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:
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In order to play on the 7th-grade basketball team, you must buy a team uniform. Last year a uniform cost $40, but this year a uniform cost $48. What is the percent of change?
-IMPORTANT-
show work please and thanks
Answer:
1/6 or 16.666%
Step-by-step explanation:
8/48 and there is your answer.
Silvia randomly picked 12 flowers from a garden. Three of the flowers she picked were roses. What is the experimental probability that the next flower she picks will be a rose? ________
Answer:
1/4
Step-by-step explanation:
I could be wrong but that's what I would put
Answer:
P(next to be rose) = 1/4Explanation:
in general when she picked 12 flowers, 3 were roses
3/12 = 1/4
x^2-6=2-18x solve by completing the square
-1/3 – ¼
please show work if you don`t please don`t answer the question
Answer:
-1/3 - 1/4
First, make common denominators
-4/12 - 3/12
Then subtract the numerators
- 7/12
how is finding 8x3/4 similar to finding 3/4 of 8
Answer: your answer would be 6
8*3=24/4 and 24/4=6
Step-by-step explanation: Hope this help :D
Answer:
Because in order to find 3/4 of 8, you must solve for 8 * 3/4.
A helpful tip is that "of" is one of the giveaways of a multiplication problem. Others include but are not limited to, "multiply, " "product," "by," "times," "area," "twice," "double," "thrice," "triple," and "quadruple."
I would appreciate Brainliest, but no worries.
Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2
solve for x leave answer in simplest radical form.
Answer:
4sqrt(15)
Step-by-step explanation:
a² + b² = c²
x² + 7² = 17²
x² + 49 = 289
x² = 240
[tex]\sqrt{x^2} =\sqrt{240}[/tex]
[tex]x=4\sqrt{15}[/tex]
Linda just bought 7 bags of 14 cookies each. She already had 8 cookies in a jar. How many cookies does Linda have now?
Answer:
106
Step-by-step explanation:
Answer:
106
Step-by-step explanation:
(14 x 7) + 8 = 106
there are 6 rows of chairs 4 rows are empty
Answer:
then only 2 rows are full
Step-by-step explanation:
im confused but if thats it then thats the answer if im right mark me brainliest
:>
For BRAINLIST!!
Which statement is best supported by the information in the dot
plots?
Answer: D
Step-by-step explanation: because the The plot has 20 dots and it cannot be greater than or less then
increase R700 in the Ratio 3:2
Step-by-step explanation:
³93521586335445555554555554488807799654
change 7 3/8 from a mixed. number to to an improper fraction
Answer:
59/8
Step-by-step explanation:
Multiply the whole number by the denominator.
[tex]7 * 8 = 56[/tex]
Add the numerator to the product.
[tex]56 + 3 = 59[/tex]
Write the sum over the denominator.
[tex]\boxed{\frac{59}{8}}[/tex]
Hope this helps.
The Frill family and the Smith family go to the movies.
The Frill family buys 6 adult tickets and 2 child tickets for $124.
The Smith family buys 3 adult tickets and 5 child tickets for $100.
Find the prize of an adult ticket and the prize of a child ticket.
Step-by-step explanation:
Let a be the price of 1 adult ticket.
Let c be the price of 1 child ticket.
given,
[tex]6a + 2c = 124[/tex]
as equation 1,
and
[tex]3a + 5c = 100[/tex]
as equation 2.
Now we will solve for a and c using elimination method of simultaneous equations.
Now we multiply equation 2 by 2 to eliminate a and solve for c.
[tex]3a \times 2 + 5c \times 2 = 100 \times 2 \\ 6a + 10c = 200[/tex]
This new equation will be equation 3.
Now we will use equation 1 - equation 3 to eliminate a and solve for c.
[tex](6a - 6a) + (2c - 10c) = 124 - 200 \\ 0 + ( - 8c) = - 76 \\ - 8c = - 76 \\ c = - 76 \div - 8 \\ = 9.5[/tex]
Now substitute c into equation 2.
[tex]3a + 5(9.5) = 100 \\ 3a + 47.5 = 100 \\ 3a = 100 - 47.5 \\ 3a = 52.5 \\ a = 52.5 \div 3 \\ = 17.5[/tex]
Therefore one adult ticket will cost $17.50 and one child ticket will cost $9.50.
Someone please answer this without trying to send me a link
Answer:
y=-2x+5
Step-by-step explanation:
y=-2x+5
Six children want to share five chocolate bars fairly. How much chocolate will each child get?
Answer:
0.8 of a chocolate bar
Step-by-step explanation:
Bc 5 divided by 6 is 0.8
Use the figure below to complete the sentence.
B
A
E
39°
o
BGC and ZFGE are (select)
angles, so mZFGE =
Answer:
<BGC and <FGE are vertical angles
<BGC=90°-42°=48°
So m<FGE=48°
Hope it helps...
(-8, -1); slope = - 3/4
Pleaseee this onee!!
Answer:
y = -3/4x - 7
Step-by-step explanation:
Slope intercept:
y - y1 = m(x - x1)
y + 1 = -3/4(x + 8)
y + 1 = -3/4x - 6
y = -3/4x - 7
PLS HELP DO NOT TRIY THE FAKE I CANT UPLOAD STUFF
The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m.
Write a question that could be answered by solving the equation 10−0.035d=4.
Answer:
By solving this equation for the variable ' d ', you learn how many days after you fill the tank you'll have to send somebody back to fill it again.
Step-by-step explanation:
Steve earns $6.50 an hour. He worked 25 hours in the previous 1-week pay period. If Steve's employer withholds 10% of each of Steve's paychecks to pay Steve's income tax, how much will Steve take home in this week's paycheck?
Answer:
$146.25
Step-by-step explanation:
$6.50 per hour
for 25 hours = 25 × 6.50 = $162.5
10% of 162.5
162.5 × 10 ÷ 100
= 16.25
his week paycheck
162.5 - 16.25
= $146.25
Answer:
146.25$ is the a answer for sure
Greta bought a bunch of grapes that weighed 3 pounds 6 ounces. How many ounces is this?
Answer:
54
Step-by-step explanation:
16 x 3 is 48 then plus 6 is 54
I don’t get this question and need help. please hell
Maximizing revenue. Edwards University wants to determine what price to charge for tickets to football games. At $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 to the ticket price adds 10,000 people to the average attendance. Every person at a game spends an average of $4.50 on concessions. What price per ticket will maximize revenue
Answer:
New price is $12.75
New attendance is 57500
Step-by-step explanation:
For starters, we use the relation.
18 - 3x
Since we don't know the number of times we're expected to deduct $3 from the price.
Again, we have 40000 + 10000x on another hand. Question says to add 10000 people everytime $3 is deducted.
Since (40000 + 10000x) is the number of people, we multiply it by $4.50, the average amount each person spends is then gotten to be
(18 - 3x) (40000 + 10000x) + (40000 + 10000x) (4.5) = 0
Expanding the bracket, we have
[720000 + 60000x - 30000x²] + [180000 + 45000x] = 0, solving further, we have
900000 + 105000x - 30000x² = 0 or
-30000x² + 105000x + 900000 = 0
Then, we find the maximum of a quadratic, by finding the axis of symmetry. Use x = -b/2a
x = -105000 / 2 * -30000
x = -105000 / -60000
x = 1.75
From our earlier equations, the new price then is
18 - 3(1.75) = 18 - 5.25 = $12.75
The new attendance also is
40000 + 10000(1.75) =
40000 + 17500 = 57500
Which graph represents exponential decay?
On a coordinate plane, a straight line has a negative slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up in quadrant 1.
On a coordinate plane, a straight line has a positive slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2.
The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2 thus, option (D) is correct.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
As per the given,
The exponential function is a function that changes rapidly, for example, y = 6^x here as x approaches higher the y approaches rapidly higher.
Exponential decay is the exponential function that rapidly decreases as x increases for example y = 6^(-x).
The graph of the exponential decay has been graphed below.
Hence "The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2".
For more about exponential function,
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Answer:
D
Step-by-step explanation:
edge
hope this helps :)
Stephanie is going to paint the walls and ceiling of her bedroom. Her room is 18 feet long, 17 feet wide and 9 feet high.
What is the square footage (area) of the walls and ceiling that Stephanie will be painting?
The square footage Stephanie will be painting is ________ square feet. (Enter the number only)
How many gallons of paint does Stephanie have to purchase if each gallon of paint covers 250 square feet?
Stephanie will have to buy _____ gallons of paint. (Remember, you can only purchase a WHOLE number of gallons;Enter the number only)
If each gallon cost $23.75, how much will Stephanie spend on paint?
Stephanie will spend $________ on paint. (Enter the number only)
Answer:
55
Step-by-step explanation:
A young couple wants to save $40,000 over the next 5 years and then use this money as a down payment on a home. How much money must they deposit at the end of each quarter in an account that earns 5% compounded quarterly?
5% of 40,000 is 2,000
What is the solution to the equation 3(x-2)=3(x+4)=27
Ox= 12
OX= 14
x= 16
Ox= 26
pls help me answer number 2.
Answer: x=3, elimination method
Step-by-step explanation:
x=3
-7x-2y=-13 -> -7x-2y=-13
-(x-2y=11) -> -x+2y=-11
-----------------
-8x=-24
x = 3
elimination method
because you can easily eliminate one variable (y) using the elimination method
repersent 3 and 1/3 on a number line
Answer:
Step-by-step explanation:
To address 1/3 on a number line, we split the hole among O and An into 3 equivalent parts. Leave T and Q alone the marks of division. At that point, T addresses 1/3 and Q addresses 2/3, since 2/3 methods 2 sections out of 3 equivalent parts as demonstrated beneath. By utilizing a similar system, point O addresses 0/3 and point An addresses 3/3.
Another way of saying it is:
In portrayals of divisions on a number line we can show parts on a number line. To address 1/2 on the number line, draw the number line and imprint a direct A toward address 1.
Presently, split the hole among O and An into halves. Leave T alone the mark of division. At that point, point T addresses 1/2.
Portrayals of Fractions on a Number Line
To address 1/3 on a number line, we split the hole among O and An into 3 equivalent parts. Leave T and Q alone the marks of division. At that point, T addresses 1/3 and Q addresses 2/3, since 2/3 methods 2 sections out of 3 equivalent parts as demonstrated underneath.
Portions on a Number Line
By utilizing a similar technique, point O addresses 0/3 and point An addresses 3/3
brainliest?
Jason can water all the plants at the botanical
garden in 32 minutes. Celia can water them in
25 minutes. If they work together, about how long
will it take for them to water the plants?
Answer:
If they water the plants in the garden together then it will take about 15 minutes because when they do it seperatly it takes about 30 minutes. So if they do it together, they are cutting work in half. And half of 30 is 15.
Step-by-step explanation:
32 rounded is 30.
25 rounded is 30.
30/ 2 = 15
If x -9 is a factor of x^2 -5 -36, what is the other factor?
Answer:
Factors are (x-9)(x+4)
Step-by-step explanation: