Answer:
400-105-x bigger than or = 72
Answer:400-105-x
= 72
Step-by-step explanation:
Calculate the length of AC in ABAC to 1 decimal place.
The length of AC in triangle BAC is equal 10.7 units
Cosine RuleIn trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
AC² = AB² + BC² - 2(AB)(BC) cos AC
AC² = 6² + 7² - 2(6)(7)cos110
AC = 10.7
Using cosine rule, the length of AC is 10.7 unit.
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Find the value of the test statistic z using z=^p−p√pq/n.
The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.
a. -4.71
b. -3.96
c. 4.71
d. 3.96
Answer:
Option C - 4.71
Step-by-step explanation:
We are given the Test statistic for proportion as;
z = (^p − p)/√pq/n
From the question;
^p = 0.15
p = 0.1
q = 1 - 0.1 = 0.9
n = 800
z = (0.15 - 0.1)/√(0.1 × 0.9/800)
z = 0.05/√(0.09/800)
z = 4.71
Given the third order homogeneous constant coefficient equation y′′′+y′′−y′−y=0 1) the characteristic polynomial ar3+br2+cr+d is 2) The roots of auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). 4) Given the initial conditions y(0)=4,y′(0)=−1 and y′′(0)=2 find the unique solution to the IVP y=
The characteristic polynomial for the given third order homogeneous constant coefficient equation is ar^3 + br^2 + cr + d.
the roots of the auxiliary equation, we substitute r for y in the characteristic polynomial and set it equal to zero: ar^3 + br^2 + cr + d = 0. Solve this equation to find the values of r.
A fundamental set of solutions is a set of linearly independent solutions to the given differential equation. It is obtained by using the roots obtained in step 2 and applying them to the general solution form.
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1) The characteristic polynomial for the given third-order homogeneous constant coefficient equation is ar^3 + br^2 + cr + d.
2) The roots of the auxiliary equation are the values of r that satisfy the characteristic polynomial ar^3 + br^2 + cr + d = 0.
3) The fundamental set of solutions is {e^(r1t), e^(r2t), e^(r3t)}, where r1, r2, and r3 are the distinct roots of the auxiliary equation.
4) The unique solution to the initial value problem (IVP) is determined by substituting the initial conditions y(0) = 4, y'(0) = -1, and y''(0) = 2 into the general solution obtained from the fundamental set of solutions.
We can explain further:
1) The characteristic polynomial of the given third-order homogeneous constant coefficient equation is obtained by substituting y=e^(rt) into the equation, where r is a constant. This yields the equation ar^3 + br^2 + cr + d = 0. So, the characteristic polynomial for this equation is ar^3 + br^2 + cr + d.
2) To find the roots of the auxiliary equation, we need to solve the characteristic polynomial ar^3 + br^2 + cr + d = 0. By finding the roots of this equation, we can determine the values of r. The roots of the auxiliary equation are the values of r that satisfy the characteristic polynomial.
3) To find a fundamental set of solutions, we need to find three linearly independent solutions to the differential equation. Each solution corresponds to a distinct root of the auxiliary equation. For example, if the roots of the auxiliary equation are r1, r2, and r3, then the fundamental set of solutions is {e^(r1t), e^(r2t), e^(r3t)}.
4) Given the initial conditions y(0) = 4, y'(0) = -1, and y''(0) = 2, we can use these values to determine the unique solution to the initial value problem (IVP). By substituting the initial conditions into the general solution obtained from the fundamental set of solutions, we can find the specific solution that satisfies the given initial conditions.
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no.8
8. Find the geometric mean radius of the unconventional conductors in terms of the radius r of an individual strand. A. 1.074r C. 1.402r D. 1.953r ooo B. 1.583r
The geometric mean radius of the unconventional conductors in terms of the radius r of an individual strand is 1.583r.
To find the geometric mean radius of the unconventional conductors, we need to understand the concept of geometric mean. The geometric mean of two numbers is the square root of their product. In this case, we are looking for the geometric mean radius of multiple strands.
First, we need to determine the number of strands in the unconventional conductors. The question does not provide this information explicitly, so we assume there are at least two strands.
We know that the geometric mean radius is the square root of the product of the individual strand radii. Let's assume there are n strands, and the radius of each strand is r. Therefore, the product of the individual strand radii would be r^n.
Now, we can calculate the geometric mean radius by taking the square root of r^n. Mathematically, it can be expressed as (r^n)^(1/n) = r^((n/n)^(1/n)) = r^1 = r.
Therefore, the geometric mean radius in terms of the radius r of an individual strand is 1.583r.
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How many gallons of water will it take to fill up a swimming pool 26 ft in diameter and 4 feet deep
Answer:
\(15887.55\ \text{gallons}\)
Step-by-step explanation:
d = Diameter of pool = 26 ft
r = Radius = \(\dfrac{d}{2}=\dfrac{26}{2}=13\ \text{ft}\)
h = Height of pool = 4 ft
Volume of the pool is
\(V=\pi r^2h=\pi\times 13^2\times 4\\\Rightarrow V=2123.72\ \text{ft}^3\)
Converting to gallons
\(1\ \text{ft}^3=7.481\ \text{gallons}\\\Rightarrow 2123.72\ \text{ft}^3=2123.72\times 7.481\\ =15887.55\ \text{gallons}\)
So, the gallons of water required to fill the pool is \(15887.55\ \text{gallons}\).
When multiplying units, use the same principle that you use for multiplying fractions. In addition, ifone unit is in the numerator and the identical unit is in the denominator, they cancel each other out (to essentially equal 1). Any remaining units are used in the answer. ( centimheter) ( centimeter meter )=1 meter = meter You can also multiply several units together at once using the same principle as for fractions containing numbers. ( second centipheters )( centimeter meter )( meters kilopreter )( kilopeter megameter )= second megameter It is very important to note that if a unit appears only once in the numerator but more than once in the denominator, we can only cancel one of the unit expressions in the denominator. Think of this concept in terms of fractions. If the number 4 is in the numerator, and two 45 are in the denominator of different fractions, we only cancel out one of the 45 on the bottom, not both. (54)(43)(41)=(5∗4)(3∗1)=203=0.15 Evaluate the following unit expression. Enter the resulting units as your answer. Do not abbreviate the units and do not use parentheses. Parentheses mean multiplication. ( kilogram )( kilogram grams )( gram milligrams )= Evaluate the following unit expression. Enter the resulting units as your answer. Do not obbreviate the units and do not use parentheses. Parentheses mean multiplication. ( mole )( mole grams )( gram liter )= Evaluate the following unit expression. Enter the resulting units as your answer. Do not abbreviate the units. Enter units exactly as they anpear in the problem. Use ^ for exponents (so ft∧2forft2 ). Use " for multiplication and / for division. Do not include any spaces and not use parentheses. Parentheses mean multiplication. (mL)(cmmg)( mLcm3)=(mL)(cmmg)( mLcm∗ cm∗ cm)= Evaluate the following unit expression. Enter the resulting units as your answer. Do not abbreviate the units. Enter units exactly as they annear in the problem. Use ∧ for exponents ( so ft∧2for22). Use " for multiplication and / for division. Do not include any spaces and not use parentheses. Parentheses mean multiplication. (f2g)(mLft)(gmL)=(ft∗ftg)(mLft)(gmL)=
The resulting units are kilograms grams milligrams, mole grams liter, ft^2g mL ft gmL
To evaluate the given unit expressions, we can apply the rules of multiplying units similar to multiplying fractions.
(kilogram)(kilogram grams)(gram milligrams):
The units cancel out as follows:
(kilogram)(kilogram grams)(gram milligrams) = (kilogram)(grams)(milligrams)
Therefore, the resulting units are kilograms grams milligrams.
(mole)(mole grams)(gram liter):
The units cancel out as follows:
(mole)(mole grams)(gram liter) = (mole)(grams)(liter)
Therefore, the resulting units are mole grams liter.
(mL)(cmmg)(mLcm3):
The units cancel out as follows:
(mL)(cmmg)(mLcm3) = (mL)(cm mg)(cm^3)
Therefore, the resulting units are mL cm mg cm^3.
(f^2g)(mLft)(gmL):
The units cancel out as follows:
(f^2g)(mLft)(gmL) = (ft^2g)(mLft)(gmL)
Therefore, the resulting units are ft^2g mL ft gmL.
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Completely factor 40^4 - 324.
Answer:
40^4 - 324 = 2,559,676
Step-by-step explanation:
First we need to factor the left side of the equation, which is 40 to the 4th power. 40*40*40*40 is 2,560,000, now we need to subtract 324 from it which is 2,559,676.
solve the system of linear equations using subsitution. {y=2x-1. {y=x-8
Answer:Linear Algebra Examples ... Linear Algebra. Solve by Substitution y=x+3 , y=2x-1 ... Eliminate the equal sides of each equation and combine. ... Subtract 1 1 from 8 8 . ... The solution to the system of equations can be represented as a point.
Step-by-step explanation:
The measures of the angles of a quadrilateral are in the
ratio 2:3:6:7. Find the number of degrees in the largest
angle of the quadrilateral.
Answer:
140
Step-by-step explanation:
Consider a square for just a second. It has 4 angles each of 90 degrees. The total number of degrees in a square is 4 * 90 = 360.
It should be at least an appeal to your intuition to say that a quadrilateral has a total of 360 degrees.
Therefore the ratio you have been given must have 4 angles that add to 360.
2x + 3x + 6x + 7x = 360
18x =360
x = 20
So the 4 angles are
2* 20 = 40
3*20 = 60
6*20 = 120
7*20 = 140
Total 360
The largest angle is 140
What's 9 in index form
Answer:
3²
Step-by-step explanation:
On a planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 10kg weighs 80 N. Calculate the weight of an object whose mass is 3 kg.
Answer:
\(f = mg\\ 80 = 10g \\ g = 8 \: m .{s}^{ - 2} \\ w = 3 \times 8 = 24 \: newton \\ \: on \: that \: planet\)
Please answer this. Thank you! :)
Protein of \(125 g\) Yoghurt A is \(6,5 g\)
Protein of \(150 g\) Yoghurt B is \(4,0 g\)
How many grams of protein are provided by \(100 g\) of yoghurt A?
First, find the ratio of the weight of the yogurt A
\(125 g : 100 g\)
125 and 100 have the same factor is 25. then divide both numbers by 25 to simplify it.
\(\frac{125}{25}:\frac{100}{25} =5:4\)
Find grams of protein are provided by \(100 g\) of yoghurt A use comparison \(5:4\)
\(\frac{4}{5}(4)=\frac{16}{5}=3,2 g\)
\(3,2g\) of protein are provided by \(100 g\) of yoghurt A.
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If a population of 1000 people were to increae by 5% every year, what would the population be in 20 year?
The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.
How to estimate future population?
The future population can be estimated by the following equation:
P = P₀ × (1 + i)ⁿ
Where
P = population in the expected yearP₀ = current populationi = growth raten = number of periodsIf the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?
The population in the next 20 years would be
P = P₀ × (1 + i)ⁿ
P = 1000 × (1 + 0.05)²⁰
P = 1000 × (1.05)²⁰
P = 1000 × 2.6533
P = 2653 people
Hence, the population in the next 20 years would be 2653 people.
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Part A;
If 2 is the equation created as the product of − 3 and 1, Which of the following is an expression for 2?
Part B;
Then complete the polynomial equation.
Answer:
see explanation
Step-by-step explanation:
y₂ = - 3 × y₁
= - 3(4x² - 5x + 1) ← distribute parenthesis by - 3
= - 12x² + 15x - 3 → (a)
B
y₁ - y₂
= 4x² - 5x + 1 - (- 12x² + 15x - 3) ← distribute parenthesis by - 1
= 4x² - 5x + 1 + 12x² - 15x + 3 ← collect like terms
= 16x² - 20x + 4
The Happy Animals Kennel has $18$ cages in a row. They allocate these cages at random to $6$ dogs, $6$ cats, and $6$ pot-bellied pigs (with one animal per cage). All arrangements are equally likely. Let $A$ be the number of times in the row of cages that two animals of the same species are adjacent. For example, in the arrangement DCPCDPPPDCDPCDCCPD (where D
The probability that Fido and Rover (two dogs) are in adjacent cages is
\frac{17}{\binom{18}2}=\frac19,
because there are \binom{18}2 choices for the (unordered) pair of cages to put them in, and 17 pairs of adjacent cages.
To get the expected value, multiply this probability of a random number of same-species pairs of animals:
\frac19\cdot3\cdot\binom62=5.
The expected value is 5.
Randomness has many uses in fields such as science, art, statistics, cryptography, games, and gambling. For example, random assignment in randomized controlled trials helps scientists test hypotheses, and random or pseudo-random numbers are useful in video games like video poker.
In computing, a hardware random number generator (HRNG) or true random number generator (TRNG) is a device that generates random numbers through a physical process rather than an algorithm.
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PLEASEEE HELPPPPP ASAPPPP
Answer:
Draw 2 squares as in the picture below
Step-by-step explanation:
U 2 can help me by marking as brainliest.....
A surveyor spots a cliff 160 meters tall. He measures the angle of elevation to the top of the cliff as 71°. How far away is the surveyor from the base of the cliff? Round to the nearest meter.
Therefore, the surveyor is approximately 61 meters away from the base of the cliff. Rounded to the nearest meter, the answer is 61 meters.
What is distance?Distance is a numerical measurement of the physical space between two points or objects. It is often expressed in units such as meters, feet, miles, or kilometers, depending on the system of measurement being used. Distance is a scalar quantity, meaning that it has only magnitude and no direction. It is different from displacement, which is the vector quantity that describes the overall change in position of an object, taking into account both magnitude and direction. Distance can be calculated using various methods depending on the context, such as using a ruler or tape measure for small distances or using GPS or other advanced technologies for larger distances.
by the question.
We can use trigonometry to solve this problem. Let's call the distance from the surveyor to the base of the cliff "x". Then, we can use the tangent function to find x:
\(tan(71°) = opposite/adjacent\)
In this case, the opposite side is the height of the cliff (160 meters) and the adjacent side is x, so we have:
\(tan(71°) = 160/x\)
To solve for x, we can multiply both sides by x and divide both sides by tan (71°):
\(x = 160 / tan(71°)\)
Using a calculator, we find that tan (71°) is approximately 2.62, so:
\(x = 160 / 2.62\)
x ≈ 61.07 meters
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A rectangle has sides measuring (3x + 5) units and (6x + 11) units. Part a: what is the expression that represents the area of the rectangle? show your work to receive full credit. Part b: what are the degree and classification of the expression obtained in part a? part c: how does part a demonstrate the closure property for polynomials?.
Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).
Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.
Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.
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The picnic shelter must be at least overline 10 feet from any edge of the park. On graph paper with the distance between grid lines representing 10 feet, a city engineer makes a scale drawing of the park, as shown below. The region where the picnic shelter CANNOT be built is shown shaded. The corners of both the park and the region where the picnic shelter may be built are at the intersections of grid lines. The corners of the picnic shelter must also be at the intersections of grid lines. How many different locations in the park are possible for the placement of the picnic shelter?
Answer:
52
Step-by-step explanation:
since the shaded region is an exclusive counting the grid between 13*4 gives 52
We can see here that the number of locations in the park that are possible for the placement of the picnic shelter is C. 52
What is graph paper?Graph paper, also known as grid paper or coordinate paper, is a type of paper that has a grid of equally spaced horizontal and vertical lines drawn on it. The lines form a pattern of squares or rectangles, which facilitates drawing graphs, charts, diagrams, and geometric shapes with precision.
We can see here that multiplying the length and breadth of the picnic shelter using the unshaded boxes, we have:
13 × 4 = 52
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find all the zeros of the quadratic function
\(y = x^{2} - x - 20\)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\(y = {x}^{2} - x - 20\)
\(y = (x - 5)(x + 4)\)
To find the zeroes , Just need to put 0 instead of y .
\(0 = (x - 5)(x + 4)\)
\((x - 5)(x + 4) = 0\)
_________________________________
Hint :
\(a \times b = 0\)
\(a = 0 \: \: \: or \: \: \: b = 0\)
_________________________________
\(x - 5 = 0\)
Add sides 5
\(x - 5 + 5 = 0 + 5\)
\(x = 5\)
Or
\(x + 4 = 0\)
Subtract sides 4
\(x + 4 - 4 = 0 - 4\)
\(x = - 4\)
Thus the zeroes are :
( - 4 , 0 ) and ( 5 , 0 ) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Anne picked out 3 board games from her cabinet to take to a game night with her friends. She still has more than 10 board games in the cabinet, so she thinks she could bring a few more. Let x represent how many board games were in Anne’s cabinet to start. Which inequality describes the problem?
Answer:
x - 3 > 10
There were more than
13
board games in Anne's cabinet to start.
Step-by-step explanation:
The variable x represents how many board games were in Anne's cabinet to start. Since she has already picked out 3 board games to bring, the expression x–3 represents how many board games are still in the cabinet.
And, since Anne has more than 10 board games still in her cabinet, x–3 must be greater than 10.
This inequality shows the relationship.
x–3>10
Now, solve for x.
x–3
> 10
x–3+3
> 10+3 Add 3 to both sides
x
> 13 Simplify
So, there were more than 13 board games in Anne's cabinet to start.
a college prep school advertises that their students are more prepared to succeed in college than other schools. to verify this, they categorize gpa's into 4 groups and look up the proportion of students at a state college in each category. they find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in gpa. they then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. can they conclude that the grades of their graduates are distributed differently than the general population at the school? test at the 0.05 level of significance.
Answer:
Yes, they can conclude that the grades of their graduates are distributed differently than the general population at the school. This is because the test statistic, chi-squared, is greater than the critical value, which is 7.81. This means that the difference between the observed and expected frequencies is statistically significant.
Step-by-step explanation:
There is a difference between the general population and college prep students in GPA.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Numbers Observed Proportion Expected (O - E) (O - E)² (O - E)²/E
0 - 0.99 19 0.07 14 5 25 1.79
1 - 1.99 28 0.21 42 -14 196 4.67
2 - 2.99 82 0.37 74 8 64 0.865
3 - 3.99 71 0.35 70 1 1 0.0142
Now, X² = the sum of (O - E)²/E
= 8.33
The P-Value is .039662. The result is significant at p < .05.
Hence,
H₀: There is no difference between the general population and the college prep students in GPA.
H1: There is a difference between the general population and the college prep students in GPA.
Test statistic = 8.33
p - Value = 0.039662
Therefore, the alternate hypothesis is true.
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What is the next 2 numbers in the sequence?
343,131413,11131114113
Answer:
111113111114111113 and 111111131111111411111113
Step-by-step explanation:
Here we want to know the next two numbers in the sequence.
The key here is that we shall be placing the same number of digit 1 between each of the digits 3 4 3
We went from a single 1 to triple, so the next will be 5 digit 1 and the next will be 7 digit 1
So the next number after the third will be;
111113111114111113
The next number after this will be;
111111131111111411111113
Donna is a computer repair person. She charges a flat fee of $20 for each computer plus an hourly charge of $9 per hour. Yesterday she worked on 6 computers and spent a total of 3 hours working. How much money did she make?
Answer:
$147
Step-by-step explanation:
20×6=120 9×3=27. 120+27=147
HELPPP!!
tom and jerry have to stuff and seal 63 envelopes for a new marketing campaign jerry can stuff and seal 15 envelopes alone in 2 minutes tom can do 3 envelopes per minute
a) enter the equation that can be used to find the number of minutes, t it takes tom and jerry to stuff and seal envelopes
b) enter the number of minutes t it takes tom and jerry to stuff and seal 63 envelopes together
Answer:
right your relly right and super right
What is the slope of the line shown below?
Answer:
c
Step-by-step explanation:
Find the slope of the line that passes through the points \left(10,8\right)(10,8) and \left(4,12\right)(4,12).
Write your answer as a simplified fraction.
3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).
What is the Equation of line?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
Given, two coordinates of a line \(\left(10,8\right) and \left(4,12\right)\)
The slope of the line formula is:
\(m = \frac{y₂ - y₁}{ x₂ - x₁}\)
Let's substitute our numbers.
\(m = -\frac{8 -12}{4-10}\) = -4/6
The GCF of these two numbers is 2
So, our slope = -2/3
The general equation of a line is y = mx +c
Therefore the equation of the line is y = -2/3x + c
Since, this line passes through ( 10, 8 )
Hence, it must satisfy these coordinates
8 = -2/3 * 10 + c
44/3 = c
Thus the equation of the line is y = -2/3x +44/3
the equation of the line is 3y + 2x = 44.
Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.
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Which of the following is not a property of quadrilaterals?
A.
There are four sides.
B.
There are four diagonals.
C.
There are four vertices.
D.
The measures of the interior angles add up to 360 degrees
Please select the best answer from the choices provided
Answer:
The correct answer for this question is letter "(B) There are four diagonals." It is not a property of quadrilaterals.
Answer:
b
it has 2 diagonals crossing each other
I need help with Trigonometric Ration
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios
Sin θ Opposite Side to θ/Hypotenuse
Cos θ Adjacent Side to θ/Hypotenuse
Tan θ Opposite Side/Adjacent Side & Sin θ/Cos θ
Cot θ Adjacent Side/Opposite Side & 1/tan θ
Sec θ Hypotenuse/Adjacent Side & 1/cos θ
Cosec θ Hypotenuse/Opposite Side & 1/sin θ
Note: Opposite side is the perpendicular side and the adjacent side is the base of the right-triangle. Also, check out trigonometric functions to learn about each of these ratios or functions in detail.Trigonometric Identities
Definition
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The three sides of the right triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
What do you notice about the equation y=2 to the power of X