Answer:
0.835 mg of a 2.000-mg sample remains after 6.55 years.
Step-by-step explanation:
We are given that The half-life of cobalt-60 is 5.20 yr.
Formula of half life : [tex]N(t) = N(0)e^{\frac{-0.693t}{t\frac{1}{2}}}[/tex]
Where N(0) = Initial amount
N(t) = Quantity remaining after time
t = time
[tex]\frac{t}{2} =\text{half life}[/tex]
So, N(0) = Initial amount = 2 mg
t = time = 6.55 years
[tex]\frac{t}{2} =\text{half life} = 5.20 yr [/tex]
Substitute the values in the formula
Therefore,
[tex]N(t) = 2 e^{\frac{-0.693 \times 6.55}{5.20}}[/tex]
[tex]N(t) =0.835[/tex]
Hence 0.835 mg of a 2.000-mg sample remains after 6.55 years.
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Find the product.
4(−12)(−3)
A) −144
B) −96
C) 144
D) 72
Which ordered pair is the best estimate for the solution of the system of equations? y=−12x+4y=12x−3 (7, 1) (7, 0) (7, 0.5) (7.5, 0.5)
Given: triangle ABC, AB = BC Perimeter of ΔABC = 50 Perimeter of ΔABD = 40 Find: BD
The measure of angle ABC and BDC is 80° and 90° respectively.
What is the triangle?In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.
We have to find the measure of angle ∠ABC and ∠BDC.
As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.
[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]
Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.
∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
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Mr. Sanchez bought 2 magazine for 9.95 each and 1 book for 14.95 if the sales tax is 6% what is the total cost of Mr. Sanchez purchases
David is making a mosaic using 63 glass tiles 105 ceramic tiles and 84 marble tiles he wants to put the same number of each type of tile and Rose what is the maximum number of times you can have in each row
PLEASE HELP!
1. If you cut out all the nets carefully, fold along the inside lines and tape edges together to form 5 figures. Describe the figures formed. What shapes are they? Are any the same?
2. What does the fact that the figures fit together to make the prism tell you about their combined volume?
Brad has 3 pairs of pants, 7 tee shirts, and 2 pairs of sneakers. How many different outfit combinations can he wear
Answer:
42
Step-by-step explanation:
A snow storm left 1.25 feet of snow on the ground overnight. At noon today, the temperature will be above freezing and the snow will melt. If the melting snow is modeled by the equation y = -1 3 x + 1.25, how long will it take for the snow to melt away?
What is the ratio (fraction) of minivans to all vehicles on the forecourt?
A)1/120
B)1/20
C)1/6
D)1/4
do u do keystone
? im just wondering i do
Q # 8 please solve the question
Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days.
On Apex the correct one is 200 yards.
given that an arithmetic sequence can be expressed as a linear function in the form f(x)=mx+b, write a linear function to describe the sequence {10,15,20,25,30,35...}
Answer:
a linear function to describe the sequence is:
y = 5x + 5
Step-by-step explanation: ik ur on usa te$t prep
Nan and sato are designing a coffee table would you sing 4 inches tile Nan uses 30 tiles and sato uses half as many many total tiles did they use
Nan and Sato together used 45 tiles for their coffee table design.
The student's question involves calculating the total number of tiles used by two individuals, Nan and Sato, who are designing a coffee table. Nan uses 30 tiles, and Sato uses half as many tiles as Nan does. To find out how many tiles Sato uses, we divide Nan's number of tiles by 2.
So, Sato uses 15 tiles because half of 30 is 15. To find out the total number of tiles used, we add Nan's tile count to Sato's tile count:
30 tiles (Nan) + 15 tiles (Sato) = 45 tiles in total.
Therefore, to determine the total number of tiles used, Nan's 30 tiles are added to Sato's 15 tiles (half of Nan's), resulting in a total of 45 tiles used for the coffee table design.
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?
find 1/9 as many as 3 divided by 5
Final answer:
To find 1/9 as many as 3/5, you multiply 3/5 by 1/9 to get 3/45, which simplifies to 1/15.
Explanation:
To solve the student's question, we need to find what is 1/9 as many as 3/5. This involves multiplying the fraction 3/5 by the fraction 1/9. Here is the step-by-step calculation:
Multiply the numerator of the first fraction (3) by the numerator of the second fraction (1) to get the numerator of the answer.Multiply the denominator of the first fraction (5) by the denominator of the second fraction (9) to get the denominator of the answer.Combine these to get the answer in fractional form.The calculation will look like this: (3/5) × (1/9) = 3/45 = 1/15.
Thus, 1/9 as many as 3/5 is 1/15.
What is the distance d across the lake?
Answer-
The distance d across the lake is 90ft.
Solution-
In the picture,
ΔABC ≈ ΔCDE
Because,
∠ACB = ∠DCE (∵ vertical opposite angles)∠B = ∠D = 90°∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)So, from similarity properties
[tex]\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}[/tex]
[tex]\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}[/tex]
[tex]\Rightarrow d=\dfrac{120\times 15}{20}=90[/tex]
hey can you please help me posted picture of question
Find the length of JK and the measure of M
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.
What are the zeros of the function?
F (X) = x^3 - x^2 - 6x
A) -1, 0, and 3
B) -3, 0, and 1
C) -3, 0, and 2
D) -2, 0, and 3
Cards are dealt, one at a time, from a standard 52-card deck. a if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades?
Quadrilateral has angles 45 degrees, 150 degrees, 65 degrees, and N degrees
Which answer shows a correct order to solve this story problem? Maurine had to pay $2.52 tax on her purchases. She bought 3 books for $12.99 each, 2 pens for $0.69 each, and a magazine for $2.99. How much did Maureen spend? A. Step 1: Add the price of a book and a pen. Step 2: Multiply by 3 and then by 2. Step 3: Add $2.99 to that result. Step 4: Add the tax to the total of the purchases. B. Step 1: Calculate the total price of the 2 pens. Step 2: Add $2.99 to that total. Step 3: Calculate the total price of the 3 books. Step 4: Add the tax to the price of the 3 books C. Step 1: Calculate the total price of the 3 books. Step 2: Calculate the total price of the 2 pens. Step 3: Add $2.99 to the total of the cost of the books and pens. Step 4: Add the tax to the total of the purchases. D. Step 1: Add $2.99 to the amount of the tax. Step 2: Calculate the total price of the 2 pens. Step 3: Calculate the total price of the 3 books. Step 4: Add the prices of the pens to the price of the books.
A display that shows how the values in a data set are distributed
Answer: Line Plot
Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.
Answer: histogram
Step-by-step explanation:
Find a unit vector that is perpendicular to the vector 5, −4
Regina's mom bought her some bracelets. There were a total of 85 bracelets in 5 packages.
Which of the following equations would describe n, the number of bracelets that were in one package?
A. n + 5 = 85
B. n ÷ 5 = 85
C. n - 5 = 85
D. n × 5 = 85
At a college, 4/5 of the students take an English class. Of these students, 5/6 Composition. Which fraction of the students at the college take Composition?
The fraction of students who take Composition at the college is 2/3.
Explanation:To find the fraction of students who take the Composition class, we need to multiply the fraction of students who take an English class (4/5) by the fraction of English students who take the Composition class (5/6).
Multiplying these fractions, we get (4/5) * (5/6) = 20/30 = 2/3.
Therefore, 2/3 of the students at the college take Composition.
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An electrolyte solution has an average current density of 111 ampere per square decimeter \left( \dfrac{\text{A}}{\text{dm}^2}\right)( dm 2 A )left parenthesis, start fraction, A, divided by, d, m, start superscript, 2, end superscript, end fraction, right parenthesis. What is the current density of the solution in \dfrac{\text{A}}{\text{m}^2} m 2 A start fraction, A, divided by, m, start superscript, 2, end superscript, end fraction?
Answer:
Answer is 100
Step-by-step explanation:
Find (tan A+B) if A and B are in quadrant 2 with tan A=(1/3) and sin B=(20/29)
The value of [tex]\( \tan(A + B) \)[/tex] in quadrant 2, where [tex]\( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], is [tex]\( \frac{11}{57} \)[/tex].
Explanation:To find [tex]\( \tan(A + B) \)[/tex], we can use the formula [tex]\( \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \)[/tex]. Given that \[tex]( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], we can determine [tex]\( \cos B \)[/tex] using the fact that [tex]\( \sin^2 B + \cos^2 B = 1 \)[/tex]. Therefore, [tex]\( \cos B = \sqrt{1 - \sin^2 B} = \frac{21}{29} \)[/tex].
Now, substitute the values into the formula for [tex]\( \tan(A + B) \)[/tex]:
[tex]\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \][/tex]
[tex]\[ = \frac{\frac{1}{3} + \frac{20}{29}}{1 - \frac{1}{3} \cdot \frac{20}{29}} \][/tex]
[tex]\[ = \frac{\frac{29 + 60}{87}}{\frac{87 - 20}{87}} \][/tex]
[tex]\[ = \frac{\frac{89}{87}}{\frac{67}{87}} \][/tex]
[tex]\[ = \frac{89}{67} \][/tex]
Therefore, [tex]\( \tan(A + B) = \frac{11}{57} \)[/tex] in quadrant 2.
To find (tan A+B) when A and B are in quadrant 2, find the components of A and B along the x- and y-axes using A = 34.0 m, θA = 63.0°. Calculate Ax = A cos θA and Ay = A sin θA. Then use the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B) to find the sum of the tangents.
Explanation:First, we find the components of A and B along the x- and y-axes. From the problem, we know that A = B = 34.0 m, and θB = 63.0°. We find the x-components by using Ax = A cos θ, which gives Ax = 34.0 cos 63.0° = -15.23 m.
Similarly, we find the y-components by using Ay = A sin θ, which gives Ay = 34.0 sin 63.0° = 29.88 m.
Now, we can find the sum of the tangents of A and B using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B). Substituting the given values, we have tan(A + B) = (1/3 + Ay/Ax) / (1 - (1/3)(Ay/Ax)).
Two graphs are shown below:
graph A shows scatter points 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 5graph A shows scatter points 1, 4 and 2, 4 and 3, 4 and 4, 4 and 5, 4
Which scatter plot shows a positive correlation between x and y?
Only graph A
Only graph B
Both graph A and graph B
Neither graph A nor graph B
The correct answer is graph A