Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?
Answer:
[tex]t \: = 3.92 \: sec[/tex]
Step-by-step explanation:
When (t =0)
Height of cliff = 248 feet = 75.5m
Using Newton's equations of motion:
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
75.5 = 0 * t + 4.9 * t^2
Solving further :
[tex]t \: = 3.92 \: sec[/tex]
The image of (-4,6) reflected along the y-axis is
a. (4, -6)
b. (-4,-6)
c. (4, 6)
d. (-4, 6)
Answer:
C(4,6)
Step-by-step explanation:
the x turns into its opposite when reflected across y same thing for y when reflected across x
Answer:
c. (4, 6)
Step-by-step explanation:
The rule of an reflection about the y-axis is: [tex]A(x,y)\rightarrow A'(-x,y)[/tex]
Apply the rule to point (-4, 6):
[tex]\frac{(-4,6)\rightarrow\boxed{(4,6)}}{(x,y)\rightarrow(-x,y)}[/tex]
Option C should be the correct answer.
Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)
Answer:
[tex] f(x) = 4x^2 - 3x + 6 [/tex]
Step-by-step explanation:
Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]
Let's find a, b and c:
Substituting (0, 6):
[tex] 6 = a(0)^2 + b(0) + c [/tex]
[tex] 6 = 0 + 0 + c [/tex]
[tex] c = 6 [/tex]
Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.
Substituting (2, 16), and c = 6
[tex] f(x) = ax^2 + bx + c [/tex]
[tex] 16 = a(2)^2 + b(2) + 6 [/tex]
[tex] 16 = 4a + 2b + 6 [/tex]
[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]
[tex] 10 = 4a + 2b [/tex]
[tex] 10 = 2(2a + b) [/tex]
[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]
[tex] 5 = 2a + b [/tex]
[tex] 2a + b = 5 [/tex] => (Equation 1)
Substituting (3, 33), and c = 6
[tex] f(x) = ax^2 + bx + x [/tex]
[tex] 33 = a(3)^2 + b(3) + 6 [/tex]
[tex] 33 = 9a + 3b + 6 [/tex]
[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]
[tex] 27 = 9a + 3b [/tex]
[tex] 27 = 3(3a + b) [/tex]
[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]
[tex] 9 = 3a + b [/tex]
[tex] 3a + b = 9 [/tex] => (Equation 2)
Subtract equation 1 from equation 2 to solve simultaneously for a and b.
[tex] 3a + b = 9 [/tex]
[tex] 2a + b = 5 [/tex]
[tex] a = 4 [/tex]
Replace a with 4 in equation 2.
[tex] 2a + b = 5 [/tex]
[tex] 2(4) + b = 5 [/tex]
[tex] 8 + b = 5 [/tex]
[tex] 8 + b - 8 = 5 - 8 [/tex]
[tex] b = -3 [/tex]
The quadratic function that represents the given 3 points would be as follows:
[tex] f(x) = ax^2 + bx + c [/tex]
[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]
[tex] f(x) = 4x^2 - 3x + 6 [/tex]
Solve the following equation algebraically:
3x^2=12
a.+3
b. +2
C.+3.5
d. +1.5
Answer:
Step-by-step explanation:
answer is c just took test
|3(x–2)|=12 pls help i need assistance
Answer:
x1 = -4
x2 = 6
Step-by-step explanation:
The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive
For Example
|-3| = 3
So we can ignore if the answer we get is positive or negative because it will forced to be a positive
|3 x 4| = 12
|x - 2| = 4
x1 = 6
x2 = -2
A person tosses a fair coin until a tail appears for the first time. If the tail appearson thenth flip, the person winsndollars. LetXdenote the player’s winnings.ComputeE(X).
Answer: The answer in a is No while the answer in b is Yes
Step-by-step explanation:
Find the explanation in the attached file.
Which ordered pair is a solution to the following linear system? y = x y = –x
Answer:
(2,2) (-1,-1)
Step-by-step explanation
i think this is there answer im sorry if im wrong
A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.
a. Find the probability x = 2 cents.
b. Find the probability x = 6 cents.
c. Find the probability x = 10 cents.
d. Find the probability x = 11 cents.
e. Find the probability x = 15 cents.
f. Find the probability x = 20 cents.
g. Find the expected value of x.
Answer:
a. The probability x = 2 cents = 7/22
b. The probability x = 6 cents = 35/66
c. The probability x = 10 cents = 5/33
d. The probability x = 11 cents= 28/33
e. The probability x = 15 cents = 20/33
f. The probability x = 20 cents = 14/33
g. The expected value of x = 5.9
Step-by-step explanation:
This is a binomial probability distribution. The number of trials is known .
a. The probability x = 2 cents.
Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2
= 21 / 66 = 7/22
b. The probability x = 6 cents.
Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2
= 5*7 / 66 = 35/66
c. The probability x = 10 cents.
Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)
= 10/ 66 = 5/33
d. The probability x = 11 cents.
Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)
= 8*7 / 66 = 56/66= 28/33
e. The probability x = 15 cents.
Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)
= 8*5 / 66 = 40/66= 20/33
f. The probability x = 20 cents.
Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)
= 28 / 66 = 14/33
g. The expected value of x.
E(X) = np
E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20
=2(59)/20= 5.9
If there are 25 students in a class - 11 are guys and 14 are girls what is the probability that one of the students on the class is a guy?
Answer:
0.44
Step-by-step explanation:
11/25 = 0.44 = 44%
Answer:
11/25
Step-by-step explanation:
since there are 25 students, there will be 25 choices, and the 25 will be the denominator
and there are 11 guys so there will be 11 choices of guys and the 11 will go on top
the point p(-3,4) is reflected in the line x +2=0. find the coordinate of the image x
Answer:
(- 1, 4 )
Step-by-step explanation:
The line x + 2 = 0 can be expressed as
x + 2 = 0 ( subtract 2 from both sides )
x = - 2
This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2
Thus (- 3, 4 ) is 1 unit to the left of - 2
Under a reflection in the line x = - 2
The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.
Thus
(- 3, 4 ) → (- 1, 4 )
The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. A random sample of 50 part-time seasonal employees in 2010 had a mean of 38.5 years with a standard deviation of 16 years. Required:a. At the 5 percent level of significance, does this sample show that the average age was different in 2010? b. Which is the right hypotheses to test the statement?c. What are the test statistic and critical value?
Answer:
No the sample does not show that the average age was different in 2010
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The sample mean is [tex]\= x = 38.5[/tex]
The population mean is [tex]\mu = 37[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
The level of significance is [tex]\alpha = 5 \% = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 37[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 37[/tex]
The critical value of the level of significance obtained from the normal distribution table is ([tex]Z_{\alpha } = 1.645[/tex] )
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]
[tex]t = 0.663[/tex]
Now looking at the value t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False
Answer:
False
Step-by-step explanation:
The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.
36 minus 20 minus 32 times 1/4
Answer:
6
Step-by-step explanation:
36 - 20 - 32 x 1/4
=> 36 - 20 - 32/4
=> 36 - 20 - 8
=> 36 - 28
=> 6
Question
Consider these functions.
f(x) = -9x + 14
g(x)=-3x2
Select the correct answer from each drop-down menu.i
If x = 6, then f(6)
If g(x) -48, then x =
and x =
Submit
Answer:
[tex]\large \boxed{-40, \ 4, \ -4}[/tex]
Step-by-step explanation:
[tex]f(x)=-9x+14[/tex]
[tex]\sf Put \ x \ as \ 6.[/tex]
[tex]f(6)=-9(6)+14[/tex]
[tex]f(6)=-54+14[/tex]
[tex]f(6)=-40[/tex]
[tex]g(x)=-3x^2[/tex]
[tex]\sf Put \ g(x) \ as \ -48.[/tex]
[tex]-48=-3x^2[/tex]
[tex]\displaystyle \frac{-48}{-3} =\frac{-3x^2 }{-3}[/tex]
[tex]16=x^2[/tex]
[tex]\sqrt{16} =\sqrt{x^2 }[/tex]
[tex]x= \pm 4[/tex]
Answer:
F(6) = -9(6) + 14 = -54 + 14. f(6) = -40
G(x) = -48 / g(x) = -3(16) / g(4) = -48
Step-by-step explanation:
For the first one the drop answer is -40
For the second one its 4 then 16
I think because that whats im seeing but these are the right answers :)
Common ratio 2/3, -2, 6
Answer:
The common ratio is - 3Step-by-step explanation:
To find the common ratio between the terms of the sequence divide the previous term by the next term.
That's
[tex] - 2 \div \frac{2}{3} = - 2 \times \frac{3}{2} = - 3[/tex]Or
[tex] \frac{6}{ - 2} = - 3[/tex]Therefore the common ratio of the sequence is - 3
Hope this helps you
Answer:
-3
Step-by-step explanation:
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if rho is a density function, then rhoave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the plane z = 0.
Answer:
An aluminum bar 4 feet long weighs 24 pounds
Step-by-step explanation:
Look at parallelogram below d1 and d3 Are both 35 degrees what is the measurement of d2
Answer:
145 degrees
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary.
d2 = 180° -d1 = 180° -35°
d2 = 145°
Maria operates a taco truck in her neighborhood. She has created a graph based on her business performance in the previous year. The price she currently sells tacos for is $2.30. Which two statements correctly interpret this graph? Revenue and Cost Functions 1)Maria’s business is incurring losses. 2)Maria’s costs are rising over time. 3)Maria is running a profitable business. 4)Maria’s total revenue exceeds her total profit. 5)Maria’s total profit exceeds her total revenue.
Answer:
3)Maria is running a profitable business.
4)Maria’s total revenue exceeds her total profit.
Step-by-step explanation:
The graph shows variation of revenue and cost with respect to price of product and not with respect to time .
The price of the product is 2.30 . From this graph , we see that at this price revenue exceeds total cost . So maria is running a profitable business .
Total profit can not exceed total revenue as
Total revenue - total cost = total profit .
So total profit will always be less than total revenue .
This table shows a linear relationship.
The slope of the line is ?
Answer:
2
Step-by-step explanation:
2,8 to 4,12 has a rise of 4 and a run of 2.
4/2 = 2
The slope is 2.
Remember rise/run!
Answer:
2
Step-by-step explanation:
We take take two points and use the slope formula
m = (y2-y1)/(x2-x1)
m = (12-8)/(4-2)
= 4/2
= 2
Pablo rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 80 cents for each mile driven. Pablo had to pay
$221.59 when he returned the truck. For how many miles did he drive the truck?
Answer:
252 miles
Step-by-step explanation:
19.99 + .80x = 221.59
,80x = 201.60
x = 252
Benjamin’s and David’s ages add up to 36 years. The sum of twice their respective ages also add up to 72 years. Find their ages
Answer:
It can be any two numbers that sum up to 36.
eg:18+18,30+6,15+21
Step-by-step explanation:
Given:
Let Benjamin's age be x and David's age y.
x+y=36
2x+2y=72
Solution:
As twice of 36=72, any two numbers that add up to 36 ,will give a sum of 72 after multiplying them with 2.Therefore ,Benjamin's and David's age can be any set of numbers that sum up to 36.
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
a) 5[tex]cm^{3}[/tex]
Step-by-step explanation:
Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.
When raising to 3, these dimensions are included and therefore 5[tex]cm^{3}[/tex] is a measure of volume.
Answer:
5cm^3
Step-by-step explanation:
Volume for a form will always be in cubic units.
Area of a shape will always be in squared units.
Length will not be in cubic or squared units.
Hence, the first option is a measure for volume.
The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.
The third option represents a measurement of length, for example the length of a line segment or the height of a figure.
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Rational equation of 3/x+1=2/x-3
Answer:
x = 11
Step-by-step explanation:
3/x+1=2/x-3
Solve by using cross products
2 (x+1) = 3 (x-3)
Distribute
2x+2 = 3x-9
Subtract 2x
2x+2-2x = 3x-2x-9
2 = x-9
Add 9 to each side
2+9 =x-9+9
11 =c
Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
-----------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
-----------------
The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
-----------------
The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
Given the following diagram, find the required measures. Given: l | | m m 1 = 120° m 3 = 40° m 2 = 20 60 120
Step-by-step explanation:
your required answer is 60°.
Hello,
Here, in the figure;
angle 1= 120°
To find : m. of angle 2.
now,
angle 1 + angle 2= 180° { being linear pair}
or, 120° +angle 2 = 180°
or, angle 2= 180°-120°
Therefore, the measure of angle 2 is 60°.
Hope it helps you.....
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
If SSR is 2592 and SSE is 608, then A. the standard error would be large. B. the coefficient of determination is .23. C. the slope is likely to be insignificant. D. the coefficient of determination is .81.
Answer:
D. the coefficient of determination is .81.
Step-by-step explanation:
SST = SSE + SSR
where
SST is the summation of square total
SSE is the summation of squared error estimate = 608
SSR is the summation of square of residual = 2593
with these in mind we put the values into the formula
= 2592 + 608
=3200
Coefficient of determination = SSR/SST
= 2592/3200
= 0.81
Therefore option D is the correct answer to the question.
