1. Mr. John received more than 2 cords of wood based on the sizes of the stacked piles.
2. Based on the stacked piles, Mr. John received approximately 11,974 pieces of actual wood.
3. The cost per standard piece of wood is approximately $0.0417.
1. To determine if Mr. John received more or less than 2 cords of wood, we need to calculate the volume of each pile and compare it to the volume of a standard cord of wood.
Calculating the volume of each pile:
PILE #1:
Volume = 72 inches * 167 inches * 16 inches = 1,523,584 cubic inches
PILE #2:
Volume = 65 inches * 266 inches * 16 inches = 2,068,480 cubic inches
Calculating the volume of a standard cord of wood:
Volume of a standard cord = 4 feet * 4 feet * 8 feet = 128 cubic feet
Since 1 foot = 12 inches, the volume in cubic inches is 128 * 12 * 12 * 12 = 221,184 cubic inches.
Comparing the volumes:
Pile #1: 1,523,584 cubic inches
Pile #2: 2,068,480 cubic inches
Standard cord: 221,184 cubic inches
It is evident that both piles have significantly more volume than a standard cord of wood. Therefore, Mr. John received more than 2 cords of wood.
2. To determine the number of standard pieces of wood received, we need to calculate the number of pieces that can be obtained from the total volume of the piles.
Total volume of the piles = Volume of Pile #1 + Volume of Pile #2
Total volume = 1,523,584 cubic inches + 2,068,480 cubic inches = 3,592,064 cubic inches
Volume of a standard piece of wood = 5 inches * 5 inches * 12 inches = 300 cubic inches
Number of standard pieces of wood received = Total volume of the piles / Volume of a standard piece of wood
Number of pieces = 3,592,064 cubic inches / 300 cubic inches = 11,973.55 pieces (rounded to the nearest whole number)
Therefore, Mr. John received approximately 11,974 pieces of actual wood based on his stacked piles.
3. To calculate the cost per standard piece of wood, we need to divide the total cost of the two cords by the number of standard pieces received.
Total cost for both cords of wood = 2 cords * $250/cord = $500
Cost per standard piece of wood = Total cost / Number of standard pieces
Cost per piece = $500 / 11,974 = $0.0417 (rounded to four decimal places)
Therefore, the cost per standard piece of wood is approximately $0.0417.
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A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x.
A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x.
What is the value of y?
3
4
5
6
To find the value of y, we can use the fact that opposite sides of a parallelogram are equal in length. Therefore, we can set up the following equations:
10 = 10 + 2x
2y + 4 = 18
Simplifying the first equation, we get:
2x = 0
Solving for x, we get:
x = 0
Substituting x = 0 into the second equation, we get:
2y + 4 = 18
Simplifying this equation, we get:
2y = 14
Dividing both sides by 2, we get:
y = 7
Therefore, the value of y is 7.
A restaurant Serves 80 Costumers 20% do not Order drinks How many. People do Order drinks?
Among the 80 customers, 64 individuals choose to order drinks at the restaurant.
To find the number of people who order drinks at the restaurant, we can start by calculating the percentage of customers who do not order drinks.
Given that 20% of the customers do not order drinks, we can calculate the number of customers who do not order drinks by multiplying 80 (total customers) by 0.20 (20% expressed as a decimal):
Number of customers who do not order drinks = 80 * 0.20 = 16.
Since the total number of customers is 80, and 16 customers do not order drinks, we can subtract the number of customers who do not order drinks from the total number of customers to find the number of customers who do order drinks:
Number of customers who order drinks = 80 - 16 = 64.
Therefore, 64 people order drinks at the restaurant.
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Which of the following amounts are equal to 24 pints? Select all that apply.
A.
48 cups
B.
192 fluid ounces
C.
3 gallons
D.
48 quarts
The amount that is equal to 24 pints can be determined by using the conversion factors between different units of volume. The following amounts are equal to 24 pints:
A. 48 cups: There are 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups.
B. 192 fluid ounces: There are 8 fluid ounces in 1 cup, and 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups = 48 × 8 fluid ounces = 384 fluid ounces. Hence, 192 fluid ounces are equal to 24 pints.
C. 3 gallons: There are 8 pints in 1 gallon. Therefore, 24 pints = 24/8 gallons = 3 gallons.
D. 48 quarts: There are 2 pints in 1 quart. Therefore, 24 pints = 24/2 quarts = 12 quarts. Hence, 48 quarts are not equal to 24 pints.
Therefore, the correct answers are A, B, and C.
Sample Answer: The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.
Which did you include in your response?
Draw vertical lines to intersect on a graph.
The relation is a function if there’s only one point of intersection on a graph.
The relation is not a function if there’s more than one point of intersection on a graph.
The vertical line test is used to determine if each input has exactly one output.
Answer: All of the choices in the response would be correct.
Step-by-step explanation:
saleswoman sells a dried-fruit mixture for $ 5.90 per pound and nuts for $ 14. 75per pound. She wants to blend the two to get a -15lb mixture that she will sell for $ 9.44per pound. How much of each should she use? Solve using matrices.
To get a 15-lb mixture, she should use enter your response here( = -lb )of dried-fruit mixture and enter your response here( = lb )of nuts.
A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.
Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1 1 | | x | | 15 |
| 5.90 14.75 | | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x | | 1 1 |^-1 | 15 |
| y | = | 5.90 14.75 | | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877 -0.0576 |
| -0.0059 0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x | | 0.0877 -0.0576 | | 15 |
| y | = | -0.0059 0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.
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Find the inverse of the function. y=x2+4x+4
The inverse of the function [tex]y = x^2 + 4x + 4 is f^(-1)(x) = -2 ± √(x - 2).[/tex]C
is correct answer
To find the inverse of the function y = x^2 + 4x + 4, we can follow the steps for finding the inverse of a function:
Step 1: Replace y with x and x with y:
[tex]x = y^2 + 4y + 4[/tex]
Step 2: Solve the equation for y:
[tex]x = y^2 + 4y + 4[/tex]
Step 3: Rearrange the equation:
[tex]y^2 + 4y + 4 - x = 0[/tex]
Step 4: Solve the quadratic equation for y using factoring or the quadratic formula. In this case, the equation can be factored:
[tex](y + 2)(y + 2) - x = 0(y + 2)^2 - x = 0[/tex]
Step 5: Expand and rearrange the equation:
[tex]y^2 + 4y + 4 - x = 0y^2 + 4y = x - 4y^2 + 4y = x - 2^2y^2 + 4y = (x - 2^2)[/tex]
Step 6: Complete the square on the left side of the equation:
[tex](y^2 + 4y + 4) = (x - 2^2) + 4(y + 2)^2 = (x - 2)[/tex]
Step 7: Take the square root of both sides:
[tex]y + 2 = ±√(x - 2)[/tex]
Step 8: Solve for y:
[tex]y = -2 ± √(x - 2)[/tex]
The inverse function of y = x^2 + 4x + 4 is given by:
[tex]f^(-1)(x) = -2 ± √(x - 2)[/tex]
Therefore, the inverse of the function y = [tex]x^2 + 4x + 4 is f^(-1)(x) = -2 ± √(x - 2).[/tex]
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Assignment
Practice using function notation.
The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
O
f(3) is
O
f(x) = -5 when x is
In the first row, the ordered pair can be expressed as f(8) = -6 in function notation.
Of(3) is 18.
Of(x) = -5 when x is -2.
The given table represents a function, and we need to express the values in function notation and determine specific inputs that correspond to certain outputs.
In the table's first row, the ordered pair are shown which can be expressed as function notation:
f(8) = -6
This means that when the input (x) is 8, the corresponding output (f(x)) is -6.
f(x) = -5 when x is -2.
This means that when the input (x) is -2, the value of the function (f(x)) is -5.
In the table, the function is defined by the equation f(x) = 8x - 6. Each input value (x) is multiplied by 8 and then subtracted by 6 to determine the corresponding output (f(x)).
By substituting different values for x into the function, we can find the corresponding values for f(x) in the table.
when x = 3, we have:
f(3) = 8(3) - 6
f(3) = 24 - 6
f(3) = 18
So, f(3) is 18.
Similarly, when x = -2, we have:
f(-2) = 8(-2) - 6
f(-2) = -16 - 6
f(-2) = -22
Thus, when x is -2, f(x) is -22.
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The triangles shown below must be congruent.
True or false
True because corresponding sides and angles of the triangles are congrent.
For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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What are the solutions to the equation 0=|3x+3|+3
Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.
To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.
First, let's isolate the absolute value term on one side of the equation:
|3x + 3| = -3
Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.
To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:
3x + 3 = -3
-(3x + 3) = -3
Solving equation 1:
3x + 3 = -3
3x = -6
x = -2
Solving equation 2:
-(3x + 3) = -3
-3x - 3 = -3
-3x = 0
x = 0
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2+2=? ???¿??????¿????????
Answer:4
Step-by-step explanation:1+1 is 2, so if you take 2+2 it is 4, same as 2×2 is 4.
Which fraction is represented by point A on the number line?
The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.
With these details, you can calculate the fraction accurately.
Point A on the number line represents a fraction that requires additional information to determine its precise value.
I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.
A number line represents a range of values, typically with a specific scale or interval.
The scale can be divided into equal parts, such as units or fractions.
To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.
Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.
If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).
If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.
Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.
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The period of y = 3cot(4x - 3x) is
the period of y = 3cot(x) remains as π. the period of y = 3cot(4x - 3x) is also π.
To find the period of the function y = 3cot(4x - 3x), we need to determine the length of one complete cycle of the function.
First, let's simplify the expression inside the cotangent function: 4x - 3x = x.
Now, the cotangent function has a period of π, which means it repeats every π units.
To find the period of the given function y = 3cot(x), we need to determine how the variable x affects the period. Since the coefficient of x is 1, it means that the period is not affected by any scaling or stretching.
In summary, the period of the function y = 3cot(4x - 3x) is π, which means the function repeats every π units along the x-axis.
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Find the missing side.
+
18
12
x = [?]
Round to the nearest tenth.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{18}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ x=\sqrt{ 18^2 - 12^2}\implies x=\sqrt{ 324 - 144 } \implies x=\sqrt{ 180 }\implies x\approx 13.4[/tex]
The missing side of a right-angled triangle, assuming it to be the hypotenuse with other sides as 12 and 18, can be calculated using the Pythagorean theorem. The square root of the sum of 12^2 and 18^2 gives the length of the hypotenuse, which is approximately 21.6 when rounded to the nearest tenth.
Explanation:This question relates to the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
Assuming that the missing side in your question (x) is the hypotenuse and the other two sides are 12 and 18, you can calculate it using the aforementioned theorem. Therefore, you find x by calculating the square root of (12² + 18²), or √(144 + 324) which equals to √468. This value, rounded to the nearest tenth, is 21.6.
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Please awnser asap I will brainlist
The number of vans, small truck and large truck they can buy is 130, 65 and 65 respectively.
How many of each vehicles can be bought?Total cost of vehicles = $10 million
Total number of vehicles = 260
Cost of each commercial van = $25,000
Cost of each small truck = $50,000
Cost of each large truck = $50,000
Let
c = commercial van
s = small truck
l = large truck
v = 2s
s = l
So,
v + s + l = 260
2s + s + s = 260
4s = 260
divide both sides by 4
s = 260/4
s = 65
Therefore,
v = 2s
= 2(65)
= 130
s = l
l = 65
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
To determine if the event of rolling a pair of dice and getting doubles or a sum of 6 is mutually exclusive, we need to assess whether the two outcomes can occur simultaneously or if they are mutually exclusive.
Let's analyze the two outcomes separately:
1. Getting doubles: When rolling a pair of dice, getting doubles means that the numbers on both dice are the same. The possible outcomes for getting doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). There are a total of 6 outcomes that satisfy this condition.
2. Getting a sum of 6: To get a sum of 6, the numbers on the two dice should add up to 6. The possible outcomes for this condition are (1,5), (2,4), (3,3), (4,2), and (5,1). There are a total of 5 outcomes that satisfy this condition.
Now, to determine if the two outcomes are mutually exclusive, we need to check if there are any outcomes that satisfy both conditions. In this case, the outcome (3,3) satisfies both conditions (doubles and sum of 6).
Since there is one outcome that satisfies both conditions, we can conclude that the event of rolling a pair of dice and getting doubles or a sum of 6 is not mutually exclusive.
To find the probability of this event, we need to determine the total number of possible outcomes when rolling a pair of dice. Each die has 6 sides, so there are 6 possible outcomes for each die, resulting in a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice.
The probability is calculated by dividing the number of favorable outcomes (satisfying the condition) by the total number of possible outcomes.
Favorable outcomes = 6 (for doubles) + 5 (for sum of 6) - 1 (for the overlapping outcome) = 10
Probability = Favorable outcomes / Total number of outcomes = 10 / 36 ≈ 0.2778
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
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How do we do
700/3.14 without a calculator please show a method that would work with any whole number divided by a decimal?
If answer and explanation are correct and they are understandable and useable I will rate five stars , 13PTS, a thanks and BRAINLIEST
700 divided by 3.14 is approximately 2.23.
To divide a whole number by a decimal without using a calculator, you can follow these steps:
Convert the decimal divisor into a whole number by multiplying both the numerator and denominator by a power of 10 that eliminates the decimal. In this case, we have 3.14, so we can multiply it by 100 to get 314 as the new divisor.
700 ÷ (3.14 × 100)
Perform the division using the converted divisor. Divide 700 by 314:
700 ÷ 314 = 2.229...
Round the result to the desired number of decimal places, if necessary. Since the question does not specify the level of precision required, we will round the result to two decimal places:
2.229... ≈ 2.23
Therefore, 700 divided by 3.14 is approximately 2.23.
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Describe how the graph of h(x) = -2x - 4 can be obtained from one of the basic graphs. Then graph the function.
To obtain the graph of h(x) = -2x - 4, start with the graph of y = x. Stretch vertically by multiplying each x-coordinate by 2. Then reflect it across the x-axis and shift it down by 4 units
Describing how the graph of h(x) = -2x - 4 can be obtainedFrom the question, we have the following parameters that can be used in our computation:
h(x) = -2x - 4
The parent function is
f(x) = x
First, stretch vertically by a factor of 2
So, we have
f'(x) = 2x
Next, we reflect across the x-axis
So, we have
f''(x) = -2x
Lastly, we shift down by 4 units
So, we have
h(x) = -2x - 4
The graph is attached
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I completed 2/3 of my project last month and 1/4 of it this week, what fraction of my project is not completed
Hello!
Answer:
11/12
Step-by-step explanation:
To solve this problem, we would need to find the denominator of the 2 numbers. In this case, it is 12. We will now convert the fractions to twelfths.
2/3 = 8/12
1/4 = 3/12
After we add 8/12 and 3/12, we get our answer 11/12.
Wanahton purified a portion of water with
900
900900 grams of contaminants. Each hour, a third of the contaminants was filtered out.
Let
�
(
�
)
g(n)g, left parenthesis, n, right parenthesis be the amount of contaminants (in grams) that remained by the beginning of the
�
th
n
th
n, start superscript, start text, t, h, end text, end superscript hour.
�
gg is a sequence. What kind of sequence is it?
the sequence g is a decreasing sequence.
Here is the step-by-step solution to the problem based on the information given in the question:
Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour. g is a sequence. We need to determine the kind of sequence.The amount of contaminants in the beginning
= 900 grams
Amount of contaminants filtered out
= (1/3) * 900 = 300
grams Amount of contaminants left after first
hour = 900 - 300 = 600
gramsAmount of contaminants filtered out in the second
hour = (1/3) * 600 = 200
grams Amount of contaminants left after the second
hour = 600 - 200 = 400 grams
Amount of contaminants filtered out in the third
hour = (1/3) * 400 = 133.33 grams
(rounded to two decimal places)Amount of contaminants left after the third
hour = 400 - 133.33 = 266.67 grams
(rounded to two decimal places)In this way, the sequence will continue. We can observe that the amount of contaminants in the beginning is decreasing and the sequence is decreasing as well
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You are given the great circle of a sphere is a length of 25 miles. What is the volume of the sphere
Answer: 268
Step-by-step explanation:
onsider the following ordered pairs that represent a relation.
{(–4, –7), (0, 6), (5, –3), (5, 2)}
What can be concluded of the domain and range for this relation? Check all that apply.
The domain is the y values of the ordered pairs.
The range is the set of output values.
The given relation is a function.
Zero is included in the range of the relation.
5 is included in the domain of this relation.
the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
if we observe the given ordered pairs we can easily determine that,The domain is the set of all x-values from the ordered pairs in the relation.
So, the domain of the given relation is {−4,0,5} because we have only three unique x-values from the given ordered pairs.
The range is the set of all y-values from the ordered pairs in the relation.
So, the range of the given relation is {−7,−3,2,6} because we have four unique y-values from the given ordered pairs.
Also, we can conclude that the given relation is not a function since we have the same x-value (5) corresponding to two different y-values (−3,2).
And it is true that the zero is included in the range of the relation since we have the ordered pair (0,6) which gives the y-value of 6.
So, the statement “The given relation is a function” is incorrect. But the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
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7 3/8 as an inpropuar fracition
A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle. A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle.
Based on the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we can use this to find the possible values of the third side of the triangle.
The two given sides are 15 cm and 17 cm. We can label the unknown side as "x". Then, we can set up an equation:
15^2 + 17^2 = x^2
Simplifying this equation, we get:
225 + 289 = x^2
514 = x^2
x = sqrt(514)
Therefore, the possible value of the third side that would make it a right triangle is approximately 22.72 cm.
In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?
محے
A. No, because 26 and 21 are not congruent.
B. Yes, because 22 and 23 are congruent.
C. No, because 21 and 22 are not congruent.
D. Yes, because 22 and 26 are congruent.
The lines c and d are not parallel.
The correct answer is A. No, because 26 and 21 are not congruent.
In order for two lines to be parallel, the corresponding angles formed by a transversal should be congruent. However, in this case, angles 26 and 21 are not congruent, as indicated by their different measures of 40° and 140°, respectively.
Therefore, we can conclude that lines c and d are not parallel. The congruence of angles 22 and 23, mentioned in option B, or the congruence of angles 22 and 26, mentioned in option D, does not provide sufficient information to determine the parallelism of lines c and d.
The key factor in determining parallel lines is the congruence of corresponding angles, which is not met in this scenario.
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Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 5 feet. Container B has
a diameter of 6 feet and a height of 9 feet. Container A is full of water and the water is
pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of water remaining in Container A,
to the nearest tenth of a cubic foot?
The nearest tenth of a cubic foot, the volume of water remaining in Container A is approximately 138.2 cubic feet.
To find the volume of water remaining in Container A after it is completely filled and transferred to Container B, we need to calculate the difference in their volumes.
The volume of a cylinder can be calculated using the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Container A:
Diameter = 10 feet
Radius (r) = 10/2 = 5 feet
Height (h) = 5 feet
Container B:
Diameter = 6 feet
Radius (r) = 6/2 = 3 feet
Height (h) = 9 feet
Now, let's calculate the volumes of both containers:
Volume of Container A = π(5^2)(5) = 125π cubic feet
Volume of Container B = π(3^2)(9) = 81π cubic feet
To find the volume of water remaining in Container A, we subtract the volume of Container B from the volume of Container A:
Volume remaining in Container A = Volume of Container A - Volume of Container B
= 125π - 81π
= 44π cubic feet
To get the volume to the nearest tenth of a cubic foot, we can use an approximation for the value of π, which is approximately 3.14:
Volume remaining in Container A ≈ 44(3.14) ≈ 138.16 cubic feet
Therefore, to the nearest tenth of a cubic foot, the volume of water remaining in Container A is approximately 138.2 cubic feet.
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State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
The triangles EFG and WVU are similar by SSS
Identifying the similar triangles in the figure.from the question, we have the following parameters that can be used in our computation:
Triangle EFG and WVU
The triangles in this figure are
EFG and WVU
These triangles are similar because:
The triangles do have similar corresponding sides
i.e. Ratio = 525/252 = 875/420 = 825/396
Evaluate
Ratio = 2.083 = 2.083 = 2.083
Hence, the triangles EFG and WVU are similar
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Please help with the attached math problem…
The missing values for the inverse matrix A⁻¹ are:
a = -78b = 2c = 59d = 20e = -3The solution is:
x = -9200y = 7025z = 2375.How to convert the system of equations to matrix form?In Mathematics and Geometry, a square matrix refers to a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.
Next, we would convert the system of three linear equations in standard form to matrix form as follows;
[tex]\left[\begin{array}{ccc}1&1&1\\10&-20&98\\5&10&-10\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}200\\250\\500\end{array}\right][/tex]
By using technology, the solutions to this system of three linear equations include the following:
x = -9200
y = 7025
z = 2375.
By using technology, the inverse of this matrix is given by;
[tex]A^{-1}=\left[\begin{array}{ccc}-78&2&11.8\\59&-1.5&-8.8\\20&-0.5&-3\end{array}\right][/tex]
Therefore, the missing values are as shown in the inverse of this matrix A⁻¹ above.
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Mahmud Mahtab company's shareholders equity December 30.2020 are given below-
Sources of equity capital Common stock (Tk.100par 30.000 shares) = 30,00,000 TK, Additional paid up capital = 15,00,000 TK, Retained earnings = 55,00,000 TK,
Shareholders total equity = 1,00,00,000 TK.
The price of the stock on December 30 was Tk.500, On December 31,2020 Mahmud Mahtab declared:
(1) 10% stock dividend.
(2) 2 for I stock split.
(3) 1 for 5 reverse stock split.
REQUIREMENT :
What would happen to the accounts for the above decision?
1) 10% stock dividend: Increase in shares, no change in equity value.
2) 2 for 1 stock split: Doubles shares, no change in equity value.
3) 1 for 5 reverse stock split: Decreases shares, no change in equity value.
The decisions made by Mahmud Mahtab regarding stock dividend, stock split, and reverse stock split would result in the following changes to the accounts:
1) 10% Stock Dividend:
A stock dividend is a distribution of additional shares of stock to existing shareholders. In this case, a 10% stock dividend means that for every 10 shares held, shareholders will receive an additional share. As a result, the following changes would occur:
- Common stock: The number of shares would increase by 10% (3,000 additional shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be a reduction of the amount equal to the market value of the shares issued as dividends.
2) 2 for 1 Stock Split:
A stock split involves dividing existing shares into a larger number of shares. In a 2 for 1 stock split, each existing share would be split into two shares. The following changes would take place:
- Common stock: The number of shares would double (60,000 shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be no change.
3) 1 for 5 Reverse Stock Split:
A reverse stock split combines a number of existing shares into a smaller number of shares. In a 1 for 5 reverse stock split, every five shares would be consolidated into one share. The accounts would be affected as follows:
- Common stock: The number of shares would decrease by 80% (24,000 shares).
- Additional paid-up capital: There would be no change.
- Retained earnings: There would be no change.
Note: The above changes would affect the number of shares and their par value, but the total shareholders' equity (1,00,00,000 TK) would remain unchanged.
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