Answer:
[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex]
Step-by-step explanation:
According to the Question,
Given that, Byron is working in a lab testing bacteria populations. After starting out with a population of 288 bacteria, he observes the change in population and notices that the population triples every 16 minutes.Therefore, the equation for the population P in terms of time t in minutes is[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex] .
$1400 is invested at 4% per annum simple interest. How long will it take for the amount to reach $1624? Show you working.
Answer:
4 years
Step-by-step explanation:
I = prt
F = p + prt
F = 1400 + 1400 * 0.04 * t
1624 = 1400 + 1400 * 0.04 * t
224 = 56t
t = 4
Answer: 4 years
Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. You may use technology to compute your answers. 20–30 30–40 40–50 50–60 Total Private Practice 16 40 38 94 Hospital 8 44 59 111 Total 24 84 97 205
Answer:
1. The correct option is:
B. H0: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.
Ha: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.
2. The test statistic is -0.97.
3. The correct option is E. We fail to reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.
Step-by-step explanation:
Note: This question is not complete and it contains some inconsistency errors in thee data. The correct complete question is therefore provided before answering the question. See the attached pdf for the correct complete question.
The explanation of the answer is now provided as follows:
1. State the null and alternative hypotheses.
Since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is:
B. H0: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.
Ha: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.
2. What is the test statistic?
Note: See the attached excel file for the calculation of total of (f1 * x), total of (f2 * x), total of (f1 * x^2) and total of (f2 * x^2).
From the attached excel file, we have:
N2 = Total of f2 = Sample size of Hospital = 150
M1 = Mean of Private-Practice = Total of (f1 * x) / N1 = 38.40
M2 = Mean of Hospital = Total of (f2 * x) / N2 = 43.60
S1^2 = Variance of Private-Practice = Total of (f1 * x^2) / N1 = 1,541.00
S2^2 = Variance of Hospital = Total of (f2 * x^2) / N2 = 1,975.67
Therefore, we have:
t = (M1 - M2) / ((S1^2 / N1) + (S2^2 / N2))^0.5 = (38.40 - 43.60) / ((1,541 / 100) + (1,975.67 / 150))^0.5 = -0.97
Therefore, the test statistic is -0.97.
3. What can you conclude at the 5% significance level?
At 5% significance level, the test statistic from the Z distribution table known as t-tab is 1.96.
Since our calculated test statistic is -0.9727 is less than 1.96, this implies that we fail to reject the null hypothesis (H0).
Again, since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is E. We fail to reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.
5 scientific calculators are being sold for $135 at a school supply store, Mary needs to
buy 35 calculators for her students. How much should she expect to pay at this rate?
Mary expects to pay $954 at this rate for 35 calculators
How do you find the rate per item?If you have a rate, such as a price per a certain number of things, and the denominator quantity is not 1, you may determine the unit rate or price per unit by dividing the numerator by the denominator.
How to find 35 calculator's price?Five 5 scientific calculators are being sold for $135.
then the per calculator's cost is 135/5= $27.
And Mary needs to buy 35 calculators for her students
then 35 calculators is 35×27 = $954.
Hence she expects to pay $954.
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Find an antiderivative F(x) with F′(x) = f(x) = 6 + 24x^3 + 18x^5 and F(1)=0.
Answer:
The antiderivative is [tex]F(X) = 6x + 6x^4 + 3x^6 - 15[/tex].
Step-by-step explanation:
Antiderivative F(x)
This is the integral of [tex]F^{\prime}(x)[/tex]
So
F′(x) = f(x) = 6 + 24x^3 + 18x^5
Then:
[tex]F(x) = \int (6 + 24x^3 + 18x^5) dx[/tex]
[tex]F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K[/tex]
[tex]F(x) = 6x + 6x^4 + 3x^6 + K[/tex]
F(1)=0
[tex]F(X) = 0[/tex] when [tex]x = 1[/tex]. We use this to find K.
[tex]F(x) = 6x + 6x^4 + 3x^6 + K[/tex]
[tex]0 = 6 + 6 + 3 + K[/tex]
[tex]K = -15[/tex]
Thus
The antiderivative is [tex]F(X) = 6x + 6x^4 + 3x^6 - 15[/tex].
You deposit $ 755 each month into an IRA earning 1.3 % interest compounded monthly
How much will you have in the account in 23 years?
Answer:
FV= $242,731.14
Step-by-step explanation:
Giving the following information:
Annual investment (A)= $755
Number of periods (n)= 23*12= 276 months
Interest rate (i)= 0.013/12= 0.0010833
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {755*[(1.0010833^276) - 1]} / 0.0010833
FV= $242,731.14
Layla is cutting bows out of ribbon which will be used to wrap gifts. If Layla needs 21/22of a foot of ribbon to make a bow, and she has 21 feet of ribbon, then how many bows can Layla make?
Answer:
21 bows
Step-by-step explanation:
Since 21/22 is just 1 short of a whole 1, we can first round it up to a whole 1, and subtract it later. 21 divided by 1 is just 21, and now is the time to subtract the part in which we rounded out. 1/22 times 21 is 21/22, so Layla can't make an entire bow with it.
Please help me with this question!!! I'm
desperate!
Suppose you take a survey of all the schools in your state. What would you expect the relationship between the number of students and the number of teachers in each school to be?
Answer:
25 students:1 teacher
Step-by-step explanation:
in ever class in my school there is 1 teacher and we have between 20 and 30 students therefor 20 + 30 / 2 is 25
Question
Find the volume of a rectangular solid with the given dimensions: length 25 feet, width 7 feet, height 10 feet. Give your
answer without units.
Answer:
1750
Step-by-step explanation:
The formula to find the volume of a rectangular prism is
[tex]v=lwh[/tex]
We are given
[tex]l=25\\w=7\\h=10[/tex]
We can then plug those values into the volume equation.
[tex]v=(25)(7)(10)\\v=1750[/tex]
Please help me in this! you get 30 points!
Answer:
y=3x-2
Step-by-step explanation:
You can verify it's not D because the y-intercept is at -2.
You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.
You can verify it's not B because that would mean the x-intercept is 1.5
Given the functions below,find (f -g) (-1).
f(x) = x2 + 3
g(x) = 4x - 3
Answer:
f(x)=-1,(-1)2+3=-2+3=1g(x)=-1 4(-1)-3=4-3=1(Step-by-step explanation:
(f-g)=1
The negative sqaure root 75 fall between which consecutive integers.
Answer:
8 and 9
Step-by-step explanation
g The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9 hour. What assumptions must be true to use the result of the central limit theorem to obtain a valid approximation for probabilities about the average daily downtime
Answer:
To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.
If one dog eats 5 pounds of food each week, how many dogs will 65 pounds of food feed for a week
Answer:
It will feed 13 dogs.
Step-by-step explanation:
1 dog = 5 lbs
Set up an equation:
Variable x = number of dogs
1/5 = x/65
Cross multiply:
1 × 65 = 5 × x
65 = 5x
Divide both sides by 5:
13
Check your work:
13 dogs × 5 lbs = 65 lbs
65 = 65
Correct!
PLEASE HELP I WILL GIVE BRAINLIEST AND 25 POINTS!!!
The following function represents the value of a truck, in dollars, after x years:
f(x) = 29,000(0.88)x
What does 0.88 represent?
The decrease in the value of the truck, which is 12%
The present value of the truck
The value of the truck after x years
The decrease in the value of the truck, which is 88%
9514 1404 393
Answer:
(a) The decrease in the value of the truck, which is 12%
Step-by-step explanation:
The only reasonable choice among the offered answers is the one shown above.
__
We would describe the value 0.88 as the annual multiplier of the truck's value, which decreases 12% each year.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 590(1.79)
Answer:
growth
79% rate of increase
Step-by-step explanation:
1.79 is > than 1
therefor growth
1.79 = 79% rate of increase
What is the standard form of 14587.25
Answer:
fourteen thousand five hundred and eighty seven point twenty five.
Step-by-step explanation:
The given number is 14587.25.
We need to write it in standard form.
7 is in ones place, 8 is in tens place, 5 is in hundreds place, 4 is in thousands place and 1 is in ten-thousands place.
So,
14587.25 = fourteen thousand five hundred and eighty seven point twenty five.
A cone has a diameter of 4 inches and a height of 9 inches. Find the volume of the cone. Use 3.14 for \large \pi.
Answer:
37.68 in.^3
Step-by-step explanation:
diameter = 4 in.
radius = diameter/2 = 2 in.
height = 9 in.
[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \blue{37.68~in.^3} [/tex]
Eduardo purchased a car for $18,500 with 6.5% sales tax, a freight charge of $450, a registration fee of $155, and an ownership fee of $45. Eduardo made a down payment
of $2.500, the total amount financed would be:
$18.056.50
$17.852.50
$17.398.75
$18.235.75
None of these choices are correct
Answer: $17,852.50
Step-by-step explanation:
First find the total cost of the car including the various charges:
Sales tax = 18,500 * 6.5%
= $1,202.50
Total cost = Purchase price + sales tax + Freight charge + Registration fee + Ownership fee
= 18,500 + 1,202.50 + 450 + 155 + 45
= $20,352.50
Subtract the down payment to find out the amount that will be financed:
= 20,352.5 - 2,500
= $17,852.50
Slope is -1 and (3,2) is on the line
what is 5.73 as a mixed number
Answer:
[tex]5 \ \frac{73}{100} [/tex]
Step-by-step explanation:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are
2 numbers to the right of the decimal point, place the decimal number over 10^2 (100). Next, add the whole number to the left of the decimal.
Answer:
5 73/100
Step-by-step explanation:
5.73 = 573
100
= 573
100
as a fraction
To convert the decimal 5.73 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
5.73 = 5.73
1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,
5.73
1
= (5.73 × 100)
(1 × 100)
= 573
100
.
(This fraction is alread reduced,
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 573
100
is also equal to 5 73/100
when expressed as a mixed number.
Solve the system of equations.
y = 3x
y = x2 - 10
A. (2,6) and (5, 15)
B. (2,6) and (-5, -15)
C. (-2,-6) and (-5, -15)
D. (-2,-6) and (5, 15)
Answer:
D. (-2, -6) and (5,15)
Step-by-step explanation:
When you set the equations together, you get x^2-3x-10. You then set this equation equal to zero and get (x-5)(x+2) or x=-2 and x=5. Then, plug these x-values into each equation to get your y-values.
Evaluate 5|7 - 9| - 2.
-12
0
1
8
[tex]\longrightarrow{\green{ D. \:8 }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex]5 \: |7 - 9| - 2[/tex]
[tex] = 5 \: | - 2| - 2[/tex]
[tex] = 5 \times 2 - 2[/tex]
[tex] = 1 0- 2[/tex]
[tex] = 8[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Identify two segments that are marked congruent to each other on the diagram
below. (Diagram is not to scale.)
K
H
#
is congruent to
Answer:
segments LJ and LI are congruent
Step-by-step explanation:
look for the little lines (tick marks)
similar marks mean congruent to each other
The two congruent segments in the figure are LJ and LI.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
An included angle is found between two sides that are under consideration. Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.
In the figure, the two segments marked are LI and LJ these two segments are congruent to each other. Congruency means the shape and the size of the segments will be equal to each other.
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Which statement correctly describes the end behavior of y = 3x8 + 5x2 +2x - 1
es
A)
The graph rises to the left and falls to the right.
B)
The graph falls to the left and rises to the right.
C)
The graph rises to the left and rises to the right.
D)
The graph falls to the left and falls to the right.
I need help with this last question plz
Answer:
C) The graph rises to the left and rises to the right.
Step-by-step explanation:
The highest expone tis even and it's coefficient is positive
therefor
The graph rises to the left and rises to the right.
This are diferente question help me please
Step-by-step
28.26 in84.9 m5024 cm277.45 mi 452.16 in1.36 mi44.15 m3.14 cmI hope it helps you
I don’t get this at all
Answer:
0.21
Step-by-step explanation:
There's 21 kids with a cell phone and no tablet
so 21/100 = 0.21
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
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Which table represents a linear function
Answer:
First table
Step-by-step explanation:
the ratio between length and breadth of a rectangle is 7 : 5 find its length and breadth if it its perimeter is 60 m
Answer:
length= 17.5 m , breadth = 12.5 m
Step-by-step explanation:
The ratio of length : breadth = 7 : 5 = 7x : 5x ( x is a multiplier )
Then
2l + 2b = perimeter ( l is length, b is breadth )
2(7x) + 2(5x) = 60
14x + 10x = 60
24x = 60 ( divide both sides by 24 )
x = 2.5
Then
length = 7x = 7 × 2.5 = 17.5 m
breadth = 5x = 5 × 2.5 = 12.5 m