a) length = 24 + 2x
width = 16 + 2x
b) The area of the new garden space = 384 + 48x + 4x².
c) The area of the border can be represented by the polynomial expression 32x+2x².
What is a polynomial expression?
A polynomial expression is a mathematical expression that is a sum of terms, each term consisting of a constant coefficient multiplied by one or more variables raised to a non-negative integer power.
a.) Let x represent the width of the border. The length of the new garden space would be 24 feet + 2x (since the border is added to both the length and width). The width of the new garden space would be 16 feet + 2x (since the border is added to both the length and width).
length = 24 + 2x
width = 16 + 2x
b.) The area of the new garden space can be represented by the trinomial (24+2x)(16+2x) = (24*16) + (48x) + (4x^2)
c.) The area of the border can be represented by the polynomial expression 2x(16+x) = 32x + 2x^2.
Hence,
a) length = 24 + 2x
width = 16 + 2x
b) The area of the new garden space = 384 + 48x + 4x².
c) The area of the border can be represented by the polynomial expression 32x+2x².
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help please need to submit now
Answer:
∠HKJ = 180 (STRAIGHT ANGLE)
∠HKI = 180-106 = 74
Common Fac
Greatest common Factor:
reth is not correct because.
3
4
8 Luis buys 16 bellflowers and 20 roses. He wants to plant an equal number
of bellflowers and an equal number of roses in each of his flower boxes.
What is the greatest number of flower boxes Luis can plant using all the
bellflowers and roses? Show your work.
7161
With the greatest common factor method all of the roses and bellflowers, Luis can plant a maximum of 8 flower boxes.
How can you discover the approach of the greatest common factor?Three techniques—listing out the common factors, primal factorization, and division method—can be used to determine the biggest common factor of two or more natural numbers. To get the GCF, each procedure needs to be multiplied and divided. For instance, 14 and 35 have a GCF of 7.
According to the given information:Luis buys 16 bellflowers and 20 roses.
Factors of 16 : 4 x 4 x 2 x 2 x 2 x 2
Factors of 20 : 5 x 4 x 2 x 2
The GCF is the greatest common factor.
∵ The GCF of the numbers 16 and 20 is 4 x 2 = 8.
So,
the greatest number of flower boxes Luis can plant using all the bellflowers and roses is 8.
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write an equation in slope intercept from perpendicular to y = 1/5x - 9 through (7, -3)?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x-9\qquad \impliedby \qquad \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]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{1} \implies -5}}[/tex]
so we're really looking for the equation of a line whose slope is -5 and it passes through (7 , -3)
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- 5}(x-\stackrel{x_1}{7}) \implies y +3= -5 (x -7) \\\\\\ y+3=-5x+35\implies {\Large \begin{array}{llll} y=-5x+32 \end{array}}[/tex]
The prime number 7 is the average of which two different numbers?
Answer:
many, many answers
Step-by-step explanation:
as we know an avarage is the number in between all given values. so it can be 6.5 and 7.5, 6 and 8 5 and 9, 4 and 10 and so on
What is a line segment in 4th grade math?
A line segment is a straight line of points that start at one point and end at another point. A Line segment AB is written down as AB'.
In geometry, the line segment is edged by two definite points on a line. In another word, we can a segment of a line is part of the line that joins two points.
A line has no terminal points and expands limitlessly in both directions but a line segment has two definite endpoints. The dissimilarity between a line segment and a ray is that a ray has only one endpoint and its other end extends infinitely.
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Jed sells desserts for $24 each.
Each dessert costs $12.80.
Percentage profit: 87.5%
The cost to make each dessert increases to $13.60. Jed wants to make the same percentage profit.
Work out the new selling price.
Using percentage profit formula, the selling price must be $24.8
What is Percentage ProfitProfit percentage is calculated by dividing the net profit by the total revenue and multiplying it by 100. For example, if a business has a net profit of $50,000 and total revenue of $500,000, its profit percentage is 10%.
The initial cost of the desert can be calculated using the formula of percentage profit.
percentage profit = [(selling price - cost price) / cost price] * 100
87.5 / 100 = 24 - x / x
0.875 = 24 - x / x
0.875x = 24 - x
24 = 1.875x
x = 12.8
The cost price is 12.8
The profit will be = 24 - 12.8 = 11.2
In order to keep making same percentage profit with the new cost of production.
Selling price = 11.2 + 13.60
Selling price = 24.8
The selling price is $24.8
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A linear equation that solution is equal to 3
Answer:
is 9
Step-by-step explanation:
If $3,000 is loaned for 4 months at a 4. 5% annual rate, how much interest is earned?.
If $3,000 is loaned for 4 months at 4.5% AR , He earned $45 interest .
What is interest ?
Interests are subjects that fascinate you and want to learn more about. Interests are usually more about learning and discovering ideas, concepts, and knowledge like history, animal behavior, or even pop culture. For example, if your interest is history, going to museums would be your hobby.
Have given ,
$3,000 is loaned for 4 months at a 4.5% annual rate ,
To find how much interest is earned ,
annual rate is 4.5% then 4 months rate will be [tex]\frac{4.5}{3}[/tex] = 1.5%
So, he earned 1.5% interest for $3,000 ,
Let's calculate , [tex]\frac{3000*1.5}{100}[/tex]
[tex]\frac{4500}{100}[/tex] = $45
If $3,000 is loaned for 4 months at 4.5% AR , He earned $45 interest .
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question in picture. Geometry. Acellus.
Examining the figure properly shows that chord AB in the circle has its length to be equal to 16
How to find the length of ABInformation given from the question is interpreted as
let the center of the circle be O
BE = opposite = ?
OE = adjacent = 6
OB = OA = hypotenuse = radius = 10
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
10² = BE² + 6²
100 = BE² + 36
BE² = 100 - 36
BE = √64
BE = 8
Since line OE is the perpendicular bisector, BE = AE
and from the figure AB = BE + AE
= 8 + 8
= 16
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hurry please and thank you
The last option is equivalent to the slope of the linear function and this is given by
2/5
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m is calculated using the formula
m = (y₀ - y₁) / (x₀ - x₁)
The value of the slope is constant for a linear function
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Find the outer perimeter of this figure.
Round your answer to the nearest
hundredth. Use 3.14 to approximate IT.
12 m
P = 2 = Tr = [ ? ]m
12 m
P = 12m + 12m = [ ]m
10 m
P = 10m + 10m = [ ]m
The outer perimeter of the figure is calculated as 62.84m
What is Perimeter of a FigurePerimeter is the distance around the edge of a shape. It is the sum of all the sides of a shape.
Perimeter is the total length of the outside boundary of a shape. It is calculated by adding up all of the sides of the shape.
In this problem, we already have the values given to us and we simply need to compute them.
a) P = 18.84m
b) 12m + 12m = 24m
c) 10m + 10m = 20m
The total outer perimeter of the figure is calculated as
P = 18.84 + 24 + 20 = 62.84m
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the number of boys in each class varies directly with the number of girls. in one class there are 14 boys and 7 girls.
using b=kG, find k
The value of k could be 2 by using the given expression B = kG.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables, constants.
Given ,
the number of boys in each class varies directly with the number of girls. in one class there are 14 boys and 7 girls.
using b=kG
So here we have to find the value of k.
From the given expression
that is ,
B = kG
where by substituting the given values ,
we get,
14 = k * 7
k = 14/7
k = 2
Hence, The value of k could be 2 by using the given expression B = kG.
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A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled. A) 60 B) 50 C) 7.1 D) 5.9
The number of 3s that will be rolled when dice is rolled 360 times will have a standard deviation of 7.1.
Define standard deviation.The standard deviation (or ) is a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What does standard deviation tells you?The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.
Let X = the total number of 3s produced by rolling the die 360 times. As a result, the number of 3s that will be rolled will have a standard deviation of 7.1.
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For a school fundraiser, Ernie sold 66 gift cars, Jessie sold 24 gift cards, and Makayla sold 78 gift cards. Choose the expression that uses GCF and the Distributive Property to find the total number of gift cards that Ernie, Jessie, and Makayla sold
Answer:
168
Step-by-step explanation:
Gift Cards sold by Ernie = 66
Gift cards sold by Hessie = 24
Gift Cards sold by Makayala = 78
Common Factor = 6
66 = 6 x 11
24 = 6 x 4
78 = 6 x 13
The total number of gift cards sold is the sum of each person, that being 66 + 24 + 78 which equals 168
Total number of gift cards that all three sold = 168
What is the easiest way to learn an angle?
The easiest way to learn about angles depends on the individual learner, methods like Visualization, Practice Problems, and Hands-on activities can be utilized.
Visualization: For visual learners, using drawings and diagrams can help them comprehend the idea of angles. They may practice sketching and measuring angles with a protractor, as well as observing the angle in real-life settings like doors, windows, and stairs.Practice problems: Practice problems will help you reinforce your understanding of angles and get more familiar with the various methods for calculating angles. Learning exercises such as finding, categorizing, and measuring angles in various contexts might be beneficial.Hands-on activities: Hands-on activities, such as making angle puzzles or building constructions with varied angles, can help make angles more solid and easier to grasp.Learn more about the easiest way to learn an angle here: https://brainly.com/question/29211013
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the product of two consectuitve natural numbers os 1.5 times the square of the lesser number find the two squares
The two squares of the the product of two consectuitve natural numbers os 1.5 times the square of the lesser number are 2 and 3.
How can the two squares be calculated?The expression that of the statement that the two squares where the product of two consecutive natural integers is 1.5 times the square of the smaller number can be written as
x(x+1)=(1.5)(x^2)
we can open the bracket
x^2 +x = 1.5x^2
then we can re arrange
0.5x^2 -x=0
then we can factorize
x(0.5x-1)=0
x=0 or 0.5x=1
x=0 or x=2
Therefore, The number can be 0 and 1 or 2 and 3
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Draw the prime factor trees for 90 and 135.
Use the prime factor trees to find the lowest common multiple (LCM) of
90 and 135.
The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.
What is the least common factor (LCM)?The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.
The numbers are given below.
90 and 135
The prime factors of the number 90 will be given as,
90 = 2 × 3 × 3 × 5
90 = 2 × 3² × 5
The prime factors of the number 135 will be given as,
135 = 3 × 3 × 3 × 5
135 = 3³ × 5
The prime factor trees of the numbers 90 and 135 will be 2 × 3² × 5 and 3³ × 5.
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Find the area of the figure. Round to the nearest hundredth if nessary.
Answer:
7.3 m²
Step-by-step explanation:
Area of a rectangle = length x width
A = 2.9m x 2.5m = 7.25 m²≅7.3 m²
A result is called "statistically significant" whenever. O The null hypothesis is true. O The significant level a = 0.05. O The p-value Greaterthanorequalto 0.05. O The p-value is less than the significant level.
A result is called "statistically significant" when the p-value is less than the significant level, typically 0.05.
This means that there is less than a 5% chance that the results are due to chance alone, and suggests that there is a real effect present in the data.
The Null Hypothesis is the assumption that there is no significant difference between the measured phenomenon and a certain value or set of values. A statistically significant result means that the observed data are inconsistent with the assumption of no difference, or no effect.
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Compute C5,2. (Enter an exact number.)
The value of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.
The Combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.
A combination is the choice of r things from a set of n things without replacement and where order does not matter.
[tex]_{n} C_{r} =(\frac{n}{r})= \frac{_{n}P_{r} }{r!} =\frac{n!}{r!(n-r)!}[/tex]Here We have to find. [tex]${ }^5 \mathrm{C}_2$[/tex]
[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=\frac{5 !}{2 ! \times(5-2) !}[/tex]
[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 !}{3 ! \times 2 !}[/tex]
[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =\frac{5 \times 4 \times 3 !}{2 \times 1 \times 3 !}[/tex]
[tex]${ }^5 \mathrm{C}_2$[/tex][tex]& =5 \times 2[/tex]
[tex]${ }^5 \mathrm{C}_2$[/tex][tex]=10\end{aligned}[/tex]
Therefore, the exact number of [tex]${ }^5 \mathrm{C}_2$[/tex] is 10.
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WHO EVER TELLS ME THIS AND GETS IT RIGHT GET BRAINIEST
The product of 1.3 and 0.7 based on the grid is option D 0.91.
What are decimals?Decimals are a form of number in algebra that have an integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.
According to the grid 1.3 is represented using 13 squares in a row, while 0.7 is represented using 7 squares in column.
The product of 1.3 and 0.7 can thus be calculated by counting all the number of squares in the 13 rows and 7 columns.
The total number of squares in the grid id 91. Since, there are two decimal places we divide 91 by 100.
Thus, the product is 0.91.
The product can be calculated as follows:
(1.3) (0.7) = 0.91
Hence, the product of 1.3 and 0.7 is 0.91.
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What is the fraction 3/4 called?
Answer:
3 out of 4
Step-by-step explanation:
the denominator represent the whole number and numerator represent the amount
one way colors are represented in computers is with rgb, where 3 integers ranging from 0-255 inclusive are used to represent a color. if 2 integers $a$ and $b$ are used to represent a color, how many pairs $(a,b)$ are there such that their sum is divisible by 12?
There are 256 expected value for both a and b, so there are 256 x 256 = 65536 possible pairs of (a,b). Of these, there are 2112 pairs for which the sum of a and b is divisible by 12.
1. There are 256 possible values for both a and b. That means there are 256 x 256
= 65536 possible pairs of (a,b)
2. To find the number of pairs for which the sum of a and b is divisible by 12, we can look at the numbers 0 to 255 and see how many multiples of 12 there are. There are 21 multiples of 12 from 0 to 255, so
21 x 21
= 441.
3. Each multiple of 12 can be paired with any other number from 0 to 255, so there are 21 x 256 = 2112 pairs of (a,b) for which the sum is divisible by 12.
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A frequency table lists
O the times per second variations occur in various wave bands.
O the number of scores at each value.
O Othe intensity of a variable over all the participants studied.
O the average value of each variable.
A frequency table is a form of data presentation that shows the number of occurrences of each value of the variable being studied. It can be used to show the average value of the variable, the intensity of the variable, and the number of times a certain value appears.
A frequency table is a data presentation tool that is used to show the number of occurrences of each value of a variable being studied. It is often used to show the average value of a variable, the intensity of a variable, and the number of times a certain value appears. To construct a frequency table, you first need to list all the possible values of the variable that you are studying. Next, count the number of occurrences of each value, and then list this count for each value. You can then use this data to calculate the average value of the variable, the intensity of the variable, and the number of times a certain value appears. Additionally, frequency tables can be used to show the times per second variations occur in various wave bands.
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A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 90% confidence interval with a maximum error of 0.17 reproductions per hour. Assuming that the mean is 11.9 reproductions and the variance is known to be 4, what is the minimum sample size required for the estimate? Round your answer up to the next integer.
If a research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The minimum sample size required for the estimate is: 374.54.
How to find the sample size?n=((z⍺/2×sigma)/E)^2
Confidence interval ,c =90%
Maximum error, E =0.17
Variance, sigma^2=4
Z-score for 90% confidence interval=1.645
sigma=√4
sigma =2
Sample size = ((1.645×2)/0.17)^2
Sample size = 374.54
Therefore the sample size is 374.54.
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HELP PLEASE! 13 POINTS!! {simplify (3x - 8) + (2x + 5) - (4x - 8).}
(A) x + 21
(B) 9x - 11
(C) 9x + 5
(D) x - 11
(E) x + 5
anton wants to make 5 lb of sugar syrup.how much water and how much sugar does he need to make each concentration of sugar syrup? 5% syrup
The amount of water and sugar he needs respectively to make 5% syrup are; 4.75 lbs and 0.25 lbs
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. and a single variable.
Now, we are told that Anton wants to make 5 lb of sugar syrup. To get the amount of sugar that he needs to make 5% syrup. Thus;
Let x represent the number of pounds of sugar he needs to make 5% syrup
Thus;
x/5 = 5%
x/5 = 0.05
Multiply both sides by 5 to get;
x = 0.25
Thus, he needs 0.25 lbs of sugar and amount of water required = 5 - 0.25 = 4.75 lbs of water
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Find the area of the shaded figure
Answer:
138
Step-by-step explanation:
Divide the shaded area to a rectangle and a triangle
Shaded rectangle area = 10 * 12 = 120
Shaded triangle area = (6 * 12)/2 = 72/2 = 36
Area of unshaded rectangle
Shaded area= 120 + 36 - 18 = 156 - 18 = 138
Hope this helps :)
Have a great day!
(02.01 MC)
Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week. He
rounds his answer to 20 years. Is Eugene's answer viable?
Yes, Eugene can use traditional rounding rules to show the time required to earn the full million dollars.
No, Eugene would need to round down to show the time required to earn the full million dollars.
Not enough information to determine viability.
Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.
If Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week.: D. Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.
How to find if Eugene's answer is viable?To determine if Eugene's answer is viable, we need to find how long it will take him to earn his first million dollars at an average gross pay of $975.00 per week.
$1,000,000 / $975.00 per week
= 1025.64 weeks
So, it will take Eugene approximately 1025.64 weeks or approximately 19.71 years (rounded to the nearest year) to earn his first million dollars.
Therefore the correct option is D.
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Owners are also charged a $10 registration fee. The Kittle family boarded their dog at the kennel for 7 days. What was the total, with registration fee, of boarding their dog?
The total cost of boarding their dog including the registration fee is $237.50.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
We have to find the cost of boarding dog for 1 day.
Cost for three days = $97.50
Cost for 1 day = $97.50 / 3 = $32.50
Given that, the Kittle family boarded their dog at the kennel for 7 days.
Cost for 7 days = $32.50 × 7 = $227.50
Also given, owners are also charged a $10 registration fee.
Total cost = $227.50 + $10
= $237.50
Hence the total cost is $237.50.
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The complete question is as follows :
The table show the cost of boarding a dog at a dog kennel. Owners are also charged a $10 registration fee. The Kittle family boarded their dog at the dog kennel for 7 days what was the total, with registration fee, of boarding their dog?
Days Cost($)
3 97.50
4 130.00
5 162.50
6 195.00
