Answer:
2,188,180
Step-by-step explanation:
since 0 can't give anything to 8 the number would stay the same
HELP ASAP
This figure represents a planter
How much soil will it take to fill the planter?
Enter your answer in the box
the amount of soil needed is 27 cubic feet.
Tania is riding a train for $43.6$ miles to get to her destination. The train has $14.3$ more miles to travel before arriving at Tania's destination.
Which equation and solution correctly represent how many miles, $m$ , the train has already traveled?
Responses
Answer:
The answer to your problem is:
m +14.3 =43.6
m =29.3
Step-by-step explanation:
Miles to travel: 43.6
Miles left to travel: 14.3
To find the amount of miles that the train has already traveled (m), we know that the sum of that value (m) and the miles left to travel (14.3) is equal to the total miles (43.6)
m +14.3 = 43.6
m = 43.6-14.3= 29.9
Thus the answer to your problem is,
m +14.3 =43.6
m =29.3
What type of triangle is shown below?
Answer:
equalateral
Step-by-step explanation:
each side is equal to the next
Answer:
2. Equilateral
Step-by-step explanation:
Step 1: Process Of Elimination-
1. Right: No
This triangle is not a right triangle because it does not have a right triangle indicator nor does it equal 90°.
2. Equilateral: Yes
This triangle is an equilateral triangle because all 3 sides are equal and they add up to 180° meaning each side equal 60°.
3. Acute: No
A acute triangle is a triangle that is less then 90° but this triangle equals 180°.
4. Scalene: No
A scalene triangle is a triangle that has different side angles but they all add up to 180° but here we can see that the sides are equal.
what are the parameters of the relevant standard beta distribution?
The parameters of the relevant standard beta distribution are alpha and beta.
Determine the shape of the beta distributionThese are two parameters that determine the shape of the beta distribution
.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.
The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.
The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.
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Kevin ate 5/12 of a pizza. Which is a better estimate for the amount of pizza that he ate: about half of the pizza or almost all of the pizza?
Answer:
Step-by-step explanation:
answer: about half the pizza as 5/12 is closer to half(6/12) then the full pizza (12/12)
someone pls answer this!!
doing more questions after on this topic worth 100 points
do simple working
Answer:
ii. is the answer
hope this helped
PLEASE HELP! What similarity statement can you write relating the three triangles in the diagram?
The answer of the given question based on the finding the similarity statement by relating the three triangle is the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.
What is Angle-Angle (AA) similarity theorem?The Angle-Angle (AA) similarity theorem is statement used in geometry to determine whether two triangles are similar. It states that if two angles of one triangle are congruent to two angles of another triangle, then two triangles are similar.
More specifically, this theorem states that if two pairs of corresponding angles in two triangles are congruent, then triangles are similar. In other words measure of one angle in one triangle is equal to corresponding angle in other triangle, and measure of another angle in first triangle is equal to corresponding angle in other triangle.
Based on the given diagram, the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.
In the diagram, we can see that all three triangles have two pairs of congruent angles, which are labeled as angle A and angle B. Therefore, we can conclude that the three triangles are similar by AA similarity.
We can write this similarity statement as: Triangle ABC ~ Triangle DEF, Triangle ABC ~ Triangle GHI, and Triangle DEF ~ Triangle GHI.
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Gina was shopping and saw a t-shirt she really liked, but could not decide which color to buy. The clerk said she would reduce the price by $2.50 per shirt if Gina bought more than one. She purchased 5 shirts all in different colors, for a total of $47.50. Write an equation to find the original cost of one shirt.
Let x represent the original cost of one shirt. The equation is 5x - 47.50 = 0, which can be solved to find that x = $9.50.
Gina was shopping and saw a t-shirt she liked, but couldn't decide which color to buy. The clerk offered to reduce the price by $2.50 per shirt if Gina bought more than one. She decided to purchase 5 shirts in different colors and the total cost of all 5 shirts was $47.50. To find the original cost of one shirt before the discount, we can set up an equation. Let x represent the original cost of one shirt. The equation would be 5x - 47.50 = 0, since the total cost of the 5 shirts was $47.50. When this equation is solved, x = $9.50, which is the original cost of one shirt before the discount. Therefore, the total cost of all 5 shirts was reduced by $2.50 for each shirt, from $9.50 to $7.00.
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What is the term-to-term rule of the linear sequence below? 1 , 7 , 13 , 19 , 25
Answer:6n-5
Step-by-step explanation:
1,7,13,19,25
It goes up in 6 each time, so you will need to go back 6 back on the number one, so it will be -5 so the answer will be 6n-5.
6(2)-5 = 7
6(3)-5 =13
Carlos has scored 24, 19, 20, and 28 points in his four basketball games so far. How many points does he need to score in the next game so that his average (mean) is 24 points per game?
Carlos needs to score 29 points in the next game to have an average of 24 points per game.
What is the mean and standard deviation?The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
According to the given information:Let x be the number of points Carlos needs to score in the next game to have an average of 24 points per game.
To find the solution, we can use the formula for the mean of a set of numbers:
(mean) = (sum of numbers) / (number of numbers)
In this case, we want the mean to be 24, and we have 5 numbers (4 previous game scores and the score in the next game), so:
24 = (24 + 19 + 20 + 28 + x) / 5
Multiplying both sides by 5, we get:
120 = 91 + x
Subtracting 91 from both sides, we get:
x = 29
Therefore, Carlos needs to score 29 points in the next game to have an average of 24 points per game.
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[tex]\frac{2}{3}a + 2 = \frac{1}{3}(4a + 1)[/tex]
solve for "a"
Answer:
a=5/2
Step-by-step explanation:
Answer:
a = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] a + 2 = [tex]\frac{1}{3}[/tex] (4a + 1)
multiply through by 3 to clear the fractions
2a + 6 = 4a + 1 ( subtract 4a from both sides )
- 2a + 6 = 1 ( subtract 6 from both sides )
- 2a = - 5 ( divide both sides by - 2 )
a = [tex]\frac{-5}{-2}[/tex] = [tex]\frac{5}{2}[/tex]
Natalie uses a 50% off coupon when she buys a camera. The original price of the camera is
$46. 00
$46. 0. How much money does Natalie save by using the coupon?
Natalie saved amount $23 by using the coupon.
What is meant by the discount rate?
The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the present.
The data is available from the question is:
The discount through coupon is d = 50%.
The original price of camera is c = $46.00
The discount on the amount is:
[tex]d = (\frac{50}{100}) 46[/tex]
d = 23
Thus, the amount saved is $23.
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Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?
A.
XY = 8 mm , YZ = 12 mm , XZ = 23 mm
B.
XY = 11 mm , YZ = 9 mm , XZ = 23 mm
C.
XY = 11 mm , YZ = 12 mm , XZ = 20 mm
D.
XY = 14 mm , YZ = 12 mm , XZ = 29 mm
The combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.
For a set of three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Using this property, we can determine which of the given combinations of side lengths will form a triangle with vertices X, Y, and Z.
A. XY = 8 mm, YZ = 12 mm, XZ = 23 mm
Here, XY + YZ = 8 mm + 12 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.
B. XY = 11 mm, YZ = 9 mm, XZ = 23 mm
Here, XY + YZ = 11 mm + 9 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.
C. XY = 11 mm, YZ = 12 mm, XZ = 20 mm
Here, XY + YZ = 11 mm + 12 mm = 23 mm, which is greater than XZ = 20 mm. Therefore, this combination of side lengths will form a triangle.
D. XY = 14 mm, YZ = 12 mm, XZ = 29 mm
Here, XY + YZ = 14 mm + 12 mm = 26 mm, which is greater than XZ = 29 mm. Therefore, this combination of side lengths will form a triangle.
Therefore, the combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.
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Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?
A.XY = 8 mm , YZ = 12 mm , XZ = 23 mm
B.XY = 11 mm , YZ = 9 mm , XZ = 23 mm
C.XY = 11 mm , YZ = 12 mm , XZ = 20 mm
D.XY = 14 mm , YZ = 12 mm , XZ = 29 mm
What is the purpose of doing a multiple comparison? Choose the correct answer below. O A. O B. O C. ○ D. A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA. A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations. When at least one of the variances is different, a multiple comparison shows the relationship between the variances. When the null hypothesis of an ANOVA test is rejected, a multiple comparison shows the relationship between the population means. Click to select vour answer
The purpose of doing a multiple comparison is to show the relationship between the population means when the null hypothesis of an ANOVA test is rejected.
What is meant by the multiple comparison?Multiple comparison is a statistical process that entails making a large number of comparisons, thus raising the chances of erroneously detecting false positives or type I errors.
When using multiple comparisons, there is a possibility that a statistical inference drawn for a single comparison is no longer valid.
Therefore, it is critical to adjust the p-values or confidence levels of these tests accordingly. As a result, multiple comparison methods have been devised.
The following are the purposes of doing multiple comparisons:
The relationship between the population means is shown when the null hypothesis of an ANOVA test is rejected.
A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA.
A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations.When at least one of the variances is different, a multiple comparison shows the relationship between the variances.
The most important objective of multiple comparisons is to estimate, compare, and control the likelihood of making false conclusions.
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Let B and C be two ordered bases of Rº, and consider a linear transformation T:RR. Suppose that the change of base matrix Ic,B is given by 1-3 -1 1] -1 2 -1 -1 -3 -2] and the coordinate matrix Tc,c of T with respect to C is given by -2 -2 -27 |-1 -3 -1. | 2 0 -1] Use this to determine coordinate matrix TB,B of T with respect to B! TB,B =
The coordinate matrix TB,B of a linear transformation T with respect to bases B and C is found to be [2 5 4; 1 1 2; -1 -1 -1].
To find the coordinate matrix TB,B of T with respect to B, we can use the formula:
TB,B = Ic,B * Tc,c * Ib,c
where Ib,c is the change of basis matrix from basis B to basis C.
To find Ib,c, we can use the inverse of Ic,B:
Ib,c = (Ic,B)^(-1)
We can use a calculator to find the inverse of Ic,B:
Ib,c = [1/4 1/4 -1/4]
[ 0 1 1 ]
[-1/4 -3/4 3/4]
Now, we need to calculate Ic,B * Tc,c:
Ic,B * Tc,c = [ 1 -3 -1 ] [-2 -2 -27 ] [ 1/4 1/4 -1/4 ] = [ 23 29 68 ]
[-1 2 -1 ] [-1 -3 -1 ] [ 0 1 1 ] [-15 -23 -48]
[-1 -3 -2 ] [ 2 0 -1 ] [-1/4 -3/4 3/4 ] [ 3 11 25]
Finally, we can calculate TB,B:
TB,B = (Ic,B * Tc,c * Ib,c)^(-1)
We can use a calculator to find the inverse of Ic,B * Tc,c * Ib,c:
TB,B = [ 2 5 4 ]
[ 1 1 2 ]
[-1 -1 -1 ]
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Tammy is planning to garden a plot of land in the shape of a right triangle.
The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches.
Answer: 7.5 square inches
Step-by-step explanation: the ratio is 1:2 meaning we cut the numbers in half, then we can find area normally
5/2=2.5
12/2=6
2.5x6=15
15/2=7.5
The gcf of 18,36 and me is 2.
I am a multiple of 5
I am greater than 18 and less than 30
Based on the information provided, the only possible number that satisfies all the conditions is 20.
What is GCF?
GCF stands for "Greatest Common Factor". It is also sometimes referred to as the "Greatest Common Divisor" (GCD). The GCF of two or more numbers is the largest positive integer that divides evenly into each of the numbers. In other words, it is the largest factor that the numbers have in common.
The GCF (Greatest Common Factor) of 18, 36, and a number N is 2. Since 18 and 36 are both even numbers with a common factor of 2, any number that satisfies this condition must also be even and have a factor of 2.
The number N is a multiple of 5. Since the number is even and has a factor of 2, the only even multiple of 5 between 18 and 30 is 20.
Finally, we are given that N is greater than 18 and less than 30. The only number that satisfies all the given conditions is therefore 20.
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Write the equation of the parabola that has its vertex at (3,-12) and passes through the point (0,6)
Answer:
y=2(x-3)²-12
Step-by-step explanation:
If x and y are in direct proportion and y is 30 when x is 6,find y when x is 14
Answer:
70
Step-by-step explanation:
If y=30 when x=6, 5x=y (because they are in direct proportion).
So, when x=14 replace x.
5*14=y
y=70
you can prove this because 70/14=30/6=5
so, the proportions are equal
(Adding Integers MC) What is the value of 209 + −142 + −52? 15 −15 67 −194
The answer is positive 15 because the final result is 15 units to the right of zero on the number line.
To solve this problem, we simply need to add the three integers together.
Starting with 209, we add -142 to get 67. Then, we add -52 to get a final result of 15. Therefore, the answer is 15.
To understand why the answer is positive, negative, or zero, we can think of integers on a number line. Positive integers are to the right of zero, negative integers are to the left of zero, and zero is at the center.
Starting with 209, we move 209 units to the right of zero on the number line. Then, adding -142 means moving 142 units to the left of zero, resulting in a position of 67 units to the right of zero. Finally, adding -52 means moving 52 units to the left of 67, resulting in a position of 15 units to the right of zero.
Therefore, the answer is positive 15 because the final result is 15 units to the right of zero on the number line.
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Algebraic expressions for geometry( just beginning geometry) please help this is 2 months late
We can see here:
4. Given: 6x + 7 = 8x - 17. Prove: x = 12
Statements Reasons
1. 6x + 7 = 8x - 17 Given
2. 7 = 2x - 17 Subtracted 6x from both sides
3. 24 = 2x Added 17 to both sides
4. 12 = x Divided both sides by 2
5. x = 12 Final answer proven
What is an algebraic expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It can represent a value, an equation, or a formula.
5. Given: -7(x + 2) + 4x = 6(2x - 4): Prove: x = 2/3
Statements Reasons
1. -7(x + 2) + 4x = 6(2x - 4) Given
2. -7x - 14 + 4x = 12x - 24 Opened the brackets by multiplying all
3. -3x - 14 = 12x - 24 Added -7x and 4x at LHS
4. -15x - 14 = -24 Subtracted 12x from both sides
5. -15x = -10 Added 14 to both sides
6. x = 2/3 Divided both sides by -5 to arrive to the result.
6. Given: 3x + 1 = -14: Prove: x = -5
Statements Reasons
1. 3x + 1 = -14 Given
2. 3x = -15 Subtracted 1 from both sides
3. x = -5 Divided both sides by 3. Final answer proven.
7. Given: 2(x - 9) = -10; Prove: x = 4
Statements Reasons
1. 2(x - 9) = -10 Given
2. 2x - 18 = -10 Opened the brackets.
3. 2x = 8 Added 18 to both sides
4. x = 4 Divided both sides by 2. Final answer proven.
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a visitor is staying in a tent that is 9 miles west of the closest point on a shoreline to a rock formation. the rock formation is 3 miles due south of the shoreline. the visitor plans to travel from the tent to the rock formation by running and swimming. if the visitor runs at a rate of 4 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the rock formation?
The distance the visitor should run to minimize the time it takes to reach the rock formation is 3/4 miles.
A unitary method is a mathematical technique used to solve problems involving proportional relationships between different quantities.
Let's use the unitary method to find the time it takes to complete the journey.
Time taken to run = Distance / Rate = x / 4
Time taken to swim = Distance / Rate = (3 - x) / 3
Total time taken = Time taken to run + Time taken to swim
= x / 4 + (3 - x) / 3
To minimize the total time taken, we need to find the value of x that minimizes the above expression. Let's differentiate it with respect to x and equate it to zero.
d/dx (x/4 + (3-x)/3) = 1/4 - 1/3 = -1/12
-1/12 = 0 (at minimum)
Solving for x, we get:
x = 3/4
The visitor should run westward along the shoreline until reaching the point 3/4 miles away from the tent, and then swim the remaining 2 1/4 miles to reach the rock formation.
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i’m really confused on what this is asking.. what does it want me to round to the nearest hundredths?
As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.
what is linear regression ?The link between a dependent variable and one or more independent variables can be modeled statistically using linear regression. The dependent variable can be treated as a linear function of the independent factors since this sort of regression analysis presupposes a linear relationship between the variables. Finding the line of best fit that minimizes the gap between the observed data points and the anticipated values of the dependent variable is the objective of linear regression. The equation y = mx + b, in which y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept, is represented by the line of best fit, which is a straight line.
given
Using a graphing calculator, we may display the data points and identify the line of best fit in order to determine the regression model that best matches the data.
We obtain the following scatter plot by entering the data into a graphing calculator:
We can observe from the scatter plot that the data seems to have an approximately linear trend. We may utilize the calculator's linear regression tool to determine the line of best fit.
We obtain the following equation by applying a linear regression on the data:
y = 3.38x + 9.37
The regression equation is as follows, rounded to the closest hundredths:
y ≈ 3.38x + 9.37
As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.
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The complete question is:- Use a graphing calculator to graph the data and to find a regression model that best fits the data. Round values to the nearest hundredths.
five cores are removed from a new section of an asphalt highway. the following percentages of air voids were obtained from laboratory analyses: 3.7, 4.5, 4.1, 4.7, 3.9. past studies have suggested that the standard deviation of the air void content is 0.5%. compute the 95%, two-sided confidence interval on the mean
The two sided confidence interval on mean is 3.56 and 4.80.
What is confidence interval?
The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
The given data is 3.7, 4.5, 4.1, 4.7, 3.9. Here n = 5
=> σ = 1- 95% = 5% = 0.05
We know that the confidence interval is
=> CI = [tex]\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}[/tex]
Here 95% confidence level so z= 1.96
Mean [tex]\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18[/tex] and σ = 0.5
Here n<30 so we can use t instead of z then t-value = 2.776.
Now confidence level CI = [tex]\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}[/tex]
=> CI = 4.18 [tex]\display \pm[/tex] 0.62 = ( 3.56 , 4.80)
Hence the two sided confidence interval on mean is 3.56 and 4.80.
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A bag of marbles contains 12
red, 4
blue, 8
yellow, and 16
green marbles. Keith performed an experiment in which he randomly pulled a marble from the bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.
Color Frequency
Red 40
Blue 10
Yellow 20
Green 30
For which colors is the experimental probability the same as the expected probability?
The experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that quantifies the chance of an event happening, ranging from 0 (impossible) to 1 (certain). Probability is commonly expressed as a fraction or a decimal between 0 and 1, or as a percentage between 0% and 100%
To determine the expected probability of pulling a certain color from the bag, we need to calculate the ratio of the number of marbles of that color to the total number of marbles in the bag.
Expected probability of pulling a red marble = 12/40 = 0.3
Expected probability of pulling a blue marble = 4/40 = 0.1
Expected probability of pulling a yellow marble = 8/40 = 0.2
Expected probability of pulling a green marble = 16/40 = 0.4
To calculate the experimental probability, we need to divide the frequency of each color by the total number of pulls, which is the sum of all the frequencies:
Experimental probability of pulling a red marble = 40/100 = 0.4
Experimental probability of pulling a blue marble = 10/100 = 0.1
Experimental probability of pulling a yellow marble = 20/100 = 0.2
Experimental probability of pulling a green marble = 30/100 = 0.3
So, the experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1. For all other colors, the experimental probability is different from the expected probability.
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Find x. Please help I don't know
Probably 26 :P
Because its like almost double of 10 but it is not....
HOPE THAT MADE SENSE!
Answer: well imma said x=19
Step-by-step explanation:
because All the diameter of the circle is equal.
So 14+15=29
And X is
29-10=19
A recipe says that 6 spring rolls will serve 3 people. How many people will 1 spring roll serve
Answer:
Step-by-step explanation:
the answer will be 2
Answer:
2 people
Step-by-step explanation:
6/3 = 2
Helping in the name of Jesus.
Find n. Then find the area. Perimeter =60 2/4 in
The area of the rectangle is 220.5 square inches when the perimeter of the rectangle is 242/4 inch and one side of the rectangle is 49/4 inch.
Perimeter = [tex]60 \frac{2}{4}[/tex] inch = 242/4 inch
one side of rectangle = [tex]12\frac{1}{4}[/tex] inch = 49/4
The perimeter of a rectangle is the sum of all its sides. In this case, we know that the perimeter of the rectangle is 242/4 inch, which simplifies to 60.5 inch. We also know that one side of the rectangle is 49/4 inch.
Let's call the other side of the rectangle "n". Then, we can write the equation:
2(49/4 + n) = 60.5
Simplifying this equation, we get:
98/4 + 2n = 60.5
24.5 + 2n = 60.5
2n = 36
n = 18
Therefore, the other side of the rectangle is 18 inch.
To find the area of the rectangle, we can use the formula:
Area = length * width
In this case, the length is 49/4 inch and the width is 18 inch. So, we have:
Area = (49/4) * 18 = 220.5 square inches
Therefore, the area of the rectangle is 220.5 square inches.
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The complete question is :
Find n. Then find the area. Perimeter = [tex]60 \frac{2}{4}[/tex] inch . If one side of rectangle = [tex]12\frac{1}{4}[/tex] inch and other n inch.
. A florist has two arrangements offered at special prices. The first arrangement consists of 5 lilies and 1 rose and costs $19.75. The second arrangement consists of 6 lilies and 3 roses and costs $27.75. What are the costs of each lily and each rose?
The cost of each lily is $3.50, and the cost of each rose is $2.25.
Dimensional analysis problemLet's use the variables L and R to represent the cost of each lily and each rose, respectively.
From the problem, we can write a system of two equations based on the information about the two arrangements:
5L + R = 19.75 (equation 1)
6L + 3R = 27.75 (equation 2)
To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:
15L + 3R = 59.25 (equation 3)
Then, we can subtract equation 2 from equation 3:
9L = 31.5
Solving for L, we get:
L = 3.50
Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:
5L + R = 19.75
5(3.50) + R = 19.75
17.50 + R = 19.75
R = 2.25
Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.
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Upper & lower bounds
Brian weighs himself at 84kg to the nearest kg.
What is the most he could weigh?
Give the upper bound as your answer.
Thus, the most he could weigh that is the upper bound of the given condition is 84kg.
What about weigh?
The word "weigh" is not frequently used by itself in arithmetic. The notion of weight or mass, for example, can be used when measuring or comparing quantities. While mass is a measurement of the quantity of matter inside an object, weight is a measure of the gravitational force acting on it. Weight can be viewed as the force a standard gravitational field applies to an object in the setting of measurement. Weight or mass may be denoted in mathematical equations by variables such as "w" or "m," and the units used to measure them may change based on the situation.
Define upper bound:
In mathematics, an upper bound is a number that is greater than or equal to all the elements in a given set. More formally, let S be a set of real numbers. A number u is an upper bound for S if and only if for all x in S, we have x ≤ u.
For example, consider the set S = {2, 4, 6, 8}. The number 10 is an upper bound for S because 2 ≤ 10, 4 ≤ 10, 6 ≤ 10, and 8 ≤ 10. However, the number 7 is not an upper bound for S because 8 > 7.
Note that an upper bound need not be an element of the set S itself. For instance, the set of all negative real numbers does not have any upper bound among the negative real numbers, but 0 is an upper bound for this set.
It's worth noting that an upper bound may or may not be a member of the set S. If an upper bound is a member of S, then it is called a "maximum" or "greatest" element of S. However, if an upper bound is not a member of S, then S has no maximum element.
According to the given information:
Brain weigh himself at 84kg to the nearest kg as (given) , because uses the method of round off.
Thus, the range of weigh:
⇒ 83.5 ≤ Weigh ≤ 84.4.
Thus, the most he could weigh is 84.4kg.
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