Answers
Answer:
(2x+16) + (x) = 180
Step-by-step explanation:
The opposite angles of a quadrilateral inscribed inside a circle will be supplementary angles, meaning that A+C=180, and B+D=180. A+C is not given in the answers below, but B+D is, so that is the correct answer.
Hope this helps! Please give brainliest!!
Answer:
C
Step-by-step explanation:
Opposite angles of a quadrilateral are supplementary
Related Questions
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answers
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Determine whether the pair of equations represent parallel lines, perpendicular lines, or neither.
12x + 4y = 16
24x + 8y = 36
Answers
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5
Use the place value chart to write 9.807.
Answers
Answer:
9 ones, 8 tenths, 0 hundredths, 7 thousandths
Step-by-step explanation:
Answer:
9 thousands
8 hundreds
0 tens
7 ones
Step-by-step explanation:
Hope it helped!
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answers
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2
y
X
Find the slope of the line that passes through the points
(2, -5) and (7, 1).
y
-5
6
2
7
1
Step 1: Choose (X1,Y1).
4
2.
-4
-2
2
4
6
8
Answers
Answer:
slope = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 5) and (x₂, y₂ ) = (7, 1)
m = [tex]\frac{1+5}{7-2}[/tex] = [tex]\frac{6}{5}[/tex]
The required slope of the line passes through the points (2, -5) and (7, 1) is m = 6/5
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Let's apply this formula to the given points:
m = (1 - (-5)) / (7 - 2)
m = 6 / 5
Thus, the required slope of the line passes through the points (2, -5) and (7, 1).
Learn more about slopes here:
https://brainly.com/question/3605446
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Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answers
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $43,000 and $61,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.
Required:
a. What is the planning value for the population standard deviation (to the nearest whole number)?
b. How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?
1. $500?
2. $200?
3. $100?
Answers
Answer:
a. 4650
b.
1. 332
2. 2076
3. 8306
Step-by-step explanation:
a. The planning value for population standard deviation is,
s = (maximum - minimum) / 4
s = (61600 - 43000) / 4
s = 4650
that is, it would be 4650, the planning value for population standard deviation
b. we have to:
n = (z * s / E) ^ 2
z for confidence level 95% is 1.96, E = 500; 200; 100
replacing:
1.
n = (1.96 * 4650/500) ^ 2
n = 332.2 = 332
2.
n = (1.96 * 4650/200) ^ 2
n = 2076.6 = 2076
3.
n = (1.96 * 4650/100) ^ 2
n = 8306.4 = 8306
A glass vase has a circular rim with a diameter of 5in. How many inches of ribbon are needed to go once around the rim? Use 3.14
Answers
Answer:
31.4 inches
Step-by-step explanation:
The circumference of a circle has the formula 2πr.
2 × π × 5
= 10 × 3.14
= 31.4
31.4 inches of ribbon is needed to go once around the rim.
Answer:
15.7 inches of ribbon.
Step-by-step explanation:
This question is basically asking for the circumference of the glass vase's rim. We can calculate that by multiplying the diameter by π, which in this case, is 3.14.
The diameter is 5 inches, so all you need to do is 5 * 3.14 = 15.7 inches of ribbon.
Hope this helps!
1/3 times the difference of a number and five is -2/3 which equation best shows this
Answers
Answer:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Step-by-step explanation:
Let the number be x
Difference of a number & 5 : x-5
1/3 time the difference of a number & 5: 1/3 (x-5)
Equation:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Solution:
[tex]x-5=\frac{-2}{3}*\frac{3}{1}\\\\x-5=-2\\\\x=-2+5\\x=3[/tex]
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
Answers
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Population divided into groups. Some members of each group are surveyed. This is stratified sampling
a water storage tank is in the shape of a hemisphere. If the radius is 29ft, approximate the volume of the tank in cubic feet
Answers
Answer:
The answer is 51080.2 cubic feetStep-by-step explanation:
Volume of a hemisphere is given by
[tex]V = \frac{2}{3} \pi {r}^{3} [/tex]
where r is the radius of the hemisphere
From the question
r = 29 ft
Substitute the value of r into the formula
That's
[tex]V = \frac{2}{3} \pi \times {29}^{3} [/tex]
[tex]V = \frac{48778}{3} \pi[/tex]
We have the final answer as
V = 51080.2 cubic feetHope this helps you
GO DEEPER
In the last six months, Sonia's family used 456, 398,655, 508,
1,186, and 625 minutes on their cell phone plan. In an effort to spend less
time on the phone each month, Sonia's family wants to try and keep the
mean cell phone usage at 600 minutes or less. Over the last 6 months,
by how many minutes did the mean number of minutes exceed their goal?
Answers
Answer:
46
Step-by-step explanation:
- (3/4) times (- 3/8) times ___= -3/4
Answers
Answer:
x = -8/3
Step-by-step explanation:
Step 1: Write equation
-3/4(-3/8)(x) = -3/4
Step 2: Multiply
9/32(x) = -3/4
Step 3: Divide
x = -3/4/(9/32)
x = -3/4(32/9)
x = -8/3
Answer:
-8/3
Step-by-step explanation:
-(3/4) x (-3/8)= 9/32
9/32 times (-8/3) = -3/4
Answer: -8/3
What is 75miles/hr in feet/second?(1mile = 5280feet)
Answers
Answer:
110 feet/sec
Step-by-step explanation:
75 miles x 5280 feet
= 396000
396000/60 min
=6600
6600/60 secs
=110 feet/second
a)3x-1/5=2x+3/7
b)4x/5-3x/10=2
Answers
is this what u need.....
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. c) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144d) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
Answers
Answer:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Step-by-step explanation:
Confidence interval:
Confidence level of x%
We build from a sample.
Between a and b.
Intepretation: We are x% sure that the population mean is between a and b.
In this question:
90%
45 CEO's
Between ($139,048, $154,144).
So
We are 90% sure that the mean salary of all CEO's falls within this interval.
The correct answer is:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Select the correct answer. Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v? A. v = B. v = C. v = D. v =
Answers
Answer:
Step-by-step explanation:
vector u=<(11-(-7),(-5-2)>=<18,-7>
as direction is opposite to u
so vector v=-3(18,-7)=(-54,21)
Please answer this correctly
Answers
Answer:
80%
Step-by-step explanation:
The probability of getting a four is 1/5
The probability of getting a odd is3/5
So u add them and it gives u 4/5 which in decimal is .8 which in percent is 80%
Hope this helps
Please only answer if you are 100% sure about the answer.
Answers
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answers
Answer:
4 and 4
Step-by-step explanation:
We have 2 numbers that will be X and Y
X * Y = 16 => Y = 16 / X
We must minimize the sum, therefore:
S = X + Y
S = X + 16 / X
we derive and equal 0 and we are left with:
dS / dA = 1 - 16 / (X ^ 2) = 0
1 = 16 / X ^ 2
X ^ 2 = 16
X = 4
in the case of Y:
Y = 16/4 = 4
Therefore the numbers are 4 and 4.
The two positive numbers are 4 and 4
Let the two numbers be x and y
If the product of both numbers is 16, hence;
xy = 16 ........................... 1
If the sum will be at the minimum, hence x + y = minimum
From equation1, x = 16/ y
Substitute into the second equation to have;
16/y + y = A(y)
A(y) = 16/y + y
For the expression to be at a minimum, hence dA/dy = 0
dA/dy = -16/y² + 1
0 = -16/y² + 1
0 - 1 = -16/y²
-y² = -16
y = √16
y = 4
Recall that xy = 16
4x= 16
x = 4
Hence the two positive numbers are 4 and 4
LEarn more here: https://brainly.com/question/13598452
Please answer this correctly
Answers
Answer:
8/25
Step-by-step explanation:
The probability of picking a number less than 9 is 4/5.
The probability of picking an even number is 2/5.
[tex]4/5 \times 2/5[/tex]
[tex]=8/25[/tex]
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answers
Answer:
Option (c).
Step-by-step explanation:
It is given that, I paid twice as much by not waiting for a sale and not ordering online.
Let the cost of items ordering online be x.
So, now i am paying twice of x = 2x
Now, we have find 2x is what percent of x.
[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]
It means, I paid 200% of what I could have online and on sale.
Therefore, the correct option is (c).
what expression is equivalent to 6+(-x)+2x(-7)+2x
Answers
Answer:
I hope this will help you :)
Step-by-step explanation:
6+(-x)+2x(-7)+2x
6-x+2x✖️(-7)+2x
6-x-14+2x
6-14-x+2x
-8+x
Please answer this correctly
Answers
Answer:
75%
Step-by-step explanation:
The numbers that are not 5 are 6, 7, and 8.
3 numbers are not 5 out of 4 total numbers on the spinner.
3/4 = 0.75
= 75%
Answer:
75%
Step-by-step explanation:
Total no.s = 4
Divided in parts = 25%
P(not 5) = 75%
A pair of surfers collected data on the self-reported numbers of days surfed in a month for 30 longboard surfers and 30 shortboard surfers. Complete parts a and b below.
Longboard: 2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Shortboard: 17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
a) Compare the typical number of days surfing for these two groups.
The median for the longboards was________ days, and the median for the shortboards was_______ days, showing that those with________ typically surfed more days in this month
b) Compare the interquartile ranges.
The interquartile range for the longboards was________ days, and the interquartile range for the shortboards was_______ days, showing more variation in the days surfed this month for the________
Answers
Answer:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Step-by-step explanation:
Longboard:
2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Sorting in ascending order, we have:
[tex]2, 3, 5, 6, 7, 7, \boxed{8, 8}, 9, 10, 10, 11, 11, 12, \boxed{13, 14,} 15,15, 16, 16, 16, 17, \boxed{18, 18}, 19, 20, 21, 22, 24 , 24[/tex]
Median [tex]=\dfrac{13+14}{2}=13.5[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{18+18}{2}=18\\$Interquartile range, Q_3-Q_1=18-8=10[/tex]
Shortboard
17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
Sorting in ascending order, we have:
[tex]5, 6, 6, 7, 7, 7, \boxed{8, 8,} 8, 10, 10, 10, 12, 12, \boxed{13, 13} 14, 15, 16, 16, 16, 16, \boxed{17, 20,} 22, 23, 23, 24, 24, 25[/tex]
Median [tex]=\dfrac{13+13}{2}=13[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{17+20}{2}=18.5\\$Interquartile range, Q_3-Q_1=18.5-8=10.5[/tex]
Therefore:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Decide whether the Experiment is a Binomial Experiment. If it is not, explain why:
You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
Answers
Answer:
Experiment 1 and 3 are clear binomial experiments.
Experiment 2 needs tweaking to be a binomial experiment.
Check Explanation.
Step-by-step explanation:
A binomial experiment is one in which
1) The probability of success doesn't change with every run or number of trials.
2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.
3) The outcome of each trial/run of a binomial experiment is independent of one another.
Checking each of the experiments one at a time
- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
For this experiment,
1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.
2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).
3) The probability of each trial being a boy is independent from all the other trials.
Hence, this experiment is a binomial experiment.
- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
For this experiment,
1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.
2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.
3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.
This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.
- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.
2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).
3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.
Hence, this experiment is a binomial experiment.
Hope this Helps!!!
Solve the equation. Round the solution to the nearest tenth . Enter the solution set of the equation . 2P o =P 0 (1.053)^ t
Answers
Answer: t= 13.4
Step-by-step explanation:
The given equation is [tex]2P_0=P_0(1.053)^t[/tex]
To solve this equation for 't', we first divide both sides by [tex]P_0[/tex], we get
[tex]2=(1.053)^t[/tex]
Taking log on both the sides, we get
[tex]\log 2= \log(1.053)^t[/tex]
Since [tex]\log a^b=b\log a[/tex]
Then,
[tex]\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=\dfrac{0.30103}{0.02243}\\\\\Rightarrow t=13.4208649131\approx13.4[/tex]
Hence, the value of t is 13.4.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. If he can ride 10 mph faster than he can walk, how much time (in hr) should he allow to walk a 25-mile trail? (Hint: How fast can he walk?) ________ hr. (enter a fraction)
Answers
Answer:
The answer is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Velocity formula:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:
This means that:
[tex]v = \frac{8}{t}[/tex]
And
[tex]v + 10 = \frac{28}{t}[/tex]
[tex](v + 10)t = 28[/tex]
From the first equation:
[tex]vt = 8[/tex]
So
[tex]vt + 10 = 28[/tex]
[tex]8 + 10t = 28[/tex]
[tex]10t = 20[/tex]
[tex]t = \frac{20}{10}[/tex]
[tex]t = 2[/tex]
He walks 8 miles in two hours, so:
[tex]v = \frac{8}{2} = 4[/tex]
4 miles per hour.
How much time (in hr) should he allow to walk a 25-mile trail?
This is t when [tex]d = 25[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{25}{t}[/tex]
[tex]4t = 25[/tex]
[tex]t = \frac{25}{4}[/tex]
The answer is [tex]\frac{25}{4}[/tex]
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?
Answers
Answer:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Step-by-step explanation:
Given:
There are two types of boxes i.e. Large and Small
Let the weight of Large boxes = L kg
Let the weight of Small boxes = S kg
As per given statement:
A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.Writing equation for above:
[tex]8L + 4S = 201[/tex] ....... (1)
A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.Writing equation for above:
[tex]3L + 2S = 82 ....... (2)[/tex]
Now, by solving the equations (1) and (2), we can get the values of L and S.
Multiplying equation (2) with 2 and subtracting from equation (1):
[tex]8L + 4S = 201[/tex]
-
[tex]2 \times (3L + 2S) = 82 \times 2[/tex]
[tex]8L + 4S = 201[/tex]
-
[tex]6L + 4S = 164[/tex]
--------------------
[tex]2L = 37[/tex]
L = 18.5 Kg
Putting value of L in equation (1):
[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]
So, the answer is:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Given that triangle DAE ~ triangle BAC, what is the length of side AE?
Answers
Answer:
12
Step-by-step explanation:
For polygons that are similar to each other, the ratio of their corresponding sides are usually equal to each other, as they are proportional.
Therefore, given that ∆DAE is similar to ∆BAC, AD = 6, AB = 6+4 = 10, AE = x, AC = x + 8, therefore:
AD/AB = AE/AC
6/10 = x/(x+8)
Cross multiply
6*(x+8) = x*10
6x + 48 = 10x
Subtract 6x from both sides
48 = 10x - 6x
48 = 4x
Divide both sides by 4
48/4 = x
x = 12
Length of side AE = 12