Answer:
Step-by-step explanation:
A 2% decrease each year means that the population at the end of a year is 98% of what it was at the start of the year. Apply this for t consecutive years and you get the relation
P(t) = Po (0.98)t
Po = 100,000
P(t) = 100,000 (0.98)t
Riya is applying mulch to her garden. she applies it at a rate of 250{,}000\text{ cm}^3250,000 cm 3 250, comma, 000, start text, space, c, m, end text, cubed of mulch for every \text{ m}^2 m 2 start text, space, m, end text, squared of garden space.
The area of her garden where Riya is applying Mulch is 0.25m³.
To understand this answer, we will analyze the information in the question statement. So, we know that Riya is applying Mulch to her Garden. The application of Mulch is at the rate of 250 000 cm^3 for every m^2. Now to find the rate for every m^3, we will use the basic conversion formula for converting cm to m:
we know that,
100 cm = 1m
Now we can write this formula as follows,
1 cm = 1 / 100 m
1 cm = 0.01 m
We will use the same relation for the values given to us in the question:
250, 000 cm^3 = 250, 000 x 1 cm x 1cm x 1cm
1 cm^3 = 1 cm x 1cm x 1cm
250, 000 cm^3 = 250, 000 x 0.1 x 0.1 x 0.1
From, 1 cm = 0.01 m
250, 000 cm^3 = 250, 000 x 0.000001
250, 000 cm^3 = 0.25 m^3
Hence Riya is applying at 0.25 m^3 per m^2 (meter square).
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which answer choice correctly represents the quotient of 738/13 you will be reported if wrong
Answer:
Quotient = 60
Remainder = 3
Full calculation: 783 = 13 × 60 + 3
Answer:
Step-by-step explanation:
Remainder = 3
Quotient = 60
Full calculation: 13 × 60 + 3=783
Evaluate the determinant of each matrix.
[4 -1 8 2]
For the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
The determinant is equal to 16.
How to find the determinant of the given matrix?Remember that for a general 2 by 2 matrix:
[tex]\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\\\end{array}\right][/tex]
The determinant is given by the simple formula:
D = a₁*b₂ - b₁*a₂
This is the only thing we need to use in this problem, we will use this formula to find the determinant of the given 2 by 2 matrix.
In this case we have the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
Then we can just use the given formula for the determinant, we will get
D = 4*2 - (-1)*8
We just need to solve that expression, we will get:
D = 8 - (-8) = 8 + 8 = 16
We can see that the determinant of the given matrix is equal to 16.
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Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
c. Open-Ended Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
We will know 8 complete names after 2 days and 20 complete names after 8 days. Whether or not this function represents your learning rate will vary from person to person.
Here, we are given an exponential function: f(t)= c{1- e^(-kt)}
where
f(t) = number of tasks learned.
c = total number of tasks to be learned
k = rate of learning
t = time
Now, when we move to a new school, number of names we need to learn ⇒ c = 25
learning rate for new tasks = 20%
⇒ k = 0.2
and time = 2 days
⇒ t = 2
Substituting these values in the function we get-
f(2) = 25{1- [tex]e^{-0.2 * 2}[/tex]}
= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]
= 0.67
Thus, f(2) = 25( 1-0.67 )
f(2) = 25(0.33)
f(2) = 8.25
Thus, we will be able to learn 8 complete names in 2 days.
If t = 8f(8) = 25{1- [tex]e^{-0.2*8}[/tex]}
= 25{1- [tex]e^{-1.6}[/tex]}
= 25(1- 0.20)
= 25(0.80)
= 20
Thus, we will be able to learn 20 complete names in 8 days. Whether of not this function describes your own learning rate will vary from person to person. Some people are fast learners whereas others take their time. A fast learner will have a higher learning rate whereas a slow learner will have a lower learning rate as depicted by k. You can change the value of k to adjust the function as per your learning abilities.
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Your question was incomplete, check for full content below-
Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days?
b. After 8 days?
c. Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
Round this number to the
nearest hundredth.
1.2983
Answer: 1.3
Step-by-step explanation:
Answer:
1.3
Step-by-step explanation:
9 is the hundredth and we round up with 8 so we’d round up 1 and we get 1.3
Find the sum of (7.3 × 106) and (4.6 × 105). write the final answer in scientific notation. 11.9 × 1011 1.19 × 1010 7.76 × 106 7.76 × 105
The sum in scientific notation will give:
7.76*10⁶
How to find the sum in scientific notation?
Here we want to find the sum between the numbers (7.3*10⁶) and (4.6*10⁵).
To sum these numbers, we need to have the same exponent in the "10", then we can rewrite:
7.3*10⁶ = 73*10⁵
Now the sum will be:
73*10⁵ + 4.6*10⁵
Taking a common factor we get:
73*10⁵ + 4.6*10⁵ = (73 + 4.6)*10⁵ = 77.6*10⁵
Now we want to go back to scientific notation, so we need to move the decimal point one time to the left, we will get:
77.6*10⁵ = 7.76*10⁶
That is the outcome of the sum.
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If a polygon has 5 sides, then it is a pentagon.
Write the inverse of the conditional statement and determine whether it is true or false.
If a polygon does not have 5 sides, then it is not a pentagon.; FALSE
If a polygon is a pentagon, then it has 5 sides.: TRUE
If a polygon is a pentagon, then it has 5 sides; FALSE
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
Answer:
Step-by-step explanation:
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
r(x)=-x-7 when x=-2,0, and 5
The output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
What are the output values when x = -2, 0, and 5?Given the data in the question;
r(x) = -x - 7r(-2) = ?r(0) = ?r(5) = ?When x = -2. replace all the occurrence of x with -2 in the function and simplify to determine the output value.
r(x) = -x - 7
r(-2) = -(-2) - 7
r(-2) = 2 - 7
r(-2) = -5
When x = 0. replace all the occurrence of x with 0 in the function and simplify to determine the output value.
r(x) = -x - 7
r(0) = -(0) - 7
r(0) = 0 - 7
r(0) = -7
When x = 5. replace all the occurrence of x with 5 in the function and simplify to determine the output value.
r(x) = -x - 7
r(5) = -(5) - 7
r(5) = -5 - 7
r(5) = -12
Therefore the output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
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PLSS HELP :((
will mark brianlist if its the correct answer ty
The step 2 should be m∠p + m∠o = 180 degrees(supplementary angles)
How to find the angles of a triangle?The external angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles(remote interior angles) .
Therefore,
Step 1
m∠m + m∠n + m∠o = 180°(sum of angles of a triangle)
It's very correct
Step 2
m∠p - m∠o = 90 degrees(Alternate angles)
This is incorrect.
It should be m∠p + m∠o = 180 degrees(supplementary angles)
The angles m∠p and m∠o are supplementary angles. This simply implies the angles add up to 180 degrees.
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PRACTICAL APPLICATIONS: DO YOU ADD, SUBTRACT, MULTIPLY, OR DIVIDE
36. ELECTRICAL TRADES: From a roll of no. 12 wire an electrician cut the following lengths:
9, 13, 42, and 12 feet. How many feet of wire did he use?
Using addition, Total length of wire used by the electrician is 76 feet.
What would you say about addition?Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.
What does addition serve as?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
We will use simple addition here,
Total length used by electrician is
(9 + 13 + 42 + 12) feet.
= 76 feet
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Using the division properties, how can the expression 2/5÷(−5/5) be simplified? Drag and drop your answers into the boxes to complete the statement.
The required solution of the given expression is -2/5 as a simplified form.
What is expression?
An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined
Given:
The given expression is
2/5÷(−5/5)
According to given question we have
The expression is
2/5÷(−5/5)
=2/5÷(-1)
=2*(-1)/5
=-2/5
Therefore, the required solution of the given expression is -2/5 as a simplified form.
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Which function represents the equation of the line?
Answer:
A linear function is of the form f(x)= mx+b
5⋅f(1)+5⋅g(9)=5, dot, f, left parenthesis, 1, right parenthesis, plus, 5, dot, g, left parenthesis, 9, right parenthesis, equals A coordinate plane. The x- and y-axes both scale by one. There is a graphed function, y equals f of x, which is made up of line segments. A line segment connects negative ten, negative six to negative eight, negative six. A line segment connects negative eight, negative six to negative seven, negative seven. A line segment connects negative seven, negative seven to negative six, negative seven. A line segment connects negative six, negative seven to negative five, negative six. A line segment connects negative fix, negative six to negative three, negative six. A line segment connects negative three, negative six to negative two, negative five. A line segment connects negative two, negative five to negative one, negative seven. A line segment connects negative one, negative seven to zero, negative five. A line segment connects zero, negative five to two, negative five. A line segment connects two, negative five to three, negative three. A line segment connects three, negative three to four, negative three. A line segment connects four, negative three to five, negative two. A line segment connects five, negative two to six, negative three. A line segment connects six, negative three to seven, negative two. A line segment connects seven, negative two to eight, negative two. A line segment connects eight, negative two to ten, negative four. There is another graphed function, y equals g of x, which is also made up line segments. A line segment connects negative ten, one to negative nine, two. A line segment connects negative ten, zero to negative nine, zero. A line segment connects negative nine, zero to negative eight, two. A line segment connects negative eight, two to negative seven, three. A line segment connects negative seven, three to negative six, three. A line segment connects negative six, three to negative five, two. A line segment connects negative five, two to negative four, ze
I don't know I really needed help on this one
Expand each binomial.
(2 x-3)⁷
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (2x - y)⁴
By using binomial expansion theorem, we get
(2x - 3)⁷ = 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187
(2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
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f(x)= x; translation 2 units right followed by a horizontal stretch by a factor of 2
Answer: f(x) = | x |
Step-by-step explanation:
when transforming and translating a function, you use the form a | x - h | + k
a= vertical shrink/stretch factor
h = horizontal movement ( right or left)
k = vertical movement ( up or down )
So a = 1/2 h = 0 and k =2
g(x) = 1/2 | x-0 | + 2
g(x) = 1/2 | x | + 2 [which means vert shrink of 1/2 and up 2 units ]
Scott borrowed $985 for a new TV and game system. He made 6 monthly payments to repay the loan. He paid $155 interest. What is his simple interest rate?
Based on the amount that Scott borrowed for the new TV and game system, and the interest paid, the simple interest rate is 15.7%
What is the simple interest rate?The simple interest rate can be found by the formula:
= Interest paid by Scott on the loan / Amount Scott borrowed x 100%
Solving for the simple interest rate gives:
= 155 / 985 x 100%
= 0.1573604060913705583756345177665 x 100%
= 0.157 x 100%
= 15.7%
This means that Scott paid 15.7% on the loan he borrowed.
In conclusion, Scott's simple interest rate is 15.7%.
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An arrow is modeled on the coordinate plane as shown. What is the area of the arrow? Round your answer to the nearest tenth, if necessary.
y
(0,3)
(0, 1)
O
(4,4)
(4.5,3)
(4.5,1)
(4,0)
(8, 2)
square units:
X
l o o k i t u p o n g a u t h m a t h c o p y u r q e s t i o n t h e r e
Step-by-step explanation: You're welcome
Use the graph to answer the following question.
If ∆ PQR is translated left 2 and down 6, what would be the coordinates of R' ?
The coordinate of the point R' after translation will be (0, - 4).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
If ∆PQR is translated left 2 and down 6. Then the translation rule is given as,
(x', y') → (x - 2, y - 6)
From the graph, the coordinate of point R will be at (2, 2). Then the coordinate of the point R' after translation will be
(x', y') → (2 - 2, 2 - 6)
(x', y') → (0, - 4)
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SOMEONE PLEASE HELP 100 points
Answer:
A) No solution
B) No solution
Step-by-step explanation:
[tex]A)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Which in this case leads to no solution because c cannot be less than 0 logically)
[tex]B)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Whether you change the </> sign or not, c cannot be any less than 0 or it will lead to no solution.)
Answer:
All real numbers im pretty sure
Step-by-step explanation:
A holiday company offer a 12% discount if you book before 31st March. How much
would you pay today for a holiday to France if the full price is £1,245?
Dan's has a current credit card statement of $785. his credit card apr is 24.42%. what would be his finance charge if he does not pay the balance in full?
A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.
If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.
Current Balanced Owned =$785
APR = 24.42%
Let’s suppose the billing cycle is 30 days, then
Finance charge = $15.76
The new balance you owe = $800.76.
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GSE Geometry
Unit 3
Check For Understanding!!
Parallel Lines cut by a Transversal
1. Given and m/8 = 119, find the measures of all the
numbered angles in the figure.
m<1=_
m<2=_
m<3=_
m<4 = _
m<5 =_
m<6 =_
m<7=_
The measure of all the angles are :
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
According to the question we have been given two parallel lines which is cut by a transversal line. There total 8 angles and given is the measure of
∠8 = 119°.
We need to find the measure of all other 7 angles.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
So according to the rules given above the measure of all the angles are:
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
Hence measure of all the angles is given above
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The 3rd term of (a-b)4 is
The third term of the expansion is 6a^2b^2
How to determine the third term of the expansion?The binomial term is given as
(a - b)^4
The r-th term of the expansion is calculated using
r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)
So, we have
3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)
Evaluate the sum and the difference
3rd term = C(4, 2) * (a)^2 * (-b)^2
Evaluate the exponents
3rd term = C(4, 2) * a^2b^2
Evaluate the combination expression
3rd term = 6 * a^2b^2
Evaluate the product
3rd term = 6a^2b^2
Hence, the third term of the expansion is 6a^2b^2
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T is known that 3% of people whose luggage is screened at an airport have questionable objects in their luggage. what is the probability that a string of 15 people pass through screening successfully before an individual is caught with a questionable object? what is the expected number of people to pass through be- fore an individual is stopped?
The probability that a string of 15 people passes through screening successfully before an individual is caught with a questionable object is 0.3040 and the expected number of people to pass through be- fore an individual is stopped 49
3% of people whose luggage is screened at an airport have questionable objects in their luggage i.e
P(x)=3/100=0.03
The probability of people whose luggage is screened at an airport and have no questionable object in their luggage is
〖P(x)〗^1=1-P(x)
〖P(x)〗^1=1-0.03
〖P(x)〗^1=0.97
Using Binomial probability which states that
P(x)=(nCx) (p)^x (q)^(n-x)
N= 16 total number in consideration
p= probability with no questionable luggage
q= probability with questionable luggage
P(15)=(16C15) (p)^15 (q)^(16-15)
P(15)=(16C15) (0.97)^15 (0.03)^(16-15)
16C15=16!/((16-15)!(15!))
15C15=15!/((1)!(15!))
16C15=20922789888000/((1)(1307674368000))
16C15=20922789888000/1307674368000
16C15=16
P(15)=(16) (0.97)^15 (0.03)^1
P(15)=(16)(0.63325)(0.03)
P(15)=0.3040
P(x) =(Required outcome)/(Total outcome)
0.3040 =15/(Total outcome)
Total outcome=15/0.3040
Total outcome=49.34
Total outcome=49
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n + 30 + 2n - 10 + 70 =180
Answer:
n=30
Step-by-step explanation:
n+30+2n-10+70=180
We move all terms to the left:
n+30+2n-10+70-(180)=0
We add all the numbers together, and all the variables
3n-90=0
We move all terms containing n to the left, all other terms to the right
3n=90
n=90/3
n=30
Please Help! Determine the range of the following graph:
the range of the function in the graph is:
-4 ≤ y ≤ 2
How to determine the range of a given graph?For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.
Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.
If we look at the graph, we can see that the minimum value of y is:
y = -4
And we can see that the maximum value of y is:
y = 2
Then the range of the function in the graph is:
-4 ≤ y ≤ 2
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2.) Which represents the part of the 10-by-
10 grid that is shaded?
A
B
C
D
10
3
1-
20
A garden center is recording the heights of its available trees. Which of the following displays could be used to represent the data, and why?
A. Bar chart, because tree height is numerical
B. Box plot, because tree height is numerical
C. Histogram, because tree height is categorical
D. Stem-and-leaf-plot, because tree height is categorical
When the garden is recording the heights of its available trees. the display that can be used to represent the data by a Bar chart, because tree height is numerical. The correct option is A.
What is a bar chart?
A bar chart or bar graph uses rectangular bars with heights or lengths proportional to the values they represent to show categorical data. A bar plot could be either vertical or horizontal. A vertical bar graph is sometimes known as a column chart.
A bar chart is used to show the distribution of data points or to compare metrics across different subgroups of your data. We may see how different groups compare to one another and which groupings are most common or prevalent using a bar graph.
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Answer:
Step-by-step explanation:
i think its A., bart chart
Suppose the function f(x)=0.15 x represents the number of U.S. dollars equivalent to x Chinese yuan and the function g(y)=14.07 y represents the number of Mexican pesos equivalent to y U.S. dollars.
a. Write a composite function that represents the number of Mexican pesos equivalent to x Chinese yuan.
A composite function that represents the number of Mexican pesos equivalent to x Chinese yuan. h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
What is the composite function that represents the number of Mexican pesos equivalent to x Chinese yuan ?x yuan to y dollars = f(x)
f(x) = 0.15 x
y dollars to x yuan
y= 0.15 x
x = y / 0.15
y dollars to x pesos =g(y)
g(y) =14.07 y
x pesos to y dollars
x = 14.07 y
y = x / 14.07
Substituting the result of second into first,
pesos → dollars → yuan
Lets call this function, h(x) = converts x pesos into y yuan.
h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
= 0.474 x
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i need help with this
Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.
How to illustrate the information?It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.
In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.
Therefore, it should be noted that 8.33 will be:
= 8 + 1/3
It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...
Therefore, the appropriate fraction for 8.33 will be 8 1/3.
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