Solve the triangle PQR (find the measures of ∠P, ∠Q, and side PQ).
(I need help finding both angle measure and side measure, please and thank you!)
Answers
Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
What precisely is a triangle?A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.
Here,
The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:
=> PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)
=> PQ² = 9² + 12² - 2(9)(12)cos(62°)
=> PQ² ≈ 110.03
=> PQ ≈ 10.49
As a result, side PQ is roughly 10.49 units long.
The rule of sines can then be used to determine the dimensions of angles P and Q:
=> sin(∠P) / PQ = sin(62°) / PR
=> sin(∠P) / 10.49 = sin(62°) / 9
=> sin(∠P) ≈ 0.6322
=> ∠P ≈ 39.39°
=> sin(∠Q) / PQ = sin(77°) / QR
=> sin(∠Q) / 10.49 = sin(77°) / 12
=> sin(∠Q) ≈ 0.8559
=> ∠Q ≈ 58.10°
As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
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Related Questions
Write each function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. cos(α+20∘)
Answers
The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.
The complementary angle of 20° is 70° because 20° + 70° = 90°.
So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).
Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:
cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)
Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
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Suppose the water depth during low tide at a certain bay is about 3.0 m, and at high tide it is about 9.0 m. The natural period of oscillation is about 12 hours, and on a particular day, high tide occurred at 6:45 a.m. Find the amplitude (in meters) of the model. Xm
Answers
The amplitude of the model is 3.0 meters.
The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.
The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.
The amplitude of the model can be found using the formula:
Xm = (H - L)/2
where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.
Substituting the given values, we get:
Xm = (9.0 - 3.0)/2
Xm = 3.0 meters
Therefore, the amplitude of the model is 3.0 meters.
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Will make you brainlist!
Answers
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
Please help me please it would be very appreciated.
Answers
the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x²
The equation of a quadratic function is generally given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and "a" determines the shape of the parabola.
To move the function to the left by three units, we need to replace "x" with "(x + 3)" inside the parentheses:
[tex]y = a(x + 3 - h)^2 + k[/tex]
To move the function up by four units, we need to add four to the value of "k":
[tex]y = a(x + 3 - h)^2 + (k + 4)[/tex]
To stretch the function by a scale factor of two, we need to multiply "a" by two:
[tex]y = 2a(x + 3 - h)^2 + 2(k + 4)[/tex]
Combining these transformations, we get the final equation:
[tex]y = 2(x + 3 - 0)^2 + (0 + 4)[/tex]
[tex]y = 2(x + 3)^2 + 4[/tex]
Therefore, the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
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Which statements are true? Select each correct answer.
A. 40m^6 -4=4(10m^6-1)
B. 32m^4 +12m^3 =4m^3(8m +3)
C. 15m^3-6m=3m(5m^2 -6m)
D. 6m^2+18m=6m^2(1+3m)
Answers
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
A. 40m^6 -4=4(10m^6-1) is not true.
B. 32m^4 +12m^3 =4m^3(8m +3) is not true.
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
Step-by-step explanation:
Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
Answers
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The measure of an angle is 40.6°. What is the measure of its supplementary angle?
Answers
Answer: 139.4
Step-by-step explanation:
a supplementary angle is equal to 180 so all we have to do is subtract 40.6 from 180
180 - 40.6 = 139.4
On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .
Which statements about the triangles are true?
Select each correct answer.
AC BC
a c is greater than b c
AC>AB
a c is greater than a b
AC
Answers
Answer:
AC<BC = 30+60=90 < 60+90= 150
Step-by-step explanation:
AC>AB 30+90= 120 > 30+60=90
AC<BC 30+60=90 < 60+90= 150
need help finding the letter u
Answers
In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd
What is a triangle?A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd
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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd
What is a triangle?A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd
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Transaction ID
Items
1
Bread, Milk
2
Bread, Diaper, Beer, Eggs
3
Milk, Diaper, Beer, Coke
4
Bread, Milk, Diaper, Beer
5
Bread, Milk, Diaper, Coke
6
Bread, Coke, Eggs
7
Beer, Coke
8
Beer, Milk, Bread, Diaper, Eggs
9
Eggs, Diaper
10
Diaper, Beer
Calculate the support, Confidence, and Lift for each of the following rules
Please show work.
3
Rule:
Support
Confidence
Lift
1)
{Bread} -> {Milk}
2)
{Beer} -> {Eggs}
3)
{Beer, Bread} -> {Milk}
4)
{Bread, Eggs} -> {Diapers}
5)
{Milk, Bread} -> {Eggs, Coke}
6)
{Beer, Milk} -> {Bread, Diapers}
7)
{Bread, Milk, Eggs} -> {Diapers}
8)
{Bread, Eggs, Coke} -> {Diapers, Beer}
Answers
Confidence in math is the belief in one's ability to understand and solve mathematical problems. Developing confidence in math is important because it can help individuals overcome anxiety and fear of math, which can limit their performance and success in the subject.
1) {Bread} -> {Milk}:
Support: 5/10
Confidence: 5/7
Lift: 5/2.4
2) {Beer} -> {Eggs}:
Support: 4/10
Confidence: 4/9
Lift: 4/3
3) {Beer, Bread} -> {Milk}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
4) {Bread, Eggs} -> {Diapers}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
5) {Milk, Bread} -> {Eggs, Coke}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
6) {Beer, Milk} -> {Bread, Diapers}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
7) {Bread, Milk, Eggs} -> {Diapers}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
8) {Bread, Eggs, Coke} -> {Diapers, Beer}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
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I am in need of some help with this
Answers
The required volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
What is volume?A measurement of three-dimensional space is volume. It is frequently expressed mathematically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are linked.
First, let's find the volume of the cylinder:
[tex]$$V_{cylinder} = \pi r^2 h = \pi (5)^2 (8) = 200\pi$$[/tex]
Next, let's find the volume of the hemisphere:
[tex]$V_{hemisphere} = \frac{2}{3}\pi r^3 = \frac{2}{3}\pi (5)^3 = \frac{250\pi}{3}$$[/tex]
To find the volume of the entire shape, we simply add the volume of the cylinder and hemisphere:
[tex]$$V_{shape} = V_{cylinder} + V_{hemisphere} = 200\pi + \frac{250\pi}{3} = \frac{850\pi}{3}$$[/tex]
Therefore, the volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
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What is the meaning of mean, meadian and mode?
(With explanation)
Answers
Step-by-step explanation:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Please mark as brainliestAnswer:
Step-by-step explanation:
Certainly! "Mean," "median," and "mode" are three different measures of central tendency used in statistics to describe a dataset. They help provide insight into the typical or central value within a set of data points.
1. **Mean:**
- **Definition:** The mean, also known as the average, is calculated by adding up all the values in a dataset and then dividing by the total number of values.
- **Calculation:** Mean = (Sum of all values) / (Number of values)
- **Explanation:** The mean gives you the "typical" or "average" value in a dataset. It's the sum of all the values divided by the number of values. For example, if you have test scores of 80, 85, 90, 92, and 95, the mean score would be (80 + 85 + 90 + 92 + 95) / 5 = 88.4.
2. **Median:**
- **Definition:** The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
- **Explanation:** The median is the middle value that separates the dataset into two equal halves. It is not influenced by extreme values (outliers) as much as the mean. For example, in the dataset 4, 7, 9, 12, 15, the median is 9 because it's the middle value.
3. **Mode:**
- **Definition:** The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode if all values occur with the same frequency.
- **Explanation:** The mode represents the most common value or values in a dataset. For example, in the dataset 2, 3, 3, 4, 4, 4, 5, the mode is 4 because it appears more frequently than any other value.
In summary, the mean is the average value, the median is the middle value, and the mode is the most frequently occurring value in a dataset. Each of these measures provides different insights into the central tendency of data and can be useful for various statistical analyses and interpretations.
Identifying and naming congruent angles 
Answers
In response to the stated question, we may state that As a result, the figure's pairs of congruent angles are: ∠BAC ≅ ∠EDF; ∠ABC ≅ ∠DEF; ∠ACB ≅ ∠DFE
What are angles?An angle is a form in Euclidean geometry that is constructed from two rays, known as the tone's sides, that connect at a central location known as angle's vertex.
Two beams may combine to generate an inclination in the plane in which they are located. They are known as dihedral angles. In plane geometry, an angle is a potential arrangement of two rays or planes that meet a termination.
The English term “angle” derives from the Latin phrase "angulus," which means "horn." The vertex is the point at where the twin rays, also termed as the angle's sides, converge.
The congruent angles in the illustration are:
BAC and EDF are vertically opposed angles with the same measurement.
ABC and DEF are equivalent angles with the same measure.
ACB and DFE are equivalent angles with the same measure.
Therefore, the figure's pairs of congruent angles are:
∠BAC ≅ ∠EDF
∠ABC ≅ ∠DEF
∠ACB ≅ ∠DFE
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Rose graphs this equation as shown x^2-4x+y^2=0 Rose correctly found the what but incorrectly found the what to correct her graph she could what
Answers
The equation [tex]x^2-4x+y^2=0[/tex] can be rewritten as [tex]x^2-4x+4+y^2=4[/tex], which is equivalent to [tex](x-2)^2 + y^2 = 2^2[/tex]. This is the equation of a circle centered at (2,0) with a radius of 2.
How to graph this equation?To graph this equation, you could plot the center point (2,0) and then draw a circle with a radius of 2 around that point. Alternatively, you could find a few points on the circle by plugging in values for x and solving for y (or vice versa), and then plot those points to sketch the circle.
If Rose found the correct equation but incorrectly graphed it, she could try using the correct center point and radius to sketch the circle more accurately. Alternatively, she could check her work to see where she made a mistake in graphing the equation.
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10340000000 in standard form
Answers
Answer:
1034 x 10⁷
Step-by-step explanation:
the seven just means to multiply by 10 seven times
Let me know if this helps.
All 5 students in Mr. Arthur's class score 50 on a test. What is the average score on this test?
Answers
If all the 5 students in Mr. Arthur's class scores 50 on a test then the average score of the test is 50.
To find the average score on the test, we need to sum up the scores of all the students and then divide by the number of students.
In this case, all 5 students scored 50 on the test.
So the total score of all 5 students is:
Total score = 5 x 50 = 250
The average score is then calculated by dividing the total score by the number of students:
Average score = Total score / Number of students
Average score = 250 / 5
Average score = 50
Therefore, the average score on the test is 50.
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solve the linear system using elimination. -5x+3y=19 and -5x+7y+11
Answers
Answer:
x = -5
y = -2
Step-by-step explanation:
-5x + 3y = 19
-5x + 7y = 11
Time the first equation by -1
5x - 3y = -19
-5x + 7y = 11
4y = -8
y = -2
Now put -2 in for y and solve for x
-5x + 3(-2) = 19
-5x - 6 = 19
-5x = 25
x = -5
Let's Check
-5(-5) + 3(-2) = 19
25 - 6 = 19
19 = 19
So, x = -5 and y = -2 is the correct answer.
A triangle has one side with length 9 and another side with length 6. The angle opposite the side of length 6 measures 40. what is the measure of the angle opposite the side of length 9?
Answers
Answer: the angle opposite the side length 9 is 74.62 degrees I think .
Step-by-step explanation:
an arm wrestler is the champion for a period of 75 hours. (here, by an hour, we mean a period starting from an ex- act hour, such as 1 p. m ., until the next hour.) the arm wrestler had at least one match an hour, but no more than 125 total matches. show that there is a period of consec- utive hours during which the arm wrestler had exactly 24 matches.
Answers
In the following question, among the conditions given, There must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
The arm wrestler had at least 75 matches and no more than 125 total matches. This means that the arm wrestler had a maximum of 50 matches in any consecutive period of 75 hours. Therefore, there must be a period of consecutive hours during which the arm wrestler had exactly 24 matches.
To show this, let us consider the following: in the 75-hour period, there must have been at least 3 periods of consecutive 24-hour periods (24 matches per period). If we subtract 3 x 24 matches from the total of 75 matches, we are left with 3 matches. Therefore, there must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
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The volume of this prism is 4950cm3. The area of the cross-section is 110cm2. Work out x .
Answers
Answer:
answer will be my albert enistein calculation is 4500000⁹7765⁵44³=6425786
Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?
Answers
Answer:
To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.
For last week's test, the ratio of correctly spelled words to total words is:
16/20 = 0.8
For this week's test, the ratio of correctly spelled words to total words is:
13/15 ≈ 0.867
Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.
Kernels as Dot Products 2 1 point possible (graded) Which of the following feature vectors (x) produces the kernel K(x,x) = (x) - (x') (x) = [x1, x2, x3] O(x) = [₁ + x₂ + x3] (x) = [x₁, x₂ + x3] (x) = [x₁ + x3, x1 + x2] = x₁x₁ + x2x₂ + x3 x3 + x 2 x 3 + x 3 x 2
Answers
The feature vector that generates the kernel K(x, x) = (x) - (x') is given by (x) = [x1, x2 + x3].
The formula for kernel is K(x, y) = φ(x) · φ(y) and the dot product of two vectors is defined as (x) · (y) = x^Ty where x^T denotes the transpose of x.
Therefore, we can expand the given kernel to: K(x, x') = φ(x) · φ(x')= [x1, x2 + x3] · [x1, x2 + x3]'= [x1, x2 + x3] · [x1, x2 + x3]= x1x1 + (x2 + x3)(x2 + x3) The correct option is (x) = [x1, x2 + x3]
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find the length of the cord pt.3
Answers
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
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researchers analyzed data from more than 5000 adults and found that the more diet sodas a person drank, the greater the person's weight gain. does this mean that drinking diet soda causes weight gain?
Answers
Based on the analyzed data from more than 5,000 adults, researchers found that the more diet sodas a person drank, the greater the person's weight gain.
But it is not true that drinking diet soda causes weight gain.
The causal link between drinking diet soda and weight gain is not established. People who drink diet soda may be consuming more calories and sugars from other sources or may be leading an unhealthy lifestyle that results in weight gain.
the artificial sweeteners used in diet soda may interfere with the body's natural ability to regulate calorie intake, leading to increased cravings for high-calorie foods and, ultimately, weight gain. However, more research is needed to understand the impact of artificial sweeteners on weight gain fully.
Therefore, it can be concluded that drinking diet soda does not directly cause weight gain. Instead, a healthy lifestyle and balance between calorie intake and energy expenditure is necessary to maintain a healthy weight.
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45/43 as a percentage rounded to the nearest tenth of a percent
Answers
Answer:
104.7% to the nearest tenth.
Step-by-step explanation:
Multiply the fraction by 100:
= (45 x 100) / 43
= 104.651.
Select the correct solution for the expression. 2 5 + 3 8 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
Answers
In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:
2/5 = 16/40
3/8 = 15/40
We can now sum the two fractions:
16/40 + 15/40 = 31/40
As a result, the proper answer is:
B. 16/40 + 15/40 = 31/40
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Can some one solve this and show their work please
Answers
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
----------------------------------
check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
-----------------------------------
7 + 6 = 2 x 7 - 1
13 = 13
this answer is good
The amount of daily daylight is unrelated to levels of depression in older adults. What type of hypothesis is this?
a) Null hypothesis
b) Alternative hypothesis
b) Research hypothesis
d) Nonsignificant hypothesis
Answers
The amount of daily daylight is unrelated to levels of depression in older adults. The hypothesis "The amount of daily daylight is unrelated to levels of depression in older adults" is an example of the null hypothesis.
A null hypothesis is a statement that there is no significant difference between two variables or a relationship between them.The null hypothesis assumes that the observed results or changes in the experiment or data are due to random fluctuations or errors in the measurement process. It is the default hypothesis that is typically tested against an alternative hypothesis.
A researcher tries to disprove or reject the null hypothesis by conducting experiments or collecting data to support the alternative hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. However, if the null hypothesis cannot be rejected, then it remains as the plausible explanation for the observations or outcomes in the experiment.
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What’s the area of 5feet 12feet and 13feet, using 4(bxh)
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The area of 5feet 12feet and 13feet, 30 square feet
Area calculation.the formula 4(bxh) is used to calculate the area of a rectangle, not a triangle. However, the dimensions 5 feet, 12 feet, and 13 feet are actually the sides of a right triangle (known as a Pythagorean triple), so we can use the formula for the area of a right triangle:
Area = 1/2 x base x height
where the base and height are the two legs of the right triangle.
Using the Pythagorean theorem, we can determine that the legs of the triangle are 5 feet and 12 feet, and the hypotenuse is 13 feet. Therefore, the area of the triangle is:
Area = 1/2 x 5 feet x 12 feet
Area = 30 square feet
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find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid(x^2/4) + (y^2/64) + (z^2/49) = 1Hint: By symmetry, you can restrict your attention to the first octant (where x,y,z=0), and assume your volume has the form V=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant.What is the maximum volume?
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The volume of the rectangular box is given by using the Lagrangian multiplier theorem is 172.435 cubic units.
It states that any local maxima or any local minima of the function are calculated under the equality constraints.
The equation of ellipsoid is given as,
[tex]\frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} =1[/tex]
Let the edges of the required rectangular box be x, y, and z.
Then, the volume of the box in the first quadrant is V = xyz
Then we have,
[tex]\phi(x,y,z) = \frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} -1[/tex]
By the Lagrange multiplier,
[tex](V_x,V_y,V_z) = \lambda (\phi_x, \phi_y,\phi_z)\\\\(yz,xz,xy)=\lambda(\frac{2x}{4},\frac{2y}{64},\frac{2z}{49} )\\\\xyz = \lambda\frac{x^2}{2},xyz =\lambda\frac{y^2}{32} ,xyz=\lambda\frac{2z^2}{49} \\\\x^2 = 2k, y^2=32k,z^2=49k/2[/tex]
Solving for k we have the value of k as k = 2/3.
Put k=2/3 in equation 2, we have
x² = 2*2/3 , y² = 32*2/3, z² = 49/2*2/3
x =±2/√3 , y= ±8/√3 , z = ±7/√3
Then the volume of the rectangular box will be
Volume = [tex]\frac{2}{\sqrt{3} } \frac{8}{\sqrt{3} } \frac{7}{\sqrt{3} }[/tex]
Volume = 172.435 cubic units.
Therefore, the value of volume of the rectangular box is 172.435 cubic units.
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