Step-by-step explanation:
The reserve ratio is the central bank's mandate for banks to keep a certain reserve requirements, which are excess cash deposits that must be kept on hand and not loaned out.
Raising the ratio is contractionary since less loans can be made, but this also solidifies banks' balance sheets.
If the Federal Reserve instead lowers the reserve ratio through an expansionary monetary policy, commercial banks are required to hold less cash on hand and can make more loans.
The lowering of the interest rate on reserves, considered an expansionary monetary policy, as it encourages banks to lend money instead of keeping it in reserve.
Hence, option 1 is correct.
Lowering the interest rate on reserves is considered an expansionary monetary policy because it incentivizes banks to lend out their excess reserves rather than keeping them idle in reserve accounts. When the central bank reduces the interest rate on reserves, it effectively lowers the opportunity cost for banks to hold reserves.
As a result, banks are more inclined to lend money to consumers and businesses at lower interest rates, which stimulates borrowing and spending in the economy. Increased lending and spending contribute to economic expansion and growth, making it an expansionary monetary policy.
Thus, lowering the interest rate encourages banks to lend money instead of keeping it in reserve.
Learn more about monetary policy here:https://brainly.com/question/28199887
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Pls answer this pls pls
1) 520
2)60
3)2600
4)3760
Answer:
1. 520
2. 60
3. 2600
4. 3760
Step-by-step explanation:
[tex]{hope it helps}}[/tex]
Find the area of a circle with radius, R = 6.37m.
Give your answer rounded to 2 DP
Answer:
A = 127.48 rounded
Step-by-step explanation:
Area of a circle:
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi[/tex][tex](6.37)^{2}[/tex]
A = 127.48 rounded
Answer:
It's 127.47
First we take the radius and square it
6.37^2
then we multiply it by pi
40.5769 x π = 127.47
Relationships between x and y
Answer:
so both tables are proportional
1. in the green table
y divided by x =
1/5 for each row
2. in the blue table
y divided by x =
2/5 for each row
Step-by-step explanation:
/ means divided by
divide y by x
for both tables
in each table
if y divided by x
show the same number
for every row
then its proportional
1. in the green table
y divided by x =
1/5 for each row
2. in the blue table
y divided by x =
2/5 for each row
so both tables are proportional
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=5
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
5²+5²=h²
50=h²
h=[tex]\sqrt{50}[/tex]
x=[tex]\bold{5\sqrt{2}}[/tex]
please help me please help me
Answer:
the answer is 1
Step-by-step explanation:
(√4 / √6) + (√6 / √4)
(2 / 2√3) + (2√3 / 2)
√3 / √3
= 1
Mark rolls a fair dice 48 times. How many times would Mark expect to roll a one?
Answer:
8 Times, Mark would expect to roll a one 'Eight times'
The difference between $500.02 - $79.3 add explanation if possible
Answer:
420.72
Step-by-step explanation:
60
What is the value of x in the equation x - y = 30, when y= 15?
O. 4
O. 8
O. 80
O. 200
Answer:
Step-by-step explanation:
x - y = 30
Substitute 15 for y.
x - (15) = 30
Add 15 to both sides.
x = 45
h (t) = -10t + 6
h ( ? ) = -44
I'm looking for the T that goes in the parenthesis
This is from Algebra 1 - Khan Academy, Unit Functions
Answer:
[tex]{ \tt{h(t) = - 10t + 6}} \\ - 44 = - 10t + 6 \\ - 10t = - 50 \\ t = 5[/tex]
Answer:
h(5)
Step-by-step explanation:
Equate - 10t + 6 and - 44 and solve for t
- 10t + 6 = - 44 ( subtract 6 from both sides )
- 10t = - 50 ( divide both sides by - 10 )
t = 5 , that is
h(5) = - 44
solve for x
[tex] \sqrt{x^2-4x+8} +x=2 - x[/tex]
please show all workings
Answer:
[tex]\displaystyle x=-\frac{2}{3}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]
We can isolate the square root. Subtract x from both sides:
[tex]\sqrt{x^2-4x+8}=2-2x[/tex]
And square both sides:
[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]
Expand:
[tex]x^2-4x+8=4-8x+4x^2[/tex]
Isolate the equation:
[tex]3x^2-4x-4=0[/tex]
Factor:
[tex]\displaystyle (3x+2)(x-2)=0[/tex]
Zero Product Property:
[tex]3x+2=0\text{ or } x-2=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]
Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.
Testing x = -2/3:
[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]
Since the resulting statement is true, x = -2/3 is indeed a solution.
Testing x = 2:
[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]
Since the resulting statement is not true, x = 2 is not a solution.
Therefore, our only solution to the equation is x = -2/3.
Step-by-step explanation:
Hey there!
Given;
[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]
Take "X" in right side.
[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]
Squaring on both sides;
[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]
Simplify;
[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]
[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]
[tex]3 {x}^{2} - 4x - 4 = 0[/tex]
[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]
[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]
[tex]3x(x - 2) + 2(x - 2) = 0[/tex]
[tex](3x + 2)(x - 2) = 0[/tex]
Either;
3x+2 = 0
x= -2/3
Or;
x-2 = 0
x= 2
Check:
Keeping X= -2/3,
√(x²-4x+8 ) +X = 2-x
√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3
8/3 = 8/3 (True)
Now; Keeping X= 2
√{(2)²-4*2+8}+2 = 2-2
8 ≠0 (False)
Therefore, the value of X is -2/3.
Hope it helps!
A bottling company marks a 0 for every bottle that comes out correct and a 1 for every defective bottle. Estimate the probability that the next bottle is defective
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]0 \to[/tex] Correct
[tex]1 \to[/tex] Defective
Required
The probability that the next is defective
The question is incomplete because the list of bottles that came out is not given.
However, the formula to use is:
[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]
Take for instance, the following outcomes:
[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]
We have:
[tex]Total = 14[/tex]
[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's
So, the probability is:
[tex]Pr = 9 \div 14[/tex]
[tex]Pr = 0.643[/tex]
Answer:
1/20
Step-by-step explanation:
000000000000100000
It is asking the probability of a defective bottle
there is one defective bottle out of 20
what is the measure of 2?
Answer:
Value of x:
[tex]{ \tt{(7x + 1) \degree + (18x + 4) \degree = 180 \degree}} \\ { \tt{25x + 5 = 180}} \\ { \tt{25x = 175}} \\ x = 7[/tex]
Finding m‹2 :
[tex]{ \tt{m \angle2 = (7x + 1) \degree}} \\ { \tt{m \angle2 = (7 \times 7) + 1}} \\ { \bf{m \angle2 = 50 \degree}}[/tex]
Answer:
m∠2 = 50
Step-by-step explanation:
7x + 1 and 18x + 4 are angles in a linear pair.
Sum of linear pair angles is supplementary.
7x + 1 + 18x + 4 = 180
7x + 18x + 1 + 4 = 180
25x + 5 = 180
25x = 180 - 5
25x = 175
x = 175 / 25
x = 7
Substitute x = 7 in 7x + 1,
7x + 1
= 7 ( 7 ) + 1
= 49 + 1
= 50
7x + 1 and ∠2 are vertically opposite angles and vertically opposite angles are equal.
∠2 = 7x + 1
∠2 = 50
3. The following are the scores you shot in five rounds of golf: 70,80,75,75,80. The variance is: A. 3.74 C. 14 B. 196 D. 70
Answer:
Option C.
Step-by-step explanation:
For a given set of N elements:
{x₁, x₂, ..., xₙ}
The mean is given by:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
And the variance is given by:
[tex]v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}[/tex]
Then for our set:
{70, 80 ,75, 75, 80}
We have 5 elements, then N = 5
The first thing we need to find is the mean.
[tex]M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76[/tex]
Then the variance will be:
[tex]v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14[/tex]
The correct option is C, 14.
Helppp and explain thankyouuu
We have that
x - 3y = 12 and -x + y = 4
We add the 2 equations together
x - 3y + (-x + y) = 16
-> -2y = 16
-> y = -8 (1)
We plug y = -8 into -x + y =4
-> -x - 8 = 4
-> -x = 12
-> x = - 12 (2)
From (1) and (2) we could conclude that the answer is B
how many 20p coins in £4
Answer two 20p coins make 40p
Step-by-step explanation:
Answer:
20 number of 20p makes £4.
Step-by-step explanation:
Let the number of 20p be x
Therefore,
[tex]x \times 0.20 = 4\\\\x = \frac{4}{0.20} = \frac{4 \times 100}{ 20} = 4 \times 5 = 20[/tex]
Three different non-zero digits can be arranged in six different ways to
form six three-digit numbers. If the smallest three of these numbers add
to 540, what is the sum of the largest three numbers?
Answer:
1134
Step-by-step explanation:
We have 3 digits:
a, b, c
a 3 digit number can be written as:
a*100 + b*10 + c*1
Such that these numbers can be:
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Let's assume that:
a < b < c
Then the 3 smaller numbers are:
a*100 + b*10 + c
a*100 + c*10 + b
b*100 + a*10 + c
The 3 larger numbers are:
b*100 + c*10 + a
c*100 + a*10 + b
c*100 + b*10 + a
We know that the sum of the 3 smaller numbers is equal to 540, then:
(a*100 + b*10 + c) + (a*100 + c*10 + b) + (b*100 + a*10 + c) = 540
Let's simplify this:
(a + a + b)*100 + (b + c + a)*10 + (c + b + c) = 540
(2a + b)*100 + (b + c + a)*10 + (2c + b) = 540
The sum of the 3 larger numbers is equal to X, we want to find the value of X:
(b*100 + c*10 + a) + (c*100 + a*10 + b) + (c*100 + b*10 + a) = X
Now let's simplify the left side:
(b + c + c)*100 + (c + a + b)*10 + (a + b + a)*1 = X
(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X
Then we have two equations:
(2a + b)*100 + (b + c + a)*10 + (2c + b) = 540
(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X
Notice that the terms are inverted.
By looking at the first equation, we can see that:
(2c + b) = 10 (because the units digit of 540 is 0)
Then, we can see that:
(b + c + a + 1 ) = 14 (the one comes from the previous 10)
finally:
(2a + b + 1) = 5 (the one comes from the previous 14)
Then we can rewrite:
(2*c + b) = 10
(b + c + a) = 14 -1 = 13
(2a + b) = 5 - 1 = 4
Now we can replace these 3 in the equation:
(b + 2*c)*100 + (c + a + b)*10 + (2a + b) = X
(10)*100 + (13)*10 + 4 = X
1000 + 130 + 4 = X
1134 = X
The sum of the 3 largest numbers is 1134.
Emmy just bought a new laptop! She used a student discount code that took $50.75 off the original price. The discounted price of the laptop was $349.24. Let p represent the original price of the laptop. Which equation models the problem?
Answer:
can you show the equations?
Evaluate the expression,
32 +6*22-42=23
Answer:
d
Step-by-step explanation:
Given a list of candy in a field called Item and prices called Price on an empty PivotTable, how would you find out how many of each type of candy you have?
Answer:
Drag Item to both the VALUES and the ROWS area
Step-by-step explanation:
To find out how many of each type of candy you have; Drag Item to both the VALUES and the ROWS area
Find the measure of the angle indicated.
1
2
4
3
151°
6
8
7
The measure of angle 7 is
............................
...............................................................................................................................................................................................................................................................................................................
Solve the inequality. q/3 < 11
Answer:
[tex]q < 33[/tex]
Step-by-step explanation:
[tex] \frac{q}{3} < 11[/tex][tex]q < 11 \times 3[/tex]
[tex]q < 33[/tex]
Hope it is helpful....Answer:
33
Step-by-step explanation:
q/3<11
q=11×3
q=33
:. The answer is 33.
I have like no clue what this means, please help! :)
Answer:
1/9
You are being asked to "complete the square"
you need to find a value to make the quadratic a "perfect square:
the focus is -2/3 you need to "add" one half of -2/3 squared to the
equation (1/2 * -2/3)^2 .... (-2/6)^2 .... 4/36 .... 1/9
Step-by-step explanation:
Evaluate –3 2nd power + (2 – 6)(10).
Answer:
-49
Step-by-step explanation:
-3^2=-9
(2-6)*10=-40
(-9) + (-40) = -49
at a grocery store, an uncooked beef roast is on sale for $5.99/lb. At the same grocery store, prepared roast beef is available at the deli for $2.99/100g. How much more expensive is the deli roast compared to the uncooked roast?
Answer:
$7.58/lb
Step-by-step explanation:
raw roast: $5.99 per lb
deli roast: $2.99 for 100g
We know the price per lb of the raw roast.
Let's find the price per lb of the deli roast.
1 lb = 454 grams
454 grams / 100 grams = 4.54
1 lb is 4.54 times 100 g
If we multiply the price of 100g of deli roast by 4.54, we get teh price per lb.
$2.99/lb * 4.54 = $13.57/lb
raw roast: $5.99/lb
deli roast: $13.57/lb
difference in price of 1 lb: $13.57 - $5.99 = $7.58
Answer: $7.58/lb
Answer:
.01669 $/g or $7.57 $/lb
Step-by-step explanation:
$2.99/100g = .0299 $/g
1 lb = 453.59237 g.
$5.99/453.59237 g= .0132$/g
The difference of a number and seven is twelve
Write an equation to represent the sentence
Answer:19 You can use addition 12+7=19 19-7=12
Ayden's monthly bank statement showed the following deposits and withdrawals:
-−$21.78, -−$26.26, -−$91.08, $63.64, $100.54
If Ayden's balance in the account was $40.85 at the beginning of the month, what was the account balance at the end of the month?
Solve the formula c = pi d for d
A. d = pi c
B. d = c/pi
C. d = c - pi
D. d = pi/c
Answer:
B
Step-by-step explanation:
C=pi×d
C÷pi = Pi×d÷Pi
C/pi=d
Answer:
B
Step-by-step explanation:
Given
C = πd ( isolate d by dividing both sides by π )
[tex]\frac{C}{\pi }[/tex] = d
Given Q(x) = 7x − 3 and P(x) = 7x3 − 3x2 + 42x − 27, find P(x) Q(x) . (Divide using long division.)
Complete question:
Given Q(x) = 7x − 3 and P(x) = 7x3 − 3x2 + 42x − 27, find P(x) ÷ Q(x) . (Divide using long division.)
Answer:
[tex]\frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}[/tex]
The quotient = x² + 6 and the remainder = - 9
Step-by-step explanation:
Given;
Q(x) = 7x − 3
P(x) = 7x³ − 3x² + 42x − 27
To divide P(x) by Q(x) using long division, we apply the following method;
x² + 6
---------------------------------
7x − 3 √ 7x³ − 3x² + 42x − 27
− (7x³ - 3x²)
-------------------------------------
42x − 27
− (42x − 18)
----------------------------------------
− 9
[tex]Therefore, \ \frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}[/tex]
The quotient = x² + 6 and the remainder = - 9
help plsssssssssssss i really need helpppp
1. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
Answer:
y= x + 3
Step-by-step explanation:
we know that
The linear equation in slope-intercept form is equal to
y= mx + b
where
m is the slope
b is the y-intercept
step 1:
Find the slope
Take two points from the graph
see the attached figure
about (37,40) and (47,50)
The formula to calculate the slope between two points is equal to: y2-y1
x2-x1
substitute
M= 50-40/47-37
10/10 = 1
step 2:
Find the y-intercept
we have: m=1
point (37,40)
substitute in the linear equation: 40= (1) (37) + b
solve for b: 3
therefore
The linear equation is: y = x + 3
Determine if the conditional statement is true or false given the following: p is false. q is false. Is -q -p true or false?
Hello,
if p is false then ~p is true
if q is false then ~q is true
if ~p is true and ~q is true then ~q and ~p is true
