One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.
Hope this helped!
A scale drawing of a rectangular painting has a scale factor of 1:4 which statements are true
Answer:
object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .
Step-by-step explanation:
What a scale factor of 1:4 means.
Simply it means that the reals size of the object on land have been reduced in the drawing in the paper.
Now for scale factor of 1:4 in particular it means that the object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .
Example if the drawing has measurements of 4 inches on paper, then on land it will be 16 inches
The hypotenuse of a right triangle is 95 inches long. One leg is 4 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.
Answer:
65.1 and 69.1
Step-by-step explanation:
a^2+b^2=c^2
c=95
b=a+4
Solve for a^2+(a+4)^2=95^2
a=65.1
b=a+4=69.1
Answer:
65.1 and 69.1
Step-by-step explanation:
c² = a² + b²
c= 95
a - one leg
b= (a + 4) - second leg
95² = a² + (a + 4)²
9025 = a² + a² + 2*4a + 16
2a² + 8a - 9009 = 0
[tex]a= \frac{-b +/-\sqrt{b^2 - 4ac} }{2a} \\\\a = \frac{-8 +/-\sqrt{8^2 - 4*2*9009} }{2*2} \\\\a=65.1 \ and \ a=- 69.1[/tex]
A leg length can be only positive. a = 65.1
b = 65.1 + 4 = 69.1
82
R5
6
,92 5
4 8
12
12
0
Answer:
see below
Step-by-step explanation:
The first subtraction has a zero result (blue) from the thousands digit, so we know the dividend has 4 in that place. The 5 in the 1s place of the dividend is brought down to fill the space on the bottom line. 6 goes into that number 0 times, so the final quotient digit is 0.
4,925 = 6×820 +5
or
4,925 ÷ 6 = 820 r5
Carefully review the research matrix presented below. If this is a within subjects design, how many total participants will be used in the experiment?
Immaculate Appearance Neat Appearance Sloppy Appearance
15 participants 15 participants 15
participants
a. 15
b. 30
c. 45
d. 60
Answer:
c. 45
Step-by-step explanation:
there are 15 participant in each category, and there are 3 categories, so total participants = 15 * 3
= 45
Hope this helps, and please mark me brainliest if it does!
If a number is added to the numerator of 7/9 and the same number is subtracted from the denominator, the result is 3. Find the number.
Answer:
5
Step-by-step explanation:
[tex]\frac{7+x}{9-x}=3\\ 7+x = 3(9-x)\\7+x=27-3x\\x+3x=27-7\\4x=20\\x=5[/tex]
A small college has 1460 students. What is the approximate probability that more than six students were born on Christmas day? Assume that birthrates are constant throughout the year and that each year has 365 days.
Answer:
The approximate probability that more than six students were born on Christmas day is P=0.105.
Step-by-step explanation:
This can be modeled as a binomial variable, with n=1460 and p=1/365.
The sample size n is the total amount of students and the probability of success p is the probability of each individual of being born on Christmas day.
As the sample size is too large to compute it as a binomial random variable, we approximate it to the normal distribution with the following parameters:
[tex]\mu=n\cdot p=1460\cdot (1/365)=4\\\\\sigma=\sqrt{n\cdot p(1-p)}=\sqrt{1460\cdot(1/365)\cdot(364/365)}=\sqrt{3.989}=1.997[/tex]
We want to calculate the probability that more than 6 students were born on Christmas day. Ww apply the continuity factor and we write the probability as:
[tex]P(X>6.5)[/tex]
We calculate the z-score for X=6.5 and then calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{6.5-4}{1.997}=\dfrac{2.5}{1.997}=1.252\\\\\\P(X>6.5)=P(z>1.252)=0.105[/tex]
In a manufacturing process, a machine produces bolts that have an average length of 5 inches with a variance of .08. If we randomly select five bolts from this process, what is the standard deviation of the sampling distribution of the sample mean
Answer:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] \mu= 5. \sigma^2 =0.08[/tex]
And the deviation would be [tex] \sigma = \sqrt{0.08}= 0.283[/tex]
For this case we select a sample size of n = 5 and the distirbution for the sample mean would be:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
(like Ross 6.28) The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.’s car is ready before L.M.’s car? Assume that service times are independent and service begins upon arrival of the car.
Answer: provided in the explanation section
Step-by-step explanation:
The complete question says:
The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.'s car is ready before L.M.'s car? Assume that service times are independent and service begins upon arrival of the car Be sure to: 1) define all random variables used, 2) explain how independence of service times plays a part in your solution, 3) show all integration steps. (b) If both cars are brought in at time 0, with work starting on S.C. 's car only when L.M.'s car has been completely serviced, what is the probability that S.C.'s car is ready before time 2?
Ans to this is provided in the images uploaded as it is not possible to put the symbols here...
i hope you find this helpful.
cheers !!
~Help me with this please I will mark as BRANLIEST and give you 55 POINTS! (If you answer correctly)
Answer:
[tex]y=50x+75[/tex]
Step-by-step explanation:
When writing a linear equation from a graph, we need to find two things: the y-intercept (what y is when x is 0) and the slope.
First, let us find the y-intercept.
To do this, we can just look at the graph. When x=0, y=75, so 75 is our y-intercept, which is also known as b.
To find the slope of this line, we will need to look at two points
We already know that (0,75) is a point. From the graph, we can see that (1,125) is also a point on this line.
Now, we can find the slope of this line using the following formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{125-75}{1-0} \\\\m=\frac{50}{1} \\\\m=50[/tex]
Now that we have both the y-intercept and slope, we can put them together in the form of [tex]y=mx+b[/tex]
[tex]y=50x+75[/tex]
Answer:
Slope: 50
Equation: y = 50x + 75
Step-by-step explanation:
Take two points:
(2,175)
(3,225)
Find the slope:
225 - 175/3 - 2
50/1 = 50
So we get this equation:
y = 50x + b
Now to find b, insert one of those points from before back in:
175 = 50(2) + b
175 = 100 + b
b = 75
So the equation is:
y = 50x + 75
The line y = kx + 4, where k is a constant, is
graphed in the xy-plane. If the line contains the
point (c,d), where c ≠ 0 and d ≠ 0, what is the slope
of the line in terms of c and d ?
Answer:
(d - 4) / c
Step-by-step explanation:
The slope of the line in terms of c and d is (d - 4) / c.
Here, we have,
To find the slope of the line in terms of the coordinates of the point (c, d), we can use the slope-intercept form of a line, y = mx + b, where m represents the slope.
In the given equation, y = kx + 4, we can see that the coefficient of x is k, which represents the slope of the line.
Since the line contains the point (c, d), we can substitute these values into the equation:
d = kc + 4
To isolate the slope term, we rearrange the equation:
d - 4 = kc
Now, divide both sides by c:
(d - 4) / c = k
Therefore, the slope of the line in terms of c and d is (d - 4) / c.
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A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, V2V3 might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.
Required:
a List the sample points in this experiment of ordering paper on two successive days.
b Assume the vendors are selected at random each day and assign a probability to each sample point.
c Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P( A), P( B), P( A U B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
Find the given attachments
Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. Group of answer choices
Answer:
(71.28, 78.72)
Step-by-step explanation:
We have the following information from the statement:
mean (m) = 75
sample standard deviation (sd) = 5
Sample size (n) = 13
Significance level (alpha) = 1 - 0.98 = 0.02
Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12
The critical value would be:
t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)
Margin of error equals:
E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:
E = 2,681 * 5/13 ^ (1/2)
E = 3.72
Therefore, the interval of 98% confidence interval would be:
75 + 3.72 = 78.72
75 - 3.72 = 71.28
(71.28, 78.72)
8. A biotech company is looking for a user experience researcher to organize and report on some user experience data for a health and wellness app. They need to know the demographics of the users and the average time the app is open for each demographic. In the technical interview, you are asked to describe your approach to the initial analysis. When describing your analysis plan for the request, with what type of statistics would you tell the interviewer you would start your analysis
Answer:
Descriptive statistics
Step-by-step explanation:
Descriptive statistics describes and summarizes the basic features of a given dataset. It explains features from a collection of information, it is also said to be a form of summary statistics. Here data is characterized using its properties.
In this case, I was asked to describe my approach to the initial analysis. When describing the analysis plan for the request, I would tell the interviewer to start analysis using descriptive statistics.
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
Answer:
Step-by-step explanation:
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
solution[tex]t=\frac{\text {estimated slope}}{\text {std error}}[/tex]
a)
Estimated Slope Std error t - calculated
-0.027 0.009 -3
-0.070 0.018 -3.89
-0.006 0.003 -2
4.8 1.7 2.82
0.159 0.062 2.56
-0.124 0.032 -3.87
0.041 0.018 2.28
11.8 6.66 1.77
-0.639 0.36 -1.78
b) Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
at an ice cream shop, thirty cups of ice cream costs $105. what is the cost of one cup of ice cream? what is the cost of 18 cups of ice cream??
Hey there! :)
Answer:
Price per cup: $3.5
Price for 18 cups: $63.
Step-by-step explanation:
To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.
30x = 105
Divide both sides by 30:
x = $3.5.
To find the cost of 18 cups, simply multiply this price by 18:
18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.
Marcus is trying to find 4 5/6-1 3/6. His work shown. What is Marcus's mistake?
Step 1: Subtract the wholes. 4-1=3
Step 2: Subtract the fractions. 5/6-3/6=2/6
Step 3: Subtract the differences. 3-2/6=2 4/6
Answer:
Step 3
Step-by-step explanation:
The mistake was made in Step 3.
Step 1: Subtract the wholes. 4 - 1 = 3
Step 2: Subtract the fractions. 5/6 - 3/6 = 2/6
After Step 2, He should have added them instead of subtracting them:
3 + 2/6 = 3 2/6
So, step 3 was his mistake.
Answer:step 3
Step-by-step explanation: he should have added
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is
Answer:
63.25 not an integer
Step-by-step explanation:
HCF(a,b)*LCM(a,b)=ab
11*368=64*x
x=11*368/64
x=63.25 not an integer, one of the given numbers must be incorrect
but you may use this method to find it yourself
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket , to the nearest 100th of a foot. y=-16x^2+230x+112
Answer:
The maximum height reached by the rocket is of 938.56 feet.
Step-by-step explanation:
The height y, after x seconds, is given by a equation in the following format:
[tex]y(x) = ax^{2} + bx + c[/tex]
If a is negative, the maximum height is:
[tex]y(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]y(x) = -16x^{2} + 230x + 112[/tex]
So
[tex]a = -16, b = 230, c = 112[/tex]
Then
[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]
[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]
The maximum height reached by the rocket is of 938.56 feet.
Simplify the expression and then evaluate it for the given value of the variable: (6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!
Answer:
20
Step-by-step explanation:
The simplified expression is -5x+21
-5(0.2)+21=
-1+21= 20
Answer:
24
Step-by-step explanation:
f(x)= (6−2x)+(15−3x)
x=-0.2
f(-0.2)=(6−2(-0.2)+(15−3(-0.2))
f(-0.2)=(6+0.4)+(15+0.6)
f(-0.2)=6.4+15.6
f(-0.2)=22
3ab-9ab+7ab and hurry up
Answer:ab
Step-by-step explanation:3-9=-6 +7=1 1ab also equals just ab
Answer:
Since its adding and subtracting just add the coefficients of similar terms (coefficient is the number in front, term is the coefficient. and variables, similar terms are terms that have the same variables)
3ab-9ab+7ab
3-9=-6: -6ab+7ab
-6+7=1: 1ab or ab :)
A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 4 men. Based on chance alone, what is the probability that one woman and one man will be chosen to be on the committee
Answer:
53.33% probability that one woman and one man will be chosen to be on the committee
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the members are chosen is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that one woman and one man will be chosen to be on the committee?
Desired outcomes:
One woman, from a set of 2, and one man, from a set of 4. So
[tex]D = C_{2,1}*C_{4,1} = \frac{2!}{1!1!}*\frac{4!}{1!3!} = 8[/tex]
Total outcomes:
Two members from a set of 2 + 4 = 6. So
[tex]T = C_{6,2} = \frac{6!}{2!4!} = 15[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{8}{15} = 0.5333[/tex]
53.33% probability that one woman and one man will be chosen to be on the committee
What is the area of the rhombus?
Answer: 24 square units
Explanation: The diagonals are 4+4 = 8 and 3+3 = 6 units long. Multiply the diagonals to get 8*6 = 48. Then divide this in half to get 48/2 = 24.
An alternative is to find the area of one smallest triangle, and then multiply that by 4 to get the total area of the rhombus. You should find the area of one smallest triangle to be 0.5*base*height = 0.5*4*3 = 6, which quadruples to 24.
The relationship of variance and mean informs researchers about the spread of data. If a researcher calculates the mean abundance per unit area of a species, and then calculates the variance, the relationship between mean and variance will reflect the distribution pattern.
Which distribution pattern pictured below will have variance greater than the mean?
Answer:
The distribution pattern that will have variance greater than mean is one where the population of species is clustered and thus far from the mean abundance of species per unit area.
This distribution pattern can be found, using the POISSON distribution.
Step-by-step explanation:
Variance is a measure of dispersion while Mean is a measure of central tendency.
The mean is the average of all values (in this case, the abundance or concentration of species per unit area). It is the sum total of all values, divided by the number of values there are.
The variance of a given set of data, on the other hand, is a measure of the spread or distance or dispersal of the data from the mean. It measures the spread between each datum/value and the mean value.
The relationship between mean and variance surely reflects the pattern that the distribution will take. The kind of distribution pattern that will have a greater variance than mean is a Poisson distribution. Sample size is usually large here. Since the variance is greater than the mean, the population is a clustered or clumped distribution.
Express loga 6 + loga 70 as a single logarithm
Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
A motorboat can maintain a constant speed of 28 miles
per hour relative to the water. The boat makes a trip
upstream to a certain point in 35 minutes; the return trip
takes 21 minutes. What is the speed of the current?
Answer:
7mph
Step-by-step explanation:
Given
Time Taken to go upstream Tup = 35 min
Time Taken to go downstream Tdown=21 min.
Let the absolute speed (i.e speed relative to the stationary riverbed) be :
Vup : going upstream
Vdown: going downstream.
We know that the distance traveled upstream = distance traveled downstream, hence we can equate both distances, i.e. :
Distance Traveled Upstream = Distance Traveled Downstream
Vup · Tup = Vdown · Tdown (substituting the values for time above)
35Vup = 21Vdown
Vup = (21/35) Vdown ------------(eq 1)
We are also given that the motorboat can travel at V = 28 mph relative to the water.
Since going upstream, we are going AGAINST the current, relative to the riverbed, we expect to be travelling slower. In fact, the absolute difference between the speed relative to the water (i.e V = 28 mph) and the speed relative to the seabed (i.e Vup), is equal to the speed of the current.
The same can be said for going downstream WITH the current, that the absolute difference between V = 28mph and Vdown is also equal to the speed of the current.
Hence we can equate the two:
28 - Vup = Vdown - 28
Vup + Vdown = 2(28)
Vup + Vdown = 56 ---------------------(eq 2)
If we solve the system of equations (eq 1) and (eq2), we will get
Vup = 21 mph and Vdown = 35 mph
(sanity check tells us that this makes sense because we expect to be going slower upstream because we are going against the current)
Hence current speed
= 28-Vup
= 28 - 21
= 7 mph. (answer)
Sanity Check:
Current speed can also be written:
= Vdown-28
= 35 - 28
= 7 mph (same as what we found above, so this checks out)
The speed of the current motorboat = 7 mph
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Speed of boat in still water = 28 mph
Let the speed of stream = w
Here, The upstream time is 35 min = 35/60 h = 7/12 h
downstream time is 21 min = 21/60 h = 7/20 hours
Since, The distance (d = vt) traveled either way is the same, but at different speeds and times.
Hence, Set upstream and downstream distances (vt) equal and solve for w as;
⇒ (28 - w)(7/12) = (28 + w)(7/20)
⇒ 20 (28 - w) = 12 (28 + w)
⇒ 5(28 - w) = 3(28 + w)
⇒ 140 - 5w = 84 + 3w
⇒ 140 - 84 = 5w + 3w
⇒ 56 = 8w
⇒ w = 7
Thus, The speed of the current = 7 mph
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In a class of 30 students, there are four more girls than boys. a)Using x as the number of boys, write down an equation b)Solve the equation and find the number of girls in the class.
easy claps!!
Answer: 30=2x+4 and there are 17 girls in the class.
Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.
It's BASIC prealgebra so you should probably practice bit more with linear equations!
Noaya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let y represent the number of pages left to read after x hours.
Answer: –55x + 570
Step-by-step explanation:
The person above me completely missed the question so this is the right one
What is the value of p ?????
Answer:
d) 50
Step-by-step explanation:
40 + 90 + p = 180
p = 50
Mrs Van Roijen decides to abseil down the Shard in London. The journey down normally takes 33 minutes. However, on her way down, she stops for 18 minutes to take some photos. Eventually she arrives at the bottom of the Shard. Looking at her watch she sees that it is now 12:15. At what time did she set off? 11: 34
11: 24
11: 44
11: 54
Answer:
11.24
Step-by-step explanation:
If she arrived at 12.15, to find the time of departure we have to deduct 33 mins and the time she spent for photos,18 mins from this to get time of departure.
Total time spent for journey
33mins +18 mins = 51mins
time of departure = 12.15 - 51mins
so the time of departure is 11.24
Solve:
5 thousands
ones
5 thousand ones is the same as 5,000. Each one takes up one place.
Answer:
5000
Step-by-step explanation: