Answers
The amount a student received in merit scholarships was $3,456 ($478 per student). The cost of full tuition was $4,200. This means that the difference between the amount of the scholarship and the cost of tuition was $744.
What is amount ?Amount is a numerical value that represents a quantity of something. It is used to measure the size, amount, or degree of something, often in terms of money, time, or distance. Amounts are usually expressed in a specific unit, such as dollars, minutes, or kilometers. Amounts can also refer to the total number of something, such as the amount of people in a room or the amount of items in a box. Amounts can also be used to describe a portion or percentage of something, such as the amount of a discount or the amount of interest earned.
To find the percentage of students who did not receive enough to cover full tuition, we need to divide the difference ($744) by the amount of the scholarship ($3,456). This gives us a percentage of 21.5%.
Rounded to the nearest whole percent, the answer is 22%. This means that 22% of students who received a merit scholarship did not receive enough to cover full tuition.
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Related Questions
Find the generating functions and the associated sequences of: (x+4) ^ 4
Answers
Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
What is the generating functions and associated sequences of the functionTo find the generating function of (x+4)^4, we expand it using the binomial theorem:
[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
Therefore, the generating function of (x+4)^4 is:
[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.In this case, the sequence is given by the coefficients of G(x):a₀ = 256a₁ = 256a₂ = 96a₃ = 16a₄ = 1To find the generating function of (x+4)^4, we expand it using the binomial theorem:
(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256
Therefore, the generating function of (x+4)^4 is:
G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.
In this case, the sequence is given by the coefficients of G(x):
a₀ = 256
a₁ = 256
a₂ = 96
a₃ = 16
a₄ = 1
Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
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how do you solve this? (-3a+56)+(5a+40)
Answers
Answer:To simplify the expression, you need to combine the like terms, which are the terms that have the same variable and power. In this case, the like terms are -3a and 5a:
(-3a + 56) + (5a + 40)
= (-3a + 5a) + (56 + 40)
= 2a + 96
Therefore, the simplified expression is 2a + 96.
Enjoy (:
Step-by-step explanation:
What is the equation of the line graphed?
Answers
Answer:
The simplest possible equation for the line on the graph would be x = - 2
Annie is concerned over a report that "a woman over age 40 has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40 -year-old university-educated American woman was 2.5% . To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 546 never-previously-wed, university-educated, American women who were single at the beginning of their 40 s and who are now 45 . Of these women, 20 report now being married. Does this evidence support Annie’s claim, at the 0.01 level of significance, that the chances of getting married for this group is greater than 2.5% ? Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: p=0.025: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.025
Answers
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
what is null hypothesis ?The null hypothesis, which is an assertion or assumption that there is no significant difference or association between two or more variables or populations, is used in statistical hypothesis testing. It is frequently indicated by the letter H0 and is typically the hypothesis that is tested against a competing hypothesis. The objective of the hypothesis test is to either reject or fail to reject the null hypothesis based on the evidence or data seen. The null hypothesis serves as the default or baseline assumption. If the alternative hypothesis is supported by evidence, the null hypothesis is likely to be rejected.
given
The test's null and alternate hypotheses are as follows:
H0: p 0.025 (The percentage of American women with university educations who had never previously been married at the start of their 40s and are now 45 and married is less than or equal to 2.5%)
Ha: p > 0.025 (More than 2.5% of American women with college degrees who were unmarried at the start of their 40s and are now 45 and married are never before married).
Due to the directed nature of the alternative hypothesis, a one-tailed test is being used (greater than).
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A bank requires that the Dotkoms pay their homeowner's insurance, property taxes, and
mortgage in one monthly payment to the bank. If their monthly mortgage payment is $1,711.22,
their semi-annual property tax bill is $3,239, and their annual homeowner's insurance bill is
$980, how much do they pay the bank each month?
Answers
Answer: $2,162.06
Step-by-step explanation:
To calculate the total monthly payment to the bank, we need to add up the monthly mortgage payment, the monthly portion of the semi-annual property tax bill, and the monthly portion of the annual homeowner's insurance bill.
First, we need to find the monthly portion of the semi-annual property tax bill. To do this, we divide the semi-annual property tax bill by 6 (since there are 6 months in half a year):
Monthly property tax payment = Semi-annual property tax bill / 6
Monthly property tax payment = $3,239 / 6
Monthly property tax payment = $539.83
Next, we need to find the monthly portion of the annual homeowner's insurance bill. To do this, we divide the annual homeowner's insurance bill by 12 (since there are 12 months in a year):
Monthly homeowner's insurance payment = Annual homeowner's insurance bill / 12
Monthly homeowner's insurance payment = $980 / 12
Monthly homeowner's insurance payment = $81.67
Now we can add up the monthly mortgage payment, the monthly property tax payment, and the monthly homeowner's insurance payment to find the total monthly payment to the bank:
Total monthly payment = Monthly mortgage payment + Monthly property tax payment + Monthly homeowner's insurance payment
Total monthly payment = $1,711.22 + $539.83 + $81.67
Total monthly payment = $2,332.72
Therefore, the Dotkoms pay the bank $2,332.72 each month.
Answer:
Step-by-step explanation:
Using proportions, it is found that they pay the bank $2332.72 each month.
What is a proportion?
A proportion is a fraction of a total amount.
Using proportions, it is found that they pay the bank $2332.72 each month.
What is a proportion?
A proportion is a fraction of a total amount.
Their payments are given by:
Monthly mortgage of $1,711.22.
Semi-annual property tax bill is $3,239, that is, it is paid every 6 months, hence 3239/6 = $539.83.
Consider the function h(x) = a(−2x + 1)^5 − b, where a does not=0 and b does not=0 are constants.
A. Find h′(x) and h"(x).
B. Show that h is monotonic (that is, that either h always increases or remains constant or h always decreases or remains constant).
C. Show that the x-coordinate(s) of the location(s) of the critical points are independent of a and b.
Answers
Answer:
A. To find the derivative of h(x), we can use the chain rule:
h(x) = a(-2x + 1)^5 - b
h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4
To find the second derivative, we can again use the chain rule:
h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3
B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.
C. To find the critical points, we need to find where h'(x) = 0:
h'(x) = -10a(-2x + 1)^4 = 0
-2x + 1 = 0
x = 1/2
Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.
Bret needs to put a logo on a business card. He prints the logo the wrong way up by mistake. Bret needs to turn the logo the correct way up. What fraction does Bret need to turn the logo?
Answers
The fraction Bret needs to turn the logo is 1 / 2.
How to find the fraction Bret needs to turn the logo?Bret needs to put a logo on a business card. He prints the logo the wrong way up by mistake. Bret needs to turn the logo the correct way up.
Therefore, the fraction he needs to turn the logo can be represented as follows:
For a complete turning, it will be 360 degrees. according to the diagram he has already turned the logo 180 degrees.
Therefore, for Bret to turn the logo correctly, he needs to turn it 180 degrees.
Hence, the fraction he needs to turn the logo is as follows:
180 / 360 = 18 /36 = 1 / 2
Hence, Bret needs to turn the logo half way(1 / 2)up.
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Which of the following is a true statement?The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1.The area under the standard normal curve between 0 and 2 is half the area between -2 and 2.For the standard normal curve, the IQR is approximately 3.For the standard normal curve, the area to the left of 0.1 is the same as the area to the right of 0.9.
Answers
For the standard normal curve, the area to the left of 0.1 is the same as the area to the right of 0.9 is true . So, the correct answer is D.
The standard normal curve is a normal distribution with a mean of 0 and a standard deviation of 1. This curve is often used in statistics to model natural phenomena, and it has many important properties.
Option A is incorrect because the area under the standard normal curve between 0 and 2 is not twice the area between 0 and 1. The area under the curve increases as we move away from the mean, so the area between 0 and 2 will be greater than the area between 0 and 1.
Option B is also incorrect because the area under the standard normal curve between 0 and 2 is not half the area between -2 and 2. The area between -2 and 2 covers more of the curve than the area between 0 and 2, so the area between 0 and 2 will be smaller than half the area between -2 and 2.
Option C is incorrect because the standard normal curve does not have a fixed IQR (interquartile range). The IQR depends on the quartiles of the distribution, which can vary depending on the sample size and the distribution's shape.
Option D is the correct answer because the standard normal curve is symmetric around the mean of 0. This means that the area to the left of any point on the curve is the same as the area to the right of its negative counterpart. Therefore, the area to the left of 0.1 is equal to the area to the right of 0.9.
Therefore, Correct option is D.
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Construct an example of a function that satisfies the following conditions:
a) Its domain and range are both all real numbers except 5.
b) Its domain is all positive numbers greater than 1, including 1.
c) Its domain is all positive numbers greater than 1, but not including 1.
Answers
Answer:
f(x) = (x^2 - 25) / (x - 5)
Step-by-step explanation:
Note that this function is undefined at x=5, which satisfies condition (a). Also, the function is defined for all other real numbers, which satisfies the domain and range requirement of (a).
For condition (b), note that the function is defined for all positive numbers greater than 1, including 1, since the denominator (x-5) will be positive for these values of x.
For condition (c), note that the function is undefined at x=1, since the denominator (x-5) will be negative for x slightly less than 1. Therefore, the function is defined for all positive numbers greater than 1, but not including 1.
Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using
limits.
Y=(1/6) ^-x
Answers
Answer:
The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.
To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.
As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.
As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.
Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.
Please answer these questions correctly :)
Answers
Find the percent of each number :-
1.) 64% of 75 tiles :
[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]
Hence, 64% of 75 tiles is 48 tiles.
2.) 20% of 70 plants.
[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]
Hence, 20% of 70 plants is 14 plants.
3.) 32% of 25 pages .
[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]
Hence, 32% of 25 pages is 8 pages.
4.) 85% of 40 e -mails.
[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]
Hence, 85% of 40 e -mails is 34 e-mails.
5.) 72% of 350 friends.
[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]
Hence, 72% of 350 friends is 252 friends.
6.) 5% of 220 files.
[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]
Hence, 5% of 220 files is 11 files.
define a re for the language {w | w is at least 6 symbols long and contains at least one 0 and at least one 1}
Answers
The regular expression is (0|1)[0(0|1)1(0|1)] | (0|1)[1(0|1)0(0|1)], which matches any string that is at least 6 symbols long and contains at least one 0 and at least one 1.
One possible regular expression for the language {w | w is at least 6 symbols long and contains at least one 0 and at least one 1} is:
(0|1)[0(0|1)1(0|1)] | (0|1)[1(0|1)0(0|1)]
This regular expression matches any string that satisfies the following conditions:
The string contains at least one 0 and at least one 1.
The string is at least 6 symbols long.
The string can have any number of 0s and 1s before and after the first 0 or 1, but it must contain at least one of each before and after the first 0 or 1.
For example, this regular expression matches strings like "0101010", "1000001", "1110010", but does not match strings like "101", "11111", "0000000".
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Complete question:
Alphabet = {0,1}.
Define a regular expression for the language {w | w is at least 6 symbols long and contains at least one 0 and at least one 1}
WILL GIVE BRAINLIEST NEED ANSWERS FAST!!!
Find the missing length indicated
Answers
Step-by-step explanation:
4)
based on similar triangles and the common ratio for all pairs of corresponding sides we know
LE/LM = LD/LK = DE/EM
because E and D are the midpoints of the longer sides, all of these ratios are 1/2.
1/2 = DE/8
8/2 = 4 = DE
5)
same principle as for 4)
BQ/BA = BR/BC = QR/AC
again, Q and R are the midpoints, so all these ratios are 1/2.
1/2 = QR/10
QR = 10/2 = 5
Trigonometric Functions
pls help and be sure to show all your work !! the second pic is the graph that needs to be plotted for the first question.
Answers
A) Values of y will be 1, 0, -1, 0, 1
B) and C) plot the values as shown in below figure.
Define the term Trigonometric Function?Trigonometric functions are a set of mathematical functions that relate the angles and sides of right triangles.
A) for f(x) = cos x; the values of x-y chart are:
x y = f(x)
0 1
[tex]\frac{\pi }{2}[/tex] 0
[tex]\pi[/tex] -1
[tex]\frac{3\pi }{2}[/tex] 0
[tex]2\pi[/tex] 1
B) the points are plotted as given figure below.
C) Connects the dots to show the graph of y = cos x; sown in figure below please check it.
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There are two coins. One of them is a biased coin such that P (head): P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
Answers
Answer:
Step-by-step explanation:
Let B be the event that the selected coin is biased, and F be the event that the selected coin is fair. Let H be the event that the coin toss shows a head.
We want to find P(B|H), the probability that the selected coin is biased given that the coin toss shows a head. By Bayes' theorem, we have:
P(B|H) = P(H|B) * P(B) / P(H)
We know that P(H|B) = 1/4 (since the biased coin has a probability of 1/4 of showing a head), and that P(B) = 1/2 (since there are two coins, one of which is biased).
To find P(H), we can use the law of total probability:
P(H) = P(H|B) * P(B) + P(H|F) * P(F)
P(H) = (1/4) * (1/2) + (1/2) * (1/2)
P(H) = 3/8
Putting it all together:
P(B|H) = P(H|B) * P(B) / P(H)
P(B|H) = (1/4) * (1/2) / (3/8)
P(B|H) = 1/3
Therefore, the probability that the selected coin is biased given that the coin toss shows a head is 1/3.
Pls help! Due tmrrww!!
Answers
Answer:
1. basement: 1,4,7,10,13
middle : 2,5,8,11,14
top: 3,6,9,12,15
2. you just need to skip count ten times then we will have 30. so she lives in apartment 30.
Step-by-step explanation:
You have a map that is missing a scale. The distance from Point A to Point B is
five inches on the map, and after driving it, you know it is 250 miles in reality.
Answers
The scale of the map in the question is 1 inch = 50 miles.
What is the scale of the map?A scale in a map is a relation that tells us how many units each unit in the map represents. In this case, we know that the distance between two points A and B on the map is 5 inches, while the actual distance between these two places is 250 miles.
Then we start with the relation:
5 inches = 250 miles.
But to get the scale of the map we need to see how many miles one inch represents in the map, then we can divide both sides of the equation by 5 to geT:
5 in = 250 mi
1 in = 250mi/5
1 in = 50 mi
The scale of the map is 1 inch to 50 miles.
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Can someone solve this
Note: in dark pen is the questions to solve in light pencil is my answer probably are wrong
Answers
The open circle at 3 indicates that 3 is not included in the solution set. This inequality can be read as "X is less than 5" or "X is strictly less than 5."
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators that represents a value. Expressions can be as simple as a single number or variable, or they can be complex combinations of mathematical operations. For example, 2 + 3 is a simple expression that represents the value 5, while (2 + 3) x 4 - 1 is a more complex expression that represents the value 19. Expressions can be evaluated or simplified using the rules of arithmetic and algebra.
Here,
1. Simplify:
3(4x-2)+ 7X (2-1) + 4 (6+4)+(-8)
Multiplying inside the parentheses first:
12x - 6 + 7x + 4 + 40 - 8
Combining like terms:
19x + 30
Final answer: 19x + 30
2. Graph:
3 > X
This is a simple inequality in one variable (X). To graph it on a number line, we first draw a dot at 3 (since the inequality is strict), and then shade all values less than 3:
<=========o---
The open circle at 3 indicates that 3 is not included in the solution set.
3. Write the inequality:
X < 5
This is a simple inequality in one variable (X). The inequality sign is "less than," and the number on the right-hand side is 5. This inequality can be read as "X is less than 5" or "X is strictly less than 5."
4. Solve for x:
3x - 7 = 42
Adding 7 to both sides to isolate the variable:
3x = 49
Dividing both sides by 3 to solve for x:
x = 16.33 (rounded to two decimal places)
Final answer: x = 16.3
5. Find 32% of $542.50:
To find 32% of $542.50, we can use the formula:
percent * amount = part
where "percent" is the percentage expressed as a decimal, "amount" is the whole amount, and "part" is the result we're looking for.In this case, we have:
0.32 * $542.50 = part
Multiplying:
$173.60 = part
Final answer: $173.60
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Suppose the current cost of gasoline is $2.93 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
Answers
Answer:
Step-by-step explanation:
To find the current price index number using the 1975 price of 56.7 cents as the reference value, we can use the formula:
Price Index = (Current Price / Base Price) x 100
Where "Current Price" is the current cost of gasoline, and "Base Price" is the 1975 price of 56.7 cents.
Substituting the values given in the problem, we get:
Price Index = ($2.93 / $0.567) x 100
Price Index = 516.899
Therefore, the current price index number, using the 1975 price of 56.7 cents as the reference value, is 516.899.
Let V be a 3 dimensional vector space with A and B its subspace of dimension 2 and 1 respectively if A
∩
B
=
0
then A
V=A-B
B
V=A+B
C
V=AB
D
none of the above
Answers
The 3-dimensional vector space represented in the form subspace dimensions A and B is given by option B. V = A + B.
V be 3-dimensional vector space.
Subspace of dimensions of A and B are 2 and 1 respectively.
And A ∩ B = 0.
It follows that every vector in A is linearly independent of every vector in B.
This implies,
Any vector v in V can be expressed uniquely as a sum of a vector in A and a vector in B.
Let v be an arbitrary vector in V.
A has dimension 2, it has a basis of two linearly independent vectors.
Let {a1, a2} be such a basis.
B has dimension 1, it has a basis consisting of a single nonzero vector b.
Then, any vector v in V can be expressed uniquely as
v = c1a1 + c2a2 + cb,
where c1, c2, and c are scalars.
Thus,
V = A + B.
Therefore, the correct answer to represents 3 dimensional vector space V as option(B). V = A + B.
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factorise completely[tex]3x²-12xy
Answers
Answer:
3x(x - 4y)
Step-by-step explanation:
3x² - 12xy ← factor out 3x from each term
= 3x(x- 4y)
The breadth of a rectangular playground is 5m shorter than its length. If its perimeter is 130m,find ids length and breadth.
Answers
Answer:
Length is 35 m and breadth is 30 mStep-by-step explanation:
Given,
The breadth of a rectangular playground is 5m shorter than its length.Perimeter is 130 mLet length be x and breadth (x - 5).
Perimeter of rectangle is calculated by :
[tex] \: \: \boxed{ \pmb{ \sf{Perimeter_{(rectangle)} = 2(l + b)}}} \\ [/tex]
On substituting the values we get :
[tex]\dashrightarrow \: \: 130 = 2(x + x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 130 = 2(2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \dfrac{130}{2} = (2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 65 = 2x - 5 \\ [/tex]
[tex]\dashrightarrow \: \: 65 + 5 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: 70 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: \frac{70}{2} = x \\ [/tex]
[tex]\dashrightarrow \: \: 35 = x \\ [/tex]
Hence,
Length = x = 35 m.Breadth = x -5 = (35 -5) = 30 mWhen a researcher wants to report the average cost of college tuition from the 1950s until present time, he or she enlists _______ statistics.a) Inferentialb) Descriptivec) Correlationald) Predictive
Answers
Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.
When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.
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2 cities are 210 miles apart. If the distance on the map is 3 1/4 inches, find the scale of the map
Answers
The scale of the map = 682.5.
How would you define distance in one sentence?We kept a safe distance and followed them. She perceives a separation between her and her brother that wasn't there before. Although they were previously close friends, there was now a great deal of gap between them.
We must calculate the ratio of the distance shown on the map to the real distance between the cities in order to ascertain the scale of the map.
We are aware that there are 210 miles separating the two cities. Let x represent the precise location of this distance on the map. From that, we may establish the ratio:
Actual distance / Map Distance = 210 / x
The distance on the map is indicated as 3 1/4 inches, which is also known as 13/4 inches. When we enter this into the percentage, we obtain:
Actual distance divided by (13/4) = 210 / x
We can cross-multiply and simplify to find x's value:
Actual distance: 682.5 = x * 210 x = 3.25 when 210 * (13/4) Equals x.
Consequently, 3.25 inches on the map represent the actual distance between the cities. We can write: To determine the map's scale:
Actual distance divided by 1 inch on the chart equals 210 miles.
When we replace the values we discovered earlier, we obtain:
1 / 210 = 3.25 / scale
If we solve for the scale, we obtain:
scale = 682.5.
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In an examination,x pupils take the history paper and 3x take the mathematics paper. A. illustrate the data on a venn diagram indicating the number of pupils I'm each region.
B. if the number of pupils taken the examination is 46, find the value of x
Answers
If we round up, we get x = 12, which means that 12 students took history and 36 students took mathematics.
What is venn diagram?A Venn diagram is a graphical representation of sets, often used to show relationships between different sets of data. It consists of one or more circles, where each circle represents a set. The circles are usually overlapping to show the relationships between the sets. The region where the circles overlap represents the elements that belong to both sets. The non-overlapping parts of each circle represent the elements that belong to only one of the sets.
Here,
A. To illustrate the data on a Venn diagram, we need to draw two overlapping circles, one for history and one for mathematics. We can label the regions as follows:
The region where the circles overlap represents the students who took both history and mathematics.
The region outside both circles represents the students who did not take either history or mathematics.
The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics.
The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history.
In this diagram, let's assume that x students took history and 3x students took mathematics. Then the total number of students who took the examination is x + 3x = 4x. We can label the regions on the diagram accordingly:
The region where the circles overlap represents the students who took both history and mathematics. Since there are 3x students who took mathematics, and all of them are included in the overlap region, the number of students who took both is 3x.
The region outside both circles represents the students who did not take either history or mathematics. Since there are 46 students in total, and 4x of them took the examination, the number of students who did not take either is 46 - 4x.
The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics. Since x students took history, and 3x took mathematics, the number of students who took history but not mathematics is x - 3x = -2x. However, since we cannot have a negative number of students, we can assume that this region is empty.
The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history. Since there are 3x students who took mathematics, and some of them also took history, the number of students who took mathematics but not history is 3x - 3x = 0. Therefore, this region is also empty.
B. We know that the total number of students who took the examination is 46. Therefore, we have:
x + 3x = 46
4x = 46
x = 11.5
However, since x represents the number of students who took history, it must be a whole number. Therefore, we can round x up or down to the nearest whole number. If we round down, we get x = 11, which means that 11 students took history and 33 students took mathematics.
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Use the parabola tool to graph the quadratic function f(x) = -√² +7.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola HELP ME PLEASEEE
Answers
Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).
What is parabola?
A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function.
Assuming you meant [tex]f(x) = -x^2 + 7[/tex], here's how you can graph the parabola using the parabola tool:
Find the vertex
The vertex of the parabola is located at the point (-b/2a, f(-b/2a)), where a is the coefficient of the [tex]x^2[/tex] term and b is the coefficient of the x term. In this case, a = -1 and b = 0, so the vertex is located at the point (0, 7).
Plot the vertex
Using the parabola tool, plot the vertex at the point (0, 7).
Plot a second point
To plot a second point, you can choose any x value and find the corresponding y value using the quadratic function. For example, if you choose x = 2, then [tex]f(2) = -2^2 + 7 = 3[/tex]. So the second point is located at (2, 3).
Therefore, Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).
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Complete Question:
Use the parabola tool to graph the quadratic function.
f(x) = -√² +7
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Solve for the short leg of the 30-60-90 triangle.
Answers
Answer:
2
Step-by-step explanation:
The basic 30-60-90 triangle ratio is:
Side opposite the 30° angle: x
Side opposite the 60° angle: x√3
Side opposite the 90° angle: 2x
Here, the side opposite the 90° angle is 4.
This means that 2x = 4 and, thus, x = 2.
Since b is the side opposite the 30° angle, b = x, so it is 2.
find an ordered pair (x, y) that is a solution to the equation. -x+6y=7
Answers
Step-by-step explanation:
(-1, 1) is a solution.
because
-(-1) + 6×1 = 7
1 + 6 = 7
7 = 7
correct.
every ordered pair of x and y values that make the equation true is a solution.
(5, 2) would be another solution. and so on.
if y is given and you need to find third derivative of y (given as y'''), what are the steps: explain what one needs to do and say it in your words.
Answers
The steps for finding out the third derivative of y (given as y''') are explained and given below.
To find the third derivative of y (y'''), you would need to differentiate the function y three times with respect to the independent variable. Here are the steps:
Start by differentiating y once to get the first derivative, y'.
Differentiate y' again to get the second derivative, y''.
Finally, differentiate y'' to get the third derivative, y'''.
You can use the chain rule, product rule, quotient rule, and other differentiation rules as needed to find each derivative.
Here's an example of finding the third derivative of y for the function y = x^4 + 2x^3 - 5x:
y' = 4x^3 + 6x^2 - 5
y'' = 12x^2 + 12x
y''' = 24x + 12
So the third derivative of y is y''' = 24x + 12.
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What is the difference between the longest and
shortest pieces of scrap wood?
Answers
The difference in length between the two pieces of scrap wood is 7/8 inches.
What is the difference between the longest and shortest pieces of scrap wood?
To get the difference we just need to take the difference between the two lenghs.
Remember that we only have pieces of scraph wood if we have an "x" over the correspondent value in the line diagram.
By looking at it we can see that the longest pice measures 5 inches, while the shortest one (there are two of these) measure (4 + 1/8) inches.
The difference is:
5 - (4 + 1/8) = 7/8
The longest piece is 7/8 inches longer.
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