[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &7\\ t=\textit{elapsed time}\dotfill &127\\ h=\textit{half-life}\dotfill &64.8 \end{cases} \\\\\\ A=7\left( \frac{1}{2} \right)^{\frac{127}{64.8}}\implies A=7\left( \frac{1}{2} \right)^{\frac{635}{324}}\implies A\approx 1.80[/tex]
The half-life of sr-85, which may be used in bone scans, is 64.8 days. 1.80 milligrams of a 7 mg sample will be left after 127 days.
What is half-life?Half-life is defined as the time required for a quantity to reduce to half of its initial value.
The half-life of sr-85, which may be used in bone scans, is 64. 8 days.
We need to find how many milligrams of a 7 mg sample will be left after 127 days.
[tex]\rm A = P\frac{1}{2} ^{t/h}[/tex]
here A = current amount
P = inital amount
t = time
h = half life
So,
[tex]\rm A = 7\frac{1}{2} ^{127/64.8}[/tex]
[tex]\rm A = 7\frac{1}{2} ^{635/324}\\A = 1.80[/tex]
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A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have an average of 787
83, 81, 70, 74
The minimum grade he must get on the last test in order to have an average of 78 is
Answer:
82
Step-by-step explanation:
The sum of his previous grades were 308. In order to get an average grade of 78, he needs to have a score of 78*5 or 390. His necessary grade minus his current grade is 390 - 308, which is 82. The minimum score the student needs to get on his test in order to have an average of 78 is 82
Answer:
82.
Step-by-step explanation:
The sum of the 5 tests must be 5*78 = 390 for the average to be 78.
So in the last test is grade must be 390 - (83+81+70+74)
= 390 - 308 = 82.
A fair coin is tossed 3 consecutive times. What is the probability that the result of the first toss is heads and the results of the next two are tails?
A: 1/8
B: 1/6
C: 1/2
D: 1/4
Answer: a). 1/8
Step-by-step explanation:
If the coin is fair, then the odds of getting heads or tails should be equal, 12.
Then 3 tosses of tails will have a chance of 12⋅12⋅12=18.
The graph of a function g is shown below.
Find g (2) and find one value of x for which g(x) = -2.
Answer:
a. 1
b. 1
Step-by-step explanation:
by looking at the graph you can deduce the answer.
The equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation for the function is,
g(x) = x²-3
The graph of a quadratic function that has something bowl-shaped. Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
To find the value of g (2) the value of the function is,
g(2) = 2²-3
g(2) =8-3
g(2) =5
Thus, the equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
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What is the volume of this sphere?
1024π m^3
972π m^3
729π m^3
81π m^3
Answer:1024π m^3
Step-by-step explanation:
i got 100 on the quiz
which trig ratio
determine which trig ratio to use to solve for x
Answer:
sin = opp / hyp
cos = Adj / hyp
tan = opp / adj
7. cos 41 = x / 86
8. sin x = 5/13
9. cos x = 9/37
10. tan 61 = x/28
11. sin 41 = x/65
12. tan x = 79/84
Step-by-step explanation:
can someone answer this please
Answers:
Reason 23: Given
Reason 24: Reflexive Property
Reason 25: AAS
========================================================
Explanation:
Reason 23 is given because we simply restate the initial facts word for word. Whatever is said at the top "given" is copy/pasted into the table below. This explains why the second reason is "given" as well.
Reason 24 is "Reflexive Property" because any segment is congruent to itself. Think "reflexive" as in "mirror reflection".
For reason 25, we will use the AAS (angle angle side) congruence theorem. This is because we have two pairs of congruent angles (statement 1 and statement 2) as well as a pair of congruent sides (statement 3). We don't use ASA because the side FY is not between the angles mentioned. The order is important. Check out the diagram below. Take note of the color coding for the angles.
Which of the following tables represents a proportional relationship?
A
y=4x
8/2=4. .and the rest too have the same value
a rectangle has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat.
Then find the area, in square feet, of the mat.
❍ Concept :-
⠀
We have been provided with some information regarding a rectangular shaped mat. And on the basis of that information, we will create some assumptions and create and equation and equate it to get our required answer.
⠀
✱ Given Information :-
⠀
A rectangular mat with,
Perimeter = 36 ft. Length = twice the width⠀
✱ To Find :-
⠀
The dimensions of the matArea of the mat⠀
✱ Formula Used :-
⠀
[tex] \diamond \: \underline{ \boxed{\begin{array}{cc} \sf1. \: Perimeter_{Rectangle} = 2(l+b) \\ \\ \sf 2. ~Area_{Rectangle} = l\times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}}} \: \star \\ [/tex]
⠀
✱ Solution :-
⠀
Let the breadth of the mat be x, therefore,
Length = 2x⠀
Now, according to the question,
⠀
[tex] \sf \hookrightarrow 36 \: = 2(2x + x) \\ \\ \\ \sf \hookrightarrow 6x = 36 \: ft. \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow x = \cancel\frac{36}{6} = 6 \: ft. \: \: \\ [/tex]
Thus,
Length = 2x = 2 x 6 = 12 ft. Breadth = x = 6 ft.⠀
Now, we have to find out the area of the mat, thus,
⠀
[tex] \sf \hookrightarrow Area=6 \times 12 \\ \\ \\\sf \hookrightarrow Area=72 \: sq. ~ft. \\ \\ [/tex]
Thus, the area of the mat is 72 sq. ft.
⠀
[tex]\underline {\rule{221pt}{2.5pt}} \\ \\ [/tex]
Answer:
72 sq. feet
Step-by-step explanation
Since the perimeter is 36 feet and the length is 2w, you have to do the guess and check method.
I already did the guess and check method. So, here's how it became:
length =12
width=6
because 6x2=12 or 12 divide 2=6.
12 + 6 + 12 + 6.
12+6= 18. 12+6=18. 18+18=36 feet.
To find the area of a rectangle, you have to do L times W.
Which means 12x6.
12x6=72 sq. feet.
I hope this helps!!!
help please? requestig help to a smart person?
[tex] \frac{150}{10} = \frac{300}{20} = \frac{450}{30} = \frac{600}{40} = 15[/tex]
[tex]for \: x = 15y[/tex]
[tex]50x = 50(15) = 750.00[/tex]
Option B :)In a survey of some tourists, 80% of the tourists have been to India and 35% of the tourists have been to china.If all the tourists who have been to china also been to India and 260 have not been either of the countries, find the number of tourists who have been india but not china.
Answer:
585
Step-by-step explanation:
This sort of problem can be solved using a 2-way table that categorizes tourists by combination of destinations. Of the four possible combinations, one is ruled out (China, but not India). We can determine percentages and numbers for the combinations of interest using the given data.
__
80% have been to India, so 20% have not. All of those have also not been to China. Since tourists in that category number 260, there must be ...
260/20% = 1300 . . . tourists surveyed
Of the 80% who have been to India, 35% have been to China. That leaves 45% who have been to India, but not China. This number is ...
45% × 1300 = 585
The number of tourists who have been to India, but not China, is 585.
Evaluate each expression.
Check
Match the algebraic expression on the left to the correct value when evaluated on the right.
j+ş evaluate when= 1
350
n
7
evaluate when n = 35
to
up
5
70a: evaluate when a = 5
1.5
X-9; evaluate when x = 10.5
11
12
Answer:
I showed the answers in the pic above ^
Step-by-step explanation:
I hope this helps you!
Answer:
Step-by-step explanation:
HELPPPPPPPPP URGENT :(((((((((
Answer:
Step-by-step explanation:
a and b are the parallel sides of the trapezoid.
In the graph, each unit = 2
a = 8 & b= 4
height = h = 8
[tex]\bf \boxed{ \text{Area of trapezoid = $\dfrac{(a+b)*h}{2}$} }[/tex]
[tex]\bf = \dfrac{(8+4)*8}{2}\\\\\\ = \dfrac{12*8}{2}\\\\\\ = 6*8\\\\ = 48 \ square \ units[/tex]
Please help! will give brainlest!
Answer:
1
Step-by-step explanation:
[tex] \tan \bigg( \frac{5\pi}{4} \bigg) \\ \\ = \tan \bigg( \pi + \frac{\pi}{4} \bigg) \\ \\ = \tan \bigg(\frac{\pi}{4} \bigg) \\ \\ = 1[/tex]
[tex]\tan \left(\dfrac{5 \pi}4 \right)\\\\\\=\tan \left(2 \cdot \dfrac{\pi}2 + \dfrac \pi4\right)\\\\\\=\tan \left(\dfrac{\pi}4 \right)\\\\\\=1[/tex]
How do you change a radical expression into an expression with radical exponents
Step-by-step explanation:
The answer is in the picture
Help me please! I’ll give Brainliest to the right answer!
Answer:
(x,y) ---> (x+9, y+8)
Step-by-step explanation:
you simply take one point (ex point R to R^1) and count the distance from left to right/right to left which is 9 so that is your X and count up which will be your Y in this case is 8.
ILL GIVE THE BRAINLIEST TO THE PERSON WHO DOES THIS FOR ME THANK YOU
(Statistics hw)
11% of the total are left handed
so if we take random 100 students then 11% will be applicable to it also
so :-
[tex] \frac{11}{100} \times 100 \\ 11students[/tex]
Round each decimal to the nearest whole number.
6.85
0.37
2.5
16.1
Answer:
7
0.37 is closest to 0 but probably 1
3
16
Which angle measures 30 degrees?
Answer:
angle e o f and c o e
Step-by-step explanation:
please mark me brainliest
Acute angle is the answer which is A
15-16) 4, 6, 9, 11, 14, 16, _____, 21, ______
Pattern:
Missing Terms:
17-18) 3, 6, 7, 14, 15, _____, ______
Pattern:
Missing Terms:
Answer:
first pattern: +2, +3 (repeated)
first missing terms: 19, 24
second pattern: *2, +1
second missing terms: 30, 31
Step-by-step explanation:
first pattern:
1. subtract the second term with the first, (6-4=2) then then third with the second (9-6=3).
2. repeat until to prove the pattern, +2, +3
3. apply pattern to missing term, (16+2=19) and (21+3=24)
second pattern:
1. since subtracting the terms does not give us a pattern, try dividing when possible, (6/3=2) and (14/7=2). then subtract the other terms (7-6=1) and (15-14=1)
2. find pattern from calculation, *2, +1.
3. apply pattern to missing terms, (15*2=30) and (30+1=31).
hope this helped! ♡
How many times more sunscreen is in Bottle B than in Bottle A? Provide
your answer using a decimal.
Using the volume of the rectangular prisms, it is found that there is 1.5 times more sunscreen in Bottle B than in Bottle A.
What is the volume of a rectangular prism?The volume of a rectangular prism of dimensions l, w and h is given by:
V = lwh.
For bottle A, we have that, in inches, l = 1, w = 2, h = 6, hence the volume in cubic inches is given by:
Va = 1 x 2 x 6 = 12 in³.
For bottle B, we have that, in inches, l = 1.5, w = 3, h = 4, hence the volume in cubic inches is given by:
Vb = 1.5 x 3 x 4 = 18 in³.
The ratio between the volumes is given by:
r = Vb/Va = 18/12 = 1.5.
Hence, there is 1.5 times more sunscreen in Bottle B than in Bottle A.
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HURRY ASAP WILL GIVE BRAINLY
please help me with the question in the picture
Answer:
(x - 5) / (x - 6) (don't put them in brackets, i'm doing this to signify that all of x - 5 is being divided by all of x - 6).
Step-by-step explanation:
x² + 2x - 35:
what multiplies into -35 and adds into 2?
7 and -5
so the top is now (x + 7)(x - 5)
x² + x - 42
what multiplies into -42 and adds into 1?
-6 and 7
so the bottom is now (x + 7)(x - 6)
the 2 lots of (x + 7) cancel and you are left with (x - 5) / (x - 6)
Answer:
[tex]\frac{x-5}{x-6}[/tex]
Step-by-step explanation:
Let's start with the numerator to factor it.
We need two numbers adding up to 2 and multiplying to -35. Easy to see the number are +7 and -5. You can then factor as [tex]x^2+2x-35=(x+7)(x-5)[/tex]
Denominator then. Same story, Two number adding to 1 and multiplying to -42. Numbers are +7 again and -6. Factors as before:
[tex]x^2+x-42=(x+7)(x-6)[/tex].
Now you can simplify
[tex]\frac{x^2+2x-35}{x^2+x-42} = \frac{(x+7)(x-5)}{(x+7)(x-6)}= \frac{x-5}{x-6}[/tex]
is x-1 taking away an x or adding an x?? im trying to find the perimeter of area tiles, and the perimeter is x + x + x + (x-1) + 1 + 1 + 1 so would it be 2x+3 or 4x + 3??
Answer:
4x + 2
Step-by-step explanation:
x - 1 is adding an x and subtracting a 1 ,so
x + x + x + (x - 1) + 1 + 1 + 1
= x + x + x + x - 1 + 1 + 1 + 1 ← collect like terms
= 4x + 2
Solve the system using substitution
y+8x=10
2y-4x=40
(_,_)
Step-by-step explanation:
i used the two methods....I hope this will help you!
2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation
h(t) = -4.91? + 24.5t + 1
a) How high is the ball after 1 second?
b) Find the maximum height of the ball to one decimal place.
c) When does the ball reach its maximum height?
d) When does the ball hit the ground?
Answer:
I'll assume the ? is supposed to be t^2
See the answers below.
Step-by-step explanation:
h(t) = -4.91t^2 + 24.5t + 1
a) How high is the ball after 1 second?
h(1) = -4.91*(1)^2 + 24.5*(1) + 1
h(1) = 20.59 meters
b) Find the maximum height of the ball to one decimal place.
We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):
First Derivative
h(t) = -4.91*(t)^2 + 24.5*(t) + 1
'h(t) = -9.82*(t) + 24.5
0 = -9.82*(t) + 24.5
9.82t = 24.5
t = 2.49 seconds is the time the ball reaches maximum height. Use that is the equation to find the height:
h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1
h(2.49) = 31.6 meters
Graph
See attached graph. The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.
c) When does the ball reach its maximum height?
From the first derivative calculation above, t = 2.49 seconds to reach maximum height. The graph also shows 2.49 seconds. Better hurry.
d) When does the ball hit the ground?
The can be determined by either direct calculation of from the graph (attached).
Calculation:
h(t) = -4.91t^2 + 24.5t + 1
0 (ground) = -4.91t^2 + 24.5t + 1
4.91t^2 - 24.5t - 1 = 0 Solve with the quadratic equation. I get t = 5.04 seconds
Graph:
The graph shows 4.95 seconds. Both agree when rounded to one decimal point: 5.0 seconds.
19. Which of the following statements about the number line is true?
A. Numbers get smaller as you move to the left on the number line.
B. Number lines can't help you compare numerals.
O C. Numbers get larger as you move to the left on the number line.
D. Number lines end with the number 10.
Answer:
A. Numbers get smaller as you move to the left on the number line.
Step-by-step explanation:
A number line is typically drawn so that smaller, more negative numbers are on the left, and larger, more positive numbers are on the right.
__
Numbers get smaller as you move to the left on the number line.
_____
Additional comment
Number lines can be drawn with any scale and range, depending on what they are intended to represent. For representation of small integers, it is not uncommon for a number line to range from -10 to +10. However, that is not the only possible range that might be used.
Any number line can be used to show number order (least to greatest ≡ left to right). A number line with a linear scale can also be used to show relative differences between numbers: a greater distance on the number line corresponds to a greater difference between numbers.
Use the diagram below for Questions 1 and 2. It would be helpful to draw and label the diagram in your journal. Labeling the angle and arc measures will make the problems easier.
A local TV news station has their cameras positioned at Points A, X, and B for their newscasts.
Answer: 110 degrees
Step-by-step explanation:
A local TV news station has its cameras positioned at Points A, X, and B for their newscasts.
So the m<1 = 110°
Is the measure of arc and angle the same?
An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the center. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
Please check the attached file for an explanation.
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The figure1 can be transformed to create figure 2 using a single transformation which transformation can be used to accomplish this
The figure 1 can be transformed to create figure 2 by reflecting across the y axis.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.
The figure 1 can be transformed to create figure 2 by reflecting across the y axis.
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This figure represents the base of an fish tank that is 6 inches high.
What is the volume of the fish tank?
390 in³
330 in³
270 in³
240 in³
Answer:
270
Step-by-step explanation:
5 x 7 x 6= 210
2 x 5 x 6= 60
210 + 60= 270
The required volume of the fish tank is 240 cubic inches. option D is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The requried volume of the figure is given as,
Volume = height [area of the plot]
Since the area of the plot is given as,
area = area of the left rectangle + area of the right triangle.
area = 5 × 7 + 1/2 × [12-7]×[5-3]
area = 35 + 5
area = 40 square inches.
Volume = 6 [40]
Volume = 240 in³
Thus, the required volume of the fish tank is 240 cubic inches. option D is correct.
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