The half-life h is calculated to be approximately 2.41.
To determine the half-life h from the given half-life function:
[tex]\[ Q(t) = 28550 \cdot \left( \frac{3}{4} \right)^{\frac{t}{h}} \][/tex]
we need to solve for h in the equation:
[tex]\[ \left( \frac{3}{4} \right)^h = \frac{1}{2} \][/tex]
To solve for h , we take the natural logarithm (ln) of both sides of the equation:
[tex]\[ \ln \left( \left( \frac{3}{4} \right)^h \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Using the logarithmic property [tex]\(\ln(a^b) = b \ln(a)\)[/tex], we get:
[tex]\[ h \ln \left( \frac{3}{4} \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Now, solve for h :
[tex]\[ h = \frac{\ln \left( \frac{1}{2} \right)}{\ln \left( \frac{3}{4} \right)} \][/tex]
Calculate the natural logarithms:
[tex]\[ \ln \left( \frac{1}{2} \right) = \ln(0.5) \approx -0.6931 \\\[ \ln \left( \frac{3}{4} \right) = \ln(0.75) \approx -0.2877 \][/tex]
Now, divide these values to find h :
[tex]\[ h = \frac{-0.6931}{-0.2877} \approx 2.41 \][/tex]
So, the half-life h is approximately:
[tex]\[ h \approx 2.41 \][/tex]
Therefore, the half-life h rounded to the nearest hundredth is:
h = 2.41
How many squares will be in the fifth figure
Answer: 30
Step-by-step explanation:
see photo for work
Write an integer for the following situation a gain of 20 pounds
Answer:
+20
Step-by-step explanation:
This is meaning to add when it says to gain
A shoe company sends out 7 trucks loaded with nursing shoes that cost the company $ 1,572per truck if they send out 750 boxes per truck what would be the profit if the cost per box is $ 125.40
1572*7=11004
750*125.40=94050
94050-11004=83046
the profit is $83046
Find the measure of 3. Help Plz
Answer:
∠3 = 135°
Step-by-step explanation:
∠3 = ∠1 = 135° ( corresponding angles are congruent )
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 7 14 28 35
y 1 2 4 5
x 1 2 3 4
y 4 10 12 16
x 2.5 3 5 6
y 5 6 10 15
Which table shows a proportional relationship between x and y?
PLS HELP!!!!
Answer:
Second table
Step-by-step explanation:
Proportional relationships between x and y satisfied the following equation y = k*x, where k is some constant. Rearranging we get: k = y/x. So, if we take every pair y-x and divided them, we have to find the same k.
- Division y/x for the first table:
2/1 = 2
5/3
8/4 = 2
14/7 = 2 It is not a proportional relationship
- Division y/x for the second table:
1/7
2/14 = 1/7
4/28 = 1/7
5/35 = 1/7 It is a proportional relationship
- Division y/x for the third table:
4/1 = 4
10/2 = 5
12/3 = 4
16/4 = 4 It is not a proportional relationship
- Division y/x for the fourth table:
5/2.5 = 2
6/3 = 2
10/5 = 2
15/6 = 5/2 It is not a proportional relationship
What are the solutions to x2 + 8x + 7 = 0?
O
O
O
O
x=-8 and x = -7
x=-7 and x=-1
x = 1 and x = 7
x = 7 and x = 8
Answer:
x = - 1 and x = - 7
Step-by-step explanation:
Given
x² + 8x + 7 = 0 ← in standard form
(x + 1)(x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 7 = 0 ⇒ x = - 7
What percent of 400 is 3?
Answer:
0.75%
Step-by-step explanation:
In order for us to obtain the answer, we first write 3 over 400 as a fraction, we then multiply it by 100 as percentage is always out of 100, so 3/400 x 100
Which equation is equivalent to 16x – 8 + 2x = 100?
Answer:
x=6
Step-by-step explanation:
16x-8+2x=100
18x-8=100
18x=100+8
18x=108
x=108/18
x=6
14x=108 is the equivalent equation of the equation 16x – 8 + 2x = 100.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 16x – 8 + 2x = 100.
Sixteen times of x minus eight plus two times of x equal to hundred.
16x – 8 + 2x = 100.
We need to add the variable terms to get the equivalent equation.
Equivalent equation is an equation which looks different but the result will be same.
14x-8 = 100.
Add 8 on both sides.
14x=100+8
14x=108.
Hence, 14x=108 is the equivalent equation of the equation 16x – 8 + 2x = 100.
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A pregnant woman learns she is having twins
Assuming the probability of having a girl and boy are the same, what is the probability that the twins are two girls
Enter your answer as a percent to one decimal place like this : 42.5%
I’ll put you as brainliest
Answer: I think the answer would be 50%
If the chance of having a boy or girl would be 50%, then having twins would be that probability as well.
Answer:The answer is 25%
Step-by-step explanation: 0.5x 0.5= 0.25
If its 50 % to have a boy or girl then you just multiply them.
What is 68−−√ in simplest radical form?
I think you mean [tex]\sqrt{68}[/tex] so I will just simplify that.
[tex]\sqrt{68}=\sqrt{4}*\sqrt{17}=2\sqrt{17}[/tex]
answer: [tex]2\sqrt{17}[/tex]
the answer is 2√17
hope this helps :)))
I WILL GIVE BRAINLIEST!!!! PLZ HELP!!!! ASAP!!!!
m - 7 < 6
A. m < -1
B. m ? 1
C. m < 13
D. < - 13
What is the acceleration of this object? The object's mass is 2 kg. 11 m/s2 4 m/s2 0 m/s2 7 m/s2
Answer:
The acceleration of the object is 4 [tex]m/s^2[/tex]
Step-by-step explanation:
Given:
The mass of the object is = 2 kg
To Find:
Acceleration of the object = ?
Solution:
From the diagram below we know that
The resultant force is 8N along the east Direction
we know the acceleration is the"Rate of change of Velocity"
And Expressed as
F = ma
Where
F is the Force
m is the mass
Now substituting the known values we get
[tex]8 = 2 \times a[/tex]
[tex]a =\frac{8}{2}[/tex]
a=4 [tex]m/s^2[/tex]
Answer:
b the object is 4 m/s
Step-by-step explanation:
PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!
X= ____________
Y= ____________
Answer:
x = 11, y = 3
Step-by-step explanation:
9x + 25 and 13x - 19 are corresponding angles and congruent, thus
13x - 19 = 9x + 25 ( subtract 9x from both sides )
4x - 19 = 25 ( add 19 to both sides )
4x = 44 ( divide both sides by 4 )
x = 11
Thus
13x - 19 = (13 × 11) - 19 = 143 - 19 = 124°
13x- 19 and 17y + 5 form a straight angle and are supplementary, thus
13x - 19 + 17y + 5 = 180, that is
124 + 17y + 5 = 180
129 + 17y = 180 ( subtract 129 from both sides )
17y = 51 ( divide both sides by 17 )
y = 3
Find the value of x when y = 6 and z = -1/2, If
Answer:
[tex]x=-\frac{261}{46}[/tex]
Step-by-step explanation:
we have the expression
[tex]\frac{3x+2y-5z}{y-4z}=\frac{x}{3y}[/tex]
we have
[tex]y=6,z=-\frac{1}{2}[/tex]
To find the value of x, substitute the given values of y and z in the expression
[tex]\frac{3x+2(6)-5(-\frac{1}{2})}{6-4(-\frac{1}{2})}=\frac{x}{3(6)}[/tex]
solve for x
[tex]\frac{3x+12+\frac{5}{2}}{6+2}=\frac{x}{18}[/tex]
[tex]\frac{3x+12+\frac{5}{2}}{8}=\frac{x}{18}[/tex]
Multiplying in cross
[tex](3x+12+\frac{5}{2})18=8x[/tex]
[tex]54x+216+45=8x[/tex]
[tex]54x-8x=-216-45[/tex]
[tex]46x=-261[/tex]
[tex]x=-\frac{261}{46}[/tex]
Help me with this math problem
Answer:
Weight of each large box [tex]x=15.75kg[/tex]
Weight of each small box [tex]y=13.75kg[/tex]
Step-by-step explanation:
Given:- Two equations are given,
Equation 1 :- [tex]7x+9y=234[/tex]
Equation 2:- [tex]5x+3y=120[/tex]
let,
x=weight of large box in Kilogram.
y=weight of small box in Kilogram.
Now,
multiply Equation 1 by 2 and Equation 2 by 6,
So we get 2 new equations,
Equation 3:- [tex]14x+18y=468[/tex]
Equation 4:- [tex]30x+18y=720[/tex]
Now after subtracting Equation 3 from Equation 4 we will get a new equation,
i.e. Equation 5:- [tex]16x=252[/tex]
therefore [tex]x=15.75[/tex]
now, put the value of x in Equation 1, so we will get
[tex](7x15.75)+9y=234[/tex]
[tex]110.75+9y=234[/tex]
[tex]9y=234-110.75[/tex]
[tex]9y=123.75[/tex]
[tex]y=123.75/9[/tex]
[tex]y=13.75[/tex]
So, weight of each large box i.e. [tex]x=15.75 kilogram[/tex]
and weight of each small box i.e. [tex]y=13.75 kilogram[/tex]
If m1 + m2 = 137°, what is m3?
Answer:
m3=43°
Step-by-step explanation:
The total has to add up to 180° so 180-137 = 43°
The line y=-3 is what I need help
Answer:
Look at the attachment below :)
Step-by-step explanation:
When we are given just a X or a Y coordinate, we just graph that. In this example, y will always be -3 and x will be anything so its a straight line.
Which expression is equivalent? 7 − 4(2x − 3)
Answer:
19-8x
Step-by-step explanation:
7-4(2x-3)
7-8x+12
19-8x
Answer:
19-8x
Step-by-step explanation:
7-4(2x-3)
7-8x+12
19-8x
2/3*5/15+-24+-18 pls help asap
Answer:
-42 2/9
Step-by-step explanation:
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Asa saves dimes and quarters so that he will have exact change for he bus. He dabs and then dumps the container that he has been using for collecting his coins and finds he has 47 coins that are worth $9.50. How many of each coin does he have?
Answer:
He have 32 quarters and 15 dimes.
Step-by-step explanation:
Given:
Asa saves dimes and quarters so that he will have exact change for the bus.
He has 47 coins that are worth $9.50.
Now, to find the number of coin each he have.
Let the number of quarters be [tex]x.[/tex]
And the number of dimes be [tex]y.[/tex]
So, the total number of coins are:
[tex]x+y=47.[/tex]
[tex]y=47-x.[/tex].........(1)
As given the total worth of coins = $9.50
And the value of a quarter = $0.25 and the value of a dime = $0.10.
Now, the total worth of coins are:
[tex]0.25x+0.10y=9.50[/tex]
Putting the equation (1) in the place of [tex]y[/tex] we get:
[tex]0.25x+0.10(47-x)=9.50[/tex]
[tex]0.25x+4.7-0.10x=9.50[/tex]
[tex]0.15x+4.7=9.50[/tex]
Subtracting both sides by 4.7 we get:
[tex]0.15x=4.80[/tex]
Dividing both sides by 0.15 we get:
[tex]x=32.[/tex]
The number of quarters = 32.
Now, putting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=47-32.[/tex]
[tex]y=15.[/tex]
The number of dimes = 15.
Therefore, he have 32 quarters and 15 dimes.
80 95 90 80 100 _ what goes on the blank to get a mean of 90
Answer:
95
Step-by-step explanation:
(80 + 95 + 90 + 80 + 100 + x) / 6= 90
x = 95
Answer:
95.
Step-by-step explanation:
The are a total of 6 numbers so to make the mean 90 the total must be 6*90 = 540.
So the number in the blank is 540 - (80 + 95+90+80+100)
= 540 - 445
= 95.
a bag contains 5 red, 6 white, and 5 blur marbles. a marble is drawn from the bag and replaced 32 times. the table shows the results. for which color is the experimental probability of drawing the color the same as the theoretical probability?
red:12 white: 12 blue:8
Answer:
White.
Step-by-step explanation:
Theoretical probabilities are:
Red: 5 / ( 5 + 6 + 5) = 5/16
White: 6/16 = 3/8.
Blue: 5/16.
The answer is white because it is drawn 12 times which equals its theoretical probability: 12/32 = 3/8.
The probability of drawing the color the same as the theoretical probability is 3/8.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A bag contains 5 red, 6 white, and 5 blue marbles.
Theoretical probabilities for the colors are:
Red:
= 5 / ( 5 + 6 + 5)
= 5/16
White:
= 6/16
= 3/8.
Blue: 5/16.
So, the probability of drawing the color the same as the theoretical probability is white because the theoretical probability is 3/8.
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Choose the solution set graphic until the correct one is displayed.
A.Infinite set of points on the line
B.Empty set
C.Points on negative x-axis
Final answer:
The solution set graphic is C - Points on negative x-axis.
Explanation:
The correct solution set graphic for this question is C - Points on negative x-axis.
To determine the solution set graphically, you would need to plot all the possible values of the equation or inequality on a coordinate plane. Option A - Infinite set of points on the line would represent a linear equation or inequality with multiple solutions. Option B - Empty set would mean that there are no solutions to the equation or inequality. Option C - Points on negative x-axis would indicate that the equation or inequality has solutions only on the negative x-axis.
Which of the following rational numbers represents a repeating decimal 11 / 40 ,3/25, 25/48,or 7/32
[tex]\frac{25}{48}[/tex] represents repeating decimal
Solution:
We are asked to find the rational number that represents repeating decimal
A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely)
Option 1
[tex]\frac{11}{40} = 0.275[/tex]
So here the decimal part is not repeating. So [tex]\frac{11}{40}[/tex] does not represent repeating decimal
Option 2
[tex]\frac{3}{25} =0.12[/tex]
So here the decimal part is not repeating. So [tex]\frac{3}{25}[/tex] does not represent repeating decimal
Option 3
[tex]\frac{25}{48} = 0.52083333333[/tex]
So here in decimal part "3" is repeating and goes on forever
So [tex]\frac{25}{48}[/tex] represents repeating decimal
Option 4
[tex]\frac{7}{32} = 0.21875[/tex]
So here the decimal part is not repeating. So [tex]\frac{7}{32}[/tex] does not represent repeating decimal
The following shows a corn maze for participants to walk through. The participants can only go forward and when there is a fork in the path you may assume that people are equally likely to take any one of the paths. It costs $5.00 to enter the maze and each participant gets $10.00 if they come out in a prize area.
I'm not really sure but I know that the answer is definitely not 0.25 or 0.5.
Answer:
D. 0.472
Step-by-step explanation:
I guessed on my test and got it correct trust me.
The first three steps of completing the square to solve the quadratic equation x² + 4x - 6 = 0, are
shown below.
Step 1: x2 + 4x = 6
Step 2: x2 + 4x + 4 = 6 + 4
Step 3: (x + 2)2 = 10
What are the next 3 steps?
Answer:
The next 3 steps are
Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]
Step 5: [tex]x=-2\pm \sqrt{10}[/tex]
Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]
Step-by-step explanation:
Given:
Quadratic Equation is
x² + 4x - 6 = 0
To Find:
x = ?
Solution:
Step 1: x2 + 4x = 6
Step 2: x2 + 4x + 4 = 6 + 4
Step 3: (x + 2)2 = 10
Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]
Step 5: [tex]x=-2\pm \sqrt{10}[/tex]
Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]
Introduction to the triangle midsegment theorem‼️Can someone help me with this problem ❓
Answer:
see explanation
Step-by-step explanation:
Given a line joining the midpoints of 2 sides of a triangle, the midsegment
Then the midsegment is parallel to and half the measure of the third side of the triangle, thus
XY = 2KL = 2 × 42 = 84
Since J is the midpoint of XY, then
JY = 0.5XY = 0.5 × 84 = 42 and
JK = 0.5YZ = 0.5 × 76 = 38
In right triangle JKL, ZL is a right angle, mZJ = 62°, and JK = 17.
sin 62° 0.88
cos 62° 0.47
tan 62° 1.88
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What is the measurement of JL?
If necessary, round your answer to one decimal place, like this: 42.5
Please the attachment for question.
Answer:
Measurement of JL=8
Step-by-step explanation:
Given:-
[tex]\triangle JKL\ is\ right\ angle\ triangle[/tex]
[tex]m\angle J=62\ degree[/tex]
JK=17
[tex]sin\ 62\ degree= 0.88[/tex]
[tex]cos\ 62\ degree= 0.47[/tex]
[tex]tan\ 62\ degree= 1.88[/tex]
To find measurement of JL=?
Now,
[tex]cos\theta=\frac{adjacent\ side}{hypotenuse}[/tex]
[tex]cos\ 62\ degree=\frac{JL}{17}[/tex]
[tex]0.47=\frac{JL}{17}[/tex]
[tex]JL=0.47\times 17[/tex]
[tex]JL=7.99[/tex]
[tex]JL=8[/tex]
Therefore measurement of JL=8
About 4/5 of the weight of a pineapple is water. About how much water would you expect to find in 2 1/2 pounds of pineapple?
Answer:
2 pounds
Step-by-step explanation:
all you have to do is 2 1/2 x 4/5 because 4/5 is equal to 1. So if you multiply that by 2 1/2 you will get the answer
Find the greatest common factor of 10, 30 and 45
Answer:
The greatest common factor is 5.
Step-by-step explanation:
The prime factorisation of 10, 30 and 45 is,
10 = 2 × 5
30 = 2 × 3 × 5
45 = 3 × 3 × 5
The prime factor '5' is common in the factorisation of 10, 30 and 45
So, the greatest common factor of 10, 30 and 45 is 5.