Answer:
[tex]90[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the volume of a rectangular prism is [tex]V=lwh[/tex]
Let's substitute the number for the length, width, and height now.
[tex]V=(6)(5)(3)[/tex]
[tex]V=(30)(3)[/tex]
[tex]V=90[/tex]
--------------------
Hope this is helpful.
The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500. Is there sufficient evidence at the ?= 0.05 level to conclude that the mean cost has increased. Solve the question by traditional approach.
Answer:
The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.
Step-by-step explanation:
The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.
At the null hypothesis, we test if the mean cost is still the same, that is:
[tex]H_0: \mu = 13252[/tex]
At the alternative hypothesis, we test if the mean cost has increased, that is:
[tex]H_1: \mu > 13252[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
13252 is tested at the null hypothesis:
This means that [tex]\mu = 13252[/tex]
The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.
This means that [tex]n = 20, X = 15560, s = 3500[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}[/tex]
[tex]t = 2.95[/tex]
P-value of the test and decision:
The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.
The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.
Given the following numbers: a = 12500000 b = 0.00125 c = 1120000
Calculate (ab)÷ (c) and write the answer in standard form. (2.5 marks)
d) Express the interval (-1.5, 4] as an inequality and then graph the interval.
Answer:
Answer to the following question is as follows.
Step-by-step explanation:
Given:
a = 12500000
b = 0.00125
c = 1120000
Calculate (ab) ÷ (c)
Given:
d) Express the interval [-1.5, 4] as an inequality and then graph
Computation:
(ab) ÷ (c) = (a)(b) / c
(ab) ÷ (c) = (12500000)(0.00125) / (1120000)
(ab) ÷ (c) = 25 / 1,792
Express the interval [-1.5, 4]
{x : -1.5 < x ≤ 4}
Graph.
._________._________.
-1.5 0 4
There are twelve shirts in my closet. Five are red, four are blue, and three are green. What is
the probability that I choose a red or blue shirt to wear tomorrow?
O 65%
0 75%
0 80%
60%
58%
Answer:
the probability that I chose red or blue is 75%
75%
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
OMG THIS IS SO HARD
Answer:
Answer to the first question is D. Answer to the second question is also D.
Step-by-step explanation:
First question:
All the sides of the square are equal meaning you just have to multiply 1 side by 4 to get the perimeter(all the sides added together.) If one side is (s+3) then you either add that to itself 4 times or multiply it by 4. It's the same thing so it's 4(s+3) and (s+3)+(s+3)+(s+3)+(s+3).
Second question:
Adding a negative number is equivalent to subtracting a positive number. In this case, 59.2-84.7 = 59.2+(-84.7)
6. Lerato wants to purchase a house
that costs R 850 000. She is required to
pay a 12% deposit and she will borrow
the balance from a bank. Calculate
the amount that Lerato must borrow
from the bank.
Answer:
J
Step-by-step explanation:
Answer: 748,000
Step-by-step explanation: Multiply 850,000 by 0.12 and you would get 102,000 then you would subract 102,000 from 850,000 getting 748,000
Determine how much interest you would earn on the following investment:
$190,000 invested at a 6.9% interest rate for 9 months.
Estimate 620 / 17 by first rounding each number so that it has only 1 nonzero digit.
no links plz
Step-by-step explanation:
620 / 17 =36.47058.. ≈ 36.5
Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.
Answer:
[tex]P = (7, -\frac{3}{5})[/tex]
Step-by-step explanation:
Given
[tex]A = (-9,5)[/tex]
[tex]B = (11,-2)[/tex]
[tex]m : n = 4 : 1[/tex]
Required
Point P
This is calculated as:
[tex]P = (\frac{m * x_2 + n * x_1}{m + n}, \frac{m * y_2 + n * y_1}{m + n})[/tex]
So, we have:
[tex]P = (\frac{4 * 11 + 1 * -9}{4 + 1}, \frac{4 * -2 + 1 * 5}{4+1})[/tex]
[tex]P = (\frac{35}{5}, \frac{-3}{5})[/tex]
[tex]P = (7, -\frac{3}{5})[/tex]
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5)(x-3) / (x+5)(x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
what’s the answer to this problem please and thank you
Answer:
1.8574 hours
Step-by-step explanation:
Solve for t.
Take the natural log of both sides.
[tex] 3000 = 75000e^{-1.733t} [/tex]
[tex] 1 = 25e^{-1.733t} [/tex]
[tex] \dfrac{1}{25} = e^{-1.733t} [/tex]
[tex] \ln \dfrac{1}{25} = \ln (e^{-1.733t}) [/tex]
[tex] -3.218875 = -1.733t [/tex]
[tex] t = 1.8574[/tex]
If f(x)=5x and g(x)=2x-1, what is the composition f(g(x))?
Answer:
10x-5
Step-by-step explanation:
f(x)=5x
g(x)=2x-1
To create a composite function, replace x in f(x) with g(x)
f(g(x)) = 5(g(x) = 5(2x-1) = 10x-5
Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the mixture flows out at the rate of 3 gallons per minute, how many pounds of salt will remain in the tank after 16 minutes if 28 pounds of salt are in the mixture initially? (Give your answer correct to at least three decimal places.)
Answer:
Step-by-step explanation:
This is a differential equation problem most easily solved with an exponential decay equation of the form
[tex]y=Ce^{kt}[/tex]. We know that the initial amount of salt in the tank is 28 pounds, so
C = 28. Now we just need to find k.
The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is [tex]\frac{dy}{dt}[/tex]. Thus, the change in the concentration of salt is found in
[tex]\frac{dy}{dt}=[/tex] inflow of salt - outflow of salt
Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:
[tex]3(\frac{y}{400})[/tex]
Therefore,
[tex]\frac{dy}{dt}=0-3(\frac{y}{400})[/tex] or just
[tex]\frac{dy}{dt}=-\frac{3y}{400}[/tex] and in terms of time,
[tex]-\frac{3t}{400}[/tex]
Thus, our equation is
[tex]y=28e^{-\frac{3t}{400}[/tex] and filling in 16 for the number of minutes in t:
y = 24.834 pounds of salt
Match the pairs of equivalent exMatch the pairs of equivalent expressions.
pressions.
Answer:
Give us the picture or numbers please.
Step-by-step explanation:
Answer: add pic pls
Step-by-step explanation:
Which statement is true regarding the functions on the
graph?
f(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
Answer:
f(3) = g(3)
Step-by-step explanation:
on the graph the only point, where both lines cross (both functions create the same functional value) is at x=3.
since both lines have the same y-value there, we express this in math by the "=" sign. and both functions have the same input value (x=3) there.
A professor is interested in whether or not college students have a preference (indicated by a satisfaction score) for reading a textbook that has a layout of one column or layout of two columns. In the above experiment, what is the dependent variable
Answer:
Satisfaction score
Step-by-step explanation:
The dependent variable may be described as the variable which is being measured in a research experiment. In the scenario described above, the dependent variable is the satisfaction score which is used to measure preference for a one or two column textbook. The dependent variable can also seen as the variable which we would like to predict, also called the predicted variable . The predicted variable here is the satisfaction score.
DE is tangent to Circle C at point D.
What is the measure of
Enter your answer in the box.
Answer:
39°
Step-by-step explanation:
A radius of a circle (segment CD) drawn to the point of tangency (D) intersects the tangent (line DE) at a 90-deg angle.
That makes m<D = 90.
m<D + m<C + m<E = 180
90 + 51 + m<E = 180
m<E = 39
if an angle is bisected to form two new 20 degree angles, what was the measure of the original angle?
Answer:
10 degrees
Step-by-step explanation:
The angle bisected so that mean it was divided into 2 parts, so if it's 20 degree angles bisected it's divided by 2:
20/2= 10°
So the measure of the original angle is 10° degrees!
Answer:40
Step-by-step explanation: i took the lesson this was the answer
1. Which of the following ARE integers? (choose ALL that are integers
a. 35%,
b.-10,
c. 34,
d. 0.25,
e. 3105.
2. Which integer is between -3 and 4? (choose ONE answer)
a. 10
b. 3.14
c. O
Answer:
(1) -10, 34 and 3105
(2) 0
Step-by-step explanation:
Solving (a): Select all integers
The integers are numbers without decimal.
So, we have: -10, 34 and 3105
Other options are not integers
Solving (b): Select all integers between -3 and 4
Using the same explanation in (1) but with the range of -3 and 4. the integer is 0.
Other options are not integers
what is the greatest common factor of 160 and 198?
Hey there!
[tex]\large\textsf{FACTORS OF 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, \& 160}[/tex]
[tex]\large\textsf{FACTORS OF 198: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, \& 198}[/tex]
[tex]\large\text{Go through the factors to see if there’s any like terms and if you find any,} \\\large\text{look for the greatest one the numbers share together.}[/tex]
[tex]\large\text{Like terms: \boxed{\textsf{\bf 1 \& 2}}}[/tex]
[tex]\large\checkmark\boxed{\large\text{GCF: \bf 2 }}\large\checkmark[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge the GCF \underline{G}reatest \underline{C}ommon \underline{F}actor is \bf 2}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
3. Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years. Calculate a 96% CI on the death rate from lung cancer.
Answer:
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.
This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
2. What facts are needed to solve the problem?
Answer:
firstly we have to identify the problems, understand carefully and chose the best way to solve problems.
F(x) =-2x-4 find x if f(x)=14
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
An initial deposit of $212 is placed in
a bank account and left to grow, with
interest compounded continuously.
what will it be after 6 years?
Round your answer to the nearest dollar.
Answer:
$224.932
Step-by-step explanation:
Note: The question is not complete
say the rate is 10%
Given data
Initial depostite= $212
TIme= 6years
rate= 10%
the expression for the compound interest is given as
A=P(1+r)^t
substitute
A=212(1+0.1)^6
A=212(1.01)^6
A=212*1.061
A= $224.932
Hence the final amount at the rate of 10% is $224.932
Which of the following best describes the relationship between angle a and angle bin the image below?
express the ratio as a fraction in the lowest term.3600s:2hours
Step-by-step explanation:
3600s=1hr
so, 1hr:1hr
1:1
Based on the concept of fractions and the information in the question, the fraction form in the lowest term is 1/2.
What is Fraction?Fraction is a term that is used to describe the portion/part of the whole thing. It represents the equal parts of the whole.
Generally, the term fraction has two parts, namely numerator and denominator.
Hence, in this case, to express the ratio as a fraction in its lowest term, convert both units to the same unit of time.
1 hour is equal to 3600 seconds so 2 hours is equal to 2 * 3600 = 7200 seconds.
Now the ratio is 3600 seconds to 7200 seconds.
To simplify this ratio we can divide both terms by their greatest common divisor which is 3600.
So the simplified ratio is 1:2.
Therefore, in this case, it is concluded that the fraction form in the lowest term is 1/2.
Learn more about fraction here: https://brainly.com/question/30154928
#SPJ2
Student received 10 different resistors for a laboratory setup with five slots to attach resistors, where each slot can accommodate only one resistor. In how many ways those 10 resistors can be attached to the laboratory setup?
Answer:
The number of ways of attaching the 10 resistors = 5¹⁰ = 9,765,625 ways
Step-by-step explanation:
Given;
total number of resistors, n = 10
number of slots available, = 5
The first resistor can be attached in 5 ways,
The second resistor can also be attached in 5 ways,
The third resistor can also be attached in 5 ways, etc
Each of the resistors can be attached in 5 different ways;
The number of ways of attaching the 10 resistors = 5¹⁰ = 9,765,625 ways
The mean number of words per minute (WPM) typed by a speed typist is 149 with a standard deviation of 14 WPM. What is the probability that the sample mean would be greater than 147.8 WPM if 88 speed typists are randomly selected
Answer:
78.81%
Step-by-step explanation:
We are given;
Population mean; μ = 149
Sample mean; x¯ = 147.8
Sample size; n = 88
standard deviation; σ = 14
Z-score is;
z = (x¯ - μ)/(σ/√n)
Plugging in the relevant values;
z = (147.8 - 149)/(14/√88)
z = -0.804
From z-distribution table attached, we have; p = 0.21186
P(X > 147.8) = 1 - 0.21186 = 0.78814
In percentage gives; p = 78.81%
This graph shows the solution to which inequality?
(32)
(-3.-6);
A ys 1/x - 2
B. y> fx-2
C. yzfx-2
***-2
Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x)→0 . f(x)=lnx, a=
Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
[tex]f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...[/tex]
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
[tex]f(x) = ln(a) + \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....[/tex]
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
