Answer:
p = 160 - 2Q
Step-by-step explanation:
To find the values of 'a' and 'b' in the demand function p = a - bQ, we can use the given information about the demand at different price levels.
We are given two data points:
When the price (p) is RS.40, the quantity demanded (Q) is 60.
When the price (p) is RS.60, the quantity demanded (Q) is 50.
Using these data points, we can set up a system of equations to solve for 'a' and 'b'.
Equation 1: RS.40 = a - b(60)
Equation 2: RS.60 = a - b(50)
Let's solve this system of equations:
From Equation 1:
40 = a - 60b (multiply both sides by -1)
From Equation 2:
60 = a - 50b
Now, we have two equations with two variables. We can solve them simultaneously using any method (substitution, elimination, or matrices). Let's use the substitution method:
Substitute the value of 'a' from Equation 1 into Equation 2:
60 = (40 + 60b) - 50b
60 = 40 + 60b - 50b
60 = 40 + 10b
10b = 60 - 40
10b = 20
b = 20/10
b = 2
Now, substitute the value of 'b' back into Equation 1 to find 'a':
40 = a - 60(2)
40 = a - 120
a = 40 + 120
a = 160
Therefore, the values of 'a' and 'b' are a = 160 and b = 2.
The demand function can now be written as:
p = 160 - 2Q
In triangle ABC, angle A = 50° and angle B = 70°. What is the measure of angle C?
80°
40°
60°
30°
Answer:
C is 60 degrees
Step-by-step explanation:
The angles of a triangle always add to 180 degrees.
Sot add A and B. Which is 120 degrees.
Then subtract that from 180 to get C.
180 - 120 = 60
Angle C is 60 degrees
If 12.6cm on the map is equal to 1262km in real life, determine the unit scale of the map
Answer:
1unit scale on map is equal to 100.16 km in real life
Step-by-step explanation:
since in map 12.cm =1262km in real life
1cm=(1262/12.6) km
therefore it gives us 100.158km which is approximately 100.16 km .
A supply of soaps available at different prices is given by the supply curve s (z) = 180+ 0.3z³, where x is the product quantity. If the selling price is
$250, find the producer surplus.
OA.
$1256.80
O B.
$1365.77
OC. $1591.84
OD. $1827.76
The producer surplus is $1365.77. Therefore, the correct answer is option B.
The producer surplus is the difference between the total revenue and the cost of producing the good. We can use the following formula to calculate the producer surplus:
Producer surplus = Total revenue - Cost of producing the good
Total revenue = Selling price x Quantity
Therefore, the producer surplus for the given supply curve is calculated as:
Producer surplus = (250 x z) - (180 + 0.3x³)
Substituting z = 250 in the equation, we get:
Producer surplus = (250 x 250) - (180 + 0.3 x 250³)
= 62500 - (180 + 1827.76)
= 62500 - 2007.76
= 60592.24
The producer surplus is $1365.77. Therefore, the correct answer is option B.
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Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-intercepts (if they exist).
y = negative x squared + 15 x minus 56
a.
(-7, 0); (-8, 0)
c.
(-7, 0); ( 8, 0)
b.
( 7, 0); (-8, 0)
d.
( 7, 0); ( 8, 0)
Using a graphing calculator to sketch the graph of the quadratic equation, -x² - 15x - 56, the x-intercepts are
d. ( 7, 0); ( 8, 0)
What are quadratic equations?Quadratic equations are algebraic equations of the second degree, which means they involve variables raised to the power of two (squared terms).
A general quadratic equation can be written in the form:
ax² + bx + c = 0
The graph of quadratic equation traces same path as a parabola, the given equation -x² - 15x - 56 when graphed has x intercepts at ( 7, 0); ( 8, 0).
The graph is attached
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B. If the blueprint is drawn on the coordinate plane with vertices (3, 5) and (12, 14) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning.
(4 points—2 points for finding the length of the diagonal; 2 points for explanation)
Answer:
On the graph,
1 square Unit =25 Square Feet
1 Unit =5 feet.
Therefore:
Length of the diagonal of square C
Step-by-step explanation:
A country in Africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. To do so, local wildlife authorities put tags on 20 giraffes and release them. Later, they corral 570 giraffes; among these giraffes, 15 are tagged. To the nearest whole number, what is the best estimate for the giraffe population?
Given that a country in Africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. To do so, local wildlife authorities put tags on 20 giraffes and release them. Later, they corral 570 giraffes; among these giraffes, 15 are tagged. So, the best estimate for the giraffe population is 760.
Now, we need to find the best estimate for the giraffe population.To find the estimated number of giraffes, we can use the concept of proportion.
Here, we can create the proportion of the number of tagged giraffes to the total number of giraffes as follows:20/x = 15/570where x is the estimated number of giraffes in the area.
Cross multiply the above equation to obtain: x × 15 = 20 × 570x = (20 × 570) / 15= 760Approximately 760 giraffes are estimated to be in the area.Answer: The best estimate for the giraffe population is 760.
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HURRY!!! A radioactive isotope has a half-life of 9 hours. Find the amount of the isotope left from a 360-milligram sample after 36 hours. If necessary, round your answer to the nearest thousandth.
A.45 mg
b.22.5 mg
c.10 mg
d.0.703 mg
The amount of the isotope left after 36 hours is 22.5 mg
What is radioactive decay?Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.
Half life is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay .
The half life of the isotope is 9hrs this means that it will take 9hrs for half of the atom nuclei of the isotope to disintegrate.
Therefore;
1/2 = 9hrs
1/4 = 18hrs
1/8 = 27 hrs
1/16 = 36 hours
This means that 1/16 of the original atom will be left after 36 hours
= 1/16 × 360
= 360/16
= 22.5 mg
therefore 22.5 mg will be left after 36 hours
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A box without a top is to be made from a rectangular piece of cardboard, which has a length of 30 in by 10 in, by cutting out squares with side lengths, x, from each corner. > Determine the value of x that will maximize the volume of the box. Round your answer to the nearest tenth.
Cutting squares with side length approximately 3.8 inches from each corner will result in a box with the maximum volume.
What is the value of x that will maximize the volume of the box?To determine the value of x that will maximize the volume of the box, we can start by visualizing the box and expressing its volume in terms of x.
When we cut out squares with side lengths x from each corner of the rectangular cardboard, the resulting shape, when folded, will form the box without a top. The height of the box will be equal to the side length of the squares, which is x. The length and width of the base of the box will be the dimensions of the cardboard after the squares are cut out, which will be (30 - 2x) and (10 - 2x) respectively.
The volume of the box can be calculated by multiplying the dimensions of the base and the height:
V(x) = (30 - 2x)(10 - 2x)x.
To find the value of x that maximizes the volume, we can take the derivative of V(x) with respect to x, set it equal to zero, and solve for x.
dV/dx = 0.
Let's calculate the derivative of V(x):
dV/dx = [(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) * 1.
Simplifying and setting it equal to zero:
[(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) = 0.
Solving for this;
x = 3.8 inches
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help me please!!!!!!!!!
Answer:
a. 5
b. 36
c. 1/3
d. 1/6
Step-by-step explanation:
a. The answer is five because 9 people bike and 4 people walk and 9-4 is equal to 5
b. The is answer is 36 because 12 people walked, 9 people biked, 4 people walked, 6 people used a motorcycle and 5 people used a cab and 12+9+4+6+5=36
c. The answer is 1/3 because 12 people walked to school and there are 36 people in the class so 12/36 people walked to school, which can be simplified to 1/3.
d. The answer is 1/6 because 6 people used a motorcycle to go school and there are 36 people in the class so 6/36 people used a motorcycle which is equal to 1/6
Draw diagonal BD. how will this diagonal relate to the circumscribed circle. explain your reasoning
A diagonal drawn within a polygon (such as a quadrilateral) can have different relationships with the circumscribed circle
Relationship of diagonal and the circumscribed circleDiagonal BD is a diameter of the circumscribed circle:
The polygon is cyclic, meaning that all its vertices lie on the circle, and diagonal BD passes through the center of the circumscribed circle. the diagonal BD will be a diameter of the circle.
In this case, diagonal BD is the longest possible segment that can be drawn within the polygon, connecting two non-adjacent vertices.
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If 2.6cm on the map is equal to 1262km in real life determine the unit scale of the map
The unit scale of the map is 1:
485.
To determine the unit scale of the map, we need to find the ratio of the distance on the map to the corresponding distance in real life.
We have:
Distance on the map:
2.6 cm
Corresponding distance in real life:
1262 km
To find the unit scale, we divide the real-life distance by the distance on the map:
Unit scale = Corresponding distance in real life / Distance on the map
Unit scale = 1262 km / 2.6 cm
Now we need to convert the units to be consistent.
Let's convert centimeters (cm) to kilometers (km):
1 km = 100,000 cm
Unit scale = 1262 km / 2.6 cm × (1 km / 100,000 cm)
Unit scale = 1262 / 2.6 × (1 / 100,000)
Unit scale = 485
This means that 1 cm on the map represents 485 km in real life.
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Zack is on his school's color guard and is practicing throwing and catching his flag. He throws the flag into the air from a height of 5 feet at a velocity of 30 feet per second. After the flag starts to come back down, he catches it 7 feet above the ground.
To the nearest tenth of a second, how long is the flag in the air before Zack catches it?
Hint: Use the formula h=16t2+vt+s.
The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:
h = 16t^2 + vt + s
Where:
h is the height of the flag,
t is the time in seconds,
v is the initial vertical velocity of the flag,
s is the initial height of the flag.
In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).
We can rewrite the equation as:
7 = 16t^2 + 30t + 5
To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.
The quadratic equation in this case is:
16t^2 + 30t + 5 - 7 = 0
16t^2 + 30t - 2 = 0
Now, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the quadratic equation, we have:
t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)
Simplifying further:
t = (-30 ± √(900 + 128)) / 32
t = (-30 ± √1028) / 32
Using a calculator, we find two solutions:
t ≈ -1.08 seconds or t ≈ 0.06 seconds
Since time cannot be negative in this context, we discard the negative solution.
Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
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Cinético 5, torres 3, unido _
Answer:14
Step-by-step explanation: just trust me
Which of the following scenarios could be represented by the
inequality shown: 2.5x - 10> 45
To solve the inequality 2.5x - 10 > 45
What is Inequality?
To determine which scenarios could be represented by the inequality 2.5x - 10 > 45, we need to solve the inequality for x and analyze its meaning.
Let's solve the inequality step by step:
2.5x - 10 > 45
Add 10 to both sides:
2.5x - 10 + 10 > 45 + 10
2.5x > 55
Now, divide both sides by 2.5:
(2.5x)/2.5 > 55/2.5
x > 22
The solution to the inequality is x > 22. This means that any value of x greater than 22 would satisfy the inequality.
In terms of scenarios, here are a few examples:
This discrepancy shows that the person must have more than 22 years of experience to qualify if x is the number of years of experience needed for a certain job.This inequality shows that the corporation needs to sell more than 22 units to generate a profit larger than 45 if x is the number of units it sells.This inequality means that a person must be older than 22 years to satisfy a certain requirement if x is the individual's age.Learn more about Inequality
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What is the meaning of "each partition P of X defines an equivalence relation on X"?
The statement indicates that when a set X is partitioned, each partition forms an parity relation by grouping together rudiments that are considered original within each subset, thereby creating distinct and non-overlapping subsets within the original setX.
The statement" each partition P of X defines an parity relation on X" means that when a set X is divided into non-overlapping subsets or partitions, each partition creates an parity relation on the original set X.
An parity relation is a relation that satisfies three parcels reflexivity, harmony, and transitivity. In the environment of partitions, when a set X is divided into subsets, each partition forms an parity relation by grouping together rudiments that partake a common characteristic or property.
Within each partition, the rudiments are considered original or affiliated to each other, and they're distinct from rudiments in other partitions. The meaning of" each partition P of X" refers to every possible way of dividing the set X intonon-overlapping subsets.
It implies that different partitions may live grounded on different criteria or conditions for grouping rudiments.
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Joe is anxious for the big game. He couldn't get tickets for the game, but he heard it's being broadcast on a large
screen at a local megaplex. Since Joe doesn't want to miss a minute of this game, he decides to check out the megaplex
the day before the game.
The megaplex was empty, so Joe was able to take some measurements. He found that the 9 foot high screen is placed
on a wall with its base 7 feet above his eye level. Now he just needs to figure out how far away from the wall he needs
to stand to get the best view. He'll do this by maximizing angle theta.
Joe should arrive earlier to the game, engage in a dynamic warm-up routine, and include regular hamstring strengthening and flexibility exercises in his workout regimen to reduce the risk of straining his hamstring tendon during softball games.
A practical recommendation for Joe, the weekend warrior, who keeps straining his hamstring tendon during softball games, would be to incorporate a more comprehensive warm-up routine before the game.
As an ACSM-EP (American College of Sports Medicine - Exercise Physiologist), I would suggest that Joe arrive at least 20-30 minutes prior to the game and follow a dynamic warm-up routine.
This routine should include exercises that engage the whole body, especially focusing on the hamstrings and surrounding muscles. Some examples are leg swings, high knees, butt kicks, and dynamic stretches such as walking lunges.
These movements not only increase blood flow and muscle temperature, but also improve flexibility and joint mobility, reducing the risk of injury during the game.
Additionally, Joe should consider incorporating regular hamstring strengthening and flexibility exercises into his overall fitness routine, as this can help prevent future strains.
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Product of two whole numbers is 10000. If neither numbers contain a zero digit, what are the two numbers?
Answer:
Step-by-step explanation:
To find two whole numbers whose product is 10,000 and do not contain the digit zero, we can systematically examine the possible combinations.
The prime factorization of 10,000 is 2^4 * 5^4. We need to find two numbers that can be formed using these prime factors without including the digit zero.
Let's start with the power of 2. The highest power of 2 that can divide 10,000 is 2^4. So, the possible combinations for the power of 2 are 2^0 * 2^4, 2^1 * 2^3, 2^2 * 2^2, 2^3 * 2^1, and 2^4 * 2^0.
For the first combination, 2^0 * 2^4, it results in 1 * 16 = 16. Since 16 contains the digit zero, it doesn't meet the given condition.
Moving on to the next combination, 2^1 * 2^3, we have 2 * 8 = 16. Again, it contains the digit zero.
Continuing with 2^2 * 2^2, we get 4 * 4 = 16. This combination also doesn't satisfy the condition.
Next, we have 2^3 * 2^1, which equals 8 * 2 = 16. As before, it contains the digit zero.
Finally, we have 2^4 * 2^0, which gives us 16 * 1 = 16. Once again, it contains the digit zero.
After examining all the combinations involving powers of 2, we can conclude that there are no suitable combinations that satisfy the given conditions. Therefore, there are no two whole numbers without a zero digit that multiply to give 10,000.
can yall help me with this i gotta turn it in by 12:30 pm
The Multiplication of the fraction is shown below.
To multiply the numerators (the numbers on top) of the fractions to get the new numerator.
Multiply the denominators (the numbers on the bottom) of the fractions to get the new denominator.
1. 2/3 x 3
= 2/3 x 3/1
= 6/3
=2
2. 1/2 x 30
= 30/2
= 15
3. 4 x 3/4
= 12/4
=3
4. 1/2x 24
= 24/2
= 12
5. 3/5 x 15
= 45/5
= 9
6. 2/3x 18
= 36/3
= 12
7. 4/5 x 50
= 200/5
= 40
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Here's a box plot that summarizes how
many hot dogs contestants ate in a contest.
•
20 22 24 26 28 30 32 34 36
Number of hot dogs
Which of these best describes the shape of
the distribution?
The shape of the distribution is negatively skewed, due to the larger difference of the median and Q1 then of Q3 and the median.
What does a box and whisker plot shows?A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:
The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.The left side of the box in this problem is greater than the right side of the box, hence we have a negatively skewed distribution.
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Determine the amount of money you need to invest to accumulate $7,000 dollars in 4 years if you invest it at 2.5% annual interest, compounded quarterly.
An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.
To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.
The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.
A = P(1+r/n)^(nt)
A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
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A square has an area that is less than 100 m2. What is a reasonable range for the graph of the square’s side?
The reasonable range for the graph of the square’s side is (0, 10)
What is a reasonable range for the graph of the square’s side?From the question, we have the following parameters that can be used in our computation:
A square has an area that is less than 100 m²
The area of a square is calculated as
Area = Length²
The area is less than 100
So, we have
Length² < Area
substitute the known values in the above equation, so, we have the following representation
Length² < 100
Evaluate
Length < 10
Hence, the reasonable range for the graph of the square’s side is (0, 10)
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Number of car sold are 98.
Number of trucks sold are 66.
Given,
Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .
Let number of cars sold are x.
Let number of cars sold of y .
Now,
For dealership 1 equation will be,
x + y = 164 ......(1)
For dealership 2 equation will be,
As the cars are sold twice and trucks are sold half .
2x + y/2 = 229......(2)
Solving 1 and 2,
y = 66
x = 98
Thus number of car sold are 98.
Thus number of trucks sold are 66.
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What is the amplitude for the function graphed below.
a. 1
b. 2
c. 3
d. 4
e. 5
The amplitude of the function graphed will be 3.
Since, We know that,
The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.
We have,
A graph,
Here, The highest value = 5
Lowest value = -1
So,
From the definition mentioned above,
Amplitude = (5 + |- 1|) / 2
= 6 / 2
= 3
We get,
Amplitude = 3
Hence, we can say that the amplitude of the function graphed will be 3.
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On 1 April mazibane has R540, 00 in his credit card account. He buys a lounge suit for R8300, 00 on credit. There is no interest on the debit amount for the first month. Thereafter the interest is 16% per year calculated daily but compounded monthly. On 1 June Mazibane pays R5000 into the account.
How much must Mazibane pay into the account on 30 June to have no debt in the account
According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.
How to calculate the amount Mazubane must pay on 30 June?To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.
Initial Debt:
On 1 April, Mazibane had a credit card debt of R8300.Interest Calculation:
The interest on the debt is 16% per year, calculated daily but compounded monthly. From 1 April to 1 June, a period of two months, there is no interest charged on the debt.Previous Payment:
On 1 June, Mazibane paid R5000 into the account.To determine the remaining debt on 1 June, we subtract the payment from the initial debt:
Remaining debt on 1 June = R8300 - R5000 = R3300.From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.
To calculate the interest for one month, we use the formula:
Interest = Principal x (1 + (rate/100))^(time/12) - Principal,where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).
Interest for one month = R3300 x (1 + (16/100)/12)^(1/12) - R3300.To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:
Total debt on 30 June = R3300 + Interest for one month.To have no debt on 30 June, Mazibane must pay the total debt amount:
Mazibane must pay R3300 + Interest for one month on 30 June.Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.
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Define associative property
Answer:
the way in which factors are grouped in a multiplication problem does not change the product.
Step-by-step explanation:
If s bag of rice weight 55kg Find the weight of 123bags of rice
Answer: 6765kg
Step-by-step explanation:
55*123=6765
Answer:6,765
Step-by-step explanation:
just multiply 123 by 55 to get 6,765
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the Binomial Theorem to find the binomial expansion of the given expression. Show your work.
[tex](2x-3y)^5[/tex]
The expression is : [tex](2x-3y)^5 = 32x^5-240x^4y+720x^3y^2-1080x^2y^3+810xy^4-243y^5[/tex].
To expand the expression [tex](2x-3y)^5[/tex], we can use the binomial theorem or Pascal's triangle. However, using the binomial theorem can be time-consuming for large exponents. Instead, we can use Pascal's triangle to determine the coefficients of each term.
First, write out the coefficients of [tex](2x)^5[/tex] and [tex](-3y)^5[/tex] separately. Using Pascal's triangle, we get 1, 5, 10, 10, 5, and 1 for [tex](2x)^5[/tex] and 1, -3, 3, -1, 0, and 0 for [tex](-3y)^5[/tex].
Next, multiply each coefficient by its corresponding term and combine like terms. The resulting expanded form is [tex]32x^5-240x^4y+720x^3y^2-1080x^2y^3+810xy^4-243y^5[/tex].
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Solve for the value of q
Answer:
[tex]q=45[/tex]
Step-by-step explanation:
Notice that [tex](q+2)^{\circ}[/tex] and [tex](3q-2)^{\circ}[/tex] form a linear pair, that is, they sum to [tex]180^{\circ}[/tex] as follows:
[tex](q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45[/tex]
In one part of a rainforest 3/5 of the frogs are poisonous. what fraction of the frogs are not poisonous?
Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.
In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.
To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).
It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.
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A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings - - - Sauce (cups) - - - Oregano (tsp)
- - - 3- - - - - - - - - - - 6 - - - - - - - - - - - - - -1 & 1/2
8---
At this rate, how much sauce and oregano will be needed to make 8 servings?
A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
B) The recipe will need 16 cups of sauce and 4 teaspoons of oregano for 8 servings.
C) The recipe will need 14 cups of sauce and 4 teaspoons of oregano for 8 servings.
D) The recipe will need 14 cups of sauce and three and a half teaspoons of oregano for 8 servings.
The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.
According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.
Ratio of sauce to oregano:
6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano
Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:
8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano
Therefore, for 8 servings, we would need:
8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce
Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
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