Answer:
r = 15
Step-by-step explanation:
Volume of a sphere is given by
V = 4/3 pi r^3
4500 pi = 4/3 pi r^3
Divide each side by pi
4500 = 4/3 r^3
Multiply each side by 3/4
3/4 *4500 = 3/4 *4/3 r^3
3375 = r^3
Take the cube root of each side
(3375)^(1/3) = (r^3)^(1/3)
15 = r
what is x the missing side length in triangle DEF
Answer:
x = 9.75
Step-by-step explanation:
We know that Triangle ABC and DEF are congruent, therefore;
[tex]\frac{CB}{FE} = \frac{AB}{DE}[/tex]
[tex]\frac{12}{9 }=\frac{13}{x}[/tex]
=> 12*x = 9*13
=> 12x = 117
=> x = 117 / 12
=> x = 9.75
Hope this helps!
Need help ASAP please and thank you
Bob's car uses 6 L of gasoline per 100 km. How many litres of gas
will he use for a 400 km trip?
Astatine is a radioactive chemical element that was first produced at the University of California, Berkeley in 1940. The half-life of astatine is 8 hours.
Write an exponential function that models the mass in grams y remaining from a 560-gram sample after t hours.
When will approximately 198 grams remain in the sample?
How many grams will remain after 3 days? Express your answer as a decimal rounded to the nearest hundredth.
Answer:
Approximately 198 grams will remain in the sample after 12 hours.
Approximately 1.09 grams will remain after three days.
Step-by-step explanation:
We can write an exponential function to model the situation. The exponential model for decay is:
[tex]\displaystyle A=A_0(r)^{t/h}[/tex]
Where A₀ is the initial amount, r is the rate of decay, t is the time that has passed (in this case in hours), and h is the half-life.
Since the half-life of the chemical, astatine, is 8 hours, h = 8 and r = 0.5. The initial amount is 560 grams. Hence:
[tex]\displaystyle A=560\left(\frac{1}{2}\right)^{t/8}[/tex]
To find when the sample will have approximately 198 grams, remaining, let A = 198 and solve for t:
[tex]198=560(0.5)^{t/8}[/tex]
Solve for t:
[tex]\displaystyle \frac{198}{560}=\frac{99}{280}=\left(\frac{1}{2}\right)^{t/8}[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln\frac{99}{280}=\ln\left(\left(\frac{1}{2}\right)^{t/8}\right)[/tex]
Using logarithm properties:
[tex]\displaystyle \frac{t}{8}\ln\frac{1}{2}=\ln\frac{99}{280}[/tex]
So:
[tex]\displaystyle t=\frac{8\ln(99/280)}{\ln(0.5)}=11.9994...\approx 12\text{ hours}[/tex]
Approximately 198 grams remain in the sample after 12 hours.
Three days is equivalent to 72 hours. Hence, t = 72:
[tex]\displaystyle A(72)=560\left(\frac{1}{2}\right)^{72/8}=1.09375\approx 1.09\text{ grams}[/tex]
Approximately 1.09 grams of astatine will remain after three days.
A circular plate has circumference 27 inches. What is the area of this plate? Use 3. 14 for a The area of this plate is about square inches (Round the final answer to the nearest whole number as needed Round all intermediate values to the nearest thousandth as needed)
Answer:
58.01 in^2
Step-by-step explanation:
Which of the following expressions is correctly written in scientific notation?
Answer:
The 3rd choice.
Step-by-step explanation:
The third choice has what it takes to be a scientific notation.
I need a very detailed in depth explanation of laws of Sine and Cosine. (With examples, Law rules etc.)
Answer:
A law stating that the square of a side of a plane triangle is equal to the sum of the squares of the other two sides minus twice the product of the other sides multiplied by the cosine of the angle between them.As we learned, sine is one of the main trigonometric functions and is defined as the ratio of the side of the angle opposite the angle divided by the hypotenuse. It's important for finding distances or height and can also be used to find angle measures, which are measured in radians.Law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle. ... If ABC is a triangle, then as per the statement of cosine law, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.RULE OF LAW Defined
The rule of law is a principle of governance in which all persons, institutions and entities, public and private, including the State itself, are accountable to laws that are publicly promulgated, equally enforced and independently adjudicated, and which are consistent with international human rights norms and standards. It requires, as well, measures to ensure adherence to the principles of supremacy of law, equality before the law, accountability to the law, fairness in the application of the law, separation of powers, participation in decision-making, legal certainty, avoidance of arbitrariness and procedural and legal transparency.A rule of law framework that includes the following:
Constitution or its equivalent, as the highest law of the land;A clear and consistent legal framework, and implementation thereof;Strong institutions of justice, governance, security and human rights that are well structured, financed, trained and equipped;Transitional justice processes and mechanisms; A public and civil society that contributes to strengthening the rule of law and holding public officials and institutions accountable.[tex]\color{yellow}{}[/tex]
Given v = u + 5t; Find v when u= -15 and t=4
v = u + 5t
v = -15 + 5(4)
v = -15 + 20
v = 5
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
[tex]v = u + 5t[/tex]
Given,
[tex]u = - 15 \\ t = 4 \\ v = \: ?[/tex]
To find the value of v, we must substitute the values of u & t in the equation ⇻ v = u + 5t.
[tex]v = u + 5t \\ v = ( - 15) + 5(4) \\ v = - 15 + 20 \\ v = 5[/tex]
✐ The value of v is 5.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
What is the solution set for -2n – 2 > 2?
Answer:
n < -2
Step-by-step explanation:
-2n – 2 > 2
-2n (– 2 + 2) > 2 + 2
-2n > 4
-2n/-2 > 4/-2
n < -2
[please help]What are the values of x and y
Answer:
536363663737272727 4th july and im present
A sighting is made of a sailboat from a lighthouse. If the lighthouse is 123.5 m above
the level of the water, how far is the sailboat from the shore if the angle of depression
is 18°?
△ABC is congruent to △DEF. What is the value of x? Explain how you determined your answer.
Answer:
3
Step-by-step explanation:
It is 3 because fi you multiply 5 by 3 you get 15, and if you multiply 10 by 3 you get 30. Subtract 30 by 6 and get 24. And finally, if you multiply 2 by 3 it gives you 9. 9+12= 21.
Harold, the handyman, builds two similar sheds for a farm. The smaller shed is 6 feet tall and weighs 500 pounds. If it takes three times as much paint to cover the larger shed, approximately how tall is the larger shed and approximately how much does it weigh?
Answer:
18 ft
1500 pounds
Step-by-step explanation:
6 x 3 = 1 8
500 x 3 = 1500
I'm tired :( too many missing assignments. I've been working all day
Answer:
aw its fine, take a break and get some fresh air
Answer:
oof its ok u got this
drink some coffee or take a quick break or finish everything tomorrow
Step-by-step explanation:
The original price of a computer was reduced by $250.
If p= the computer’s original price in dollars, which algebraic expression represents the reduced price?
a. 250p
b. 250 + p
c. p - 250
d. 250 - p
Answer:
the awnser is c. p-250 + p
What is the equation of the line?
Answer:
y = -7
Step-by-step explanation:
This is a horizontal line
The y value does not change
It is of the form y=
y = -7
Answer:
y = -7
Step-by-step explanation:
A horizontal line has an equation of the form
y = k
where k is the y-coordinate of every point on the line.
We see that every point on this line has y-coordinate -7, so the equation is
y = -7
Mrs. Lia has 11 pounds of modeling clay. She divides the clay into 1 2 - pound blocks. If Mrs. Lia sets aside 7 of the blocks and gives the rest to the students in her art class, how many 1 2 - pound blocks of clay does Mrs. Lia give to her class?
Answer:
Assuming she is dividing into 1/2 lb blocks.
15 of the 1/2 lb are given to the class.
Step-by-step explanation:
She can make 22 of the 1/2 lb blocks out of 11 lbs. If she sets aside 7, then 22-7=15. She has 15 of the 1/2lb blocks left to give to the class.
¿Cuál es la energía cinética de un objeto de masa igual a 30 kg que se desplaza a una velocidad de 25 m/s?
Answer:
9,375 J
Step-by-step explanation:
According to the scenario, calculation of the given data are as follows,
Mass (m) = 30 kg
Moving speed or Velocity (v) = 25 m/s
So, we can calculate kinetic energy by using following formula,
Kinetic energy = (1/2)m[tex]v^{2}[/tex]
By putting the value in the formula, we get
Kinetic energy = (1/2) 30 × [tex]25^{2}[/tex]
= 15 × 625
= 9,375 J
Can someone please help me out
Answer:
x = 8, A = 182 units²
Step-by-step explanation:
The perimeter P of a rectangle is calculated as
P = 2l + 2b ( l is the length and b the breadth )
Given P = 66, then
2(7) + 2(3x + 2) = 66 ← distribute and simplify left side
14 + 6x + 4 = 66
6x + 18 = 66 ( subtract 18 from both sides )
6x = 48 ( divide both sides by 6 )
x = 8
Then
3x + 2 = 3(8) + 2 = 24 + 2 = 26, so
A = 7 × 26 = 182 units²
value of x? with work
Given:
The figure of a circle.
Measure of arc = 176°
Measure of angle = (27x+7)°
To find:
The value of x.
Solution:
We know that the measure of central angle is equal to measure corresponding intercepted arc and the measure of central angle is twice of the measure of subtended angle on that arc.
So, the measure of arc is twice of measure of subtended angle on that arc.
[tex]m(arc FH)=2\times m\angle FGH[/tex]
[tex]176^\circ=2\times (27x+7)^\circ[/tex]
[tex]\dfrac{176^\circ}{2}=(27x+7)^\circ[/tex]
[tex]88^\circ=(27x+7)^\circ[/tex]
Now,
[tex]88=27x+7[/tex]
[tex]88-7=27x[/tex]
[tex]\dfrac{81}{27}=x[/tex]
[tex]3=x[/tex]
Therefore, the value of x is 3.
The level of the tide in a harbor changes from 813 8 1 3 feet to 256 2 5 6 feet above sea level over a period of 212 2 1 2 hours. What is the change in tide level per hour over this period of time? Feet per hour
Answer:
-2.63 ft./hour
Step-by-step explanation:
The level of the tide in a harbor changes from 813 feet to 256 feet above sea level over a period of 212 hours. What is the change in tide level per hour over this period of time?
Solution:
The initial tide level was 813 feet while the final tide level was 256 feet above sea level within a period of 212 hours.
The change in tide level per hour is the ratio of the change in tide level to the period taken. Hence:
Change in tide level per hour = (Final tide level - initial tide level) / time taken
Change in tide level per hour = (256 ft. - 813 ft.) / 212 hours
Change in tide level per hour = -2.63 ft./hour
A paint shop mixes colours to the customers taste. To make 1 litter of base white, 2 milliliters of B and 0,25 milliliter of C. how much of each component will he use for mixture containing 750 litres of base white? write each answer in litres.
Answer:
Mixing quantity of B = 1.5 liter
Mixing quantity of C = 0.1875 liter
Step-by-step explanation:
Given:
Mixing ratio;
1 liter white base , 2 milliliter of B , 0.25 milliliter of C
Find:
Mixing quantity in 750 liters
Computation:
2 milliliter of B = 0.002 L
0.25 milliliter of C = 0.00025 L
Mixing quantity of B = 750 x 0.002
Mixing quantity of B = 1.5 liter
Mixing quantity of C = 750 x 0.00025
Mixing quantity of C = 0.1875 liter
Which expression is equivalent to
НЕ
оооо
Answer:
q^12
Step-by-step explanation:
q^6^2
We know that a^b^c = a^(b*c)
q^6^2 = q^(6*2) = q^12
Which ratio is equivalent to the ratio 32:40?
A 16 to 20
B 30:16
C 16 to 30
D 20:16
Answer:
A, 16 to 20
Step-by-step explanation:
32 / 2 = 16
40 / 2 = 20
How many quarts are in 583.7 liters? Round to the nearest tenth.
Answer:
616.8
Step-by-step explanation:
look it up
Answer:
616.8 quarts
Step-by-step explanation:
Find the information in the diagram can you prove FDG and FDE
Given:
A diagram of two triangles.
To find:
Whether the triangles are congruent or not.
Solution:
In triangles DEF and DGF,
[tex]m\angle EDF\cong m\angle GDF[/tex] (Given)
[tex]\overline{DF}\cong \overline{DF}[/tex] (Reflexive property)
[tex]m\angle DFE\cong m\angle DFG[/tex] (Given)
Two corresponding angles and their included angles are congruent, so the triangles are congruent by ASA postulate.
[tex]\Delta DE F\cong \Delta DGF[/tex] (ASA congruence postulate)
Therefore, yes the triangles are congruent by ASA. Hence the correct option is A.
Answer: I’m going towards no bc they all are aaa and there no aaa in geometry
Step-by-step explanation:
Express as a trinomial
(2x - 6)(3x - 2)
Answer:
[tex]6 {x}^{2} - 22x + 12 [/tex]Step-by-step explanation:
(2x - 6)(3x - 2)
= 2x(3x - 2) - 6(3x - 2)
[tex] = 6 {x}^{2} - 4x - 18x + 12[/tex]
[tex] = 6 {x}^{2} - 22x + 12 \: (ans)[/tex]
Two positive integers are 3 units apart on a number line. Their product is 108.
Which equation can be used to solve for m, the greater integer?
a). m(m – 3) = 108
b.) m(m + 3) = 108
c.) (m + 3)(m – 3) = 108
d.) (m – 12)(m – 9) = 108
Answer:
d) the numbers are 9 and 12
Step-by-step explanation:
set each factor equal to 108:
m-12=108
m = 120
*************
m-9=108
m=117
*************
120 and 117 are 3 units apart
****************
9 x 12 = 108
If f(x) = 4x-3 and g(x) = x+4, find (f-g)(x).
A. 5x-1
B. 3x-7
C. 5x-7
D. 7-3x
Answer:
B. 3x - 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 4x - 3
g(x) = x + 4
(f - g)(x) is f(x) - g(x)
Step 2: Find
Substitute in functions: (f - g)(x) = 4x - 3 - (x + 4)[Distributive Property] Distribute negative: (f - g)(x) = 4x - 3 - x - 4[Subtraction] Combine like terms (x): (f - g)(x) = 3x - 3 - 4[Subtraction] Combine like terms: (f - g)(x) = 3x - 7what are the factors of the expression below? 2bx+4by-3ax-6ay
Answer:
Step-by-step explanation:
2bx + 4by -3ax -6ay
= 2b (x +2y) - 3a (x +2y)
= (x +2y) (2b-3a)
