The main answer is that the confidence intervals for the population proportion of subjects with syncope or near syncope who also have cardiovascular disease, at 90%, 95%, and 99% confidence levels, are as follows:
90% Confidence Interval: Approximately 51.84% to 70.53%
95% Confidence Interval: Approximately 49.77% to 72.60%
99% Confidence Interval: Approximately 46.48% to 76.89%
In the study, out of the 136 subjects with syncope or near syncope, 75 reported having cardiovascular disease.
To construct the confidence intervals, we can use the formula for a proportion's confidence interval. The formula is based on the normal distribution assumption when sample size is large enough, which is satisfied here.
By plugging in the sample proportion (75/136) and the appropriate critical values based on the desired confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%), we can calculate the lower and upper bounds for each confidence interval.
These confidence intervals provide an estimate of the likely range within which the true population proportion lies.
For example, with 95% confidence, we can say that we are 95% confident that the true proportion of subjects with syncope or near syncope who also have cardiovascular disease falls between approximately 49.77% and 72.60%.
The wider the confidence interval, the lower the precision of the estimate, but the higher the level of confidence.
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Determine the surface area and volume
The surface area of the cone is: 213.66 cm²
The volume of a cone is: 7.33 cm³
How to find the surface area and volume?The formula for the surface area of a cone is:
T.S.A = πrl + πr²
where:
r is radius
l is slant length
From the diagram and using Pythagoras theorem,we have:
l = √(7² + 5²)
l = √74
Thus:
TSA = (π * 5 * √74) + (π * 5²)
TSA = 213.66 cm²
Formula for the volume of a cone is:
V = ¹/₃πr²
V = ¹/₃π * 7
V = 7.33 cm³
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Five angels of a hexagon are 123,124,118,130’110. Calculate the six angle
Answer:
The sixth angle is 115°.
Step-by-step explanation:
Number of sides in a hexagon = n =6
Sum of interior angles = (n−2)180°
= (6−2)180 ∘
= 720
∴ Let the six angle of hexagon be x.
⇒ x + 123 + 124 + 118 + 130 + 110 = 720°
⇒ x + 605 = 720°
⇒ x = 720 - 605
⇒ x = 115
Match the example on the left with the corresponding property on the right.
11(4-2x3)
Match the example on the left with the corresponding property on the right.
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
Let X and Y have joint pdf .
a. Compute P(X < 1/2 Ç Y > 1/4).
b. Derive the marginal pdfs of X and Y.
c. Are X and Y independent? Show some calculations in support of your answer.
d. Derive f(x|y) = {the conditional pdf of X given Y=y}
Answer:
To answer the questions, I'll assume that you're referring to continuous random variables X and Y. Let's go through each part:a. To compute P(X < 1/2 ∩ Y > 1/4), we integrate the joint probability density function (pdf) over the given region:P(X < 1/2 ∩ Y > 1/4) = ∫∫ f(x, y) dx dyb. To derive the marginal pdfs of X and Y, we integrate the joint pdf over the other variable. The marginal pdf of X can be obtained by integrating the joint pdf over Y:fX(x) = ∫ f(x, y) dySimilarly, the marginal pdf of Y can be obtained by integrating the joint pdf over X:fY(y) = ∫ f(x, y) dxc. To determine if X and Y are independent, we need to check if the joint pdf can be expressed as the product of the marginal pdfs:f(x, y) = fX(x) * fY(y)If this condition holds, X and Y are independent.d. The conditional pdf of X given Y = y can be derived using the joint pdf and the marginal pdf of Y:f(x|y) = f(x, y) / fY(y)By substituting the values from the given joint pdf, we can obtain the conditional pdf of X given Y = y.Please provide the specific joint pdf for X and Y, and I'll be able to assist you further with the calculations.Hope this help youThe marginal pdf of X is fX(x) = x + 1/2
How do you compute P(X < 1/2, Y > 1/4)?We need to integrate the joint pdf over the given region. This can be done as follows:
P(X < 1/2, Y > 1/4) = ∫∫[x + y] dx dy over the region 0 ≤ x ≤ 1/2 and 1/4 ≤ y ≤ 1
= ∫[x + y] dy from y = 1/4 to 1 ∫ dx from x = 0 to 1/2
= ∫[x + y] dy from y = 1/4 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1/2
= ∫[x + y] dy from y = 1/4 to 1/2
= [(x + y)y] evaluated at y = 1/4 and y = 1/2
= [(x + 1/2)(1/2) - (x + 1/4)(1/4)]
= (1/2 - 1/4)(1/2) - (1/4 - 1/8)(1/4)
= (1/4)(1/2) - (1/8)(1/4)
= 1/8 - 1/32
= 3/32
Therefore, P(X < 1/2, Y > 1/4) = 3/32.
The marginal pdfs of X and Y can be done as follows:
For the marginal pdf of X:
fX(x) = ∫[x + y] dy over the range 0 ≤ y ≤ 1
= [xy + (1/2)y^2] evaluated at y = 0 and y = 1
= (x)(1) + (1/2)(1)^2 - (x)(0) - (1/2)(0)^2
= x + 1/2
Therefore, the marginal pdf of X is fX(x) = x + 1/2.
For the marginal pdf of Y:
fY(y) = ∫[x + y] dx over the range 0 ≤ x ≤ 1
= [xy + (1/2)x^2] evaluated at x = 0 and x = 1
= (y)(1) + (1/2)(1)^2 - (y)(0) - (1/2)(0)^2
= y + 1/2
Therefore, the marginal pdf of Y is fY(y) = y + 1/2.
To determine if X and Y are independent, we need to check if the joint pdf factors into the product of the marginal pdfs.
fX(x) * fY(y) = (x + 1/2)(y + 1/2)
However, this is not equal to the joint pdf f(x, y) = x + y. Therefore, X and Y are not independent.
To derive the conditional pdf of X given Y = y, we can use the formula:
f(xy) = f(x, y) / fY(y)
Here, we have f(x, y) = x + y from the joint pdf, and fY(y) = y + 1/2 from the marginal pdf of Y.
Therefore, the conditional pdf of X given Y = y is:
f(xy) = (x + y) / (y + 1/2)
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Which property is illustrated by the following statement? If A ABC = A DEF,
and ADEF=AXYZ, then AABC=AXYZ.
B.
A
с
E
D
O A. Reflexive
O B. Symmetric
O C. Transitive
O D. Commutative
F
Z
The property that is illustrated by the statements is Transitive. Option C
How to determine the propertyUsing the principle of transitivity, if two objects are equal to a third, they are also equal to one another.
From the information given, we have that;
< ABC = <DEF
< DEF = < XYZ
This simply proves that < ABC and < XYZ are both equivalent to < DEF in this situation.
By using the transitive property, we can determine that A ABC and A XYZ are also equal. This attribute enables us to construct relationships between many elements based on their equality to a shared third element and to connect logically equalities.
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29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
The ordered pair that is a solution for both inequalities is (-2, 2).
Which ordered pair makes both inequalities true?Here we have the system of inequalities:
y < -x + 1
y > x
And we want to see which one of the given points makes both of them true.
To find that, just replace the values in both inequalities and see if both become true or not.
For example, for the first point:
(-3, 5)
We will get:
5 < -(-3) + 1 = 4
5 > -3
The first one is false, and the second one is true.
The correct option is the second point:
2 < -(-2) +1 = 3
2 > -2
Both are true.
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guys give examples of cylinder volume word problems pls
The volume of a cylinder is given by the equation presented as follows:
V = πr²h.
In which:
r is the radius.h is the height.How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
Hence the measures must be identified and have it's values replaced into the formula to obtain the volume of a cylinder.
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Find the exact value of sec(-135)
The exact value of sec(-135°) is 1.
To find the exact value of sec(-135°), we need to use the relationship between secant and cosine functions.
The secant function is defined as the reciprocal of the cosine function:
sec(theta) = 1 / cos(theta).
We know that the cosine function has a period of 360°, which means that cos(theta) = cos(theta + 360°) for any angle theta.
In this case, we want to find sec(-135°). Since the cosine function is an even function (cos(-theta) = cos(theta)), we can rewrite sec(-135°) as sec(135°).
Now, let's focus on finding the value of cos(135°). The cosine function is negative in the second and third quadrants.
In the second quadrant, the reference angle is 180° - 135° = 45°. The cosine of 45° is equal to √2/2.
Therefore, cos(135°) = -√2/2.
Now, we can find sec(135°) using the reciprocal property:
sec(135°) = 1 / cos(135°).
Substituting the value of cos(135°), we have:
sec(135°) = 1 / (-√2/2).
To simplify further, we multiply the numerator and denominator by -2/√2:
sec(135°) = -2 / (√2 * -2/√2).
Simplifying the expression:
sec(135°) = -2 / -2,
sec(135°) = 1.
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Determine the range of the following graph:
Answer: [-2,7]
Step-by-step explanation: The range of a graph is just the range of minimum and maximum outputs of the y axis. The minimum y axis value is -2, while the maximum is 7. Putting your answer in brackets means that the endpoints (-2 and 7) are inclusive, which is the case since the dots are filled in. If the dots are hollow, the range does not include those endpoints and you would use parentheses instead.
A rotation of a figure can be considered
A rotation is a geometric transformation that preserves the shape and size of a figure while changing its orientation in space. It is a fundamental concept in geometry and is used in various fields, including art, design, and engineering.
A rotation of a figure can be considered as a transformation that rotates the figure around a fixed point, known as the center of rotation. During the rotation, each point of the figure moves along an arc around the center, maintaining the same distance from the center.
To perform a rotation, we specify the angle of rotation and the direction (clockwise or counterclockwise). The center of rotation remains fixed while the rest of the figure rotates around it. The resulting figure is congruent to the original figure, meaning they have the same shape and size but may be in different orientations.
Rotations are commonly described using positive angles for counterclockwise rotations and negative angles for clockwise rotations. The magnitude of the angle determines the amount of rotation. For example, a 90-degree rotation would result in the figure being turned a quarter turn counterclockwise.
In general, a rotation is a geometric transformation that keeps a figure's size and shape while reorienting it in space. It is a fundamental idea in geometry that is applied in a number of disciplines, including as engineering, design, and the arts.
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To bake some cakes, a baker used 40g of strawberries for every220g of flour. If the total amount of strawberries and flour that the baker used was 1040g, what was the amount of flour the baker used?
Answer:
880g of flour
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
The ratio the baker uses (strawberries: flour) is:
40g: 220gAdding the two of these together gives us:
40g + 220 = 260gThis means that for 1 batch of cakes, 260g of flour and strawberries is needed in total.
Now that we know that, we can take 1040g and divide that by 260g.
1040g ÷ 260g = 4
This means that the baker made 4 batches of cakes using 1040g total.
Taking the amount of flour and multiplying that by 4 to get the amount of flour used:
220g × 4 = 880g
Therefore the baker uses 880g of flour for every 1040g total.
What is the vertex for the graph of v - 3 = - (x+2)^2
The vertex for the graph of the equation [tex]v - 3 = - (x+2)^2 is (-2, 3).[/tex]
To find the vertex of the graph of the equation [tex]v - 3 = - (x+2)^2,[/tex] we can rewrite it in the standard vertex form: [tex]v = a(x - h)^2 + k,[/tex]
where (h, k) represents the vertex coordinates.
First, let's rearrange the given equation:
[tex]v - 3 = - (x+2)^2[/tex]
[tex]v = - (x+2)^2 + 3[/tex]
Comparing this with the standard vertex form, we can see that h = -2 and k = 3.
Therefore, the vertex of the graph is (-2, 3).
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Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
[tex]\displaystyle \text{To solve this problem, let's assume the distance of the run is denoted by 'x' miles, and the distance of the bicycle race is denoted by '48 - x' miles.}[/tex]
[tex]\displaystyle \text{We can use the formula: time} = \text{distance/velocity to find the time taken for each segment of the race.}[/tex]
[tex]\displaystyle \text{For the run:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_1 = \frac{x}{5}[/tex]
[tex]\displaystyle \text{For the bicycle race:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_2 = \frac{48 - x}{23}[/tex]
[tex]\displaystyle \text{Given that the total time for the race is 6 hours, we can write the equation:}[/tex]
[tex]\displaystyle t_1 + t_2 = 6[/tex]
[tex]\displaystyle \text{Substituting the expressions for } t_1 \text{ and } t_2, \text{ we get:}[/tex]
[tex]\displaystyle \frac{x}{5} + \frac{48 - x}{23} = 6[/tex]
[tex]\displaystyle \text{To solve this equation, we can simplify it by multiplying through by the common denominator, which is 115:}[/tex]
[tex]\displaystyle 23x + 5(48 - x) = 6 \times 115[/tex]
[tex]\displaystyle \text{Simplifying further:}[/tex]
[tex]\displaystyle 23x + 240 - 5x = 690[/tex]
[tex]\displaystyle 18x = 450[/tex]
[tex]\displaystyle x = \frac{450}{18}[/tex]
[tex]\displaystyle x = 25[/tex]
[tex]\displaystyle \text{Therefore, the distance of the run is 25 miles, and the distance of the bicycle race is } 48 - 25 = 23 \text{ miles.}[/tex]
Find the measure of the indicated angle.
99⁰
96⁰
98⁰
92°
L
120°
K
N
M
64
Answer:
? = 92°
Step-by-step explanation:
the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
? = [tex]\frac{1}{2}[/tex] (LM + AK) = [tex]\frac{1}{2}[/tex] (120 + 64)° = [tex]\frac{1}{2}[/tex] × 184° = 92°
PLSSSSSSSSSSSSSSS HELP!!!
Answer:
15
Step-by-step explanation:
5x = 4x + 3
x = 3
BC = 5x = 5(3) = 15
Answer: 15
Please answer ASAP I will brainlist
The system has no solution. Option C is correct.
To solve the given system of equations using row operations, we can write the augmented matrix and perform Gaussian elimination. The augmented matrix for the system is:
1 1 -1 | 6
3 -1 1 | 2
1 4 2 | -34
We'll use row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. Let's proceed with the row operations:
R2 = R2 - 3R1:
1 1 -1 | 6
0 -4 4 | -16
1 4 2 | -34
R3 = R3 - R1:
1 1 -1 | 6
0 -4 4 | -16
0 3 3 | -40
R3 = R3 + (4/3)R2:
1 1 -1 | 6
0 -4 4 | -16
0 0 0 | -4
Now, we can rewrite the augmented matrix in equation form:
x + y - z = 6
-4y + 4z = -16
0 = -4
From the last equation, we can see that it leads to a contradiction (0 = -4), which means the system is inconsistent. Therefore, the system has no solution.
The correct answer is (C) This system has no solution.
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What is -2( 3x + 12y - 5 - 17x - 16y + 4 )simplified?
-40x + 8y + 2
28x + 8y + 2
28x + 6y + 2
-28x - 8y + 2
Answer:
-2(3x + 12y - 5 - 17x - 16y + 4)
-6x - 24y + 10 + 34x + 32y - 8
-6x + 34x - 24y + 32y + 10 - 8
28x + 8y + 2
Urvi solved a fraction division problem using the rule “multiply by the reciprocal.” Her work is shown below.
StartFraction 14 divided by StartFraction 2 Over 7 EndFraction. StartFraction 1 Over 14 EndFraction times StartFraction 2 Over 7 EndFraction = StartFraction 2 Over 98 EndFraction or StartFraction 1 Over 49 EndFraction
Which is the most accurate description of Urvi’s work?
"1/49," accurately represents the result of Urvi's work.The correct answer is option D.
Urvi's work is accurate and follows the correct rule of "multiply by the reciprocal" to solve the fraction division problem.
In the given problem, she is dividing 14 by the fraction 2/7. According to the rule, to divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction.
In Urvi's work, she first takes the reciprocal of 2/7, which is 7/2. Then, she multiplies 14 by the reciprocal, which gives us (14 * 7/2).
Simplifying the multiplication, we get 98/2, which simplifies further to 49. Therefore, the correct answer to the fraction division problem is 1/49.
Option D, which states "1/49," accurately represents the result of Urvi's work. This option is the most accurate description of her work because it correctly shows the final simplified fraction after applying the "multiply by the reciprocal" rule.
Overall, Urvi's work demonstrates a correct understanding and application of the rule for solving fraction division problems.
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The Probable question may be:
Urvi solved a fraction division problem using the rule “multiply by the reciprocal.” Her work is shown below.
A StartFraction 14 divided by StartFraction 2 Over 7 EndFraction.
B. StartFraction 1 Over 14 EndFraction times
C. StartFraction 2 Over 7 EndFraction = StartFraction 2 Over 98
D. EndFraction or StartFraction 1 Over 49 EndFraction
Which is the most accurate description of Urvi’s work?
On her breakfast tray, Aunt Lily had a little vase of flowers - a mixture of primroses and celandines. She counted up the petals and found there were 39. "Oh, how lovely!" she said, "exactly my age; and the total number of flowers is exactly your age, Rose!" How old is Rose?
(NB: Primroses have five petals on each flower and Celandines have eight petals on each flower). Please show working
Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Let's assume the number of primroses in the vase is p, and the number of celandines is c.
Each primrose has 5 petals, so the total number of primrose petals is 5p.
Each celandine has 8 petals, so the total number of celandine petals is 8c.
According to the given information, the total number of petals is 39. Therefore, we can set up the equation:
5p + 8c = 39 (Equation 1)
Aunt Lily mentions that the total number of flowers is exactly Rose's age. Since Rose's age is not provided, we'll represent it with the variable r.
The total number of flowers is p + c, which is also equal to Rose's age (r). Therefore, we have another equation:
p + c = r (Equation 2)
We need to find the value of r (Rose's age). To do that, we'll solve the system of equations by eliminating one variable.
Multiplying Equation 2 by 5, we get:
5p + 5c = 5r (Equation 3)
Now we can subtract Equation 1 from Equation 3 to eliminate the p term:
(5p + 5c) - (5p + 8c) = 5r - 39
This simplifies to:
-3c = 5r - 39
Now, let's rearrange Equation 2 to solve for p:
p = r - c (Equation 4)
Substituting Equation 4 into the simplified form of Equation 3, we have:
-3c = 5r - 39
Substituting r - c for p, we get:
-3c = 5(r - c) - 39
Expanding, we have:
-3c = 5r - 5c - 39
Rearranging the terms, we get:
2c = 5r - 39
Now we have a system of two equations:
-3c = 5r - 39 (Equation 5)
2c = 5r - 39 (Equation 6)
To solve this system, we can eliminate one variable by multiplying Equation 5 by 2 and Equation 6 by 3:
-6c = 10r - 78 (Equation 7)
6c = 15r - 117 (Equation 8)
Now, let's add Equation 7 and Equation 8 to eliminate c:
-6c + 6c = 10r + 15r - 78 - 117
This simplifies to:
25r = 195
Dividing both sides by 25, we get:
r = 7.8
Since Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Therefore, Rose is 8 years old.
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Determine the surface area and volume. Note: The base is a square.
The volume of the square based pyramid would be =60cm³.
How to calculate the volume of square pyramid?To calculate the volume of a square based pyramid, the formula that should be used would be given below as follows;
Volume = 1/3× base²× height
where base length = 6cm
height = 5cm
Volume = 1/3× 6×6×5
= 60cm³
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Select the incorrect phrases in the paragraph.
Given:
is a right angle
is a right angle
Prove:
Four lines M A, M B, M C, and M D that starts from point M are drawn such that angle A M C equals 90 degrees, and angle B M D equals 90 degrees.
1. Angle A M C is a right angle. It leads to angle A M B and angle B M C are complementary 2. Angle B M D is a right angle. It leads to angle B M C and angle C M D are complementary. 1 and 2 lead to Angle A M B which approximately equals angle C M D.
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
is a right angleis given.
is a right angleis also given.Since
is a right angle,
and
are complementary.Since
is a right angle,
and
are complementary.By the Congruent Complements Theorem,
.
The incorrect phrases in the paragraph are as follows:
Since ∠AMC is a right angle, ∠BMC and ∠CMD are complementary.
Since ∠BMD is a right angle, ∠AMB and ∠BMC are complementary.
How to identify the wrong phrasesTo identify the wrong phrases, note that a right angle is an angle that forms 90° when inclined to another line. Also, complementary angles are those whose sum is 90°.
A close look at the angles will show that ∠BMD is a right angle but ∠BMC and ∠CMD are complementary. Also, the following is correct: ∠AMC is a right angle, ∠AMB and ∠BMC are complementary.
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Identify the vertex of the parabola.
(−2, −1)
(−3, 2)
(−1, −2)
(1, 2)
The vertex of the parabola is located at (-1, -2).To identify the vertex of the parabola given the points (-2, -1), (-3, 2), (-1, -2), and (1, 2), we can use the fact that the vertex of a parabola is the highest or lowest point on the graph.
From the given points, we can observe that the y-coordinate of the vertex will be either the highest or lowest among the y-coordinates of the points.By examining the y-coordinates, we see that the point (-3, 2) has the highest y-coordinate of 2, while the point (-1, -2) has the lowest y-coordinate of -2.
Therefore, the vertex of the parabola is the point (-1, -2), as it is the lowest point on the graph. The x-coordinate of the vertex is -1, and the y-coordinate is -2.
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A metalworker cuts out a large semicircle with a diameter of 28 centimeters.Then the metalworker is a smaller sine ait of the larger one and rives it. The der of the ticular pince that is removed a 14 centimeters. Find the distance wound the shape after the smaller circle is removed. Use 22/7
The distance around the shape after the smaller semicircle is removed is 29 cm.The correct answer is option D.
To find the distance around the shape after the smaller semicircle is removed, we need to calculate the circumference of the larger semicircle and subtract the circumference of the smaller semicircle.
The circumference of a semicircle is given by the formula:
Circumference = π * radius + diameter/2
For the larger semicircle:
Radius = diameter/2 = 28/2 = 14 cm
Circumference of the larger semicircle = π * 14 + 28/2 = 22/7 * 14 + 14 = 44 + 14 = 58 cm
For the smaller semicircle:
Radius = diameter/2 = 14/2 = 7 cm
Circumference of the smaller semicircle = π * 7 + 14/2 = 22/7 * 7 + 7 = 22 + 7 = 29 cm
Therefore, the distance around the shape after the smaller semicircle is removed is:
58 cm - 29 cm = 29 cm
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The Probable question may be:
A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. What will be the distance around the shape after the smaller semicircle is removed? Use 22/7 as an approximation for π.
A. 80cm
B. 82cm
C. 85cm
D. 86cm
Please answer ASAP I will brainlist
Using Gauss-Jordan method, the value of x, y and z are 0, -2 and 1
What is the solution of the system of equation?To solve the system of equations using the Gauss-Jordan method, we'll perform row operations to transform the augmented matrix into row-echelon form and then further transform it into reduced row-echelon form. Here are the steps:
1. Write the augmented matrix for the system of equations:
[1 -2 4 | 20]
[1 1 13 | -31]
[-2 6 -1 | -69]
2. Perform row operations to transform the matrix into row-echelon form:
R2 = R2 - R1
R3 = R3 + 2R1
[1 -2 4 | 20]
[0 3 9 | -51]
[0 2 7 | -29]
3. Perform row operations to further transform the matrix into reduced row-echelon form:
R2 = R2 / 3
R3 = R3 - 2R2
[1 -2 4 | 20]
[0 1 3 | -17]
[0 0 1 | 1]
4. Perform row operations to obtain a diagonal of 1s from left to right:
R1 = R1 + 2R2 - 4R3
R2 = R2 - 3R3
[1 0 0 | 0]
[0 1 0 | -2]
[0 0 1 | 1]
The resulting matrix corresponds to the system of equations:
x = 0
y = -2
z = 1
Therefore, the solution to the given system of equations is x = 0, y = -2, and z = 1.
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The number of books on Diana's
bookshelf by male and female authors is
shown in the table below. Some of the
numbers are missing.
How many of the non-fiction books were
written by female authors?
Fiction
Non-fiction
Total
Male
36
68
Female
Total
77
142
Answer:
The table shows that there are a total of 142 books on Diana's bookshelf, with 77 books written by female authors and the rest by male authors. However, the number of non-fiction books written by female authors is missing from the table, so it is impossible to determine the exact number without more information.
Step-by-step explanation:
Answer:
104 books
Step-by-step explanation:
Fiction Non-Fiction Total
Male 36 38
Female x
Total 77 142
----------------------------------------------------------------------------
x = 142 - 38 = 104
Sydney is trying to pick out an outfit for the first day of school. She can choose from 3 pairs of pants, 7 t-shirts, 8 sweaters or hoodies, and 4 pairs of shoes. How many different outfits does Sydney have to choose from?
Answer:
We have to multiply everything to find the amount of different possible outcomes so 3*7*8*4 = 672 unique outfits
Step-by-step explanation:
Hope this helps!
50 points. Will give brainliest.
Write a polynomial equation that has roots: 3, √2 and -4i.
Answer:
Step-by-step explanation:
Given x=3, [tex]\sqrt{2}[/tex], and -4i
y= (x-3)([tex]x^{2}[/tex]-2)([tex]x^{2}[/tex]+16)
Answer:
x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0
Step-by-step explanation:
If the roots of a polynomial equation are 3, √2 and -4i, then the factors of that polynomial are (x - 3), (x - √2) and (x + 4i), since each factor represents one of the roots.
However, since -4i is a complex number, its conjugate 4i is also a root of the polynomial. So we also need the factor (x - 4i).
Thus, the polynomial equation is:
(x - 3) (x - √2) (x + 4i) (x - 4i) = 0
To simplify this equation, we can use the fact that (a + bi)(a - bi) = a^2 - b^2i^2 = a^2 + b^2:
(x - 3) (x - √2) (x^2 + 16) = 0
Expanding this equation yields:
x^4 - 3x^3 + 16x - 16√2x^2 + 48√2x - 48 = 0
So the polynomial equation with roots 3, √2, and -4i is:
x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0
This is one appointments the same distance from other points or lines geometry
The concept of equidistant points or lines is fundamental in geometry and plays a significant role in many geometric constructions and properties.
In geometry, an "equidistant" point is a point that is at the same distance from other points or lines. This concept is often used in various geometric constructions and proofs.
For example, in a circle, the center of the circle is equidistant from all points on the circumference. This property is what defines a circle.
In terms of lines, an equidistant point can be found by drawing perpendicular bisectors. A perpendicular bisector of a line segment is a line that is perpendicular to the segment and divides it into two equal parts. The point where the perpendicular bisectors of a triangle intersect is called the circumcenter, and it is equidistant from the vertices of the triangle.
Another example is the concept of an equidistant curve. In some cases, there may be a curve or path that is equidistant from two fixed points. This curve is called the "locus of points equidistant from two given points" and is often referred to as a "perpendicular bisector" when dealing with line segments.
All things considered, the idea of equidistant points or lines is essential to geometry and is important to many geometrical constructions and features.
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HELP CAN SOMEONE ANSWER THIS
Answer:
JLK = PRQ
Step-by-step explanation:
We already know that JL = QR and KL = PR.
If we know the angle between the two sides is equal or if the other side lengths are equal, then that would prove the two triangles to be equal.
Since the option for the two other side lengths (JK = PQ) to be equal is not listed, then the option that shows the angles are equal is the correct answer.
Since both JKL and PRQ are between the line segments already said to be equal, the answer is JLK = PRQ
Answer:
C. This would be a true statement due to the fact the to sides touch are equal. The sides are going to come at the same angle giving you a SAS which is possible to show for congruent triangles.