The examples match with the following properties:
1. C. Distributive Property
2. A. Commutative Property
3. B. Associative Property
4. B. Associative Property
The correct matching of the examples on the left with the corresponding properties on the right is as follows:
1. 3(x + 3) = 3x + 9 : C. Distributive Property
This example demonstrates the distributive property, where we distribute the factor 3 to both terms inside the parentheses, resulting in 3 times x and 3 times 3, which simplifies to 3x + 9.
2. 2 + 3 + 4 = 4 + 3 + 2 : A. Commutative Property
This example illustrates the commutative property of addition, which states that the order of adding numbers does not affect the sum. Here, the numbers are rearranged on both sides of the equation, but the sum remains the same.
3. 4(2 x 3) = (4 x 2)3 : B. Associative Property
This example showcases the associative property of multiplication, where the grouping of factors does not affect the product. The expression on the left side is calculated as 4 times the product of 2 and 3, while the expression on the right side is calculated as the product of 4 and 2, followed by multiplying the result by 3. Both calculations yield the same result.
4. 6 + (7 + x) = (6 + 7) + x : B. Associative Property
This example also demonstrates the associative property, but in the context of addition. The expression on the left side associates the addition of 7 and x first, while the expression on the right side associates the addition of 6 and 7 first. Both expressions ultimately add up to the same sum.
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The question probable may be:
Match the example on the left with the corresponding property on the right.
1. 3(x + 3) = 3x + 9
2. 2 + 3 + 4 = 4 + 3 +2.
3. 4(2 x 3) = (4 x 2)3
4. 6 + (7 + x) = (6 + 7) + x
A. Commutative Property
B. Associative Property
C. Distributive Property
Give me Author/year in mathemathics,?
Answer:
Isaac Newton (late 17th century) - Newton made significant contributions to calculus and mathematical physics. His book "Philosophiæ Naturalis Principia Mathematica" laid the groundwork for classical mechanics.
Please answer ASAP I will brainlist
Answer:
(a) $556 billion
(b) $581 billion
(c) $693 billion
Step-by-step explanation:
The given function is:
[tex]\boxed{A(x)=314e^{0.044x}}[/tex]
where A(x) is the assets (in billions of dollars) for a financial firm .
If x = 7 corresponds to the year 2007 then:
x = 13 corresponds to the year 2013.x = 14 corresponds to the year 2014.x = 18 corresponds to the year 2018.Therefore, to find the assets for each of the given years, substitute the corresponding value of x into the function.
[tex]\begin{aligned}A(13)&=314e^{0.044 \cdot 13}\\&=314e^{0.572}\\&=314(1.77180712...)\\&=556.34743707...\\&=556\; \sf (nearest\;billion)\end{aligned}[/tex]
[tex]\begin{aligned}A(14)&=314e^{0.044 \cdot 14}\\&=314e^{0.616}\\&=314(1.851507181...)\\&=581.3732549...\\&=581\; \sf (nearest\;billion)\end{aligned}[/tex]
[tex]\begin{aligned}A(18)&=314e^{0.044 \cdot 18}\\&=314e^{0.792}\\&=314(2.20780762...\\&=693.2515954...\\&=693\; \sf (nearest\;billion)\end{aligned}[/tex]
Which graph represents a function
Answer:
The one at the bottom right above the next button
Step-by-step explanation:
Whats the answer for this questions?
Answer:
7(20) + (1/2)(20)(9) = 140 + 90 = 230 cm²
How much fencing is required to enclose a circular garden whose radius is 21 m
Answer:182.12 meters of fencing required.
Step-by-step explanation:
Maricella solves for x in the equation 4 x minus 2 (3 x minus 4) + 4 = negative x + 3 (x + 1) + 1. She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
B. In order to combine like terms on one side of the equation, the inverse operation must be used.
C. When the problem is worked in the correct order, the numbers that Maricella added are not actually like terms.
D. Maricella did not combine all three constants on both sides of the equation; she combined only two.
Answer:
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
Step-by-step explanation:
You want to know the error that adding -4+4 on the left and 1+1 on the right represents in the solution of the equation ...
4x -2(3x -4) +4 = -x +3(x +1) +1SolutionThe correct solution procedure would be to eliminate the parentheses using the distributive property as a first step:
4x -6x +8 +4 = -x +3x +3 +1
Comparing this to Maricella's first step, we see that she ignored the step of using the distributive property to multiply the constants inside parentheses by the factor outside. The appropriate description of Maricella's mistake is ...
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
__
Additional comment
Adding like terms would give ...
-2x +12 = 2x +4
8 = 4x . . . . . . . . . . . add 2x-4 to both sides
2 = x . . . . . . . . . . divide by 4
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Find the area of the shape shown below.
Answer:
The answer is 32
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
((base 1 + base 2)/ 2 )* h
Now all you have to do is substitute the numbers in.
Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.
Answer:
32 square units
Step-by-step explanation:
[tex]\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32[/tex]
Note that [tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of each base of the trapezoid, so it doesn't matter which is which.
at castleton university alex bought three mathematics textbook and four programming textbooks athe same school rick bought eight mathematic textbooks and a single programming textbook of alex spent 854.14 rick spend 1866.39 on textbooks what was the average cost of each book
Answer:
math = 227.98
programming = 42.55
Step-by-step explanation:
We have
3m + 4p = 854.14 -eq(1)
8m + 1p = 1866.39 -eq(2)
rq(2) x 4: 32m + 4p = 7465.56 -eq(3)
eq(3)-eq(1):
32m + 4p = 7465.56
- ( 3m + 4p = 854.14)
--------------------------------
29m = 6611.42
--------------------------------
⇒ m = 6611.42/29
m = 227.98
sub in eq(1)
3(227.98) + 4p = 854.14
4p = 854.14 - 683.94
4p = 170.2
p = 170.2/4
p = 42.55
Which statement can be concluded using the true statements shown?
If two angles in a triangle measure 90° and x degrees, then the third angle measures (90-x) degrees.
In triangle ABC, angle A measures 90 degrees and angle B measures 50°.
Angle C must measure 50 degrees.
Angle C must measure 40 degrees.
O Angle C must measure (90 - 40) degrees.
O Angle C must measure (90-30) degrees.
Answer:
Angle C must measure 40 degrees.
Step-by-step explanation:
All angles in a triangle add up to 180 degrees
(90-50)=40 degrees
We can check our answer by adding all the angles up
90+50+40=180
Angle C must be 40 degrees
Question #4
Find the measure of the indicated arc.
160 °
D
R
?
U
S
56°
T
Answer:
D. 48
Step-by-step explanation:
When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
56 = 1/2(160 - ?)
112 = 160 - ?
? = 160 - 112 = 48
Determine algebraically, the solution interval for the quadratic inequality 2x²-7x≤-3
Interval
Test Point
Substitution
True/False?
Solution:
Answer:
violence figer in the past two years
Find the sample variance and standard deviation. 21, 12, 6, 7, 10 O Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal place as needed.) A. s²= = OB. ² Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.). O A. OB. S = = 0= في
The sample variance (s²) is approximately 29.5 and the sample standard deviation (s) is approximately 5.4.
To find the sample variance and standard deviation,
Calculate the mean (average) of the given data set.
21 + 12 + 6 + 7 + 10 = 56
Mean = 56 / 5 = 11.2
Square the result of subtracting the mean from each data point.
(21 - 11.2)² = 96.04
(12 - 11.2)² = 0.64
(6 - 11.2)² = 27.04
(7 - 11.2)² = 17.64
(10 - 11.2)² = 1.44
Calculate the sum of the squared differences
96.04 + 0.64 + 27.04 + 17.64 + 1.44 = 142.8
Divide the sum by (n-1), where n is the number of data points (in this case, 5).
142.8 / (5-1) = 35.7
The result is the sample variance (s²).
Take the square root of the sample variance to determine the sample standard deviation (s).
s = √35.7 ≈ 5.4
Therefore, the sample variance is approximately 29.5 (rounded to one decimal place) and the sample standard deviation is approximately 5.4 (rounded to one decimal place).
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Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs $2, and a piece of fudge costs $3
This system of inequalities models the scenario:
2x + 3y <15
x+y≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points).
***PLEASE MAKE IT EASY FOR ME SO ITS EASY TO TYPE*** 15 POINTS
Step-by-step explanation:
Part A: The graph of the system of inequalities consists of two lines and a shaded region.
The line 2x + 3y = 15 is a solid line (because of the "less than" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 5, and when x = 7.5, y = 0.
The line x + y = 3 is a solid line (because of the "greater than or equal to" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 3, and when x = 3, y = 0.
The shaded region represents the solution set. It is the area below the line 2x + 3y = 15 and above or on the line x + y = 3. This shaded region satisfies both inequalities simultaneously.
Part B: To determine if the point (5, 1) is included in the solution area, we substitute x = 5 and y = 1 into both inequalities:
2x + 3y < 15:
2(5) + 3(1) < 15
10 + 3 < 15
13 < 15
Since 13 is less than 15, the point (5, 1) satisfies the first inequality.
x + y ≥ 3:
5 + 1 ≥ 3
6 ≥ 3
Since 6 is greater than or equal to 3, the point (5, 1) satisfies the second inequality.
Since the point (5, 1) satisfies both inequalities, it is included in the solution area for the system.
Part C: Let's choose the point (2, 2) as another example from the solution set.
Interpretation in real-world context:
When we have x = 2 and y = 2, it means Michael decides to buy 2 cupcakes and 2 pieces of fudge. This combination of sweets satisfies the conditions set in the inequalities, ensuring that he can feed at least three siblings.
The point (2, 2) represents a valid solution in which Michael spends a total of $10 (2 cupcakes * $2/cupcake + 2 fudges * $3/fudge = $4 + $6 = $10). With this choice, he can afford to buy enough treats to feed his three siblings while staying within his budget of $15.
will give 100 points The box plots display measures from data collected when 15 athletes were asked how many miles they ran that day.
A box plot uses a number line from 0 to 13 with tick marks every one-half unit. The box extends from 1 to 3.5 on the number line. A line in the box is at 2. The lines outside the box end at 0 and 5. The graph is titled Group A's Miles, and the line is labeled Number of Miles.
A box plot uses a number line from 0 to 13 with tick marks every one-half unit. The box extends from 1 to 5 on the number line. A line in the box is at 2.5. The lines outside the box end at 0 and 11. The graph is titled Group C's Miles, and the line is labeled Number of Miles.
Which group of athletes ran the least miles based on the data displayed?
Group A, with a median value of 2 miles
Group C, with a median value of 2.5 miles
Group C, with a narrow spread in the data
Group A, with a wide spread in the data
The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
x y x2 xy
100 600 10,000 60,000
144 850 20,736 122,400
225 1,300 50,625 292,500
324 1,900 104,976 615,600
400 2,300 160,000 920,000
∑x=1,193 ∑y=6,950 ∑x2=346,337 ∑xy=2,010,500
Which regression equation correctly models the data?
y = 5.83x – 1.04
y = 5.83x + 17
y = 5.71x + 29
y = 5.71x + 27.6
The regression equation that correctly models the data is: y = 5.71x + 27.6.
The correct answer to the given question is option D.
Regression equations are mathematical models that relate two or more variables to find the relationship between them. One variable, denoted as y, is considered the dependent variable. The other variable, denoted as x, is considered the independent variable.
In this case, the independent variable is the size of the outdoor deck, while the dependent variable is the estimated cost to construct it.
There are different types of regression equations. The one that fits this scenario is the linear regression equation, which has the form y = mx + b, where m is the slope of the line and b is the y-intercept.
The slope represents the change in y for each unit change in x, while the y-intercept represents the value of y when x is zero. To find the regression equation that correctly models the data, we need to calculate the slope and the y-intercept using the given values.
We can use the following formulas:
Slope: m = [(n∑xy) - (∑x)(∑y)] / [(n∑x2) - (∑x)2]
Y-intercept: b = (∑y - m∑x) / n Where n is the number of data points, which is 6 in this case.
Using the given values, we get: Slope: m = [(6)(2,010,500) - (1,193)(6,950)] / [(6)(346,337) - (1,193)2] = 5.71
Y-intercept: b = (6,950 - (5.71)(1,193)) / 6 = 27.6
Therefore, the regression equation that correctly models the data is: y = 5.71x + 27.6
The answer is option D.
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19
Select the correct answer.
This table represents function f.
0
2
I
f(x)
0
-2
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the inter
-3
-4.5
-2
-2
-1
-0.5
1
-0.5
3
-4.5
OA. The average rate of change of fis less than the average rate of change of g.
O B.
The average rate of change of fis more than the average rate of change of g.
'O C.
The average rate of change of fis the same as the average rate of change of g.
OD. The average rates of change of f and g cannot be determined from the given information.
The correct statement is OB. The average rate of change of f is more than the average rate of change of g.
To determine the average rate of change (slope) of the functions f and g, we can use the formula:
Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)
For function f, using the given table, we can calculate the average rate of change between the points (0, 0) and (2, -2):
Average Rate of Change (f) = (-2 - 0) / (2 - 0) = -2 / 2 = -1
For function g, using the given points (-3, 5) and (0, 14), we can calculate the average rate of change:
Average Rate of Change (g) = (14 - 5) / (0 - (-3)) = 9 / 3 = 3
Comparing the average rates of change, we find that the average rate of change of f is -1, while the average rate of change of g is 3.
Therefore, the correct statement is:
OB. The average rate of change of f is more than the average rate of change of g.
The average rate of change of f is greater than the average rate of change of g, indicating that the function f is increasing at a faster rate than function g over the given interval.
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Naomi wants to save $100,000, so she makes quarterly payments of $1,500 into an account that earns 4.4%/a compounded quarterly. (If you are using TVM Solver, please ensure you provide screenshots of your work or breakdown how you entered everything into the solver).
How long will it take her to reach her goal?
Would doubling her payment amount save her half the time needed to save? Support your statement.
Naomi will take approximately 93 quarters (around 23 years and 3 months) to save $100,000 by making quarterly payments of $1,500 with a 4.4% interest rate.
Doubling her payment amount would save her time, but the exact time saved would require recalculating with the new payment amount.
To calculate the time it will take for Naomi to reach her goal of $100,000, we can use the future value formula for a series of periodic payments:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (goal amount) = $100,000
P = Payment amount per period = $1,500
r = Interest rate per period = 4.4% per year / 4 (quarterly compounding) = 1.1% per quarter
n = Number of periods (quarters) to reach the goal (what we need to find)
Plugging in the values, we have:
$100,000 = $1,500 * [(1 + 0.011)^n - 1] / 0.011
Simplifying the equation, we have:
[(1 + 0.011)^n - 1] = $100,000 * 0.011 / $1,500
[(1.011)^n - 1] = 0.073333...
Now, we can solve this equation for n using logarithms:
n = log(0.073333...) / log(1.011)
Using a financial calculator or an online calculator, we find that n ≈ 92.33 quarters.
Since Naomi is making quarterly payments, we round up to the next whole number, giving us a total of 93 quarters.
Therefore, it will take Naomi approximately 93 quarters (or around 23 years and 3 months) to reach her goal of $100,000.
Doubling her payment amount to $3,000 per quarter would indeed save her time in reaching her goal. The higher payment amount means she would accumulate the desired amount faster. However, to determine the exact time saved, we would need to recalculate using the same formula as above with P = $3,000. The time saved will depend on the specific calculation result.
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Suppose the bear population in the Allegheny National Forest have weights that produce a normal density curve as shown.
74——————-200————————-326
From the graph shown, use the 69-95-99.7% (empirical) rule to estimate the standard deviation of the bear weights.
The estimated standard deviation of the bear weights, based on the given graph and using the 69-95-99.7% rule, is approximately 63.
The 69-95-99.7% (empirical) rule, also known as the 3-sigma rule, is a rule of thumb that applies to data that follows a normal distribution. According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In the given graph, if we assume the bear weights follow a normal distribution, we can estimate the standard deviation using the 69-95-99.7% rule.
Based on the graph, we know that the midpoint of the distribution (mean) is 200. Assuming the graph is symmetric, we can estimate one standard deviation as half the distance between the mean (200) and either end (74 or 326).
To calculate this, we subtract the mean from one of the endpoints and divide by 2:
Standard Deviation ≈ (326 - 200) / 2 ≈ 126 / 2 ≈ 63
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Use the side lengths to prove which triangles form a right triangle.
Select all the triangles that form a right triangle
The side length that prove a right angle triangle is √2, √3 and √5.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, a right angle triangle can be proved by using the Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
(√2)² + (√3)² = (√5)²
Hence, the right angle triangle is the triangle with sides √2, √3 and √5.
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determine the value of x
Answer:
[tex]x = 5\sqrt3[/tex]
Step-by-step explanation:
We can solve for the side length x in this 30-60-90 triangle by using the ratio of side lengths for that specific type of right triangle:
1 : [tex]\sqrt3[/tex] : 2In this triangle, we can identify the smallest side (corresponding to 1 in the ratio) as 5. This means we can solve for x by multiplying 5 by [tex]\sqrt3[/tex]. Thus:
[tex]\boxed{x = 5\sqrt3}[/tex]
Which ordered pairs are in the solution set of the system of linear inequalities?
y > Negative one-halfx
y < One-halfx + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.
(5, –2), (3, 1), (–4, 2)
(5, –2), (3, –1), (4, –3)
(5, –2), (3, 1), (4, 2)
(5, –2), (–3, 1), (4, 2)
The ordered pairs which are in the solution set of the system of linear inequalities are (5, –2), (3, 1), (4, 2).
The correct answer to the given question is option C.
The system of linear inequalities is:y > -1/2 x y < 1/2 x + 1
On a coordinate plane, two straight lines are shown.
The first solid line has a negative slope and goes through (0, 0) and (4, -2).
Everything above the line is shaded.
The second dashed line has a positive slope and goes through (-2, 0) and (2, 2).
Everything below the line is shaded.
We will check which of the given ordered pairs lie in the solution set of this system of linear inequalities. 1. (5, -2) Putting x = 5 and y = -2, we get:
y > -1/2 x ⇒ -2 > -1/2 (5) ⇒ -2 > -2.5 which is false.
xy < 1/2 x + 1 ⇒ (5)(-2) < 1/2 (5) + 1 ⇒ -10 < 3.5 which is false.
Therefore, the ordered pair (5, -2) is not in the solution set of the system of linear inequalities. 2. (3, 1) Putting x = 3 and y = 1, we get:
y > -1/2 x ⇒ 1 > -1/2 (3) ⇒ 1 > -1.5 which is true.
xy < 1/2 x + 1 ⇒ (3)(1) < 1/2 (3) + 1 ⇒ 3 < 2.5 which is false.
Therefore, the ordered pair (3, 1) is not in the solution set of the system of linear inequalities. 3. (-4, 2) Putting x = -4 and y = 2, we get:y > -1/2 x ⇒ 2 > -1/2 (-4) ⇒ 2 > 2 which is false. xy < 1/2 x + 1 ⇒ (-4)(2) < 1/2 (-4) + 1 ⇒ -8 < -0.5 which is true.
Therefore, the ordered pair (-4, 2) is in the solution set of the system of linear inequalities. Hence, the answer is (5, –2), (3, 1), (4, 2).
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A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?
T1, –9(x, y)
T–1, –9(x, y)
T–9, 1(x, y)
T–9, –1(x, y)
The function rule that describes the given translation is T-9, 1(x, y).
The first value in the function rule represents the horizontal translation, while the second value represents the vertical translation. In this case, the square is translated 1 unit to the right, indicating a positive horizontal translation.
Additionally, the square is translated 9 units down, indicating a negative vertical translation. Therefore, the correct function rule is T-9, 1(x, y).
In the coordinate plane, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. When we apply the function rule T-9, 1 to the coordinates of the square, we subtract 9 from the y-coordinate and add 1 to the x-coordinate.
This results in the square being moved 9 units down and 1 unit to the right from its original position.
The negative sign in front of the 9 indicates a downward movement, and the positive sign in front of the 1 indicates a rightward movement. Hence, the translation is accurately described by the function rule T-9, 1(x, y).
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Answer:
C
Step-by-step explanation:
ily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold?
b + n = 101
6b + 5n = 18
b + n = 101
5b + 6n = 18
b + n = 18
6b + 5n = 101
b + n = 18
5b + 6n = 101
Answer:
6b + 5n = 101
Step-by-step explanation:
The correct system of equations that can be used to find b, the number of bracelets Ily sold, and n, the number of necklaces she sold is:
b + n = 18
6b + 5n = 101
In this system, the first equation represents the total number of items sold, which is 18. Since b represents the number of bracelets and n represents the number of necklaces, the equation b + n = 18 reflects that the total number of bracelets and necklaces sold should add up to 18.
The second equation represents the total amount of money Ily earned from selling bracelets and necklaces. Since bracelets were sold for $6 each and necklaces for $5 each, the equation 6b + 5n = 101 represents the total amount of money earned, which is $101.
Therefore, the correct system of equations is:
b + n = 18
6b + 5n = 101
Choose an amount between $60.00 and $70.00 to represent the cost of a grocery bill for a family. Be sure to include dollars and cents.
Part A: If the family has a 25% off coupon, calculate the new price of the bill. Show all work or explain your steps. (6 points)
Part B: Calculate a 7% tax using the new price. What is the final cost of the bill? Show all work or explain your steps. (6 points)
Answer:
A: $51.00
B: $54.57
Step-by-step explanation:
Let amount = $68.00
Part A:
Since the coupon is for 25%, the family pays 75% of $68.00
75% of $68.00 = 0.75 × $68.00 = $51.00
The new price is $51.00
Part B:
The tax is 7% of $51.00
7% of $51.00 = $3.57
The total price is the sum of $51.00 and the amount of tax, $3.57
Total price = $51.00 + $3.57 = $54.57
A wooden board in the shape of a rectangle prism measures 0.3 m by 2.1 m by 0.1 m and has a mass of 0.17 kilogram. What is the density of the board?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the density of the wooden board, we need to divide the mass of the board by its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given:
Length (l) = 0.3 m
Width (w) = 2.1 m
Height (h) = 0.1 m
Mass (m) = 0.17 kg
Volume (V) = l × w × h
V = 0.3 m × 2.1 m × 0.1 m
V = 0.063 m³
Density (ρ) = mass / volume
ρ = 0.17 kg / 0.063 m³
ρ ≈ 2.7 kg/m³
The density of the wooden board is approximately 2.7 kg/m³.
Find the value of the combination. 13C5
Answer:
[tex]_{13}C_5=1287[/tex]
Step-by-step explanation:
[tex]\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\\\\_{13}C_5=\frac{13!}{5!(13-5)!}\\\\_{13}C_5=\frac{13!}{5!\cdot8!}\\\\_{13}C_5=\frac{13*12*11*10*9}{5*4*3*2*1}\\\\_{13}C_5=\frac{154440}{120}\\\\_{13}C_5=1287[/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(13 - 5)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(8)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times \cancel{8!}}{5! \times \cancel{8!}} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 }{5 \times 4 \times 3 \times 2 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 110 \times 9 }{20 \times 6 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 990 }{20 \times 6 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{154440 }{120 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = 1287 \\ [/tex]
QUESTION 3 Find the value of x in the figure below. (4 marks) a) (5x15) +5+45- 45°
The calculated value of x in the triangle is 40°
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure (see attachment)
Using the theorem of linear pair, we have
∠DBA + ∠ABC = 180°
Using the given values, we have
∠100° + ∠ABC = 180°
Collect the like terms
∠ABC = 180° - 100°
Evaluate
∠ABC = 80°
The sum of angles of a triangle is 180° .
So, in triangle ABC
∠A + ∠B + ∠C = 180°
Using the given values, we have
x + 80 + 60 = 180°
Evaluate the sum
x + 140 = 180°
Collect the like terms
x = 180° - 140°
Evaluate
x = 40°
Hence, the value of x is 40°
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Find the center of the ellipse defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
The center of the ellipse defined by the equation 9x^2 + 4y^2 + 18z - 23 = 0 is (0, 0, 0).
9x^2 + 4y^2 + 18z - 23 = 0 must be rearranged to its standard form in order to determine the location of the ellipse's centre. The ellipse equation has the following standard form:
(x - h)^2/a^2 + (y - k)^2/b^2 + (z - l)^2/c^2 = 1,
where (h, k, l) represents the center of the ellipse, and a, b, and c are the semi-major, semi-minor, and semi-vertical axes, respectively.
Let's rearrange the given equation to match the standard form:
9x^2 + 4y^2 + 18z - 23 = 0
Dividing by 23 to simplify the equation:
(9x^2)/23 + (4y^2)/23 + 18z/23 - 1 = 0
Now, we can rewrite the equation as:
(9x^2)/23 + (4y^2)/23 + 18z/23 = 1
Comparing this with the standard form, we can identify the values of a, b, and c:
a^2 = 23/9
b^2 = 23/4
c^2 = 23/18
Taking the square roots of these values:
a ≈ √(23/9) ≈ 1.53
b ≈ √(23/4) ≈ 1.92
c ≈ √(23/18) ≈ 1.23
Therefore, the semi-major axis (a) is approximately 1.53, the semi-minor axis (b) is approximately 1.92, and the semi-vertical axis (c) is approximately 1.23.
The center of the ellipse is represented by the values (h, k, l). Since the equation does not involve any shifts or translations, the center is located at the origin (0, 0, 0).
As a result, (0, 0, 0) is the centre of the ellipse formed by the equation (9x2 + 4y2 + 18z - 23 = 0).
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Answer:
Center: (-3, 1)
Step-by-step explanation:
The center of an ellipse is always the point that is equidistant from the two foci and the two vertices.
In order to find the center of the ellipse, we can complete the square in both the x and y terms.
First, we move the constant term to the right side of the equation:
[tex]9x^2+18x + 4y^2-8y = 23[/tex]
In order to complete the square in x, we take half of the coefficient of x and square it, then add it to both sides of the equation.The coefficient of x is 18, so half of it is 9, and squaring that gives us 81. Adding 81 to both sides of the equation gives us:
[tex]9x^2+18x + 81 = 23 + 81[/tex]
which combines the terms in x into a squared term:
[tex](9x+9)^2 = 104[/tex]
Similarly:
In order to complete the square in y, we take half of the coefficient of y and square it, then add it to both sides of the equation. The coefficient of y is -4, so half of it is -2, and squaring that gives us 4. Adding 4 to both sides of the equation gives us:[tex]4y^2-8y + 4 = 23 + 4[/tex]
which combines the terms in y into a squared term:
[tex](2y-2)^2 = 27[/tex]
Now that we have completed the square in both x and y, we can write the equation in standard form for an ellipse:
[tex]\frac{(x+3)^2}{11^2} + \frac{(y-1)^2}{3^2} = 1[/tex]
The standard form for an ellipse is:
[tex]\boxed{\bold{\frac{(x-h)^2}{a^2} +\frac{ (y-k)^2}{b^2} =1 }}[/tex]
where (h, k) is the center of the ellipse, a is the radius in the x-direction, and b is the radius in the y-direction.
In the equation for our ellipse, (h, k) = (-3, 1).
So the center of the ellipse is at the point (-3, 1).
In the nearest tenth, this is (-3.0, 1.0).
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
StartFraction 5 Over 12 EndFraction
StartFraction 7 Over 12 EndFraction
StartFraction 5 Over 7 EndFraction
La semana pasada, una tienda de velas recibió $355,60 por vender 20 velas. Las velas pequeñas se vendieron a $10,98 y las velas grandes a $27,98. ¿Cuántas velas grandes vendió la tienda?
Answer:
Para resolver este problema, podemos plantear un sistema de ecuaciones. Si definimos "p" como el número de velas pequeñas y "g" como el número de velas grandes, podemos expresar la información del problema de la siguiente manera:
p + g = 20 (la tienda vendió un total de 20 velas) 10.98p + 27.98g = 355.60 (el ingreso total por la venta de velas fue de $355.60)
Podemos resolver este sistema de ecuaciones utilizando el método de sustitución. Despejando "p" de la primera ecuación, obtenemos:
p = 20 - g
Luego, sustituimos esta expresión de "p" en la segunda ecuación:
10.98(20 - g) + 27.98g = 355.60
220.20 - 10.98g + 27.98g = 355.60
17.00g = 135.40
g = 8
Por lo tanto, la tienda vendió 8 velas grandes.
Step-by-step explanation: