Answer:
[tex]V(t) = 425(0.952)^{t}[/tex]
Step-by-step explanation:
The amount of water in the bucket after t hours, in mL, can be modeled by an equation in the following format:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial amount, and r is the constant decay rate, as a decimal.
Bucket contains 425 mL of water.
This means that [tex]V(0) = 425[/tex]
The capacity of water in the bucket decreases 4.8% each hour.
This means that [tex]r = 0.048[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 425(1-0.048)^{t}[/tex]
[tex]V(t) = 425(0.952)^{t}[/tex]
Jenna worked 13 hours more than Jose last month. If Jenna worked 9 hours for every 4 hours that Jose worked, how many hours did they each work?
Which could be the side lengths of a triangle? (A) 2,2,4 (B) 3,4,7 (C) 4,5,8 (D) 5,5,10 (E) 7,3,10 PLEASE HELP
Answer:
(C) 4,5,8
Step-by-step explanation:
Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.
Answer:
Option C { 4,5,8 }
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.
* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.
______
{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.
______
Solution = { 4,5,8 }
Simplify 4 + (−3 − 8)
Answer:
-7
Step-by-step explanation:
4 + (−3 − 8)
PEMDAS
Parentheses first
4 + (-11)
Add and subtract next
-7
Answer:
first I'm using BODMAS
4+(-11)
= -7
hope it helps
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Find the sum. Please
Answer:
[tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]
Step-by-step explanation:
It usually works to factor the denominators, so you can determine the least common denominator.
[tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]
Find the fourth term in the expansion of the binomial
(4x + y)^4
a) 16xy^3
b) 256x^4
c) 64y^4
d) 4xy^3
Answer:
a) 16xy³
Step-by-step explanation:
For a binomial expansion (a + b)ⁿ, the r+1 term is:
nCr aⁿ⁻ʳ bʳ
Here, a = 4x, b = y, and n = 4.
For the fourth term, r = 3.
₄C₃ (4x)⁴⁻³ (y)³
4 (4x) (y)³
16xy³
Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]
Answer:
B. [tex]4^2[/tex]
Step-by-step explanation:
[tex]4^7 \times 4^{-5}[/tex]
Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]
[tex]4^{7 + -5}[/tex]
Add exponents.
[tex]=4^2[/tex]
Answer:
[tex] {4}^{2} [/tex]Step by step explanation
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
Use product law of indices
i.e
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
[tex] = {4}^{7 + ( - 5)} [/tex]
[tex] = {4}^{7 - 5} [/tex]
[tex] = {4}^{2} [/tex]
Hope this helps...
Best regards!
Please answer this correctly
Step-by-step explanation:
pnotgrt8rthan4 = 3 ÷ 7 × 100
= 42.8571428571 / 43%
Please answer this correctly
Answer:
2/3
Step-by-step explanation:
There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.
Answer:
2/3Step-by-step explanation:
This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.
The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.
flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,
193, 209, 215, 192, 179, 196, 225, 199, 196, 210,
199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().
b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.
c) What is the statistical decision at the significance level α = .01?
Answer:
a) The sample mean is M=200.
The sample standard deviation is s=13.19.
b) Right-tailed. The null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
c) At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Step-by-step explanation:
We start by calculating the sample and standard deviation.
The sample size is n=30.
The sample mean is M=200.
The sample standard deviation is s=13.19.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the arrival rate is significantly higher than 195. As we are interested in only the higher tail for a significant effect, this is a right-tailed test.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
The significance level is 0.01.
The standard deviation of the population is known and has a value of σ=13.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.107)=0.018[/tex]
As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Please answer this correctly
Answer:
1/7
Step-by-step explanation:
There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7
Answer:
1/7
Step-by-step explanation:
The number from the list that is less than 2 is 1.
1 number out of a total of 7 numbers.
= 1/7
7
х
45
Find x.
x=
V(14)
7
07/2
Answer:
7
Step-by-step explanation:
This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time
Of one of the equal side is 7 than the other one too must be 7
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
PLEASE HELP!!!! Find the common difference
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
What is the measure of PSQ?
Answer:
Do you have an image because I'm a bit confused with you just asking the measure of PSQ.
Step-by-step explanation:
HELP!! Im not sure what i did wrong!!
I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...
Will give brainliest answer
Answer:
[tex]153.86 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]
Answer:
153.86 [tex]units^{2}[/tex]
Step-by-step explanation:
Areaof a circle = πr^2
[tex]\pi = 3.14[/tex](in this case)
[tex]r^{2} =7[/tex]
A = πr^2
= 49(3.14)
= 153.86
PLSSSSSSS HELP WILL MARK BRAINLIEST Doug owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If he has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
Answer:
i think this person answered but idrk perseusharrison79
Step-by-step explanation:
For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.
Not drawn to scale
StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction
StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction
StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction
One-half = StartFraction 6 over x EndFraction
Step-by-step explanation:
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answer:
by using distance formula
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
by putting the values of coordinates
[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]
[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]
[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]
[tex]d=\sqrt{6.25+100}[/tex]
[tex]d=\sqrt{106.25}[/tex]
[tex]d=10.3[/tex]
Step-by-step explanation:
i hope this will help you :)
An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 13.00 and a standard deviation equal to 0.2 seconds. What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
Answer:
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 13, \sigma = 0.2[/tex]
What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
We have to find the pvalue of Z when X = 13.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13.36 - 13}{0.2}[/tex]
[tex]Z = 1.8[/tex]
[tex]Z = 1.8[/tex] has a pvalue of 0.9641
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°
Answer:
(190-5a)°
Step-by-step explanation:
Sum of internal angles of a triangle equals to 180°
If the third angle is x, then we have:
(2a-32)°+(3a+22)° +x = 180°(5a- 10)° +x= 180°x= (180+10-5a)°x= (190-5a)°The third angle is: (190-5a)°
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
I travelled at 60km/h and took 2 hours for a certain journey. How long would it have taken me if I had travelled at 50km/h?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
2 hours at 60 km/h means you have travelled 2*60=120 km
120 km at 50 km/h takes 120/50 = 2.4 hours
2.4 hours is 2 hours and 0.4*60 = 24 minutes.
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
HELP! will give brainlest or whatever its called... Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis. A’ B’ C’
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)Point B = (0, 3) becomes B ' = (0, -3)Point C = (-1, -1) becomes C ' = (-1, 1)The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer:
(-2,-3)...(0,-3)...(-1,1)
Step-by-step explanation:
The length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. Find the domain in this situation.
Answer:2/3
Step-by-step explanation:
Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).
What is domain of a function?The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).
Learn more about domain of a function here
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Rebecca collected data from a random sample of 500 homeowners in her state asking whether or not they use electric heat. Based on the results, she reports that 51% of the homeowners in the nation use electric heat. Why is this statistic misleading?
Answer:
She makes conclusion about a population that is not well represented by the sample.
Step-by-step explanation:
The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.
The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.
Answer: The sample is biased