Answer:
[tex]a < 0.287[/tex]
Step-by-step explanation:
we have
[tex]13^{4a} < 19[/tex]
Solve for a
Apply log both sides
[tex]log(13^{4a}) < log(19)[/tex]
Remember the rule
㏒(a^n) = n ㏒(a)
so
[tex](4a)log(13) < log(19)[/tex]
Divide by 4 log(13) both sides
[tex]a < log(19)/[4log(13)][/tex]
[tex]a < 0.2870[/tex]
15.5
tons
155 tons =how many
pounds
square root of 3 x^2 times square root of 4x
[tex]\bf \sqrt{3x^2}\cdot \sqrt{4x}\implies \sqrt{3x^2\cdot 4x}\implies \sqrt{12x^2x}\implies \sqrt{4\cdot 3\cdot x^2x} \\\\\\ \sqrt{2^2\cdot 3\cdot x^2x}\implies 2x\sqrt{3x}[/tex]
Determine if the two figures are congruent and explain your answer.
To determine if two figures are congruent, we need to check if one can be obtained from the other through a combination of rigid transformations. The specific transformations that can be applied to one figure to make it coincide with the other need to be described to explain if the figures are congruent or not.
If two figures are congruent, we need to check if one can be obtained from the other through a combination of rigid transformations. Rigid transformations include translations, rotations, and reflections. If we can apply a series of these transformations to one figure to make it coincide exactly with the other, then the figures are congruent.
Without specific information about the figures, I can provide a general explanation of how you might approach this:
Translation (Slide): Check if one figure can be translated (slide) to coincide with the other. If you can move one figure to overlap with the other without rotating or reflecting it, they might be congruent.Rotation (Turn): Check if one figure can be rotated to match the orientation of the other. If a rotation can make the two figures coincide, they may be congruent.Reflection (Flip): Check if one figure can be reflected (flipped) to match the other. If a reflection can be applied to one figure to make it coincide with the other, they may be congruent.To explain your answer, describe the specific transformations (translations, rotations, reflections) that can be applied to one figure to make it coincide with the other. If you can perform a sequence of these transformations to superimpose one figure onto the other, then the figures are congruent. If not, they are not congruent.
Given the function f(x) = 2x – 1 and the linear function g(x), which function has a greater value when x = 3?
A.f(x) is greater.
B.g(x) is greater.
C.f(x) and g(x) are the same when x=3
D.g(x) is undefined when x=3
Answer:
Option B. g(x) is greater
Step-by-step explanation:
step 1
Find the value of f(x) when the value of x is equal to 3
we have
f(x)=2x-1
substitute the value of x=3
f(3)=2(3)-1=5
step 2
Find the value of g(x) when the value of x is equal to 3
Observing the graph
when x=3
g(3)=7
step 3
Compare the values
f(x)=5
g(x)=7
so
g(x) > f(x)
g(x) is greater
Answer:
Correct option is:
B. g(x) is greater
Step-by-step explanation:
Firstly, we find the value of f(x) when x=3
f(x)=2x-1
substitute the value of x=3
f(3)=2×3-1=5
On observing the graph, we see that g(x)=7 when x=3
Now, on Comparing the values of f(x) and g(x) when x=3
f(3)=5
g(3)=7
so, g(x) > f(x) when x=3
So, Correct option is:
B. g(x) is greater
Find the shortest distance from A to B in the diagram below.
Answer: 14 m
Step-by-step explanation:
8 m + 6 m = 14 m
Answer:
10 cm.
Step-by-step explanation:
We have been given a cuboid. We are asked to find the shortest distance from A to B is the given diagram.
We know that shortest distance from A to B will be equal to hypotenuse of right triangle with two legs 8 meters and 6 meters.
[tex]AB^2=8^2+6^2[/tex]
[tex]AB^2=64+36[/tex]
[tex]AB^2=100[/tex]
Now, we will take square root of both sides of our given equation as:
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the shortest distance from A to B is 10 cm.
The polynomial P(x) = 2x^3 + mx^2-5 leaves the same remainder when divided by (x-1) or (2x + 3). Find the value of m and the remainder.
The polynomial also leaves the same remainder also leaves the same remainder when divided by (qx+r), find
the values of q and r.
Answer:
m=7
Remainder =4
If q=1 then r=3 or r=-1.
If q=2 then r=3.
They are probably looking for q=1 and r=3 because the other combinations were used earlier in the problem.
Step-by-step explanation:
Let's assume the remainders left when doing P divided by (x-1) and P divided by (2x+3) is R.
By remainder theorem we have that:
P(1)=R
P(-3/2)=R
[tex]P(1)=2(1)^3+m(1)^2-5[/tex]
[tex]=2+m-5=m-3[/tex]
[tex]P(\frac{-3}{2})=2(\frac{-3}{2})^3+m(\frac{-3}{2})^2-5[/tex]
[tex]=2(\frac{-27}{8})+m(\frac{9}{4})-5[/tex]
[tex]=-\frac{27}{4}+\frac{9m}{4}-5[/tex]
[tex]=\frac{-27+9m-20}{4}[/tex]
[tex]=\frac{9m-47}{4}[/tex]
Both of these are equal to R.
[tex]m-3=R[/tex]
[tex]\frac{9m-47}{4}=R[/tex]
I'm going to substitute second R which is (9m-47)/4 in place of first R.
[tex]m-3=\frac{9m-47}{4}[/tex]
Multiply both sides by 4:
[tex]4(m-3)=9m-47[/tex]
Distribute:
[tex]4m-12=9m-47[/tex]
Subtract 4m on both sides:
[tex]-12=5m-47[/tex]
Add 47 on both sides:
[tex]-12+47=5m[/tex]
Simplify left hand side:
[tex]35=5m[/tex]
Divide both sides by 5:
[tex]\frac{35}{5}=m[/tex]
[tex]7=m[/tex]
So the value for m is 7.
[tex]P(x)=2x^3+7x^2-5[/tex]
What is the remainder when dividing P by (x-1) or (2x+3)?
Well recall that we said m-3=R which means r=m-3=7-3=4.
So the remainder is 4 when dividing P by (x-1) or (2x+3).
Now P divided by (qx+r) will also give the same remainder R=4.
So by remainder theorem we have that P(-r/q)=4.
Let's plug this in:
[tex]P(\frac{-r}{q})=2(\frac{-r}{q})^3+m(\frac{-r}{q})^2-5[/tex]
Let x=-r/q
This is equal to 4 so we have this equation:
[tex]2u^3+7u^2-5=4[/tex]
Subtract 4 on both sides:
[tex]2u^3+7u^2-9=0[/tex]
I see one obvious solution of 1.
I seen this because I see 2+7-9 is 0.
u=1 would do that.
Let's see if we can find any other real solutions.
Dividing:
1 | 2 7 0 -9
| 2 9 9
-----------------------
2 9 9 0
This gives us the quadratic equation to solve:
[tex]2x^2+9x+9=0[/tex]
Compare this to [tex]ax^2+bx+c=0[/tex]
[tex]a=2[/tex]
[tex]b=9[/tex]
[tex]c=9[/tex]
Since the coefficient of [tex]x^2[/tex] is not 1, we have to find two numbers that multiply to be [tex]ac[/tex] and add up to be [tex]b[/tex].
Those numbers are 6 and 3 because [tex]6(3)=18=ac[/tex] while [tex]6+3=9=b[/tex].
So we are going to replace [tex]bx[/tex] or [tex]9x[/tex] with [tex]6x+3x[/tex] then factor by grouping:
[tex]2x^2+6x+3x+9=0[/tex]
[tex](2x^2+6x)+(3x+9)=0[/tex]
[tex]2x(x+3)+3(x+3)=0[/tex]
[tex](x+3)(2x+3)=0[/tex]
This means x+3=0 or 2x+3=0.
We need to solve both of these:
x+3=0
Subtract 3 on both sides:
x=-3
----
2x+3=0
Subtract 3 on both sides:
2x=-3
Divide both sides by 2:
x=-3/2
So the solutions to P(x)=4:
[tex]x \in \{-3,\frac{-3}{2},1\}[/tex]
If x=-3 is a solution then (x+3) is a factor that you can divide P by to get remainder 4.
If x=-3/2 is a solution then (2x+3) is a factor that you can divide P by to get remainder 4.
If x=1 is a solution then (x-1) is a factor that you can divide P by to get remainder 4.
Compare (qx+r) to (x+3); we see one possibility for (q,r)=(1,3).
Compare (qx+r) to (2x+3); we see another possibility is (q,r)=(2,3).
Compare (qx+r) to (x-1); we see another possibility is (q,r)=(1,-1).
If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =
Answer:
The value of k is -11
Step-by-step explanation:
If (x+2) is a factor of x3 − 6x2 + kx + 10:
Then,
f(x)=x3 − 6x2 + kx + 10
f(-2)=0
f(-2)=(-2)³-6(-2)²+k(-2)+10=0
f(-2)= -8-6(4)-2k+10=0
f(-2)= -8-24-2k+10=0
Solve the like terms:
f(-2)=-2k-22=0
f(-2)=-2k=0+22
-2k=22
k=22/-2
k=-11
Hence the value of k is -11....
(x)=3log(x+5)+2 what is the x intercept
Answer:
[tex]\large\boxed{x-intercept=-2+\sqrt[3]{0.01}}[/tex]
Step-by-step explanation:
[tex]f(x)=3\log(x+5)+2\to y=3\log(x+5)+2\\\\\text{Domain:}\ x+5>0\to x>-5\\\\\text{x-intercept is for }\ y=0:\\\\3\log(x+5)+2=0\qquad\text{subtract 2 from both sides}\\\\3\log(x+5)=-2\qquad\text{divide both sides by 3}\\\\\log(x+5)=-\dfrac{2}{3}\qquad\text{use the de}\text{finition of logarithm}\\\\(\log_ab=c\iff b^c=a),\ \log x=\log_{10}x\\\\\log(x+2)=-\dfrac{2}{3}\\\\\log_{10}(x+2)=-\dfrac{2}{3}\iff x+2=10^{-\frac{2}{3}}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n[/tex]
[tex]x+2=\left(\dfrac{1}{10}\right)^\frac{2}{3}\qquad\text{use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\\\\x+2=\sqrt[3]{0.1^2}\qquad\text{subtract 2 from both sides}\\\\x=-2+\sqrt[3]{0.01}\in D[/tex]
the system of equations graphed below has how many solutions? y=-3/2x-3 y=-3/2x+5
Answer:
No solutions.
Step-by-step explanation:
The value of y cannot be equal to both -3/2x - 3 and -3/2x + 5.
Kevin’s car requires 5 liters of diesel to cover 25 kilometers. How many liters of diesel will Kevin need if he has to cover 125 kilometers?
Answer: 25 litres
Step-by-step explanation: If it takes 5 litres of diesel to cover 25km, it means it will take more litres to cover 125km. So you have to divide 125km by 25km then you will get 5 which you will then multiply by 5 litres to get 25 litres of diesel.
which of the following recursive formulas represent the same arithmetic sequence as the explicit formula an=5+(n-1)2
a. a1=5
an=an-1+2
b. a1=5
an=(an-1+2)5
c. a1=2
an=an-1+5
d. a1=2
an=an-1*5
Answer:
Choice A:
[tex]a_1=5[/tex]
[tex]a_{n}=a_{n-1}+2[/tex]
Step-by-step explanation:
[tex]a_n=5+(n-1)2[/tex]
means we looking for first term 5 and the sequence is going up by 2.
In general,
[tex]a_n=a_1+(n-1)d[/tex]
means you have first term [tex]a_1[/tex] and the sequence has a common difference of d.
So it is between the first two choices.
The explicit form of an arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
An equivalent recursive form is [tex]a_n=a_{n-1}+d \text{ where } a_1 \text{ is the first term}[/tex]
So d again here is 2.
So choice a is correct.
[tex]a_1=5[/tex]
[tex]a_{n}=a_{n-1}+2[/tex]
Answer: Option a
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
Step-by-step explanation:
The arithmetic sequences have the following explicit formula
[tex]a_n=a_1 +(n-1)*d[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
The recursive formula for an arithmetic sequence is as follows
[tex]\left \{ {{a_1} \atop {a_n=a_{(n-1)}+d}} \right.[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
In this case we have the explicit formula [tex]a_n=5+(n-1)*2[/tex]
Notice that in this case
[tex]a_1 = 5\\d = 2[/tex]
Then the recursive formula is:
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
The answer is the option a.
Nolan buys baseball bats to sell in his store. Each bat costs him $19.99 and he is using a mark up rate of 85%. At what selling price will Nolan sell each bat?
Answer:
The selling price of each bat is $36.98
Step-by-step explanation:
* Lets explain how to solve the problem
- Nolan buys baseball bats to sell in his store
- Each bat costs him $19.99
- He is using a mark up rate of 85%
- The selling price = cost price + markup
* Lets solve the problem
∵ The cost price of each bat is $19.99
∵ The markup is 85%
- To find the markup multiply its percent by the cost price
∴ The markup = 19.99 × 85/100 = $16.9915
∵ The selling price = the cost price + the markup
∴ The selling price = 19.99 + 16.9915 = 36.9815
* The selling price of each bat is $36.98
the following table shows the distance from school as a function time
time in minutes. distance in meters
x. f(x)
0 36
3 32
6 28
9 24
12 20
find and intercept the meaning of the x intercept in this scenario
36,0 the distance away from the school
27,0 the time it takes to reach the school
36,0 the time it takes to reach the school
27,0 the distance away from the school
Answer:
27,0 the distance away from the school
Step-by-step explanation:
Apply the formula for equation of a straight line;
y=mx+c where c is the y intercept , and m is the gradient
From the graph, the slope is negative where speed decreases with increase in time
Find the gradient by applying the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking y₁=24, y₂=20, x₁=9, x₂=12
Then;
[tex]m=\frac{20-24}{12-9} =\frac{-4}{3}[/tex]
write the equation of the function as ;
y=mx+c, c=36( the y-intercept when x=0) hence the equation is;
[tex]y=mx+c\\\\y=\frac{-4}{3}x+36[/tex]
To get x-intercept, substitute value of y with 0
[tex]y=mx+c\\\\\\y=-\frac{4}{3} +36\\\\\\0=-\frac{4}{3} x+36\\\\\frac{4}{3}x =36\\\\\\4x=36*3\\\\\\x=108/4=27[/tex]
This means that the x-intercept is 27 ,and this means you will require 27 minutes to cover the whole distance to the school.
Answer:
A: 36,0 the distance away from the school
Step-by-step explanation:
At 0 it means you have spent 0 minutes going to school which means you haven't left the starting point yet.
36 is the distance left (in meters) from your current position and school. This means that the school is 36 meters away from the starting point.
What is the missing side length in this right triangle? A. 15 B. 21 C. 225 D. 441
9,12?
Answer:
A. 15.
Step-by-step explanation:
9^2 + 12^2
= 81 + 144
= 225.
Taking the square root: we get 15.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the two sides of the triangle, therefore, using the Pythagorean theorem, the third side of the triangle can be written as,
x² = 12² + 9²
x² = 144 + 81
x² = 225
x = 15
Hence, the missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
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An ant can run an inch per second. How long will it take the same ant to run a foot?
Answer:
12 seconds.
Step-by-step explanation:
There are 12 inches in a foot so the ant can run a foot in 1 *12 = 12 seconds.
PLEASE HURRY
WILL GIVE BRAINLIEST
What is the equation for the hyperbola shown?
Find the answer in the attachment.
The hyperbola's equation is x² / 3600 - y² / 121 = 1, centered at the origin (0,0). Its vertices are at (60,0), (-60,0) on the x-axis, and (0,11), (0,-11) on the y-axis.
To find the equation of the hyperbola, we need to determine its center and the distances from the center to the vertices along the x and y axes. The general equation of a hyperbola centered at (h, k) is given by:
(x - h)² / a² - (y - k)² / b² = 1
Where (h, k) is the center of the hyperbola, and 'a' and 'b' are the distances from the center to the vertices along the x and y axes, respectively.
In this case, since the hyperbola is symmetric along the x and y axes, the center is at the origin (0, 0). Also, we know the distance from the center to the vertices along the x-axis is 60 units (60 and -60) and along the y-axis is 11 units (11 and -11).
So, a = 60 and b = 11.
Now we can plug these values into the equation:
x² / (60)² - y² / (11)² = 1
Simplifying further:
x² / 3600 - y² / 121 = 1
And that's the equation of the hyperbola.
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What is the distance between the points (4,3) and (1,-1) on the coordinate plane?
If a scalene triangle has its measures 4 m, 11 m and 8 m, find the largest angle.
A. 129.8
B. 90.0
C. 34.0
D. 16.2
Answer:
129.8 approximately
Step-by-step explanation:
So this sounds like a problem for the Law of Cosines. The largest angle is always opposite the largest side in a triangle.
So 11 is the largest side so the angle opposite to it is what we are trying to find. Let's call that angle, X.
My math is case sensitive.
X is the angle opposite to the side x.
Law of cosines formula is:
[tex]x^2=a^2+b^2-2ab \cos(X)[/tex]
So we are looking for X.
We know x=11, a=4, and b=8 (it didn't matter if you called b=4 and a=8).
[tex]11^2=4^2+8^2-2(4)(8)\cos(X)[/tex]
[tex]121=16+64-64\cos(X)[/tex]
[tex]121=80-64\cos(X)[/tex]
Subtract 80 on both sides:
[tex]121-80=-64\cos(X)[/tex]
[tex]41=-64\cos(X)[/tex]
Divide both sides by -64:
[tex]\frac{41}{-64}=\cos(X)[/tex]
Now do the inverse of cosine of both sides or just arccos( )
[these are same thing]
[tex]\arccos(\frac{-41}{64})=X[/tex]
Time for the calculator:
X=129.8 approximately
What is the solution of 4.5x-100>125
Answer:
x > 50Step-by-step explanation:
[tex]4.5x-100>125\qquad\text{add 100 to both sides}\\\\4.5x-100+100>125+100\\\\4.5x>225\qquad\text{divide both sides by 4.5}\\\\\dfrac{4.5x}{4.5}>\dfrac{225}{4.5}\\\\x>50[/tex]
The solution to the inequality 4.5x - 100 > 125 is x > 50.
The given inequality is 4.5x - 100 > 125.
To solve it, first, add 100 to both sides to get 4.5x > 225. Then, divide by 4.5 to find x > 50. Therefore, the solution to the inequality is x > 50.
Steps for solving 3x + 18 = 54 are shown.
Explain how Step 1 helps solve the equation.
3x+18 = 54
3x + 18-18 = 54 -18
3x = 36
3x_36
33
X = 12
Original equation
Step 1
Step 2
Step 3
Step 4
) A. Adding 18 to both sides undoes the subtraction.
O
B. Adding 18 to both sides combines like terms.
O
C. Subtracting 18 from both sides isolates the variable term.
O
D. Subtracting 18 from both sides isolates the variable.
C
By subtracting 18 to both sides you are separating the 3x because you are not ready to isolate the variable (x) in step 1
Answer:
WELP i got little different answers and for me it was A
A.
Adding 18 to both sides isolates the variable term.
B.
Adding 18 to both sides isolates the variable.
C.
Subtracting 18 from both sides undoes the subtraction.
D.
Subtracting 18 from both sides combines like terms.
Question 12 Multiple Choice Worth 1 points)
(03.07 LC)
Choose the equation of the horizontal line that passes through the point (-8, -7).
Answer:
linear inqution
Step-by-step explanation:
relationship
ANSWER
[tex]y = - 7[/tex]
EXPLANATION
A horizontal line that passes through (a,b) has equation
[tex]y = b[/tex]
This is because a horizontal line is a constant function.
The y-values are the same for all x belonging to the real numbers.
The given line passes through (-8,-7).
In this case, we have b=-7.
Therefore the equation of the horizontal line that passes through the point (-8, -7) is
[tex]y = - 7[/tex]
Which graph shows the line y-2 = 2(x + 2)?
A/B/co
A. Graph A
B. Graph B
C. Graph D
D. Graph c
Answer:
The answer is Graph A.
Step-by-step explanation:
i got the answer from the teachers answer key
Graph A shows the line y-2 = 2(x + 2).
The answer is option A
What is a straight line graph?
The graph follows a straight line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.solving the equation:-
y-2 = 2(x + 2)
y=2x+4+2
Y=2x+6
y-intercepts = 6 (Graph A represents this).
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In a pet shop, there are 3 hamsters for every 2 guinea pigs, and there are 2 giant cloud rats for every 3 guinea pigs. If n is the total number of hamsters, guinea pigs, and giant cloud rats, and n>0, then what is the smallest possible value of n?
Answer:
n = 19.
Step-by-step explanation:
If there are x guinea pigs then there are 3/2 x and 2/3 x rats.
So n = x + 3/2 x + 2/3 x
n = 19x / 6
19x = 6n
Let x = 6 , then n = 19*6 / 6 = 19.
Now n and x must be whole numbers so x is 6 and n = 19 are the smallest possible values.
Answer:
n=19
Step-by-step explanation:
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What is the slope of st.line xcosa+ysina=p? ( Find by using derivative)
Answer:
Assume that [tex]a[/tex] and [tex]p[/tex] are constants. The slope of the line will be equal to
[tex]\displaystyle -\frac{\cos{(a)}}{\sin{(a)}} = \cot{(a)}[/tex] if [tex]\sin{a} \ne 0[/tex];Infinity if [tex]\sin{a} = 0[/tex].Step-by-step explanation:
Rewrite the expression of the line to express [tex]y[/tex] in terms of [tex]x[/tex] and the constants.
Substract [tex]x\cdot \cos{(a)}[/tex] from both sides of the equation:
[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].
In case [tex]\sin{a} \ne 0[/tex], divide both sides with [tex]\sin{a}[/tex]:
[tex]\displaystyle y = - \frac{\cos{(a)}}{\sin{(a)}}\cdot x+ \frac{p}{\sin{(a)}}[/tex].
Take the first derivative of both sides with respect to [tex]x[/tex]. [tex]\frac{p}{\sin{(a)}}[/tex] is a constant, so its first derivative will be zero.
[tex]\displaystyle \frac{dy}{dx} = - \frac{\cos{(a)}}{\sin{(a)}}[/tex].
[tex]\displaystyle \frac{dy}{dx}[/tex] is the slope of this line. The slope of this line is therefore
[tex]\displaystyle - \frac{\cos{(a)}}{\sin{(a)}} = -\cot{(a)}[/tex].
In case [tex]\sin{a} = 0[/tex], the equation of this line becomes:
[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].
[tex]x\cos{(a)} = p[/tex].
[tex]\displaystyle x = \frac{p}{\cos{(a)}}[/tex],
which is the equation of a vertical line that goes through the point [tex]\displaystyle \left(0, \frac{p}{\cos{(a)}}\right)[/tex]. The slope of this line will be infinity.
If a fair coin is tossed 11 times, in how many different ways can the sequence of heads and tails appear?
2048 different ways can the sequence of heads and tails appear.
What is possibility?The definition of a possibility is something that may be true or might occur, or something that can be chosen from among a series of choices.
According to the question
Fair coin is tossed 11 times
There are two possibilities for each flip (Heads or Tails). You multiply those together to get the total number of unique sequences.
Here’s an example for 2 flips: HH - HT - TT - TH. (That’s 2 × 2, or [tex]2^{2}[/tex])
Here’s 3 flips: HHH - HHT - HTH - HTT - THH - THT - TTH - TTT. (That’s
2× 2 × 2, or [tex]2^{3}[/tex]).
For ten flips, it’s [tex]2^{10}[/tex]… which is 1024.
For 11 flips, it's [tex]2^{11}[/tex].......Which is 2048
2048 different ways can the sequence of heads and tails appear.
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Final answer:
There are 2048 different ways that a sequence of heads and tails can appear after tossing a fair coin 11 times, because each coin toss has two possible outcomes and the events are independent.
Explanation:
If a fair coin is tossed 11 times, the number of different sequences of heads and tails that can appear is calculated using the formula for the number of outcomes of binomial events. Since each toss of the coin has two possible outcomes (either a head or a tail), and we are tossing the coin 11 times, we use the power of 2 raised to the 11th power, which gives us 211 = 2048. Therefore, there are 2048 different ways a sequence of heads and tails can appear after tossing a coin 11 times.
The reason why there are so many combinations is that each coin toss is independent of the previous one, with a 50 percent chance of landing on either side. This principle is used in probability theory to calculate the possible outcomes of repeated binary events. As an interesting note, if we were to look at possibilities of a specific number of heads and tails, such as 10 heads and 1 tail or vice versa, this would be represented in Pascal's triangle, which reflects the coefficients in the binomial expansion.
If 20% of a = b, then b% of 20 is same as?
[tex]20\%\text{ of } a=b \Longleftrightarrow0.2a=b\\\\b\%\text{ of } 20 \Longleftrightarrow \dfrac{b}{100}\cdot20\\\\\dfrac{b}{100}\cdot20=\dfrac{b}{5}=\dfrac{0.2a}{5}=\boxed{\boxed{a}}[/tex]
The Montanez family is a family of four people. They have used 3,485.78 gallons of water so far this month. They cannot exceed 7,250.50 gallons per month during the drought season. Write an inequality to show how much water just one member of the family can use for the remainder of the month, assuming each family member uses the same amount of water every month.
Answer:
x ≤ 3764.72
Step-by-step expl anation:
The Montanez family cannot use more than 7250.50 gallons, this means that they can use less than or equal to 7250.50 gallons, this tells you which sign to use. The variable x can be used to describe how much water they have left to use and then you add 3,485.78 gallons to x.
x + 3485.78 ≤ 7250.50 This inequality means that the amount of water the family has yet to use added to 3485.78 gallons cannot exceed 7250.50 gallons.
Next, you simplify the inequality using the property of inequalities.
x ≤ 7250.50 - 3485.78
x ≤ 3764.72
The required inequality is x<941.18 for the Montanez family if they have used 3485.78 gallons of water.
What is inequality?It is also a relationship between variables but this is in greater than , less than, greater than or equal to , less than or equal to is used.
How to form an inequality?Let the water used by a member be x
so
x*4=7250.50-3485.78
4x=3764.72
x=941.18
Hence one member can only use 941.18 gallons of water in the month.
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A jet plane travels 2 times the speed of a commercial airplane. The distance between Vancouver
and Regina is 1730 km. If the flight from Vancouver to Regina on a commercial airplane takes
140 minutes longer than a jet plane, what is the time of a commercial plane ride of this route? (please show steps:))
Answer:
The time of a commercial airplane is 280 minutes
Step-by-step explanation:
Let
x -----> the speed of a commercial airplane
y ----> the speed of a jet plane
t -----> the time that a jet airplane takes from Vancouver to Regina
we know that
The speed is equal to divide the distance by the time
y=2x ----> equation A
The speed of a commercial airplane is equal to
x=1,730/(t+140) ----> equation B
The speed of a jet airplane is equal to
y=1,730/t -----> equation C
substitute equation B and equation C in equation A
1,730/t=2(1,730/(t+140))
Solve for t
1/t=(2/(t+140))
t+140=2t
2t-t=140
t=140 minutes
The time of a commercial airplane is
t+140=140+140=280 minutes
The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.
Part a) Total Cost
Total Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.
The total cost is ( $65,000 fixed) + (15,000 x $7.5)
=$65,000+$112,500
=$177,500
Part b) Total Revenue
Revenue from 1 tire = $25
Total tires recapped = 15000
So, Total revenue = 15000 tires x $25/tire
Total Revenue =$375,000
Part c) Total Profit
Total Profit = Revenue - Cost
Using the above values, we get:
Profit = $375,000 - $177,500
Profit = $197,500
Part d) Break-even Point
Break-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:
For break-even point
Cost of recapping x tires = Revenue from x tires
65,000 + 7.5 x = 25x
65,000 = 17.5 x
x = 3714 tires
Thus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.
Use the intercepts from the graph below to determine the equation of the function.
A) 4x-3y=12
B) -4x-3y=12
C) 4x-3y=-12
D) -4x+3y=-12
ANSWER
C) 4x-3y=-12
EXPLANATION
The intercept form of a straight line is given by:
[tex] \frac{x}{x - intercept} + \frac{y}{y - intercept} = 1[/tex]
From the the x-intercept is -3 and the y-intercept is 4.
This is because each box is one unit each.
We substitute the intercepts to get:
[tex] \frac{x}{ - 3} + \frac{y}{4} = 1[/tex]
We now multiply through by -12 to get
[tex] - 12 \times \frac{x}{ - 3} + - 12 \times \frac{y}{4} = 1 \times - 12[/tex]
[tex]4x - 3y = -12[/tex]
The correct choice is C.