Consider the series ∑n=1[infinity]1n(n+6) Determine whether the series converges, and if it converges, determine its value. Converges (y/n): Value if convergent (blank otherwise):
Answers
The series converges to approximately 0.1615.
To determine whether the series ∑n = 1 [infinity] 1n (n+6) converges, we can use the limit comparison test.
We compare it to the series ∑n = 1 [infinity] 1n 2, which we know converges (by the p-series test with p=2).
lim n→∞ =1
Since the limit is finite and non-zero, by the limit comparison test, we conclude that the series ∑n=1[infinity]1n(n+6) also converges.
To find its value, we can use partial fractions.
1n(n+6) = \(\frac{A}{n}\) + \(\frac{B}{n+6}\)
Multiplying both sides by n(n+6) and setting n=0 and n=-6, we get:
The value of r can be done by dividing the second term (1(n+6)) by the first term (1n), which gives us r = (n+6)/n.
When we plug in n = 1, we get r = 7/1, which is greater than 1.
Since the common ratio is greater than 1, the series is divergent.
A = \(\frac{1}{6}\)
B = \(-\frac{1}{6}\)
Therefore:
1n(n+6) = \(\frac{1}{6}\) (\(\frac{1}{n}\) - 1/(n+6)\(\frac{1}{n+6}\))
Hence:
∑n = (\(\frac{1}{6}\))(\(\frac{1}{1}\) - \(\frac{1}{7}\) + \(\frac{1}{2}\) - \(\frac{1}{8}\) + \(\frac{1}{4}\) - \(\frac{1}{9}\) + ...)
= (\(\frac{1}{6}\)) ln (\(\frac{80}{49}\))
≈ 0.1615
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Related Questions
Use the SIN to find x?
190m
Xm
1. Set Up
2. Operation
3. Answer
52.2
Answers
Answer:
sine=opposite/hypotenuse
sin52.2=x/150
sin0.790=x/150
x=118.5
Consider the following vector field.
F(x, y, z) =
9ex sin(y), 2ey sin(z), 8ez
sin(x)
(a)
Find the curl of the vector field.
curl(F) =
(b)
Find the divergence of the vector field.
div(F) =
Answers
The curl of the vector field
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
The divergence of the vector field
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.
(a) Curl of F:
The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k
In this case, we have:
P(x, y, z) = 9ex sin(y)
Q(x, y, z) = 2ey sin(z)
R(x, y, z) = 8ez sin(x)
Taking the partial derivatives, we get:
∂P/∂y = 9ex cos(y)
∂Q/∂z = 2ey cos(z)
∂R/∂x = 8ez cos(x)
∂R/∂y = 0 (no y-dependence in R)
∂Q/∂x = 0 (no x-dependence in Q)
∂P/∂z = 0 (no z-dependence in P)
Substituting these values into the curl formula, we have:
curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k
= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
Therefore, the curl of the vector field F is given by:
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
(b) Divergence of F:
The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z
In this case, we have:
∂P/∂x = 9e^x sin(y)
∂Q/∂y = 2e^y sin(z)
∂R/∂z = 8e^z
Substituting these values into the divergence formula, we have:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
Therefore, the divergence of the vector field F is given by:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
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A square patio has a perimeter of (32x+8) feet. What is the length of the patio?
Answers
The perimeter of the square patio is the sum of its side lengths
The length of the patio is: 8x + 2
The given parameters are:
\(\mathbf{Shape = Square}\)
\(\mathbf{Perimeter = 32x + 8}\)
The perimeter of a square is:
\(\mathbf{Perimeter = 4 \times Length}\)
So, we have:
\(\mathbf{4 \times Length = 32x + 8}\)
Divide both sides by 4
\(\mathbf{Length = 8x + 2}\)
Hence, the length of the patio is: 8x + 2
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Consider a perfectly shuffled 52-card deck dealt to 4 players. Find the probability that one player (any one of the four players) gets all aces.
Answers
The probability that one player gets all aces is 0.0467
Finding the probability that one player gets all aces.From the question, we have the following parameters that can be used in our computation:
Cards, n = 52
Players, r = 4
The 52 cards can be shared to the the 4 players in C(n + r - 1, r - 1) ways
So, we have
C(52 + 4 - 1, 4 - 1) = C(55, 3)
When evaluated, we have
C(52 + 4 - 1, 4 - 1) = 26235
Next:
The remaining 48 cards can be shared to the other 3 players in C(n + r - 1, r - 1) ways
C(48 + 3 - 1, 3 - 1) = C(50, 2)
C(48 + 3 - 1, 3 - 1) = 1225
So, we have
P = 1225/26235
Evaluate
P = 0.0467
Hence, the probability is 0.0467
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What is g(x)?
A. g(x) = -2
B. g(x) = -x
C. g(x) = -|x|
D. g(x) = -x^2
Answers
Answer:
A. g(x) = -2^x.
Step-by-step explanation:
If g(x) = -2, it would be a straight line running horizontally.
If g(x) = -x, it would be a linear equation.
If g(x) = -|x|, it would be an absolute value function, which is a graph in a v-shape.
So, the remaining answer is that A. g(x) = -2^x.
Hope this helps!
Its A, \(-2^x\).
For inputs x you can find corresponding y-values on the graph of function:
\(x=1\implies y=-2^1=-2\)
\(x=2\implies y=-2^2=-4\)
\(x=3\implies y=-2^3=-8\)
.
.
.
Hope this helps.
Solve for x in the equation x2-10x+25= 35-
X=5+2√ √5
O x=5± √√35
x=10+2√√/5
x = 10+ √√√35
0 0 0 0
Answers
The solution of the quadratic equation is x=5±√35 .
A quadratic equation is given by the equation which can be written in the form ax²+bx +c.
There are two solution of x for a quadratic equation. the graph of a quadratic equation is in the shape of a parabola in the cartesian plane.To solve a quadratic equation various methods are used:Completing of squaresMiddle term factorizationusing the quadratic formulathe given quadratic equation is :
x²-10x+25=35
Simplifying the equation we get:
or, x²-10x+25-35=0
or, x²-10x-10=0
Now we will solve the equation by completion squares method:
x²-10x-10=0
or, x²-2×x×5+5²-5²-10=0
or, (x-5)²=35
or, x-5=±√35
or, x= 5±√35
Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .
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Computer equipment was acquired at the beginning of the vear at a cout of $73,700 that has an estimatod resduat value of 34,600 and an eatimated ustul life of 5years. a. Determine the depreciable cost. b. Determine the straight-tine rate. \% c. Determine the annual straight-hine depreciation.
Answers
The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.
a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.
b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.
c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.
By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.
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NEEP HELP ASAP LAST DAY OF SCHOOL PLS SHOW YOUR WORK
A rectangular field is 80 meters wide and 120 meters long. Give the length and width of another rectangular field that has the same perimeter but a larger area.
Width= ----- Meters
Length= ------ Meters
Answers
The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.
To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:
1. Calculate the perimeter of the given rectangular field:
Perimeter = 2 * (Length + Width)
= 2 * (120 meters + 80 meters)
= 2 * 200 meters
= 400 meters
2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:
Side length = Perimeter / 2
= 400 meters / 2
= 200 meters
3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.
4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:
Width = Perimeter / 2 - Length
= 400 meters / 2 - 200 meters
= 200 meters - 200 meters
= 0 meters
5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.
In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.
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which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials
Answers
None of the options are commutative for the given binary operations.
Define the term commutative property?According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. With addition and multiplication, the principle is true, but not for division or subtraction.commutative property:
a*b = b*a
* is any binary operation.
Consider option a: subtraction of integers
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Option b: . division of nonzero real numbers
Let a = 2, b = 3
a/b = b/ a (commutative property)
But
2/3 ≠ 3/2 not commutative
Option c. function composition of polynomials.
Let polynomial be a - b
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Thus, none of the options are commutative for the given binary operations.
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The rectangle below was enlarged using a scale factor.
What is the area of the original rectangle
Answers
Answer:
8
Step-by-step explanation:
do 8÷1.6 that gives you 5
so then to get your bottom length do 5×5=25
so then do 1.6×5 and that gives you 8
the length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 8 cm/s. when the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm2/s)?
Answers
The rate at which the area is increasing is 95cm/sec² .
Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.
We know that the area of the rectangle is given by A=a × b
Now differentiating with respect to t we get :
\(\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}\)
Substituting the values we get that the rate of increase in the area is :
Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²
A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.
A line segment represents the graph of a single variable.In this context, a function that is also a linearly map may be referred to as a homogeneous linear function or a linear form (the other meaning). In the context of linear algebra, the scalar-valued affine mappings are functions of degree 0 or 1.To learn more about area visit:
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reaching into the change drawer, sue notices that she only has nickels (worth 5 cents) and dimes (worth 10 cents). from prior experience, she knows that the variance of the number of nickels is 8, the variance of the number of dimes is 10 and the covariance of the number of nickels to the number of dimes is 5. what is the covariance of the number of coins to the value of the coins (in cents)?
Answers
The covariance between the number of coins and the value of the coins is 240.
The covariance between the number of coins (N) and the value of the coins (V) can be calculated as
Cov(N, V) = Cov(n nickels + n dimes, 5n nickels + 10n dimes)
= 5 Cov(n nickels, n nickels) + 10 Cov(n nickels, n dimes) + 5 Cov(n dimes, n nickels) + 10 Cov(n dimes, n dimes)
= 5 * Var(n nickels) + 10 * Cov(n nickels, n dimes) + 5 * Cov(n dimes, n nickels) + 10 * Var(n dimes)
= 5 * 8 + 10 * 5 + 5 * 5 + 10 * 10
= 40 + 50 + 50 + 100
= 240
So the covariance between the number of coins and the value of the coins is 240.
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how to find the magnitude and direction of a vector using trig?
Answers
To find the magnitude and direction of a vector using trigonometry, you can follow these steps:
1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).
2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
magnitude(A) = √(Ax^2 + Ay^2)
3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
angle = arctan(Ay / Ax)
b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).
4. Convert the direction to degrees or radians, depending on the required format.
Let's consider an example to illustrate these steps:
Suppose we have a vector A with components Ax = 3 and Ay = 4.
1. Identify the components: A = (3, 4).
2. Calculate the magnitude:
magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
3. Find the direction:
angle = arctan(4 / 3) ≈ 53.13 degrees.
4. Convert the direction:
angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.
So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.
Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.
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Which of the following statements is true regarding the influence of a small alpha level in the context of hypothesis testing? O a. A small alpha level reduces the effect size. O b. A small alpha level increases statistical power. c. A small alpha level reduces the likelihood of a Type I error. O d. A small alpha level increases the likelihood of detecting statistical significance
Answers
The influence of a small alpha level in the context of hypothesis testing is:
c. A small alpha level reduces the likelihood of a Type I error.
What is null hypothesis?A hypothesis known as the null hypothesis states that sample observations are the result of chance.
The correct statement regarding the influence of a small alpha level in the context of hypothesis testing is:
c. A small alpha level reduces the likelihood of a Type I error.
A small alpha level (typically denoted as α) is the significance level used in hypothesis testing to determine the threshold for rejecting the null hypothesis. By setting a small alpha level, such as 0.01 or 0.05, we are reducing the probability of making a Type I error, which is the incorrect rejection of a true null hypothesis.
In other words, a small alpha level provides a stricter criterion for rejecting the null hypothesis, making it less likely to reject the null hypothesis when it is true. This reduces the likelihood of claiming a significant result when there is no true effect or relationship in the population.
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Please someone help with this question ASAP
Answers
Answer:
x= -2; y= -2
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, and therefore we can make two observations:
9=-9x-9
19=-10y-1
Then we can just solve each of the equations to get x and y:
9 = -9x - 9
+ 9 +9
18=-9x
----------
-9
-2=x
19=-10y-1
+1 +1
20=-10y
------------
-10
-2=y
Hi ok so like im back w another question and like i need help so like if you could help me you would actually make my day.. like ACTUALLY *3*
Answers
Answer:
B
Step-by-step explanation:
You simplify it using radicals.
A new type of pump can drain a certain pool in 9 hours. An older pump can drain the pool in 11 hours. How long will ittake both pumps working together to drain the pool?
Answers
Given:
A new type of pump can drain a certain pool in 9 hours.
An older pump can drain the pool in 11 hours.
To find:
The required time when both pumps work together to drain the pool.
Explanation:
One hour's work of the new pipe is,
\(\frac{1}{9}\)One hour's work of the old pipe is,
\(\frac{1}{11}\)So, one hour's work of both the pipe together is,
\(\begin{gathered} \frac{1}{9}+\frac{1}{11}=\frac{11+9}{9(11)} \\ =\frac{20}{99} \end{gathered}\)Therefore, the time taken to drain the pool for both the pipes together is,
\(\begin{gathered} \frac{99}{20}hours \\ (or) \\ 4\text{ }hours\text{ 57minutes} \end{gathered}\)Final answer:
The required time to drain the pool for both the pipes together is 4 hours 57 minutes.
What is the surface
area of a box in the
shape of a rectangular
prism with a length of 8
inches, width of 9 inches,
and height of 4 inches?
Answers
Answer:
Surface Area (S.A.) = 2(8x9 + 8x4 + 9x4)
Surface Area = 2(72 + 32 + 36)
Surface Area = 280
Hope this helps!
Answer:
Step-by-step explanation:
The formula for surface area for this kind of figure is
SA = 2*l*w + 2*l*h + 2*w*h
l = 8w=9h = 4SA = 2*8*9 + 2*8*4 + 2*9*4
SA = 144 + 64 + 72 in^2
SA = 280 sqr inches
To win a game, Roger needs to score 2,000
points. So far, he has scored 837 points.
How many more points does Roger need
to score?
Answers
Answer:
Step-by-step explanation:
the answer is 1163 :)
Tom bought 3 1/2 gallons of ice cream. If a pint is 1/8 of a gallon, how many pint-sized servings are there
Answers
24 and a half pint sized servings
Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4547 patients treated with the drug, 114 developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p.
Answers
Answer:
The best point estimate of the population proportion p is 0.0251.
The 99% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
In clinical trials, among 4547 patients treated with the drug, 114 developed the adverse reaction of nausea.
This means that \(n = 4547, \pi = \frac{114}{4547} = 0.0251\)
The best point estimate of the population proportion p is 0.0251.
99% confidence level
So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).
The lower limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 - 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0191\)
The upper limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 + 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0311\)
The 99% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).
Find the missing side length, k.
Answers
Step-by-step explanation:
by using pythagorean theorema²+b²=c²a & c are given
to find k, let us use k as b
c²- a²=k²41²- 9²=k²1681-81=1600✓1600=40If the ratio of boys to girls is 3 : 11 and there are 66 girls in the play, how many students are boys?
Answers
Answer:
18 boys
Step-by-step explanation:
boys/girls = 3/11 = b/66
3/11 = b/66
11b = 3 × 66
b = 3 × 6
b = 18
There are 18 boys.
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 11 percent, has a YTM of 9 percent, and has 15 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 9 percent, has a YTM of 11 percent, and also has 15 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today?
Answers
Answer:
Price of Bond X : $1,162.89
Price of bond Y : $854.66
Step-by-step explanation:
Given the following information :
Bond X :
Face value = $1000
Yield to maturity (YTM) / market interest rate = 9%
Coupon rate = 11%
Years to maturity = 15 years
Compounding frequency = semianually
Using the online bond price calculator, The bond price will be $1,162.89. The bond is sold at premium, since the par value is lesser than the bond price.
For Bond Y:
Face value = $1000
Yield to maturity (YTM) / market interest rate = 11%
Coupon rate = 9%
Years to maturity = 15 years
Compounding frequency = semianually
Using the online bond price calculator, The bond price will be $854.66. The bond is sold at a discount , since the par value is greater than the bond price.
What is the y-intercept of y = sinx?
Answers
Answer:
The y-intercept is 0
Step-by-step explanation:
Here, we want to get the y-intercept value of y = sin x
From the plot of the graph, we can see that the graph of sin x touches the y-axis at the point y = 0
So therefore, the y-intercept of y = sin x is 0
Let’s say you want to play a new card game called Pokee. Every player is dealt 4 cards and everyone compares what hands they have to see who wins. Our job is to figure out what the hierarchy of the hands should be. Below is a list of several scoring hands that we wish to compare. For each hand, count how many hands of that type there are (include the expression you used to get that value) along with a simple explanation of how you got that expression. Assume a standard 52 card deck with 4 suits.
a) Presidential Flush (J, Q, K, Ace, all the same suit)
b) Straightish (4 consecutive cards)
c)Flushed (4 cards of the same suit)
d) House (Two pairs of different cards)
Answers
can you guys help me
Answers
Answer:
m<1 = 140
Step-by-step explanation:
m<1 = 140 because of alternate interior angles
Use the properties of radicals to simplify the expression. Explain.
Answers
Because both 2 and 72 under the radical are positive numbers, we can apply this rule:
\(\sqrt{2}\cdot\sqrt{72} = \sqrt{2\cdot72}\)
Now that new version, \(\sqrt{2\cdot 72}\) is the same thing as \(\sqrt{144}\), because \(2\cdot72=144\).
And \(\sqrt{144}=12\).
12 is your answer.
The rule we used is \(\sqrt{a}\cdot\sqrt{b} = \sqrt{a\cdot b}\), but it only works if both \(\sqrt{a}\) and \(\sqrt{b}\) are real numbers (AKA if a and b are both non-negative).
Hal types 32 words per minute. Which equation could be used to find the number of minutes m it would take him to type 640 words?
Answers
Answer:
32m = 640------------------
The rate of typing is 32 words per minute.
For m minutes Hal can type 32m words.
If he types 640 words, we can set this as equation:
32m = 640By solving we get:
m = 20 minutesFind the volume of a pyramid with a square base, where the perimeter of the base is
18.1
ft
18.1 ft and the height of the pyramid is
28.1
ft
28.1 ft
Answers
Answer: the answer is mostly likely : 74.3
Step-by-step explanation:
if im not wrong: 18.1 + 28.1 + 28.1 is the equation.