Greg, Albert, Joseph, and Finn are playing hide-and-seek and taking turns being 'it'. In how many different orders could the children take their turns being 'it'? orders
There are 24 different orders in which Greg, Albert, Joseph, and Finn can take their turns being 'it' in the game of hide-and-seek.
To determine the number of different orders in which the children can take their turns being 'it' in a game of hide-and-seek, we can use the concept of permutations.
Since there are four children (Greg, Albert, Joseph, and Finn), we need to find the number of permutations of these four children. A permutation represents an arrangement of objects in a specific order.
The formula for calculating permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (children) and r is the number of objects (children) to be arranged.
In this case, we have n = 4 (four children) and r = 4 (all four children will take their turns as 'it'). Plugging these values into the formula, we get:
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4! / 1
= 4 × 3 × 2 × 1 / 1
= 24
Therefore, there are 24 different orders in which Greg, Albert, Joseph, and Finn can take their turns being 'it' in the game of hide-and-seek.
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Select the correct answer. The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units Function g is represented by the table. x -2 -1 0 1 2 g(x) 0 2 8 26 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept and the same end behavior as x approaches ∞. C. They have different x- and y-intercepts but the same end behavior as x approaches ∞. D. They have the same x- and y-intercepts.
The correct statement is that they have different x- and y-intercepts, but we cannot determine their end behavior based on the given information.
Based on the information provided, we can compare the two functions f and g as follows:
Function f:
- It passes through the points (-10, -1) and (2, 8).
- It intercepts the x-axis at -2 units and the y-axis at 2 units.
Function g:
- It is represented by the table with x-values -2, -1, 0, 1, 2, and corresponding y-values 0, 2, 8, 26.
Comparing the two functions based on their intercepts and end behavior:
A. They have the same y-intercept and the same end behavior as x approaches ∞: This statement is incorrect because the y-intercepts of f and g are different. Function f intercepts the y-axis at 2 units, while function g intercepts the y-axis at 0 units. Additionally, we do not have information about the end behavior of either function.
B. They have the same x-intercept and the same end behavior as x approaches ∞: This statement is incorrect because the x-intercepts of f and g are different. Function f intercepts the x-axis at -2 units, while function g does not intercept the x-axis.
C. They have different x- and y-intercepts but the same end behavior as x approaches ∞: This statement is partially correct. Function f and g have different x- and y-intercepts, but we don't have information about their end behavior.
D. They have the same x- and y-intercepts: This statement is incorrect as the x- and y-intercepts of f and g are different.
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Given: Quadrilateral DEFG is inscribed in circle P.
Prove: m∠D+m∠F=180∘
It is given that quadrilateral DEFG is inscribed in circle P. Because a circle measures 360°, mEFG + mGDE =360∘. By the Response area, 12mEF + 12mGDE =180∘. By the inscribed angles theorem, Response area = 12mGDE and Response area = 12mEFG This means m∠D+m∠F=180∘ by the
The solution to the gaps in the angle proof are:
Multiplication Property of equality
m∠D = ¹/₂ * [arc EFG] and m∠F = ¹/₂ * [arc GDE]
substitution property
How to prove the missing angles?The inscribed angle Theorem states that the inscribed angle measures half of the arc of which it is composed.
Thus, we can say that:
m∠D = ¹/₂ * [arc EFG]
and
m∠F = ¹/₂ * [arc GDE]
Therefore:
arc EFG + arc GDE = 360°-------> full circle
Applying multiplication property of equality, we have:
¹/₂ * arc EFG + ¹/₂ * arc GDE = 180°
Applying substitution property of equality, we have:
m∠D = ¹/₂ * [arc EFG]
m∠F = ¹/₂ * [arc GDE]
¹/₂ * arc EFG + ¹/₂ * arc GDE = 180° ----> m∠D + m∠F = 180°
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7. Find the trig function
Find sin 0 if cos 0= 15/17
Sin 0 is approximately 0.4709.
To find sin 0 given that cos 0 = 15/17, we can use the Pythagorean identity:
[tex]sin^2 0 + cos^2 0 = 1[/tex]
Rearranging the equation, we have:
[tex]sin^2 0 = 1 - cos^2 0[/tex]
Since we know that cos 0 = 15/17, we can substitute this value into the equation:
[tex]sin^2 0 = 1 - (15/17)^2[/tex]
Calculating this, we find:
[tex]sin^2 0 = 1 - (225/289)\\sin^2 0 = (289/289) - (225/289)\\sin^2 0 = 64/289[/tex]
Taking the square root of both sides, we get:
sin 0 = √(64/289)
Now, we need to determine the sign of sin 0. Since cos 0 is positive (15/17), sin 0 will also be positive in the first and second quadrants.
sin 0 = √(64/289)
sin 0 ≈ √0.2213
sin 0 ≈ 0.4709 (rounded to four decimal places)
Therefore, sin 0 is approximately 0.4709.
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Miranda likes to have wine with her dinner on Friday and Saturday nights. She usually buys two bottles of wine for the weekend. she really needs to cut back on spending. She decides to buy only one bottle per week. on average a bottle of wine cost $15. How much does she save in one year?
We subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend. Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.
To calculate how much Miranda saves in one year by buying only one bottle of wine per week instead of two, we can follow these steps:
Determine the number of bottles of wine she buys in a year:
Miranda used to buy 2 bottles of wine per weekend, so in a week, she bought 2 bottles.
Since there are 52 weeks in a year, the number of bottles she bought in a year is 2 bottles/week * 52 weeks = 104 bottles.
Calculate the total cost of wine for the year:
Since each bottle costs $15, the total cost of wine for the year when buying 2 bottles per week would be 104 bottles * $15/bottle = $1560.
Calculate the cost of wine for one year when buying only one bottle per week:
With Miranda's decision to buy one bottle per week, the total number of bottles she buys in a year is 1 bottle/week * 52 weeks = 52 bottles.
Therefore, the cost of wine for one year when buying only one bottle per week would be 52 bottles * $15/bottle = $780.
Calculate the amount saved in one year:
To determine the amount saved, we subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend.
Amount saved = $1560 - $780 = $780.
Therefore, Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.
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What is the shortest distance from the surface +15+2=209 to the origin?
We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
Given the equation of the surface is xy + 15x + z^2 = 209.
Let's determine the shortest distance from the surface to the origin.
The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:
Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.
For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).
The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.
Here, the normal vector is ∇f = (y + 15, x, 2z).
Now, let's consider a point A on the surface which is closest to the origin.
Let the coordinates of A be (a, b, c).
Therefore, the position vector of A is given by: OA = ai + bj + ck.
The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.
Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.
Since A lies on the surface, we have: a*b + 15a + c^2 = 209.
We also know that OA passes through the origin.
Therefore, the position vector of A is perpendicular to the direction vector OA.
This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0
Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0
Also, we know that OA passes through the origin.
Therefore, the magnitude of OA is equal to the distance of A from the origin.
Hence, we can write: |OA| = √(a^2 + b^2 + c^2)
The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))
Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k
Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|
The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.
Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.
Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
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[tex]24\ \textgreater \ 6x-3[/tex]
Answer:
x < 4.5
Step-by-step explanation:
To solve the inequality 24 > 6x - 3, we can follow these steps:
Start by adding 3 to both sides of the inequality to isolate the term with the variable:
24 + 3 > 6x - 3 + 3
This simplifies to:
27 > 6x
Divide both sides of the inequality by 6 to solve for x:
27/6 > 6x/6
Simplifying further:
4.5 > x
Therefore, the solution to the inequality 24 > 6x - 3 is x < 4.5.
Hope this helps!
The solution to the inequality is :
↬ [tex]\bf{x < \dfrac{9}{2}}[/tex]
Solution:
Let's solve [tex]\bf24\:\textgreater\:6x-3}[/tex].
First, add 3 to each side:
[tex]\sf{24+3\:\textgreater \:6x}[/tex]
[tex]\sf{27 > 6x}[/tex]
Divide each side by 6
[tex]\sf{27/6 > x}[/tex]
[tex]\sf{x < 27/6}[/tex]
[tex]\sf{x < 9/2}[/tex]
Hence, x < 9/2Joel Friedlander es un corredor de la Bolsa de
Valores de Nueva York y tiene curiosidad acerca del tiempo que transcurre entre la colocación de una
orden de venta y su ejecución. Joel hizo un muestreo de 45 órdenes y encontró que el tiempo medio
para la ejecución fue 24.3 minutos, con una desviación estándar de 3.2 minutos. Ayude a Joel con la
construcción de un intervalo de confianza del 95% para el tiempo medio para la ejecución de una
orden
We are 95% confident that the true mean time for the execution of an order is between 23.36 and 25.24 minutes.
How to explain the confidence intervalconfidence interval = mean ± 1.96 * standard deviation / ✓(sample size)
In this case, the mean is 24.3 minutes, the standard deviation is 3.2 minutes, and the sample size is 45. Plugging these values into the formula, we get the following confidence interval:
confidence interval = 24.3 ± 1.96 * 3.2 / ✓(45)
= 24.3 ± 0.94
= (23.36, 25.24)
This means that we are 95% confident that the true mean time for the execution of an order is between 23.36 and 25.24 minutes.
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Joel Friedlander is a stockbroker from New York Securities and you are curious about the time that elapses between the placement of a
sales order and its execution. Joel sampled 45 orders and found that the mean time for execution it was 24.3 minutes, with a standard deviation of 3.2 minutes. Help Joel with the construction of a 95% confidence interval for the mean time for the execution of an order
Por favor necesito el ejercicio para ahora
En la carnicería hemos comprado 2 kg y cuarto de ternera, 5 kg y dos cuartos de pollo y
4 kg y tres cuartos de lomo de cerdo. Expresa en forma de fracción y número decimal el
total de carne que hemos comprado
The total amount of meat bought is 46/4 or 11.5 kg (or 11.5 kilograms).
To express the total amount of meat bought in fraction and decimal form, we need to add up the quantities of each type of meat.
The given quantities are:
2 kg and a quarter of beef
5 kg and two quarters (or a half) of chicken
4 kg and three quarters of pork loin
To find the total amount of meat bought, we can add these quantities:
2 kg and 1/4 + 5 kg and 1/2 + 4 kg and 3/4
To add these mixed numbers and fractions, we need to find a common denominator. The common denominator here is 4.
2 kg and 1/4 can be converted to 9/4 by multiplying 2 by 4 and adding 1.
5 kg and 1/2 can be converted to 9/2 by multiplying 5 by 2 and adding 1.
4 kg and 3/4 remains the same.
Now we can add the fractions:
9/4 + 9/2 + 4 + 3/4
To add the fractions, we need to find a common denominator, which is 4.
9/4 + 9/2 + 16/4 + 3/4
Now we can add the numerators and keep the denominator:
(9 + 18 + 16 + 3) / 4
The numerator becomes 46, so the total amount of meat bought is 46/4.
To express this as a decimal, we can divide the numerator by the denominator:
46 ÷ 4 = 11.5
Therefore, the total amount of meat bought is 46/4 or 11.5 kg (or 11.5 kilograms).
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Mark’s cost does not vary directly with time spent talking because
Mark's cost does not vary directly with time spent talking, it indicates the presence of other factors, such as pricing structure, additional services, peak hours, bundled packages, or promotions, that influence the overall cost. These factors can lead to non-linear cost variations and a lack of direct proportionality between the cost and time spent talking.
If Mark's cost does not vary directly with the time spent talking, it means that there is not a simple proportional relationship between the two variables. In other words, doubling the time spent talking does not necessarily result in doubling the cost. This indicates that there are other factors influencing Mark's cost besides just the time spent talking.
There can be several reasons why Mark's cost does not vary directly with time spent talking:
Pricing structure: Mark's cost may be determined by a pricing structure that includes fixed fees or additional charges based on certain conditions. For example, there might be a base rate for a certain duration of talk time, and any additional time may be billed at a different rate.
Additional services: Mark's cost might include additional services or features that are not solely dependent on talk time. For instance, there could be charges for international calling, call forwarding, or other value-added services.
Peak hours or special rates: Mark's cost might be affected by peak hours or special rates. Some service providers offer different pricing during certain times of the day or specific days of the week. This could result in non-linear cost variations with respect to time spent talking.
Bundled packages: Mark's cost might be part of a bundled package that includes other services like internet or television. In such cases, the overall cost may be influenced by factors other than talk time.
Promotions or discounts: Mark's cost may be subject to promotional offers or discounts that are not directly related to the time spent talking.
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You are using a magnifying glass that shows the image of an object that is six tin image of the termite seen through the magnifying glass. 9.5 mm The image length through the magnifying glass is millimeters.
When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.
When using a magnifying glass, the image of an object appears larger. In this case, the termite is being viewed through a magnifying glass that magnifies the image by a factor of six. The actual length of the termite is not mentioned in the given information. However, it is stated that the length of the image seen through the magnifying glass is 9.5 mm.To determine the actual length of the termite, we can divide the length of the image by the magnification factor. Therefore, the actual length of the termite would be 9.5 mm divided by 6, which is approximately 1.58 mm.Therefore, when viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.For more questions on magnifying glass
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Using the image below, find the missing part indicated by the question mark.
(3 separate questions)
The missing part indicated in the figures are ? = 12, TX = 9 and x = 20
How to find the missing part indicated in the figuresFigure a
The missing part can be calculated using the following equation
?/(11 - 5) = 22/11
Evaluate the difference
?/6 = 22/11
So, we have
? = 6 * 22/11
Evaluate the expression
? = 12
Figure b
The missing part can be calculated using the following equation
TX/3 = 6/2
So, we have
TX = 3 * 6/2
Evaluate
TX = 9
Figure c
The value of x can be calculated using the following equation
1/4x + 6 = 2x - 29
So, we have
x + 24 = 8x - 116
Evaluate
-7x = -140
Divide
x = 20
Hence, the value of x is 20
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How many 20kobo make up #20
Answer:
100
Step-by-step explanation:
#20 naira - 20 * 100
= 2000kobo
2000/20
100
QED✅✅
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Use the image to determine the type of transformation shown.
A. Reflection across the x-axis
B. Horizontal translation
C. Vertical translation
D. 180° clockwise rotation
The type of transformation shown is vertical translation.
Since, Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Given a polygon EFGH.
It is transformed to another polygon with the same size E'F'G'H'.
Here the polygon EFGH is just moved downwards as it is and mark is as E'F'G'H'.
If it is rotation or reflection, the points will change it's correspondent place.
Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.
Therefore, here translation is done.
Since the shifting is done vertically, it is vertical translation.
Hence the transformation is vertical translation.
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Find the length of side X in simple radical form with a rational denominator
The length of side X in simple radical form with a rational denominator is 25/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 5 × 5/√3
Hypotenuse, x = 25/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Indica cuáles de las funciones son afines y=-5 y=1-5x^2 y=-2x^2 y=3x+0,5
Based on the given functions, y = -5 and y = 3x + 0.5 are said to be affine functions. Hence option A and D are correct.
What is the function?An affine function is seen as a function that can be shown as y = mx + b, where m and b are constants.
So looking at the functions given:
y = -5
This function is one that has a constant function with a slope of 0. It can be shown as y = 0x - 5, thus is affine.y = 1 - 5x²
This function is seen as a quadratic function with a squared term. so it is not an affine.y = -2x²
This is the same with the upper function as it is a quadratic function with a squared term, so it is not an affine.y = 3x + 0.5
This function is a linear function with a slope of 3 as well as a y-intercept of 0.5. It can be shown as y = 3x + 0.5, thus, this function is affine.Learn more about functions from
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Which table matches the equation for y = 3/2x-3
Answer: I think it's H, if it isn't and you get a second try it should be N
Step-by-step explanation: Both H and N start with 0/-3 except F which means F is wrong. Maybe you should wait for a better answer...but it shouldn't be F
algebra 2 equality’s
The algebra 2 is a vast field that deals with various mathematical concepts, such as equations and inequalities.
Algebra 2 is a branch of mathematics that mainly deals with equations and inequalities. An equation is a mathematical statement that implies that two expressions are equal.
Similarly, an inequality implies that two expressions are not equal but are related by a certain operation.There are different types of equations that one may encounter in Algebra 2.
A linear equation is an equation that can be represented by a straight line on the coordinate plane. A quadratic equation is one that can be written in the form ax² + bx + c = 0.
There are also exponential, logarithmic, and trigonometric equations that one may come across.Inequalities are statements that two expressions are not equal. Inequalities can be represented graphically on a coordinate plane, just like equations.
There are different types of inequalities such as linear, quadratic, exponential, and logarithmic inequalities.In conclusion, These concepts help in solving real-world problems by providing a framework to analyze them mathematically.
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Calculate.
12C4
Note: Cr=
n
n!
r!(n−r)!
Answer:
495
Step-by-step explanation:
using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1
then
12[tex]C_{4}[/tex]
= [tex]\frac{12!}{4!(12-4)!}[/tex]
= [tex]\frac{12!}{4!(8!)}[/tex]
cancel 8! on numerator/ denominator
= [tex]\frac{12(11)(10)(9)}{4!}[/tex]
= [tex]\frac{11880}{4(3)(2)(1)}[/tex]
= [tex]\frac{11880}{24}[/tex]
= 495
ASAP!!! Please help me solve
Answer: j(x) = (x-1)(x+2)
The x-1 part is because of the root x = 1
The root x = -2 leads to the factor x+2
Mikey johnson shipped out 34 2/7 pounds of electrical supplies . The supplies are placed in individual packets that weigh 2 1/7 pounds each . How many packets did he ship out ?
Mikey Johnson shipped out 34 2/7 pounds of electrical supplies. The supplies are placed in individual packets that weigh 2 1/7 pounds each. Therefore, Mikey shipped out 16 packets of electrical supplies.
To solve the problem, we can use the following steps.Step 1: Find the weight of each packet.
We are given that the weight of each packet is 2 1/7 pounds.
To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.
This gives us: 2 1/7 = (2 × 7 + 1) / 7= 15 / 7 pounds.
Therefore, the weight of each packet is 15/7 pounds.
Now, divide the total weight by the weight of each packet.
We are given that the total weight of the supplies shipped out is 34 2/7 pounds.
To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.
This gives us: 34 2/7 = (34 × 7 + 2) / 7= 240 / 7 pounds.
Therefore, the total weight of the supplies is 240/7 pounds.
To find the number of packets that Mikey shipped out, we can divide the total weight by the weight of each packet.
This gives us: 240/7 ÷ 15/7 = 240/7 × 7/15= 16.
Therefore, Mikey shipped out 16 packets of electrical supplies.
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lim (cosec 2x - xcosec³x)
x approaches 0
The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.
We have,
To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.
The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).
Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.
Substituting these into the expression,
We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).
Now, let's evaluate the limit term by term:
lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).
lim(x approaches 0) (x (1/(sin(x))³))
= 0 (1/(sin(0))³)
= 0 x 1/0 (which is also undefined).
Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.
Therefore,
The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.
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WHAT IS THE CORRELATION R FOR THE DATA SET
I WILL MARK YOU BRAINLIEST!
The correlation coefficient (r) is -0.96.
Given the data:
x: 0, 1, 2, 2, 3, 4, 5, 5, 6
y: 12, 9.5, 9, 8.5, 8.5, 6, 5, 5, 3.5
Step 1: Calculate the mean (average) of x and y.
Mean of x = (0 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 6) / 9 = 3
Mean of y = (12 + 9.5 + 9 + 8.5 + 8.5 + 6 + 5 + 5 + 3.5) / 9 = 7
Step 2: Calculate the deviations from the mean for x and y.
Deviation of x (dx) = x - X
Deviation of y (dy) = y - Y
x: -3, -2, -1, -1, 0, 1, 2, 2, 3
y: 5, 2.5, 2, 1.5, 1.5, -1, -2, -2, -3.5
Step 3: Calculate the product of the deviations of x and y.
(dx * dy): -15, -5, -2, -1.5, 0, -1, -4, -4, -10.5
Step 4: Calculate the sum of the products of the deviations (Σ(dx * dy)).
Σ(dx * dy) = -15 - 5 - 2 - 1.5 + 0 - 1 - 4 - 4 - 10.5 = -43
Step 5: Calculate the standard deviations of x (σx) and y (σy).
Standard deviation of x (σx) = √(Σ(dx²) / (n-1))
Standard deviation of y (σy) = √(Σ(dy²) / (n-1))
Calculating dx²:
dx^2: 9, 4, 1, 1, 0, 1, 4, 4, 9
Σ(dx²) = 33
Calculating dy²:
dy²: 25, 6.25, 4, 2.25, 2.25, 1, 4, 4, 12.25
Σ(dy²) = 61
Calculating the standard deviations:
σx = √(33 / (9-1)) = √(33 / 8) ≈ 1.84
σy = √(61 / (9-1)) = √(61 / 8) ≈ 2.70
Step 6: Calculate the correlation coefficient (r).
r = Σ(dx dy) / (√(Σ(dx²) Σ(dy²)))
r = -43 / (√(33 61))
r ≈ -43 / (√(2013))
r ≈ -43 / 44.87
r ≈ -0.96
Therefore, the correlation coefficient (r) is approximately -0.96.
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A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
Any help on this study?
The Equation of circle for Circle B is (x - 2) ² + (y + 4)² = 38.4.
For circle A:
Radius of circle A = √36 = 6
Area of circle A = π(6)^2 = 36π
Let's assume the radius of circle B is r.
Circumference of circle A = 2π(6) = 12π
Circumference of circle B = 3.2 x Circumference of circle A
= 3.2 x 12π
= 38.4π
Since the ratio of the areas is equal to the ratio of the circumferences, we have:
Area of circle B / Area of circle A = (r^2π) / (36π) = 38.4π / 36π
Simplifying, we get:
r² / 36 = 38.4 / 36
Cross-multiplying, we have:
36 x r² = 38.4 x 36
Dividing both sides by 36:
r^2 = 38.4
Taking the square root of both sides:
r = √38.4
Now we have the radius of circle B. Let's substitute this value into the equation for circle B:
(x - 2) ² + (y + 4)² = (√38.4)²
Simplifying:
(x - 2) ² + (y + 4)² = 38.4
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NO LINKS!! URGENT HELP PLEASE!!!
Given the explicit formula for a geometric sequence find the first five terms and the 8th term.
36. a_n = -3^(n-1)
37. a_n = 2 * (1/2)^(n - 1)
Answer:
see explanation
Step-by-step explanation:
to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula
36
a₁ = - [tex]3^{1-1}[/tex] = - [tex]3^{0}[/tex] = - 1 [ [tex]a^{0}[/tex] = 1 ]
a₂ = - [tex]3^{2-1}[/tex] = - [tex]3^{1}[/tex] = - 3
a₃ = - [tex]3^{3-1}[/tex] = - 3² = - 9
a₄ = - [tex]3^{4-1}[/tex] = - 3³ = - 27
a₅ = - [tex]3^{5-1}[/tex] = - [tex]3^{4}[/tex] = - 81
the first 5 terms are - 1, - 3, - 9, - 27, - 81
to find a₈ substitute n = 8 into the explicit formula
a₈ = - [tex]3^{8-1}[/tex] = - [tex]3^{7}[/tex] = - 2187
37
to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula
a₁ = 2 × [tex](\frac{1}{2}) ^{1-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{0}[/tex] = 2 × 1 = 2
a₂ = 2 × [tex](\frac{1}{2}) ^{2-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{1}[/tex] = 2 × [tex]\frac{1}{2}[/tex] = 1
a₃ = 2 × [tex](\frac{1}{2}) ^{3-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{2}[/tex] = 2 × [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{2}[/tex]
a₄ = 2 × [tex](\frac{1}{2}) ^{4-1}[/tex] = 2 × ([tex]\frac{1}{2}[/tex] )³ = 2 × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{4}[/tex]
a₅ = 2 × [tex](\frac{1}{2}) ^{5-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{4}[/tex] = 2 × [tex]\frac{1}{16}[/tex] = [tex]\frac{1}{8}[/tex]
the first 5 terms are 2 , 1 , [tex]\frac{1}{2}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{8}[/tex]
to find a₈ substitute n = 8 into the explicit formula
a₈ = 2 × [tex](\frac{1}{2}) ^{8-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{7}[/tex] = 2 × [tex]\frac{1}{128}[/tex] = [tex]\frac{1}{64}[/tex]
Answer:
The explicit formula for a geometric sequence is:
a_n = a_1 * r^(n - 1)
where:
a_n is the nth term in the sequencea_1 is the first term in the sequencer is the common ratio between the terms in the sequenceIn equation 36,
we can see that the first term is -3 and the common ratio is -3. Therefore, we can write the explicit formula for this sequence as:
a_n = -3 * (-3)^(n - 1)
Using this formula, we can find the first five terms and the 8th term in the sequence:
a_1 = -3
a_2 = -3 * (-3) = 9
a_3 = -3 * (-3)^2 = -27
a_4 = -3 * (-3)^3 = 81
a_5 = -3 * (-3)^4 = -243
a_8 = -3 * (-3)^7 = 6561
In equation 37,
we can see that the first term is 2 and the common ratio is 1/2. Therefore, we can write the explicit formula for this sequence as:
a_n = 2 * (1/2)^(n - 1)
Using this formula, we can find the first five terms and the 8th term in the sequence:
a_1 = 2
a_2 = 2 * (1/2) = 1
a_3 = 2 * (1/2)^2 = 1/2= 0.5
a_4 = 2 * (1/2)^3 =1/4= 0.25
a_5 = 2 * (1/2)^4 = 1/8=0.125
a_8 = 2 * (1/2)^7 = 1/64=0.015625
The point P (x, y) is moving along the curve y = x² -10/3 x^3/2+ 5x in such a way that the rate of change of y is constant.
Find the values of x at the points at which the rate of change of x is equal to half the rate of change of y.
Answer:
To find the points where the rate of change of x is half the rate of change of y, we need to solve the equations:
dy/dx = k
dy/dt = k
where k is a constant representing the rate of change.
Step-by-step explanation:
What equation is graphed?
10
8
6
SK
-10-8-8/ 2 4 6 8 10
-8
-10
16
9
=1
=1
po
first off, let's take a peek at the picture above
hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.
now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}[/tex]
In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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which system has no solution? x>2 x<7 , x<2 x>7 , x<2 x<7 , X>2 x>7
The only system of inequalities that has no solution is x<2 and x>7.(option-b)
The system of inequalities that has no solution is x<2 and x>7.
If x is less than 2, it cannot be greater than 7 at the same time. These two inequalities are contradictory, and there is no number that could satisfy both of them simultaneously.
The system of inequalities x>2 and x<7 forms an open interval between 2 and 7. Any value of x within this interval can satisfy both inequalities, so this system has a solution.
The system of inequalities x<2 and x<7 forms an inequality that is satisfied by any value of x that is less than 7, so this system also has a solution.
Lastly, the system of inequalities x>2 and x>7 forms an inequality that is not satisfied by any value of x, as there is no number that is simultaneously greater than 2 and greater than 7.(option-b)
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