Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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The half life of a drug in 3 hours. If the drug is administered with a dose of 640mgs and the patient in not allowed to drive untold only 80mgs are present. How long before the patient can drive p
Answer: 12 hours
Step-by-step explanation: 6 h = 360 min,9 h = 540 min, 12 h = 720 min
640-360=280 , 640-540=100 , 640-720=-80
A particular fruit's weights are normally distributed, with a mean of 572 grams and a standard deviation of 19 grams.
If you pick 23 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
If you pick 23 fruits at random, then 11% of the time, their mean weight will be greater than 577 grams.
How to determine the required mean weight?First of all, we would calculate the standard deviation of the sampling distribution by using this mathematical expression:
Standard deviation, σy = σ/√n
Where:
σ represents the standard deviation.n represents the number of items.Substituting the given parameters into the formula, we have;
Standard deviation, σy = 19/√23
Standard deviation, σy = 19/4.7958
Standard deviation, σy = 3.962.
Since 23 fruits are to be picked randomly, then 11% of the time, their mean weight would be greater than is given by this mathematical expression:
P(x > c) = 0.11
P(x > (c - 572)/3.962) = 0.11
P(x > 1.23) = 0.11 (z-core from p-value using the z-score table).
(c - 572)/3.962 = 1.23
Cross-multiplying, we have:
c - 572 = 4.8733
c = 572 + 4.8733
c = 576.8733 ≈ 577 grams.
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Which are correct representations of the inequality 6x 2 3+ 4(2x - 1)? Select three options.
12 2x
6x 23+ 8x -4
-1.5
-1
-0.5
0 0.5
1
1.5
|--1.5
-1
-0.5
0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1.5
Answer:
The third option
Step-by-step explanation:
I did the math x less than or equal to 0.5
Brainliest for the correct answer :>
Answer:
it can be A or B it doesn't matter because 25-5>10 and 20-5>10
Answer:
Move all terms not containing a to the right side of the inequality.
Inequality Form:
X> 15
Interval Notation:
(15
Step-by-step explanation:
By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for sh.56 , gain is as much as percent as its cost in dollars . What is the cost price ?
The cost price of the table is $40.
What is Gain ?Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
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Some questions supply a data set, like the one below, which must be used in order to answer the question.
4
8
9
5
2
7
7
5
8
You can copy the data set into another program, such as a spreadsheet or a statistical software program
Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.
The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.
1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.
A
1 4
2 8
3 9
4 5
5 2
6 7
7 7
8 5
9 8
2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.
3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.
4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.
5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.
Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.
In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.
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Calc question — related rates
The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
How to determine rate?The volume of the liquid in the bowl is given by the following integral:
\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)
where r = radius of the bowl and y = height of the liquid.
The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:
r = √{(4/(8-x)) - 1}² + 1²
The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:
h = (4/(8-x)) - 1
Substituting these equations into the volume integral:
\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)
Evaluate this integral using the following steps:
Expand the parentheses in the integrand.
Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.
Integrate each part separately.
The integral of the square root term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)
The integral of the linear term can be evaluated using the following formula:
\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)
Substituting these formulas into the integral:
V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h
Evaluating this integral:
V = π { 16/27 (8-h)³ - 16/18 (8-h)² }
The rate of change of the volume of the liquid is given by:
dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }
The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.
Substituting these values into the equation for dV/dt:
dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π
Solving this equation for the rate of change of the depth of the liquid:
dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹
Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.
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My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
Please help urgent thank you
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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Given that f(x) = 4x V3x + 3 and g(x) = 2vx + 1, find x(*)(). х Ox3 20x +3 OxVx+3 +3 O 2x 73
Answer: The answer is the last option, Option D.
Please anyone that can help me
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
In AIJK, i = 25 inches, j = 46 inches and k=24 inches. Find the measure of ZJ to the nearest degree.
Answer:
140
Step-by-step explanation:
6. The measure of angle Q is 70 degrees. Find the measure of angle P.
Р
Q
R
Answer:
angle P measures 40 degrees
Step-by-step explanation:
triangle with 2 equal sides has 2 equal angles also (isosceles triangle)
if angle Q is 70, then R is 70
sum of all interior angles of a triangle is 180; therefore, angle P must be 180-140
Please explain your answer to the question in the picture with steps.
Please help really urgent
Answer:
0.0909
Step-by-step explanation:
4 blue + 5 red + 3 black = 12 chips in total.
p=probability
1st draw:
p (blue) = 4/12
there are now 11 chips in the bag, 4-1 =3 are blue.
2nd draw?
p (blue) = 3/11
probability of pulling one blue chip followed by another blue chip is:
(4/12) X (3/11) = (4X3)/12X11)
= (12)/(132)
= 1/11
0.0909
2) (-8, -9). (4.-10)
Answer: √
145 or 12.04159457 for the decimal ways try 12
Step-by-step explanation: 12.0415945787923
Midpoint (−2,−9.5)
Slope −0.0833333333333333
x intercept −116.00
y intercept −9.67
Answer:
√
145 or 12.04159457 for the decimal wise try 12
Factor 6x^2 + x − 2
Answer:
(2−1)(3+2)
Step-by-step explanation:
Rewrite in product form
2x(3x+2) - 1(3x+2)
(2x-1) (3x+2)
help me please i need it now
Answer:
1.75
Explanation:
Take two points: (0, -3), (4,4)
\(\sf rate \ of \ change: \dfrac{y_2- y_1}{x_2 - x_1} = \dfrac{rise}{run}\)
Here rate of change:
\(\sf \rightarrow \dfrac{4-(-3)}{4-0}\) (insert values)
\(\sf \rightarrow \dfrac{7}{4}\) (in fraction)
\(\sf \rightarrow 1.75\) (in decimals)
Answer:
1.75
Step-by-step explanation:
Rate of change = slope of the line
Taking two points (4,4) and (0, -3) :
slope (m) = 4 + 3 / 4 - 0slope (m) = 7/4slope (m) = 1.75
x+2y+3z = 12
x-3y + 4z=27
-x+y+2z=7
Show work
Answer:
x=1
y=−2
z=5
(heres how i got the answer)
Step-by-step explanation:
x+2y+3z=12
x−3y+4z=27
−x+y+2z=7
Solve x+2y+3z=12 for x.
x=−2y−3z+12
Substitute −2y−3z+12 for x in the second and third equation.
−2y−3z+12−3y+4z=27
−(−2y−3z+12)+y+2z=7
Solve equations for y and z respectively.
y=−3+
5
1
z
z=
5
19
−
5
3
y
Substitute −3+
5
1
z for y in the equation z=
5
19
−
5
3
y.
z=
5
19
−
5
3
(−3+
5
1
z)
Solve z=
5
19
−
5
3
(−3+
5
1
z) for z.
z=5
Substitute 5 for z in the equation y=−3+
5
1
z.
y=−3+
5
1
×5
Calculate y from y=−3+
5
1
×5.
y=−2
Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.
x=−2(−2)−3×5+12
Calculate x from x=−2(−2)−3×5+12.
x=1
The system is now solved.
x=1
y=−2
z=5
find the surface area
Answer:
225 cm 2
Step-by-step explanation:
Answer:
Surface Area = 6* (5 inches) 2 = 6* (25 square inches)
Step-by-step explanation:
The factors of the polynomial are
A.(x + 1)(2+ix)(2-ix)
B.(x-1)(2+ix)(2-ix)
C.(x-1)[x-(3+1)][x-(4-1)]
D.(x+1)(x+(2+1)][x- (2-1)]
E.(x-1)[x+(2+1)][x- (2-1)]
Answer: c
Step-by-step explanation:
Si una mosca real tiene una longitud de 9mm y su maqueta mide 18cm.cual a q escala se realizo la maqueta
The scale factor used is:
1 centimeter equals half millimiter.
How to find the scale factor?The scale factor tells us how many units in the sculpture represent a real unit.
We know that:
Real length = 9mm
Length in the sculpture = 18cm
Then we have the relation between the lengths:
18cm = 9mm
Dividing both sides by 18 we will get:
1cm = 9mm/18
1cm = 0.5mm
So the scale is 1 centimeter equals half millimiter.
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If y = -24 when x = -3,find x when y = -6 ???
Answer:
-0.75
Step-by-step explanation:
first, you find a way to get from -24 to -6 and that is by dividing by 4 so you have to also divide the old x value by 4 to get the new x value which means -3 ÷ 4 which equals -0.75
pls give me brainliest i really need it
For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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You deposit $400 into a savings account that earns 5% annual
interest compounded annually. The graph shows the balance of
your investment account over time.
Step-by-step explanation:
F=400(1+0.05/1)^1*t
After 1 year= $ 400.20
2= 400.40
3=$ 400.60
4= $ 400.80
5=$ 401.00
6= $ 401.20
7=$ 401.40
8= $ 401.60
9=$ 401.80
10= $ 402.00
The graph of the balance over every year is plotted. Here, we can see the increase in balance over the years.
What is compound interest?"Compound interest is the addition of interest to the principal sum of a deposit, or in other words, interest on principal plus interest."
Here, the principal is (P) = $400
The interest rate(r) = 5% = 0.05
The time period is = n years
Therefore, after n years balance is = P(1 + r)ⁿ
After 1 year, balance is = $400(1 + 0.05)¹ = $420
After 2 years, balance is = $420(1 + 0.05)¹ = $441
After 3 years, balance is = $441(1 + 0.05)¹ = $463.05
After 4 years, balance is = $463.05(1 + 0.05)¹ = $486.20
After 5 years, balance is = $486.20(1 + 0.05)¹ = $510.51
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Helppppp plz
Times New Roman, 14px
1.5pt B I U Ꭶ A Ꭺ
Part 1: Use a sequence to represent the air loss in a bike tire.
A manufacturer of bicycle tires performs an experiment to determine the daily loss of air when the cap on
a bicycle inner tube is loose. At the end of the experiment, the company concluded that customers can
expect to lose an average of 2.8 psi (pounds per square inch) per day when the bike is not in use.
1. One bike owner fills his tires to 98 psi on the first day of August, but does not realize that the caps are
loose.
I
a) Make a table showing the expected daily psi for the tires if no air is added for a week. (3 points)
b) What type of sequence can be used to represent the expected psi of the tires? Explain. (2 points)
c) Write the formula for the nth term in the sequence. (2 points)
Answer:
Have you gotten the answers yet?
Step-by-step explanation:
Answer:
here you go
Step-by-step explanation:
the second picture is to part D if you can't see it
What is the area of this figure? 6 m 14 m 4 m 20 m 4 m 12 m 6 m
Answer:
what figure
Step-by-step explanation:
From their locations in the diagram, what are two possible values for n and m?
The letters n and m represent two unknown numbers.
Explanation:
The mixed number 3 & 1/4 is the same as the improper fraction 13/4. It is a rational number since it's a fraction or ratio of two integers.
13/4 = 3.25 is not an integer. So that's why n is outside of the "integer" box, but inside the "rational" box.
In contrast, \(m = 2\pi\) is irrational because we cannot represent pi as a fraction of two integers. We can get an approximation like 22/7, but that won't be exact.
need help with geometry
To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:
Volume = π * r² * h
Substituting the given values, we have:
\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)
To solve for h, we divide both sides of the equation by 153.86:
h = 1500 / 153.86
h ≈ 9.75
Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.
Therefore, the height of the cylinder is 9.75 inches.
Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.
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I need help with questions 1,2, and 3. This class is microeconomics
Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.
What is budget?A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.
What is consumption?Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.
According to the given information:
To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.To know more about budget and consumption visit:
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