We need to use the concept of proprotionality for the given question.The value of y is 25.7, value of R is 1 and value of t is 144.
It is given that y varies directly as the square root of x which means that y is directly proportional to x, we can write it as
y∝[tex]\sqrt{x}[/tex] which can again be written as y=[tex]\sqrt{x} k[/tex] where k is a proportionality constant,we need to find the value of k inorder to find the value of y.We know that y=12 when x=49
12=[tex]\sqrt{49} k[/tex]=7k⇒12=7k⇒k=[tex]\frac{12}{7}[/tex]
when x=225 then y=[tex]\sqrt{225}[/tex]×[tex]\frac{12}{7}[/tex]=15×[tex]\frac{12}{7}[/tex]=25.7
R is inversely proportional to the cube of S,we can write it as
R∝[tex]\frac{1}{S^{3} }[/tex] ⇒R=[tex]\frac{k}{S^{3} }[/tex]
We need to find the value of k inorder to find the value of R, it is given that R=8 when S=3
8=[tex]\frac{k}{27}[/tex]
k=27x8=216
Value of R when S=6 will be
R=[tex]\frac{216}{6^{3} } =\frac{216}{216} =1[/tex]
It is given that n varies directly as the square root of t and inversely as l,we can write it as
n∝[tex]\frac{\sqrt{t} }{l}[/tex] which can be again written as n=[tex]\frac{\sqrt{t} }{l} k[/tex] where k is a proportionality constant,we need to find the value of k first to find the value of t
We know that n=5 when t=16 and l=2
5=[tex]\frac{\sqrt{16} }{2}k=\frac{4}{2} k=2k[/tex]
k=[tex]\frac{5}{2}[/tex]
We know that n=10,l=3 and k=[tex]\frac{5}{2}[/tex] substituting these values we can get the value of t
t=[tex](\frac{nl}{k} )^{2}[/tex]=[tex](\frac{10.3.2}{5} )^{2} =12^{2} =144[/tex]
Thus we can see that using the concept of proportionality we found out the values of y,R and t. Value of y is 25.7, R is 1 and t is 144.
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Margot draws a shape with one pair of parallel lines that are four centimeters apart. She then flips the shape across a horizontal line.
How many pairs of parallel lines are in the flipped shape?
The flipped shape has a pair of parallel line
What are parallel lines?A pair of line is said to be parallel lines when the lines tend to maintain equal distance apart and never intersect at any point. such lines has peculiar properties and are useful in mathematics.
Since a pair of parallel line do not intersect their is not angle between them.
What happens when a shape is flipped ?Flipping a shape will change the position of the flipped shape to a new one. This activity does not add to the size of a shape or to the property of the shape.
Margot flipping a pair of parallel lines will not add or reduce the number of the parallel lines. It however creates point of intersection between the parallel line and horizontal line crossing the parallel line.
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4.05 repeating as a mixed number
4.05 with (05) repeating if converted to a fraction or mixed number will be
[tex]4\frac{5}{99}[/tex].
As per the question statement, we are provided with a repeating decimal, 4.05 with (05) repeating.
We are required to convert the repeating decimal into a mixed number.
To solve this question, we need to know the formula to convert any repeating decimal number to a fraction which goes as:
[tex]\frac{[(DN*F)-NRF]}{D}[/tex]
Where, DN denoted the concerned Decimal Number,
(F = 10) if one repeating is number, 100 if two repeating numbers, 1000 if three repeating numbers and so on.
NRP denotes the Non-repeating part of decimal number.
And, D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, and so on, similar to F.
Then, using our given data in the above formula, we get
4.05 with (05) repeating = [tex]\frac{(4.05*100)-4}{99}=\frac{(405-4)}{99}=\frac{401}{99}=4\frac{5}{99}[/tex].
Repeating Decimal: A repeating decimal, also called as Recurring Decimal, is a decimal number that consists of digits repeating after a fixed interval after the decimal point.To learn more about Repeating Decimal, click on the link below.
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please hurry I really need help!
13. The table shows the times of runners completing a
marathon. To qualify for the next marathon, a
runner's time must be less than 3 hours. Which
runners qualify?
Cho
Kevin
Runner
Ojas
Sydney
Time (h)
3-1/
3.2
8
30
13
360
3-
Answer:
Step-by-step explanation:
the answer is 30
What is the remainder when f(x) = x4 + 7x3 + 17x2 + 20x is divided by x2 + 4?
a
\large x^2+13x+7+\frac{-52}{x^2+4}
b
\large x^2+7x+\frac{13x-8}{x^2+4}
c
\large x^2+7x+13+\frac{5x-52}{x^2+4}
d
\large x^2+1+\frac{1}{x^2+4}
The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4) so none of the given option is correct.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Given the dividend f(x)= x⁴ + 7x³ + 17x² + 20x and diviser x² + 4
The first time it will go to x²
Then,
Quotient = x²
Remainder = 7x³ - 13x²
The second time goes to 7x
Quotient = 7x
Remainder = -13x² - 28x
The third time it is not divisible so (-13x² - 8x)/(x² + 4) will be the reminder.
Together it is x² + 7x + (-13x² - 8x)/(x² + 4).
Hence "The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4)".
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express 2^6 × 2^2 in the form 8^p
The value of the expression 2^6 × 2^2 is 8^2 * 4
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?The expression is given as
2^6 × 2^2
Apply the product law of indices to the above expression
So, we have
2^6 × 2^2 = 2^(6 + 2)
Evaluate the sum in the above expression
So, we have
2^6 × 2^2 = 2^8
Expand the expression
So, we have
2^6 × 2^2 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
This gives
2^6 × 2^2 = 8 * 8 * 4
So, we have
2^6 × 2^2 = 8^2 * 4
Hence, the value of the expression 2^6 × 2^2 is 8^2 * 4
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what is the answer to 5g/8-1/2=-3
plssss help
Answer:
g = -4
Step-by-step explanation:
Hope this helps :)
x^3=-115 pleasess i need the answer now
Answer:
x = -∛115
Step-by-step explanation:
x^3 - (-115) = 0
= x^3 + 115
Factoring
(a+b) • (a^2-ab+b^2) =
a^3-a^2b+ab^2+ba^2-b^2a+b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=
a^3+0+0+b^3=
a^3+b^3
(115 isn't a cube.)
Polynomial roots
P: -1, -5, -23, -115, 1, 5, 23, 115
Q: 1
P/Q: -1, -5, -23, -115, 1, 5, 23, 115
Divisor(s): None
In these sets of data, there are no rational roots shown.
Step-by-step explanation(part 2):
x^3 + 115 = 0
x^3 = -115
x = ∛-115
Negative numbers will always have real cube roots.
∛ -115 = ∛ -1 × 115 = ∛ -1 × ∛ 115 = (-1) × ∛ 115
Therefore,
x = -∛115
First try was inco
Lemon earns a 3.2% commission as a salesperson. She sold a drone
for $146.97. What is the amount of Lemon's commission? Round your
answer to the nearest penny.
label required
The amount of Lemon's commission is $4.7
According to the question we have been given that
Commission earned by Lemon = 3.2%
Selling price of drone which is sold by Lemon = $146.97
We need to find the amount of commission she earned by selling the drone.
The formula to be used to find the amount of commission is
= percentage of commission * selling price
putting the required value we get
= 3.2% of $146.97
here 'of' is denoted as multiplication
thus, =0.032 * 146.97
= $4.7
Hence the amount of Lemon's commission is $4.7
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Suppose that a single die with 6 sides (numbered 1, 2, 3, ... , 6) is rolled twice. what is the probability that the sum of the two rolls equals 5 ?
The probability that the sum of the two rolls equals 5 is 1/16.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given a single die with 8 sides (numbered 1, 2, 3, ..., 8) is rolled twice, the total outcome will be:
Total outcome = 8^2
Total outcome = 64
For the sum of two rolls, the expected outcome will be:
E = {(1, 4), (4, 1), (3, 2), (2, 3)}
n(E) = 4
Pr(sum of the two rolls is 5) = 4/64
Pr(sum of the two rolls is 5) = 1/16
Hence the probability that the sum of the two rolls equals 5 is 1/16
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Land's bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 8 sales receipts for mail-order sales results in a mean sale amount of $61.80 with a standard deviation of $17.75. A random sample of 13 sales receipts for internet sales results in a mean sale amount of $77.40 with a standard deviation of $29.75. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
A. Find the critical value that should be used in constructing the confidence interval. B. Find the standard error of the sampling distribution to be used in constructing the confidence interval.
C. Construct the 80% confidence interval.
The assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.
What is a random sample?A simple random sample (or SRS) in statistics is a subset of individuals (a sample) chosen at random from a larger set (a population) with the same probability. It is the process of selecting a sample at random.To assume that the population variances are not equal and that the two populations are normally distributed:
Given:
n1 = 11 sample sizex1 = 79 for the sample means1 = 18.25 standard deviationn2 = 18 sample sizex2 = 96.70 for the sample means2 = 20.25 standard deviationSo, df = n1 + n2 - 2; 11 + 18 - 2 = 27.
T critical = T0.01, 27 = 2.473
Let,
S = sqrt[(s1²/n1) + (s2²/n2)]S = sqrt[(18.25^2 / 11) + (20.25^2 / 18)]S = 7.284Then,
(μ1 - μ2) = (x1 - x2) ± T critical × S(μ1 - μ2) = (79 - 96.70) ± 2.473*7.284(μ1 - μ2) = - 17.7 ± 18.013332Now,
-17.7 - 18.013332 ; - 17.7 + 18.013332−35.713332 ; 0.313332Therefore, the assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.
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What is the difference between 0.2 and 0.2 repeating? How can you operate with both 0.2 and 0.2 repeating? Will the results from operating with the two rational numbers be the same or different? Provide Justification and examples to prove your reasoning.
The difference between 0.2 and 0.2 repeating is that 0.2 is that rational number and 0.2 repeating is the rational number.
What is defined as the rational and irrational numbers?Irrational numbers are real numbers that can't be depicted as a ratio-like fraction, p/q, where q and p are integers. In other words, irrational numbers are real numbers which are not rational numbers.Rational numbers are written in the form p/q, where p and q are any integer and q 0 respectively.Q represents the set of rational numbers. A rational number is one that can be demonstrated as a fraction with both the numerator and denominator being integers.For the two given values;
0.2 is the rational number as it can written in the fraction form as;
0.2 = 2/10
0.2 = 1/5 which is in the p/q form.
For the value of 0.2... repeating is also the rational number as it can be also written in the form of p/q.
0.2... = 0.2 bar is the correct representation.
Therefore, the number 0.2 and 0.2 repeating are the rational numbers.
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The recommended mass m of a baseball is 145 grams. The actual mass is allowed to vary by up to 2 grams. What are the minimum and maximum allowed baseball masses?
The minimum and maximum allowed baseball masses are 143 grams and 147 grams
What are the minimum and maximum allowed baseball masses?The given parameters are
Mass = 145 grams
Vary = 2 grams
This means that the allowed baseball masses are
Allowed baseball masses = Mass ± Vary
This gives
Allowed baseball masses = (145 - 2, 145 + 2) grams
Evaluate
Allowed baseball masses = 143 grams, 147 grams
Hence, the minimum and maximum allowed baseball masses are 143 grams and 147 grams
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,-1) and (-9,3).
Answer: Determine the mid-point.
Determine the slope between the two points.
The slope of perpendicular is negative reciprocal
Use slope and mid-point is point slope form.
Step-by-step explanation:
What is the slope of the line? Coordinate grid ranging from negative five to five on the x and y axes. A line passes through points (negative two, one) and (two, negative one). Responses −12 negative fraction 1 over 2 end fraction 2 2 12 1 half −2
The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
The Slope(m) of the line is defined as the change in y coordinate with respect to change in x coordinate ,
The Slope(m) of line passing through the points A(a,b) and B(c,d) is calculated using the formula
m = (d-b)/(c-a)
In the question
it is given that the line passes through the points (-2,1) and (2,-1) .
name the points as A(-2,1) and B(2,-1) .
the values are a=-2 , b=1 , c=2 , d=-1 .
Substituting the values in the formula of Slope we get
m = (-1-1)/(2-(-2))
= -2/(2 + 2)
= -2/4
= -1/2
Therefore , the slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
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Answer:
Step-by-step explanation:
The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
Your bank offers you a 36-month, 3 pr car loan for a $50000 new mercedes slk300 roadster. what will your monthly payment be?
The monthly payment will be $1454.06048
You can calculate the Car Loan EMI Amount with the help of the mathematical formula: EMI Amount = [P x R x (1+R)^N]/[(1+R)^N-1] , where P, R, and N are the variables. This also means that the EMI value will change, each time you change any of the three variables. Let’s discuss these three variables in detail.
‘P’ stands for the Principal Amount. It is the original loan amount given to you by the bank on which the interest will be calculated.
‘R’ stands for the Rate of Interest set by the bank.
N is the number of years given for the repayment of the loan. As you must pay the EMIs each month, the duration is calculated in the number of months.
Here , P=$50000,R=3/12/100=0.0025,N=36 Months.
EMI=[50000 x 0.0025 x (1+0.0025)^36]/[(1+0.0025)^36-1]
= $1454.06048
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Find the greatest common factor for each list of numbers 12,18,26,32
Simplify the radical expression that does NOT simplify to 10.
Answer:
A.
Option A√10 ≈ 3
2 × 3 ≈ 6
Option B√25 = 5
√4 = 2
5 × 2 = 10
Option C[tex]\frac{300}{3}=100\\\sqrt{100}\\100=10^2\\\sqrt{10^2}\\\sqrt{10^2}=10[/tex]
Option D[tex]1000=10^3\\\sqrt[3]{10^3}\\\sqrt[3]{10^3}=10(\mathrm{Radical\:rule)}\\[/tex]
Thus,
option A. is correct.
Solve the quadratic equation by completing the square.
x²+18x+79=0
[tex]x^2 + 18x=-79 \\ \\ x^2 + 18x+81=2 \\ \\ \boxed{(x+9)^2=2} \\ \\ x+9=\pm \sqrt 2 \\ \\ x=-9 \pm \sqrt{2} \\ \\ \boxed{x=-9+\sqrt{2}, -9-\sqrt{2}}[/tex]
3. Solve the formula v + f -e = 2 for e
O Ae-v-f-2
O BC v+f-2
O ce-v-f+2
O De-u+f+2
Answer:
B is the correct answer.
Step-by-step explanation:
Add -2+e to both sides
v + f − e -2+e = 2 -2+e
Which will give you v + f -2 = e.
Dilate the figure by the scale factor. Then enter the new coordinates. A(-3,1) C(0,-4) B(2,4) K=7 A'([?], []) B'(11) C'([],[])
The new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).
Dilating the given triangle by the scale factor means multiplying each coordinate by the given scale factor.
Given coordinates are A(-3, 1), B(2, 4), and C(0, -4).
The scale factor k = 7.
Let, the new coordinate obtained by dilating A with scale factor k be A'.
Then x-coordinate of A' = k × x-coordinate of A
⇒ x-coordinate of A' = 7 × (-3)
⇒ x-coordinate of A' = -21
And y-coordinate of A' = k × y-coordinate of A
⇒ y-coordinate of A' = 7 × 1
⇒ y-coordinate of A' = 7
So, A' → (-21, 7)
Let, the new coordinate obtained by dilating B with scale factor k be B'.
Then x-coordinate of B' = k × x-coordinate of B
⇒ x-coordinate of B' = 7 × 2
⇒ x-coordinate of B' = 14
And y-coordinate of B' = k × y-coordinate of B
⇒ y-coordinate of B' = 7 × 4
⇒ y-coordinate of B' = 28
So, B' → (14, 28)
Let, the new coordinate obtained by dilating C with scale factor k be C'.
Then x-coordinate of C' = k × x-coordinate of C
⇒ x-coordinate of C' = 7 × 0
⇒ x-coordinate of C' = 0
And y-coordinate of C' = k × y-coordinate of C
⇒ y-coordinate of C' = 7 × -4
⇒ y-coordinate of C' = -28
So, C' → (0, -28)
Refer to the image attached for the new triangle formed.
Therefore, the new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).
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If I buy a disc that costs $16.30 but there's a 10% discount how much I'm I going to pay
Answer:
$14.67
Step-by-step explanation:
The value of the discount is,
→ (10/100) × 16.30
→ 0.1 × 16.30
→ $1.630
Then the amount he should pay is,
→ 16.30 - 1.630
→ $14.67
Hence, he must pay $14.67.
Answer:
=14.67
Step-by-step explanation:
0.10×16.30=1.63 or
16.30-1.63=14.67 or[tex]\frac{1467}{100}[/tex]
i
answer the questions on the pdf
1. true or false. if false, correct the statement to make it true. explain ur reasoning
If f(x) = x³, then -4f(x - 1) + 2 can be written as -4(x3 − 1) + 2
pls!!!! asap!!!
Answer: False
The correct expression is -4(x-1)^3+2
====================================================
Work Shown:
[tex]f(x) = x^3\\\\f(x-1) = (x-1)^3\\\\-4f(x-1) = -4(x-1)^3\\\\-4f(x-1)+2 = \boldsymbol{-4(x-1)^3+2}\\\\[/tex]
So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3
Side note: (x-1)^3 expands to x^3-3x^2+3x-1
Which relationships are likely to have a positive association? select all that apply.
a. the distance traveled on a trip and the travel time
b. the distance remaining on a trip and the travel time
c. the amount of money spent and the number of shirts bought
d. the height of an eighth- grade student and the time to complete a puzzle
e. the amount of money owed on a computer and the time making payments
would be great if someone helped :))
The relationships
a. the distance traveled on a trip and the travel time
c. the amount of money spent and the number of shirts bought
are have the positive associations.
Positive associations:
Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase.
Given,
Here we have the following relationships,
a. the distance traveled on a trip and the travel time
b. the distance remaining on a trip and the travel time
c. the amount of money spent and the number of shirts bought
d. the height of an eighth- grade student and the time to complete a puzzle
e. the amount of money owed on a computer and the time making payments
We need to find the positive associations in it.
Based on the definition of positive association,
The options (a) and (c) are the relationships that are in positive association.
Because while we look into the option (a),
When the traveling distance is increased then the time taken for it also increased.
Similarly in option (c),
While we increase the amount then the number of shirt we brought will also be increased.
The other options are not fit in this case.
So, option (a) and (c) are in positive association.
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The following are the weights of 10 young dogs, in pounds:
7, 5, 11, 8, 14, 19, 16, 15, 13, 27
what proportion of the measurements lie in the interval?
The proportion which falls within the range is 0.9.
Given that data:
x : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27
Mean = Σx / n
Using calculator :
Mean (m) = 13.5
Standard deviation (s) = 6.433
Proportion that lies in mean ± 2s
Lower = Mean - 2s
13.5 - 2(6.433) = 0. 632
Upper = Mean + 2s
13.5 + 2(6.433) = 26.376
Mean ± 2(sd) = (0.632, 26.276)
The only digit from the data which falls outside the defined range = 27
Proportion within interval = 9 / n
Proportion which falls within range = 9/10 = 0.9
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A right triangle has side lengths 8, 15, and 17 as shown below.
Use these lengths to find sin.X, tanX, and cos.X.
Answer:
please demonstrate how tha triangle looks like
Value of x
Pls show steps
Answer:
x = 18
Step-by-step explanation:
Vertical angles are congruent.
4x + 3 = 75 Subtract 3 from both sides of the equation
4x = 72 Divide both sides by 4
x = 18
Name a pair of adjacent complementary angles.
4. Name a pair of adjacent supplementary angles.
5. Name a pair of nonadjacent complementary angles.
6. Name a pair of nonadjacent supplementary angles.
3. A pair of adjacent complementary angles is: ∠LJM and ∠NJM.
4. A pair of adjacent supplementary angles is: ∠KJL and ∠NJL
5. A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP
6. A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM
What are Complementary and Supplementary Angles?Supplementary angles have a sum that is equal to 180 degrees, while complementary angles equal 90 degrees.
What are Adjacent Angles?Angles that share the same side and vertex are adjacent angles.
3. m∠LJM + m∠NJM = 56 + 34 = 90°
A pair of adjacent complementary angles is: ∠LJM and ∠NJM.
4. m∠KJL + m∠NJL = 90 + (56 + 34) = 180°
A pair of adjacent supplementary angles is: ∠KJL and ∠NJL
5. m∠EGF + m∠NJP = 41 + 49 = 90°
A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP
6. m∠FGH + m∠LJM = 124 + 56 = 180°
A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM
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two students are running on a circular path. it takes the first student 25 minutes to complete one lap, and it takes the second student 30 minutes to complete one lap. if they both start at the same time and run in the same direction, when will they meet each other at the starting point? 175 minutes 150 minutes 25 minutes 5 minutes
150 Minutes
We need to find the Lcm of 25 and 30
Student 1 and Student 12 start from the same point, at same time and in same direction. So they meet again after lcm of the times taken by them individually.
What is LCM?
Least common multiple
To get the LCM we have to factorize the numbers,
25=5*5
30=2*5*3
LCM of 25 and 30 is 5*2*3*5 is 150
Therefore in 15 minutes they meet each other at the starting point
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Answer: 175
Step-by-step explanation:
Which of the following values is less than −|62|?
Answer:
-63, -90, -1924. -|63|, etc
Step-by-step explanation:
