Answer:Rules for rotating points about the origin
1. The point (a,b) rotated 90° counterclockwise about the origin
becomes (-b,a).
A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)
A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)
B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)
C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)
D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)
Step-by-step explanation:
Suppose that X is a Bernoulli random variable with success probability 0.8. (Note: If this number is not already rounded to two decimal places, round it to two decimal places before proceeding.)
Calculate the mean of X. Round your answer to two decimal places.
5. A 12-ounce jar of jam costs $2.40. A 16-ounce jar costs $4.00. What is the
difference in the cost per ounce?
$
per ounce
The difference in the cost per ounce is $0.05 per ounce
Fractions and proportionFractions are written as the ratio of two integers
If a 12-ounce jar of jam costs $2.40, the cost per ounce will be:
Unit cost = 2.40/12
Unit cost = $0.2
Similarly, if a 16-ounce jar costs $4.00, the price of a ounce will be:
Unit cost = 4/16
Unit cost. =$0.25
difference = $0.25 - $0.2
difference = $0.05
Hence the difference in the cost per ounce is $0.05 per ounce
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The point (–1, 0.5) lies on the graph of
f –1(x) = 2x. Based on this information, which point lies on the graph of f(x) = log2x?
The point which would lie on the graph of f(x) = log2x is; (1, 0.301).
Which point would lie on the graph of f(x) = log2x?Since it follows from the task content that the given point (–1, 0.5) lies on the graph of f –1(x) = 2x.
The subsequent graph of f(x) = log2x would result from taking logarithms in which case, we have the graph passing through points determined as follows;
f(x) = log2^x
f(x) = x log2
Hence, when x = 1;
f(1) = 1log 2
Hence, we have point; (1, 0.301).
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
The width of the cooling tower at the base of the structure is 40 meters.
Width of the cooling towerGiven equation
x²/400 -(y-90)²/1600=1
Solving for the width
Cooling tower width =2√400
Cooling tower width=2×20
Cooling tower width=40 meters
Therefore the correct option is D. 40 meters.
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Answer:
40
Step-by-step explanation:
Evaluate function expressions
Answer:
Your answer is -24.
Step-by-step explanation:
Given information.
The graph of f(x) and g(x)
Solving for
-6 * f(3) - 6 * g(-1) = ?
think of f(x) = y as x is the input and y is the output.
Input a value of x into f(x) or g(x) gets us a y value.
Looking at the graph of f(3) = -2 and the graph of g(-1) = 6
Now substitute that and solve.
-6 * -2 -6 * 6 = 12 - 36 = -24
Answer: -24
Step-by-step explanation:
We should first find the outputs to the functions f and g with inputs 3 and -1 respectively. We can do this by looking at the graph and finding the y value for each desired x value.
Thus, we can see that f(3) = -2 and g(-1) is 6.
We can replace these into the expression to get
[tex]-6*-2-6*6[/tex]
We should first multiply, so we get
[tex]12 -36[/tex]
[tex]-24[/tex]
Hence, the answer is -24.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
1.The center of the circle lies on the x-axis
2.The radius of the circle is 3 units.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
(2^x+y , 3^x-y )= (16,9) find the value of x and y
Answer:
x=3,y=1
Step-by-step explanation:
2^x+y=16,3^x-y=9
16=2^4,9=3^2
x+y=4,x-y=2 add both
2x=6,x=3
3-y=2,y=1
If f(x) = 3x +3, which of the following is the inverse of
f(x)?
Answer: [tex]f^{-1}(x)=\frac{x-3}{3}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=3y+3\\\\x-3=3y\\\\y=\frac{x-3}{3}\\\\\therefore f^{-1}(x)=\frac{x-3}{3}[/tex]
What effect will replacing x with (x - 4)have on the
graph of the equation y = (x - 3)²?
A. slides the graph 4 units up
B. slides the graph 7 units down
OC. slides the graph 4 units right
D. slides the graph 1 unit right
Answer: D. slides the graph 1 unit right
Step-by-step explanation:
See attached image.
a bag contains 15 counters:7 red 4 blue and 4 green.a counter is taken out of the bag at random.what is the probability of choosing the following: a red or blue counter.
[tex]|\Omega|=15\\|A|=7+4=11\\\\P(A)=\dfrac{11}{15}\approx73.3\%[/tex]
Answer:
RED COUNTER: 7/15
BLUE COUNTER: 4/15
Hope it helps,
for further explanation do contact me
Suppose that the functions p and q are defined as follows. p(x)=x+1
q(x)=2x^2-2
The value of (p*q)(5) and (q*p)(5) is 288
How to determine the composite functions?The functions are given as:
p(x)=x+1
q(x)=2x^2-2
Calculate p(5) and q(5)
p(5)=5+1 = 6
q(5)=2(5)^2-2 = 48
The functions are then calculated as:
(p*q)(5) = p(5) * q(5)
(p*q)(5) = 6 * 48
(p*q)(5) = 288
Also, we have:
(q*p)(5) = (p*q)(5)
(q*p)(5) = 288
Hence, the value of (p*q)(5) and (q*p)(5) is 288
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Complete question
Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)
Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes.Solve the inequality. How many pounds of tomatoes can Lisa buy
Answer:
At maximum, she can buy 5 tomatoes.
Step-by-step explanation:
If you solve the inequality, as so:
1.2x+1.8 <=7.8
1.2x <= 6
x <= 5
A dry Waller wants to order core board for a 15-story elevator shaft. Each floor uses 18.5 sheets.Calculate the number of boards needed. Add 10%of the total for waste.
Answer:
305.25
Step-by-step explanation:
18.5 for one floor, multiply by 15 to get the amount for 15 floors: 18.5*15 = 277.5 sheets
We need to add 10% for waste, meaning 277.5 plus the waste: 1.1*277.5 = 305.25
The drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
How to determine the number of boards needed. Add 10%of the total for wastecalculate the number of core boards needed for the 15-story elevator shaft, we can follow these
Calculate the total number of sheets for all floors:
Total sheets = Number of floors × Sheets per floor
Total sheets = 15 floors × 18.5 sheets per floor
Total sheets = 277.5 sheets
Add 10% of the total for waste:
Waste percentage = 10% = 0.10 (in decimal form)
Waste sheets = Total sheets × Waste percentage
Waste sheets = 277.5 sheets × 0.10
Waste sheets = 27.75 sheets
Calculate the final number of boards needed (including waste):
Number of boards = Total sheets + Waste sheets
Number of boards = 277.5 sheets + 27.75 sheets
Number of boards = 305.25 sheets
Since you can't have a fraction of a sheet, we need to round up to the nearest whole number.
Therefore, the drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
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Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if thefoot of the ladder is placed 2.5 ft away from the wall
Answer:
sqrt(601)/2 ft
Step-by-step explanation:
The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.
The length of ladder used is 12.25 ft.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
example:
The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.
Solution:
Given : Hypotenuse = 16 units
Let us consider the given side of a triangle as the perpendicular height = 8 units
On substituting the given dimensions to the Pythagoras theorem formula
Hypotenuse^2 = Base^2 + Height^2
16^2 = B^2 + 8^2
B^2 = 256 - 64
B = √192 = 13.856 units
Therefore, the measure of the third side of a triangle is 13.856 units.
given:
base= 2.5 ft,
perpendicular= 12 ft
Using Pythagoras theorem,
H² = B² + P²
H² = 2.5² + 12²
H² = 6.25+ 144
H= 12.25 ft
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A set of 3 pens costs $1.68. At that unit price, how much would one pen cost?
Answer:
$.56
Step-by-step explanation:
To find the cost of one pen, take the total cost and divide by the number of pens
$1.68/ 3
$.56 per pen
A smart-phone is thrown upwards from the top of a 384-foot building with an initial velocity of 32 feet per
second. The height h of the smart-phone after t seconds is given by the quadratic equation
h 16t² + 32t + 384. When will the smart-phone hit the ground
Answer:
When t = 4
Step-by-step explanation:
The phone will hit the ground when h = 0.
[tex]16t^2 + 32t + 384 =0 \\ \\ t^2 + 2t + 24=0 \\ \\ (t+6)(t-4)=0 \\ \\ t=-6, 4[/tex]
However, as time cannot be negative, we know the answer is when t = 4.
Solve the inequality. -3x + 2x - 34 Enter the exact answer in interval notation.
Answer:
x = -34
Step-by-step explanation:
-3x + 2x -34 = 0
sum the x
-3x + 2x = -x
replace -x in the equation
-x -34 = 0
move -34 to other side
-x = 34
divide the two sides by -1 to get x value
x = -34
now replace x value in the equation:
-3(-34) + 2(-34) -34 =
102 -68 -34 =
102 -102 = 0
Find the value of x. Round to the
nearest tenth.
X
26
12
X
x = [?]
Answer:
Step-by-step explanation:
This is classic right triangle trig, cos specifically. Our reference angle is the one marked 26°, the hypotenuse is given as 12, and the side adjacent to the reference angle is our unknown. This is the cosine ratio. Setting up to solve for x:
[tex]cos26=\frac{x}{12}[/tex] and
12cos(26) = x Plug this into your calculator in degree mode to get that
x = 10.8
A tower is composed of a prism with a square base and a pyramid. The base length is 20 meters, and the height of the prism is 40 meters, while the slant height of the pyramid is 10√2 meters. What is the total surface area, including the bottom base? 400√2 + 3,600 m2 200√2 + 3,600 m2 400√2 + 400 m2 4000√2 m2
The total surface area of the tower composed of a prism with a square base and a pyramid is 3600 + 400√2 m²
How to find the surface are of a composite figure?Total surface area of the tower = area of the base + 4(area of the rectangular surface) + 4(area of the triangular surface)
Therefore,
area of the base = 20² = 400 m²
4(area of the rectangular surface) = 4(40 × 20) = 3200 m²
4(area of the triangular surface) = 4(1 / 2 × 10√2 × 20) = 4(100√2) = 400√2 m²
Therefore,
total surface area = 400 + 3200 + 400√2
total surface area = 3600 + 400√2 m²
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Answer:
a)400V2 plus 3,600 m2
Step-by-step explanation:
You randomly select an integer from 0 to 9 (inclusively) and then randomly select and integer from 0 to 7 what is the probability of selecting a 2 both times
Reason:
Set A = {0,1,2,3,4,5,6,7,8,9}
Set B = {0,1,2,3,4,5,6,7}
The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.
The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.
Multiply those fractions mentioned (1/10)*(1/8) = 1/80
This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.
Questions on a statistics exam are considered good questions provided the questions discriminate between students who have
studied for the exam and those who have not studied. Suppose that on a particular statistics exam the students were separated
into two gnpups, Group 1 that studied and Group 2 that had not studied. Data was collected and a 95% confidence interval for
the difference in the proportion of those passing the exam from Group 1 that studied and the proportion of those passing the
exam from Group 2 that had not studied. The confidence interval turned out to be (0.005, 0.125). Select the best answer.
Let P, = the proportion of Group 1 students that passed the exam
Let Py = the proportion of Group 2 students that passed the exam
The data fails to show with 95% confidence that these questions discriminated between those who studied and those who did
not study.
© We are 95% confident that those who studied had a higher passing rate than those who did not study.
We are 95% confident that those who studied had a lower passing rate than those who did not study.
None of the above
Using the interpretation of the confidence interval, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
The confidence interval of the difference is:
(0.005, 0.125).
Since the entire interval is positive, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
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What is the angle of rotation of the following figure?
This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.
What is the angle of rotation of a snow flake?
Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.
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The mean length of 3 childrens' index finger is 9.9cm.
The mean length of 3 adults' index finger is 13.2cm.
What is the mean length (rounded to 2 DP) of these 6 people's index finger?
The mean length of the 6 people's index finger is 11.55
How to determine the mean length?The given parameters are:
Mean length of 3 children = 9.9 cmMean length of 3 adults = 13.2 cmThe mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{3 * 9.9 + 3 * 13.2}{3 + 3}[/tex]
Evaluate
[tex]\bar x = \frac{69.3}{6}[/tex]
Divide
[tex]\bar x = 11.55[/tex]
Hence. the mean length of the 6 people's index finger is 11.55
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y>2 and ysx
B. y 22 and y
C. x>2 and y2x
D. x22 and y> x
Answer: B
Step-by-step explanation:
The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].
This allows us to eliminate all the options except for B.
find x and y pls help
30 + 110 + 30 + 110 = 280
360-280 = 80
2y = 80
y = 40 degrees
If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.
30 + 40 = 70
The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.
In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180
Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.
Angles in triangle add to 180.
180 - 110 - 30 = 40.
Thus, x = 40 degrees
There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)
Hope this helps!
Which equation could possibly represent the graphed function?
Answer: A
Step-by-step explanation:
The polynomial has roots at [tex]x=-4, -2, 4[/tex].
So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].
This eliminates everything except for A.
the sum of a number increased by three and the number decreased by seven
Answer is (n + 3) + (n - 7)
Simplified to 2n - 4
Using “n” for number
Which number line represents the solutions to |x + 4| = 2?
Answer: Option 1
Step-by-step explanation:
[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]
Solve Absolute Value.
| x + 4 | = 2
We know either x + 4 = 2 or x + 4 = −2
x + 4 = 2 (Possibility 1)
x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)
x = -2
x + 4 = −2 (Possibility 2)
x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)
x = -6
Answer: x = - 2 or x = -6
Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.
please give detailed answer of the question.
The resulting coordinates for each row are (-2, 2), (0, 4),()2, 6), (6, 10) and (8,12) respectively
Functions and valuesGiven the linear function expressed as;
y = x + 4
where
x are the input values and y are the output values
If x = -2
y = -2+4
y = 2
The coordinate (x, y) will be (-2, 2)
If x = 0
y = 0+4
y = 4
The coordinate (x, y) will be (0,4)
If x = 2
y = 2+4
y = 6
The coordinate (x, y) will be (2, 6)
If x = 6
y = 6+4
y = 10
The coordinate (x, y) will be (6,10)
If x = 8
y = 8+4
y = 12
The coordinate (x, y) will be (8, 12)
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Using the following accounts and balances, prepare the “Stockholders’ Equity” section of the balance sheet. 60,000 shares of common stock authorized, and 4,000 shares have been reacquired.
Common Stock, $50 par $2,400,000
Paid-In Capital from Sale of Treasury Stock 48,000
Paid-In Capital in Excess of Par—Common Stock 576,000
Retained Earnings 1,368,000
Treasury Stock 25,000
The total Stockholders’ Equity is $4,367,000
Total Stockholders’ EquityCommon Stock, $50 par $2,400,000
Paid-In Capital in Excess of Par—Common Stock $576,000
Paid-In Capital from Sale of Treasury Stock $48,000
Total paid in capital $3,024,000
Retained Earnings $1,368,000
Less Treasury stock $25,000
Total Stockholders’ Equity $4,367,000
Therefore the total Stockholders’ Equity is $4,367,000.
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