Final answer:
The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.
Explanation:
If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:
Ratio = Volume of Saline / Total Volume of Solution
Ratio = 90 µL / 150 µL
By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.
The dilution ratio is therefore 3:5.
What is the slope intercept form of 6x+2y=8
Answer: y = -3x + 4
Step-by-step explanation:
subtract the 6x on both sides (2y = -6x + 8)
divide on both sides by 2 to isolate y ( y = -3x + 4)
Done :)
Solve each inequality
X + 15 > 3
Answer:
It can be anything
Step-by-step explanation:
It just has to be grater.
Name the property the equation illustrates.
(ab)3 = a (63)
Accociative Property of addition
Name the property the equation illustrates
(ab)3 = a(b3)
A. Commutative property of addition
B. Associative property of Multiplication
C. Associative Property of Addition
D. Inverse Property of Multiplication
Answer:Associative property of Multiplication
Solution:From given equation
(ab)3 = a(b3)
We have to find the property used here
We find the brackets are interchanged
So here, given is a multiplication equation
Therefore, Associative property of Multiplication is used
Associative property of Multiplication:This property says that when we are multiplying it does not matter where you put the parenthesis
The result will be same wherever we put the parenthesis in multiplying two or more numbers
Which means,
[tex]a \times (b \times c) = (a \times b) \times c[/tex]
Therefore, from given,
[tex]a \times (b \times 3) = (a \times b) \times 3[/tex]
Thus associative property of multiplication is used
A business woman invests $41,500 into two accounts: one that returns 8% annual interest and one that returns 15% annual interest. After 1 year, she earns $5490. How much did she invest in each account?
$10,500 in the 8% interest account, $31,000 in the 15% interest account.
$11,500 in the 8% interest account, $30,000 in the 15% interest account.
$9,500 in the 8% interest account, $32,000 in the 15% interest account.
$32,000 in the 8% interest account, $9,500 in the 15% interest account.
Answer:
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
Step-by-step explanation:
Let
x ---> the amount invested in the 8% interest account
41,500-x ----> the amount invested in the 15% interest account
we know that
The amount invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490
so
The linear equation that represent this problem is
[tex]0.08x+0.15(41,500-x)=5,490[/tex]
solve for x
[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]
so
[tex]41,500-x=41,500-10,500=\$31,000[/tex]
therefore
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
x+13/2=4 what x equal
Step-by-step explanation:
x+13÷2×2=4×2
x+13=8
x+13-13=8-13
x=8-13
x=-5
Answer:-2.5
Step-by-step explanation:
13/2=6.5. 4-6.5 =-2.5
what is x+3y=15 and 4×2y=30
Answer:
For the first one, x is 9 and y is 2. 9 + 3(2) = 15. The second is y = 3.75
i need help on 1 & 2
Answer:
1 - Avenue A is perpendicular to South St.
2 - 70°
Step-by-step explanation:
1 - North, Center, and South St. are parallel lines. Therefore Ave A will be perpendicular to the three lines.
2 - Ave B and Center street forms a 70° angle. Since Center and South St. are parallel lines, they have corresponding angles. Therefore, Ave B and South St also form a 70° angle. The same is true for Ave B and North St.
4 friends share 5 medium pizzas equally once a week after school when they study for their math quiz. James wants to know how much pizza he’s eaten this year. If they’ve been meeting for 14 weeks, how much pizza had James eaten while at his study group? Show your work.
Answer:
17 pies and one half pie
Step-by-step explanation:
Write the numbers in order from greatest to least.
-5, 1 1⁄5, -5 3⁄4, 5⁄12
Answer:
-5 3/4, -5, 5/12, 1 1/5
Step-by-step explanation:
Negatives are opposite of positives when least to greatest
I really need help can ya'll please help. ://
Thank you
a) Wayne's savings before he spent $28 is $30
b) Stef's savings after she spent $28 is $8
Step-by-step explanation:
step 1 :
let,
Wayne's savings = 5x
Stef's savings = 6x
step 2 :
After spending $28 each of them, The ratio becomes 1/4.
⇒ (28 - 5x) / (28 - 6x) = 1/4
⇒ 4(28 - 5x) = 1 (28 - 6x)
⇒ 112 - 20x = 28 - 6x
⇒ 112 - 28 = 20x - 6x
⇒ 84 = 14 x
x = 84/4 = 6
step 3 :
a) Wayne's savings before he spent $28 = 5x
substitute x=6,
Wayne's savings = 5(6) = $30
step 4 :
b) Stef's savings after she spent $28 = Total savings - $28
= 6x - 28
= 6(6) - 28
∴ Stef's savings after she spent $28 = 36 - 28 =$8
(a) Wayne's savings before he spent $28 is $30.
(b) Stef's savings after she spent $28 is $8.
Solution:
Ratio of Wayne's savings to Stef's savings = 5 : 6
Let x be the common amount they have.
After spending $28 each, the ratio becomes 1 : 4.
5x – 28 : 6x – 28 = 1 : 4
This can be written in a fraction form.
[tex]$\Rightarrow\frac{5x-28}{6x-28}=\frac{1}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 4(5x-28)}=1({6x-28})[/tex]
[tex]$\Rightarrow 20x-112=6x-28[/tex]
Arrange like term one side.
[tex]$\Rightarrow 20x-6x=112-28[/tex]
[tex]$\Rightarrow 14x=84[/tex]
⇒ x = 6
(a) Wayne's savings before he spent $28 = 5x = 5(6) = $30
(b) To find stef's savings after spent $28:
Stef's savings before she spent $28 = 6x = 6(6) = $36
Stef's savings after she spent $28 = $36 – $28 = $8
Hence Wayne's savings before he spent $28 is $30
Stef's savings after she spent $28 is $8.
Determine whether the statement is true of false and support your reasoning:
Mr. Flores has 100 pictures in a photo album. Of these pictures, 20 show his friends, 50 show his family, and 30 show his pet dachshund, Frou-Frou.
Based on this information, the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family.
Answer:
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
Step-by-step explanation:
the probability of randomly selecting a picture of Frou Frou is = 30/100 = 0.3
The probability of randomly selecting a picture of his family = 50/100 = 0.5
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
A cyclist traveled 9 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 45 kilometers, the skater had gone 30 kilometers. What’s the speed of the skater?
Final answer:
The speed of the skater is 18 km/h.
Explanation:
To find the speed of the skater, we can set up a proportion using the information given. Let's let the speed of the skater be x km/h. Since the cyclist traveled 9 km/h faster than the skater, the speed of the cyclist would be x + 9 km/h. Now, we can set up the proportion:
(x + 9 km/h)/(45 km) = x km/h)/(30 km).
To solve this proportion, we can cross-multiply and solve for x:
(x + 9 km/h)(30 km) = (x km/h)(45 km)
30x + 270 = 45x
270 = 45x - 30x
270 = 15x
x = 18
Therefore, the speed of the skater is 18 km/h.
An office remodeling project costs $15,880. If you pay $3,680
towards the project, how much do you finance?
Answer:
23.17%
Step-by-step explanation:
The project costs $15,880 of which you contributed $3,680. To know the percentage of how much you finance,
(amount paid / cost)*100%
= (3680/15880)*100%
= (0.231738035)*100%
= 23.1738035%
Thus the amount contributed is 23.17% of the cost.
Find the missing side length, m.
Answer:
m=5
Step-by-step explanation:
Since we know that triangle ABC is similar to QRS, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
Choose whole numbers to make the division easier
[tex]\frac{QR}{AB} = \frac{QS}{AC} \\\frac{10}{6} = \frac{m}{3} \\\frac{10*3}{6} =m\\m=10*3/6 = 5[/tex]
The missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
The missing side length, [tex]$m$[/tex], can be found using the fact that triangles [tex]$ABC$[/tex] and[tex]$QRS$[/tex] are similar. This means that their corresponding side lengths are proportional. We can set up a proportion like this:
(m)/(3)=(10)/(6)
Cross-multiplying, we get:
[tex]$$6m[/tex] =[tex]30$$[/tex]
Solving for [tex]$m$[/tex], we get:
[tex]$$m[/tex] =[tex]5$$[/tex]
Therefore, the missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
What percent of 140 is 50.4?
Answer:
36
Step-by-step explanation:
X/100% x 140 = 50.4
X x 140 = 50.4 x 100
X x 140 = 5040
X = 5040/140
X = 36
“An A grade will be given to students having at least 450 total test points. There are two more tests to take before the semester is over. Lesha wants to know what she needs to score in order to get an A. Write and solve an equation to determine what score she needs to average on the next two tests if each question is with 1 point. Explain your reasoning.”
The required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
Solution:
An A grade will be given to students having at least 450 total test points
Let p represent her present test point total, and t represent the necessary average on the next two tests
There are two more tests to take before the semester is over
Therefore,
[tex]p+2t\geq 450[/tex]
A grade is given to students having at least 450 total test points
"at least" means greater than or equal to
So we have used greater than or equal to symbol
Solve the inequality for "t"
[tex]p+2t\geq 450\\\\Subtract\ p\ from\ both\ sides\\\\2t\geq 450-p\\\\Divide\ both\ sides\ by\ 2\\\\t\geq \frac{450-p}{2}[/tex]
Thus the required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
What is the quotient 212,960\1000
The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.
Explanation:The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.
Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.
Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary and that the measure of ∠J is 41 degrees, 38 minutes, 9 seconds. What is the measure of ∠K?
Pleaseee answer now!!!
The measure of ∠K is 49 degrees 22 minutes 51 seconds.
Step-by-step explanation:
Given that ∠J and ∠K are complementary.
∠J = 41°38'9".
∠K = ?
When a sum of two angles result is 90°, then it is called as complementary angles.
Since ∠J and ∠K are complementary, then their sum is 90°.
∠J +∠K=90°.
∠K= 90° - ∠J.
=90°60'60" - 41°38'9".
=49°22'51".
∠K= 49 degrees 22 minutes 51 seconds.
Write 80/100 as tenths in fraction form and decimal form
Answer:
0.8
Step-by-step explanation:
Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options.
The equivalent expressions are:
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Solution:
Given expression is:
[tex]7(-\frac{3}{4}x - 3)[/tex]
We have to find the equivalent expressions
By distributive property,
a(b + c) = ab + ac
Therefore,
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Thus equivalent expressions are found
Answer:
Im pretty sure its a and e
Step-by-step explanation:
lmk if im wrong or right
The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $3. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
Answer:
Option D
Just took test on ed2020 it is the last graph. Option D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
which question represents a line that passes through (2,-1/2) and has a slope of 3?
Answer:
y=3x-13/2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1/2)=3(x-2)
y+1/2=3x-6
y=3x-6-1/2
y=3x-12/2-1/2
y=3x-13/2
the table shows the distance a small motor scooter can travel using one gallon of gasoline comeplete the table to find the number of miles the scooter can travel for other amounts of gasoline
By using the information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference, we calculate that it can travel 11.8 miles with 0.1 gallons and 1180 miles with 10 gallons.
To complete the table and find the number of miles the scooter can travel for other amounts of gasoline, we can use the given information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference point. We can calculate the mileage for different amounts of gasoline using this information.
Here's how we can complete the table:
Gallon 0.1:
We can calculate the distance for 0.1 gallons by taking 10% of the mileage for 1 gallon:
0.1 * 118 miles = 11.8 miles
Gallon 10:
Similarly, we can calculate the distance for 10 gallons by multiplying the mileage for 1 gallon by 10:
10 * 118 miles = 1180 miles
So, the completed table would look like this:
Gallon 0.1: 11.8 miles
Gallon 1: 118 miles
Gallon 10: 1180 miles
This table provides the number of miles the scooter can travel for different amounts of gasoline, including 0.1 gallons, 1 gallon, and 10 gallons.
For more such information on: miles
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one year, super bowl commercial time sold for 4 million for 30 seconds of air time. What was the price per second? Round to the nearest cent
Final answer:
To calculate the cost per second for a $4 million Super Bowl ad that runs for 30 seconds, divide the total cost by the number of seconds, yielding a cost of approximately $133,333.33 per second.
Explanation:
The question asks us to calculate the cost per second for Super Bowl commercial air time when 30 seconds of air time sold for $4 million. To find the price per second, we divide the total cost by the total number of seconds.
Price per second = Total cost ÷ Number of seconds
Price per second = $4,000,000 ÷ 30 seconds
Price per second = $133,333.33 (rounded to the nearest cent)
Therefore, the price per second for Super Bowl commercial air time was approximately $133,333.33.
18. You run along a path at a constant speed of 5.5 miles per hour. How far do you travel in 1.5 hours? in 3.8 hours?
Answer:
the travel of only 1.5 hours:8.25
The travel in 3.8 hours:20.9
Step-by-step explanation:
1.5(5.5)
1.5(3.8)
Can someone please help first answer gets brainlist
Answer:
3/5
Step-by-step explanation:
0.6 is actually 6/10 as a fraction. You divide bot the 6 and the 10 by 2 to get 3/5
oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters. determine the density of oak in grams per cubic centimeter.
Answer:
The density of oak is 0.695 grams per cubic centimeter.
Step-by-step explanation:
Given:
Oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters.
Now, to find the density of oak in grams per cubic centimeter.
Mass (m) = 2.85 kilograms.
So, using conversion factor we convert into grams:
[tex]2.85\times 1000=2850\ grams.[/tex]
Volume (v) = 4100 cubic centimeters.
Now, to get the density by using formula:
[tex]Density=\frac{mass}{volume} \\Density=\frac{m}{v}[/tex]
[tex]Density=\frac{2850}{4100}[/tex]
[tex]Density=0.695\ grams\ per\ cubic\ centimeter.[/tex]
Therefore, the density of oak is 0.695 in grams per cubic centimeter.
what is the measure of b if a=20 and c=29. using the pythagorean theorem
Since a^2+b^2=c^2 becomes 20^2+b^2=29^2, we solve for b:
400+b^2=841
b^2=441
b=21
So the length of b is 21 units.
Hope this helped!
Answer:
Step-by-step explanation:
b=21
a Leg
20
c Hypotenuse
29
Write an equation of a line that passes through the x-intercept 4 and y-intercept -2
Answer:
[tex]y=\frac{1}{2} x-2[/tex]
Step-by-step explanation:
We have the two points (4,0) and (0,-2)
Find the slope
[tex]m=\frac{-2-0}{0-4} =\frac{-2}{-4} =\frac{1}{2}[/tex]
y-intercept is -2
[tex]y=\frac{1}{2} x-2[/tex]
What does -8/3 simplify to ?
Answer:
exact form: -8/3
decimal form: -2.6666666
mixed number: -2 2/3
Step-by-step explanation: