The required value of function F(x), when x=18 is -2
A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table
x = 2 3 5 6 7 8 9
F(x) = 21 10 10 8 9 5 6
What is line?
line, is curve showing the shortest distance between 2 points.
Now, putting x = 18 in f(x) ≈ −0.86x + 13.5
f(x) ≈ −0.86(18) + 13.5
= -1.98
≅ -2 (approximation)
Thus, the required values of x=18 in a line of best fit is -2.
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Xin and Yvonne are standing 42 m apart. If they walk towards each other, they will meet after 12 seconds. If they walk in the same direction, Yvonne will catch up with Xin after one minute. It is given that Xin and Yvonne walk at constant speeds ofx m/s and y m/s respectively.
Form a pair of simultaneous equations in x and y.
Answer:
12(x+y)=42
60(y-x)=42
Step-by-step explanation:
12(x+y)=42 (12 seconds, x+y speed each second, 42 metres)
60(y-x)=42 (1 minute = 60 seconds, x-y speed each second, 42 metres)
31) Alana ordered jeans ($28) and a sweater ($35) from a catalog. The sales tax is 8%. The shipping charges came
to $6.58. What was the total amount she was charged?
O a.) $74.62
Ob.) $77.62
Oc.) $75.62
Answer:
a) $74.62
Step-by-step explanation:
Cost of both clothes = 28+35 = $63
Tax = 0.08*63 = $5.04
Shipping: $6.54
Add: 63+5.04+6.58 = 74.62
scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use empirical rule to determine the following:
a) what percentage of people has an IQ score between 61 and 139?
b) what percentage of people has IQ score less than 87 or greater than 113?
c) what percentage of people has an IQ score greater than 113?
Using the Empirical Rule, the percentages are given as follows:
a) 99.7%.
b) 32%.
c) 16%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Item a:
61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.
Item b:
87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.
Item c:
Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.
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Solve: −(23a−13)+53a=−4
Answer:
a = -17/30
Step-by-step explanation:
So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.
Original Equation:
-(23a - 13) + 53a
Distribute negative sign
-23a + 13 + 53a
Group like terms:
(-23a + 53a) + 13
Simplify
30a + 13 = -4
Subtract 13 from both sides
30a = -17
Divide both sides by 30
a = -17/30
PLEASE HELP!!!!!!!!!!
Step-by-step explanation:
[tex] = - \frac{5}{9} - ( - \frac{14}{15} )[/tex]
[tex] = - \frac{5}{9} + \frac{14}{15} [/tex]
[tex] = - \frac{5 \times 5}{9 \times 5} + \frac{14 \times 3}{15 \times 3} [/tex]
[tex] = - \frac{25}{45} + \frac{42}{45} [/tex]
[tex] = \frac{ - 25 + 42}{45} [/tex]
[tex] = \frac{42 - 25}{45} [/tex]
[tex] = \frac{17}{45} [/tex]
Umm I don’t have 10 as a option
Answer: Look for the closes thing to 10
Step-by-step explanation:
-76 * a number minus 61 is equal to -89 less than the number
Answer: -211/76
Step-by-step explanation:
to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:
we can replace "a number" for a variable such as x
this gives:
-76·x-61=x+89
now all you have to do is solve the equation and you're done!
a2 − 6) and (a2 + 4) are the factors of
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Example: x²+3x+5 is a polynomial.
The polynomial whose factors are (a²-6) and (a²+4) is,
P(x) = (a²-6)(a²+4)
= a⁴ + 4a² - 6a² - 24
= a⁴ - 2a² - 24
Hence, The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
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Step 6: Patterns can provide a clear understanding of mathematical relationships. This can be seen very clearly in the form of multiplication tables. 3 x 2; 3 x 3; 3 x 4 are clearly examples of the relationship pattern found in multiplication. Provide two more examples of relationship patterns found in mathematics. Describe the pattern in each case. (NB: Do not use the multiplication tables). (8) Step 6 : Patterns can provide a clear understanding of mathematical relationships . This can be seen very clearly in the form of multiplication tables . 3 x 2 ; 3 x 3 ; 3 x 4 are clearly examples of the relationship pattern found in multiplication . Provide two more examples of relationship patterns found in mathematics . Describe the pattern in each case . ( NB : Do not use the multiplication tables ) . ( 8 )
Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.
What are mathematical patterns?Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.
Mathematical patterns are usually abstract.
What is a geometric sequence?A geometric sequence is a sequence of non-zero numbers. The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.
A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.
What is a Fibonacci sequence?
A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.
The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.
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What is √200in simplest form?
Answer:
10√2
Step-by-step explanation:
The square root of 200 in its simplest radical form is 10√2.
If we know the prime factorization of a number, we can write the radical form of the square root of that number. As a result, the prime factorization of 200 is 2 × 2 × 2 × 5 × 5.
As a result, the square root of 200 in the simplest radical form should be 10√2.
(3-0/4a)-(10-0.8a). Solve for a
An equation is formed of two equal expressions. The value of 'a' in the given equation is 6.452.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for 'a' as shown below,
[tex]\dfrac{(3-0)}{4a} = (10-0.8a)\\\\\dfrac{3}{4a} = (10-0.8a)\\\\[/tex]
0.75a = 10 - 0.8a
0.75a + 0.8a = 10
1.55a = 10
a = 6.452
Hence, the value of 'a' in the given equation is 6.452.
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Compare the process of solving |x – 1| + 1 < 15 to that of solving |x – 1| + 1 > 15. Check all of the following you included in your response. Both absolute values would need to be isolated first. You would need to write a compound inequality for each. Both compound inequalities would compare x – 1 to –15 and 15. The inequality with “<” would use an “and” statement, while the “>” would use an “or” statement.
The required Comparison of the inequalities are
The |x – 1| + 1 > 15 represents the value of x lies between 13<x<15.The range of values encompassing the region's junction is (-13, 15).
If x is more than or equal to 15, then x-11+1>15 indicates the value of x is greater than or equal to 13. None of the regions in the intersection are empty.What is inequality?When comparing two numbers, an inequality indicates whether one is less than, larger than, or not equal to the other.
We take into account the various variables of the inequality
|x – 1| + 1 > 15
Therefore
|-x-1|+1-1<15-1
|-x-1|-1 <14
13<x<15
The required region lies between the inequality -13 <x< 15.
Simplify the inequality Ix-11+1 > 15 we get,
|x-1|+1 > 15
|x+1| +1-1 >15-1
|x-1| > 14
x> 15
x<-13
If x has a value between -13 and x + 15, then the expression "|x-1|+1+115" is true. The range "(-13, 15)" contains the intersection of the region.If "|x-1|+1>15" then either "x >15" or "x-13" applies to the value of x. This region's intersection is unoccupied.Read more about inequalities
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Which equation is a function of x? x = 5 x = y squared 9 x squared = y x squared = y squared 16
The equation which is a function of x is x²=y.
Given an equation that is a function of x.
A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.
If we input a value of x then we get the output f(x) = y, which is the function of x.
We are given four options out of which we are to pick the one which may be a function of 'x'.
The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.
The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.
The third option is x²=y in which y contains power 1. So, option 3 is correct.
The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.
Hence, the equation which is a function of x is x²=y.
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MATH: FINDING HALF LIFE PT 1
Answer:
15.4 years
Step-by-step explanation:
An investment is doubled when it is twice its initial value. The equation can be solved for the value of t that makes this true.
SetupIn the exponential equation for investment value, the factor y₀ is the initial value of the investment. We want to find t when y = 2y₀.
2y₀ = y₀·e^(0.045t)
SolutionDividing by y₀ gives ...
2 = e^(0.045t)
Taking natural logarithms, we have ...
ln(2) = 0.045t
Dividing by the coefficient of t gives its value:
t = ln(2)/0.045 ≈ 15.4
The investment will be doubled after 15.4 years.
__
Additional comment
The continuously compounded interest rate for this investment is 4.5%. The doubling time is 0.693 divided by this: 0.693/0.045 ≈ 15.4. This relationship holds for any sort of continuous compounding.
If a + a = a then a = 0. prove
a+a=a
→a+a-a=0
→a=0
(proved)
Step-by-step explanation:
[tex]a + a = a[/tex]
[tex]2a = a[/tex]
[tex]2a - a = 0[/tex]
[tex]a = 0[/tex]
Proved.
Solve the inequality.
[tex]5x - 7 \leqslant 13 \\ add \: 7 \: on \: both \: sides \\ 5x - 7 + 7 \leqslant 13 + 7 \\ 5x \leqslant 20 \\ divide \: both \: sides \: by \: 5 \\ \frac{5x}{5} \leqslant \frac{20}{5} \\ x \leqslant 4[/tex]
Interval: (-infinity,4]If f(x) = x³ - 2, find f(3).
[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]
[tex]f(3) = 25[/tex]
Graph the function g.
f(x) = -2(x-4)² +4
g(x) = f(x) - 1
O
Answer:
19
Step-by-step explanation:
fx=16+4
fx=20
gx= 20-1
gx=19
19
The diameter of a circle is 48 meters. What is the angle measure of an arc 17 meters long?
simplest form IXL
Give 3 reason why a rectangle is not a square
Answer:
A square is a rectangle but a rectangle is not a square. A square consists of four sides of equal lengths. A rectangle has two sides shorter than the two other sides.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10< x <22
Using it's concept, the average rate of change of the function over the interval 10 < x < 22 is given by:
[tex]r = \frac{f(22) - f(10)}{12}[/tex]
What is the average rate of change of a function over an interval?It is given by the change in the output divided by the change in input.
Over the interval 10 < x < 22, the outputs are f(10) and f(22), hence the rate of change is given by:
[tex]r = \frac{f(22) - f(10)}{12}[/tex]
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The two lines below are parallel. If the slope of the red line is 3, what is the
slope of the green line?
Trigonometry Maths Question
80 points up for grabs!
Will mark brainliest to whoever answers
Answer:
x = 35.537677791974°
y = 63.434948822922°
Step-by-step explanation:
let x be the measure of the angle of elevation of the sun.
tan(x) = 10/14
Then
x = tan⁻¹ (10÷14) = 35.537677791974°
………………………………………………
let y be the measure of the angle of elevation of the sun
where the shadow decreases to 5m.
tan(y) = 10/5 = 2
Then
y = tan⁻¹ (2) = 63.434948822922°
Answer:
a) 35.54°
b) 63.43°
Given following:
length of pole: 10 meterits shadow: 14 meterDetermining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.
(a)
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{14}[/tex]
[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]
[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]
(b) If the shadow decreases to 5 meter.
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{5}[/tex]
[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]
[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]
5. Kal Tire installs automobile tires on a first-come first-served basis. A random sample of 50 customers experienced an average wait time of 93.7 minutes. Assume that the standard deviation of total wait time for all customers is 20.6 minutes. Determine the margin of error for a 95% confidence interval for this sample.
5.7099 is the margin of error.
What is standard deviation ?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
According to the question,
The standard sampling error of the sample mean is σₓ ,
The sampling distribution is: N (u,σₓ/n)
Therefore,
By using the standard deviation formula:
σₓ = √∑(xi -μ)/N
Where,
∑= population standard deviation
N= the size of the population
xi= each value from the population
μ =the population mean
So ,
σₓ = [tex]\frac{20.6}{\sqrt{50} }[/tex] = 2.913
Since, a = 1- 95% = 0.05
therefore [tex]Z\frac{a}{2}[/tex] = (1-0.005 x 2) = 1.959964
Here, the margin of error for a 95% confidence interval for this sample is given by:
[tex]Z\frac{a}{2}[/tex] * σₓ = 1.959964 x 2.913
= 5.7099
5.7099 is the margin of error for a 95% confidence interval for this sample.
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Pls help
Volume round to tenth
The volume of the cone to nearest tenth is 247. 12 cm ^3
How to determine the volumeNote that the shape is a cone
Volume for a cone =
[tex]\pi \: { {r}^{2} \frac{h}{3} } [/tex]
Given that radius = 5.3cm
height = 8.4cm
Substitute into the formula, we have
Volume = 3.142 × 5.3 × 5.3 × (8.4/3)
Volume = 3. 142× 28.09 × 2.8
Volume = 247. 12 cm ^3
Thus, the volume of the cone to nearest tenth is 247. 12 cm ^3
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A sub sandwich shop offers 22 toppings to choose from. How many ways could a person choose a 4-topping sandwich?
a)26
b)88
c)7,315
d) 175,500
pleaseee help, will mark branliest
There are 7,315 different combinations, thus, the correct option is c
How many combinations are there?
If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:
[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]
In this case we have K = 4 and N = 22, replacing that, we get:
[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]
So there are 7,315 different combinations, thus, the correct option is c.
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How many centimeters in 3.7 kilometers?
Answer:
370,000 centimeters
Step-by-step explanation:
1. There are 1000 meters in a kilometer.
2. 3.7 kilometers x 1000 = 3,700 meters
3. There are 100 centimeters in a meter
4. 3,700 x 100 = 370,000 centimeters
Use the following image to solve the problem
Answer:
The distance is √17.
Step-by-step explanation:
the step is provided in the image....
I hope it was helpful
What is the length of the track, in miles, around turn A? Round your answer to three decimal places.
Answer:
?
Step-by-step explanation:
Please explain-WHAT TRACKS?
Answer:
5.275
Step-by-step explanation:
Got the answer from Emma on Gauth Math
evaluate (-1 - 3²) - 4³/2
Answer:
-42
Step-by-step explanation:
You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.
pls brainliest Hope this helps have a nice day :>
[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]
Calculates 3 to the power of 2 and gets 9.
[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]
Subtract 9 from −1 to get −10.
[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]
Calculates 4 to the power of 3 and gets 64.
[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]
Divide 64 by 2 to get 32.
[tex]\bf{-10-32 }[/tex]
Subtract 32 from −10 to get −42.
[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }