It takes 16,064 years for the 500g of radium to decay to 5g.
How long will it take for 500g of radium to decay to 5g?
Here we have the decay equation:
[tex]Q(t) = Q_0*e^{-k*t}[/tex]
Where Q₀ is the initial amount, and k is the decay constant.
We know that:
Q₀ = 500g
k = 0.00043
And we want to find the value of t such that Q(t) = 5g, so we need to solve:
[tex]5 = 500*e^{-0.00043*t}\\\\5/500 = e^{-0.00043*t}\\\\0.001 = e^{-0.00043*t}[/tex]
Now we can apply the natural logarithm in both sides:
[tex]ln(0.001) = ln(e^{-0.00043*t})\\\\ln(0.001) = -0.00043*t\\\\\frac{ln(0.001)}{-0.00043} = t = 16,064.5[/tex]
So it takes 16,064 years for the 500g of radium to decay to 5g.
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Given: AD BC and ZBCD=
ZADC
Prove: DE CE
A
D
B
Correct! Assemble the next
statement.
Intro
Angles Segments Triangles Statements Reasons
ZADC
ZDEA
ZECD
Statements
✓ 1. ZDEA and ZCEB are
vertical angles
ZBCD
ZEDC
ZCBE
ZCEB
Reasons
1. def. of vertical angles
ZDAE
In the given triangle, it should be noted that ADC is the same as BCD due to SAS congruence.
How to illustrate the information?From the information given,
AD = BC
BCD = ADC.
This depicts the concept of SAS. In this case, the two-sided will be equivalent.
Also, it should be noted that DAC and CBD are equal according to the vertical angle theorem.
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Answer:
see picture ....
Step-by-step explanation:
Six less than the product of
twice a number and ten is
twenty.
[tex]\text{First I'd recommend replacing the number with just n.}\\\text{Now, multiply this number by 2:: 2n}\\\text{Multiply 10 by it:: 2n*10}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{6 is subtracted from (2n*10):: (2n*10)-6}[/tex]
[tex]\text{This gives a total of 20}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{(2n*10)-6=20}[/tex]
6 numbers that have a median of 8 a mean of 9 and a range of 13?
Answer:
5,6,8,8,9,18
Step-by-step explanation:
...................
A Triangle
36 cm
perimeter
square
=40cm
perimeter
put them both together
find the
perimeter?
Answer:
58 cm
Step-by-step explanation:
if both shapes are squares, then the perimeter must be divide by all 4 equal sides
36 / 4 = 9, so each side of the first shape is 9 cm
40 / 4 =10 , so each side of the second shape is 10 cm
by putting the shapes together two of the side seal 1 side of each shape but 10-9 is 1 so add all three sides of the rest of the shape,
so 9+ 9+ 9= 27, then the three side of the second shape,
so 10+ 10+ 10= 30, then that extra 1 cm of difference from the size difference when put together,
so 27+ 30+ 1= 58 cm
Chords AC and BD intersect in circle O as shown in the diagram. Two of the angle measurements are marked. What is mL CED?
Answer:
By using the formulas of circle and geometry, we find that ∠CED = 65°.
Step-by-step explanation:
We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so
∠CED = 0.5 × (arc AB + arc CD)
See the attached figure with letters to better understand the problem
arc AB = 82° (by central angle)
arc CD = 48° (by central angle)
Substitute the values in the formula above
∠CED = 0.5 × (82° + 48°)
∠CED = 0.5 × 130°
∠CED = 65°
Therefore the answer is ∠CED = 65°
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Which of the following is a ballistic stretching exercise?
A.
calf stretch
B.
arm circles
C.
yoga plow
D.
hurdle stretch
Answer:
B. Arm circles
Hope you have a great day :)
IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS
Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.
Answer:
Given function:
[tex]q(x)=9x^2-24x+16[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]ac=9 \cdot 16=144[/tex]
Two numbers that multiply to 144 and sum to -24 are: -12 and -12
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies q(x)=9x^2-12x-12x+16[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]
Factor out the common term [tex](3x-4)[/tex]:
[tex]\implies q(x)=(3x-4)(3x-4)[/tex]
Therefore:
[tex]\implies q(x)=(3x-4)^2[/tex]
PLEASE HELP FAST!!!
The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
Angle of elevation and depressionFrom the question given, we have the following parameters
Base of the building = 7feet
Height of the building = 18 feet
Required
angle of elevation
Using the SOH CAH TOA identity
tanФ = opp/adj
tanФ = 18/7
Ф = 68.73 degrees
Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
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Question:
A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.
Andy fed his dog about 16kilogram of food in one week. he fed his cat about 2 kilogram of food in one week what is the best estimate for the total amount of food he feeds his dog and cat in2 weeks. each animal represent 4 kilogram of food
Answer:
36kg
Step-by-step explanation:
The dog eats 16kg per week, which is 32kg in 2 weeks
The cat eats 2kg per week, which is 4kg in 2 weeks
32+4=36
A fuel tank is 1/6 full. When 2 gallons of gasoline are added, the tank becomes 1/4 full. What is the total fuel capacity of the tank in gallons?
Answer:
24 gallons
Step-by-step explanation:
Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.
Thus, the tank has a fuel capacity of 24 gallons.
Answer:
24
Step-by-step explanation:
Let x be the total fuel capacity of the tank, in gallons.
Then from the given information
x/6 + 2 = x/4,
Multiplying both sides by 12 to remove the fractions, we get
2x + 24 = 3x so x = 24.
Therefore, the total fuel capacity of the tank is 24 gallons.
how many nonisomorphic spanning trees does each of these simple graphs have
The characteristics of a nonisomorphic spanning tree are:
One would have 3 vertices of degree 2 and 2 of degree 1, Another spanning tree would have one vertex of degree three, The third spanning tree would have one vertex of degree four.4What is Nonisomorphic?This refers to the quality of a group of things not having the same form and is popularly used in mathematics to show and make identifications of maths objects that are structurally well-defined.
Hence, we can see that your question is incomplete so I gave you a general overview of the topic for better understanding.
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The value of x must be greater than
0
1
3
7
Answer:
The value of x should be greater than 3.
Step-by-step explanation:
Given that,
The AB is 12 units.
The AC is 15 units.
We need to find the value of BC.
Based on the above information, the calculation is as follows:
As we know that
The sum of two sides length is always more than the 3rd one.
Based on this,
12 + 15 > x
x < 27
15 + x >12
x >-3
12 + x > 15
x >3
what is the area of the trapezium?
Answer:
156 cm²
Explanation:
This figure is a trapezium.
Formula of Area of Trapezium = 1/2 × (a + b) × height
Here given:
a = 9 cmb = 30 cmh = 8 cm==============
Area of trapezium: 1/2 × (9 + 30) × 8 = 156 cm²
Answer:
area of the trapezium is 156
Step-by-step explanation:
Do the fractions and convert to repeating or terminating decimal numbers?
It should be noted that 16/25 can be converted to a terminating decimal number is 0.64.
How to explain the fraction?
Do the fractions 6/7 and 16/25 convert to repeating or terminating decimal numbers.
In this case, 6/7 converts to repeating decimal numbers. You could represent it, so you don't have to repeat the decimals infinitely, by putting a bar over the repeating decimals like 0.857142 with a bar going over from the 8 to the 2.
Also, 16/25 can be converted to a terminating decimal number which is 0.64.
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This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A B
C
D F
Frequency 5 10 15 3 2
Find the probability that a student earns a
Answer:
14.3%
Step-by-step explanation:
5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428
Write x^2+5x-7 in the form (x+a)^2+b.
Answer: −x2+
5
x
=
7
Move
7
to the left side of the equation by subtracting it from both sides.
−
x
2
+
5
x
−
7
=
0
Once the quadratic is in standard form, the values of
a
,
b
, and
c
can be found.
a
x
2
+
b
x
+
c
Use the standard form of the equation to find
a
,
b
, and
c
for this quadratic.
a
=
−
1
,
b
=
5
,
c
=
−
7
Step-by-step explanation:
The unit rate of change of yyy with respect to xxx is the amount yyy changes for a change of one unit in xxx.
Is the unit rate of change of yyy with respect to xxx less in the equation y=6.5xy=6.5xy, equals, 6, point, 5, x or in the graph below?
The unit rate of change of y with respect to x is less in the graph
How to compare the rate of change?The attached graph represents the missing information in the question
The graph passes through the following points
(0,0) and (5,1)
The rate of change of the graph is then calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{1-0}{5-0}[/tex]
Evaluate
m = 0.2
The equation is given as:
y = 6.5x
The slope of the above equation is 6.5
By comparison, 6.5 is greater than 0.2
Hence, the unit rate of change of y with respect to x is less in the graph
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Answer:
The equation
Step-by-step explanation:
i did it on khan academy
Which data set could be represented by the boxplot shown? (1 point)
{0, 2, 3, 5, 8, 9, 10, 10, 12}
{2, 3, 3, 4, 5, 5, 8, 10, 10}
{2, 3, 4, 5, 5, 7, 7, 9, 10}
{2, 3, 4, 5, 5, 5, 8, 9, 10
The second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have given a data set and a box plot shown in the picture.
From the boxplot we can see:
Minimum value = 2
Q1 = (2+4)/2 = 3
Median = (4+6)/2 = 5
Q3 = (8+10)/2 = 9
Maximum value = 10
The second data set:
{2, 3, 3, 4, 5, 5, 8, 10, 10}
Minimum value = 2
Q1 = (2+4)/2 = 3
Median = (4+6)/2 = 5
Q3 = (8+10)/2 = 9
Maximum value = 10
Thus, the second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.
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A chocolate chip recipe that produces 30 cookies calls for 2 1/4 cups of flour. If the math club decides to make fifteen dozen cookies for a bake sale, how many cups of flour will they need?
Answer:
2 1/4
Step-by-step explanation:
If f(x) = 2x - 6 and g(x) = x - 2x², find the value of f(2) + g(-3)
Answer:
-23
Step-by-step explanation:
f(2)= 2*2-6 = -2
g(-3)= -3-2*9 = -21
---> f(2)+G(-3)= -2-21 = -23
Answer: -23
Step-by-step explanation:
f(2) + g(-3) means that we will substitute 2 as x into the function f, and add that to -3 substituted as x into function g.
First, we will find the substituted and simplified values of these functions.
f(x) = 2x - 6
f(2) = 2(2) - 6
f(2) = -2
[tex]-----[/tex]
g(x) = x - 2x²
g(-3) = (-3) - 2(-3)²
g(-3) = -21
Lastly, we can add them.
f(2) + g(-3)
-2 + -21
-23
What is the inverse of this function?
f(x) = -√x +3₁ x ≥ −3
f-¹(x) =
2-
-
for x ≤
Answer:
f(x)^-1=x^2-3
Step-by-step explanation:
So I'm assuming you meant to include the 3 in the radical as well which would make sense given the domain restriction. To find the inverse you simply swap the x and y since the inverse function is when the domain and range are swapped.
[tex]y=-\sqrt{x+3}\\x=-\sqrt{y+3}\\-x=\sqrt{y+3}\\(-x)^2=y+3\\x^2-3=y\\f(x)^{-1}=x^2-3[/tex]
Question 13 (4 points) (05.03) Which of the following statements best describes the graph of -5x + 2y = 1? (4 points)
A) It is a curve joining the points (-5, 2), (2, 3), and (4, 1).
B)It is a curve joining the points (-1, -3), (-1, -3), and (1, 5).
C)It is a straight line joining the points (1, 3), (3, 8), and (-3, -7).
D)It is a straight line joining the points (4, -3), (-1, 2), and (-4, 5).
Answer:
C) straight line through (1, 3) ... (-3, -7)
Step-by-step explanation:
The linear equation will describe a straight line. The slope and general location of the line on a graph can be estimated from its x- and y-intercepts.
__
interceptsThe x-intercept is the value of x that satisfies the equation when y=0.
-5x +2·0 = 1
x = -1/5 . . . . . . divide by the coefficient of x
The y-intercept is the value of y that satisfies the equation when x=0.
-5·0 +2y = 1
y = 1/2 . . . . . . divide by the coefficient of y
nature of the graphThe intercept values mean the line crosses the positive y-axis and the negative x-axis. It will have a positive slope. Points on the line that have integer x- and y-coordinates will have coordinates that have the same sign.
Of the offered answer choices, A and B are eliminated because the graph is not a curve. D is eliminated because the suggested points have coordinates with opposite signs. The correct choice is C:
It is a straight line joining the points (1, 3), (3, 8), and (-3, -7)
What is the value of x in the triangle?
Answer:
45 degree=√2/2
√2/2=12√2
we use criss-cross method
√2x/√ 2=12√2/√ 2
×=24
Step-by-step explanation:
if it confused you this is (/)is dividing
hope I helped
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A researcher has a table of data with four-column variables and three-row variables. the value for the degrees of freedom in order to calculate the chi-squared statistic is __________.
The degree of freedom is 6.
What is degree of freedom?The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
Given:
rows= 3
column= 4
So, degree of freedom
= (row-1)(column-1)
=(3-1)(4-1)
=2*3
=6
Hence, the degree of freedom is 6.
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Answer:
The degree of freedom is 6.
Step-by-step explanation:
Got it right on the test.
Question 2(Multiple Choice Worth 1 points)
(02.02 LC)
If g(x)= x² + 3, find g(4).
11
19
16
8
Answer: 19
Step-by-step explanation:
g(4) = 4² + 3
g(4) = 16 + 3
g(4) = 19
Which length is equivalent to 12 yards?
Answer:
36 feet
Step-by-step explanation:
1 yard 3 feet
A survey participant is randomly selected. Let F be the
event that the participant's first motor vehicle had four
cylinders and let C be the event that the participant's
first motor vehicle was a car. What is the value of PIF
The probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is:
Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table(please refer to the attached picture)
A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. What is the value of P(F or C)?
A) 0.59B) 0.68C) 0.71D) 0.80We have to find the value of P(F or C):
[tex]\rm P( F \ or \ C) = \dfrac{118+6+18+16+2}{118+6+18+16+12+20+2+6+2}[/tex]
[tex]\rm P( F \ or \ C) = \dfrac{160}{200}[/tex]
P(F or C) = 0.80
Thus, the probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
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find the least nu,ber which is exactly divisible by 12 16 and 24
Answer:
The smallest number all three numbers can be divided by is 4.
Step-by-step explanation:
12/4=3
16/4=4
24/4=6
Hope this helps!
If not, I am sorry.
The __________ and the _________ are two of the most popular and useful methods of standardizing for size and comparing distributions.
The proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.
Methods of standardizationProportion is the fraction of favorable cases from the total number of cases. It is defined for both population and sample.
Median is defined as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half of it.
Therefore, the proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.
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What are the solutions of 3x² + 14x + 16 = 0?
0 x=-₁-2
0 x = -2₁-²2/
0x = ²,2
0x=-₁2
X
Answer:
x = -2, -2
Step-by-step explanation:
3x² + 14x + 16 = 0
(3x+8) (x+2)
x = -8/3
x = -2
The solutions of the quadratic equation 3x² + 14x + 16 = 0 are x = -2 and x = -8/3.
To find the solutions of the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula.
The quadratic formula states that for an equation of the form ax² + bx + c = 0
The solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation 3x² + 14x + 16 = 0,
a = 3, b = 14, and c = 16.
Substituting these values into the quadratic formula, we get:
x = (-14 ± √(14² - 4.3.16)) / (2 × 3)
x = (-14 ± √(196 - 192)) / 6
x = (-14 ± √4) / 6
Now we have two possibilities for x:
x₁ = (-14 + √4) / 6
x₂ = (-14 - √4) / 6
Simplifying each expression:
x₁ = (-14 + 2) / 6
x₁ = -12 / 6
x₁ = -2
x₂ = (-14 - 2) / 6
x₂ = -16 / 6
x₂ = -8 / 3
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