The number in standard form will be 16 thousand 6 hundred.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (9 × 10) + (4 × 100) + (6 × 1,000) + (1 × 100) + (2 × 10) + (9 × (1,000 + 100 + 10)
Simplify the expression, then we have
⇒ (9 × 10) + (4 × 100) + (6 × 1,000) + (1 × 100) + (2 × 10) + (9 × (1,000 + 100 + 10)
⇒ [(9 + 2 + 9) × 10] + [(4 + 1 + 9) × 100] + [(6 + 9) × 1,000]
⇒ 15 × 1,000 + 14 × 100 + 20 × 10
⇒ 16 × 1,000 + 6 × 100
The number in standard form will be 16 thousand 6 hundred.
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place the steps to sketch the graph of a rational function in the appropriate order
The steps to sketch the graph of a rational function in the appropriate order is in the order: 1,4,2,3
The steps to sketch the graph of a rational function will be first to find the function's zeros and vertical asymptotes, and plot them on a number line, the second step is to choose test numbers to t the left and right of each of these places, and find the value of the function at each test number., the third step is to use test numbers to find where the function is a positive and where it is negative and the last step is to sketch the function's graph, plotting additional points as guides as negative.
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Place the steps to sketch the graph of a rational function in the appropriate order.
1)find the function's zeros and vertical asymptotes, and plot them on a number line.
2) use test numbers to find where the function is positive and where it is negative.
3) sketch the function's graph, plotting additional points as guides as negative.
4)choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.
What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 80 less than the sum of the measures of the base angles?
Answer: 65 °
Step-by-step explanation:
Let x = measure of a base angle
Base angles of an isosceles triangle are equal
Sum of interior angles of a triangle is always 180:
x + x + (2x - 80) = 180
4x - 80 = 180
4x = 260
x = 65
What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
please help!
Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Jocelyn can make to earn her first free movie ticket.
Answer:
25 + 12.5v ≤ 170
Step-by-step explanation:
Given the inflation model C(t)=C0(1+r)t and given that a boat that currently sells for $385,290 sold for $142,700 7 years ago, what has the average annual rate of inflation been for the past 7 years? Round to two decimal places.
1,384,190...............
Jack wrote this solution to solve for x.
Which statement is true?
O-3 is an extraneous solution because it is negative.
6 is an extraneous solution because it creates a zero
in the denominator.
O There are no extraneous solutions.
Both-3 and 6 are extraneous solutions because
they create a 0 in the denominator.
x+3
9
x²-11x-30
1 x+3
9
x-5 x-6 (x-6xx-5)
*+3
x-6
x-x-6xx-5)=
x-6xx-5)(x-6xx-5)
x-6=(x+3xx-5)-9
x-6-²-5x+3x-15-9
9
0=²-3r-18
0=(x-6Xx+3)
x=68x=-3
(x-6xx-5)
Factor
Multiply by the LCD
Simplify
Sampaty
Combine like terms.
Zero Product Property
Solve for x
Based on the solution written by Jack to solve for x, the statement which is true is that: B. 6 is an extraneous solution because it creates a zero in the denominator.
What is an extraneous solution?In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that is not a direct solution (root) of the original equation.
This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that are not solutions to the original equation as shown below:
1/(x - 5) = (x + 3)/(x - 6) - 9/(x² - 11x + 30)
1/(x - 5) = (x + 3)/(x - 6) - 9/(x - 6)(x - 5)
When x = 6, the denominator of the given equation becomes;
1/(x - 5) = (x + 3)/(x - 6) - 9/(6 - 6)(x - 5)
1/(x - 5) = (x + 3)/(x - 6) - 9/(0)(x - 5)
1/(x - 5) = (x + 3)/(x - 6) - 9/0
1/(x - 5) = (x + 3)/(x - 6) - undefined.
Therefore, six (6) is an extraneous solution solution to the original equation because it creates an undefined expression.
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A man wants to put a fence around a
square lot with sides of 68 feet. How
many feet of fencing is needed? If
each 8-foot section of fence costs
$25.00, how much will the fence cost?
Answer:
272 feet of fencing is needed to go around the square lot. The total cost of the fence would be $6,800.00 ($25.00 x 272 feet).
Step-by-step explanation:
Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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Write the equation of the line passing through the given point that is
parallel to the given line
16. y = 2/3 x - 2: (-3, 4)
17. -2x+ 7y = 14; (-7, -3)
18. 3x - 4y = 16; (8, -5)
19. 4x + y = 7: (2,4)
The equation of the line passing through the given point that is
parallel to the given lines are;
16) y = ²/₃x + 6
17) y = ²/₇x - 1
18) y = ³/₄x - 11
19) y = -4x + 12
What is the equation of the Line?
16) We are given the equation of a line as;
y = ²/₃x - 2
The general equation of a line in slope intercept form is ;
y = mx + c
where;
m is slope
c is y-intercept
Thus, equation passing through (-3, 4) is;
y - 4 = ²/₃(x - (-3))
y - 4 = ²/₃x + 2
y = ²/₃x + 6
17) We are given the equation of a line as;
-2x + 7y = 14
7y = 2x + 14
y = ²/₇x + 2
Thus, equation passing through (-7, -3) is;
y - (-3) = ²/₇(x - (-7))
y + 3 = ²/₇x + 2
y = ²/₇x - 1
18) We are given the equation of a line as;
3x - 4y = 16
4y = 3x - 16
y = ³/₄x - 4
Thus, equation passing through (8, -5) is;
y - (-5) = ³/₄(x - 8)
y + 5 = ³/₄x - 6
y = ³/₄x - 11
19) We are given the equation of a line as;
4x + y = 7
y = -4x + 7
Thus, equation passing through (2, 4) is;
y - 4 = -4(x - 2)
y - 4 = -4x + 8
y = -4x + 12
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Can a prime number be a multiple of 11?
Multiple of 11 cant be prime number.
What are prime numbers?Prime numbers are those that are bigger than 1. Only the number itself and factor 1 are present. This indicates that no number other than 1 and the number itself may be used to divide these numbers without leaving a residue.
Now that multiples of 11 are being questioned, such as 22, 33, and 44, can they be prime numbers?
We know that prime numbers are those that can only be divided by themselves and by one , but since these multiples of 11 are all divisible by 11, they cannot be prime numbers.
The multiple of 11 cannot thus be a prime number.
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PLSSSS HELPPPP MEEEE
Answer:
Slope: positive
m = 3
Step-by-step explanation:
the slope is positive because the line goes up from left to right.
to find m:
m = (y2 - y1) divided by (x2 - x1)
x1 = -1, y1 = -4, x2 = 0, y2 = -1 <--taken from the points in the diagram
plug in the points:
m = (-1 - (-4)) divided by (0 - (-1))
m = (3) divided by (1)
m = 3
so, your m = 3
Look at the pattern.
72, 67, 62, 57
Which of these is the rule for the pattern?
a
b
d
subtract 5
add 5
subtract 9
add 9
Answer:
Subtract 5
Step-by-step explanation:
72 , 67, 62, 57,..
Each term is obtained by subtracting 5 from the previous term.
72 - 5 = 67
67 - 5 = 62
62 - 5 = 57
The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 3.50 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. The mean wait time was calculated to be 3.94 minutes. Assuming the population standard deviation is 1.30 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes with a 95% level of confidence?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The value of the test statistic is given as follows:
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes.
How to obtain the value of the test statistic?The value of the test statistic is obtained using the z-distribution, as the population standard deviation is known in the context of this problem.
The equation that gives the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value claimed at the test of the hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 3.94, \mu = 3.50, \sigma = 1.30, n = 41[/tex]
(all values are taken from the text).
Then the numeric value of the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.94 - 3.50}{\frac{1.30}{\sqrt{41}}}[/tex]
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes, as the critical value for the right-tailed test with 95% confidence is of z = 1.645, and the test statistic is greater than this.
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Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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Graph -7x+5y=35−7x+5y=35minus, 7, x, plus, 5, y, equals, 35.
Answer:
835786543225644323567
I need help on this Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
{3, 4, 6, 7, 8}
Step-by-step explanation:
For sets U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}, and C = {1, 2, 3, 4, 5}, you want the set {A∩C}'.
A∩CThe set A∩C contains the elements that are common to both sets. Those are {1, 2, 5}.
{A∩C}'The set of interest contains the elements of U that are not in A∩C. Those are ...
{3, 4, 6, 7, 8}
__
Additional comment
DeMorgan's theorem tells us the desired set is equivalent to A'∪C', or {3, 4, 7, 8}∪{6, 7, 8}. That, too, is ...
(3, 4, 6, 7, 8}
WHAT WILL YOU WEAR?
You are getting ready for Thanksgiving dinner and trying to find the perfect outfit. You want to wear your new sweater from Infinity21. The manufacturer advertises that this sweater is most comfortable to wear when the temperature satisfies |t-56| ≤6 degree: Fahrenheit. The weaather report says it will be 53°F on Thanksgiving Day at mealtime.
Can you wear your new sweater comfortably?
By solving a linear inequation, it can be concluded that
The sweater can be worn comfortably
What is a linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥
A one degree inequation is known as linear inequation.
Here, the given linear inequation is
[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]
As 53° F lies between 50 and 62, the sweater can be worn comfortably
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if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
P is equal to 8700% for population x time in hours.
What is population growth model?P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29
K's model must be solved. ln%28p%29=ln%288700%29%
2Bkx%2Aln%28e%
29\skx%
2A1=ln%28p%29-ln%288700%
29\sk=%281%
2Fx%29%
28ln%28p%29-ln%288700%29%29
Replace the point (1,10000).
k=%281%
2F1%29%
28ln%2810000%
29-ln%288700%
29%
29\sk=ln%2810000%
29-ln%288700%
29 k=0.13926, which you might only desire to three or maybe even two significant figures.
You may just enter 10000% if you want p after two hours.
And it SHOULD be the same as 8700% (2810000%2F8700%).
Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.
Determine how long to double x.
Take the logs on both sides, then find x.
To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29
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if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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1 Select the correct answer. Each statement describes a transformation of the graph of . Which statement correctly describes the graph of y = f(x − 7) + 3? A. It is the graph of f translated 3 units up and 7 units to the left. B. It is the graph of f translated 7 units down and 3 units to the right. C. It is the graph of f translated 7 units up and 3 units to the right. D. It is the graph of f translated 3 units up and 7 units to the right.
Using translation concepts, it is found that the correct option is:
D. It is the graph of translated 3 units up and 7 units to the right.
The parent function is:
[tex]f(x)=y=1nx[/tex]
Shifting a function a units to the right is equivalent to finding f(x - a), thus:
[tex]f(x-7)=1n(x-7)[/tex]
Shifting a function a units up is equivalent to finding f(x) + a, thus:
[tex]f(x-7)+3=1n(x-7)+3[/tex]
Which means that the function was shifted 7 units to the right and 3 up, thus, option D is correct.
Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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What is the equation of the line of symmetry for the parabola represented by the equation y=−2(x−7^)2+11?
Enter your answer as the correct equation, like this: x = 42
Answer:
x = 7
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given equation:
[tex]y=-2(x-7)^2+11[/tex]
The given equation is in vertex form.
The axis of symmetry of a parabola with a vertical axis of symmetry is:
x = hwhere h is the x-value of the vertex.
As the vertex of the given equation is (7, 11), the axis of symmetry is:
x = 7help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
what are the 12 kinds of polygons
The 12 kinds of polygons are:
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Tridecagon
Tetradecagon
Polygons:
A polygon is a closed shape figure that has a minimum of three sides and three vertices.
Poly → many
gon → angle
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A recipe for flapjacks uses only syrup, butter and oats, in the ratio 1: 2: 3
a) Trevor makes some flapjacks using this recipe and uses 200g of syrup.
(i) What quantity of butter should he use? _________g
(ii) What quantity of oats should he use? _________g
b) Using this recipe, 150g of syrup are needed to make 8 flapjacks. Find the quantity of oats needed to make 16 of these flapjacks.
Answer: _____g
By using Unitary method, it can be calculated that
a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) 900 g of oats is required to make 16 flapjacks
What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here Unitary method will be required
a) Let Trevor use x g Syrup, 2x g butter and 3x g oats
Trevor uses 200 g syrup
So x = 200
i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) To make 8 flapjacks 150 g of syrup is used
To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used
To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used
To make 16 flapjacks 300g of syrup is used
To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used
To make 16 flapjacks 900 g of oats is used
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You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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-18-18 Swap sides variables are on the 1eft and
changes sign direction. Please help me graph answer x2>-18 thanks
The graph of the expression x² > -18 does not exist
How to determine the graph of the expression?From the question, we have the following inequality expression that can be used in our computation:
x2 > -18
This expression can be rewritten properly
So, we have the following representation
x² > -18
Next, we take the square roots of both sides of the expression
This gives
√x² > √-18
Evaluate the exponents
So, we have
x > 3√-2
The radical is a complex number
This means that the inequality expression cannot be graphed (because of the presence of the complex expression)
Read more about inequality at
https://brainly.com/question/25275758
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