The simplified mοnοmial is [tex]-9x^9y^5[/tex].
What is mοnοmial ?In algebra, a mοnοmial is an expressiοn that has a single term, with variables and a cοefficient. Fοr example, 2xy is a mοnοmial since it is a single term, has twο variables, and οne cοefficient. Mοnοmials are the building blοcks οf pοlynοmials and are called 'terms' when they are a part οf larger pοlynοmials. In οther wοrds, each term in a pοlynοmial is a mοnοmial.
Mοnοmial is defined as an expressiοn that has a single nοn-zerο term. It cοnsists οf different parts like the variable, the cοefficient, and its degree. The variables in a mοnοmial are the letters present in it. The cοefficients are the numbers that are multiplied by the variables οf the mοnοmial. The degree οf a mοnοmial is the sum οf the expοnents οf all the variables.
When we multiply mοnοmials with the same base, we add their expοnents. Using this prοperty, we can simplify the expressiοn as fοllοws:
[tex](-8x^4y^3)(2x^5y^2)+7x^9y^5[/tex]
[tex]= (-8 * 2)(x^4 * x^5)(y^3 * y^2) + 7x^9y^5[/tex]
[tex]= -16x^9y^5 + 7x^9y^5[/tex]
[tex]= (7 - 16)x^9y^5[/tex]
[tex]= -9x^9y^5[/tex]
Therefοre, the simplified mοnοmial is [tex]-9x^9y^5[/tex].
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The two-way frequency table below shows data on playing a sport and playing a musical instrument for students in a class.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
Plays sports Does not play sports
Plays a musical instrument 666 777
Does not play a musical instrument 888 333
Plays a sport Does not play a sport Row total
Plays a musical instrument
1.001.001, point, 00
Does not play a musical instrument
1.001.001, point, 00
The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.
What is frequency?Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.
Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.
This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.
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helpppp again please
Answer: Volume = 23816.41
Which answer choice is the correct solution set for the function, f(x)=-2x^(2)-2x+4?
Answer:
Step-by-step explanation:
Do what the picture says.Right answer gets brainilest!!!!
Answer:
142.5 ft^2
Step-by-step explanation:
You need to calculate each figure separately
area of the first rectangle = 5 x 4 = 20
area of the second rectangle = (5+6)x(4) = 44
area of 1/4 circle = 1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5
area of figure: 78.5 + 20 + 44 = 142.5
Answer:
To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.
Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:
Area = (b1 + b2) / 2 * h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
Plugging in the values, we get:
Area = (6ft + 10ft) / 2 * 5ft
Area = 8ft * 5ft
Area = 40 sq ft
Area ≈ 3.73 sq m (rounded to two decimal places)
Therefore, the area of this figure is approximately 3.73 square meters.
(If it wasn't in decimals, it would be 40 square feet.)
Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
A bag of peanuts could be divided among
8 children, 9 children, or 10 children with each
getting the same number, and with 2 peanuts
left over in each case. What is the smallest
number of peanuts that could be in the bag?
The smallest number of peanuts that could be in the bag is 4320.
Let's use the Chinese Remainder Theorem to solve this problem.
Let:
x be the number of peanuts in the bag.
Then we know that x ≡ 2 (mod 8), x ≡ 2 (mod 9), and x ≡ 2 (mod 10).
Using the Chinese Remainder Theorem, we can find a solution for x as follows:
Let
M = 8 * 9 * 10 = 720, and let M1, M2, and M3 be the remainders when M is divided by 8, 9, and 10 respectively.
That is, M1 = 720 mod 8 = 0, M2 = 720 mod 9 = 0, and M3 = 720 mod 10 = 0.
Let b1 = 1, b2 = 1, and b3 = 1.
Then we need to find integers a1, a2, and a3 such that a1 * M1 * b1 + a2 * M2 * b2 + a3 * M3 * b3 = 1.
One solution is a1 = 5, a2 = -4, and a3 = 1,
so we have 5 * 720 * 1 + (-4) * 720 * 1 + 1 * 720 * 1 = 7201
= M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2.
This means that x = M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2 is a solution to the system of congruences.
Since M1 = 0, we have x ≡ 0 (mod 8).
Since M2 = 0, we have x ≡ 0 (mod 9).
Since M3 = 0, we have x ≡ 0 (mod 10).
Therefore, the smallest positive integer solution for x is x = 720 * 1 * 2 + 720 * 1 * 2 + 720 * 1 * 2 = 4320.
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I’m really bad at these problems can someone please help!?
The value of x, y, z are 14√2, 4√7, 2√21
What is trigonometric ratio?Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Tan (45) = 14√2/x
1 = 14√2/x
x =14 √2
the third side(hypotenuse) = √14√2)²+14√2)²
= √56+56
= √112
= 4√7
sin(30) = y/4√7
1/2 = y/4√7
2y = 4√7
y = 2√7
cos 30 = z/4√7
√3/2 = z/4√7
2z = 4√21
z = 2√21
therefore the value of x , y , z are 14√2, 4√7, 2√21
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Jack has 7 yards of rope. He wants to cut it into pieces of different sizes. Jack needs 84 inches of rope to tie some packages and 4 feet of rope for another project. Does Jack have enough rope? Explain. Pls help
No, Jack does not have enough rope. First, we need to convert all units to the same measurement.
Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.
To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.
Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.
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A New York Times/CBS News Poll asked a random sample of U.S. adults the question "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Based on this poll, the 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). Based on this poll, a reporter claims that more than two-thirds of U.S. adults favor such an amendment. Use the confidence interval to evaluate the reporter's claim.
a. Because the value 2/3 = 0.667 (and values greater than 2/3) are in this interval, it is plausible that more than 2/3 of the population favor such an amendment. Thus, there is convincing evidence that more than 2/3 of U.S. adults favor such an amendment.
b. Because 2/3 = 0.667 is included in this interval, it is plausible that more than 2/3 of U.S. adults favor such an amendment.
c. 95% of the time there will be more than two-thirds of U.S. adults in favor of such an amendment. Because 0.95 > 0.667, the reporter's claim is correct.
d. Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S. adults favor such an amendment.
e. Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is convincing evidence that more than 2/3 of U.S. adults fuvor such an amendment.
The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.
Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.
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An international company had 19700 employes in one country that is 22. 9 percent of there employies
The given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees.
The given statement implies that the international company has a total number of employees working in various countries. Out of these, 22.9% of the employees are working in a particular country, which amounts to 19700 employees in that country.
To find out the total number of employees working in all countries, we can use the following formula:
Total number of employees = Number of employees in the given country / Percentage of employees in the given country
Substituting the values given in the problem, we get:
Total number of employees = 19700 / 0.229
Total number of employees = 85939.3
Therefore, the international company has approximately 85939 employees working in various countries.
It's important to note that this calculation assumes that the proportion of employees working in the given country is representative of the proportion of employees working in other countries. However, if the proportion of employees working in other countries is significantly different, then the actual number of employees in the company could be different from the calculated value.
In conclusion, the given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees. We can use this information to approximate the total number of employees working in all countries.
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complete question :
An international company had 19700 employes in one country that is 22. 9 percent of there employies. Find the total number of employes in the company ?
Hello please help, the table is attached Task 1.B
The average speed of the bus between Bradbury Place and Broomhills Park is 31 km/hl. Work out how many kilometres the bus travels between these two stops. If your answer is a decimal, give it to 1 d.p.
Answer:
7.8 km
Step-by-step explanation:
You want the distance between two points when the travel time is 15 minutes at an average speed of 31 km/h.
DistanceThe relation between time, speed, and distance is ...
distance = speed × time
Here, the time is the difference between 14:50 and 14:35, which is 50-35 = 15 minutes. In terms of hours, that is 15/60 = 1/4 hours.
The speed is given as 31 km/h, so the distance is ...
(31 km/h)×(1/4 h) = 31/4 km = 7.75 km ≈ 7.8 km
The distance between the two bus stops is about 7.8 km.
Answer:7.75 km so approximately 7.8 km
Step-by-step explanation:
i am not sure but i think the answer is 7.8 km
14:50 - 14:35= 15 minutes
because in every hour the bus travel 31 km/h so,
31 km/h divided by 60
multiply the answer by 15 = 7.75 km
State the range of this quadratic function.
Answer:
[-4, +∞)
Step-by-step explanation:
[-4, +∞)
Please ASAP Help
Will mark brainlest due at 12:00
The midpoint of the line segment with the endpoints is (-2, 5).
option B.
What is the coordinates of the midpoint of a line segment?To find the coordinates of the midpoint of a line segment with endpoints K(-9, 3) and H(5, 7), we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Where;
(x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.Plugging in the coordinates of K and H, we get:
Midpoint = [(-9 + 5)/2, (3 + 7)/2]
= [-2, 5]
Therefore, the midpoint of the line segment with endpoints K(-9, 3) and H(5, 7) is (-2, 5).
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Fill in the blank with the correct term or number to complete the sentence.
A _____ expression like (3+5) x (4-1) is a combination of numbers and at least one operation
An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.
i need help on this please
Answer:[tex]847\pi[/tex]
Step-by-step explanation:
[tex]v=\pi r^{2} h\\v=\pi 11^{2} 7\\v=847\pi[/tex]
The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3
If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.
Let's start by using the formula for the square of a binomial:
(a + b)^2 = a^2 + 2ab + b^2
In this case, we have:
(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)
(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)
We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:
(x + 1)^2 = (x - 3)^2 + 120
Substituting the expressions we found above, we get:
x^2 + 2x + 1 = x^2 - 6x + 9 + 120
Simplifying, we get:
8x = 110
Therefore, the solution is:
x = 13.75
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Complete question is:
The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?
-x + 12y = -27 and -5x + 3y = -21
Answer:
x = 3
y = -2
Step-by-step explanation:
-x + 12y = -27
-5x + 3y = -21
Time the first equation by -5
5x - 60y = 135
-5x + 3y = -21
-57y = 114
y = -2
Now put in -2 for y and solve for x
-5x + 3(-2) = -21
-5x -6 = -21
-5x = -15
x = 3
Let's check
-5(3) + 3(-2) = -21
-15 - 6 = -21
-21 = -21
So, x = 3 and y = -2 is the correct answer.
Pleas answer this question
find cos X
Answer:
110x
Step-by-step explanation:
its 110x
CEREAL The volume of a box of cereal in square inches can be represented by
the expression 2x² + 30x + 108. Factor the expression.
Answer:
2(x+6)(x+9)
Step-by-step explanation:
Factor out a 2.
The result is 2(x^2+15x+54).
From here, many ways are possible, but for simplicity, we’ll go for a guess and check method. Assuming you know how it works, 2 numbers (we’ll call them a and b) satisfy a+b=15 and ab=54. After a bit of guessing, we can derive that the 2 numbers are 6 and 9. Our factored expression resembles 2(x+a)(x+b), so our factored expression is
2(x+6)(x+9)
Suppose at an appliances store, the price of a toaster increased from ₹400 to ₹800, while that of a microwave increased from ₹10000 to ₹10400. The increase in price for both appliances is the same, which is ₹
The increase in price for both appliances is the same, which is ₹400
Let's first find the increase in price for the toaster:
Increase in price = New price - Old price
Increase in price = ₹800 - ₹400
Increase in price = ₹400
Now, let's find the increase in price for the microwave:
Increase in price = New price - Old price
Increase in price = ₹10400 - ₹10000
Increase in price = ₹400
As we can see, the increase in price for both appliances is the same, which is ₹400.
The increase in price for both appliances is ₹400. This is found by subtracting the old price from the new price for each appliance. For the toaster, the increase is ₹800 - ₹400 = ₹400. For the microwave, the increase is ₹10400 - ₹10000 = ₹400. Since both appliances had the same increase in price, we can conclude that the percentage increase is different for each appliance. In this case, the percentage increase for the toaster is 100% [(₹800 - ₹400)/₹400 x 100%], while the percentage increase for the microwave is only 4% [(₹10400 - ₹10000)/₹10000 x 100%].
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what is an equation that is parallel to y=1/2x + 1/4 and passes through the points (-6, 5)
Answer: o find an equation that is parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 1/2, so any parallel line must also have a slope of 1/2.
Now we can use the point-slope form of a line to find the equation of the parallel line that passes through (-6, 5):
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in m = 1/2 and (x1, y1) = (-6, 5), we get:
y - 5 = 1/2(x - (-6))
Simplifying:
y - 5 = 1/2(x + 6)
y - 5 = 1/2x + 3
y = 1/2x + 8
So the equation of the parallel line that passes through (-6, 5) is y = 1/2x + 8.
Brainliest is Appreciated.
Given the function
` f(x)= {( -6, x<0), ( sqrt(7 x^2 + 9), x\geq 0):}`
Calculate the following values:
`f(-6)= ` `f(0)= ` `f(6)= `
Answer:
f(-6) = -6 (since -6 is less than 0)
f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)
f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)
Step-by-step explanation:
To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.
For x less than 0:
f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)
For x greater than or equal to 0:
f(x) = sqrt(7x^2 + 9)
Therefore:
f(-6) = -6 (since -6 is less than 0)
f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)
f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)
simplify the expression 16+(-3)-3/7j-6/7j+4
Step-by-step explanation:
To simplify the expression 16+(-3)-3/7j-6/7j+4, we first need to combine like terms. The real numbers (16, -3, and 4) can be added together, and the imaginary numbers (-3/7j and -6/7j) can also be added together. So we have:
16 + (-3) + 4 + (-3/7j) + (-6/7j)
Simplifying the real numbers:
= 16 - 3 + 4
= 17
Simplifying the imaginary numbers:
= (-3/7j) + (-6/7j)
= (-9/7j)
Putting it all together, we get:
16 + (-3) - 3/7j - 6/7j + 4 = 17 - 9/7j
So the simplified expression is 17 - 9/7j.
I NEED HELP ASAP!!!!
I got ya.
I wrote the answers in the boxes.
Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be
15
3
4
15
4
3
​
inches. Find the sink’s volume in cubic inches. Round your answer to the nearest tenth if necessary
The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.
The volume of hemisphere is calculated by the formula -
Volume = 2/3πr³, where r represents radius of the hemisphere.
Before beginning the calculation, convert radius from mixed fraction to fraction.
Radius = (15×4)+3/4
Performing multiplication and addition
Radius = 63/4 inches
Volume =
[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]
Performing multiplication and taking cube
Volume = 8182.77 inches³
Rounding to nearest tenth
Volume = 8182.8 cubic inches
Hence, the volume of hemisphere is 8182.8 cubic inches.
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The complete question is -
Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be
15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary
If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly 5 threes?
Answer:
0.119
Step-by-step explanation:
No. of sides a die has= 6 sides
No. of times it is rolled= 7 times
Total pairs= 6 x 7
= 42 pairs
No. of 5 threes= 5 x 1
= 5
Probability of getting 5 threes= Favorable outcomes/Total outcome
= [tex]\frac{5}{42}[/tex]
= 0.119 chance
∴ probability of getting 5 threes is 0.119
Find -3 3/4+1/2 on a number line
Answer: - 3 1/4
Step-by-step explanation:
- 3 3/4 + 1/2
Get a common denominator
-3 3/4 + 2/4
-3 1/4
A sample of 10 widgets has a mean of 32.500 and standard
deviation of 6.050. At 90% confidence, the lower limit with 3
decimal places is
The lower limit with 3 decimal places at 90% confidence is 29.266.
To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.
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Use the relative frequency table shown to the right to calculate the number of the 300
measurements falling into each of the measurement classes. Then graph a frequency histogram for these data.
Measurement Class Relative Frequency
00.5-2.50 0.15
02.5-4.50 0.1
04.5-6.50 0.1
06.5-8.50 0.05
08.5-10.5 0.1
10.5-12.5 0.2
12.5-14.5 0.2
14.5-16.5 0.1
Calculate the number of measurements that fall into each class.
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
What is relative frequency ?
Relative frequency is a measure used to calculate the proportion or percentage of occurrences of an event in relation to the total number of events or observations. It is calculated by dividing the frequency of an event by the total number of observations in a dataset. The relative frequency is expressed as a decimal, fraction, or percentage. It is useful for comparing the occurrence of events in different datasets or for comparing the distribution of events in a single dataset.
According to the question:
To calculate the number of measurements that fall into each class, we need to multiply the relative frequency of each class by the total number of measurements, which is 300.
For the 00.5-2.50 class: 0.15 x 300 = 45
For the 02.5-4.50 class: 0.1 x 300 = 30
For the 04.5-6.50 class: 0.1 x 300 = 30
For the 06.5-8.50 class: 0.05 x 300 = 15
For the 08.5-10.5 class: 0.1 x 300 = 30
For the 10.5-12.5 class: 0.2 x 300 = 60
For the 12.5-14.5 class: 0.2 x 300 = 60
For the 14.5-16.5 class: 0.1 x 300 = 30
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
To graph a frequency histogram for these data, we can plot the number of measurements in each class on the vertical axis and the measurement classes on the horizontal axis, with the bars for each class touching each other. The resulting histogram should have eight bars of varying heights, with the tallest bars representing the classes with the most measurements.
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PLEASE ANSWER!!! WILL GIVE BRAINLIEST!!!
Question 3: A rectangle has sides measuring (7x - 1) units and (2x + 3) units.
Part A:
Create an expression that represents the area of the rectangle:
Calculate the area. SHOW ALL WORK:
Write the expression in standard form:
Part B: Identify the following by using the expression below. 4x^2 + 3y - 6x^4y + 4
Degree:__
#Terms:__
Drag & Drop, write the expression in standard form.
A) -6x^4 + 4x^2 + 3y + 4
B) 4x^2 + 3y - 6x^4 + 4
C) -6x^4 + 3y + 4x^2 + 4
D) 4x^2 - 6x^4 + 3y + 4
Part C: Choose the term that makes the statement true.
Adding, subtraction or multiplying two polynomials _____ results in another polynomial.
A) Always
B) Sometimes
C) Never
Answer:
Part A:
The expression that represents the area of the rectangle is:
Area = length × width
Area = (7x - 1)(2x + 3)
Area = 14x^2 + 19x - 3
To calculate the area, we multiplied the length (7x - 1) by the width (2x + 3).
To write the expression in standard form, we rearrange the terms in descending order of degree:
Area = -3 + 19x + 14x^2
Part B:
The expression in standard form is:
-6x^4 + 4x^2 + 3y + 4
Degree: 4
Terms: 4
Part C:
Adding, subtracting, and multiplying two polynomials always results in another polynomial. Therefore, the term that makes the statement true is A) Always.
Step-by-step explanation:
21. A triangle has a base of 3 centimeters and
a height of 6 centimeters. Explain how the
area of the triangle will change if the base is
doubled.
Answer:
The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.
If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.
In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:
A = 1/2 * 6 cm * 6 cm = 18 cm²
Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.
Step-by-step explanation: