Answer: [tex]t_9=\dfrac{1}{2^8}[/tex]
Step-by-step explanation:
[tex]t_n=t_1\times r^{n-1}\\\\Given: t_1=1,\quad r=\dfrac{1}{2}\\\\\\t_9=1\times\bigg(\dfrac{1}{2}\bigg)^{9-1}\\\\\\.\quad =\large\boxed{\dfrac{1}{2^8}}[/tex]
how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Which equation describes the line graphed above? A. -4x-5 B. -1/5x-4 C. -5x-4 C. -4x-1/5
The equation is -1/5x-4 represented by the graph. The correct option is B.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Let us check the equation -1/5x-4. The line goes down one and turns right 5. The Slope is -1/5x and the y-intercept is at -4. The graph of the equation is attached with the answer below.
Hence, option B is correct.
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URGENT!!! Please help me with this question!!!
Answer:
Step-by-step explanation:
The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle. The inscribed angle's arc measures 36%, and the central angle's arc measure 72%
Answer:
75
%Step-by-step explanation:
The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle.
18. In a recent survey, 75% of the community favored building a police substation in their neighborhood. If 10 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.
Answer: 0.28157
Step-by-step explanation:
Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75
Number of citizens are chosen: n= 10
Let x be the binomial variable that represents the number of citizens favor the building of the police substation.
Then, the probability that exactly 8 of them favor the building of the police substation will be :
[tex]P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2[/tex]
[Using binomial probability function [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]]
[tex]=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157[/tex]
Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157
Is (0, 3) a solution to the following system?
Y=-x+3
Y=2x-3
A No, because it does not check in either equation.
B. No, because it does not check in the first equation.
C. No, because it does not check in the second equation.
D. Yes, because it checks in both equations.
Solve each equation with (0, 3)
y = -x + 3
3 = -0 + 3
y = 3 (correct since y = 3 in (0, 3))
y = 2x - 3
3 = 2(0) - 3
3 = 0 - 3
3 = -3 (incorrect since it isn't equal)
So... No, because it does not check in the second equation.
Best of Luck!
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.
The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713
Given that:
[tex]Entrance\ Fee = \$18[/tex]
[tex]Rate = \$0.08[/tex] per ball
Let:
[tex]B \to Balls[/tex]
The amount (A) Carolina can spend on B balls is:
A = Entrance Fee + Rate * B
This gives:
[tex]A = 18 + 0.08 * B[/tex]
[tex]A = 18 + 0.08B[/tex]
To get $10, Carolina must spend $75 or more.
This means:
[tex]A \ge 75[/tex]
So, the inequality is:
[tex]18 + 0.08B \ge 75[/tex]
The smallest number of balls is calculated as follows:
[tex]18 + 0.08B \ge 75[/tex]
Collect like terms
[tex]0.08B \ge 75 - 18[/tex]
[tex]0.08B \ge 57[/tex]
Divide both sides by 0.08
[tex]B \ge 712.5[/tex]
Round up
[tex]B \ge 713[/tex]
Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713
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Using a linear function, it is found that:
1. [tex]18 + 0.08B \geq 75[/tex], given by option B.2. She has to buy at least 713 paintballs.-----------
The linear function for the cost of B paintballs has the following format:
[tex]C(B) = C(0) + aB[/tex]
In which
C(0) is the fixed cost.a is the cost per paintball.-----------
Question 1:
Entrance fee of $18, thus [tex]C(0) = 18[/tex].Cost of $0.08 per ball, thus, [tex]a = 0.08[/tex]Thus:
[tex]C(B) = 18 + 0.08B[/tex]
The promotion is valid if the cost is of at least 75, thus:[tex]C(B) \geq 75[/tex]
[tex]18 + 0.08B \geq 75[/tex], given by option B.
-----------
Question 2:
The smallest number is the solution of the inequality for B, thus:[tex]18 + 0.08B \geq 75[/tex]
[tex]0.08B \geq 57[/tex]
[tex]B \geq \frac{57}{0.08}[/tex]
[tex]B \geq 712.5[/tex]
Rounding up, she has to buy at least 713 paintballs.
A similar problem is given at https://brainly.com/question/24583430
Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t is the time in seconds. For which interval of time is the height of the ball less than 17 feet?
Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
[tex]-16t^2+81<17[/tex] The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
[tex]-16t^2<-64[/tex] then divide both sides by -16:
[tex]t^2>4[/tex] Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
Answer:
A on edg
Step-by-step explanation:
find the center of the circle (x-2)^2+(y-8)^2=33
Answer:
The center is (2,8)
Step-by-step explanation:
The equation of a circle is written as
(x-h)^2+ (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
(x-2)^2+(y-8)^2=33
The center is (2,8) and the radius is sqrt(33)
Hi, I don't know how to do these, if you could help me answer them, that would be great
Answer:
137°Step-by-step explanation:
From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°
From the diagram, mAB = 43°. Substituting this value into the above equation;
mAB + mAD = 180°
43° + mAD = 180°
mAD = 180°-43°
mAD = 137°
Hence, the measure of angle mAD is 137°
What is an equivalent equation for 3 x = 12 minus 4 y when solved for x? X = 4 minus four-thirds y x = 4 + four-thirds y x = negative 4 + four-thirds y x = negative 4 minus four-thirds y
Answer:
[tex]x = 4 - \frac{4}{3}y[/tex]
Step-by-step explanation:
If we have the equation [tex]3x = 12-4y[/tex], we can simplify this equation down.
Divide both sides by 3:
[tex]x = 4 - \frac{4}{3}y[/tex] .
Hope this helped!
Answer:
X = 4 minus four-thirds y
Step-by-step explanation:
Well to solve for x we single it out.
3x = 12 - 4y
Divide 3 by everything,
x = 4 - 4/3y
Thus,
X = 4 minus four-thirds y.
I do hope this helps :)
A circle has a radius of sqrt 45 units and is centered at -2.4, -4.8 write the equation of the circle
Answer:
(x+2.4)^2+(y+4.8)^2=2025
If you'd like additional help with math or another subject, check out growthinyouth.org!
Step-by-step explanation:
2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
What is the measure of ∠XBC? m∠XBC = m∠BAC + m∠BCA 3p – 6 = p + 4 + 84 3p – 6 = p + 88 2p – 6 = 88 2p = 94 m∠XBC
Find the equation of the line.
Answer:
y = 2x + 4
Step-by-step explanation:
y = mx + b
b = y-intercept = 4
m = slope = rise/run = 4/2 = 2
y = 2x + 4
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
The third option is correct.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
Step-by-step explanation:
Sara bought a cell phone for $200 and its value has decreased at rate of $5 per month.
V(t) is the value of the phone and t is the number of months.
The domain of the function is the possible values of the number of months t.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is the values of V(t) that we get after substituting the possible values of the number of months t.
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
When the number of months is t = 0 then the value of the function is maximum V(t) = 200
When the number of months is t = 40 then the value of the function is minimum V(t) = 0
Therefore, the third option is correct.
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answer:
3x (x - 2) (x + 3)
Answer 4
Hope this helps :)
Please help, ty if you do
Answer:
C
Step-by-step explanation:
4,800 times 7% is 336, and 1200 times 14% is 168, and 168 is half as much as 336, so the correct answer is c
Answer:
C
Step-by-step explanation:
Multiply .7 to 6000 and solve
What is the equation of the circle shown below?
Answer:
( x+2)^2 + ( y+2) ^2 = 9
Step-by-step explanation:
The center is at (-2,-2)
The radius is 3 which is the number of units from the center to the circles edge
The equation of a circle can be written as
( x-h) ^2 + (y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x--2) ^2 + (y--2) ^2 = 3^2
( x+2)^2 + ( y+2) ^2 = 9
Write the function in standard form.
Y=(3x-2)(3x+6)
Answer:
y = 9x^2 + 12x - 12.
Step-by-step explanation:
y = (3x - 2)(3x + 6)
y = 9x^2 - 6x + 18x - 12
y = 9x^2 + 12x - 12.
Hope this helps!
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of the object.
Answer:
v=√E/m or v=√E /√m
Step-by-step explanation:
Complete question below:
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of
the object.
E = mv^2
Solve the formula for v.
Solution
E=mv^2
Where,
E=kinetic energy
m=mass
v=speed of the object
E=mv^2
Divide both sides by m
E/m=mv^2/m
E/m=v^2
It can be rewritten as
v^2=E/m
Square root both sides
√(v^2)=√E/m
v=√E/m
Or
v=√E/√m
This is to say speed (v)=square root of kinetic energy (E) Over masa(m)
A shoe salesperson earns a 5% bonus on weekly sales over $3,000. Consider these functions to answer the following questions. f(x) = x – 3,000 g(x) = 0.05x Part A In your own words, explain what each of the functions represents.
Answer:
g(x)= 0.05x represents the amount of bonus, f(x)=x-3,000 represents weekly sales over $3,000.
Step-by-step explanation:
The function f(x) represents how much money earned by sales person weekly over $3000.
And function g(x) represents the amount of bonus earned by salesperson.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
The percent of bonus earned by salesperson weekly on sales over $3,000 is 5%.
Also, we have two functions.
[tex]f(x) = x - 3000[/tex]
and [tex]g(x) = 0.05x[/tex]
For the function, f(x) if x is the amount of money earned salesperson in a week, then f(x) will represents how much money salesperson earned apart form $3000.
And the function g(x) represents the amount of bonus earned by the salesperson.
Hence, the function f(x) represents how much money earned by sales person weekly over $3000. And function g(x) represents the amount of bonus earned by salesperson.
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Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
Answer: Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
We must work with linear equations, remember that the general shape is:
y = a*x + b
where a is the slope and b is the y-intercept.
Ok, first we want to find the rate of change (or the slope) of the graphed line:
We know that for a line that passes through the points (x1, y1) and (x2, y2)
The slope is:
a = (y2 - y1)/(x2 - x1)
Then for the graphed function, we can see that it passes through the points:
(0, -2) and (4, 0)
Then the slope is:
a = (0 -(-2))/(4 - 0) = 2/4 = 1/2
Now, the slope of the second line is 15/4.
Let's calculate the difference between the slopes:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
(notice that we are calculating slope2 - slope1)
Then the correct option is:
Function 2 has a greater rate of change by 13/4
Answer:
B) Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
Maximize the objective function P = 2x + 1.5y for the feasible region shown. State the maximum value for P and the ordered pair at which the maximum value occurs.
Incomplete question. However, let's assume this are feasible regions to consider:
Points:
- (0, 100)
- (0, 125)
- (0, 325)
- (1, 200)
Answer:
Maximum value occurs at 325 at the point (0, 325)
Step-by-step explanation:
Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.
- For point (0, 100): P= 2(0) + 1.5 (100) =150
- For point (0, 125): P= 2(0) + 1.5 (125) =187.5
For point (0, 325): P= 2(0) + 1.5 (325) = 487.5
For point (1, 200): P= 2(1) + 1.5 (200) = 302
Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.
Which of the following is a like radical to 3x sqrt 5
Answer:
The last option
Step-by-step explanation:
Source: Trust bro
Answer:
d) y sqrt 5
Step-by-step explanation:
radicals are like if they have the same index and radicand, here they are both square roots and have a radicand of five
Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees. What is the measure of angle O in parallelogram LMNO? 35° 75° 105° 155
Answer:
C, 105 Degrees
Step-by-step explanation:
So the two opposite sides of a parallelogram is equal to each other and the two adjacent angles are supplementary. So if (x+40)+3x=180, this means that 4x+40=180. This gives us 4x=140, so x=35. If we plug it back into the equation it ascertains as such: 3(35)= 105. The answer for this question and angle O is 105 degrees, or C.
The measure of angle O in this parallelogram is 105°.
The properties of a parallelogramThe opposite angles of a parallelogram are equal.The Opposite sides of the parallelogram are equal and parallel.The diagonals of the parallelogram bisect each other.The Sum of the angles = 360°
Solution
Because the properties says that opposite angles are equal.
Angle L = (x + 40)
angle O = (3 x)
Applying the first property
x+40+x+40+3x+3x = 360
collect the like termsx+x+3x+3x+40+40 = 360
8x+80 = 360
8x = 360-80
8x = 280
Divide through the equation by 8
x = 280/8
x = 35
The question wants us to find the value of angle O
O = 3x
O = 3*35
= 105
The value of angle O is equal to 105°
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which expression is equal to 5/ square root 11 ?
Answer:
5√11 ÷ 11 (The very last choice)
Step-by-step explanation:
I first found out what 5/√11 was and got 1.507556723 and checked all the other options and found that 5√11 ÷ 11 was the only option that had the exact same quotient as 5/√11.
Bella is going back to school shopping and her favorite store is having a sale. She sees there are 4 packages of 15 tops for $18 and 5 packages of 10 tops for $16 which is the better deal? How do you know
Answer:
The 4 packages of 15 tops for $18 is a better deal
Step-by-step explanation:
We can see which set of tops have the lowest unit price.
4 packages of 15 tops for $18:
4*15=60
There is a total of 60 tops for $18, which means each top costs 18/60 dollars, or $0.30.
5 packages of 10 tops for $16
5*10=50
There is a total of 50 tops for $16, which means that each top costs 16/50 dollars, or $0.32.
0.32>0.3
The 4 packages of 15 tops for $18 is a better deal :)
Have a great day
Find the sum of two consecutive odd numbers is 56 find the numbers
Answer:
[tex]\boxed{\sf 27 \ and \ 29}[/tex]
Step-by-step explanation:
Let the first consecutive odd integer be [tex]\sf x[/tex].
Let the second consecutive odd integer be [tex]\sf x+2[/tex].
The sum of the two numbers is 56.
[tex]\sf x+x+2=56[/tex]
[tex]\sf 2x+2=56[/tex]
[tex]\sf 2x=54[/tex]
[tex]\sf x=27[/tex]
Put x as 27 for the second consecutive odd integer.
[tex]\sf 27+2=29[/tex]
The two numbers are 27 and 29.
Which expression is equal to 5(2x^2-1)+3(7x^2+1)
Answer:
31x² - 2
Step-by-step explanation:
5(2x²-1)+3(7x²+1) = 5*2x² - 5*1 + 3*7x² + 3 = 10x² - 5 + 21x² + 3 = 31x² - 2
Use Descartes' Rule of Signs to find the number of possible positive real roots and the number of possible negative real roots for the function f(x) = x^4+ 2x^3-3x^2- 8x - 4.
a positive 1; negative 3 or 1
b. positive 1; negative 3 or 5
C. positive 3; negative 3 or 1
d. positive 3; negative 3 or 5
Answer:
a positive 1; negative 3 or 1
Step-by-step explanation:
To determine the number of positive roots, we have to determine the number of sign changes for f(x) = x⁴ + 2x³ - 3x² - 8x - 4.
The coefficients in f(x) are +1, +2, -3, -8, -4.
Since there is only one sign change from +2 to -3, we have 1 positive root.
To determine the number of negative roots, we have to determine the number of sign changes for f(-x) = (-x)⁴ + 2(-x)³ - 3(-x)² - 8(-x) - 4 = x⁴ - 2x³ - 3x² + 8x - 4
The coefficients in f(-x) are +1, -2, -3, +8, -4.
Since there is three sign change from +1 to -2, from -3 to +8, and from +8 to -4. So,we have 3 or 1 negative root, since the number of negative roots is equal to the number of sign changes or an even number less than the number of sign changes. So, 3 -2 = 1
So, the number roots are of positive 1; negative 3 or 1
Answer:
a.positive 1; negative 3 or 1
Step-by-step explanation:
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