interesting puzzle,
total CDs=[tex]39[/tex]
country CDs $c$ is half of rock CDs $r$, $r=2c$
and one fourth of soundtrack $s$ as country CDs , $c=4s$
express in common variable s, $r+c+s=39$
$2(4s)+4s+s=39 \implies s=3$
so $c=12$ and $r=24$
after borrowing 3 rock CDs, there be $21$ rock CDs rest will be same
A 10 gram sample of a substance that’s used to detect explosives has a k-value of 0.1356.Find the substances half life in days.Round your answer to the nearest tenth.
Answer:
t ≈ 5.1 days
Step-by-step explanation:
A 10 gram sample of a substance thats used to detect explosives has a k-value of 0.1356. Find the substances half-life in days. round your answer to the nearest tenth. N=N₀ e^-kt N₀= initial mass (at time t = 0) N = mass at time t k= a positive constant that depends on the substance itself and on the units used to measure time t=time in days
The initial condition is that, at time t = 0, the amount of substance contains originally 10 grams
Find the value of N₀
N=N₀ e^-kt
We substitute:
10 = N₀ {e^(-0.1356)*0}
10 = N₀ (e^0)
10=N₀(1)
10=N₀
N₀ = 10
When the substance is in half-life
That is, half of the original substance (5 grams)
Find t
N=N₀ e^-kt
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Bring down t by multiplying natural log on both sides
ln(0.5) = -0.1356*t
Divide both sides by -0.1356
t = -(ln(0.5) / 0.1356
t ≈ 5.11 days
To the nearest tenth
t ≈ 5.1 days
Answer:
5.1 days in Plato
Step-by-step explanation:
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
a shop has a sale and reduces all the prices by 15k in naira.find the sale price of an article of an article marked at 750naira
Answer:
Question (i):
Reduce = 15% of Rs 40 = 0.15 x 40 = Rs 6
Price after reduced = Rs 40 - Rs 6 = Rs 36
Answer: Rs 36
-
Question (ii):
Reduce = 15% x 20.40 = 0.15 x 20.40 = Rs 3.60
Price after reduced = Rs 20.40 - Rs 3.60 = Rs 17.34
Answer: Rs 17.34
-
How would I solve this? (y-z) ÷ z y=-2 and z=4/5
Answer:
-3.5
Step-by-step explanation:
The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5
Answer:
[tex]\large\boxed{-3.5}[/tex]
Step-by-step explanation:
(y - z) ÷ z y = -2 and z = 4/5
Substitute in the given values for y and z into the equation
(y - z) ÷ z
(-2 - 4/5) ÷ 4/5
Subtract inside the parenthesis (-2 - 4/5)
-2.8 ÷ 4/5
Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)
4/5 = (4 * 20) / (5 * 20) = 80 / 100
80 / 100
Divide numerator and denominator by 10
8/10 = 0.8
Substitute into previous equation
-2.8 ÷ 4/5 = -2.8 ÷ 0.8
Divide
[tex]\large\boxed{-3.5}[/tex]
Hope this helps :)
if the morning temperature started at -7 celsius but warmed during the day to 24 celsius . What is the temperature change
Answer:
31° change
Step-by-step explanation:
If we want to find the change between two numbers, we need to imagine it like a number line.
<-------------0------------->
Let's plot -7 and 24 on this number line.
<----------[tex]-7[/tex]--0------------24>
If we want to get from -7 to 0, we increase by 7. To get from 0 to 24, we increase by 24.
So the total change is [tex]7 + 24 = 31[/tex].
Hope this helped!
A man gave his 8000$ as pocket money and his son 1000$ less.Express the girls money as a percentage of the total sum of money.
Answer:
About 89%
Step-by-step explanation:
8000 + 1000 = 9000.
To find the girls money as a percentage of the total sum of money, you must take 8000 and divide it by 9000.
8000/9000 = .8888 = 88.88 = 88.9% or about 89%.
Ali was supposed to meet his friend in th evening every sunday. The first time he came at 4.30,the next time at5. 20,then at 6.30.Then at8. 00.When did he turn up the last time after that?
Answer:
9:50
Step-by-step explanation:
Given the following information :
First meeting = 4:30
Second meeting = 5:20
Third meeting = 6:30
Fourth meeting = 8:00
Frim careful observation of the meeting times :
Difference between the ;
Second and first meeting:
5:20 - 4:30 = 50 minutes
After that 20 minutes is added to the subsequent meetings as observed from the third and fourth meetings
6:30 - 5:20 = 70 minutes
8:00 - 6:30 = 90 minutes
Therefore, next meeting time :
(90 + 20) minutes = 110 minutes
8:00 + 110 minutes = 9:50
1. An atom consist of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of -1.Remember number of electrons is equal to number of protons, while answering these questions i) What is the charge on an atom? Ii) What will be the charge of an atom if it loses an electron? Iii) What will be the charge of an atom if it gains an electron?
Answer:
I) no charge
ii) it will be positively charged
iiI) it will be negatively charged
Step-by-step explanation:
An atom is composed of electrons, neutrons and protons. Electrons are negatively charged while protons are positively charged. The number of electrons and protons in a neutral atom are exactly the same. This ensures the electrical neutrality of the atom.
However, if an atom looses an electron, there are now more protons than electrons present in the atom hence the atom is positively charged.
Similarly, if an atom gains an electron, it now contains more electrons than protons, hence it is negatively charged.
a 6 foot tall man casts a shadow that is 9 ft long. At the same time, a tree nearby casts a 48 ft shadow. how tall is the tree
Answer:
32 ft tall
Step-by-step explanation:
Since a 6 ft man casts a shadow 9 ft long, the shadow is 3/2 of the actual object/person.
SINCE THE TREE'S SHADOW IS AT THE SAME TIME, THE HEIGHT IS THE SAME RULE.
We know the tree's shadow is 48 ft.
--> 48/3 = 16
16 x 2 = 32
32 ft tall
Hope this helps!
Answer: 32ft tall
Step-by-step explanation:
sandra is playing a trivia game.on her first turn she lost 75 points. on her second turn,she lost 35 points. on her third turn,she scored 100 points. What is sandras score after three turns?
Answer: -10 points
Step-by-step explanation:
She lost 110,so that loss -the gain(100) is the total score at the end of three games
[tex]\frac{63,756×60}{70×5,280}[/tex]
Answer:
[tex]1035[/tex]
Step-by-step explanation:
(63756×60)/(70×5280)
=1035
The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?
Answer:
5 hours
Step-by-step explanation:
From the question, we are told that:
Time required to drive a fixed distance varies inversely as the Speed
T ∝ 1/S
k = proportionality constant hence,
T =k × 1/S
T = k/S
Step 1
Find k
It takes 2 hr at a speed of 200 km/h to drive a fixed distance
T = 2 hours, S = 200km/h
T = k/S
2 = k / 200
k = 2 × 200
k = 400
Step 2
How long will it take to drive the same distance at a speed of 80 km/h?
S = 80km/h
T = k/S
k = 400
T = 400/80
T = 5
Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr
Is it true or false that this is the graph of f(x) = 3^x?
Answer: False, this is not the graph of f(x) = 3^x
=====================================================
Explanation:
Plug in x = 0 to get
f(x) = 3^x
f(0) = 3^0
f(0) = 1
That means (0,1) is on the graph. So far so good.
-------
But let's try x = 1
f(x) = 3^x
f(1) = 3^1
f(1) = 3
Meaning (1,3) should be on the graph of y = 3^x. Instead, the graph shows (1,4) is on the red curve. We don't have a match.
The red curve shows the equation y = 4^x.
Keenan currently does a total of 8 pushups each day. He plans to increase the number of pushups he does each day by 2 pushups until he is doing a total of 30 pushups each day. Which equation can we use to determine x, the number of days that it will take Keenan to reach his goal? In an expression
Answer:
Number of push up = 8 + 2x
Step-by-step explanation:
Keenan can do 8 push ups each day. He plans to do 2 extra day until he is doing 30 push ups. Each day he does an additional 2 push up, on the first day he does 8 + 2 = 10 push up, on the second day he does 10 + 2 = 12 push ups. This can be represented by the expression:
Number of push up = 8 + 2x
where x is the number of days.
To do 30 push ups, we can calculate the number of days needed:
30 = 8 + 2x
2x = 30 - 8
2x = 22
x = 11
Answer:
8+2x its from khan academy
Step-by-step explanation:
give person above brainliest :)
2x-15=3(2x+3)
It’s multi step equations
Answer:
x = -6
Step-by-step explanation:
Hello!
2x - 15 = 3(2x + 3)
Distribute the 3
3 * 2x = 6x
3 * 3 = 9
2x - 15 = 6x + 9
Subtract 2x from both sides
-15 = 4x + 9
Subtract 9 from both sides
-24 = 4x
Divide both sides by 4
-6 = x
Hope this helps!
Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get
Answer:
3x(x+8)=0
x=0,-8
This is how to solve for x.
Choose all properties that were used to simplify the following problem:
(38 +677) + (-38)
[677 + 38) + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The properties 1‚ 2‚ 4‚ and 5. are used
The properties used to simplify problem are 1 , 2 and 4.
A problem which is simplified is given ; (38 +677) + (-38).
What are the correct options ?
How will you represent the associative properties of addition ?
Associative properties are represented by ; (A + B ) + C = A + ( B + C ).
As per the data given in question ;
Let's check which options are suitable.
( 38 + 677 ) + ( -38 ) = 38 + ( 677 - 38 )
(A + B ) + C = A + ( B + C )
So , this is the associative property.
677 + 0 = 677
A + 0 = A
So , this is the additive identity.
677 + [38 + (-38)]
Here ; 38 + ( -38 ) represents ;
A + (-A) = 0.
So , this is the additive inverse.
Thus , the properties used to simplify problem are 1 , 2 and 4.
To learn more about addition properties click here ;
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A watermelon weighs 6.45 kilograms. How many grams does the watermelon weigh?
Answer:
6450g
Step-by-step explanation:
1kg = 1000g
6.45kg = 6450
The watermelon weighs 6450 grams.
Given that a watermelon weighs 6.45 kilograms.
We need to convert its unit into grams.
To convert kilograms to grams, you need to multiply the weight in kilograms by 1000, as there are 1000 grams in 1 kilogram.
The watermelon weighs 6.45 kilograms, you can use the following formula to convert it to grams:
Weight in grams = Weight in kilograms × 1000
Let's do the math:
Weight in grams = 6.45 kilograms × 1000 = 6450 grams
So, the watermelon weighs 6450 grams.
Learn more about Unit conversion click;
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solve for v. 27= -v/2
Answer:
v = -54
Step-by-step explanation:
27= -v/2
Multiply each side by -2
27 *-2= -v/2 *-2
-54 = v
Answer:
-54
Step-by-step explanation:
[tex]27=\frac{-v}{2}[/tex] .... Equation to start with
[tex]27 x 2= \frac{-v}{2} x2[/tex] ..... Cancelling out the denominator and multiplying on the other side
[tex]54 = -v[/tex] .... Multipling
[tex]-54 =v[/tex] ..... Solving for v, not -v, so bring the negative over to the other side
Hope you understood:)
A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 2 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Answer:
16. 1 miles
Step-by-step explanation:
Using Pythagorean Theorem,
a^2 + b^2 = c^2
Since the road that goes from his home to work directly is c^2...
Plug in the rest of the numbers
16^2 + 2^2 = c^2
256 + 4 = c^2
260 = c^2
The reverse square of 260 is
16. 1 miles
Given triangle ABC is similar to triangle DEF , calculate the value of BC. Picture is below
Hello! :)
Answer:
[tex]\huge\boxed{BC = 6.4 }[/tex]
Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:
[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]
Let BC = x:
[tex]\frac{8}{15} = \frac{x}{12}[/tex]
Cross multiply:
[tex]8 * 12 = 15 * x[/tex]
[tex]96 = 15x[/tex]
[tex]x = 6.4[/tex]
Therefore, BC = 6.4 units.
Hope this helped you!
Classify the triangle.
B) isosceles
Step-by-step explanation:If the median to the base is perpendicular to the base =>
= > isosceles triangle
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be times the original volume.
Answer:
The answer is below
Step-by-step explanation:
From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch
The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³
While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25
The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³
Volume of the flask = The volume of the cylinder + The volume of the sphere = 2.36 + 47.71 = 50.07 in³
If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025
The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³
While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125
The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³
New Volume of the flask = The new volume of the cylinder + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³
The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125
The resulting volume would be 0.125 times the original volume
Answer:
50.07 and 8 times
Step-by-step explanation:
1) Calculate volume of each figure using according formulas.
You should get:
Sphere: 47.71in^3
Cylinder: 2.36in^3
Now let's add, and you should get 50.07.
2) Let's dilate the dimensions/flask by 2 (multiply by 2)
4.5 * 2 = 9
1 * 2 = 2
3 * 2 = 6
Now with these dimensions you should get:
Sphere: 381.7in^3
Cylinder: 18.85in^3
This should add up to 400.55in^3
Divide new by original. 400.55 / 50.07 = 8
So it is 8 times larger.
what’s the equation of line ?
y =__x + __
Answer:
y=3/4x-2
Step-by-step explanation:
two points from graph (0-2) and (8,4)
find slope m: y2-y1/x2-x1
m=4+2/8-0
m=6/8=3/4
x=0 then y=b=-2
y=3/4x-2
evaluate 5!+2!. Thank you!
Answer:
122
Step-by-step explanation:
5!=5 x 4 x 3 x 2 x 1 = 120
2!=2 x 1 = 2
120+2=122
I REALLY need help with these 3 questions plz!!!!
Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
how many are 4 raised to 4 ???
Answer:
256Step-by-step explanation:
The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;
[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]
Hence the expression 4 raised to 4 is equivalent to 256
Claire and Richard are both artists who use square canvases. Claire
uses the polynomial 50%? + 250 to decide how much to charge for her paintings
and Richard uses the polynomial 40x² + 350 to decide how much to charge for
his paintings. In each polynomial, x is the height of the painting in feet.
a. How much does Claire charge for a 20-foot-tall painting?
b. How much does Richard charge for a 15-foot-tall painting?
c. To the nearest tenth, for what height will both Claire and Richard charge
the same amount for a painting? Explain how to find the answer.
d. When both Claire and Richard charge the same amount for a painting,
how much does each charge?
Answer:
A. [tex]Claire = 20250[/tex]
B. [tex]Richard = 9350[/tex]
C. Height = 3.2 feet
D. Charges = $760
Step-by-step explanation:
Given
[tex]Claire = 50x^2 + 250[/tex]
[tex]Richard = 40x^2 + 350[/tex]
Solving (a): Claire's 20ft charges
In this case, x = 20
Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(20)^2 + 250[/tex]
[tex]Claire = 50(400) + 250[/tex]
[tex]Claire = 20000 + 250[/tex]
[tex]Claire = 20250[/tex]
Solving (b): Richard's 15ft charges
In this case, x = 15
Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(15)^2 + 350[/tex]
[tex]Richard = 40(225) + 350[/tex]
[tex]Richard = 9000 + 350[/tex]
[tex]Richard = 9350[/tex]
Solving (c): Height which they both charge the same;
This implies that
[tex]50x^2 + 250 = 40x^2 + 350[/tex]
Solving for x [Collect Like Terms\
[tex]50x^2 - 40x^2 = 350 - 250[/tex]
[tex]10x^2 = 100[/tex]
Divide both sides by 10
[tex]x^2 = 10[/tex]
Take square roots of both sides
[tex]x = \sqrt{10}[/tex]
[tex]x = 3.2ft[/tex] (Approximated)
Hence; Height = 3.2 feet
Solving (d): How much they charge when the charge the same amount.
Substitute 3.2 for x in any of the given equation
[tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(3.2)^2 + 250[/tex]
[tex]Claire = 50*10.24 + 250[/tex]
[tex]Claire = 512 + 250[/tex]
[tex]Claire = 762[/tex]
[tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(3.2)^2 + 350[/tex]
[tex]Richard = 40 * 10.24 + 350[/tex]
[tex]Richard = 409.6 + 350[/tex]
[tex]Richard = 759.6[/tex]
The reason for the difference is due to approximation
Hence, they both charge approximately 760
Find the vertex of the parabola.
f (x) = x squared minus 6 x + 13
a.
( 4, 0)
c.
( 3, 4)
b.
(0, 3)
d.
( 4, 3)
Answer:
The vertex is (3,4)
Step-by-step explanation:
f (x) = x^2 - 6 x + 13
Completing the square
-6/2 = -3 and squaring it = 9
= x^2 -6x +9 +4
= ( x-3) ^2 +4
The equation is now in vertex form
a( x-h) ^2 +k
where the vertex is ( h,k)
The vertex is (3,4)
Answer:
C on edge
Step-by-step explanation:
Simplify -1-7 +41. N
Answer:
-3
Step-by-step explanation:
-7+4=-3
The absolute value of -3 is 3
The negative sign in front of the absolute value bracket makes it -3
