Answer:
[tex]a^9 + b^ 5 + c^{13}[/tex]
Step-by-step explanation:
[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]
When bases are same and it is multiplication, then add the exponents.
[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]
[tex](a^9)+(b^ 5) + (c^{13})[/tex]
Apply rule : [tex](a^b)=a^b[/tex]
[tex]a^9 + b^ 5 + c^{13}[/tex]
Answer:
[tex]a^9+b^5-c^{13[/tex]
Step-by-step explanation:
[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]
When bases are same, powers are to be added.
=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]
=> [tex]a^9+b^5-c^{13[/tex]
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the amount of electrical energy that is put into the bulb. An illustration of a wide arrow with a light bulb at the tail of it labeled electrical energy 100 J, breaks into a small arrow going forward labeled light 10 J and a larger curling away labeled heat 90 J. The goal of the bulb is to produce light. What is the efficiency of this bulb as it works to put out light? 10% 80% 90% 100%
Answer:
10%
Step-by-step explanation:
Using the given formula with the given data, we have ...
efficiency = output work / input work
= (10 J)/(100 J) = 0.10 = 10%
Answer:
A) 10%
Step-by-step explanation:
10/100=10
If the 2nd and 5th terms of a
G.P are 6 and 48 respectively,
find the sum of the first four
terms
Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
Answer:
11.2≤[tex]\mu[/tex]12.8Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)
A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".
StatisticsAccording to the question,
Sample mean, [tex]\bar x[/tex] = 12.5
Z score at 99%, Z = 2.576
Standard deviation, S = √Variance
= √2.4
= 1.5492
Sample size, n = 25
We know the formula,
Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])
By substituting the given values, we get
= 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])
= 12.5 [tex]\pm[/tex] 2.576 (0.30984)
= 12.5 [tex]\pm[/tex] 0.7981
Now,
Cl = (12.5 - 0.7981, 12.5 + 0.7981)
= (11.2019, 12.7981) or,
= (11.2, 12.8)
Thus the above answer is appropriate.
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determining the probability of events. please help :)
Answer:
C. 1/8
Step-by-step explanation:
Probability of shooting a goal on a throw is 2/4 = 1/2.
Probability of 3 in a row is (1/2)³ = 1/8.
6th grade math, help me pleasee:)
Answer:
8 pounds
Step-by-step explanation:
2 x 3 = 6 tb of chili powder in pot 2
find pounds per tablespoon: 48 / 6 = 8 pounds
Answer:
1/2 pound per tablespoon
Step-by-step explanation:
Jaden sure does like his chili!
In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
Answer:
x>3
Step-by-step explanation:
Six human skulls from around 4000 b.c. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9
mm. If you want to construct a 95% confidence interval estimate of the mean length of all such skulls, assume that the requirements
are satisfied. Find the critical values that would be used to construct a 95% confidence interval estimate of o
Answer:
Step-by-step explanation:
Hello!
You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.
You know that
n= 6 human skulls
[tex]\frac{}{X}[/tex]= 94.2mm
S= 4.9
Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:
[[tex]\frac{}{X}[/tex] ± [tex]t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }[/tex]]
[tex]t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571[/tex]
[94.2 ± 2.571 * [tex]\frac{4.9}{\sqrt{6} }[/tex]]
[89.06; 99.34]mm
With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.
I hope this helps!
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. _______________
b. Determine the installment price.b. _________________
c. Determine the finance charge.c. _________________
Answer:
see details below
Step-by-step explanation:
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. ___$23450____________
29450 - 6000 = 23450
b. Determine the installment price.b. ___$792,22______________
"monthly payment of $792.22"
c. Determine the finance charge.c. __$5069.92_______________
A = 792.22
n = 36
finance charge = total paid - amount to be financed
= 36*792.22 - 23450
= 5069.92
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability [tex]\hat p = \dfrac{320}{400}[/tex]
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]
where;
[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960
SO;
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]
[tex]=0.8 \pm 1.960 \times 0.02}[/tex]
[tex]=0.8 \pm 0.0392[/tex]
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
omplete)
HWS
X 3.3.13-BE
The manufacturer's suggested retail price (MSRP) for a particular car is $25,495, and it is expected to be worth $20,081 in 2 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 4 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
f(x) =
(Simplify your answer. Do not include the $ symbol in your answer.)
Answer:
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Step-by-step explanation:
Value now: $25,495
Value in 2 years: $20,081
Loss of value in 2 years: $25,495 - $20,081 = $5,414
Loss of value per year: $5,414/2 = $2,707
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. What is the margin of error associated with the confidence interval
Answer:
Margin of Error = ME =± 5.2592
Step-by-step explanation:
In the given question n= 20 < 30
Then according to the central limit theorem z test will be applied in which the standard error will be σ/√n.
Sample Mean = μ = 64
Standard Deviation= S= σ = 12
Confidence Interval = 95 %
α= 0.05
Critical Value for two tailed test for ∝= 0.05 = ±1.96
Margin of Error = ME = Standard Error *Critical Value
ME = 12/√20( ±1.96)=
ME = 2.6833*( ±1.96)= ± 5.2592
The standard error for this test is σ/√n
=12/√20
=2.6833
M angle D=? What is the degree of the angle?
Answer:
80°Step-by-step explanation:
In ACB and ECD
AC =~ CE [ Given ]
BC =~ CD [ Given ]
<ACD =~ <ECD [ Vertical angles ]
Hence, ∆ ACB =~ ECD by SAS congruency of triangles.
Then, <B = <D
In ∆ABC , sum of all three angles must be 180°
<A + <B + <C = 180°
plug the values
[tex] 30 + < d \: + 70 = 180[/tex]
Add the numbers
[tex]100 + < d = 180[/tex]
Move constant to R.H.S and change it's sign
[tex] < d = 180 - 110[/tex]
Subtract the numbers
[tex] < d = 80[/tex] °
Hope this helps..
Best regards!!
A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
what is 1.8÷0.004? using long division
Answer:
Hi! Answer will be below.
Step-by-step explanation:
The answer is 450.
If you divide 1.8 and 0.004 the answer you should get is 450.
Below I attached a picture of how to do long division...the picture is an example.
Hope this helps!:)
⭐️Have a wonderful day!⭐️
Probability of landing on even # on a spinner; probability of rolling an odd # on a die
Answer:
Spinner: 50%
Die: 50%
Step-by-step explanation:
Well for the spinner it depends on the amount of numbers it has,
in this case we’ll use 6.
So The probability of landing on the even numbers in a 6 numbered spinner.
2, 4, 6
3/6
50%
Your average die has 6 sides so the odd numbers are,
1, 3, 5
3/6
50%
Louden County Wildlife Conservancy counts butterflies each year. Data over the last three years regarding four types
of butterflies are shown below. What is the average number of Variegated Fritillaries for all three samples?
A. 55 B.83 C.106 D.165
Answer:
A). 55
Step-by-step explanation:
Number of Variegated Fritillaries for each year is
2009 = 7
2010= 95
2011= 63
The sum total of the samples= 7+95+63
The sum total of the samples= 165
Number of years= 3
The average= total/number of years
The average= 165/3
The average= 55
Answer: A
Step-by-step explanation: I have a massive brain (•-*•)
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
A sample size of 2080 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that [tex]\pi = 0.6[/tex]
How large of a sample size is required?
We need a sample of n.
n is found when [tex]M = 0.025[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]
[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]
[tex]n = 2079.3[/tex]
Rounding up
A sample size of 2080 is needed.
The product of 6 and a number (n) is 48 . Which equation shows this relationship? ANSWER CHOICES: 6n=48 n+6=48 48n=6 n-6=48
Answer:
6n=48
Step-by-step explanation:
product means multiplication
6×n=48
6n=48
An equation that shows this relationship is: A. 6n = 48.
How to determine the equation representing the product?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;
6 × n = 48
6n = 48
n = 48/6
n = 8.
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Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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A necklace was on sale for 20% discount off the original price of
$1250.00. What was the final sale price if 12.5% VAT has to be
paid?
Answer:
= $ [tex] \mathsf{1125}[/tex]Step-by-step explanation:
[tex] \mathrm{Given}[/tex],
[tex] \mathrm{Discount\% = 20\%}[/tex]
[tex] \mathrm{Marked \: price = 1250}[/tex]
[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]
[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]
[tex] \mathrm { = 20\% \: of \: 1250}[/tex]
[tex] \mathrm{ = 250}[/tex]
[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]
[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]
[tex] \mathrm{ = 1250 - 250}[/tex]
= $ [tex] \mathrm{1000}[/tex]
[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]
[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]
[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]
= $ [tex] \mathrm{ 125}[/tex]
[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]
[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]
[tex] \mathrm{ = 1000 + 125}[/tex]
= $ [tex] \mathrm{1125}[/tex]
Therefore, The final sale of the necklace is $ 1125
Hope I helped
Best regards!
3.01)Which statement best describes the area of the triangle shown below?
9
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
O It is one-half the area of a square of side length 4 units.
Ont is twice the area of a square of side length 4 units.
Answer:
C. It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
Hey there!
Well if a square has side lengths of 4 units,
the area would be 16 because of l*w.
Now the formula for the area of a triangle is,
b*h/2
b = 4
h = 4
4*4=16
16 ÷ 2 = 8
So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,
meaning the area of a triangle is one-half the area of a square.
Hope this helps :)
From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).
a. The normal distribution can be used.
b. The t distribution with 6 degrees of freedom must be used.
c. The sample size must be increased.
d. The t distribution with 5 degrees of freedom must be used.
Answer:
d) The t-distribution with 5 degrees of freedom must be used
Step-by-step explanation:
For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.
The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.
Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger), we can assume that the curve of t-student is the same as for normal distribution
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
Which of the following points is a solution of y > Ixl + 5?
A. (0, 5)
B. (1, 7)
C. (7, 1)
Answer:
B. (1,7)
Step-by-step explanation:
We can substitute the x and y values of each coordinate into the inequality and test if they work.
Let's start with A, 5 being y and 0 being x .
[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]
5 IS NOT greater than 5, they are the exact same, so A is out.
Let's try B, 1 being x and 7 being y.
[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]
7 IS greater than 6, so B. (1,7) does work for this inequality!
Let's do C for fun, when 7 is x and 1 is y.
[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]
1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.
Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].
Hope this helped!
Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The set where p1(t) = t, p2(t) = t2, p3(t) = 2t + 3t2 C: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t + t2
Answer:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
[tex]\alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]
[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]
Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:
[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{1} = -2\cdot k[/tex]
[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{2} = -3\cdot k[/tex]
It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} + \alpha_{3} = 0[/tex]
[tex]3\cdot \alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
Does anyone know the answers to these?
Step-by-step explanation:
a. The point estimate is the mean, 47 days.
b. The margin of error is the critical value times the standard error.
At 31 degrees of freedom and 98% confidence, t = 2.453.
The margin of error is therefore:
MoE = 2.453 × 10.2 / √32
MoE = 4.42
c. The confidence interval is:
CI = 47 ± 4.42
CI = (42.58, 51.42)
d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.
e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.
Arrange the cards below to show the solution to 40.091 x 10³
Answer:
40091.
Step-by-step explanation:
Multiply 40.091 by 10 three times to get the answer.
40.091 * 10 = 400.91
400.91 * 10 = 4009.1
4009.1 * 10 = 40091.
The expression 40.091 x 10³ can be represented as 40091.
What are exponents?The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.
How to solve the given question?In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.
Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.
Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.
∴ The expression 40.091 x 10³ can be represented as 40091.
Learn more about exponents at
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