f(5) = -4(5 - 1)
f(5) = -4(4)
f(5) = - 16
f(x) = |x+1|-1; vertical stretch by a factor of 3
The image of the function after vertically stretched by a factor of 3 is f'(x) = 3|x + 1| - 3
How to determine the equation of f(x) after the transformation?From the question, the given parameters are:
f(x) = |x + 1| - 1
The transformation is given as
Vertical stretch by a factor of 3
This implies that we stretch the function f(x) by a factor of 3 across the origin
Mathematically, this transformation can be represented as
(x, y) = (x, 3y)
When represented as a function, we have
f'(x) = 3 * f(x)
Substitute the equation f(x) = |x + 1| - 1 in the equation f'(x) = 3 * f(x)
So, we have the following equation
f'(x) = 3 * (|x + 1| - 1)
Remove the bracket
So, we have
f'(x) = 3 * |x + 1| - 3 * 1
Evaluate the products
So, we have
f'(x) = 3|x + 1| - 3
Hence, the equation of f'(x) is f'(x) = 3|x + 1| - 3
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Hits to a high-volume Web site are assumed to follow
a Poisson distribution with a mean of 10,000 per day.
Approximate each of the following:
(a) The probability of more than 20,000 hits in a day
(b) The probability of less than 9900 hits in a day
(c) The value such that the probability that the number of hits
in a day exceeds the value is 0.01
(d) Approximate the expected number of days in a year (365
days) that exceed 10,200 hits.
(e) Approximate the probability that over a year (365 days)
more than 15 days each have more than 10,200 hits
Given the following, (a) 100 (a) 0 (b) 0.1587 (c) 10233 (d) 8.322 (e) 0.0096
How can I tell if the distribution of my data is Poisson?The ratio of variance to mean in a sample in n counts from a distribution with a Poisson coefficient ought to correspond to a Chi-square population with n-1 angles of freedom. This test depends on the fact that the mean and variance of the Poisson distribution are identical.
a)
Here for Poisson distribution
Here mean of distribution=μ=λ= 10000
Variance =σ2=λ= 10000
Standard deviation σ=√λ= 100.000
Considering that λ is big, we can approximate:
a)
Probability of more than 20000 hits in a day:
Probability =P(X>20000)=P(Z>(20000-10000)/100)=P(Z>100)=1-P(Z<100)=1-1=0
if using ti-84 press -2nd -vars - command :normal cdf(20000,1 2nd EE 99,10000,100)
b)
P(less than 9900 hits):
Probability =P(X<9900)=(Z<(9900-10000)/100)=P(Z<(-1)=0.1587
If using ti-84 press 2nd -vars - command :normalcdf(-1 2nd EE 99,9900,10000,100)
c)
For top 0.01 or 99th percentile critical value of z=2.33
Therefore corresponding value=mean+z*std deviation=10233
If using ti-84: press 2nd-vars-invNorm(0.99,10000,100)
d)
Probability of exceeding 10200:
Probability =P(X>10200)=P(Z>(10200-10000)/100)=P(Z>2)=1-P(Z<2)=1-0.9772=0.0228
Therefore expected number of days that exceed 10200 hits =np=365*0.0228=8.322
e)
Mean of distribution=μ=np= 8.3220
and standard deviation σ=sqrt(np(1-p))= 2.8517
For normal distribution z score =(X-μ)/σx
P(more than 15 days has more than 10200 hits):
Probability =P(X>15)=P(Z>(15-8.322)/2.852)=P(Z>2.34)=1-P(Z<2.342)=1-0.9904=0.0096
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how many ice cream servings can the 5 sisters buy if they only want to spend 10.00$ on ice creams. Write an inequality. Ice creams is 2.80$
Let the number of ice-cream serving the sisters can buy be "s".
Each serving is $2.80, so the cost of "s" ice-creams will be:
[tex]2.80s[/tex]This cost cannot exceed 10 dollars.
10 dollars is the maximum.
So, we can say that "2.80s" is equal to or less than 10.
We write it in inequality notation:
[tex]2.80s\leq10[/tex]Solving for "s":
[tex]\begin{gathered} 2.80s\leq10 \\ s\leq\frac{10}{2.80} \\ s\leq3.57 \end{gathered}[/tex]So, the logical solution is that the 5 sisters can buy 3 ice-cream servings with their budget.
The lengths of two sides of a triangle are 8 and 17. What is one possible length of the third side?
One possible length of the third side of the given triangle is 15
Determining a possible length of a side of a triangleFrom the question, we are to determine a possible length of the third side of the triangle
From one of the properties of a triangle, we know that
The sum of any two sides of a triangle is greater than the third side and the positive difference of any two sides of a triangle is lesser than the third side.
Thus,
8 + 17 is greater than the third side
25 is greater than the third side
and
17 - 8 is lesser than the third side
9 is lesser than the third side
If the third side of the triangle is x,
Then,
9 < x < 25
Hence, a possible value of x is 15
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7 1/4 dividend by 1 2/3
Answer:
6.2
Step-by-step explanation:
i got this answer by guessing, srry.
2x2 and the times tables
Explanation:
The question asked for
[tex]2\times2,and\text{ }the\text{ }times\text{ }table[/tex]Concept:
2 times 2 means the addition of 2 in 2 places
[tex]\begin{gathered} 2\times2=2+2 \\ 2\times2=4 \end{gathered}[/tex]The time table is given below as
Hence,
The final answer is
[tex]\Rightarrow2\times2=4[/tex]An artist mixes yellow and blue paint to make the perfect shade of green.she uses 2 ounces of blue paint for every 7 ounce of yellow. How many ounces of yellow will the artist need to add to 12 ounces of blue
- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. What is thelength of the shortest side?
Let's name the a, b, c
let side a = x
let side b = 4+x
Let side c = hypotenuse = 20
Using the law of pythagoras
opposite² + adjacent² = hypotenus²
x² + (x+4)² = 20²
open the parenthesis
x² + x² + 4x +16 = 400
2x² + 4x + 16 = 400
2x² + 4x + 16 - 400 = 0
2x² + 4x - 384 = 0 --------------------------------(1)
The is now a quadratic equation
so we will solve and find x
Using the formula method
Quadratic formula is
[tex]x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Comparing equation (1) with ax² + bx + c = 0
a = 2 b = 4 and c= -384
Inserting the values into the formula
[tex]x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}[/tex]simplifying the above
[tex]x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}[/tex][tex]undefined[/tex](7, 17)
(-4,0)
(-3,-13)
(2,2)
(5,10)
Understanding Ratios
Eliza is a chef at a restaurant. She is making spaghetti sauce and put 21 tomatoes and 6 onions in the pot. Wh
tomatoes to onions in the pot?
Answer: The Answer is 7:2
Step-by-step explanation:
is 7:2
EspanA parachutist's speed during a free fall reaches 75 meters per second. What Is this speed in feet per second? At this speed, how many feet will the parachutistfall during 20 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.Speed:Distance fallen in 20 Seconds:
The speed of the parachutist is falling is 75m/s.
You have to express the speed of the fall in ft/s.
1m is equal to 3.3ft
To express the speed in ft per second, given that the time unit is the same, you have to multiply 75m/s by 3.3
[tex]75\cdot3.3=247.5[/tex]The speed, expressed in feet per second, is 247.5ft/s
This means that the parachuter falls 247.5ft every second, to determine the distance fallen in 20 seconds, you have to multiply the speed by the time:
[tex]247.5\cdot20=4950[/tex]After 20 seconds he will fall 4950ft
Write an equation for this phrase "2 cubed is equal to the square root of x"
2 cubed means that you have to make the axponent of 2 by 3, symbolically:
[tex]2^3[/tex]The square root of x can be symbolized:
[tex]\sqrt[]{x}[/tex]If both terms are equal then you can put them together as:
[tex]2^3=\sqrt[]{x}[/tex]This is the expression that sumbolizes the phrase.
Solve on the interval [0,27): 2 cscx -3 = -5 ОА. Зл 2 O 2T 4T B. 3.3 7 T 1 IT c O T O D. IS
Answer:
[tex]x\text{ = }\frac{3\pi}{2}[/tex]Explanation:
We want to get the value of x on the interval for which the identity holds true
We have this as follows:
[tex]\begin{gathered} \csc \text{ x = }\frac{1}{\sin \text{ x}} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -5+3} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -2} \\ \\ \sin \text{ x = -1} \\ \\ x\text{ = }\sin ^{-1}\text{ (-1)} \\ \\ x\text{ = }\frac{3\pi}{2} \end{gathered}[/tex]If m∠4 = 96 and m∠5 = 138, what is m∠3?
Applying the triangle sum theorem, the measure of angle 3 = 54°.
What is the Triangle Sum Theorem?The triangle sum theorem is the theorem that justifies why the sum of all the interior angles of a triangle is equal to 180 degrees.
Given the following measures:
Measure of angle 4 = 96°Measure of angle 5 = 138°Measure of angle 1 = 180 - m∠4 [linear pair have a sum of 180 degrees]
Substitute
Measure of angle 1 = 180 - 96
Measure of angle 1 = 84°
Measure of angle 2 = 180 - m∠5 [linear pair have a sum fo 180 degrees]
Substitute
Measure of angle 2 = 180 - 138
Measure of angle 2 = 42°
Therefore:
Measure of angle 3 = 180 - m∠1 - m∠2 [triangle sum theorem]
Substitute
Measure of angle 3 = 180 - 84 - 42
Measure of angle 3 = 54°
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complete the two way relative frequencies using decimels, and round to three places.
To complete the second table, you need to divide all cells in the first table by 41. obtaining:
Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.70.09Enter a number as an exact integer or decimal.eBookSubmit Answer
The given fraction is
[tex]\frac{0.7}{0.09}[/tex]Using a calculator, we have
[tex]\frac{0.7}{0.09}=7.77777777777\ldots[/tex]However, rounded to the nearest tenth would be
[tex]7.7777777777\ldots=7.8[/tex]Therefore, the answer is 7.8.Stretch or compress each linear function. Let g(x) be a vertical stretch of f(x)=2x-2 by a factor of 5. Write the rule for g(x).
If g(x) = cf(x), then g(x) is a vertical stretch of f(x) by a factor of c. It means that the rule for g(x) is:
g(x) = 5*f(x)
Replacing f(x) by 2x - 2, we get:
g(x) = 5*(2x - 2)
g(x) = 5*2x - 5*2
g(x) = 10x - 10
Answer: g(x) = 10x - 10
Find the domain of f and write your answer in interval notation. f(x) = 9/10 + 4x + 6
The domain of a function is the set of all posible values that its input can take.
To find it, we should analyze the rule of correspondence of the function to see if it includes restrictions over the variable that works as input. In this case, we can see that x appears inside a square root. The expression inside the square root must be greater or equal to 0. Then:
[tex]\begin{gathered} 10+4x\ge0 \\ \Rightarrow4x\ge-10 \\ \Rightarrow x\ge-\frac{10}{4} \\ \Rightarrow x\ge-\frac{5}{2} \end{gathered}[/tex]The domain of f is the set of all real numbers x such that:
[tex]-\frac{5}{2}\le x[/tex]In interval notation:
[tex]x\in\lbrack-\frac{5}{2},\infty)[/tex]Therefore, the domain of the function is:
[tex]\lbrack-\frac{5}{2},\infty)[/tex]which expression represents the sum of 173and32,times by 5
EXPLANATION
The expression that represents the sum of 173 and 32 times by 5 is
(172+32)x5 [OPTION C]
Use the following situation to complete Exercise 7. 7. The school photography club charges $10 for each photo in its annual pet photolontest. The club wants to save $75 of its earnings for a pizza party. The club members also want to have at least $50 left over after the pizza party to pay for other club expenses. Write an expression for: a. how much money the club earns by taking p pet photos
Answer:
10p
Explanation:
We are told that the photography club charges $10 for each photo; therefore, if we have p number of photos then the total amount charged will be 10 * p = 10p
is 10% greater than or less than 1/8
is 10% greater than or less than 1/8 ?
Convert both of the given to decimals
So, 10% = 10/100 = 0.1
And 1/8 = 0.125
so, 10% is less than 1/8
Find the distance between the two points:(7,12), (1,4)
In order to find the distance between the given points, use the following formula:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]where (x1,y1) and (x2,y2) are the given points,
In this case, you have:
(x1,y1) = (1 , 4)
(x2,y2) = (7 , 12)
By replacing the previous values into the formula for d, you obtain:
[tex]\begin{gathered} d=\sqrt[]{(12-4)^2+(7-1)^2} \\ d=\sqrt[]{8^2+6^2^{}} \\ d=\sqrt[]{64+36} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]Hence, the distance between the given points is 10
Graph the function f(x)=3/2x−4.Use the line tool and select two points to graph.
We are meant to graph the function
f(x)=3/2x − 4.
Please answer with a detailed explanation.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The Domain of the function is [0,230].
Given that,
In the picture there is a question with a graph.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The graph displays the height of the golf ball above the ground in yards as a quadratic function of x, the golf ball's horizontal distance from the box in yards.
We have to find the domain of the function in the situation.
The domain is nothing but All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a graph is every value in the graph, from left to right. The graph's entire range, from lower to higher numbers, represents the range.
Therefore, the Domain of the function is [0,230].
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A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.
Labor-Hours per Ski
Maximum Labor-Hours
Available per Day
Department
Fabricating
Finishing
Trick Ski
6
1
Slalom Ski
4
1
132
30
If the profit on a trick ski is $50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maxi
What is the maximum profit?
The maximum profit will be $2,700.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The profit on a trick ski is $50 and the profit on a slalom ski is $30.
Let the number of Trick ski manufactured = x
And, Number of slalom ski manufactured = y
So, Maximize;
P = 50x + 30y
Subject to we get;
6x + 4y ≤ 108
And, x + y ≤ 24
And, xy ≤ 0
Now, We have to find set of feasible solutions graphically for the number of each type of ski that can be produced.
So, Linear equation in slope form;
6x + 4y = 108
y = -1.5x + 27
And, x + y = 24
y = - x + 24
So, By the graph we get;
The points,
(x , y) = (0, 24) , (6 , 18) (18, 0)
Hence, The maximum profit when 6 trick ski and 18 slalom ski manufactured.
maximum profit = 6 x 50 + 18 x 30 = 840
And, The maximum profit when 18 trick ski and 0 slalom ski manufactured.
maximum profit = 18 x 50 = 900
The maximum profit when 0 trick ski and 24 slalom ski manufactured.
maximum profit = 24 x 40 = 960
Thus, The maximum profit = 840 + 900 + 960
= $2,700
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4 - 3(x-3) = 5(x+2) - 8xSolve for the variable in the equation shown
Given:
The equation is,
[tex]4-3(x-3)=5(x+2)-8x[/tex]Simplify the equation,
[tex]\begin{gathered} 4-3\mleft(x-3\mright)=5\mleft(x+2\mright)-8x \\ \text{LHS}=4-3(x-3) \\ =4-3x-3\times(-3) \\ =4-3x+9 \\ =13-3x\ldots\ldots\text{.}\mathrm{}(1) \\ \text{RHS}=5(x+2)-8x \\ =5x+5(2)-8x \\ =-3x+10\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Now,
[tex]\begin{gathered} 13-3x=-3x+10 \\ -3x=-3x+10-13 \\ -3x=-3x-3 \\ \Rightarrow-3=0 \\ \Rightarrow No\text{ solution} \end{gathered}[/tex]Which inequality is true for all real numbers? Check all that apply.
a-b
ac≥ bc
If az b, then a + c≥ b + c
If c> d, then a-c
If a
The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
What do math inequalities mean?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality. Some people receive better and more skilled care in the medical field than others.The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
The alternate options are incorrect. For instance, the first option, a - b a + b, is false because the expression would be ruined if you don't apply the same adjustment to both sides of the inequality.
Both options 2 and 5 are incorrect.
The proper responses are thus 3 and 4.
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Answer:
3,4
Step-by-step explanation:
The perimeter of a square is equal to four times the length of its side. Write the direct variation equation that represents this situation.
Let y be the dependent variable and let x be the independent variable.
The linear equation representing this situation will be y = 4x, where y is the dependent variable and x is the independent variable.
As per the question statement, it is given that the perimeter of a square is equal to four times the length of its side and we are supposed to write the direct variation equation that represents this situation.
Also given that we have to use "y" and "x" which are dependent and independent variables respectively.
Perimeter = 4*side
So we conclude that perimeter is dependent on the independent value of side of the square.
Therefore, y = 4x would be the appropriate linear equation depicting the situation given.
Linear equation: An equation is said to be linear if the maximum power of all the variables are consistently 1.Dependent Variable: A quantity whose value relies on how the independent variable is altered is referred to as a dependent variable.Independent variable: A variable that indicates a quantity being altered in an experiment is known as an independent variable.To learn more about the concept of linear equations and dependent / independent variables, click on the link given below:
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A new energy drink advertises 120 calories for 5 oz. How many calories are in 15 oz of drink
A new energy drink advertises 120 calories for 5 oz.
How many calories are in 15 oz?
We can set up a proportion to solve this problem
[tex]\frac{120}{5}=\frac{x}{15}[/tex]Where x is the number of calories in 15 oz
Let us solve the above equation for x
[tex]\begin{gathered} \frac{120}{5}=\frac{x}{15} \\ \frac{x}{15}=\frac{120}{5} \\ x=\frac{120}{5}\cdot15 \\ x=120\cdot3 \\ x=360 \end{gathered}[/tex]Therefore, there are 360 calories in 15 oz of drink.
Which equation is equivalent to 0.05n+ 0.1d = 4.55?
O 5n+d=455
O 0.5n+d=455
O5n+10d=455
0.05d + 0.1n = 455
Answer:
[tex]5n+10d=455[/tex]
Step-by-step explanation:
Multiply both sides of the equation by 100.
