Answer:
r = e or 2.718282
Step-by-step explanation:
a) simplify both sides of the equation
2.718282 = r
b) flip the equation
r = 2.718282
Write each number in standard form.
2. eight and fifty-nine hundredths
3. seven and three thousandths
1
4.3 +2× +4×
1,000
The values given in standard form are 8.59 and 7.003
Writing in standard formThe standard form of a number is a way of writing the number in a form that follows certain rules. Any number that has exponents and decimals is said to be a standard notation.
Given the following statements
eight and fifty-nine hundredths
8 + 59/100
8 + 0.59
8.59
For the expression seven and three thousandths
7 + 3/1000
7 + 0.003
7.003
Hence the values given in standard form are 8.59 and 7.003
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Translate the point (5, -3) 3 units left and 1 unit up.
The image point is located at ____.
Answer:
(2,-2)
Step-by-step explanation:
In the given figure AB = AC, BAD = 50 and AD = AE. find the value of x
Answer:
[tex]x=25^o[/tex]
Step-by-step explanation:
Angle sum of a triangle: [tex]< A + < B+ < C=180^o\\[/tex]
Types of Triangles: Isosceles, Equilateral, Scalene
Given AB = AC are two sides of the big triangle, then ΔABC is Isosceles.
Isosceles triangles are defined to have two equal sides and two equal angles (opposite the congruent(equal) sides).
Also, since ABC is defined as a triangle, BC is a straight line, a.k.a., it is a [tex]180^o[/tex] angle. As the image shows, the line, AD creates a right angle on one side, therefore it creates a right angle([tex]90^o[/tex]) on the other side.
Back to Isosceles Triangles, AD = AE means ΔADE is isosceles and <ADE = <AED
Using the Angle sum formula of a triangle, you can fill in <A, <B, and <C with the following:
<A=[tex]50^o[/tex]
<B=<C=y [This is because <ADE = <AED]
[tex]50^o+2y=180^o\\2y=130^o\\y=65^o[/tex]
Now, this means that <ADE=[tex]65^o[/tex] and <ADC =[tex]90^o[/tex]
<x is better seen as <EDC
<EDC+<ADE=<ADC
Since we know <ADE is 65 and <ADC is 90, we can plug in these to the formula above.
[tex]x+65^o=90^o\\x=25^o[/tex]
Which number sentence is not true?
A) -4.51 4.5
B) |0| < |-45|
C) |45|> 0
D) 14.5| |-45|
One way to simplify an expression containing trigonometric functions is to first write the expression in terms of
---Select---
and
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only.
One way to simplify an expression containing trigonometric functions is to first write the expression in terms of sines and cosines only.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
The law of cosine.In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Similarly, the law of sine can be used to determine the missing side length of a geometric figure with the opposite and hypotenuse side lengths are given:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
In this context, we can reasonably infer and logically deduce that an expression containing trigonometric functions can be simplified by first writing the expression in terms of sines and cosines only.
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A = P(1+r)tn
The formula above is used to calculate compound interest. A represents the amount of money accumulated after n years, including interest; P is the initial principal amount (i.e.,
the initial amount deposited); stands for the annual rate of interest as a decimal; and t
represents the number of years and in the number of times the interest is compounded, per
year. If Serina deposits $500 in an account earning 5% interest compounded semiannually and keeps the money in her account for three years, how much money will she have at the end of the five years? Round your answer to the
nearest dollar.
A $515.00
B $530.00
C $670.05
D$710.10
Answer:
670.05
Step-by-step explanation:
Rounding to the nearest dollar, Serina will have $515 at the end of five years. Therefore, correct option is A.
To calculate the amount Serina will have at the end of five years, we can use the formula for compound interest:
A = [tex]P(1 + r)^{(nt)[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, Serina deposits $500 with an annual interest rate of 5%, compounded semiannually (n = 2), and keeps the money in her account for three years (t = 3).
Plugging in the values, we get:
A = 500(1 + 0.05)⁶
A = 500(1.005)⁶
A ≈ 500(1.030)
A ≈ $515
Therefore, correct option is A.
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aaron, brandon, and clara sit in class so that they are at the vertices of a triangle. it is 15 feet from aaron to brandon, and it is 8 feet from brandon to clara. give the range of possible distance from aaron to clara
The range of distance between Aaron and Clara is 7<d<23.
What is the triangle?Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees. Every triangle has three sides and three angles, which may or may not be the same. In the case of a right triangle, the sides are given special names, with the side opposite the right angle being known as the hypotenuse and the other two sides being known as the legs.The range of possible distance from Aaron to Clara:
15+d > 8 ⇒ d > -78+d > 15 ⇒ d>715+8 > d ⇒ d < 23So, the range is: 7<d<23
Therefore, the range of possible distance from Aaron to Clara is 7<d<23.
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how to write 673465 in standerd form
6 hundred and 73 thousand and 65..
17. In the number below,
which digit is in the
thousandths place?
7459.31890
Answer:
hey from where are you...
2) a number v divided by 12
1) determine the result when 2x^2+4x+2 is subtracted from 4x^2-8x+3
Answer:
[tex]2x^2 - 12x + 1[/tex]
Step-by-step explanation:
Hello!
Given the expression: [tex]4x^2 - 8x + 3 - (2x^2 + 4x + 2)[/tex]
Simplify by combining like terms.
Like terms are terms with the same variable and raised to the same power.
Simplify[tex]4x^2 - 8x + 3 - (2x^2 + 4x + 2)[/tex][tex]4x^2 - 8x + 3 - 2x^2 - 4x - 2[/tex][tex]4x^2 - 2x^2 - 8x - 4x +3 - 2[/tex][tex]2x^2 - 12x + 1[/tex]The simplified form is [tex]2x^2 - 12x + 1[/tex].
To convert kilograms to pounds, Abby halves the number of kilograms, n, then subtracts 10% from the result of that calculation, whereas Renato subtracts 10% first and then halves the
result. (a) Write an algebraic expression for each method.
Abby's expression:
Renato's expression:
(b) Do the methods give the same answer?
Abby's method and Renato's method of converting kilograms to pounds gives the same answer.
Algebraic expressionNumber of kilograms = nAbby:
1/2n - 10%
= 1/2n - 0.1
Renato:
-10% + 1/2n
= -0.1 + 1/2n
Therefore, Abby's method and Renato's method of converting kilograms to pounds gives the same answer.
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the sum of three consecutive odd integers is 321. what are the three consecutive odd integers?
define in words variables for the unknown values
create an equation
solve using algebra
The consecutive odd numbers that sum up to 321 are 105, 107 and 109.
How to find the three consecutive odd numbers?The sum of three consecutive odd integers is 321.
Odd numbers are numbers that when divided by 2 produces a remainder.
let
x = first odd numbers
Therefore,
x + x + 2 + x + 4 = 321
combine the like terms
x + x + x + 2 + 4 = 321
add the like terms
x + x + x + 2 + 4 = 321
3x + 6 = 321
subtract 6 from both sides
3x + 6 = 321
3x + 6 - 6 = 321 - 6
3x = 315
divide both sides by 3
x = 315 / 3
x = 105
Therefore, the consecutive odd numbers that sum up to 321 are 105, 107 and 109.
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Answer this question please
The solution to the inequality is w ≥ 470 or w ≤ 530
How to determine the solution to the inequality?The given parameters are:
Number of words = 500
Absolute deviation = 30
Acceptable number of words = w
The absolute value inequality is represented as
|w - Number of words| ≥ Absolute deviation
So, we have
|w - 500| ≥ 30
Remove the absolute bracket
So, we have
w - 500 ≥ -30 or w - 500 ≤ 30
Add 500 to both sides of the inequality
So, we have
w ≥ 470 or w ≤ 530
Hence, the solution to the inequality is w ≥ 470 or w ≤ 530
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Question
If the point (1, 4) is on the graph of an equation, which statement must be
true?
о A. The values x= 1 and y = 4 are the only values that make the
equation true.
O B. The values x = 1 and y = 4 make the equation true.
C. There are solutions to the equation for the values x= 1 and x = 4.
OD. The values x = 4 and y = 1 make the equation true.
SUBMIT
Please help me
Find the slope of the line on the graph
Answer:
slope = 6/10
Step-by-step explanation:
Point 1: (0,2)
Point 2: (10,8)
m= Slope= Rise/run = (y2-y1)/(x2-x1) = (8-2)/(10-0) = 6/10
Write a formula for the perimeter of the rectangle in terms of its length, l.
a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.
We know that the perimeter of rectangle is given by:
Perimeter ( P ) = 2 ( l + b )
Now, we need to represent this formula in terms of length that is l.
So, we get that:
P = 2 l + 2 b
Now subtract 2 b from both the sides:
P - 2 b = 2 l + 2 b - 2 b
P - 2 b = 2 l
2 l = P - 2 b
Divide both the sides by 2:
2 l / 2 = (P - 2 b) / 2
l = P / 2 - b
Therefore, we get that, a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.
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(3x-5) + (x +1) = 180
Answer:
46
Step-by-step explanation:
4x-4=180
4x=184
x=46
Answer:
x=46
Step-by-step explanation:
used by scientific calculator.
the information in the following table for the next few questions. The following statistics represent samples of copper wire submitted by two companies for tensile strength testing (psi).
Statistic Company A Company B
Arithmetic Mean 500 600
Median 500 500
Mode 500 300
Standard Deviation 40 20
Mean Absolute Deviation 32 16
Quartile Deviation 25 14
Range 240 120
Sample Size 100 80
The middle 95% of the wires from Company A tested between _____ and _____ . Record ONLY the lower limit as a whole number.
The middle 50 percent of the wires of Company A tested between _____ and _____. Record ONLY the lower limit as a whole number.
Which company's distribution has the larger dispersion (answer either 'A' or 'B')?
The variance for Company A is _____? (whole numbers only)
Using the normal distribution, we have that:
A.
The middle 95% of the wires from Company A tested between 420 and 580 psi.The middle 50% of the wires of Company A tested between 473 psi and 527 psi.B. Due to the higher coefficient of variation, Company A has the larger dispersion.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For Company A, the mean and the standard deviation are given as follows:
[tex]\mu = 500, \sigma = 40[/tex]
The Empirical Rule is applicable for a normal variable, meaning that 95% of the measures are within 2 standard deviations of the mean, hence:
500 - 2 x 40 = 420.500 + 2 x 40 = 580.The middle 95% of the wires from Company A tested between 420 and 580 psi.
The middle 50% is the measures between the 25th percentile(X when Z = -0.675) and and the 75th percentile(X when Z = 0.675), hence:
25th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-0.675 = (X - 500)/40
X - 500 = -0.675(40)
X = 473.
75th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 500)/40
X - 500 = 0.675(40)
X = 527.
The middle 50% of the wires of Company A tested between 473 psi and 527 psi.
Which Company had the larger dispersion?The company with the larger dispersion has the highest coefficient of variation, given by the standard deviation divided by the mean.
Hence:
Company A: 40/500 = 0.08.Company B: 20/600 = 0.033.Hence Company A has the larger dispersion.
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help me please I need a good grade
Answer: x=32
Step-by-step explanation:
x-7+2x+1=90
x+2x-7+1=90
3x-6=90
3x=96
x=32
Which of the following numbers is irrational? -4.8237, pi/2, the square root of 4 to the third power, or 4 + the square root of 25
Answer:
Did you already get the answer?
Step-by-step explanation:
Evaluate the following expression: (3x+2)+5
Answer:
3x + 7
Step-by-step explanation:
Hope this helps you :)
one seventh times the absolute value of the quantity x minus 3 end quantity minus 2 equals 9
The solutions of "one seventh times the absolute values of the quantity x minus 3 minus 2 equals 9" is 80 and -74
The absolute value of the quantity x minus 3 = |x-3|
The one seventh time the absolute value of the quantity x minus 3 minus 2 equal to 9
Then the equation will become
(1/7)×|x-3|-2=9
Solve the equation
(1/7)×|x-3|-2= 9
(1/7)×|x-3|= 11
|x-3| = 11×7
|x-3|= 77
The absolute value equation will become
x-3= 77
x-3 = -77
Solve both equation
x-3=77
x= 80
x-3 = -77
x= -74
Hence, the solutions of "one seventh times the absolute values of the quantity x minus 3 minus 2 equals 9" is 80 and -74
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The price of 3 citrons and 4 fragrant wood apples is 51 units. The price of 4 citrons and 3 fragrant wood apples is 54 units. Find the price of a citron and the price of a wood apple.
Answer:9 citronella and 6 fragrant wood apples
Step-by-step explanation:
Given n(J) = 255, n(K) = 186 and n(J ∪ K) = 429, find n(J ∩ K).
Answer:
12
Step-by-step explanation:
[tex]n(J \cap K)=n(J)+n(K)-n(J \cup K) \\ \\ =255+186-429 \\ \\ =12[/tex]
Choose the estimate closest to the length of a pen: 30cm, 160mm, or 16mm.
The estimate closest to the length of a pen is 160mm
How to estimate the closest length of a pen?Estimation is when we use approximate values in a calculation to give an approximate, predicted answer rather than an exact answer.
We can estimate some lengths and distances using approximate values for measurements.
For example, 16 cm is approximately the length of a pen.
Therefore, the estimate of a pen is 16 cm.
Since the length in cm is not in the option, we have to convert.
Hence,
1 centimetres = 10 millimetres
16 centimetres = ?
cross multiply
estimated length of a pen = 160 millimetres.
Therefore, the estimate closest to the length of a pen is 160mm
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A lacrosse field is rectangular with a length of 110 yards and a width of 60 yards. Which side lengths could be used to create a scale drawing of the field?
The side lengths could be used to create a scale drawing of the field is 6600 yard².
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
A lacrosse field is rectangular with a length of 110 yards and a width of 60 yards.
According to given question we have
We know that
Area of rectangle= Length × width
Area of rectangle= 110 × 60
Area of rectangle= 6600 yard².
Scale ratio can be 1:55
Therefore, the side lengths could be used to create a scale drawing of the field is 6600 yard².
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Can someone help me pls
Answer:
See below
Step-by-step explanation:
What are the scale factors
Answer:
10 if going from the smallest to the largest or 1/10 if going from the smallest to the largest.
Step-by-step explanation:
Let s = scale factor
10s = 100 Divide both sides by 10
s = 10
The function f is given in three equivalent forms.
Which form most quickly reveals the y-intercept?
Choose 1 answer:
Answer:
c
Step-by-step explanation:
C is straight forward that the value of the y intercept is 8, unlike the A and B where you must first simply by removing the brackets