The items are classified as M1, M2, or neither based on their liquidity and spendability. A line of credit and traveler's checks are neither M1 nor M2 as they are not actual money. Physical currency and money in a checking account are classified as M1, while money in a money market account is classified as M2.
Explanation:M1 refers to the narrowest definition of the money supply, which includes only the most liquid forms of money that can be easily spent. M2 is a broader measure of the money supply and includes M1 as well as other less liquid forms of money. Neither refers to items that do not fit into either M1 or M2.
a. Your $5,000 line of credit on your Bank of America card is neither in M1 nor M2 as it is not actual money but a credit limit.
b. $50 dollars' worth of traveler's checks you have not used yet is neither in M1 nor M2 as they need to be exchanged for cash before they can be spent.
c. $1 in quarters in your pocket is in M1 as it is physical currency that can be spent.
d. $1200 in your checking account is in M1 as it is a liquid form of money that can be spent.
e. $2000 you have in a money market account is in M2 as it is a less liquid form of money that can be accessed but may have restrictions or penalties for withdrawal.
An experimental vehicle is able to travel 3/8 mile on 1/16 gallon of water. What is the rate at which the vehicle can travel, in miles per gallon of water?
The rate at which the vehicle can travel is 6 miles per gallon
Solution:
Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water
To find: Rate at which the vehicle can travel, in miles per gallon of water
distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]
gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]
Miles per gallon is given as:
[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]
Substituting the given value we get,
[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]
So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon
Find cos A if a=5, c=13
Answer:
You're not giving enough details about the figure
I GIVEBRAINLIEST AND ANSWER UR WUETSIONI GAVE AWAY 20 pts SO BETTER ANSWER CORRECT AND HURRY !!
△MAD ≅ △SUN
What is the value of x?
30°
60°
90°
180°
Answer:
Step-by-step explanation:
x = 60
ΔMAD ≅ Δ SUN
So corresponding parts of congruent triangle are congruent.
∠MDA = ∠NSU
Answer:
x = 90
Step-by-step explanation:
Remember you have to post complete questions in order to get good and exact answers. So here I'll assume a diagram shown below. From the statement. we know that:
△MAD ≅ △SUN
This implies that triangle MAD is congruent to triangle SUN meaning that corresponding sides and angles measure the same. In other words:
∠M = ∠S
∠A = ∠U
∠D = ∠N
And:
MA = SU
AD = UN
MD = SN
So, from the figure:
∠S = ∠M = 30°
As the sum of internal angles of every triangle measures 180°, then:
∠S + ∠U + ∠N = 180°
And:
∠U = x°
So:
30° + x° + 60° = 180°
x° = |80° - 30° - 60°
x° = 90°
So:
x = 90
_________________________________________________________
Brainliest?, also let me know if i am wrong, Good Luck.
The area of a mirror is 225 Square inches, it's width is
[tex]13 \frac{3}{4} [/tex]
inches. Will the mirror fit in a space that is 15 inches by 16 inches? Explain.
NO. The mirror will not fit in a space that is 15 inches by 16 inches
Solution:
Given that area of mirror is 225 square inches
[tex]width = 13\frac{3}{4} \text{ inches }[/tex]
Converting the above mixed fraction we get,
[tex]width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }[/tex]
Let us find the length of mirror
The area of mirror is given as:
area of mirror = length x width
Substituting the given values,
[tex]225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36[/tex]
Thus length of mirror is 16.36 inches
Will the mirror fit in a space that is 15 inches by 16 inches?
NO. The mirror will not fit in a space that is 15 inches by 16 inches
Because length of mirror is 16.36 inches whereas the given space is 15 inches long
16.36 > 15 so the length of mirror will not fit inside the space
Also width of mirror is [tex]\frac{55}{4} = 13.75[/tex] inches which is less than the given space whose width is 16 inches
13.75 < 16 so the width of mirror will not fit inside the space
is 2×3×4the prime factorization of 24 Explain you reasoning
Answer:
see the prime factors
Step-by-step explanation:
24= 6*4=3*2*2*2
=2*3*4
Answer:
No
Step-by-step explanation:
First off, the number 4 is not a prime number and the prime factorization of a number has to consist of all prime numbers. 2*3*4 does result in 24 but 4 is not prime because a prime number is a whole number with exactly two factors, itself and 1. 4 has more than two factors; the factors of 4 are 1, 2, and 4 so 4 isn't prime.
2*2*2*3 is the prime factorization of 24 because when you break down 24 into prime numbers, the results are 2*2*2*3.
24=2*12(here, we broke the number 24 into two factors 2 and 12. it doesn't matter which factors you break the number into because you still get the same result.)
2*12=2*2*6(we broke the number 12 into 2*6 because 12 isn't prime. we have to break each number into prime numbers.)
2*2*6=2*2*2*3(finally, we broke down 6 because it is the only number left that is not prime. 2*3=6 and 2 and 3 are prime so we break down 6 into 2*3)
Now you have the prime factorization of 24!
24=2*2*2*3
You and your guest have eaten in a restaurant which had excellent service. Your bill comes to $23.00. If you leave exactly a 15% tip, what would the amount of the tip be?
Answer:
23*0.15=$3.45
Step-by-step explanation:
23*0.15=$3.45
Ms.Graves gave her class 18 minutes to read. Carrie read 6 1/2 pages in that time. At what rate, in pages per hour, did Carrie read?
Answer:
Carrie read at a rate of 21 2/3 pages per hour
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Time Ms. Graves gave her class to read = 18 minutes
Number of pages Carrie read in 18 minutes = 6 1/2 pages
2. At what rate, in pages per hour, did Carrie read?
Rate = Number of pages/Time given
For getting the exact rate per hour, we should use the Rule of Three Simple, this way:
Number of pages in 60 minutes * 18 = 6 1/2 * 60
Number of pages in 60 minutes = (6.5 * 60)/18
Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3
Carrie read at a rate of 21 2/3 pages per hour
Linear or Non - Linear
Answer:
linear
Step-by-step explanation:
This graph is linear
pls helpppppp!! before 12!
The answer is 25.12 exactly
Select the equation of the line that passes through the point (–2, –1) and has slope 5 in point-slope form. a (y + 1) = 5(x + 2) b (x + 2) = 5(y – 1) c (y – 1) = 5(x – 2) d (x – 2) = 5(y + 1)
Answer:
y+1=5(x+2)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=5(x-(-2))
y+1=5(x+2)
Factorise 1 - 25 (a+b)^2
Answer:
Step-by-step explanation:
1 - 25 (a+b)^2 = 1 - 5² (a+b)²
= 1 - (5*[a + b) ]² { [tex]a^{m} *a^{n} = a^{m+n}[/tex] }
= 1 - (5a +5b)²
= (1 + 5a +5b) (1 - [5a + 5b]) { a² - b² = (a + b)(a - b) }
=(1 + 5a +5b) (1- 5a - 5b)
Question 4
We mapped 2 triangles with a series of basic rigid motions, and showed they are
congruent. Will it be true for the opposite?
A.Yes
B.No
Question 5 (1 point)
Order does not matter with sequencing of transformations,
A.True
B.False
Give an example of an event for which the probability equals 1. Justify your answer
Answer:
If today is Saturday, the probability that tomorrow is Sunday.
Step-by-step explanation:
given f(x)=2x^2+3x-5 for what values of x is f(x) positive
Answer:
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
Step-by-step explanation:
we have
[tex]f(x)=2x^{2}+3x-5[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
The coordinates of the vertex is the point (h,k)
step 1
Find the vertex of the quadratic function
Factor the leading coefficient 2
[tex]f(x)=2(x^{2}+\frac{3}{2}x)-5[/tex]
Complete the square
[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}[/tex]
[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}[/tex]
Rewrite as perfect squares
[tex]f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}[/tex]
The vertex is the point (-\frac{3}{4},-\frac{49}{8})
step 2
Find the x-intercepts (values of x when the value of f(x) is equal to zero)
For f(x)=0
[tex]2(x+\frac{3}{4})^{2}-\frac{49}{8}=0[/tex]
[tex]2(x+\frac{3}{4})^{2}=\frac{49}{8}[/tex]
[tex](x+\frac{3}{4})^{2}=\frac{49}{16}[/tex]
take the square root both sides
[tex]x+\frac{3}{4}=\pm\frac{7}{4}[/tex]
[tex]x=-\frac{3}{4}\pm\frac{7}{4}[/tex]
[tex]x_1=-\frac{3}{4}+\frac{7}{4}=1[/tex]
[tex]x_2=-\frac{3}{4}-\frac{7}{4}=-2.5[/tex]
therefore
The function f(x) is negative in the interval (-2.5,1)
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
see the attached figure to better understand the problem
Identify all sets to which the number belongs.
-0.249851765....
a. integer
b. irrational
c.rational, integer, whole
d.rational, integer, whole, natural
Option B
-0.249851765 is a irrational number
Solution:
Given number is -0.249851765
We have to classify the number
Let us first understand about irrational, real, whole, integer and rational numbers
Integers:An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043
Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.
Thus -0.249851765 has non zero digits after decimal point. So it is not a integer
Whole numbers:Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."
But the given number -0.249851765 is negative number. So it is not a whole number
Natural numbers:A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.
A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero
So the given number -0.249851765 is a negative number and so it is not a natural number
Rational numbers:A rational number is a number that can be expressed as a fraction (ratio) in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q is not zero.
The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.
When a rational number fraction is divided to form a decimal value, it becomes a terminating or repeating decimal.
So -0.249851765 is not a rational number
Irrational number:An irrational number is real number that cannot be expressed as a ratio of two integers.
When an irrational number is expressed in decimal form, it goes on forever without repeating
So the given number -0.249851765 is irrational number
We can conclude that:
-0.249851765 is a irrational number, So Option B is correct
Carol's monthly take home pay is $1500.she spends $250.a month on food. What the ratio of food costs to take home dollars
Answer:
The answer is 6 ratio because when you divide these two number then the anwer is 6
Answer:
ratio of food costs to take away home 1:6
Step-by-step explanation:
$1500: $250
150:25
30:5
6:1
Anyone for geometry #’s 5 & 6
Answer:
5. m < 1 = 72 degrees.
6. m < 1 = 80 degrees.
Step-by-step explanation:
5. < 1 = 72 degrees.
If we draw a line through the point of < 1, We see that We have have 2 angles of 40 and 32 ( alternate angles).
6. By the same reasoning m < 1 = 60 + 20
= 80 degrees.
Quadrilateral ABCD is translated up and to the right, and then
rotated about point Q. Which congruency statement is
correct?
ABCD = WXYZ
ABCD = ZYXW
ABCD WZYX
ABCD = ZWXY
When a triangle is translated, the resulting triangle will be congruent to the original triangle.
The congruency statement is ABCD = ZYXW
From the complete question, corresponding points are:
Point A and point ZPoint B and point YPoint C and point XPoint D and point WThis means that:
Points A and Z are correspondingPoints B and Y are correspondingPoints C and X are correspondingPoints D and W are correspondingHence, the congruency statement is ABCD = ZYXW
Read more about congruency at:
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The combined height of one fir tree and one pine tree is 21 meters. The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree. How tall are the types of trees?
The fir trees are 9 meters tall and the pine trees are 12 meters tall
Solution:
Let f be the height of one fir tree
Let p be the height of one pine tree
Given that combined height of one fir tree and one pine tree is 21 meters
So we get,
height of one fir tree + height of one pine tree = 21
f + p = 21 ----- eqn 1
Also given that height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree
height of 4 fir trees stacked on top of each other = 24 + height of one pine tree
4f = 24 + p ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "f and "p"
From eqn 1,
f = 21 - p ----- eqn 3
Substitute eqn 3 in eqn 2
4(21 - p) = 24 + p
84 - 4p = 24 + p
-4p - p = 24 - 84
-5p = - 60
p = 12Substitute p = 12 in eqn 3
f = 21 - 12 = 9
f = 9Summarizing the results:
height of one fir tree = 9 meters
height of one pine tree = 12 meters
Dere me pest answer for the question.
14. 20 is what percent of 50?
O A. 30%
OB. 10%
O C.40%
D.250%
Mark for review (Will be highlighted on the review page)
Answer:
C : 40%
Step-by-step explanation:
20 ÷ 50 = 0.40 also to solve just divide the smaller number from the greater number in order to be able to get the correct percentage.
Answer:
Step-by-step explanation
is / of = % / 100.....proportion formula
20 is what percent of 50...
20 / 50 = x / 100
cross multiply
50x = 2000
x = 2000/50
x = 40.......so 20 is 40% of 50
Corresponding sides of similar triangles are
A opposite
B proportional
C equals
What is the equation of the following graph in vertex form?
y = (x − 3)^2 − 1
y = (x + 3)^2 − 1
y = (x − 4)^2 − 2
y = (x − 4)^2 + 8
============================================
How I got that answer:
The vertex is the lowest point of parabolas that open upward.
(h,k) = vertex
(h,k) = (-3,-1)
h = -3
k = -1
For each of the answer choices, a = 1.
The general template of a quadratic in vertex form is
y = a(x-h)^2 + k
Plug a = 1, h = -3, k = -1 into that equation. Simplify.
y = a(x-h)^2 + k
y = 1(x-(-3))^2 + (-1)
y = (x+3)^2 - 1
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola. The provided equations have vertices at different points. You must match the vertex of your graph with the correct equation.
Explanation:In order to find the equation of the graph in vertex form, we need to locate the vertex on the graph. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.
Considering the options provided:
y = (x − 3)² − 1: The vertex is at (3, -1)y = (x + 3)² − 1: The vertex is at (-3, -1)y = (x − 4)² − 2: The vertex is at (4, -2)y = (x − 4)² + 8: The vertex is at (4, 8)However, without a graph or specific vertex provided, we won't be able to define the equation of the graph precisely in vertex form. You need to match the vertex of your graph to one of the above options.
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Which number line shows the solution set |h-3|<5 on a number line
Step-by-step explanation:
|h-3|<5
This implies that
h-3<5 or h-3<-5
h<5+3 or h<-5+3
h<8 or h<-2
Hence the solution set is {h:h<-2 or h<8 }
Therefore the number line in the picture shows the solution set for |h-3|<5
The inequality |h-3|<5 means that h is a numerical value between -2 and 8. A number line representing this solution set would be marked between these two values.
Explanation:The inequality |h-3|<5 represents all numbers that are less than 5 units from 3 on the number line. It leads to two simple inequalities. When we remove the absolute value we get -5 < h-3 < 5, which simplifies to -2 < h < 8. So the number line that shows the solution set will have a line drawn between -2 and 8, indicating all the numbers between these two values satisfy the inequality.
Learn more about Inequality here:https://brainly.com/question/32625151
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A bicycle store costs $3850 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $155. How many bicycles must the store sell each month to break even?
155-45=110
3850÷110=385 bicycles
Answer:
35
Step-by-step explanation:
3850/(155-45)
3850/110
35
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Select the correct answer.
A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2).
What is a reasonable time for it to take the baseball to land on the ground?
A.
7 seconds
B.
2 seconds
C.
9 seconds
D.
5 seconds
Answer:The reasonable time for the base ball to land on the ground is 5 seconds
Step-by-step explanation:
To get the time we will differentiate
h(t) = -16t2 + 80t + 224, w.r.t t
dh(t)/dt= 0
-32t +80=0
32t=80
t=80/32
t= 2.5 seconds This is the time the base ball has been in the air
The reasonable time for it to take the baseball to land on the ground is T= 2×t
T= 2×2.5
T=5 seconds
An Atlas moth has a wingspan of 11 inches. What is the wingspan of 26 Atlas moths?
Answer:
The wingspan of 26 atlas moths are 286 inches.
Step-by-step explanation:
Given:
An Atlas moth has a wingspan of 11 inches.
Now, to find the wingspan of 26 atlas moths.
So, we use unitary method:
As given an atlas wingspan has 11 inches.
Then for wingspan of 26 atlas we multiply it by 11 inches:
⇒ [tex]26\times 11\ inches[/tex]
[tex]=286\ inches.[/tex]
Therefore, the wingspan of 26 atlas moths are 286 inches.
Final answer:
To find the total wingspan of 26 Atlas moths, multiply the wingspan of one moth, 11 inches, by 26, resulting in a total of 286 inches.
Explanation:
The question involves simple multiplication to determine the total wingspan of 26 Atlas moths. If one Atlas moth has a wingspan of 11 inches, then the wingspan of 26 Atlas moths can be found by multiplying 11 inches by 26.
Step-by-step calculation:
Determine the wingspan of one Atlas moth, which is already given as 11 inches.
Multiply the wingspan of one moth by the total number of moths: 11 inches * 26 = 286 inches.
Therefore, the total wingspan of 26 Atlas moths is 286 inches.
Which equation represents the line that passes through the points (-3,7) and (3,3)
Answer:
The equation of the line is 2 x +3 y = 15.
Step-by-step explanation:
Here the given points are ( -3, 7) & ( 3, 3) -
Equation of a line whose points are given such that
[tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-
y - [tex]y_{1}[/tex] = [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex] ( x - [tex]x_{1}[/tex] )
i.e. y - 7= [tex]\frac{3 - 7}{3 - (-3)}[/tex] ( x- (-3))
y - 7 = [tex]\frac{-4}{3 + 3}[/tex] ( x + 3 )
y - 7= [tex]- \frac{2}{3}[/tex] ( x + 3 )
3 ( y - 7) = - 2 ( x + 3)
3 y -21 = -2 x - 6
2 x + 3 y = 21 - 6
2 x + 3 y = 15
Hence the equation of the required line whose passes trough the points ( - 3, 7) & ( 3, 3) is 2 x + 3 y = 15.
Find the length of line segment GF
right triangle E F G; angle G is a right angle; side EF has a length of 9 point 4; side EG has a length of 6 point 8
Final answer:
To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. Plug in the given values of the lengths of the legs EF and EG, and solve the equation to find the length of GF.
Explanation:
To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is line segment GF. Let's label the length of EF as x, and the length of EG as y.
Using the Pythagorean theorem, we can set up the following equation: x^2 + y^2 = GF^2.
Plugging in the given values, x = 9.4 and y = 6.8, we get: 9.4^2 + 6.8^2 = GF^2. Solving this equation will give us the length of line segment GF.
Write an equation of the line passing through point P that is perpendicular to the given line. P(4,−3), y=−x−5
Answer:
all work is shown and pictured
A farmer in China discovers a mammal hide that contains 37% of its original amount of C-14. Find the age of the mammal hide to the nearest year.
Answer: 54678 years
Step-by-step explanation:
This can be solved by the following equation:
[tex]N_{t}=N_{o}e^{-\lambda t}[/tex] (1)
Where:
[tex]N_{t}=54\%=0.54[/tex] is the quantity of atoms of carbon-14 left after time [tex]t[/tex]
[tex]N_{o}=1[/tex] is the initial quantity of atoms of C-14 in the mammal hide
[tex]\lambda[/tex] is the rate constant for carbon-14 radioactive decay
[tex]t[/tex] is the time elapsed
On the other hand, [tex]\lambda[/tex] has a relation with the half life [tex]h[/tex] of the C-14, which is [tex]5730 years[/tex]:
[tex]\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}[/tex] (2)
Substituting (2) in (1):
[tex]0.54=1e^{-(0.000121 years^{-1}) t}[/tex] (3)
Applying natural logarithm on both sides of the equation:
[tex]ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})[/tex] (4)
[tex]-0.616=-(0.000121 years^{-1}) t[/tex] (5)
Isolating [tex]t[/tex]:
[tex]t=\frac{-0.616}{-0.000121 years^{-1}}[/tex] (6)
[tex]t=54677.68 years \approx 54678 years[/tex] (7) This is the age of the mammal hide
The age of the mammal hide to the nearest year is approximately 11,239 years.
To find the age of the mammal hide with 37% of its original amount of C-14 remaining, we can use the decay formula for a substance undergoing exponential decay, which is described by the equation N(t) = N0(1/2)t/T, where N(t) is the remaining amount of substance, N0 is the original amount of substance, t is the time that has elapsed, and T is the half-life of the substance.
In this case, the half-life of C-14 is 5,730 years. Since we know the remaining amount of C-14 is 37% of the original amount, we can set up the equation 0.37 = (1/2)t/5730. To solve for t, we take the natural logarithm of both sides:
ln(0.37) = ln((1/2)t/5730)
ln(0.37) = (t/5730) * ln(1/2)
t = (ln(0.37)/ln(1/2)) * 5730
When we compute the value for t, we get the age of the mammal hide. By performing this calculation, we find that t is approximately 11,239 years. This is the estimated age of the mammal hide to the nearest year.