The number of terms for the following sequence:
90, 98, 86,....16, 14 is 39
What is sequence?Sequence is defined as defined as an array of numbers in a particular order of arrangment. It can be AP or GP.
But the sequence given in this question is an AP with the following
Last term = 14,
First term = 90,
Common difference = -2
The nth term of a sequence (AP) when the last term is given is denoted by
L=a + (n-1)d
14= 90 + (n-1)*-2
14=90-2n+2
Rearrange the equation to have
14-90-2=-2n
122=-2n
Making n the subject to get
Therefore number of terms is =61
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Wednesday was 5 degrees warmer than Tuesday.
What was the temperature on Wednesday?
Answer: The temperature on Wednesday is 5 degrees hotter than Tuesday
Step-by-step explanation:
An online clothing company sells custom sweatshirts. The company charges $2.99 for shipping plus $8.00 for each sweatshirt. Write a linear function rule that models the total cost y (in dollars) for any number of sweatshirts x.
Use pencil and paper. Describe how the linear function rule would change if the shipping charge applied to each sweatshirt.
Answer:
y = 8x + 2.99
y =10.99x if the shipped was charger per shirt.
Step-by-step explanation:
For the first equation, the shipping charge in 2.99 if you buy 1 shirt or 100 shirts. It is an initial or one time fee, but you have to pay $8 for each shirt. I shirt 8, 2 shirts 16, 3 shirts 24 and so on.
In the second equation you are paying 2 and the shipping for each shirt.
That function is when the shipping charge is a one time fee.
If the shipping charge applied to each sweatshirt, then the total cost function would be y = 10.99x
===================================================
Explanation:
x = number of sweatshirts
Since each shirt costs $8, the expression 8x is the total cost of the shirts if we ignore shipping. Add on shipping to get 8x+2.99 as the actual total cost. This wouldn't include taxes or any other potential fees.
Adding on the 2.99 means it's a one time charge. This assumes all of the sweatshirts you buy is able to be shipped in one box.
---------------
If we changed it so that the shipping applied to each shirt (instead of each box), then the 2.99 would become 2.99x
That would mean the total cost becomes y = 8x+2.99x which fully simplifies to y = 10.99x
It says that the cost per shirt is really $10.99
In the triangles, and . If is greater than , then is ________ . congruent to longer than shorter than the same length as
If angle C is greater than angle E, then AB is greater than. Therefore, option B: 'greater than' is the correct answer.
In the figure attached, it is seen that
BC = DE and AC= FE
Now it is required to find the relation between sides AB and DF of the two given triangles.
Since it is given that angle C of the first triangle is greater than angle E of the second triangle. So it is concluded that the opposite sides of the two triangles are in the same ratio as their angles.
Hence, the AB is greater than DF.
"
Complete question:
In the triangles,BC = DE and AC = FE. If mC is greater than mE, then AB is ________ .
A: congruent to
B: longer than
C: shorter than
D: the same length as
"
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write a scientific national 6.3×10^3
The scientific notation 6.3 × 10³ can be written as 6300 in regular notation
Scientific Notation is a way of writing big and small numbers very easily. It is also known as the Standard form in Britain. It is used when a number can be multiplied by a power of 10.
When we write a scientific notation, it has two parts.
Only the digits are written with decimal points put after the first digit.The digits are followed by ×10 to a power (eg 10² or 10³) that shows how many places exactly we should move our decimal point to get the actual number.In the question instead of writing 6.3 × 10³, we can also write 6.3 × 10^4 which is easy to type but means the same.
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The complete question will be:
How is the Scientific Notation 6.3 × 10³ can be written as regular notation?
Given (Multiplug)
MP= 500
discount percent= 11.5
What percentage of VAT can be added to the customer purchase price after the discount so that the Multiplug can be obtained for the same amount as marked price. Find it.
Answer:
To find the percentage of VAT that can be added to the customer purchase price after the discount, you can use the following formula:
VAT% = (MP - (MP * (discount%/100))) / ((MP * (discount%/100)) * (1 + (VAT%/100))) * 100
Plugging in the values you provided, we get:
VAT% = (500 - (500 * (11.5/100))) / ((500 * (11.5/100)) * (1 + (VAT%/100))) * 100
Solving for VAT%, we get:
VAT% = 15.384615384615385
Therefore, you can add 15.384615384615385% VAT to the customer purchase price after the discount so that the Multiplug can be obtained for the same amount as the marked price.
Answer:
19.6%
If this help please set brainliest.
Step-by-step explanation:
To find the percentage of VAT that can be added to the customer purchase price after the discount, you can use the following formula:
VAT % = (MP - (MP * (discount percent / 100))) / (MP * (discount percent / 100)) * 100
Plugging in the given values, we get:
(500 - (500 * (11.5 / 100))) / (500 * (11.5 / 100)) * 100 = 19.6%
This means that you can add 19.6% VAT to the customer purchase price after the discount in order to obtain the Multiplug for the same amount as the marked price.
Question 3 of 10
What is the solution to the system of equations?
-5
y = 3x + 1
5.
-5.
OA. (-2, 1)
OB. (1, -2)
OC. (-2,-1)
OD. (-1,-2)
5
y=-2x-4
Option D: The solution of the system of equation is (-1,-2)
What is System of Equation ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
The equations are :
y = 3x + 1 ⇒ y - 3x = 1 (i)
y = -2x -4 ⇒ y + 2x = -4 (ii)
Subtracting (i) from (ii) we get ,
2x +3x = -4 -1
⇒ 5x = -5
⇒x = -1
for x = -1
y = 3x + 1 = 3*(-1) + 1 = -2
The solution of the system of equation is (-1,-2)
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If Michael is 63 inches tall and he can jump to touch the top of the doorframe which is 94 inches tall, how high can Michael jump?
Answer:
Michael can jump 31 inches high. This can be calculated by subtracting his height (63 inches) from the height of the doorframe (94 inches), which gives a difference of 31 inches.
The Hendricksons are in charge of bringing treats for 505050 football players. They brought 333 coolers of popsicles and 222 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat
If the Hendricksons are in charge of bringing treats for 505050 football players. The statement that best predicts how many football players will get a popsicle is: C. There will be exactly 30 football players who get a popsicle.
How to find the football players that will get a popsicle?First step is to find the total cooler
Total cooler = 3+2
Total cooler = 5
Since play we have 3:2 type of color
Hence,
Number of player with popsicles = 3/5 × 50
Number of player with popsicles = 30
Number of player with sandwiches = 2/5 × 50
Number of player with sandwiches = 20
Therefore the correct option is C.
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The complete question is:
The Hendricksons are in charge of bringing treats for 50 football players. They brought 3 coolers of popsicles and 2 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat. Which statement best predicts how many football players will get a popsicle? Choose 1 answer:
A. There will be exactly 20 football players who get a popsicle.
B. There will be close to 20 football players but not exactly 20 who get a popsicle.
C. There will be exactly 30 football players who get a popsicle.
D. There will be close to 30 football players who get a popsicle but not exactly 30 who get a popsicle
HELP PLEASE
Consider the equation xy = 0. In this equation, two variables are multiplied and the result is 0. Can the equation be true if neither variable is equal to 0? Can the equation be true if only one variable is equal to 0? If so, which one needs to be equal to 0? Can the equation be true if both variables are equal to 0?
Answer:
It is not true unless one or both variables is equal to zero. If either x, y or both is 0, then the equation will be true.
There are seven different books to choose from. In how many ways can you arrange these books on three different shelves of a bookcase?
The number of ways to arrange the seven books on three different shelves as required is; 210 ways.
What is the number of ways to arrange the books on different shelves?It follows from the task content that the number of possible arrangements of all seven books on three different shelves be determined.
On this note, the number of possible arrangements is best described by the number of possible permutations.
On this note, the permutation which represents the number of possible arrangements is;
⁷P₃
= 210 ways.
Ultimately, the number of possible arrangements is: 210.
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What is the volume of each cylinder?
The cylinder's capacity is 1.25 x [tex]10^{5}[/tex] and 3.28077× [tex]10^{5}[/tex] its radius and height are indicated in the illustration, accordingly.
what is volume ?The area contained by an object's limits in three-dimensional space is referred to as its volume. Another name for it is an object's capacity. The quantity of space a 3-dimensional item occupies is another way to quantify volume. A vessel's liquid content is measured in standard units and is known as the liquid measurement. Additionally, we call it the vessel's "volume" or "capacity." Both the juice bottle and the infant milk bottle have milliliter measuring marks.
given
a) r = 20 cm
h = 100 cm
V = [tex]\pi r^{2}h[/tex]
V = [tex]\pi * 20^{2} * 100[/tex]
= 1.25 x [tex]10^{5}[/tex]
b) d = 118 m = 118 / 2 = 59 m
h = 30 m
V = [tex]\pi r^{2}h[/tex]
V = [tex]\pi * 59^{2} * 30[/tex]
= 3.28077× [tex]10^{5}[/tex]
The cylinder's capacity is 1.25 x [tex]10^{5}[/tex] and 3.28077× [tex]10^{5}[/tex] its radius and height are indicated in the illustration, accordingly.
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What is the image of (3, 3) after a dilation by a scale factor of centered at the origin
The image point of (3, 3) is (3/n, 3/n).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given point (3, 3).
Let n be the scale factor.
The image of (3, 3) after dilation,
by a scale factor of n centered at the origin will be,
= (3/n, 3/n).
= (3/n, 3/n).
Therefore, (3/n, 3/n) is the image point.
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A set of sweater prices are normally distributed with a mean of 58 5858 dollars and a standard deviation of 5 55 dollars. What proportion of sweater prices are between 48. 50 48. 5048, point, 50 dollars and 60 6060 dollars?.
The proportion of sweater prices falling between 48.50 dollars and 60 dollars can be found by calculating the area under the normal curve for the two endpoints which is 78.38%
This can be calculated using the z-score formula, which is defined as
(x-μ)/σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.
For 48.50 dollars, the z-score is
(48.50-58)/5.5 = -1.454545.
For 60 dollars, the z-score is
(60-58)/5.5 = 0.363636.
Using a z-table, the proportion of sweater prices between 48.50 and 60 dollars is 0.7838, or 78.38%.
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Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make copper balls that have a radius of 6 in. If copper costs $0.75 per in^(3), how much will the copper cost to make one ball? Use 3.14 for \pi , and do not round your answer.
The cost of making the ball is $678.24.
What is the cost of the ball?
We are told in the question that Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make copper balls that have a radius of 6 in. If copper costs $0.75 per in^(3).
Now we have to obtain the volume of the ball. Let us recall that the ball has the shape of a sphere hence volume of a sphere is;
V = 4/3πr^3
V = 4/3 * 3.14 * (6)^3
V = 904.32 in^3
The cost of the ball is; 904.32 in^3 * $0.75
= $678.24
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Which operation must be done on both sides of the given equation in order to solve them 1 8x =24?
Kellan burns 348
calories in 3 hours. How
long will it take her to
burn 870 calories?
Answer:
7.5 Hours
Step-by-step explanation:
Given:
Kellan burns 348 calories in 3 hours.
Question:
How long will it take her to burn 870 calories?
Solve:
Since, it given that KelIan burns 348 calories in 3 hours. Then we need to find how much KeIlan burns per hour.
To do that, divide the calories by the hours.
Thus, 348 divided by 3 which equals 116.
Now knowing that KeIlan burns 116 per hour will help us know how much hours it would take to burn up 870 calories.
To do that,
We have to divide 870 by 116 which equals 7.5.
Hence, it would take 7.5 hours to burn 870 calories.
RevyBreeze
Lucía and Quinn train for a bike race. Lucía bikes 46 miles in 240 minutes.
Quinn bikes 51 miles in 5 hours. Who bikes at a faster rate? Show your work
Answer:
Lucia has a faster rate.
Step-by-step explanation:
Lucia's unit rate
46/4 = 11.5 240 minutes is the same as 4 hours 240/60
Lucia can travel 11.5 miles in 1 hour.
Quinn's unit rate:
51/5 = 10.2
Quinn can travel 10.2 miles in 1 hour
Answer:Lucia is faster
Step-by-step explanation:
speed= distance / time Lucia:46miles /240
I NEED HELP ASAP what is -5/9 divided by (-1/3)?!
answers choices
- 5/27
- 1 2/3
- - 1 2/3
- 1 1/3
I hope you’re having an amazing day! :)
The simplified form of the expression -5/9 ÷ -1/3 is 1 2/3.
What is -5/9 divided by (-1/3)?Given the expression in the question;
-5/9 ÷ -1/3
To divide a fraction by another fraction, multiply by its reciprocal.
Hence;
-5/9 × -3/1
Note that; - × - = +
5/9 × 3/1
Multiply 5 and 3
( 5 × 3 ) / 9
15 / 9
Cancel out the common factor of 3
5/3
Convert the improper fraction
5/3
1 2/3
Therefore, the result is 1 2/3.
Option B) 1 2/3 is the correct answer.
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After completing your analysis of the rating system, you determine that any rating greater than or equal to 3. 75 points can be considered a high rating. You also know that chocolate and tea considers a bar to be super dark chocolate if the bar's cocoa percent is greater than or equal to 80%. You decide to create a new data frame to find out which chocolate bars meet these two conditions. Assume the first part of your code is: best_trimmed_flavors_df <- trimmed_flavors_df %>% you want to apply the filter() function to the variables cocoa. Percent and rating. Add the code chunk that lets you filter the new data frame for chocolate bars that contain at least 80% cocoa and have a rating of at least 3. 75 points.
The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.
filter(cocoa.percent >= 80, rating >= 3.75)
1. Start by creating a new data frame called best_trimmed_flavors_df that uses the trimmed_flavors_df data frame
2. Use the %>% operator to pipe the trimmed_flavors_df data frame into the new data frame
3. Use the filter() function to filter the new data frame for chocolate bars with at least 80% cocoa and a rating of at least 3.75 points
The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.
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Examine the equation. –2(–x 9) = 2(x – 9) 2x – 18 = 2x – 18 this equation has .
Answer:
infinitely many solutions
Step-by-step explanation:
If the circle is dilated by a scale factor of one-fourth, what will be the length of the new radius? a circle with radius of 16 centimeters. 1 cm 4 cm 20 cm 64 cm
Answer:
4
Step-by-step explanation:
A dilation of a shape's area will proportionately affect its diagonal (or in the case of a circle, its radius). Thus, we can simply multiply the scale factor (1/4) by the circle's original radius to get the length of new radius.
[tex]16 \left(\dfrac{1}{4} \right)[/tex]
[tex]= \dfrac{16}{4}[/tex]
[tex]= 4[/tex]
What is the factored form of 4x² 9?
After taking the common, the factored form of [tex]4x^2-9[/tex] is (2x+3)(2x-3).
In the given question, we have to find the factored form of [tex]4x^2-9[/tex].
The following is how we factor the GCF out of a polynomial:
(1) Determine the polynomial's GCF for each term.
(2) Present each term as the GCF and another factor's product.
(3) To factor out the GCF, use the distributive property.
To solve this question we use the formula [tex](a^2-b^2) = (a+b)(a-b)[/tex]
We can write [tex]4x^2-9[/tex] as
[tex]4x^2-9[/tex] = [tex](2x)^2-(3)^2[/tex]
[tex]4x^2-9[/tex] = (2x+3)(2x-3)
Hence, the factor form of [tex]4x^2-9[/tex] is (2x+3)(2x-3).
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The complete question is:
What is the factored form of [tex]4x^2-9[/tex]?
Combine and simplify the following radical expression.
The radical value of the expression is 144⁵/³
What is a radical expression?You should be aware that a radical expression is defined as any expression containing a radical (√) symbol.
The given expression to be ex[pressed is
(2∛12)(3∛2)
To express this, we multiply two two brackets together to have
6∛24
Taking the cube root of 24 we have
6¹ * 24¹/³
Applying the multiplication law of indices we have
144⁵/³
In conclusion this is to say that the radical expression is 144⁵/³
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Multiply.
15x(1/3)
A)1/45
B)1/5
C)5
D)45
Answer:
5
Step-by-step explanation:
15/3 = 5
Answer:
c. 5
Step-by-step explanation:
15 ×1/3
= 5
note: three goes into fifteen 5 and goes into itself 1 living 5 .
all numbers with an absolute value greater than 3 but less than 7
The solution of the statement is,
⇒ - 6, - 5, - 4, - 4, 5 , 6
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The algebraic statement is,
''All numbers with an absolute value greater than 3 but less than 7''.
Now,
The mathematical expression of the given statement is,
⇒ 3 < |x| < 7
Thus, All the possible values are;
⇒ |x| = 4, 5, 6
⇒ x = - 6, - 5, - 4, - 4, 5 , 6
Thus, All the solution of the given statement is,
⇒ x = - 6, - 5, - 4, - 4, 5 , 6
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What is the domain and range of a logarithmic function f/x LOGB X?
The domain of the function [tex]f(x) = log_{b} x[/tex] is (0, ∞) and the range of the function is (-∞, ∞) which means that all real numbers is the range for the given function.
The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.
Given, [tex]y = log_{b} x[/tex]
To calculate the domain of given function we put argument greater than 0
[tex]x > 0[/tex]
Now we have to express the domain in the form of interval
Domain = (0, ∞)
Now put the domain in logarithmic expression to get range:
∴ Range = (-∞, ∞)
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In an arithmetic sequence, the first term is $100$ and the fourth term is $76$. What is the value of the first term that is less than $0$
The value of the first term that is less than 0 is -4
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
Where a₁ is the first term in the sequence, d is the common difference between terms, and n is the position of the term that we are trying to find.
If in an arithmetic sequence, the first term is 100 and the fourth term is 76, then the common difference is
aₙ = a₁ + (n - 1)d
76 = 100 + (4 - 1)d
76 = 100 + 3d
3d = 76 - 100
3d = -24
d = -8
Solve for aₙ that is less than 0.
aₙ = a₁ + (n - 1)d
aₙ = 100 + (n - 1)(-8) < 0
100 - 8n + 8 < 0
8n > 108
n > 13.5
a₁₄ = 100 + (14 - 1)(-8) = -4
Therefore, the value of the first term that is less than 0 is -4.
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q17 ANSWER FOR 20 POINTS
Answer:
18√3
Step-by-step explanation:
To simplify the expression 2√48 + 5√12, you can first simplify each of the terms inside the parentheses. The square root of 48 is equal to 4*√3, so you can rewrite the first term as:
2√48 = 2*(4√3) = 8√3
The square root of 12 is equal to 2*√3, so you can rewrite the second term as:
5√12 = 5*(2√3) = 10√3
Now that you have simplified the terms inside the parentheses, you can add them together to get:
(8√3) + (10√3) = 18*√3
So, the simplified expression is equal to 18*√3
At what point is the tangent to horizontal?
The tangent is horizontal when the slope of the tangent is 0.
A horizontal tangent line is a mathematical feature on a graph, located where a function's derivative is zero.
Where the derivative of a function is zero, a graph's horizontal tangent line is a mathematical feature.
This is so that the derivative, by definition, can provide the slope of the tangent line.
The slope of horizontal lines is zero. As a result, the tangent line is horizontal when the derivative is zero.
Use the function's derivative to get the zeros and then insert them back into the original equation to find horizontal tangent lines.
Calculus considers horizontal tangent lines significant because they show local maximum or minimum points in the original function.
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true or false the functional baseline describes the required fuctionality of a system and identifies all top level fuctions that the system must perform
Yes, it is true that the functional baseline identifies all top-level functions that a system must carry out as well as the functionality that is expected of it.
Functional Baseline:The functional baseline describes the system functionality that is necessary, as well as the functional and interface features of the overall system and the verification that is necessary to show that the given functional characteristics have been achieved. An activity's effectiveness and progress can be tracked and evaluated both during implementation and after completion using the data from a baseline study as a benchmark.
The functional baseline is the authorized configuration documentation that details a system's or top-level CI's performance requirements (functional, interoperability, and interface characteristics), as well as the verification necessary to show the accomplishment of those specified characteristics.
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