Answer:
D
Step-by-step explanation:
Reminder: A function returns ONLY ONE y value for each input value.
We immediately discard possible answer A, since 2 points have input 1 with different outputs.
Same for B: discard this.
Same for C: discard this.
D is a function. All of the inputs are unique (no duplication).
Suppose f(x) = x^2. What is the graph of g(x) =f(4x)?
Answer:
your y-intercept is 0 and slope is 4 so any line with zero slope it will be horizontal
Answer: On mine it is D
Step-by-step explanation:
It is the small one facing up
Joe Bob wanted to find out how many hours of exercise the students at his school gets each week. He went to the school's gym and asked the following question:
"Do you work out every day like a healthy person, or are you a lazy couch potato who only works out once in a while?"
What is another way Joe Bob could word his question so that it does not contain any bias?
Although I am unsure what this question has to do with Mathematics, Joe Bob could simply say "How often do you work out in a week?"
A company makes batteries with an average life span of 300
hours with a standard deviation of 75 hours. Assuming the
distribution is approximated by a normal curve fine the
probability that the battery will last:(give 4 decimal places for
each answer)
a. Less than 250 hours ___________
b. Between 225 and 375 hours __________
c. More than 400 hours ______________
Answer:
a) 0.2514
b) 0.6827
c) 0.0918
Step-by-step explanation:
Average life span of batteries = u = 300 hours
Standard deviation = s = 75 hours
Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.
Part a) Less than 250 hours
In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{250-300}{75}=-0.67[/tex]
From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514
P(z < -0.67) = 0.2514
Thus, the the probability that the life span of battery will be less than 250 hours is 0.2514
Part b) Between 225 and 375 hours
In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.
225 into z-score will be:
[tex]z=\frac{225-300}{75}=-1[/tex]
375 into z-score will be:
[tex]z=\frac{375-300}{75}=1[/tex]
Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:
P(-1 < z < 1 ) = 0.6827
Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827
Part c) More than 400 hours
In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{400-300}{75}=1.33[/tex]
From the z-table the probability of z score being more than 1.33 comes out to be:
P( z > 1.33) = 0.0918
Thus, the probability that the life span of battery will be more than 400 hours is 0.0918
Does anyone know how to do this ? Please help !
Ah, all you have to do is combine 2/5m and 3/5m.
In this case:
=2/5m - 4/5 - 3/5m
=-1/5m - 4/5
=-m/5-4/5
Answer:
[tex]\frac{-1}{5}m-\frac{4}{5}[/tex]
Step-by-step explanation:
You are given:
[tex]\frac{2}{5}m-\frac{4}{5}-\frac{3}{5}m[/tex]
Reorder using commutative property (putting like terms together):
[tex]\frac{2}{5}m-\frac{3}{5}m-\frac{4}{5}[/tex]
Now we are going to bring down the -4/5 (there is nothing to do there).
(2/5)m and -(3/5)m have the same denominator all we have to do is figure out what is 2-3 which is -1
[tex]\frac{-1}{5}m-\frac{4}{5}[/tex]
Which polynomial is prime?
3x3 + 3x2 – 2x – 2
3x3 – 2x2 + 3x – 4
4x3 + 2x2 + 6x + 3
4x3 + 4x2 – 3x – 3
The prime polynomial out of the given options is 3x^3 + 3x^2 - 2x - 2.
Explanation:Out of the given polynomials, the polynomial that is prime is 3x3 + 3x2 - 2x - 2.
A polynomial is considered prime if it cannot be factored into a product of lower degree polynomials with integral coefficients.
In this case, the polynomial 3x3 + 3x2 - 2x - 2 is a cubic polynomial and cannot be factored further, so it is prime.
The temperature rose 9*F in three hours. If the starting temperature was -15*F what was the final temperature? Explain.
Answer:
-6*F
Step-by-step explanation:
-15+9=-6
what is the area of the figure. please help show steps
Answer: [tex]143.99\ ft^2[/tex]
Step-by-step explanation:
We need to find the lenght AC and BC of the triangle by applying these identities:
[tex]cos\alpha=\frac{adjacent}{hypotenuse} \\\\sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Then, AC is:
[tex]sin(45\°)=\frac{AC}{24}\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft[/tex]
And BC is:
[tex]cos(45\°)=\frac{BC}{24}\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft[/tex]
The area will be:
[tex]A=\frac{AC*BC}{2}[/tex]
Substituting values, we get:
[tex]A=\frac{(16.97\ ft)(16.97\ ft)}{2}=143.99\ ft^2[/tex]
What is the sign of 3xy when x>0 and y<0?
Let see.
Numbers which are bigger than 0 are defined as positive numbers and have a prefix of + (plus).
Numbers which are smaller than 0 are defined as negative numbers and have a prefix of - (minus).
Let say number a is equal to the expression,
[tex]a=3xy[/tex]
Since y is negative we can change its prefix to -,
[tex]a=3x\cdot(-y)[/tex]
Any number (in this case 3x) multiplied by negative number will produce a negative number.
Therefore the sign or prefix of number a will be -.
Hope this helps.
r3t40
When you multiply a positive number and a negative number, the result is a negative number. Therefore, the sign of 3xy, when x > 0 and y < 0, is negative.
Explanation:The question is asking for the sign of the product of two numbers, x and y, when x is positive (x > 0) and y is negative (y < 0). In mathematics, when you multiply a positive number and a negative number, the result is always a negative number.
So, the product of x and y or 3xy in this case, would be negative. This is due to the principle that the product of different signs (in this case, positive and negative) is always negative.
Learn more about Multiplication of positive and negative numbers here:https://brainly.com/question/34274159
#SPJ3
If x + y = 12 and x - y = 3, then
x2 - y2 =
[tex]x^2-y^2=(x-y)(x+y)\\\\x^2-y^2=3\cdot12=36[/tex]
How many deciliter are equivalent to 5 cups
Answer:
11.8294Step-by-step explanation:
Answer:
Step-by-step explanation:
How many deciliters are equivalent to 5 cups?
2.1097 deciliters
11.85 deciliters
118.5 deciliters
210.97 deciliters
ANSWER IS 11.85
perform the indicated operation: (-1 1/2)(-3/2)
The operation (-1 1/2)(-3/2) gives 9/4 or 2 1/4 as a mixed number.
To perform the indicated operation: (-1 1/2)(-3/2), we need to multiply the two numbers.
First, convert the mixed number -1 1/2 to an improper fraction. It is -3/2 because 1 1/2 is equal to 3/2 and we keep the negative sign.Now, multiply the two fractions: -3/2 * -3/2.Since the signs are the same (both negative), the answer will be positive.Multiply the numerators: 3 * 3 = 9.Multiply the denominators: 2 * 2 = 4.So, the answer is 9/4, or 2 1/4 when converted to a mixed number.What is the following sum? Assume x > 0 and y > 0 sqrt x^2y^2+2 sqrt x^3y^4+xy sqrt y
Answer:
[tex]xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
Step-by-step explanation:
Given expression,
[tex]\sqrt{x^2y^2}+2\sqrt{x^3y^4}+xy\sqrt{y}[/tex]
[tex]=(x^2y^2)^\frac{1}{2} + 2(x^3y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex]\because (\sqrt{x}=x^\frac{1}{2})[/tex]
[tex]=(x^2)^\frac{1}{2} (y^2)^\frac{1}{2} + 2(x^3)^\frac{1}{2} (y^4)^\frac{1}{2} + xy\sqrt{y}[/tex]
[tex](\because (ab)^n=a^n b^n)[/tex]
[tex]=x^{2\times \frac{1}{2}} y^{2\times \frac{1}{2}} + 2(x^{3\times \frac{1}{2}})(y^{4\times \frac{1}{2}})+xy\sqrt{y}[/tex]
[tex]\because (a^n)^m=a^{mn}[/tex]
[tex]=x^1 y^1 + 2x^{1\frac{1}{2}} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2x.(x)^\frac{1}{2} y^2 + xy\sqrt{y}[/tex]
[tex]=xy+2xy^2\sqrt{x}+xy\sqrt{y}[/tex]
[tex]=xy(1+2y\sqrt{x}+\sqrt{y})[/tex]
Answer:
B is the right option
Step-by-step explanation:
On edg :))
Suppose you and some friends are going to the movies. The amount of money you spend for tickets varies directly with the number of people buying
tickets. If you spend $48 for six tickets, what is the constant of variation?
e r song to the movies. The amount of money you spend for tckets vantes directly w
6
Answer:
The constant variation, and the price of one ticket is 8.
Step-by-step explanation:
Which value is equivalent to
[tex]\bf \left( \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 5\cdot 2}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3} \right)^2 \times \left( \cfrac{5^0}{2^{-3}} \right)^3\times 2^{-9}\implies \left( \cfrac{5\cdot 2}{ 3} \right)^2 \times \left( \cfrac{1}{2^{-3}} \right)^3\times 2^{-9}[/tex]
[tex]\bf \left( \cfrac{10}{ 3} \right)^2 \times \left( 2^3 \right)^3\times 2^{-9}\implies \left( \cfrac{10}{ 3} \right)^2 \times 2^9\times 2^{-9}\implies \cfrac{10^2}{3^2}\times 2^{9-9} \\\\\\ \cfrac{100}{9}\times 2^0\implies \cfrac{100}{9}\times 1\implies \cfrac{100}{9}[/tex]
Which equation represents the slope-intercept form of the line below?
Answer:
Choice B: y = 1/2x + 8
Step-by-step explanation:
Given
slope = 1/2
y-intercept = (0,8)
Put in y = mx + b form
slope is indicated by m
y-intercept is indicated by b
y = 1/2x + 8
Answer
y = 1/2x + 8
Answer: B. [tex]y=\dfrac{1}{2}x+8[/tex]
Step-by-step explanation:
We know that the equation of a line in slope-intercept form is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line and c is the y-intercept of the line.
For the given graph , we have
y-intercept = (0,8)
i.e. c=8
Slope =[tex]\dfrac{1}{2}[/tex]
i.e. m=8
Then, the equation of the given line in slope-intercept form will be :-
[tex]y=\dfrac{1}{2}x+8[/tex]
Find the student's error in solving the following
inequality.
31 <-5x + 6
25 <-5x
-5
x>7
Step-by-step explanation:
when dividing by a (-)
the inequality sign changes
Answer:
"The student should have switched the direction of the inequality sign to get –5> x for a final answer."
and the second one is:
The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.
Step-by-step explanation:
i got that on edge
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
"All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid."
As of today, Susan's movie is currently five days late. She knows that if she doesn't get the movie back tonight, she will be charged $9.99, the purchase price of the movie, plus five days' worth of late fees. A round trip cab ride to the video store will cost about $10.
Which of the following statements is true?
a.
Taking a cab to return the movie is the cheapest action. Susan should call a cab.
b.
It would cost about the same to keep or return the movie. Susan should keep it.
c.
Keeping the movie and paying the purchase price and late fees is the cheapest option.
d.
If Susan returns the movie, she should not have to pay late fees. She should return it.
ANSWER IS D
Answer:
c. Keeping the movie and paying the purchase price and late fees is the cheaper option.
Step-by-step explanation:
1. If Susan takes a cab and pays late fees
Cost of cab = $10.00
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.50
2. If Susan keeps the movie
Purchase price of movie = $9.99
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.49
Keeping the movie and paying the purchase price and late fees is the cheapest option.
a. is wrong. Taking a cab is the more expensive option.
b. is wrong. Susan contracted to return the movie, so she should try to do so.
c. is correct. This is a statement of fact, not a judgement call.
d. is wrong. Susan contracted to pay the late fees if she did not return the video (but she should still return it).
What is the number three thousand eighty expressed in scientific notation?
Answer:
3.08 x [tex]10^{3}[/tex]
Step-by-step explanation:
3080 = 3.08 x 1000 = 3.08 x [tex]10^{3}[/tex]
Solve for x.
5(x + 1) = 4(x + 8)
Answer:
x =27
Step-by-step explanation:
5(x + 1) = 4(x + 8)
Distribute.
5x + 5 = 4x + 32
Move x term onto one side.
x + 5 = 32
Move integer onto one side.
x = 27
if a+b+c=-2 and x+y=-9 what is 9x + 4b + 9y +4c + 4a
Answer:
-89
Step-by-step explanation:
9x + 4b + 9y +4c + 4a (9x+9y)+(4a+4b+4c) =9(x+y)+4(a+b+c)
but : a+b+c = -2 and x+y = -9
9x + 4b + 9y +4c + 4a = 9(-9)+4(-2) = - 81 -8 =-89
The sum of two numbers is 12, their product is 96. Compute these two numbers. Explain.
Answer:
The numbers are
[tex]6+2\sqrt{15}i[/tex] and [tex]6-2\sqrt{15}i[/tex]
Step-by-step explanation:
Let
x and y -----> the numbers
we know that
[tex]x+y=12[/tex] -----> [tex]y=12-x[/tex] ------> equation A
[tex]xy=96[/tex] ----> equation B
substitute equation A in equation B and solve for x
[tex]x(12-x)=96\\12x-x^{2}=96\\x^{2} -12x+96=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -12x+96=0[/tex]
so
[tex]a=1\\b=-12\\c=96[/tex]
substitute
[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(1)(96)}} {2(1)}[/tex]
[tex]x=\frac{12(+/-)\sqrt{-240}} {2}[/tex]
Remember that
[tex]i^{2}=\sqrt{-1}[/tex]
[tex]x=\frac{12(+/-)\sqrt{240}i} {2}[/tex]
[tex]x=\frac{12(+/-)4\sqrt{15}i} {2}[/tex]
Simplify
[tex]x=6(+/-)2\sqrt{15}i[/tex]
[tex]x1=6+2\sqrt{15}i[/tex]
[tex]x2=6-2\sqrt{15}i[/tex]
we have two solutions
Find the value of y for the first solution
For [tex]x1=6+2\sqrt{15}i[/tex]
[tex]y=12-x[/tex]
substitute
[tex]y1=12-(6+2\sqrt{15}i)[/tex]
[tex]y1=6-2\sqrt{15}i[/tex]
Find the value of y for the second solution
For [tex]x2=6-2\sqrt{15}i[/tex]
[tex]y2=12-x[/tex]
substitute
[tex]y2=12-(6-2\sqrt{15}i)[/tex]
[tex]y2=6+2\sqrt{15}i[/tex]
therefore
The numbers are
[tex]6+2\sqrt{15}i[/tex] and [tex]6-2\sqrt{15}i[/tex]
Is the following function an example
of exponential growth or decay?
f(x) = 198(0.73)x+1
Answer:
Exponential decay
Step-by-step explanation:
b = 0.73
Since the b is less than 1 (b<1), the rate is decreasing.
I need help please.
Answer:
Step-by-step explanation:
p^8 q^6 / p ^4 q^3
In this expression the base of numerator and denominator is same:
We will change the division into multiplication and the denominator will become numerator will negative exponents:
p^8 q^6 * p ^-4 q^-3
Now simplify the terms with same base
The exponents of the same base will be added
=p^8+(-4) q^6+(-3)
=p^8-4 q^6-3
=p^4 q^3
The answer is p^4 q^3....
Rationalize the denominator and simplify.
let's use the conjugate of the denominator and multiply top and bottom by it, recall the conjugate of a binomial is simply the same binomial with a different sign in between.
[tex]\bf \cfrac{2\sqrt{x}-3\sqrt{y}}{\sqrt{x}+\sqrt{y}}\cdot \cfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\implies \cfrac{2\sqrt{x}\sqrt{x}-2\sqrt{x}\sqrt{y}~~-~~3\sqrt{x}\sqrt{y}+3\sqrt{y}\sqrt{y}}{\underset{\textit{difference of squares}}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}} \\\\\\ \cfrac{2\sqrt{x^2}-2\sqrt{xy}-3\sqrt{xy}+3\sqrt{y^2}}{(\sqrt{x})^2-(\sqrt{y})^2}\implies \cfrac{2x-5\sqrt{xy}+3y}{x-y}[/tex]
Answer:
[tex]\dfrac{2x-5\sqrt{xy}+3y}{x-y}\\[/tex]
Step-by-step explanation:
In Rationalize the denominator we multiply both numerator and denominator by the conjugate of denominator.
In Conjugate we change the sign of middle operator.
Example: Congugate of (a + b) = a - b
Now Solving the given expression,
[tex]\dfrac{2\sqrt{x} - 3\sqrt{y}}{\sqrt{x} + \sqrt{y}} = \dfrac{2\sqrt{x} - 3\sqrt{y}}{\sqrt{x} + \sqrt{y}}\times \dfrac{\sqrt{x} - \sqrt{y}}{\sqrt{x} - \sqrt{y}}\\\\\Rightarrow \dfrac{(2\sqrt{x} - 3\sqrt{y})(\sqrt{x} - \sqrt{y})}{( \sqrt{x} + \sqrt{y}){(\sqrt{x} - \sqrt{y}})}\ \ \ \ \ \ \ \ \ \ \ [\because (a-b)(a+b)=(a^{2} +b^{2})]\\\Rightarrow \dfrac{2x-2\sqrt{xy}-3\sqrt{xy}+3y}{x-y}\\\\ \Rightarrow \dfrac{2x-5\sqrt{xy}+3y}{x-y}\\[/tex]
Describe the steps you used to solve the equation and find the amount of Carrie’s allowance. Linear equation: 1 4 a + 1 3 a + 8 = 22
Sample Response: First, the like terms had to be combined using the lowest common denominator (LCD). Then the subtraction property of equality was used to isolate the variable term. Finally, both sides of the equation were multiplied by the reciprocal of the coefficient to solve for a.
Terry invested money in a biotech stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 2 to day 10.
Answer:
The average rate of change is 1.275
Step-by-step explanation:
The average rate of change of f(x) from x=a to x=b is given by:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The money Terry invested is modeled by the function [tex]f(x)=0.01(2)^x[/tex] where x represents number of days.
The average rate of change from day 2 to day 10 is given by:
[tex]\frac{f(10)-f(2)}{10-2}[/tex]
[tex]f(10)=0.01(2)^{10}=10.24[/tex]
[tex]f(2)=0.01(2)^{2}=0.04[/tex]
The average rate of change becomes:
[tex]\frac{10.24-0.04}{8}[/tex]
[tex]=\frac{10.2}{8}=1.275[/tex]
Answer:
The average rate of change is 1.275
A combination of a conditional statement and its converse written in the “if and only if” form. Both the conditional and the converse must be true before writing this statement .
Answer:
An angle is 90° if and only if it is a right angle.
Explanation:
The statement is: If an angle is 90°, then it is a right angle.
The converse of this statement would be:
If an angle is a right angle, it is 90°.
Clearly, both the conditional and converse of this statement is true.
What is the scale factor of this dilation?
[Not drawn to scale]
The scale factor of the dilation is:
[tex]1\dfrac{1}{2}[/tex]
Step-by-step explanation:Scale factor--
It is a fixed amount by which the each of the dimension of the original figure is multiplied in order to obtain the dilated image of the figure.
Here we see that there is a enlargement dilation.
( since the side of the image increases after the dilation)
Let the scale factor be k.
From the figure we see that:
The side of length 6 units is transformed to get a side of length 9 units.
i.e.
[tex]6\times k=9[/tex]
i.e.
[tex]k=\dfrac{9}{6}\\\\i.e.\\\\k=\dfrac{3}{2}\\\\i.e.\\\\k=1\dfrac{1}{2}[/tex]
You are told that a sample of size 225 the mean is 48.5 and the standard deviation is 1.8 the study is reported with 90% confidence level explain how to determine if 48.8 is within the confidence interval
Answer with explanation:
Size of the sample = n =225
Mean[\text] \mu[/text]=48.5
Standard deviation [\text] \sigma[/text]= 1.8
[tex]Z_{90 \text{Percent}}=Z_{0.09}=0.5359\\\\Z_{score}=\frac{\Bar X -\mu}{\frac{\sigma}{\sqrt{\text{Sample size}}}}\\\\0.5359=\frac{\Bar X -48.5}{\frac{1.8}{\sqrt{225}}}\\\\0.5359=15 \times \frac{\Bar X -48.5}{1.8}\\\\0.5359 \times 1.8=15 \times (\Bar X -48.5)\\\\0.97=15 \Bar X-727.5\\\\727.5+0.97=15 \Bar X\\\\728.47=15 \Bar X\\\\ \Bar X=\frac{728.47}{15}\\\\\Bar X=48.57[/tex]
→Given Confidence Interval of Mean =48.8
→Calculated Mean of Sample =48.57 < 48.8
So, the value of Sample mean lies within the confidence interval.
Answer:
sample answer
Step-by-step explanation:
To find the margin of error, multiply the z-score by the standard deviation, then divide by the square root of the sample size.
The z*-score for a 90% confidence level is 1.645.
The margin of error is 0.20.
The confidence interval is 48.3 to 48.7.
48.8 is not within the confidence interval.
What is the value of x?
Enter your answer in the box
Answer:
25
Step-by-step explanation:
Those parallel lines tell us our triangles are similar. So that means the corresponding sides are proportional.
So we have that x corresponds to x+15 and
40 corresponds to 24+40.
So we have this proportion to solve:
[tex]\frac{x}{x+15}=\frac{40}{24+40}[/tex]
Let's simplify what we can:
[tex]\frac{x}{x+15}=\frac{40}{64}[/tex]
Cross multiply:
[tex](64)(x)=(x+15)(40)[/tex]
Multiply/distribute:
[tex]64x=40x+600[/tex]
Subtract 40x on both sides:
[tex]24x=600[/tex]
Divide both sides by 24:
[tex]x=\frac{600}{24}=25[/tex]
x=25
Answer:
x = 25.
Step-by-step explanation:
24/40 = 15/x
x = (40*15) / 24
x = 600/24
= 25.