Answer:
Age of the spear head = 6349 years.
Step-by-step explanation:
Expression to be used to calculate the age of the spear head,
[tex]N_t=N_0e^{-kt}[/tex]
Here, [tex]N_t[/tex] = Final amount of C-14
[tex]N_0[/tex] = Initial amount
[tex]k[/tex] = 0.0001
[tex]t[/tex] = Time in years
If [tex]N_t[/tex] = 53% of [tex]N_0[/tex] = [tex]N_0\times (0.53)[/tex]
[tex]0.53N_0=N_0e^{-0.0001\times t}[/tex]
[tex]0.53=e^{-0.0001t}[/tex]
[tex]\text{ln}(0.53)=\text{ln}(e^{-0.0001t})[/tex]
[tex]-0.634878=(-0.0001)t[/tex]
[tex]t=6348.78[/tex] years
[tex]t[/tex] ≈ [tex]6349[/tex] years
Therefore, age of the spear head = 6349 years.
6. Solve for x!! please help!
x/2 = -7
=> x = -7 × 2
=> x = -14
Answer:
x=-14
Step-by-step explanation:
[tex]\frac{x}{2} =-7\\\\x=-14\\[/tex]
What is the solution to the system that is created by the equation y = - x + 6
Answer:
If you draw the graph of y = -x + 6 on the above graph the solution to system will be the coordinates of the point of intersection.
the equation of the line drawn above is y = 0.5x
so you can also find the solution by solving the system
y = 0.5x
y = -x + 6
0.5x = -x + 6
1.5x = 6
x = 6/1.5 = 4
and y = 0.5*4 = 2
The answer is (4, 2) - the third choice.
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
1 : 5
Step-by-step explanation:
3 students zoo
15 students aquarium
zoo : not zoo
3: 15
Divide each side by 3
3/3 : 15/3
1 : 5
.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
What is the constant of variation?
What is the equation representing the direct variation?
Answer:
The constant of variation is 1/9
The equation representing the direct variation is y/x= 1/9
Step-by-step explanation:
In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get
y/x = k
3 / 27 = k
(3/27) / (3/3) = 1/9* = k
Therefore, the constant of variation is 1/9
Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation
* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both
The constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation of direct variation is given by,
y = kx ....(i) where "k" is a constant.
Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
Given that y varies directly with x, and x = 27, then y = 3.
Substitute the values of y = 3 and x = 27 in the direct variation equation and solve for k:
⇒ 3 = 27k
⇒ k = 3/27
⇒ k = 1/9
Substitute the values of k = 1/9 in the direct variation equation :
⇒ y = (1/9)x
Thus, the constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
Learn more about the equations here:
brainly.com/question/10413253
#SPJ6
Please help me solve this!
Answer:
Step-by-step explanation:
Reference angle = 27
height = 2
Sin(27) = opposite / hypotenuse
hypotenuse = opposite / sin(27)
opposite = 2
hypotenuse = 2 / sin(27)
hypotenuse = 4.405
The ramp has to be 4.41 feet long.
If x^2-ax+b and x^2-cx+d both have a factor x-m prove that m=d-b/c-a
Answer:
see explanation
Step-by-step explanation:
Given (x - m) is a factor of both then x = m make both expressions equal to zero.
m² - am + b = 0
m² - cm + d = 0
Then
m² - am + b = m² - cm + d ( subtract m² - cm from both sides )
cm - am + b = d ( subtract b from both sides )
cm - am = d - b ← factor out m from each term on the left side
m(c - a) = d - b ← divide both sides by (c - a)
m = [tex]\frac{d-b}{c-a}[/tex] ← as required
Find the solution set of the inequality. -25 > -5(x + 2.5
Answer:
-25 > -5(x+2.5)
-25 > -5x -12.5
x > 5/2
please click thanks and mark brainliest if you like :)
Answer:
x < 2.5
Step-by-step explanation:
-25>-5(x-12.5)
-25 > -5x -12.5
add 12.5 to both sides
-25+12.5 > -5x -12.5+12.5
-12.5> -5x
divide both sides by -5
(-12.5/-5)> -5x/-5
x>2.5
since we divided by a negative,the inequality sign will flip over
x<2.5
Will Mark Brainlest Help pls
Answer:
Hello,
[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]
How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4
Answer:
OB
Step-by-step explanation:
start counting from 1
Then your significant digit is 6
Can anyone please help?
Answer:
i don't know
( lol )
heheeeee
find the missing side.
Answer:
I htink x ≈ 8
Step-by-step explanation:
Answer:
X is approximately 7.8.
Step-by-step explanation:
You can use SOH-CAH-TOA to help figure out what function (sin, cos, tan) you need to use in order to figure out the missing side.
For this one, we can see the angle is pointing to the opposite side (x length), and we have been given the hypotenuse (18). So we want to use the sin function.
[tex]sin\ (angle)=\frac{opposite}{hypotenouse}[/tex]
[tex]sin (26)=\frac{x}{18}[/tex]
[tex]0.438=\frac{x}{18}[/tex]
[tex]7.890... = x[/tex]
Using Pythagorean theorm, you can figure out the other side if need be :)
For reference:
[tex]sin (angle)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(angle)=\frac{opposite}{adjacent}[/tex]
On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from
Saugerties to Catskill be on this map?
Answer:
10miles
Step-by-step explanation:
Answer:
I have no clue what is going on wit dis g
Explain how to solve the equation
.
b – 7 = 12
Answer:
19
Step-by-step explanation:
Add 7 onto 12 to find answer.
Answer:
b = 19
Step-by-step explanation:
b = 12 + 7
Simplify 12+7 to 19.
Write an inequality and show on a number line all numbers:
less than 4 but greater than or equal to 0
Answer:
the inequality is 0<x<4
Step-by-step explanation:
(0,4)
Find the measure of
Answer:
74 degrees
.................
Answer:
74
Step-by-step explanation:
BEC and CED form a straight line so they add to 180
BEC+CED = 180
106+ CED = 180
CED = 180-106
CED = 74
I just need help on this and fast
hope this helps you understand the concept
Can someone plz help me
Answer:
37500
Step-by-step explanation:
pattern is multiplying by -5.
-7,500*-5 = 37,500
Have a nice day! :-)
HELP PLS HELP MEEEEE IM FAILING PYTHAGOREAN THEOREM
7^2 + 6^2 = h^2
49 + 36 = h^2
85 = h^2
√85 = h
h = 9.21m
Answered by Gauthmath must click thanks and mark brainliest
The surface area of a sphere is a function of the radius of the sphere: A = 41182.
Evaluate the function for a basketball with a radius of 11.5 cm.
The value of the function of the surface area of a sphere when the radius is 11.5 cm is approximately 1661.9 cm²
The process of arriving at the above value is as follows;
The known parameter
The function of the radius representing the surface area of a sphere is, f(r) = A = 4·π·r²
The radius of the basketball, r = 11.5 cm
Required;
To evaluate the function, f(r), for the basketball
Method;
The process of evaluating a function, is to find the value of the function at a given value of the input or independent variable of the function
The input variable is the variable that determines the output value of the function, it is the variable which is the function is about
In the question, the function given is dependent on the radius, r
To evaluate the value of the function, we substitute the value of r in the equation of the functionTherefore;
When r = 11.5 cm (the radius of the basketball), from the function, the surface area of the basketball, A = f(11.5) = 4 × π × (11.5 cm)² ≈ 1661.9 cm²
Therefore;
The evaluation of the function which is the value of the function, f(r) = A,
when the radius, r, is 11.5 cm, which is the surface area of the spherical
basketball, is A ≈ 1661.9 cm²
Learn more about evaluation of functions here;
https://brainly.com/question/11743679
Please answer this!!
Answer:
C, 5/12
Step-by-step explanation:
The tangent of an angle is defined as the side opposite to that angle divided by the side adjacent to that angle. The tangent of angle A would be equal to the value of side BC divided by side AB. The value of side BC is 5, and the value of side AB is 12. The answer is 5/12.
Answer: ∠A=[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Tangent is opposite over adjacent.
Find the value of z
A.110
B.141
C.80
D.100
Answer:
Option A 110degree is the answerSelect all decimals that are equivalent to
(
9
×
100
)
+
(
2
×
10
)
+
(
3
×
1
10
)
+
(
5
×
1
100
)
.
A.
92.35
B.
920.350
C.
902.35
D.
92.350
E.
920.35
F.
920.035 I really need help
Answer:
B, E
Step-by-step explanation:
( 9 × 100 ) + ( 2 × 10 ) + ( 3 × 0.10 ) + ( 5 ×0.01 ) = 920.35
A. 92.35
B. 920.350
C. 902.35
D. 92.350
E. 920.35
F. 920.035
Find the slope of the line that passes through (-26, 9) and (32, 71).
Answer:
[tex]Slope = \frac{31}{29}[/tex]
Step-by-step explanation:
Step 1: Define the slope formula
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Step 2: Find the slope
[tex]Slope = \frac{71-9}{32-(-26)}[/tex]
[tex]Slope = \frac{62}{58}[/tex]
[tex]Slope = \frac{31}{29}[/tex]
Answer: [tex]Slope = \frac{31}{29}[/tex]
Find the measure of <3. 90 50 40 130
=============================================================
Explanation:
This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.
One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.
The measure of ∠3 is 90°
Because in a kite the diagonals bisects at 90°
Therefore ∠3 is 90°
Answered by Gauthmath must click thanks and mark brainliest
A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?
Answer:
160 chemistry books and 80 history books
Step-by-step explanation:
C=chemistry books sold, H=history books sold
C=2H
C+H=240, 3H=240, H=80, C=160
Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?
Answer:
where is the figure without figure how to find out
17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.
Answer:
Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.
Each coffee pot hold 6 cups of coffee we sell 10 cups of coffee every fifteen minutes how many pots of coffee do I need to make in an hour?
Answer:
7 pots of coffee (If you want to be precise its 6 2/3)
Step-by-step explanation:
So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)
What is the period of the graph of y=1/2 sin (2πx) -3?
A. 1
B. 1/2
C. 3
D. 2π
Answer:
A. 1
Step-by-step explanation:
Since this graph is in the form A sin (B(x+c))+d, where
the amplitude is the absolute value of AThe period is 2pi/BPhase Shift is CMidline is y=DTherefore, the values are
A=1/2
B=2pi
C=0
D=-3
So the period is 2pi/2pi which is 1.
3/5 of 1 hour is? pls give me the answer
1hr=60min
[tex]\\ \sf\longmapsto \dfrac{3}{5}\;of\;60min[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{5}\times 60[/tex]
[tex]\\ \sf\longmapsto \dfrac{180}{5}[/tex]
[tex]\\ \sf\longmapsto 36min[/tex]