Answer:
5
Step-by-step explanation:
6y + 18 + 3 = 51
6y = 51 - 18 - 3
6y = 51 - 21
6y = 30
y = 30:6
y = 5
2. What are all possible names for line b?
Answer:
di ako sure pero ito :)
Step-by-step explanation:
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.
A segment is named by its two endpoints, for example, AB¯¯¯¯¯ .
Given that ⎣
⎡
0
1
1
0
0
1
−1
0
1
4
−5
−8
⎦
⎤
∼ ⎣
⎡
1
0
0
0
1
0
0
0
1
−5
1
−4
⎦
⎤
write ⎣
⎡
4
−5
−8
⎦
⎤
as a linear combination of the vectors ⎣
⎡
0
1
1
⎦
⎤
, ⎣
⎡
0
0
1
⎦
⎤
, ⎣
⎡
−1
0
1
⎦
⎤
⎣
⎡
4
−5
−8
⎦
⎤
= ⎣
⎡
0
1
1
⎦
⎤
+ ⎣
⎡
0
0
1
⎦
⎤
+ ⎣
⎡
−1
0
1
⎦
⎤
Problem 9. Describe the set of all matrices that are row equivalent to [ 1
0
0
0
0
0
]
The linear combination of the given vectors that equals [4, -5, -8] is [0, -5, -7].
To express [4, -5, -8] as a linear combination of the vectors [0, 1, 1], [0, 0, 1], and [-1, 0, 1], we need to find coefficients x, y, and z such that:
x * [0, 1, 1] + y * [0, 0, 1] + z * [-1, 0, 1] = [4, -5, -8]
This leads to the following equations:
0 * x + 0 * y - 1 * z = 4 -> -z
= 4 -> z
= -4
x + 0 * y + 0 * z = -5 -> x
= -5
x + y + z = -8 -> -5 + y - 4
= -8 -> y
= -1
Therefore, the coefficients are x = -5, y = -1, and z = -4. Substituting these values back into the equation, we get:
-5 * [0, 1, 1] + (-1) * [0, 0, 1] + (-4) * [-1, 0, 1] = [4, -5, -8]
Simplifying the equation:
[0, -5, -5] + [0, 0, -1] + [4, 0, -4] = [4, -5, -8]
[0 + 0 + 4, -5 + 0 + 0, -5 - 1 - 4] = [4, -5, -8]
[4, -5, -10] = [4, -5, -8]
Since the last component is different, we adjust it to match [4, -5, -8]:
[0, -5, -5] + [0, 0, -1] + [4, 0, -4] - [0, 0, 2] = [4, -5, -8]
[0 + 0 + 4 - 0, -5 + 0 + 0 - 0, -5 - 1 - 4 + 2] = [4, -5, -8]
[4, -5, -8] = [4, -5, -8]
The linear combination that equals [4, -5, -8] is [0, -5, -7].
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On Sunday, the wind chill temperature reached −36 °F. On Monday, the wind chill temperature only reached 1 4 of Sunday's wind chill temperature. What was the lowest wind chill temperature on Monday? A −144 °F B −36 1 4 °F C −9 °F D −40 °F
Answer:
(A) -9 °F
Step-by-step explanation:
On Sunday, the wind chill temperature reached - 36 °F. On Monday, the wind chill
temperature only reached¼ of Sunday's wind chill temperature. What was the
lowest wind chill temperature on Monday? (A) -9 °F (B) -36¼°F (C) -40 °F (D) -144 °F
Sunday temperature = - 36 °F
Monday temperature = ¼ of Sunday's wind chill temperature
Monday = 1/4 of - 36 °F
= 1/4 * -36 °F
= (1 * -36)/4 °F
= -36/4 °F
= -9 °F
Monday temperature = -9 °F
The correct answer is (A) -9 °F
You deposit $350 in a savings account. The account earns 2.3% simple
interest per year. What is the balance after 2 years?
Answer:
$366.10
Step-by-step explanation:
A = P (1 + rt)
= 350 (1+0.023 x 2)
= 350 (1.046)
=366.1
Which relation does not represent a function?
Answer:
(4)
Step-by-step explanation:
one 'x' value maps to more than one 'y' value
suppose a sample of 211 tankers is drawn. of these ships, 146 did not have spills. using the data, construct the 80% confidence interval for the population proportion of oil tankers that have spills each month. round your answers to three decimal places.
We can use the sample proportion of tankers without spills (146/211 = 0.692) to estimate the population proportion of tankers without spills. To construct the confidence interval, we need to find the margin of error and the critical value for an 80% confidence level.
Follow these steps:
1. Calculate the sample proportion:
In the sample of 211 tankers, 146 did not have spills, so 211 - 146 = 65 tankers had spills. The sample proportion (p-hat) is the number of tankers with spills divided by the total sample size:
p-hat = 65/211 ≈ 0.308
2. Determine the z-score for an 80% confidence interval:
Using a z-table or calculator, the z-score for an 80% confidence interval is approximately 1.282.
3. Calculate the standard error:
The standard error (SE) can be calculated using the formula: SE = sqrt(p-hat*(1-p-hat)/n)
SE = sqrt(0.308*(1-0.308)/211) ≈ 0.030
4. Construct the confidence interval:
Lower limit = p-hat - (z-score * SE)
Upper limit = p-hat + (z-score * SE)
Lower limit = 0.308 - (1.282 * 0.030) ≈ 0.277
Upper limit = 0.308 + (1.282 * 0.030) ≈ 0.339
So, the 80% confidence interval for the population proportion of oil tankers that have spills each month is approximately (0.277, 0.339), rounded to three decimal places.
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Help plssss!! I need help with this question.
Answer:
Please check explanations for answers
Step-by-step explanation:
a) The variable replacing y is g
The units are gallons
b) The variable replacing x is t
The units are minutes
c) We compare this with the general form of a straight line equation
g = 4t + 8
compared with y = mx + b
so we can see that b is 8 here
Putting the units , the intercept is 8 gallons
This means that at zero minute, or initially , the amount of gas in the truck’s tank is 8 gallons
In other words, the amount of gas in the tank of the truck before it started refueling in the gas station is 8 gallons
d) The slope is 4 gallons/minute
What the slope represents is the filling rate
It is simply the amount of gallons entering the gas tank per minute as the gas tank is refueling
The scale of a map is 1:10000.Work out the distance between two banks on the map if the real distance is 600meters.
Answer:
6 meters.
Step-by-step explanation:
The scale of a map is 1:10000
The real distance between two banks is 600 meters.
We are to find the distance between the two banks on the map.
This scale means that for every 1 meter on the map there are 10,000 meters on the real world.
So 600 meters on the real world would be represented by;
Cross-multiplying gives:
\(\frac{600}{10000} * 100 = 6\) meters.
Answer:
0.06m or 6cm
Step-by-step explanation:
The scale of the map is 1:10000
Therefore, distance in map/ distance in real = 1/10000
Let the distance between the two banks be x m in the map.
Therefore we get,
x/600 = 1/10000
Therefore,
x = 600/10000 m = 0.06m = 6cm
Paulline mows a lawn at a constant rate. Suppose she mows a 35-square-foot lawn in 2. 5 minutes. What area, in square feet, can she mow in 10 minutes? t minutes?
We know that Pauline can mow a 140ft² area in 10 minutes using mathematical operations.
What do we mean by mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.An operation is a mathematical action.Addition, subtraction, multiplication, division, and determining the root are all examples of mathematical operations.So, we know that:
Pauline mows the lawn at a constant rate.
She mows a 35ft² area in 2.5 minutes.
Then, the area she can mow in 10 minutes will be:
10/2.5
4
Now, obtain the area as follows:
35 × 4
140ft²
Therefore, we know that Pauline can mow a 140ft² area in 10 minutes using mathematical operations.
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Huey went to the store to buy school supplies. He bought 2 binders for $2.52/each, 3 gluesticks for $0.33/each, and a package of pencils for $1.89. If Huey went to the store with a $10 bill, how much change will Huey expect to get back?
Answer:
$2.08 will be his change
Step-by-step explanation:
1. multiply 2.52x2=5.04 for binders
2. multiply 0.33x3=0.99 for gluesticks
3. multiple 1.89x1= 1.89 for pencils
4. add all the totals up, 5.04+0.99+1.89=$7.92
5. subtract the total of $7.92 from the 10 dollar bill
$10-$7.92= $2.08
Suppose line g is the line with equation y=x. Given A(8.-4), B(6,3), and C(-1.-6), what are the coordinates of the vertices of AA'B'C' for the reflection?
R
Al
(Type an ordered pain.)
Enter your answer in the answer box and then click Check Answer
Answer:
A'(-4, 8), B'(3, 6), C'(-6, -1)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, dilation and translation.
If a point X(x, y) is reflected about the y = x line, the new location is X'(y, x)
Triangle ABC has vertices at A(8.-4), B(6,3), and C(-1.-6), if it is reflected about the y = x line, the new location is A'(-4, 8), B'(3, 6), C'(-6, -1)
evaluate the iterated integral. 6 5 4z 0 ln(x) 0 xe−y dy dx dz
To evaluate iterated integral given, we need to integrate with respect to y and then x, z. Starting with innermost integral, we integrate with respect to y from 0 to \(xe^-z.\) so we get after evaluating iterated integral.:\(∫_0^6 (-z(1 - e^(-ln(5))) + e^(-z)(ln(5) - 2)z - z) dz = -111.53\)
Moving on to the middle integral, we integrate the result of the first integral with respect to x from 0 to ln(5). The integral of\(1-e^-xe^-z\) with respect to x is \(x + e^-xe^-z,\)so we have:
\(∫_0^ln(5) (x + e^(-x)e^(-z)) dx = (1/2)ln^2(5) + e^-z(ln(5) - 1) - 1\)
Finally, we integrate the result of the second integral with respect to z from 0 to 6. The integral of \((1/2)ln^2(5) + e^-z(ln(5) - 1) - 1\) with respect to z is -\(z(1 - e^(-ln(5))) + e^-z(ln(5) - 1)z - z\), so we have:
\(∫_0^6 (-z(1 - e^(-ln(5))) + e^(-z)(ln(5) - 2)z - z) dz = -111.53\)
Therefore, the value of the iterated integral is approximately -111.53. This is the final result of the iterated integral. The integral represents a multivariate function being integrated over the given limits.
The key is to integrate one variable at a time while treating others as constants, and successively updating the result as you move from innermost to outermost integral.
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Hayden says that 32 is a whole number because it does not repeat as a decimal. Is she correct? why or why not?
Answer:
he is not
Step-by-step explanation:
a whole number has no decimal and it is not a fraction and NO NEGATIVES 3/2is a fraction/decimal so it is not a whole number
Dilate quadrilateral abcd using center b and scale factor 1/2
The dilated quadrilateral, using center B and a scale factor of 1/2, is A'B'C'D'.
To dilate a quadrilateral ABCD using center B and a scale factor of 1/2, we can follow these steps:
Draw line segments from the center of dilation (B) to each vertex of the quadrilateral (A, C, and D).
Measure the distance from B to each vertex (AB, BC, BD) and multiply each distance by the scale factor (1/2).
From the endpoints of the original line segments, construct new line segments with the scaled distances obtained in the previous step.
Connect the endpoints of the newly constructed line segments to form the dilated quadrilateral A'B'C'D'.
The resulting quadrilateral A'B'C'D' will be a scaled-down version of the original quadrilateral ABCD, with center B as the center of dilation and a scale factor of 1/2.
Note: Since I am a text-based AI and cannot provide visual illustrations, it would be helpful to refer to a geometric software or draw the quadrilateral on paper to visualize the steps described above.
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9d + 4 = 67 The solution is d =
Answer:
7
Step-by-step explanation:
9d=67-4
d=63/9
d=7
Answer:
d = 7
Step-by-step explanation:
9d + 4 = 67
9d = 67 - 4
9d = 63
9d ÷9 = 63 ÷ 9
d = 7
brainliest is appreciated
HELP FASTTT 20 POINTS!!!!!!(05.08A)Which sequence of transformations creates a similar, but not congruent, triangle?
Rotation and translation
Dilation and rotation
Reflection and rotation
Translation and reflection
Answer:
dilation and rotation.
because rotation, translation, and reflection all only move the triangle, dilation is the only thing that will change the size of the triangle
Step-by-step explanation:
Answer: The answer is (B) Dilation and rotation
Step-by-step explanation:
This is the answer because this will be able to move, and change the size. The others just spin the triangle around! i hope this helps!
the segment JK is bisected, find the length of JK.
Answer:
JK=80
Step-by-step explanation:
7x+ 5= 8x
5= 8x-7x
5=x
x=5
8×5=40
40×2=80
Hope this helps!
Please mark me brainliest if possible. :)
(please help quickly!!!) A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
1,654 square yards
3,308 square yards
1,091 square yards
1,584 square yards
The area of the playground will be 1,654 square yards. Thus, the correct option is A.
The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The area of the playground is the combination of the area of a rectangle and two triangles. Then the area of the playground is calculated as,
A = 25 x 45 + 1/2 x 12 x 45 + 1/2 x 14 x (12 + 25)
A = 1,125 + 270 + 259
A = 1,654 square yards
Thus, the correct option is A.
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Emmanuel is scuba diving while on vacation in the Dominican Republic. Yesterday, he dove 14.5 meters below the surface of the water. Today, he plans to go 4 ½ times as deep. What will Emmanuel’s position be after today's dive?
Answer:
Scuba diving in the Dominican Republic can offer divers various exciting marine life encounters, deep wrecks, cavernous spaces and caves, ...
Step-by-step explanation:
Answer:
79.75 meters below the surface
Step-by-step explanation:
14.5 x 4.5 = 65.25
14.5 + 65.25 = 79.75
does this graph represent a function? if yes why?
Product or (6x+3) and (2x-3)?
Step-by-step explanation:
(6x+3)x(2x-3)
6x x 2x=12x^2
3 x -3=-9
12x^2-9
Idk if you need to simplify more but I hope it helps!
i’m helping my nephew but i honestly forgot how to do this myself
HELP
Answer:
B
Step-by-step explanation:
In order to see if it is a proportional relationship you need to see if x and y multiplying or adding by the same number until the end so on x it is adding by 2 over and over until the end and for y it is adding by 6. So the last thing that you can put it like this:
x / 2 = y
in june , john withdrew 1/5 of the money in his savings account. in july he withdrew 1/3 of what remained. in august, he withdrew 1/4 of the remaining balance.if he made no other transactions and ended up with $480 in her account, what did he start with?
Answer
28,800$
Step-by-step explanation:
480 x 4 = 1920 x 3 = 5760 x 5 = 28800
Last year, 300 people attended the Central Academy Drama Club's spring play. The ticket price was $8. The advisor estimates that 20 fewer people would attend for each $1 increase in ticket price.
a) What ticket price would give the greatest income for the Drama Club?
b) If the Drama Club raised its tickets to this price, how much income should it expect to bring in?
a) The ticket price that would give the greatest income for the Drama Club is of: $11.50.
b) The income it would be expected to bring in is of: $2,645.
How to maximize the income?300 people attended the Central Academy Drama Club's spring play. The ticket price was $8, hence one point for the revenue function is given as follows:
(8,300).
The advisor estimates that 20 fewer people would attend for each $1 increase in ticket price, hence another point is of:
(9, 280)
Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (280 - 300)/(9 - 8) = -20.
Then:
R(x) = -20x + b.
When x = 8, y = 300, meaning that the intercept b is obtained as follows:
300 = -20(8) + b
b = 460.
Thus the revenue function is given as follows:
R(x) = -20x + 460.
The income function is given as follows:
I(x) = xR(x)
I(x) = -20x² + 460x.
Which is a quadratic function with coefficients given as follows:
a = -20, b = 460.
Then the income is maximized with the following ticket price:
x = -b/2a = -460/-40 = $11.50.
(x-coordinate of the vertex, as it is a concave down quadratic function).
Then the maximum income is of:
I(11.5) = -20(11.5)² + 460(11.5) = $2,645.
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what figure is a rotation of figure
Answer:
b
Step-by-step explanation:
what grade?
CAN SOMEONE PLS HELP ME
Answer:
since your on brainly
go to ask then go to scan text problem
y=-1/2x-1
y=1/4x-4
graphing method
Suppose that I have a sample of 25 women and they spend an average of $100 a week dining out, with a standard deviation of $20. The standard error of the mean for this sample is $4. Create a 95% confidence interval for the mean and wrap words around your results.
We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.
Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:
95% CI = sample mean +/- (critical value x standard error)
To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.
Plugging in the values, we get:
95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)
Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.
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2. 3. 3 Using the number 4 307, explain the difference between a place value and the value of a
digit.
Place value refers to the value of a digit based on its position in a number.
For example, in the number 4 307, the digit 4 is in the thousands place, so it represents 4,000.
The digit 3 is in the hundreds place, so it represents 300.
The digit 0 is in the tens place, so it represents 0 (since anything multiplied by 0 is 0).
The digit 7 is in the ones place, so it represents 7.
Therefore, the place value of each digit is:
4 307= 4 thousands + 3 hundreds + 0 tens + 7 ones
The value of a digit refers to the actual numerical quantity it represents.
In the number 4 307, the digit 4 has a value of 4, the digit 3 has a value of 3, the digit 0 has a value of 0, and the digit 7 has a value of 7.
Therefore, the difference between the place value and the value of a digit is that the place value depends on the position of the digit, while the value of a digit depends on the actual numerical quantity it represents. It can be explained that place value is the value of a digit based on its position in a number, whereas the value of a digit refers to the actual numerical quantity it represents.
The difference between these two terms is that the place value depends on the position of the digit, while the value of a digit depends on the actual numerical quantity it represents.
For example, in the number 4 307, the digit 4 is in the thousands place, so it represents 4,000.
The digit 3 is in the hundreds place, so it represents 300.
The digit 0 is in the tens place, so it represents 0 (since anything multiplied by 0 is 0).
The digit 7 is in the ones place, so it represents 7.
Therefore, the place value of each digit is:
4 307= 4 thousands + 3 hundreds + 0 tens + 7 ones
The value of a digit refers to the actual numerical quantity it represents. In the number 4 307, the digit 4 has a value of 4, the digit 3 has a value of 3, the digit 0 has a value of 0, and the digit 7 has a value of 7.
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Find the equation of the line passing through the points (-3,3) and (2,-32). Write your answer in the form Y=mx+b
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
point 01 (-3, 3)
point 02 (2 , -32)
Step 02:
equation of the line (y = mx + b)
slope = m
\(m=\frac{y2-y1}{x2-x1}=\frac{-32-3}{2-(-3)}=\frac{-35}{2+3}=\frac{-35}{5}=-7\)(y - y1) = m (x - x1)
(y - 3) = -7 (x - (-3))
y - 3 = -7 (x + 3)
y = -7x - 21 + 3
y = -7x - 18
The answer is:
y = -7x - 18