Answers
Answer: 4.2%
Step-by-step explanation:
The probability the first response is correct is 1/6.The probability the second response is correct is 1/4.Multiplying these, we get (1/6)(1/4), which is about 4.2%
Related Questions
if angle X is an acute angle with tan X = 8/7, what is the value of sec X?
Answers
Answer: [tex]\frac{\sqrt{113}}{7}[/tex]
Step-by-step explanation:
As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.
Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],
[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 128t + 144. After how many seconds will the ball pass the top of the building
Answers
The time for the ball to pass the top of the building is determined as 4 s.
Time of motion of the ballThe time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.
h = -16t² + 128t + 144
v = dh/dt
v = -32t + 128
at maximum height, v = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4 s
Thus, the time for the ball to pass the top of the building is determined as 4 s.
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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
When the ball pass the top of the building, h = 144 foot
Plug h = 144 foot in h= -16t² + 128t + 144
144 = -16t² + 128t + 144
[tex]\rm -16t^2+128t=0[/tex]
t = 0 or t = 8 seconds
At t = 0, initially, the ball was thrown upward.
At t = 8 seconds, the ball passes the top of the building
Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
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226,710 - 724,435 =
How to work this out without calculator
Answers
What error did Lucia make?
Answers
Answer:
See below
Step-by-step explanation:
She combined 3x and - 9x incorrectly
she should have gotten - 6 x not - 12 x
If P(x) is a polynomial with lead term -x7, then
a) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
b) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
c) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
d) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
Answers
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity , Option B is the correct answer.
What is a Polynomial ?A polynomial is an expression which consists of variables , Coefficient , indeterminate and mathematical operations.
The polynomial given has lead term -x⁷
So when x --> ∞ , -x⁷---> - ∞
and when x ---> - ∞ , -x⁷ ----> ∞
Similarly for the function P(x)
So when x --> ∞ , P(x)---> - ∞
and when x ---> - ∞ , P(x) ----> ∞
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
Therefore Option B is the correct answer.
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Which measure of center is shown in a box plot?
mean
median
mode
range
Answers
5,1
3,1
4,1 is the correct answer
Answer:
(b) median
Step-by-step explanation:
A box-plot is a graphical representation of the 5-number summary of a data set. It includes the minimum, maximum, median, and 1st and 3rd quartiles.
__
The measure of center shown in a box plot is the median.
As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.
Answers
The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
We have:
Average x = 24375
u = 24230
SD = 523
n = 105
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is overpaid.
u > 24230
Assume significance level = 0.05
From the Z-table:
Z(critical) = 1.645
Now,
Z = (x-u)/(SD/√n)
Z = (24375-24230)/(523/√105)
Z = 2.84
Z > Z(critical)
So, reject the null hypothesis.
The average salary of sanitation workers in the city of Euonymus is overpaid.
Now, from the two-tail test:
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is 24230
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is not 24230
u ≠ 24230
Assume significance level = 0.05
From the Z-table for the two-tail test:
Z(critical) = ±1.96
Now,
Z = 2.84
Z > z(critical)
∴ The average salary of sanitation workers in the city of Euonymus is not 24230.
Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
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what is the range of the ordered pairs shown in the graph
Answers
Answer:
D.
Step-by-step explanation:
It contains all the y-values of the points.
Answer:
Coordinates of all points
first = (-1 , 3)
second = (-2, 1 )
third = (-3 , -3)
fourth = (-4 , -5)
option 3
Question 6b
6b of 6
The width of a rectangle is 15 centimeters less than its length. If the area of the
rectangle is 100 square centimeters, find the length and the width using the formula
A = lw.
O Length = 25 centimeters and Width = 10 centimeters
○ Length = 20 centimeters and Width = 5 centimeters
O Length = 115 centimeters and Width = 100 centimeters
○ Length = 5 centimeters and Width = 20 centimeters
Answers
Answer:
○ Length = 20 centimeters and Width = 5 centimeters
Step-by-step explanation:
Let the length = L
Then the width is L - 15
A = lw
100 = L(L - 15)
L² - 15L - 100 = 0
(L - 20)(L + 5) = 0
L - 20 = 0 or L + 5 = 0
L = 20 or L = -5
Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.
L = 20
width = L - 15 = 20 - 15 = 5
Answer: ○ Length = 20 centimeters and Width = 5 centimeters
In Triangle XYZ, XZ = XY and m∠Y=57°. The longest side of the triangle is ______.
YZ
XZ
XY
Both XZ and XY
Answers
Answer:
I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.
since XY=XZ, XYZ is the isosceles and naturally angle Y = angle Z = 57 degree.
so in a traingle the longest side is on the opposite side of the biggest angle.
If the congruent sides measures 57, the angle opposite the base( angle X) would mean 180-57-57 = 66. So basically the side which is opposite to X is the longest and that side being YZ.
Can anyone help me solve this? Please and thank you!
Answers
It's the sum of a geometric sequence.
Let's rewrite it a bit:
[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]
And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]
Now let's calculate the initial sum:
[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]
Derek works 43 hours at a rate of pay of $15 per hour. He receives double pay over 40 hours. What is his gross pay?
Answers
The Gross pay which Derek gets is 690 dollars.
What is Gross Pay?Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.
Here, Total hours worked by Derek = 43 hours
Rate of pay = $15 per hour
Rate of pay beyond 40 hours = $30 per hour
Now,
Rate of pay for the first 40 hours = 40 X 15 = $ 600
Since the pay rate doubles after 40 hours,
Rate of pay for the remaining 3 hours = 3 X 30 = $ 90
Gross Pay = 600 + 90 = $ 690
Thus, the Gross pay which Derek gets is 690 dollars.
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&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E S D E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E S D E
Answers
Answer:
E = [1,2,3,4,5,6,7,8,9,10,11,12]
S = [4,9]
E = [2,4,6,8,10,12]
The number that satisfies both conditions S and E is [4]
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = square numbers
This means,
1² = 1
2² = 4
3² = 9
S = {1, 4, 9}
E = even numbers
This means,
E = {2, 4, 6, 8, 10, 12}
Now,
S ∩ E = Numbers that are even and square.
S ∩ E = {4}
Thus,
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
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The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Answers
The mean and the standard deviation are 233 and 208.95 respectively.
The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.
First, we calculate the class midpoint (x) from the given intervals.
The class midpoint is the average of the intervals. So, we have:
X1 = (0+199)/2 = 99.5
X2 = (200+399)/2 = 299.5
X3 = (400+599)/2 = 499.5
X4 = (600+799)/2 = 699.5
X5 = (800+999)/2 = 899.5
X6 = (1000+1199)/2 = 1099.5
X7 = (1200+1399)/2 = 1299.5
So, the table becomes:
X values Frequency (f)
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean of the distribution is:
This gives:
Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)
Mean = 124832.5/535 = 233
Therefore, Mean = 233
The standard deviation is calculated as follows:
So, we have:
Б =
√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)
Standard Deviation = √(23357155.5)/535
= √43658.23
= 208.95
Б = 208.95
Hence, the mean and the standard deviation are 233 and 208.95 respectively.
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A company pays $20 per hour for up to 7 hours of work, and $30 per hour for
overtime hours (hours beyond 7). If x is the total hours worked, and more
than 7 hours have been worked, what is the expression for just the overtime
hours worked?
Answers
Answer:
Step-by-step explanation:
current total of hours work earnings (7hrs): $140
total earnings: $980 per week
49 hours work per week (no overtime)
immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)
total working hours: 77 hours per week
total earnings: $1,960 per week
3z^2-4z+11 -(12z^2+2z-11 find the difference . polynomials functions
Answers
Answer:
−135z
2
−2z
The 2 is representing Square
Step-by-step explanation:
(3z)
2
−4z+11−(12z)
2
+2z−11
Expand (3z)
2
.
3
2
z
2
−4z+11−(12z)
2
+2z−11
Calculate 3 to the power of 2 and get 9.
9z
2
−4z+11−(12z)
2
+2z−11
Expand (12z)
2
.
9z
2
−4z+11−12
2
z
2
+2z−11
Calculate 12 to the power of 2 and get 144.
9z
2
−4z+11−144z
2
+2z−11
Combine 9z
2
and −144z
2
to get −135z
2
.
−135z
2
−4z+11+2z−11
Combine −4z and 2z to get −2z.
−135z
2
−2z+11−11
Subtract 11 from 11 to get 0.
−135z
2
−2z
factorise 4ab +6bn-2a-3n
Answers
Answer:
(2b - 1)(2a + 3n)
-----------------------------------------------
Given polynomial
4ab + 6bn - 2a - 3nFactorize it as below:
4ab + 6bn - 2a - 3n =
(4ab - 2a) + (6bn - 3n) = Regroup
2a(2b - 1) + 3n(2b - 1) = Factorize each group using common factors
(2b - 1)(2a + 3n) Factorize using common factor
Answer:
[tex](2b-1)(2a+3n)[/tex]
Step-by-step explanation:
Given expression:
[tex]4ab+6bn-2a-3n[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]
Factor out the common term (2a + 3n):
[tex]\implies (2b-1)(2a+3n)[/tex]
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answers
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, -1][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
What is the equation of a circle with center (8, 6) and radius 5?
Answers
The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].
In the year 2015, New Jersey had 1,218 people per square mile. The land area of New Jersey is 7,354 square miles. What was the approximate population of New Jersey in 2015? In the year 2015 , New Jersey had 1,218 people per square mile . The land area of New Jersey is 7,354 square miles . What was the approximate population of New Jersey in 2015 ?
Answers
Answer:
8,957,172 people
Explanation:
Population = 1,218 people per square mile
Land area of New Jersey = 7,354 square miles
Total population:
people living in per square mile × total land area
1,218 × 7,354
8,957,172
Which expression represents a difference of squares?
A. t² +100
B. 4x² - 16x
C. 25k-64
D. 81-49y²
Answers
Answer:
D represents a difference of squares.
Answer: Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex]
Step-by-step explanation:
Hii, do you need to know which expression represents a difference of squares? No problem! (:
The Difference of SquaresLet's consider it for a moment. The "difference of squares" means we subtract two numbers squared, like [tex]\boldsymbol{a^2-b^2}[/tex].
Now let's check our choices and see where we subtract two numbers squared.
The only choice like that is Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex].
In choice A, we add 2 numbers; in choices B and C we don't subtract two numbers squared.
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]
--
) The correlation between a car’s engine size and its fuel economy (in mpg) is r= -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
Answers
The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
Given that, r= -0.774.
To solve such problems we must know about the fraction of the variability in data values or R-squared.
What fraction of the variability in fuel economy is accounted for by the engine size?The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
Fraction of the variability in data values = (coefficient of correlation)²= r²
Now, the variability in fuel economy = r²= (-0.774)²
= 0.599076%= 59.91%
Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.
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A shop is opened at 7.45 am and closed at 6.30 pm on each day from Monday to Friday. Calculate the total time the shop is opened from Monday to Friday.
Answers
Answer:
53 hours and 45 minutes
Step-by-step explanation:
since they open for 10 hours and 45 minutes a day.
10*5=50 hours, 45*5=225 minutes
add the minutes and hours together and it is 53 hours and 45 minutes
Urgent my safari wont work! 20 pts!!
What’s the square root of 32006???
Answers
Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.
Answers
Answer:
10000×(1+5%)^(15×2)=43219.4238
Transform each graph as specified below.
(a) The graph of y= f(x) is shown. Draw the graph of y=1/2f(x).
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
Answers
Answer:
x f(x)
0 0
-2 -4
4 -2
You need to draw y = 2 f (x-1)
So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values
New function
x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.
y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)
Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)
What are the following expressions simplified?
(11 √40) (9 √5)
(2 √6) (10 √8)
5 √6 ÷ √7 - √5 ÷ √6
Answers
The simplified expressions are
1. 990√2
2. 80 √3
3. 30- √35 / √42
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
(11 √40) (9 √5)
= 11*9* √40*√5
= 99*√200
= 99* 10√2
= 990√2
(2 √6) (10 √8)
= 2*10 * √6 * √8
=20* √48
= 20* 4 √3
= 80 √3
5 √6 ÷ √7 - √5 ÷ √6
=30- √35 / √42
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which function has an asymptote at x=5 and an x-intercept of (6,0)?
Answers
The function is f(x) = log(x - 5).
What is Asymptotes?A line or curve that acts as the limit of another line or curve.
The complete question is
Which function has an asymptote at x = 5 and an x-intercept of (6,0)? a. f(x) = log(x − 5) b. f(x) = log(x 5) c. f(x) = log x − 5 d. f(x) = log x 5
let us take,
f(x) = log(x - 5)
y = 0, then
0 = log(x-5)
x - 5 = [tex]e^{0}[/tex]
x - 5 = 1
x = 6
So, it can be conclude that the x-intercept is at (6, 0)
Hence, the function is f(x) = log(x - 5).
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60 milllimeter equals kilograms
Answers
Answer: .00006kg
Step-by-step explanation:
PLEASE HELP
The function
shown.
Select from the drop-down menus to correctly describe the end
f (x).
behavior of
f(x) = -2(0.25) + 1is
As x decreases without bound, the graph of
Choose...
Choose...
As x increases without bound, the graph of
f (x)
‹ƒ (x)
f(x)
1 2
5
4
3
2
1
-4-3-2-11.
3
1
2 3
4 5
4
6
5 6
7 8