When the Federal Reserve decreases the reserve rate from 7% to 5%, the amount of money resulting from fraction-reserve banking increases. In this case, an initial deposit of $30,000 would result in $28,500 due to the change in reserve rate.
Explanation:When the Federal Reserve decreases the reserve rate from 7% to 5%, it means that banks are required to hold a smaller percentage of deposits as reserves. This change allows banks to lend out a larger portion of the initial deposit. In this case, if the initial deposit into a bank is $30,000, the amount that would result from fraction-reserve banking would increase because the bank can now lend out a greater percentage of the deposit.
To calculate the new amount that would result from fraction-reserve banking, we need to calculate the reserve amount and the loan amount.
Therefore, the amount that would result from fraction-reserve banking from an initial deposit of $30,000 would be $28,500.
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−42v+33<8v+91 solve for v
The value of v is v > -1.16.
What are Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given linear inequality is
−42v + 33 < 8v + 91
We have to take like terms on one side.
-42v and 8v are like terms and 33 and 91 are like terms.
Subtracting 8v from both sides,
−42v + 33 - 8v < 8v + 91 - 8v
-50v + 33 < 91
Subtracting 33 from both sides,
-50v + 33 - 33 < 91 - 33
-50v < 58
Dividing both sides by -50, the inequality sign changes.
v > -58 / 50
v > -1.16
Hence the solution for the inequality is v > -1.16.
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Ellen walks dogs on weekends. She gets paid $8.50 per hour. Each day she works five hours and 45 minutes. How much does Ellen get paid per weekend?
what's the answer to this equation?
The perimeter p of a rectangle is related to the length l and width w through the equation p=2l+2w. determine the width in terms of the perimeter and length.
Of the ice cream cones sold yesterday at percy's ice cream shop, 1/3 were chocolate and another 1/2 were vanilla. what fraction of the ice cream cones sold were either chocolate or vanilla
The required fraction of the ice cream cones sold were either chocolate or vanilla is 5/6.
What is Least Common Denominator?The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.
We have been given that of the ice cream cones sold yesterday at Percy's ice cream shop, 1/3 were chocolate and another 1/2 were vanilla.
We have to determine the fraction of the ice cream cones sold were either chocolate or vanilla
1/3 equals 2/6
According to the given question,
The fraction of either vanilla or chocolate will be:
⇒ 1/3 + 1/2
Change into a lowest common denominator,
⇒ 2/6 + 3/6
Apply the addition operation to get
⇒ 5/6
Therefore, the required fraction of either vanilla or chocolate is 5/6.
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an ice cream factory makes 260 quarts of ice cream in 10 hours. How many quarts could be made in 36 hours? What was that rate per day?
Final answer:
The ice cream factory can make 936 quarts in 36 hours and the rate per day is 624 quarts.
Explanation:
To find out how many quarts of ice cream can be made in 36 hours, we can set up a proportion based on the rate of production. The rate of production is 260 quarts of ice cream in 10 hours. We can set up the proportion:
260 quarts / 10 hours = x quarts / 36 hours
Cross-multiplying, we get:
10x = 260 * 36
Simplifying, we find:
x = (260 * 36) / 10 = 936
Therefore, 936 quarts of ice cream can be made in 36 hours.
To find the rate per day, we need to calculate how many quarts can be made in 24 hours. We can set up the proportion:
260 quarts / 10 hours = y quarts / 24 hours
Cross-multiplying, we get:
10y = 260 * 24
Simplifying, we find:
y = (260 * 24) / 10 = 624
Therefore, the rate per day is 624 quarts of ice cream.
I need help with #12. I have to show work too.
Explain why the equation 6|x| + 25 = 15 has no solution. When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution. When one solves, they arrive at a step where |x| is equal to a fraction that may not be represented as an integer. Since | x| must be an integer, there is no solution. When one solves, they arrive at a step where x is equal to a negative number. Since x can never be negative inside of the absolute value bars, there is no solution. The statement is false. There is a solution.
The equation 6|x| + 25 = 15 has no solution because it implies that |x| equals a negative number after simplification, and absolute values cannot be negative.
Explanation:The equation 6|x| + 25 = 15 has no solution because the absolute value of x, denoted by |x|, represents the distance of x from zero on the number line, and as such, it can never be negative. When we solve the given equation, we isolate the absolute value on one side which gives us 6|x| = -10 after subtracting 25 from both sides. Dividing by 6, we obtain |x| = -10/6, which is a negative number. However, since an absolute value cannot equal a negative number, this indicates that there is no valid solution to the equation.
What is the slope of the line shown?
Answer:
Option (b) is correct.
The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]
Step-by-step explanation:
Given: A graph with an equation of line having two points (1,6) and (-6, -3)
We have to find the slope of the given line in graph and choose the correct from the given options.
Consider the two points (1,6) and (-6, -3).
Slope between two points can be calculated using the formula as,
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex]\left(x_1,\:y_1\right)=\left(1,\:6\right),\:\left(x_2,\:y_2\right)=\left(-6,\:-3\right)[/tex]
Thus, Slope is
[tex]m=\frac{-3-6}{-6-1}=\frac{9}{7}[/tex]
Thus, The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]
Plz help! Convert 3/5 into fractions with a denominater of 15 A.9/15 B. 3/15 C.5/15 D. 6/15
Angles L and M are supplementary. What is the sum of their measures? The sum of the measures of angles L and M is
a group of 10 people ran an average of 2.7 miles in one week. if the first 4 people in the group averaged 3 miles, what did the last 6 people average
Seven years ago, kodi found a box of old baseball cards in the garage. since then, he has added a consistent number of cards to the collection each year. he had 52 cards in the collection after 3 years and now has 108 cards. kodi looking into his box of baseball cards. how many cards were in the original box? is this t(0) or t(1)? write the first few terms of the sequence. kodi plans to keep the collection for a long time. how many cards will the collection contain 10 years from now? write an equation that determines the number of cards in the collection after n years. what does each number in your rule represent?
The required equation is y = 14x + 10 which is the number of cards in the collection and he will have 150 cards after 10 years
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
As per the question, we take the two points are (3,52) (7,108)
So slope = (108 - 52) / (7 - 3) = 56/4 = 14
y = mx + b
slope(m) = 14
Substitute the value of x = 3 and y = 52 in the equation
52 = 3(14) + b
52 = 42 + b
52 - 42 = b
10 = b
So the original amount of cards is 10
If x represents the number of years, while y is the total number of cards.
y = 14x + 10
He began with 10 cards and has added 14 cards every year thereafter.
So after 10 years
y = 14(10) + 10
y = 140 + 10
y = 150
Therefore, he will have 150 cards after 10 years
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What types of triangles can have an obtuse angle?
Scalene
Right
Acute
Isosceles
What is the median of the data set?
30 52 68 65 69 61 68 75 85 78
Question 2 options:
61
65.1
68
69
Answer: The answer is 68
The above answer is incorrect.
Step-by-step explanation:
if that is the wrong answer then what is the right answer .
y+6x=11; x= -1, 0, 4
solve the equation for y then find the value of y for each value of x
What is the difference of the polynomials?
Answer:
2x^3 + 2x
Step-by-step explanation:
subtract the 2 x^4's
x^3 +x^3 = 2x^3
x +x = 2x
answer is 2x^3 + 2x
The difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]
Given the polynomials:
[tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex],We are required to find their difference which can be solved as follows:
[tex](x^4 + x^3 + x^2 + x ) - ( x^4 - x^3 + x^2 - x)[/tex]
First, open the bracket by multiplying every term you have in [tex]( x^4 - x^3 + x^2 - x)[/tex] by -1:
Thus:[tex]x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x[/tex]
Group like terms together and add them together[tex]x^4 - x^4 + x^3 + x^3 + x^2 - x^2 + x + x\\\\\mathbf{2x^3 + 2x}[/tex]
Thus, the difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]
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6(r+3)-4=2r+10+4r how do you slove that
Line SV is an angle bisector of angle RST if angle RSV = (3x+5) and angle RST = (8x-14) find x
Answer:
x=12
Step-by-step explanation:
Line SV is an angle bisector of angle RST
<RSV = <VST
Both angles are equal
m<RSV = (3x+5)
<RSV = <VST, so m<VST = (3x+5), m<RST= 8x-14
m<RST= m<RSV +m<VST
[tex]8x-14= 3x+5+3x+5[/tex]
Combine like terms and solve for x
[tex]8x-14= 6x+10[/tex]
Subtract 6x from both sides
[tex]2x-14=10[/tex]
Add 14 on both sides
[tex]2x=24[/tex]
Divide both sides by 2
x=12
in a word game, you choose a tile from the bag, replace it, and then choose another. if there are 28 vowels and 12 constants, what is the probability you will choose a constant
4. Your Turn: Find the measure of angle B. Enter only the number as your answer. *
Amy is eight years older than twice her cousin Alicia’s age. The sum of their ages is less than 32. Let x represent Alicia's age. Which inequality represents Alicia’s possible age? 0
0
0
0
Factor the polynomial given a common factor.
Suppose it took 12 riders a total of 11 days 21 hours to ride from St.joseph to Sacremento. If they all rode the same number of hours how many hours did each rider ride
can someone help me out
I don't see in the problem what she is paid for over time but it is normally 1.5 times per hour
so 40 hours at 25 = 1000
51-40 = 11 hours of over time
25 *1.5 = 37.50 per hour for over time
11 * 37.50 = 412.50
1000+412.50 = 1412.50 total
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h
A=H(A+B)/2
Solve for b.
A. B=Ah/2-a
B. B=2A/h+a
C. B=2A/h-a
D. B=2A-a/h
Answer:
The answer is b=2A/h-a
How many times as heavy is the Golden Eagle as the Red Tailed Hawk? The Golden Eagle weighs 13 9/10 lbs and the red tailed hawk weighs 3 1/2 lbs?
The Golden Eagle, weighing 13.9 lbs, is approximately 4 times as heavy as the Red Tailed Hawk, which weighs 3.5 lbs.
Explanation:To find out how many times as heavy the Golden Eagle is compared to the Red Tailed Hawk, we need to divide the weight of the Golden Eagle by the weight of the Red Tailed Hawk. The Golden Eagle weighs 13 9/10 lbs, which can be converted into an improper fraction as 139/10 or a decimal as 13.9 lbs. The Red Tailed Hawk weighs 3 1/2 lbs, which can be converted into an improper fraction as 7/2 or a decimal as 3.5 lbs.
To perform the division, we'll use the decimal form of the weights:
Golden Eagle: 13.9 lbsRed Tailed Hawk: 3.5 lbsDividing the Golden Eagle's weight by the Red Tailed Hawk's weight:
13.9 lbs ÷ 3.5 lbs = 3.9714 (approximately)
So, the Golden Eagle is approximately 4 times as heavy as the Red Tailed Hawk.
What is the radius of a circle with circumference 27 in.?
The radius of a circle with a circumference of 27 inches can be calculated using the formula for the circumference of a circle which is 2πr. Calculating this, the radius is approximately 4.3 inches.
Explanation:The subject of this question is Mathematics, more specifically, Geometry which deals with shapes, sizes and properties of figures. In this case, we are being asked to find the radius of a circle given its circumference. The circumference of a circle is calculated as 2πr, where r represents the radius and π is approximately equal to 3.14.
To find the radius (r), you would divide the circumference by 2π. Given that the circumference of the circle is 27 inches, we divide 27 by 2π (approximately 6.28). This can be further simplified to approximately 4.3 inches.
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Evaluate cot675°. i will give brainlist
The value of expression cot 675° is, - 1
We have to given that,
To find the value of cot 675°.
Now, We can find the value as,
⇒ cot 675°
⇒ cot (2 × 360 - 45)°
⇒ - cot 45°
⇒ - 1
Hence, The value of expression cot 675° is, - 1
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