Answer:
so 6x = -6y + 5
divide by 6
x = 5
Step-by-step explanation:
The function y=-16r^2+38 represents the height y (in feet) of a water droplet t seconds after falling from an icicle. After how many seconds does the water droplet hit the ground? Round your answer to two decimal places. A second water droplet falls from a height of 41 feet. After how many seconds does that water droplet hit the ground? Round your answer to one decimal place.
Answer:
The first droplet will hit the ground after about 1.54 seconds.
The second droplet will hit the ground after about 1.6 seconds.
Thus, the first hits the ground first.
Step-by-step explanation:
We are given the function:
[tex]y=-16r^2 + 38[/tex]
Which represents the height y in feet of a water droplet t seconds after falling from an icicle.
Part A)
We want to find the time it took for the water droplet to hit the ground.
When it hit the ground, its height y above ground will be zero. Therefore, we can let y = 0 and solve for r:
[tex]0=-16r^2+38[/tex]
Subtract 38 from both sides:
[tex]-38 = -16 r^2[/tex]
Divide:
[tex]\displaystyle r^2 = \frac{38}{16} = \frac{19}{8}[/tex]
And take the principal square root of both sides:
[tex]\displaystyle r= \sqrt{\frac{19}{8}} = \frac{\sqrt{38}}{4} \approx1.54\text{ seconds}[/tex]
So, the first water droplet hits the ground after about 1.54 seconds.
Part B)
We want to determine how long it will take for a water droplet to hit the ground from a height of 41 feet.
From the original equation, if r = 0, then y = 38. So, the initial height was 38 feet.
Then we can modify the function into:
[tex]y= -16r^2 + 41[/tex]
In this case, when r = 0, the starting height y is 41 feet.
Again, let y = 0 and solve for r:
[tex]0 = -16r^2 + 41[/tex]
Isolate:
[tex]\displaystyle r^2 = \frac{41}{16}[/tex]
And take the principal square root of both sides:
[tex]\displaystyle r = \sqrt{\frac{41}{16}} = \frac{\sqrt{41}}{4} \approx 1.6\text{ seconds}[/tex]
So, the second drop will hit the ground after approximately 1.6 seconds.
And in conclusion, the first drop will hit the ground sooner (as expected).
vvorth 1 points
(01.02 MC)
Which of the following describes the correct process for solving the equation 2x - 4 = 20 and arrives at the correct solution?
O Add 4 to both sides, and then divide by 2. The solution is x = 12.
O Divide both sides by -4, and then subtract 2. The solution is x = -7.
O Subtract 4 from both sides, and then divide by 2. The solution is x = -12.
O Multiply both sides by -4, and then divide by 2. The solution is x = -40.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Add 4 to both sides, and then divide by 2. The solution is x = 12."
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
To solve for 'x', we would have to use inverse operations. We would first have to add four to both sides to undo the negative four. Addition is the opposite of subtraction. We would then divide by 2 to isolate 'x'. Division is the opposite of multiplication.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\2x - 4 = 20\\------------\\\rightarrow 2x - 4 + 4 = 20 + 4\\\\\rightarrow 2x = 24\\\\\rightarrow \frac{2x=24}{2}\\\\\rightarrow \boxed{x = 12}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA model. SS (Treatment) in the one-way ANOVA model is ________ the SS (Treatment) in the randomized block design ANOVA model.
a. Always equal to.
b. Always greater than.
c. Always less than.
d. Sometimes greater than.
Answer: Always equal to
Step-by-step explanation:
A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.
Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 6/5x-1
Step-by-step explanation:
We have two points so we can find the slope
(-5,-7) and (5,5)
The slope is
m = ( y2-y1)/(x2-x1)
= ( 5- -7)/( 5 - -5)
= (5+7)/(5+5)
= 12/10
= 6/5
The slope intercept form of a line is
y = mx+b
y = 6/5x+b
Using the point (5,5)
5 = 6/5(5)+b
5=6+b
b=-1
y = 6/5x-1
A son is 8 years old. his father is 5 times as old. How old will the father be when he is twice as old as his son?
If it takes 5 years for an animal population to double, how many years will it take until the population
triples?
9514 1404 393
Answer:
7.92 years
Step-by-step explanation:
We want to find t such that ...
3 = 2^(t/5)
where 2^(t/5) is the annual multiplier when doubling time is 5 years.
Taking logs, we have ...
log(3) = (t/5)log(2)
t = 5·log(3)/log(2) ≈ 7.92 . . . years
It will take about 7.92 years for the population to triple.
Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
In this question, the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Parameter of 5.2 per square yard:
This means that [tex]\mu = 5.2r[/tex], in which r is the radius.
How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?
We want:
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.99[/tex]
Thus:
[tex]P(X = 0) = 1 - 0.99 = 0.01[/tex]
We have that:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}[/tex]
Then
[tex]e^{-5.2r} = 0.01[/tex]
[tex]\ln{e^{-5.2r}} = \ln{0.01}[/tex]
[tex]-5.2r = \ln{0.01}[/tex]
[tex]r = -\frac{\ln{0.01}}{5.2}[/tex]
[tex]r = 0.89[/tex]
Thus, the radius should be of at least 0.89.
Another example of a Poisson distribution is found at https://brainly.com/question/24098004
(7/8*9)*3/4*(9/3*5)=
Answer:
2835/32 or 88 19/32Step-by-step explanation:
(7/8 × 9) × 3/4 × (9/3 × 5)= 63/8 × 3/4 × (3 × 5)= 63/8 × 3/4 × 15= 2835/32 or 88 19/32[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
[tex]88 \frac{19}{32} [/tex]
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed on data from a random selection of 15 of the marathons to determine if there was evidence to indicate that the women's winning wheelchair time is faster than the men's winning running time, on average. What must be true about the population of differences in the women's wheelchair winning times and men's winning times at this marathon for conclusions from the paired t-test to be valid? Choose the correct answer below. A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal. B. Because there were at least 5 years of observations, the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem. C. Because the sample size is large enough, the distribution of differences for all years will be normal. D. Because of the small sample size of differences in winning times between the women's wheelchair winner and the men's running winner, the distribution of sample means of the differences cannot be normal.
Answer:
A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.
Step-by-step explanation:
In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.
Find the shortest distance from A to D in the diagram
Answer:
I will choose (a) I did a problem like this last week
Anyone?? Help????
Please!!!
Answer:
625 (answer A)
Step-by-step explanation:
Sorry for no explanation I can't explain stuff I just do it.
ulwazi's Father offered to pay for Ani's wedding ring, which cost R1349 excluding 14%VAT calculate the selling price
9514 1404 393
Answer:
₹1537.86
Step-by-step explanation:
With the 14% tax added, the final cost is ...
₹1349 × (1 +14%) = ₹1349×1.14 = ₹1537.86
Để tuyển nhân viên, một công ty tổ chức kiểm tra 3 vòng độc lập. Một người tham gia thi tuyển với xác suất qua các vòng lần lượt là 0,8 và 0,6 và 0,25.
a) Tìm xác suất để người đó không được nhận vào công ty?
b) Tìm xác suất để người đó thi đỗ ít nhất 1 vòng.
c) Tìm xác suất để người đó thi không đỗ ở vòng 2.
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
please ask in English
Step-by-step explanation:
then I can help
Students apply for admission to different academic programs within a college. Because of space, each program can only accept a limited number of students. The table below shows the acceptance data for a selection of majors in the college.
Acceptance Status
Accepted Rejected Total
College Major Chemistry 72 18 90
Business 65 35 100
Spanish 45 15 60
Total 182 68 250
What is the probability that a student was accepted, given that the student applied to the business program?
26.0%
35.0%
35.7%
65.0%
I think the answer is (A). 26%. Can someone check?
Answer:
Your wrong, it's 65%.
Step-by-step explanation:
The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.
yw :)
The probability that a student was accepted is 5.0% since option b be the correct answer.
ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,
How to find probability?We have to find out the probability of the selection of a student applied for the business program.
We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events
So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.
Learn more about probability here- https://brainly.com/question/11234923
#SPJ2
Write a situation that can be represented by 2x + 6 > 20.
Hm, interesting inequality.
If you know that it slightly simplifies to [tex]2x\gt14[/tex] then you could go about representing something in real life,
Buying shoes is always done in pairs, if u buy two pairs of shoes you bought 4 shoes. You can only ever buy an even number of shoes which is represented by [tex]2x[/tex].
So you are asking yourself how many pairs you had to buy in order to have more than 14 shoes. The answer is of course, 7 pairs means exactly 14 shoes but since you need more the answer is 8 pairs. Represented by,
[tex]x\gt7=\{8,9,10,\dots,\aleph_0\}[/tex]
assuming [tex]x\in\mathbb{N}[/tex], which is appropriate since you cannot buy negative shoe or [tex]0.43819[/tex] of a shoe pair.
However, if you cannot change the inequality at all, you can use the above paragraph but simply add, you have 3 pairs (6 shoes) of shoes that are indispensable and you want to know the minimum number of shoe pairs you need to buy so that you always have more than 20 shoes.
Notes
[tex]\aleph_0[/tex] is the number of natural numbers [tex]\mathbb{N}[/tex] there are.
[tex]\{\dots\}[/tex] is explicit set notation, ie. which values concretely satisfy the inequality.
Hope this helps :)
Answer:
= 2x > 20-6
= 2x > 14
= x > 7... then the answer includes the numbers greater than seven
Alan's aunt gave him $95 to spend on clothes at the mall. He bought 5 shirts that cost $6 each and a pair of pants that cost $17. How much money does Alan have left to buy more clothes? (one more)
Answer:
he has 48 dollars left to spend on clothes
What is the classification for this polynomial?
-9m^2n^3
Answer:
(a) Monomial
(b) Cubic
Step-by-step explanation:
Given
[tex]-9m^2n^3[/tex]
Required
Classify
By number of terms
The above polynomial is single term.
Single term polynomials are referred to as monomial
By degrees
To determine the degree, we consider the variable farthest from the constant.
In this case, n is farther from 9 than m.
And the power or degree of n is 3.
Polynomials with degree 3 are referred to as cubic polynomial
(d) 320 If the measurement of two angles of a triangle are 72º and 70%, find third ange in degrees. If the measurement of two angles of a triangle are 630 and 100
75,000 live bacteria are present in a culture in a flask. When an antibiotic is
added to the culture, the number of live bacteria is reduced as shown by the
equation. Approximately how many hours have passed when there are 4500
bacteria left alive?
4500 = 75,000 e-0.1733t
Answer:
16.23 hours
Step-by-step explanation:
To obtain the number of hours that have passed ; we have to solve for t on the equation ;
4500 = 75,000 e^-0.1733t
Divide both sides by 75000
4500/75000 = e^-0.1733t
0.06 = e^-0.1733t
Take the In of both sides ;
In(0.06) = - 0.1733t
-2.813410 = - 0.1733t
Divide both sides by - 0.1733
t = 16.23 hours
The correlation between a student’s shoe size and their score on a final exam is −0.79.What conclusions can be drawn based on the correlation coefficient? Select all that apply.
There is a relationship between a student’s shoe size and their final exam score.Big shoe sizes correlate to low exam scores.Large shoe sizes cause students to do poorly on the final exam.As the shoe size decreases, the final exam score increases.Small shoe sizes cause students to do well on the final exam.
(1,2,4) (A,B,D)
Answer:
The first one, the second, and fourth one are correct.
Select A,B, and D.
ED2021
Answer:
A, B, and C
Step-by-step explanation:
I got it right ;)
P = 14.7e-0.21x, where x is the number of miles above sea level. To the nearest foot, how high
is the peak of a mountain with an atmospheric pressure of 8.743 pounds per square inch?
9514 1404 393
Answer:
13064 feet
Step-by-step explanation:
We can rewrite the formula so that x is in feet. Equating the new formula to 8.743 PSI, we have ...
8.743 = 14.7e^(-0.21x/5280)
Dividing by 14.7 and taking natural logs, we have ...
ln(8.743/14.7) = -0.21x/5280
Multiplying by the inverse of the coefficient of x gives ...
x = 5280·ln(8.743/14.7)/-0.21 ≈ 13064.0806
The peak of the mountain is about 13,064 feet high.
Please answer in detail
Answer:
y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1
Twelve residents from the city of Rocklin were randomly selected and asked "How many TVs are in your household?". The following data were obtained: 2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, and 3.
According to Nielsen Media Research the national average is 2.7 TVs per household. Is this sufficient sample evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average of 2.7 TVs per household? Use ! = 5% and assume that the number of TVs in Rocklin households is normally distributed.
Answer:
There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .
Step-by-step explanation:
This is a one sample mean test ;
H0 : μ = 2.7
H1 : μ > 2.7
Given the data :
2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3
Sample size, n = 12
The sample mean, xbar = ΣX / n = 33/12 = 2.75
The sample standard deviation, s = 1.215 ( from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.75 - 2.7) ÷ (1.215/√(12))
T = 0.05 / 0.3507402
T = 0.1426
The critical value from Tscore ;
df = 12 - 1 = 11
Critical value = 1.796
Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.
Answer:
3/56
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
The total number of marbles in the box
= 1 + 3 + 2 + 2
= 8 marbles
The probability that the first marble is white and the second marble is blue
= 3/8 * 1/7
= 3/56
Find h(-5) when: h(x) = x2 + 2x + 2
Answer:
17
Step-by-step explanation:
h(x) = x^2 + 2x + 2
Let x = -5
h(-5) = (-5)^2 + 2(-5) + 2
= 25 -10 +2
= 17
11
find the number of ways of forming
an executive Committee of four in a
social club consisting of 15 members,
If a particular man must be in
the comittee
There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members
Understanding Permutation and CombinationIf a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:
14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364
Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.
Learn more about combination here:
https://brainly.com/question/28065038
#SPJ1
Write a quadratic equation having the given numbers as solutions. -7 and -5
The quadratic equation is ___ =0.
Answer:
x²+12x+35
Step-by-step explanation:
in factored form it would just be
(x+7)(x+5)=0
expand this
x²+12x+35=0
Question 7 of 10
What is the slope of the line described by the equation below?
y-9 = -2(x-8)
Answer:
The slope is -2 and a point on the line is (8,9)
Step-by-step explanation:
The equation is in point slope form
y -y1 = m(x-x1) where (x1,y1) is a point on the line and m is the slope
y-9 = -2(x-8)
The slope is -2 and a point on the line is (8,9)
