Answer:
[tex]\huge\boxed{2400}[/tex]
Useful Information:
The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]
Step-by-step explanation:
To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.
The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.
The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]
To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.
1) Divide 5 by 100.
[tex]\frac{5}{100}=0.05[/tex]
2) Add 1 to 0.05.
[tex]1+0.05=1.05[/tex]
3) Substitute the values into the formula.
[tex]initial.amount*1.05^{3}=2778.30[/tex]
4) Divide 2778.30 by [tex]1.05^3[/tex].
[tex]\frac{2778.30}{1.05^3}=2400[/tex]
* GEOMETRY
please help me show the work for 9, 10, and 11!!
9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm
10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm
11) Based on Question 9, MN=13.5 cm
Use the law of cosines to find each missing side. Round to the nearest tenth
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
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Decrease 80g by 12.5%
complete each
1. 570 mL = _______________ L
2. 623 cm3 = _______________ m3
3. 38 gal. = _______________c
4. 585mL = ________________tbsp
5. 20 fl. oz. = ________________ tsp
6. 12 hrs =________________ min
Answer:
1. 570 mL = 0.57 L
2. 623 cm3 = 0.000623 m3
3. 38 gal. = 608 cups
4. 585mL = 39.5624 tbsp
5. 20 fl. oz. = 120 tsp
6. 12 hrs = 720 min
Step-by-step explanation:
1. 570 mL to L
divide the volume value by 1000, 570 / 1000 = 0.57
2. 623 cm3 to m3
divide the volume value by 623/10^6 = 0.000623
3. 38 gal. to c
1 gallon is 16 cups,
multiply the volume value by 16, 38 x 16 = 608c
4. 585mL to tbsp
for an approximate result, divide the volume value by 14.787
14.787 x 585 = 39.5624
5. 20 fl. oz. to tsp
multiply the volume value by 6, 20 x 6 = 120
6. 12 hrs to min
1 hour is 60 minutes
multiply the time value by 60
12 x 60 = 720
Suppose you flip two coins. What is the probability of getting at most one heads? give your answer as a reduced fraction.
The probability of getting at most one heads is 1/2
How to determine the probability?Let H represents Head and T represents Tail.
The sample space of two coin is:
S=(H,T),(T,T),(T,H),(H,H).
In the above sample, we have:
At most one head = 2
Total = 2
The required probability is then calculated as:
P = 2/4
Simplify
P = 1/2
Hence, the probability of getting at most one heads is 1/2
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find sizes of unknown angles
Answer:
a=75
b=70
c=110
d=105
e=110
f=105
Step-by-step explanation:
divide: 8x^3 y^5 / 4x^2 y^3
[tex]2 {x}^{5} {y}^{8} [/tex]
Step-by-step explanation:
yes
Simplify cubed 5 -10/27
The correct answer for the given expression is 99.22.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
The expression will be solved as:-
E = [tex]({5 -\dfrac{10}{27}})^3[/tex]
E = [tex](\dfrac{135-10}{27})^3[/tex]
E =[tex]\dfrac{125}{27}^3[/tex]
E = 99.22
Therefore the correct answer for the given expression is 99.22.
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What is the measure of ∠z
Answer:
155°
Step-by-step explanation:
z = 65° + y
y is a right angle
=> y = 90°
=> z = 65° + 90° = 155°
Evaluate the expression for the given values of the variables:
2a³-7b²+ 3c - (d + e) a = 3, b = 2, c = 4, d = 11, and e = 7
Answer:
yes
Step-by-step explanation:
it's hard but you'll figure it out so don't worry
Sofia is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Sofia's test score (out of 100) if she got 8 questions wrong? What would be her score if she got xx questions wrong?
Score with 8 questions wrong:
Score with xx questions wrong:
need answer quickly
Answer:
60 points
100 - 5x
Step-by-step explanation:
If she got 8 questions wrong she missed (8 * 5) points or 40 points. This means she only got 60 points
This can be further generalized by simply subtracting the amount of questions someone got wrong by 5 from the total available points of 100
100 - 5x
The basic equation for calculating compound interest is A = P(1 + nt.
If $1,200 is invested at an interest rate of 8% per year, compounded quarterly, how much will the
investment be worth at the end of 10 years?
Show your work!
The amount of the investment at the end of the 10 years period if compounded quarterly is $2,649.6.
Compound interestPrincipal, P = $1200Interest rate, r = 8% = 0.08Time, t = 10Number of period, n = 4A = P(1 + r/n)^nt
= 1200(1 + 0.08/4)^(4×10)
= 1200(1 + 0.02)^40
= 1200(1.02)^40
= 1200(2.208)
= $2,649.6
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2(2x – 1) + 7 < 13 or –2x + 5≤-10
Answer:
2, 7.5
Step-by-step explanation:
2(2x - 1) + 7 < 13
4x - 2 + 7 < 1
4x + 5 < 13
4x < 8
x < 2
-2x + 5 ≤ -10
-2x ≤ -10 - 5
-2x ≤ -15
x ≤ -15 / -2
x ≤ 7.5
help______________________________________
The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.
Meaning of Simultaneous Equation.A simultaneous equation can be defined as an equation that possesses two unknowns and one constant.
The solution to the problem can only be gotten by solving it side by side with another equation of the same format.
In conclusion, The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.
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What is the missing number below in the solution to 968 divided by 10
Answer: 484/5
Step-by-step explanation:
For this word problem, it seems confusing with the wording but the equation would just be:
968÷10=x
solving for x, we get 484/5.
after 1 year, 80% of the initial amount of a radioactive substance remains. what is the half-life of the substance? half-life is
If a radioactive substance remains 80% of the initial amount then the half life of the radioactive substance is 2.5 years.
Given 80% of the initial amount of a radioactive substance remains.
If after 1 year the value or weight of the radioactive substance remains 80% means the rate of disappearing is 20% per annum.
If we clearly observe then it is forming a geometric progression and the rate is 80%.
Geometric progression will be if we assume the initial quantity be 100
is:
100,80,64,.........
we have to calculate the value of years in the value of term is 0.
the value of nth term of a geometric progression is [tex]ar^{n-1}[/tex]
so,
r is 0.8
100*[tex]0.8^{n-1}[/tex]=0
[tex]0.8^{n-1}[/tex]=0
if we calculate this we will find n-1=11
n=12
So the full life of radioactive substance is 12 and the half life will be 6 years.
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\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Answer:
5
Step-by-step explanation:
Given expression:
[tex]\dfrac{6^{n+2}-6^n}{6^{n+1}+6^n}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies \dfrac{6^n6^2-6^n}{6^n6^1+6^n}[/tex]
Factor:
[tex]\implies \dfrac{6^n(6^2-1)}{6^n(6^1+1)}[/tex]
Cancel [tex]6^n[/tex] :
[tex]\implies \dfrac{(6^2-1)}{(6^1+1)}[/tex]
Simplify:
[tex]\implies \dfrac{36-1}{6+1}[/tex]
[tex]\implies \dfrac{35}{7}[/tex]
[tex]\implies 5[/tex]
Three years ago, dedrick's age was a third of francisca's age. in 13 years, francisca's age will be twice dedrick's age. how old are they now?
Answer:
Step-by-step explanation:
According to the first statement, "Three years ago, Dedrick's age was a third of Francisca's age":
D - 3 = (1/3) * (F - 3)
According to the second statement, "In 13 years, Francisca's age will be twice Dedrick's age":
F + 13 = 2 * (D + 13)
Now, we have a system of two equations. We can solve these equations to find their current ages.
Step 1: Solve the first equation for D in terms of F:
D - 3 = (1/3) * (F - 3)
3D - 9 = F - 3
3D = F + 6
D = (F + 6) / 3
Step 2: Substitute the expression for D into the second equation:
F + 13 = 2 * ((F + 6) / 3 + 13)
Step 3: Solve for F:
F + 13 = 2 * ((F + 6) / 3 + 13)
F + 13 = 2 * (F + 6 + 39)
F + 13 = 2 * (F + 45)
F + 13 = 2F + 90
F - 2F = 90 - 13
-F = 77
F = -77
Step 4: Find D using the expression we found earlier:
D = (F + 6) / 3
D = (-77 + 6) / 3
D = -71 / 3
Now, we have found their ages, but we encounter a problem. Both Francisca and Dedrick's ages are coming out as negative, which is not meaningful in this context. It suggests that there might be an error in the initial information provided or in the equations derived from it.
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please help
(a) Is it safe to place the plant box on a window ledge that can support a maximum weight of 2400 grams? Explain why or why not.
(b) Would the density of the soil change if the plant box was only half full? Explain.
Answers:
(a) The ledge can support the plant box. It is safe to put it there.
(b) No the density would not change.
=========================================================
Explanation for part (a)
We'll need the volume of the cube.
volume = side*side*side
volume = 13*13*13
volume = 2,197
Or you could do
volume = (side)^3
volume = (13)^3
volume = 2,197
The volume of the cube is 2,197 cubic cm. Multiply this with the density to determine its weight.
1.33*2197 = 2,922.01
The soil weighs 2,922.01 grams which is below the 2400 gram weight limit. Therefore, the ledge can support the planter.
------------------------------------
Explanation for part (b)
The weight would go down if you only put in half the soil, but the density would not change regardless of how much soil is in there. Why doesn't the density change? Because the density is the amount of stuff per unit volume. The density tells us how packed in a material is. We can scale the amount of material up or down, and retain the same density.
This is based off physics concepts which are bit beyond the scope of this math course, but different materials have different densities. It's common to use a reference table to look up densities of various materials. For instance, ice is less dense than water. This is why ice floats rather than sinks. As another example, gold is more dense than iron. So 1 cubic unit of gold will weigh more compared to 1 cubic unit of iron.
How many hours did theo and kade do separately?
Solve (x - 2 < 5) ∩ (x + 7 > 6).
1. Ø
2. {x | x < -1 x < 7}
3. {x | -1 < x < 7}
Answer:
c2
Step-by-step explanation:
Solve using a proportion.
Mario spends 8 hours each week practicing soccer. How many hours will Mario spend on soccer practice after 21 weeks?
A. 168 hours
B. 186 hours
C. 160 hours
D. 29 hours
There are eight shirts in your closet, three blue, two are black, one is green, and two are white. You randomly select one to wear on Monday and then a different one on Tuesday. What is the probability that you wear blue shirts on both days?
(please write an explanation)
The probability of wearing blue shirts on both days is 3/28.
What is probability?Probability is the measure of the likelihood of an occurrence.
Given:
8 shirts are available out of which 3 are blue, 1 is green and 2 are white.
P(blue on Monday) = 3/8
Now, 7 shirts are left to wear on Tuesday
P(blue on Tuesday) =2/7
So,
the probability of wearing blue shirts on both days = 3/8 * 2/7 = 3/28
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enlist any five common social rules all kinds of society
Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.
Step-by-step explanation:trust me
HELPPPPP ITS URGENTTTTT
click on the photo
Answer:
x=67.4
Step-by-step explanation:
well sin30:1/2
So y is not 30 since 5/13 doesn’t equal 1/2
So it’s either the the third or fourth option
And x>y
So option 4 is correct
What is the area of rectangle ABCD?
coordinate plane with rectangle ABCD at A 0 comma 1, B 0 comma 4, C 4 comma 4, and D 4 comma 1
12 square units
14 square units
16 square units
18 square units
The area of a 2D form is the amount of space within its perimeter. The area of the rectangle is 12 units². Thus, the correct option is A.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
As per the given information, the graph of the rectangle can be made as shown below. It can be observed from the graph that the length of the rectangle and width of the rectangle are 4 units and 3 units, respectively. Therefore, the area of the rectangle is,
Area = 4 units × 3 units = 12 units²
Hence, the area of the rectangle is 12 units². Thus, the correct option is A.
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perimeter =
help me please thank u :)
Answer:
[tex]\fbox {Perimeter = 37.92}[/tex]
Step-by-step explanation:
Finding the missing side :
⇒ Take the tan value of the listed angle
⇒ tan 60° = √3 = 6/x
⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46
Solving :
⇒ Perimeter = 10 + 2(6 + 3.46)
⇒ Perimeter = 10 + 2(9.46)
⇒ Perimeter = 19 + 18.92
⇒ Perimeter = 37.92
The slope-intercept form of the equation of a line that passes through point (-2,-13) is y=5x-3. What is the point-slope form of the equation for this line?
Answer:
y + 13 = 5(x + 2)
Step-by-step explanation:
Point - slope form of equation:[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
Slope intercept of the line : y =5x - 3
Comparing with y = mx +b , m =slope = 5
m = 5 and Point (-2 ,-13)
y - [-13] = 5(x - [-2])
y + 13 = 5(x + 2)
Which points would you find on the graph for |x| +1 < 3?
-1
-3
0
1
The points would you find on the graph for |x| +1 < 3 are -1, 0 and 1
How to determine the points?The inequality is given as:
|x| + 1 < 3
Subtract 1 from both sides
|x| < 2
This means that the absolute value of x is less than 2
From the list of options, the true values are -1, 0 and 1.
Because their absolute values are less than 2
Hence, the points would you find on the graph for |x| +1 < 3 are -1, 0 and 1
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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³
How to find volume?The volume of the air space surrounding the cone inside the cylinder is as follows:
volume of the air space = volume of cylinder - volume of a cone
volume of cylinder = πr²h
volume of cylinder = π16 × 5²
volume of cylinder = 400π
volume of the cone = 1 / 3 πr²h
volume of the cone = 1 / 3 × π × 12 × 4²
volume of the cone = 64π
Therefore,
volume of the air space = 400π - 64π
volume of the air space = 336π
volume of the air space = 1055.04 cm³
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