Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
A random sample of 149 recent donations at a certain blood bank reveals that 76 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of appropriate hypotheses using a significance level of 0.01. Would your conclusion have been different if a significance level of 0.05 has been used?
Answer:
Yes it suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.
Well if a significance level of 0.05 is used it will not affect the conclusion
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 149[/tex]
The number that where type A blood is k = 76
The population proportion is [tex]p = 0.40[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
=> [tex]\r p = \frac{76}{149}[/tex]
=> [tex]\r p = 0.51[/tex]
The Null hypothesis is [tex]H_o : p = 0.41[/tex]
The Alternative hypothesis is [tex]H_a : p \ne 0.40[/tex]
Next we obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is
[tex]Z_{\alpha } = Z_{0.01} = 1.28[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1-p)}{n} } }[/tex]
substituting values
[tex]t = \frac{0.51 - 0.40 }{ \sqrt{ \frac{0.40 (1-0.40 )}{149} } }[/tex]
[tex]t =2.74[/tex]
So looking at the values for t and [tex]Z_{0.01}[/tex] we see that [tex]t > Z_{0.01}[/tex] so we reject the null hypothesis. Which means that there is no sufficient evidence to support the claim
Now if [tex]\alpha = 0.05[/tex] , the from the z-table the critical value for [tex]\alpha = 0.05[/tex] is [tex]Z_{0.05} = 1.645[/tex]
So comparing the value of t and [tex]Z_{0.05} = 1.645[/tex] we see that [tex]t > Z_{0.05}[/tex] hence the conclusion would not be different.
What is the slope of the line?
A. −9/5
B. 5/9
C. −5/9
D. 9/5
Answer: -9/5
Step-by-step explanation: To find the slope, we must understand that the slope of a line is defined as the ratio rise/run.
The rise is the vertical direction of the line and the
run is the horizontal direction of the line.
So to start, I am going to pick 2 points on this line.
You want to find points where the line crosses the four corners.
In the diagram, those would be the points (-4, 5) and (1, -4).
Now, we can use slope formula.
Slope = y₂ - y₁ / x₂ - x₁
So we have -4 - 5/1 - -4 which simplifies to -9/5.
So the slope is -9/5.
Answer:
the answer is -9/5 100%
Step-by-step explanation:
In a study of treatments for very painful "cluster" headaches, 140 patients were treated with oxygen and 158 other patients were given a placebo consisting of ordinary air. Among the 140 patients in the oxygen treatment group, 113 were free from headaches 15 minutes after treatment. Among the 158 patients given the placebo, 35 were free from headaches 15 minutes after treatment. Use a significance level to test the claim that the oxygen treatment is effective. A) Find test statistic z B) Find the P-value C) Construct the appropriate confidence interval D) determine if the oxygen treatment is effective
Answer:
A
[tex]t = 10.1[/tex]
B
[tex]p-value = p(t > 10.1)= 0.000[/tex]
C
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
D
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 140[/tex]
The number of patient which the oxygen cured is k = 113
The second sample size is [tex]n_2 = 158[/tex]
The number of patient that placebo cured is l = 35
The first sample proportion is
[tex]\r p_1 = \frac{ 113}{140 }[/tex]
[tex]\r p_1 = 0.8071[/tex]
The second sample proportion is
[tex]\r p_2 = \frac{ 35}{ 158 }[/tex]
[tex]\r p_2 = 0.222[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 > p_2[/tex]
Let assume the level of significance be[tex]\alpha = 0.05[/tex]
Generally the pooled proportion is mathematically evaluated as
[tex]p = \frac{p1 * n1 + p2 * n2}{n1 + n2}[/tex]
substituting values
[tex]p = \frac{0.8071 * 140 + 0.222 * 158}{140 + 158}[/tex]
[tex]p = 0.4969[/tex]
Generally the standard error is mathematically represented
[tex]SE = \sqrt{ p(1- p ) * [ \frac{1}{n_1} + \frac{1}{n_1}] }[/tex]
substituting values
[tex]SE = \sqrt{ 0.4969(1- 0.4969 ) * [ \frac{1}{140} + \frac{1}{158}] }[/tex]
[tex]SE = 0.0580[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p_1 - \r p_2}{ SE}[/tex]
[tex]t = \frac{ 0.8071 -0.222}{ 0.0580}[/tex]
[tex]t = 10.1[/tex]
The p-value is from the normal distribution table as
[tex]p-value = p(t > 10.1)= 0.000[/tex]
given that [tex]t< \alpha[/tex] the null hypothesis is rejected
From the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically the represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
[tex]E = 1.96 * 0.0580[/tex]
[tex]E = 0.1137[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2) - E < p_1 - p_2 < (\r p_1 - \r p_2) + E[/tex]
substituting value
[tex](0.8071 - 0.222) - 0.1137 < p_1 - p_2 < (0.8071 - 0.222) + 0.1137[/tex]
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
Andrea is told that the means of two groups in a study were statistically significant. She knows the means and standard deviations of the two groups and is interested in calculating an estimate of effect size. Given this information, which effect size estimate should she calculate
Answer:
Cohen's D
Step-by-step explanation:
Cohen's D is a statistic that measures effect size. It shows standardised difference between 2 means.
Effect size is defined as how large the effect of a something is or its magnitude.
Cohen's D works effectively when the sample is >50 (that is for large samples). However a correction factor can be used to make results from small samples more accurate
The formular for Cohen's D is:
D = (mean1 - mean2) ÷ (√({standard deviation1}^2 + {standard deviation 2}^2)/2)
This is the most appropriate method in the given scenario
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 20°. How far away from the building is the sculpture? Round your answer to the nearest hundredth.
Answer:
219.80 feet
Step-by-step explanation:
Tan 20= 80/b
Tan 20= 0.363970234266
(0.363970234266)b=80
b= 219.80 feet
The distance between the sculpture and the bottom of the building is required.
The distance between the building and sculpture is 219.80 feet.
Trigonometry[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]
p = Height of building = 80 feet
b = Required length
From the trigonometric ratios we have
[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]
Learn more about trigonometry:
https://brainly.com/question/23899312
Which equations has no solution?
Answer: I think it is C
Step-by-step explanation:
There is no answer because A can be many solutions, B is x = -25, you just cannot solve C, and D is y = 7/6
What value does the 2 in the number 0.826?
Answer:
.02
Step-by-step explanation:
2 is in "Hundredths' place in .826
So, the number is multiplied with 1/100 or .01
=> 2 x 1/100
=> 2/100
=> .02
=> 2 x .01
=> .02
The value of 2 in .826 is .02
A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly skill, which was described as a task requiring visual spatial skills related to mathematical competence. The 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0 Use a 0.05 significance level to test the claim that prenatal cocaine exposure is associated with lower scores of four year old children on the test of object assembly.
What are null and alternative hypothesis? What is test statistics?
Answer:
We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
Step-by-step explanation:
We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.
Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.
[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.
So, Null Hypothesis, : = 490 {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}
Alternate Hypothesis, : 490 {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3
[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2
[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3
[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3
[tex]n_1[/tex] = sample of children born to cocaine users = 190
[tex]n_2[/tex] = sample of children not exposed to cocaine = 186
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3
So, the test statistics = ~
= -2.908
The value of t-test statistics is -2.908.
Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.
Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:
Null and alternative hypothesis:Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by
[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]
Null hypothesis:
[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]
Test statistic:
[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]
Alternative Hypothesis:
[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]
Rejection Criterion
[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]
Given value:
[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]
here
[tex]\to t_0 < -t_{0.05,374}[/tex]
hence rejecting the [tex]H_0[/tex]
Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.
Find out more about the alternative hypothesis here:
brainly.com/question/18831983
A random variable is not normally distributed, but it is mound shaped. It has a mean of 14 and a standard deviation of 3. If you take a sample of size 10, can you say what the shape of the sampling distribution for the sample mean is
Answer:
Step-by-step explanation:
from the question,
the mean 14
the standard deviation is 3
and sample size is 10.
since the n which is the sample size is 10, then the distribution is mound shaped.
why?
this is due to the fact that the random variable from which we took the sample is mound shaped.
The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.
the standard deviation of the mean is
3/√10
= 0.948
first second and last term of Ap are a,b,2a respectively, find its sum
Answer:
(3ab)/(2(b-a))
Step-by-step explanation:
The n-th term of an arithmetic progression is ...
an = a1 +d(n -1)
Then the value of n is ...
n = (an -a1)/d +1
The sum of an arithmetic progression is the product of the number of terms and the average of the first and last terms. In this sequence, the common difference d is ...
d = (b -a)
So, the sum is ...
Sn = (a +2a)/2·((2a -a)/(b -a) +1)
Sn = (3ab)/(2(b-a)) . . . . sum of the arithmetic progression
__
Example:
The sequence 1, 1.5, 2 has ...
a = 1, b = 1.5
Its sum is given by the above formula as ...
Sn = 3(1)(1.5)/(2(1.5 -1)) = 4.5/(2(.5)) = 4.5 = 1 + 1.5 + 2 . . . . yes
What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24
Answer:
D question,somewhat confusing, itsit's like simultaneous equation,but values are different
Answer:
x = 4 + 2y/3
Step-by-step explanation:
Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
Answer:
rose. is. 18/2=9 years old
Answer:
Stephanie is 18years old and she is twice older than her sister
so rosa is 18÷2(since stephanie is twice older than rosa
so rosa is 9 years old
The base of a right rectangular prism has an area of 173.6 square centimeters and a height of 9 centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?
Answer:
D) 1562.4 cubic centimeters
Step-by-step explanation:
volume = area of the base × height
volume = 173.6cm² × 9 cm
volume = 1562.4 cm³
I need help please, m bda =
And m bca =
Step-by-step explanation:
Exterior angle BOA = 250°
Interior angle BOA = 360°- 250° = 110°
Now,
(A) BDA = interior angle BOA / 2 = 55°( Property of circles)
(B) From the figure, we observe that AOBC is a cyclic quadrilateral (i.e. sum of opposite angles is 180°).
Therefore, BCA + BOA = 180°
BCA = 180° - 110° = 70°
Determine the value of x in the figure. Question 1 options: A) x = 90 B) x = 85 C) x = 45 D) x = 135
Answer:
A.) x=90°
Step-by-step explanation:
Note:
The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.
We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:
[tex]180=135+y[/tex]
y is the unknown angle. Solve for y:
[tex]180-135=y\\\\y=45[/tex]
y is 45°. Since this and the other angle are congruent, add:
[tex]45+45=90[/tex]
Note:
Triangles angles will always add up to a total of 180°.
To find the missing angle x°, use:
[tex]180=a+b+c[/tex]
These are the angles in a triangle. Substitute any known values and solve:
[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]
The missing angle x° is 90°.
:Done
What is the perimeter of the image attached?? (PLEASE HELP I WILL MARK BRAINLIEST)
Answer:
[tex] Perimeter = 3x + 3 [/tex]
Step-by-step explanation:
Perimeter of the given triangle in the figure is the sum of all three sides.
The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].
Therefore,
[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]
Simplify,
[tex] Perimeter = x + x - 3 + x + 6 [/tex]
Collect like terms
[tex] Perimeter = x + x + x - 3 + 6 [/tex]
[tex] Perimeter = 3x + 3 [/tex]
An Internet service provider is implementing a new program based on the number of connected devices in each household currently,customers are charged a flat rate of $175 per month.the new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network.find the number of devices,x,for which the cost of the new plan is less than the cost of the current plan.
Answer:
(x=6) is less than 18 which would give you the cost of the current plan
Step-by-step explanation:
If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.
quanto e 45x12 (500-450-550)
Answer:
see below
Step-by-step explanation:
the simple answer is -270000
PLEASE HELP ME I DONT HAVE THAT MANY POINTS AND ITS DUE TODAY I NEED HELP ASAP
The table contains the data for your first weeks sales. Complete the table by calculating your commission and earnings for each day of the week
Answer with explanation:
Sales Commission(10% of sales)
$2,200 0.1×$2,200= $220
$2,000 0.1× $2,000= $200
$3,134 0.1×$3,134=$313.4
$2,417 0.1×$2,417=$241.7
$2,579 0.1×$2,579 =$257.9
The completed table is given as follows
Day Sales Commission Non-Sales pay Earning
(10% of sales) (Commission +Non Sales pay)
Mon $2,200 $220 $9.50 $220+ $9.50=$229.50
Tue $2,000 $200 $9.50 $200 +$9.50=$209.50
Thurs $3,134 $313.4 $9.50 $313.4+ $9.50=$322.9
Fri $2,417 $241.7 $9.50 $241.7+$9.50= $251.2
Sat $2,579 $257.9 $9.50 $257.9+$9.50=$267.4
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!
Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score? % (b) What percentage were above?
Answer:
Step-by-step explanation:
From the given information;
Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting.
What percentage of the scores were at or below her score?
The percentage of scores that were at or below her score is
Percentage P = 90%
This benchmark is more than average, so we can typically say more of the scores were at or below her score
What percentage were above?
Since The percentage of scores that were at or below her score is
Percentage P = 90%
Then the percentage of the scores that were above will be : (100 -90)%
= 10 %
We can see here that less percentage of score were above Angela's Score.
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
When traveling with the wind, it takes an airplane 3 hours to travel 1800 miles. It takes the same airplane 3.6 hours to travel the same 1800 miles when traveling against the wind. Assuming the airplane travels at a constant speed during both trips, what is the speed of the airplane and the speed of the wind?
Answer:
The speed of the airplane in still air is 550 mph.
The speed of the wind is 50 mph.
Step-by-step explanation:
speed = distance / time
distance = speed * time
or simply
d = st
Let v be the speed of the airplane with no wind.
Let w = speed of wind
With the wind:
d = 1800; s = v + w; t = 3
1800 = 3(v + w)
Against the wind:
d = 1800; s = v - w; t = 3.6
1800 = 3.6(v - w)
We have a system of two equations:
3(v + w) = 1800
3.6(v - w) = 1800
Divide both sides of the first equation by 3. Divide both sides of the second equation by 3.6.
v + w = 600
v - w = 500
Add the equations.
2v = 1100
v = 550
The speed of the airplane in still air is 550 mph.
v + w = 600
550 + w = 600
w = 50
The speed of the wind is 50 mph.
Please help me solve for the median !!!
Answer:
50.93
Step-by-step explanation:
Add up the frequencies:
2 + 5 + 14 + 15 + 21 + 18 + 15 + 9 + 2 = 101
Divide by 2: 101/2 = 50.5
So the median is the 51st number, with 50 below and 50 above.
Add up the frequencies until you find the interval that contains the 51st number.
2 + 5 + 14 + 15 = 36
2 + 5 + 14 + 15 + 21 = 57
So the median is in the group 49.5 − 51.5. To estimate the median, we use interpolation. Find the slope of the line from (36, 49.5) to (57, 51.5).
m = (51.5 − 49.5) / (57 − 36)
m = 2/21
So at x = 51:
2/21 = (y − 49.5) / (51 − 36)
y = 50.93
Combine like terms to create an equivalent expression. 1/7 - 3 (3/7n - 2/7)
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▹ Answer
1 - 9/7n
▹ Step-by-Step Explanation
1/7 - 3(3/7n - 2/7)
Remove the parentheses (Distribute -3 among the parentheses):
1/7 - 9/7n + 6/7
Calculate:
1 - 9/7n
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1-9/7n
Step-by-step explanation:
[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]
What is f(0) given f(x) = 5(x + 2)2 – 10?
Answer:
10
Step-by-step explanation:
f(o) is given when x= 0 in f(x)
f(0) = 5 ( 0 + 2 ) 2 - 10
= 20 - 10
= 10
Answer:
[tex] \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}[/tex]
Step-by-step explanation:
Given, f ( x ) = 5 ( x + 2 )² - 10
Let's find f ( 0 ) :
[tex] \sf{f(0) = 5( {0 + 2)}^{2} - 10}[/tex]
Add the numbers
⇒[tex] \sf{f(0) = 5( {2)}^{2} - 10}[/tex]
Evaluate the power
⇒[tex] \sf{f(0) = 5 \times 4 - 10}[/tex]
Multiply the numbers
⇒[tex] \sf{ 20 - 10}[/tex]
Subtract 10 from 20
⇒[tex] \sf{10}[/tex]
Hope I helped !
Best regards !!
Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-floor manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, two independent, random, representative samples of planks were examined. One sample contained 200 planks which were sawed using the old method. The other sample contained 400 planks which were sawed using the new method. Sixty-two of the 200 planks were scrapped under the old method of sawing, whereas 36 of the 400 planks were scrapped under the new method.
Required:
a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively.
b. Write the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.
c. Using the part a results, can we conclude at the 10% significance level that the scrap rate of the new method is different than the old method?
Answer:
The critical value for two tailed test at alpha=0.1 is ± 1.645
The calculated z= 9.406
Step-by-step explanation:
Formulate the hypotheses as
H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods
Ha : p1≠ p2
Choose the significance level ∝= 0.1
The critical value for two tailed test at alpha=0.1 is ± 1.645
The test statistic is
Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]
p1= scrap rate of old method = 62/200=0.31
p2= scrap rate of new method = 36/400= 0.09
p = an estimate of the common scrap rate on the assumption that the two rates are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.31) + 400 (0.09) / 600
p= 62+ 36/600= 98/600 =0.1633
now q = 1-p= 1- 0.1633= 0.8367
Thus
z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)
z= 0.301/√ 0.13663( 3/400)
z= 0.301/0.0320
z= 9.406
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.
The Rogers family drove 220 miles in 5.5 hours. How many miles would they drive at this same rate in 4 hours? A. 88 mi B. 147 mi C. 160 mi D. 179 mi Please show ALL work! <3
Answer:
160 miles
Step-by-step explanation:
We can use a ratio to solve
220 miles x miles
--------------- = ----------------------
5.5 hours 4 hours
Using cross products
220 *4 = 5.5x
880 = 5.5x
Divide each side by 5.5
880/5.5 = x
160 miles
Answer:
[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]
Step-by-step explanation:
We can solve this problem by ratios.
Let x be the missing value.
[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]
Cross multiply.
[tex]5.5 \times x = 220 \times 4[/tex]
[tex]5.5x=880[/tex]
Divide both sides by 5.5.
[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]
[tex]x=160[/tex]
qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
32.8 miles
Step-by-step explanation:
Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?
Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :
y = -0.95x + c
Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:
48 = -0.95(31) + c
c = 48 + 0.95(31)
c = 48 + 29.45
c = 77.45
The equation of the line is
y = -0.95x + 77.45
After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.
y = -0.95(47) + 77.45
y = -44.65 + 77.45
y = 32.8 miles
The points (0,3) and (1,12) are solutions of an exponential function. What is the equation of the exponential function?
Answer:
[tex]f(x) =3\,*\,\,4^x[/tex]
Step-by-step explanation:
to find the equation of an exponential function, just points on the function's graph are needed.
Recall that the exponential function has a general expression given by:
[tex]f(x) = a \,e^{b\,x}[/tex]
so we impose the condition for the function going through the first point (0,3) as:
[tex]f(0) = a \,e^{b\,(0)}= 3\\a\,e^0=3\\a\,(1)=3\\a = 3[/tex]
Now,knowing the parameter a, we can find the parameter b using the other point:
[tex]f(1) = 3 \,e^{b\,x}= 12\\3\,e^{b\,(1)}=12\\e^b=12/3\\e^b=4\\b=ln(4)[/tex]
Therefore, the function can be written as:
[tex]f(x) = 3 \,e^{ln(4)\,x}=3\,\,\,4^x[/tex]
Answer:
C)
h(x) = 3(4)x
