Answer:
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
Step-by-step explanation:
In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.
We take a sample of size n=64.
Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004[/tex]
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
For what value of the variable: 1. are the values of the expressions 2m−13 and m+3 equal? 2. is the value of 2x+1 twenty greater than 8x+5? 3. is the value of 9−y twice as much as the value of y?
Answer:
1.- m = 13
2.- [tex]x<-\frac{2}{3}[/tex]
3.- y = 3
Step-by-step explanation:
In all cases we need to start with an equation or an inequality and slove for the variable:
Case 1. : 2 m - 13 = m + 3
[tex]2m-13=m+3\\2m-m=3+13\\m=16[/tex]
Case 2. : 2 x + 1 > 8 x + 5 + 20
[tex]2x+1>8x+25\\1-25>8x-2x\\-24>6x\\-4 >x\\x<-4[/tex]
Case 3. : 9 - y = 2 y
[tex]9-y=2y\\9=2y+y\\9=3y\\y=3[/tex]
Name the triangle with the following characteristics. sides: 5 cm, 6 cm, 7 cm; Angles: 75° and 60°. yeah
Answer:
Step-by-step explanation:
this triangle is regular one
we can't apply the pytahgorian theorem 5²+6²≠7² the angles have different sizes 75≠60≠45the sides have different lengths 5≠6≠7Answer:
obtuse scalene triangle
Pls help me pick the right answer! Please
I NEED ANSWER SUPER BAD PLEASE!!!!!!!!!!!What is the greatest integer less than 100 for which the greatest common divisor of that integer and 12 is 4?
Answer:
92
Step-by-step explanation:
We will list out the numbers which are factors of 12. They include:
1, 2, 3, 4, 6, 12.
We need to get the highest number that has its greatest factor to be 4. It means that 6 and 12 cannot divide it.
To do this, we will write out the multiples of 4. They include:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88,92,96.
We will have to choose the highest number which only 4 can divide and 6 and 12 cannot divide.
Since we are looking for the largest, We can try dividing all the numbers by 4, 6, and 12 starting from 96.
We will quickly see that 4 can divide 92 but 6 and 12 cannot.
This gives us 92 as the answer.
Answer:
92
Step-by-step explanation:
Please answer this correctly
Answer:
0
Step-by-step explanation:
The probability of picking a even number is 1/3
If u don’t replace it then the probability of picking an even number is 0/3
Multiply and u get 0/9 or 0
Hope this helps
Answer:
0
Step-by-step explanation:
The number 2 is even.
The probability of picking an even number is 1/3.
You don't put the first card back.
1 and 3 are odd.
1/3 × 0 = 0
How much interest is earned if $2500 is invested for 25 years at 8% simple
interest?
*
0500
50000
250
O 5000
Answer: $5,000
Step-by-step explanation: First begin with the interest formula.
Interest = Principal × Rate × Time
In this problem, we're solving for the interest.
The principal is the amount invested or $2,500.
The rate is 8% which we can write as .08.
The time is 25 years.
So we have I = (2,500)(.08)(25).
Now we multiply.
(2,500)(.08) is equal to 200.
Now, multiply 200(25) to get 5,000.
This means that the interest earned is $5,000.
Complete the steps to solve this linear equation: 2x + 9(x – 1) = 8(2x + 2) – 5 1.Apply the distributive property: 2x + 9x– 9 = 16x + 16 – 5 2.Combine like terms on each side: 11x – 9 = 16x + 11 3.Use the subtraction property of equality to isolate the variable term: –9 = 5x + 11 Use the subtraction property of equality to isolate the constant: –20 = 5x 4. Use the division property of equality to solve: = x
Answer:
it should be -4=x.
Answer: -4
Step-by-step explanation:
Which statement best describes the function below?
f(x)=x2-x2-9x+9
Answer:
B. It is a many-to-one function.
Step-by-step explanation:
To find what the function below is, you can use the Function Grapher and Calculator from Math is Fun to graph the function.
As you can see, the graph passes the vertical line test, since each x-value has exactly one y-value.
According to the diagram below, the function will be a many-to-one function, since there are y-values that have three different x-values.
So, your answer will be B. it is a many-to-one function.
Hope this helps!
Which of the following theorems verifies that WVU= RST
Answer:
C. HL
Step-by-step explanation:
The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.
Couple more! Running out of time lol!
Answer:
A translation; (x,y) --> (x-4,y-5)
Step-by-step explanation:
This is because the figures are congruent and in the same orientation but just in different locations on the coordinate plane.
A(0,3) --> A'(-4,-2)
So, the rule is (x,y) --> (x-4,y-5)
Please answer this correctly
it would be possible because if it's 6 it's even if it 4 it's even if it's 2 it's even so you okay so it is certain and possible babes
A loan of $25,475 is taken out at 4.6% interest, compounded annually. If no payments are
made, after about how many years will the amount due reach $37,500? Round to the
nearest year.
Please helpppp
Answer:
It will take 9 years
Step-by-step explanation:
use formula A=P(1+ r/n)^nt
37,500= 25,475(1+.046/1)^1*x
37,500/25,475=1.046^x
1.47203= 1.046^x
try out different numbers for x and use whole number since it asks for the nearest year
1.046^8 = 1.43302 and 1.046^9 = 1.4989
so we know its inbetween
8 and 9 to figure out one is the closest whole number try raising it to the power of 8.5 and if it passes 1.47203 then its 9, if it doesnt then its 8
1.046^8.5 = 1.46561
1.46561< 1.47203
since 1.046561 is lower than 1.47203 its safe to assume that the year is between 8.5-8.99 thus we can round up to 9
When testing for current in a cable with sixsix color-coded wires, the author used a meter to test threethree wires at a time. How many different tests are required for every possible pairing of threethree wires?
Answer:
20 tests
Step-by-step explanation:
There are six different wires, and for each test the author picks three, this means that each test is a combination of three out of six wires (₆C₃) . The number of total combinations possible is given by:
[tex]_6C_3=\frac{6!}{(6-3)!3!}\\_6C_3=\frac{6*5*4}{3*2*1}\\_6C_3=20[/tex]
20 tests are required to verify every possible pairing of three wires.
9/3 *[(18-10)-2^2]
36
12
0.25
0.75
Answer:
12
Step-by-step explanation:
Use the PEMDAS
there is a parenthesis and exponents
9/3{(8) - 4)}
Multiply and divide 9/3= 3
Also subtract 8-4 = 4
3{8-4}
3(4)= 12
circumference of 6cm ? help plz <3 heyyy b a e (bet you won't reply :)
Answer:
If r = 6 cm, the the circumference is c = 2π(6) = 12π cm
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps. This system of equations models the given information for both stamp types. x – y = 34 x + y = 212
Step-by-step explanation:
x - y = 34
x + y = 212
2x = 246
x = 123
123 + y = 212
y = 89
(123, 89)
You buy a 33-pound bag of flour for $9 or you can buy a 1- pound bag for $0.39. Compare the per pound cost for the large and small bag. How much is the pounds per dollar
Answer:
see below
Step-by-step explanation:
9 dollars / 33 lbs = .272727 dollars per lb
.39 / 1 lbs = .39 per lb
The large bag is less expensive
Step-by-step explanation:
33lb bag = $9.00
1lb = $0.39
$9.00 bag per pound is $.0.27 per pound
If I bought 33, 1 pound bags it would cost $12.87
cheaper by $ 3.87 to buy the 9lb bag.
I NEED HELP PLEASE, THANKS! :)
Answer: C
Step-by-step explanation:
We can automatically eliminate D because since both matrices are 2x2, the product exists.
[tex]\left[\begin{array}{ccc}1&5\\-3&4\end{array}\right] \left[\begin{array}{ccc}2&6\\6&-1\end{array}\right] =\left[\begin{array}{ccc}1*2+5*6&1*6+5*(-1)\\(-3)*2+4*6&(-3)*6+4*(-1)\end{array}\right]=\left[\begin{array}{ccc}32&1\\18&-22\end{array}\right][/tex]
A 7 cm x 5 cm rectangle sits inside a circle with radius of 6 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. Please answer fast!
Answer:78.14cm^2
Step-by-step explanation:
Which best describes thermal energy?
Answer:
It's the third Answer: It is the portion of internal energy that can be transferred from one substance to another.
Hope this helps
Answer:
c
Step-by-step explanation:
A professor gives a statistics exam. The exam has 100 possible points. The scores for the students in the second classroom are as follows:
88 88 92 88 88 72 96 88 84
Calculate the sample size, n, and the sample mean, M n = M =
While grading the exam, the professor realizes that one of the questions covered material that was not yet covered in the lectures. This question was worth 20 points, so he decides to add 20 points to everyone's score.
Calculate the new n and M.
Answer:
N = 9
M = 87.11
Step-by-step explanation:
According to the situation, the data provided and the solution are as follows
The scores for the student in the classroom is
= 88 88 92 88 88 72 96 88 84
The different student's number of scores is 9
The solution of new n and M is shown below:-
Sample size (n) = 9
Sample mean (m) is
[tex]= \frac{Sum\ of\ all\ data\ values}{Sample\ size}[/tex]
= [tex]\frac{88 + 88 + 92 + 88 + 88 + 72 + 96 + 88 + 84}{9}[/tex]
[tex]= \frac{784}{9}[/tex]
= 87.11
s defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Banking officials claim that the mean bad debt ratio for all Midwestern banks is 3.5%, but that Ohio’s is different. Suppose that a random sample of seven Ohio banks is selected and that the bad debt ratios for these banks are: 7%, 4%, 6%, 3%, 5%, 4%, and 2%. Assuming that bad debt ratios are approximately normal, test at the 0.05 level of significance whether the mean bad debt ratio for Ohio banks is different than the Midwestern average.H0: Mu = 3.5Ha: Mu neq 3.5Hint: data <- c(7, 4, 6, 3, 5, 4, 2) # you can find xbar=mean(data) and s=sd(data) of the sample in R.a) What type of hypothesis test do you need to use? (3 points)b) Determine the test statistic? (3 points)c) Determine the critical value? Stat your conclusion. (5 points)d) Determine the p-value? State your conclusion. (4 points)
Answer:
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).
Test statistic t = 1.431
Critical values tc = ±2.447
P-value = 0.203
Step-by-step explanation:
This is a hypothesis t-test for the population mean.
The claim is that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).
Then, the null and alternative hypothesis are:
H_0: \mu=3.5\\\\H_a:\mu\neq 3.5
The significance level is 0.05.
The sample has a size n=7.
We calculate the sample mean and standard deviation as:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(7+4+6+3+5+4+2)\\\\\\M=\dfrac{31}{7}\\\\\\M=4.43\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((7-4.43)^2+(4-4.43)^2+(6-4.43)^2+. . . +(2-4.43)^2)}\\\\\\s=\sqrt{\dfrac{17.71}{6}}\\\\\\s=\sqrt{2.95}=1.72\\\\\\[/tex]
The sample mean is M=4.43.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.72.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.72}{\sqrt{7}}=0.65[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.43-3.5}{0.65}=\dfrac{0.93}{0.65}=1.431[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=7-1=6[/tex]
This test is a two-tailed test, with 6 degrees of freedom and t=1.431, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.431)=0.203[/tex]
As the P-value (0.203) is bigger than the significance level (0.05), the effect is not significant.
If we use the critical value approach, for this level of confidence, the critical values are tc = ±2.447. The test statistic is within the bounds of the critical values and falls within the acceptance region.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).
Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B? 2:6 4:36 1:3 1:27
Answer:
1:27 (D)
Step-by-step explanation:
Given:
Sphere A has a diameter of 2
Sphere A is dilated to create sphere B
Scale factor = 3
Volume of a sphere = 4/3 πr³
Radius = r = diameter/2 = 2/2
r = 1
Volume of sphere A = 4/3 ×π(1)³
Volume of sphere A = 4/3 × π
Volume of sphere B = 4/3 πR³
Since the diameter was dilated, the diameter of B = diameter of A × scale factor
diameter of B = 2×3 = 6
Radius of B = R = diameter/2 = 3
Volume of sphere B = 4/3 × π(3)³
Volume of sphere B = (4/3)(27)π
Ratio of the volume of sphere A to volume of sphere B
= [4/3 ×π]: [(4/3)(27)π]
= (4π/3)/[(4π/3)×27] = 1/27
= 1:27
Answer: 1:27
Step-by-step explanation:
The original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27, so the ratio is 1:27
The quick ratio, Q, is calculated using the formula Q= CA-I-P/ CL, where CA is the value of the company’s current assets, I is inventory, P is prepaid expenses, and CL is current liabilities. Rearrange the formula for current assets
Answer:
CA = Q·CL +I +P
Step-by-step explanation:
Multiply by the denominator, then add the opposite of all terms that are not CA.
[tex]Q=\dfrac{CA-I-P}{CL}\\\\Q\cdot CL=CA-I-P\\\\Q\cdot CL+I+P=CA\\\\\boxed{CA=Q\cdot CL+I+P}[/tex]
An equilateral triangular plate with sides 6 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.) rhog^3(3)^1/2 _______ dx = _______ N
Answer:
26,400 N
Step-by-step explanation:
PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION
a classical music concert is to constist of 3 cello pieces, 3 choral works, and 3 pieces for piano. In how many ways can the program be arranged if a piano piece must come first
Answer:
120,960 ways
Step-by-step explanation:
Assuming that each piece is unique, then the order of each piece matters.
There are 9 pieces in total, there are 3 options for the first piece (3 piano pieces), and the remaining 8 pieces can be permuted. The number of possible arrangements is:
[tex]n=3*\frac{8!}{(8-8)!}\\ n=3*8*7*6*5*4*3*2*1\\n=120,960\ ways[/tex]
The program can be arranged in 120,960 ways.
Progress
Question ID: 470099
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24 minutes. Working together, how long will it
take for them to paint the wall?
Answer:
8 minStep-by-step explanation:
Try this:
1 wall 1 288
------------------------ = --------------- = --------------- min = 8 min
1 wall 1 wall 24 + 12 36
(---------) + (---------) ------------
12 min 24 min 288
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) μ = 24; σ = 4.2 P(x ≥ 30) = ?
Answer:
Step-by-step explanation:
x is a random variable. Since we are assuming that x has a normal distribution, then we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 24
σ = 4.2
The indicated probability to be determined is P(x ≥ 30)
P(x ≥ 30) = 1 - P(x < 30)
For P(x < 30),
z = (30 - 24)/4.2 = 1.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.9236
Therefore,
P(x ≥ 30) = 1 - 0.9236 = 0.0764
"a. How many study subjects were cases? b. How many study subjects were controls? c. What was the ratio of controls to cases?"
Answer:
The description is provided following.
Step-by-step explanation:
The given question is incomplete. The complete question will be:
Brain tumors No Brain tumors
Cell Phones 63 185
No Cell Phones 96 292
The further explanation is given below.
a...
Subjects with these symptoms/diseases are recognized as "cases." Consequently, the majority of the instances would be as follows:
⇒ [tex]63+96[/tex]
⇒ [tex]159[/tex]
b...
Subjects who might not have the disorder or infection are classified as "controls." Therefore, the amount of controls is as follows:
⇒ [tex]185+292[/tex]
⇒ [tex]477[/tex]
c...
The proportion of control and monitoring of instances:
⇒ [tex]\frac{478}{159}[/tex]
⇒ [tex]3.006[/tex]
6 out of 9 pairs of your jeans are blue. What percentage of you
jeans are NOT blue?
Answer:
33.333333%
Step-by-step explanation:
If 6/9 (66.66666666%) of the jeans are blue it means that 3/9 of the jeans are not blue. 3/9 as a percentage is 33.333333%
Answer:
33.3%
Step-by-step explanation:
6 ÷ 9 = 66.66666667%
100% - 66.66666667% = 33.3% (Or you can put 33.33333333)
Hope this helped! :)