For square a of perimeter 24 cm and square b has an area equal to one-fourth the area of the square a, the perimeter of square b is 12 cm.
Given that a square has a perimeter of 24 cm. And another square b has an area equal to one-fourth of the area of square a. To find the perimeter of square b, we need to find the length of the side of square b using the area of square
Area of the square a = side² of the square a
The perimeter of the square a = 4 × side of the square a
Given that, Perimeter of square a = 24 cm⇒ 4 × side of square a = 24 cm⇒ side of square a = 24 / 4 cm⇒ side of square a = 6 cm.
Area of square b = 1/4 × Area of square a = 1/4 × side² of square a= 1/4 × 6² cm²= 9 cm²
Side of square b = √9 cm = 3 cm
Perimeter of square b = 4 × 3 cm = 12 cm
Therefore, the perimeter of square b is 12 cm.
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PLEASE HELP!
The sum of the roots of a monic quadratic is -6, and the product of its roots is 7. What is the quadratic?
Answer with a quadratic expression using the variable x such as x^2 + 10x + 20
Answer:
x^2 +6x+7
Step-by-step explanation:
for roots a and b
x^2 - (a+b)x + ab = (x-a)(x-b)
What is the standard form of the equation of the circle with the center and a radius of square 2 divided by 4
The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.
We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).
This means that h = 1/2 and k = -1/2.
The radius of the circle is r = square 2 divided by 4.
We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.
Now we can substitute these values into the standard form equation to get:
(x - 1/2)² + (y + 1/2)² = 1/8
So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
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What is the solution to the equation 3x - 2 = 2(2x - 1/2)?
ALGEBRA 1
Answer:
First, you distribute 2(2x-1/2)
2(2x) and 2(-1/2)
Now, you have 3x-2=4x-1
Then, you move 2 to the right side by adding so you can cancel it out.
Then, you move 4x to the left side by doing the same thing with 2
Now, divide both sides by -1
The answer is C, z= -1.
3x-2=2(2x-1/2)
3x-2=4x-1
3x=4x+1
-x=1
-x/-1 = 1/-1
= x=-1
Does 3 divided by 8 = 3/8
Answer:
yes
Step-by-step explanation:
The answer to 3 divided by 8 can also be written as a mixed fraction as follows: 0 3/8 Note that the numerator in the fraction above is the remainder and the denominator is the divisor.
An angle measures 62° more than the measure of its complementary angle. What is the measure of each angle?
A student solved the equation extraneous? Explain. 5/x-4 = x/x-4 and got 4 and 5 as solutions. Which, if either, of these is extraneous? Explain.
Therefore , the solution of the given problem of equation comes out to be x = 5 is a correct answer to the problem.
What is equation?Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in a + 7 rather than a separate algorithm who divides 12 onto two separate components and is able to evaluate data obtained from x + 7.
Here,
We can begin by making the provided equation simpler:
=> 5/(x - 4) = x/(x - 4)
=> 5 = x
Consequently, x = 5 is the answer to the problem.
The result of adding x = 4 to the initial equation is:
=> 5/(4 - 4) = 4/(4 - 4)
That amounts to:
=> 5/0 = 4/0
However, since division by zero is undefinable, the answer x = 4 is superfluous and does not satisfy the equation.
The result of the initial equation with x = 5 is:
=> 5/(5 - 4) = 5/(5 - 4)
That amounts to:
=> 5/1 = 5/1
As a result, x = 5 is a correct answer to the problem.
In conclusion, only one of the solutions -x = 5 is correct, and the other
-x = 4 is unnecessary because it results in a divide by zero.
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Which of these is a pythagorean triple?
Responses
9, 40, 41
7, 26, 89
1, 2, 3
36, 48, 62
Answer:
The first one
Step-by-step explanation:
Use the pythagoras theorem=a ^2+b^2 =c^2
Use a is 9 b is 40 because the largest value is always the hypotenuse and the hypotenuse is always c.
so you do 9 squared add 40 squared to find c squared.
Square root the answer and you get 41 so it is a pythagoras triple
The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What is the number?
The smaller number is 5.5 and the larger number is 15.5.
Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.
From the problem statement, we know that:
x + y = 25 (the sum of the two numbers is 25)
y = 3x - 3 (the larger number is 3 less than three times the smaller)
We can use the second equation to solve for y in terms of x, by adding 3 to both sides:
y + 3 = 3x
Then, we can substitute this expression for y into the first equation:
x + (y + 3) = 25
Substituting y + 3 with 3x, we get:
x + 3x = 22
Combining like terms, we get:
4x = 22
Finally, we solve for x by dividing both sides by 4:
x = 5.5
Now that we know x, we can use the equation y = 3x - 3 to find y:
y = 3(5.5) - 3 = 15.5
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Luca owns a food truck called The Muffin Man, and this week, he is making a specialty flavor by adding cheddar cheese and hot peppers to corn muffin mix. The mix comes in a box shaped like a rectangular prism with a volume of 60 cubic inches. The box has a length of 5 inches and a height of 8 inches
The width of the rectangular prism box is 1.5 inches if the length of the box is 5 inches and the height of the box is 8 inches.
The volume of a rectangular prism = 60 cubic inches.
The length of the box = 5 inches
The height of the box = 8 inches
To calculate the width of the rectangular prism, we can use the formula for volume:
Volume = length * width * height
Mathematically,
V = l*w*h
60 = 5w * 8
w = 60 / (5 * 8)
w = 1.5 inches
Therefore we can conclude that the width of the rectangular prism box is 1.5 inches.
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for each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by:
For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.
Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.
A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.
If the line slopes up from left to right, it has a positive slope. As the value of x increases by one, the value of y also increases by the slope. If the line slopes downward from left to right, it has a negative slope. As the value of x increases by one, the value of y decreases by the slope.The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.
Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis
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ray fills his car with 45 liters of gasoline every week how many kiloleters of gasoline does his car use in 2 years?
Ray's car will use 4.68 kiloliters of gasoline and travel 39.54 kilometers
Every week, Ray fills his car with 45 liters of gasoline. To calculate the total amount of gasoline used by Ray's car over two years, we must first convert liters to kiloliters. One kiloliter is equal to 1,000 liters, so 45 liters is equal to 0.045 kiloliters. Therefore, in two years, Ray's car will use 0.045 kiloliters x 104 weeks (2 years x 52 weeks per year) = 4.68 kiloliters of gasoline.
To calculate how many kilometers the car will travel with 4.68 kiloliters of gasoline, we need to know the car's fuel efficiency rating. Assuming the car has an average fuel efficiency rating of 8.5 kilometers per liter, we can calculate that the car will travel 8.5 kilometers x 4.68 kiloliters = 39.54 kilometers with 4.68 kiloliters of gasoline.
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4. Davie has sent the following number of text messages in the past 7 days: 10, 2, 5, 22, 19, 11, 8. (1 point)
Gabby has sent the following number of text messages in the past 7 days: 19, 15, 25, 24, 20,
29, 21. Using IQR, who has had a higher variability of text messages per day?
ODavie had a higher variability because his IQR is 8 more than Gabby's.
OGabby had a higher variability because her IQR is 7 more than Davie's.
ODavie had a higher variability because his IQR is 6 more than Gabby's.
OGabby had a higher variability because her IQR is 6 more than Davie's.
Answer:
Step-by-step explanation:
4. The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle
6. The cοrrect οptiοn is D) The IQR For both sets is 8.
What is the descriptive statistics?Descriptive statistics is a branch οf statistics that invοlves the cοllectiοn, presentatiοn, and characterizatiοn οf a set οf data.
4) Given
1. Number οf text messages frοm David 10, 2, 5, 22, 19, 11, 8
2. Number οf text messages frοm Gabrielle 19, 15, 25, 24, 20, 29, 21
Find the median fοr the data οf David
10, 2, 5, 22, 19, 11, 8
Arrange in ascending οrder
2, 5, 8, 10, 11, 19, 22
Median οf the data is (n + 1)/2
= (7 + 2)/2
= 4
= 4th term = 10
Nοw Find Q1 and Q3
Q1 = 5 and Q3= 19
IQRD=Q3−Q1
IQRD=19−5
IQRD=14 Equatiοn (1)
Find the median fοr the data οf Gabrielle
19, 15, 25, 24, 20, 29, 21
Arrange in ascending οrder
15, 19, 20, 21, 24, 25, 29
Median οf the data is 4th term 21
Nοw Find Q1 and Q3
Q1=19 and Q3=25
IQRG=Q3−Q1
IQRG=25−19
IQRG=6 Equatiοn (2)
Frοm equatiοn 1 and 2 we can say that
David had a higher variability because his IQR is 8 mοre than Gabrielle.
Hence, The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle.
5) Seventh grade = 6 10 14 18 22 26
Median = 4th value = (18 + 14)/2 = 16
Q1=10 and Q3=22
IQR = 22 - 14 = 8
Eighth grade = 22 26 30 34 38
Median (n + 1)/2 = 3rd value = 30
Q1=22 and Q3=38
IQR = 34 - 26 = 8
Thus, The IQR For both sets is 8.
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Physics graduate student Laura Van Ertia has conducted a complete randomized design with a single factor, hoping to solve the mystery of the unified theory and complete her dissertation. The results of this experiment are summarized in the following ANOVA display:What is the sum of squares for the factor?
Remember, accurate interpretation of the results is essential for the success of Laura's dissertation.
The sum of squares for the factor in Laura Van Ertia's experiment can be found in the ANOVA display. ANOVA stands for Analysis of Variance, and it is a statistical method used to compare the means of two or more groups. The sum of squares is a measure of the variation within the data, and it helps to determine whether the differences between groups are statistically significant.
In the given question, you have not provided the actual ANOVA display, which is necessary to determine the sum of squares for the factor. The ANOVA table typically consists of columns for sources of variation (such as between groups and within groups), degrees of freedom, sum of squares, mean squares, F-ratio, and p-value. The sum of squares for the factor can be found in the 'sum of squares' column corresponding to the between-group variation row.
Once you have the ANOVA display, locate the sum of squares for the factor and use it in your analysis to understand the results of the experiment and its implications on the unified theory.
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Can someone please
Help me on this? I’ll give 20 points for this
Answer:
a) 6x10^-6 b) 0.000006 c) I would not be concerned
Step-by-step explanation:
a)
50% is just half and more just means added onto.
Half of 4x10^-6 is 2x10^-6
If you add that onto the original value, you will have:
6x10^-6 (standard form)
b)
0.000006 (ordinary number)
c)
I would not be concerned about the increase in probability of a side effect while using the new medicine. The probability to begin with is extremely low, almost insignificant. While the 50% increase may sound intimidating, it is just a 50% increase on a number that is already very very small. Honestly, it makes almost no difference.
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, brad has scored 87 , 89 , and 78 on the first three. what range of scores on the fourth test will give brad a c for the semester (an average between 70 and 79 , inclusive)?
Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.
To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.
In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Enter the four constraints into the graphing calculator.
What are the vertices of the feasible region?
Hint: input your answers from questions 3, 4, and 5 into Desmos to find the vertices.
Answers from questions 3, 4, and 5
[tex]4x+2y≤16\\3x+3y≤15\\x≥0\\y≤0[/tex]
Answer:huh,
Step-by-step explanation:I don’t understand you’re saying
a cable tv receiving dish is in the shape of a paraboloid of revolution. find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.
the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).To find the location of the receiver, we first need to determine the equation of the paraboloid.
The standard equation for a paraboloid of revolution with a vertical axis is:
z = [tex](x^2 + y^2)[/tex]/(4f)
Where:
z is the height at any point (x, y) on the paraboloid.
x and y are the horizontal coordinates of the point.
f is the focal length of the paraboloid, which is half the depth of the dish.
In this case, the dish is 6 feet across at its opening, so the diameter is 6 feet and the radius is 3 feet. Therefore, the maximum value of x and y is 3 feet. The depth of the dish is given as 2 feet.
Using these values, we can solve for the focal length:
2 = [tex](3^2 + 3^2)[/tex]/(4f)
2 = 18/(4f)
f = 18/8 = 9/4 = 2.25 feet
Now that we have the value of f, we can find the location of the receiver, which is placed at the focus of the paraboloid. The focus is located at (0, 0, f).
Therefore, the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).
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the value of a boat is 21 200. it loses 6 of its value every year. find the approximate monthly percent decrease in value.
The approximate monthly percent decrease in value of the boat is 0.5%.
The given value of a boat is 21 200, and it loses 6% of its value every year. We are to find the approximate monthly percent decrease in value.
The given information is as follows: The value of a boat = $21,200The percentage decrease in value = 6%We are to find the approximate monthly percent decrease in value. Annual decrease in value of a boat is 6% of $21,200= $1,272Monthly decrease in value of a boat will be 1/12 of the annual decrease = $1,272/12≈ $106Thus, the approximate monthly percent decrease in value of the boat will be
[tex]$\frac{106}{21,200}*100\%=0.5\%$[/tex]
Therefore, the approximate monthly percent decrease in value of the boat is 0.5%.
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Your question is incomplete, but probably the complete question is :
The value of a boat is $21,200. It loses 6% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
Which of the following statements are true? Select all that apply. The correlation coefficient, r , is equal to the number of data points that lie on the regression line divided by the total number of data points. The correlation coefficient gives us information about the number of outliers compared to the number of data points. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive. The correlation coefficient, r , gives us information about the strength and direction of a linear relationship between any two variables. If r is the correlation between two variables x and y then -r is the correlation between y and x . The larger r is in absolute value, the stronger the relationship is between the two variables.
The correlation coefficient measures the linear relationship between two variables, meaning that it assumes that the relationship between the two variables can be described by a straight line. Thus option C, D, E, F is correct.
What is the correlation coefficient?The following statements are true:
The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.
The correlation coefficient, r, gives us information about the strength and direction of a linear relationship between any two variables.
If r is the correlation between two variables x and y then -r is the correlation between y and x.
The larger r is in absolute value, the stronger the relationship is between the two variables.
The statement "The correlation coefficient gives us information about the number of outliers compared to the number of data points" is false.
The statement "The correlation coefficient, r, is equal to the number of data points that lie on the regression line divided by the total number of data points" is also false.
Therefore, The larger r is in absolute value, the stronger the relationship is between the two variables.
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who in 1706 first gave the greek letter pi its current mathematical definition
The mathematician William Jones is credited with first using the Greek letter π
The mathematician William Jones is credited with first using the Greek letter π to represent the ratio of a circle's circumference to its diameter in a 1706 publication. He wrote, "there is no other more proper than Pi," and thus the symbol caught on among mathematicians. However, it's important to note that the concept of pi and its calculation had been around for thousands of years prior to Jones' use of the symbol.
Ancient Egyptian, Babylonian, and Indian mathematicians all had methods for approximating pi, and Archimedes famously used a geometric method to calculate it to a high degree of accuracy in the third century BCE.
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an old piano has 88 keys, and 56 of them are out of tune, while the remaining keys are tuned properly. a child strikes a key on the piano at random. what is the probability that the child strikes a properly tuned key?
Answer: I think It is 63.64%. If I'm wrong I'm sorry.
Step-by-step explanation:
Ask yourself what is 56% out of 88%. I did it in my head, but I got 63.6363636% then I rounded it to 63.64%.
Work out m and c for the line: y = 5 − x
Answer:
m = -1, c = 5
Step-by-step explanation:
Provided in the attachment.
answer for this algebra question (2⋅3) 2 −5 2 =
Answer:
First, we evaluate the expression inside the parentheses: 2⋅3 = 6.
Next, we evaluate the exponent: 6² = 36.
Finally, we subtract 5² = 25 from 36: 36 - 25 = 11.
Therefore, the value of the expression (2⋅3)² − 5² is 11.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral tris are all 9 feet long, and the height of the equilateral triangle is 7.8 feet. The pyramid's slant heigh feet. What is its surface area?
If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.
How to find the surface area?To solve this problem, we can use the formula for the surface area of a pyramid:
Surface area = base area + (1/2) x perimeter of base x slant height
First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:
Area = (square root of 3) / 4 x (side length)^2
Substituting the given values, we get:
Area = (square root of 3) / 4 x 9^2
Area = (square root of 3) x 20.25
Area = 11.06 (rounded to two decimal places)
Next, we need to find the perimeter of the base, which is simply 3 times the side length:
Perimeter = 3 x 9
Perimeter = 27
Finally, we can use the given slant height to find the surface area:
Surface area = 11.06 + (1/2) x 27 x 8.1
Surface area = 11.06 + 109.35
Surface area = 120.41 square feet (rounded to two decimal places)
Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.
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in an experiment to determine whether or not a person is talking on a cell phone affects the number of driving errors they make, what is the independent variable?
The independent variable is whether or not a person is chatting on a cell phone in an experiment to ascertain whether or not this influences the number of driving errors they commit.
What is a variable?A variable is any aspect that can be changed or changed over time.
For example, in an experiment, a researcher can manipulate the independent variable (such as the amount of light that a plant receives) to see how it affects a dependent variable (like how much the plant grows).
What is an independent variable?An independent variable is a variable that stands on its own and is not affected by the other variables being measured. In the given situation, the independent variable is whether or not the person is talking on a cell phone.
The dependent variable is the variable that changes in response to the independent variable. In the given situation, the dependent variable is the number of driving errors they make.
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A man loses 10 percent by selling his watch for 450 find the cost price of the watch
If a man loses 10 percent by selling his watch for 450 then the cost price of the watch would be 500.
Let's assume the cost price of a watch is 100.
So, after selling at a loss of 10 percent, the selling price of the watch is 90.
By comparing the assumed selling price of the watch with the original selling price, 450/90 = 5.
So, the original selling price is 5 times the assumed selling price.
Thus original cost price should also be 5 times of assumed cost price, so the original cost price × 5 = 100 × 5 = 500.
Hence the original cost price of the watch is 500.
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Helppppppppppppppppp
A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table
To determine the most likely distribution of the colors of candies in the bag before it was opened, we can analyze the data from the table and try to find a distribution that would result in the observed frequencies.
If we add up the number of candies of each color that were pulled out by the four students, we get:
Red: 75 + 80 + 85 + 90 = 330
Blue: 45 + 55 + 60 + 50 = 210
Green: 50 + 45 + 40 + 55 = 190
Yellow: 20 + 20 + 30 + 25 = 95
Orange: 10 + 5 + 25 + 30 = 70
We can see that the most frequently pulled color was red, followed by blue and then green. This suggests that the bag may have had more red candies than the other colors before it was opened.
Looking at the answer choices, the distribution in option B (300 red, 250 blue, 200 green, 100 yellow, and 150 orange) seems to match the observed frequencies the closest, as it has the highest number of red candies. Therefore, option B is the most likely distribution of the colors of candies in the bag before it was opened.
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Correct question:
A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
Which number correctly completes the ratio table?
2 8 13 14
16 Square 104 112
A. 64
B. 48
C. 40
D. 32
Using a constant factor, the number that completes the ratio table is calculated as: A. 64.
How to Solve Ratio Table?To complete the ratio table, we can observe that each number in the second row is obtained by multiplying the corresponding number in the first row by a constant factor of 8.
Thus, the ratio of the first row number to the second row number is 1:8.
This means that:
2 * 8 = 16
13 * 8 = 104
8 * 8 = 64.
Therefore, we can also get the correct number that completes the ratio table by multiplying 8 by 8, which is:
8 * 8 = 64.
So, the missing number in the ratio table is: A. 64.
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(1/32)^x=8^3-x solve for x
We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:
(1/32)^x = (2^3)^3-x
Simplifying the right side:
(1/32)^x = 2^(9-3x)
We can write both sides using a common base, say 2:
2^(-5x) = 2^(9-3x)
Now we equate the exponents and solve for x:
-5x = 9 - 3x
-2x = 9
x = -4.5
Therefore, the solution to the equation is x = -4.5.