Answer:
Therefore it has been draining 48 hours.
Step-by-step explanation:
Given that a water body is being drained it begins with 700 gallons of water.
Let after x hours the amount of water in the water body will 388 gallons.
The water body is draining 6.5 gallons each hour
It means
The amount of water that drain in 1 hour is 6.5 gallons.
The amount of water that drain in 2 hour is (6.5+6.5) gallons.
=(2×6.5)gallons.
The amount of water that drain in 3 hour is( 6.5+6.5+6.5) gallons.
=(3×6.5) gallons.
Therefore
The amount of water that drain = time ×6.5
The amount of water that drain in x hour is (x×6.5) gallons=6.5x gallons.
Therefore the remaining water
= initial amount of water- drainage water
=(700-6.5x)gallons
According to the problem,
700-6.5x= 388
⇒ -6.5x = 388-700
⇒ - 6.5x = - 312
[tex]\Rightarrow x=\frac{-312}{-6.5}[/tex]
⇒ x= 48
Therefore it has been draining 48 hours.
Few students manage to complete their schooling without taking a standardized admissions test such as the Scholastic Achievement Test, or SAT (used for admission to college); the Law School Admissions Test, or LSAT; and the Graduate Record Exam, or GRE (used for admission to graduate school). Sometimes, these multiple-choice tests discourage guessing by subtracting points for wrong answers. In particular, a correct answer will be worth +1 point, and an incorrect answer on a question with five listed answers (a through e) will be worth −1/4 points.
What is the expected value of eliminating one answer and guessing among the remaining four possible answers?
What is the expected value of eliminating three answers and guessing between the remaining two possible answers?
Answer:
Step-by-step explanation:
Assuming there is a punitive removal of one point for an incorrect response.
Five undiscernable choices: 20% chance of guessing correctly -- Expectation: 0.20*(1) + 0.80*(-1) = -0.60
Four undiscernable choices: 25% chance of guessing correctly -- Expectation: 0.25*(1) + 0.75*(-1) = -0.50
I'll use 0.33 as an approzimation for 1/3
Three undiscernable choices: 33% chance of guessing correctly -- Expectation: 0.33*(1) + 0.67*(-1) = -0.33 <== The approximation is a little ugly.
Two undiscernable choices: 50% chance of guessing correctly -- Expectation: 0.50*(1) + 0.50*(-1) = 0.00
And thus we see that only if you can remove three is guessing neutral. There is no time when guessing is advantageous.
One Correct Answer: 100% chance of guessing correctly -- Expectation: 1.00*(1) + 0.00*(-1) = 1.00
The expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16. The expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.
Explanation:To find the expected value of eliminating one answer and guessing among the remaining four possible answers, we need to consider the probabilities associated with each outcome.
Since there are four possible answers remaining, the probability of guessing the correct answer is 1/4. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:
Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)
Expected Value = (1/4 * 1) + (3/4 * (-1/4)) = 1/4 - 3/16 = 1/16.
So, the expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16.
For eliminating three answers and guessing between the remaining two possible answers, the probabilities change.
Since there are now two possible answers remaining, the probability of guessing the correct answer is 1/2. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:
Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)
Expected Value = (1/2 * 1) + (1/2 * (-1/4)) = 1/2 - 1/8 = 3/8.
So, the expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.
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The final cost of a bookstore purchase with a $5 coupon in a state that chargers 8% sales tax is given by the expression. The variable x represents the amount of the purchase before the sales tax and the coupon is applied. 1.08 ( x-5) What does ( x-5) represent ? The cost before applying the coupon The total charge before applying sales tax The rate at which the total cost increases The total charge after tax
Answer: 5.37.
Step-by-step explanation:8 percent markup which in this case is 8 cents per dollar and s in nice its 5 multiply 5 by 8 and that gives you the cents part.
Two trains leave the station at the same time. One is traveling east at rate of 78mph. The other is traveling west at rate of 72 mph. How long to they have to travel until they are 1,162.5 miles apart?
Answer:
The time the both trains have to travel for making a distance of 1162.5 miles apart T = 7.75 hour
Step-by-step explanation:
Speed of the first train = 78 [tex]\frac{mi}{h}[/tex]
Speed of the second train = 72 [tex]\frac{mi}{h}[/tex]
Suppose the both trains have to travel for time = T hour
The distance traveled by first train ( [tex]D_{1}[/tex] ) = Speed × time
⇒ [tex]D_{1}[/tex] = 78 × T --------- (1)
The distance traveled by second train ( [tex]D_{2}[/tex] ) = 72 × T --------- (2)
Total distance D = [tex]D_{1}[/tex] + [tex]D_{2}[/tex]
⇒ D = 78 × T + 72 × T
⇒ 1162.5 = 150 T
⇒ T = 7.75 hour
This is the time the both trains have to travel for making a distance of 1162.5 miles apart.
Find the value of c that makes each trinomial a perfect square.
x^2-13x+c
Answer:
169/4
Step-by-step explanation:
x² - 13x + c
x² -2(x)(13/2) +(13/2)²
(13/2)² = 169/4 or 42 ¼
A home owner has a monthly budget of $400 to spend on their homes landscaping. If they spent 35% of their budget this month on landscaping, how much was spent?
Answer:
$140
Step-by-step explanation:
If the Monthly Budget for Landscaping=$400
and the Percentage of Landscaping Budget Spent this Month=35%
The Amount Spent on Landscaping=35% of Total Landscaping Budget
=35 percent of $400
Recall that percentage is always over 100, therefore 35%=35/100
=[tex]\frac{35}{100}X400[/tex]
=$140
The homeowner spent $140 on landscaping this month.
Answer:
$260 was spent.
Step-by-step explanation:
The main problem is about proportion, specifically direct proportion.
$400 is the total budget, wich means is 100% of the budget.
They spent 35%, so we need to substract the amount of spent budget to total budget, in order to know how much was spent, we will call it remaining budget:
total budget=100%
spent budget=35%
remaining budget=total budget - spent budget
remaining budget= 100% - 35% = 65%
remaining budget= %65
As a result of the substraction we have the percentage of remaining budget, 65%. The next step is to transform that percentage into an amount of money. To do that we use the Mathematical Rule of Three.
The Rule of Three is a method to solve direct proportion problems, when we have three quantities related to each other. For this case %100 equals $400 and %65 equals to unknown, that's the cuantitie we want to know, that is, remaining budget, as shown below:
%100 -> $400
%65 -> x
On a general form it could be understood as a relation between a-b and c-x:
a -> b
c -> x
Next we will apply the following formula
[tex]x= \frac{c*b}{a} [\tex]
For this case:
[tex]x= \frac{65*400}{100} [\tex]
[tex]x= $260[\tex]
The remaining budget is $260
Two ships leave a harbor together, traveling on courses that have an angle of 135°40' between them. If they each travel 402 miles how far apart are they?
Final answer:
The distance between two ships leaving a harbor can be calculated using vector addition and the cosine law formula, resulting in an approximate distance of 565 miles.
Explanation:
The distance between the two ships can be calculated using vector addition.
To find the distance apart, we can add the vectors representing the paths of the two ships. Using the cosine law formula, we calculate the magnitude of the resultant vector to be approximately 565 miles.
help me, someone, I really need it
Answer:
Point B
Step-by-step explanation:
Because the x coordinate is -2
Move two to the left.
The y-coordinate is 2
After we are at -2 for x, then move up to reach the y=2 line. \
Then that will be your point.
Answer:
it would be point b
ASAP
Brianna invested $480 in an account paying an interest rate of 6 1/2% compounded continuously. Adam invested $480 in an account paying an interest rate of 6 3/4 % compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Brianna's money to double than for Adam's money to double?
Answer: it would take 7 years more for Brianna's money to double than for Adam's money to double
Step-by-step explanation:
Considering Brianna's investment,
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = $480
r = 6.5% = 6.5/100 = 0.065
A = 2 × 480 = $960
Therefore,
960 = 1800 x 2.7183^(0.065 x t)
960/1800 = 2.7183^(0.065t)
2 = 2.7183^(0.065t)
Taking ln of both sides, it becomes
Ln 2 = 0.065tln2.7183
0.693 = 0.065t
t = 0.693/0.065
t = 10.66
Approximately 17 years
Considering Adam's investment, we would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 480
A = 960
r = 6.75% = 6.75/100 = 0.0675
n = 4 because it was compounded 4 times in a year.
Therefore,.
960 = 480(1 + 0.0675/4)^4 × t
960/480 = (1 + 0.016875)^4t
960/480 = (1.016875)^4t
Taking log of both sides, it becomes
Log 2 = 4t log 1.016875
0.301 = 0.0291t
t = 0.301/0.0291
t = 10.34
Approximately 10 years
A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is
Final answer:
The median is a more accurate indicator of the average student's SAT score at Groveland High School in a right-skewed distribution because it is not affected by outliers, unlike the mean.
Explanation:
The question addresses why the median is a more accurate indicator of the SAT score of the average student at Groveland High School rather than the mean when the data is strongly skewed to the right. This is because the median is the middle value that divides the number set into two equal halves, and it is not affected by outliers or extremely high scores that are present in a right-skewed distribution. In contrast, the mean is the average of all values and can be significantly influenced by outliers, leading to a value that may not accurately represent the 'central' tendency of the data. Thus, for a right-skewed data set, the median provides a better measure of center for what can be considered a typical score because it is not skewed by unusually high values.
A survey of 550 male managers and 650 female managers was conducted. All 1,200 managers identified whether, for each of six characteristics, the characteristic is important to consider when hiring a new employee. For each of the six characteristics, the percent of managers surveyed who identified that characteristic as important to consider is given in the following table. SURVEY RESULTSCharacteristic Percent Work Experience 72%Proficiency in English 68%Ability to Follow Directions 65%Specific Occupational Skill 60%Computer Expertise 58%Appropriate Attire and Behaviour 55%The number of managers surveyed who identified work experience as an important characteristic to consider was approximately what percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider?
A. 15%
B. 20%
C. 25%
D. 30%
E. 35%
Answer:
Correct option is (B). 20%.
Step-by-step explanation:
The number of managers is, 1200.
The percentage of managers who identified work experience as an important characteristic to consider is, P (W) = 72%.
The percentage of managers who identified appropriate attire and behavior as an important characteristic to consider is, P (AB) = 55%.
Compute the number of managers who identified work experience as an important characteristic to consider as follows:
[tex]n(W)=1200\times P(W)\\=1200\times\frac{72}{100}\\=864[/tex]
Compute the number of managers who identified appropriate attire and behavior as an important characteristic to consider as follows:
[tex]n(AB)=1200\times P(AB)\\=1200\times\frac{55}{100}\\=660[/tex]
Compute approximately what percent greater is P (W) than P (AB) as follows:
[tex]P(W>AB)=\frac{n(W)-n(AB)}{1200}=\frac{864-660}{1200}=\frac{204}{1200}=0.17\approx0.20[/tex]
Thus, the number of managers surveyed who identified work experience as an important characteristic to consider was approximately 20% percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider.
Correct option is (B).
There are a dozen eggs in a basket. 4 are white. The rest are brown. Tell what fraction of the eggs are brown. The write the fraction in simplest form.
Out of a dozen eggs, with 4 being white, the fraction that represents the brown eggs is 8/12. Simplified, this fraction is 2/3.
Explanation:The question is asking us to find what fraction of the eggs are brown if there are 4 white eggs out of a dozen in a basket. Since there are 12 eggs in a dozen, and we know 4 are white, we can subtract the 4 white eggs from the total to find out how many are brown.
12 eggs (total) - 4 white eggs = 8 brown eggs.
Therefore, the fraction of the basket that contains brown eggs is 8/12. To simplify this fraction, we look for the greatest common divisor of both the numerator (8) and the denominator (12), which is 4. Dividing both by 4, we get:
8 ÷ 4 = 2
12 ÷ 4 = 3
So the fraction of the eggs that are brown in simplest form is 2/3.
A child, 1 m tall, is walking directly under a street lamp that is 6 m above the ground. If the child walks away from the light at the rate of 20 m/min, how fast is the child's shadow lengthening?
Final answer:
The child's shadow is lengthening at a rate of 6 m/min as they walk away from the street lamp.
Explanation:
The child's shadow lengthens as they walk away from the street lamp because the angle between the child and the light source increases. To find the rate at which the shadow lengthens, we can use similar triangles. The ratio of the length of the shadow to the height of the child remains constant. So, if the child's height increases by 1 meter, the shadow length increases by 6 meters. Therefore, the child's shadow is lengthening at a rate of 6 m/min.
The rate of lengthening of the child's shadow is 4 meters per minute.
Step 1: Defining the variables.
Let:
h = height of the street lamp = 6 my = height of the child = 1 mx = distance of the child from the lamp posts = length of the child's shadowIt is given that the child walks away from the light at a rate of 20 m/min. This is:
[tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]
Step 2: Relating the variables using similar triangles.
The two triangles formed (one by the lamp post and its shadow, and the other by the child and the child's shadow) are similar. Therefore, the following proportion:
[tex]\frac{x+s}{h} = \frac{s}{y}[/tex]
Substituting the known values (h = 6 m and y = 1 m), we get:
[tex]\frac{x+s}{6} = \frac{s}{1}[/tex]
Step 3: Solving for s.
Cross-multiplying gives:
[tex]6s=x+s[/tex]
Rearranging terms:
[tex]5s=x[/tex]
So the length of the shadow, s, in terms of the child's distance from the lamp, x, is:
[tex]s = \frac{x}{5}[/tex]
Step 4: Differentiate with respect to time.
Differentiating both sides with respect to t:
[tex]\frac{ds}{dt} = \frac{1}{5}\frac{dx}{dt}[/tex]
Substituting the known rate of change [tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]:
[tex]\frac{ds}{dt} = \frac{1}{5}*20 = 4\ meters\ per\ min[/tex]
Therefore, the child's shadow is lengthening at a rate of 4 meters per min.
College basketball team has won 14 games and lost 6 games. If they continue to win at this rate, how many games would the team win in a 50 game schedule?
Answer:
42 games
Step-by-step explanation:
If the college basketball team has won 14 games and lost 6 games,
The Probability of recording a win is given as:
Probability(of a win)[tex]=\frac{Number of Outcomes }{Total Number o trials}[/tex]=[tex]\frac{14}{20}[/tex]
In experimental probability, this can also be taken as the Relative Frequency of a win.
Therefore: Number of Expected Wins
=Relative Frequency of a win X Total Number of Trials
[tex]\frac{14}{20}X60=42[/tex]
The team would expect to win 42 games in a 60 game schedule
Final answer:
The team would win 35 games in a 50 game schedule.
Explanation:
To find out how many games the team would win in a 50 game schedule, we can use a proportion. The team has won 14 out of 20 games so far, which can be written as 14/20. We can set up a proportion with x representing the number of games the team would win in a 50 game schedule:
14/20 = x/50
Now we can cross-multiply and solve for x:
20x = 14 * 50
20x = 700
x = 700/20
x = 35
So, if they continue to win at this rate, the team would win 35 games in a 50 game schedule.
IXL Geometry help pls !
Answer:
Step-by-step explanation:
It’s 34
Answer:
The answer to your question is Area = 9 yd²
Step-by-step explanation:
Data
Big square Small square
Area = 36 yd² Area = x
Side = 6 yd Side = 3 yd
Process
1.- Use the formula of Area of a square to find it
Area = side x side
2.- Substitution
Area = 3 x 3
3.- Simplification and result
Area = 9 yd²
A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?
A) Block on dog breed and randomly assign puppies to existing and new formula groups within each
breed.
B) Block on geographic location and randomly assign puppies to existing and new formula groups
within each geographic area.
C) Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by
breed to either the existing or the new formula.
D) Stratify on geographic location of the puppies and randomly sample puppies within each
geographic area. Then assign puppies by geographic area to either the existing or the new formula
E) Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by
gender to either the existing or the new formula.
To reduce the variable of natural differences in puppy growth rates, the investigators should block on dog breed. Breed significantly impacts growth rates compared to geographic location or gender.
Explanation:In designing an experiment to test whether a new high-protein puppy food promotes faster weight gain than an existing formula, the strategy that would most effectively reduce variability due to natural differences in puppy growth rates would be option A- Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
Puppy growth rates can vary significantly by breed, with larger breeds often growing faster than smaller ones. By blocking on breed, the researchers can ensure that any differences in weight gain are due to the food, not differences in breed-specific growth rates.
The other strategies - blocking or stratifying on geographic location, or stratifying on gender - would not be as effective, because these factors have less influence on a puppy's growth rate compared to its breed.
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Will Give BRAINLIEST for CORRECT answer! Please Help! A can of vegetables holds 454 mL of food and is 4.5 in. tall. What is the diameter of the can? Please how all steps!!
Answer: the diameter of the can is 2.8 inches
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
height = 4.5 inches
Volume of can = 454 millilitres
1 cubic inch = 16.387 millilitres
Converting 454 millilitres to cubic inches, it becomes
454/16.387 = 27.7 cubic inches
Therefore
27.7 = 3.14 × r² × 4.5
27.7 = 14.13r²
r² = 27.7/14.13
r² = 1.96
r = √1.96
r = 1.4
Diameter = 2 × radius
Diameter = 2 × 1.4 = 2.8 inches
Solve the following equation: -3 = 1 3/5 + m.
-2 3/5
-4 3/5
-4 2/5
-1 25
Answer:
-4 2/5
Step-by-step explanation:
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)
Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is orange or yellow.
Compute the probability that three randomly selected peanut M&M's are all red.
If you randomly select two peanut M&M's, compute that probability that neither of them are red.
If you randomly select two peanut M&M's, compute that probability that at least one of them is red.
Answer:
Step-by-step explanation:
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.
Colour Brown Yellow Red Blue Orange Green total
Prob 0.12 0.15 0.12 0.23 0.23 0.15 1
The probability that a randomly selected peanut M&M is not yellow
=[tex]1-P(Yellow) = 0.85[/tex]
the probability that a randomly selected peanut M&M is orange or yellow.
= [tex]0.23+0.15=0.38[/tex]
the probability that three randomly selected peanut M&M's are all red.
= [tex](0.12)^3 = 0.001728[/tex]
(assuming large number of peanuts and thus independent )
If you randomly select two peanut M&M's, compute that probability that neither of them are red.
= [tex](1-0.12)^2\\= 0.7744[/tex]
If you randomly select two peanut M&M's, compute that probability that at least one of them is red
=[tex]1-P(both non red)\\= 1-0.88^2\\= 0.2256[/tex]
nearest foot horizontal distance
The horizontal distance the plan has covered when it has flown 4,000 feet is 694 feet.
Step-by-step explanation:
Step 1:
For the given triangle, assume the opposite side has a length of x units, the hypotenuse of the triangle measures 4,000 feet. The given angle of the triangle is 10°. To calculate the opposite side's length of the triangle, we use the sine of the given angle.
[tex]sin A = \frac{oppositeside}{hypotenuse}[/tex]
Step 2:
The length of the opposite side = x feet.
The length of the hypotenuse side = 4,500 feet.
[tex]sin A = \frac{oppositeside}{hypotenuse}, sin 10 = \frac{x}{4000}.[/tex]
[tex]x = sin10 (4000), sin 10 = 0.1736, x = 0.1736(4000) = 694.4 feet[/tex].
So the horizontal distance is 694.4 feet, rounding this off to the nearest foot, we get the horizontal distance as 694 feet.
Last year, 31 2 acres of strawberry fields produced approximately 14,700 pounds of strawberries. This year the number of acres planted with strawberries increased to 5 acres. Use proportional reasoning to estimate the farm's income from the sale of strawberries this year.
So in 5 acres of land produces 21,000 pounds of strawberries.
Step-by-step explanation:
Step 1:
Last year, [tex]3\frac{1}{2}[/tex] acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.
To do this we divide the total number of strawberries produced by the number of acres it was produced in.
The number of strawberries produced per acre[tex]= \frac{14,700}{3.5} = 4,200[/tex] pounds.
Step 2:
To determine the number of strawberries in 5 acres of land, we multiply the number of strawberries per acre by the number of acres.
The number of strawberries produced in 5 acres[tex]= 5(4,200) = 21,000[/tex] pounds.
So in 5 acres of land produces 21,000 pounds of strawberries.
Solve the two-step equation. − 2 3 x – 21 4 = 27 4
Answer:
Step-by-step explanation:
I'm going to assume that the problem is -23x -214 = 274
And in that case...
1. First isolate the x-value by adding 214 to both sides of the equation:
-23x = 488
2. Then, divide both sides by -23 to truly get x alone:
x = [tex]-\frac{488}{23}[/tex] or -21.22
Answer:
x = -18
Add the opposite of the constant on the left:
-2/3x = 21/4 +27/4 = 48/4 = 12
Multiply the equation by the inverse of the coefficient of x:
x = (-3/2)(12) = -18
The solution is x = -18.
Step-by-step explanation:
A wooden structure has the shape of a right triangle with a base of 12 feet and a height of 8 feet. It is supported by a wire stretched from point C to the ground at point D such that the support wire is perpendicular to the top of the structure, AC.
(1) how far away from point b should point d be placed? give an exact answer in feet and inches.
(2) to the nearest tenth of a foot what is the length of the support wire?
Answer:
(1)5 ft 4 in
(2)9.6 ft
Step-by-step explanation:
We are given that
AB=12 ft
BC=8 ft
All right triangles are similar
(1)Let BD=x
Triangle ABC and DBC are similar
When two triangle are similar then , the ratio of their corresponding sides are equal.
[tex]\frac{12}{8}=\frac{8}{x}[/tex]
[tex]x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft[/tex]
[tex]x=\frac{64}{12}\times 12=64 inches[/tex]=5 ft 4in
1 feet=12 inches
(2)In triangle DBC
[tex]CD^2=BC^2+DB^2[/tex]
Using Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(perpendicular\;side)^2[/tex]
[tex]CD^2=(8)^2+(5.3)^2[/tex]
[tex]CD=\sqrt{64+28.09)}=9.6 feet[/tex]
Hence, the length of support wire=9.6 feet
The distance from point B that point D should be placed in the triangle is 5 feet 4 inches.
How to solve the triangle?The distance from point B that point D should be placed in the triangle will be calculated thus:
Let the distance be represented by x
12/8 = 8/x
x = (8 × 8) / 12
x = 5 ft 4 in
The length of the support wire will be calculated thus:
CD² = 8² + 5.3²
CD² = 64 + 28.09
CD² = 92.09
CD = ✓92.09
CD = 9.6 feet
Therefore, the length of the support wire is 9.6 feet.
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HELP PLS 20 POINTS! I WILL MARK BRAINLIEST
Answer:
I believe it is 2 for $5.08
Step-by-step explanation:
1.27 times 2 is 2.54
2.54 times 5 is 12.70
Answer:
D 2(1/2) for $6.25
Step-by-step explanation:
a. 5.08/2=2.54
b.12.7/5=2.54
c.1.27/0.5=2.54
d.6.25/2.5=2.5
1. Graph the polar equation
2. Find each quotient and express it in rectangular form.
2(cos150°+isin150°)/ 8(cos210°+isin210°)
-0.22+0.12i
1/4[sin(-60°)+icos(-60°)]
0.12-0.22i
1/4[cos(-60°)+isin(-60°)]
3. Write the rectangular equation (x+5)^2+y^2=25 in polar form.
R= -10sin theta
R= 5
R= 5cos theta
R= -10cos theta
To graph the polar equation, plot points based on r and θ values. To express the quotient of complex numbers in rectangular form, operate division, simplify, then convert. To convert a rectangular equation to polar form, substitute x and y with their polar form.
Explanation:1. To graph the polar equation, you would plot points based on the r (magnitude/distance) and θ (angle) values from the origin (0,0). As you've not provided the specific polar equation, I cannot provide a full step-by-step explanation.
2. To divide complex numbers and express the quotient in rectangular form, you multiply the numerator and the denominator by the conjugate of the denominator, simplify, and convert the result into rectangular coordinates (x+iy) form. For example,
2(cos150° + isin150°) / 8(cos210° + isin210°)
After calculating the division, you end up with the cosine and sine of an angle in the numerator. Then, convert this to rectangular form. Unfortunately, as Brainly platform constraints, computational solutions cannot be provided through this medium.
3. To convert the rectangular equation (x+5)^2+y^2=25 in polar form, replace x = rcosθ and y = rsinθ in the equation. Then simplify the equation to get a polar equation.
Learn more about Converting across Coordinate Systems here:https://brainly.com/question/33236198
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An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which of the following is NOT true? 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. 2. The margin of error is 34. 3. The value z in the margin of error is 1.96. 4. A total of 95% of all SRS of size n contain the true mean BMI
Answer:
Option 1) A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.
Step-by-step explanation:
We are given the following in the question:
95% confidence interval of mean body mass index (BMI) for girls between 13 and 19 years of age is:
[tex](19.5, 26.3)[/tex]
Lower limit = 19.5
Upper limit = 26.3
1. A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.
The given statement is false. This is not the right interpretation for confidence interval.
2. The margin of error is 3.4
The confidence interval can be found as
[tex]\text{sample mean}\pm \text{Margin of error}[/tex]
Let x be the sample mean and y be the margin of error, thus, we can write
[tex]x - y =19.5\\x + y = 26.3\\2x =45.8 \\x = 22.9\\y = 22.9 - 19.5\\y = 3.4[/tex]
Thus, the margin of error is 3.4
Thus, the given statement is true.
3. The value z in the margin of error is 1.96.
The statement is true.
The z-multiplier for a 95% confidence interval used is 1.96
4. A total of 95% of all SRS of size n contain the true mean body mass index
The given statement is true. It is the right interpretation of 95% confidence interval.
Among the provided statements, 'A total of 95% of all teenage girls have BMI between 19.5 and 26.3' is NOT accurate. A 95% confidence interval does not indicate that 95% of the data is in that range.
Explanation:In this case, the statement that is NOT true about the confidence interval for estimating the mean body mass index (BMI) for girls between 13 and 19 years of age is: 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3.
A 95% confidence interval does not claim that 95% of the population data falls within this range. Instead, it asserts that if we were to take many samples and build a confidence interval from each sample, then about 95% of the confidence intervals would contain the true mean BMI (this is the meaning of statement 4).
Statement 2 is incorrect since the margin of error is not 34. It is calculated as (26.3 - 19.5)/2 = 3.4.
Statement 3 is correct as the value for 'z' in a 95% confidence interval is indeed 1.96. This is because 1.96 is the z-score that cuts off the top 2.5% and bottom 2.5% of data in a standard normal distribution, leaving 95% of the data in between.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
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In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2015, there were 10,000,000 residents in the city and 800,000 in the suburbs. Set up a difference equation that describes this situation, where Subscript[x, 0] is the initial population in 2015. Then estimate the populations in the city and in the suburbs two years later, in 2017.
Answer:
City @ 2017 = 8,920,800
Suburbs @ 2017 = 1, 897, 200
Step-by-step explanation:
Solution:
- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:
0.94*p_c + 0.04*p_s = p_c'
0.06*p_c + 0.96*p_s = p_s'
- Assuming 6% moved while remaining 94% remained settled at the time of migrations.
- The matrix representation is as follows:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right][/tex]
- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1[/tex]
- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1[/tex]
- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.
[tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o[/tex]
- Where,
[tex]x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right][/tex]
- The population in 2017 x_2 would be:
[tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right][/tex]
The estimated populations in 2017 are approximately 9,792,000 for the city and 807,360 for the suburbs
To set up the difference equation for this situation, let's denote the city population in a given year as [tex]\( C_n \)[/tex] and the suburban population as [tex]\( S_n \),[/tex] where [tex]\( n \)[/tex] represents the number of years since 2015. The initial populations in 2015 are given as [tex]\( C_0 = 10,000,000 \)[/tex] and[tex]\( S_0 = 800,000 \)[/tex].
Each year, 6% of the city's population moves to the suburbs, which can be represented as [tex]\( 0.06C_n \)[/tex]. Similarly, 4% of the suburban population moves into the city, which is [tex]\( 0.04S_n \).[/tex]
The difference equations describing the change in population each year are:
[tex]\[ C_{n+1} = C_n - 0.06C_n + 0.04S_n \][/tex]
[tex]\[ S_{n+1} = S_n + 0.06C_n - 0.04S_n \][/tex]
Now, let's calculate the populations for 2016 (one year after 2015,[tex]\( n = 1 \))[/tex]:
[tex]\[ C_1 = C_0 - 0.06C_0 + 0.04S_0 \][/tex]
[tex]\[ S_1 = S_0 + 0.06C_0 - 0.04S_0 \][/tex]
Plugging in the initial values:
[tex]\[ C_1 = 10,000,000 - 0.06 \times 10,000,000 + 0.04 \times 800,000 \][/tex]
[tex]\[ S_1 = 800,000 + 0.06 \times 10,000,000 - 0.04 \times 800,000 \][/tex]
Calculating the values:
[tex]\[ C_1 = 10,000,000 - 600,000 + 32,000 \][/tex]
[tex]\[ S_1 = 800,000 + 600,000 - 32,000 \][/tex]
[tex]\[ C_1 = 9,432,000 \][/tex]
[tex]\[ S_1 = 1,368,000 \][/tex]
Next, we calculate the populations for 2017 [tex](\( n = 2 \)):[/tex]
[tex]\[ C_2 = C_1 - 0.06C_1 + 0.04S_1 \][/tex]
[tex]\[ S_2 = S_1 + 0.06C_1 - 0.04S_1 \][/tex]
Using the populations from 2016:
[tex]\[ C_2 = 9,432,000 - 0.06 \times 9,432,000 + 0.04 \times 1,368,000 \][/tex]
[tex]\[ S_2 = 1,368,000 + 0.06 \times 9,432,000 - 0.04 \times 1,368,000 \][/tex]
Calculating the values:
[tex]\[ C_2 = 9,432,000 - 565,920 + 54,720 \][/tex]
[tex]\[ S_2 = 1,368,000 + 565,920 - 54,720 \][/tex]
[tex]\[ C_2 = 9,792,000 \][/tex]
[tex]\[ S_2 = 807,360 \][/tex]
dont skip please
In which quadrant would point (2, -5) be located?
Quadrant II
Quadrant III
Quadrant IV
Quadrant I
Answer:
This would be quad III
Step-by-step explanation:
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points. Write an equation to determine the total number of questions (q)(q)(, q, )on Tim's math test.
Answer:
q = 29
Step-by-step explanation:
4(q -10) = 76
Noah bought a new car costing 25350. He made a 20% down payment on the car and financed the remaining cost of the car for 5 years at 6.5%. How much interest did Noah pay on his car loan?
Answer: Noah paid $6591 on his car loan.
Step-by-step explanation:
The amount of money paid as down payment for the car is
20/100 × 25350 = 5070
Therefore, the amount paid to finance the remaining cost of the car is
25350 - 5070 = $20280
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
From the information given,
P = 20280
R = 6.5%
T = 5 years
I = (20280 × 6.5 × 5)/100 = $6591
Answer:its $6591
Step-by-step explanation:
The amount of money paid as down payment for the car is
20/100 × 25350 = 5070
Therefore, the amount paid to finance the remaining cost of the car is
25350 - 5070 = $20280
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
From the information given,
P = 20280
R = 6.5%
T = 5 years
I = (20280 × 6.5 × 5)/100 = $6591
Fill each blank with sometimes, always or never to make each statement true
a. the diagonals of a parallelogram_______ bisect each other.
b. the opposite sides of a parallelogram will_________ have different lengths
c. parallelograms are________ rectangles
Answer:
a.always
b.never
c.sometimes
Final answer:
The blank spaces in the statements regarding properties of parallelograms should be filled with 'always' for diagonals bisecting each other, 'always' for opposite sides having the same length, and 'sometimes' when referring to parallelograms being rectangles, as not all parallelograms have right angles.
Explanation:
The given question asks you to fill in the blanks with sometimes, always, or never to make each statement about a parallelogram true. Here are the completed statements with explanations:
The diagonals of a parallelogram always bisect each other.The opposite sides of a parallelogram will always have the same length. (Here 'always' is used to imply that because it's a property of parallelograms, the opposite sides will indeed be equal in length.)Parallelograms are sometimes rectangles. (This is true because rectangles are a specific type of parallelogram with right angles, but not all parallelograms are rectangles.)To understand these properties, consider that a parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Additionally, the diagonals of a parallelogram bisect each other, which means they cut each other exactly in half at the point where they cross. This property is invariant under any affine transformation, so it holds true regardless of how the parallelogram is oriented or scaled.