Answer:
[tex]E=5.76\times 10^{-8}N/C[/tex]
Step-by-step explanation:
We are given that
Charge of atomic nucleus,q=+40 e=[tex]40\times 1.6\times 10^{-19}C[/tex]
Because
1 e=[tex]1.6\times 10^{-19} C[/tex]
Charge of atomic nucleus=[tex]64\times 10^{-19}C[/tex]
Distance of charge form the center of nucleus=r=1 m
We have to find the magnitude of electric field at distance r
[tex]E=\frac{Kq}{r^2}[/tex]
Where K=[tex]9\times 10^9Nm^2/C^2[/tex]
Using the formula
[tex]E=\frac{9\times 10^9\times 64\times 10^{-19}}{1}=576\times 10^{-10}N/C[/tex]
[tex]E=\frac{576}{100}\times 10^2\times 10^{-10}=5.76\times 10^{2-10}=5.76\times 10^{-8}N/C[/tex]
Using identity[tex]a^x\cdot a^y=a^{x+y}[/tex]
Hence, the magnitude of electric field=[tex]E=5.76\times 10^{-8}N/C[/tex]
In a certain state the maximum speed permitted on freeways is 75 mi/h and the minimum speed is 50 mi/h. The fine for violating these limits is $25 for every mile per hour above the maximum speed or below the minimum speed. Express the amount of the fine F as a function of the driving speed x.
Answer: The amount of fine F as a function of the driving speed x would be
[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]
Step-by-step explanation:
Since we have given that
Maximum speed = 75 mi/hr
Minimum speed = 50 mi/hr
Fine for every mile per hour above the maximum speed or below the minimum speed = $25
So, Amount of fine for below the minimum speed would be
[tex]25(50-x)\ ;\ 0\leq x<50[/tex]
Amount of fine for above the maximum speed would be
[tex]25(x-75)\ ;\ x> 75[/tex]
There will be no fine in between the following range:
[tex]0\ ;\ 50\leq x\leq 75[/tex]
Hence, the amount of fine F as a function of the driving speed x would be
[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]
The function that represents the given situation is required.
The required function is
[tex]f(x)=\begin{cases}25(50-x) & \text{ if } 0\leq x<50 \\0 & \text{ if } 50\leq x\leq75\\25(x-75) & \text{ if } x>75 \end{cases}[/tex]
Let [tex]x[/tex] be the speed of the car
Maximum speed limit is 75 mi/h
Minimum speed limit is 50 mi/h
Any speed above the maximum speed and any speed below the minimum speed the fine is $25 dollar per mile per hour.
[tex]f(x)=25(50-x),\ 0\leq x<50[/tex]
[tex]f(x)=25(x-75),\ x>75[/tex]
There is no fine if the speed is between the given limits.
[tex]f(x)=0,\ 50\leq x\leq75[/tex]
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If n denotes a number to the left of 0 on the number line such that the square of n is less than [tex]\small \frac{1}{100}[/tex], then the reciprocal of n must be _________.
The reciprocal of n must be less than –10
Solution:
Given n denotes a number to the left of 0 means n < 0.
Square of n is less than [tex]\frac{1}{100}[/tex] means [tex]n^2<\frac{1}{100}[/tex].
Therefore, we have [tex]n<0[/tex] and [tex]n^2<\frac{1}{100}[/tex].
⇒ [tex]n^2<\frac{1}{100}[/tex]
Taking square root on both sides, we get
⇒ [tex]n<\± \frac{1}{10}[/tex]
⇒[tex]\frac{-1}{10}<n<\frac{1}{10}[/tex]
⇒ But we know that n < 0, so [tex]n<\frac{1}{10}[/tex] false.
It should be [tex]\frac{-1}{10}<n[/tex].
To equal the expression, multiply both sides of the equation by –10n.
⇒ [tex]-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}[/tex] (symbol < changed to > when multiply by minus)
⇒ [tex]\frac{1}{n}>-10[/tex]
Hence, the reciprocal of n must be less than –10.
The circular blade on a saw has a diameter of 6.25 inches and rotates at 4500 revolutions per minute. (a) Find the angular speed of the blade in radians per minute. (Round your answer to three decimal places.)
Answer:angular speed=471.429rad/sec
Step-by-step explanation:
One revolution is :
2×pi×radians
Then 4500 revolution will be:
2×pi×4500rad= 9000pi rad
1minutes = 60seconds
So the angular speed is :
=(9000×pi rad) / minutes
=9000×(22/7)rad /60seconds
=471.42857143 rad/sec
=471.429rad/sec to 3 d.p
The angular speed of the blade is [tex]471[/tex] radian per minute.
In one revolution, angle made is [tex]2\pi[/tex] radian.
In 4500 revolutions = [tex]2\pi *4500=9000\pi[/tex] radian.
We know that ,
1 hour = 60 minute.
Angular speed = [tex]\frac{9000\pi radian}{60minute} =\frac{9000*3.14}{60}=471radian/minute[/tex]
Therefore, the angular speed of the blade is [tex]471[/tex] radian per minute.
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In a research report, Richard H. Weindruch of the UCLA Medical School claims that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40 if 64 mice that are placed on this diet have an average life of 38 months with a standard deviation of 5.8 months? Use a P-value in your conclusion.
Answer:
The average life of the mice that are placed on this diet is less than 40 months.
Step-by-step explanation:
Consider the provided information.
When 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40.
The null and alternative hypothesis are:
[tex]H_0:\mu=40\\H_a:\mu<40[/tex]
64 mice that are placed on this diet have an average life is 38 months with a standard deviation of 5.8 months.
Therefore, [tex]n = 64, \bar x=38\ and\ \sigma=5.8[/tex]
Use the formula: [tex]z=\dfrac{\bar x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]
Substitute the respective values in the above formula.
[tex]z=\dfrac{38-40}{\frac{5.8}{\sqrt{64} }}[/tex]
[tex]z=-\dfrac{2}{\frac{5.8}{8}}\approx-2.76[/tex]
Now using the table [tex]P(Z<z)=0.029[/tex]
The p value is smaller than 0.05 so reject the null hypothesis.
Therefore, the average life of the mice that are placed on this diet is less than 40 months.
Fat cat starts at 9 am and goes at 75 yards per minute then skinny cat starts at 9:02 am and goes at 100 yards per minute. How long does it take for skinny cat to catch up to fat cat?
Answer:
It would take skinny cat 6 mins to reach fat cat.
Step-by-step explanation:
Given:
Speed of Fat cat = 75 yd/min
Speed of skinny cat = 100 yd/min
We need to find the time taken by skinny cat to reach fat cat.
Let the distance covered by both be 'd'.
Also let the time taken by Fat cat to cover distance 'd' be 't' mins.
Now we know that skinny cat started 2 mins later so time taken by Skinny cat will be [tex]t-2 \ mins[/tex].
Now we know that;
Distance is equal to speed times time.
framing in equation form we get;
Distance cover by fat cat = [tex]75t[/tex]
Distance cover by skinny cat = [tex]100(t-2) =100t-200[/tex]
Both distance have to made same since we need to find the time required more to reach the other cat.
[tex]100t-200=75t[/tex]
Combining like terms we get;
[tex]100t-75t=200\\\\25t =200[/tex]
Dividing both side by 25 we get;
[tex]\frac{25t}{25}=\frac{200}{25}\\\\t = 8\ mins[/tex]
Time taken by skinny cat = [tex]t-2 =8-2=6 \ mins[/tex]
Hence it would take skinny cat 6 mins to reach fat cat.
Skinny Cat catches up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am. This is calculated by determining the head start that Fat Cat has and the faster pace at which Skinny Cat moves.
We are presented with a problem where two cats, one named Fat Cat and the other Skinny Cat, start at different times and move at different speeds. Fat Cat starts at 9:00 am moving at 75 yards per minute, and Skinny Cat starts at 9:02 am moving at 100 yards per minute. The question is to find out how long it takes for Skinny Cat to catch up to Fat Cat.
Calculate the head start Fat Cat has by finding out how much distance they cover before Skinny Cat starts. Since Fat Cat starts at 9:00 am and Skinny Cat starts at 9:02 am, there is a 2-minute difference. In 2 minutes, Fat Cat travels 75 yards/minute × 2 minutes = 150 yards.Next, determine the speed difference between the two cats. Skinny Cat is moving at 100 yards per minute, and Fat Cat is moving at 75 yards per minute. The difference in speed is 100 yards/minute - 75 yards/minute = 25 yards/minute.Finally, calculate the time taken for Skinny Cat to catch up. Since Skinny Cat is going 25 yards per minute faster than Fat Cat, you would divide the head start by the speed difference: 150 yards / 25 yards/minute = 6 minutes.So, Skinny Cat will catch up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am.
Candy has been saving her pocket money she began the month with 25 and ended with 75 she said the end of the month mount was 250 of her original amount
The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e?
Answer:
[tex]V_{avg} = \frac{ln2}{e} = 0.255fts^{-1}[/tex]
Step-by-step explanation:
The question asks for the average velocity and not the instantaneous velocity (which would have meant to differentiate). So, the right formula is
[tex]V_{avg} = \frac{s(t_{2}) - s(t_{1} ) }{t_{2} -t_{1} } =[/tex]
From the question, [tex]t_{1}[/tex] corresponds to e seconds and [tex]t_{2}[/tex] corresponds to 2e seconds. So, we have
[tex]V_{avg} = \frac{ln(2e) - ln(e)}{2e - e}[/tex]
One of the laws of logarithms says that
[tex]ln(\frac{a}{b} )= ln(a) - ln(b). \\\\ Therefore, ln(2e) - ln(e) = ln(\frac{2e}{e} ) = ln(2)[/tex]
[tex]V_{avg} = \frac{ln(2)}{e} = 0.2550fts^{-1}[/tex] ≅ [tex]0.255fts^{-1}[/tex]
Determine the 6-day simple moving averages for the ten consecutive day closing prices.
97.70, 97.70, 98, 98.45, 99, 99.68, 101, 101.50, 100, 100.56
1 ; 2 ; 3 ; 4 ; 5
Answer:
40.112
Step-by-step explanation:
In a production process, the diameter measures of manufactured o-ring gaskets are known to be normally distributed with a mean diameter of 80 mm and a standard deviation of 3 mm. Any o-ring measuring 75 mm or less in diameter is defective and cannot be used. Using Excel, determine the percent or proportion of defective o-rings that will be produced.
Answer:
DIRECT WAY EXCEL
"=NORM.DIST(75,80,3,TRUE)"
And we got: [tex] P(X\leq 75)= 0.04779[/tex]
OTHER WAY
[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]
And we can find this probability using the normal standard table or excel:
[tex]P(Z<-1.67)=0.04779[/tex]
Step-by-step explanation:
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".
Solution to the problem
Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(80,3)[/tex]
Where [tex]\mu=80[/tex] and [tex]\sigma=3[/tex]
And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:
[tex] P(X\leq 75)[/tex]
One way to do this in excel is with the following formula:
"=NORM.DIST(75,80,3,TRUE)"
And we got: [tex] P(X\leq 75)= 0.04779[/tex]
And the other way is use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]
And we can find this probability using the normal standard table or excel:
[tex]P(Z<-1.67)=0.04779[/tex]
HFM & PST
What is the perimeter of HFM
Enter the answer in the box.
Answer:
50.75 units
Step-by-step explanation:
In this problem
Triangles HFM and PST are similar
we know that that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
step 1
Find the scale factor
Let
z ----> the scale factor
[tex]z=\frac{HF}{PS}[/tex]
substitute the given values
[tex]z=\frac{14}{8}=1.75[/tex]
step 2
Find the perimeter of triangle PST
[tex]P=8+9+12=29\ units[/tex]
step 3
Find the perimeter of triangle HFM
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor
so
[tex]29(1.75)=50.75\ units[/tex]
A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?(A) [tex]\sqrt{3}[/tex] : 1
(B) 1 : 1
(C) [tex]\frac{1}{2}[/tex] : 1
(D) [tex]\sqrt{2}[/tex] : 1
(E) 2 : 1
Answer:B
Step-by-step explanation:
Given
Right circular cone is inscribed in a hemisphere so that the base of the cone coincides with base of hemisphere
Height of cone is equal to radius of hemisphere
so ratio of the height of cone to the radius of the hemisphere is 1:1
Given the equation y = 4x - 3.A) If x increases by 1 unit, what is the corresponding change in y? B) If x decreases by 5 units, what is the corresponding change in y?
A) When x increases by 1 unit, y increases by 4 units.
B) When x decreases by 5 units, y decreases by 20 units.
Use the concept of linear equation defined as:
The equation having degree one is called a linear equation.
The point-slope of the linear equation is:
y = mx + c
The given equation is:
y = 4x - 3
A) To find the corresponding change in y when x increases by 1 unit,
Use the given equation y = 4x - 3.
By substituting x+1 in place of x, we get
y = 4(x+1) - 3.
Simplifying this expression,
y = 4x + 4 - 3,
y = 4x + 1.
Comparing this equation with the original equation,
That the coefficient of x is the same (4),
Which means that the rate of change remains constant.
Therefore, when x increases by 1 unit, y will increase by 4 units.
B) Similarly, to find the corresponding change in y when x decreases by 5 units,
Substitute x-5 in place of x in the original equation.
This gives us y = 4(x-5) - 3.
Simplifying further, we get
y = 4x - 20 - 3,
y = 4x - 23.
Comparing this equation with the original equation,
Again the coefficient of x remains the same (4), indicating a constant rate of change.
Therefore, when x decreases by 5 units, y will decrease by 20 units.
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Final answer:
For the equation y = 4x - 3, an increase of x by 1 unit results in an increase of y by 4 units, and a decrease of x by 5 units results in a decrease of y by 20 units, due to the slope of the line being 4.
Explanation:
The equation in question is y = 4x - 3.
A) Change in y when x increases by 1 unit:
For the linear equation given, the coefficient in front of x represents the slope of the line, which is 4. This indicates that for every 1 unit increase in x, y will increase by 4 units (since the slope is the rate of change of y with respect to x). Therefore, if x increases by 1 unit, y will increase by 4 units.
B) Change in y when x decreases by 5 units:
If x decreases by 5 units, we again use the slope of the line to determine the change in y. Since the slope is 4, a decrease in x by 5 units will result in a decrease in y by 20 units (5 units × 4 = 20 units).
Bobby Borrowed 24,000 from two different banks to start a business One Bank charge the equivalent of 4% simple interest in the other charge 5.5% interest if the total interest after 1 year was $990 determine the amount borrowed from each Bank
Answer:he borrowed $22000 from bank 1.
He borrowed $2000 from bank 2
Step-by-step explanation:
Let x represent the amount of money that he borrowed from bank 1.
Let y represent the amount of money that he borrowed from bank 2.
Bobby Borrowed 24,000 from two different banks to start a business. This means that
x + y = 24000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time
Considering the money borrowed from bank 1,
P = x
R = 4%
T = 1
I = (x × 4 × 1)/100 = 0.04x
Considering the money borrowed from bank 2,
P = y
R = 5.5%
T = 1
I = (y × 5.5 × 1)/100 = 0.055y
if the total interest after 1 year was $990, it means that
0.04x + 0.055y = 990 - - - - - -1
Substituting x = 24000 - y into equation 1, it becomes
0.04(24000 - y) + 0.055y = 990
960 - 0.04y + 0.055y = 990
- 0.04y + 0.055y = 990 - 960
0.015y = 30
y = 30/0.015 = $2000
Substituting y = 2000 into
x = 24000 - y, it becomes
x = 24000 - 2000
x = 22000
A food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets. Should she park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude
Answer:
Angle bisector
Step-by-step explanation:
Given that a food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets.
We have to find out where she should park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude
We know the perpendicular bisector is the locus of points equidistant form two points.
But here two streets can be treated as straight lines only.
The angle bisector of two lines will have all the points on the bisector.
Median is not applicable since here no triangle is there neither altitude
So right answer is angle bisector.
She should park her truck on the angle bisector of angle formed by intersection of two roads.
General Motors wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company. What type of sampling is used? Cluster Convenience Simple random Systematic Stratified
Answer: Simple random
Step-by-step explanation:
Since , the company randomly selects customers and asks them about their level of satisfaction with the company.
So the chances for each customer to get selected are equal.
This technique of sampling is known as simple random sampling .
Definition:
A simple random sampling is a sampling technique in which the researcher randomly selects individuals from the whole population of interest for his sample.Here , the probability for each individual to get selected is equal as [tex]\dfrac{1}{N}[/tex] , where N = Population size.
In the rest of sampling method (convenience , systematic , stratified and cluster) , the individuals in the population do not have equal chances to get selected. .
The type of sampling used is Cluster Sampling.
Explanation:The type of sampling used in this scenario is Cluster Sampling.
Cluster sampling involves dividing the population into smaller groups or clusters, and then selecting a random sample of clusters to survey.
In this case, the customers are grouped based on their respective clusters in the customer database, and then a random sample of 30 clusters is selected to participate in the satisfaction survey.
Select all polynomials that are divisible by (x-1).
Choose all answers that apply:
*A(x)=3x^3+2x^2-x
*B(x)=5x^3-4x^2-x
*C(x)=2x^3-3x^2+2x-1
*D(x)=x^3+2x^2+3x+2
Answer:
The answer to your question is below
Step-by-step explanation:
*A(x)=3x³ + 2x² - x This polynomial is not divisible by (x - 1)
Factor completely 3x(x + 1)(3x - 1)
*B(x)=5x³ - 4x² - x This polynomial is divisible by (x - 1)
factor completely 3x(x - 1)(5x + 1)
*C(x)=2x³ - 3x² + 2x - 1 This polynomial is divisible by (x - 1)
Synthetic division 2 - 3 + 2 -1 1
2 -1 1
2 -1 1 0
*D(x)=x³ + 2x² + 3x + 2 This polynomial is not divisible by (x - 1)
Synthetic division 1 2 3 2 1
1 3 6
1 3 6 8
Answer:
B(x) and C(x)
Step-by-step explanation:
B(x) and C(x)
In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coofficient as being linear?
A. The term linear refers to a straight line, and r measures the fraction of the points the best line passes trough.
B. The term linear refers to a straight line that passes through the average values of the paired data, and r measures how well a scatterplot fits a straight-line pattem
C. The term linear refers to a straight line, and r measures how well a scatterplot fits a straight-line pattern
D. The term linear refers to the straight line that passes through the greatost number of points, and r meansures the fraction of the points the line passes through
Answer:
C. The term linear refers to a straight line, and r measures how well a scatter plot fits a straight-line pattern
Step-by-step explanation:
In statistics, when two variables are being investigated, the location of the co-ordinates on a rectangular co-ordinates ystem is called a scatter diagram.
The amount of linear correlation between two variables is expressed by a coefficient of correlation, given the symbol r. This is defined in terms of the deviations of the co-ordinates of two variables from their mean values and is given by the product-moment formula
For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists.
Select the margin of error that corresponds to the sample mean that corresponds to each population: A population mean of 0.45, a standard deviation of 0.001, and margin of error of 0.5%
A)0.44
B)0.46
C)0.45
Answer:
C) 0.45
Step-by-step explanation:
Given that a population mean is 0.45, standard deviation is 0.001 and margin of error stands at 0.5% we have the following
0.45 + 0.001 = 0.451
Population mean with standard deviation is 0.451.
0.451 * 0.5% = 0.448745
We now reduce the number to two decimals and get the final marigin of error
0.45 as result
Answer:
Confirmation it is 0.45
Step-by-step explanation:
All the students you know taking a biology class are going to a picnic hence you concluded all students in the biology class are going for picnic This type of reasoning is an example of
a) Deduction
b) Induction
c) Inaccurate information
d) None of the above
Answer:
Induction
Step-by-step explanation:
This is an example of induction. When you take a (possibly false) conclusion according to the information you know. In this case, since you dont know of any case of a biology student not going for picnic, then you conclude that every biology student go for picnic .
It isnt deduction because the reasoning is not based on logic, rather, it is based on the partial information you know. You can argue that, since you know many students that went for a picninc, then the whole class should go to the picnic because they organized it that way, however you might need a bit more of information to reach this conclussion, for example, that the teacher went with them. Maybe, for example, a small group of students decided to go elsewhere instead.
There isnt inaccurate information here. It is incomplete, yes, but it doesnt lack accuracy: all you know is true. There isnt innacurate information.
Theresa is planning on making a fleece blanket for her nephew. She learns that the fabric she wants to use is $7.99 per yard . Find the total cost of 4 yards of fabric
When it is 11:00 a.m. in Riyadh, it is 4:00 p.m. in Manila. If your flight from Riyadh to Manila lasts 11 hours and 40 minutes, and you land at 2:00 a.m. on Monday (Manila time), what time was it in Riyadh when you left?
Final answer:
The departure time in Riyadh when flying to Manila can be calculated by subtracting the flight duration from the arrival time in Manila.
Explanation:
To determine the time in Riyadh when you left for Manila, we need to calculate the time difference between the two cities. We know that when it's 11:00 a.m. in Riyadh, it's 4:00 p.m. in Manila, giving us a time difference of 5 hours. Since your flight duration is 11 hours and 40 minutes, we need to subtract this time from the arrival time in Manila to find the departure time in Riyadh. Subtracting 11 hours and 40 minutes from 2:00 a.m. on Monday gives us 2:00 p.m. on Sunday. Therefore, it was 2:00 p.m. on Sunday in Riyadh when you left for Manila.
Feather color in budgies is determined by two different genes, Y and B, one for pigment onthe outside and one for the inside of the feather. YYBB, YyBB, or YYBb is green; yyBB or yyBbisblue; YYbb or Yybb is yellow; and yybb is white. A blue budgie is crossed with a white budgie.Which of the following results is NOT possible?
A) green offspring only
B) yellow offspring only
C) blue offspring only
D) green and yellow offspring
Answer:
Therefore, the following results are not possible:
A) green offspring only
B) yellow offspring only
D) green and yellow offspring.
Step-by-step explanation:
We know that feather color in budgies is determined by two different genes. For blue color are combinations yyBB or yyBb. For white color is combination yybb.
By combining these two colors we can not get green and yellow.
Because green and yellow colors are in this form:
Green: YYBB, YyBB, or YYBb
Yellow: YYbb or Yybb.
Therefore, the following results are not possible:
A) green offspring only
B) yellow offspring only
D) green and yellow offspring.
The most fundamental unit of computing is the ______, which is represented as an on (1) or off (0) value.
Answer:
Byte
Step-by-step explanation:
We use byte to represent 1 and 0 in computing..
The most basic unit of computing is the 'bit', which can be represented as either 1 (on) or 0 (off). This binary information is used in digital circuits to perform tasks in computing devices. The use of bits was crucial to the development of modern computing.
Explanation:The most fundamental unit of computing is the bit, which is represented as an on (1) or off (0) value. In digital circuits found in modern devices, transistors behave like switches that can be either on or off, encoding information in a binary code of ones and zeros. These bits are utilised to perform a variety of tasks like data manipulation and transmission of signals. Over time, scientists have found ways to amplify the computing capacity of bits by integrating vast collections of transistors on single silicon wafers, creating the integrated circuits (IC), which is foundational to the modern digital computer revolution.
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Amanda can spend no more than $85 to rent a car for day trip. A rental car cost 35 per day plus $20 per mile. Write and solve an inequality to find the possible distance in miles and the Amelia can drive without exceeding her budget
Answer: 2miles/ 2.5miles.
Step-by-step explanation:
If rentals for a car costs $35
subtracting this $35 from budget of $85 gives us
$85-$35= $50
By travelling one mile, we subtract $20, we're then left with
$50 - $20 = $30.
By travelling another mile, we subtract another $20, which gives
$30-$20= $10.
Since this $10 is not enough to cater for another mile, the maxmimum number of miles is 2miles.
But if allowed in halves, the $10 can cover half a mile and the longest possible distance she can travel is 2.5miles
(30 Points, please explain your answer)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Answer:
B: Based on the data, this is an example of correlation.
Step-by-step explanation:
It's the correct answer because there somewhat related and as the ice cream trucks get more sales the weather gets warmer. They both have a positive increase.
Based on the data, this is an example of correlation and causation. Option A is correct
Correlation is defined as the two things depends on each other.
Here,
People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.
Thus, Based on the data, this is an example of correlation and causation.
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A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism as shown. What is the volume of the resulting figure? A. 882 cubic centimeters B. 888 cubic centimeters C. 960 cubic centimeters D. 1,032 cubic centimeters
Answer:888 cubic centimeters
Step-by-step explanation:
The formula for determining the volume of a rectangular prism is expressed as
Volume = length × height × width
Length = 10 centimeters
Width = 8 centimeters
Height = 12 centimeters
Therefore, the volume of the rectangular prism would be
10 × 8 × 12 = 960 centimeters³
A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism. The height of the hole would also be 12 centimeters.
Therefore, the volume of the rectangular hole would be
2 × 3 ×12 = 72 cm³
the volume of the resulting figure would be
960 - 72 = 888 cm³
Fernando works between 12 and 25 hours each week. The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works. Which statement best represents the domain of this function for any given week?
Answer:
Step-by-step explanation:
The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, that he works.
The domain of a function are the set of possible values of x, the independent variable that satisfies the function.
Fernando works between 12 and 25 hours each week. It means that the statement that best represents the domain of this function for any given week would be
12 ≤ x ≤ 25
The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
Fernando works between 12 and 25 hours each week.
The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works.
The domain is the set of values x for which the given function is defined.
Or The independent variable that satisfies the function.
The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.
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The cost of an adult ticket to a football game was 1.75. The cost of a student ticket 1.25. The number of student tickets sold was twice the number of adult tickets. The total income from the sale of tickets was 850. How many tickets of each type were sold?
ANSWER: Adult tickets: 200 Student tickets:400
STEP-BY-STEP EXPLANATION:
n = number of adult tickets sold
2n = number of student tickets sold
2n(1.25) + n(1.75) = $850
2.50n + 1.75n = $850
4.25n = $850
n = 200
2n= 2 × 200= 400
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.)(a) List all outcomes in the event A that all three vehicles go in the same direction.A = (b) List all outcomes in the event B that all three vehicles take different directions.B = (c) List all outcomes in the event C that exactly two of the three vehicles turn right.C = (d) List all outcomes in the event D that exactly two vehicles go in the same direction.D = (e) List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =
Answer:
a. A = {RRR,LLL,SSS}
b. B = {RLS, RSL, LSR, LRS, SRL, SLR}
c. C = {RRS, RRL, RSR, RLR, LRR, SRR}
d. D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
e. C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
C n D = {RRS, RRL, RSR, RLR, LRR, SRR}
Step-by-step explanation:
a..
All three vehicles go in the same direction
This means that all the three vehicles either go straight, or right or left at the same time.
So, A { {RRR, LLL, SSS}
b..
All three vehicles take different directions
Thus means that all the vehicle take different routes
If a vehicle takes the the straight direction, the other 2 vehicles take right and left directions respectively
So, B = {RLS, RSL, LSR, LRS, SRL, SLR}
c..
Exactly two of the three vehicles turn right
This means that two vehicles take right direction while the last vehicle either tske the straight route or left route.
C = {RRS, RRL, RSR, RLR, LRR, SRR}
d..
Exactly two vehicles go in the same direction.
The means that if two vehicles pass straight direction then the third vehicle takes either the right or left direction.
Also, if two vehicles pass right direction, the third vehicle either takes the left direction or straight direction
Lastly, if two vehicles pass left direction then the third vehicle either pass the straight direction or right direction.
D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
e. C U D = the union of items in C and D without repetition
So,
C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
C n D = Common items in C and D
C n D = {RRS, RRL, RSR, RLR, LRR, SRR}
List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =
The question presents various scenarios of successive vehicles choosing directions. Outcomes are determined in cases where all vehicles choose the same direction, all choose different directions, exactly two choose right, exactly two choose the same direction (any), and the negation of the latter case. The outcomes of combining these scenarios (union and intersection) are also defined.
Explanation:The events refer to the outcomes of the directions three successive vehicles could potentially take. There are three possibilities: right (R), left (L), or straight (S).
(a) Event A where all three vehicles go in the same direction, would include these outcomes: A = {RRR, LLL, SSS}.
(b) Event B where all three vehicles take different directions, would look like this: B = {RLS, RSL, LRS, LSR, SRL, SLR}.
(c) Event C where exactly two of the three vehicles turn right would include these outcomes: C = {RRS, RRL, SRR, LRR, RSR, RLR}.
(d) Event D where exactly two vehicles go in the same direction, would include these outcomes: D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR}.
(e) Event D' which stands for everything that's not in event D, includes these outcomes: D' = {RLS, SLR, LRS, RSL, LSR, SRL}.
The union of events C and D, C ∪ D, combines the outcomes of both C and D, but without repetition: C ∪ D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR, RSR, RLR}.
Finally, the intersection of event C and D, C ∩ D, includes only outcomes common to both C and D: C ∩ D = {RRS, RRL, SRR, LRR, RSR, RLR}.
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Georgia pay $2.75 for four granola bars and one apple. Addison paid $2.25 for two granola bars and three apples find a cost of one granola bar in the cost of one apple.
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Step-by-step explanation:
Let,
Cost of one granola bar = x
Cost of one apple = y
According to given statement;
4x+y=2.75 Eqn 1
2x+3y=2.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]
Putting y=0.35 in Eqn 2
[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Keywords: linear equation, elimination method
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The cost of one granola bar is $0.60, and the cost of one apple is $0.35.
To solve the problem, we need to set up a system of linear equations based on the information given:
Georgia paid $2.75 for 4 granola bars and 1 apple.
Addison paid $2.25 for 2 granola bars and 3 apples.
Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25
Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35
Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.