Answer:
Step-by-step explanation:
figure out the answer by figuring out how much each bar is
Answer:
2b + 5b = b(2+5) = 7b
Step-by-step explanation:
Have a good day :)
Sam 2 granola bars
ADD
Haley 5 granola bars
Equal 7 granola bars
Which angles are coterminal with an angle drawn in standard position measuring 282°?
Select all correct angle measures.
−438∘
−78∘
78°
572°
642°
Answer:
−438°, -78°, 642°
Step-by-step explanation:
Given angle:
282°
To find the co-terminal angles of the given angle.
Solution:
Co-terminal angles are all those angles having same initial sides as well as terminal sides.
To find the positive co-terminal of an angle between 360°-720° we will add the angle to 360°
So, we have: [tex]282\°+360\°=642\°[/tex]
To find the negative co-terminal of an angle between 0° to -360° we add it to -360°
So, we have: [tex]282\°-360\°=-78\°[/tex]
To find the negative co-terminal of an angle between -360° to -720° we add it to -720°
So, we have: [tex]282\°-720\°=-438\°[/tex]
Thus, the co-terminal angles for 282° are:
−438°, -78°, 642°
The correct coterminal angles with 282° are -78° option(2) and 642° option(5). The angles -438°, 78°, and 572° are not coterminal with 282°.
In mathematics, coterminal angles are angles that share the same initial and terminal sides. To find coterminal angles for a given angle, we add or subtract multiples of 360° (a full rotation). For the angle 282°:
1. Subtracting 360°:
⇒ 282° - 360° = -78°
2. Adding 360°:
⇒ 282° + 360° = 642°
Therefore, the angle measures -78° and 642° are coterminal with 282°. The other values, -438°, 78°, and 572°, are not coterminal with 282° as they do not share the same position after full rotations.
In summary, the correct coterminal angles with 282° are -78° and 642°.
Complete question:
Which angles are coterminal with an angle drawn in standard position measuring 282°?
Select all correct angle measures.
−438°−78°78°572°642°If the standard deviation of the sampling distribution of sample means is 5.0 for samples of size 16, then the population standard deviation must be
Answer:
20
Step-by-step explanation:
The question states that the sample size is 16 and standard deviation of sampling distribution of sample mean also known as standard error is 5. This information can be written as
σxbar=standard error=5 ,n=sample size=16.
We have to find population standard deviation σ.
We know that
[tex]Standard error=\frac{population standard deviation}{\sqrt{n} }[/tex]
[tex]population standard deviation=\sqrt{n} *(standard erorr)[/tex]
[tex]\sqrt{n} =\sqrt{16} =4[/tex]
Population standard deviation=σ=4*5=20
Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude?
Answer: The resultant would be the sum and the difference between the vectors.
Step by step explanation: 1. The possible resultant is between the sum of the 2 vectors and the difference between the two vectors.
2. The greatest magnitude is when the vectors lie in the same direction and the sum would be the scalar sum of the two vectors. The angle between the two would be zero degree.
Julia purchased a new car and traveled 356 miles before refueling. If she needed 15.6 gallons of gas to fill the car's tank, estimate her gas mileage.
Answer:
22.8 MPG
Step-by-step explanation:
356 divided by 15.6 = 22.8
The scores of 12th-grade students on the national assessment of educational progress year 2000 mathematics test have a distribution that is approximately normal with mean of 300 and standard deviation of 35.
Answer:
a)[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]
[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]
b)[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]
[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]
Step-by-step explanation:
Assuming the following questions:
a) Choose one twelfth-grader at random. What is the probability that his or her score is higher than 300? Higher than 335?
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(300,35)[/tex]
Where [tex]\mu=300[/tex] and [tex]\sigma=35[/tex]
We are interested on this probability
[tex]P(X>300)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]
We find the probabilities with the normal standard table or with excel.
And for the other case:
[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]
b) Now choose an SRS of four twelfth-graders. What is the probability that his or her mean score is higher than 300? Higher than 335?
For this case since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
[tex] \bar X = \sim N(\mu = 300, \sigma_{\bar x} = \frac{35}{\sqrt{4}}=17.5)[/tex]
The new z score is given by:
[tex]z=\frac{\bar X -\mu}{\sigma_{\bar x}}[/tex]
And using the formula we got:
[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]
We find the probabilities with the normal standard table or with excel.
And for the other case:
[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]
A researcher is curious about the average IQ of registered voters in the state of FL. The entire group of registered voters in FL is an example of a(n) ___________.
a. sampleb. statisticc. populationd. parameter
Answer:
Option C) population
Step-by-step explanation:
We are given the following situation in the question:
A researcher is curious about the average IQ of registered voters in the state of FL.
Sample:
It is a part of a population. It is always smaller than the population.
Statistic:
Any numerical value or any other measure describing a sample of a population is known as statistic.
Population:
It is the universal data set. Every observation belongs to this group which is of interest. Sampling is done within population to obtain small groups of sample.
Parameter:
Any numerical value or any other measure describing the population is known as a parameter.
In this situation, the entire group of registered voters in FL is an example of a population because it contains all the individual for variable of interest.
Variable of interest:
Average IQ of registered voters in the state of FL.
Individual of interest:
Registered voters in the state of FL.
simplifying inside parentheses first pt. 2
Answer:
The answer to your question is the second option
Step-by-step explanation:
Process
Simplify using exponents laws, first inside the parentheses and then outside the parentheses.
[tex][\frac{a^{-2}b^{2}}{a^{2}b^{-1}} ]^{-3}[/tex]
a) Simplify a
a⁻² a⁻² = a⁻⁴
b) Simplify b
b² b¹ = b³
c) Write the result
[tex][\frac{b^{3}}{a^{4}}]^{-3}[/tex]
d) [tex][\frac{a^{4}}{b^{3}}]^{3}[/tex]
e) Simplify
[tex]\frac{(a^{4})^{3}}{(b^{3})3}[/tex]
f) Result
[tex]\frac{a^{12}}{b^{9}}[/tex]
If x2 + y2 = 25, what is the value of
at the point (4,3)?
O A. -25/27
OB.-7/27
OC. 7/27
D. 3/4
OE. 25/27
Answer:
A. -25/27
Step-by-step explanation:
Given:
The equation is given as:
[tex]x^2+y^2=25[/tex]
To find: [tex]\frac{d^2 y}{dx^2}[/tex] at (4, 3)
Differentiating the above equation with respect to 'x', we get:
[tex]\frac{d}{dx}(x^2+y^2)=\frac{d}{dx}(25)\\\\2x+2yy'=0\\\\x+yy'=0\\\\yy'=-x\\\\y'=\frac{-x}{y}------- (1)[/tex]
Value of [tex]y'[/tex] at (4,3) is given as:
[tex]y'_{(4,3)}=-\dfrac{4}{3}-------- (2)[/tex]
Now, differentiating equation (1) with respect to 'x' again, we get:
[tex]y''=\frac{d}{dx}(\frac{-x}{y})\\\\y''=\frac{y(-1)-(-x)y'}{y^2}\\\\y''=\frac{-y+xy'}{y^2}[/tex]
Now, value of [tex]y''[/tex] at (4,3) is given as by plugging 4 for 'x', 3 for 'y' and [tex]\frac{-4}{3}[/tex] for [tex]y'[/tex]
[tex]y''_{(4,3)}=\frac{-3+(4)(-\frac{4}{3})}{3^2}\\\\y''_{(4,3)}=\frac{-3-\frac{16}{3}}{9}\\\\y''_{(4,3)}=\frac{-9-16}{3}\div 9\\\\y''_{(4,3)}=\frac{-25}{3}\div 9\\\\y''_{(4,3)}=\frac{-25}{3}\times \frac{1}{9}\\\\y''_{(4,3)}=-\frac{25}{27}[/tex]
Therefore, the value of the second derivative at (4, 3) is option (A) which is equal to -25/27.
THE NUMBER OF STUDENTS FRON SCHOOL LAST WEEK WAS 145. This week there were only 110 students sick. What was the percent decrease of the number of students home sick?
The percent decrease of the number of students home sick is 24.14%.
Solution:
The number of students home this last week was 145
This week there were only 110 students home sick
To find: Percent decrease
The percent decrease is given by formula:
[tex]\text{Percent Decrease } = \frac{\text{Final value-initial value}}{\text{Initial value}} \times 100[/tex]
Here given that,
Initial value = last week = 145
Final value = this week = 110
Substituting the values in formula, we get,
[tex]\text{Percent Decrease } = \frac{110-145}{145} \times 100\\\\\text{Percent Decrease } = \frac{-35}{145} \times 100\\\\\text{Percent Decrease } = -24.14[/tex]
Here negative sign denotes decrease in percent
Thus the percent decrease of the number of students home sick is 24.14%.
Diego measured the length of a pain to be 22 cm the actual length of the pen is 23 cm which of these is the closest to the percent error For Diego measurement
The percent error For Diego measurement is 4.3 % decrease
Solution:
Given that, Diego measured the length of a pain to be 22 cm
The actual length of the pen is 23 cm
To find: percent error
Percent error is the difference between a measured and actual value, divided by the actual value, multiplied by 100%
The formula for percent error is given as:
[tex]\text{Percent error } = \frac{\text{Measured value - actual value}}{\text{Actual value}} \times 100[/tex]
Here given that,
Measured value = 22 cm
Actual value = 23 cm
Substituting the values in formula,
[tex]Percent\ Error = \frac{22-23}{23} \times 100\\\\Percent\ Error = \frac{-1}{23} \times 100\\\\Percent\ Error = -0.043 \times 100\\\\Percent\ Error = -4.3[/tex]
Here, negative sign denotes percent decrease
Thus percent error For Diego measurement is 4.3 % decrease
Scott and Tom rent a boat at Stow Lake. They start at 10:15 and end at 11:45. The boat rental costs $1.50 for every 15 minutes. How much will they pay?
Answer:they would pay a total amount of $9
Step-by-step explanation:
Scott and Tom rent a boat at Stow Lake. They start at 10:15 and end at 11:45. The number of hours for which they rented the boat would be
11:45 - 10:15 = 1 hour 30 minutes = 1.5 hours.
Converting to minutes, It becomes
60 + 30 = 90 minutes.
The boat rental costs $1.50 for every 15 minutes. Therefore, the total amount of money that they would pay is
90/15 × 1.5 = $9
A rectangular box 4 meters long, 3 meters wide and 2 meters tall. On the box is a cat, and the box is floating in water such that half the box is under water. The density of the box is 300 kg/m³. What is the mass of the cat?
Answer:
Mass of the cat = 16800kg
Step-by-step explanation:
The volume of the box = its length * its breath * its height- 4m × 3m × 2m = 24[tex]m^{3}[/tex]
The standard density of water is 1000 Kg/[tex]m^{3}[/tex]
By Archimedes principle, the mass of a body floating body is equivalent to the mass of the volume liquid displaced
in this case we have
Mass of water displaced = Density of the water × Volume of the water displaced = 1000 Kg/[tex]m^{3}[/tex] × 24[tex]m^{3}[/tex] = 24000kg
The mass of the box = Box density × Box volume = 24[tex]m^{3}[/tex] × 300kg/[tex]m^{3}[/tex] = 7200 kg Hence the mass of water displaced = mass of the foating box + mass of th cat
24000kg = mass of cat +7200kg
mass of cat = 24000kg - 7200kg = 16800kg
John is a new college graduate working at his first job. After years of living in an apartment he has decided to purchase a home. He has found a great neighborhood from which he can walk to work. Before buying a home in the area he has decided to collect some data on the homes in this neighborhood. A data set has been compiled that represents a sample of 100 homes in the neighborhood he is considering. The variables included in this data set include:* Value: the current value of the home as determined by the county tax assessor. * Size: the size of the home in square feet. * Year: the year the homes were built. * Basement: does the home have a basement
When analyzing data on homes in a neighborhood, focus on variables like value, size, year built, and basement presence. The sample data set of lawn areas is quantitative and continuous.
Data Analysis Process:
When collecting data on homes in a neighborhood, you can analyze it by looking at variables like value, size, year built, and basement presence. To make sense of the data, you can calculate statistics like the median home value and the variation in values to get a clearer picture of the housing market.
Data Types:
The areas of lawns in square feet sampled from five houses represent quantitative data, specifically continuous data, as they can take on any value within a range without restrictions.
Which expressions are equivalent to -6(b+2)+8−6(b+2)+8minus, 6, left parenthesis, b, plus, 2, right parenthesis, plus, 8 ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -6b+2+8−6b+2+8minus, 6, b, plus, 2, plus, 8 (Choice B) B -6b-4−6b−4minus, 6, b, minus, 4 (Choice C) C None of the above
Answer:
B. [tex]-6b-4[/tex]
Step-by-step explanation:
Given expression is [tex]-6(b+2)+8[/tex]
Simplifying the expression now
Lets use distributive property of multiplication to solve it.
As given, [tex]-6(b+2)+8[/tex]
Distributing -6 with b and 2.
= [tex](-6b-12)+8[/tex]
Opening the parenthesis
= [tex]-6b-12+8[/tex]
= [tex]-6b-4[/tex]
∴ As from the given options, [tex]-6b-4[/tex] is the correct choice.
Answer:
B
Step-by-step explanation:
Its right got it from khan
76.8 is 32% of what number
Answer: 240
Step-by-step explanation:
gina pasted 3 stickers in a book. if she added one sticker to her collection every day, what equation represents the relationship between x (number of days) and y (number of stickers)?
Answer:
The answer to your question is
Number of stickers = number of days + 3
Step-by-step explanation:
- To find the equation of the line that represents the situation, first, find the slope.
Slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{4 - 3}{1 - 0} = \frac{1}{1} = 1[/tex]
- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 1(x - 1)
y - 4 = x - 1
y = x - 1 + 4
y = x + 3
y = number of stickers
x = days
Number of stickers = number of days + 3
Answer:
is x = y + 3
Step-by-step explanation:
If y = e^5t is a solution to the differential equation d^2 y/dt^2 - 13 dy/dt + ky = 0, find the value of the constant k and the general form y = Ae^5t + Be^at of the solution to the above equation, (i.e. find a). (Use constants A, B, etc., for any constants in your solution formula.)
Answer:
k = -12/5
A = 125/12
B = -325/12
a = 5
Step-by-step explanation:
y = e^5t
Dy/dt = 5e^5t
d2y/dt2 = 25e^5t
Inputting the values of dy/dt and d2y/dt2 into the equation above, we have:
25e^5t - 13e^5t + 5k(e^5t) = 0
12e^5t + 5k(e^5t) = 0
e^5t(12 + 5k) = 0
12 + 5k = 0
k = -12/5
The equation becomes,
d2y/dt2 - 13dy/dt -12/5y = o
So rearranging the equation,
-5/12d2y/dt2 + 65/12dy/dt + y = 0
y = 5/12(25e^5t) - 65/12(5e^5t)
y = 125/12e^5t - 325/12e^5t
Therefore,
k = -12/5
A = 125/12
B = -325/12
a = 5
The value of the constant k is 40. The general form of the solution is y = A[tex]e^{5t}[/tex] + B[tex]e^{8t}[/tex]
Let's start by recognizing that if y = [tex]e^{5t}[/tex] is a solution to the differential equation d²y/dt² - 13 dy/dt + ky = 0, we need to find the value of the constant k and the general form y = A[tex]e^{5t}[/tex] + B[tex]e^{at}[/tex] of the solution. To do this, we need to determine k and a.
1. First, calculate the first and second derivatives of y = [tex]e^{5t}[/tex]
First derivative: dy/dt = 5[tex]e^{5t}[/tex]Second derivative: d²y/dt² = 25[tex]e^{5t}[/tex]2. Substitute these into the differential equation:
d²y/dt² - 13 dy/dt + ky = 0
3. Substituting, we get:
25[tex]e^{5t}[/tex] - 13(5[tex]e^{5t}[/tex]) + k[tex]e^{5t}[/tex] = 0
25[tex]e^{5t}[/tex] - 65[tex]e^{5t}[/tex] + k[tex]e^{5t}[/tex]= 0
(25 - 65 + k)[tex]e^{5t}[/tex] = 0
(-40 + k)[tex]e^{5t}[/tex] = 0
4. For this to hold true, the following must be true:
k - 40 = 0
Thus:
k = 40
The general solution to the differential equation can be expressed as:y = A[tex]e^{5t}[/tex] + B[tex]e^{at}[/tex]
1. To find a, substitute y = [tex]e^{at}[/tex] into the equation:
d²([tex]e^{at}[/tex])/dt² - 13 d([tex]e^{at}[/tex])/dt + 40[tex]e^{at}[/tex] = 0
We get:
a²[tex]e^{at}[/tex]- 13a[tex]e^{at}[/tex] + 40[tex]e^{at}[/tex]= 0
(a² - 13a + 40)[tex]e^{at}[/tex] = 0
2. The characteristic equation is:
a² - 13a + 40 = 0
3. Solve for a using the quadratic formula:
a = [13 ± √(13² - 4⋅40)] / 2
a = [13 ± √(169 - 160)] / 2
a = [13 ± √9] / 2
a = [13 ± 3] / 2
4. The roots are:
a = 8a = 5Since y = [tex]e^{5t}[/tex] is a solution already, the other root a = 8 is the additional solution. Thus, the general solution to the differential equation is:
y = A[tex]e^{5t}[/tex] + B[tex]e^{8t}[/tex].
Determine which of the following passages are arguments. For those that are, identify the conclusion. For those that are not, determine the kind of nonargument. Since the 1950s a malady called whirling disease has invaded U.S. fishing streams, frequently attacking rainbow trout. A parasite deforms young fish, which often chase their tails before dying, hence the name.
Answer:
Non Arguement passage.
Step-by-step explanation:
The passage given is a non arguement passage , the passage is more of a report especially the introductory part where the author said ''Since the 1950s a malady called whirling disease has invaded U.S. fishing streams, frequently attacking rainbow trout.'' this highlighted phrase is a report gathered or investigated by the author which was gotten as a result of his own personal findings or from history. For an argument passage, the introductory part will have portrayed what the author implied, there will be an indication of the authors stance or favoured opinion which of course will be backed by evidence from his or her findings. as such, there is nothing of such which may serve as a precursor to indicate or informed us if the passage is that of an arguement. Again, the passage is a report and not an argument. as nothing can be inferred from the paragraph to point to us if it is an argument passage.
However, there is a conclusion in the passage and conclusions has arrived by the author must have been from a detailed findings and research, if possible an experimental study before a conclusion can be reached as the last line of the paragraph says ''A parasite deforms young fish, which often chase their tails before dying, hence the name.'' The conclusion is that parasite are known to cause deformation in young fish.
A fast food restaurant sold 30 burgers with cheese if the ratio burger soup with cheese compared to without cheese was 5 : 1 one how many burgers did they sell total
Answer:36 burgers were sold.
Step-by-step explanation:
Let x represent the total number of burgers, with or without cheese that was sold.
The total number of burgers with cheese that the fast food sold is 30.
if the ratio burger sold with cheese compared to without cheese was
5 : 1 , the total ratio would be the sum of both proportions. It becomes
5 + 1 = 6
Therefore
5/6 × x = 30
5x/6 = 30
Cross multiplying by 6, it becomes
5x = 30 × 6 = 180
x = 180/5 = 36
Therefore, the number of burgers without cheese sold would be
36 - 30 = 6
ASAP! I NEED THIS DONE AS QUICKLY AS POSSIBLE WITH WORKING OUT
After t seconds, a particle P has position vector
r = [(3t³- t + 3)i + (2t²+ 2t - 1)j] m
(a) Find an expression for the velocity of P in terms of t
(b) Find an expression for the acceleration of P in terms of t
Answer:
See explanation.
Step-by-step explanation:
Let us first analyze some principle theory. By definition we know that the velocity ( [tex]v[/tex] ) is a function of a distance ( [tex]d[/tex] ) covered in some time ( [tex]t[/tex] ), whilst acceleration ( [tex]a[/tex] ) is the velocity achieved in some time. These can also been expressed as:
[tex]v = \frac{d}{t}\\[/tex] and [tex]a=\frac{v}{t}[/tex]
We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the velocity and the acceleration, by differentiating the vector with respect to time, once and twice, respectively.
Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of [tex]i-j[/tex] ) as:
[tex]r=(3t^3-t+3)i+(2t^2+2t-1)j[/tex] Eqn.(1)
Let us solve.
Part (a) Velocity: we need to differentiate Eqn.(1) with respect to time as:
[tex]v(t)=\frac{dr}{dt}\\\\ v(t)=[(3)3t^2-1]i+[(2)2t+2]j\\\\v(t)=(9t^2-1)i+(4t+2)j[/tex] Eqn.(2)
Part (b) Acceleration: we need to differentiate Eqn.(2) with respect to time as:
[tex]a(t)=\frac{dv}{dt}\\ \\a(t)=[(2)9t]i+4j\\\\a(t)=(18t)i+4j[/tex]
Thus the expressions for the velocity and the acceleration of particle P in terms of t are
[tex]v(t)=(9t^2-1)i+(4t+2)j[/tex] and [tex]a(t)=(18t)i+4j[/tex]
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan could of ran any day this week
An inequality that shows the distance Johnathan could of ran any day this week is:
[tex]x\leq 3.5[/tex]
Solution:
Let "x" be the distance Johnathan can run any day of this week
Given that,
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles
Therefore,
Number of days ran = 5
The most he ran in 1 day = 3.5 miles
Thus, the maximum distance he ran in a week is given as:
[tex]distance = 5 \times 3.5 = 17.5[/tex]
The maximum distance he ran in a week is 17.5 miles
If we let x be the distance he can run any day of this week then, we get a inequality as:
[tex]x\leq 3.5[/tex]
If we let y be the total distance he can travel in a week then, we may express it as,
[tex]y\leq 17.5[/tex]
PLZ, HELP WORTH 30 PTS!!!! WILL MARK BRANLIEST!!!
Answer:
Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.
Step-by-step explanation:
i) when x = -2 then y = 3 so the line from x = -2 to x = 2 has the point (-2, 3)
ii)when x = 2 then y = 1 so the line from x = -2 to x = 2 has the point (2, 1)
iii) if two points in a line are given then slope of equation passing through the lines is given by
slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{1 - 3}{2 - (-2)}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
So from the general equation of a line y = mx + c
we get y = [tex]\frac{-1}{2}[/tex]x + c and substituting for x and y with (-2, 3) respectively we get
3 = 1 + c. Therefore c = 2.
Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.
Solve the system using elimination.
3x – 4y = 9
–3x + 2y = 9
(–27, –9)
(3, 9)
(–3, –6)
(–9, –9)
Answer:
(-9,-9)
Step-by-step explanation:
Answer:
(-9,-9)
Step-by-step explanation:
I half dozen cupcakes cost $15. What constant of proportionality relates to the numbers of cupcakes and the total cost? Write an equation that represents its relationship
Answer:
The constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].
Step-by-step explanation:
Given:
Let the number of cupcakes be represent by [tex]'x'[/tex]
Also let the total cost be represented by [tex]'y'.[/tex]
We know that two proportional quantities are in for;
[tex]y=kx[/tex]
where, k⇒ represents constant of proportionality.
Now we know that;
1 dozen = 12
Half dozen = 6
Now Given:
half dozen cupcakes cost $15.
So Let us substitute [tex]x=6[/tex] and [tex]y=15[/tex] in above equation we get;
[tex]15 =k \times 6[/tex]
Dividing both side by 6 we get;
[tex]\frac{15}{6}=\frac{k6}{6}\\\\k= 2.5 \ \$/cupcake[/tex]
Hence the constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].
Final answer:
The constant of proportionality relating the number of cupcakes to the cost is $2.50 per cupcake. The equation representing the relationship is C = $2.50 × n.
Explanation:
To find the constant of proportionality for the number of cupcakes and total cost, we use the given information: half a dozen cupcakes (which is 6 cupcakes) cost $15. Therefore, we can divide 15 by 6 to find the cost per cupcake.
C = k × n
Where C is the total cost, n is the number of cupcakes, and k is the constant of proportionality (cost per one cupcake). First, find the constant:
k = C/n = $15/6 cupcakes = $2.50 per cupcake
The equation that represents the relationship between the number of cupcakes (n) and the total cost (C) is:
C = $2.50 × n
50 POINT QUESTION!! A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
This has already been answered but something seemed off so if u could answer it for that would be great thx
See the attached picture.
Answer could change slightly depending on how all the steps are rounded.
Six students from a statistics class reported the number of hours of television they watch per week. Here are their data: 8, 10, 5, 14, 3, 6. What is the standard deviation of the number of hours of television watched per week for this sample of six students?
Answer:
3.93
Step-by-step explanation:
Let x is the number of hours of television watched per week by six students.
X 8 10 5 14 3 6
Standard deviation for sample data is
[tex]Standard deviation=S=\sqrt\frac{{sum(x-xbar)^2} }{n-1}[/tex]
[tex]xbar=\frac{sum(x)}{n}[/tex]
[tex]xbar=\frac{8+10+5+14+3+6}{6}[/tex]
[tex]xbar=\frac{46}{6}[/tex]
xbar=7.67
[tex]sum(x-xbar)^2=(8-7.67)^2+(10-7.67)^2+(5-7.67)^2+(14-7.67)^2+(3-7.67)^2+(6-7.67)^2[/tex][tex]sum(x-xbar)^2=0.11+5.44+7.11+40.11+21.78+2.78=77.33[/tex]
[tex]Standard deviation=S=\sqrt\frac{{(77.33)} }{5}[/tex]
[tex]S=\sqrt15.466[/tex]
S=3.93
1. Given the below sequence: -1, -3, -5, -7, . . . (a) What are the next 3 terms? (b) Is this an arithmetic or geometric sequence? (c) Why? (d) What is the 27th term? (Show how to find it and tell me what the 27th term is.)
Answer:
(a) -7 , - 9 , - 11
(b) Arithmetic sequence
(c) There is a common difference of -2
(d) -53
Step-by-step explanation:
(a) To find the next three terms , we must firs check if it is arithmetic sequence or a geometric sequence . For it to be an arithmetic sequence , there must be a common difference :
check :
-3 - (-1) = -5 - (-3) = -7 - (-5) = -2
This means that there is a common difference of -2 , which means it is an arithmetic sequence.
The next 3 terms we are to find are: 5th term , 6th term and 7th term.
[tex]t_{5}[/tex] = a + 4d
[tex]t_{5}[/tex] = - 1 + 4 ( -2 )
[tex]t_{5}[/tex] = -1 - 8
[tex]t_{5}[/tex] = - 9
6th term = a +5d
[tex]t_{6}[/tex] = -1 + 5(-2)
[tex]t_{6}[/tex] = -1 - 10
[tex]t_{6}[/tex] = - 11
[tex]t_{7}[/tex] = a + 6d
[tex]t_{7}[/tex] = -1 + 6 (-2)
[tex]t_{7}[/tex] = -1 - 12
[tex]t_{7}[/tex] = -13
Therefore : the next 3 terms are : -9 , -11 , - 13
(b) it is an arithmetic sequence because there is a common difference which is -2
(c) Because of the existence of common difference
(d) [tex]t_{27}[/tex] = a + 26d
[tex]t_{27}[/tex] = -1 + 26 ( -2 )
[tex]t_{27}[/tex] = -1 - 52
[tex]t_{27}[/tex] = - 53
In 2014, the populations of China and India were approximately 1.355 and 1.255 billion people,45 respectively. However, due to central control the annual population growth rate of China was 0.44% while the population of India was growing by 1.25% each year. If these growth rates remain constant, when will the population of India exceed that of China?
Answer:
in the year 2023
Step-by-step explanation:
Initial population of China = 1.355 billion
Initial population of India = 1.255 billion
Annual population growth rate of China = 0.44% = 0.0044
Annual population growth rate of India = 1.25% = 0.0125
Now,
Final population = P₀ [tex]\times e^{\text{rate}\times t}[/tex]
Here,
P₀ = initial population
t = time
Thus,
Population of India > Population of China
1.255[tex]\times e^{\text{0.0125}\times t}[/tex] > 1.355[tex]\times e^{\text{0.0044}\times t}[/tex]
or
[tex]e^{0.0081t}[/tex] > 1.07968
taking natural log both sides
0.0081t > ln (1.07968 )
or
0.0081t > 0.0766
or
t > 9.465
Hence,
9.465 year after 2014
i.e
in 2014 + 9.465 = 2023.46
in the year 2023
Using the formula for exponential growth and the provided population data for China and India, we can approximate that India's population will exceed China's in roughly 20 years.
Explanation:In order to determine when India's population will exceed that of China, we can use the formula for exponential growth, which is P = P_0 * ert , where P is the future population, P_0 is the initial population, r is the growth rate, and t is time. As per the data provided, for China, P = 1.355 billion, r = 0.44%, and for India, P = 1.255 billion, r = 1.25%. We have to find time t when population of India will exceed that of China. This requires solving the equation: 1.355 * e0.0044t = 1.255 * e0.0125t.
This equation can be solved using algebra and logarithms. However, by making some approximations and using a spreadsheet or calculator, we can find that the population of India will exceed that of China after approximately 20 years, based on the growth rates provided.
Learn more about Population Growth here:https://brainly.com/question/18415071
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A individual has a body fat percentage of 17.7% and weighs 129 pounds.How many pounds of his weight is made up of fat?Round ur answer to the nearest tenth
Answer: 21.9 pounds of his weight is made up of fat.
Step-by-step explanation:
The total weight of the individual is 129 pounds. The individual has a body fat percentage of 17.7%.
Therefore, the number of pounds of his body that is made up of fat would be
17.7/100 × 129 = 0.177 × 129 = 21.93 pounds.
Approximating to the nearest tenth, it becomes 21.9 pounds.
Please help asap, brainliest,thanks, and 50 points. Thank you soooo much! <3
Answers:
1) [tex]x^{8} y^{8}[/tex]
2) [tex]y^{3} \sqrt{y}[/tex]
3) [tex]5x^{4} \sqrt{6}[/tex]
4) [tex]\sqrt{7}[/tex]
5) [tex]\frac{\sqrt{z}}{z}[/tex]
Step-by-step explanation:
1) [tex]\sqrt{x^{16} y^{36}}[/tex]
Rewriting the expression:
[tex](x^{16} y^{36})^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]x^{\frac{16}{2}} y^{\frac{36}{2}}[/tex]
Simplifying:
[tex]x^{8} y^{8}[/tex]
2) [tex]\sqrt{y^{7}}[/tex]
Rewriting the expression:
[tex]\sqrt{y^{6} y}=(y^{6} y)^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]y^{\frac{6}{2}} y^{\frac{1}{2}}[/tex]
Simplifying:
[tex]y^{3} y^{\frac{1}{2}}=y^{3} \sqrt{y}[/tex]
3) [tex]\sqrt{150 x^{8}}[/tex]
Rewriting the expression:
[tex]\sqrt{(6)(25) x^{8}}[/tex]
Since [tex]\sqrt{25}=5[/tex]:
[tex]5x^{4}\sqrt{6}[/tex]
4) [tex]\frac{7}{\sqrt{7}}[/tex]
Multiplying numerator and denominator by [tex]\sqrt{7}[/tex]:
[tex]\frac{7}{\sqrt{7}} (\frac{\sqrt{7}}{\sqrt{7}})=\frac{7}{7\sqrt{7}}[/tex]
Simplifying:
[tex]\sqrt{7}[/tex]
5) [tex]\frac{5z}{\sqrt{25 z^{3}}}[/tex]
Rewriting the expression:
[tex]\frac{5z}{5z \sqrt{z}}[/tex]
Simplifying:
[tex]\frac{1}{\sqrt{z}}[/tex]
Since we do not want the square root in the denominator, we can multiply numerator and denominator by [tex]\sqrt{z}[/tex]:
[tex]\frac{1}{\sqrt{z}}(\frac{\sqrt{z}}{\sqrt{z}})[/tex]
Finally:
[tex]\frac{\sqrt{z}}{z}[/tex]