Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7
To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as
lim_x→0 [(4^(2x) - 1)/x]/(7/2)
Now, we can apply L'Hopital's rule to the numerator
lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0
So we get:
lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0
Therefore, the limit is 0.
Now let's verify the given answer using logarithmic properties
(4^(2x) - 1)/(7x) = (2 log(4))/7
Multiplying both sides by 7x
4^(2x) - 1 = 2x log(4)
Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:
(4^x + 1)(4^x - 1) = 2x log(4)
Dividing both sides by (4^x - 1)
4^x + 1 = (2x log(4))/(4^x - 1)
Now, taking the limit as x approaches 0, we get:
lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7
Therefore, the given answer is verified.
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At the party Ashia and her friend at 2 1/2 pizzas after the party there were 1 1/8 pizza left how many pizzas were there at the start of the party?
Answer: 3 5/8 pizzas were there at the start of the party.
Step-by-step explanation:
At the party let number of pizzas were = x Aisha and her friends ate 2 1/2 pizzas after which 1 1/8 pizzas were left.
Therefore the equation formed will be
x- 2 1/2= 1 1/8
x-(5/2)= 9/8
x= 9/8 + 5/2
x= 29/8= 3 5/8
Therefore 3 5/8 pizzas were there at the start of the party.
Given triangle XYZ with ZX = 30°, ZY= 20° and ZZ = 2aº, what is the value of a?
A. 130
B. 65
C. 40
D. 20
According to the question, we are given a triangle XYZ
where,
∠X = 30° ∠Y = 20° ∠Z = 2a°Angle sum property states that sum of all the angles of triangle is 180°. So by adding all the three angles we will get the required value of a.
∠X + ∠Y + ∠Z = 180°
30° + 20° + 2a° = 180°
50° + 2a° = 180°
2a° = 180° - 50°
2a° = 130°
a° = 130/2
a° = 65°
Therefore, required value of a is 65°
Answer:
B
Step-by-step explanation:
remember : the sum of all angles in a triangle is always 180°.
are you sure the third angle is called ZZ ?
I am rather sure it would be called XY !
so,
180 = ZX + ZY + XY = 30 + 20 + 2a
130 = 2a
a = 130/2 = 65°
calculate the probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460. (use salt. round your answer to four decimal places.)
The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.
To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.
Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula
z = (x - μ) / σ,
where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.
In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula
z = (470 - 460) / (σ / √n),
where n is the sample size.
If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as
=> z = (470 - 460) / (1 / √100) = 10.
We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.
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What is 5 1/2 x 5 = ?
Answer:27.5
Step-by-step explanation:
i did this with a calculator, but the answer is
27.5
Do anybody know this?
The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)
What are the coordinates of the division of the line segment?The formula for the division of line segments in the ratio m:n is
P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}
We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)
Thus, if the ratio is 2:5, we have:
U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}
U(x, y) = (84/7), (42/7)
U(x, y) = (12, 6)
Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.
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There are a number of factors that alter the bioavailability of minerals from foods. Complete each sentence with either increases or decreases. decreases increases Phytic acid the absorption of zinc from grains. ces Oxalic acid the absorption of calcium from spinach. Refinement of grains the mineral content of grain products. Vitamin C the absorption of iron from foods. the absorption of calcium from foods. Vitamin D < Prev 5 of 15 !!! Next > raw
In this particular question, the following statements can be used to complete each sentence with either "increases" or "decreases":
- Phytic acid decreases the absorption of zinc from grains.
Oxalic acid decreases the absorption of calcium from spinach.
- Refinement of grains decreases the mineral content of grain products.-
Vitamin C increases the absorption of iron from foods.-
Vitamin D increases the absorption of calcium from foods.
Explanation:
Bioavailability refers to the proportion of a nutrient that is absorbed from food and made available for use in the body. Factors that alter bioavailability of minerals from foods include phytic acid, oxalic acid, refinement of grains, and vitamins C and D. Phytic acid, for instance, decreases the absorption of zinc from grains while oxalic acid decreases the absorption of calcium from spinach.
Refinement of grains, on the other hand, decreases the mineral content of grain products. Conversely, vitamin C increases the absorption of iron from foods while vitamin D increases the absorption of calcium from foods.
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Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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the area of the figure is
The area of the parallelogram above is 490 metres squared.
How to find the area of a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
The area of a parallelogram can be calculated as follows:
area of a parallelogram = bh
where
b = baseh = heightTherefore,
b = 49 metres
h = 10 metres
Therefore,
area of a parallelogram = 10 × 49
area of a parallelogram = 490 metres squared
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It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box, which holds 15 cups of sugar. Double the dimensions of the box. Hint: given k, areas are scaled by ____ and volumes are scaled by ____ Approximately how much paint would the new box need? How much sugar would it hold?
The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
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A student was asked to factor
Answer:
Step-by-step explanation:
1) [tex]6x^4 \times 6x^4 = 36x^8[/tex] (needs to be [tex]36x^{16}[/tex] )
2) [tex](4y^2) \times (4y^2) =16y^4[/tex] (needs to be [tex]25y^4[/tex] )
1) Change both [tex]6x^4 \text{ terms to } 6x^8.[/tex]
2) Change both [tex]4x^2 \text{ terms to } 5y^2.[/tex]
Bonus:
Need to change a minus to a plus,
[tex]36x^{16}-25y^4=(6x^8+5y^2)(6x^8-5y^2)[/tex]
does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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write the equation of an exponential decau function with a range of (-inifinage,10) verticlal shrink of 3/4 and vertical shift up 10 units
The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.
We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
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Which set of ordered pairs is NOT A FUNCTION?
(5,3) , 6,3) , (7,3) , (8,3)
(2,1) (3,3) , (4,6) , (2,3)
(1,6) , (8,4) , (3,8) , (7,`)
(9,8), (7,6) , (5,3) , (2,1)
The set of ordered pairs (2,1), (3,3), (4,6), (2,3) is NOT a function because the input value of 2 corresponds to both the output values of 1 and 3.
For a set of ordered pairs to be a function, each input (x-value) must correspond to only one output (y-value). Therefore, if there exists an input (x-value) that corresponds to more than one output (y-value), then the set of ordered pairs is NOT a function.
Let's check each set of ordered pairs:
(5,3), (6,3), (7,3), (8,3): Each input (x-value) corresponds to the output (y-value) of 3. This set of ordered pairs is a function.(2,1), (3,3), (4,6), (2,3): The input value of 2 corresponds to both the output values of 1 and 3. Therefore, this set of ordered pairs is NOT a function.(1,6), (8,4), (3,8), (7,`): The output value for the fourth ordered pair is missing, so we cannot determine whether this set of ordered pairs is a function or not.(9,8), (7,6), (5,3), (2,1): Each input (x-value) corresponds to a unique output (y-value). This set of ordered pairs is a function.Therefore, the set of ordered pairs that is NOT a function is (2,1), (3,3), (4,6), (2,3).
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a die is continuously rolled 104 104 times. what is the probability that the total sum of all rolls does not exceed 375 375 ?
The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165
Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.
Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:
E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365
The variance of X is
Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312
The standard deviation of X is
SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67
To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375
P(X <= 375) = F(375)
where F(x) = P(X <= x) is the CDF of X.
Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67
Z = (X - E(X)) / SD(X)
Z follows a standard normal distribution with mean 0 and standard deviation 1.
P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))
= P(Z <= (375 - 365) / 17.67)
= P(Z <= 0.566)
Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.
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The given question is incomplete, the complete question is :
A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?
suppose the amount of time (in minutes) per day that you spend watching netflix is in the 90th percentile of all account users. which interpretation(s) of this quantity are correct? select all that apply.
The correct interpretations of the given quantity are C and E.
C. Your daily viewing time is greater than 90% of all Netflix users.
E. 90% of all Netflix users viewing times per day are less than your daily viewing time.
To understand the correct interpretation, we need to first understand what the 90th percentile means. It refers to the value below which 90% of the data falls.
If your daily viewing time is in the 90th percentile of all Netflix users, it means that your viewing time is greater than 90% of all users. In other words, only 10% of users watch more Netflix than you, and your viewing time is greater than the viewing time of 90% of users.
Therefore, options C and E are the correct interpretations.
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Complete Question:
Suppose the amount of time (in minutes) per day that you spend watching Netflix is in the 90th percentile of all account users. Which interpretation(s) of this quantity are correct? Select ALL that apply.
A. You spend approximately 90 minutes per day watching Netflix.
B. 90% of all viewers spend more time on Netflix per day than you.
C. Your daily viewing time is greater than 90% of all Netflix users.
D. There is a 90% probability that a randomly selected viewer spends less time than you watching Netflix per day.
E. 90% of all Netflix user viewing times per day are less than your daily viewing time.
F. 90% of all Netflix user viewing times per day are less than or equal to your daily viewing time.
Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. Two lines L I and I J are formed by connecting points (Negative 4,3), (5,3), and (5, Negative 3).
I(5, 3), J(5, -3), and L(-4, 3) are three vertices of rectangle IJKL. What are the coordinates of the fourth vertex, K, of rectangle IJKL?
A.
(-4, -3)
B.
(5, 3)
C.
(5, -3)
D.
(-4, 3)
The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
Thus, οptiοn D is cοrrect.
What is the cοοrdinate geοmetry?Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.
The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).
Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
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The Computer has labeled the lines you graphed a and b. What are the equations of the lines? Enter them into the table below
The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.
Consider two points on the blue line.
The points are (5, -8) and ( -3,1 ).
Equation of the blue line is:
y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]
8 (y - 1) = -9 ( x + 3)
8y - 8 = -9x -27
9x + 8y + 19 = 0
Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.
Consider two points on the red line.
The points are (-3, 1) and ( 1,6 ).
Equation of the red line is:
y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]
4 (y - 1) = 5 (x + 3)
4y - 4 = 5x + 15
5x - 4y+ 19 = 0
Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.
Hence, the equations for the given blue and red lines are completed.
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To fill a pool, Barb uses two hoses. The first hose is rated to fill the pool in
10 hours. The second hose is rated to fill it in 5 hours. If Barb adds a third
hose that uses the slower rate, how long will it take to fill the pool.
It will take [1] hours to fill the pool.
Using division operation, the length it will take the three hoses to fill the pool is 8.33 hours.
What is the division operation?The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves the dividend, the divisor, and the result called the product.
In this situation, it will take Hose A 10 hours to fill the pool and Hose B 5 hours. If the two hoses are in use, it will 7.5hours (10 + 5)/2.
When the third hose is added, it will take 8.33 hours (10 + 5 + 10)/3.
The first hose's filling rate for the pool = 10 hours
The second hose's filling rate for the pool = 5 hours
The third hose's filling rate for the pool = 10 hours (the slower rate)
The total number of hours used by the three hoses = 25 hours (10 + 5 + 10)
The number of hoses used = 3
The length of time it will take the 3 hoses to fill the pool = 8.33 hours (25/3)
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Can anybodyhelp me with these please? I need help please!
1: The measure of arc JML is: arc JML = 176°
3: m∠WXY = 59°
5: The measure of the arc is: arc FE = 54°
7: The measure of the angles are: m∠A = 79° and m∠B = 112°
9: The value of x is: x = 9
How to find the angle or arc measure in a circle?
No. 1
The measure of inscribed angle is half the measure of its intercepted arc. That is:
∠ JKL = 1/2 * arc JML
88 = 1/2 * arc JML
arc JML = 2 * 88
arc JML = 176°
No. 3
arc WY = 360 - 86 - 156 = 118° (sum of angles in a circle)
m∠WXY = 1/2 * arc WY
m∠WXY = 1/2 * 118
m∠WXY = 59°
No. 5
An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°
m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)
m∠EDF = 1/2 * arc FE
27° = 1/2 * arc FE
arc FE = 2 * 27
arc FE = 54°
No. 7
The opposite angle in a cyclic quadrilateral add up to 180°. That is:
m∠A + m∠C = 180°
m∠A + 101 = 180
m∠A = 180 - 101
m∠A = 79°
m∠B + m∠D = 180°
m∠B + 68 = 180
m∠B = 180 - 68
m∠B = 112°
No. 9
67 = 1/2 * (16x - 10)
67 * 2 = (16x - 10)
16x - 10 = 134
16x = 134 + 10
16x = 144
x = 144/16
x = 9
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The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
Answer:
g(x) = (x + 3)2 - 2
Step-by-step explanation:
I think that's the one I just did this class so
A trazpodizi has an aera of 35 mm2 what is the height
The height of the trapezium is 5mm, given that the two parallel sides have lengths of 6mm and 8mm, and the area of the trapezium is 35mm².
To find the height of a trapezium given its area and the lengths of its parallel sides, we use the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, h is the height, and Area is the area of the trapezium.
In this case, we are given that the area of the trapezium is 35mm², and we know that the two parallel sides have lengths 6mm and 8mm. So, we can substitute these values into the formula and solve for h:
35 = (6+8) x h/2
Simplifying the right-hand side of the equation, we can combine the two lengths of the parallel sides and multiply by h, and then divide by 2 to get:
35 = 14h / 2
Multiplying both sides by 2, we get:
70 = 14h
Dividing both sides by 14, we get:
h = 5
Therefore, the height of the trapezium is 5mm.
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On pose, pour tout n E N, Un = Un - 5.
(a) Montrer que (Un) est une suite géométrique; préciser sa raison et son premier terme.
(b) Donner l'expression de Un en fonction de n: en déduire l'expression de un en fonction de n.
(c) En déduire la valeur de U12
Answer:
(a) Pour montrer que la suite (Un) est géométrique, il suffit de vérifier que le quotient de deux termes consécutifs est constant. Soit n un entier naturel non nul. Alors :
Un+1 / Un = (Un-4) / (Un) = 1 - 5/Un
Donc, pour tout n E N*, on a :
Un+1 / Un = 1 - 5/Un = (Un / Un) - (5/Un) = (Un - 5) / Un
On a bien trouvé une raison q = -5/1, et un premier terme U1 = U1 - 5.
(b) La raison de la suite (Un) est q = -5/1. En utilisant la formule générale de la suite géométrique, on obtient :
Un = U1 * q^(n-1) = (U1 - 5) * (-5)^(n-1)
En particulier, on a :
U_n = U_1 * q^{n-1} = (U_1 - 5) * (-5)^{n-1} = U_12 = (U_1 - 5) * (-5)^{12-1}
(c) On n'a pas suffisamment d'informations pour déterminer la valeur de U1, donc on ne peut pas calculer directement la valeur de U12.
how far will 560J raise a block weighing 8 N
a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
How to calculate work?
To calculate the height to which a block weighing 8 N can be raised by a force of 560J, we need to use the formula for work done:
Work (W) = force (F) x distance (d) x cos(theta)
where theta is the angle between the force and the displacement. In this case, the force is the weight of the block (8 N), the distance is the height the block is raised (h), and theta is 0 degrees because the force is acting vertically upward and the displacement is in the same direction.
So, we can rearrange the formula to solve for the height (h):
h = W / (F x cos(theta))
Substituting the values we have, we get:
h = 560 J / (8 N x cos(0 degrees))
Since the cosine of 0 degrees is 1, we can simplify to:
h = 560 J / 8 N
h = 70 meters
Therefore, a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
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Please Help Me I need help
In response to the stated question, we may state that therefore, the expressions value of vector will be n = 25.73.
what is expression ?An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
to find vector and magnitude we have
[tex]n^2 = (22.5)^2 + (12.5)^2\\n^2 = 506.25 + 156.25\\n^2 = 662.5\\n = \sqrt(662.5)\\n = 25.73[/tex]
therefore, the value of vector will be n = 25.73.
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Answer: rectangleular pyramid
Step-by-step explanation:
Can someone explain this correctly to me?
Answer:
2.80
Step-by-step explanation:
It asks to find the shipping and handling price.
The first step is take that percentage, 20% and convert into decimal form. Then you need to multiply that by the original price. So it would be 0.2 x 14.
That gives you 2.80 which is the shipping and handling price. That's all you have to do.
The 15 Chihuahua puppies ate 63 cups of food last week. If each puppy ate the same amount of food, how many cups of puppy food did each puppy eat?
15 StartLongDivisionSymbol 63.0 EndLongDivisionSymbol minus 60 = a remainder of 30 and a quotient of 4.blank.
How many cups of food did each puppy eat?
4 cups
4.1 cups
4.2 cups
4.ModifyingAbove 2 with bar cups
Answer:c 4.2 cups
Step-by-step explanation:
just do 63 divided 15
the smith family has $4$ cats and $3$ dogs. in how many ways can these $7$ pets be placed in a row of $7$ chairs such that at least $2$ cats are next to each other?
There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.
Arrangement of entities can be done using permutation and combination in mathematics.
Consider the distributions where 2 cats are not next to each other as
C D C D C D C.
There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144
There are a total of 7!=5040 possible ways to seat both cats and dogs.
At least 2 cats seat together= All possible arrangements- None of the cat seat together.
Thus the number of seatings where at least 2 cats are adjacent is
5040-144 = 4896
So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.
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A video goes viral on social media, the number of views per day can be modeled with the equation y = -0.75x² +9.75x where is the number of days after the video is posted and y is the number of views per day in thousands. According to the model, after how many days do people stop watching the video?
Answer:
Step-by-step explanation:
To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.
The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.
Using the formula with a = -0.75 and b = 9.75, we get:
x = -9.75 / 2(-0.75)
x = -9.75 / -1.5
x = 6.5
Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.
To determine when people stop watching the video, we need to check the values of y after this point.
When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).
Describe how it is possible to calculate the enthalpy of formation for a compound that cannot be synthesized directly from the constituent elements.
The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.
The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.
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