The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,
(18,000 - x) × 0.0275 + 0.0475x = 579
495 - 0.0275x + 0.0475x = 579
0.02x = 84
x = $4,200
Then the value of ($18,000 - x) is given as,
$18,000 - x = $18,000 - $4,200
$18,000 - x = $13,800
The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
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product p of three numbers x ,y,and z
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
I will give brainliest and ratings if you get this correct
The quotient rule is proved below.
What is derivative of a function?In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Given is the expression -
Q(x) = F(x)/G(x)
Quotient rule -Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -
f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Proof -Now, let f(x) = u(x) and g(x) = v(x).
Q(x) = u(x)/v(x)
Q(x) = u(x) v⁻¹(x)
Using the product rule -
Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}
Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)
Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)
Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Therefore, the quotient rule is proved above.
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What is the value of r^2 for the following data yo three decimal places ?
The correlation coefficient of the data-set in this problem is given as follows:
C. r² = 0.931.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The points from the table in this problem are given as follows:
(3,2), (4,4), (5,5), (7,6), (10,20).
Inserting these points into a calculator, the correlation coefficient is obtained as follows:
r² = 0.931.
Meaning that the correct option is given by option C.
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Find the equation of the line L
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +1}{-3 +1} \implies \cfrac{ 2 }{ -2 } \implies - 1[/tex]
[tex]\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}{- 1}(x-\stackrel{x_1}{(-1)}) \implies y +1 = - 1 ( x +1) \\\\\\ y+1=-x-1\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}[/tex]
Which represents the solution to the inequality 5.1(3+2.2x)>-14.25-6(1.7x+4)?
X=<-2.5
x>2.5
(-2.5,~)
(-~,2.5)
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one
of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is
answer
C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123
explanation
The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).
The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Equations 4 and 5 are not equivalent to any of the other equations.
What is a equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The equations that are equivalent are:
2 + x = 5
Negative 5 + x = negative 2
x + 1 = 4
Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
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Please help:) calculus asking about delta functions
The required solution of the given expression δ = 0.0002. as of the given conditions
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.
Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,
|5x - 15| = |5(3 + δ) - 15|
= |15 + 5δ- 15|
= |5δ|
Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,
|5δ|/5 < 0.001/5
|δ| < 0.001/5
Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.
Similarly, if x = 3 - delta, we have:
|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|
|-5δ|/5 < 0.001/5
|δ| < 0.001/5
So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.
Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.
So, δ= 0.001/5 = 0.0002.
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This right circular cylinder has a radius of 8 in. And a height of 15 in. What is its volume, v?.
The volume of the cylinder is approximately 9,558.4 cubic inches.
The volume V of a right circular cylinder is given by the formula:
V = πr^2h
where r is the radius of the circular base and h is the height of the cylinder.
In this case, the radius is 8 inches and the height is 15 inches. Substituting these values into the formula, we get:
V = π(8^2)(15)
= π(64)(15)
= 3,040π cubic inches
Therefore, the volume of the cylinder is 3,040π cubic inches. If you want an approximate value, you can use the approximation π ≈ 3.14 and calculate:
V ≈ 3,040(3.14)
≈ 9,558.4 cubic inches
So, the volume of the cylinder is approximately 9,558.4 cubic inches.
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Describe the transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4
A:The graph is vertically stretched by a factor of 1/3 and shifts up 4 units.
B:The graph is vertically stretched by a factor of 1/3 and shifts down 4 units.
C:The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
D:The graph is horizontally compressed by a factor of 1/3 and shifts down 4 units.
The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
How to explain the transformationThe parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.
This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.
The correct option is C.
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1. Is Event 1 and Event 2 Mutually Exclusive of each other? Event 1: Pre- Schooler is a girl Event 2: Pre- Schooler prefers the color blue to the color pink Select one: a. No, A girl pre-schooler can prefer the color blue to the color pink. b. Yes, The gender of pre-schooler has no affect on color preference c. Yes, Girls prefer the color pink to the color blue 2. 70 preschoolers were asked whether they preferred blue or pink. 35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color. Assuming one of the pre-schoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
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To encourage bulk buying, a company reduces the list price of $4,000 per unit by
three cents times the number of units bought. Write a function statement for the
company's revenue (R) from a particular distributor that buys x units.
R(x) =
The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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The angles of a triangle are in the ratio of 2 : 3 : 7. Find the measure of the two greatest angles of the triangle.
Answer:
Step-by-step explanation:
The measure of the two greatest angles is 105° and 45°
Let the angles be 2x, 3x and 7x ...... (i)
According to the 'Angle Sum Property' of triangle,
2x + 3x + 7x = 180°
12x = 180°
x = 15°
Now, put value of x in (i)
2x = 2 × 15 = 30°
3x = 3 × 15 = 45°
7x = 7 × 15 = 105°
so, the two greatest angles are 105° and 45°
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could you please help me find out how to add m+x
Answer:
i got u i have your email
Step-by-step explanation:
A bank developed a model for predicting the average checking and savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth
The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.
Given that;
The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.
Now,
-17,732 is a constant amount credited from the savings acount
367 is the amount saved per year of age
1300 is the amount saved per year of education
0.116 is the amount save per household wealth
Therefore, the following are the interpretations of the equation.
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Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...
Answer:
The [tex]66[/tex]th term is [tex]363[/tex].
Step-by-step explanation:
To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have
[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].
Answer:
a₆₆ = 363
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then
a₆₆ = - 92 + (65 × 7)
= - 92 + 455
= 363
Find the exact value of x
Answer:
When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.
You want to subtract 9 and 24 to get the x value:
24 - 9 = 15
x = 15
Step-by-step explanation:
Hope it helps! =D
Hi there, here's your answer:
Given a right angled triangle
With the hypotenuse as 24 units and one of the legs as 9 units
To find:
The 3rd side denoted as 'x'
Solution:
We use Pythagoras Theorem:
[tex]a^2 + b^2 = c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
We know the value of c and b
And a = x
Thus,
[tex]x^2 = c^2 - b^2[/tex]
[tex]x^2 = 576 - 81\\[/tex]
[tex]== > x^2 = 495\\[/tex]
Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units
Hope it helps! Please mark as Brainliest!
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Subtract 5m + 11 and m + 8
The expression (m + 8) - (5m + 11) simplifies to -4m - 3.
How to subtract the expresisonsFrom the question, we have the following parameters that can be used in our computation:
Subtract 5m + 11 and m + 8
To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:
(m + 8) - (5m + 11)
Open the brackets
= m + 8 - 5m - 11
Evaluate the like terms
= -4m - 3
Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.
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Use the distributive property to evaluate 4(2x - 1) when x = 6.
O44
04
40
O 47
The value of the expression 4(2x - 1) when x = 6 is 44. Option A
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.
They are also identified with arithmetic operations, such as;
AdditionMultiplicationDivisionSubtractionBracketParenthesesFrom the information given, we have that;
4(2x - 1)
expand the bracket, we get;
8x - 4
Substitute the value of x as , we have;
8(6) - 4
Multiply
48 -4
Subtract the values
44
Hence, the value is 44
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Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?
Answer: your mom
Step-by-step explanation:
Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
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what must be added to each term of the ratio 49:64 , so that it becomes 3:4 ?
Answer:
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.
Step-by-step explanation:
have a nice day.
What else would need to be congruent to show that AABC= APQR by SSS?
B
A
A. AC = PQ
B. AB BA
C. BC= QR
D. ZAZP
C
Q
P
R
Given:
AC PR
AB=PQ
The condition which satisfy the congruency of the given triangle is
BC≈QR.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
To show that triangle ABC≈triangle PQR by SSS,
In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.
Given, AC≅PR, AB≅PQ.
The another one condition is BC≅QR.
Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.
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Using The Distance Formula: What is the length of AB
With A(3,4) and B(-4,6)
A'B' = D2/3 (AB)
LEVEL 3
Record the letters
in your triangle from
left to right.
Example:
ABCDEFGHI
Enter the correct 9 letter sequence (no spaces) Use all capital letters *
Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.
What is a triangle?A triangle is a polygon with 3 sides. Also, It has three vertices.
As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.
Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.
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