Answer:
Follows are the solution to this question:
Step-by-step explanation:
[tex]T: 1 \ R^n \to 1 \ R^n[/tex] is invertible lines transformation
[tex]S[T(x)]=x \ and \ V[T(x)]=x \\\\t'x \ \varepsilon\ 1 R^n\\\\[/tex]
T is invertiable linear transformation means that is
[tex]T(x) =A x \\\\ where \\\\ A= n \times n \ \ matrix[/tex]
and [tex]\ det(A) \neq 0 \ \ that \ is \ \ A^{-1} \ \ exists[/tex]
Let
[tex]V \varepsilon\ a\ R^{n} \ consider \ \ u= A^{-1} v \varepsilon 1 R^n\\\\T(u)= A(A^{-1} v)=(A \ A^{-1}) \\\\ v= I_{n \times n} \cdot v = v[/tex]
so,
[tex]s[T(u)]=v[T(u)]\\\\s(v)=v(v) \ \ \forall \ \ v \ \ \varepsilon \ \ 1 R^n[/tex]
Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario picks one marble at random, what is the probability that he selects a red marble or a yellow marble?
Answer:
not simplified: 18/44
Simplified: 9/22
Step-by-step explanation:
Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below arc summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage?
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Please find the complete question in the attachment file.
[tex]n_1 = 26 \\\\ x_1 = 16.12 \\\\s_1 = 3.58\\\\n_2 = 26\\\\ x_2 = 19.85 \\\\ s_2 = 4.51[/tex]
[tex]H_0: u_1 = u_2\\\\H_1: u_1 \neq u_2[/tex]
Using formula:
[tex]\to S^{2}_{p}=\frac{S^{2}_{1}(n_1 -1)+ S^{2}_{2}(n_2-1)}{n_1+n_2-2}[/tex]
[tex]\to Sp^2 = \frac{((26-1) \times (3.58^2) + (26-1) \times (4.51^2))}{(26+26-2)}[/tex]
[tex]= \frac{((25) \times 12.8164 + (25) \times 20.3401 )}{(26+24)}\\\\ = \frac{(320.41 + 508.5025)}{(50)}\\\\ = \frac{(828.9125)}{(50)}\\\\=16.57825[/tex]
[tex]\to Sp = 4.0716[/tex]
Calculating the value of standard error:
[tex]\to SE = Sp \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}[/tex]
[tex]=4.0716 \times \sqrt{\frac{1}{26}+\frac{1}{26}}\\\\=4.0716 \times \sqrt{\frac{1+1}{26}}\\\\=4.0716 \times \sqrt{\frac{2}{26}}\\\\=4.0716 \times \sqrt{\frac{1}{13}}\\\\=4.0716 \times 0.277 \\\\=1.1278332\\\\= 1.1293[/tex]
Calculating the value of test statistic:
Formula:
[tex]\to t = \frac{(x_1-x_2)}{SE}[/tex]
[tex]= \frac{(16.12 -19.85)}{1.1293}\\\\= \frac{(-3.73)}{1.1293}\\\\=-3.303[/tex]
Calculating the value of Degree of freedom:
[tex]= n_1+n_2 -2 \\\\= 26+26 -2 \\\\= 52 -2 \\\\= 50[/tex]
Because the P-value is a 2-tailed test = 0.0018
Thus they reject H0, because of P-value < 0.05,
Yeah, certain data show clearly that the means are different.
A company sells 100 - 0.5x shirts
when it charges %x per shirt. How
many dollars per shirt should the
company charge in order to make
$5,000 on shirt sales?
Answer:
$100
Step-by-step explanation:
We are given that
Company sells shirts=100-0.5x
Charge per shirt=x
We have to find the charge per shirt in order to make $5000 on shirt sales.
According to question
[tex]x(100-0.5x)=5000[/tex]
[tex]100x-0.5x^2=5000[/tex]
[tex]0.5x^2-100x+5000=0[/tex]
[tex]5x^2-1000x+50000=0[/tex]
[tex]x^2-200x+10000=0[/tex]
[tex]x^2-2\times x\times 100+(100)^2=0[/tex]
[tex](x-100)^2=0[/tex]
[tex]x=100,100[/tex]
Hence, charge per shirt=$100
can someone please help me with this math problem thank you.
please help. It’s really easy just the question is worded weirdly and I don’t get it.
Answer:
d
Step-by-step explanation:
A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns are possible if the first 4 digits must be even and the last digit cannot be zero, one or two?
Number of possible codes =
Answer:
g
Step-by-step explanation:
5 x 1 3/45 * 1 3/4
What is the answer?
reatest to Smallest which is correct?
1. 50 16 5 -64
2. 16 5 50 -64
3. 5 16 -64 50
4. -64 50 16 5
Answer:
1. 50 16 5 - 64
Step-by-step explanation:
have a nice day
nine times a number decreased by four
Answer: 9x - 4
Step-by-step explanation:
We know that a number must be decreased by four. Let's break it up a little.
Nine times some number. We don't know what nine will be multiplied by, so we will just write a placeholder number: x. This number will be multiplied by nine. So it will turn into 9x.
We must decrease (subtract) from this by four. Subtracting 9x by four can be written as 9x - 4.
Find both the area and the perimeter of the semi circle
Answer/Step-by-step explanation:
Area of a semicircle = ½πr²
Perimeter of a semicircle = πr + d
7. d = 14 m
r = ½ of d = 7 m
Area = ½*π*7² = ½*π*49
✅Area = 76.97 m² (nearest hundredth)
Perimeter = π*7 + 14
✅Perimeter = 35.99 m (nearest hundredth)
8. d = 35 in.
r = ½ of d = 17.5 in.
Area = ½*π*17.5² = ½*π*306.25
✅Area = 481.06 in.² (nearest hundredth)
Perimeter = π*17.5 + 35
✅Perimeter = 89.98 in (nearest hundredth)
Sumita buys a set of earphones for £12.17. She pays with £15. How much change does she get? Give your answer in £.
She will get $8.01. Hope this helped.
Simplify.
34x−7+2(x−2)
Answer:36x-11
Step-by-step explanation:
Answer: 36x-11
34x-7+2(x-2)
34x-7+2x-4
36x-11
Step-by-step explanation:
Helppppppp it’s due tomorrow
Answer:
A to f equals 2.5
A to e equals 1.5
a to d equals .5
a to c equals 2
a to I equals 3.5
a to g equals 3
a to h equals 4.5
a to j equals 4
a to k equals 5.5
use the big numbers as landmarks! that's the number before the decimal ( . ) to find the number after the decimal, count the little lines!
Clare bought a photo for 19 cents and paid with a $1 bill. How much change should she receive? ASAP
Multiply.
(3x + 1)(x + 7)
Answer:
the answer is 3x^2 + 22x + 7
Step-by-step explanation:
Expand the polynomial using the FOIL method.
hoped this helped!
brainly, please?
Answer:
3x^2+22x+7
Step-by-step explanation:
Kevin draws out one M&M without looking.
· What is P(green)?
· What is P(red)?
· What is P(~Yellow)?
· What is P(~Orange)?
Answer:
1/6
Step-by-step explanation:
M&M comes in 6 colors.
So, P(green), = 1/6
P(red) = 1/6
· P(Yellow) = 1/6
· P(Orange) = 1/6
Aliyah's school is selling tickets to a play. On the first day of ticket sales the school sold 9 adult tickets and 14 student tickets for a total of $220. The school took in $188 on the second day by selling 11 adult tickets and 7 student tickets. What is the price each of one adult ticket and one student ticket? Write answer as an ordered pair.
Answer:
Step-by-step explanation:
a and s are the numbers of adult and student tickets, respectively.
9a + 14s = 220
11a + 7s = 188 Multiply by -2 and add to first equation.
-22a - 14s = -376
9a + 14s = 220
-----------------------
-13a = -156
a = 12
9(12) + 14s = 220
14s = 112
s = 8
Adult tickets cost $12. Student tickets cost $8.
The function f(x) is defined below. What is the end behavior of f(x)?
Answer:
first choice
Step-by-step explanation:
A bag contains 1 dollar, 50 cents and 25 cents coins in the ratio 3:5:7. The total amount is $ 1856.
Find the number of each denomination.
Answer:
There are 768 1 dollar coins, 1280 50 cent coins and 1792 25 cent coins
Step-by-step explanation:
The total amount of coins is given by x.
Ratio 3:5:7
[tex]\frac{3}{3+5+7} = \frac{3}{15}[/tex] are worth $1.
[tex]\frac{5}{3+5+7} = \frac{5}{15}[/tex] are worth 50 cents = $0.5.
[tex]\frac{7}{3+5+7} = \frac{7}{15}[/tex] are worth 25 cents = $0.25.
The total amount of money is $1856.
This means that:
[tex]\frac{3x}{15} + 0.5\frac{5x}{15} + 0.25\frac{7x}{15} = 1856{/tex]
Multiplying everything by 15
[tex]3x + 2.5x + 1.75x = 27840[/tex]
[tex]7.25x = 27840[/tex]
[tex]x = \frac{27840}{7.25}[/tex]
[tex]x = 3840[/tex]
Amount of coins of 1 dollar:
[tex]\frac{3*3840}{15} = \frac{3840}{5} = 768[/tex]
Amount of 50 cent coins:
[tex]\frac{5*3840}{15} = \frac{3840}{3} = 1280[/tex]
Amount of 25 cent coins:
[tex]\frac{7*3840}{15} = 1792[/tex]
There are 768 1 dollar coins, 1280 50 cent coins and 1792 25 cent coins
Find the square root of the following decimal numbers.
Answer:
[tex] \huge \boxed{ \tt i)1.6} \\ \huge \boxed{ \tt ii)4.3} \\ \huge \boxed{ \tt iii)8.3} \\ \huge \boxed{ \: \: \: \: \tt iv)9.2 \: \: \: }[/tex]
Step-by-step explanation:
to understand thisyou need to know about:square rootfinding square root by division methodconverting decimal to a fractionPEMDAStips and formulas:tips for finding square root by division method
Group the digits in pairs, starting with the digit in the units placeThink of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. Repeat steps till all the periods have been taken uptips for converting decimal to a fraction
Write down the decimal divided by 1Multiply both top and bottom by 10 for every number after the decimal pointreduce the fractionlet's solve:solve the square roots using division method:
the picture is attachedsolve the square roots by converting decimals into fraction:
[tex] \tt i) \sqrt{2.56} \\ \tt \sqrt{ \frac{256}{100} } \\ \tt \sqrt{ \frac{1 {6}^{2} }{ {10}^{2} } } \\ \tt\frac{16}{10} \\ \tt \: 1.6[/tex]
[tex] \tt ii) \sqrt{18.49} \\ \tt \sqrt{ \frac{1849}{100} } \\ \tt\sqrt{ \frac{ {43}^{2} }{ {10}^{2} } } \\ \tt \frac{43}{10} \\ \tt 4.3[/tex]
[tex] \tt iii) \sqrt{ 68.89} \\ \tt \sqrt{ \frac{6889}{100} } \\ \tt \sqrt{ \frac{ {83}^{2} }{ {10}^{2} } } \\ \tt \frac{83}{10} \\ \tt 8.3[/tex]
[tex] \tt iv) \sqrt{84.64} \\ \tt\sqrt{ \frac{8464}{100} } \\ \tt\sqrt{ \frac{ {92}^{2} }{ {10}^{2} } } \\ \tt \frac{92}{10} \\ \tt9.2[/tex]
Answer:
1.6
4.3
8.3
9.2
Step-by-step explanation:
Hope it is helpful....
A 1 km long train travelling at a speed of 60km/h enter a tunnel 1km long. What time will the train take to come out of the tunnel fully.
Answer:
2 minutes
Step-by-step explanation:
The front of the train enters the tunnel and travels 1 km before the rear of the train enters the tunnel. Thus, the total distance traveled by the front of the train is 2 km, and this is covered in a certain number of hours:
Since distance = rate times time, time = distance / rate. In this particular case we have:
2 km
time = distance / rate = ------------------- = (1/30) hr
60 km/hr
(1/30) hr converts to 2 minutes, since 1 hr = 60 minutes
Which of the following does the graph below represent?
A. Ratios that are not equivalent
B. Equivalent ratios
C. Cannot tell from the graph
Answer:
Step-by-step explanation:
You cannot tell from the wiggly line! If that is supposed to be a straight line, you have equivalent ratios from point to point.
Suppose that the local sales tax rate is 7% and you purchase a car for $14,100
a. How much tax is paid ?
B. What is the car's total cost ?
I don't understand you're language
d = (4 x 180) - (3 x 90)
Answer:
d = (4 x 180) - (3 x 90) = 450Step-by-step explanation:
d = (4×180) - (3×90)
d = (720) - (270)
d = 720 - 270
d = 450
HOPE THIS HELPS YOU
Follw me = 10 thanks
Mark as brainliest = 10 thanks
1 thanks to me = 2 thanks
A square has sides of 10x. Write and simply an expression for the perimeter square
Answer:
4(10x) = 40x
Step-by-step explanation:
Assuming you meant that each side has 10x, and not the sum of each side is 10x. Since each side has 10x, and every square has equal sides of 4, we can utilize parenthesis.
4 = number of sides
10x = given length of each side
4(10x) = 40x
Same as saying 4 × 10x = 40x.
Help Asapppppppppppp
Answer:
(-15,0) and (0,-3)
Step-by-step explanation:
(-15,0) = x- intercept
(0,-3) = y-intercept
plz help me brainlest for the 1st answer
Nigel has 138 fluid ounces of lemonade. How many 6-fluid-ounce serving of lemonade can he make
Answer:
23, because 138 divided by 6 is 23
He can make 23 servings.
Suppose the half-life of a certain radioactive substance is 20 days and there are 50g present initially.
a)
Write an equation that models this situation.
b)
How much radioactive substance is remaining after 12 days?
c)
Find the time when there will be 1g of the substance remaining.
Answer:
a) 10(5g + 2r) weight loss over time
b) 20/12 = 1.66667 = 50 / 1.67 = 29.999 gm = 5(6g -1/50) or 5(5 + g) = 30g
c) 30g = 12 days = 3/5 therefore 5/5 -3/5 = 2/5 = 2/5 x 50 (g) = 20g in 8 days lost
8/20 = 0.4 loss each day 50g - 0.8g = 20-2 = 18 days.
Step-by-step explanation:
A full body treatment costs £125.00 Today there is a 10% discount, how much do you pay ?
Step-by-step explanation:
[tex] \frac{10}{100} \times 125 = 12.5 \\ 125 - 12.5 = 112.5[/tex]
112.5 £