The measure of arc CAD is either 240 or 260.
How to do measure of arc?Without additional information, it is not possible to determine the measure of arc CAD with certainty. The measure of an arc depends on the central angle that subtends it.
If the central angle is known, the measure of the arc can be calculated using the formula: measure of arc = (central angle / 360) x circumference of the circle. However, without knowing the central angle, we cannot determine the measure of arc CAD.
Therefore, we need to be provided with additional information such as the measure of another angle that is related to the central angle, or the length of a chord that subtends the arc in order to determine the central angle and the measure of arc CAD.
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The table shows the
average rainfall, in inches, in Miami for each
of the first six months of 2020. Write ordered
pairs for the data in the table
The ordered pairs for the data in the table include the following:
(1, 2.09)(2, 2.42)(3, 3.00)(4, 3.20)(5, 4.98)(6, 8.27)What is an ordered pair?In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Based on the table shown in the image attached below, we can reasonably infer and logically deduce that all of the coordinate points or ordered pairs would be located in quadrant 1.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter
The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
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given the expression, (n⁵)⁶ what will exponent be in the simplified exponential form?
The expression given in a simplified form is n³⁰
What are index forms?Index forms are described as those mathematical forms that are used to write numbers that are too large or small in more convenient forms.
They are also expressed as a number or variable that is raised to an exponents.
Index forms are also referred to as standard forms or scientific notations.
Following the rules of index forms, we have that;
Add the exponent with like bases and are being multipliedIn expanding the bracket, also multiply the exponentsFrom the information given, we have that;
(n⁵)⁶
Multiply the exponents
n³⁰
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The polynomial â 2x2 + 700x represents the budget surplus of the town of Alphaville.
Betaville's surplus is represented by x2 - 100x + 80,000. If x represents the tax revenue in
thousands from both towns, enter the expression that represents the total surplus of both
towns together.
The expression that represents the total surplus of both towns together is ?
The total surplus of both towns together is represented by the polynomial [tex]3x^2 + 600x + 80,000.[/tex]
The expression that represents the total surplus of both towns together is (â 2x2 + 700x) + (x2 - 100x + 80,000).?To find the total surplus of both towns together, we need to add the budget surplus of Alphaville and Betaville.
The budget surplus of Alphaville is represented by the polynomial [tex]2x^2 + 700x.[/tex]
The budget surplus of Betaville is represented by the polynomial x^2 - 100x + 80,000.
Therefore, the expression that represents the total surplus of both towns together is:
[tex](2x^2 + 700x) + (x^2 - 100x + 80,000)[/tex]
Simplifying this expression, we get:
[tex]3x^2 + 600x + 80,000[/tex]
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Please help asap I need this until tmr
The following table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.
To complete the table, we need to use the information that the directions on the small cans of cat food say to feed a cat 1 can of food each day for every 4 pounds of body weight.
For example, for a cat weighing 4 pounds, we need to give 1 can of food each day.
For a cat weighing 5 pounds, we need to give more than 1 can but less than 2 cans of food each day.
To find the exact number of cans, we can use the formula:
cans per day = weight in pounds / 4
Substituting the given values, we get:
cans per day = 5 / 4
cans per day = 1.25
Therefore, for a cat weighing 5 pounds, we need to give 1.25 cans of food each day. We can round this to the nearest tenth to get 1.3 cans per day.
Similarly, we can use the formula to complete the rest of the table:
KIT-E-KAT weight in pounds cans per day
4 1
5 1.3
6 1.5
7 1.8
8 2
9 2.3
10 2.5
11 2.8
12 3
13 3.3
14 3.5
15 3.8
Therefore, the completed table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.
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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. Initial Balance (dollars) $5,000 $5,000 $5,000 $5,000 Monthly Deposit (dollars) $100 $200 $300 $400 Account Value in Five Years (dollars) $11,000 $17,000 $23,000 $29,000 Problem The student wants to have enough money saved in four 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? A $200 B $100 C $300 D $400
$23,000 is more than the $19,000 needed for tuition and fees for the first two years, the minimum amount the student should deposit in the savings account every month is $300 (option C).
What is the account value in five years with a monthly deposit of $300?The minimum monthly deposit the student should make in order to save enough money for her first two years of college tuition and fees in four years, we need to calculate how much she would need to have in her savings account at the end of four years.
Since the student estimated she needs $9,500 per year for tuition and fees, she will need $19,000 for her first two years. Since she already has $5,000 in her savings account, she needs to save an additional $14,000 in four years.
Looking at the table, we can see that the account value in five years with a monthly deposit of $200 is $17,000. To find out how much the account value would be in four years, we need to calculate the future value of $17,000 with a 4-year time frame and an annual interest rate of 0%, which gives:
Future value = $17,000 x (1 + 0%)^(4 x 12/12) = $17,000
Since the account value with a $200 monthly deposit is only $17,000 after 5 years, which is not enough to cover the $19,000 needed for tuition and fees for the first two years, the student needs to make a higher monthly deposit.
Looking at the table again, we can see that the account value in five years with a monthly deposit of $300 is $23,000. To find out how much the account value would be in four years, we need to calculate the future value of $23,000 with a 4-year time frame and an annual interest rate of 0%, which gives:
Future value = $23,000 x (1 + 0%)^(4 x 12/12) = $23,000
$23,000 is more than the $19,000 needed for tuition and fees for the first two years, the minimum amount the student should deposit in the savings account every month is $300 (option C).
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The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is 35 meters wide at the base and 20. 6 meters tall, what was the minimum amount of glass needed to construct the pyramid?
The minimum amount of glass needed to construct the Louvre pyramid is approximately 3133 square meters.
What is the minimum amount of glass needed to construct the glass pyramid in front of the Louvre museum in Paris, if the pyramid is 35 meters wide at the base and 20.6 meters tall?
The surface area of a square base pyramid can be calculated by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the square base is simply the width of the base squared:
Area_base = (35 m)^2 = 1225 square meters
The area of each triangular face can be calculated using the formula:
Area_triangle = (1/2) * base * height
For the Louvre pyramid, the base of each triangular face is equal to the width of the base of the pyramid, which is 35 meters. The height of each triangular face can be found using the Pythagorean theorem:
[tex]height^2 = (1/2 * width)^2 + height^2[/tex]
[tex]height = sqrt((1/2 * 35 m)^2 + (20.6 m)^2)[/tex]
height = 29.2 m
Therefore, the area of each triangular face is:
Area_triangle = (1/2) * (35 m) * (29.2 m) = 508.5 square meters
The total surface area of the pyramid is:
Surface_area = Area_base + 4 * Area_triangle
Surface_area = 1225 + 4 * 508.5
Surface_area = 3133 square meters
Since the pyramid is made of glass, we need to calculate the minimum amount of glass needed to construct it. Assuming the glass is thin and flat, we can simply use the surface area of the pyramid to estimate the amount of glass needed.
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There are 4 times as many chickens as ducks, there are 72 more chickens than ducks how many chickens and ducks are there
c = number of chickens
d = number of ducks
c = 4d because there are 4 times as many chickens as ducks
c = d+72 because there are 72 more chickens
4d = d+72 after using substitution
4d-d = 72
3d = 72
d = 72/3
d = 24
c = 4d = 4*24 = 96 ...or... c = d+72 = 24+72 = 96
Answer: There are 96 chickens and 24 ducksA spinner has 10 equally sized sections, 6 of which are gray and 4
of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray.
Step-by-step explanation:
since both spins are independent events (one does not have any impact on the other), the sequence does not matter. the probability of first blue and then gray is the same as first gray and then blue.
it is the probability of getting 1 gray and 1 blue result.
a probability is always the ratio
desired cases / totally possible cases.
since 6/10 of the area of the spine are gray, and 4/10 of the area are blue, the probability for any single spin to result in gray is 6/10 = 3/5 = 0.6.
and the probability to result in blue is 4/10 = 2/5 = 0.4
the probability to get 1 gray and 1 blue is then the product of both probabilities :
0.6 × 0.4 = 0.24
it is like rolling a die twice and asking for e.g. two 6s or any other combination of 2 specific numbers. that probability is
1/6 × 1/6 = 1/36
FYI :
the probability of getting gray twice is then
0.6 × 0.6 = 0.36
the probability of getting blue twice is
0.4 × 0.4 = 0.16
as mentioned to get gray first and blue second is
0.6 × 0.4 = 0.24
to get blue first and gray second
0.4 × 0.6 = 0.24
and these are all the possible results you can get in 2 spins.
therefore, the probability for any of them is
0.36 + 0.16 + 0.24 + 0.24 = 1
The number of bacteria in a certain colony doubles every 5 days. At the same rate, how long will the colony need to triple in number?
The colony will need to triple in number after about 7.58 days.
How to find the number of bacteria in a certain colony?Since the number of bacteria doubles every 5 days, we can write the relationship between the number of bacteria and time as an exponential function:
N(t) = N0 x 2^(t/5)
where N0 is the initial number of bacteria and t is the time in days.
To find out how long it will take for the colony to triple in number, we need to solve the equation:
N(t) = 3N0
Substituting the expression for N(t) from above, we get:
N0 x 2^(t/5) = 3N0
Dividing both sides by N0, we get:
2^(t/5) = 3
Taking the logarithm of both sides (with base 2) gives:
t/5 = log2(3)
Multiplying both sides by 5, we get:
t = 5 x log2(3)
Using a calculator or a computer program to evaluate the logarithm, we get:
t ≈ 7.58
Therefore, the colony will need to triple in number after about 7.58 days.
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The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In ( - x3 + 9x2 +21x + 1) (0 sxs 10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? a) The number of units that should be sold in order to maximize the total profit is (Simplify your answer.) b) The maximum profit is approximately $. (Do not round until the final answer. Then round to the nearest dollar as needed.)
Final Answer: a. The number of units that should be sold in order to maximize the profit is 7 thousand units.
b. The maximum profit is approximately $5.51
Conceptual part: a. In order to find maximum profit we need to differentiate the profit function
so, p(x)= [tex]ln(-x^3+9x^2+21x+1)[/tex][tex]dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1[/tex] = 0
[tex]-3x^2+18x+21=0[/tex]
[tex](x-7) (x+1) = 0[/tex]
as profit can't be negative.
hence x=7.
b. We can determine the maximum profit by substituting x=7 in profit function.
[tex]p(7) = ln(-7^3+9*7+21*7+1)[/tex]
[tex]p(7) = ln(246)[/tex]
p(7) = 5.51
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The table gives a set of outcomes and their probabilities. Let a be the event "the outcome is a divisor of 4". Let b be the event "the outcome is prime". Find p(a|b)
The probability that the outcome is a divisor of 4 given that it is prime is 0.125, or 12.5%.
Since we are given the probabilities of different outcomes, we can use the definition of conditional probability to find p(a|b), which represents the probability that the outcome is a divisor of 4 given that it is prime.
The formula for conditional probability is:
p(a|b) = p(a ∩ b) / p(b)
where p(a ∩ b) represents the probability of both events happening simultaneously.
Looking at the table of outcomes and their probabilities, we can see that there are four prime numbers: 2, 3, 5, and 7. Of these, only 2 is a divisor of 4.
Therefore, p(a ∩ b) is the probability that the outcome is 2, which is 0.1.
The probability of the outcome being prime is the sum of the probabilities of the four prime outcomes, which is:
p(b) = 0.1 + 0.2 + 0.3 + 0.2 = 0.8
Substituting these values into the formula for conditional probability, we get:
p(a|b) = p(a ∩ b) / p(b) = 0.1 / 0.8 = 0.125
Therefore, the probability that the outcome is a divisor of 4 given that it is prime is 0.125, or 12.5%.
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4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question
The difference between the radii of the two circular tracks is 15ft
How do we calculate?The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft
we find the diameter of each track.
The circumference of a circle can be found using the formula
P = πd
d = P /π
track 1, we have
d1 = P1 / π
d1 = 220 / π
d1 = 70.03 ft.
track 2, we have
d2 = P2 / π
d2 = 126 / π
d2 = 40.11 ft.
radius of tract 1 = 35.01 ft
radius of track 2 = 20.05 ft
The difference between the two track radius is
∆r = r1 - r2
∆r = 110 / π - 63 / π
∆r = (110 - 63) / π
∆r = 47 / π
∆r = 14.96 ft.
∆r = 15 ft
In conclusion, difference between the radii of the two circular tracks is 15ft
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#complete question:
What is the difference between the radii of the two circular tracks? Answer the questions to find out.
1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?
Evaluate the limit using L'Hospital's rule
lim (e^x + 2x - 1)/2x
To evaluate the limit using L'Hospital's rule, we need to take the derivative of both the numerator and denominator separately until we get a determinate form. We have:
lim (e^x + 2x - 1) / (2x)
Taking the derivative of the numerator:
lim (e^x + 2) / 2
Taking the derivative of the denominator:
lim 2
Since we now have a determinate form, we can evaluate the limit by plugging in the value of x. We get:
(e^x + 2) / 2
As x approaches infinity, e^x also approaches infinity, so the limit diverges to positive infinity. Therefore, the limit does not exist.
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Franklin is helping his aunt sew a lace border onto 2 quilts. Each quilt is 2. 2 meters wide by 2. 7 meters long. At the craft store, they buy a 20-meter roll of lace. To their surprise, they use up almost all of it. How many millimeters of lace do they have left after finishing the quilts?
The amount in millimeters of lace they have left after finishing the quilts is 400 millimeters.
Determine how much lace is needed for each quilt. Each quilt has a perimeter that we need to cover with lace. The perimeter is the sum of all sides of a rectangle, which is (2 x width) + (2 x length).
Each quilt is 2.2 meters wide and 2.7 meters long. So, the perimeter of one quilt is (2 x 2.2) + (2 x 2.7) = 4.4 + 5.4 = 9.8 meters.
Since there are 2 quilts, the total lace needed for both quilts is 9.8 meters x 2 = 19.6 meters.
They bought a 20-meter roll of lace. To find out how much lace is left, subtract the total lace used from the initial length of the roll: 20 meters - 19.6 meters = 0.4 meters.
To convert this to millimeters, multiply by 1,000: 0.4 meters x 1,000 = 400 millimeters.
So, Franklin and his aunt have 400 millimeters of lace left after finishing the quilts.
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A bottel of orange juice contains 750 mg of vitamin C and has 6 servings. A bottek of cranbery juice contains 134 mg of vitamin C and has 1. 5 servings. Mrs khan wants to compare the amount of vitamin c in the juices. How many milligrams of vitamin c are in 1 serving of each type of juice complete the statment. One serving of________ juice has __________Mg More vitamin C per serving Than one serving of _________ Juice
After evaluating the conclusion is that one serving of orange juice has 35.7 mg more vitamin C per serving than one serving of cranberry juice.
According to the provided data , a bottle of orange juice has 750 mg of vitamin C and provides 6 servings. A bottle of cranberry juice has 134 mg of vitamin C and provides 1.5 servings.
Now to evaluate how many milligrams of vitamin C are in 1 serving of each type of juice, we have to perform division to evaluate the total amount of vitamin C by the number of servings.
For orange juice
750 mg / 6 servings
= 125 mg/serving
For cranberry juice
134 mg / 1.5 servings
= 89.3 mg/serving
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Hydrologists sometimes use Manning's equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe a flowing full; the slope S of the pipe, which gives the vertical drop in foot for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by the following. v = 1.486/n R^2/3 S^1/2 For a certain brass pipe, the roughness coefficient has been measured to be n = 0.014. The pipe has a diameter of 3 feet and a slope of 0.4 foot per foot. (That is, the pipe drops 0.4 foot for each horizontal foot.) If the pipe is flowing full, find the hydraulic radius of the pipe. () Find the velocity of the water flowing through the pipe. ()
The velocity of the water flowing through the pipe is approximately 7.83 feet per second. The hydraulic radius of the pipe can be calculated as follows:
R = d/4
where d is the diameter of the pipe. In this case, the diameter is 3 feet, so the hydraulic radius is:
R = 3/4 = 0.75 feet
Now, we can use the given formula to calculate the velocity of the water:
[tex]v =[/tex][tex]1.486/n[/tex] [tex]R^(2/3) S^(1/2)[/tex]
Substituting the given values, we get:
v = 1.486/0.014 (0.75[tex])^(2/3)[/tex] (0.4[tex])^(1/2)[/tex] ≈ 7.83 feet per second
Therefore, the velocity of the water flowing through the pipe is approximately 7.83 feet per second.
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I have tried doing this question for 20 minutes but I just can't get the answer, (add maths circular measure)
the answer is 17.2cm² supposedly
Answer:
17.2 cm²
Step-by-step explanation:
Alr let me try
The angle is 1.2 you got it right. The rest is in the pics
Answer: A(shaded)=17.15 cm²
Step-by-step explanation:
What you did so far is correct.
Given:
r=5
s=6
Solve for Ф angle:
s=[tex]\frac{part circle}{wholecircle} 2\pi r[/tex] This way help you find the portion/percent you want
6=(Ф/360) (2[tex]\pi[/tex]5) >solve for Ф Divide by (2[tex]\pi[/tex]5) and multiply by 360
Ф=68.75
Solve for pie/sector
Now that you have the angle, you can use the same concept for area
Area of sector = [tex]\frac{part circle}{wholecircle} \pi r^{2}[/tex]
Area of sector = [tex]\frac{68.75}{360} \pi 5^{2}[/tex]
Area of sector = 15.0 cm²
Now let find y so we can plug into area of triangle
use tan Ф = opposite/adjacent
tan 68.75 = y/5
y=5 * tan 68.75
y=12.86 cm
Area of triangle = 1/2 b h b=y=12.86 h =5
Area of triangle = 1/2* 12.86*5
Area of triangle = 32.15 cm²
Now subtract area of sector from triangle
A(shaded)=A(triangle)-A(sector)
A(shaded)=32.15- 15.0
A(shaded)=17.15 cm²
To the nearest cubic centimeter, what is the volume of the regular hexagonal prism?
a hexagonal prism has a height of 7 centimeters and a base with a side length of 3 centimeters. a line segment of length 2.6 centimeters connects a point at the center of the base to the midpoint of one of its sides, forming a right angle.
the volume of the regular hexagonal prism is about ___ cm3
Rounded to the nearest cubic centimeter, the volume of the regular hexagonal prism is approximately 82 [tex]cm^3.[/tex]
To calculate the volume of the regular hexagonal prism, we need to find the area of the base and multiply it by the height.
The base of the prism is a regular hexagon with side length 3 centimeters. The formula for the area of a regular hexagon is:
[tex]Area = (3√3/2) * (side length)^2.[/tex]
Substituting the given side length of 3 centimeters:
[tex]Area = (3√3/2) * 3^2[/tex]
= (3√3/2) * 9
= (27√3/2).
Now, let's calculate the volume by multiplying the base area by the height:
Volume = Area * height
= (27√3/2) * 7
≈ 81.729[tex]cm^3[/tex].
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To conduct a science experiment, it is required to decrease the temperature from 36 c at the rate of 4 c every hour. what will be the temperature 10 hours after the process begins?
To conduct the science experiment, the temperature needs to be decreased from 36°C at a rate of 4°C every hour.
So, after 1 hour, the temperature will be 36°C - 4°C = 32°C. After 2 hours, the temperature will be 32°C - 4°C = 28°C. Continuing this pattern, after 10 hours, the temperature will be 36°C - (4°C x 10) = 36°C - 40°C = -4°C.
However, this temperature is below freezing and unlikely to be accurate for a science experiment.
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In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?
Linda contributed $3,355.56 to social security in 2003.
The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.
The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).
In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.
To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.
Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062
Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56
Linda contributed $3,355.56 to social security in 2003.
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What is the quotient of 223 + 3x2 + 5x – 4 divided by 22 +2+1?
Pls I need help
The quotient is -58x2 + 131x - 234 with a remainder of -5898.To solve this problem, we need to use long division. The dividend is 223 + 3x2 + 5x - 4 and the divisor is 22 + 2 + 1, which simplifies to 25.
We start by dividing 2 into 22, which gives us 11. We then write 11 above the 2 and multiply it by 25, which gives us 275. We subtract 275 from 223, which gives us -52. We bring down the 3, which gives us -523. We then repeat the process by dividing 2 into 52, which gives us 26. We write 26 above the 5 and multiply it by 25, which gives us 650. We subtract 650 from -523, which gives us -1173. We bring down the 1, which gives us -11731. We divide 2 into 117, which gives us 58.
We write 58 above the x and multiply it by 25, which gives us 1450. We subtract 1450 from -1173, which gives us -2623. We bring down the -4, which gives us -26234. We divide 2 into 262, which gives us 131. We write 131 above the 5 and multiply it by 25, which gives us 3275. We subtract 3275 from -2623, which gives us -5898. Therefore, the quotient is -58x2 + 131x - 234 with a remainder of -5898.
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PLEASE HELP
Which inequality is true?
A number line going from negative 3 to positive 3 in increments of 1.
One-fourth less-than negative 1 and StartFraction 2 Over 4 EndFraction
Negative 2 and three-fourths less-than negative 1 and one-half
Negative 2 and one-fourth greater-than negative 1 and one-fourth
Negative three-fourths greater-than 1 and three-fourths
The inequality that is true is Negative 2 and three-fourths less-than negative 1 and one-half.
How to find the true inequality ?The first inequality from the number line can be shown to be :
( 1 / 4 ) < - 1 1 / 2
This is not possible as a negative cannot be larger than a positive.
The second inequality is:
- 2. 75 < - 1. 5
This is true as larger negative numbers are lower than smaller negative numbers.
The third inequality is:
- 2. 25 > - 1. 25
This is not possible for the reason explained.
In conclusion, option B is correct.
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24. Anna, Berta, Charlie, David and Elisa baked biscuits at the weekend. Anna baked 24, Berta
25, Charlie 26, David 27 and Elisa 28 biscuits. By the end of the weekend one of the children had
twice as many, one 3 times, one 4 times, one 5 times and one 6 times as many biscuits as on
Saturday. Who baked the most biscuits on Saturday?
(A) Anna (8) Berta (C) Charlie (D) David (E) Elisa
At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.
To determine who baked the most biscuits on Saturday, we need to calculate how many biscuits each child had at the end of the weekend.
Anna had 24 biscuits, Berta had 25, Charlie had 26, David had 27, and Elisa had 28.
Let's start with the child who had twice as many biscuits as on Saturday. We can divide their total number of biscuits by 2 to get the number they had on Saturday.
If we try this calculation for each child, we find that only Elisa's total number of biscuits (28) is evenly divisible by 2. Therefore, Elisa must be the child who had twice as many biscuits as on Saturday, meaning she had 14 biscuits on Saturday.
We can use a similar process to determine how many biscuits each child had on Saturday:
- The child who had three times as many biscuits as on Saturday must have had a total of 42 biscuits, which means they had 14 biscuits on Saturday.
- The child who had four times as many biscuits as on Saturday must have had a total of 56 biscuits, which means they had 14 biscuits on Saturday.
- The child who had five times as many biscuits as on Saturday must have had a total of 70 biscuits, which means they had 14 biscuits on Saturday.
- The child who had six times as many biscuits as on Saturday must have had a total of 84 biscuits, which means they had 14 biscuits on Saturday.
Now we can add up the number of biscuits each child had on Saturday:
- Anna had 24 biscuits.
- Berta had 25 biscuits.
- Charlie had 26 biscuits.
- David had 27 biscuits.
- Elisa had 14 biscuits.
Therefore, David baked the most biscuits on Saturday with 27.
To determine who baked the most biscuits on Saturday, we need to consider the information given about the multiplication factors (twice, 3 times, 4 times, 5 times, and 6 times) and the initial number of biscuits baked by each child.
1. Anna baked 24 biscuits.
2. Berta baked 25 biscuits.
3. Charlie baked 26 biscuits.
4. David baked 27 biscuits.
5. Elisa baked 28 biscuits.
Now, let's apply the multiplication factors and see which child had the most biscuits at the end of the weekend:
1. Anna: 24 x 2 = 48
2. Berta: 25 x 3 = 75
3. Charlie: 26 x 4 = 104
4. David: 27 x 5 = 135
5. Elisa: 28 x 6 = 168
At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.
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Question 7 Determine the way in which the line (x, y, z) = (2, -3, 0] + k[-1, 3, -1) intersects the plane [x, y, 2] = [4, -15, -8] + s[1, -3, 1] + t[2, 3, 1), if at all. [2T/2A] , - No text entered -
The line intersects the plane at the point (-4, 15, -6).
How to find the intersection of line in given plane?The line (x, y, z) = (2, -3, 0) + k(-1, 3, -1) can be expressed parametrically as:
x = 2 - k
y = -3 + 3k
z = k
The plane [x, y, 2] = [4, -15, -8] + s[1, -3, 1] + t[2, 3, 1) can be expressed in scalar form as:
x + y - 2z = 14 + s - 2t
To find the intersection of the line and the plane, we can substitute the parametric equations of the line into the scalar equation of the plane:
(2 - k) + (-3 + 3k) - 2k = 14 + s - 2t
Simplifying this equation, we get:
-4k + 3 = 14 + s - 2t
We can also express the line and plane equations in vector form:
Line: r = (2, -3, 0) + k(-1, 3, -1) = (2-k, -3+3k, k)
Plane: r = (4, -15, -8) + s(1, -3, 1) + t(2, 3, 1) = (4+s+2t, -15-3s+3t, -8+s+t)
To find the intersection of the line and the plane, we need to find the values of k, s, and t that satisfy both equations simultaneously. We can do this by equating the vector forms of the line and plane and solving for k, s, and t:
2 - k = 4 + s + 2t
-3 + 3k = -15 - 3s + 3t
k = -8 - s - t
Substituting k into the first equation, we get:
2 + 8 + s + t = 4 + s + 2t
Simplifying this equation, we get:
t = 4
Substituting t = 4 and k = -8 - s - t into the second equation, we get:
-3 + 3(-8 - s - 4) = -15 - 3s + 3(4)
Simplifying this equation, we get:
s = -2
Substituting t = 4 and s = -2 into the first equation, we get:
k = 8 - s - t = 8 + 2 - 4 = 6
Therefore, the line intersects the plane at the point (x, y, z) = (2, -3, 0) + 6(-1, 3, -1) = (-4, 15, -6).
So the line intersects the plane at the point (-4, 15, -6).
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A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip, parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?
Assume that a procedure yields a binomial distribution with n trials and a probability of success of p. use a binomial probability table to find the probability that the number of successes x is exactly .
To find the probability that the number of successes x is exactly a certain value in a binomial distribution with n trials and a probability of success of p, we can use a binomial probability table. The table will provide us with the probability of getting x successes out of n trials, given a specific value of p.
For example, let's say we want to find the probability of getting exactly 3 successes in a binomial distribution with 10 trials and a probability of success of 0.5. We can use a binomial probability table to find the probability of getting exactly 3 successes, which is 0.117.
It is important to note that the probability of getting a specific number of successes in a binomial distribution is dependent on both the number of trials and the probability of success. Therefore, if we change either of these values, the probability of getting a certain number of successes will also change.
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A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. What is the shape of the cross section?
A. Trapezoid
B. Rectangle
C. Triangle
D. Cylinder
The shape of the cross section of a right rectangular pyramid sliced vertically (down) by a plane not passing through the vertex of the pyramid m is a trapezoid. (A)
This is because when a pyramid is sliced vertically, the resulting cross section is always a two-dimensional representation of the pyramid's base.
Since the base of a right rectangular pyramid is a rectangle, slicing it vertically will result in a trapezoid-shaped cross section. The top and bottom sides of the trapezoid will be parallel, and the other two sides will be slanted.
In a right rectangular pyramid, the vertex m is located directly above the center of the rectangle base. When a plane is passed through this vertex, it will result in a triangular cross section. However, when a plane is passed through a different point, as described in the question, it will result in a trapezoidal cross section.(A)
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9. the square footage and monthly rental of 15 similar one-bedroom apartments yield the linear
regression formula y = 1.3485x + 840.51, where x represents the square footage and y represents
the monthly rental price. round answers to the nearest whole number.
Based on the linear regression formula y = 1.3485x + 840.51, you can calculate the monthly rental price (y) for a one-bedroom apartment by plugging in the square footage (x) of the apartment.
The linear regression formula for the 15 similar one-bedroom apartments is y = 1.3485x + 840.51, where x represents the square footage and y represents the monthly rental price. This means that for every square foot increase in the apartment size, the monthly rental price is predicted to increase by $1.35.
The y-intercept of the formula is $840.51, which represents the predicted monthly rental price for an apartment with 0 square footage (this is not possible in reality, but is used in the formula for mathematical purposes). To get the rental price, round your answer to the nearest whole number. For example, if an apartment has 500 square feet, you'd calculate: y = 1.3485(500) + 840.51 ≈ 1344.76, which rounds to $1,345 as the monthly rental price.
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a professor gives his students 6 essay questions to prepare for an exam. only 4 of the questions will actually appear on the exam. how many different exams are possible?
The different possible exams for the 6 essay questions from which only 4 appear is equal to 15.
n is the total number of items in the set = 6 essay questions
r is the number of items we want to choose = 4 questions
Using combinations,
which is a way of counting the number of ways to choose a certain number of items from a larger set without regard to order.
Choose 4 out of the 6 essay questions, without regard to the order in which they appear on the exam.
Use the formula for combinations,
C(n, r) = n! / (r! × (n - r)!)
Plugging in the values, we get,
⇒C(6, 4) = 6! / (4! × (6 - 4)!)
⇒C(6, 4) = 6! / (4! ×2!)
⇒C(6, 4) = (6 × 5 × 4 × 3) / (4 × 3 × 2 × 1)
⇒C(6, 4) = 15
Therefore, there are 15 different exams possible, each consisting of 4 out of the 6 essay questions provided by the professor.
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