in square , point is the midpoint of side and point is the midpoint of side . what is the ratio of the area of triangle to the area of square ? express your answer as a common fraction.
Answers
The ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\).
State the formula for the triangle's area?
The formula for the area of a triangle can be calculated using the base and height of the triangle. The general formula is:
Area = \(\frac{(base\ *\ height) }{2}\)
In this formula, the base refers to the length of any side of the triangle, and the height refers to the perpendicular distance from the base to the opposite vertex.
Let's assume the square has side length s. Since the given points are the midpoints of two sides, they divide each side into two equal segments, each with length \(\frac{s}{2}\).
We can construct a triangle by connecting these two points and one of the vertices of the square. This triangle will have a base of length s and a height of \(\frac{s}{2}\).
The area of a triangle is given by the formula:
Area = \(\frac{(base\ *\ height) }{2}\)
Substituting the values, we have:
\(Area of traingle=\frac{(s\ *\frac{s}{2}) }{2}\\=\frac{(\frac{s^2}{2})}{2}\\=\frac{s^2}{4}\)
The area of the square is given by the formula:
Area of square =\(s^2\)
Now, we can calculate the ratio of the area of the triangle to the area of the square:
\(Ratio =\frac{ (Area of triangle)}{ (Area of square)} \\=\frac{(\frac{s^2}{ 4})}{s^2} \\\\= \frac{s^2 }{4 * s^2}\\\\=\frac{1}{4}\)
Therefore, the ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\), expressed as a common fraction.
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Related Questions
the probability associated with failing to reject the null hypothesis when it is false is called
Answers
The probability associated with failing to reject the null hypothesis when it is false is called the Type II error rate.
This error rate is the likelihood of incorrectly accepting the null hypothesis when the alternative hypothesis is actually true. It is denoted as beta (β) and is often calculated before conducting a hypothesis test. The probability of making a Type II error depends on several factors, including the sample size, the significance level, and the effect size.
It is important to minimize the Type II error rate in order to increase the power of a hypothesis test, which is the probability of correctly rejecting the null hypothesis when it is false. A higher power means that the test is more likely to detect a true effect and avoid false negative results. However, reducing the Type II error rate usually requires increasing the sample size or relaxing the significance level, which may not be feasible or desirable in some cases. Therefore, it is crucial to carefully consider the trade-offs between the Type II error rate, the power, and the practical implications of the hypothesis test before making any conclusions.
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From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
Answers
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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The sets of numbers 3, 4, 5, and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples!
Answers
Answer:
Pythagorean Theorom: a^2+b^2=c^2
Take the largest number of each as C (hypotenuse)
3,4,5
(3)^2+(4)^2= (5)^2
25=25
Therefore it is a Pythagorean Triple.
8,15,17
(8)^2+(15)^2=(17)^2
289=289
Therefore it is a Pythagorean Triple.
6 in
10 in
8 in
a. What is the volume of the prism, in cubic inches?
12 in
b. What is the surface area of the prism, in square inches?
Answers
The total surface area and volume of prism are:
Volume = 576 in³
Total Surface Area = 336 in²
How to find the surface area and volume of the prism?The volume of the prism is calculated as:
Volume = Base Area * Height
Thus, we have:
Volume = (12 * 8) * 6
Volume = 576 in³
The total surface area is the sum of the surface area of all individual surfaces and as such we have:
Total Surface Area = (8 * 12) + (12 * 6) + (12 * 10) + 2(0.5 * 8 * 6)
Total Surface Area = 96 + 72 + 120 + 48
Total Surface Area = 336 in²
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if points C, D and E are on a line and CD=20 and CD=32, what are the possible value of DE?
Answers
The length of line segment DE is 10 units
A line CE is given, on which three points C, D and E lies in such a way that
length of line segment CD = 20
length of line segment CE = 32
We need to find the length of line segment DE
We know from the property of a straight line that, sum of all the length of line segments of a line is equal to the total length of the straight line
Therefore, CD + DE = CE
Putting values, we will get
20 + DE = 32
DE = 32 -20
DE = 10
Hence, the length of line segment DE is 10 units
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A solid with surface area 50units^2 is dilated by a scale factor of K to obtain a solid surface area 200units^2. Find the value of K.
Answers
The value of K is 2.
Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.
We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.
Using the formula for the surface area, we have:
Initial surface area * (scale factor)^2 = Final surface area
50 * K^2 = 200
Dividing both sides of the equation by 50:
K^2 = 200/50
K^2 = 4
Taking the square root of both sides:
K = √4
K = 2
Therefore, the value of K is 2.
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(laws of exponents with integer exponents lc) simplify (24)−1. one over two raised to the power of negative four one over two raised to the fourth power −24 23
Answers
By using the law of exponent the value of (24)⁻¹ is equal to 1/24.
To simplify (24)⁻¹, we can apply the rule for negative exponents.
The rule states that any non-zero number raised to the power of -n is equal to the reciprocal of that number raised to the power of n.
Applying this rule to (24)⁻¹, we have,
(24)⁻¹
= 1 / (24)¹
= 1 / 24
Therefore, applying the law of exponent (24)⁻¹ simplifies to 1/24.
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The above question is incomplete, the complete question is:
Using laws of exponents with integer exponents ,simplify (24)⁻¹.
one over two raised to the power of negative four one over two raised to the fourth power .
150 litres of water are poured into a cylindrical drum of diameter 48 cm.Find the depth of the water in the drum
Answers
Answer:
82.89 cm to the nearest hundredth.
Step-by-step explanation:
Volume = πr^2h where r = radius, h = height of the water.
r = 1/2 * 48 = 24 cm and the volume = 150 * 100 = 150,000cm^3 (as there are 1000 cm^3 in 1 litre).
So, substituting, we have:
150000 = π*24^2*h
h = 150000/π*24^2
= 82.893 cm
A science class has a ratio of 3 boys to 2 girls. Can there be 24 students in the class
Answers
Answer:
no
if you Let 3x be the number of boys
Let 2x be the number of girls
3x + 2x = 24
5x = 24
x = 4.8
3(4.8) = 14.4 boys
2(4.8) = 9.6 girls
There can't be 24 students for a ratio of 3 boys and 2 girls, because there can't be 14.4 boys and 9.6 girls, it has to be an exact number, otherwise it wouldn't make any sense
An analytical chemistry lab is conducting quality control tests on a drug. A single dosage of the drug should contain 8 mg of active ingredient. Of course, there will be a small amount of variability due to imperfections in the production process, but the mean of all dosages produced should be 8 mg. In 25 random dosages, the mean amount of active ingredient is 10.3 mg and the standard deviation is 2 mg. Do the data suggest that the mean amount of active ingredient in all dosages produced is different from 8 mg? (Use 1 % significance level).
Let μ be the population mean of the active ingredient (in mg)
(A) Set up the null- and alternative hypothesis.
(B) Compute the value of the test statistic. (Include the formula and show all work).
(C) Determine the critical value or the p-value.
(D) State your conclusion in practical terms. (Not just reject or fail to reject).
Answers
A) H0: μ = 8mg, Ha: μ ≠8mg.
B) \(t = (x̄ - μ) / (s / sqrt(n)) = (10.3 - 8) / (2 / sqrt(25)) = 5.5\).
C) Degrees of freedom = n - 1 = 24, two-tailed t-test, α = 0.01, critical values are ±2.492. p-value < 0.01.
D) We reject the null hypothesis and conclude that there is strong evidence that the mean amount of active ingredient in all dosages produced is different from 8 mg. The sample mean is significantly higher than 8 mg, indicating that the production process needs improvement.
(A) The null hypothesis is that the population mean of the active ingredient is equal to 8 mg, while the alternative hypothesis is that it is different from 8 mg. In symbols, H0: μ = 8 vs. Ha: μ ≠8.
(B) We apply the t-test formula to determine the value for the test statistic:
\(t = (xbar - μ) / (s / sqrt(n))\)
where Î14 is the estimated population mean, n is the number of samples size, x bar represents the sample mean, and s is the standard deviation of the sample. Plugging in the values from the problem, we get:
\(t = (10.3 - 8) / (2 / sqrt(25)) = 3.25\)
(C) To determine the critical value or the p-value, we look up the t-distribution with 24 degrees of freedom ( df = n - 1) and a two-tailed significance level of 0.01. The critical values are ±2.492, while the p-value is less than 0.01.
(D) Based on the results, we reject the null hypothesis and conclude that the mean amount of active ingredient in all dosages produced is different from 8 mg at the 1% significance level. In practical terms, this means that the drug production process needs to be investigated and improved to ensure that the correct amount of active ingredient is consistently delivered in each dosage.
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A family of four realized their water bill was high and that a lot of water was being wasted in the shower. They replaced their 5-gallon-per-minute showerheads with ones that only use 3 gallons per minute. If each family member showers for 5 minutes per day and a typical month is 30 days long, how many gallons of water will the family save per month with the new showerheads
Answers
Answer:
\(5 \times 5 = 25 \)
\(25 \times 30 = 750\)
The set of whole numbers is not a subset OF --
A. Natural Numbers
B. Integers
C. Rational Numbers
D. Real Numbers
Answers
please helpp!!
Ron asked 18 classmates whether they prefer granola bars over muffins. He used a calculator to compare the number of classmates who said yes to the total number he surveyed. The calculator showed the result as 0.66666667. Write this number as a fraction.
Answers
Answer:
2/3
Step-by-step explanation:
0.6666667 as a fraction is 2/3
Answer:
Part A = 2/3
Part B = 12
Step-by-step explanation:
2/3 of 18 would be 12
Hope this helped, have a great day
Cho sells kakigori, a Japanese frozen dessert flavored with sweet syrup, at a street stand.
The scatter plot shows the daily high temperature and the number of servings of kakigori
Cho sells each day for 12 days. Based on a line of best fit for the data, about how many
servings of kakigori will Cho sell on a day when the high temperature is 29° Celsius?
Number of Servings Sold
115
110
105
100
95
90
85
80
75
70
65
60
55
50
0
18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)
94
101
88
111
Answers
We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.
From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.
By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.
Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
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please please please help me! the question is: calculate the size of ABC, thank you!
Answers
Just add the two numbers that make the big circle.
36 plus 26 which is 62
is that an awnser?
please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answers
==========================================================
Explanation:
Check out the diagram below to see what's going on.
a = 8.2 feetb = unknownc = 9 feetUse the pythagorean theorem to find b
\(a^2 + b^2 = c^2\\\\b = \sqrt{c^2 - a^2}\\\\b = \sqrt{9^2 - (8.2)^2}\\\\b = \sqrt{81 - 67.24}\\\\b = \sqrt{13.76}\\\\b \approx 3.709 447\\\\b \approx 3.7\\\\\)
The length is roughly 3.7 feet.
A 10-mile bike race is divided into 4 equal sections.
Which equation shows how to find the number of miles in each section?
Math item stem image
CLEAR CHECK
4÷10=410 mile
4÷10=104 miles
10÷4=410 mile
10÷4=104 miles
Answers
Answer:
Step-by-step explanation:
read the question it says
a 10 mile bike rade is DIVIDED into 4 equal sections
10 DIVIDED BY 4
10÷4=104 miles
1.Given the following:
D: μ≥1000;
E: μ<1000
D and E represent respectively.
Select one:
a. H(a) and H(0)
b. H(0) and H(a)
c. Type I error and Type II error
Answers
Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.
How to determine D: μ≥1000; E: μ<1000?Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).
The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.
The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.
Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.
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Help meh plzzzzzzzz Quick
Answers
Answer:
51..................................................................................
Step-by-step explanation:
ggs bad anwser
Answer:
Sales tax is $5.6 Total cost is $75.6
Step-by-step explanation:
It's called math :D
Calculate the circumference of a circle with diameter 5 cm. Round to 2 d.p.
Answers
Answer:
15.71 cm
Step-by-step explanation:
Equation for the circumference of a circle: 2πr or dπ where r is the radius & d is the diameter.
5*π = 15.71
Answer:
15.71 cm
Step-by-step explanation:
Use the circumference formula, C = 2\(\pi\)r
Since the radius of half of the diameter, the radius will be 2.5 cm
Plug in the radius into the formula and solve:
C = 2\(\pi\)r
C = 2\(\pi\)(2.5)
C = 15.71
So, the circumference of the circle is approximately 15.71 cm
Select all the fractions that are represented by a repeating decimal .
Answers
Answer:
A e f
Step-by-step explanation:
Hope this was helpful!!!
What table represents a function?
Answers
Table A represents a function.
Define functions.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.
Given,
Table A represents a function,
A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.
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The graph shows the relationship between miles and kilometres.
a)
Convert 20 miles
to km.
b)
Convert 64 km
to miles.
Answers
By cross multiplication, we have found the following results:
a) 20 miles are equal to 32.180 kilometers.
b) 64 kilometers are equal to 39.776 miles.
How to convert a distance value into another distance unit
In this problem we must convert a given value in a unit into its equivalent quantity in another unit of same kind. We must convert miles to kilometers and viceversa by using conversion rates and cross multiplication.
First, we must convert a distance of 20 miles to kilometers by cross multiplication:
x = 20 mi × (1.609 km / 1 mi)
x = 32.180 km
Second, we must convert a distance of 64 kilometers to miles by cross multiplication:
x = 64 km × (1 mi / 1.609 km)
x = 39.776 mi
RemarkThe graph is missing, but this question can resolved by using conversion rates, that is, a mile equal 1.609 kilometers.
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Answer:
here is the answer⬇️
5. 32 = 4(x + 9)
6. 2(x-3) = -4.
7. Z(X + 6) = 77
8
8.-9(x - 8) = 27
9. 5(2c + 7) = 75
10. 6(3d +5) = 84
i might as well do this in one, this is due today and i don’t get it, someone help with explaining for the equations
Answers
4(x + 9) = 32
[4(x + 9)]/4 = 32/4
x + 9 = 8
x = 8 - 9
x = -1
6) 2(x - 3) = -4
2(x - 3) = -4
2x - 6 = -4
2x - 6 + 6 = -4 + 6
2x/2 = 2/2
x = 1
7) Z(X + 6) = 77
[Z(X + 6)]/Z = 77/Z
X + 6 = 77/Z
X + 6 - 6 = 77/Z - 6
X = 77/Z - 6
a. Sketch the vector PQ in the plane from initial point P(0, -4) to terminal point Q(4, – 1), then b. Sketch the equivalent position vector.
Answers
The sketches of the vector PQ and the equivalent vector are added as an attachment
The sketch of the vector PQGiven that
Initial point, P = (0, -4)
Terminal point, Q = (4, -1)
To sketch the vector PQ, we can plot the initial point P(0, -4) and the terminal point Q(4, -1) in a coordinate plane and draw an arrow from P to Q.
See attachment for the sketch such that the arrow represents the vector PQ, which starts at P and ends at Q.
The sketch of the equivalent vectorTo sketch the equivalent position vector, we can place the initial point of the vector at the origin (0,0) and draw an arrow from the origin to the terminal point Q(4, -1).
See attachment for the sketch
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is the table proportional
Answers
Answer:
Yes
Step-by-step explanation:
13 x 2 = 26
12 x 3 = 39
A game designer used 9 ounces of clay to make 24 identical pieces for a game
A. 3/8 B. 5/8 C. 8/5 D. 8/3
Answers
According to the unitary method, the amount of clay required to make one piece of the game is 3/8 ounces (option a).
The unitary method is a method of solving a problem by finding the value of one unit, and then using that value to find the value of another unit. In this case, we need to find the value of one piece of the game, given the total amount of clay used and the number of identical pieces made.
To solve this problem using the unitary method, we first need to find the value of one unit, which in this case is the amount of clay used to make one piece of the game. To do this, we will divide the total amount of clay used (9 ounces) by the number of pieces made (24):
Value of one unit = Total amount of clay used / Number of pieces made
= 9 ounces / 24 pieces
= 3/8 ounces per piece
Therefore, option A in the given choices is correct.
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What is the best answer to report for (515 x 0.0025) +24.57? A. 25.858. B. 25.85.
C. 25.8575. D. 26. E. 25.9
Answers
The best answer to submit for (515 x 0.0025) + 24.57 is 25.8575.
A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. Decimal notation is the name for the method used to represent numbers in the decimal system. The Hindu-Arabic numeral system has been expanded to include non-integer values.
To find the answer to the expression (515 x 0.0025) +24.57, we can simplify it by performing the multiplication and addition in the correct order:
(515 x 0.0025) + 24.57 = 1.2875 + 24.57 = 25.8575
Therefore, the best answer to report is C. 25.8575.
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Help me out!! Pleaseeeeee
Answers
Answer:
A. The slope is \(\frac{3}{2}\)
B. the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point.
Step-by-step explanation:
PART A: Slope
Given tangent line;
\(y = \frac{3x}{2} + \frac{9}{2}\)
The slope of the tangent line is equal to the derivative of the function;
\(\frac{dy}{dx} =\frac{3}{2}\)
the slope = \(\frac{3}{2}\)
PART B: Correct statement that describe the slope of a tangent line:
A secant line is a straight line joining two points on a function and the slope of the function is equal to average rate of change of the function between the two points.
A tangent line is a straight line that touches a function at only one point, and the slope of the function is equal to the instantaneous rate of change of the function at that one point.
Thus, the correct statement is " the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point".
1.5 m
7.1 m
7.1 m
V=
Answers
Answer:
75.615 m^3
Step-by-step explanation:
volume is length x width x height
7.1*7.1*1.5
75.615 m^3
Answer:
POINTS
Step-by-step explanation: