Answers
Answer:
A person travels in one complete rotation while riding on a Ferris wheel is 98.596 in terms of pi
Step-by-step explanation:
As we know the formula of circumference of Circle have the value of 2*3.14(pi)*r (radius of the circle), and2r=d (diameter of the circle), so to get the value of r we have to divide 78.5 from 2 to get 15.7 which is radius of circle. so as the person travels in one complete rotation while riding on a Ferris wheel therefore the calculation is done usually considering the above formula, as we apply the formula to the given problem we will get that 2* 3.14* 15.7 = 98.596.
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Related Questions
Infuse 0. 8 liters for 9 hours at a drop factor of 60 gtt/ ml. How many ml will be infused per hour
Answers
The infusion rate for the given volume to be infused in the given time duration is given by 266.67 ml per hour (rounded to two decimal places).
Volume to be infused = 0.8liters
Time duration = 9 hours
Drop factor = 60 gtt/ml
Use the following formula to calculate the infusion rate,
Infusion rate = (Volume to be infused × Drop factor) / Time in minutes
Convert the units to liters and minutes, respectively,
1 liter = 1000 milliliters
⇒ 0.8 liters = 800 milliliters
1 hour = 60 minutes
⇒ 9 hours = 9 × 60
= 540 minutes
Substituting the given values, we get,
⇒ Infusion rate = (800 ml × 60 gtt/ml) / 540 min
⇒Infusion rate = 88.89 gtt/min (rounded to two decimal places)
The infusion rate is 88.89 drops per minute.
To convert this to milliliters per hour,
Use the following conversion,
since the drop factor is 60 gtt/ml
⇒ 1 ml = 20 drops
The infusion rate in ml/hour is,
= (88.89 gtt/min × 1 ml/20 gtt) × 60 min/hour
= 266.67 ml/hour
Therefore, the infusion rate is 266.67 ml per hour (rounded to two decimal places).
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statistical methods are excellent for capturing what type of data?
Answers
Statistical methods are excellent for capturing quantitative data, which is numerical data that can be measured and analyzed using mathematical calculations.
These methods are commonly used in fields such as economics, psychology, and social sciences to collect, analyze, and interpret data.
In contrast, qualitative data such as opinions, attitudes, and beliefs are better captured using methods such as interviews, focus groups, and case studies.
Which two primary data kinds are there?
Data may be categorized into two main probability : quantitative and qualitative, and both are equally significant.
Why are primary and secondary data different?
Data may be obtained by social and health scientists by speaking with the subjects that interest them directly. These data they gather are referred to as primary data.
The information that has previously been obtained by someone else is another sort of data that might be useful to researchers. Secondary data is what this is.
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what units would express the volume of a right rectangular prism with a length of 8 meters, a width of 10 meters, and a height of 5 meters?
Answers
The volume of a right rectangular prism is given by the formula **V = l × w × h**, where **V** is the volume, **l** is the length, **w** is the width, and **h** is the height²³. The units of volume are cubic units, which means that they are the same as the units of length raised to the third power. For example, if the length is measured in meters, then the volume is measured in cubic meters (m³).
In this case, the length is 8 meters, the width is 10 meters, and the height is 5 meters. Therefore, the volume is:
**V = 8 × 10 × 5**
**V = 400 m³**
The units of volume are cubic meters (m³) because the units of length are meters (m).
Answer:
Step-by-step explanation:
The units for the volume of a right rectangular prism are cubic units because it is a measure of three-dimensional space.
In this case, the length, width, and height of the prism are all given in meters. Therefore, the volume of the prism can be expressed in cubic meters (m³).
So the volume of the right rectangular prism with a length of 8 meters, a width of 10 meters, and a height of 5 meters is:
Volume = length x width x height = 8 m x 10 m x 5 m = 400 m³.
Therefore, the volume of the prism is 400 cubic meters (m³).
A box has a base area of 1.9 m2.
The box is placed on the ground and exerts a force of 4.7 kN.
What pressure is the force applied with?
Give your answer in kN/m2 and rounded to 2 dp.
Answers
Answer:
The pressure exerted by the box on the ground is given by the force divided by the area of the base. Let's convert the force from kN to N, and the area from m^2 to cm^2, for convenience:
4.7 kN = 4.7 × 10^3 N
1.9 m^2 = 1.9 × 10^4 cm^2
Now we can calculate the pressure:
pressure = force / area
pressure = (4.7 × 10^3 N) / (1.9 × 10^4 cm^2)
pressure ≈ 0.247 kN/m^2
Rounding this to 2 decimal places, we get:
pressure ≈ 0.25 kN/m^2
Therefore, the pressure exerted by the box on the ground is approximately 0.25 kN/m^2.
What is the value of x?
Answers
Answer: 101
Step-by-step explanation:
180 - 76 - 48 = 56
180 - 56 - 23 = 101
Please answer 1-6 and tell me where to graph each one. 20 points and will mark brainliest for best answer!
Answers
Answer:
1) 3w - 10 > 4
3w > 6, so w > 2
Put a 2 below the third vertical line on
the number line. Draw and fill in the
circle over 2, then draw a line going to
the arrow on the right.
2) 2x + 4 < 8
2x < 4, so x < 2
Put a 2 below the third vertical line on
the number line. Draw (but do not fill in)
the circle over 2, then draw a line going
to the arrow on the left.
3) 3 < 1.5p - 9
1.5p > 6, so p > 4
Put a 4 below the third vertical line on
the number line. Draw (but do not fill in)
the circle over 4, then draw a line going
to the arrow on the right.
4) (b/5) + 9 < 10
b/5 < 1, so b < 5
Put a 5 below the third vertical line on
the vertical line. Draw (but do not fill in)
the circle over 5, then draw a line going
to the arrow on the left.
5)
[tex] \frac{1}{3} c - 2 \frac{1}{2} \geqslant \frac{1}{2} [/tex]
[tex] \frac{1}{3} c \geqslant 3[/tex]
[tex]c \geqslant 9[/tex]
Put a 9 below the third vertical line on the number line. Draw and fill in the circle over 9, then draw a line going to the arrow on the right.
6) (4/5)(x - 2) < 6
x - 2 < 7.5, so x < 9.5
Put a 9.5 below the third vertical line on
the number line. Draw and fill in the
circle over 9.5, then draw a line going to
the arrow on the left.
2 x (1⁄4 + 11⁄8 + 3) =
Answers
The value of the expression is 9 1/4.
We have,
We can simplify the expression step by step using the order of operations (PEMDAS).
2 x (1/4 + 11/8 + 3)
First, let's add the fractions inside the parentheses:
1/4 + 11/8 = 2/8 + 11/8 = 13/8
Now we can substitute this result back into the original expression:
2 x (13/8 + 3)
Next, we add the two terms inside the parentheses:
13/8 + 3 = 13/8 + 24/8 = 37/8
Now we can substitute this result back into the expression:
2 x 37/8
Finally, we multiply the coefficient 2 by the fraction 37/8:
2 x 37/8 = 74/8 = 9 1/4
Therefore,
The value of the expression is 9 1/4.
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An artist recreated a famous painting using an 8:1 scale. The dimensions of the scaled painting are 12 inches by 16 inches. What are the dimensions of the actual painting?
96 inches by 128 inches
36 inches by 112 inches
20 inches by 24 inches
1.5 inches by 2 inches
Answers
Answer:
If the dimensions of the scaled painting are 8 times smaller than the actual painting, then the actual dimensions can be found by multiplying the scaled dimensions by 8.
So, the actual dimensions of the painting are:
12 inches x 8 = 96 inches (width)
16 inches x 8 = 128 inches (height)
Therefore, the dimensions of the actual painting are 96 inches by 128 inches.The table of values represents a
quadratic function.
Answers
The equation of the function in standard form is f(x) = x² + 4x - 12.
How to find the quadratic equation of a table?Quadratic equation can be represented as follows:
ax² + bx + c
where
a, b and c are constantTherefore, let's write the equation of the function in standard form.
-12 = a(0)² + b(0) + c
c = -12
Let's use -1 and -15
-15 = a(-1)² + b(-1) + -12
-15 = a - b - 12
a - b = - 3
Let's use -2 and -16.
-16 = a(-2)² + b(-2) + -12
-16 = 4a - 2b - 12
4a - 2b = -4
2a - b = -2
Therefore,
a - b = - 3
2a - b = -2
subtract the equations
a = 1
b = a + 3
b = 1 + 3
b = 4
Therefore, the equation is as follows:
f(x) = x² + 4x - 12
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suppose that you would like to construct a 95% confidence interval to estimate the proportion of all uconn students who graduate in 4 years. you would like to use a maximum error of 2.5%. a. how large a sample is needed if you know that in the past few years approximately 70% of all students have graduated in 4 years? note: always round up to the next integer value if your answer is not an integer. b. how large a sample is needed if you have no knowledge of what % of students typically graduate in 4 years? always round up to the next integer value if your answer is not an integer.
Answers
The required sample size to construct a 95% confidence interval to estimate the proportion is 602 students.
a. To estimate the sample size needed to construct a 95% confidence interval with a maximum error of 2.5% when the past few years' graduation rate is 70%, we can use the following formula:
n = [Z² × p × (1-p)] / E²
where:
Z = the Z-value for the desired confidence level (95% in this case), which is 1.96
p = the estimated proportion of students who graduate in 4 years (70%)
E = the maximum error, which is 0.025 (2.5%)
Plugging in the values, we get:
n = [(1.96)² × 0.7 × (1-0.7)] / 0.025²
n = 381.16
Always round up to the next integer, so the sample size needed is 382.
b. To estimate the sample size needed when there is no knowledge of the typical graduation rate, we can use a conservative estimate of 50% for p. Plugging in the values, we get:
n = [1.96² × 0.5 × (1-0.5)] / 0.025²
n = 601.64
Always round up to the next integer, so the sample size needed is 602.
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Ali is putting money into a savings account. He starts with $450 in the savings account, and each week he adds $70.
Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Ali has
been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings
account after 17 weeks.
Answers
Answer:
The total amount of money in the savings account can be represented by the sum of the initial amount of money and the amount of money added each week multiplied by the number of weeks:
S = 450 + 70W
To find the total amount of money in the savings account after 17 weeks, we can substitute W = 17 into the equation:
S = 450 + 70(17)
S = 450 + 1190
S = 1640
Therefore, after 17 weeks of adding $70 to the savings account each week, the total amount of money in the account will be $1640.:)
Name these decimal numbers. a) 7.8 b) 8.25....
Answers
The decimal numbers in this problem are classified as follows:
a) 7.8 is a rational number.
b) 8.25... is an irrational number.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.In the context of this problem, we have that:
The number 7.8 is a rational number, as it is a terminating decimal.The number 8.25... is an irrational number, as the ... indicates that the decimal is non-terminating.More can be learned about rational and irrational numbers at brainly.com/question/5186493
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A weather report for Eastern Ontario was a 40% probability of snow the next day. What are the odds against it snowing the next day?
Answers
Answer:
The odds against it snowing the next day can be found by subtracting the probability of it snowing (40%) from 100% (the total possible outcomes) and then expressing it as a ratio of non-snowing outcomes to snowing outcomes.
100% - 40% = 60%
The odds against it snowing the next day are 60:40 or 3:2 (simplifying the ratio).
1 - 0.4 = 0.6
To express this as odds against it snowing, we divide the probability of it not snowing by the probability of it snowing:
0.6 / 0.4 = 1.5
Therefore, the odds against it snowing the next day are 1.5 to 1.
An eighth-grade student estimated that she needs $9,500 for tuition and fees for each year of college She already has $5,000 in a savings account. The table shows the projected future value of the account in five years based on different monthly deposits.
The student wants to have enough money saved in five years to pay the tuition and fees for her first two years of college.
Based on the table, what is the minimum amount she should deposit in the savings account every month?
400
300
100
200
Answers
Answer: 300
1 year of tution and college fee: $9,500
= $9,500 × 2 = $19,000
2 years of tution and college fee: $19,000
Money already in Account = $5,000
If we deposit $100 every month for 5 years we would get $11,000 that is less than $19,000.
If we deposit $200 every month for 5 years qe would get $17,000 which is still less.
If we deposit $300 every month we would get $23,000 which is not less so the correct answer is $300.
Spring break homework due tonight!! Please help!!
Answers
the missing angle measurement using the angle addition postulate are:
DBC = 42 degreesL. ABD= 78 degreesLHFG = 56 degreesL HJK = 32 degreesLHFG = 59 degrees L PQS = 79 degreesLFGH = 34 degrees LOPQ = 91 degrees What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. Angles are typically measured in degrees or radians.
According to the given information:
The angle addition postulate is a rule used to find the measure of an angle created by two adjacent angles. If two adjacent angles are known, then their sum will equal the measure of the larger angle formed by the two adjacent angles. To use the angle addition postulate, add the measures of the known adjacent angles to find the measure of the larger angle.
In the given set of angles, we are asked to use the angle addition postulate to find the missing angle measures. We can use this rule to find the missing angles by adding the measures of the known adjacent angles. By doing so, we can find the measure of the larger angle formed by the two adjacent angles. It is essential to note that this rule only applies to adjacent angles. Therefore, we can only use the angle addition postulate to find the missing angle measurements for angles that share a common vertex and side
LABC = 60 degrees (angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the larger angle formed by the two adjacent angles)L
DBC = 42 degrees (angle addition postulate)L. ABD= 78 degrees (angle addition postulate)LHFG = 56 degrees (angle addition postulate)L HJK = 32 degrees (angle addition postulate)LHFG = 59 degrees (angle addition postulate)L PQS = 79 degrees (angle addition postulate)LFGH = 34 degrees (angle addition postulate)LOPQ = 91 degrees (angle addition postulate)To know more about angles visit:
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Sofia built a model of the great pyramid with a voulme of 90 cubic inches. The base of the pyramid has a side length of 7. 5 inches. Find the height of of sofias pyramid
Answers
As per the given volume, the height of Sofia's pyramid is approximately 4.8 inches.
Sofia's model of the great pyramid has a volume of 90 cubic inches. This means that if we were to fill the pyramid with water, it would hold 90 cubic inches of water.
The formula for the volume of a pyramid is:
Volume = (1/3) x base area x height
In this case, we know that the volume of the pyramid is 90 cubic inches, and the base of the pyramid has a side length of 7.5 inches. We need to find the height of the pyramid.
We can start by plugging in the values we know into the formula for the volume of a pyramid:
90 = (1/3) x base area x height
We know the base has a side length of 7.5 inches, so the base area is:
base area = (7.5)² = 56.25 square inches
Now we can plug in the base area and solve for the height:
90 = (1/3) x 56.25 x height
270 = 56.25 x height
height = 270 / 56.25
height ≈ 4.8 inches
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Radioactive phosphorus decays continuously at the rate of 5% per day. This means that an initial amount of 9 grams of radioactive phosphorus decays t days according to the formula
Answers
The formula for the amount of radioactive phosphorus remaining after "t" days is A = 9 × [tex](0.95)^t[/tex]
Radioactive decay is a process by which the nucleus of an unstable atom emits radiation in the form of particles or energy in order to reach a more stable state. In the case of radioactive phosphorus, the nucleus decays by emitting beta particles, which leads to a decrease in the number of radioactive atoms over time.
The amount of radioactive phosphorus remaining after "t" days can be calculated using the formula
A = A₀ × [tex](0.95)^t[/tex]
Where
A0 = initial amount of radioactive phosphorus (9 grams in this case)
A = amount of radioactive phosphorus remaining after "t" days
t = number of days
So, substituting the given values in the formula, we get
A = 9 × [tex](0.95)^t[/tex]
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A bag contains five red marbles, four orange marbles, one yellow marble, and three green marbles. Two marbles are drawn from the bag.
What is the approximate probability one of the chosen marbles is orange and the other is green?
Answers
The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.
To find the approximate probability of drawing marbles, we can use the following formula
probability = (number of favorable outcomes) / (total number of outcomes)
We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.
The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is
13C2 = (13 x 12) / (2 x 1) = 78
Thus, the approximate probability of drawing one orange marble and one green marble is
probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154
Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.
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Malik bought a pizza with 153.86 in² for him and his friends to eat. What is the diameter of the pizza?
Answers
Answer:
153.86 = π(r^2)
r = √(153.86/π) = 6.998 = 7 inches
d = 2r = 14 inches
Answer:
Diameter of pizza = 14 inches
Step-by-step explanation:
Pizza is shaped like a circle
If the radius of the pizza is r, the area which is the area of a circle of radius r is given by
[tex]A = \pi r^2[/tex]
Here we are given the area as 153.86 in²
153.86 = π · r²
r² = 153.86 /π
r = √( 153.86 /π )
= 6.998 in
≈ 7 inches
Diameter = 2 x radius
= 14 inches
the hydrate CoCl2 x XH2O decomposes to CoCl2, whose mass is 53.9% of the hydrate mass. What is the value of X in the hydrate formula?
Answers
Answer:
4
Step-by-step explanation:
Let's start by assuming that the initial mass of the hydrate CoCl2 x XH2O is 100 grams. This means that the mass of the anhydrous compound CoCl2 after decomposition is 53.9 grams (since it is 53.9% of the hydrate mass).
The mass of water lost during the decomposition is therefore:
Mass of water lost = Initial mass of hydrate - Mass of anhydrous compound
Mass of water lost = 100 g - 53.9 g
Mass of water lost = 46.1 g
The molar mass of CoCl2 is 129.8 g/mol, and the molar mass of H2O is 18.0 g/mol. Therefore, the molar mass of the hydrate CoCl2 x XH2O is:
Molar mass of hydrate = Molar mass of CoCl2 + Molar mass of H2O × X
Molar mass of hydrate = 129.8 g/mol + 18.0 g/mol × X
We can set up a proportion to solve for X:
Mass of water lost / Molar mass of water = X / Molar mass of hydrate
Plugging in the values we found:
46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)
Solving for X:
46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)
2.56 mol = X / (129.8 g/mol + 18.0 g/mol × X)
2.56 mol × (129.8 g/mol + 18.0 g/mol × X) = X
331.968 g/mol × X + 46.368 g/mol × X = X
378.336 g/mol × X = X
X = 4
Therefore, the value of X in the hydrate formula CoCl2 x XH2O is 4, and the formula of the hydrate is CoCl2 x 4H2O.
Jack went for a mountain hike. On his way up, he traveled at a speed of 2 mph. He reached the summit in 3 hours. On his way back down, Jack jogged at a speed of 5 mph. Write the formula that describes how the distance Jack covered during the hike depends on the amount of time that he traveled.
Answers
The formula that describes the distance Jack covered during the hike is: S(t) = vt for v = 5 and t is the time
How to solve linear equation word problems?The form of a linear equation in slope intercept form is:'
y = mx + c
where:
m is slope
c is y-intercept
Now, the formula for distance here is:
s(t) = vt
where:
v is speed
t is time
For a speed of 2 mph and a time of 3 hours, we can arriave at:
s(3) = 2 * 3 = 6 m for 2 seconds
Similarly:
s(t) = 5t
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I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)
Answers
The probability of picking a T and an N is 1/81.
The correct option is (B).
From the geometric shape we can see that the total number of different letter is = 9
that are M, A, T, H, I, S, F, U, N
Now T is one of the letter from that 9 letters.
Now if we pick T then the probability of that = 1/9
Therefore, P(T) = 1/9
now we again replace T in previous position before picking the next letter.
Again the total number of letters = 9
Again, N is one of the letter from that 9 letters.
So the probability of picking N = 1/9
Therefore, P(N) = 1/9
The required probability of picking T and N
= probability of picking T followed by picking N
= P(T)*P(N)
= (1/9)*(1/9)
= 1/(9*9)
= 1/81
Hence the correct option is (B).
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a computer company hired interns from a group of 234 applicants. the table shows the numbers of applicants who were or were not computer science majors, and the numbers of applicants who were or were not hired. match the probabilites with the description. column a 1. what is the probability that the intern had a computer science major and did not get hired.: what is the probability that the intern had a computer science major and did not get hired. 2. what is the probability that the intern had a major other than computer science?: what is the probability that the intern had a major other than computer science? 3. what is the probability that a computer science major was hired?: what is the probability that a computer science major was hired? 4. what is the probability that an intern with a major other than computer science was not hired?: what is the probability that an intern with a major other than computer science was not hired? column b a.conditional - 36.2% b.conditional - 48.6% c.joint - 43.6% d.joint - 51.2% e.marginal - 68.3% f.marginal - 31.6%
Answers
For computer company hired interns from a group of 234 applicants.
a) Probability that intern had a computer science major and did not get hired is [tex] \frac{112}{234} [/tex]
b) Probability that interns had a major other than computer science is [tex] \frac{38}{234} [/tex]
c) Probability that interns had a computer science and get hired = [tex] \frac{58}{234} [/tex].
4) probability that an intern with a major other than computer science was not hired is [tex] \frac{38}{234}[/tex].
Probability is defined as the chance of occurrence of an event. It is calculated by the ratio of favourable outcomes to the total possible outcomes. We have a table data of computer company that hired interns. Total number of applicants = 234
the table shows data of the numbers of applicants who were or were not computer science majors, and the numbers of applicants who were or were not hired. Number of outcomes for an intern had a computer science major and did not get hired = 112
1) Probability that intern had a computer science major and did not get hired = [tex] \frac{112}{234} [/tex].
2) Number of interns had a major other than computer science = 38
Probability that interns had a major other than computer science = [tex] \frac{38}{234} [/tex].
3) Number of interns had a computer science major and hired = 58
Probability that interns had a computer science and get hired = [tex] \frac{58}{234} [/tex].
4) Number of interns had a major other than computer science was not hired
= 38
Probability that an intern with a major other than computer science was not hired = [tex] \frac{38}{234} [/tex]. Hence, required value is [tex] \frac{38}{234} [/tex].
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Complete question:
a computer company hired interns from a group of 234 applicants. the table shows the numbers of applicants who were or were not computer science majors, and the numbers of applicants who were or were not hired. match the probabilites with the description. column a 1. what is the probability that the intern had a computer science major and did not get hired.
2. what is the probability that the intern had a major other than computer science?
3. what is the probability that a computer science major was hired?
4. what is the probability that an intern with a major other than computer science was not hired
column b a.conditional - 36.2% b.conditional - 48.6% c.joint - 43.6% d.joint - 51.2% e.marginal - 68.3% f.marginal - 31.6%.
The area of a quarter circle is 0. 785 square miles. What is the quarter circle's radius?
Answers
The radius of the quarter circle is 1 mile.
The formula for calculating the area of a circle is given by A = πr², where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant equal to approximately 3.14.
To find the radius of a quarter circle, we first need to find the area of the circle. Since the area of a quarter circle is given as 0.785 square miles, we can calculate the area of the circle as follows:
Area of circle = 4 × Area of quarter circle
Area of circle = 4 × 0.785 square miles
Area of circle = 3.14 square miles
Now that we know the area of the circle, we can use the formula for the area of a circle to find the radius. We rearrange the formula as follows:
r² = A/π
r² = 3.14/π
r² = 1
r = √1
r = 1 mile
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Angela’s parents have allowed her to watch TV for a maximum of 7 hours each week. She has already watched TV for hours this week. She wants to watch some episodes of her favorite shows that are each of an hour long. How many episodes, x, can Angela watch this week? Sketch the graph of the inequality that represents the maximum amount of episodes she can watch.
Answers
If each episode is 30 minutes long (0.5 hours), then Angela can watch up to eight episodes this week.
Angela has already watched a certain number of hours of TV this week, but we don't know how many. Let's call that number "h". We know that her parents allow her to watch a maximum of 7 hours per week, so we can set up an inequality:
h + x ≤ 7
where "x" is the number of additional hours of TV Angela wants to watch, and "≤" means "less than or equal to". We can simplify this inequality by subtracting "h" from both sides:
x ≤ 7 - h
This inequality tells us the maximum number of hours of TV Angela can watch this week, based on how many hours she has already watched. Now we need to figure out how many episodes she can watch, given the length of each episode.
Let's call the length of each episode "e". We know that each episode is "e" hours long, and Angela can watch "x" hours of TV. So the number of episodes she can watch is:
x ÷ e
where "÷" means division. Putting it all together, we get:
Number of episodes = x ÷ e = (7 - h) ÷ e
Now let's sketch the graph of this inequality. We can plot "x" on the horizontal axis and "h" on the vertical axis, and shade in the region where the inequality is true:
[Insert graph here]
The shaded region represents all the possible values of "x" and "h" that satisfy the inequality. For example, if Angela has already watched 3 hours of TV this week (so h = 3), then the maximum number of hours she can watch is:
x ≤ 7 - h = 7 - 3 = 4
And the maximum number of episodes she can watch is:
Number of episodes = (7 - h) ÷ e = 4 ÷ e
So if each episode is 30 minutes long (0.5 hours), then Angela can watch up to:
Number of episodes = 4 ÷ 0.5 = 8
eight episodes this week.
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Alex used the data to make the graph below.
In what way could the graph be misleading?
How could you redraw the graph so that it is less misleading?
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the starting numbers on the left don't start at 0. Make sure to make the graph on the x axis starts at 0
Mental Math Rectangle QUAD has coordinates Q(0.0). U(0,5), A(7.5), and D(7.0). Q'U'A'D' is the image of QUAD after a
dilation with center (0.0) and scale factor 6. What are the coordinates of point U'?
The coordinates of point U' are
(Type an ordered pair.)
Answers
The coordinates of point U’ are (0, 30).
Explain the term coordinates
Coordinates refer to a system used to locate a point in space or on a plane. They consist of a set of values, often expressed as ordered pairs or triples, which represent the position of the point along each axis. Coordinates are used in various fields, such as mathematics, geography, and physics.
According to the given information
The coordinates of point U’ are (0 , 30). Here’s how to find it:
The scale factor for Q’U’A’D’ is 6.
The coordinates of point U are (0 , 5).
To find the coordinates of point U’, we multiply the y-coordinate of U by the scale factor which gives us 5 * 6 = 30.
Therefore, the coordinates of point U’ are (0 , 30)
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Find the center and radius of a circle with the equation below.
(x+3)2+(y−2)2=144
Answers
As per the given equation, the center and radius of the circle are (-3, 2) and 12, respectively.
Radius is the distance between the center of a circle and any point on its circumference. It is half the length of the diameter of the circle.
The center-radius form of a circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
Comparing the given equation with the standard form, we have:
[tex](x + 3)^2 + (y - 2)^2 = 144[/tex]
This means that the center of the circle is (-3, 2) and the radius is the square root of 144, which is 12.
Therefore, the center and radius of the circle are (-3, 2) and 12, respectively.
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Tyler takes out a loan of £1800. It gathers simple interest at a rate of 2.5% per annum. He pays back the loan after 10 years. How much money does he have to pay back? Give your answer to the nearest £1.
Answers
A bowling ball shaped like a sphere had a diameter of 21. 6 centimeters. Calculate a measurement closest to the volume of the bowling ball iin cubic centimeters
Answers
Answer:
5,234 cubic centimeters
Step-by-step explanation:
The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
Since the diameter of the bowling ball is 21.6 centimeters, the radius is half of that:
r = d/2 = 21.6/2 = 10.8 centimeters
Substituting this value into the formula, we get:
V = (4/3)πr^3 = (4/3)π(10.8)^3 ≈ 5,233.8 cubic centimeters
Rounding this to the nearest whole number, we get a measurement closest to the volume of the bowling ball of 5,234 cubic centimeters.
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