The summation notation of the sum is:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
The total amount is $84.
How to use summation notation to write the sum?Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.
Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.
Let n represent the number of weeks
Thus, this can be written using summation notation as:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
Thus, the total amount = 4¹ + 4² + 4³ = $84
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I Need Help I’m Desperate
For the graph with points (-2, 2) and (2,0), the slope, linear equation and y-intercept is m = -1/2, y = -1/2x + 1 and y = 1 respectively.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first graph shows the points (-2, 2) and (2,0).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[0 - 2]/[2 - (-2)]
(-2)/(2 + 2)
-2/4
-1/2
So, the slope point is obtained as m = -1/2.
The equation becomes - y = -1/2x + b
To find the value of b substitute the values of x and y in the equation -
2 = -1/2(-2) + b
2 = 1 + b
b = 2 - 1
b = 1
So, the value for b is 1.
Now, the equation becomes -
y = -1/2x + 1
To find the y-intercept substitute the value of x = 0 in the equation -
y = -1/2(0) + 1
y = 0 + 1
y = 1
Therefore, the slope is 1, equation is y = -1/2x + 1 and y-intercept is y = 1.
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Select all equations that represent the situation.
a) 4 · 2 5= ?
b) ? · 2 5= 4
c) 2 5÷ 4 = ? d)
4 ÷ 2 5= ?
e) ? ÷ 2 5= 4
Answer: b) ? · 2 5= 4
d) 4 ÷ 2 5= ?
e) ? ÷ 2 5= 4
The equations that represent the situation are b) ? · 2 5= 4 , d) 4 ÷ 2 5= ?, e) ? ÷ 2 5= 4
The question is asking for an unknown quantity and it is asking to find it by using the 4 and 25, so the equations that represent the situation are the ones that have 4 and 25 in them and have the unknown quantity on one side of the equation and the known quantity 4 on the other side.
a) 4 · 2 5= ? is not a valid equation as it is asking to multiply 4 and 25, which is known and doesn't have any unknown quantity.
c) 2 5÷ 4 = ? is also not a valid equation as it is asking to divide 25 by 4 and doesn't have any unknown quantity.
Step-by-step explanation:
you may not cross a single broken white or yellow line: When doing so would interfere with traffic.
When turning left into a driveway.
When the car in front of you is disabled.
When passing to the right on a one-way street.
You may not cross a single broken white or yellow line, when doing so would interfere with traffic unless it is safe to do so and without interfering with traffic.
The yellow line on the road serves as a barrier between opposing lanes of traffic as a traffic safety measure. It is intended to alert drivers to the fact that they are moving in the opposite directions and should keep a safe distance while driving.
The yellow line is typically placed in the centre of the road to indicate the separation of traffic. On highways and interstates, the yellow line is frequently used to mark the separation between two lanes of traffic moving in the same direction.
Drivers should always follow the yellow line and never cross it because doing so can be risky and result in accidents. The yellow line can also be used to show when passing other vehicles is dangerous.
On the driver's side, it is prohibited to pass other cars when a yellow line is interrupted by a solid line. Overall, the yellow line is an important safety measure for drivers to be aware of and obey when on the road.
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Shaquana went shopping for a new phone. The sales tax where she lives is 3.5%. If the price of the phone is pp dollars and cents, which expression represents the total price plus tax?
After applying the sales tax, the expression for the total price of the phone is 1.03p.
What is sales tax?
The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.
The amount for phone is represented as - p dollars and cents
The sales tax percentage is - 3% = 0.03
The sales tax applied on the phone is - 0.03p
The total price of the phone is denoted by the expression -
Total Price = Price of phone + Sales Tax
Total Price = p + 0.03p
Total Price = 1.03p
Therefore, the total price is obtained as 1.03p.
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A function f(x) increases by a factor of 10 over every unit interval in x and f(0)=1.
Which could be a function rule for f(x)?
Answer: A function that increases by a factor of 10 over every unit interval in x and starts at f(0)=1 could be represented by the function rule f(x) = 10^x.
This function starts at f(0) = 10^0 = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. For example:
f(1) = 10^1 = 10
f(2) = 10^2 = 100
f(3) = 10^3 = 1000
and so on.
Another possible function rule could be f(x) = 10x +1 it starts at f(0) = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. for example:
f(1) = 101 +1 = 11
f(2) = 102 +1 = 21
f(3) = 103 +1 = 31
and so on.
Both functions have similar behavior and answer the given conditions.
Step-by-step explanation:
Write the pair of fractions as a pair of fractions write a common denominator 6/9 and 1/3
The variable X varies jointly with Y and Z. When Y = 2 and Z = 4, X = 14. What is the value of X when Y = 10 and Z = 16?
The value of x when y = 10 and Z = 16, in the given joint variation is: 1120.
How to Solve a Joint Variation Problem?If X varies jointly with Y and Z, then we can use the formula X = k * Y * Z, where k is the constant of proportionality.
Using the given information, we can find k by plugging in the values of Y, Z, and X and solving for k:
14 = k * 2 * 4
k = 14 / (2 * 4)
k = 7/2
Now that we know the value of k, we can use it to find the value of X when Y = 10 and Z = 16:
X = k * Y * Z
X = (7/2) * 10 * 16
X = 70 * 16
X = 1120
So the value of X when Y = 10 and Z = 16 is 1120.
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i need help with all a b and c.
second attachment are the correct answers, please explain how to get to those answers.
Answer:
(a) A(x) = (12 -2x)√(3x -9)
Step-by-step explanation:
You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.
(a) Heron's formulaHeron's formula for the area of a triangle with side lengths a, b, c is ...
A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter
Given a perimeter of 12, and two sides x, this becomes ...
A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))
A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares
A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6
The domain is such that the radical and the area are non-negative.
(b) MaximumThe derivative of the area function is ...
[tex]A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}[/tex]
The derivative is zero at the maximum, so ...
-9x +36 = 0 ⇒ x = 4 . . . . . . . an equilateral triangle
The maximum area is ...
A(4) = (12 -2·4)√(3·4 -9) = 4√3
The maximum area is 4√3.
Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...
2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4 ⇒ x = 1/3
The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.
(c) Scaled and translatedThe function ...
z = 2A(3x+3) +1 = 2A(3(x+1)) +1
Compare this to ...
z = p·A(q(x -r)) +s
which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.
We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.
Applying these transformations to the original A(x) domain and range, we find the domain is ...
1/3[3, 6] -1 = [0, 1] . . . . . domain of z
And the range is ...
2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z
PLEASE HELP!!! I need to know the hypotenuse to this triangle.
The bottom side adjacent to the right triangle is 14.4 by the way. You should solve this using trig.
Answer:
hypotenuse = 14.8
Step-by-step explanation:
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]3.2^2 + 14.4^2 = c^2\\10.24 + 207.36 = c^2\\\sqrt{217.6} = c\\c = 14.751...\\c = 14.8[/tex]
A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall a: what does the 1 inch represent in the model? what is the scale? b: what is the scale factor model ?
Answer: 30
Step-by-step explanation: 600/20=30 so each inch on the scale represents 30 feet in real life.
Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not yellow) when choosing one marble from the bag.
8%
24%
36%
64%
Answer:
c, 64 percent
Step-by-step explanation:
3+3+10+9=25
25-9(yellow)=16
25/16=64
Answer: D: 64%
Step-by-step explanation: 3 + 3 + 9 + 10 = 25, 3 + 3 + 10 = 16 (Alternative: 25 - 9) 16 / 25 = 64. So the answer is 64%
56) a player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?
If a player who is off the field of play to receive medical treatment trips a player who is on the field of play , then (c) the referee cautions the player and the play is restarted with a indirect free kick.
On the field of play of football , the medical treatment of any player is not permitted under any circumstances.
When the player is bleeding, the player is required to leave the field immediately.
When the play has been restarted, only time the injured player is allowed to return to field of play is after game has started again.
It is exclusive responsibility of match referee to decide whether or not an injured player may return to the game.
The given question is incomplete , the complete question is
A player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?
(a) A. The referee shows a red card and sends off the player. Play is restarted with an indirect free kick.
(b) The referee shows a yellow card and cautions the player. Play is restarted with an indirect free kick.
(c) The referee cautions the player and Play is restarted with an direct free kick.
(d) The referee cautions the player and restarts with a dropped ball.
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write a formula that expresses the distance between p and 17
Step-by-step explanation:
The f O U r M U la is 72inc hes
PLEASE HELP ASAP!!!!!!!!!
Answer:2x
Step-by-step explanation:
Answer: the correct answer would be 2x
Step-by-step explanation:
The cost of a fishing pole has risen to $48 this week. Last week's cost was $43 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
11.6%
Step-by-step explanation:
First, we have to find how much it increases
48 - 43 = $5
We know it increases by $5
Then we take
5 divided by 43, then times 100 = 11.6%
So, it increases 11.6%
100 pts: Which of the following tables represents a linear function? x 1 1 0 1 1 y −2 −1 0 1 2 x 0 1 2 3 4 y −3 2 0 −2 3 x −2 −1 0 1 2 y 2 0 −1 0 2 x −2 −1 0 1 2 y 3 1 −1 −3 −5
Table (D) represents a linear function which the graph has been attached below.
What is the Linear function?A linear function is defined as an equation in which the highest exponent of the variable is always one. In mathematics, independent and dependent variables are values that vary in relation to one another.
The table is given in the question, as an option (D)
x: −2 −1 0 1 2
y: 3 1 −1 −3 −5
According to the above table, we plot the graph through the points then we can see that the graph of a function looks linear.
Thus, this table represents a linear function.
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a box contains one red ball, one purple ball, and one blue ball. two balls are drawn from the box one after the other without replacing the first ball. how many outcomes are possible for this experiment?
There are 6 possible outcomes for this experiment.
The total number of outcomes possible for an experiment of drawing two balls one after the other without replacing the first ball, depends on the number of possible outcomes for the first draw, multiplied by the number of possible outcomes for the second draw, given that the first ball was not replaced.
The total number of ways to choose one ball out of three is 3, and the number of ways to choose the second ball out of two remaining balls is 2. Therefore, the total number of outcomes possible for this experiment is 3 x 2 = 6.
The possible outcomes are:
(Red, Purple), (Red, Blue), (Purple, Red), (Purple, Blue), (Blue, Red) and (Blue, Purple)
It's important to notice that this method is called the Multiplication Rule for counting the total number of outcomes of two or more independent events.
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What is the difference between 3x^2-4x-5 and 2x^2-7x-3?
Answer:
Shown Below
Step-by-step explanation:
The difference between the two polynomials 3x^2-4x-5 and 2x^2-7x-3 is the result of subtracting the second polynomial from the first one.
3x^2 - 4x - 5 (first polynomial)
(subtraction operator)
2x^2 - 7x - 3 (second polynomial)
= x^2 - 3x - 2 (difference)
So the difference between 3x^2-4x-5 and 2x^2-7x-3 is x^2 - 3x - 2
This is a polynomial with a degree of 2 (quadratic) and the coefficient of x^2 is 1, x is -3 and the constant is -2.
Please help Due in 20 min
Evaluate
1/6x+7/12 when x= 1/2.
Answer: 8/12
Step-by-step explanation:
First you multiply 1/6 with 1/2 that would give us 1/12
Then you add 1/12 with 7/12
Our answer would be 8/12
Answer:
2/3 or in Decimal its 0.6
Step-by-step explanation:
1/6x+7/12 when x= 1/2.
1/6(1/2)+7/12
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
The graph that represents the situation is given in the attached image.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A gymnast joined a yoga studio to improve his flexibility and balance.
He pays a monthly fee and a fee per class he attends.
The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
The graph of the linear equation is given in the attached image.
And the graph that is equivalent to the graph is also given in the attached image.
Therefore, the equivalent graph is given in the attached image.
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Four students draw a design for a class flag. Each flag is black and white
Shown below are four designs. Which designs have the same fractions o
black and white? Explain how you know.
Designs have the same fractions o black and white is 16/2
Which designs have the same fractions?
Given,
Four student, each with 2 distinct colors, and no two subsequent flag may share the same color. Hence, the first stripe may be colored in any of 4 different ways.
The second student can be colored in 4 different ways after it is not the same color as the first.
The third flag should not be the same color as the second; it can be colored in 4 different ways.
The fourth flag should not be the same color as the third, allowing for a total of 4 different color combinations. total = 4 * 2 * 2 = 16
designs have the same fractions o black and white is 16/2
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Simplify
45y/30y (7x+49)
Plsss help
By simplifying 45y/30y (7x+49) this we get 3 / 2(7x + 49).
What is the simplifying?Simple implies to make anything easier to understand. Reducing an expression, fraction, or mathematical problem to its simplest form is known as simplification. Using calculations and solving the problem makes it simple. simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form. simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.45y/30y (7x+49)
45y / 30y(7x +49) : 3 / 2(7x + 49)
45y / 30y(7x + 49)
45y / 30(7x + 49)
Factor the number :45 = 15 . 3
=15.3 / 30(7x + 49)
Factor the Number : 30 = 15 . 2
15.3 / 15.2(7x + 49)
Cancel the common factor : 15
= 3 / 2(7x + 49).
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X-intercept:
y-intercept:
Answer: I believe your x-intercept is (-7,0) and your y-intercept is (0,2)
Step-by-step explanation: I hope this helps! (It's kind of sad how this is the only bit of math I'm good at)
For what value of p and q the root of quadratic equation x^2 (2p-4)x-(3q5)=0 vanih
Answer:
A quadratic equation of the form ax^2 + bx + c = 0 has solutions (or roots) that are either real or complex. The solutions of the equation vanish (or become equal to zero) when the equation is equal to zero.
For the equation x^2 (2p-4)x-(3q5)=0 to have a solution that vanishes, the discriminant (b^2 - 4ac) must be equal to zero.
Therefore, the roots of the quadratic equation x^2 (2p-4)x-(3q5)=0 vanish when p = 4 and q = 0
5. Quarterly payments of 300 for 9 years that will start 1 year from now,
What is the period of deferral in the deferred annuity?
help me
Period of deferral in the deferred annuity = 3 periods or 3 quarters.
Given: Quarterly payment of 300 for 9 years that will start 1 year from now.
To find the Period of deferral in the deferred annuity.
A deferment period is an agreed-upon time during which a borrower does not have to pay the lender interest or principal on a loan.
Solution: Formula for Period of deferral
K = nt - 1
K- Period of deferral
n- number of times compounded
t- time of start
K= nt - 1
K= 4(1) - 1
K= 3
Period of deferral = 3 periods / 3 quarters.
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2. Which number is NOT a
common denominator of the
fractions being added?
29
2 + 151/20
9
A 108
B 72
C 36
D 24
2.D movi
Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.
What is an example of common denominator?Common denominators are used to describe fractions with the same denominators. Take a look at the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 The fractions' denominators are both common, making it simple to calculate the variable result in both situations.
Here,
Given :
=>29 + 151/20
=> 580 + 151/20
=> 731/20
=> 36.55
As a zero denominator would result in an infinite fraction, a finite fraction can never have a denominator of 0.
Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.
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There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.
a. Write an equation that represents the volume V as a function of the radius r.
b. Complete this table for the function, giving three possible examples
Volume of the cone with height 18 meters and radius 'r' is given by :
a. Equation to represents the volume of the cone is 6πr²( cubic meters).
b. Three possible examples:
r (meters ) : 2 4 6
V (cubic meters ) : 24π 96π 216π
Height 'h' of the cone is 18meters.
Radius of the cone is 'r' meters.
a. Equation to represents volume of a cone as function 'r'
Volume 'V' of the cone is = ( 1 / 3 )π ×r² × h
Substitute value h = 18 meters we get,
V = ( 1 / 3 )π ×r² × 18
⇒ V = 6πr² cubic meters
b. Three possible examples for different values of 'r'
When r = 2
V = 6π × ( 2)²
⇒ V = 24π cubic meters
When r = 4
V = 6π × ( 4)²
⇒ V = 96π cubic meters
When r = 6
V = 6π × ( 6)²
⇒ V = 216π cubic meters
Therefore, the required volume of the cone with radius 'r' and height 18meters is:
a. Equation to represents volume is 6πr².
b. Table completion:
r (meters ) : 2 4 6
V (cubic meters ) : 24π 96π 216π
The above question is incomplete , the complete question is:
There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.
a. Write an equation that represents the volume V as a function of the radius r.
b. Complete this table for the function, giving three possible examples.
r : 2 _ _
V: ? ? ?
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Please help I’m very confused?
By means of angle properties and algebra properties, the measure of the missing angle equals 136°.
How to determine the measure of a missing angle
In this problem we find the representation of two consecutive angles, whose sum of measures equals 180°. The measure of an angle is equal to 44° and the measure of the other one must be determined by using the following algebraic expression:
m ∠ x + 44° = 180°
Now we proceed to solve the expression by algebra properties:
m ∠ x = 180° - 44°
m ∠ x = 136°
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4. If 2 is subtracted from three times a number, the result is equal to 5 less than three times
the number. Find the number.
The resulting equation: 3x - 2 = 3x - 5
This equation does not have any true answer, meaning either the question asked is wrong or you have typed this equation wrong.
The only answer you could write for this is No Solution.
a classroom has two rows with nine seats in each row. there are 15 students named s1, . . . , s15, where s1, . . . , s4 always sit in the front row and s5, . . . , s10 always sit in the back row. (the students s11, . . . s15 may sit in either row). in how many ways can the students be seated?
Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.
The open seats in the front row can be filled by the remaining 5 students in 5! ways.
The open seats in the back row can be filled by the remaining 5 students in 5! ways.
So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400
Step-by-step explanation: