Answer:
* The value of a1 = 945.65 ⇒ answer c
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Progression:
- U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, n is the position
of the term
- The sum of first n terms of a Geometric series is calculate
from Sn = [a1 (1 - r^n)]/(1 - r) , where a1 is the first term, r is the
common ratio and n is the number of the terms
* Lets solve the problem
∵ Sn = 88,560
∵ r = 2.2
∵ n = 6
∵ Sn = [a1 (1 - r^n)]/(1 - r)
∴ 88,560 = [a1 (1 - 2.2^6)]/(1 - 2.2) ⇒ simplify up and down
∴ 88,560 = [a1 (-112.379904)]/(-1.2) ⇒ simplify the fraction
∴ 88,560 = a1 (93.64992) ⇒ divide both sides by 93.64992
∴ a1 = 945.6494998 ≅ 945.65
* The value of a1 = 945.65
4x - 22 = 62 + 2x
15 points
4x-22=62+2x
4x-2x=62+22
2x=84
x=84/2= 42
x= 42 is the answer
[tex]x=42[/tex]
Step-by-step explanation:Move the variables to one side and the constants to the other. [tex]4x-2x=62+22[/tex]
Combine the variables. [tex]2x=62+22[/tex]
Combine the constants. [tex]2x=84[/tex]
Divide both sides by 2. [tex]x=42[/tex]
charles deposited $12,000 in the bank. He withdrew $5,000 from his account after one year. If he recives a total amount of $9,340 after 3 years, find the rate of simple interest.
Answer:
The rate of simple interest is 9%
Step-by-step explanation:
* Lets talk about the simple interest
- The simple Interest Equation (Principal + Interest) is:
A = P(1 + rt) , Where
# A = Total amount (principal + interest)
# P = Principal amount
# I = Interest amount
# r = Rate of Interest per year in decimal r = R/100
# R = Rate of Interest per year as a percent R = r * 100
# t = Time period involved in months or years
- The rule of the simple interest is I = Prt
* lets solve the problem
- Charles deposited $12,000
∴ P = $12,000
- He withdrew $5,000 from his account after one year
- He receives a total amount of $9,340 after 3 years
∴ A = $9340 and t = 3
- Lets find the inetrest after 1 year
∵ I = Prt
∵ P = 12000
∵ t = 1
∴ I = 12000(r)(1) = 12000r
- Lets subtract the money that he withdrew
∵ He withdrew $5000
∵ He deposit at first 12000
∴ He has after the withdrew 12000 - 5000 = 7000
- The new P for the next 2 years is 7000
- This amount will take the same rate r for another two years
- The total money is $9340
∵ I = A - P
∵ A = 9340
∵ P = 7000
∴ The amount of interest = 9340 - 7000 = 2340
- The amount of interest after 3 years is 2340
- Lets find the amount of interest in the two years
∴ I = 7000(r × 2) = 14000r
- The amount of interest after the 3 years is the sum of the interest in
the 1st year and the other 2 years
∴ 2340 = 14000r + 12000r
∴ 2340 = 26000r ⇒ divide both sides bu 2340
∴ r = 2340 ÷ 26000 = 0.09
∵ The rate R in percentage = r × 100
∴ R = 0.09 × 100 = 9%
∴ The rate of simple interest is 9%
Question 9 (1 point)
32% of 300 is what number?
Hello There!
32% of 300 is 96
Work shown in image attached.
Answer:
96
Step-by-step explanation:
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 300 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 300 is 100%, so we can write it down as 300=100%.
4. We know, that x is 32% of the output value, so we can write it down as x=32%.
5. Now we have two simple equations:
1) 300=100%
2) x=32%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
300/x=100%/32%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 32% of 300
300/x=100/32
(300/x)*x=(100/32)*x - we multiply both sides of the equation by x
300=3.125*x - we divide both sides of the equation by (3.125) to get x
300/3.125=x
96=x
x=96
now we have:
32% of 300=96
What is the slope of the line passing through the points (3, 3) and (5, 7) ?
1. 2
2. 1/2
3. −2
4. −1/2
Answer:
1.) 2
Step-by-step explanation:
We have points (3,3) and (5,7) on the line.
Slope of a line = change in y ÷ change in x
i.e Slope = [tex]\frac{7 - 3}{5 - 3}[/tex] = 2
The slope of the line passing through the points (3, 3) and (5, 7) is 2. Therefore, the correct answer is option 1.
The given coordinate points are (3, 3) and (5, 7).
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Here, slope = (7-3)/(5-3)
= 4/2
= 2
So, the slope is 2.
Therefore, the correct answer is option 1.
To learn more about the slope of a line visit:
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Can someone help me with this
Hello There!
It could not be C because there corresponding angles could not be congruent.
It also could not be B all the sides are proportional to each other.
I don’t think it could be D because that’s similar as well.
The only option that makes sense is “C”
PLEASE HELP ASAP
You’re supposed to find volume but the answer is set up weird (a fraction and a square root) Please set up your answer like that. Thank you!
Step-by-step explanation:
The volume of a prism is:
V = AH
where A is the area of the base and H is the height.
The base is a triangle, so the area is:
A = 1/2 b h
We know that b = 3. To find h, we can split the triangle in half. Then we can either use Pythagorean theorem to find h, or properties of a 30-60-90 triangle.
The short leg is 3/2, so the height is 3/2 √3.
A = 1/2 (3) (3/2 √3)
A = 9/4 √3
Therefore:
V = (9/4 √3) (6)
V = 27/2 √3
The temperature is 45F. The temperature will decrease by 2F each hour. Let h be the number of hours. When will the temperature be below 2 f
Answer:
23rd hours
Step-by-step explanation:
This is problem based on arithmetic progression in which our first term is 45 , and the common difference is -2
we have to find the n when the nth term is 2.
The formula for nth term of an AP is
[tex]a_{n}=a+(n-1)d[/tex]
replacing the values in the formula
[tex]a_{n}=a+(n-1)d\\2=45+(n-1)(-2)\\2=45-2(n-1)\\-43=-2(n-1)\\21.5 = n-1\\n=22.5\\[/tex]
hence at 22.5 hours it will reach 2F or we can say that after 23 hours the temperature will be below 2F
Simplify completely quantity 6 x squared minus 54 x plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus
Answer:
We can easily simplify the expression by using a computational tool
The expression is
"6 x squared minus 54 x plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus "
Please, see attached images below, for a full explanation
HELPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!!!!
can you explain how a table can be used to find a rate of change?
Answer: You can use it because the value of the integers tell you where a point might be located.
Hope this helps!
Force (denoted by F) can be defined as a function of mass (denoted by m) and acceleration (denoted by a) using this formula F=ma mass is measured in kg, and acceleration is measured in m/s
Units are written in bracelets.
[tex]F=ma \: \{kg\cdot\dfrac{m}{s^2}\}[/tex]
[tex]F=ma \: \{\boxed{\dfrac{kg\cdot m}{s^2}}=N\}[/tex]
Hope this helps.
r3t40
Answer:
Step-by-step explanation:
Force is defined as a function of mass (denoted by m) and acceleration (denoted by a) using this formula F=ma
units for mass m is kg
units for acceleration is metre/sec^2
Hence together we can write unit as
unit for force = [tex]Kg m/sec^2[/tex]
This can also be expressed as newtons
Unit for force = newtons also.
Using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 7 years. Original cost = $23,500. The cost of maintenance and repairs is $ .
Final answer:
The labor charge for a car repair job that takes 3.5 hours is $267.50. The difference in labor charges between a job that takes 2.4 hours and one that takes 6.3 hours is $214.50. Choosing between two similarly priced used cars requires additional information beyond the asking price.
Explanation:
The question asks for different computations related to the costs of car maintenance and repairs. Here is a solution to one of the calculations:
Labor Charge Calculation
The independent variable is the number of hours worked, and the dependent variable is the total labor charge. The equation to represent this situation is:
Labor Charge = $75 + ($55 × number of hours)
The slope is $55 as it represents the increase in charge per hour, and the y-intercept is $75 since it's the flat fee charged regardless of the hours worked.
For a job taking 3.5 hours:
Labor Charge = $75 + ($55 × 3.5) = $75 + $192.50 = $267.50
Difference in labor costs for two jobs (2.4 and 6.3 hours):
Labor Charge for 2.4 hours = $75 + ($55 × 2.4) = $75 + $132 = $207
Labor Charge for 6.3 hours = $75 + ($55 × 6.3) = $75 + $346.50 = $421.50
Difference = $421.50 - $207 = $214.50
In the context of Marvin shopping for a used car, it is not possible to provide a suggestion on which car to buy (the $4,000 or the $4,600 one) without additional information. Factors such as overall condition, future maintenance costs, and personal budget would need to be considered.
Use the equation and type the ordered-pairs. y = 2 ^x
Find the ordered pairs for y = 2ˣ by substituting various values of x into the equation, calculate y, and list the pairs. These can then be plotted on a graph to show the exponential relationship.
To determine the ordered pairs for the given function y = 2ˣ, you will perform substitutions for x with various values and calculate the corresponding y values. Once this is done, you can plot these points on a graph to visualize the function.
Choose a range of x-values (for example, -3, -2, -1, 0, 1, 2, 3).
Calculate the corresponding y-values using the equation y = 2ˣ.
List the ordered pairs (x,y).
Plot each pair on a coordinate graph.
Connect the points to represent the exponential graph.
Remember, shifting an exponential graph parallel to the x-axis can be done by adjusting the exponent's value.
What is the greatest common denominator of 110 40 and 120
The prime factorizations of the numbers are
[tex]110 = 2\times 5 \times 11,\quad 40= 2^3\times 5,\quad 120=2^3\times 3\times 5[/tex]
The greatest common factor is composed by all common primes, taken with the lowest exponent possible. In this case, it will be
[tex]2\times 5 = 10[/tex]
Which system of equations could be graphed to solve the equation below?
[tex]\bf \begin{cases} \boxed{y}=\log(2x+1)\\ y=3x-2 \end{cases}\qquad \stackrel{\textit{doing substitution on the 2nd equation}}{\boxed{\log(2x+1)}=3x-2}[/tex]
a quick note, I must say that writing y₁ and y₂ is a bit misleading, since it makes it appear as if they're two different variables, when they're the same one.
Answer:
B
Step-by-step explanation:
B) y1=log(2x+1), y2=3x-2
which fraction is not equivalent to 9/12
24/32 6/8 5/20 16/24
Answer:
[tex]\large\boxed{\dfrac{9}{12}\neq\dfrac{5}{20}\ \text{and}\ \dfrac{9}{12}\neq\dfrac{16}{24}}[/tex]
Step-by-step explanation:
[tex]\dfrac{9}{12}=\dfrac{9:3}{12:3}=\dfrac{3}{4}\\\\\dfrac{24}{32}=\dfrac{24:8}{32:8}=\dfrac{3}{4}\\\\\dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\\\\\dfrac{5}{20}=\dfrac{5:5}{20:5}=\dfrac{1}{4}\\\\\dfrac{16}{24}=\dfrac{16:8}{24:8}=\dfrac{2}{3}[/tex]
Answer:
6/8
Step-by-step explanation:
Solve kx + 8 = 4 for x
Answer:
x = k/-4
Step-by-step explanation:
Answer:I got it wrong the answer is actually x=-4/k
Step-by-step explanation:
Apex approved
(50 Points)
Drag each description to the correct location on the table. Each description can be used more than once.
Some systems of equations and their graphs are given in the table. For each system, place the description(s) in the box that correctly describe the type of system shown.
Please helppppp :((((
Answer with explanation:
1.→→→ 3x-5y=15------(1)
6 x-10 y=30----(2)
Line 2 =2 * Line 1
These two lines are coincident.
Dependent
2.→→→ -2 x+4 y=-6-------(1)
Dividing both sides by , 2 we get
-x+2y= -3-----------------(1)
x+6 y=3------------(2)
These two are distinct lines ,it means they have a common point of intersection.
Consistent, and Independent
3.→→→
x-4y = -12-----------------(1)
3x-12 y= -9--------------(2)
Equation (2)=3 * Equation (1)
These two lines are coincident.
Dependent
4.→→→
3 x+y=3------(1)
6x+2y=-4------(2)
Dividing both sides by ,2 we get
3 x+y= -2
Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.
Inconsistent
1.→→→ 3x-5y=15------(1)
6 x-10 y=30----(2)
Line 2 =2 * Line 1
These two lines are coincident.
Dependent
2.→→→ -2 x+4 y=-6-------(1)
Dividing both sides by , 2 we get
-x+2y= -3-----------------(1)
x+6 y=3------------(2)
These two are distinct lines ,it means they have a common point of intersection.
Consistent, and Independent
3.→→→
x-4y = -12-----------------(1)
3x-12 y= -9--------------(2)
Equation (2)=3 * Equation (1)
These two lines are coincident.
Dependent
4.→→→
3 x+y=3------(1)
6x+2y=-4------(2)
Dividing both sides by ,2 we get
3 x+y= -2
Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.
Do you notice clusters or outliners in the data ? Explain your reasoning
Answer:
1,110 is a cluster because it’s a very large number for 52 degrees and 189 is because it’s a very large number for 16 degrees.
Step-by-step explanation: I'm happy to help...
Choose the graphs that indicate equations with no solution.
Answer:
It will be any graphs that show a parallel line relationship.
Explanation:
Any graph that shows parallel lines will always be no solution.
Answer:
It have to be a graph that shows functions that doesn't have points in common. The figure show some examples.
A circle has a circumference of 28.36 units what is the diameter of the circle
Answer:
d= 9.032 units
Step-by-step explanation:
Given
[tex]Circumference = 28.36[/tex]
We will use the formula for circumference of a circle to find it's radius and then diameter will be found using radius.
So,
[tex]C=2\pi r\\Putting\ the\ value\ of\ \pi and \C\\28.36 = 2 * 3.14 *r\\28.36=6.28* r\\r=\frac{28.36}{6.28}\\ r=4.516\ units[/tex]
Now to find the diameter:
d = r*2
d = 4.516*2
d= 9.032 units
Answer:
The diameter of the circle is 9.03 units
Step-by-step explanation:
The formula for calculating the circumference of a circle is [tex]C=\pi d[/tex].
From the question, the diameter of the circle is 28.36 units.
Since the circumference is rounded to the nearest hundredth, we substitute [tex]\pi=3.14[/tex] and [tex]C=28.36[/tex] into the formula and solve for d.
[tex]\implies 28.36=3.14d[/tex]
Divide both sides by 3.14
[tex]\implies \frac{28.36}{3.14}=\frac{3.14d}{3.14}[/tex]
[tex]\implies 9.03=d[/tex].
Hence the diameter of the circle is 9.03 units to the nearest hundredths
Which is the correct first step in finding the area of the base of a cylinder with a volume of 26x cubic meters and a height of 6.5 meters?
v=bh 6.5=b(26x)
v=bh v=26pi+(6.5)
v=bh v=26pi(6.5)
v=bh 26pi=b(6.5)
Answer:
[tex]\large\boxed{V=Bh,\ 26x=B(6.5)\to B=4x}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of cylinder:}\\\\V=Bh\\\\\text{We have}\ V=26x\ m^3\ \text{and}\ h=6.5\ m.\\\\\text{Substitute:}\\\\26x=B(6.5)\qquad\text{divide both sides by 6.5}\\\\\dfrac{26x}{6.5}=B\to B=4x[/tex]
ABCD ~ EFGH
z=?
Please help me!!!
Answer:
z = 110°
Step-by-step explanation:
Since the figures are similar, then corresponding angles are congruent, thus
∠H = ∠D, that is
z = 110°
Since the figures are similar, then corresponding angles are congruent, thus
ABCD ~ EFGH
∠H = ∠D, that is
z = 110°.
What is Similar angle.Two angles in one triangle are equal to two angles in another triangle, then the triangles are similar
What is Congruent anglesCongruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines
What is Congruent Angles TheoremThere are many theorems based on congruent angles. Using the congruent angles theorem we can easily find out whether two angles are congruent or not. Those theorems are listed below:
Vertical angles theoremCorresponding angles theoremAlternate angles theoremCongruent supplements theoremCongruent complements theoremTo learn more about the Congruent angle, refer
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Find the slope of a line perpendicular to 2y = -6x +8
[tex]\bf 2y=-6x+8\implies y=\cfrac{-6x+8}{2}\implies y=\cfrac{-6x}{2}+\cfrac{8}{2} \\\\\\ y=-3x+4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{3}\implies \cfrac{1}{3}}}[/tex]
A ball is thrown vertically in the air with a velocity of 100ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the ball is at a height of 150ft
Answer:
Step-by-step explanation:
2.5, 3.8
To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve the quadratic equation -16t^2 + 100t = 150. By using the quadratic formula, we find two possible values for t: t = 3.75 seconds and t = 2.5 seconds.
Explanation:The equation given in the question is h = -16t2 + v0t, where h is the height, t is the time, and v0 is the initial velocity. To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve for t.
150 = -16t2 + 100t
Rearranging the equation, we get 16t2 - 100t + 150 = 0. This is a quadratic equation which can be solved using the quadratic formula.
The quadratic formula is t = (-b ± √(b2 - 4ac)) / (2a). In this equation, a = 16, b = -100, and c = 150.
Plugging in these values, we get t = (100 ± √(1002 - 4 * 16 * 150)) / (2 * 16).
Simplifying further, we have t = (100 ± √(10000 - 9600)) / 32.
This simplifies to t = (100 ± √400) / 32.
Taking the square root, we get t = (100 ± 20) / 32.
This gives us two possible values for t: t = (100 + 20) / 32 = 120/32 = 3.75 and t = (100 - 20) / 32 = 80/32 = 2.5.
Therefore, the ball is at a height of 150ft at two times: t = 3.75 seconds and t = 2.5 seconds.
Gigi earned $65 for 5 hours of gardening. She earned $90 for 9 hours of office work. Which statement correctly compares Gigi’s earning per hour for gardening and office work?
She earned $3 more per hour for office work than for gardening.
She earned $4 more per hour for office work than for gardening.
She earned $3 more per hour for gardening than for office work.
She earned $4 more per hour for gardening than for office work.
Hello There!
First we have to see how much does Gigi earns per hour.
For gardening, we are going to divide.
65 ÷ 5 ≈ 13
Gigi earns $13 for gardening for only 1 hour.
Second, we have to see how much Gigi earns per hour for office work.
We will divide
90 ÷ 9 ≈ 10
Now, we can see that Gigi earned $3 more per hour for gardening than for office work.
please help! ill mark you as brain if your right!!!!
Answer:
SA = 1099 square inches.
Step-by-step explanation:
Just plug into the formula
SA = 2pir^2 + 2pi r h where pi = 3.14, r = 5 and h = 30
SA = 2 (3.14) (5^2) + 2 (3.14)(5)(30)
SA = 157 + 942
SA = 1099 square inches.
Answer:
1099.56 or 1099.6 dependong on what you wanna round to
Step-by-step explanation:
2×pi×5^2+2×pi×5×30
last one for tonight.asdfvgbhnjmgytfredtufyi ugi
Answer:
(1/6)^3 = 1/216, these events are independent.
Step-by-step explanation:
What happens in one roll has no effect on the other rolls, so these events are independent. The probility of any roll outcome is 1/6 since there are 6 sides. Since you want to roll a 6 AND a 5 AND a 4 you have to multiply the probabilities.
(03.03 MC) Choose the graph below that correctly represents the equation 2x + 4y = 24. (5 points) Select one: a. line through the points 0 comma 6 and 12 comma 0 b. line through the points 0 comma negative 6 and 12 comma 0 c. line through the points 0 comma negative 12 and 6 comma 0 d. line through the points 0 comma 12 and 6 comma 0
Answer:
your line goes through both (0,6) and (12,0)
Step-by-step explanation:
Ok so you are describing some lines you see I think:
I see some of these as points you mentioned:
(0,6) , (0,-6) , (6,0)
So let's see which of these work:
(0,6)?
2(0)+4(6)=24
24=24
(0,6) does work!
The other point you have listed with (0,6) is (12,0).
Let's try (12,0)
2(12)+4(0)=24
24+0=24
24=24
(12,0) works!
So your line goes through both (0,6) and (12,0)
Answer:
The correct option is A) Line through the point (0,6) and (12,0).
Step-by-step explanation:
Consider the provided equation 2x + 4y = 24.
Substitute x = 0 in the provided equation.
2x + 4y = 24
2(0) + 4y = 24
4y = 24
y = 6
Thus, the points which satisfy the equation is (0,6).
Now, substitute x = 12 in the provided equation.
2x + 4y = 24
2(12) + 4y = 24
24 + 4y = 24
4y = 0
y = 0
Thus, the points which satisfy the equation is (12,0).
Therefore, the correct option is A) Line through the point (0,6) and (12,0).
Ajar contains a mixture of 20 black marbles, 16 red marbles, and 4 white marbles, all the same size. Find the probability
of drawing a white or red marble on the first draw.
125
12
01
NEXT QUESTION
ASK FOR HELP
TURN IT IN
[tex]|\Omega|=20+16+4=40\\|A|16+4=20\\\\P(A)=\dfrac{20}{40}=\dfrac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
16+4 =20 red and white marbles
40 marbles in all
20/40= 1/2
What is common ratio
Answer:
B
Step-by-step explanation:
The common ratio in this case, is something that is going to make the geometric sequence go down. Your will make it go up.
Common ratio = second term / first term
common ration = 125/625 = 25/125 which is obtained by dividing both top and bottom of the fraction by 5.
Its not the best possible answer, but it is the best among those given.
Answer:
1/5
Step-by-step explanation:
Notice that 125 is 1/5 th of 625; 25 is 1/5 th of 125; 5 is 1/5 of 25, and so on.
Thus, the common ratio is 1/5.
\