Answer:
supplementary angles
Step-by-step explanation:
1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given
2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.
3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive
4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality
5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence
Lee.com accepted a $70,000, 634% , 120-day note on July 26. Lee discounted the note on October 28 at LB Bank at 6%. What proceeds did Lee receive? (Use Days in a year table) (Round your answer to the nearest cent.)
On October 28, Lee received proceeds of $71,153.66 from the discounted note.
What is note discounting?Discounting a note involves receiving immediate cash by selling it to a financial institution at a discount.
The implication of discounting a note is that the receiver gets less than the maturity value.
The maturity value is the face value of the note plus the computed interest.
Face value of the note receivable = $70,000
Interest rate = 6.34%
Note period = 120 days
July 26 - October 28 = 94 days
Maturity value of the note receivable = The Face Value + Interest
= $71,459.07 [$70,000 + ($70,000 x 6.34% x 120/365)]
Bank discount rate = 6%
The discount period from October 28 to Nov 22 = 26 days (120 - 94)
Bank discount = Maturity Value x Discount Rate x Discount Period
= $305.41 ($71,459.07 x 6% x 26/365)
Proceeds = Maturity value - Bank discount
= $71,153.66 ($71,459.07 - $305.41)
Thus, by discounting the note receivable at LB Bank at 6%, Lee received $71,153.66 instead of the $71,459.07 it would have received at maturity.
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The odds in favor of an event occurring are given. Compute the probability of the event occurring. (Enter the probability as a fraction.) 8 to 9
The probability expression when converted from odd's expression is 8/17
How to determine the probability?From the question, we have the following odd parameters
Odd = 8 to 9
To start with, we need to express the odd as ratio
So, we have the following representation
Odds ratio = 8 : 9
Solving further, we need to express the ratio as fraction
So, we have the following representation
Odds fraction = 8/9
To convert the above odd's expression to probability expression, we make use of the following equation
This is represented as
P = Odds/(Odds + 1)
Substitute the known values in the above equation
So, we have the following equation
P = (8/9)/(8/9 + 1)
Evaluate the sum
This gives
P = (8/9)/(17/9)
Express the quotient as product
P = (8/9) * (9/17)
Evaluate
P = 8/17
Hence, the probability is 8/17
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x− ℎ)^2+kand how they can be identified from the equation.
From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
As given in the question,
Given equation is :
y = A(x-h)² +k
Standard basic parabola equation is y = x² where parabola pass through (0, 0) .
In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .
Value of A > 0 then it open in upward direction .
Value of A <0 then it is open in downward direction.
Vertex of the given parabola y = A(x-h)² +k is (h, k).
Line of symmetry is given by vertical line x =h.
Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
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find the number that is exactly halfway between 5 and 17
the difference of ten times a number and six is fourteen as a equation and solve it
The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.
According to the question,
We have the following information:
The difference of ten times a number and six is fourteen.
Now, let's take the number to be x.
So, we have the following expression:
10x-6 = 14
Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:
10x = 14+6
10x = 20
x = 20/10
x = 2
Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.
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Solve for X in the equation;
2x+5=7
Answer:
x=1
Step-by-step explanation:
Answer: x=1
Step-by-step explanation:
2x + 5 = 7
2x + 5 - 5 = 7 - 5
2x = 2
2x/2 = 2/2
x=1
What pattern do you see?
Gallons
0.1
10
Miles
118
Step-by-step explanation:
why ? the same pattern your saw yourself, as the handwritten numbers indicate.
it is 1:118.
event on the left is multiplied by 118 to create the numbers on the right.
I need help with Part 2 only
algebra please helppp
Addition of the given polynomial functions (5a³ + 4a² - 3a + 2) and (a³ - 3a² + 3a - 9) gives 8a³ + a² - 7
What is polynomial function?A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.
How to find the addition of the polynomialAddition of polynomial is achieved term by term
= (5a³ + 4a² - 3a + 2) + (a³ - 3a² + 3a - 9)
= 5a³ + 3a³+ 4a² - 3a²- 3a + 3a + 2 - 9
= 8a³ + a² - 7
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I need help with solving problem.
Answer:
x=-1,x=3/5
Step-by-step explanation:
Those are the two values of x
Suppose you want to have $600,000 for retirement in 35 years. Your account earns 5% interest. How
much would you need to deposit in the account each month?
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To have $600,000 for retirement in 35 years at 5% interest, one would need to deposit $528.13 in the account each month.
What are periodic deposits?Periodic deposits are monthly cash inflows into a retirement account that accumulates interest by compounding.
To find periodic deposits, we can use an online finance calculator, defining the parameters as follows.
N (# of periods) = 420 months (35 years x 12)
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $600,000
Results:
Monthly Deposits (PMT) = $528.13
Sum of all periodic deposits = $221,814.60
Total Interest = $378,185.40
Thus, monthly deposits of $528.13 can accumulate to $600,000 in 35 years at 5% interest.
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Complete the chart to show similarities and differences between multiplying by 0.1, 0.01, 10, 100. Tell how many places the decimal point appears to move and in which direction when you multiply by each
Answer:
they all are being multiplied by 10
Step-by-step explanation:
0.01 x 10 = 0.1
0.1 x 10 = 1
1 x 10 = 10
10 x 10 = 100
8x^(3)-27=0
find the roots of x
Answer:
[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
Step-by-step explanation:
[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
The quotient is a multiple of 4 the dividend is a multiple of 9 the divisior is a factor of 12 possible solution
The birth weights of the 908 babies born at Valley Hospital in 2019 were normally
distributed with a mean of 7.2 pounds with a standard deviation of 1.5. Use the Z-
Score Table from the book to determine the number of babies that weighed more
than 10 pounds.
Round your answer to the nearest whole number, but do not include the word
"babies" in your response.
PLEASE HELP I POSTED THIS QUESTION LIKE TWICE AND NO ONE IS HELPING ME
Using the z-score tables, the number of babies that weighed more than 10 pounds is; 43
How to find the p-value from z-score?A probability distribution that can be considered to be symmetric about the mean is the normal distribution, which can often be referred to as the Gaussian distribution. This depicts to us the concept of data being close to the mean occurring more often than data that are considered far from the mean. The normal distribution usually has a bell curve graph.
We are given that;
The total number of babies is 908.
Mean of the normal distribution is 7.2 pounds.
Standard deviation of the normal distribution is 1.5 pounds.
The formula of z score is given by;
z = (x - μ)/σ
where;
x is sample mean
μ is population mean
σ is standard deviation
We are given that;
x = 10
μ = 1.5
σ = 7.2
Thus;
z = (10 - 7.2)/1.5
z = 1.86667
The P-value from Z-Table gives us:
P(x > 10) = 1 - P(x < 10) = 0.030974
The number of babies that weighed more than 10 pounds is;
(0.030974 × 908) ≈ 43
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Complete the table: (Enter your answers as a whole dollar amount.) Units Unit Cost Dollar Cost Beg. Inventory Jan. 1 10 $ 7.00 A Apr. 11 30 $ 12.00 B May 17 40 $ 13.00 C Dec. 5 20 $ 15.00 D
The completion of the inventory table is as follows:
A = $70B = $360C = $520D = $300.What are the inventory methods?Some of the inventory methods that are used in completing the inventory table are:
FIFO (First-in, First-out) lies on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.Specification Identification does not rely on any assumptions in allocating the costs of goods sold and ending inventory.Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 10 $7.00 $70
Apri. 11 Purchases 30 $12.00 $360
May 17 Purchases 40 $13.00 $520
Dec. 5 Purchases 20 $15.00 $300
Total 100 $1,250
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help please need this rn
The equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.
Given function:
g(x) = 6/x-1
vertical asymptote for any function is denominator is equal to zero.
x - 1 = 0
x = 1.
Therefore the equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.
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A bag contains 3 gold marbles, 5 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
The expected value if you play this game will be -$0.205.
Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.
Given, The bag contains,
Number of gold marbles (P1) = 3
Number of silver marbles (P2) = 5
Number of black marbles (P3) = 26
Also given,
The winning value if a gold marble is selected = $3
The winning value if a silver marble is selected = $2
The losing value if a black marble is selected = $1
Probability = Expected value/ Sum of the total number of events
Probability of picking a gold marble,
P1 = 3/ (3+ 5+ 26)
= 3/34.
Probability of picking a silver marble,
P2 = 5/ (3+ 5+ 26)
= 5/34.
Probability of picking a black marble,
P3 = 26/ (3+ 5+ 26)
= 26/34.
The expected value if you play the game will be,
Value = ($3) P1 + ($2) P2 + (-$1) P3
= ($9/34) + ($10/34) - ($26/34)
= - ($7/34)
= -$ 0.205
Thus, you will face a loss of 0.205 cents.
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Determine the next three terms in the following sequence:
-1, 1/2, -1/4, 1/8, __, __, __,….
A. 1/12, 1/24, 1/48
B. 1/16, 1/32, 1/64
C. -1/16, 1/32, -1/64
D. -1/12, 1/24, -1/48
The next three terms in the sequence are -1/16, 1/32, -1/64
The correct option is option C)
What is a sequence?
A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression
We are given a sequence of -1, 1/2, -1/4, 1/8,
We have to describe the next three terms of the sequence
If we notice closely the given sequence is an geometric sequence
Hence they have a common factor known as common ratio
in it we divide a term by its previous term
Hence
Ratio= (1/2)/-1
Ratio = -1/2
Now to find the next terms we multiply this with the last term we get
1/8*-1/2= -1/16
Now Hence the next three terms are -1/16, 1/32, -1/64
The correct option is option c)
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Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 when y = 600000, hence:
[tex]y = 641000(0.99)^x[/tex]
[tex]600000 = 641000(0.99)^x[/tex]
[tex](0.99)^x = \frac{600000}{641000}[/tex]
[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]
x = 6.6 decades.
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rearrange the perimeter forumula for a rectangle to find the width.
P=2w+ 2l
The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle
Perimeter of RectangleThe perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
In this question, we simply need to make the width (w) the subject of formula.
The equation given is
p = 2w + 2l
p = perimeter of rectanglew = width l = lengthp = 2w + 2l
p = 2(w + l)
p / 2 = w + l
w = p/2 - l
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Graph the function.
h(x)=x²-5
Answer: Look at the graph
Step-by-step explanation:
Direction: Opens upVertex: (0,-5)Axis of Symmetry: x = 0Directrix: y= -21/4x: -2 -1 0 1 2y: -1 -4 -5 -4 -1HELP PLEASE HELP I NEED HELP PLEASEEEEEEEEEEE
The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.
What is a linear relation?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
The first and the second differences are:
x y first differences second differences
4 18 ----
5 28 10 ------
6 35 7 -3
7 39 4 -3
8 40 1 -3
9 38 -2 -3
The values of second differences are constant, therefore, the relation is linear.
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Match each number on the left with the correct description of the number on the right.
Answer:a, c and d
Step-by-step explanation:bc i got it right on edge
Please help me with the attached question
The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, equivalent expressions are expressions that have the same value.
Therefore, the expression that is equivalent can be calculated as follows:
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]
Hence, let's simplify the expression to find it's equivalent,
open the bracket
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]
[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2
Therefore,
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]
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Given: ∠2≅∠3 Prove: ∠1 and ∠3 are supplementary
The proof to the above diagram is ∠1 + ∠3 = 180
What are Supplementary angles?Supplementary angles are angles whose sum equals 180°
If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.
∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3
Also ∠1 + ∠2 = 180°( sum of angles on a straight line)
making ∠2 the subject of the equation
∠2 = 180 - ∠1
But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3
substituting ∠2 for ∠3 in the equation, we have
∠3 = 180 - ∠1
which is further simplified as,
∠1 + ∠3 = 180°
Which means both angles are also supplementary.
In conclusion, both angles are supplementary as ∠1 + ∠3 = 180
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The ratio of 7th grade students to 8th grade students in a soccer league is 7:13, if there are 100 students in all ,how many are in 7th grade ?
What is the equation of the line shown in the graph? Drag and drop the expressions to write the equation of the line in slope-intercept form. Giving Brainlist
y =_+_
Answer:
Step-by-step explanation:
76 points and brainlist
The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
2 x 102
2 x 103
0.7 x 101
6.67 x 102
Answer:
d the last one I think
Step-by-step explanation:
I am not really sure
Answer:
D.) 6.67 X 10^2
HELP MIDDLE SCHOOL MATH BRAINLIEST 30 POINTS
Answer:
Step-by-step explanation:
A. -1/3x
B. -x
c.-5/4x