Answer:
$1137
Step-by-step explanation:
Solution:-
We will define the random variable as follows:
X: Monthly social security (OASDI) payments
The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).
The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:
X ~ Norm ( μ , σ^2 )
We will define the normal distribution for (OASDI) payments as follows:
X ~ Norm ( μ , 116^2 )
We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:
P ( X > 1214.87 ) = 0.25
We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.
Using standard normal tables, determine the Z-score value corresponding to:
P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75
z-score = 0.675
- Now use the standardizing formula as follows:
[tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]
Answer: The mean value is $1137
Question 8(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc DF. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees. 50° 90° 100° 140°
Answer: 90°
Step-by-step explanation:
As known ∡EGC=(arcEC+arcDF)/2
arcEC+arcDF=70°*2
5x+10+11x+2=140
16x+12=140
16x=128
x=128:16
x=8
So arcDF=11*x+2=11*8+2=90°
The measure of arc DF is 90°.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Given, Circle A with chords EF and CD that intersect at point G,
arc EC = 5x + 10°
arc DF = 11x + 2°
∠EGC = 70°
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite
so
∠EGC=(1/2)[arc EC+arc DF]
substitute the values
70 = 1/2(5x + 10 + 11x + 2)
70 = 1/2(16x + 12)
140 = 16x + 12
16x = 128
x = 128/16 = 8
so ac DF = 11x + 2
arc DF = 11(8) + 2
arc DF= 88 + 2 = 90°
Hence the value of arc DF is 90°.
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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!
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 :)
What is 3/4 improper or proper or mixed
Answer:
proper because the numerator is lower than the denominator
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
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
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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What are the dimensions of the rectangle? PLEASE HELP!!
Answer:
2(x^2 + 8x -55)
Step-by-step explanation:
Well to do the box method we first need to simplify the given equation further to,
[tex]2x^2 + 16x - 110\\[/tex],
For this quadratic the box method doesn't work so we can divide everything by 2 make make it
2(x^2 + 8x -55)
Thus,
[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).
Hope this helps :)
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
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.
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!⭐️
Which is hyperplane is better between B1 and B2? a. B1 is better than B2 b. B2 is better than B1 c. Both B1 and B2 are the same d. Neither B1 nor B2
Answer:
a. B1 is better than B2.
Step-by-step explanation:
Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by [tex]\frac{2}{||W||}[/tex]. The correct option is a.
Answer:
A
Step-by-step explanation:
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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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%
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 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a box with the maximum volume
Answer:
The size square removed from each corner = 32.15 cm²
Step-by-step explanation:
The volume of the box = Length * Breadth * Height
Let r be the size removed from each corner
Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]
The original length of the cardboard is 119 cm, if you remove a size of r (This typically will be the height of the box) from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:
Length, L = 119 - 2r
Similarly for the breadth, B = 24 - 2r
And the height as stated earlier, H = r
Volume, V = L*B*H
V = (119-2r)(24-2r)r
V = r(2856 - 238r - 48r + 4r²)
V = 4r³ - 286r² + 2856r
At maximum volume dV/dr = 0
dV/dr = 12r² - 572r + 2856
12r² - 572r + 2856 = 0
By solving the quadratic equation above for the value of r:
r = 5.67 or 42
r cannot be 42 because the size removed from the corner of the cardboard cannot be more than the width of the cardboard.
Note that the area of a square is r²
Therefore, the size square removed from each corner = 5.67² = 32.15 cm²
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!
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
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps
What is the missing term in this arithmetic sequence? 9, 14, 19, __, 29, 34, …
Answer: 24 because you add 5 for every number ex: 9+5=14
Answer:
24
Step-by-step explanation:
The difference can be calculated by subtracting the second term with the first term.
d = 14 - 9
d = 5
The difference is 5.
Add 5 to 19.
19 + 5 = 24
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
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.
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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
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.
by what number 7whole 2/3be divided to get 4whole1/3
Answer: 1 30/39
Step-by-step explanation:
Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.
Hope it helps <3
.If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3; however, if '
you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4. For what fraction is this true?
Answer:
The fraction that this is true for = 7/13
Step-by-step explanation:
From the above question
Let the numerator be represented by a
Let the denominator be represented by b
If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
Cross Multiply
3(a + 5) = 2(b + 5)
3a + 15 = 2b + 10
Collect like terms
3a - 2b = 10 - 15
3a - 2b = -5..........Equation 1
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
Cross Multiply
4(a - 5) = 1(b - 5)
4a - 20 = b - 5
Collect like terms
4a - b = 20 - 5
4a - b = 15..........Equation 2
b = 4a - 15
3a - 2b = -5..........Equation 1
4a - b = 15..........Equation 2
Substitute 4a - 15 for b in equation 1
3a - 2b = -5..........Equation 1
3a - 2(4a - 15) = -5
3a - 8a + 30 = -5
Collect like terms
3a - 8a = -5 - 30
-5a = -35
a = -35/-5
a = 7
Therefore, the numerator of the fraction = 7
Substitute 7 for a in Equation 2
4a - b = 15..........Equation 2
4 × 7 - b = 15
28 - b =15
28 - 15 = b
b = 13
The denominator = b is 13.
Therefore,the fraction which this is true for = 7/13
To confirm
a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
7 + 5/ 13 + 5 = 2/3
12/18 = 2/3
Divide numerator and denominator by of the left hand side by 6
12÷ 6/ 18 ÷ 6 = 2/3
2/3 =2/3
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
7 - 5/13 - 5 = 1/4
2/8 = 1/4
Divide the numerator and denominator of the left hand side by 2
2÷2/8 ÷ 2 = 1/4
1/4 = 1/4
From the above confirmation, the fraction that this is true for is 7/13
[PLEASE HELP] in the function above, the slope of it will be multiplied by 1/2 and it’s y value of its y intercept will be increased by 3 units, which of the graphs below best shows the new function???
Answer:
The graph at the bottom left in your group of possible answers.
Step-by-step explanation:
Notice that the original given graph corresponds to the equation:
[tex]y=2x+1[/tex]
since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).
So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:
[tex]y=x+4[/tex]
A line of slope 1 and y-intercept at (0, 4)
Notice that the graph at the bottom left in your possible answers is representing such function.
Answer:
Answer Y: or Bottom Left of Given Answers
Step-by-step explanation:
The ratio of oranges in a fruit salad to people it will serve is 9/40, or 9:40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
The correct answer is 180 oranges
Explanation:
In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:
[tex]\frac{9}{40} = \frac{x}{800}[/tex] - 1. Multiply 9 x 800 and 40 x x (cross multiplication)
[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40
[tex]\frac{7200}{40} = x[/tex]
[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which can be expressed as 180: 800
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.
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