We have
Initial mass of Polonium-210
[tex]N_0=10\text{ micrograms}[/tex]Decay rate, r = 0.502% = 0.00502
Time, t = 190 days
Then, We know that left amount is given by
[tex]N=N_0e^{-rt}[/tex]Solving
[tex]N=10e^{-0.00502(190)}=10e^{-0.9538}=3.853[/tex]Answer: 3.853 micrograms
Construct a triangle with the given measures. Label all sides and angle measurements. 1. 4 cm, 6cm
Given the two sides measurement,
• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :
• We can find the value of side h by using Pythagorean theorem:
[tex]\begin{gathered} \text{ h = }\sqrt[]{x^2+y^2}\text{ } \\ \text{where x = 4}cm\text{ and y = 6}cm\text{ , } \\ \therefore\text{ h = }\sqrt[]{4^2+6^2} \\ \text{ = 7.2 }cm \end{gathered}[/tex]• Subsequently, we will find angle angle , as shown in the diagram above as follows:
[tex]\begin{gathered} \text{For angle }\beta \\ Tan\text{ }\beta\text{ = opposite /adjacent } \\ \text{Tan }\beta\text{ = }\frac{AB}{BC\text{ }} \\ Tan\text{ }\beta\text{ = }\frac{6}{4} \\ \beta\text{ = }\tan ^{-1}(\frac{6}{4}) \\ \text{ =56.3}\degree \end{gathered}[/tex]• Since we have angle ,= 56.3 °, ,we can find, angle :
,• + + 90° = 180 °,....(angles in a triangle adds up to 180°)
∴ = 180° -90° -56.3°
=33.7°
a line contains the point ( -3, -1 ) and has a slope of 1/3. which equation represents this line?
Given:
Slope = 1/3
Contain the point = ( -3,-1 )
Find-:
The equation of a line.
Explanation-:
The general equation of a line is:
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]Given the slope is 1/3, then the equation of the line become.
[tex]\begin{gathered} m=\frac{1}{3} \\ \\ y=mx+c \\ \\ y=\frac{1}{3}x+c \end{gathered}[/tex]The value of y-intercept is:
The point (-3,-1) contains the line so its satisfied the equation.
[tex]\begin{gathered} (x,y)=(-3,-1) \\ \\ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{3}x+c \\ \\ -1=\frac{1}{3}(-3)+c \\ \\ -1=-1+c \\ \\ c=-1+1 \\ \\ c=0 \end{gathered}[/tex]So equation of line become:
[tex]\begin{gathered} y=mx+c \\ \\ y=\frac{1}{3}x+0 \\ \\ y=\frac{1}{3}x \\ \\ 3y=x \\ \\ x-3y=0 \end{gathered}[/tex]The final equation of line is:
[tex]x-3y=0[/tex]please help meeee i am lost
Answer:
The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit
Find g(x), where g(x) is the reflection across the y-axis of f(x) = -9x - 4.
Write your answer in the form mx + b, where m and b are integers.
g(x) =
Answer: [tex]9x-4[/tex]
Step-by-step explanation:
Reflecting across the y-axis means [tex]f(x) \longrightarrow f(-x)[/tex].
[tex]g(x)=-9(-x)-4=9x-4[/tex]
3/5 × 2/9 and 5/6 × 4/7 and 3/10 × 5/6 and 6/7 × 7/15
1
Step
Multiple both numerator and both denominator
[tex]\frac{3}{5}\text{ x }\frac{2}{9}\text{ = }\frac{3\text{ x 2}}{5\text{ x 9}}\text{ = }\frac{6}{45}\text{ = }\frac{2}{15}[/tex]2
[tex]\frac{5}{6}\text{ x }\frac{4}{7}\text{ = }\frac{5\text{ x 4}}{6\text{ x 7}}\text{ = }\frac{20}{42}\text{ = }\frac{10}{27}[/tex]3
[tex]\frac{3}{10}\text{ x }\frac{5}{6}\text{ = }\frac{3\text{ x 5}}{10\text{ x 6}}\text{ = }\frac{15}{60\text{ }}\text{ = }\frac{1}{4}[/tex]4
[tex]\frac{6}{7}\text{ x }\frac{7}{15}\text{ = }\frac{6\text{ x 7}}{7\text{ x 15}}\text{ = }\frac{42}{105}\text{ = }\frac{2}{5}[/tex]the sum of two consecutive natural number is 36 find the number
Select the correct answer.
What is the product of (7) (-16)(-7) (-1)?
A.
B.
-7
9
B. -16
C. -
D. 192
The product of (7) (-16)(-7) (-1) is - 784 by using simple multiplication.
What is multiplication?Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
7 × -16 = -112
-112 × -7 = 784
784 × -1 = -784
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What is the correct formula for the volume of a cone? Is the correct answer option A B or C?
The formula for the volume of a cone is a third of the product of pi, its height h and the square of its radius r. Then, it is:
[tex]\frac{1}{3}\pi r^2h[/tex]Answer: C
72.7% to nearest 10th percent
Answer:
72.7% to nearest 10th percent would be 73%!
Step-by-step explanation:
Hope it helps! =D
Find the vertex of the parabola y=2x^2+8x+7.
Hi i hope this helps you out
2. Math on the Spot Solve each equation.
A. 3n+ 1 = 19
B. 21 = -2p - 5
A.
[tex]3n =19 - 1 \\ 3n = 18 \\ \frac{3n}{3} = \frac{18}{3} \\ n = 6[/tex]
B.
[tex]21 + 5 = - 2p \\ 2p = - 26 \\ \frac{2p}{2} = \frac{26}{2} \\ p = 13[/tex]
HOPE THIS HELPS.
Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-20y=-160
The equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .
The equation of the line in slope intercept form is written as
y = mx + c ,
where m is the slope of the line , and c is the y intercept .
In the question ,
the equation of the line is given
equation of line is given as 4x-20y = -160
to convert the equation in slope intercept form , we rewrite it as
20y = 4x+160
dividing both sides by 20 ,
we get
20y/20 = 4x/20 + 160/20
y = x/5 + 8
hence ,the slope intercept form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .
Therefore , the equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .
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cost equationcost of producing 7 unitswhat is the break point
Answer:
Part A: C(x) = 0.068x+0.8
Part B: 1.28
Part C: 9.76
Explanation:
Part A:
The cost C equals
cost = revenue - profit
[tex]C(x)=R(x)-P(x)[/tex]which is
[tex]C(x)=0.15x-(0.082x-0.8)[/tex][tex]C(x)=0.15x-0.082x+0.8[/tex][tex]\boxed{C\mleft(x\mright)=0.068x+0.8}[/tex]Part B:
The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives
[tex]C(7)=0.068(7)+0.8[/tex][tex]C(7)=1.28[/tex]Hence, the cost of producing 7 items is 1,28 million dollars.
Part C:
To break even, the cost must equal the revenue
[tex]R(x)=C(x)[/tex]or
[tex]0.15x=0.068x+0.8[/tex]subtracting 0.068 from both sides gives
[tex]0.082x=0.8[/tex]dividing both sides by 0.082 gives
[tex]\boxed{x=9.76}[/tex]which is the break-even point
PLEASE HURRY
What is the value of the expression 45x − 16 if x is equal to −6?
Answer:
-286
Step-by-step explanation:
45(-6)-16
= -270 - 16
= -286
Step-by-step explanation:
45x - 16
x = -6
45(-6) - 16
-270 - 16
-286
Hope this helps! :)
May I please get help with this for I am confused and have tried many times to re-create the reflection of the triangle
We have to reflect the triangle across the y-axis.
If we have a point P = (x,y) and we reflect it across the y-axis, we will change the x-coordinate to its opposite value and and the y-coordinate is kept the same.
The image point then is P' = (-x,y).
Then, to reflect the triangle, we have to reflect the three vertices and then join the vertices.
We can then reflect the vertices as:
3.Justify each step of the solution by stating the name of the property that was used to get to each step.Given: Step 1: 1.________________________________Step 2: 2. _______________________________Step 3: 17x = 403. _______________________________Step 4: 4. _______________________________Answer:
We are given the following equation:
[tex]2(10-13x)+9x=-34x+60[/tex]In the first step we will use the distributive property on the left side:
[tex]20-26x+9x=-34x+60[/tex]In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:
[tex](20-20)+(-26x+9x)=-34x+(60-20)[/tex]Solving the operations we get:
[tex]-17x=-34x+40[/tex]In step 3 we will add 34x to both sides, this is the inverse additive inverse:
[tex](-17x+34x)=(-34x+34x)+40[/tex]Solving the operations:
[tex]17x=40[/tex]In step 4, we divide both sides by 17, this is the division property of equality:
[tex](\frac{17x}{17})=\frac{40}{17}[/tex]Solving the operations:
[tex]x=\frac{40}{17}[/tex]The area of the floor of a square play pen is 6 square meters. What is the perimeter of the play pen? Approximate your answer by rounding to the nearest integer.
Help must be done in less than 10 minutes
Answer:
10 m
Step-by-step explanation:
Area of a square
[tex]A=s^2[/tex]
where s is the side length.
If the area of the floor is 6 m²:
[tex]\begin{aligned}A&=s^2\\\implies 6&=s^2\\\sqrt{6}&=\sqrt{s^2}\\s&=\sqrt{6}\end{aligned}[/tex]
Therefore, the side length of the square is √6 m.
Perimeter of a square
[tex]P=4s[/tex]
where s is the side length.
Substitute the found value for s into the formula to find the perimeter:
[tex]\begin{aligned}P&=4s\\\implies P&=4 \cdot \sqrt{6}\\P&=4 \sqrt{6}\\P&=9.79795897...\\ P&=10 \sf \;m\;(nearest\:integer)\end{aligned}[/tex]
Therefore, the perimeter is 10 m to the nearest integer.
The table shows the number of restaurants in five different cities Cities numbers of restaurants Carlsbad 489 potters vale 261 little hath 282 edgbaston 216 barrow 317 how many more restaurants are there in Carlsbad than in barrow?
To answer this question, we will use the next table (obtained from the Question Tab):
City -------- Number of restaurants
Carlsbad 489
Potter Valley 261
Little Heath 282
Edgbaston 216
Barrow 317
If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:
[tex]489-317=172[/tex]From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow.
We can check this as follows:
In summary, we can say that there are 172 more restaurants in Carlsbad than in Barrow.
Name the segments in the figure below.Q R S ISelect all that apply.
Answer
Options A, F, G, N
The line segments include
QR
QS
QT
RS
RT
ST
Note that the segments only have a dash on top of them and not an arrow.
Explanation
A line segment is a region of a line bounded by two different endpoints and contains all the points on the line that are between the two endpoints.
From the attached image, we can see that there is a line with infinite length (the arrows at the two endpoints indicate that this line continues till infinity), has points Q, R, S and T.
So, the line segments will be any space from one endpoint to another. They'll include
QR
QS
QT
RS
RT
ST
Note that the segments only have a dash on top of them and not an arrow.
Hope this Helps!!!
Use fundamental identities to find the value. Step by step can u explain.
To answer this question, we will use the following diagram as reference:
To determine the tangent of θ, we have to find the value of x.
To find x, we use the Pythagorean theorem and get:
[tex]4^2=3^2+x^2.[/tex]Therefore:
[tex]x=\sqrt{4^2-3^2}=\sqrt[]{7}.[/tex]Therefore:
[tex]\tan \theta=\frac{3}{\sqrt[]{7}}.[/tex]Answer:
[tex]\tan \theta=\frac{3}{\sqrt[]{7}}.[/tex]Dalia's living room is 12 feet long and 10 feet wide. Her dining room
is also 10 feet wide. Write two equivalent expressions that each
represent the combined area of the two rooms.
10ft
12 ft-
Living
Room
xft-
Dining
Room
(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined area of the two rooms.
the given dimensions of the living room are given as follows,
length =12
width/breadth =10
thus the area of the living room will be,
length x breadth, i.e.
=12 x 10
=120 sq. feet
the given dimensions of the dining room are given as follows,
length= x
width/breadth=10
thus the area of the dining room can be calculated as
length x breadth
=10x sq. feet
Now, to calculate the combined area of both the rooms, we have to add the area of the dining room and the area of the living room,
that is,
(120 + 10x) sq. feet
What is area?
The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
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6. Suppose the class takes a test and the following averages are obtained: mean = 80, median= 90, and mode = 70. Tom, who scored 80, would like to know if he did better than half the class. What is your response?
We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.
However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.
Hence, he did not do better than half of the class.Solve the following linear equation using equivalent equations to isolate the variable. Express your answer as an integer, as a simplified fraction, or as a decimal number rounded to two places.
ANSWER
[tex]u=\frac{1}{5}[/tex]EXPLANATION
We want to solve the given linear equation:
[tex]-6u=\frac{-6}{5}[/tex]To do this, divide both sides of the equation by -6 to isolate u and simplify:
[tex]\begin{gathered} \frac{-6u}{-6}=\frac{-6}{5}\cdot\frac{1}{-6} \\ \Rightarrow u=\frac{1}{5} \end{gathered}[/tex]That is the solution to the linear equation.
A number with an absolute value of 42 was divided by a number with an absolute value of 7 The quotient -6. Write two posibble numeric equations
Answer:
-42/7 and 42/-7
Explanation:
The absolute value of a number is represented by:
[tex]|x|[/tex]The lines represent absolute value of a number x, and what it does is that it makes everything into a positive number.
For example |-5|=5 and |5|=5, so we always have two options with an absolute value: that it comes from a negative number or that it comes from a positive number.
In this case we have that a number with an absolute value of 42 (it could be |-42|=42 or |42|=42) divided by a number with an absolute value of 7 (it could be |-7|=7 or |7|=7) the quotient is -6.
One possible numberic equation is:
[tex]\frac{-42}{7}=-6[/tex]Since this meets all the above conditions
Another possible numeric equation is:
[tex]\frac{42}{-7}=-6[/tex]Since this too meets all the above conditions.
Can I please get answer for a and b. I just need the answers. Thanks
When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:
[tex]f(a+2)=(a+2)^2-2(a+2)+1[/tex]Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:
[tex]f(a+2)=a^2+4a+4-2a-4+1[/tex]Now, we group the like-terms and add them:
[tex]\begin{gathered} f(a+2)=a^2+4a-2a+4+4+1 \\ f(a+2)=a^2+2a+1 \end{gathered}[/tex]For yhe other one, Let's do each term and then make the substraction:
[tex]\begin{gathered} f(a+h)=(a+h)^2-2(a+h)+1 \\ f(a+h)=a^2+2ah+h^2-2a-2h+1 \\ f(a+h)=a^2+h^2+2ah-2a-2h+1 \end{gathered}[/tex][tex]f(a)=a^2-2a+1[/tex]So:
[tex]\begin{gathered} f(a+h)-f(a)=a^2+h^2+2ah-2a-2h+1-(a^2-2a+1) \\ f(a+h)-f(a)=a^2-a^2+h^2+2ah-2a+2a-2h+1-1 \\ f(a+h)-f(a)=h^2+2ah-2h \end{gathered}[/tex]Which of the following is the correct mathematical expression for:
The difference between three times a number and 4
Answer:
3x - 4
Step-by-step explanation:
"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.
"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.
"the difference of ___ and ___" means to subtract those two things.
So we get 3x - 4
Point DD is located at (-6,-5)(−6,−5) on the coordinate plane. Point DD is reflected over the xx-axis to create point D'D ′ . What ordered pair describes the location of D'?D ′ ?
The ordered pair that describes the location of N is (2,6)
Given:
N's coordinates are: (-2,-6)
Point N ′ is produced by reflecting point N over the y-axis.
By reflecting point N' over the x-axis, the final point N" is produced.
x , y = -x , y
N(-2 -6) = N'(2 6)
To locate the ordered pair describing where N" is located.
Point N's coordinates are (-2,-6). Point N ′ is produced by reflecting point N over the y-axis.
x , y = -x , y
N(-2 -6) = N'(2 6)
The resultant point N" is created by reflecting point N' over the x-axis.
The ordered pair for point N" is therefore (2,6) gives its location.
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Miss sheet,owner of the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40percent markup on selling price what is most that Misu can pay for a comforter?
The price that Misu can pay for a comforter based on the markup percentage is $103.57.
How to calculate the value?From the information, the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40 percent markup on selling price.
Let the selling price be represented as x. Based on the information given, this will be illustrated as:
x + (40% × x) = 145
x + 0.4x = 145
1.4x = 145
Divide
x = 145/1.4.
x = 103.57
The selling price will be $103.57.
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I need help on these questions
Question 16
[tex](f(x), g(x))=x^2, (x-9)[/tex]
Note it wants the pair, so you just include the definitions of the functions, not f(x)= and g(x)=Question 17
[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]
The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.
A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).
in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.
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El área de un sector circular de un círculo con radio igual a 8cm y ángulo central igual a 56° es aproximadamente
The sectorial area of the circle is equal 31.3cm^2
Area of a SectorThe formula for the b of the sector of a circle is /360o (r2) where r is the radius of the circle and is the angle of the sector.
Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.
Data;
Radius - 8cmangle = 56 degreesThe area of the sector can be calculated using the formula given
[tex]A = \frac{\theta }{360} * \pi r^2[/tex]
Substituting the values into the formula;
[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]
The area is equal 31.3cm^2
Translation:
The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.
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