Answer:
6 seconds
Step-by-step explanation:
The area of interest increases from 4 square feet to 16 square feet, an increase of 12 square feet. Since the area increases by 2 square feet each second, the time required for it to increase 12 square feet is ...
(12 square feet)/(2 square feet/second) = 6 seconds
A painter leans a 10 ft ladder against a building.
The base of the ladder is 7 ft from the building.
To the nearest foot, how high on the building
does the ladoer reach?
Answer:
7.14 ft I hope it helps :)Step-by-step explanation:
[tex]Hypotenuse = 10\\Opposite = 7\\Adjacent = x\\ \\Using Pythagoras theorem ;\\Hyp^{2} =opp^{2} +adj^{2} \\10^{2} = 7^{2} +x^{2} \\100 = 49+x^{2} \\x^{2} =100-49\\x^{2} =51\\\sqrt{x^{2} } =\sqrt{51} x = 7.14 ft[/tex]
How many ordered pairs (x, y) of positive integers satisfy the inequality 4x + 5y < 20?
Answer:
6
Step-by-step explanation:
The ordered pairs that satisfy the inequality are shown in the attachment. There are 6 of them.
A marketing consulting group wants to see whether placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales. The average sales of the seasonal cookie for this region was 650 units. A sample of 36 stores that placed the cookie on an end cap showed a sample mean of 671 units sold with a standard deviation of 81. The resulting p-value is 0.1288; thus, the null hypothesis is not rejected. The marketing consulting group concludes that placing the cookies on an end cap does not affect sales. What type of error is possible in this situation
Answer:
Type II error.
Step-by-step explanation:
We have a hypothesis test for the claim that placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales.
The null hypothesis will state that there is no difference, while the alternative hypothesis will state that there is significant positive difference.
The result is a P-value of 0.1288 and the null hypothesis failing to be rejected.
As the null hypothesis failed to be rejected, if an error has been made in the conclusion, is that we erroneusly accept a false null hypothesis.
This is a Type II error, where the null hypothesis is accepted although the alternative hypothesis is true.
Let v be the vector from initial point Upper P 1P1 to terminal point Upper P 2P2. Write v in terms of i and j. Upper P 1P1equals=(negative 8−8,44), Upper P 2P2equals=(66,44)
Answer:
The expression of [tex]\vec v[/tex] in terms of i and j is:
[tex]\vec v = 74\cdot i + 0\cdot j[/tex]
Step-by-step explanation:
Let [tex]\vec P_{1}[/tex] and [tex]\vec P_{2}[/tex] vectors with respect to origin, so that [tex]\vec P_{1} = (-8,44)[/tex] and [tex]\vec P_{2} = (66,44)[/tex]. [tex]\vec v[/tex] is a vector of the form:
[tex]\vec v = \vec P_{2} - \vec P_{1}[/tex]
Then,
[tex]\vec v = (66,44)-(-8,44)[/tex]
[tex]\vec v = (66 + 8, 44 - 44)[/tex]
[tex]\vec v = (74, 0)[/tex]
The expression of [tex]\vec v[/tex] in terms of i and j is:
[tex]\vec v = 74\cdot i + 0\cdot j[/tex]
which term represents a perpendicular segment joining the two bases of a right prism?
A: altitude
B: slant height
C: lateral area
D: surface area
Answer:
A: altitude
Step-by-step explanation:
The perpendicular segment joining the bases of a prism is the
altitude.
While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems. The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013. Is this an unusually high number of faulty modems
Answer:
We conclude that this is an unusually high number of faulty modems.
Step-by-step explanation:
We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.
The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.
Let p = population proportion.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.013 {means that this is an unusually high number of faulty modems}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion faulty modems= [tex]\frac{10}{367}[/tex] = 0.027
n = sample of modems = 367
So, the test statistics = [tex]\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }[/tex]
= 2.367
The value of z-test statistics is 2.367.
Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that this is an unusually high number of faulty modems.
Recently, TWA reported an on-time arrival rate of 78.4%. Assume that a later random sample of 750 flights results in 630 that are on time. If TWA were to claim that its on-time arrival rate is now higher than 78.4%, would the claim be supported at the 0.02 level of significance? Please show all 4 steps of the classical approach.
Answer:
Step-by-step explanation:
1. Null hypothesis: u <= 0.784
Alternative hypothesis: u > 0.784
2. Find the test statistics: z using the one sample proportion test. First we have to find the standard deviation
Using the formula
sd = √[{P (1-P)}/n]
Where P = 0.84 and n = 750
sd =√[{0.84( 1- 0.84)/750]}
sd=√(0.84 (0.16) /750)
SD =√(0.1344/750)
sd = √0.0001792
sd = 0.013
Then using this we can find z
z = (p - P) / sd
z = (0.84-0.784) / 0.013
z =(0.056/0.013)
z = 4.3077
3. Find the p value and use it to make conclusions...
The p value at 0.02 level of significance for a one tailed test with 4.3077 as z score and using a p value calculator is 0.000008254.
4. Conclusions: the results is significant at 0.02 level of significance suck that we can conclude that its on-time arrival rate is now higher than 78.4%.
i need help on this lol
Answer:
the math problem is incomplete
polygon P'Q'R'S'T' shown on the grid below is an image of polygon PQRST after dilation with a scale factor of 3, keeping the origin as the center of dilation:
Answer: d) SR and S'R' have the ratio 1:3
Step-by-step explanation:
In order for the polygons to be similar, they must have congruent angles and proportional side lengths.
a) ∠Q and ∠Q' have the ratio 1:3
FALSE - The angles must be congruent (not proportional)
b) TS and T'S' have equal lengths
FALSE - We can see that there is a dilation so they cannot be congruent.
c) RT and R'T' have equal lengths
FALSE - We can see that there is a dilation so they cannot be congruent.
d) SR and S'R' have a ratio of 1:3
TRUE! - The sides are proportional so we can use this to prove similarity.
Answer:
D- The lengths of side SR and side S'R' are in the ratio 1:3.
Step-by-step explanation:
I took the test and it was right
Pleasssseeeeee hhhhheeeelllpppp
Answer:
what can I help you miss
Answer: A' = (1, 5)
B' = (-3, 5)
C' = (-3, 2)
D' = (1, 2)
Step-by-step explanation:
Reflecting across the y-axis provides the opposite x-value.
Z = (x, y) --> Z' = (-x, y)
A = (-1, 5) --> A' = (1, 5)
B = (3, 5) --> B' = (-3, 5)
C = (3, 2) --> C' = (-3, 2)
D = (-1, 2) --> D' = (1, 2)
Pls answer either of these questions with step by step explanation
Answer:
C and B
Step-by-step explanation:
31. Thrice means 3 times as much. Let's call Rahul and Shivam's present ages r and s respectively. We can write:
r = 3s
r + 8 = 1 + (s + 8) * 2
Simplifying the second equation gives us r + 8 = 2s + 17. When we substitute r = 3s into the second equation we get 3s + 8 = 2s + 17 which gives us s = 9. This means r = 9 * 3 = 27 so Rahul's age 8 years before the present is 27 - 8 = 19.
32. Let's call Ravi and Kishan's ages r and k. We can write:
r + k = 69
r - 8 = 2(k - 8) - 4
Rewriting the first equation gives us r = -k + 69 and when we substitute this into the second equation we get -k + 69 - 8 = 2k - 16 - 4. Solving for k we get k = 27 which means r = 42. 42 - 27 = 15.
A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 54 specimens and counts the number of seeds in each. Use her sample results (mean = 81.1, standard deviation = 8.4) to find the 90% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.
Answer:
90% confidence interval for the number of seeds for the species
(78.8073 ,83.3927)
Step-by-step explanation:
Step(i):-
Given sample size 'n' =54
Mean of the sample x⁻ = 81.1
standard deviation of the sample 'S' = 8.4
90% confidence interval for the number of seeds for the species
[tex](x^{-} -t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} -t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} })[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 54-1 =53
[tex]t_{\frac{0.10}{2} } = t_{0.05} = 2.0057[/tex]
[tex](81.1 -2.0057\frac{8.4}{\sqrt{54} } , 81.1 +2.0057\frac{8.4}{\sqrt{54} })[/tex]
(81.1- 2.2927 ,81.1 + 2.2927 )
(78.8073 ,83.3927)
Final answer:-
90% confidence interval for the number of seeds for the species
(78.8073 ,83.3927)
g Your underground used-book business is booming. Your policy is to sell all used versions of Calculus and You at the same price (regardless of condition). When you set the price at $10, sales amounted to 100 volumes during the first week of classes. The following semester, you set the price at $30 and sales dropped to zero. Assuming that the demand for books depends linearly on the price, what price gives you the maximum revenue?
Answer:
The price that maximizes the revenue is $15 per book.
Step-by-step explanation:
We have a demand that has a linear relation to price.
The two points we will use to calculate the demand function are:
Price p=10, Demand q=100Price p=30, Demand q=0We have the equation:
[tex]q=m\cdot p+b[/tex]
Then, we replace:
[tex]q(30)=0=m(30)+b\\\\q(10)=100=m(10)+b\\\\\\b=-30m\\\\100=10m+(-30m)=-20m\\\\m=-100/20=-5\\\\b=-30(-5)=150\\\\\\q(p)=-5p+150[/tex]
The revenue R can be calculated as the multiplication of price and quantity.
We can maximize R by deriving and equal that to 0:
[tex]R=p\cdot q=p(-5p+150)=-5p^2+150p\\\\\\\dfrac{dP}{dp}=-5(2p)+150=0\\\\\\-10p+150=0\\\\p=150/10=15[/tex]
The price that maximizes the revenue is $15 per book.
The price that will offer the maximum revenue would be as follows:
$15
Find the priceWhat information do we have,
When Price = $10, Q = 100 Units
When Price = $ 30, Q = 0 units
With the above information, we can take the equation:
Q = Maximum (p + b)
by putting the values in both the above situations,
30 = 0 = m30 + b
10 = 0 = m10 + b
we get b = -30m. by putting this, we get
100 = 10m + (-30m) = -20m
∵ q(p) = -5p + 150
Through the equation and putting the above values, we get:
[tex]R = p.q.[/tex]
[tex]= p(-5p + 150)[/tex]
[tex]= -5p^2 + 150p[/tex]
$15 as the maximum price.
Thus, $ 15 is the correct answer.
Learn more about "Price" here:
brainly.com/question/18117910
How many of these equations have the solution
x
=
12
x
=
12
?
x
−
2
=
10
x
−
2
=
10
x
2
=
24
x
2
=
24
10
−
x
=
2
10
−
x
=
2
2x1=25
2x−1=25
Answer:
a)x−2=10
b) 2x=24
Two equations have have the solution
x = 12
Question:
How many of these equations have the solution x=12 ?
x−2=10
2x=24
10−x=2
2x−1=25
Step-by-step explanation:
To determine which of the above equations have x= 12, we would solve for x in each of the equations.
a) x−2=10
Collecting like terms
x = 10+2
x = 12
This equation has x= 12 as a solution
b) 2x =24
Divide through by coefficient of x which is 2
2x/2 = 24/2
x = 12
This equation has x= 12 as a solution
c) 10−x=2
Collecting like terms
10-2 - x = 0
8 - x = 0
x = 8
d) 2x−1=25
Collecting like terms
2x = 25+1
2x = 26
Divide through by coefficient of x which is 2
2x/2 = 26/2
x = 13
Note: that (b) x2 = 24 from the question isn't clear enough. I used 2x = 24.
If x2 = 24 means x² = 24
Then x = √24 = √(4×6)
x = 2√6
Then the number of equations that have the solution x = 12 would be 1. That is (a) x−2=10 only
Answer:
1/2x + 12 >10
Step-by-step explanation:
2 Points
If f(x) = x + 8 and g(x) = -4x - 3, find (f+ g)(x).
O A. (f+ g)(x) = -3x + 5
O B. (f+ g)(x) = 5x + 11
O C. (f+g)(x) = -5x - 11
O D. (f+ g)(x) = 3x - 5
SUBMI
Answer: A
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Since we are given f(x) and g(x), we cna add them together.
x+8+(-4x-3)
x+8-4x-3
-3x+5
Please answer this correctly
An insurance company has 10,000 automobile policyholders. The expected yearly claim per policyholder is $240, with a standard deviation of $800. Approximate the probability that the total yearly claim exceeds $2.7 million.
Answer:
almost 0%
Step-by-step explanation:
Given that for an insurance company with 10000 automobile policy holders, the expected yearly claim per policyholder is $240 with a standard deaviation of 800
using normal approximation, the probability that the total yearly claim exceeds $2.7 million is calculated as follows:
Sea sumatoria de x = SUMX, tenemos que:
[tex]P (SUMX \geq 2700000) = P(\frac{SUMX - 240*10000}{800 *\sqrt{10000} } \geq \frac{2700000 - 240*10000}{800 *\sqrt{10000} })[/tex]
[tex]= P (z\geq \frac{2700000 - 240*10000}{800 *\sqrt{10000}})[/tex]
= P (z => 3.75)
= 1 - P ( z < 3.75)
P = 1 - 0.999912
P = 0.000088
Which means that the probability is almost 0%
What is the value of f(x) when x=3?
-3
o -2
o 1
O
Find the volume of this cone.
Round to the nearest tenth.
10ft
8ft
[? ] ft
Answer:
V ≈ 670.2 [tex]ft^3[/tex]
Step-by-step explanation:
Use the formula of the volume of a cone, which is [tex]V=\pi r^{2} \frac{h}{3}[/tex]
Plug in your given components and solve for V:
[tex]V=\pi (8)^2\frac{10}{3} \\V=\pi (64)\frac{10}{3} \\V=\pi (64)(3.33)\\V=\pi (213.33)\\V=670.2[/tex]
For which equations is x = 9 a possible solution?
|x|= 9
-|x|=9
-|-x|=9
-|-x|=-9
|x|=-9
|-x|=9
|-x|=-9
Answer:
Step-by-step explanation:
|x|= 9 is a solution. The range of the absolute value function is [0, infinity).
-|x|=9 not a solution. No absolute value function will return a negative result.
-|-x|=9 not a solution. -(x) = 9 is not true for x = 9.
-|-x|=-9 solution. -9 = -9 is true.
1.5 * 10 exponent -5 covert to decimal form
Answer:
The decimal form of [tex]1.5\times 10^{-5}[/tex] is [tex]0.000015[/tex].
Step-by-step explanation:
We need to convert [tex]1.5\times 10^{-5}[/tex] into decimal form. It is given in the standard form. The following steps are to be done to convert it into decimal form.
[tex]1.5\times 10^{-5}\\\\=\dfrac{15}{10}\times 10^{-5}\\\\=15\times 10^{-5}\times 10^{-1}\\\\\=15\times 10^{-5-1}\\\\=15\times 10^{-6}\\\\=\dfrac{15}{1000000}\\\\=0.000015[/tex]
So, the decimal form of [tex]1.5\times 10^{-5}[/tex] is [tex]0.000015[/tex]. Hence, this is the required solution.
Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points. A graph shows the horizontal axis numbered negative 4 to positive 4 and the vertical axis numbered negative 4 to positive 4. Points show an upward trend. Which is the residual value when x = 2? –2 –1 1 2
Answer
its -1
Step-by-step explanation:
ED 2020 boiiiii
The residual value of the line of the best fit when x = 2 is -1
How to determine the residual value?The equation of the line is given as:
y = 0.5x + 1
When x = 2, we have:
y = 0.5 * 2 + 1
Evaluate
y = 2
The residual is the difference between the actual value and the predicted value.
From the complete graph, the actual value is 1.
So, we have:
Residual = 1 - 2
Evaluate
Residual = -1
Hence, the residual value when x = 2 is -1
Read more about residuals at:
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I have been stuck on this question for a bit. I need some help on it me and 2 other people can't seem to figure it out.
Answer:
1080
Step-by-step explanation:
The surface area is the sum of the areas of the faces.
This L-shaped prism has 8 faces: the 2 Ls on the ends, and the 6 rectangular faces along the sides of the L.
The area of each L is 14×10 − 10×8 = 60.
The total surface area is therefore:
A = 2(60) + 20×4 + 20×8 + 20×10 + 20×2 + 20×14 + 20×10
A = 1080
The surface area is 1080 cm².
A pen and its ink refill together cost $\;\$1.10$. The pen costs $\;\$1$ more than the ink refill. What is the cost of the pen in dollars?
Answer:
$1.05
Step-by-step explanation:
Let the cost of ink refill be $x
given
The pen costs 1$ more than the ink refill
Then, cost of pen in terms of x is $( x + 1)
Total cost of pen and refill in terms of x = x + x+ 1 = 2x + 1
It is also given
A pen and its ink refill together cost $\;\$1.10$
Thus,
2x + 1 = 1.10
=> 2x = 1.10 - 1 = 0.1
=> x = 0.1/2 = 0.05
Thus, cost of refill = $0.05
cost of pen = 1+ x = 1 + 0.05 = 1.05
Thus, cost of pen in $ is 1.05.
The fuel A costs $4 per gallon, and fuel B costs $8 per gallon. Peter can spend at
most $24 on fuel. Write the system of linear inequalities to represent this situation.
Answer:
24= 8x+4x
Step-by-step explanation:
.
What is the standard deviation of the following data set round to the nearest 10th 60, 40, 35, 45 and 39
See work attached: Answer is 9.7
Which statement is best represented by the inequality p greater-than 48? A. The basketball team scored less than 48 points.
B. The basketball team scored 48 fewer points than last year’s team.
C. The basketball team scored greater than 48 points.
D. The basketball team scored exactly 48 points.
Answer:
C. The basketball team scored greater than 48 points.
Step-by-step explanation:
pls mark as brainliest
Answer:
c
Step-by-step explanation:
Dialiting a triangle changes the angles and side length of the triangle true or false
Answer:
False
Step-by-step explanation:
Dilation changes the side lengths, but not the angles. The given statement is FALSE.
The checking accounts of USF Credit Union are categorized by age of account and balance in account. We are going to select an account at random from this group of 2000 accounts.What is the conditional probability that the account has a balance at least $500, given that it is at least 3 years old, that is P(>=$500 | >=3 years)?
a. 1/2
b. 1/10
c. 1/4
d. None of these
Missing details to question is attached
Answer:
c) [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
S
Required:
Find the probability that the account has a balance at least $500, given that it is at least 3 years old.
Which means: P(≥$500 | ≥3 years)
To find the probability, use the formula below:
P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)
Where from th given information:
Number of accounts with balance≥ 500 and age ≥3 years = 200
Number of accounts with age≥3 years = 600 + 200 = 800
Therefore,
P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]
The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]
Find StartFraction dy Over dx EndFraction for y equals StartFraction negative 5 x cubed minus 5 x squared plus 3 Over negative 5 x Superscript 4 Baseline plus 2 EndFraction . Do not simplify.
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{(-5x^4+2)(-15x^2-10x)+(-5x^3-5x^2+3)(-20x^3)}{(-5x^4+2)^2}[/tex]
Step-by-step explanation:
Given: [tex]y=\dfrac{-5x^3-5x^2+3}{-5x^4+2}[/tex]
We are required to find the derivative of y with respect to x, [tex]\dfrac{dy}{dx}[/tex] .
We apply the quotient rule:
For a fractional expression,
[tex]\dfrac{u}{v},$ \dfrac{dy}{dx}=\dfrac{vu'+uv'}{v^2}[/tex]
[tex]u=-5x^3-5x^2+3,$ $u'=-15x^2-10x\\\\v=-5x^4+2, v'=-20x^3[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{(-5x^4+2)(-15x^2-10x)+(-5x^3-5x^2+3)(-20x^3)}{(-5x^4+2)^2}[/tex]
Since we are asked not to simplify, we simply leave our answer in the substituted form above.
