Answer:
6%
Step-by-step explanation:
Got it right on the test.
ejercicio de estadistica
Answer:
no habla espanol
Step-by-step explanation:
write each number as a logarithm with base 2:-3
The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
What are logarithms?As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
How to rewrite the number as a logarithm?The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
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what is ordinary numbers
What is ordinary number?
1 : a number designating the place (such as first, second, or third) occupied by an item in an ordered sequence — see Table of Numbers. 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number.
write and solve an inequality that means a number plus four than or equal to twelve.
The correct answer for the solution of inequality is [tex]x\geq 8[/tex].
Let the unknown number be "[tex]x[/tex]."
The statement "a number plus four" can be written as "[tex]x+4[/tex]."
The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]
Put these together, the inequality becomes:
[tex]x + 4\geq 12[/tex]
solve for "[tex]x[/tex]," isolate the variable on one side of the inequality:
Subtract -[tex]4[/tex] from both side of the expression:
[tex]x + 4 - 4 \geq 12 - 4[/tex]
[tex]x\geq 8[/tex]
The correct expression for the inequality is [tex]x\geq 8[/tex]
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Which number can each term of the equation be multiplied by to illuminate the fractions before solving 6-3/4x+1/3=1/2x+5
[tex]\boldsymbol{\sf{6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]
Convert 6 to the fraction 18/3.
[tex]\boldsymbol{\sf{\dfrac{18}{3} -\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]
Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.
[tex]\boldsymbol{\sf{\dfrac{18+1}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 \ \longmapsto \ \ [Add \ 18+1] }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 }}[/tex]
Subtract [tex]\bf{\frac{1}{2}x }[/tex] on both sides.
[tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x-\dfrac{1}{2}x=5 }}[/tex]
Combine [tex]\bf{-\frac{3}{4}x}[/tex] and [tex]\bf{-\frac{1}{2}x}[/tex] to get [tex]\bf{-\frac{5}{4}x}[/tex].
[tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{5}{4}x=5 }}[/tex]
Subtract 19x from both sides.
[tex]\boldsymbol{\sf{-\dfrac{5}{4}x=5-\dfrac{19}{3} }}[/tex]
Convert 5 to the fraction 15/3.
[tex]\boldsymbol{\sf{-\dfrac{4}{5}x=\dfrac{15}{3}-\dfrac{19}{3} }}[/tex]
Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.
[tex]\boldsymbol{\sf{-\dfrac{5}{4}x=\dfrac{15-19}{3} \ \longmapsto \ \ [Subtract \ 15-19] }}[/tex]
[tex]\boldsymbol{\sf{-\dfrac{5}{4}x=-\dfrac{4}{3} }}[/tex]
Multiply both sides by -4/3, the reciprocal of -4/3.
[tex]\boldsymbol{\sf{x=-\dfrac{4}{5}\left(-\dfrac{4}{5}\right) }}[/tex]
Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\boldsymbol{\sf{x=\dfrac{-4(-4)}{3\times5} \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=\frac{16}{15} }}}}}[/tex]
The length and width of a rectangle is 42cm and 28cm respectively. The ratio between the two
quantities is ____________.
Answer:
The ratio is 3 : 2.
Step-by-step explanation:
42 cm : 28 cm
= 21 : 14 (Divide both sides by 2)
= 3 : 2 (Divide both sides by 7)
The ratio between the length and width of the rectangle is 3:2.
We have,
The concept used here is the concept of ratio.
In mathematics, a ratio is a comparison of two quantities.
It expresses how many times one quantity contains another or how many times it is greater or smaller than the other quantity.
The ratio between the length and width of the rectangle can be found by dividing the length by the width:
Ratio = Length / Width
= 42 cm / 28 cm
= 7 x 6 / 7 x 4
Cancel out the common factor.
= 6/4
= 2 x 3 / 2 x 2
Cancel out the common factor.
= 3/2
Thus,
The ratio between the length and width of the rectangle is 3:2.
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Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1% interest compounded monthly. She just turned 33, and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time.
Answer:
A convenient formula to use is
S = ((1 + i)^n - 1) / i where S is the value of 1$ deposited for n periods at an interest rate of i
in this case n = 12 * 28 = 336 periods of deposit at an interest rate of
.0021 / 12 = .00175 = i
S = (1.00175^336 - 1) / .00175 = 456.8338 the value of 1$ after 336 periods
350 * 456.8338 = 159891.81 the value of 350 deposited monthly
Note that 350 * 336 would be 117,600
One must be careful to distinguish the above formula from
(1 - (1 + i)^-n) / i which gives the value of 1$ when the borrower is "paying" an interest rate of i - this would be the case for a mortgage - or what is the value of 1$ paid for n periods when paying an interest rate of i
Which of the following is the equation of the line that passes through the points (-3,4) and (6,7)?
The equation of the line that passes through the given points is
y = 1/3x + 5.
What is the formula for calculating the equation of a line passing through two points?The formula for the equation of a line passing through two points (x1, y1) and (x2, y2) is
[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
Where the fraction (y2 - y1)/(x2 - x1) is the slope of the line denoted by 'm'.
Calculation:It is given that, a line passes through the points (-3,4) and (6,7).
So, the equation of the line is
[tex](y-y1) = \frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
On substituting x1 = -3, y1 = 4, x2 = 6, and y2 = 7
(y - 4) = [(7 - 4)/(6 + 3)](x + 3)
⇒ (y - 4) = (3/9)(x + 3)
⇒ (y - 4) = 1/3(x + 3)
⇒ y- 4 = 1/3x + 1
⇒ y = 1/3x + 1 + 4
∴ y = 1/3x + 5
Thus, the equation of the line passing through the points (-3,4) and (6,7) is y = 1/3x + 5. Where the slope m = 1/3.
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1. Graph the linear function f(x) = -2x + 1
Answer: The slope is -2 and the y-intercept is (0,1)
Step-by-step explanation:
Prove: In an equilateral triangle the three medians are equal
Step-by-step explanation:
Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .
In 5-card poker, find the probability of being dealt the following hand. Refer to the table. Note that
a standard deck of playing cards has 52 cards-4 suits (clubs, diamonds, hearts, spades), where
each suit has 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
no pair
The probability of being dealt no pair is
(Type an integer or decimal rounded to eight decimal places as needed.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
Number of
Outcomes
Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favourable outcomes = 1302540
The probability of being dealt no pair:
P(no pair) = 1302540/2598960
P(no pair) = 0.5011
In percentage:
P(no pair) = 50.11%
Thus, the probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
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A project is expected to provide cash flows of and over the next four years , respectively . At a required return of 8.5 percent , the project has a profitability Index of .898 . For this to be true , what is the project's cost at Time ? \$12.150,\$12.600,\$15.700,; \$10.200
Project's cost at time 0 is $46,272.84
What is profitability index?
Profitability index is the present value of future cash flows divided by the project cost at time 0.
The present value of each future cash flow can be determined using the present value formula of a single cash flow as below;
PV=FV/(1+r)^N
FV=future cash inflows in years 1-4
r=discount rate=8.5%
N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.
PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4
PV of future cash flow=$41,553.01
Profitability index=PV of future cash flows/Project cost
Profitability index= .898
Project cost=unknown(assume it is X)
.898=$41,553.01 /X
X=$41,553.01/ .898
X=project's cost=$46,272.84
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select the correct answer. What is the area of the triangle in the diagram
Answer:
B
Step-by-step explanation:
The area of the triangle is half the base time the height. The height is y sub 1. The length is the distance between the x values.
Se tiene 10 fichas, las 5 primeras de color
azul numeradas del 1 al 5 y las 5 restantes
blancas también numeradas del 1 al 5. Se
colocan en una caja sacando una ficha y
posteriormente otra más, entonces la
probabilidad de que ambas estén
numeradas con el valor 1, es:
Usando la distribución hipergeométrica, la probabilidad de que ambas estén numeradas con el valor 1, es: 0.0222 = 2.22%.
¿Qué es la fórmula de distribución hipergeométrica?
La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 10, k = 2, n = 2.
La probabilidad de que ambas estén numeradas con el valor 1, es P(X = 2), entonces:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,2) = \frac{C_{2,2}C_{8,0}}{C_{10,2}} = 0.0222[/tex]
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Graph the following conditions. {(x, y): x + 2y > 6}
See attachment for the graph of the inequality expression x + 2y > 6
How to graph the conditions?The condition is given as:
{(x, y): x + 2y > 6}
This means that
x + 2y > 6
The above is an inequality expression, where the variables are x and y
So, we simply plot the graph of the inequality expression x + 2y > 6
See attachment for the graph of the inequality expression x + 2y > 6
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find the slope of the line that passes through each pair of points a. (-4, 5), (1, 1)
I need help with the question
Answer:
0.7
Step-by-step explanation:
Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.
Find the measures of angles a and b when 0=44
Agri-Small Business limited expenses on petrol for their fleet is R 4 850.00 at the end of September and they have a balance of R106 360.00 remaining in their account. The company has used 25% of its September income on salaries, 11% on electricity, rates and taxes, and 42% of the remaining on insurance and investments. The total income and expenditure in September are
a. Income is R 299 596.00 and expenditure is R 193 236.00.
b. Income is R 193 236.00 and expenditure is R 4 850.00.
c. Income is R 106 360.00 and expenditure is R 4 850.00.
d. Income is R 106 360.00 and expenditure is R 299 596.00
The total income and expenditure in September are "Income is R 106 360.00 and expenditure is R 4 850.00." Option C. This is further explained below.
What are the total income and expenditure in September?Generally, the equation for Insurance and investment is mathematically given as
II= 42% of the balance
II = 0.42*0.64A
II= 0.2688A
Generally, the equation for Total After All other exp is mathematically given as
Texp = 0.64A – 0.2688A
Texp= 0.3712A
Total After All other exp = 111210
subbing ahead and equating we have
111210 = 0.3712 A
Therefore
A = 299596
The total income is 299596
Therefore, the calculation for the expense is given as
Expense = 0.25A + 0.11A + 0.2688A + 4850
Expense= 0.6288A + 4850 = (0.6288*299596) + 4850
Expense= 193236
The Expense is 299596
In conclusion, At the end of September, Agri-Small Business's minimal spending on gasoline for their fleet amounted to R 4 850.00, and they still had a balance of R106 360.00 in their account. The majority of the remaining revenue was allocated to insurance and investments by the business, which accounted for 42% of the total. Wages and salaries accounted for 25% of the company's income in September. The overall revenue and expenses for the month of September were as follows: the income was R 106 360.00, and the expenses were R 4 850.00. Option C.
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SOMEBODY PLEASE HELP ASAP
Answer:
40
Step-by-step explanation:
[tex]\frac{RW}{24}=\frac{30}{18} \\ \\ RW=40[/tex]
Q.2. Solve the following. a) How many triangles can you find in the figures below? b) How many different edges are used in these triangles? c) If the area of each of the 4 smallest triangles is the same and thi area is 1 square unit, what is the area of each triangle in the figure?
Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.
According to the statement
we have given that a figure and we have to the number of triangle present in it and the area of each square and the number of edges used in all triangles.
So, For this purpose, we know that the
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
So,
A. The number of triangles present in figure:
There is a rectangle provided with two diagonals and due to this structure
Firstly 4 triangles are formed with 2 diagonals (big size).
And 4 triangles are formed in diagonals because diagonals cut each other (small size).
So, Total 8 triangles are formed in figure.
B. Edges used to form triangle :
there are 4 edges used to form triangles because of presence of overall shape of rectangle because triangles are formed in a rectangle shape.
So, 4 edges used to make triangles.
C. Area of the triangle:
If the area is 1 square unit and area of all triangles are same
So, The area of all triangle is 1 square unit.
So, Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.
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Find the length indicated
Show work
Answer: 5 units
Step-by-step explanation:
x+2+2x-7=13
solve for x
3x=18
x=6
∴SR: 2x-7
=2(6)-7
=12-7
=5
Answer:
SR = 5
Step-by-step explanation:
[tex]TR=x+2+2x-7=3x-5[/tex]
[tex]3x-5=13[/tex]
[tex]3x=13+5[/tex]
[tex]x=18/3=6[/tex]
[tex]SR=2x-7=2(6)-7=12-7=5[/tex]
Hope this helps
sirs is making lemonade to sell at her lemonade stand. she made a batch of 8 pitchers of lemonade using 24 lemons, 12 cups of sugar, and 20 liters of water. she decides to make a second batch of 6 pitchers of lemonade. how many liters of water should she use to make the second batch of lemonade?
Answer:15
Step-by-step explanation: 20 divided by 8=2.5 x 6=15
There are 40 students in Mrs. Rusczyk's first grade class. if there are three times as many students with blond hair as with blue eyes, 3 students with blond hair and blue eyes, and 15 students with neither blond hair nor blue eyes, how many students have blue eyes?
by solving a system of equations, we conclude that there are 7 students with blue eyes in the class.
How many students have blue eyes?
We know that there are 40 students in the first-grade class, and we also know that:
Let's define the variables.
B = number of students with blue eyes.H = number of students with blond hair.We know that:
H = 3*B
We also know that there are 3 students that have both blue eyes and blond hair.
And there are 15 students with none of these traits, so:
40 - 15 = 25
There are 25 students that have blue eyes, blond hair, or both.
Because we know that 3 students have both traits, we can write:
B + H - 3 =25
(Where we subtract 3 because we don't want to add these students twice).
Then we created a system of two equations:
H = 3*B
B + H - 3 =25
Replacing the first equation into the second one, we get:
B + (3*B) - 3 = 25
4*B = 25 + 3 = 28
B = 28/4 = 7
Then, by solving that system of equations, we conclude that there are 7 students with blue eyes in the class.
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Please help me answer this question
Answer: A
Step-by-step explanation:
The total value of the prizes is [tex]1000+500+2(50)=1600[/tex].
The total cost of the tickets is [tex]1000(4.00)=4000[/tex].
So, the total loss is $2400.
Dividing this by 1000 tickets gives $-2.40.
Jose wants to walk to the store from his house but he is not sure how far away it is. Find the distance between his house (-8, -9) and the store (-4, -10). Each unit is equal to one mile.
Answer:
4.12 miles
Step-by-step explanation:
Use distance formula
d^2 = (-8- -4)^2 + ( -9 - -10)^2
d^2 = 16 + 1
d^2 = 17
d = sqrt 17 = 4.12 miles
ball is thrown vertically upward at an initial speed of Its height (in feet) after t seconds is given by h(t)t(16t). After how many seconds does the ball reach its maximum height? Round answer to two decimal places.
If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].
We are required to find the time after which the ball will attain its maximum height.
The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.
h(t)=52t-16[tex]t^{2}[/tex]
Differentiate with respect to t.
dh/dt=52-32t
Again differentiate with respect to t.
[tex]d^{2}h/dt^{2}[/tex]=-32t
Because tim cannot be negative means the height is maximum.
Put dh/dt=0
52-32t=0
-32t=-52
t=52/32
t=1.625
Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Question is incomplete as the right and complete equation is
h(t)=52t-16[tex]t^{2}[/tex] .
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[tex]h(x) = x -1 + \frac{1+ ln {}^{2} (x) }{x}[/tex]
[tex]\displaystyle \lim_{x\to0} h(x)= \: ? \\ \displaystyle \lim_{x\to \infty } h(x)= \: ?[/tex]
Apply L'Hôpital's Rule if possible
Answer:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]
Step-by-step explanation:
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]
= +∞ + 0
= +∞
[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]
[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]
= -1 + +∞
= +∞
Solve the following equation for x
5x-30y=-35.
5x-30y=-35
Divide both the side by 5 and we get
x-6y = -7
x = 6y -7
Answer:
x=-7+6y
You simply need to add 30y and then divide by 5 to isolate the variable.
HELP!
ANGLE 1 = 52°
(Show work)
The measure of the unknown angles are as shown below;
m<2 = 128 degrees = m<4
m<5 = 128 degrees
m<6 = 52 degrees
m<3 = 52 degrees = m<8
m<7 = 128 degrees
Lines and anglesAn angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.
Given the following parameters
m<1 = 52 degrees
From the given diagram, the following are true
m<1 = m<3 (corresponding angle)
m<3 = m<8 (vertical angles)
m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)
m<4 = m<7 (vertical angles)
Also;
m<1 + m<2 = 180
m<2 = 180 - m<1
m<2 = 180 - 52
m<2 = 128 degrees = m<4
m<5 = 128 degrees
m<6 = 52 degrees
m<3 = 52 degrees = m<8
m<7 = 128 degrees
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