x-1[/tex]
Therefore, Option (4) will be the answer.
Answer:
D
Step-by-step explanation:
Correct:)
What is the slope of the line represented by the equation y = 1/5x-3?
Answer:
1/5
Step-by-step explanation:
Your equation is written in the form y=mx+b, where m is the slope and b is the y-intercept.
m=1/5, so the slope is 1/5
Find the range of y=3/2cos4x-1
Answer:
Range = [- 2.5, 0.5] = [ - 5/2, 1/2]
Step-by-step explanation:
Smallest value of cos α = - 1,
largest value of cos α = 1.
When cos 4x = - 1, y=3/2cos4x-1 = 3/2*(-1) - 1 = - 5/2 = - 2 1/2 = - 2.5
When cos 4x = 1, y=3/2cos4x-1 = 3/2*1 - 1 = 1/2 = 0.5
Range = [- 2.5, 0.5] = [ - 5/2, 1/2]
Simplify: |2-5|-(12 ÷4-1)^2
The value of the expression when simplified is -13
How to determine the valueIt is important to note:
PEDMAS is a mathematical acronym that representing;
P for ParenthesesE for exponentsD for divisionM for multiplicationA for additionS for subtractionAlso, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.
It is denoted with the symbol '| |'
Given the expression;
|2-5|-(12 ÷4-1)^2
Solve the bracket
|-3| - (12 /3)^2
Solve further
|-3| - 4^2
Find the absolute value
3 - 4^2
Find the square
3 - 16
-13
The value is - 13
Thus, the value of the expression when simplified is -13
Learn more about PEDMAS here:
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Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
0
∑
i=1 (−3i+5)
Question:
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
30
∑ (−3i+5)
i=1
Answer:
The first three terms are : 2, -1 and -4
The last term is: -85
The sum of the sequence is: -1245
Step-by-step explanation:
Given;
==================================
30
∑ (−3i+5) -------------------(i)
i=1
==================================
Where the ith term aₙ is given by;
[tex]a_{i}[/tex] = [tex]-3i + 5[/tex] -------------------(ii)
(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;
[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2
[tex]a_2 = -3(2) + 5 = -1[/tex]
[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]
Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;
[tex]a_{30} = -3(30) + 5 = -85[/tex]
(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;
[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex] -----------------(iii)
Where;
n = number of terms in the sequence = 30
[tex]a_1[/tex] = first term = 2
[tex]a_n[/tex] = last term = -85
Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;
[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]
[tex]s_n[/tex] = 15[-83]
[tex]s_n[/tex] = -1245
WILL GIVE BRAINLIEST PLEASE HELP
Answer:
the 3 one is the correct answer
Step-by-step explanation:
Answer: RS and SU
Step-by-step explanation:
Skew lines are lines that don't have points connected and are not parrelel to each other.
The only lines that are both not parrelel and have unconnected points are the lines RS and SU
The endpoints of line segment CD are C (1, -9) and D (7, 5 ). Find the coordinates of the midpoint M.
Answer:
(4, -2)
Step-by-step explanation:
To find the midpoint of two points you have to take the average of those two points. So, I can do (1+8)/2, which is 4, to find the midpoint of the x coordinates. I can then do (-9+5)/2, which is -2 to find the midpoint of the y coordinates.