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
What is the length of a rectangle if its width is 7 feet and its area is 84 square feet?
Answer: The length is 12 feet.
Step-by-step explanation:
k/4 +3=14 What is the answer to this question?
Answer:
k=44
Step-by-step explanation:
Find the slope of 3y = 6x + 4
one boy s c o r e d 80% out of a total of 500 marks how many marks did that boy is scored
The boy scored:
500 x 80% = 400 (marks)
Clara has 3 bottles of paint. She buys 5 more bottles of paint. If she uses 1/4 bottle of paint to paint a picture, how many similar paintings can she paint with all the paint?
ANSWER:
She has 3+5=8 bottles of paint. 1/4 bottle paints a picture.
8 divided by 1/4 = 32 paintings possible with all the paint
Answer:
32 Paintings
Step-by-step explanation:
8 Bottles 4 per one bottle so 8x4 =32
Hoped this helped.
find the least common factor of 4,5,6 no links or photo or I will report you
Answer:
60
Explanation:
The new superset list is
2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 x 5 = 60
In exponential form:
LCM = 22 x 31 x 51 = 60
LCM = 60
Therefore,
LCM(4, 5, 6) = 60
Find the area of the garden.
Answer:
28yd²
Step-by-step explanation:
area of square = side *side
=6*6= 36²
area of rectangle (patio)= length* breadth
=4*2=8²
area of garden= area of square - area of rectangle
=36-8
=28 yd²
Answer:
28 sq. ydStep-by-step explanation:
For finding the area of the garden :First Case:
Given,
Side of the big square = 6 yd
Therefore,
Area of the big square = side × side
= 6yd × 6yd
[tex] = 36 {yd}^{2} [/tex]
Second Case:
Length of the patio = 4 yd
Breadth of the patio = 2 yd
Therefore,
Area of the patio = Length × Breadth
= 4yd × 2yd
[tex] = 8 {yd}^{2} [/tex]
Last Case:
According to first and second cases,
Area of the garden
= Area of the big square - Area of the patio
[tex] = 36 {yd}^{2} - 8 {yd}^{2} [/tex]
[tex] = 28 {yd}^{2} [/tex]
Hence,Required area of the garden is 28 sq. yd (Ans)
how do you find lateral surface area
Answer: This lateral surface area can be calculated by multiplying the perimeter of the base by the height of the prism. For a right circular cylinder of radius r and height h, the lateral area is the area of the side surface of the cylinder: A = 2πrh.
Step-by-step explanation:
I think it will be b but I don’t know
Answer:
yeah it is b
acute and scalene
Step-by-step explanation:
scalene means none of the sides equal
and also all sides are acute angles
Answer:
yep you are correct it would be answer b
Step-by-step explanation:
hope this helped you
what is the radius of a sphere whose surface area is 100cm²?
Answer:
r≈2.82
Step-by-step explanation:
Hope this helps and have a great day!!!
Step-by-step explanation:
that can help you
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}
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!1111 I REALLY NEED HELP I A, BEGGIN YOU GUYS!!!!!!!!!!!!!!!!!!!!!!!!!!! ILL GIVE BRAINLIEST AND EXTRA POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Equivalent: 6(y - 3) AND 2(3y - 9)
Not Equivalent: 3(y - 6) AND 2(y - 9)
Step-by-step explanation:
4y - 2(5 - y + 4)
4y - 2(9 - y)
4y - 18 + 2y
6y - 18 (Everything must be equivalent to this)
3(y - 6) NOT EQUIVALENT
3y - 18
6(y - 3) EQUIVALENT
6y - 18
2(y - 9) NOT EQUIVALENT
2y - 18
2(3y - 9) EQUIVALENT
6y - 18
Find the range of the data. 26, 21, 27, 33, 24, 29
Answer:
33-21=9
Step-by-step explanation:
The current population of the Earth is estimated to be about 7,440,000,000 people. Express this number using scientific notation.
Answer:
7.44 × 10⁹
Step-by-step explanation:
You would take a decimal point from the last zero to in-between 7 and 4 and see how many places you moved it then write the scientific formula.
9 spaces so it would be 7.44 × 10⁹
The scientific notation of the current population of the Earth will be;
⇒ 7.44 × 10⁹
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The current population of the Earth is estimated to be about 7,440,000,000 people.
Now,
Since, The current population of the Earth = 7,440,000,000 people
Hence, The scientific notation of the current population of the Earth is written as;
⇒ 7,440,000,000
⇒ 7.44 × 10⁹
Thus, scientific notation of the current population of the Earth is,
⇒ 7.44 × 10⁹
Learn more about the multiplication visit:
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If Brianna can read 1/4 of her book in 1/2 hour, how much of her book will she read in 1 hour?
11 feet
Find the area of the square.
A = ft2
Answer:
area of square = side²
area of square=(11 feet)²
area of square=121 feet²
In a benchmark study, a fast food restaurant had an average service time of 2.4 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that a service time is less than or equal to one minute
Answer:
[tex]P(x \le 1)= 0.9093[/tex]
Step-by-step explanation:
Given
[tex]\lambda = 2.4[/tex] -- mean
Required
Determine [tex]P(x \le 1)[/tex]
This is calculated using:
[tex]P(X \le x)= 1 - e^{-\lambda x}[/tex]
So:
[tex]P(x \le 1)= 1 - e^{-2.4 * 1}[/tex]
[tex]P(x \le 1)= 1 - e^{-2.4}[/tex]
[tex]P(x \le 1)= 1 - 0.0907[/tex]
[tex]P(x \le 1)= 0.9093[/tex]
1.give the sequence 8.5.2.-1,...at what term will the number become -25? A.11th term B.10th term C.12th term D.20th term 2.which of the following is an algebraic esprression? A.3+5 B.n-1-14 C.3+5=8 D.x=53 3.what is the sum of the first 5 even numbers? A.30 B.20 C.10 D.50
Answer: 1. C(12) 2. B(n-1-14) 3. A(30)
Step-by-step explanation: For number one the nth term with common difference d and first term a is a+(n-1)d=nth term, plug in the values you have and solve for n to get 12. For number 2 an algebraic expression has a variable and a constant but doesn't have an equal sign. So it is B. For number three just add them up. Hope this helped!
Corey spent 18 minutes coloring. She spent 6 times as many minutes reading
Answer:
18 x 6 =108. she spent 108 minutes reading.
Step-by-step explanation:
A dealer buys articles for R7500 and makes the price 30% higher.
What is the selling price of the articles?
Answer:
9750
Step-by-step explanation:
profit amount = 30% of R 7500
= 30/100 *R 7500
= 2250
now
sp = R 7500 + R 2250
= R 9750
f(x)=-2x² + 3x-6, find f (3)
Answer:
f(3) = -15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = -2x² + 3x - 6
f(3) is x = 3 for the function f(x)
Step 2: Evaluate
Substitute in x [Function]: f(3) = -2(3)² + 3(3) - 6Exponents: f(3) = -2(9) + 3(3) - 6Multiply: f(3) = -18 + 9 - 6Add: f(3) = -9 - 6Subtract: f(3) = -15Answer:
f(3) = -15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
Algebra I
Functions
Function Notation
Step-by-step explanation:
Step 1: Define
f(x) = -2x² + 3x - 6
f(3) is x = 3 for the function f(x)
Step 2: Evaluate
Substitute in x [Function]: f(3) = -2(3)² + 3(3) - 6
Exponents: f(3) = -2(9) + 3(3) - 6
Multiply: f(3) = -18 + 9 - 6
Add: f(3) = -9 - 6
Subtract: f(3) = -15
-3y-5=10 Show your work please, thank you.
Answer:
-5
Step-by-step explanation:
-3y = 10 + 5
-3y = 15
y = - 5
Answer:
hi
Step-by-step explanation:
-3y-5=10
-3y=10+5
-3y=15
y=15/ -3
y= -5
hope it helps
have a nice day
Here it is sry and thx!
Answer:
B
Step-by-step explanation:
hard to explain xD
Answer:
#2
Step-by-step explanation:
1x60+45=105
2x60+45=165
3x60+45=225
4x60+45=285
the volume of a sphere is increasing at a rate of 7 cm^3/s. Find teh rate of change when volume is 4pi/3
The question is incomplete. The complete question is :
The volume of a sphere is increasing at a rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4 pi / 3 cm^3. (Do not round your answer.)
Solution :
Volume of the sphere, [tex]$V=\frac{4}{3} \pi r^3$[/tex]
Given that [tex]$\frac{dV}{dt}= 7 \ cm^3/s $[/tex]
V = [tex]$\frac{4 \pi}{3} = \frac{4 \pi r^3}{3}$[/tex]
∴ r = 1
[tex]$\frac{dV}{dt} =\frac{4}{3} \pi .3.r^2 \ \frac{dr}{dt}$[/tex]
[tex]$7 = \frac{4}{3} ( \pi )(3) (1)^2 \frac{dr}{dt}$[/tex]
[tex]$\frac{dr}{dt}=\frac{7}{4 \pi}$[/tex] cm/s
Surface area, [tex]$A = 4 \pi r^2$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi r \ \frac{dr}{dt}$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi \times \frac{7}{4 \pi} \times 1$[/tex]
[tex]$=14 \ cm^2/s $[/tex]
What is the value of 6 in the number 762
Answer:
60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
Hi,
Since the 6 is in the tenths place, it's a 60.
I hope this helps :)
What is the volume of a cylinder with base radius 2 and height 5?
Either enter an exact answer in terms of 3.14 for pi
Answer:
V ≈ 62.83
Step-by-step explanation:
Cylinder Formulas in terms of r and h
Calculate the volume of a cylinder:
V = πr2h
Calculate the lateral surface area of a cylinder (just the curved outside):
L = 2πrh
Calculate the top and bottom surface area of a cylinder (2 circles):
T = B = πr2
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Solution
V=πr 2h = π · 22 · 5 ≈ 62.83185
Therefore, the volume of the cylinder in the nearest tenths is V ≈ 62.83
Please solve the question with steps.
9514 1404 393
Answer:
c. x + 6
Step-by-step explanation:
The factorization is ...
x(x -3)(x -6)
The factor on the list that is not part of the above expression is (x +6).
_____
More detail
Factoring x from each term gives ...
x(x^2 -9x +18)
Now, you're looking for factors of 18 that sum to -9. We know that 18=(-3)(-6) and that -3-6 = -9, so the remaining two factors are (x-3)(x-6).
= x(x -3)(x -6)
Please help with this
it's the first answer choice
Step-by-step explanation:
If you add all the pieces of data up and divide the total number by 8 (the amount of pieces of data) you will get the mean. For median you just order them from least to greatest and find the one in the middle. Lastly, for mode you just choose the number that shows up the most.
Suppose Charli D'Amelio posted 40 dance videos to TikTok. If 65% of the videos have her making up her own moves, how many of the dance videos do not have her making up her own moves?
Step-by-step explanation:
[tex]40 - (40 \div 100 \times 65) = \\ = 40 - (0.4 \times 65) = \\ = 40 - 26 = \\ = 14[/tex]
The table shows a dog’s weight over a 5-year period. Which graph could represent this data?
Answer:
A
Step-by-step explanation:
Answer:
top left
Step-by-step explanation:
