[tex](6x+5)/(x+7)\\[/tex] can be represented as in the form quotient [tex]+( remainder )/( divisor )[/tex] as [tex]6 + 47/(x+7)[/tex] using division.
The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):
The divisor, x+7, should be written in the following format: (a, b, c,... 0), where the final term is 0 and the other terms are the polynomial coefficients in descending order of degree. The divisor is already present in this form in this instance.Using the same format as the divisor and a 0 coefficient for any missing terms, write the dividend, 6x+5, in the same format. The dividend can therefore be expressed as (6, 5).Reduce the dividend's first period, which is six years.Multiply the first coefficient of the dividend by the amount that was just brought down, and then place the answer under the second coefficient of the payout. So, we multiply 7 by 6 to obtain 42, which we then place in the payout under the number 5.To determine the new dividend coefficient value, add the two coefficients from the previous step. Because of this, 5 + 42 = 47.Repeat steps 4 and 5 as necessary to process all of the dividend's terms. The leftover is the last coefficient in the dividend, and together with the other coefficients, it makes up the quotient. In this instance, the remainder is 47 and the quotient is 6.So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:
(6x+5)/(x+7) = 6 + 47/(x+7)
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How many unit angles does the smaller angle of a small pattern block turn through?explain
Therefore , the solution of the given problem of angle comes out to be the smaller angle will therefore rotate through one unit angle each time.
What does an angle mean?In Euclidean mathematics, a tilt is a shape consisting of two sides, or cylindrical faces, that separate at the wall's centre and its apex. Two rays may come together at their intersections to create an angle. Another result of two things interacting is an angle. They are characterized as dihedral angles. Two line beams can be arranged in different ways at their extremities to produce a two-dimensional curve.
Here,
A small pattern block is a geometric structure made up of six congruent isosceles triangles organised around a regular hexagon with six equal-length sides.
Two of the angles in an isosceles triangle are identical in size, while the third angle varies.
We need to first create a frame of reference in order to determine how many unit angles the smaller angle of a small pattern block turns through.
Assume that we begin by placing the little pattern block in its initial location with one of its sides vertically aligned.
This results in one of the isosceles triangles being vertically aligned after turning the block.
The smaller angle will therefore rotate through one unit angle each time if we continue to rotate the small pattern block anticlockwise by one-sixth of a complete revolution for each subsequent turn.
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a spherical snowball is melting in such a way that its diameter is decreasing at rate of 2 cm/min. at what rate is the volume of the snowball decreasing when the diameter is 6 cm?
The rate of decrease of volume of the sphere when its diameter is 6 cm is -96π cubic cm/min.
Given that the snowball is a sphere, we can use the formula for the volume of a sphere.
The formula for the volume of a sphere is
V = 4/3 πr³
We need to find out the rate of decrease of volume when the diameter is 6 cm.
To find the rate of decrease of volume, we need to differentiate the above formula. Differentiating the above formula w.r.t. time, we get
dV/dt = 4/3 π(3r²)(dr/dt)
Where r is the radius of the sphere and dr/dt is the rate of change of the radius.
Let d be the diameter of the sphere. Then we can write,r = d/2
Also, given that dr/dt = -2cm/min
Substituting the values in the equation for the rate of decrease of volume,
dV/dt = 4/3 π(3(d/2)²)(-2) = -8π/3 d²
As the diameter of the sphere is 6 cm, d = 6 cm.Substituting the value in the equation above, we get
dV/dt = -8π/3 (6)² = -96π cubic cm/min
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Use the density formula (d =) to find the density of a block of metal with a mass of 21.1
kilograms and a volume of 9.37 meters³.
Round your answer to the nearest tenth of a kg/m³
Answer:
Below
Step-by-step explanation:
Density = mass
volume
Density = 21.1 kg / 9.37 m^3 = ~ 2.3 kg/m^3
In its January 25, 2012, issue, the Journal of the American Medical Association (JAMA) reported on the effects of overconsumption of low, normal, and high protein diets on weight gain, energy expenditure, and body composition. Researchers conducted a single blind, randomized controlled trial of 25 U. S. Adults. The subjects were healthy, weight-stable, male and female volunteers, aged 18 to 35 years. All subjects consumed a weight-stabilizing diet for 13 to 25 days. Afterwards, the researchers randomly assigned participants to diets containing various percentages of energy from protein: 5% (low protein), 15% (normal protein), or 25% (high protein). The subjects were not aware of the specific protein level diet to which they were assigned. On these diets the researchers overfed the participants during the last 8 weeks of their 10 to 12 week stay in the inpatient metabolic unit. The goal was to investigate the effect of overconsumption of protein on weight gain, energy expenditure, and body composition. What is the purpose of random assignment in this experiment?
a. To generalize the experiment results to a larger group
b. To avoid bias
c. To produce treatment groups with similar characteristics
d. To control for confounding variables
Random assignment in this experiment is important to avoid bias.
By randomly assigning participants to diets with different levels of protein, the researchers are ensuring that any differences in outcomes are due to the diet, and not because of any individual characteristics of the participants. Random assignment helps to ensure that the groups being compared in the experiment are similar and that any differences seen in outcomes are due to the protein level and not other factors. Random assignment helps to eliminate any bias that could be introduced if the participants were assigned to diets based on their own characteristics. This helps to ensure that the results of the experiment are valid and accurate.
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In a binomial situation, n = 4 and π = 0.35. Find the
probabilities for all possible values of the random variable,
x. (Round your answers to 4 decimal places.)
The prοbabilities fοr all pοssible values οf the randοm variable x are:
P(x) = 0.1785 P(x) = 0.3911 P(x) = 0.3462 P(x) = 0.1124 P(x) = 0.0118.
Hοw likely is it that twο randοm variables will οccur?The jοint prοbability is the likelihοοd οf twο (οr mοre) events. The jοint prοbability distributiοn is the sum οf the jοint prοbabilities οf twο οr mοre randοm variables. Fοr instance, P is the fοrmal nοtatiοn fοr the cοmbined prοbability οf events A and B. (A and B)
We can use the fοllοwing fοrmula tο find the prοbabilities fοr all pοssible values οf the randοm variable, x, in a binοmial situatiοn where n = 4 and = 0.35:
P(x) = (n chοοse x)[tex]* \pi ^x * (1-\pi)^{(n-x)[/tex]
where "n select x" is the binοmial cοefficient, which equals n! / (x! * (n-x)!).
Then, fοr x = 0, 1, 2, 3, and 4, we can cοmpute P(x) as fοllοws:
P(x=0) = (4 chοοse 0) [tex]* 0.35^0 * 0.65^4 = 0.1785[/tex]
P(x=1) = (4 chοοse 1) [tex]* 0.35^1 * 0.65^3 = 0.3911[/tex]
P(x=2) = (4 chοοse 2) [tex]* 0.35^2 * 0.65^2 = 0.3462[/tex]
P(x=3) = (4 chοοse 3) [tex]* 0.35^3 * 0.65^1 = 0.1124[/tex]
P(x=4) = (4 chοοse 4) [tex]* 0.35^4 * 0.65^0 = 0.0118[/tex]
When we rοund these numbers tο fοur decimal places, we get:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
As a result, the prοbabilities fοr all pοssible values οf the randοm variable x are as fοllοws:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
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Step by step explanation please! Offering brainliest
Answer:
343 cubic meters.
Step-by-step explanation:
To find the volume of a cube given its surface area, we need to first find the length of one of its sides.
The formula for the surface area of a cube is:
SA = 6s^2
where SA is the surface area and s is the length of one of the cube's sides.
We are given that the surface area is 294 square meters, so we can set up the equation:
294 = 6s^2
Simplifying, we get:
49 = s^2
Taking the square root of both sides, we get:
s = 7
So the length of one of the cube's sides is 7 meters.
To find the volume of the cube, we use the formula:
V = s^3
Substituting in 7 for s, we get:
V = 7^3 = 343
Therefore, the volume of the cube is 343 cubic meters.
Answer:
343m³
Step-by-step explanation:
Surface area of a cube is A = 6a²
6a² = 294
Divide both sides by 6
a² = 49
Square root of both sides
a =7
Substitute the value of a into volume
Volume of Cube V = a³
V = 7x 7x7
V = 343m³
2. The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1. 30 pm (a) He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.
Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.
The formula to calculate the time taken is: Time = Distance/Speed
Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:
Time = 140 miles/50 mph = 2.8 hours
Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.
To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.
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The quadrilateral ABCD has vertices with coordinates A(1,4), B(2,3), C(0,-3) and D(-3,1). Graph ABCD and find its area.
The graph of quadrilateral ABCD is attached below and it's area is 25.5 squared units
What is the graph and area of ABCDTo graph the vertices of the quadrilateral ABCD, we need to use a graphing calculator to find the sides and then the area can be calculated as;
We can use the Shoelace Formula to find the area of the quadrilateral. The Shoelace Formula is based on the idea of using the coordinates of the vertices of the polygon to calculate its area.
The formula is:
Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|
where (x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices of the polygon in order, either clockwise or counterclockwise.
Using this formula, we get:
Area = 1/2 * |(13 + 2(-3) + 01 + (-3)4) - (42 + 30 + (-3)(-3) + 11)|
Area = 1/2 * |(-3 - 6 - 12 - 12) - (8 + 0 + 9 + 1)|
Area = 1/2 * |-33 - 18|
Area = 1/2 * 51
Area = 25.5
Therefore, the area of quadrilateral ABCD is 25.5 square units.
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In order to save money for prom, Tom is going to walk his neighbors dog for $6. 50 per hour and wash cars for $7 per hour. His mother told him he can work no more than 15 hours in order to keep up with his homework. Tom will need to make at least $91 to cover prom expenses.
I just need the solution
Tom is working two jobs to save money for prom, walking a neighbor's dog for $6.50 an hour and washing cars for $7 an hour, to make at least $91.
Tom is working to put money aside for the prom.. His mother has instructed him that in order to keep up with his schoolwork, he may only work a maximum of 15 hours each week. Tom has made the decision to wash cars for $7 per hour and walk his neighbor's dog for $6.50 per hour in order to achieve this aim. For his prom expenditures, he will need to earn at least $91. He must put in a maximum of 13.2 hours of work to earn $91. This implies he can stroll a dog for 8.4 hours and wash vehicles for 4.8 hours. He can also decide to simply perform one job; but, in order to earn the appropriate amount, he would need to walk his neighbor's dog for 12 hours.
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-10+30+58=9-54 X 50-4=
Answer:
Hi
Step-by-step explanation:
SOLUTION STEPS
−10+30+58=9−54×50−4=
Add −10 and 30 to get 20.
20+58=9−54×50−4
Add 20 and 58 to get 78.
78=9−54×50−4
Multiply 54 and 50 to get 2700.
78=9−2700−4
Subtract 2700 from 9 to get −2691.
78=−2691−4
Subtract 4 from −2691 to get −2695.
78=−2695
Compare 78 and −2695.
A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?
1)There is no correlation between amount of sleep and number of calories burned.
2)There may or may not be causation. Further studies would have to be done to determine this.
3)There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep
The correct answer is option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Based on the information provided, the yoga instructor can conclude that there is no correlation between the amount of sleep and the number of calories burned during class. Therefore, the correct answer is
option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Option 2) suggests that further studies would be needed to determine causation, but since there is no correlation found in this study, there is no basis for further investigation into causation.
Option 3) suggests that there is a correlation between the amount of sleep and the number of calories burned and that there is likely causation. However, this conclusion contradicts the information provided, which indicates that there is no correlation between these variables.
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If there is a 5% chance that none of the items on a scratch-off lottery ticket
will be a winner, what is the probability that at least one of the scratch-off items will win?
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, the probability that at least one of the scratch-off items will win is 95%.
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, then the probability of winning on any one item is 1 - 0.05 = 0.95 (i.e., a 95% chance of winning on any one item).
The complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring, can be used to determine the likelihood that at least one of the scratch-off items will win. In this case, the event we are interested in is winning on at least one item. The complement of this event is not winning on any item.
So, the probability of winning on at least one item is:
1 - 0.05 = 0.95
Therefore, there is a 95% chance that at least one of the items on a scratch-off lottery ticket will win.
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I need to get this done in 5 minutes and im so confused!?
Answer: line A
Step-by-step explanation:
2x is the slope and -1 is the y-intercept
2x for the slope, also 2/1x (meaning rising up 2 places for every one place on the x axis).
Line A is the only line who has 2x for the slope.
ANSWER: LINE (A)
Answer:
Line a
Step-by-step explanation:
The equation is y= 2x - 1 so....
Slope = 2
Y-intercept = -1
Slope can be put as Rise/ Run ( up/ side)
This means the slope can be written as 2/1
Line a has a slope of 2/1 from the point -1 so the answer is line a
The ability to determine the age of some individuals can be difficult if there are not quality government records of birth.
Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and
an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally
distributed with a mean of 19.1 years and a standard deviation of 16.1 months. Complete parts (a) through (d).
The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.
What is Probability?Probability of an event is a number that shows what is the possibility of an event occur.
we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.
[tex]= \frac{(17 - 18.6 years)}{1.308333 years}[/tex]
[tex]= \frac{(-1.6) }{1.308333}[/tex]
[tex]= -1.22293[/tex]
[tex]= approx. 1.22.[/tex]
The area from the mean to +ve or -ve 1.22 is .3888
We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.
So, the growth plates will fuse before age 17 [tex]= .5000-.3888 = 0.1112[/tex]
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3.6 You have a single piece remaining, 8 points from home, and it is your roll. Your opponent will surely go out if he or she gets another turn. Show that p (your winning) <1/2 , so that a double is not called for. Then explain why this does not contradict the result stated in Exercise 3.1 - namely that the expected count on a backgammon roll is 8 6 1 , exceeding the 8 points you need to win.
a) result does not contradict
To show that p(your winning) <1/2, we need to consider that the last piece you have on your board could land on various positions. Depending on the position, your opponent could end up winning even if you land a higher value on the dice. Therefore, the probability of your winning is less than 1/2. This shows that a double is not called for.Exercise 3.1 states that the expected count on a backgammon roll is 8 6 1, exceeding the 8 points you need to win. This is true since the expected count means the average count you are expected to land on if you roll the dice. It does not mean that every roll will result in a count higher than 8, and it does not mean that you will always win. The expected count is simply a statistical measure of the possible outcomes of rolling the dice. Therefore, this result does not contradict the fact that p(your winning) <1/2.
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an escalator can move 30 people per minute from the main level to the upper level. How long would it take to use the escalator to move 100 people?
Answer:
3.33 minutes
Step-by-step explanation:
first know that the escalator can move 30 people in 1 minute.
then, we can write in a mathematical expression as:
30 people = 1 minute
100 people = ? minutes.
cross multiply, i.e. 30×? = 100×1
therefore, ? = 100/30
? = 3.33 minutes.
therefore, it's going to take 3.33 minutes for the escalorr to take 100 people.
Which inequality is true when the value of w w is 13 13?
The given inequality is true when w is greater than 5: w > 5. (option 4)
To solve the inequality, we can simplify the expression inside the absolute value brackets by distributing the negative sign and combining like terms:
|13w - 5 + w + 3| - 5 + w + 3 > 5|14w - 2| - 2 > 5|14w - 2| > 7Now we can split the inequality into two cases: 14w - 2 > 7 and -(14w - 2) > 7. Solving each case for w gives:
14w - 2 > 7
14w > 9
w > 9/14
-(14w - 2) > 7
-14w + 2 > 7
-14w > 5
w < -5/14
So the solution to the inequality is w > 9/14 or w < -5/14. However, we are given that w is greater than 5, so the only valid solution is w > 5.
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Complete Question:
Which inequality is true when the value of w is 13?
w-<5 -w-3>-5 -w-3>5 w->5.i need help asap please
Answer:
2,3,4,10
Step-by-step explanation:
DIVIDE METERS BY 1000 SINCE KILO MEANS 1000
Answer:2000m=2km
3000m=3km
4000m=4km
10000m=10
Step-by-step explanation:
1kilometers is equal to 1000 meters. So, we divide meters with 1000 in order to find kilometers.
plss hellllp
plss helllp
Suppose the diameter of a circle is
4
What is its circumference?
Use 3. 14 for
π and enter your answer as a decimal
The circumference of the circle with diameter 4 is 12.56 units using 3.14 as the value of π.
The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle. If the diameter of the circle is given as 4, then we can substitute it into the formula to get:
C = πd
C = π(4)
Since we are given to use 3.14 for π, we can substitute it into the formula to get:
C = 3.14(4)
C = 12.56
It's important to note that the circumference of a circle is the distance around the edge or perimeter of the circle.
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A piece of wax has a volume of 2. 5 cm and a mass of 4. 5 g. What is the density of the wax? A. 2. 0 g/cm B. 1. 8 g/cm3 C. 11. 3 g/cm3 O D. 7. 0 g/cm
The density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams.
The density of a material is defined as its mass in line with unit volume, generally expressed in grams in line with cubical centimeter( g/ cm ³). To compute the density of the presented wax, we need to divide its mass by applying its volume.
Presented that the volume of the wax is2.5 cm ³ and its mass is 4.5 g, we will compute its density as
Density = Mass/ volume = 4.5 g/2.5 cm ³ = 1.8 g/ cm ³
Thus, the density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams. knowing the density of a fabric can help in relating the cloth or in predicting its deportment in distinct qualifications.
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If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
To find out how many sixth grade textbooks were used, divide 57.1 cm by the height of one sixth grade textbook. Then multiply that number by 23 to get the total number of sixth grade textbooks used.
If you want to find out how many sixth grade textbooks were used for the tower, you first have to calculate the height of one sixth grade textbook. Once you have that measurement, you can divide 57.1 cm by that height to get the number of sixth grade textbooks used in the tower. To get the total number of textbooks used, you then need to multiply the number of textbooks per tower by 23, since 23 fifth grade textbooks were used. In other words, if the height of one sixth grade textbook is h, the number of sixth grade textbooks used is (57.1 cm / h) * 23. This equation gives you the number of sixth grade textbooks used, based on the height of one sixth grade textbook and the total height of the tower.
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events. a. A∣B b. A∣B ′ c. A∣B ' d. Are events A and B independent? a. P(A∣B)= (Round to two decimal places as needed.) b. P(A∣B ′ )= (Round to two decimal places as needed.) c. P(A ′ ∣B ′ )= (Round to two decimal places as needed.) d. Are events A and B independent? A and B are not independent. A and B are independent.
The A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
P(A∣B)= 0.60 (Round to two decimal places as needed.)b. P(A∣B ′ )= 0.45 (Round to two decimal places as needed.)c. P(A ′ ∣B ′ )= 0.20 (Round to two decimal places as needed.)d. Are events A and B independent? A and B are not independent.Explanation:A∣B means that the event A occurs when the event B occurs. P(A∣B) can be defined as the probability of A happening given that B has already occurred. By definition, A and B are independent if P(A∣B) = P(A).a. P(A∣B)= P(A∩B)/P(B)0.60 = 0.36/0.60= 3/5 b. P(A∣B ′ )= P(A∩B ′ )/P(B ′ )0.45 = 0.27/0.60= 9/20c. P(A ′ ∣B ′ )= P(A ′ ∩B ′ )/P(B ′ )0.20 = 0.12/0.60= 1/5d. If A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
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In the figure, three lines intersect at point P. If x = 65 and y = 75, what is the value of z?
The value of angle Z is 40 degrees. (Option 3). In this problem, we are given that three lines intersect at point P and we need to find the value of angle Z.
We know that angle X is 65 degrees and angle Y is 75 degrees. We also know that all six angles formed by the intersection of the three lines add up to 360 degrees.
Using these facts, we can set up an equation as
2X + 2Y + 2Z = 360.
We can simplify this equation to
X + Y + Z = 180.
We can then substitute the given values of X and Y to get
65 + 75 + Z = 180.
Simplifying this equation, we get Z = 40, which means Z is equal to 40 degrees.
Therefore, the answer is option C.
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Complete Question:
In the figure, 3 lines intersect at point P. If x = 65 and y = 75, what is the value of z?
140804020. The jug shown below contains some water. How many litres of water does this jug contain? 300 ml 250 ml - 200 ml -150 ml 100 ml -50 ml
Answer:
250 ml
Step-by-step explanation:
300ml + 250ml =550ml
550ml - 200ml=350ml
350ml - 150ml + 100ml=300ml
300ml - 50ml=250ml
A cylinder has a volume of 72 cubic inches. What is the volue of a cone with the same height and radius as the cylinder
A cone with the same height and radius as a cylinder has a volume of 24 cubic inches.
If a cylinder has a volume of 72 cubic inches, we can use the formula for the volume of a cylinder to find its height and radius. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
72 = πr^2h
We can solve this equation for h:
h = 72/(πr^2)
Now, we can use the formula for the volume of a cone to find the volume of a cone with the same height and radius as the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
V = (1/3)πr^2(72/(πr^2))
Simplifying this equation, we get:
V = 24
Therefore, the volume of a cone with the same height and radius as the cylinder is 24 cubic inches.
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Amanda was given the following polynomial and asked to factor completely. Find the errors that she made and explain how to fix her errors.
Answer:
The error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24. Amanda also omitted the addition sign in line 3 of her calculations.
Step-by-step explanation:
To factor a quadratic polynomial in the form ax² + bx + c, find two numbers that multiply to ac and sum to b.
Therefore, for the given polynomial 4x² + 22x + 24:
⇒ ac = 4 · 24 = 96
⇒ b = 22
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Therefore, the factor pair that sums to 22 is 16 and 6.
Rewrite b as the sum of these two numbers:
⇒ 4x² + 22x + 24
⇒ 4x² + (16 + 6)x + 24
⇒ 4x² + 16x + 6x + 24
Therefore, the error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24. Amanda also omitted the addition sign in line 3 of her calculations.
The correct calculation is as follows:
4x² + 22x + 24
⇒ 4x² + 16x + 6x + 24
⇒ 4x(x + 4) + 6(x + 4)
⇒ (4x + 6)(x + 4)
Given :-
A polynomial 4x² + 22x + 24 .To find:-
The mistakes made by Amanda and how to fix the mistakes.Answer:-
Given polynomial to us is ,
[tex]\implies 4x^2 + 22x + 24 \\[/tex]
With respect to the standard form of polynomial ax² + bx + c , we have;
a = 4 and c = 24Step 1 :- Split the middle term into two parts p and q such that p × q = a × c and p + q = b
Such two numbers are 16 and 6 .
Hence, we can rewrite it as ,
[tex]\implies 4x^2 + 16x + 6x + 24 \\[/tex]
But Amanda wrote [tex] 4x^2+16x - 6x + 24[/tex] , so she made a mistake here by writing +6x as -6x .
Step 2:- Factor out the common terms .
[tex]\implies 4x( x + 4) + 6(x+4) \\[/tex]
Step 3 :- Take out [tex] x+4[/tex] as common.
[tex]\implies (x+4)(4x+6) \\[/tex]
This is our required factored form .
Hence we can see that Amanda made a mistake only in splitting the term term .
and we are done!
I NEED HELP ON THIS ASAP!!
The constraints as a system of linear inequalities include the following;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640
75x + 60y ≤ 12,900
The solution set for the system of linear inequalities is shown in the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the SOS Smartcall produced in one day.Let the variable y represent the number of SOS Basic produced in one day.Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640.
75x + 60y ≤ 12,900
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Pls help
Help Algebra1
The equivalent expression is; 4a^3b(4b - 2a^2b^4 + 3a)
How do we know equivalent expressions?Two expressions are equivalent when you can manipulate one expression algebraically to transform it into the other expression. For example, you can use the distributive property, combine like terms, factor out common factors, or simplify fractions to show that two expressions are equivalent.
We have the expression;
16a^3b^2 - 8a^5b^5 + 12a^4b
4a^3b(4b - 2a^2b^4 + 3a)
It's important to note that sometimes two expressions may look different, but they can be equivalent under certain conditions or constraints.
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1. David has designed a lawn game that uses a circular center target with alternating gray and
white rings. The circles used to make the target have radii of 0. 5 foot, 1 foot, and 1. 5 feet.
1. 5 ft
What is the total area of the gray sections of the target, to the nearest square inch?
A 452 square inches
B. 565 square inches
C 678 square inches
D. 1017 square inches
The total area of gray sections of the target is 1017 square inches. The correct option is (D).
To find the total area of the gray sections of the target, we need to first find the areas of the gray rings. We can do this by subtracting the area of the smaller circle from the area of the larger circle for each ring.
The area of a circle is given by the formula A = πr^2, where r is the radius.
For the outer gray ring, the radius is 1.5 feet. So, the area of the gray ring is:
A_gray_outer = π(1.5)^2 - π(1)^2
= 7.06858 - 3.14159
= 3.92699 square feet
For the middle gray ring, the radius is 1 foot. So, the area of the gray ring is:
A_gray_middle = π(1)^2 - π(0.5)^2
= 3.14159 - 0.78540
= 2.35619 square feet
For the inner gray ring, the radius is 0.5 feet. So, the area of the gray ring is:
A_gray_inner = π(0.5)^2 - 0
= 0.78540 square feet
The total area of the gray sections of the target is the sum of these three areas:
A_total_gray = A_gray_outer + A_gray_middle + A_gray_inner
= 3.92699 + 2.35619 + 0.78540
= 7.06858 square feet
To convert this to square inches, we multiply by the conversion factor (12 inches/foot)^2:
A_total_gray = 7.06858 * (12)^2
= 1016.7048 square inches
Rounding this to the nearest square inch gives:
A_total_gray ≈ 1017 square inches
So the correct answer is (D). 1017 square inches.
To know more about Area of circle:
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