The new area of the park that will not be wooded after expansion is represented by the expression 41.25x³ - 24.75x² + 15x - 13.5.
Explanation:The current area of the park is given by the polynomial 11x² + 4x + 6. If the city expands the park by a factor of 5x - 3, the total new area of the park becomes (11x² + 4x + 6) * (5x - 3), which represents the expansion of the park.
However, the question asks for the part of the park that will not be wooded, which we know is three-fourths of the total park. So, we multiply our expanded park equation by 3/4 (or 0.75) to find this area:
(3/4) * [(11x² + 4x + 6) * (5x - 3)]
Using distributive property, we can further expand the expression:
=(3/4) * [(55x³ - 33x² + 20x - 18)]
So the area that will not be wooded after expansion is expressed as 41.25x³ - 24.75x² + 15x - 13.5.
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Given that the current area of the park is represented by a second degree equation, the expansion of the park will proportionally increase its area. The new area after expansion will be the product of the current area and the expansion factor, so we will need to multiply our current area, which is given by 11x^2 + 4x + 6, by the expansion factor, which is 5x - 3.
This will yield: (5x - 3)*(11x^2 + 4x + 6) as the total new area of the park.
Now that we've calculate the total new area of the park, we need to find out the area of the park that will be wooded and the area that will not be. We know that the wooded area will be one-fourth of the total area, so we can find this by dividing our total area by 4.
This yields: (5x - 3)*(11x^2 + 4x + 6) / 4 as the wooded area of the park.
After discovering the area that will be wooded, we can find the non-wooded area by subtracting the wooded area from the total area of the park.
Therefore, the new area of the park that is not wooded is given by:
3*(5x - 3)*(11x^2 + 4x + 6) / 4
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A map of Scotland is drawn to scale of 1:325,000.
how many CM on the map would show 65KM?
On a map of Scotland, drawn to the scale of 1:325,000, 65 KM of real-world distance will be represented by 20 cm on the map.
Explanation:The question pertains to the scale existing on a map. A map scale enables us to convert the measurements on the map into the corresponding real-world distances. Here, we have a map of Scotland that is drawn to the scale of 1:325,000. This signifies that 1 cm on the map equates to 325,000 cm in reality.
To ascertain how many cm on the map would represent 65 KM, we first need to convert 65 KM into cm. As we know, 1 KM is equal to 100,000 cm. Therefore, 65 KM will be equivalent to 65 * 100,000 = 6,500,000 cm.
Now, we divide the real-world cm (6,500,000 cm) by the scale (325,000), which gives us the cm on the map. Thus, 6,500,000 cm / 325,000 = 20 cm
So, on this map, 65 KM will be denoted by 20 cm.
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A pizza parlor uses square prisms for their pizza boxes. Due to the crust rising, the height of their boxes is always 2 inches. Additionally, the volume of the pizza box must be 450 cubic inches to fit their standard-sized pizza. A worker determined that the equation below could be used to find the side length, x, of the box needed to reach that volume.
Answer:
The solutions are -15 and 15, but only 15 is a reasonable side length.
Step-by-step explanation:
Got it right on the test.
Which is greater 9/8ths or 2 halves?
The correct answer is [tex]\frac{9}{8}[/tex] is greater than 2 halves.
To compare 9/8ths and 2 halves, we need to convert them to equivalent fractions with the same denominator, and then compare their numerators.
[tex]\text{Step 1: Convert 2 halves to an equivalent fraction with the denominator of 8}[/tex]
[tex]2\text{ halves} = 2 \times \left(\frac{4}{8}\right) = \frac{8}{8}[/tex]
[tex]\text{Step 2: Compare the numerators of }\frac{9}{8}\text{ and }\frac{8}{8}[/tex]
[tex]\text{Since }9 > 8\text{, therefore, }\frac{9}{8} > \frac{8}{8}[/tex]
Therefore, [tex]\frac{9}{8}[/tex] is greater than 2 halves.
Steve opened a bank account.he plans to deposit $35 every month.write an equation that models the total amount of money,t,deposited after m months
Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) = 1/3. What is P(X) written as a decimal? Round to the nearest tenth, if necessary.
Answer:option C
Step-by-step explanation: edge
What is the expression of one less than the quotient of four and a number x
Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. How can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? What does a positive correlation tell you about the dependent and independent variables?
Round 6 4/9 to nearest whole number
dividing mixed fractions
A gift box in the shape of a triangular prism has a volume of 36 cubic inches, a base height of 4 inches, and a height of 3 inches. What is the length of the base?
Answer:
6 inches is the base
Step-by-step explanation:
So you have to think back to what the formula to volume is. From there plug in numbers until you get your answer
Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C)
1
2
x + 8 = 10
D)
1
2
(2x - 6) = -6
The answer is C
for X=-3
In order to survive, organisms must maintain stable conditions in their bodies, even though their external environments are always changing.
For example, humans need to maintain an internal temperature around 37°C. Blood needs to have a pH around 7.4 and an oxygen saturation close to 100%.
What needs to happen in order to maintain these conditions?
A) Organ systems must interact with one another.
B) Organisms must be at rest.
C) Genes must be altered each time cells replicate.
D) All of these.
Organ systems must interact with one another.
Write two equivalent fractions for 2/3
A classmate believes that a triangle can have both a right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect?
Sum of internal angles in a triangle is 180 degree.
∠A + ∠B + ∠C = 180°
Now we have three cases:
Case 1 : For right anlge triangle.
in this case one angle is 90°. and rest of two angle's sum is 90 degree
it means measure of rest two anles is less than 90 degree.
So, this type trianlge holds one right anlge and two acute angle.
Case 2: If one angle is Obtuse angle(more than 90°)
In this case , rest of two angle's sum is less than 90°
So, this type trianlge holds one obtuse anlge and two acute angle.
Case 3: All angles are acute
In this case all three anles are less than 90°
So, triangle has one obtuse angle, that means rest of two anlges must be less than 90°
Engineers must consider the breadths of male heads when designing motorcycle helmets. men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in. (based on anthropometric survey data from gordon, churchill, et al.). if one male is randomly selected, find the probability that his head breadth is less than 6.2 in. use 4 decimals for your answer.
Answer: 0.9772 (the answer above wasn't the right one;)
Using z-score formula, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.
What is z-score formula?When you have multiple samples and want to describe the standard deviation of those sample means (the standard error), you would use this z score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
This z-score will tell you how many standard errors there are between the sample mean and the population mean.
We have been given that men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. We are asked to find the probability that a man's breadth is less than 6.2 inches.
First of all, we will find z-score corresponding to sample score of 6.2 as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where,
z = Z-score,
x = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{6.2-6.0}{1.0}[/tex]
[tex]z=\frac{0.2}{1.0}[/tex]
z = 0.2
Now, we need to find the probability that a z-score is less than 0.2.
Using normal distribution table, we will get:
P(z < 0.2) = 0.57926
0.579261 ≈ 57.9261 %
Therefore, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.
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6 surfaces 2 small stand tall what shape
Of the 180 days of school last year, Grace was absent 15 days. What percent of the day was she absent?
Luca has a box of dog toys. There are 3 bones, 5 balls, and a stuffed animal. What is the ratio of balls to stuffed animals?
Answer:
5.1
Step-by-step explanation:
I Has This Study Island Before
The area of a trapezoid is found using the formula A=1/2h(b^1+b^2), where b^1 and b^2 are the parallel sides of the trapezoid and h is the height. The area of a trapezoid is 18km^2 , with bases 5 km and 7 km. What is the height, in
Answer:
40
Step-by-step explanation:
Just did it on Time4Learning. Please give brainliest.
A store advertises that it is offering a 14% discount on all articles purchased at the store. if yao pays $670.80 for an article, what was the marked price for the article?
contractor A estimated a job would cost $54,000 to complete in 90 days. contractor B estimated he could complete the same job for $49,500 in 120 days. how much per day does each contractor charge
Contractor A estimated a job would cost $54,000 to complete in 90 days.
Per day charge of Contractor A = $54,000 / 90 = $ 600 / day
Contractor B estimated he could complete the same job for $49,500 in 120 days.
Per day charge of Contractor A = $49,500 / 90 = $ 412.50 / day
Therefore, Contractor A charges $ 600 per day and contractor B charges $412.50 per day.
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How does one find the equation y=ax²+bx+c when you are only provided with the coordinates of the turning point, (-6,-9)? Note: a is +1 or -1
Is 2 miles greater too 3,333 yards or is 3,333 yards greater than 2 miles?
What words can you use to read 14.895
Suppose a family starts out 50 miles from home at time t = 0. They travel away from home at a constant speed of 45 miles an hour. What's the equation that tells you how far they'll be from home t hours later? (Assume d is distance in miles.) A. d = 45t + 50 B. d = 45t C. d = 50t D. d = 50t + 45
Sayed gave an answer of 6 6/7 for the problem 4 2/7 x 1 3/5. using estimates, is this a reasonable answer?
When ordering hot cocoa, Jackson is asked if he wants milk chocolate, dark chocolate, or chocolate mint flavor. He also must choose between a small or large mug, and has the option of adding marshmallows. How many ways can Jackson order his hot cocoa? A). 10
B).6
C).7
D).12
There are 12 ways Jackson can order his hot cocoa by choosing from three flavors, two mug sizes, and the option of adding marshmallows. Option D is correct,
To find the total number of ways Jackson can order his hot cocoa, we need to consider all the possible combinations of choices he has.
1. Flavor: Jackson has 3 options: milk chocolate, dark chocolate, or chocolate mint flavor.
2. Mug Size: Jackson has 2 options: small or large mug.
3. Marshmallows: Jackson has 2 options: with or without marshmallows.
To find the total number of combinations, we multiply the number of options for each choice:
[tex]\[ \text{Total combinations} = \text{Number of options for flavor} \times \text{Number of options for mug size} \times \text{Number of options for marshmallows} \]\[ \text{Total combinations} = 3 \times 2 \times 2 \]\[ \text{Total combinations} = 12 \][/tex]
So, there are 12 ways Jackson can order his hot cocoa. Therefore, the correct answer is option D) 12.
you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty-five percent of the olive oil remains. How many quarts of olive oil remain?
Solution:
we are given that
You have a large container of olive oil. You have used [tex]22 \frac{1}{2}[/tex] quarts of oil.
Twenty-five percent of the olive oil remains.
we have been asked to find how many quarts of olive oil remain?
Let there were x quarts of olive oil.
It mean , we can write
[tex]x-22 \frac{1}{2}=\frac{1}{4}*x[/tex]
[tex]x-\frac{1}{4}*x=22 \frac{1}{2}[/tex]
[tex] \frac{3x}{4}=22 \frac{1}{2}[/tex]
[tex] 3x=4*22 \frac{1}{2}[/tex]
[tex] x=\frac{4}{3}* \frac{45}{2}[/tex]
[tex] x=30[/tex]
Hence quarts of olive oil remain [tex] =30-\frac{45}{2}=\frac{15}{2}=7\frac{1}{2}[/tex]
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A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.
1 The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
2 The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.
3 The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4 The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5 The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
6 The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
Answer:
A,C,D,E
Step-by-step explanation:
An equation is formed of two equal expressions. The correct options are 1, 3, 4, and 5.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Also, x represents the price of the small boxes and y represents the price of the large boxes. Therefore,
The equation for the first student can be written as,
5x + 13y = 232
The equation for the second student can be written as,
12x + 7y = 218
Now, the multiplication that can be done to eliminate the variables are,
1.) The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
3.) The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4.) The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5.) The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
Hence, the correct options are 1, 3, 4, and 5.
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What is the sum of the arithmetic series below? Use the formula for the sum of an arithmetic series.
Answer: The required sum is 504.
Step-by-step explanation: We are given to find the sum of the following arithmetic series using the formula for the sum of an arithmetic series :
[tex]\sum_{i=1}^{18}(2i+9).[/tex]
The given arithmetic series can be written, in expanded form, as follows :
[tex]11+13+15+17+~.~.~.~+43+45.[/tex]
We know that
the sum of first n terms of an arithmetic series with first term a and common difference d is given by
[tex]S=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]
In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.
Therefore, the sum up to 18 terms will be
[tex]S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.[/tex]
Thus, the required sum is 504.
The sum of the arithmetic series ∑₁¹⁸(2i + 9) using the arithmetic series formula is 504.
To find what is the sum of the arithmetic series ∑₁¹⁸(2i + 9) below using the formula for the sum of an arithmetic series, we proceed as follows
The formula for the sum of therms of an arithmetic series is given by
Sₙ = n/2(a + Tₙ) where
n = number of termsa = first term and Tₙ = last termNow, since we have that arithmetic series, ∑₁¹⁸(2i + 9), the nth terms is U = 2i + 9
Now, the first term is when i = 1.
So, U₁ = a = 2(1) + 9
= 2 + 9
= 11
Also, the last term is when i = 18
So, U₁₈ = T₁₈ = 2(18) + 9
= 36 + 9
= 45
So, the sum of terms Sₙ is when n = 18
S₁₈ = 18/2(11 + 45)
= 9(56)
= 504