Answer:
A. Makes the most sense. If you are using multiplication you'd get 18 1/16
The logarithm of a number to the base V2 is k. What is its logarithm to the base 2v2 ?
Answer:
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
Step-by-step explanation:
Given
Let the number be X
From the first statement, we have:
[tex]log_{\sqrt 2} X = k[/tex]
Required
Find [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{\sqrt 2} X = k[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
So:
[tex]log_{\sqrt 2} X = k[/tex]
[tex]X = \sqrt{2}^k[/tex]
Substitute: [tex]X = \sqrt{2}^k[/tex] in [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)[/tex]
[tex]log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}[/tex]
Apply the following law:
[tex]log_ab = \frac{log\ b}{log\ a}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}[/tex]
Express the square roots as power
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}[/tex]
Rewrite as:
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}[/tex]
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
The length of a rectangle is x feet more than its width. The area of the rectangle is 5x + 25. What is the width of the rectangle?
Answer:
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
(Anyone can correct me if I'm wrong)
Step-by-step explanation:
Before we start the solving, we can make the following statements:
Area = l x w
Area = 5x + 25
therefore,
l x w = 5x + 25
Since the question states that the length is x more than the width, so we can make the following statement:
w = l + x
With this, we can substitute it to the first statement we made, l x w = 5x + 25,
l x (l + x) = 5x + 25
[tex]l^{2}[/tex] + lx = 5x + 25
lx - 5x = 25 - [tex]l^{2}[/tex]
x(l - 5) = 25 - [tex]l^{2}[/tex]
x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]
From this, we can find w by substituting it in the statement we made earlier, w = l + x,
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
Suppose the probability that it will rain tomorrow is 0.59. What is the probability that it will not rain tomorrow?
Answer:
0.41
Step-by-step explanation:
All probability equals 1. So if the probability that something will happen is x, then the probability that it will not happen is 1-x
ANSWER THIS PLZZ I WILL GIVE TOP COMMENT :)!!!!!
Answer:
D, -42 multiply 6 on both sides
D. because when it is multiplied, the inequality is no longer true.
There are 20 pieces of fruit in a basket and 12 of them are oranges. What percentage of the pieces of fruit in the basket are oranges? Show your work in the box and circle your answer
Answer:60 percent
Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.
Which expression is equivalent to sqrt -108 - sqrt -3?
A) 5 sqrt 3i
B) 6 sqrt 3i
C) 7 sqrt 3i
D) 8 sqrt 3i
2/6+1/4
Show work please
And no links
Answer:
7/12
Step-by-step explanation:
1/3+1/4
convert to twelfths
4/12+3/12
7/12
Answer:
7/12
Step-by-step explanation:
2/6 + 1/4
Change the denomintors to be alike (Change the denominators to 12) 4/12 + 3/12
Multipy the top and bottom
Add
Get 7/12
Brainliest?
The following figure is made of a square and a rectangle.
4 cm
4 cm
7
10 cm
What is the perimeter of the figure?
cm
What is the value of x in the equation 2/3x = 12
Answer:
x = 8
The value of 'x' is 8
Step-by-step explanation:
2/3(8)=12
2/(24)=12
Good luck!!
If 65% of Americans are overweight, how many people would be overweight in a city of 1.5 million?
Answer:
hey There
Step-by-step explanation:
This compares with 27.5 percent of those age 55 to 64 and 25.6 percent of those age 65 to 74. With respect to being overweight, 31.8 percent of the individuals 75 and older were such, while 37.9 percent of 55 to 64 year olds and 37.8 percent of individuals age 65 to 74 were overweight (figure 1).
Answer:
66.9%
i hope thats right
un comerciante vende un artículo en $196 y obtiene como telera con tanto porciento igual al precio del costo del artículo Hallar el costo del artículo
Answer:
$196 es el precio del articulo
Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Answer:
The doomsday is 146 days
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]
First, we calculate the solution that satisfies the initial solution
Multiply both sides by
[tex]\frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]
Take integral of both sides
[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]
Integrate
[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
To find c; let t= 0
[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]
[tex]-\frac{y_0^{-c}}{c} = C[/tex]
[tex]C =-\frac{y_0^{-c}}{c}[/tex]
Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]
Multiply through by -c
[tex]y^{-c} = -ckt+y_0^{-c}[/tex]
Take exponents of [tex]-c^{-1[/tex]
[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
i.e.
[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
Next:
[tex]t= 3[/tex] i.e. 3 months
[tex]y_0 = 2[/tex] --- initial number of breeds
So, we have:
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
-----------------------------------------------------------------------------
We have the growth term to be: [tex]ky^{1.01}[/tex]
This implies that:
[tex]ky^{1.01} = ky^{1+c}[/tex]
By comparison:
[tex]1.01 = 1 + c[/tex]
[tex]c = 1.01 - 1 = 0.01[/tex]
[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:
-----------------------------------------------------------------------------
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]
[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]
[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]
Take -1/100th root of both sides
[tex]16^{-1/100} = -0.03k + 0.9931[/tex]
[tex]0.9727 = -0.03k + 0.9931[/tex]
[tex]0.03k= - 0.9727 + 0.9931[/tex]
[tex]0.03k= 0.0204[/tex]
[tex]k= \frac{0.0204}{0.03}[/tex]
[tex]k= 0.68[/tex]
Recall that:
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
This implies that:
[tex]\frac{y_0^{-c}}{c} = kT[/tex]
Make T the subject
[tex]T = \frac{y_0^{-c}}{kc}[/tex]
Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]
[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]
[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]
[tex]T = \frac{0.9931}{0.0068}[/tex]
[tex]T = 146.04[/tex]
The doomsday is 146 days
can someone help having trouble solving this question
Answer:
if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60
Answer:
x = 50°
Step-by-step explanation:
sum of exterior angles is always equal to 360°
so, we can add all the given numbers and set them equal to 360° to find x:
130° + 30° + 100° + x° + x° = 360°
260° + 2x = 360°
2x = 100°
x = 50°
what is the slope of the line passing through the points (4,7) and (-2,10)?
Answer:
-1/2
Step-by-step explanation:
Answer:
the answer is the slope is -1/2
I need help
Can you help me please!!!
Answer:
Step-by-step explanation:
The triangles are similar.
x/(x+4) = 7.2/12
x/(x+4) = 0.6
x = 0.6(x+4)
0.4x + 2.4
x = 6
What does 3 to the power of 2 minus 4 times 2 plus 6
Answer:
7 is the answer
Step-by-step explanation:
Answer:
This equals 7
Step-by-step explanation:
I used a calculator
Can I have brainliest pls
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate. Do not round your intermediate computations, and round your answer to three decimal places.
Complete question:
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 of them germinate.
Answer:
[tex]P(x = 4) = 0.1376[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex]
[tex]p = 63\%[/tex] --- proportion that germinates
[tex]p = 0.63[/tex]
Required
P(x = 4)
This question follows a binomial distribution:
[tex]P(x) = ^nC_x*p^x*(1-p)^{n-x[/tex]
When x = 4;
[tex]P(x = 4) = ^9C_4*0.63^4*(1-0.63)^{9-4[/tex]
[tex]P(x = 4) = ^9C_4*0.63^4*(0.37)^5[/tex]
[tex]P(x = 4) = 126*0.63^4*0.37^5[/tex]
[tex]P(x = 4) = 0.13763895392[/tex]
[tex]P(x = 4) = 0.1376[/tex]
if f(x)=5x-7,what isf(3)?
Answer:
Explanation:
f ( − 3 ) basically means substitute − 3 for x in the function − 5 x
f
(
−
3
)
=
−
5
(
−
3
)
−
7
f
(
−
3
)
=
15
−
7
f
(
−
3
)
=8
Step-by-step explanation:
Simplify the following expression completely, where x 20.
x5xy* + 405x’y* - 180x’y4
O xy2 5x + xy? V405x – xy2/80x
0 6xyV5x
-3xy 5x + xy? J405x
O 6xy ſ5x}
Answer:
Option B is your answer
Step-by-step explanation:
hope it helps
have a great day!!
Answer:
A.) -80X^8 + 40x^7 -5x^6 -3x^2
Its OPTION A
Step-by-step explanation:
find the product (ab-3)^2
Answer:
a^2b^2 -6ab + 9
Step-by-step explanation:
Need help 15 points pls help me
5 1/2 feet is the base of window.
Answer:
area of parllelogram =base×height
25 2/3=base×4 2/3
77/3=base×14/3
77/3×3/14=base
base=77/14=11/2=5 1/2feet
Use similar triangles to solve for the missing lengths below.
If you know how to work this out please help:)
Answer:
x = 14
y = 18
Step-by-step explanation:
By the property of similar triangles,
If two triangles are similar their corresponding sides will be proportional.
[tex]\frac{AB}{EF}= \frac{AC}{GE}[/tex]
[tex]\frac{5}{10}=\frac{7}{x}[/tex]
x = [tex]\frac{70}{5}[/tex]
x = 14
Similarly, [tex]\frac{AB}{EF}= \frac{CB}{GF}[/tex]
[tex]\frac{5}{10}=\frac{9}{y}[/tex]
y = [tex]\frac{90}{5}[/tex]
y = 18
A roofing contractor buys 30 bundles of shingles and 4
rolls of roofing paper for $1040.
In a second purchase (at the same prices), the
contractor buys 12 bundles of shingles and 16 rolls of
roofing paper for $2000.
Create and solve a system of equations in order to
determine how much each bundle of shingles (x) and
roll of roofing paper (y) would cost
Answer:
Cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.
Step-by-step explanation:
Let the cost of each bundle of shingles = x
And cost of the roofing paper = y
Contractor buys 30 bundles of shingles and 4 rolls of roofing paper for $1040.
30x + 4y = 1040
15x + 2y = 520 -----(1)
In a second purchase contractor buys 12 bundles of shingles and 16 rolls of roofing paper for $2000
12x + 16y = 2000
3x + 4y = 500 --- (2)
Equation (1) multiplied by 2 then subtracted from equation (2)
(3x + 4y) - 2(15x + 2y) = 500 - 1040
(3x - 30x) + (4y - 4y) = -540
-27x = -540
x = 20
From equation (1)
15(20) + 2y = 520
300 + 2y = 520
2y = 220
y = 110
Therefore, cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.
Find X please help me with test corrections due midnight tonight!
If HBN is congruent to LYR.
Answer:
the answer is
x=22..........
1) Find the missing angle.
31°
949
? + 31° + 94° = 180°
? + 125° = 180°
? = 180° - 125°
? = 55°
Answer: 52°
Step-by-step explanation:
Angles in a triangle always add up to 180°.
So to work out what the missing angle is, you would have to add 34 and 94 together.
34+94=128
Then you would have to take 128 away from 180.
180-128=52°
Hope this helps :)
Ralph opened up his checking account with $100. On Monday, he withdrew $45 to purchase a pair of jeans. On Wednesday, he deposited a $25 check he received for his birthday from his uncle. On Friday, he used his debit card to buy a $98 football ticket. What is the balance in Ralph's checking account?
Answer:
The answer is -18
Step-by-step explanation:
He starts off with $100 in his account. He then take so $45 to purchase a pair of jeans, so we have to subtract 45 from 100 and that gives us $55. He now has $55 in his account, he then adds another $25 to his account, so we have to add 25 to 55 and that will give us $80 in his account. Finally on Friday he takes out $98 of his checking account. He takes out more than he has in his checking account so we have to subtract $80 from $98 and we will get $18, but since he takes out more than what he has in his account the answer will be negative and we end up with -18 dollars in his checking account.
Answer:72
Step-by-step explanation:
there are 144 microscopes in boxes at a school. each box has 24 microscopes which equation could be used to find b, the number of boxes of microscopes at this school
A. 24+144= b
B. 144-b= 24
C. B divided by 24= 144
D. 24 x b= 144
The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.
Answer:
24.5
Step-by-step explanation:
3x-2y=8 2x+y=10 solve system of equations
Answer:
x=4,y=2
Step-by-step explanation:
3x-2y=8 ..........1
2x+y=10...........2
multiply equation 2 by 2 and adding equation 1 and 2 ,we get
3x-2y=8
4x+2y=20
+_________
7x=28
x=28/7=4
:.x=4
again substituting value of x in equation 1 we get
3×4-2y=8
12-8=2y
y=4/2=2
:.y=2
Helps, is it 64 111 or 90?
Answer:
111
Step-by-step explanation: