Answer:
the number of possible reading schedules is 1.064301638 × 10¹²
Step-by-step explanation:
Given that :
The English teacher needs to pick 10 books to put on her reading list for the next school year.
If the English teacher picks at most 3 poetry books i.e no more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books
Thus; the number of ways to pick the books are :
[tex]\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right][/tex]
[tex]= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}][/tex]
[tex]= [ 1*1001]+[8*2002]+[28*3003]+[56*3432][/tex]
[tex]\mathbf{= 293293}[/tex]
However, to determine how many reading schedules that are possible we use the relation:
Number of ways to pick a book × [tex]^{10}P_{10}[/tex]
[tex]= 293293* \dfrac{10!}{(10-10)!}[/tex]
= 293293 × 10!
= 1.064301638 × 10¹²
Thus , the number of possible reading schedules is 1.064301638 × 10¹²
in the formula C=5/9(F-32),If C=35, then F=?
Step-by-step explanation:
Hope this helps
Hope this is correct
Answer:
F = 95°
Step-by-step explanation:
[tex]C=\frac{5}{9}(F-32)[/tex] is the formula to convert Fahrenheit to Celsius
If we have C = 35, we just need to plug in this number to its corresponding variable and then solve for F
[tex]35=\frac{5}{9}(F-32)[/tex] then we need to multiply both sides of the equation by 9 to get rid of the fraction on the right side[tex]35(9)=[\frac{5}{9}(F-32)](9)[/tex] then simplifies to [tex]315=(5)(F-32)[/tex] Now we can distribute the 5 on the right side to the (F - 32) to get 315 = 5F - 160Adding 160 to both sides we get 475 = 5FDividing both sides by 5 we get 95 = F5. Lana pays a semiannual premium of $300 for automobile insurance, a monthly premium of $100 for health insurance, and an annual premium of $700 for life insurance.
Find her monthly expense.
Hey there! I'm happy to help!
We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.
---------------------------------------------------------------------------
AUTOMOBILE INSURANCE
$300 for automobile insurance semiannually
The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!
300/6=50
Therefore, she pays $50 a month for automobile insurance.
---------------------------------------------------------------------------
HEALTH INSURANCE
We are told here that she pays $100 every month for health insurance. We don't need do anything else here!
---------------------------------------------------------------------------
LIFE INSURANCE
We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!
700/12≈58.33
Therefore, she pays $58.33 every month on life insurance.
---------------------------------------------------------------------------
SOLUTION
Now, we just add all of these monthly totals up to find Lana's monthly expense.
50+100+58.33=208.33
Therefore, Lana's monthly expense is $208.33.
I hope that this helps! Have a wonderful day!
at the last minute deal Don and Mary booked a 7 day cruise for a total of $670. If the normal price for a couple is $1340, what discount percent did Don ans Mary recieve?
Answer:50%
Step-by-step explanation:670/1340 = 1/2 = 50%
Find the radius of a circle given that the area is three times its circumference
Answer:
Radius of the circle = 6 units
Step-by-step explanation:
Let the radius of the circle be r
According to the given condition:
Area of the circle = 3 times the circumference of the circle
[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]
PLEASE HELP ALGEBRA PROBLEM!!! 20 POINTS ANSWER A-D
Answer:
A. 1.5 seconds
B. 36 feet
C. 0 feet
D. After 3 seconds
Step-by-step explanation:
I graphed it on desmos.
Use the equation and type the ordered-pairs. y = log 2 x {(1/2, a0), (1, a1), (2, a2), (4, a3), (8, a4), (16, a5)}
Answer:
the answer is 1/2,a0
Step-by-step explanation:
Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows.
Type A
x-bar1 = 75.7 hrs.
s1 = 4.5 hrs.
n1 = 11
Type B
x-bar2 = 64.3 hrs.
s2 = 5.1 hrs.
n2 = 9
Construct a 98% confidence interval for the difference for the mean drying time between paint A and paint B.
A. 6.08 hrs < μ1 - μ2 < 16.72 hrs
B. 5.85 hrs < μ1 - μ2 < 16.95 hrs
C. 5.78 hrs < μ1 - μ2 < 17.02 hrs
D. 5.92 hrs < μ1 - μ2 < 16.88 hrs
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of type A paint
x2 = sample mean of type B paint
s1 = sample standard deviation type A paint
s2 = sample standard for type B paint
n1 = number of samples of type A paint
n2 = number of samples of type B paint
From the information given,
x1 = 75.7
s1 = 4.5
n1 = 11
x2 = 64.3
s2 = 5.1
n2 = 9
x1 - x2 = 75.7 - 64.3 = 11.4
√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709
Degree of freedom = (n1 - 1) + (n2 - 1)
df = (11 - 1) + (9 - 1) = 18
For the 98% confidence interval, the z score from the t distribution table is 2.552
Margin of error = 2.552√4.709 = 5.55
The upper boundary for the confidence interval is
11.4 + 5.55 = 16.95 hours
The lower boundary for the confidence interval is
11.4 - 5.55 = 5.85 hours
The correct option is
B. 5.85 hrs < μ1 - μ2 < 16.95 hrs
If the center of a circle is at
(5,-3) and its radius is 4, complete
its equation:
Answer:
Step-by-step explanation:
[tex](x-5)^2+(y-(-3))^2=16[/tex]
Find the percent of decrease from $2.00 to $1.25
Answer:
37.5
Step-by-step explanation:z
2.0-1.25=0.75
0.75/2.00 x 100
37.5% decrease
Choose the equation of the graph shown below:
y = |x - 1| - 3
y = |x + 1| - 3
y = |x - 1| + 3
Answer:
y=[x+1]-3 because it's at the end of the line
Which of the following are solutions to the quadratic equation? Check all that apply x^2 + 12x + 36 = 7
Answer:
x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
(x + 6)² = 7
x + 6 = + or - [tex]\sqrt{7}[/tex]
x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]
The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.
Given that the quadratic equation is x² + 12x + 36 = 7.
(x + 6)² = 7
x + 6 = ±√7
x = -6 + √7 , x = -6 - √7
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the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest
Answer:
The age difference between oldest the youngest is of 48 years.
Step-by-step explanation:
We can solve this question using a system of equations.
I am going to say that:
Kissi's age is x.
Esinam's age is y.
Lariba's age is z.
The ratio of the ages of Kissi and Esinam is 3:5
This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]
That of Esinam and Lariba is 3:5
This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]
The sum of the ages of all 3 is 147 years
This means that [tex]x + y + z = 147[/tex]
What is the age difference between oldest the youngest
z is the oldest
x is the youngest.
First i will find y.
We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]
So
[tex]x + y + z = 147[/tex]
[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]
The lesser common multiple between 5 and 3 is 15. So
[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]
[tex]49y = 147*15[/tex]
[tex]y = \frac{147*15}{49}[/tex]
[tex]y = 45[/tex]
Youngest:
[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]
Oldest:
[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]
Difference:
75 - 27 = 48
The age difference between oldest the youngest is of 48 years.
Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles.
a) To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
b) What is the critical value for the test using a 0.05 level of significance?
c) What is the test statistic?
d) What is your decision?
Answer:
a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
b) We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
Step-by-step explanation:
Information provided
[tex]\bar X=23400[/tex] represent the sample mean
[tex]s=1412[/tex] represent the sample standard deviation
[tex]n=18[/tex] sample size
[tex]\mu_o =22100[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 22100[/tex]
Alternative hypothesis:[tex]\mu \neq 22100[/tex]
Part b
We need to find the degrees of freedom given by:
[tex] df =n-1 = 18-1=17[/tex]
And the critical values for this case are:
[tex] t_{\alpha/2}= 2.110[/tex]
Part c
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]
Part d
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi
The distance between (2,0) and (5, -1) is
Answer:
(3, -1)
Step-by-step explanation:
5-2=3
0-1=-1 (keep 0, change - to a +, flip 1 to a -1)
A girl threw a marble 15 m vertically up in the air which later fell and settled at the bottom of a lake 7 m deep. Find the total distance travelled by the marble while falling down?
Answer:
22 m
Step-by-step explanation:
Total distance travelled by marble while falling down = height above surface of lake + depth of lake = 15 + 7 = 22 m
If 4000 hours= 240,000 minutes and you make a 10 minute video, how many people will need to view the video to get 4000 hours of view time?
Answer:
24000
Step-by-step explanation:
because 24000 * 10 =240000
2009-2202+1234-2 equals
Step-by-step explanation:
1039
This is the correct answer
help asap giving branlist!!!
Answer:
option 2
Step-by-step explanation:
Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.
In the circle below, CD is a diameter. If AE=10, CE=4, and AB=16, what is
the length of the radius of the circle?
Please Help ASAP
Answer:
(D)9.5 Units
Step-by-step explanation:
We have two chords CD and AB intersecting at E.
Using the theorem of intersecting chords
AE X EB =CE X ED
AE=10CE=4AB=16AB=AE+EB
16=10+EB
EB=16-10=6
Therefore:
AE X EB =CE X ED
10 X 6 = 4 X ED
ED =60/4 =15
Therefore:
CD=CE+ED
=4+15
CD=19
Recall that CD is a diameter of the circle and;
Radius =Diameter/2
Therefore, radius of the circle =19/2 =9.5 Units
A tree was 9 feet tall. One year later, the tree was 16 feet tall. Write an equation and use mental math to find how many feet f the tree grew.
Answer:
7 ftStep-by-step explanation:
let the height height of the tree be "h"
Hence the tree's height h=9 ft
one year later,let the height of the tree increased by x ft
hence
[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree
In order to solve for the added height(growth) of the tree we need to solve for x
[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]
Line segment ON is perpendicular to line segment ML
What is the length of chord ML?
0
20 units
24 units
26 units
30 units
13
P
8
M
N
Mark this and return
Answer:
The correct answer is B (24 units)
Step-by-step explanation:
Meru Peak is 765 m higher than Mt. Kilimanjaro. If the sum of their heights is 12,555 m, find the height of Mt. Kilimanjaro.
Answer:
Step-by-step explanation:
Let P=Mount Peak
Let K=Mount Killimanjaro
The equation should then be
12555=P+K ...1
P=K+765 ... 2
sub equation 2 into 1
12555=P+P+765
12555=2P+765
12555-765=2P+765-765 (subtracting 765 from both sides)
11790=2P
P=5895, now that we know P
we just make a new equation that was similiar to 1
12555=5895+K
K=6660
the height of Mount K is 6660 Metres
Arsha predicted that she would sell 225 magnets. She actually sold 240 magnets. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Magnets 225 240 a b a = Negative StartFraction 15 over 225 EndFraction; b = negative 6.7 percent a = Negative StartFraction 15 over 240 EndFraction; b = negative 6.25 percent a = StartFraction 15 over 240 EndFraction; b = 6.25 percent a = StartFraction 15 over 225 EndFraction; b = 6.7 percent
Answer:
c
Step-by-step explanation:
Please answer I need help!
Answer:
c & d
Step-by-step explanation:
the description matches the information in the table
Answer: A, B, C
Step-by-step explanation:
domain = x
range = y
One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?
Answer:
39 degrees
Step-by-step explanation:
Given
triangle is right angled i.e one angle is 90 degrees
other angle is 51 degrees.
let the third angle be x degrees
we know that sum of angles of any triangle is 180 degrees
thus,
90 + 51+ x = 180
=> 141 + x = 180
=> x = 180 - 141 = 39.
Thus, measure of other small angle is 39 degrees.
Answer:
Step-by-step explanation:
m∠A+m∠B+m∠C = 180
90+51+x1= 180
41+x=180
x=39
b. Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.) c. Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.) d. Find the expected value of X. (Round your answer to one decimal place.) e. Find the standard deviation of X. (Round your answer to three decimal places.)
Answer:
(a) Probability distribution is prepared below.
(b) The probability that two or fewer heads are observed in three tosses is 0.875.
(c) The probability that at least one head is observed in three tosses is 0.875.
(d) The expected value of X is 1.5.
(e) The standard deviation of X is 2.121.
Step-by-step explanation:
The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.
(a) Find the probability distribution of X.
(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)
(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)
(d) Find the expected value of X. (Round your answer to one decimal place.)
(e) Find the standard deviation of X. (Round your answer to three decimal places.)
Now, firstly the sample space obtained in three tosses of a fair coin is given as;
Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}
(a) The Probability distribution of X is given below;
Number of Heads (X) P(X) [tex]X \times P(X)[/tex] [tex]X^{2} \times P(X)[/tex]
0 [tex]\frac{1}{8}[/tex] = 0.125 0 0
1 [tex]\frac{3}{8}[/tex] = 0.375 0.375 0.375
2 [tex]\frac{3}{8}[/tex] = 0.375 0.75 3
3 [tex]\frac{1}{8}[/tex] = 0.125 0.375 3.375
Total 1.5 6.75
(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.125 + 0.375 + 0.375
= 0.875
(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.125
= 0.875
(d) The expected value of X = E(X) = [tex]\sum (X \times P(X))[/tex]
= 1.5
(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]
= [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]
= [tex]6.75 - 1.5^{2}[/tex] = 4.5
Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.121.
At a computer store, a customer is considering 7 different computers, 9 different monitors, 8 different printers and 2 different scanners. Assuming that each of the components is compatible with one another and that one of each is to be selected, determine the number of different computer systems possible.
Answer:
1008
Step-by-step explanation:
to find the number of combinations, just multiply everything. you will get 1008 :)
Ronald needs a morning breakfast drink that will give him at least 390 calories. Orange juice has 130 calories in 8oz. How many ounces does he need to drink to reach his calorie goal?
Answer:
24 ounces of orange juice
Step-by-step explanation:
Given-
Calories needed=390 calories
Calories in 8oz juice=130 calorie
Therefore ounces of juice=(390/130)8
=3 x 8
=24 ounces
If Ronald needs a morning breakfast drink that will give him atleast 390 calories. Orange juice has 130 calories in 8oz. Then 24 ounces does he need to drink to reach his calorie goal.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Ronald needs a morning breakfast drink that will give him at least 390 calories.
Orange juice has 130 calories in 8oz.
We need to find how many ounces does he need to drink to reach his calorie goal
Calories needed=390 calories
Calories in 8oz juice=130 calorie
Three hundred ninety divided by one hundred thirty times of eight.
Therefore ounces of juice=(390/130)8
Three hundred ninety divided by one hundred thirty is three.
=3 x 8
Three times of eight is twenty four.
=24 ounces
Hence 24 ounces of orange juice does he need to drink to reach his calorie goal.
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In 1970, 59% of college freshmen thought that capital punishment should be abolished; by 2005, the percentage had dropped to 35%. Is the difference real, or can it be explained by chance
Answer:
there is significant distinction in opinion regarding abolition of capital punishment.
Step-by-step explanation:
Compute the p cost of 2-proportion for estimating difference. The Minitab output pronounces the p valu eto be 0.000. This is less than the assumed importance degree of alpha = 0.05. Therefore, reject null hypothesis to finish that there is significant distinction in opinion regarding abolition of capital punishment.
The company produces two types of goods in quantities of x and y, with market prices of €40 and 80€, respectively. If the production cost is given by function C(x,y) =2x^2+5y^2+120 and is not exceeding €250. What is the max profit obtained?
Answer:
€ 270
Step-by-step explanation:
Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have 2x² + 5y² + 120 ≤ 250
The selling price S(x,y) = 40x + 80y
The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120
Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.
So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y
dP/dx + λdC/dx = 0
40 - 4x + 4λx = 0 (1)
4λx = 4x - 40
λ = (x - 10)/x
dP/dy + λdC/dy = 0
80 - 10y + 10λy = 0 (2)
substituting λ into (2), we have
80 - 10y + 10(x - 10)y/x = 0
multiplying through by x, we have
80x - 10xy + 10xy - 100y = 0
80x - 100y = 0
80x = 100y
x = 100y/80
x = 5y/4
substituting x into C(x,y) ≤ 250, we have
2(5y/4)² + 5y² + 120 ≤ 250
25y²/8 + 5y² + 120 ≤ 250
25y² + 40y² + 960 ≤ 2000
65y² ≤ 2000 - 960
65y² ≤ 1040
y² ≤ 1040/65
y² ≤ 16
y ≤ ±√16
y ≤ ± 4 since its quantity, we take the positive value.
So x = 5y/4 = 5(± 4)/4 = ± 5
So, x ≤ ± 5
For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have
P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120
= 200 + 320 - 50 - 80 - 120
= 520 - 250
= 270
So, the maximum profit obtained is € 270
