Answer:
4 places after the decimal.
the result is 0.0215
Step-by-step explanation:
I assume the expression is really
43 / (2⁴ × 5³)
this is the same as
(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)
since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5
the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5
the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5
the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5
in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.
and finally the fourth division to 0.5⁴.
0.5⁴ = (5/10)⁴ = 5⁴/10⁴
so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.
every divisible by 5 takes one of these powers away.
so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.
all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.
so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.
1 point
Use log10 3-0.4771; log10 5 0.699010810 7 0.8451; log10 11 1.0414 to approximate the value of each expression-
log10 14710910 (147)
Answer:
[tex]\log_{10}(147) = 2.1673[/tex]
Step-by-step explanation:
Given
[tex]\log_{10} 3 = 0.4771[/tex]
[tex]\log_{10} 5 = 0.6990[/tex]
[tex]\log_{10} 7= 0.8451[/tex]
[tex]\log_{10} 11 = 1.0414[/tex]
Required
Evaluate [tex]\log_{10}(147)[/tex]
Expand
[tex]\log_{10}(147) = \log_{10}(49 * 3)[/tex]
Further expand
[tex]\log_{10}(147) = \log_{10}(7 * 7 * 3)[/tex]
Apply product rule of logarithm
[tex]\log_{10}(147) = \log_{10}(7) + \log_{10}(7) + \log_{10}(3)[/tex]
Substitute values for log(7) and log(3)
[tex]\log_{10}(147) = 0.8451 + 0.8451 + 0.4771[/tex]
[tex]\log_{10}(147) = 2.1673[/tex]
in the diagram below, BD is parallel to XY. what is the value of y?
a. 70
b. 130
c. 110
d. 20
I can't see the diagram sorry.
Step-by-step explanation:
Is there supposed to be a picture attached?
posters n tees sold 486 items yesterday; one-third of these were t-shirts.how many t-shirts sold? how many posters?
Answer:
162 t-shirts, 324 posters
Step-by-step explanation:
Assuming they only sold t-shirts and posters, you can find the amount of t-shirts sold by dividing 486 by 3, or multiplying it by 1/3. This equals 162. This is because one third were t-shirts. To find the rest you just subtract 162 from the total of 486, or multiply 162 by 2. (since you already know the amount of 1/3, 2/3 is double that.)
Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)
Answer:
Step-by-step explanation:
Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.
Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1
4x = y + 1
[tex]x = \dfrac{y+1}{4}[/tex]
[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
By integration, the required surface area in the revolve is:
[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]
where;
g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
∴
[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]
[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]
[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]
[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/(1+x), a = 2
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = e−5x
f(x)=
[infinity]
n = 0
=
Find the associated radius of convergence R.
R =
Answer:
A) [ 7/3, (-7/9)(x/2), 7/27(x-2)^2, (-7/81)(x-2)^3 ]
B) attached below
Step-by-step explanation:
A) Using the definition of a Taylor series
The first four nonzero terms of the series for f(x) = 7/ (1 +x), a = 2
= [ 7/3, (-7/9)(x/2), 7/27(x-2)^2, (-7/81)(x-2)^3 ]
attached below is the detailed solution
B) Finding Maclaurin series for f(x)
f(x) = e^-5x
attached below
Associated radius of convergence = ∞ ( infinity )
emir is standing in a treehouse in looking down at a swing set in the yard next-door. The angle of depression from emir’s Highline to the swingset is 31.43°, and emir is 11 feet from the ground. How many feet is the base of the tree from the swing set
Answer:
18 feet
Step-by-step explanation:
The question is illustrated using the attached image.
From the image, we have:
[tex]\theta = 31.43^o[/tex] --- angle of depression
[tex]h = 11ft[/tex] --- Emir's height
Required
The distance from the base of the tree (x)
From the attached triangle, we have:
[tex]\tan(90 - \theta) = \frac{Opposite}{Adjacent}[/tex]
This gives:
[tex]\tan(90 - 31.43) = \frac{x}{11}[/tex]
[tex]\tan(58.57) = \frac{x}{11}[/tex]
Make x the subject
[tex]x = 11 * \tan(58.57)[/tex]
[tex]x = 18.00[/tex]
Answer:
18
Step-by-step explanation:
took the test
The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased
The question is incomplete. The complete question is :
The breaking strengths of cables produced by a certain manufacturer have a mean of 1900 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 150 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1902 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased?
Solution :
Given data :
Mean, μ = 1900
Standard deviation, σ = 65
Sample size, n = 150
Sample mean, [tex]$\overline x$[/tex] = 1902
Level of significance = 0.01
The hypothesis are :
[tex]$H_0 : \mu = 1900$[/tex]
[tex]$H_1 : \mu > 1900$[/tex]
Test statics :
We use the z test as the sample size is large and we know the population standard deviation.
[tex]$z=\frac{\overline x - \mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{1902-1900}{65 / \sqrt{150}}$[/tex]
[tex]$z=\frac{2}{5.30723}$[/tex]
[tex]$z=0.38$[/tex]
Finding the p-value:
P-value = P(Z > z)
= P(Z > 0.38)
= 1 - P(Z < 0.38)
From the z table. we get
P(Z < 0.38) = 0.6480
Therefore,
P-value = 1 - P(Z < 0.38)
= 1 - 0.6480
= 0.3520
Decision :
If the p value is less than 0.01, then we reject the [tex]H_0[/tex], otherwise we fail to reject [tex]H_0[/tex].
Since the value of p = 0.3520 > 0.01, the level of significance, then we fail to reject [tex]H_0[/tex].
Conclusion :
At a significance level of 0.01, we have no sufficient evidence to support that the mean breaking strength has increased.
Hi Friends!
please help me with these questions !
Answer/Step-by-step explanation:
2. a. 5y - 3 = -18
Add 3 to both sides
5y - 3 + 3 = -18 + 3
5y = -15
Divide both sides by 5
5y/5 = -15/5
y = -3
b. -3x - 9 = 0
Add 9 to both sides
-3x - 9 + 9 = 0 + 9
-3x = 9
Divide both sides by -3
-3x/-3 = 9/-3
x = -3
c. 4 + 3(z - 8) = -23
Apply the distributive property to open the bracket
4 + 3z - 24 = -23
Add like terms
3z - 20 = -23
Add 20 to both sides
3z - 20 + 20 = - 23 + 20
3z = -3
Divide both sides by 3
3z/3 = -3/3
z = -1
d. 1 - 2(y - 4) = 5
1 - 2y + 8 = 5
-2y + 9 = 5
-2y + 9 - 9 = 5 - 9
-2y = -4
-2y/-2 = -4/-2
y = 2
3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq
(3pq + 5p²q² + p³) + (p³ - pq)
3pq + 5p²q² + p³ + p³ - pq
Add like terms
= 3pq - pq + 5p²q² + p³ + p³
= 2pq + 5p²q² + 2p³
Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq
(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)
Apply distributive property to open the bracket
3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³
Add like terms
3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq
= p³ - 7p²q² + 2pq
4. Perimeter of the rectangle = sum of all its sides
Perimeter = 2(L + B)
L = (5x - y)
B = 2(x + y)
Perimeter = 2[(5x - y) + 2(x + y)]
Perimeter = 2[5x - y + 2x + 2y]
Add like terms
Perimeter = 2(7x + y)
Substitute x = 1 and y = 2 into the equation
Perimeter = 2(7(1) + 2)
Perimeter = 2(7 + 2)
Perimeter = 2(9)
Perimeter = 18 units
5. First let's find the quotient to justify if the value we get is greater than or less than 2.25
7⅙ ÷ 3⅛
Convert to improper fraction
43/6 ÷ 25/8
Change the operation sign to multiplication and turn the fraction by the left upside down.
43/6 × 8/25
= (43 × 8)/(6 × 25)
= (43 × 4)/(3 × 25)
= 172/75
≈ 2.29
Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25
find the x-intercepts y=2x^2 + 5x + 2/x^2-4x+3
Answer:
[tex]{ \tt{y = \frac{2 {x}^{2} + 5x + 2}{ {x}^{2} - 4x + 3 } }} \\ x - intercept : y = 0 \\ { \tt{ \frac{2 {x}^{2} + 5x + 2 }{ {x}^{2} - 4x + 3 } = 0 }} \\ \\ { \tt{2 {x}^{2} + 5x + 2 = 0}} \\ x = \frac{1}{2} \: \: and \: \: x = - 2[/tex]
5t/4y=3b/4c (solve for y)
I also need to know the steps.
thanks.
Answer:
[tex]y = \frac{5ct}{3b}[/tex]
Step-by-step explanation:
[tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex]
1. start by multiplying y to both sides:
y × [tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex] × y
[tex]\frac{5t}{4} =\frac{3b}{4c}y[/tex]
2. divide both sides by [tex]\frac{3b}{4c}[/tex]
[tex]\frac{5t}{4}/\frac{3b}{4c} =\frac{3b}{4c}y/\frac{3b}{4c}[/tex]
[tex]y = \frac{5ct}{3b}[/tex]
Pls answer
Subtract -37 from -53
Answer:
-37 subtract -53
-53 subtract -37 = -16
Step-by-step explanation:
Answer:
The answer is 16
Step-by-step explanation:
-37-(-53) = -37 + 53
You can flip it to 53 - 37 which equals 16.
Hope this helps! :)
*Heads up you can also search this up* ^^
why was it difficult for the woman to cross the road
the average of two number is xy.if one number is x the other i
Answer:
z = (2xy-x)
Step-by-step explanation:
Let the first number be x and the other number is z.
According to question,
The average of two number is xy i.e.
[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]
So, the value of z is (2xy-x) i.e. the other number is (2xy-x).
the campus bookshop sells exercise books and textbooks, where, the total cost of 10 exercise books and 2 textbooks is $1400.00. One also finds the total cost of 3 textbooks and 30 exercise books is $3000. Then determine the price of 1 exercise book?
Answer:
The price of 1 exercise book is $122.45.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the price of one exercise book.
y is the price of one textbook.
Total cost of 10 exercise books and 2 textbooks is $1400.00.
This means that:
[tex]10x + 2y = 1400[/tex]
Since we want x:
[tex]2y = 1400 - 10x[/tex]
[tex]y = 700 - 5x[/tex]
One also finds the total cost of 3 textbooks and 30 exercise books is $3000.
This means that:
[tex]3x + 30y = 3000[/tex]
Since [tex]y = 700 - 5x[/tex]
[tex]3x + 30(700 - 5x) = 3000[/tex]
[tex]3x + 21000 - 150x = 3000[/tex]
[tex]147x = 18000[/tex]
[tex]x = \frac{18000}{147}[/tex]
[tex]x = 122.45[/tex]
The price of 1 exercise book is $122.45.
How would I solve the 4 questions on the picture?
Answer:
l don't know
Step-by-step explanation:
What is the general form of the equation for the given circle centered at [0, 0)?
Answer:
x^2+y^2=r^2 is quation of circle whose centre is (0,0)
Round your answer to the nearest hundredth.
3
А
с
?
8
B
HELP!!!
Answer:
Step-by-step explanation:
This appears to be an SSA application of solving the triangle
We have 2 sides, so we will use the law of cosines
The law of cosines defines for a triangle ABC with side a/b/c with corresponding angles A/B/C
a^2 = b^2+c^2 - 2*b*c * (cos A)
this applies to the other 2 sides
first using the pythagorean theorem we find that BC = sqrt(55)
then we substitute all 3 sides into our equation to find angle A
55 = 64 + 9 - 2*8*3* (cos A)
18 = 2*8*3(cos A)
3/8 = (cos A)
and angle A is approximately 68 degrees
Please check if I'm correct
Answer:
67.98°
Step-by-step explanation:
Given 2 sides, you can find the missing angle of a right triangle using basic trig functions.
Since Cos∅=adjacent/ hypotenuse, we can use the adjacent side to the angle, 3 and they hypotenuse, 8 in the ratio by doing 3/8. This is 0.375. Then we use the inverse cosine function to find the angle. This gives 67.98°
Or
Cos∅=0.375
Cos^-1= 67.98
Decide if each answer will be less than or greater than the original number. Drag each to the correct category
250% of 18
35% of 300
62% of 182
300% of 250
89% of 525
120% of 72
That's a question about percentage.
Let's imagine that we want to know how much is 90% of 200. To do this calculation, we should multiply 200 by 90 and then divide the result by 100. We do that because 90% is the same thing that [tex]\frac{90}{100} =0,9[/tex]. So, 90% of 200 is equal to:
[tex]\frac{200\cdot90}{100} =\\\\\frac{18000}{100} =\\\\180[/tex]
Now, imagine that you would like to know how much is 100% of 999. First, we multiply 999 by 100 and divide the result by 999. So, 100% of a number is equal to itself. That's a very important information, because it's possible to understand this:
If the percentage is less than 100%, the result is less than original number.If the percentage is equal to 100%, the result is equal to the original number.If the percentage is greater than 100%, the result is greater than original number.Now, we can solve our problem! \o/
The options that the percentage is less than 100% are: 35% of 300, 62% of 182 and 89% of 525. Therefore, their answers will be less than the original number.
And, the option that the percentage is greater than 100% are: 250% of 18, 300% of 250 and 120% of 72. So, their answers will be greater than the original number.
On the image, you can see the answer in a table.
I hope I've helped. ^^
Enjoy your studies! \o/
Help please!!!!!!!!!!!
Answer:
y = 14
Step-by-step explanation:
[tex] \frac{15}{21} = \frac{5}{7} [/tex]
[tex] \frac{10}{x} = \frac{5}{7} [/tex]
[tex]x = 14[/tex]
Now,
10/15 = y/21
15y = 10*21
y = 210/15
y = 14
This is a Right answer...
I hope you understand..
Mark me as brainliest...
evaluate the expression when x=7 and y= -2 -x+8y
Answer:
y=-2
Step-by-step explanation:
y=-2*-7*+8y
y= 14+8y
-7y=14
y=-2
I NEED HELP ILL MARK!!!
Answer:
c) tan
Step-by-step explanation:
For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.
Answer: c) tan
Find the time required for an investment of 5000 dollars to grow to 8600 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer:
about 7.3 years
Step-by-step explanation:
[tex]8600=5000(1+\frac{.075}{4})^{4*t}\\1.72=(1.01875)^{4t}\\log_{1.01875}1.72=4t\\29.19428479=4t\\t=7.298571198[/tex]
Answer:
The answer is t=7.3
NEED HELP ASAP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth:
Exponential Decay:
y = 1700(1.25)^t
y =240(1/2)^t
y = 4000(1.0825)^t
y = 1.5(10)^t
y = 12,000(0.72)^t
y = 8000(0.97)^t
Answer:
Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t
Decay: y =240(1/2)^t, y = 12,000(0.72)^t, y = 8000(0.97)^t
Step-by-step explanation:
In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.
The circle P has a center at (0, 0) and a point on the circle at (0, 4). If it is dilated by a factor of 4, what is the distance of the diameter for circle P’.
A. 32
B. 4
C. 8
D. 16
Answer:
A. 32
Step-by-step explanation:
If the center is (0, 0) and a point is (0, 4) then the distance from the center to that point is 4 units. That distance is the radius. If you are dilating by a factor of 4, multiply the radius by 4 and you get 16. The new radius is 16 and the diameter= radius*2.
16*2=32
What is the mode of the data?
Weight of Dogs In the Pet Store
Stem Leaves
0 3, 8
1 0, 1, 4, 7,
2 2, 4, 5
3 5 0 | 3 = 3 pounds
4 0
A. 17
B. 3
C. no mode
D. 40
Answer:
No mode
Step-by-step explanation:
Mode = number that appears the most
No number appears more than 1 time
Hence there is no mode
Answer:Should be no mode tell me if i'I'm wrong
Step-by-step explanation:
Lisa bought a house The value of the house increased by 1.5% each year for 2 years. At the end of 2 years, the value of the house was £123,627. Work out the value of the house when Lisa bought it.
Answer:
$370,881
Step-by-step explanation:
firstly we we multiply 1,5% by 2yrs. the answer we get is 3,0%. we then multiply 3 % by $123,627 and get $370,881
If Lisa bought a house The value of the house increased by 1.5% each year for 2 years. The value of the house was £123,627. The initial amount of the house is 95120.7.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
Lisa bought a house The value of the house increased by 1.5% each year for 2 years
By the end of 2 years, the value of the house was £123,627.
A=P(1+rt)
A is the final amount,
r is rate of interest
t is the time
P is principle amount.
123,627=P(1+1.5/100 (2))
123657=P(1+0.15(2))
123657=P(1+0.3)
123657=1.3P
Divide both sides by 1.3
P=95120.7
The initial amount of the house when Lisa bought is 95120.7
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ2
Please HELP!
How many pairs (A, B) are there where A and B are subsets of {1, 2, 3, 4, 5, 6, 7, 8} and A ∩ B has exactly two elements?
Answer:
There are 256 pairs in all.
Use Cramer's Rule to solve (if possible) the system of linear equations.
x1 + 2x2 =8
- x1 + x2 = 1
Required:
Find the coefficient matrix.
Answer:
x1 = 2
x2 = 3
Step-by-step explanation:
[tex]x_1=\frac{D_{x1}}{D}\\\\x_2=\frac{D_{x2}}{D}[/tex]
Here D is the coefficient matrix.
Hence
[tex]x_1=\frac{6}{3}\\x_1=2[/tex]
&
[tex]x_2=\frac{9}{3}\\x_2=3[/tex]
12x + 1 - 2(y + 2) = 12x - ______ - 2y
Answer:
-3
Step-by-step explanation:
12x + 1 - 2(y + 2)
=> 12x + 1 - 2y - 4
=> 12x - 3 - 2y
Answer:
-3
Step-by-step explanation:
12x+1-2y-4
12x+1-2y-4
12x-2y-3
Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did was correct and/or incorrect.
Part 2:
Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.
3x^2 + kx - 8
If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.
The first binomial can be further factored:
8x + 12 = 4(2x + 3)Part 2The quadratic expression needs to have two roots in order to be factored as two binomials.
The discriminant must be positive or zero:
D = b² - 4ac ≥ 0We have a = 3, b = k, c = -8
So we get following inequality:
k² - 4*3*(-8) ≥ 0k² + 96 ≥ 0Since k² is positive for any value of k, the solution is any value of k:
k ∈ RHope this attachment helps you.
