Answer:
-[tex]\sqrt{3}[/tex]/2
Step-by-step explanation:
cos is negative in quad II
cos(210)= -cos(30) = -[tex]\sqrt{3}[/tex]/2
Select the correct answer from each drop-down men
menu.
What is the distance and midpoint between points D and E on the number line?
D
E
-4 -3 -2 -1 0 1 2 3 4 5
distance =
midpoint =
Reset
Next
The midpoint is M = 0.6 and the distance is D = 4.2
Given data ,
The distance between points D and E on the number line
D = 4.2
Now , the first point D = -1.8
And , the point E = 2.4
And , the distance D = 2.4 - 1.8 = 4.2 units
Thus, the midpoint between points D and E on the number line = 0.6
Hence, the distance and midpoint between points D and E on the number line 4.2 and 0.6
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The complete question is attached below :
What is the distance and midpoint between points D and E on the number line?
Find the square root of 1681
Answer: The square root of 1681 is 41.
Answer:
41
Step-by-step explanation:
It is 41
41 * 41 = 1681
41 ^ 2 = 1681
14. Jill tossed a coin three times. Draw a tree diagram to represent the sample space.
Here is a tree diagram to represent the sample space of Jill tossing a coin three times:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
What is sample space?The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.
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Consider the five points
(0,0),(0,5),(6,0),(3,4),(−1,8)
in
R
2
and name them
(x
i
,y
i
)
for
i=1,…,5
. The objective is to find two coefficients
a,b∈R
such that the boundary of the ellipse
ax
2
+by
2
=1
is as close to the above 5 points as possible. To this end, we define the error function: \[ f(a, b)=\sum_{i=1}^{5}\left(a x_{i}^{2}+b y_{i}^{2}-1\right)^{2} \] Calculate the optimal values of
(a,b)
by finding the local minima of the error function
f(a,b)
.
The optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
To find the optimal values of (a,b), we need to minimize the error function f(a,b). We can do this by taking partial derivatives of f(a,b) with respect to both a and b, and then setting them equal to zero:
∂f/∂a = 2∑([tex]x_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex]+ b [tex]y_{i}^{2}[/tex] - 1) = 0
∂f/∂b = 2∑([tex]y_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex] + b [tex]y_{i}^{2}[/tex] - 1) = 0
We can simplify these equations by defining the following sums:
Sxx = ∑[tex]x_{i}^{4}[/tex]
Syy = ∑[tex]y_{i}^{4}[/tex]
Sxy = ∑[tex]x_{i}^{2}y_{i}^{2}[/tex]
Sx = ∑[tex]x_{i}^{2}[/tex]
Sy = ∑[tex]y_{i}^{2}[/tex]
Using these sums, we can rewrite the partial derivatives as:
∂f/∂a = 2(aSx² + bSxy² - Sx)
∂f/∂b = 2(aSxy² + bSy² - Sy)
Setting these equal to zero and solving for a and b, we get:
a = (SySx - Sxy²) / (SxSyy - Sxy²)
b = (SxSy - Sxy²) / (SxSyy - Sxy²)
Plugging in the values for Sxx, Syy, Sxy, Sx, and Sy, we get:
a = 0.7205
b = 0.5369
Therefore, the optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
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Danielle got 23 out of 25 points on her math test. What percent of questions did she get correct?
To calculate the percentage of questions Danielle got correct on her math test, we can divide the number of questions she got correct by the total number of questions on the test and then multiply by 100. In this case, Danielle got 23 out of 25 questions correct, so we can calculate her percentage as follows: (23/25) * 100 = 92%. Therefore, Danielle got 92% of the questions correct on her math test.
Percent = amount per 100
23/25 = amount per 25
25 x 4 = 100
23 x 4 = 92
92/100 = 92%
Answer = 92%
Hope this helps!
ACTIVITY 3: Solve the following equations.
The value of x in each expressions are:
1) 6
2) 1
3) -3
4) -21
5) -4
We have,
The expressions are:
1)
[tex]3^x = 9^3[/tex]
And,
9³ = (3²)³ = [tex]3^6[/tex]
So,
[tex]3^x = 3^6[/tex]
And,
x = 6
2)
[tex]4^{x + 1}[/tex] = 16
16 = 4²
So,
x + 1 = 2
x = 2 - 1
x = 1
3)
[tex](1/3)^x[/tex] = 27
27 = 3³
So,
[tex]3^{-1x}[/tex] = 3³
-x = 3
x = -3
4)
[tex]5^{3x}[/tex] = [tex]25^{x - 1}[/tex] =
[tex]5^{3x}[/tex] = [tex]5^{2x - 21}[/tex]
3x = 2x - 21
3x - 2x = -21
x = -21
5)
[tex]2^{-x}[/tex] = 16
16 = [tex]2^4[/tex]
So,
-x = 4
x = -4
Thus,
The value of x in each expression are:
1) 6
2) 1
3) -3
4) -21
5) -4
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If I save 300 a week how much will I have at the end of the year?
15,653 much will I have at the end of the year in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
Earning $300 a week equals $15,587 a year. This result is obtained by multiplying the base salary by the number of hours, weeks, and months worked in a year, assuming a 40-hour work week.
15,653 much will I have at the end of the year in.
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1. Rachel has $60 to spend
on lunches this week. On
Monday she spent $5, and
on Tuesday she spent $7.
Which inequality can be
used to find, x, the amount
of money she can spend
the rest of the week?
Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.
Answer:
86.75
Step-by-step explanation:
Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.
Course gradeThe grade for the course, with fourth test score x, will be ...
0.20(63.5 +76 +87) +0.40x = 80
0.40x +45.3 = 80
Solving for x, we get ...
0.40x = 34.7 . . . . subtract 45.3
x = 86.75 . . . . . . . divide by 0.4
The minimum score you need on the fourth test is 86.75.
<95141404393>
Solve the radical equation.
√3x-2-√11+x= -1
Answer:
[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]
Stephanie bought two rugs. One rug is 15 feet long, and the other rug is 142 feet long. Each rug has a width of 10 feet.
What is the total area in square feet of the two rugs?
A 175 ft²
B 155 ft²
C 147.5 ft²
D 302.5 ft²
*please help me
The total area of the two rugs in square feet is calculated as: 1570 ft² (none of the options are correct).
How to Find the Total Area of the Rug?To find the total area of the two rugs, we first need to calculate the area of each rug by multiplying its length and width.
Area of the first rug = 15 ft x 10 ft = 150 ft²
Area of the second rug = 142 ft x 10 ft = 1420 ft²
Now, we can find the total area by adding the area of both rugs:
Total area = 150 ft² + 1420 ft² = 1570 ft²
Therefore, the answer is not one of the options provided.
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I can’t figure out what is correct to get about 8
Step-by-step explanation:
Going down the list :
8.98 rounds to 9
6.64 rounds to 7
7.03 rounds to 7
8.52 rounds to 9
7.59 rounds to 8
If the first number past the decimal point >= 5 round the units up
o/w leave the units as they are
Help please!!!!
Whoever answers right gets brainliest!
Which linear equation is represented in the graph?
*If correct giving brainlyest*
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
Answer:
C
x1=2
-2(2)+1=3
which is the answer for y1
find x, y, and z
will give brainly
Answers:
[tex]z=12\sqrt{3} \\y=12\\x=12\sqrt2[/tex]
if you have the answer please reply im having trouble need the steps.
Over a given period of time, Seth sold more water bottles than Hayden.
To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.
We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:
Average daily sales rate for Seth = (10+20+30+40)/4 = 25
The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.
Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.
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Imagine Math simple interest
The simple interest which has the least amount of interest is investment of $ 2000 at 10 % for 3 years
Given data ,
SI is the simple interest, P is the principal amount, r is the annual interest rate, and t is the time in years.
Given that P = 2000, r = 10% = 0.1, and t = 3 years, we can calculate the simple interest as:
SI = 2000 x 0.1 x 3 = 600
Hence , the simple interest earned on an investment of $2000 for 10% at SI for 3 years is $600
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Apply the United States rule to determine the balance at maturity and the total interest paid if the borrower makes two partial payments and the remainder of the loan is paid at maturity.
Principal $1450
Interest Rate % 15.0
Loan Length (Days) 280
Partial Payment
$5800.00
$4350.00
Payment on Day #
112
196
Answer: The United States rule is a method for calculating interest and balances on loans that have partial payments during their term. The rule assumes that each partial payment is applied to the interest first, then to the principal. Here's how to use the United States rule to calculate the balance and interest for this loan:
Calculate the daily interest rate by dividing the annual interest rate by 360 (the number of days in a standard year for most loans).
Daily Interest Rate = 15.0% / 360 = 0.04167%
Calculate the interest due for the first partial payment of $5800 made on day 112. Since this payment is larger than the remaining principal, it will pay off the loan entirely and no interest will accrue beyond this date.
Days between start of loan and first payment = 112 daysInterest due on first payment = (1450 x 0.04167% x 112) = $8.10Principal remaining after first payment = $0.00
Calculate the interest due for the second partial payment of $4350 made on day 196.
Days between first payment and second payment = 84 daysInterest due on second payment = (0 x 0.04167% x 84) = $0.00Principal remaining after second payment = $0.00
Calculate the interest due on the remaining principal at maturity (day 280).
Days between second payment and maturity = 84 daysInterest due at maturity = (0 x 0.04167% x 84) = $0.00
Add up the interest due from each period to get the total interest paid over the life of the loan.
Total interest paid = $8.10 + $0.00 + $0.00 = $8.10
Add up the principal amounts from each payment to get the total amount paid.
Total amount paid = $5800.00 + $4350.00 = $10,150.00
Subtract the total amount paid from the original principal to get the balance at maturity.
Balance at maturity = $1450.00 - $10,150.00 = -$8700.00 (which means the lender owes the borrower this amount)
Therefore, the balance at maturity is -$8700.00 (meaning the lender owes the borrower this amount) and the total interest paid over the life of the loan is $8.10.
cost function definition
A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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Please if you know the answer tel me thank you.
Answer:
Step-by-step explanation:
(a) currently the mode is pink. Mode means which one occurs the most.
If you take a pink out. Now P=3 G=3 and Y=3
(a) PINK
(b) Yellow, you want yellow to be the most/mode so they put a yellow back in
Please help me with this
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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100 Points! Algebra question. Please show as much work as possible. Thank you!
The first term a₁ of the geometric series is equal to 121.5
How to evaluate for a₁ of the geometric seriesFor a geometric series when the common ratio |r| > 1, then we use the formula for the sum of nth term:
Sₙ = a(rⁿ - 1)/(r - 1)...(1)
The nth term aₙ = arⁿ⁻¹
Thus for Sₙ = 4860 and aₙ = 3280.5, the value of a₁ can be derived as follows:
aₙ = arⁿ⁻¹
aₙ = arⁿ/r = 3280.5
rⁿ = a(r × 3280.5)/a
rⁿ = 9841.5/a
putting 9841.5/a for rⁿ in equation (1) we have;
Sₙ = a[(9841.5/a) - 1]/(r - 1)
Sₙ = (9841.5 - a)/(r - 1)
recall Sₙ = 4860 and r = 3 so;
(9841.5 - a)/2 = 4860
a = 9841.5 - 2(4860)
a = 121.5
Therefore, the first term a₁ of the geometric series is equal to 121.5
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Duante is wrapping a present that is 1 foot wide, 10 inches long, and 8 inches high. What is the minimum amount of
wrapping paper he will need?
592 square inches is the minimum amount of wrapping paper Duante needed.
Duante will need a minimum of 592 square inches of wrapping paper.
Lets convert the dimensions to the same units.
Since there are 12 inches in a foot, the dimensions are:
Width = 1 foot = 12 inches
Length = 10 inches
Height = 8 inches
The rectangular box is known as a cube
The surface area of a b=cuboid is given by SA = 2lw + 2lh + 2wh
where l is length, w is width and and h is the height of the cuboid
Substituting the given values, we get:
SA = 2(10)(12) + 2(10)(8) + 2(12)(8)
= 240 + 160 + 192
= 592
Therefore, Duante will need a minimum of 592 square inches of wrapping paper.
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Need help with these!!
The decimal used to figure the price of their clothing is 2.1
The improvement in Larry's test score written as a decimal is 1.52
How to write in decimals?Markup = 210%
= 210/100
= 21/10
= 2.1
Larry's increased test score percentage = 152%
= 152/100
= 1.52
In conclusion, the price of clothing and Larry's test score in decimals is 2.1 and 1.52 respectively.
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3. Arthur's mother is a mechanical engineer. She is designing
rectangular carts formoving finished goods from a factory's
manufacturing floor to the loading dock, where the goods are placed
on trucks.
She made a drawing showing where the carts must turn from a
hallway 48 inches wide to pass through a doorway 36 inches wide.
The drawing shows the longest cart that will pass through the
doorway.
to manufacturing floor 30 in.
G
E.
to loading dock
B
D
a) What kind of triangles are AABC and ACFD?
cart
36 in.
48 in.
b) In the drawing, one sixth of an inch represents 1 foot. What is the
scale factor of the drawing? Explain.
a) is Right angle Triangles both of them
b) The scale factor is 1:2.
How to solveGiven AFD = 90 degrees, So CFD = 90 degrees.
So it a Right Angle Triangle.
Again ABC = 90 degrees, It's also a Right Angle Triangle.
Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees
so if any angle is 90 deg then the other two sum is also 90 deg.
Given the scale Factor, 1/6 inch = 1 foot,
So it is a Reducing Scale so let 'x' be in inches
So the Scale Factor = 1:2
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blank g = blank kg =3/10kg
It should be noted that 3/10 kg to grams will be 300 grams.
How to convert the valueTo convert 3/10 kg to grams (g), we can use the following conversion factor:
1 kg = 1000 g
Therefore:
3/10 kg = (3/10) x 1000 g = 300 g
Hence, 3/10 kg is equal to 300 grams (g).
In conclusion, it should be noted that 3/10 kg to grams will be 300 grams.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 3.
The median is the best measure of center, and it equals 19.
An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 12.
First quartile (Q₁) = 17.
Median (Med) = 19.
Third quartile (Q₃) = 20.
Maximum (Max) = 24.
In conclusion, the best measure of center is the median and it is equal to 19.
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Point F is at [-10, 12] and point G is at [18, 12]
The midpoint of the line segment FG is the point (4, 12).
What is midpoint?In geometry, the midpoint of a line segment is the point that is exactly halfway between the endpoints of the segment. It is the point that divides the segment into two congruent segments.
The formula for finding the midpoint of a line segment with end points (x₁, y₁) and (x₂, y₂) is:
Midpoint = [(x₁ + x₂)÷2, (y₁ + y₂)÷2]
So, the midpoint of the line segment with endpoints F(-10, 12) and G(18, 12) can be found as:
Midpoint = [(-10 + 18)÷2, (12 + 12)÷2]
= [8÷2, 24÷2]
= [4, 12]
Therefore, the midpoint of the line segment FG is the point (4, 12).
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Find the sine, cosine, and the tangent of the acute angle A of the triangle. Express each answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
sina=12/20=0.6
cosa=16/20=0.8
tana=0.6/0.8=0.75