Given:
[tex]x=\log_{10}31,500[/tex]
To find:
Select the true statements from the given options about the given value.
Solution:
We have,
[tex]x=\log_{10}31,500[/tex]
It can be written as
[tex]x=\log_{10}(2^23^25^37)[/tex]
[tex]x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)[/tex] [tex][\because \log(ab)=\log a+\log b][/tex]
[tex]x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)[/tex]
[tex]x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451[/tex]
[tex]x=4.49835[/tex]
Clearly, the value of x lies between 4 and 5. So, [tex]x>4[/tex] and [tex]x<5[/tex].
Therefore, the correct options are C and D.
The true statements are: (c) x > 4 and (d). x < 5
The logarithmic expression is given as:
[tex]x = \log_{10}(31500)[/tex]
Express 31500 as a product of 100
[tex]x = \log_{10}(315 * 100)[/tex]
Apply the law of logarithm
[tex]x = \log_{10}(315) + \log_{10}(100)[/tex]
Evaluate log 100 base 10
[tex]x = \log_{10}(315) + 2[/tex]
Evaluate log 315 base 10
[tex]x = 2.50 + 2[/tex]
Add the expressions
[tex]x \approx 4.50[/tex]
4.5 is greater than 4 and less than 5
Hence, the true statements are: (c) x > 4 and (d). x < 5
Read more about logarithms at:
https://brainly.com/question/25710806
Find the area of the following trapezoid. 5 7 14
Answer:
84
Step-by-step explanation:
5+7 times 14 divided by 2 i think there's no pic
Answer:
Welp, you didn't provide a picture so I'll go with every choice.
Step-by-step explanation:
If the two bases are 5 and 7, and the height is 14, then the area is 84.
If the two bases are 5 and 14, and the height is 7, then the area is 66.5.
If the two bases are 7 and 14, and the height is 5, then the area is 52.5.
The formula for the area of a trapezoid is : (a+b)/2 * h
Suppose that the ingredients for a large bucket of popcorn cost a movie theater 80 cents
to buy. If the theater charges $9 for the bucket, what is the percent markup? Give your
answer as a percent rounded to the nearest whole percent.
Answer:
The percent markup is 91%.
Step-by-step explanation:
1. find the amount of profit per large bucket of popcorn
9 - 0.8 = $8.2
2. divide the amount of profit per large bucket of popcorn by the cost of a large bucket of popcorn
8.2 / 9 = 91%
Answer:
The percent markup is 91%.
1. find the amount of profit per large bucket of popcorn
9 - 0.8 = $8.2
2 divide the amount of profit per large bucket of popcorn by the cost of a large bucket of popcorn
8.2 / 9 = 91%
Please help this is due tomorrow!!!
Answer:
Use the Pythagorean therm
Step-by-step explanation:
A squared(one leg) + B square(one leg) = C(aka the hypotenuse)
brainlist plz
Solve by substitution the system of equations. (y = 4x + 1) (3x + 2y = 13).
Answer:
(6*y130896+1%315£&+)
(19+!re
Jeff has a square piece of art paper. He cuts across it from one corner to the opposite corner to make two pieces. What is the total number of sides and angles in both of the new shapes?
Answer:
The number of sides is 3 on each piece of paper, altogether there are 6 sides.
The total number of angles on a triangle is 180°, altogether the sum of both triangles is 360°
Find q. q/32=6 q=? Help
Answer:
q=0
Step-by-step explanation:
Hope this helped!!
the answer is 192
Step-by-step explanation:
q/32 = 6
q = 192
What fraction is less than 3/4?
Answer:1/2
Step-by-step explanation:3/4 equals 75% but 1/2 equals 50%
A dressmaker buys flannel fabric by the yard. A purchase
of 5 yards of flannel costs $40. How many yards of flannel
would the dressmaker be able to buy for $36?
Answer:
4.5yards
Step-by-step explanation:
$40 =5yards
$36 =?
36*5=180÷40
=4.5yards
The dressmaker would be able to buy 4.5 yards of flannel for $36.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that dressmaker buys flannel fabric by the yard. A purchase of 5 yards of flannel cost $40 then we need to find yards of flannel would the dressmaker be able to buy for $36.
Given ; $40 =5yards
$36 =?
Therefore, we get
36*5 = 180÷40
= 4.5yards
Hence, the dressmaker would be able to buy 4.5 yards of flannel for $36.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Using the following data, calculate the mean absolute deviation: 7 2 8 5 9 9 5 6 8 1 What is the mean absolute deviation for these data? (4 points)
Answer:
The mean absolute deviation is 2. Hope this helps
Step-by-step explanation:
7+2+8+9+9+5+6+8+1=5.5
7-5.5=1.5
5.5-2=3.5
8-5.5=2.5
9-5.5=3.5
9-5.5=3.5
5.5-5=0.5
6-5.5=1.5
8-5.5 2.5
5.5-1=4.5
1.5+3.5+2.5+3.5+3.5+0.5+1.5+2.5+4.5=2
Answer is 2.
I hope this can help!
Have a nice day :)
~Amy
Lyle uses a streaming service to watch movies. Last month he paid $26.91 and watched 9 movies. If he watches 11 movies this month, how much will he pay the streaming service?
Answer:
$32.89
Step-by-step explanation:
You pick a card at random.
6 7 8
What is P(odd)?
Write your answer as a fraction or whole number.
Answer:
1/3
Step-by-step explanation:
1/3
On a coordinate plane, how are the locations of the points (1 , -5) and (-1 , 5) related
Answer:
They are a transformation
Step-by-step explanation:
Checked using desmos graphing
Two consecutive integers have a product of 12. What is the initial equation that would be used
to solve this?
x² = 12
x(x + 1) = 12
2 (2+2) = 12
x(x − 2) = 12
Answer:
x(x+1) = 12
Step-by-step explanation:
If a number is x then it's consecutive number will be x + 1.
And their product x(x+1)
LOOK AT THE PHOTO PLEASE
Answer:
The answer to the question provided is 7.
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: 2x - 3 = x + 4 \\ \frac{ - x \: \: \: = \: - x}{x - 3 = 4} \\ \frac{ \: \: \: \: \: \: + 3 = + 3}{x = 7} [/tex]
[I apologize if the answer is inaccurate]
Clarissa wants to create more shade in her yard to block the hot sun, so she buys a sapling of an oak tree and plants it in the yard. To make sure the tree is growing at a healthy rate, she makes the following table to track its height over a period of weeks. What is the average rate of change in the tree's height from week 3 to week 9? Enter your solution into the box below.
Answer:
The answer is 7.
Step-by-step explanation:
Determine what values to use from the table to find the average rate of change.
The problem asks for the average rate of change (AROC) from week 3 to week 9. The points referring to these measurements would be (3, 41) and (9, 83), respectively.
Step 2
FInd the AROC from (3, 41) to (9, 83).
The formula for the slope of a line between two given points (which is the same as AROC from the first two the second point) is
AROC = y2−y1x2−x1
In your points, x1 is 3, x2 is 9, y1 is 41, and y2 is 83. Plug these values into the above formula and simplify.
AROC = 83−419−3=426=7
The AROC is 7.
Step 3
Enter your solution.
Enter the value 7 and move on to the next question.
find the value of x
HELP pls .
Answer:
31°
Step-by-step explanation:
The total triangle is 180°
Subtract 180-(33+116)
Which is the standard form of the equation with p = 26, theta = 3pi/4?
A. sqrt2x-sqrt2y=0
B. sqrt2x-sqrt2y + 52-0
C. sqrt2x + 52=0
D. sqrt2x + 52y=0
Help please question in picture
Answer:
10 units squared
Step-by-step explanation:
[tex]4(5)=20[/tex]
[tex]\frac{20}{2}=10[/tex]
Solve the equation for solutions over the interval [0°, 360°). 7tanθ−7/3cotθ=0
Answer:
Step-by-step explanation:
[tex]7\tan \theta-\frac{7}{3}\cot \theta=0\\\tan \theta=\frac{1}{3} \cot \theta\\\tan^2\theta=\frac{1}{3}\\\tan \theta=\pm \frac{1}{\sqrt{3}}\\when ~\tan \theta=\frac{1}{\sqrt{3}}=tan 30,tan (180+30)\\\theta=30^\circ ,210^\circ\\when~ \tan \theta=-\frac{1}{\sqrt{3}}=\tan (180-30),tan(360-30)\\\theta=150^\circ,330^\circ[/tex]
solution set is {30,150,210,330}
Draw the graph of the equation: 1.6x=4.8
Answer:
Here...
Step-by-step explanation:
x | y
3 | 0
3 | 1
The picture is the graph ( I'm not sure why I wrote that you probably already knew... but, I'm not sure if this helps but here.. :D )
X-1
Which graph shows the solution set of
1-X
O
-5 -4 -3 -2 -1 0
1
2
3 4
5
X
O
-5 -4 -3 -2 -1
0
1
2
3
4
5
x
O
54 -3 -2 -1
0
1
2
3
4
5
x
O
-5 -4 -3 -2
0
1
2
3
4
5
X
Answer:
2nd
Step-by-step explanation:
the second pic from the given figure show the correct answer
The graph (C) shows the solution set of (x-1 )/ (1-x) < 0.
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given:
According to the question, we have the Expression
(x-1 )/ (1-x) < 0
Because the function exists, the denominator is not equal to zero. That is, x does not equal 1. Because the denominator is zero when x = 1 and the function is not defined.
Thus, in the solution set of (x-1 )/ (1-x) < 0 excluding one, at every real number is function is defined.
Therefore, the correct option is C shows the solution set.
Learn more about Inequality here:
brainly.com/question/11988499
#SPJ7
what is the remainder when the polynomial f(x) = x³ - x² + 3x - 2, is divided by 2x - 1
Answer:
Equate the divisor to 0
2x-1=0
2×=1
×=1/2
Putting onto the polynomial
f(1/2) = (1/2)³-1/2)²+3(1/2)-2
=-5/8
If you borrow $500 for 6 years at an interest rate of 9%, how much interest will you pay?
What is 3^2/3 equal to
Answer:
3
Step-by-step explanation:
3^2=3×3=9
9/3=3
hope this helps
Answer:
The correct answer is 3.
Step-by-step explanation:
Hope this helped Mark BRAINLIEST!!!!
find the surface area to the nearest tenth
Work out the area of the circle and leave it in cm plz
Answer:
132.7495 cm^2
Step-by-step explanation:
area of circle=πr^2
radius=6.5
6.5^2
42.25
42.25*3.142
132.7495
Answer:
132.7495 cm
Step-by-step explanation:
13/2=6.5
6.5*6.5=42.25
42.25*3.142=132.1495
simplify-7(3x) + 2(3x - 2)
I'll give brainliest
Answer:
-15x-4
Step-by-step explanation:
-21x + 6x-4
-15x-4
a city has a population of 34000. the value k is 0.0305. what is the population of the city after 9 years
Answer:
6
Step-by-step explanation: 6 9 0
Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
Answer:
4x-3
Step-by-step explanation:
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
What are equation of a line that is parallel to that line?Two lines are said to be parallel if they always maintain the same distance apart. If two lines are drawn so that they could extend into infinity without ever meeting each other, these lines are called parallel. Parallel lines are also called Equidistant lines.
Given
Equation of line y = 4x + 1
Point = (1, 1)
Equation of the line that is parallel to y = 4x + 1 is y=kx + b
Here k =4
y = 4x + b and contains the point (1,1)
Substitute the point (1,1) in y= 4x + b
⇒ 1 = 4(1) + b
⇒ 1 - 4 = b
⇒ b = -3
y = 4x + b
⇒ y = 4x - 3
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
Find out more information about equation of line here
https://brainly.com/question/402319
#SPJ2
The amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. When 10 ohms of resistance are used in the circuit, 12 amperes of current are present. When 5 ohms of resistance are used in the same circuit, 24 amperes of current are present.
How many ohms of resistance are used in the circuit when 15 amperes of current are present? Round your answer to the nearest tenth, if necessary.
7.5 ohms
8 ohms
50 ohms
120 ohms
9514 1404 393
Answer:
(b) 8 ohms
Step-by-step explanation:
We are told that y varies inversely to x, so the relation can be modeled by ...
y = k/x
The value of k is ...
k = xy = (12)(10) = 120
Then for x=15, the resistance is ...
y = 120/15 = 8 . . . . ohms
Answer:
(b) 8 ohms
Step-by-step explanation:
We are told that y varies inversely to x, so the relation can be modeled by ...
y = k/x
The value of k is ...
k = xy = (12)(10) = 120
Then for x=15, the resistance is ...
y = 120/15 = 8 . . . . ohms