Answer:
4 months
Step-by-step explanation:
Equation for Charles City:
where l is total length and t is time in months.
\(l = 5 * 2^t^-^1\) because the total length doubles every month, except the first month where the original path length was 5km
Equation for Tinsel Town:
\(l = 21 + 5(t-1)\) because the total length increases by 5km per month and it started at 21 km. The length will not increase for the first month.
At 1 month: CC length = 5 km
TT length = 21 km
At 2 months: CC length = 10 km
TT length = 26 km
At 3 months: CC length = 20 km
TT length = 31 km
At 4 months: CC length = 40 km
TT length = 35 km
So, Charles City's total path length wil bypass that of Tinsel Town in 4 months.
f(x)=2x^3+ax^2-24x+1 has a local maximum at x=-4. find a
Step-by-step explanation:
ax2+2x3−24x+1=y
Step 2: Add -2x^3 to both sides.
ax2+2x3−24x+1+−2x3=y+−2x3
ax2−24x+1=−2x3+y
Step 3: Add 24x to both sides.
ax2−24x+1+24x=−2x3+y+24x
ax2+1=−2x3+24x+y
Step 4: Add -1 to both sides.
ax2+1+−1=−2x3+24x+y+−1
ax2=−2x3+24x+y−1
Step 5: Divide both sides by x^2.
ax2
x2
=
−2x3+24x+y−1
x2
a=
−2x3+24x+y−1
x2
Answer:
a=
−2x3+24x+y−1
x2
Find the equation of a line which is parallel to y= 2/5 x + 17 and passes through (-15,12)
Answer:
y = 2/5x + 18.
Step-by-step explanation:
The line will have the same slope of 2/5.
Using the point-slope form of a line:
y - 12 = 2/5(x - -15)
y - 12 = 2/5(x + 15)
y = 2/5x + 6 + 12
y = 2/5x + 18.
Answer:
y = (2/5)*x + 18
Step-by-step explanation:
Because the line is parallel to the line y = 2/5 x + 17, the slope of the new line has to be the same as well. So far, we have y = (2/5)*x .
Now what we can do is plug in -15 for x and see what we get for y. Because we get -6, we need 18 more to make it 12. Because of that, the y-intercept is 18 to make the equation of the line y = (2/5)*x + 18.
find hcf and lcm of algebraic terms 3pqr, 24pr², 30pq²r²
ok fine I have sent this question to algebra calculator site they will send u notif on ur phoen with answer
Step-by-step explanation:
hcm is the highest common factor, also know as the gates common divisor.
in other words, what is the biggest expression that divides all given terms without remainder ?
3 divides 24 and 30. that is fine.
every term has one p and at least one r. only 2 out of the 3 terms have a q (so that is not part of it).
therefore, the hcm or gcd is 3pr
lcm is the lowest common multiple.
that means, what is the smallest expression that can be divided by all 3 terms without remainder ?
let's start with the numbers and use the prime factor approach :
3 = 3
24 = 2×2×2×3
30 = 2×3×5
lcm of these 3 numbers is then the combination of the longest streaks of the various prime factors :
2×2×2×3×5 = 120
about the variables
pq²r² can be divided by pqr and also by pr². and, of course, by pq²r² itself too.
so, we don't need to "add" anything.
so, the lcm is 120pq²r²
The population of Champaign, Illinois is given for three years in the table below:
Year Population
1970 163488
1980 168392
2012 203276
(a)Using 1970 as t=0, create a linear model
from the first two data points in this table to
predict the population, p, as a function of the
number of years since 1970, t.
(b) If this model is used to predict the population of Champaign in the year 2012, will the model over estimate or underestimate the actual population? Explain.
Answer:
See below
Step-by-step explanation:
a) Using the first two lines to get the equation:
Since t = 0 represents a start point, the y-intercept is 163488
Slope is:
(168392 - 163488)/10 = 490.4And the equation:
P(t) = 490.4(t - 1970) + 163488b) Prediction of the population in 2012 using the function:
P(2012) = 490.4(2012 - 1970) + 163488 = 184084.8As we see the number we got is less than the one on the line 3 of the table. So the model underestimated the actual population.
Rewrite the expressions below by completing the square.
x^2 -6x +5
Step-by-step explanation:
x^2 - 6x + 5
= (x^2 - 6x + (-3)^2 - (-3)^2 + 5)
= (x - 3)^2 - 4
The mean life of a certain ball bearing can be modeled using a normal distribution with a mean of six years and a standard deviation of one year. Calculate each of the following:a) the probability that a bearing will wear-out before seven years of service b) the probability that a bearing will wear-out after seven years of service c) the service life that will provide a wear-out probability of 10%
a) To find the probability that a bearing will wear-out before seven years of service, we need to calculate the area under the normal distribution curve to the left of x = 7. We can use the z-score formula to standardize the value of x:
z = (x - μ) / σ
where μ is the mean, σ is the standard deviation, and x is the value we want to find the probability for. Substituting the given values, we have:
z = (7 - 6) / 1 = 1
Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 1 is approximately 0.8413. Therefore, the probability that a bearing will wear-out before seven years of service is approximately 0.8413.
b) To find the probability that a bearing will wear-out after seven years of service, we need to calculate the area under the normal distribution curve to the right of x = 7. Using the same z-score formula and substituting the given values, we have:
z = (7 - 6) / 1 = 1
The probability of a z-score greater than 1 is the same as the probability of a z-score less than -1, which is approximately 0.1587. Therefore, the probability that a bearing will wear-out after seven years of service is approximately 0.1587.
c) To find the service life that will provide a wear-out probability of 10%, we need to find the value of x such that the area under the normal distribution curve to the left of x is 0.10. Using a standard normal distribution table or calculator, we can find the z-score that corresponds to a cumulative probability of 0.10, which is approximately -1.28.
Using the z-score formula and substituting the given values, we have:
-1.28 = (x - 6) / 1
Solving for x, we get:
x = 6 - 1.28 = 4.72
Therefore, the service life that will provide a wear-out probability of 10% is approximately 4.72 years
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Determine μx and δx from the given parameters of the population and sample size.
μ= 84, δ = 18, n = 36
The sample mean (μx) is 84 and the sample standard deviation (δx) is 3.
Based on the given parameters, you can find the mean (μx) and standard deviation (δx) of the sample using the formulas for the sample mean and standard deviation. The given parameters are:
Population mean (μ) = 84
Population standard deviation (δ) = 18
Sample size (n) = 36
For a simple random sample, the sample mean (μx) is equal to the population mean:
μx = μ = 84
To calculate the sample standard deviation (δx), use the following formula:
δx = δ / √n
δx = 18 / √36 = 18 / 6 = 3
So, the sample mean (μx) is 84 and the sample standard deviation (δx) is 3.
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PLEASE ASAP we need to turn in in 20 mins
Answer:
14 units^2
Step-by-step explanation:
Hey there!
In order to find the area of this triangle, we need to find the base and height of the triangle
the base of the triangle is 7 units long and the height of the triangle is 4 units high
Formula for area of triangle: Base x Height x 1/2
7 x 4 x 1/2 --> 28 x 1/2 --> 14
So, the area of this triangle is 14
Now the question is asking to find the area by forming a parallelogram
All you have to do for this is duplicate that same triangle, and mirror it upside down
Then all you would have to do is find the Base and the Height and multiply them together
what is the product of 3 square root 7 and 17 square root 14 in simplest radical form
\(3 \sqrt{7} \times 17 \sqrt{14} \)
This is the problem that we need to solve. The best way to get about it is to first:
Multiply the constant numbers (3 and 17). 3×17 is 51. Next multiply the radicals. \( \sqrt{7} \times \sqrt{14} = \sqrt{7 \times 14} = \sqrt{108} \)Simplify the squareroot of 108 since it is 49 times 2. It would be equal to 7 squareroots of 2. Our final answer would be:\(51 \times 7\sqrt{2} = 357 \sqrt{2} \)51 x 7 is 357, so the answer above is right.The skills needed are multiplication, mulitplication of radicals, and simplifying radicals, so if you want to review anything use these as reference.
Hope you understood and have a nice day!!
The intersection of Beech Street and fourth Street is 150 yards east of the intersection of Fort Street and Clover Street how many yards south is it
The amount of yards south that the intersection of Fort Street and Clover Street is given as follows:
450 yards.
How to obtain the slope?The slope of an inclined object is obtained as the division of the vertical distance of the street by the horizontal distance of the object.
The distances are classified as follows:
Vertical: south is negative, north is positive.Horizontal: west is negative, east is positive.The slope of the street is given as follows:
-3.
The east distance is given as follows:
150 yards.
Thus the south distance can be identified applying the slope as follows:
-3 = S/150
S = -3 x 150
S = -450 yards.
The negative number represents that the direction is south, hence the distance is only of 450 yards.
Missing InformationThe problem is given by the image shown at the end of the answer.
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secondary data should be gathered first because this type of information is less expensive to obtain. group of answer choices false true
The statement "secondary data should be gathered first because this type of information is less expensive to obtain" is actually false because it has already been collected, there are some important factors to consider.
Primary data is data that is collected specifically for the purpose of the research project at hand. This type of data can include surveys, interviews, experiments, and observations. On the other hand, secondary data is data that has already been collected by someone else for a different purpose.
Firstly, it's important to consider the quality of the data. Secondary data may not always be reliable or up-to-date, which could impact the accuracy of your research findings. In some cases, you may need to spend time and resources verifying the accuracy of the secondary data, which could end up being more expensive in the long run.
Additionally, it's important to consider the specific needs of your research project. Depending on your research question, primary data may be necessary to obtain the specific information you need. In other cases, secondary data may be sufficient.
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How do you write 533,000, 327.5, and 0.0034 in scientific notation
Answer:
A: 5.33 x 10∧5 and B.3.4 × 10-3
Step-by-step explanation:
Answer:
533,000,327.5 and o.oo34
what is the slope between (5,0) and (6,0)
Answer:
m=0
Step-by-step explanation:
Write the linear equation that gives the rule for this table.
x y
1 10
2 5
3 0
4 –5
Write your answer as an equation with y first, followed by an equal's sign.
The linear equation that gives the rule for this table is y = -5x + 15
How to determine the linear equation?The table of values is given as:
x y
1 10
2 5
3 0
4 –5
On the above table, we can see that:
As x increases by 1, the value of y decreases by 5
This means that the slope is
Slope = -5
Also, the above table can be modified as follows (using the slope of -5)
x y
0 15
1 10
2 5
3 0
4 –5
This means that the y-intercept is
y-intercept = 15
A linear equation is represented as
y = slope * x + y-intercept
So, we have
y = -5x + 15
So, the equarion is y = -5x + 15
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I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Answer:
Answer is 71.95°
Step-by-step explanation:
Cosine formula is
a^2=b^2+c^2-2bc(cosA)
cos A =b^2+c^2-a^2/2bc
if a= 119,b=94,c=173
cos A=94^2+173^2-119^2/2(94*173)
=8836+29,929-14,161/2(16,262)
=38765-14,161/32,524
=24604/32,524
=0.7564
cos A=0.7564
cos^-1=40.85°.that's for angle A.
Using the same formula
B=31.1°
C=180-(40.85+31.1)
C=180-71.95
C=108.05
Since angle on a straight line is 180
therefore x is 71.95
Also the sum of angles A and B
solve pls brainliest
Answer:
u=7
Step-by-step explanation:
19=5u-16
5u=19+16
5u=35
u=35/5
u=7
solve the system by graphing y=-x+10 y=x+8
Answer:
Step-by-step explanation:
I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...
Donald buys a pack of 9 chocolate bars.
The pack costs £2.50
Donald sells all 9 chocolate bars for 45p each.
Work out Donald's percentage profit.
Answer:220%
Step-by-step explanation:
If Gabby wants to buy a t-shirt for $35.99 but she has a discount for 10% off, how much is her final cost?
Answer:
It's $32.39.
Step-by-step explanation:
35.99 - 35.99*10% =
=35.99 - 35.99*0.1
=35.99 - 3.599
=32.391
32.391 is close to 32.39 so we will round it to that number.
The answer is $32.39.
Real GDP in 2018 was 500 million and in 2019 it was 520 million. What is the real growth rate?
Expenditure is divided by total GDP at market price multiplied by 100.
How do you determine the rate of real GDP growth?Real GDP is computed by subtracting the most recent year’s real GDP from the previous year’s real GDP. The difference is then divided by the previous year’s actual GDP. Real GDP may also be calculated if nominal GDP and the current inflation rate are known.
GDP at market value is the total of all expenditures. The GDP market price percentage rate is computed by dividing spending by total GDP at market price and multiplying by 100. GDP may be calculated in three ways: the value added technique, the income approach (how much money is made as revenue from resources utilized to manufacture things), and the expenditures approach (how much is spent on stuff).
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URGENT!! ABCD is a quadrilateral. The point G is on the side which forms that AG=AB and CB=CG
The tangent to the circle at point A Is the along the side CD at point L
The extension of the leg CB is located at point K.
Prove AD=AG
ADG is an equilateral triangle, then, line AD is equivalent to line AG.
How to prove the statementFrom the information given, we have to prove that;
AD=AG
It is important to note that the triangle ADG is an equilateral triangle.
The properties of an equilateral triangle are;
All the sides are equalAll the angles are congruent and equal to 60°It is a polygon with three sidesSince ADG is an equilateral triangle, then, line AD is equivalent to line AG
Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.
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questions that require responses at fixed intervals along a scale of answers are called
Questions that require responses at fixed intervals along a scale of answers are called scale questions.
What are scale questions?Closed-ended questions, such as the Likert Scale, are one of the most popular methods for gauging public opinion. To gauge people's opinions, attitudes, and beliefs, they employ psychometric testing. Statements are used in the questions, and respondents are asked how much they agree or disagree with each assertion. Likert Scale questions typically have a scale from 0 to 10, while shorter scales are also conceivable.
Every sort of research has benefits and drawbacks, and this particular question type has both in spades. The fundamental benefit of Likert Scale questions is that they follow a standard way of data collection, making them simple to comprehend.
Hence, according to the definition questions that require responses at fixed intervals along a scale of answers are called scale questions.
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2x-3y=6 identity the x and y
Answer:
X=6
Y=2
Hope this hlped
The equation of line p is y= 1 4 x–8. Line q, which is parallel to line p, includes the point (6, – 3). What is the equation of line q?
Answer:
The equation of line q in slope-intercept form is
y= 1/4 x– 9/2
.
Step-by-step explanation:
Which graph represents y<-3x?
Step-by-step explanation:
Desmos Graphing Calculator
A shop sells cereal in boxes A, B and C. Box A 500 g for $1.73 Box B 750 g for $2.60 Box C 1.25 kg for $4.35. which box is the best value?
Answer:
Box C
Step-by-step explanation:
First switch the box that's in kilograms into grams. One kilogram=1000 grams. So box C is 1250 grams.
Next divide the amount in each box by the cost of each box.
Box A 500/173=2.89
Box B 750/260=2.88
Box C 1250/435=2.87
So, since box C has the lowest amount when divided, that box has the best value.
in order to conduct an experiment, four subjects are randomly chosen from a group of 20 people . how many differenty groups of four subjects are pssoibke
The total number different groups of four subjects are possible are 4845 ways.
Define the term combination?A combination is indeed a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.The formula for the combination is-
ⁿCr = n!/r!(n - r)!
We are wondering in how many distinct options there are to choose 4 subjects out of 20;
n = 20
r = 4.
Sequence is not important because the topics can be arranged in any order and still form the same group, hence we must use a combination:
Review the combination's definition:
²⁰C₄ = 20!/4!(20 - 4)!
²⁰C₄ = 20!/4!16!
²⁰C₄ = 4845
Thus, the total number of different groups four subject groupings is 4845.
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Write an equation for the line that passes through (10, 17) and (20, 37)
Simplify: –3(y + 2)2 – 5 + 6y
What is the simplified product in standard form?
Answer:
-17
Step-by-step explanation:
\( - 3{(y + 2)}^{2} - 5 + 6y \\ - 3(y + 2)(y + 2) - 5 + 6y \\ ( - 3y - 6)(y + 2) - 5 + 6y \\ - 3 {y}^{2} - 6y - 6y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y + 6y - 12 - 5 \\ - 3 {y}^{2} - 6y - 17\)
Answer\(-3y^{2}-6y-17\)
Describe how to perform one repetition of a simulation of the proportion of high school students who followed the Egyptian Revolution using blue and yellow poker chips and, once you had results, how to estimate the p-value.
You would compare the proportion of simulated samples with a proportion as extreme or more extreme than your sample proportion to estimate the p-value.
For one repetition of a simulation of the proportion of high school students who followed the Egyptian Revolution using blue and yellow poker chips, you would first need to determine the total number of high school students in your sample and the estimated proportion of them who followed the Egyptian Revolution.
Next, assign one color of poker chip (e.g. blue) to represent students who followed the revolution and the other color (e.g. yellow) to represent students who did not.
Then, mix the chips thoroughly and draw a sample of the specified size.
Count the number of blue chips in the sample and divide by the total sample size to calculate the proportion of students who followed the revolution in your sample.
Repeat this process several times to simulate multiple samples from the same population.
To estimate the p-value, you would need to compare the proportion of students who followed the revolution in your sample to the null hypothesis value.
If your null hypothesis is that the true proportion of students who followed the revolution is equal to some hypothesized value (e.g. 0.5), then you would calculate the probability of observing a proportion as extreme or more extreme than your sample proportion, assuming the null hypothesis is true.
To do this, you would need to calculate the difference between your sample proportion and the hypothesized value, divide this by the standard error of the proportion, and then look up this calculated value in a t-distribution table with n-1 degrees of freedom (where n is the number of samples you simulated).
The p-value would be the area under the curve of the t-distribution beyond the calculated value.
Alternatively, you could simulate a large number of samples from a null distribution assuming the hypothesized value for the proportion of students who followed the revolution.
Then, you would compare the proportion of simulated samples with a proportion as extreme or more extreme than your sample proportion to estimate the p-value.
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