The image of v is (49 - 7YZ, 7a + 7e, 14, 7), and the pre-image of W is (-14/3, 20/3).
To find the image of vector v = (7, 7) under the transformation T(V1, V2) = (V2V1 - YZVZ, aV1 + VZE V2, V1 + V2, 2V1 - V2), we substitute the values V1 = 7 and V2 = 7 into the expression for T.
The image of v is obtained as T(7, 7) = (7×7 - YZ×7, a×7 + 7e, 7+7, 2×7 - 7) = (49 - 7YZ, 7a + 7e, 14, 7).
To find the pre-image of vector w = (-6/2, 4, -16) under the transformation T, we need to solve the equation T(V1, V2) = (-6/2, 4, -16) for V1 and V2.
Comparing the components of T(V1, V2) and (-6/2, 4, -16), we get the following equations:
2V1 - V2 = -16 (1)
V1 + V2 = 2 (2)
V2V1 - YZVZ = -3/2 (3)
From equation (2), we can solve for V1 in terms of V2 as V1 = 2 - V2.
Substituting V1 = 2 - V2 in equation (1), we have 2(2 - V2) - V2 = -16, which simplifies to 4 - 3V2 = -16. Solving this equation, we find V2 = 20/3.
Substituting V2 = 20/3 in equation (2), we get V1 + 20/3 = 2, which leads to V1 = -14/3.
Therefore, the pre-image of w is (-14/3, 20/3).
In summary, the image of v is (49 - 7YZ, 7a + 7e, 14, 7), and the pre-image of w is (-14/3, 20/3).
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what is 3/4 divided 1/2.
Answer:
6/4 or 1 2/4
Step-by-step explanation:
hope this helps
Answer:
1.5
Step-by-step explanation:
3/4 ÷ 1/2
= 3/4 x 2
= 6/4
= 3/2
= 1.5
what is 3a + 7 -2a -4 simplified?
Answer:
3a-2a+7-4
a+3
Step-by-step explanation:
like and unlike terms arranging
and add and subtraction
You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 55% at a level of significance of a = 0.05. According to your sample, 44 out of 73 potential voters prefer the Democratic candidate.
a. For this study, we should use ______________
b. The null and alternative hypotheses would be: ___________
a. For this study, we should use the z-test.
b. The null and alternative hypotheses would be: Null hypothesis: H0: p = 0.55
Alternative hypothesis: H1: p ≠ 0.55
Explanation:
We use the z-test when we are testing the difference between the sample mean and the population mean. Here we are testing the difference between the sample proportion (p) and the population proportion (P).
We should use the z-test for this study to check whether the proportion of voters who prefer the Democratic candidate is significantly different from 55% at a level of significance of a = 0.05. This is because we are testing the proportion of people who prefer a Democratic candidate from a population. Here, we will use the sample size, sample proportion, and level of significance to calculate the test statistic (z) value.
The null hypothesis is H0: p = 0.55, which states that there is no difference between the proportion of voters who prefer the Democratic candidate and the population proportion.
While the alternative hypothesis is H1: p ≠ 0.55, which states that there is a significant difference between the proportion of voters who prefer the Democratic candidate and the population proportion.
a. For this study, we should use the z-test.
b. The null and alternative hypotheses would be: Null hypothesis: H0: p = 0.55
Alternative hypothesis: H1: p ≠ 0.55
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Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here
The question is incomplete:
Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here. Explain why Maria is incorrect and how she can find the correct answer.
Answer:
Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.
Step-by-step explanation:
You can find the number of necklaces Avan can make by dividing the number of beads she has by the amount in each necklace:
6048/24=252
According to this, you can say that Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.
Write an equation for this word
sentence: one third of a number
equals 9.
Hurry plsss
Answer:I believe D
Step-by-step explanation: Hope you get it right
Compute the indicated quantity using the following data.
sin α = 15/17 where π/2< α < 3π/2
sin β= -4/5 where π < β < 3π/2
sin (α + β) =_________
Using trigonometric identity, sin(α + β) = -28/85.
To compute sin(α + β), we can use the trigonometric identity:
sin(α + β) = sin α cos β + cos α sin β
Given the values:
sin α = 15/17 (π/2 < α < 3π/2)
sin β = -4/5 (π < β < 3π/2)
To find sin α, we can use the Pythagorean identity:
cos α = ±√(1 - sin² α)
Since α is in the range π/2 < α < 3π/2, sin α is positive, so cos α will be negative.
sin α = 15/17
cos α = -√(1 - (15/17)²)
= -√(1 - 225/289)
= -√(64/289)
= -8/17
Now, we can substitute the values into the formula for sin(α + β):
sin(α + β) = (sin α cos β) + (cos α sin β)
= (15/17) * (-4/5) + (-8/17) * (-4/5)
= -60/85 + 32/85
= -28/85
Therefore, sin(α + β) = -28/85.
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36. Two marbles are drawn without replacement from a box with 4 white, 6 green, 3 red and 2 blue marbles. Find the probability both marbles are red.
The probability of drawing both marbles as red is 1/35.
To obtain the probability of drawing two red marbles without replacement, we need to calculate the probability of drawing one red marble on the first draw, and then the probability of drawing a second red marble given that the first marble was red.
The probability of drawing a red marble on the first draw is given by:
P(Red on 1st draw) = (number of red marbles) / (total number of marbles)
= 3 / (4 + 6 + 3 + 2)
= 3 / 15
= 1/5
After the first red marble is drawn, there are now 2 red marbles remaining out of a total of 14 marbles.
The probability of drawing a second red marble given that the first marble was red is:
P(Red on 2nd draw | Red on 1st draw) = (number of red marbles remaining) / (total number of marbles remaining)
= 2 / 14
= 1/7
To find the probability of both marbles being red, we multiply the probabilities of each event:
P(Both marbles are red) = P(Red on 1st draw) * P(Red on 2nd draw | Red on 1st draw)
= (1/5) * (1/7)
= 1/35
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how do i find a formula for "1+3+5+7+......+(2n-1)
Answer:
Step-by-step explanation:
common difference d=3-1=2
first term a=1
an=a+(n-1)d
2n-1=1+(l-1)2
2n-1=1+2l-2
2n-1=2l-1
l=n
(i used l for number of terms)
number of terms=n
[tex]S_{n}=\frac{n}{2} (first ~term+last~term)\\=\frac{n}{2} (1+2n-1)\\=n^2[/tex]
Solve the initial value problem. dy dx Ex4(y – 2), y(0) = 6
This equation represents the solution to the given initial value problem.
[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]
To solve the initial value problem, we'll separate variables and integrate both sides.
Starting with the given differential equation:
[tex]dy/dx = e^{4(y - 2)}[/tex]
Separating variables:
[tex]e^{(4(y - 2))} dy = dx[/tex]
Integrating both sides:
[tex]\int e^{(4(y - 2))} dy = \int dx[/tex]
To integrate [tex]e^{4(y - 2)}[/tex], we can use the substitution u = 4(y - 2), du = 4dy:
[tex]1/4 \int e^u du = x + C[/tex]
Integrating [tex]e^u[/tex] gives us:
[tex]1/4 * e^u = x + C[/tex]
Substituting back u = 4(y - 2):
[tex]1/4 * e^{(4(y - 2))} = x + C[/tex]
Now, applying the initial condition y(0) = 6, we can solve for C:
[tex]1/4 * e^{(4(6 - 2))} = 0 + C[/tex]
[tex]1/4 * e^{(4(4))} = C[/tex]
[tex]1/4 * e^{(16)} = C[/tex]
Therefore, the solution to the initial value problem is:
[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]
This equation represents the solution to the given initial value problem.
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4/5 divided by 2/7 in simplest form
Answer:
2 4/5
Step-by-step explanation:
4/5 divided by 2/7 is 2.8. 2.8 in the form of a fraction is 2 4/5.
The fraction 4/5 divided by 2/7 in the simplest form, is 14/5.
Given that, (4/5) divided by (2/7).
To divide fractions, multiply the first fraction by the reciprocal of the second fraction
Let a, b, c and d be real numbers. Divide a fraction (a/b) by another fraction (c/d), we can multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, the reciprocal of (c/d) is (d/c).
To divide (a/b) by (c/d), multiply the first fraction by the reciprocal of the second fraction:
(a/b) ÷ (c/d) = (a/b) x (d/c)
Multiplying the numerators and denominators:
(ad) / (bc)
Therefore, the result of (a/b) divided by (c/d) is (ad) / (bc).
To simplify this expression, and multiply the first fraction by the reciprocal of the second fraction:
(4/5) x (7/2)
Multiplying the numerators and denominators:
(4 x 7) / (5 x 2)
Simplifying the numerator and denominator:
28 / 10
To further simplify the fraction, and divide both the numerator and denominator by their greatest common divisor, which is 2:
28 ÷ 2 / 10 ÷ 2
This gives us:
14 / 5
Therefore, the fraction 4/5 divided by 2/7, in the simplest form, is 14/5.
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Solve for x 345 = 5x Express the answer to the hundredths place (i.e., two digits after the decimal point).
The solution to the equation is x = 69.
To solve the equation 345 = 5x for x, we can isolate the variable by dividing both sides of the equation by 5:
345/5 = 5x/5
69 = x
Therefore, the value of x = 69.
This means that if we substitute x with 69 in the equation 5x, we will obtain the left-hand side of the equation 345. The solution is accurate to the hundredth place, as there are no decimal places involved in this particular equation. It's important to note that the solution is a whole number, and in this case, it represents the value of x that satisfies the equation.
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A cardboard box is shaped like a cube. The length of each face is 15 inches what is the volume of the box in cube inches
Answer:
3375 in³
Step-by-step explanation:
Volume of a cube = a³ ; where a = edge of the cube
Length of each face = edge of cube = 15 inches
Volume of cube = 15³
Volume of cube = 15 inch * 15 inch * 15 inch
Volume of cube = 3375 in³
Solve the system of equations using the substitution method.
x-4-5
2x + 3y - 23
Write your solution as an ordered pair:(
Answer:
(7, 3 )
Step-by-step explanation:
Given the 2 equations
x = 4y - 5 → (1)
2x + 3y = 23 → (2)
Substitute x = 4y - 5 into (2)
2(4y - 5) + 3y = 23 , that is
8y - 10 + 3y = 23
11y - 10 = 23 ( add 10 to both sides )
11y = 33 ( divide both sides by 11 )
y = 3
Substitute y = 3 into (1) for corresponding value of x
x = 4(3) - 5 = 12 - 5 = 7
solution is (7, 3 )
The mean number of words per minute (WPM) typed by a speed typist is 119 with a standard deviation of 15 WPM. What is the probability that the sample mean would differ from the population mean by greater than 4.1 WPM if 33 speed typists are randomly selected? Round your answer to four decimal places.
Answer:
the probability that the sample mean would differ is 0.1164
Step-by-step explanation:
The computation of the probability is shown below
= 1 - P(Within 4.1 WPM)
= 1 - P( -4.1 ÷ 15÷ √3 <z < 4.1 ÷ 15÷ √3)
= 1 - P(-1.57 < z < 1.57)
= 1 - 0.8836
= 0.1164
Hence, the probability that the sample mean would differ is 0.1164
Therefore the same would be applied and relevant
Help me please I will give points whenever u wanna
Answer:
x = 120 degrees or (c)
Step-by-step explanation:
It's 120 degrees...
...
I don't know how to do this, I wasn't paying attention in class
Answer:
39.837168574084177751131265854635
Step-by-step explanation:
If you plug it into a calculator, you get that.
Next time, please pay attention in class and save us all a little trouble.
What is the measure of the other acute angle.....?
I really need to get this right plsss help me ❤️ I really need to get to an 90
the answer is 30°
EXPLAINATION:
since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°
so, 90° + 60° + x = 180
150° + x = 180°
so x = 180° - 150° = 30°
hence, the other acute angle is 30°.
For this data set, the best measure of center is the
, and its value is
Answer:
median, 60
Step-by-step explanation:
Answer:
it is 60 my friend.
Step-by-step explanation:
44444444444444 help me ples
Answer:
a
Step-by-step explanation:
could someone help me with this
HELP ME PLEASEEEEEE
Answer:
-3
Step-by-step explanation:
The answer is -3 because it is the number on the x-axis
What is the slope and y intercept of 4x + 2y = 6?
NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!!
Answer:
4x−2y=6 is 21
Step-by-step explanation:
Answer:
Y intercept=3
4(0)+2y=6
y=3
slop=m=-2
y=-2x+3
y=mx+b
M=-2
Step-by-step explanation:
87392 rounded off to the nearest 5
The given number 87392 is rounded off to 87390.
What is meant by "rounding off"?Rounding off means a number is made simpler by maintaining its overall value but being closer to the next number.
The number to be rounded off is 87392.
The digit present in the once place is 2.
If the smallest place digit is greater than or equal to 5, then round up the digit.
As the digit in the smallest digit is less than 5, the digit gets rounded down.
Here, the smallest place digit is 2 which is smaller than 5.
So, the given number rounded off to 87390.
Hence, the answer is 87390.
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find x:x+x=20
please find x for me
Answer:
x = 10
Step-by-step explanation:
10 + 10 = 20
Good luck with your work!
Answer:
x = 10
Step-by-step explanation:
x + x = 20 can also be interpreted as 2x = 20. This makes it easier to solve for the variable.
To isolate x, do the inverse operation of multiplication. So, we have to divide both sides of the equation by 2.
[tex]\frac{2x}{2}[/tex] = [tex]\frac{20}{2}[/tex]
Simplify this equation for x = 10.
I hope this is helpful. Good luck ^^
what is the range of this data set?
Answer:
Range = 3.3
Step-by-step explanation:
Range = Max value - Min value
Max value = 100.1
Min Value = 96.8
Range = 100.1 - 96.8
Range = 3.3
CAN SOMEONE HELP ME FIND THE AREA OF THE LIGHT GRAY PART WITH AN EXPLANATION :)
(IF YOU WANT ME TO GO TO A LINK I'M NOT, SO YOUR ANSWER WILL BE REPORTED IF YOU DECIDE TO INCLUDE ONE)
Answer:
91 or 525
Step-by-step explanation:
Multiply the objects width (How long it is), times height. For the smaller object inside the bigger object, it is 91. For the bigger object, it is 525.
An ounce is equal to about 28 g. If 1 g of soil contains 2.5 billion bacteria, how many bacteria are in 1 oz of soil?
Answer:
About 700 billion bacteria
Step-by-step explanation:
Given
[tex]1oz \approx 28g[/tex]
[tex]1g = 25\ billion\ bacteria[/tex]
Required
Number of bacteria in 1 oz
[tex]1g = 25\ billion\ bacteria[/tex]
Multiply both sides by 28
[tex]28 * 1g = 25\ billion\ bacteria * 28[/tex]
[tex]28g = 700\ billion\ bacteria[/tex]
Recall that
[tex]1oz \approx 28g[/tex]
This means:
[tex]1oz \approx 700\ billion\ bacteria[/tex]
Can someone plz help me with this!!!
Answer:
100
Step-by-step explanation:
an isosceles triangle is equal so if one side is 100 degrees, the other side is too
Answer:100 is the answer
Step-by-step explanation
Because the isoscles triangles are those whose two sides are equal
What is the range of y = -x2 + 6x -4?
Answer:
Hope this helps :)
What is the answer. Please dont send me ‘links’. I seriously need help.
Answer:
Total Volume of composite figure = 635.2 cm³
Steps:
1.CV = h×3.14×(d/2)²
CV = 5×3.14(8/2)²
CV = 5×3.14(4)²
CV = 5×3.14×16
CV = 5×50.24
CV = 251.2 cm³
2.RV = h×w×l
RV = 4×8×12
RV = 4×96
RV = 384 cm³
3.TV = CV + RV
TV = 251.2 + 384
TV = 635.2 cm³