After 100 years:
Replace t by 100:
A (t) = 523 (1/2)^t/30
A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams
The initial amount of the sample is 523
can you tell me if my answer is correct
Answer:
(a)Vertex
(c)3 seconds
Explanation:
Part A
The maximum point on a parabola is called the Vertex.
Part C
To find out how much the plain was in the air, find the values of t at which the height, h=0.
Next, subtract the second value of t from the first value.
[tex]h=-16t^2+32t+48[/tex]First, set h=0:
[tex]\begin{gathered} h=-16t^2+32t+48=0 \\ -16t^2+32t+48=0 \end{gathered}[/tex]Factorize:
[tex]\begin{gathered} -16(t^2-2t-3)=0 \\ t^2-2t-3=0 \\ t^2-3t+t-3=0 \\ t(t-3)+1(t-3)=0 \\ (t+1)(t-3)=0 \\ t+1=0\text{ or }t-3=0 \\ t=-1\text{ or }t=3 \end{gathered}[/tex]Therefore, the plane hits the ground after 3 seconds.
a 17 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground?
The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.
From the question, we have the following;
Hypotenuse=17 foot
Height(y)=13 feet
Base(x)=(17^2-13^2)^1/2
=120^1/2 or sqrt(120)
The ladder against the wall is a right angle triangle, so we have:
x^2+y^2=17^2
x^2+y^2=289
Top slips down at 2ft/s
dy/dt=-2 ft/s, where height (y)=13ft
The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt
Now, we take the derivative with respect to time:
=x^2+y^2=17^2
=2x(dx/dt)+2y(dy/dt)=0
Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s
2(sqrt(120))(dx/dt)+2(13)(-2)=0
2(sqrt(120))(dx/dt)-52=0
We solve for dx/dt:
dx/dt=52/(2sqrt(120))
dx/dt=52/21.9089
dx/dt=2.373 ft/s
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Which number line represents the solutions to |x + 4| = 2?
Answer:
The first option is correct :)
Step-by-step explanation:
x=-6, x=-2
|x+4|=2
x+4=2, x=-2
x+4=-2, x=-6
:] (Tell me if this is incorrect!)
(brainliest would help a lot)
Answer: the first one (-2,-6)
Step-by-step explanation:
|x+4| = 2
subtract 4 from both sides and you get -2
|x+4| = -2
subtract 4 from both sides and you get -6
If you want to check your answers, plug it into the original equation
A bag contains 2 white balls, 6 orange balls and 2 red balls. If a ball is drawn, find the probability that it is a white or red ball.
First, let's calculate the total amount of balls:
[tex]2+6+2=10[/tex]Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.
So the probability is:
[tex]p=\frac{red\text{ or }white}{total}=\frac{4}{10}=\frac{2}{5}[/tex]Correct option: A
in 15 of the 100 trials of the simulation none of the 10 passengers chosen was seated in first class. does this result provide convincing evidence that the tsa officers did not carrry out a truly random samplw?
The result provides convincing evidence that the tsa officers did not carrry out a truly random sample.
What is a random sample?A simple random sample is a subset of a statistical population in which each member has an equal chance of being selected.
In statistics, a simple random sample is a subset of individuals picked at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.
In this case, it's important to note that the fact that all the people chosen were first class members means that it was bias and not a random sampling.
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Solve for u.u^2-u-12=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution."
we have the quadratic equation
[tex]u^2-u-12=0[/tex]we have that
a=1
b=-1
c=-12
Applying the formula to solve a quadratic equation
[tex]u=\frac{-(-1)\pm\sqrt{-1^2-4(1)(-12)}}{2(1)}[/tex][tex]u=\frac{1\pm7}{2}[/tex]The values of u are
u=4 and u=-3
therefore
The answer is
u=-3,4f(x)=2x^3+ax^2-24x+1 has a local maximum at x=-4. find a
Step-by-step explanation:
ax2+2x3−24x+1=y
Step 2: Add -2x^3 to both sides.
ax2+2x3−24x+1+−2x3=y+−2x3
ax2−24x+1=−2x3+y
Step 3: Add 24x to both sides.
ax2−24x+1+24x=−2x3+y+24x
ax2+1=−2x3+24x+y
Step 4: Add -1 to both sides.
ax2+1+−1=−2x3+24x+y+−1
ax2=−2x3+24x+y−1
Step 5: Divide both sides by x^2.
ax2
x2
=
−2x3+24x+y−1
x2
a=
−2x3+24x+y−1
x2
Answer:
a=
−2x3+24x+y−1
x2
what is ( -8.7) times (-10)?
Answer:
87
Step-by-step explanation:
Answer:87
Step-by-step explanation:
please help me ! please
Answer:
[tex] \sf {\large{4\pi }}[/tex]
Step-by-step explanation:
Circumference of a circle ⭕ = [tex] 2 \pi r [/tex]
Where,
r = d/2
d means diameter
r = 4/2 = 2
So, substitute to equation C = 2πr
C = 2πr
C = (2r)π
C = (2•2)π
C = 4π
WILL GIVE BRAINLIEST
Answer:
1. Hyperbole
2. Center: (0,0)
3. Vertices: (-3, 0), (3, 0)
4. Foci: (-6, 0), (6, 0)
5. Asymptotes: y = [tex]\frac{\sqrt{18}}{3} }[/tex]x and y = [tex]-\frac{\sqrt{18}}{3} }[/tex]x
Step-by-step explanation:
At a local print shop, 10 copies can be made for $4. At this rate, how much would it cost to make 75 copies?
Answer:
$30
Step-by-step explanation:
10 x 7 = 70
7 x 4 = 28
Since it's $4 to make 10 copies, it'll be $2 to make 5
28 + 2 = 30
$30 for 75 copies (a bad deal honestly)
Please mark Brainliest!!
Answer:
$30 dollars for 75 copies
Step-by-step explanation:
What we know:
$4 for every 10 copies.
How to figure out:
Divide 4/10 = .4 .4 is the cost per copy.
We do this because if it is 4 dollars per 10 copies, then we have to figure out the cost per copy. So we have to do how many dollars goes into each copy.
Now we know the cost of one copy we can multiply the amount of copies we need by the price of one.
75 x 0.4 = 30 30 is the price of 75 copies.
Which number is the greatest?
-8
-10
-7
Answer:
-7
Step-by-step explanation:
-7 is the greatest because it is closer to 0 on the number line.
3. Determine the percent of each quantity.
a. 7% of 80
c. 12% of 320
b. 15% of 55
d. 8% of 300
Answer:
a. 5.6
b. 38.4
c. 8.25
d. 24
Step-by-step explanation:
The equation of the line that is perpendicular to the line 5x + 6y = 18 and passes through the point (10,7)
Answer:
y = ( 6 / 5 )x - 5;
Step-by-step explanation:
Perpendicular Line Theoryy = - ( 1 / m )x + c;
AlgebraConvert dual intercept to standard form.
5x + 6y = 18;
Subtract 5x from both sides.
6y = - 5x + 18;
Divide both sides by 6.
y = ( - 5x + 18 ) / 6;
y = ( - 5x / 6 ) + ( 18 / 6 );
y = ( - 5 / 6 )x + 3;
Get the perpendicular line.
y = ( 6 / 5 )x + c;
Substitute the point.
7 = ( 6 / 5 )( 10 ) + c;
7 = 12 + c;
Subtract 12 from both sides.
- 5 = c;
c = - 5;
y = ( 6 / 5 )x - 5;
Which ordered pair would form a proportional relationship with the point graphed below?
Answer:
(5, 20)
Step-by-step explanation:
(5, 20) is the only ordered pair which falls on the line
PLS HELP WITH 15. (GIVING EXTRA POINTS)
Answer:
[tex]4^{6}[/tex] or 4096
Step-by-step explanation:
When the bases are the same, you add the exponents.
Answer:
Step-by-step explanation:
[tex]\boxed{\bf\\a^n*a^m=a^{n+m}}[/tex]
[tex]\displaystyle(4)^2\cdot(4)^4\cdot(4)^0=(4)^{2+4+0}=4^6=4096[/tex]
A metal pole to hang banners and advertisements is attached to a brick
building to form a right angle. A diagonal brace is placed 5 feet below the
pole to give support. What is the length in feet of the pole?
13 ft
5 ft
The length in feet of the pole is 13 ft.
What is Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.
Use the Pythagorean relationship:
c²= a² + b²
= 5² + 12²
= 25 + 144
= 169
c = 13
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You have 8 times as many dimes as nickels. You have 18 dimes and nickels altogether how much money do you have in all?
For the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
As given in the question,
Let x be the number of dimes
Then number of nickels are 8x.
As per given condition,
Total number of dimes and nickels = 18
⇒ x + 8x = 18
⇒ 9x = 18
⇒ x= 2
Number of dimes =2
Number of nickels = 8(2)
= 16
Conversion:
1 dime = 0.10$
1 nickel = 0.05$
Total amount of money in dollars
= 2 ×(0.10) + 16× (0.05)
= 0.20 + 0.80
= 1.00
Therefore, for the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
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The product of 3x^5 and 2x^4 is
Options:
1) 5x^9
2) 5x^20
3) 6x^9
4)6x^20
Answer:
6x^9
Step-by-step explanation:
Hello!
Multiply the like terms:
3 and 2x^5 and x^4Multiply3x^5 * 2x^43*2*x^5*x^46*x^(5 + 4)6x^9The correct answer is the 3rd option, 6x^9.
Renting a roller rink for your birthday costs $300 plus $9 per person. The total charge for your party was $534. Translate this information into an equation using x to represent the number of guests at your party.
The equation using x to represent the number of guests at your party is 300 + 9x = 534
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let x represent the number of guests at your party.
Here, renting a roller rink for your birthday costs $300 plus $9 per person. This will be:
300 + 9x = 534
Collect like terms
9x = 534 - 300
9x = 234
Divide
x = 234 / 9
x = 26
The number of guest is 26.
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We can desribe 15x-10 as an expression.
We would describe 6x-2<35 as an
We can describe 15x-10 as an expression.
We would describe 6x-2<35 as an inequality.
What is an inequality?In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.
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The diagram shows a quadrilateral ABCD with each of its sides extended.
AB = AD
Show that ABCD is a kite. Give a reason for each stage of your working
(The diagram is attached)
Thanks, by neve124
It is to be noted that by the proof given below, the attached shape ABCD is a kite.
What is a kite in Euclidean Geometry?A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equivalent angles and two pairs of adjacent equal-length sides as a result of its symmetry.
The proof is as follows:
AB = AD [Given]
∠ADC = 115° [Angles on a Straight line]
That is 180 - 65 = 115°
∠BCD = 20° [Vertical Angles are equal]
∠ABC = (360 - (20+115+110))
= 115° [Angles in a quadrilateral]
Hence,
ABCD = Kite [Definition of a Geometric Kit]
That is
It two equivalent angles (∠ABC and ∠ADC)It also has two pairs of adjacent equal-length sides (that is |AD| ≈ |AB|.QED
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A painter has three partially filled paint cans.1 7/8 gallonsthe second contains 1 1/5 gallonsand the third contains 1 3/4which anwer is closet to the total amount of paint?A.2B.3C.4D.5
A painter has three partially filled paint cans.
The first contains 1 7/8 gallons
The second contains 1 1/5 gallons
The third contains 1 3/4 gallons
The total amount of paint is the sum of these paint cans.
[tex]total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4}[/tex]Now let us add these mixed fraction numbers
[tex]\begin{gathered} total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4} \\ total=(1+1+1)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(1.825) \\ total=4.825 \end{gathered}[/tex]As you can see, 4.825 is closest to 5.
Therefore, the correct option would be D
an article is $68000 and sold at a profit of 14%. Find the selling price
Answer:
The selling price is: [tex]\$77,520[/tex]
Step-by-step explanation:
Step 1: Identify the profit made
A profit of 14% is made on the article.
This means that the article was sold at a price that had 14% of its original price added to it.
The 14% of the original price is:
[tex]14\% \times 68000\\=\frac{14}{100}\times 68000\\\\\text{Calculate the value}\\\frac{14}{100}\times 68000\\=9520[/tex]
So, a profit of $9520 was made
Step 2: Calculate the selling price
The selling price will be the sum of the original price and the profit.
The selling price is:
[tex]68000+9520\\=77520[/tex]
At the start of a trip, a car's gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 gallons of gasoline. How much gasoline is left in the tank? Should you represent this amount with a positive or negative value? Why?
If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:
12 - 10 = 2
Then, 2 gallons of gasoline is left in the tank
Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the House blend with the Organic Free Trade blend, but always in the same proportion. Yesterday, you mixed 140 pounds of the House blend with 168 pounds of the Organic Free Trade blend. Today, there is 130 pounds of the House coffee left in stock. How many pounds of the Organic Free Trade coffee should you mix with it to get your secret blend?
The ratio House blend/Organic Free Trade blend is the same and must remain the same.
So, the proportion is:
[tex]\frac{140}{168}=\frac{130}{x}[/tex]Where x is the unknown amount of the Organic Free Trade blend.
So, from the proportion, we have:
[tex]\begin{gathered} 140\cdot x=168\cdot130 \\ 140x=21840 \\ \frac{140x}{140}=\frac{21840}{140} \\ x=156 \end{gathered}[/tex]Answer: 156 pounds of Organic Free Trade blend
f(x) = 2x³ - 4x + 6
f(3) =
Graph the cubic using its end behaviour and a few selected points.
The leading coefficient test requires one variable only
What is the value of x?
Answer:
15
Step-by-step explanation:
can someone help me i will give brainlest :) 5, 6, 7, 8 only do those one's
Answer:
5. -2 > x
6. 4 [tex]\leq[/tex] x
7. 0 [tex]\geq[/tex] x
8. -3 < x
Step-by-step explanation:
The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same x-intercept and the same end behavior as x approaches ∞. D. They have the same y-intercept and the same end behavior as x approaches ∞.