Answer:
[tex]x = 500[/tex]
Step-by-step explanation:
Given
[tex]log20x^3 - 2logx = 4[/tex]
Required
Solve for x
[tex]log20x^3 - 2logx = 4[/tex]
Using law of logarithm which says;
[tex]nlogx = logx^n[/tex]
The expression becomes
[tex]log20x^3 - logx^2 = 4[/tex]
Also, using laws of logarithm which says:
[tex]loga - logb = log\frac{a}{b}[/tex]
The expression becomes
[tex]log(\frac{20x^3}{x^2}) = 4[/tex]
[tex]log(20x) = 4[/tex]
Also, using laws of logarithm which says
[tex]If\ loga = b\\then\ a = 10^b[/tex]
The expression becomes
[tex]20x = 10^4[/tex]
[tex]20x = 10000[/tex]
Divide through by 20
[tex]\frac{20x}{20} = \frac{10000}{20}[/tex]
[tex]x = \frac{10000}{20}[/tex]
[tex]x = 500[/tex]
Answer:
500
Step-by-step explanation:
HELP!!! How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles:
Given the figure below, find the values of x and z.
Answer:
X= 6°z= 112°Solution,
Finding the value of X,
[tex]11x + 2 = 68[/tex]
( being vertically opposite angles)
[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]
Value of X is 6
Now, finding the value of z
[tex]z + 68 = 180[/tex]
(sum of angle in linear pair)
[tex]z = 180 - 68 \\ z = 112[/tex]
Value of z is 112.
Hope this helps....
Good luck on your assignment...
Fill in the blank with a number to make the expression a perfect square.
Answer:
16
Step-by-step explanation:
[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]
Answer:
Step-by-step explanation:
a² + 2ab +b² = (a+ b)²
w² - 8w + _?___
a = w
2ab = -8w
2*w*b = -8w
b = -8w/2w
b = 4
8w = 2 * 4*w
w² - 8w + 4² =w² -8w + 16
Which letter comes next? F H K N Z ? Choose from: L M T Y
Answer:
t
Step-by-step explanation:
The letter that comes next in the given sequence is K.
The given sequence is F H K N Z.
We need to find which letter comes next in the given sequence.
What is the pattern followed in the given sequence?The pattern followed by the given sequence is they are letters of sounding board consonants.
Therefore, the letter that comes next in the given sequence is K.
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310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
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Determine the surface area of a sphere with a diameter of 16 cm. Question 4 options: A) 804.2 cm2 B) 1,024 cm2 C) 201.0 cm2 D) 3,216.9 cm2
Answer:
The answer is option A.
804.2cm²Step-by-step explanation:
Surface area of a sphere is 4πr²
where r is the radius
radius = diameter / 2
radius = 16/2 = 8cm
Surface area of the sphere is
4π (8)²
= 4(64)π
= 256π
= 804.2cm²
Hope this helps you.
From the equation, find the axis of symmetry of the parabola.
y = 4x+ 32x+ 61
a. x= 3
x=-4
C.
b. X= 4
d. X=-3
pls hurry the answer is not 36.......Given a * b=ba−ba+ab, find (2*3)×(3*2).
Answer:
36
Step-by-step explanation:
In the above question, we have been given a rule to follow
Given a * b = ba−ba+ab
We are to find (2*3)×(3*2)
Let simplify each bracket first
a * b = ba−ba+ab
2*3, a = 2, b = 3
2*3 = 3×2 - 3×2 + 2×3
= 6 - 6 + 6
= 6
a * b = ba−ba+ab
3*2, a = 3, b = 2
3*2 = 2×3 - 2×3 + 3×2
= 6 - 6 + 6
= 6
(2*3)×(3*2)
= 6 × 6
= 36
The answer is 36
A doctor prescribes 500 milligrams of a therapeutic drug that decays by about 19% each hour.
a) To the nearest minute, what is the half-life of the drug?
b)
Write an exponential model representing the amount of the drug remaining in the patient's
system after t hours. (2 points)
c)
Use your formula to find the amount of drug that would remain in the patient's system after 24
hours. Round your answer to the nearest hundredth of a gram. (2 points)
Answer:
a) half life is 3h 17 minutes
b) function of residue drug after t hours with initial quantity = 500 mg
f(t) = 500 (0.81^t)
c) drug left in patient's system after 24 hours
= 0.00 grams (to the hundredth of a gram.
Step-by-step explanation:
Given:
Drug initial active weight, A = 500 mg
Residue active weight, f(t) = A 0.81^t
t = time in hours.
a) half life
Half life is T, such that f(T) = 0.5A =>
0.5A = A(0.81^t)
0.81^t = 0.5
t*log(0.81) = log(0.5)
t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours
= 3 h 17.36 minutes
b) Equation of function of residue drug as a function of time t in hours
A=500 mg
f(t) = A(0.81^t) substitute A = 500 mg
= 500(0.81^t) mg
c) weight of residue drug after 24 hours to the hundredth of a gram.
t=24 hours
A=500
f(t) = 500(0.81^t) substitute t=24 hours
= 500(0.81^24)
= 3.181 mg
= 0.003181 g
Determine the slope of the lines parallel and perpendicular to -4x+3y=11
Answer:
parallel = 4/3
perpendicular =-3/4
Step-by-step explanation:
Solve for y
-4x+3y=11
Add 4x to each side
3y = 4x+11
Divide by 3
y = 4/3 x +11/3
This is in the form y = mx+b where m is the slope
m =4/3
The parallel line has the same slope
parallel slope is 4/3
The perpendicular line has a negative reciprocal slope
m = -(1 /4/3) = - 3/4
Answer:
[tex]\frac{4}{3}[/tex] and - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
- 4x + 3y = 11 ( add 4x to both sides )
3y = 4x + 11 ( divide all terms by 3 )
y = [tex]\frac{4}{3}[/tex] x + [tex]\frac{11}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{4}{3}[/tex]
Parallel lines have equal slopes, thus
slope of parallel line = [tex]\frac{4}{3}[/tex]
Give a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{3} }[/tex] = - [tex]\frac{3}{4}[/tex]
What are all of the real roots of the following polynomial? f(x) = x4 - x3 - 13x2 + x + 12
We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.
Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.
x - 1 = 0 gives us x = 1.
x + 1 = 0 --> x = -1.
x - 4 = 0 --> x = 4.
x + 3 = 0 --> x = -3.
our roots are x = 1, -1, 4, and -3.
write the equation of a line that is perpendicular to x=3 and that passes through the point (0 -4) will mark brainliest asap!!!
Answer:
y = -4
Step-by-step explanation:
x = 3 is a vertical line.
The perpendicular line passes through (0, -4) (x, y)
y = -4
The line is perpendicular, so the line should be also horizontal.
Answer:
y = -4
Step-by-step explanation:
The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).
Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.
steve can run 3.5 miles in 30 minutes. if he increases his rate by 1/2 mile per hour, how far will he run in 2 hours?
Answer:
15 miles
Step-by-step explanation:
Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.
Answer:
15
Step-by-step explanation:
because its correct just did the thing.
The expression 14s(s - 1) can be used to find
the total number of cards created by the ninth
grade students. Based on the given information,
which of the following statements must be true?
Select all that apply.
Answer:
B. The variable s represents the number of students in each class.
C. The coefficient 14 represents the number of classes in the 9th grade.
Step-by-step explanation:
The total number can be found by multiplying the number of the things with the number of people producing it. For example if 5 boys make 5 colored ropes the total number of ropes will be 5*5= 25.
In this question the combinations rule is used for variuos number of classes which are 14. Now we have to find the number of students which are s (s-1). Suppose s= 6 so the number of students would be 6(6-1) = 6(5) = 30
We will multiply the number of classes 14 with the number of students s(s-1) to get the total number of cards produced.
Need Help Please I'm Out Of Time ;(
Which of the following questions are statistical questions? Select all that apply
How far does Mary live from school?
How many students were absent from Mrs. Jenssen's class today?
How tall are the sixth-grade students in your school?
How many pull-ups can each student in your class do?
What was the temperature at 4 p.m. each day this week?
Answer:
last three questions are statistical question
Answer:
The last three questions
Step-by-step explanation:
simplify this please 41 =12d-741=12d−7
Answer:
Simplifying
41 = 12d + -7
Reorder the terms:
41 = -7 + 12d
Solving
41 = -7 + 12d
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-12d' to each side of the equation.
41 + -12d = -7 + 12d + -12d
Combine like terms: 12d + -12d = 0
41 + -12d = -7 + 0
41 + -12d = -7
Add '-41' to each side of the equation.
41 + -41 + -12d = -7 + -41
Combine like terms: 41 + -41 = 0
0 + -12d = -7 + -41
-12d = -7 + -41
Combine like terms: -7 + -41 = -48
-12d = -48
Divide each side by '-12'.
d = 4
Simplifying
d = 4
250 people went to a "couples only" party at 9pm.70 people left at 11pm, how many couples stayed at the party?
Answer:
90
Step-by-step explanation:
Total People = 250
Left the party at 11 pm = 70
Stayed = 250-70
=> 180
Couples that stayed = 180/2
=> 90
Answer:
90 Couples
Step-by-step explanation:
There were 250 total people at the beginning at the party. 70 people left at 11pm.
Subtract 70 from 250:
[tex]250-70=180[/tex]
There were 180 people that stayed.
A couple consists of two people. The question asks how many couples stayed at the party, not people.
Divide 180 by 2:
[tex]\frac{180}{2}= 90[/tex]
There would be 90 couples that stayed at the party.
If a sample consists of the following data values, what is the sample mean?
13, 91, 44, 68, 54, 16, 88, 74
Answer:
mean =sum of all data values
total number of data
13+91+44+68+54+16+88+74
8
448
8
=56
therefore the mean is 56
Answer: 51
Step-by-step explanation:
Question 18 (5 points)
Identify the independent and dependent variables in the following situation: The
temperature of the water decreases as a diver descends to the bottom of a lake.
The independent variable is the temperature of the water, and the dependent
variable is the depth below the surface of the lake.
The independent variable is the depth below the surface of the lake, and the
dependent variable is the temperature of the water.
The independent variable is the speed at which the diver descends, and the
dependent variable is the temperature of the water.
The independent variable is the type of boat, and the dependent variable is the
temperature of the water.
Answer:
The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water
Step-by-step explanation:
Tempeture = depth x
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned $220 in interest. How much money was invested at 3%? $2,000 $3,000 $4,000
Answer:
money invested at 3% is $4000
Step-by-step explanation:
let the money invested in 3% account be x
then money invested in 5% account = 6000 - x
we know interest = p*r*t/100
p is the principle amount invested
here t = 1 year
interest on 3% money
interest= x*3*1/100 = 3x/100
interest on 5% money
interest= (6000-x)*5*1/100
Total interest earned on both the account
3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100
given that total interest earned = $220
thus
( 30000-2x)/100 = 220
=> 30000-2x = 220*100= 22,000
=> -2x = 22,000- 30,000
=> x = -8000/-2 = 4000
Thus, money invested at 3% = x = $4000
Answer:)
$4000
Step-by-step explanation:
A trader claims that the proportion of stocks that offer dividends is different from 0.14. If the trader wants to conduct a hypothesis test, should they use a left-, right-, or two-tailed hypothesis test to analyze whether the proportion of stocks that offer dividends is different from 0.14? Select the correct answer below: Left-tailed test Right-tailed test Two-tailed test
Answer:
The correct option is;
Two-tailed test
Step-by-step explanation:
From the interpretation of the question statement, the trader wants to conduct a hypothesis test on the trader's claim that the proportion of stocks that offer dividends is different from 0.14
Given that the difference is hypothesized, then the null hypothesis, H₀ and the alternative hypothesis, H₁ should be written as follows;
H₀: Null hypothesis (no difference, or no change)
H₁: μ ≠ μ₀ which is hypothesizing difference which is known as a two-tailed test
The confidence level is then selected and the test statistic is calculated
12/ y + 8 = 4/9 Thats the question. Im dyin for help. :)
Answer:
-1 10/17
Step-by-step explanation:
Answer:
y = 1 10/17
Step-by-step explanation:
The LCD is 9y. Multiply all three terms by 9y:
(9y)(12) (9y)(4)
----------- + 8(9y) = -----------
y 9
This reduces to 108 + 72y = 4y, or 108 = -68y
Dividing both sides by 68, we get y = 1 10/17
A rectangular carton has twice the height, one-
third the length, and four times the width of a
second carton. The ratio of the volume of the
first carton to that of the second is
A)16:3
B)3:1
C)8:3
D)3:8
What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5)?
y=34x−92
y=34x+72
y=34x−74
y=34x+174
Answer:
y = 3/4x + 17/4
Step-by-step explanation:
Step 1: Find slope m
m = (5 - 2)/(1 + 3)
m = 3/4
y = 3/4x + b
Step 2: Find b
5 = 3/4(1) + b
5 = 3/4 + b
b = 17/4
Step 3: Rewrite equation
y = 3/4x + 17/4
Answer:
y = 3/4x + 17/9
Step-by-step explanation:
Find the slope:
5 - 2/ 1 - (- 3)
3/ 1 + 4
3/4
Find the y-intercept:
2 = 3/4(-3) + b
2 = -9/4 + b
17/4 = b
Put it in an equation:
y = 3/4x + 17/9
A car begins to depreciate at a rate of 24.9% annually as soon as it is driven off the lot. If a car was purchased for 26,500; how much is it worth after the second year? The equation you used is? What is the value of the car after two years?
Answer:
13197
Step-by-step explanation:
You have to do 24.9*2 and then find that percent of 26500
PLEASE!!! HELP!!! Question: If you have points on a graph that plot (1,7), (2,8), (3,5) and (4,6) what would be the slope?
Answer:
1
Step-by-step explanation:
You only need two points to find the slope.
Let's use (1,7) and (2,8).
The formula for slope is (y2-y1)/(x2-x1)
Let's plug the values in:
(8-7)/(2-1) = 1.
So, the slope is 1.
What is the new cost if a $2.75 toy is marked up by 29%?
Answer:
$3.55
Step-by-step explanation:
You need to add 29% of $2.75 to $2.75.
That means the price will be 129% of $2.75.
129% of $2.75 =
= 1.29 * $2.75
= $3.55
Please help solve i give brainliest
Answer:
(0,3)
Step-by-step explanation:
y = 2x+3
y = -3x+3
Since both equations are equal to y, set them equal to each other
2x+3 = -3x+3
Subtract 3 from each side
2x = -3x
Add 3x to each sdie
2x+3x = -3x+3x
5x =0
Divide by 5
x=0
Now solve for y
y =2x+3
y = 0+3
y=3
(0,3)
Answer:
(0,3)
Step-by-step explanation:
y = 2x+3
y = -3x+3
2x+3 = -3x+3
2x = -3x
2x+3x = -3x+3x
5x =0
x=0
The solve for y
y =2x+3
y = 0+3
y=3
(x,y)=(0,3)
Then (0,3) will be your answer!
Hope this help!
10) Spike drives for 50 miles at 60mph. He slows down and travels
another 50 miles at 40mph. For the final part of the 120 mile journey,
he speeds up to 80mph. How long does he take altogether? What is
his average speed (to the nearest mph)?
Answer:
2 1/3 hours or 2 hours 20 minutes.
51.4 mph to 1 decimal place.
Step-by-step explanation:
Time = distance speed
First 50 miles time taken = 50 / 60 = 5/6 hours
Second 50 miles - time = 50/40 = 5/4 hours.
Final 20 miles - time taken = 20 / 80 = 1/4 hours.
Total time taken = 5/6 + 5/4 + 1/4
= 5/6 + 6/4
= 10/12 + 18/12
= 28/12
= 7/3 or 2 1/3 hours or 2 hours 20 minutes.
Average speed = total distance / total time
= 120 / 7/3
= 120 * 3/7
= 51.4 mph to 1 decimal place.
⚠ PLEASE HELP ⚠ Calculate the product. (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) will award BRAINLIEST.
Answer:
5/8
Step-by-step explanation:
The value of the expression is 8/15
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)
The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)
We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n
Here, n = 15.
So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30
= 8/15
Hence, The value of the expression is 8/15
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