Answer:
[tex]2,8,14,20[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:
[tex]a_n=6n-4[/tex]
Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].
You want to open an account with $1,700. You can earn 2.7% interest each year, and you plan to leave this account for 9 years. How much more would the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest?
$2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
Given that, principal = $1700, rate of interest = 2.7% and time period = 9 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, simple interest = (1700×2.7×9)/100
= 41310/100
= $413.10
Amount = Principal + Simple interest
= 1700+413.10
= $2113.1
Compound interest:
[tex]Amount=P(1+\frac{R}{100} )^{nt}[/tex]
[tex]=1700(1+\frac{2.7}{100} )^{4\times9}[/tex]
[tex]=1700(1.027)^{36}[/tex]
= 1700×2.609
= $4435.3
Now, 4435.3-2113.1=$2322.2
Therefore, $2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
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Rohan bought some tiles for a kitchen floor. 3/5 of the tiles were white, 1/4 of the
remainder were yellow, and the rest were blue. There were 60 more white
tiles than blue tiles. Each tile cost $3. What was the total cost of the tiles?
The cost the tiles are = $182.55
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
white tiles =W = 1/4
3/5 = yellow
each tile costs= $3
= 0.25+ 0.6+ 60
= 60.85*3
$182.55
hence,The cost the tiles are = $182.55
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1. Write an addition problem that has a sum of -4 a. The two addends have the same sign. b. The two addends have different signs.
Answer:
a. -1 + (-3)
b. -9 + 5
Step-by-step explanation:
the sum of two numbers = -4
a.
two addends have the same sign
Since the sum is negative, then both addends must be negative.
Answer: -1 + (-3) =
b.
two addends have different signs
One addend is positive, and one addend is negative. Since the sum is negative, then the addend with the greater absolute value must be negative.
Answer: -9 + 5 =
PLEASE HELP ME
Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
3x - 2 (2.3x + 2.5) = -1.6x -5
5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions while 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
How to determine if the linear expressions are equivalent?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: 3x - 2 (2.3x + 2.5) = -1.6x -5 and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3
For 3x - 2 (2.3x + 2.5):
First, clear the parenthesis by using -2 to multiply what's in the parenthesis. Then add/subtract like terms:
3x - 2 (2.3x + 2.5) = 3x-4.6x- 5 = -1.6x-5
For 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3:
First, clear the parenthesis by using -3 to multiply what's in the parenthesis. Then add/subtract like terms:
5 - 3 (-1.6x - 2.1) = 5 + 4.8x + 6.3 = 4.8x + 11.3
Since 3x - 2 (2.3x + 2.5) is equal to -1.6x-5 and 5 - 3 (-1.6x - 2.1) is not equal to 4.8x - 1.3.
Therefore, 3x - 2 (2.3x + 2.5) = -1.6x-5 are equivalent expressions and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions
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Presley has (9x-10) bracelets and sells (4x + 5). How many
bracelets does Presley have left? Write an expression
to show the difference.
Presley have 1 bracelets left and the expression which shows the difference is (9x - 10) - (4x + 5) .
What is linear polynomial equation?
Any polynomial written as the equation p(x) = ax + b, with a and b being real numbers and a 0, is referred to as a linear polynomial. The largest exponent of the variable in a linear polynomial, or one, is known as the degree of the variable.
If n elements are given and x element is subtracted from the n elements, hence the remaining element is y, then expression can be expressed by n- x = y.
We have,
(9x - 10)
(4x + 5)
Initially Presley has (9x - 10) bracelets and she sells (4x + 5), hence we have to calculate the remaining bracelets.
Therefore,
(9x - 10) - (4x + 5)
By simplifying the above equation we get,
= 9x - 10 - 4x + 5
= 5x -5
x = 5 / 5
∴ x = 1
Hence, the Presley have 1 bracelets left.
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A stock’s price fluctuations are approximately normally distributed with a mean of $26.94 and a standard deviation of $3.54. You decide to sell whenever the price reaches its highest 20% of values. What is the highest value you would still hold the stock?
The highest value you would still hold the stock is $23.97
How to determine the highest value you would stock??From the question, the given parameters about the distribution are
Mean value of the set of data = $26.94
Standard deviation value of the set of data = $3.54
Proportion = Highest 20%
This means that the p value is
p = 20%
Express as decimal
p = 0.2
At a p value of 0.2, the z-score is
z = -0.84
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
-0.84 = (x - 26.94)/3.54
Cross multiply in the above equation
So, we have
x - 26.94 = -0.84 * 3.54
Evaluate the products
x - 26.94 = -2.97
Add 26.94 to both sides of the equation
So, we have the following representation
x = 26.94 -2.97
Evaluate the difference
x = 23.97
Hence, the highest value is 23.97
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how do i factor (x + 2)^2 - (y - 2)^2???
The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).
Difference of two squaresIf for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).
Given the two squares (x + 2)² and (y - 2)²
then their difference will yeild the factors derived as follows;
(x + 2)² - (y - 2)² = [(x + 2) + (y - 2)][(x + 2) - (y - 2)]
open brackets
(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)
collect like terms
(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)
so
(x + 2)² - (y - 2)² = (x + y)(x - y + 4)
Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).
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what is the answer to
$224.50- $225.00
i already did calculator many different wayss
i will report wrong answers UNLESS you actually tried
Answer:_______________________________________________
-0.5
Answer:
224.50
-225.00
$0.50
- 50 cents
Answer the questions
(1) 150 cola cans and 260 fruit juice cans need to be stacked in a school canteen. If each stack is
to be of the same height and is to contain cans of the same type, what would be the greatest
number of cans each stack can have?
The greatest number of cans each stack can have is 10.
What is Greatest Common Divisor (GCD)?
The number that divides two or more numbers most precisely by itself is said to be the greatest common divisor (GCD) of those numbers. It is also defined as the highest common factor (HCF).
If a and b are two numbers then the greatest common divisor of both numbers is denoted by GCD(a, b).
Given, Total number of cola cans = 150
Total number of fruit juice cans = 260
According to the question condition, we need to find GCD (150,260)
Now, the prime factorization of 150 and 260 are:
150= 2 x 3 x 5 x 5
260 = 2 x 2 x 5 x 13
So, common factor = 2 x 5 = 10
Then, GCD (150,260) = 10
Hence, the greatest number of cans in each stack can have 10.
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3.201 x 10^9 and 4.85 x 10^3
(3.201 x 10^9) * (4.85 x 10^3) =
15524850000000
in scientifc notation
1.552485 x 10^13
what is 2 +2
4+5
0+9
Answer:
Step-by-step explanation:
2+2=4
4+5=9
0+9=9
Answer:
4, 9 , 9 OR 4 + 9 + 9 = 22
Step-by-step explanation:
1) Use the scale factor to
determine the new area of each
scale drawing.
Scale factor = 3
2 meters
4.5 meters
To determine the size of the county's moose population, naturalists catch 65 moose, tag them and
then set them free. Months later, 48 moose are caught, of which 14 have tags.
The estimated size of the moose population is___?
. (Round to nearest whole moose.)
The size of the moose population, 65 + (48-14)=99.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
naturalists have = 65 moosetheycatch and tag = 48set them free and catch them later,= 14now total moose= 65 + (48-14)99learn more about unitary method click here:
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I would need to graph the line through the given point with the given slope, only help me answer question 12 please. Thank you.
The graph of the linear equation for question 12 can be seen in the image at the end of the answer.
How to graph the line?If we have a linear equation with a slope m and a point (h, k=, the point-slope form of that linear equation is:
y = m*(x - h) + k
Here the slope is m = -7/4 and the point is (2, -6)
Then the linear equation is:
y = (-7/4)*(x - 2) - 6
To graph the linear equation we need two points on it, and we already know one, so we need to find the other.
To do so we can evaluate in some value of x.
If we use x = -2 we will get:
y = (-7/4)*(-2 - 2) - 6
y = (-7/4)*(-4) - 6
y = 7 - 6 = 1
So we also have the point (-2, 1)
Now we just need to graph the two given points and connect them with a line.
Below you can see the graph.
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Given loga(m) = 10 and loga(n) = 20, find loga(mn2). (Enter an exact number.)
Answer:
log(mn^2) = 50
Step-by-step explanation:
assuming base a for the logs
log(mn^2) = log m + 2log n
What are the zeros of the parabola in #1? (that is, at what points does the graph cross the x-axis?)
Picture is number one
The zeroes of the parabola is -1, -5.
What is parabola and zeroes of parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:
f(x) = y= ax2 + bx + c
To find zeroes of parabola
x = -b ±[tex]\sqrt{b^{2}-4ac } /2[/tex]
Given equation is
f(x) = [tex]x^{2} +6x+5[/tex]
a = 1, b = 6, c = 5
x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2
x = -6 ±[tex]\sqrt{16} /2[/tex]
x = -6 ± 4 /2
hence,
x = -6-4/2 and x = -6 +4/2
x = -5 or x = -1
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Mrs B invested $30,000, part at 5%, part at 8%. The total interest on the investment was $2100, how much did she invest at each rate?
(Please show working)
Answer:
$10,000 invested at 5%
$20,000 invested at 8%
Step-by-step explanation:
1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.
x + y = 30,000 (the total amount invested)
0.05x + 0.08y = 2,100 (the total interest earned)
2. Solve the system by whatever method you choose.
15. Graph 6 and 6 on the number line.
A++
-6 5 4 3 2 1 0 +1 +2 +3 +4 +5 +6
Page 6
Wilson says both 6 and 6 have an absolute value of 6. Is
Wilson correct? Use the number line and words to explain why
or why not.
Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.
How Do You Define Absolute Value?Without taking into account direction, absolute value describes how far a number is from zero on the number line.A number's absolute value can never be negative.A number or phrase is most frequently represented by the absolute value sign, which consists of two vertical straight lines, around it|-6| = 6 denotes that "6 is -6 in absolute terms.""The absolute value of the phrase -2 minus x" is what |-2 - x| denotes.The meaning of -|x| is "the opposite of the absolute value of x."The number line can be used to graph equalities and inequalities that contain expressions with absolute value in addition to displaying the distance from zero.Therefore, Wilson is correct as there is no negative term in absolute value.
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14 subtracted from the product of x and -3 is 25
Answer:
14-3x=25
Step-by-step explanation:
-3x=25+14
-3x=39
-3 -3
x = -13
A person is selected at random. A is the event “the person selected earns more than $100,000 per year” and B is the event “the person selected earns more than $250,000 per year.”
The pairs of events, A and B, that are disjoint include option A and B.
What are disjoint events?It should be noted that disjoint events simony means the events that are mutually exclusive as they can't occur at the same time.
For option A, because a person can be either male or female but not both, events A and B are disjoint.
For B, because the person already earns more than $100,000, events A and B are not disjoint.
For C, because the sum of two dice cannot be three when one die is three, events A and B are disjoint.
Therefore, A and C are disjoint.
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Complete question
Which of the following pairs of events, A and B, are disjoint?
(a) A person is selected at random. A is the event "sex of the person selected is male" and B is the event "sex of the person selected is female."
disjoint / not disjoint
(b) A person is selected at random. A is the event "the person selected earns more than $100,000 per year" and B is the event "the person selected earns more than $250,000 per year."
disjoint / not disjoint
(c) A pair of dice are tossed. A is the event "one of the dice is a 3" and B is the event "the sum of the two dice is 3."
disjoint / not disjoint
Evaluate the given function for f(2).
Answer:
3
Step-by-step explanation:
You want the value of f(2) for the graphed function.
Function valueThe value of the function f(a) is the y-coordinate of the point that has 'a' as its x-coordinate.
Finding the function value requires you locate x=a on the horizontal axis. Where the graph crosses that vertical line, the y-coordinate is the function value.
ApplicationHere, the vertical line x=2 meets the function graph at the dot with coordinates (2, 3). The y-value there is 3, so ...
f(2) = 3
Answer: [D]: " 3 " ; [that is; f(2) = 3 ].
____
We are asked to:
Evaluate the given function for f(2) ; within the given image.
By examination of the graph, we can verify that the graph is, in fact, a function—by using the vertical line test.
We find that no value for x shares more than one y-value; which means that the graph is a function.
____
Note that for a function: f(x) = y .
So; To find f(2) :
____
Note: f(2) = the "[ y - coordinate/corresponding value for y ]" ;
⇒ when " x = 2 ".
So; looking at the graph: We see that when " x = 2 " ; → " y = 3 " .
→ {Examine the co-ordinate/point: (2, 3) —that is part of the graph.}
So; f(2) = 3 ; which is Answer choice: [D]: " 3 ."
______
Hope this is helpful to you. Best wishes!
______
Write an equation in standard form of the line that passes through (-4,1) and has the slope m=3
An equation in standard form is ____ = -13
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]
Urgent .. Suppose that a national testing service gives a test in which the results are
normally distributed with a mean of 550 and standard deviation of 85. If you score a
625 on the test, what fraction of the students taking the test exceeded your score?
The fraction of the students taking the test exceeded your score will be 47 / 250.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
Assume that a public testing administration gives a test in which the outcomes are regularly dispersed with a mean of 550 and a standard deviation of 85. On the off chance that you score a 625 on the test.
Then the fraction of the students taking the test exceeded your score will be given as,
z = (625 - 550) / 85
z = 75 / 85
z = 0.8824
Then the fraction is given as,
P(x > 625) = P(z > 0.8824)
P(x > 625) = 0.188
P(x > 625) = 47 / 250
The fraction of the students taking the test exceeded your score will be 47 / 250.
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What is the sum?
3
+
x+3x+3x+3
X
2
If the pediatric floor of the hospital has 165 beds how many rooms are there if each room holds 3 beds?
What will be the rule for a negative fraction?
Maybe like -m/n instead of just m/n?
The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
An algebraic expression is a quantity made up of symbols and processes + - / and multiplication Expressions utilizing indices are made simpler using the laws of indices.
Let's consider a negative fraction exponent as, [tex]a^{-m/n}[/tex]
[tex]a^{-m/n}=1/a^{m/n}[/tex]
Since,[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Therefore, the above expression converts as,
[tex]a^{-m/n} =1/(\sqrt[n]{a})^{-m}[/tex]
[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Hence "The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].".
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~ ( ~ q → p) → ~ q is a tautology or not?
The proposition ~ (~ q ⇒ p) ⇒ ~ q represents a tautology, as it is true for all combinations of p and q.
Is a given proposition a tautology?
Propositions are constructions that contains a truth value, which are two according to classical logic (T - true, F - false). There are simple propositions and compound propositions. Compound propositions are formed by combining simple propositions and operators. There are the following operators:
∧ - Conjunction (operator "and")∨ - Disjunction (operator "or")~ - Negator (operator "not")⇒ - Implicator (operator "If-then")⇔ Double implicator (operator "if-only if")A tautology is a compound proposition that is always true. We can prove whether a proposition is a tautology by the use of a truth table:
p q ~ q ~ q ⇒ p ~ (~ q ⇒ p) ~ (~ q ⇒ p) ⇒ ~ q
T T F T F T
T F T T F T
F T F T F T
F F T F T T
The proposition ~ (~ q ⇒ p) ⇒ ~ q is a tautology.
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Write the expression 3a+2y+5ay-2y-+-52-3y in simplest form. Then, answer the following questions
using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
The simplified expression is 3a + 5ay - 3y -52 .
(a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
In the question ,
the algebraic expression is given as 3a+2y+5ay-2y-52-3y
to simplify it , we first group them in like terms
the expression becomes .
= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y
= 3a + 5ay + 2y - 2y - 3y - 52
= 3a + 5ay - 3y -52
Part(a)
the number of terms in the simplified expression is 4 ,
Part(b)
as we can see that the terms -3y and -52 are negative
So , there are 2 negative terms in the expression.
Therefore , (a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
The given question is incomplete , the complete question is
Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
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Simplify the fraction
Answer:
Step-by-step explanation:
Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 474 spoons. There are currently 246 spoons. If each set on sale contains 6 spoons, use the drop-down menu below to write an inequality representing s, the number of sets of spoons Madison should buy.
38 sets
474 - 246 = 228
228 ÷ 6 = 38