Calculate the eighth term in the sequence 512, 256,128, ...
Answer:
4
Step-by-step explanation:
You want the 8th term of the geometric sequence 512, 256, 128, ....
Explicit formulaThe formula for the n-th term of a geometric sequence is ...
an = a1×r^(n-1)
where a1 is the first term (512), and r is the common ratio (1/2).
Then the 8th term is ...
a8 = 512(1/2)^(8-1) = 512/128 = 4
The eighth term of the sequence is 4.
in a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g
The number of division that will take place when the chocolate factory a machine takes a 1 kg block of chocolate is 100.
How to calculate the value?From the information, in the chocolate factory a machine takes a 1 kg block of chocolate and then divides it into rectangles each weight 10g.
It is important to note that:
1000 grams = 1 kilograms
Therefore, since the chocolate is divided into 10g, this will be:
= Total grams / 10 gram
= 1000g / 10g
= 100
Therefore, there will be 100 division.
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Complete question
In a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g. How many division will take place?
Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
y=1/3x-1
Y=1/3x+5/3
Y=1/3x-5/3
Y=1/3x+1
Considering the definition of a line, the equation of the line that passes through the point (-2, 1) and has a slope of 1/3 is y= 1/3x + 5/3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 1/3.The line passes through the point (-2, 1).Substituting the value of the slope m, you get:
y= 1/3x + b
Replacing the value of the point in previous expression, the value of the ordinate to the origin b can be obtained:
1= 1/3× (-2) + b
1= - 2/3 + b
1 + 2/3= b
5/3= b
Finally, the equation of the line is y= 1/3x + 5/3.
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how do you know that 2 to the power of 3 x 3 is not a common multiple
Answer:
512
Step-by-step explanation:
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.
OML I just gave u the answer do I need to put this in simple terms for you since u don't understand - 2 to the power of 3 x 3 is 512 and that is not a whole number a common multiple is defined as a whole number and for 512 to be an integer it has to be a whole number. UNDERSTAND NOW???
4/7 of a group of children are boys, if they are 18 more boys than girls how many children are there altogether
Answer:126 children
Step-by-step explanation:
first you want to multiply 18 times 4 (72) then 18 times 3 (54) and then you add 72+54=126
your welcome :)
Answer the question in the picture
The area of the semicircle is A = 1187.9 cm².
What is the area of a circle?The area of a circle with a radius of r is A = πr².
Given that, the diameter of the semicircle is 55 cm.
The radius of the semicircle is,
r = 55/2
The area of a semicircle is given by,
A = (1/2)πr²
Substitute the values,
A = (1/2)π(55/2)²
A = 1187.9
Hence, the area of the semicircle is A = 1187.9 cm².
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Start with the graph of
f(x) = 6x.
Then write a function
g(x)
that results from the given transformation.
shift f(x) 5 units downward
g(x) =
Describe how the graph of g(x)= –||x+2||+4 is related to the graph of the parent function.
The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.
Reflection over the x-axis.Shift left of 2 units.Shift up of 4 units.Which transformations were used?The parent function in this problem is defined as follows:
f(x) = |x|.
The transformed function in this problem is defined as follows:
g(x) = -|x + 2| + 4
The transformations are listed and described as follows:
The multiplication by -1 represents a reflection of the parent function over the x-axis.The addition by 2 in the domain, that is, x -> x + 2, represents a shift right of two units of the parent function.The addition by 4 in the range, that is, y -> y + 4, represents a shift up of four units of the parent function.More can be learned about transformations at https://brainly.com/question/28792248
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J. Lo’s Clothiers has forecast credit sales for the fourth quarter of the year: September (actual) $ 70,000 Fourth Quarter October $ 60,000 November 55,000 December 80,000 Experience has shown that 30 percent of sales are collected in the month of sale, 60 percent are collected in the following month, and 10 percent are never collected. Prepare a schedule of cash receipts for J. Lo’s Clothiers covering the fourth quarter (October through December)
The preparation of a schedule of cash receipts for J. Lo's Clothiers covering the fourth quarter from October through December is as follows:
Fourth Quarter Cash Receipts October November December
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
What is a schedule of cash receipts?A cash receipts schedule is a financial document that specifies how a business expects to collect cash from its credit sales customers based on the sales budget.
The cash collection formula can be established using the company's past collection patterns.
September
Credit Sales (actual) $ 70,000
Fourth Quarter October November December
Credit Sales $60,000 $55,000 $80,000
Cash Receipts:
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
Cash receipts in October = $60,000 ($60,000 x 30% + $70,000 x 60%)
Cash receipts in November = $52,500 ($55,000 x 30% + $60,000 x 60%)
Cash receipts in December = $57,000 ($80,000 x 30% + $55,000 x 60%)
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Then has a recipe for a marinade recipe says to mix 3/8 cup olive oil 1/4 cup soy sauce and 1/8 cup lime juice how much olive oil does he need to make 9 cups of the marinade show your work
You have to multiply 3/8 by 9 and then you get your answer which is 3.375
Assume the $26,000 Treasury bill, 5% for 13 weeks. Calculate the effective rate of interest.
Note: Use calendar year. Round your answer to the nearest hundredth percent.
Effective rate of interest
Simple interest of $325 was accrued on a principal of $26,000.00 for a period of 0.25 years (13 weeks) at a rate of 5% per year, bringing the total amount due to $26,325.00 (principal plus interest).
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.
Here,
A = $26,325.00
I = A - P = $325.00
A is equal to P(1 + rt).
The first step is to convert R percent to r a decimal, which is equal to R/100 = 5%/100 = 0.05 per year.
For ease, let's convert time to years: 13 weeks / 52 weeks / year = 0.25 years.
How to resolve our equation
A = 26000(1 + (0.05 × 0.25)) = $26,325.00
Simple interest accrued on a principal of $26,000.00 at a rate of 5% per year for 0.25 years (13 weeks) totaling $26,325.00 (principal plus interest).
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Fill in blank by finding number pattern
1,2,1,1,2,3,2,1,1,2,3,4,3,__,__,1,2,__,__,__,__,__,2
The number pattern for the missing numbers is 1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,1,2,3,2,1,2,2
A pattern of numbers formed with a definite rule is called sequence
How to find a number pattern?
In every number patter, first term of this number pattern is 1; and the terms after the first term are obtained by adding, subtracting or multiply by 1 to the previous term.
1+1=2
2-1=1
1*1=1
1+1=2
2+1=3
3-1=2
2-1=1
1*1=1
.1*1=1
1*1=1
2+1=3
3+1=4
4-1=3
3-1=2
2-1=1
1*1=1
1+1=2
2+1=3
3-1=2
2-1=1
1+2=2
2*1=2
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Does X have a binomial distribution? Give your reasons
Opinion polls find that 45% of teens say that their parents put at least some pressure on them to get into a good college. If you take an SRS of 980 teens, X has a distribution of the number in your sample who say they feel at least some pressure from their parents to get into a good college.
The variable X has a binomial distribution, as:
It has a fixed number of observations.The trials are independent.For each outcome, there are only two possible outcomes.What are the requirements for the binomial distribution?There are three requirements for the binomial distribution to represent a variable, as follows:
Fixed number of trials.The result of each trial is independent of the result of any other trial.Two possible outcomes for each trial, one representing a success and the other representing a failure.In the context of the variable X, these requirements are respected as follows:
Fixed number of 980 trials.For each trial, there is a 45% probability that the teen says that their parents put some pressure on him/her to get on good college, and 55% that the parents do not put pressure.For each trial, there are only two possible outcomes, either the parents put pressure, or they do not.Hence yes, the variable X has a binomial distribution.
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A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
Answer: median = 61
Reason:
A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.
WHAT IS THE ANSWER PLEASE HELP ME
Answer:
option 4
Step-by-step explanation:
Use distributive property: a(b +c) = (a*b) + (a*c).
Multiply each term of (-x - 5) by (-3).
-3( -x - 5) = ( -3* -x) + (-3*-5)
= ( 3x ) + ( 15)
= 3x + 15
⇒Note I am going to solve them step by step for you to understand.
1.
[tex]3(x)+3(5)=3x+5\\3x+15=3x+5\\3x-3x=5-15\\no\\solution[/tex]
since 0≠-10
2.
[tex]-3(x)-3(-5)=-3x-15\\-3x+15=-3x-15\\-3x+3x=-15-15\\0\neq -30\\no\\solution[/tex]
3.
[tex]3(-x)+3(5)=8-x\\-3x+15=8-x\\\\-3x+x=8-15\\-2x=-7\\\frac{-2x}{-2} =\frac{-7}{-2} \\x=\frac{7}{2}[/tex]
4.
[tex]-3(-x)-3(-5)=3x+15\\3x+15=3x+15\\3x-3x=15-15\\0=0\\[/tex]
Note there is no certain value for x as any value you insert as x can make the whole equation true.
No solution is the answer for Q4
Look at this graph:
10
9
8
7
9
S
4
لیا ۔
N
L
0
1 2 3 4 5 6 7 8 9 10
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
For the given graph , slope of the line is equal to ( 1 / 2 ).
As given in the question,
Form the given graph,
Scale is given by,
On x-axis each unit of the graph represent 1 unit.
On y- axis each unit of the graph represent 1 unit.
Consider two coordinates from the line of the graph,
( x₁ , y₁ ) = ( 1, 2 )
( x₂ , y₂ ) = ( 3, 3 )
Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula of the slope we get,
Slope of the line = ( 3 - 2 ) / ( 3 - 1 )
⇒ Slope of the line = 1 / 2
Therefore, for the given graph , slope of the line is equal to ( 1 / 2 ).
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A paper company needs to ship papre to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weight 35 ponds and each large box of paper wight 60 pounds. There were 7 more small boxes shipped than large boxes and the total wight of all boxes was 815 ponds. Write a system of equations that could be used to determine the number of small boxes shipped and the number boxes shipped.
Setting up a system of equation, the number of small boxes shipped is 13 and large box shipped is 6
System of EquationSystem of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Let;
x = small boxy = large boxWe can represent this using equations;
35x + 60y = 815 ...eq(i)
x = 7 + y ... eq(ii)
Solving equation (i) and (ii)
x = 13, y = 6
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The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
Answer:
A and C are correct choices========================
The difference between two consecutive integers is 1.
Test it with the given choicesA) x + (x + 1) + (x + 2) = 42,
YesB) x + (x + 2) + (x + 4) = 42
No, the difference between the pairs is 2 not 1.C) (x minus 1) + x + (x + 1) = 42
YesD) (x minus 2) + x + (x + 2) = 42
No, the difference between the pairs is 2 not 1.E) x + 2 x + 3 x = 42
No, here is the multiples of integers and the difference between the pairs is x not 1.Answer:
x + (x + 1) + (x + 2) = 42
(x minus 1) + x + (x + 1) = 42
Step-by-step explanation:
Integer: A whole number that can be positive, negative, or zero.
Consecutive integer: Integers that follow each other in order.
Let x be an integer.
Consecutive integers of x are one more or one less than each other in order.
x + (x + 1) + (x + 2) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
x + (x + 2) + (x + 4) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
(x minus 1) + x + (x + 1) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
(x minus 2) + x + (x + 2) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
x + 2 x + 3 x = 42This equation does not represent 3 consecutive integers as each value is x more than the previous value.
Solve by factoring.
6x^2 - x - 12 = 0
Answer:
x = 3/2 and -4/3
Step-by-step explanation:
[tex] \rm \implies 6 {x}^{2} - x - 12 = 0 \\ \\ \rm \implies 6 {x}^{2} - 9x + 8x - 12 = 0 \\ \\ \rm \implies 3x(2x - 3) + 4(2x - 3) = 0 \\ \\ \rm \implies (2x - 3)(3x + 4) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: \: and \: \: 3x + 4 = 0 \\ \\ \rm \implies 2x = 3\: \: and \: \: 3x = - 4 \\ \\ \rm \implies x = \frac{3}{2} \: \: and \: \: x = - \frac{4}{3} [/tex]
Solve the inequality3/2 w ≤1/2.
line m passes through the points (-4, 3) and (-4, 7) what is the slope of the line that is perpedicular to the line m
Answer:
The slope is 4 and the equation is y = 4x + 18
Step-by-step explanation:
Okay, so you start by solving for the slope. The formula for slope is
m = y1-y2 over x1-x2 (it looks lke a fraction)
then you plug in your coordinates, so it becomes:
m = 7-3 over -4 - (-4) which then you get your slope as 4, but because it has to be perpendicular, the slope becomes -1/4. this is because the slope has to be the reciprocal and the opposite sign to be perpendicular.
Then, you can continue to create the equation by using point-slope form, which is y - y1 = m (x-x1) (y1 and x1 are from the coordinates btw)
so the point-slope equation is:
y - 3 = -1/4 (x + 4)
y - 3 = -1/4x - 1
+3 +3
y = -1/4x + 2 (this is your equation in slope - intercept form)
I hope this helps!!
4) A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
As per the unitary concept,
a) There are 5/8 cups of flour would you need for half the recipe
b) There are 6 1/4 cups of flour would you need for 5 dozen cookies.
Unitary method:
The method by which first we find the value of single unit and then the value of the required number of units is known as the Unitary Method.
Given,
Here we have given that, A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
So, here we need to find the following:
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
In order to find these value, we have to calculate the amount of flour need for 1 dozen.
In order to calculate that, one we need to divide the total amount by the cups of flour need.
Then we get,
=> 3/ (2 2/5)
=> 3/ (12/5)
=> 15/12
=> 1.25
So, for half dozen cookies, we need
=> 1.25/2
=> 0.625
Which is in the fraction form of,
=> 5/8
And for 5 dozen of cookie we need.
=> 5 x 1.25
=> 6.25
The fraction equivalent is
=> 6 1/4 cups.
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5. Mrs. Hans bought a house for $35,000 ten years ago. If she sells it this year for $119,000, what percent profit will she make?
Answer:
340%
Step-by-step explanation:
119000/35000
*PRE-CALC URGENT + 100 POINTS*
A jumping spider's movement is modeled by a parabola. The spider makes a single
jump from the origin and reaches a maximum height of 20 mm halfway across a horizontal distance of 160 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Answer:
A. (x - 80)² = -320(y = 20)
B. Focus: (80, -60)
Directrix: y = 100
Axis of symmetry: x = 80
Step-by-step explanation:
Part AIf the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:
x-intercepts = (0, 0) and (160, 0)Vertex = (80, 20)Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
[tex]\textsf{Vertex}=(h, k)[/tex][tex]\textsf{Focus}=(h,k+p)[/tex][tex]\textsf{Directrix}:y=(k-p)[/tex][tex]\textsf{Axis of symmetry}:x=h[/tex]Substitute one of the x-intercepts and the vertex into the formula and solve for p:
[tex]\implies (0-80)^2=4p(0-20)[/tex]
[tex]\implies (-80)^2=4p(-20)[/tex]
[tex]\implies 6400=-80p[/tex]
[tex]\implies p=-80[/tex]
Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:
[tex]\implies (x-80)^2=4(-80)(y-20)[/tex]
[tex]\implies (x-80)^2=-320(y-20)[/tex]
Part BGiven:
h = 80k = 20p = -80[tex]\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}[/tex]
imagine it as a degree:
We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
Given that,
We have to find the power of the expressions.
a) x⁻³.x⁵
Bases are equal so powers must be added.
x⁻³⁺⁵
x²
b) m⁻³:m⁶
It is in ratio that means
m⁻³/m⁶
We can take the m⁶ to numerator
m⁻³.m⁻⁶
Bases are equal so powers must be added.
m⁻³⁻⁶
m⁻⁹
c) a⁻⁷.a⁻²
Bases are equal so powers must be added.
a⁻⁷⁻²
a⁻⁹
d) (m⁻³)⁻²
Powers are multiplied
m⁶
Therefore, We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
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what ticket price would maximize revenue?
As per the concept of system of linear equations, the maximum revenue of this basket ball match is $3.4
Linear equation:
Linear equation refers the one variable is an equation in which there is only one variable present. And it is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.
Given,
A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $10 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Assume that attendance is linearly related to ticket price.
Here we need to find the ticket price would maximize revenue.
In order to find the ticket price for the maximum revenue,
We have to identify the details from the given question,
Total seating capacity = 66,000
When ticket price $10 then the attendance 28,000
When ticket price $7 then the attendance 33,000
Let us consider the x be the maximum revenue ticket price.
Now, to solve this we have to find the slope for the equation,
That is,
=> m = (33000 - 28000)/(7 - 10)
=> m = 5000/-3
=> m = -5000/3
=> m = 1666.6
Then the revenue equation is written as,
=> y = (10 - x) * (28,000 + 1666.6x)
=> y = 280000-11334x-1666.6x²
If we plot the this function into the graph, then we get the graph like the following.
Therefore, the solution of the graph is 3.4.
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is the line through points P(-8, -10) and Q(-5, -12) perpendicular to the line through points R(9, -6) and S(17, -5) explain
Answer:
No, the lines are not perpendicularStep-by-step explanation:
Perpendicular lines have opposite-reciprocal slopes.
It means the product of the slopes is - 1.
Let's find the slopes of the two lines and their product.
m(PQ) = (- 12 - (-10)) / (- 5 - (-8)) = - 2/3m(RS) = (- 5 - (-6)) / (17 - 9) = 1/8Find the product of slopes:
- 2/3*1/8 = - 1/12This is not - 1, therefore the lines are NOT perpendicular.
Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Answer:
S: {11}
Step-by-step explanation:
Hello!
Solve the inequality for n by isolating the variable.
Solve for n 6(n − 5) < 3(n + 4) 6n - 30 < 3n + 123n - 30 < 123n < 42n < 14The solution for n is all values less than 14, so 11 would work.
Find the average rate of change of f(x) = -x² + 3x + 1 from x=2 to x = 5.
Simplify your answer as much as possible.
Answer:
The average rate of change is: -4
Step-by-step explanation:
So to solve this we just need to plug our numbers into the formula. We are using the formula f(b) - f(a)b - a where “a” and “b” are our numbers. So we are given the intervals x=2 and x=5. When we see that we can rewrite it as (2,0) and (5,0). This is because when it is telling us just “x” we know “y” (the second number in the parentheses) is 0. So just plugging in the numbers we get: (-(5)2+3(5)+1)-(-(2)2+3(2)+1)(5 - 2). Solving it we get -4.
Can someone help please? Very much appreciated
Answer:
Coefficient is 7, variable is z
Step-by-step explanation: