The solution to the system of inequalities is given by the image presented at the end of the answer.
One point on the solution set is given as follows:
(-9,3).
What is a system of inequalities?A system of inequalities is a set of two or more inequalities involving one or more variables. In a system of inequalities, the solution is a set of values for the variables that satisfy all of the given inequalities simultaneously.
The solution is the shaded region on the graph given by the image presented at the end of the answer.
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Why is brainly taking centuries for searches? This is a real pain, each one I have to wait a minimum of 3 minutes for answers to show.
High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.
What is the centuries for searches?High Traffic: If there are many users accessing the site simultaneously, the servers might get overloaded, leading to slow searches.
Large Database: Brainly has a vast database of questions and answers, which could slow down searches if the search algorithm isn't optimized.
Internet Connectivity: Slow internet connection on your side could result in slow searches
If you're experiencing slow searches, you can try the following: Check your internet connection and make sure it's stable and fast. Try clearing your browser cache and cookies and restart your browser.
If you're using an outdated browser, try updating it to the latest version. Consider reaching out to Brainly's customer support team to report the issue and seek assistance.
Therefore, High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.
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2. There are 80 girls in the sophomore class of 200 students. Find the ratio of girls to non-girls.
Answer: 2 girls to 3 non-girls
Step-by-step explanation:
80 are girls
120 are boys (200-80)
80:120
simplify
2:3
The Hack family is planning a trip to a theme park next fall for nights. After much research, they have found several deals for lodging at the theme park. They have narrowed it down to three hotels: the Contemporary Resort, the Fun Times Resort, and The Princess Resort. Based on the rates in the table below, which is the best deal?
the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
What is Total fixed cost?
Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.
The Contemporary Resort costs $239 per night, so the total cost for four nights would be:
$239 × 4 = $956.
The Fun Times Resort costs $189 per night, so the total cost for four nights would be:
$189 × 4 = $756.
The regular cost is $219 per night, so the total cost for three nights would be:
$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:
$657 + $0 = $657.
Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
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veterinary science: colts the body weight of a healthy 3-month-old colt should be about m 5 60 kg (source: the merck veterinary manual, a standard reference manual used in most veterinary colleges). (a) if you want to set up a statistical test to challenge the claim that m 5 60 kg, what would you use for the null hypothesis h0 ? (b) in nevada, there are many herds of wild horses. suppose you want to test the claim that the average weight of a wild nevada colt (3 months old) is less than 60 kg. what would you use for the alternate hypothesis h1 ? (c) suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. what would you use for the alternate hypothesis? (d) suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. what would you use for the alternate hypothesis? (e) for each of the tests in parts (b), (c), and (d), would the area corresponding to the p-value be on the left, on the right, or on both sides of the mean? explain your answer in each case
(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,
H0 : μ = 60 kg.
(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,
H1: μ < 60 kg.
(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.
(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.
(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.
For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.
For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.
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Determine whether the given set S is a subspace of the vector space V. Note: Pn(R) is the vector space of all real polynomials of degree at most n and Mn(R) is the vector space of all real n x n matrices = OA. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b). B. V = P5(R), and S is the subset of V P5(R) consisting of those polynomials satisfying p(1) > p(0). C. V = C3(1), and S is the subset of V consisting of those functions satisfying the differential equation y'" + 2y = x2. D. V = Mn(R), and S is the subset of all skew-symmetric matrices. VE. V = C2(I), and S is the subset of V consisting of those functions satisfying the differential equation y" – 4y' + 3y = 0. F. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m X n matrix. OG. V = R", and S is the set of vectors (x1 , X2, X3 ) in V satisfying x1 – 4x2 + x3 = 3
S is a subspace of the vector space V.
For four conditions are satisfied,
The set S is a subspace of C3(1)
The set S is a subspace of Mn(R)
The set S is a subspace of C2(I)
The set S is a subspace of [tex]R^n[/tex]
The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.
If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]
The set S is a subspace of C3(1).
The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.
S is closed under linear combinations.
The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.
If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.
S is a subspace of C2(I) because it is closed under addition and scalar multiplication.
If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].
Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.
Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.
The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.
The null space of a matrix is always closed under addition and scalar multiplication.
The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]
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Which statement about subnetting is correct?
A. Subnetting applies only to IPv4 networks, unless you are using classless interdomain routing.
B. Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage.
C. Subnetting in IPv4 involves the CIDR protocol, which runs at Layer 3; in IPv6, this protocol, and hence subnetting, is not used.
D. Because the subnet mask field is so much larger in IPv6, it is easier to subnet in this newer protocol stack than in IPv4.
The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.
Hence, the correct option is B.
In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.
IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.
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In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes.
Rx: (2, 5)
1. (-2, 5)
2. (-2, -5)
3. (2, -5)
In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).
What is a graph?The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.
The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)
Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).
Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).
The point (2,5) will change to if it is reflected across the line y=x (5,2).
Therefore, the correct option is 1. (-2, 5).
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A triangle has two legs measuring 21 cm and 20 cm. Which of the following leg measurement will make a right triangle?
The leg measurement will make a right triangle is 21 cm.
What is hypotenous?The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.
Pythagorean theorem :
If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then
p² = q² + r²
The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.
Now, p² = (20)² + (21)²
= 400 + 441 = 841
i.e. p = √(841) = 29
Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.
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Lin plans to swim 12 laps in the pool. She has swum 9.75 laps so far.
How many laps does she have left to swim? Use y
for the number of laps that Lin has left to swim.
Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:
y = 12 - 9.75
Simplifying the right side:
y = 2.25
Therefore, Lin has 2.25 laps left to swim.
One computer can process a payroll in 6 hours a new computer can do it in 4 hour how long would it take both computers together
Both computers working together can process the payroll in 2.4 hours.
Let's denote the time it takes for both computers working together to process the payroll as "t".
We can use the formula:
work done = rate x time
where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :
1/6 + 1/4 = 1/t
We can simplify the left-hand side of the equation:
2/12 + 3/12 = 1/t
5/12 = 1/t
Multiplying both sides by 12t:
5t = 12
t = 12/5
t = 2.4
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what is the ratio of the area of triangle to the area of triangle ? express your answer as a common fraction.
Thus, the ratio of the area of larger triangle to the area of smaller triangle
is found as 5:1.
Explain about the ratios:An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.
Given data:
Dimension of larger triangle: base B = 10 cm, Height H = 5 cm.Dimension of smaller triangle : base b = 5 cm, Height H = 2 cm.Area of triangle = 1/2* base * height
Ratios:
area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)
area of larger triangle / area of smaller triangle = B*H / b*h
area of larger triangle / area of smaller triangle = 10*5 / 5*2
area of larger triangle / area of smaller triangle = 50 / 10
area of larger triangle / area of smaller triangle = 5/ 1 = 5:1
Thus, the ratio of the area of larger triangle to the area of smaller triangle
is found as 5:1.
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Complete question:
what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.
Dimension of larger triangle: base B = 10 cm, Height H = 5 cm.
Dimension of smaller triangle : base b = 5 cm, Height H = 2 cm.
Topic 7: Tangents
For questions 19-20, determine if AB is tangent to circle C.
Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.
What is the Tangent of a Circle?In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.
19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:
4.8² + 7.2² = 12²
74.88 = 144 [not true} Therefore, AB is not tangent to circle C.
20. Also, we will have the following:
15² + 11.2² = 6.8²
350.44 = 46.24 [not true].
AB is not tangent to circle C.
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Solve for length of segment d.
= 4 cm
b = 12 cm
c = 6 cm
4. ? =
].d
Enter the segment length tha
belongs in the green box.
If two segments intersect inside
or outside a circle: ab = cd
Answer: Using the given information and the formula ab = cd, we can write:
d = (ab) / c
We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the unknown length we want to find. Substituting the given values, we get:
a^2 + 12^2 = 6^2
a^2 + 144 = 36
a^2 = -108 (which is not a possible solution)
This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.
Step-by-step explanation:
for which data frequency is seasonality not a problem? group of answer choices monthly. weekly. annual. daily. quarterly.
Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
What is annual data frequency?Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.
What is GDP?GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.
According to the given informationSeasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
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g fit the logistic regression model to predict diabetic status based on age and glucose levels. what is the odds of ratio of being diabetic for older adults compared to adults while controlling for glucose levels? round your answer to 0.01.
To calculate the odds ratio of being diabetic for older adults compared to adults while controlling for glucose levels in a logistic regression model, we exponentiate the coefficient estimate for Age. For example, if the estimate is 0.05, the odds ratio is 1.65.
To obtain the odds ratio for older adults compared to adults while controlling for glucose levels in a logistic regression model predicting diabetic status based on age and glucose levels, we would need to look at the coefficient estimate for the age variable. Let's say the logistic regression model is
logit(P(Diabetic)) = β_0 + β_1Age + β_2Glucose
where P(Diabetic) is the probability of being diabetic, Age is the age in years, and Glucose is the glucose level in mg/dL. β_1 represents the coefficient estimate for Age.
To calculate the odds ratio for older adults (e.g., those who are 10 years older than the average age in the sample) compared to adults while controlling for glucose levels, we can exponentiate the coefficient estimate for Age and round to 0.01. That is
OR = exp(β_1*10)
For example, if the coefficient estimate for Age is 0.05, then:
OR = exp(0.05*10) = 1.65
This means that for every 10-year increase in age, the odds of being diabetic compared to non-diabetic increase by a factor of 1.65 while holding glucose levels constant.
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Complex numbers [tex]z[/tex] and [tex]w[/tex] satisfy [tex]|z|=|w|=1, |z+w|=\sqrt{2}[/tex].
What is the minimum value of [tex]P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|[/tex]?
Okay, here are the steps to find the minimum value of P:
1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)
|z+w|=sqrt(2)
Find z and w such that these conditions are satisfied.
Possible solutions:
z = 1, w = i (or vice versa)
z = i, w = 1 (or vice versa)
2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
For the cases:
z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5
z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5
3) The minimum value of P is 5.
So in summary, the minimum value of
P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
is 5.
Let me know if you have any other questions!
Can someone help with this? Find the area of the shaded region. Anything helps, thank you
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
Explain about the sector of circle:Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.
Given:
radius r = 2 cminternal angle Ф = 90 degreesArea of shaded region = area of sector - area of triangle
Area of shaded region = Ф/360° * (πr²) - 1/2*base*height
Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2
Area of shaded region = 1/4*3.14*4 - 2
Area of shaded region = 3.14 - 2
Area of shaded region = 1.14 sq. cm
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
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electric utility poles in the form of right cylinders are made out of wood that costs $23.89 per cubic foot. calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 30 ft. round your answer to the nearest cent.
The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.
To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.
Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.
Using the formula, we get:
V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3
Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.
Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99
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your friend is binging half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket
Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.
Explain about the fraction:An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.
Given data:
fraction of crate brought by friend = 1/2
Total number of ice buckets = 6
Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets
Fraction of crate in each bucket = (1/2) / 6
Fraction of crate in each bucket = 1 / (2*6)
Fraction of crate in each bucket = 1/12
Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.
So, the number of atoms in 8.500 moles of chlorine atoms would be:
8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.
The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:
15.50 moles × 16.00 g/mol = 248 g of oxygen.
The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:
1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.
The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:
147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.
The molar mass of cobalt (Co) is approximately 58.93 g/mol.
The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.
The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.
Therefore, the formula mass of Ca₃(PO₄)₂ would be:
3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.
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Hello solve this, what is 9 x 5/7
Answer: 6 3/7
Step-by-step explanation:
9/1 x 5/7
If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.
Answer:
[tex]\frac{45}{7}[/tex] or 6.4285
Step-by-step explanation:
First, multiply 9 and 5, which gives you 45.
9(5)=45
Then, divide 45 by 7.
45/7=6.4285
That gives you [tex]\frac{45}{7}[/tex] or 6.4285
Hope this helps!
Solve x^2 + 6x + 9 = 0 by graphing. Please enter the number part of your answer only.
If your answer has two numbers, enter them like this: x = 6 and -1 should be entered as "6, -1" (no quotes).
Answer:
-3
Step-by-step explanation:
You want the graphical solution to x² +6x +9 = 0.
GraphThe graph of the expression on the left shows it has a value of 0 when x = -3.
The solution is x = -3.
__
Additional comment
A graphing calculator is very helpful when you want a graphical solution.
If you want to graph this by hand, you can rewrite it as ...
(x +3)² = 0
The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.
I will be given brainliest!!!!
Answer:2/3
Step-by-step explanation:
its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD
Answer: 2/3
Step-by-step explanation:
The corresponding side of AD is A'D'.
AD = 30
A'D' = 20
Scale factor = 2/3 because AD * 2/3 = A'D'
If I'm wrong, please tell me.
which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
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Please help Thank you
The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:
a)sinθ=0.5
b)cosθ=0.866
c)tanθ=0.577
What is trigonometric-ratios ?
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.
Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]
hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]
=[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]
=[tex]\sqrt{16+48}[/tex]
=8
a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]
Sin θ=[tex]\frac{4 }{8}[/tex]
Sin θ=[tex]\frac{1}{2}[/tex]
Sin θ=0.5
b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]
=[tex]\frac{4\sqrt{3} }{8}[/tex]
=[tex]\frac{\sqrt{3} }{2}[/tex]
=[tex]\frac{1.732}{2}[/tex]
Cos θ=0.866
c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]
=[tex]\frac{4}{4\sqrt{3} }[/tex]
=[tex]\frac{1}{\sqrt{3} }[/tex]
tan θ=0.577
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a doctor can complete 3 examinations in 2 hours. how many examinations can the doctor complete in 4 hours? hint: use the proportion 3 exams : 2 hours :: x exams : 4 hours. 5 exams 5 exams 6 exams 6 exams 7 exams 7 exams 8 exams
Answer:
6 examinations
Step-by-step explanation:
We Know
A doctor can complete 3 examinations in 2 hours.
How many examinations can the doctor complete in 4 hours?
We see
4 hours is 2 hours times 2
We take
3 x 2 = 6 examinations
So, the doctor can complete 6 exams in 4 hours.
In a race, 14 out of the 25 swimmers finished in less than 47 minutes. What percent of swimmers finished the race in less than 47 minutes? Write an equivalent fraction to find the percent.
We must first convert the given information into an equivalent fraction. The answer is 56%.
What is equivalent fraction?Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.
To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.
To do this, we must multiply both 14 and 25 by 4.
This gives us 14*4/25*4 = 56/100.
To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.
Therefore, 56/100 * 100 = 56%.
This result can also be found by setting up a proportion. We can set up the proportion as follows:
14/25 = x/100.
To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.
Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.
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The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be poisson with a mean of 25 veh/hr. It takes an average of 1. 5 min for the necessary tickets to be bought for occupants of each car. (a)what is the expected length of queue at the ticket gate, not including the vehicle being served? (b)what is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c)what will be the average waiting time of a vehicle?
(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.
(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.
(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.
In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is
E[N] = λW = 25 x 0.025 = 0.625 vehicles
So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).
P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5
= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5
= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)
Using a calculator or software, this probability is found to be approximately 0.0176.
(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is
W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes
So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.
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Which of the following phrases can be used to represent -11?
the opposite of -11
eleven greater than zero
eleven below zero
positive eleven
Thx
Answer:
Eleven below Zero
Step-by-step explanation:
Every number below zero (less than zero) is a negative number.
A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 2/5 of the remaining copies. How many copies does the bookstore still have
Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.
Definition of a unitary method.Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.
Here,
Let's figure out how many issues of the magazine are still available in the store.
Given: There were 90 copies in all when the bookstore opened.
1/6 of the total copies were sold at the bookstore yesterday.
=> 15 copies were sold yesterday = (1/6) * 90.
=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale
=> 2/5 of the remaining copies were sold in the bookstore today.
30 copies were sold today, which
=> (2/5) * 75.
The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:
=> 75 - 30 = 45
45 copies of the magazine are still available at the bookstore.
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