The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
Transformation of functionsTransformation is the technique used to change the position of a figure on an xy-plane.
Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
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What is the probability of rolling an even number on a
standard dice? Give your answer in its simplest form.
What is the solution for w in the equation?
w+1/2=1/4w+2
A. 4
B. 2
C. 10/3
D. 9/3
Answer:
B. 2
w=2
Step-by-step explanation:
hope this helps!
Explain how the diagram demonstrates the Pythagorean Theorem for a right triangle with legs of length 2.
|AC|^2 = |AB|^2 + |BC|^2 is indeed the Pythagorean theorem which implies that adding the hypotenuse square as well as the two sides of a right triangle equals the hypotenuse square.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
Calculating value by using the Pythagorean theorem:
The smallest side of the triangle in this instance contains 2 dots, which equals.
The triangle's bigger side has 3 dots.
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Choose the expression that is equivalent to 9w² +(20w² - 15w+10) +2w.
OA. 9w² - 17w +6
B. 21w² -7w+10
C. 21w²-7w+6
D. 9w² -w+10
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 9w² - 13w + 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + (20 {w}^{2} - 15w + 10) + 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w + 10+ 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w +2w + 10[/tex]
[tex]\qquad \tt \rightarrow \: 29 {w}^{2} - 13w + 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
For which of the given p-values would the null hypothesis be rejected when performing a level 0. 05 test?.
Using a significance level of 0.05, the null hypothesis would be rejected for p-values less than 0.05.
What is the relation between the p-value and the conclusion of test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.Hence, the null hypothesis would be rejected for p-values less than 0.05.
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Decrease the number 14.4 by 0.2 of it.
The result of the decrease of the number 14.4 by 0.2 of it is of 14.2.
What does it mean to decrease a number a by b of it?The equivalent operation is the subtraction of a by b.
In this problem, we want to decrease the number 14.4 by 0.2 of it, hence the operation is:
14.4 - 0.2 = 14.2.
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Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?
O xx-5
0 x>-5
O x>-1
O x<-1
Answer:
x > -5
Step-by-step explanation:
[tex] \frac{2}{5} (x - 1) < \frac{3}{5} (x + 1)[/tex]
[tex]2(x - 1) < 3(x + 1)[/tex]
[tex]2x - 2 < 3x + 3[/tex]
[tex] - 5 < x[/tex]
[tex]x > - 5[/tex]
Below, the two-way table is given for a class
of students.
Freshmen
Male
4
Female 3
Total
Sophomore
6
4
Juniors Seniors Total
2
6
23
2
If a student is selected at random, find the
probability the student is a freshman.
P(Freshman) = [? ]%
Round to the nearest whole percent.
Answer:
23%
Step-by-step explanation:
There are 7 Freshman total
There are 30 students total
The probability of picking a Freshman is 7/30 or 23%
Janelle has one dime and several nickels in her coin purse. The table below describes the relationship between the number of nickels, n, and the total value of the coins in her coin purse in cents, c.
n c
6 40
7 45
8 ?
9 55
If Janelle has 8 nickels in her coin purse, what is the total value of the coins?
a. 52 cents
b. 50 cents
c. 48 cents
d. 46 cents
The graph shows the speed of Sam’s car over time.
A graph titled Speed of Car. The horizontal axis shows time (hours) and the vertical axis shows speed (m p h). Both axes are unnumbered. A line appears in 4 sections, labeled A, B, C, D. Section A shows a rise in speed over time, sections B and D maintain a level speed over time, and section C shows a reduction in speed over time.
Which best describes what is happening in section C?
The car start decelerating in section c of the graph.
The graph is a demonstration of curves which gives the relationship between x and y axis.
Here, section A show the rise in speed of car over time. Meanwhile The curve is increasing curve.
B and D shows maintain level of speed means the curve is straight line and for every value of x there is only one y.
But at section C the speed of car reducing. Meanwhile, the car decelerating and the curve is of decreasing order over the time.
Thus, for section C, car is decelerating and the curve is of decreasing nature over time upto D.
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Answer:
the car is traveling at a constant speed (answer is D)
Step-by-step explanation:
im just smart like dat
It takes, on average, 6 minutes to do all the steps but the actual time can vary according to an exponential distribution with a standard deviation of 6 minutes. Assume students arrive on average every 6.6 minutes and their inter-arrival times are also exponentially distributed. What is the expected waiting time in this system according to the Kingman (PK) Formula
The expected waiting time is 1.2 minute
According the statement
We know that the kingman formula is
[tex]{ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }[/tex]
According to statement the mean value μs is 6 min.
Here the value of P is 6/36 = 1/6
And the value of ca and cs is 1
Substitute the values in formula then
[tex]{ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = 1.22[/tex]
So, the expected waiting time is 1.2 minute
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An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth, what is the area of the screw head?
The area of the screw head is 93.5m².
How to calculate the area?The area of the hexagon can be illustrated based on the formula:
A = 3✓3/2 × a²
Base = 12.
Height = 3.
Area of each triangle = 0.5 × 12 × 3 = 18
Area of the rectangle = 12 × 6 = 72
Therefore the area of the screw head will be:
= 3√3/2 × 72
= 93.5m²
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Professor Nwamabi is conducting an experiment in which he is examining the effects of air conditioning on sleep habits. 100 participants are randomly assigned into two groups, one of which sleeps for a week in an air conditioned setting and of which sleeps in a room without air conditioning. After a week he has various physiological markers assessed to see if the groups are different. In this research, the use of air conditioning represents a(n) ________ variable.
In the research of Professor Nwamabi the use of air conditioning represents independent variable.
Given 100 participants are randomly selected in a research in which effects of air conditioning on sleep habits is studied.
Dependent variable is the variable whose value is dependent on the other variables like increase in profit and production.
Independent variable is the variable whose value is not dependent on the other variables.
In the research of Professor Nwamabi in which he is examining the effects of air conditioning on sleep habits, use of air conditioning represents independent variable. In this study the effect is on sleep habits means the value of sleep habits will change due to use of air conditioning. It shows that the use of air conditioning is not depending on other variable in the research.
Hence the use of air conditioning represents the independent variable.
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If a gallon of gas costs 368 9/10 cents, how much does 1/2 gallon cost?
Answer:
[tex]737\frac{4}{5}[/tex]cents
Step-by-step explanation:
1 Gallon of Gas = 368.9 cents (Note: 9/10 = 0.9)
1/2 Gallon of gas = [tex]\frac{368.9}{\frac{1}{2} }cents\\ =368.9 * 2\\= 737.8 cents[/tex]
or [tex]737\frac{4}{5}[/tex] cents (Reduced to simplest form)
A store owner tracks the number of online orders she receives each week since the start of a new advertising campaign and graphs the data. Use the graph to select the true statement about the function that models the given situation. A. The function is linear and is growing by equal differences over equal intervals. B. The function is exponential and is growing by equal percentages over equal intervals. C. The function is exponential and is growing by equal differences over equal intervals. D. The function is linear and is growing by equal percentages over equal intervals.
The true statement about this function which models the given situation is: A. the function is linear and is growing by equal differences over equal intervals.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
By critically observing the graph which models the given situation, we can infer and logically deduce that the true statement about this function is that the function is linear and is growing by equal differences over equal intervals.
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A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
c = 4 times h
Linear equation: 1.5c + 2h = 360
Hello!
Your answer should be..
c=4h ( as there are 4 hours )
1.5c+2h=360
c is 1.50 and h is 2.00 so you must add them to reach 360
Hope this helps! :)
PLEASE HELP I DONT UNDERSTAND I HAVE A FEW MIN TO SUBMIT
Answer:
Increasing: [tex](\infty, -1) \cup (2, \infty)[/tex]
Decreasing: [tex](-1, 2)[/tex]
Step-by-step explanation:
So when an equation has and odd degree, it will go in the opposite direction on both ends, so if y went towards infinity as x went towards infinity, then y would go towards negative infinity as x goes towards negative infinity. In this case, by looking at the graph it has an odd degree, due to opposite end behaviors, although on both ends it's increasing because even though it appears that it's going down on the left side, that's only if you start from the right and go towards the left. So it's really increasing from negative infinity to -1, and then it decreases from -1 to 2, until it once again starts increasing from 2 to infinity. This can be represented as (-infinity, -1) U (2, infinity) for increasing and (-1, 2) as decreasing
What is the area of the triangle side whose sides are 51cm, 37cm and 30cm respectively find
The area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².
The area of a triangle can be computed by the formula √{s(s - a)(s - b)(s - c)}, where a, b, and c, are the three sides of the triangle, and s is the semi-perimeter of the triangle, that is, s = (a + b + c)/2.
In the question, we are asked to find the area of the triangle, whose sides are 51cm, 37cm, and 30cm.
Thus, we take a = 51cm, b = 37cm, and c = 30cm.
The perimeter of the triangle = a + b + c = 51cm + 37cm + 30cm = 118cm.
Hence, the semi-perimeter of the triangle, s = (a + b + c)/2 = 118cm/2 = 59cm.
Hence, using the formula for the area of the triangle:
√{s(s - a)(s - b)(s - c)}
= √{59(59 - 51)(59 - 37)(59 - 30)} cm²
= √{59 * 8 * 18 * 29} cm²
= √246384 cm²
= 496.37 cm².
Thus, the area of the triangle with sides of 51cm, 37cm, and 30cm, is calculated to be 496.37cm².
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Directions: Find the product and simplify
Answer:
x^4-9x^2+26x-24
Step-by-step explanation:
Answer:
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
Step-by-step explanation:
[tex](x - 3)( {x}^{2} - 6x + 8)[/tex]
[tex] {x}^{3} - 6 {x}^{2} + 8x - 3 {x}^{2} + 18x - 24[/tex]
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
Find y. right triangles
Answer:
√2
Step-by-step explanation:
Angle ( θ ) = 45
Hypotenuse side = 2
Opposite side = x
Formula : -
sin θ = Opposite side / Hypotenuse side
Note :
The value of sin 45 = 1/√2
sin 45 = x/2
1/√2 = x/2
Cross multiply,
x*√2 = 2*1
x√2 = 2
2 can be simplified as √2 * √2
x√2 = √2*√2
Divide √2 on both sides,
x = √2
2. when a newspaper poll produces a statistic that is biased, it means that
When a newspaper poll produces a statistic that is biased, it mean that
(b) Repeated polls would give, results that are very different from each other.
What is biased in statistics?Statistical bias is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters when people say that the newspaper poll is biased, they mean that:
(b) Responding was voluntary, and only these with access and interest would answer.
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Complete question:
When a newspaper poll produces a statistic that is biased, it means that
(a) Repeated polls would give the truth, about the population, in the same direction.
(b) Repeated polls would give results that are very different from each other.
(c) Repeated polls would give results that would not yield a normal distribution.
(d) Repeated polls would give results that are very similar to each other.
If 7846, 7896 and 8802 are rounded to the nearest hundred and then added, the answer will be
Answer:
the answer is 24500
Step-by-step explanation:
7800+7900+8800
=24500
GEOMETRY) The question is on the picture below!
Answer:
C = 100 degrees
B = 70 degrees
Step-by-step explanation:
OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTARY, WHENEVER YOU ADD THEM THEY SHOULD GIVE YOU 180 DEGREES.
SOLUTION
A + C = 180
80 + C = 180
C = 100
D + B = 180
110 + B = 180
B = 70
PLEASE HELP!! ASAP!!!!!
Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (3, 4) and (5, 0). a A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14. b A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6. c A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5. d A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is labeled y with entries negative 26, negative 14, 34, 46.
The linear function with the same y-intercept with the graphed function is: table A.
What is a Linear Function?The equation that models a linear function is, y = mx + b, where m is the slope and b is the y-intercept.
Slope of the graphed function = rise/run = - 2/1 = -2
Using one of the points on the line (x, y) = (5, 0) and the slope, m = -2, find the y-intercept (b) by substituting the values into y = mx + b:
0 = -2(5) + b
0 = -10 + b
10 = b
b = 10
The slope (m) of the graphed function is -2, and the y-intercept (b) is: 10.
Slope (m) of table A = change in y/change in x = (14 - 8)/(3 - 1) = 3
Substitute a point (x, y) = (1, 8) and slope (m) = 3 into y = mx + b to find the y-intercept (b):
8 = 3(1) + b
8 - 3 = b
5 = b
b = 5
Therefore the table with the same y-intercept as the graphed function is table A.
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The function P(t) = 21e^0.01823t represents the population of Texas, in millions, t years after 2000. What was the population of Texas in the year 2000? Write your answer in millions (for example 4,000,000 would be expressed as 4).
The population in the year 2000 is 21
How to determine the population in 2000?The function is given as:
P(t) = 21e^0.01823t
The year 2000 is 0 years after 2000.
This means that
t = 0
So, we have:
P(0) = 21e^(0.01823 *0)
Evaluate the product
P(0) = 21e^0
Evaluate the expression
P(0) = 21
Hence, the population in the year 2000 is 21
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A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). If two cards are drawn from the deck and then replaced back into the deck each time, what is the probability of drawing a heart and a spade from the deck of cards?
answer options:
1/8
1/26
1/16
1/32
[tex]\large\boxed{\frac{1}{16}}[/tex]
The answer is equal to the probability of drawing a heart multiplied by the probability of drawing a spade.
The probability of a given suit being drawn is [tex]\frac{13}{54}[/tex], which simplifies to [tex]\frac{1}{4}[/tex]. This is because there are 13 outcomes we would like out of 54 possible outcomes in total.
Multiply [tex]\frac{1}{4}[/tex] by itself (square it) to get the final answer of [tex]\frac{1}{16}[/tex].
Answer corrected. Originally said [tex]\frac{1}{8}[/tex] as the final answer. Thank you, sangers1959!
Solve the following problem using linear systems: You have a bottle of a 2% solution of iodine and a bottle of a 66% solution of iodine. You need 16 liters of a 47% solution. How many liters of the 2% and 66% solutions should you mix together?
The quantity of liters of the 2% and 66% solutions should you mix together is 4.75 and 11.25 liters.
let
x = liters of 2% solutiony = liters of 66% solutionx + y = 16
0.02x + 0.66y = 0.47 × 16
from (1)
x = 16 - y
Substitute into (2)
0.02x + 0.66y = 0.47 × 16
0.02(16 - y) + 0.66y = 7.52
0.32 - 0.02y + 0.66y = 7.52
- 0.02y + 0.66y = 7.52 - 0.32
0.64y = 7.20
y = 7.20/0.64
y = 11.25 liters
Substitute y = 11.25 liters into (1)
x + y = 16
x + 11.25 = 16
x = 16 - 11.25
x = 4.75 liters
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1. Write the following rational numbers as quotients of two integers.
a) -0.5 b) - 2/1/4 c) -5/6/7 d) 7.2
Answer:
a) -0.5 = -1/2
b) -2/1/4 = -2/4
c) -5/6/7 = -5/42
d) 7.2 = 72/10
Step-by-step explanation:
Please help I need this by tommorrow
Answer:
I think you would have to do 2 times 7
Answer:
h = 2.5cm or 5/2 cm
Step-by-step explanation:
Vol = Basearea•h
In your question, the base is the triangle shape. The rectangles go around the sides of the 3-d shape and on top is another triangle that we can't really see. In your image it is kind of laying on its side. So if we stand it up properly, the triangles are on the top and bottom. The triangle is the base.
Volume was given; it is 35. Also given is one side of the rectangles, that is 7.
So we can fill in 35 and 7 into the volume formula and calculate the Basearea.
V = B • h
35 = B • 7
35 = 7B
Divide by 7.
5 = B.
We have calculated the Basearea. This is the area of the triangle shaped bottom. The area formula for a triangle is:
A = 1/2bh
We just found that A=5 and we were given that the base of the triangle is 4.
A = 1/2bh
5 = 1/2•4•h
5 = 2h
Divide by 2.
5/2 = h
This is the height of the triangle, h in the picture. (The h in the volume formula and h in the triangle are different)
This is what the question is asking for, h = 5/2 or in decimals, h = 2.5cm
If m/BOC= 27 and m/AOC = 47, then what is the measure of ZAOB? The diagram is not to scale.
D.
B
40
Ob 24
Oc
20
Od
54
74
30
e
Of
The measure of m ∠A0B is 20. Option C
How to determine the value of angle AOBm ∠BOC = 27
m ∠AOC = 47
m∠A0B = unknown
But note that the sum of m ∠BOC + m ∠A0B = m ∠AOC
We have,
27 + m ∠A0B = 47
m ∠A0B = 47 - 27
m ∠A0B = 20
Therefore, the measure of m ∠A0B is 20. Option C
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