Answer:
1) [tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
2) [tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
Step-by-step explanation:
Information given
n=300 represent the random sample taken
X=21 represent the number of peanuts empty
[tex]\hat p=\frac{21}{300}=0.07[/tex] estimated proportion of peanust empty
[tex]p_o=0.06[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Part 1
We want to test if the true proportion is 6% or no the system of hypothesis are:
Null hypothesis:[tex]p=0.06[/tex]
Alternative hypothesis:[tex]p \neq 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]
We can calculate the p value with the following formula:
[tex]p_v =2*P(z>0.729)=0.466[/tex]
The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.
Part 2
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]
And rounded up we have that n=2167
In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine the number of CFUs, the sample is prepared, spread uniformly on an agar plate, and then incubated at some suitable temperature. Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with μ = 15.
(a) If the area of the agar plate is 75 square centimeters (cm2), what is the probability of observing fewer than 4 CFUs in a 25 cm2 area of the plate? (Round your answer to four decimal places.)
(b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs? Use the Poisson distribution to obtain this probability. (Round your answer to four decimal places.)
(c) Repeat the probability calculation in part (b) but now use the normal approximation. (Round your answer to four decimal )
(d) Find the difference between this value and your answer in part (b). (Round your answer to four decimal places.)
Answer:
(a) 0.2650
(b) 0.0111
(c) 0.0105
(d) 0.0006
Step-by-step explanation:
Given that:
In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.
Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15. &;
If the area of the agar plate is 75cm²;
what is the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate.
We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;
75cm²/25cm² = 3
Since;
mean μ = 15
mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs
Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:
= P(X < 4)
Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )
we have ;
P(X < 4) = 0.2650
b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?
Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates = 15×5 = 75 CFUs
The probability is therefore = P( X > 95 )
= 1 - P(X ≤ 95)
= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)
= 0.0111
c) Repeat the probability calculation in part (b) but now use the normal approximation.
Let assume that the mean and the variance of the poisson distribution are equal
Then;
[tex]X \sim N (\mu = 75 , \sigma^2 = 75)[/tex]
We are to repeated the probability calculation in part (b) from above;
So:
P( X > 95 )
use the normal approximation
From standard normal variable table:
P(Z > 2.3094)
Using normal table
P(Z > 2.3094) = 0.0105
(d) Find the difference between this value and your answer in part (b).
So;
the difference between the value in part c and part b is;
= 0.0111 - 0.0105
[tex]= 6*10^{-4}[/tex]
= 0.0006 to four decimal places
What’s the correct answer for this?
Answer:
what is this it is not understand able
Answer:
11
Step-by-step explanation:
<TKF = 90° ( BECAUSE OF THE BISECTOR)
BUT
<TKF = 5(x+7)
So
5(x+7) = 90
5x+35 = 90
5x = 90-35
5x = 55
Dividing by 5(both sides)
x = 11
If f(x)= 5x + 40, what is f(x) when x = -5?
Answer:
f(x) = 15
Step-by-step explanation:
"If f(x)= 5x + 40, what is f(x) when x = -5?"
Substitute x for -5:
f(x) = 5x + 40
f(x) = 5(-5) + 40
f(x) = -25 + 40
f(x) = 15
What’s the value of x?
Answer:
x =20
Step-by-step explanation:
7x- 99 = 2x+1 ( vertically opposite angles)
7x - 2x = 1 +99
5x = 100
x =100/5
x =20
hope it helps
What is 2-2x greater than negative 20?
Answer:
no.
Step-by-step explanation:
Answer: -2x-18
Step-by-step explanation:
At a fundraiser, a school group charges $8 for tickets for a "grab bag." You choose one bill at random from a bag that contains 38 $1 bills, 20 $5 bills, 7 $10 bills, 5 $20 bills, and 1 $100 bill. Is it likely that you will win enough to pay for your ticket?
It is that you will win enough to pay for your ticket because the probability of winning enough to pay for your ticket as a simplified fraction is
Answer:
a. It is not likely that a winning ticket will be selected
b. The probability of winning enough to pay for the ticket expressed as a simplified fraction is 13/71
Step-by-step explanation:
To answer this question, there are some important notes to know.
1. The selection is only once
2. To win, you have to select a note which has a greater value than $8
Now, the total number of notes that we have = 38 + 20 + 7 + 5 + 1 = 71
The number of bills present that are greater than $8 are; 7 $10 bills , 5 $20 bills and 1 $100 bill
This makes a total of 7 + 5 + 1 = 13
Thus, the probability of selecting a bill which would pay for the charges is 13/71
Now, the probability of not selecting is 1- probability of selecting = 1-13/71 = 58/71
Since the probability of not selecting is greater than the probability of selecting, it means that it is not likely that a winning ticket will be selected
On your second day of measuring living trees you find a tree with a diameter of 24 inches! Should you predict the volume of this tree? Why or why not? Group of answer choices Yes! Extrapolation is fine. Don't worry about it. No! That would be extrapolation, and extrapolation is bad. (Notice in the plot that we only collected date for diameters between 8 and 22 inches).
Answer:
Yes! Extrapolation is fine. Don't worry about it.
Step-by-step explanation:
Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.
What is the solution to the equation below?
Answer:
A
Step-by-step explanation:
2/3x=1-5
2/3x=-4
x=-4/2/3
x=-6
Solve the equation, keeping the value for x as an improper fraction. 2/3 x = − 1/2 x + 5
Answer:
[tex]x= 30/7[/tex]
Step-by-step explanation:
[tex]2/3 x = -1/2 x + 5[/tex]
[tex]2/3x+1/2x = + 5[/tex]
[tex]7/6x=5[/tex]
[tex]x=5 \times 6/7[/tex]
[tex]x= 30/7[/tex]
can someone help me?
Answer: 26
Step-by-step explanation:
32-6 = 26
if 36-k=4+k what is the value of K?
36 - k = 4 + k
36 - 4 = k + k
32 = 2k
32/2 = k
16 = k
Steps:
Step 1: Simplify both sides of the equation
36−k=4+k
36+−k=4+k
−k+36=k+4
Step 2: Subtract k from both sides
−k+36−k=k+4−k
−2k+36=4
Step 3: Subtract 36 from both sides
−2k+36−36=4−36
−2k=−32
Step 4: Divide both sides by -2
−2k/−2 = −32/−2
Description:
Since we are trying to find the value of K, we need to simplify both sides of the equation. After that your answer will come as −k+36=k+4. Now the second step is to subtract k from both sides, your equation will come as −2k+36=4. Thirdly we need to subtract 36 from both sides, your equation will come as −2k=−32. Now you need to divide both sides by -2. After you do that, you will get your answer which is k=16.
Answer: k=16
Please mark brainliest
Hope this helps.
Eric's average income for the four months of the year 1450 point to $5 what must be his average income for the remaining eight months so that his average for the year is $1780.75
Answer:
$2668.63
Step-by-step explanation:
If the average of 4 months is $5
Meaning the total sum for 4 months
4×5 =$20
If the average for the year was $1780.75
It means the total sum for a year is;
$1780.75×12 =$21369
This means the money received for the remaining 8 months is;
$21369-$20=$21349
Hence the average income for the remaining 8months is ;
The total amount for 8 months / 8;
$21349/8= $2668.625
$2668.63
Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation of kilometers per hour, and the mean speed for a sample of motorcycles was kilometers per hour with a standard deviation of kilometers per hour. Construct a confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let denote the mean speed of motorcycles and round the answers to at least two decimal places. A confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
Construct the 98% confidence interval for the difference μ 1-y 2 when x 1 475.12, x 2-32134, s 1-43.48, s 2-21.60, n 1-12, and n 2-15. Use tables to find the critical value and round the answers to two decimal places. A 98% confidence interval for the difference in the population means is ________.
Answer:
Step-by-step explanation:
Hello!
X₁: speed of a motorcycle at a certain intersection.
n₁= 135
X[bar]₁= 33.99 km/h
S₁= 4.02 km/h
X₂: speed of a car at a certain intersection.
n₂= 42 cars
X[bar]₂= 26.56 km/h
S₂= 2.45 km/h
Assuming
X₁~N(μ₁; σ₁²)
X₂~N(μ₂; σ₂²)
and σ₁² = σ₂²
A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
The parameter of interest is μ₁-μ₂
(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71[/tex]
[(33.99-26.56) ± 1.654 *([tex]3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }[/tex])]
[6.345; 8.514]= [6.35; 8.51]km/h
Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06[/tex]
[(475.12-321.34) ± 2.485 *([tex]33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }[/tex])]
[121.96; 185.60]
I hope this helps!
A 6lb weight is attached to a spring suspended from a ceiling. The weight stretches the spring 4 inches. The external force is f(t)=27sin(4t)-3cos(4t). The medium offers a resistance of 3dy/dt (ft/sec). Find the equation of the motion.
Answer:
displacement x = - 0.046sin4t +0.006cos4t
Step-by-step explanation:
The model of the equation of motion is a forced motion equation and to determine the displacement of the weight as a function of time; we have:
the weight balances of the elastic force in the spring to be expressed by the relation:
mg = kx
where;
x=4 in (i.e 1/3 ft )
mass m = 6lb
let make k the subject; then:
k = mg/x = 6×32/(1/3) = 576
assuming x to be the displacement form equilibrium;
Then;
[tex]F = 27sin 4t-3cos4t +k(x+1/3) - mg -3v[/tex]
(since F(t)=27sin 4t-3cos4t somehow faces downwards, mg=downwards and k(x+1/3)= upwards and medium resistance 3v = upwards)
SO;
[tex]d2x/dt2 = 27sin 4t-3cos4t +kx - 3dx/dt[/tex]
[tex]d2x/dt2 +3dx/dt - 576x = 27sin 4t-3cos4t[/tex]
Assuming : [tex]x = asin4t + bcos4t[/tex]
[tex]dx/dt = 4acos4t - 4bsin4t[/tex]
[tex]d2x/dt2 = -16asin4t - 14bcos4t[/tex]
replacing these values in the above equation
[tex]= -16asin4t - 14bcos4t + 12acos4t - 12bsin4t -576asin4t-576bcos4t = 27sin 4t-3cos4t[/tex]
[tex]= sin4t (-592a-12b) + cos4t(12a -590b) = 27sin 4t-3cos4t[/tex]
equating sin and cos terms
a = - 0.046 ; b = 0.006
displacement x = - 0.046sin4t +0.006cos4t
A family is taking a trip. During the first 2 hours, they travel at a rate of 25 miles per hour. They then take a break for 2 hours and do not travel during that time. They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day. What is the average speed for their first day of travel? How much time elapsed from the start of their trip until they stopped for the day? Δt=
Answer:
Average speed v = 24.29 mph
Total time taken ∆t = 7 hours
Step-by-step explanation:
Given;
the first 2 hours, they travel at a rate of 25 miles per hour
t1 = 2 hours
v1 = 25 mph
then take a break for 2 hours and do not travel during that time
t2 = 2 hours
v2 = 0
They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day.
t3 = 3 hours
v3 = 40 mph
Total time taken ∆t = sum of time taken for the day travel
∆t = t1 + t2 + t3
Substituting the values;
∆t = 2 + 2 + 3 = 7 hours
The average speed v = total distance travelled/total time taken
v = d/∆t .......1
Total distance travelled d = Σ(velocity × time)
d = v1t1 + v2t2 + v3t3
d = 25 × 2 + 0×2 + 40 × 3
d = 50 + 0 + 120
d = 170 miles
Substituting into equation 1.
v = 170 miles ÷ 7 hours
Average speed v = 24.29 mph
The Thrill amusement park charges an entry fee of $40 and an additional $5 per ride, x. The Splash water park charges an entry fee of $60 and an additional $3 per ride, x Based on this information, which system of equations could be used to determine the solution where the cost per ride of the two amusement parks, y, is the same?
Answer:
40+5x=y
60+3x=y
Step-by-step explanation:
The first park is 40+5x
The second park is 60+3x
Now set them both equal to y
Please help I’ll mark you as brainliest if correct!
Answer:
(x+7)^2+(y-8)^2=1
(x-x value of center)^2+(y-y value of center)^2=radius
Answer:
(x + 7)² + (y - 8)² = 1
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = - 7, k = 8, r = 1
(x -(-7))² + (y - 8)² = 1²
(x + 7)² + (y - 8)² = 1
dentify the reference angle for each given angle, . degrees. degrees. degrees. degrees.
Answer:
S, Z, F
Step-by-step explanation:
i know its not the question but its for anyone who found this and needs it for edge lol
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
a) 95% of the widget weights lie between _______ and ________.
b) What percentage of the widget weights lie between 37 and 67 ounces?c) What percentage of the widget weights lie above 49 ?
Answer:
a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
Step-by-step explanation:
For this case our random variable of interest for the weights is bell shaped and we know the following parameters.
[tex]\mu = 55, \sigma =6[/tex]
We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.
Part a
For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
Part b
For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
Part c
We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
2]a^4+(root under 2b)^4
3]x^4+5x^2+9
4]p^2-10xp+16x^2-q^2+6xq
solve it
Answer:
1) a^4 + 16b^4
2) x^4 + 5x^2 + 9
3) p^2 − 10px − q^2 + 6qx + 16x^2
Step-by-step explanation:
1) a^4 + (2b)^4
= a^4 + 16b^4
2) x^4 + 5x^2 + 9
There are no like terms.
Answer:
= x^4 + 5x^2 + 9
3) p2 − 10xp + 16x2 − q2 + 6xq
= p^2 − 10px − q^2 + 6qx + 16x^2
Four interior angles of a pentagon measure 88°, 118, 132, and 100°. What is the measure of the fifth interior angle?
82
92
102
112
Answer:
fifth angle = 102°
Step-by-step explanation:
A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles .And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will be 180 × 3 = 540°. The sum of interior angles of a pentagon = 540°.
The general rule for calculating sum of the interior angles of a polygon is
sum of interior angle = (n−2) × 180°
where
n = number of sides
n = 5 since we are dealing with a pentagon.
sum of interior angle of a pentagon = 540°
The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.
fifth angle = 540 - (88 + 118 + 132 + 100)
fifth angle = 540 - 438
fifth angle = 102°
Answer:
its C on edg
Step-by-step explanation:
Make r the subject of the formula
Answer:
[tex]r=\frac{-a+p}{a+p}[/tex]
Step-by-step explanation:
[tex]-pr+p=ar+a[/tex]
[tex]-ar-pr+p=a[/tex]
[tex]-ar-pr=a-p[/tex]
[tex]r(-a-p)=a-p[/tex]
[tex]r=\frac{-a+p}{a+p}[/tex]
Answer:
[tex]r = \frac{p - a}{(p + a)} [/tex]
Step-by-step explanation:
[tex]p = \frac{a(1 + r)}{(1 - r)} \\ p(1 - r) = a(1 + r) \\ p - pr = a + ar \\ p - a = pr + ar \\ p - a = r(p + a) \\ \frac{p - a}{(p + a)} = \frac{r(p + a)}{(p + a)} \\ \frac{p - a}{(p + a)} = r[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
How do I write the formula?
Answer:
1/5x = h(x)
Step-by-step explanation:
6x+y = 4x+ 11y
Subtract y from each side
6x+y -y = 4x+ 11y-y
6x = 4x+10y
Subtract 4x from each side
6x-4x = 4x+10y-4x
2x = 10y
Divide each side by 10
2x/10 = 10y/10
1/5x = y
1/5x = h(x)
At hockey practice., Lars has the puck in front of the net, as shown. He is exactly 8 m away from the middle of the net, which is 2 m wide. Within what angle must Lars fire his shot in order to get it in the net, to nearest degree?
Answer:
14.25°
Step-by-step explanation:
distance from middle of the net = 8 m
width of the net = 2 m
this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.
We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.
We use the trigonometric function; tan∅ = opp/adj
opp is the side facing the angle = 1 m
adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)
adj = 8 m
tan∅ = [tex]\frac{1}{8}[/tex] = 0.125
∅ = [tex]tan^{-1}[/tex] 0.125 = 7.125°
Angle within which Lars must fire his shot = 2 x ∅
= 2 x 7.125° = 14.25°
Find three times five-twelfths, expressed as a decimal.
Answer:
The answer will be 1.25
Step-by-step explanation:
In order to make 512 into a decimal, you take the top number or numerator, which is 5 , and take your bottom number or your denominator, which is 12 , and divide 5 by 12 which will give you0.416666667
Hey there! :)
Answer:
1.25
Step-by-step explanation:
Begin by multiplying the fractions:
[tex]\frac{3}{1}* \frac{5}{12}= \frac{3*5}{1*12} = \frac{15}{12}= \frac{5}{4}[/tex]
Convert [tex]\frac{5}{4}[/tex] into a decimal:
5/4 = 1.25.
A factory ship the 100 boxes with 15 skateboards in each box and 10 boxes with 15 helmets in each box
Answer:
150(10s + h)
Step-by-step explanation:
We need to write an expression for the total items they shipped.
Let each skateboard be s.
Let each helmets be h.
The factory ships 100 boxes with 15 skateboards in each box. That is:
100 * (15 * s) = 1500s
The factory ships 10 boxes with 15 helmets in each box. That is:
10 * (15 * h) = 150h
The total number of items shipped is therefore:
1500s + 150h = 150(10s + h)
This expression represents the total number of items shipped.
A company makes two types of biscuits: Jumbo and Regular. The oven can cook at most 400 biscuits per day. Each jumbo biscuit requires 2 oz of flour, each regular biscuit requires 1 oz of flour, and there is 600 oz of flour available. The income from each jumbo biscuit is $0.08 and from each regular biscuit is $0.11. How many of each size biscuit should be made to maximize income? What is the maximum income?
Answer:
$ 44
Step-by-step explanation:
If we analyze the statement well, we can observe something very crucial to solve it, the jumbo biscuits require 2 oz of flour and give a profit of $ 0.08, the Regular one that only requires 1 oz of flour leaves a profit of $ 0.11, which means that requiring a smaller quantity of flour leaves a greater profit, so in terms of profit it is not profitable to make Jumbo, only Regular.
Therefore, since you can make 400 biscuits, they would all be regular since there are 600 oz of flour available, it is enough to make 400, therefore the maximum profit would be:
$ 0.11 * 400 = 44
The maximum possible profit is $ 44
A random sample of 10 college students was drawn from a large university. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. We want to determine if we can infer at the 5% significance level that the population mean is not equal to 20.
Answer:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
Step-by-step explanation:
Information given
22, 17, 27, 20, 23, 19, 24, 18, 19, and 24
The sample mean and deviation for these data are:
[tex]\bar X=21.3[/tex] represent the ample mean
[tex]s=3.199[/tex] represent the sample standard deviation for the sample
[tex]n=10[/tex] sample size
[tex]\mu_o =20[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is equal to 20 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 20[/tex]
Alternative hypothesis:[tex]\mu \neq 20[/tex]
The statistic would be:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
Brian is finishing a meal at his favorite restaurant. The check shows that the cost of the food is $42. He adds a 15% tip to the amount on the check. What is the total amount Brian paid? Write your answer up to two decimal places
Answer:
48.30
Step-by-step explanation:
First determine the tip
42 *15%
42 *.15 =6.30
Add this to the amount of the tip
42 + 6.30 =48.30
The total amount is 48.30
Answer:
Step-by-step explanation:
$48.30