Answer:
AB: size 4 x 4
BA: size 2 x 2
Step-by-step explanation:
When we want to multiply two matrices, we need first to check if the number of columns of the first matrix is equal the number of rows of the second matrix. Then, the resulting matrix would have the number of rows equal the number of rows of the first matrix, and the number of columns equal the number of columns of the second matrix.
That is, if we have a matrix A with dimensions a x b and a matrix B with dimensions c x d, to calculate the product AB we must have b = c, and the resulting product would have dimensions a x d.
Finally, if A is 4 x 2 and B is 2 x 4, we would have:
AB = (4 x 2) (2 x 4)
2 = 2 -> product is possible.
Dimensions of the result: 4 x 4
BA = (2 x 4) (4 x 2)
4 = 4 -> product is possible.
Dimensions of the result: 2 x 2
The size of a matrix is its dimension,
The size of AB and BA are 4 x 4 and 2 x 2, respectively
The dimension of matrix A is given as 4 x 2, while the dimension of matrix B is 2 x 4
Product AB
The dimension of matrix AB is the row of matrix A by the column of matrix B.
Matrix A has 4 rows, while matrix B has 4 columns.
So, the dimension of matrix AB is 4 x 4
Product BA
The dimension of matrix BA is the row of matrix B by the column of matrix A.
Matrix B has 2 rows, while matrix A has 2 columns.
So, the dimension of matrix BA is 2 x 2
Hence, the size of AB and BA are 4 x 4 and 2 x 2, respectively
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Are 4x and 15 + x equivalent expressions? Explain your reasoning.
If we transform the parabola y = (x + 1)2 + 2 by shifting 7 units to the right and 5 units down, what is the vertex of the resulting parabola? ( a0, a1)
Answer:
(6,-3)
Step-by-step explanation:
Need Help With This
Answer:
Area: 28 square ft
Perimeter: 22 ft
Step-by-step explanation:
To find the area:
A=Lw
A is area, L is length, w is width
A=4*7
A=28
The area is 28 square feet
To find the perimeter:
P=2L+2w
P=2(7)+2(4)
P=14+8
P=22
The perimeter is 22 feet.
Hope this helps!
Solve Two-thirds x minus one-fifth greater-than 1. x >
Answer:
x > 9/5Step-by-step explanation:
The above statement is written as
[tex] \frac{2}{3} x - \frac{1}{5} > 1[/tex]
Multiply through by the LCM of 3 and 5 which is 15
So we have
[tex]15 \times \frac{2}{3} x - 15 \times \frac{1}{5} > 15 \\ \\ 10x - 3 > 15 \\ \\ 10x > 15 + 3 \\ \\ 10x > 18 \\ \\ x > \frac{18}{10} \\ \\ x > \frac{9}{5} [/tex]
Hope this helps you
Answer: The answer is x > 9/5.
Hope this helps!! Also please put as brainlist answer really need it would really aprecite it please.
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a particular tire of this brand will last longer than 57,100 miles
Answer:
84.13% probability a particular tire of this brand will last longer than 57,100 miles
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 60000, \sigma = 2900[/tex]
What is the probability a particular tire of this brand will last longer than 57,100 miles
This is 1 subtracted by the pvalue of Z when X = 57100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57100 - 60000}{2900}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
1 - 0.1587 = 0.8413
84.13% probability a particular tire of this brand will last longer than 57,100 miles
For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 8:25 AM and 3:30 PM on both days? a) O 0.2951 b) 0.9137 c) 0.0871 d) 0.2938 e) 0.0863 f) None of the above.
Answer:
c) 0.0871
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d is given by the following formula.
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
On a single day:
24 hours, so [tex]a = 0, b = 24[/tex]
8:25 P.M. is 8:25 = 8.4167h
3:30 P. M. is the equivalent to 12 + 3:30 = 15:30 = 15.5h
Probability of rain between these times:
[tex]P(8.4167 \leq X \leq 15.5) = \frac{15.5 - 8.4167}{24 - 0} = 0.2951[/tex]
On both days:
Two days, each with a 0.2951 probability
0.2951*0.2951 = 0.0871
The correct answer is:
c) 0.0871
cube root of 99 is 4.626 find the cube root of 792
Answer:
the answer is: 9.25
Step-by-step explanation:
the cube root of 792 is approximately 9.252.
To find the cube root of 792, we can use the relationship between cube roots and cube numbers.
If the cube root of 99 is approximately 4.626, we can use this information to find the cube root of 792.
Let's calculate the cube root of 792 using the relationship:
(cube root of 792) = (cube root of 99) * (cube root of 8)
Since 792 is equal to 99 multiplied by 8 (792 = 99 * 8), we can rewrite the equation as:
(cube root of 792) = (4.626) * (cube root of 8)
Now, we need to find the cube root of 8:
(cube root of 8) = 2
Substituting this value back into the equation, we get:
(cube root of 792) = (4.626) * (2) = 9.252
Therefore, the cube root of 792 is approximately 9.252.
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Which is an expression in square units that represents the area of the shaded segment of C. Geometry
Answer:
[tex] \frac{1}{2} {r}^{2} ( \frac{1}{2}\pi - 1)[/tex]
option D is the right option.
solution,
Area of shaded region:
Area of sector-Area of ∆
[tex] = \frac{90}{360} \times \pi {r}^{2} - \frac{1}{2} \times r \times r \\ = \frac{1}{4} \pi {r}^{2} - \frac{1}{2} {r}^{2} \\ = \frac{1}{2} {r}^{2} ( \frac{1}{2} \pi - 1)[/tex]
Hope this helps...
Good luck on your assignment..
The expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]
Calculation of the expression:Since we know that
The area of the shaded region = Area of the sector - an area of a triangle
So,
[tex]= \frac{90}{360} \times \pi r^2 - \frac{1}{2} \times r\times r\\\\ = \frac{1}{4}\pi r^2 - \frac{1}{2}r^2 \\\\= \frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]
hence, The expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]
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True or False?
2+3x=5
If x is 1.1?
Answer:
False
Step-by-step explanation:
2 + 3x = 5
Put x as 1.1.
2 + 3(1.1) = 5
2 + 3.3 = 5
5.3 = 5
False.
Answer:
FalseSolution,
X=1.1
[tex]2 + 3x = 5 \\ 2 + 3 \times 1.1 = 5 \\ 2 + 3.3 = 5 \\ 5.3 = 5 \: \: \\ hence \: it \: is \: false[/tex]
can you answer with explanation how its answer is 0.63?? Aja's favorite cereal is running a promotion that says 1-in-4 boxes of the cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this cereal, and let X represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes. What is the probability that she wins at most 1 prize in the 5 boxes
Let n = total boxes (5)
Probability (p) = 1 out of 4 = 1/4 = 0.25
Probability she wins at most 1 out of 5 is p(x <=1) Which is also = p (x =0) + p(x=1)
Probability of not winning would be 0.75 ( 1-0.25)
No prizes in 5 boxes = 0.75^5
1 prize in 5 boxes = 5 x 0.25 x 0.75^4
Total probability = 0.75^5 + 5 x 0.25 x 0.75^4 = 0.63
Answer: 0.63
Step-by-step explanation:
Fill in the green box.
Answer:
y=6solution,
Similar Right triangles:
[tex] \frac{c}{h} = \frac{h}{d} \\ {h}^{2} = cd \\ {y}^{2} = 4 \times 9 \\ {y = 36 }^{2} \\ y = \sqrt{ {(6)}^{2} } \\ y = 6[/tex]
Hope this helps..
Good luck on your assignment..
Answer:whats the measure of x i really need help
Step-by-step explanation:
Mandy and Priscilla shared a packet of stickers.At first, the number of stickers Mandy had was 1/4 of the number of stickers Priscilla had. When the girls bought another 28 stickers each, the number of stickers Priscilla had was 1/5 more than the number of stickers Mandy had. How many stickers were there in the packet? Solve if you can, using ALGEBRA ONLY, pls.
Answer:
10 stickers.
Step-by-step explanation:
Let's say that Mandy has m stickers, and Priscilla has p stickers.
m = 1/4p
6/5(m + 28) = p + 28
6/5(1/4p + 28) = p + 28
1/4p + 28 = 5/6p + 23 and 1/3
5/6p - 1/4p = 28 - 23 and 1/3
10/12p - 3/12p = 84/3 - 70/3
7/12p = 14/3
p = (14/3)(12/7)
p = 8
At the beginning, Priscilla had 8 stickers. That means that Mandy had 1/4 * 8 = 8 / 4 = 2 stickers.
So, in the packet, there were 8 + 2 = 10 stickers.
Hope this helps!
In how many ways can the letters of the word POLICEMAN be arranged if the 'word' must begin with L and end with a vowel? & What is the probability the 'word will begin with L and end with a vowel?
Answer:
20160 ways
Probability = 0.0556
Step-by-step explanation:
We have 9 different letters, so the total number of words we can make is:
[tex]Total = 9! = 362880\ words[/tex]
If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:
[tex]N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words[/tex]
The probability is calculated by the division of the number of words we want over the total number of words:
[tex]P = N / Total = 20160 / 362880 = 0.0556[/tex]
An insurance company reported that, on average, claims for a certain medical procedure are $942. An independent organization constructed a 95% confidence interval of ($930 , $950) for the average amount claimed for the particular medical procedure. What conclusion best evaluates the truthfulness of the number reported by the insurance company?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
An insurance company reported that, on average claims for a certain medical procedure are $942. an independent organization constructed a 95% confidence interval of ($930, $950) for the average amount claimed for the particular medical procedure. what conclusion best evaluates the truthfulness of the number reported by the insurance company?
a) with 95% certainty, the average claim for this medical procedure is $942.
b) with 95% certainty, the average claim for this medical procedure is not $942.
c) the confidence interval is consistent with an average claim of $942 for this medical procedure
Solution:
Confidence interval is used to express how confident we are that the population parameter that we are looking for is contained in a range of given values. Looking at the given confident interval, the lower limit is $930 and the upper limit is $950. We can see that the population mean, $942 lies within these values. The correct option would be
c) the confidence interval is consistent with an average claim of $942 for this medical procedure
Using rigid motion, which statement is true
about the triangles?
Answer:
The triangles are not congruent
Step-by-step explanation:
Triangle ABC is congruent to triangle DEF
Triangle ABC is congruent to triangle FED
Two trianges ABC and DEF are given on a coordinate plane
In the diagram circle o, what is the measure of angle abc
Answer:
34°
Step-by-step explanation:
Because AB and CB are tangents, the measure of angle B is the supplement of the measure of arc AC:
180° -146° = 34°
Find the missing side of the triangle.
11 yd
10 yd
Answer:
Step-by-step explanation:
a^2+b^2=c^2
assuming that 11 and 10 are the shorter sides of the triangle
11^2+10^2=c^2
121+100=c^2
221=c^2
[tex]\sqrt{221}=\sqrt{c^2}[/tex]
this will equal 14.87 approximately
The missing side of the triangle is √221 yd .
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Let recall the Pythagorean theorem formula:
a² + b² = c²
Replacing by the values we have;
11² + 10² = c²
c² = 121 + 100
c² = 221
c = √221 yd
Therefore, the correct answer is √221 yd .
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Which of the following are the four primary principles of experimental design? Check all that apply.
A. Blindness
B. Control
C. Replication
D. Blocking
E. Randomization
If a population proportion is believed to be 0.60, how many items must be sampled to ensure that the sampling distribution of the sample proportion will be approximately normal
Answer:
[tex]n \geq 42[/tex]
Step-by-step explanation:
Data provided
P = 0.6
The calculation of sample size is shown below:-
Here the sampling distribution of proportion will be approximately normal, then follow the rule which is here below:-
[tex]np\geq 10\ and\ np (1 - p)\geq 10[/tex]
Now we will consider condition 2
[tex]np(1 - p)\geq \ 10[/tex]
[tex]n(0.6) (1 - 0.6) \geq \ 10[/tex]
[tex]n(0.6) (0.4) \geq\ 10[/tex]
[tex]n\geq \frac{10}{0.24}[/tex]
[tex]n \geq 41.66667[/tex]
or
[tex]n \geq 42[/tex]
Therefore for computing the required sample size we simply solve the above equation.
Susan can pick 4 pounds of coffee beans in an hour or gather 2 pounds of nuts. Tom can pick 2 pounds of coffee beans in an hour or gather 4 pounds of nuts. Each works 6 hours per day. a. Together, what is the maximum number of pounds of coffee beans the two can pick in a day
Answer:
144
Step-by-step explanation:
Susan can pick 4 pounds of coffee beans in an hour. Tom can pick 2 pounds of coffee beans in an hour. Together, they can pick 6 pounds of coffee an hour.
4 + 2 = 6
There are 24 hours in a day. Multiply the time by the amount that can be picked to find the answer.
24 × 6 = 144
Together, the maximum number of pounds of coffee beans the can pick in a day is 144 pounds.
Together they can pick a maximum of 36 pounds of coffee
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
given:
Susan can pick 4 pounds of coffee or 2 pounds of nuts.
Tom can pick 2 pounds of coffee or 4 pounds of nuts.
So, In 6 hours
Susan will pick
= 4 * 6
= 24 pounds of coffee.
In 6 hours,
Tom will pick
=2 * 6
= 12 pounds of coffee.
Hence, together they can pick a maximum of 36 pounds of coffee
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Simplify. (-2)^-3 please help
Answer:
Exact Form:
- 1 /8
Decimal Form:
-0.125
Answer:
- 1/8
Step-by-step explanation:
- 2⁻³ =
= - 1/2³
= - 1/8
Which ordered pair can be removed so that the resulting graph represents a function (-2, 2) (1, 3) (5, -4) (-4, -4)
Answer:
D: (-4,-4)
Step-by-step explanation:
x and y cant be the same
Answer:
b. (1,3)
Step-by-step explanation:
Take the risk!
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that m
Answer:
M = 90 for a sample of n = 100
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance or M = 90 with s sample of n = 100. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
Express as a ratio in the lowest term
1. 360 metres to 3 kilometres
2. 2 minutes to 14 seconds
Answer:
1. 3:25
2. 60:7
Step-by-step explanation:
To express the ratio in the lowest terms:
1. 360 metres to 3 kilometres
First of all, we need to convert both the terms in same unit.
Let us convert kilometres to metres for simplicity.
We know that 1 km = 1000 m
So, 3 km = 3000 m
Hence, the ratio can be represented as:
[tex]360\ m: 3000\ m\\\Rightarrow \dfrac{360}{3000}\\ \\\text{Dividing by 10:}\\\Rightarrow \dfrac{36}{300}\\\\\text{Dividing by 12:}\\\Rightarrow \dfrac{3}{25}\\\Rightarrow 3:25[/tex]
So, the simplest ratio is 3:25.
2. 2 minutes to 14 seconds
Converting minutes to seconds.
1 minute = 60 seconds
2 minutes = 120 seconds
So, the ratio can be written as:
120 seconds : 14 seconds
Dividing by 2:
60:7
So, the simplest form is 60:7.
The answers are:
1. 3:25
2. 60:7
Write the equation of each line in slope intercept form (If possible please show work)
Answer:
y= -2/3 x - 9
Step-by-step explanation:
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -2/3 x+b
We have a point to substitute into the equation
-5 = -2/3(-6) +b
-5 = 4 +b
Subtract 4 from each side
-5-4 = 4-4+b
-9 = b
y= -2/3 x - 9
A family has a phone plan that includes 4 GB of data per month. 10 days into a 30-day month, the family has used 1 GB. At that rate, how many GB will the family use for the entire month?
Answer:
3 GB
Step-by-step explanation:
Since the family has used 1 GB in 10 days. With the same rate in 30 days they would have 3 GB
if f(x) = 2x-1 and g(x) =3x + 5, what is the f(g(5)
Answer:
39
Step-by-step explanation:
g(5) = 3(5) + 5 = 20
f(20) = 2(20) - 1 = 39
Answer:
f ( 2 x + 1 ) = 6 x − 2
Step-by-step explanation:
Set up the composite result function.
f ( g ( x ) )
Evaluate f ( g ( x ) )
by substituting in the value of g into f
. f ( 2 x + 1 ) = 3 ( 2 x + 1 ) − 5
Simplify each term.
Apply the distributive property.
f ( 2 x + 1 ) = 3 ( 2 x )+ 3 ⋅ 1 − 5
Multiply 2 by 3 .
f ( 2 x + 1 ) = 6 x + 3 ⋅ 1 − 5
Multiply 3 by 1 .
f ( 2 x + 1 ) = 6 x + 3 − 5
Subtract 5 from 3 . f ( 2 x +1 ) = 6 x− 2
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
S(t) = 7 â 6(cubedroot(t))
Answer:
66.992%
Step-by-step explanation:
[tex]Sales, S(t)=7-6\sqrt[3]{t}[/tex]
Since we want to maximize revenue for the government
Government's Revenue= Sales X Tax Rate
[tex]R(t)=t \cdot S(t)\\R(t)=t(7-6\sqrt[3]{t})\\=7t-6t^{1+1/3}\\R(t)=7t-6t^{4/3}[/tex]
To maximize revenue, we differentiate R(t) and equate it to zero to solve for its critical points. Then we test that this critical point is a relative maximum for R(t) using the second derivative test.
Now:
[tex]R'(t)=7-6*\frac{4}{3} t^{4/3-1}\\=7-8t^{1/3}[/tex]
Setting the derivative equal to zero
[tex]7-8t^{1/3}=0\\7=8t^{1/3}\\t^{1/3}=\dfrac{7}{8} \\t=(\frac{7}{8})^3\\t=0.66992[/tex]
Next, we determine that t=0.6692 is a relative maximum for R(t) using the second derivative test.
[tex]R''(t)=-8*\frac{1}{3} t^{1/3-1}\\R''(t)=-\frac{8}{3} t^{-2/3}[/tex]
R''(0.6692)=-3.48 (which is negative)
Therefore, t=0.66992 is a relative maximum for R(t).
The tax rate, t that maximizes revenue for the government is:
=0.66992 X 100
t=66.992% (correct to 3 decimal places)
I NEED HELP PLEASE, THANKS! :)
Answer:
x = 6.
Step-by-step explanation:
The general form is r = ep / (1 + e cos Ф)
where e is the eccentricity, p is the distance of the directrix from the focus.
Changing our formula to the above we divide top and bottom by 4:
r = (26.4)/ 4 / (4/4 + 4.4/4 cos Ф)
r = 6.6 / (1 + 1.1 cos Ф)
e is > 1 so we have an hyperbola here.
e = 1.1 and ep = 6.6
giving p = 6.6 / 1.1 = 6.
The equation of the directrix is x = 6.
Translate into an algebraic expressions: a x is increased by 50% and decreased by 30% . What is the result?
Answer:
Step-by-step explanation:
If x is increased by 50%, it means that the amount by which x is increased is
50/100 × x = 0.5 × x = 0.5x
The new value of x would be
x + 0.5x = 1.5x
If the new value is further decreased by 30%, it means that the amount by which it was decreased is
30/100 × 1.5x = 0.3 × 1.5x = 0.45x
The new value of x would be
1.5x - 0.45x = 1.05x
Therefore, the result is 1.05x