if the federal reserve decreases the reserve rate from 5% to 2.5% how does this affect the amount of money that would result because of fractional reserve banking from an initial deposit into a bank of $35000
It increases the amount by 700,000
A candy bar has 12 grams of fat. The company producing the candy bar also sells a reduced-fat version that has 25% less fat. How many grams of fat are in the reduced-fat candy bar? Do not include units in your answers
Answer:
it's 9 grams for apex
Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t^2 + cos(t) and v(0) = 2.
v(t) = t^3 + sin(t) + 2
v(t) = t^3 - sin(t) + 3
v(t) = 6t - sin(t) + 2
v(t) = t^3 - sin(t) + 2
The velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
What is instantaneous acceleration?The acceleration at any instant of time is called instantaneous acceleration. Mathematically -
a = dv/dt
dv = a dt
∫dv = ∫a dt
Given is the acceleration function as -
a(t) = 3t² + cos(t)
We know that -
a = dv/dt
dv = a dt
∫dv = ∫a dt
v{t} = ∫{3t² + cos(t)} dt
v(t) = sin(t) + t³ + C
Now -
v(0) = 2
sin(0) + 0 + C = 2
C = 2
So, we can write the velocity function as -
v{t} = sin(t) + t³ + 2
Therefore, the velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
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Which linear equation has a slope of 3 and a y-intercept of –2?
y = 3x + 2
y = 3x – 2
y = –2x + 3
y = –2x – 3
Answer: y = 3x - 2
Step-by-step explanation:
Equation of a straight line is
y=mx + c
m is the slope and c is the intercept
comparing it with the equation
y=3x - 2
m = slope =3
and c= intercept= -2
(4.5+7.6)-8*2.5 I really need help with this problem
What is the quotient when (x+3) is divided into the polynomial 2x2+3x-9
A quotient is a quantity that is obtained by dividing two integers. The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).
What is a quotient?A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.
The quotient of the division (2x²+3x-9) ÷ (x+3) can be found as shown below,
[tex]\dfrac{2x^2+3x-9}{(x+3)}\\\\=\dfrac{2x^2+6x - 3x -9}{(x+3)}\\\\=\dfrac{2x(x+3)-3(x+3)}{(x+3)}\\\\=\dfrac{(2x-3)(x+3)}{(x+3)}\\\\[/tex]
= (2x - 3)
Hence, The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).
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Margaret is reading a book. the number of pages she has left to read is 276 - 35d, where d represents the number of days she has been reading.
what does each part of the expression represent?
(note - not all options may be used)
a) the number of pages she has read during 1 week
b) the total number of pages in the book
c) the number of pages in the book
d) the number of pages she has read during d days
Answer:
Option b , c and d are the part of the expression .
Step-by-step explanation:
We are given that the number of pages she has left to read is 276 - 35d
d represents the number of days she has been reading.
276 denotes the total number of pages
35 pages denotes the number of pages read per day
35 d represents the number of pages she has read during d days
276 - 35d represents teh reamining pages
So, Option b , c and d are the part of the expression .
1.Which statement is true about this argument?
Premises:
If two lines are parallel, then the lines do not intersect.
Lines m and n do not intersect.
Conclusion:
Lines m and n are parallel.
Which statement is true about the argument?
The argument is not valid because the premises are not true.
The argument is valid by the law of syllogism.
The argument is valid by the law of detachment.
The argument is not valid because the conclusion does not follow from the premises.
2.Which statement is true about this argument?
Premises:
If a quadrilateral is a square, then the quadrilateral has four right angles.
Quadrilateral JKLM has four right angles.
Conclusion:
Quadrilateral JKLM is a square.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is valid by the law of detachment.
The statements that are true about the arguments in the question are;
1) Option C; Law of detachment
2) Option B; Law of detachment
1) We are given the premise that;
If two lines are parallel, then the lines do not intersect.
This premise is true because we know from parallel and perpendicular lines property that parallel lines never intersect each other.
With that premise, we are now given a conclusion that; Lines m and n do not intersect.
This kind of condition is known as law of detachment which states that;
If x is true, then y is also true.
Thus, Option C is correct
2) We are given the premise that;
If a quadrilateral is a square, then the quadrilateral has four right angles.
The given premise is true because from the definition of a square, all sides must be equal and all angles must be right angles.
We are now given the conclusion that;
Quadrilateral JKLM has four right angles.
This conclusion is valid because it follows the given premise.
Again like in 1 above, this follows the law of detachment.
Option B is correct
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if x-2m=p make m the subject. answer must be written as fraction.
To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.
Explanation:To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:
Start with the original equation: x - 2m = p.Add 2m to both sides to get x = p + 2m.Subtract p from both sides to get x - p = 2m.Divide both sides by 2 to isolate m: m = (x - p)/2.Now m is the subject of the equation, and it is represented as a fraction as requested.
Ax + by = c find Y show steps
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation mc026-1.jpg. Which statement best describes the relation (c, f)? It is a function because –40°C is paired with –40°F. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. It is not a function because 0°C is not paired with 0°F. It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.
Answer:
B
Step-by-step explanation:
edge
What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ?
Enter your answer in the box. Do not round any side lengths.
What is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ?
Enter your answer in the box.
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units
(1) the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
To find area of rectangle we need to find the length and width
Length = distance between (−6, 3) and (−2, −1)
Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-2-(-6))^2 + (-1-3)^2}[/tex]
= [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]
width = Distance between (−6, 3) , (−3, 6)
Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]
=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]
Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]
(2) the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1)
Area of triangle = [tex]\frac{1}{2} * base * height[/tex]
base is the distance between (0,-2) and (8,-2)
Distance = [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8
To find out height we take two vertices (8,-2) and (9,1)
Height is the change in y values = 1- (-2) = 3
base = 8 and height = 3
So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]
(3) the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1)
To find perimeter we add the length of all the sides
Distance between (−2, 1) and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3
Distance between(−2, 4) and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5
Distance between (2, 7) and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5
Distance between (6, 4) and (6, 1) = [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3
Distance between (6, 1) and (−2, 1) = [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8
Perimeter = 3 + 5 + 5 + 3 + 8 = 24
(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)
Length = Distance between (3,-3) and (4,2) = [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]
Width = Distance between (-6,4) and (4,2) = [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]
Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )
= 30.6 units
The area of the rectangle is [tex]24\;square\;units[/tex].
1. According to the question, the vertices of the rectagle are at [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].
The distance between two vertices on the coordinate plane is
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So,
[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]
Similarly,
[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]
The area of the rectangle is equals to product of length and width of the rectabgle.
So,
[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]
Hence, the area of the rectangle is [tex]24\;square\;units[/tex].
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What is the remainder when 314^162 is divided by 7?
Final answer:
To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.
Explanation:
The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.
Let's consider the powers of 314 mod 7:
3141 mod 7 = 2
3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4
3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.
Convert 30 feet per second to miles per minute.
5280 ft = 1 mi
Round to the nearest hundredth.
Answer:
0.34 miles per minute
Step-by-step explanation:
We have to convert 30 feet per second to miles per minute.
1 minute = 60 seconds
Therefore, in one minute = 60 × 30 = 1800 feet
5280 feet = 1 mile
180 feet = [tex]\frac{1800}{5280}[/tex]
= 0.3409 ≈ 0.34 mile
Therefore, 0.34 mile per minute.
Which phrase matches the algebraic expression below? (1 point)
2(x − 7) + 10
Two times the sum of x and seven plus ten
Two times the difference of x and seven plus ten
Two times x minus seven plus ten
Two times x minus the sum of seven and ten
Answer:
Two times the difference of x and seven plus ten
Step-by-step explanation:
Which expression represents the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides?
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
What is the probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.
[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]
Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
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Unless otherwise indicated, a line in geometry is understood to be _____. straight curved either
A man’s age is two years more than four times his son’s age. His son is now 8. How old is the man?
Tom has been given 35 chores to complete today. This morning he finished 7 of them. How many chores does he now have left to do?
28 chores he now has left to do.
What is subtraction?An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreased and became lower when people eliminated it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.
35 tasks have been assigned to Tom for today.
He accomplished 7 of them this morning.
The remaining days are:
= 35-7
= 28 chores
The remaing chores are 28.
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Petro had $15 dollars. He spent $9 dollars on a book. His friend had $12 how much money did pedro have left
Determine which of the following terms is a function: a. (1,2) (2,4) (3,5) c. (1,2) (2,4) (2,6) b. (1,2) (2,3) (1,5) d. (1,2) (3,5) (3,7)
Answer:
A is the mofluffin answer
Step-by-step explanation:
A line passes through the origin and has a slope of 4. What is the equation of the line that is parallel to the first line and passes through the point (1, –2)? A. y = 4x + 9 B. y = –4x + 2 C. y = 4x – 6 D. 2003-10-03-00-00_files/i0160000.jpg
Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
A line passes through the origin and has a slope of 4
y=4x is the equation of the line.
We have to find the equation of the line that is parallel to the first line and passes through the point (1, –2)
Slope is 4 as it is parallel.
We have to find the y intercept
-2=4(1)+b
b=-6
So equation is y=4x-6
Hence, Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)
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Help me with this question plzzzz
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
14.6 units
15.5 units
21.0 units
21.6 units
see the attached figure to better understand the problem
we know that the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Let
[tex]A(-3,3)\ B(3,4))\ C(3,-3)[/tex]
Step 1
Find the distance AB
[tex]A(-3,3)\ B(3,4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-3)^{2}+(3+3)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(6)^{2}}[/tex]
[tex]dAB=\sqrt{37}\ units[/tex]
Step 2
Find the distance BC
[tex]B(3,4))\ C(3,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-4)^{2}+(3-3)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(0)^{2}}[/tex]
[tex]dBC=7\ units[/tex]
Step 3
Find the distance AC
[tex]A(-3,3)\ C(3,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-3)^{2}+(3+3)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(6)^{2}}[/tex]
[tex]dAC=\sqrt{72}\ units[/tex]
Step 4
Find the perimeter of the triangle
we know that
the perimeter of the triangle is the sum of the length sides of the triangle
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=\sqrt{37}\ units+7\ units+\sqrt{72}\ units=21.6\ units[/tex]
therefore
the answer is
the perimeter of the triangle is [tex]21.6\ units[/tex]
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
27°
36°
54°
72°
The measure of the vertex angle is 72 degrees
Isosceles triangleThe sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;
54 + 54 + x = 180
where
x is the vertex angles
Simplify
108 + x = 180
x = 180 - 108
x = 72 degrees
Hence the measure of the vertex angle is 72 degrees
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what is the decimal equivalent to 15 1/4
The equivalent decimal number will be 15.25.
What is Decimal number?
A decimal number is a number that consists of a whole and a fractional part.
Given that;
The number is,
⇒ 15 1/4
⇒ 61 / 4
Now,
Solve the number in decimal form as;
The number is,
⇒ 15 1/4
⇒ 61 / 4
⇒ 61 ÷ 4
After divide we get;
⇒ 61 ÷ 4 = 15.25
Thus, The equivalent decimal number will be 15.25.
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In a triangle, two of the angles measure 78o and 56o. What is the measure of the third angle?
You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $120 and you pay 80% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?
An equation is formed when two equal expressions. The number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that you are choosing between two plans at a discount warehouse.
The cost for x number of merchandise under plan A, which offers an annual membership fee of $120 and you pay 80% of the manufacturer's. Therefore, the cost will be,
Cost = 120 + 0.8x
The cost for x number of merchandise under plan B, which offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. Therefore, the cost will be,
Cost = 40 + 0.9x
Now, in order to find the number of merchandise that you would have to purchase in a year to pay the same amount under both plans, you need to equate the two equations together. Therefore,
Cost from Plan A = Cost from Plan B
120 + 0.8x = 40 + 0.9x
120 - 40 = 0.9x - 0.8x
80 = 0.1x
x = 80 / 0.1
x = 800
Hence, the number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
Further, the cost for each plan for 800 merchandise can be written as,
PlanA,
Cost = 120 + 0.8(800)
= $760
Plan B,
Cost = 40 + 0.9(800)
= $760
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What’s the best answer
Sine: the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.
What is the Sine of angle A?
3/4
4/3
3/5
4/5