The point (0, 5) lies on a circle with the center at (0, 0). What is the area of the circle?
How do you tell if a log function is increasing or decreasing?
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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Determine which point from the specified that satisfies each system of equations
The required point that satisfies each system of equation is (12, -1). Option B is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
To equations are given as,
y = -1/3x + 3 - - - - (1)
y = -3/4x + 8 -- - - - (2)
From equation 1 and 2
-1/3x + 3 = -3/4x + 8
3/4x - 1/3x = 8 - 3
9x - 4x / 12 = 5
5x = 60
x = 12
Now, to evaluate the y ordinate put the above x in equation 1
y = -1/3(12) + 3
y = -4 + 3
y = -1
Thus, the required point that satisfies each system of equation is (12, -1). Option B is correct.
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what is pie over 2 pls this is needed now
big reward
Técnica de conteo en estadística 6. Regla multiplicativa. Para el experimento de un lanzamiento de dado y sacar una carta de una baraja de Poker (52 cartas). a. Calcule la cantidad de elementos del espacio muestral. b. Calcula la probabilidad de que salga un número par en el dado un AS en la baraja.
Answer:
Para el punto a. tenemos 312 elementos en el espacio muestral
Para el punto b. la probabilidad pedida es [tex]\frac{1}{26}[/tex]
Step-by-step explanation:
Comencemos explicando el principio de multiplicación. Supongamos que se tiene un experimento por etapas, es decir, una primera etapa que se puede llevar a cabo de '' [tex]x_{1}[/tex] '' maneras distintas, una segunda etapa que se puede llevar a cabo de '' [tex]x_{2}[/tex] '' maneras distintas y así sucesivamente hasta una etapa final que se puede llevar a cabo de '' [tex]x_{n}[/tex] '' maneras distintas. La cantidad total de formas de desarrollar todo el experimento se puede calcular como el producto de las distintas maneras en que se puede ejecutar cada etapa :
Formas de desarrollar todo el experimento = [tex]x_{1}x_{2}[/tex] ... [tex]x_{n}[/tex]
Para el punto a. del ejercicio vamos a utilizar este principio para calcular la cantidad de elementos del espacio muestral. La primera etapa del experimento sería el lanzamiento del dado y una segunda etapa el sacar una carta de una baraja de poker (52 cartas distintas). Entonces, para un dado tenemos 6 posibles opciones y cuando sacamos una carta podemos obtener 52 resultados distintos. Por lo tanto ⇒
[tex](6)(52)=312[/tex]
Tenemos un total de 312 elementos en el espacio muestral (todos distintos) y con la misma probabilidad de ocurrencia ya que suponemos que en el dado tenemos la misma probabilidad de obtener un uno, un dos, etc; así como en la baraja tenemos la misma probabilidad de sacar cada una de las cartas.
Para el punto b. utilizaremos el hecho de que estamos frente a un espacio muestral equiprobable y calcularemos la probabilidad del evento ''sale un número par en el dado y un AS en la baraja'' contando los casos favorables a este evento y dividiendo por la cantidad de elementos totales del espacio muestral. Podremos hacerlo de esta manera ya que el espacio muestral es equiprobable. Definimos para ello
[tex]A:[/tex] ''Sale un número par en el dado y un AS en la baraja''
[tex]P(A)=\frac{CasosFavorablesAlEventoA}{CasosTotales}[/tex]
Los casos totales son 312 (calculados en el inciso a.)
Los casos favorables al evento A se pueden escribir utilizando el principio de multiplicación como
[tex](3)(4)=12[/tex]
El 3 es por los tres números pares que podemos obtener del dado (estos números son el dos, cuatro y el seis).
El 4 se debe a la cantidad de ases en una baraja de Póker de 52 cartas (estos son el as de corazones, el as de picas, el as de trébol y el as de diamantes).
Reemplazando en la expresión de [tex]P(A)[/tex] obtenemos :
[tex]P(A)=\frac{12}{312}=\frac{1}{26}[/tex]
Otra forma de haber calculado esta probabilidad es utilizando el hecho de que tirar el dado y sacar una carta de la baraja son dos eventos independientes. Por ende, la probabilidad se puede calcular como el producto de la probabilidad parcial de cada evento. Esto es :
B : ''Sale un número par en el dado''
C : ''Saco un as en la baraja''
[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]
Tres casos favorables a que salga un número par de seis posibles.
[tex]P(C)=\frac{4}{52}[/tex]
Cuatro casos favorables a obtener un as de la baraja de 52 casos posibles.
Ahora escribimos
P ( B ∩ C ) = P(B).P(C)
Por ser B y C dos eventos independientes. Entonces
[tex]P(B)P(C)=(\frac{1}{2})(\frac{4}{52})=\frac{1}{26}[/tex]
Obteniéndose la misma probabilidad ya calculada.
Find the interet and total amount due on 1200 after 1 year 5 month at a rate
of interet of 4% p. A
Total interest earned = 68
Total amount collected = 1268
What is simple Interest ?Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.
Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.
Since nothiong mentioned the interest is considered simple
Total amount = 1200 (principal)
Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]
rate = 4 %
Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68
Total amount generated = 1200 + 68 = 1268.
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Line s passes through the points (3,4) and (2,1).line t passes through the point (4,2) and is parallel to line s.
What is the equation for line t
Answer:
y=3x-10
Step-by-step explanation:
first, we need to find the slope of line s, as that will determine the slope of line t
the formula for the slope calculated from 2 points is (y2-y1)/(x2-x1)
we can label the points for (3,4) and (2,1)
x1=3
y1=4
x2=2
y2=1
substitute into the formula:
m=(y2-y1)/(x2-x1)
m=(1-4)/(2-3)
m=-3/-1
m=3/1
m=3
the slope of line s is 3
as said above, parallel lines have the same slope, but different y intercepts.
that means that line t will have the same slope as line s (3).
typically, lines are written in the form y=mx+b, where m is the slope and b is the y intercept
here's what is line t so far:
y=3x+b
we need to find b
because the line passes through the point (4,2), we can use it to solve for b
plug 4 in as x and 2 as y
2=3(4)+b
2=12+b
-10=b
so that means that b is -10
therefore the equation for line t is y=3x-10
Hope this helps! Good luck on your assignment!
b)
What is the Lowest Common Multiple of 42 and 90?
Answer:
630
Step-by-step explanation:
you can search it up if you want.
Answer:
630
Step-by-step explanation:
solve -2.3 - (4.5-3.5)
Answer:
-3.3
Step-by-step explanation:
-2.3 - (4.5-3.5)
-2.3 - (1.)
-3.3
trigonometry, please help thanks
Answer:
x = 3.25 m
Step-by-step explanation:
First, find the height of the triangle using sin31:
sin 31 = h/9 ---> h = 9sin31 = 4.64 m
Next, we can now solve for x using tan55:
tan 55 = h/x --> x = (4.64 m)/(tan 55) = 3.25 m
IF YOU KNOW SPANISH AND ALGEBRA PLEASE HELP
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A:
f(x) = -x² + 4x - 10
f(2) = -(2)² + 4(2) - 10
f(2) = -4 + 8 - 10
f(2) = 4 - 10
f(2) = -6
Part B:
g(x) = 5x + 1
g(6) = 5(6) + 1
g(6) = 30 + 1
g(6) = 31
Part C:
f(x) = -x² + 4x - 10
f(-1) = -(-1)² + 4(-1) - 10
f(-1) = -1 - 4 - 10
f(-1) = -5 - 10
f(-1) = -15
Part D:
g(x) = 5x + 1
16 = 5x + 1
15 = 5x
3 = x
x = 3
You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7.5%, and the license and title charges are $175.13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent.
9514 1404 393
Answer:
total purchase price: $27,722.01
Step-by-step explanation:
The price of the car plus tax is ...
$25,625 × (1 +7.5%) = $27,546.88
Adding license and title charges brings the total to ...
$27,546.88 +175.13 = $27,722.01 . . . total purchase price
_____
Additional comment
10% of that, or $2,772.20, will be the required down payment, leaving a balance due of $24,949.81. The payments on a 36-month loan at 9% will be $793.40, for a total loan cost of $28,562.30. Then the full cost of the car, including financing, is $31,334.50. The cost of the financing is $3,612.49.
Tyler drove 52\tfrac{1}{2}52
2
1
mile in 1\tfrac{2}{3}1
3
2
hour. If he drove at a contant rate, how far did he travel in one hour? Enter your anwer a a whole number, proper fraction, or mixed number in implet form
Tyler drove 40 miles in one hour.
To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.
So, we have:
(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour
= (52 21/32) * (3/32)
= (52 213/3232)
= (52 63/32) miles/hour
= 40 miles/hour
So, Tyler drove 40 miles in one hour.
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A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
Whatever the case a quadrilateral has always a sum of interior angles = 360°.
What is quadrilateral?A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.
A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.
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Graph the line that passes through the points (8, -3) and (4, 1) and
determine the equation of the line.
Answer:
y = -x + 5
Step-by-step explanation:
The equation is y= mx + b
m = the slope or rise/run or (y2 - y1) / (x2 - x1)
b = y-intercept
The slope here is -1, and the y-intercept is 5, so our equation is
y = -x + 5
Can you pls help me
Z= [?]° i dont know how to type out the question
Answer: first u have to find the perimiter for each side
Step-by-step explanation:
the answer is 100 d z
Unit sales for new product ABC have varied in the first seven months of this year as follows: Feb 285 Mar Apr May Jun Jul Month Jan 314 158 482 284 310 281 Unit Sales What is the (population) standard deviation of the data? Please round your answer to the nearest integer. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel
The population standard deviation of the data is 111.
1. Find the mean of the data:
Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5
2. Find the difference between each data point and the mean:
Feb: (314 - 171.5) = 142.5
Mar: (158 - 171.5) = -13.5
Apr: (482 - 171.5) = 310.5
May: (284 - 171.5) = 112.5
Jun: (310 - 171.5) = 138.5
Jul: (281 - 171.5) = 109.5
3. Square each of the differences:
Feb: (142.5)^2 = 20,312.5
Mar: (-13.5)^2 = 182.25
Apr: (310.5)^2 = 95,822.25
May: (112.5)^2 = 12,656.25
Jun: (138.5)^2 = 19,082.25
Jul: (109.5)^2 = 11,982.25
4. Sum all of the squared differences:
20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5
5. Divide the sum of the squared differences by the number of data points minus one:
149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5
Square root of 29,809.5 = 111 (rounded to the nearest integer)
Therefore, the population standard deviation of the data is 111.
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PLEASE HELP ME THIS IS DUE TODAY AND I WILL MARK BRAINLEST.
which graph represents a function?
Answer:
first graph is a function
Step-by-step explanation:
find the gradient of a line passing through each of the following pair of points (0,-5) and (6,3)
You know that 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77. You also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91. How much does a ticket in Virginia cost?
The cost of one ticket in Virginia is $8
What is a system of linear equations?A System of Linear Equations is when we have two or more linear equations working together.
Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.
To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,
Let V represents the cost in Virginia that of in Maryland be M
Therefore,
4v+5m = 77.......(i)
8v+3m = 91........(ii)
Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]
(8v+10m = 154) - (8v+3m = 91)
7m = 63
m = 9
Put m = 9 in eq(i)
4v+5(9) = 77
4v = 77-45
4v = 32
v = 8
Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.
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SOMEONE PLS PLS HELP ME
Answer:
6
Step-by-step explanation:
I counted
What is the volume of the rectangular prism?
Answer:
200
Step-by-step explanation:
whats the length of A, B and C
Answer:
B should be 3 inches long because the area of the square above is 48 inches squared, so that long side is probably 8. B is 3 inches long. As for A, this should be simple. since we know the longer side of the room has the area of 27, we can tell the length(longest side) is 9. 14 minus 9 is equal to 4. A's width is 4 inches long.
Step-by-step explanation:
for the rest, since we know one of the widths is 6 inches, we know that the length of the room with an area of 32 inches is 8. therefore, since 8 times 4 equals the number 32, C is 4 inches long. back to B. since we know that c is 4 inches long and that there is a length of 11 inches, we can tell the longest side of room A is 7. 4 Times 7 equals 28, so B is 28 inches squared.
PLEASE HELP !! WILL MARK BRAINLIEST
Answer:
(8,-2)
Step-by-step explanation:
Use the distributive property to simplify 5( x + 3).
(A). 8 x
(B). 5 x + 3
(C). 5 x + 8
(D). 5 x + 15
Answer:
D) 5x+15
Step-by-step explanation:
5×x+5×3
5x+15
plz mark as brainliest
Please solve with explanation
Answer:
a) -1535.5
b) 0
Step-by-step explanation:
A) We do this problem according to its parenthesis. First, let's evaluate the first half, -2[(-1/4)-12(-1)^2]. We have to do (-1)^2 first, because of PEMDAS. (-1)^2 is just 1. Now, our equation is -2[(-1/4)-12*1]. Thus, we get -2[(-1/4)-12] because 12*1 is just 12. Then, we do (-1/4)-12, giving us -12.25. Our equation becomes -2(-12.25). Then, we just get 24.5.
The next half, -5[24+2(-12)^2] is similar. We first evaulate (-12)^2 because of PEMDAS, giving us 144. Then, we have -5[24+2(144)]. 2 times 144 is 288, so we get -5[24+288]. 24 + 288 is 312, so we have -5(312). This finally gives us -1560.
Putting the two together, we get 24.5 - 1560, which is -1535.5.
--------------------------------------------------------------------------------------------------------------B) We substitute a = -1/3 and b = -1 into the equation, -a^2b^2 - 3a^3b^2.
We plug in -1/3 where a is and -1 where b is. So:
-(-1/3)^2(-1)^2 - 3(-1/3)^3(-1)^2.
The tricky part of this problem is making sure you follow PEMDAS. We evaluate the exponents first.
-1/9 * 1 - 3(-1/27) * 1
= -1/9 + 1/9
= 0
Step-by-step explanation:
good answer .qanda app Also use
find the distance between the points (-2,8) and (7,13) on a corrdiante plane
Answer: d = √(5² + 9²) = √106, or approximately 10.3 units.
Why is 15.6 divided by 3.12 the same as 1560 divided by 312
Answer:
they are proportionate
Step-by-step explanation:
1560/100 = 15.6
312/100 = 3.12
Answer: Because they're based off the power of 10.
Step-by-step explanation:
I think the answer is correct because, to make 15.6 to 1560 you just need to multiply by 100, and to get 3.12 to 312 all you have to do is multiply by 100. So if you divided 1560 and 312 which is 5, all you have to do is divide by 100 and you get the same answer thats why its basically considered the same because of the power of tens.
Hope This Helps!
Brady took 80 shots on his pop- a- shot basketball hoop . If he made 90%of his shots into the basket, how many shots did he make
Answer: Brady made 72 shots
Step-by-step explanation:
Number of shots taken on his pop- a- shot basketball hoop=80
Percentage of shots made into the basket=90%
Number of shots made into the basket= 90% x 80
= 90/100 x 80
= 72