Answer:5.5
Step-by-step explanation:
Graph the line with slope -1 passing through the point (1,-5)
Answer:
please review the attachment
X=a+b+4, a is directly Propotional to y² and b is inversely propotional to y, when Y= 2₁ X=18 and y=1, X=-3, Find X when y=4
Answer:
x = 81
Step-by-step explanation:
If a is directly proportional to y²:
[tex]\boxed{a \propto y^2 \implies a=ky^2}[/tex]
If b is inversely proportional to y:
[tex]\boxed{b \propto \dfrac{1}{y} \implies b=\dfrac{m}{y}}[/tex]
Given equation:
[tex]x=a+b+4[/tex]
Substitute the derived expressions for a and b into the given equation:
[tex]\implies x=ky^2+\dfrac{m}{y}+4[/tex]
Substitute the given values of x and y into the equation to create two equations in terms of k and m.
Given that x = -3 when y = 1:
[tex]\implies -3=k+m+4[/tex]
Given that x = 18 when y = 2:
[tex]\implies 18=4k+\dfrac{m}{2}+4[/tex]
Rewrite the first equation to isolate k:
[tex]\implies k=-m-7[/tex]
Substitute the expression for k into the second equation and solve for m:
[tex]\implies 18=4(-m-7)+\dfrac{m}{2}+4[/tex]
[tex]\implies 18=-4m-28+\dfrac{m}{2}+4[/tex]
[tex]\implies -4m+\dfrac{m}{2}=42[/tex]
[tex]\implies -8m+m=84[/tex]
[tex]\implies -7m=84[/tex]
[tex]\implies m=-12[/tex]
Substitute the found value of m into the expression for k and solve for k:
[tex]\implies k=-(-12)-7[/tex]
[tex]\implies k=5[/tex]
Substitute the found values of k and m into the equation to create an equation for x in terms of y:
[tex]\boxed{x=5y^2-\dfrac{12}{y}+4}[/tex]
Finally, to find the value of x when y = 4, substitute y = 4 into the equation and solve for x:
[tex]\implies x=5(4)^2-\dfrac{12}{4}+4[/tex]
[tex]\implies x=5(16)-3+4[/tex]
[tex]\implies x=80-3+4[/tex]
[tex]\implies x=81[/tex]
A sample of blood pressure measurements is taken for a group of adults, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two samples; then compare the variation.
Systolic
116
130
157
94
155
122
115
138
124
122
Diastolic
82
78
74
51
89
88
56
63
72
83
Answer:
To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.
1. For the systolic sample:
•Find the mean:
mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130
•Find the standard deviation:
sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2
sum = 165.4
std = sqrt(sum/9) = 7.3
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%
2. For the diastolic sample:
•Find the mean:
mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5
•Find the standard deviation:
sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2
sum = 624.75
std = sqrt(sum/9) = 12.24
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%
So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.
composite functions homework
The value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.
What is composite function?In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Given that, h(x) = 4x + 6 and g(x) = -5x.
The value of h(g(x)) is calculated by substituting x = -5x in the equation of h(x).
h(g(x)) = 4(-5x) + 6
h(g(x)) = -20x + 6
Hence, the value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.
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Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=x²
t(x) = 4x³
Write the expressions for (t+s) (x) and (t.s) (x) and evaluate (t-s) (2).
(r+s)(x) =
=
(-) (2) =
X
S
The value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².
What are composite functions?In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a composite function is essentially applied to the output of another function.
Given that,
s(x)=x²
t(x) = 4x³
The value of the composite functions is given as:
(t + s)(x) = t(x) + s(x) = 4x³ + x²
(t.s)(x) = (4x³)x² = [tex]4x^5[/tex]
(t - s)(x) = t(x) - s(x) = 4x³ - x²
Hence, the value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².
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Given the costs associated with insurance, why do companies provide insurance plans to employees?
Company should provide insurance policies to employees because the employees are assets to them.
What is meant by Insurance Policies?An insurance policy is a contract between the insurance company and the person getting the insurance.
Employees are assets of a company.
Companies should look after by insuring this asset like any other asset.
Although it is not the only factor for an employee to stick to a company, it is also one of the contributing factor for the employees to stick to a company longer.
It is a very good benefit for the employee since the premium is paid by the employer for the employee.
Hence companies should provide insurance policies to employees.
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A computer can do 50 trillion additions per second. How many additions can it do in 10 hours? (1 trillion = 10^12)
Answer:
1.8 quintillion or 1,800,000,000,000,000,000
Step-by-step explanation:
What is the standard deviation of the discrete random variable if the variance is 1.56?
Reason:
The standard deviation is the square root of the variance.
[tex]\text{Standard deviation} = \sqrt{\text{variance}}\\\\\text{Standard deviation} = \sqrt{1.56}\\\\\text{Standard deviation} \approx 1.24899959967968\\\\\text{Standard deviation} \approx 1.25\\\\[/tex]
Round the answer however you need to, or however your teacher instructs. I rounded to two decimal places since 1.56 is to two decimal places.
The standard deviation of the discrete random variable if the variance is 1.56 is 1.25
Given that, a discrete random variable has a variance of 1.56, we need to find its standard deviation
We know that,
The standard deviation is the square root of the variance.
Standard deviation = √ variance
Standard deviation = √1.56
Standard deviation = 1.24899959967968
Standard deviation = 1.25
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The width of a table is 4 2/5
feet. The length of the table is 2 1/5
times as long as its width.
Which equation shows the length of the table?
Please answer ASAP
The equation that shows the length of the table is length = 11/5 × 22/5
What is a fraction?A fraction can be defined as the part of a whole number, variable or element.
The different types of fractions are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
Length = 2 1/5 × Width
Width = 4 2/5 feet
Turn into improper fractions
Width = 22/5 feet
Then, length = 11/5 × 22/5
Hence, the equation is 11/5 × 22/5
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What is the solution to the image below?
5
10
-5
10
Answer: x=10
Step-by-step explanation:
Solve the question with Steps
The solution of the question sin(50)sin(80)cos(50)cos(80) is cos^2(80o), the correct option is D.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Given;
sin(50)sin(80)cos(50)cos(80)
Now,
=sin(20°)cos(80°) – cos(20°)sin(80°)
=sin(A-B) = sinA.cosB – cosA.sinB
=sin(20°-80°)
=sin(-60°)
=cos^2(80o)
Therefore, by trigonometry the answer will be cos^2(80o).
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what is 4y - 2x= -8 in slope-intercept form
Find the average rate of change, problem in picture
The average rate of change of the function over the interval (-1, 2) is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
Difference quotient of a function over an interval is also the same concept as the average rate of change of a function.
Average rate of change of a function f(x) over an interval (a, b) is [tex]\frac{f(b) - f(a)}{b-a}[/tex].
Given interval is (-1, 2).
From the graph, f(-1) = -4 and f(2) = 5
Average rate = [tex]\frac{f(2) - f(-1)}{2--1}[/tex] = (5 - -4) / (3) = 9/3 = 3
Hence the given function has an average rate of change over the interval (-1, 2) at 3.
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Find the length of CB
C is 22 and B is 20, then the length of CB is √(22² + 20²) = √(884) = 29.
What is length?Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.
The length of CB can be determined by using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. Since CB is the hypotenuse of a right triangle, the length of CB can be determined by solving the following equation:
C² + B² = CB²
Therefore, when given the lengths of sides C and B, the length of CB can be calculated by taking the square root of the sum of the squares of C and B.
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For every 12 loaves of bread that a bakery bakes for sale, 5 cakes are baked. If 96 loaves of bread were baked, how many cakes would have been baked?
Answer:
Step-by-step explanation:
Here's a step by step explanation of how to calculate the number of cakes baked if the bakery baked 96 loaves of bread:
First, determine the number of sets of 12 loaves of bread that were baked:
96 loaves of bread ÷ 12 loaves per set = 8 sets of 12 loaves
Next, determine the number of cakes baked for each set of 12 loaves of bread:
For every set of 12 loaves, 5 cakes are baked.
Finally, multiply the number of sets by the number of cakes baked per set to find the total number of cakes baked:
8 sets × 5 cakes per set = 40 cakes
So, if the bakery baked 96 loaves of bread, they would have baked 40 cakes.
Answer:
40
Step-by-step explanation:
12 times 8 equals 96 and 5 times 8 equals 40, there for 40 cakes will be backed
Please help me with this !
The length of side AB within quadrilateral ABCD is 14.301 meters.
How to determine the length of a missing by trigonometry
In this problem we find a geometric system formed by a quadrilateral and two diagonals, whose parameters are listed below:
CD = 20 m
m ∠ BCD = 20°
m ∠ ACB = 40°
m ∠ ADC = 45°
m ∠ ADB = 50°
The missing side can be found by combining law of sine and law of cosine:
Law of sine
20 / sin 65° = BD / sin 20°
BD = 7.548
20 / sin 75° = AD / sin 60°
AD = 17.932
Law of cosine
AB = √(AD² + BD² - 2 · AD · BD · cos ADB)
AB = √(17.932² + 7.548² - 2 · 17.932 · 7.548 · cos 50°)
AB = 14.301
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A survey is taken at a movie theater in Wayside. The first 100 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 100 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the total number of people who go to the movie theater, and the sample is the first 100 people at the theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Wayside.
The population is the number of people in the town of Wayside, and the sample is the number of people who go to the movie theater.
What is true about the population and sample of the survey is that;'
The population is the total number of people who go to the movie theater, and the sample is the first 100 people at the theater.
How to Identify the Population and sample of the data?In statistics, the population is defined as the entire group that you want to draw conclusions about. However, the sample is defined as the specific group that you will collect data from. The size of the sample is always less than the total size of the population. In research, a population doesn't always refer to people.
Now, we are told that a survey is taken at a movie theater in Wayside. The first 100 people who entered the theater were asked about their favorite type of movie.
Thus, the sample will be 100 people surveyed as they are part of the entire people at the movie theater.
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a grocery store got a delivery of 24 pounds of almonds into containers of 0.75 pounds of almonds in each how many containers can they fill with almonds?
Answer:32
Step-by-step explanation: 24 divided by .75=32
Help me with this question
The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The radius and height of the cone and the cylinder are the same. Then the ratio of the volume of the cylinder to the volume of the cone is 3. Then we have
(Volume of the cylinder) / (Volume of the Cone) = 3
Volume of the cylinder / 222 = 3
Volume of the cylinder = 666 cubic cm
The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.
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Which is a counterexample of the following conditional? "If a number is divisible by seven, then it is odd." 28 21 7 1
PLS JUST DROP THE ANSWER
The counterexample of the given conditional statement is "14 is even number and is divisible by 7."
What is a counterexample?Counterexamples are used in math to contradict a statement. Counterexamples are used to prove the limitations of possible theorems.
The given statement is "If a number is divisible by seven, then it is odd."
Number, 14, 28, 42, 56 are even numbers and they are divisible by seven.
Therefore, the counterexample of the given conditional statement is "14 is even number and is divisible by 7."
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Answer: the answer is 28
Step-by-step explanation: 28 is divisible by 7 and it is a even number
(a) The perimeter of a rectangular parking lot is 330 m.
If the length of the parking lot is 92 m, what is its width?
Answer: Width = 73 m
Step-by-step explanation:
Perimeter = Length(2) + Width(2)
330 - (92 x 2)
330 - 184 = 146
146 = Width of 2 sides
146/2 = 73 m
A soccer player has a large cylindrical water cooler that measures 3.5 feet in diameter and is 2 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
575.44 gallons
143.86 gallons
76.93 gallons
19.23 gallons
There are approximately 205.33 gallons of water in the water cooler when it is completely full.
What is the volume of the cylinder?
The volume of a cylinder is given by the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height of the cylinder.
The volume of the cylindrical water cooler is:
V = πr^2h
where r is the radius and h is the height. Substituting the given values:
V = 3.14 x (3.5/2)^2 x 2
= 27.44 cubic feet
To convert cubic feet to gallons, we can multiply by 7.48 gallons/cubic foot:
V = 27.44 x 7.48
= 205.32 gallons
Rounding to the nearest hundredth, the answer is:
205.32 ≈ 205.33 gallons
Hence, there are approximately 205.33 gallons of water in the water cooler when it is completely full.
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Answer:
The correct answer is 143.86 gallons
Step-by-step explanation:
PLEASEEEEE HELPPPPP!!!
The required trigonometric ratios are as follows: sin t = 1/2 and cos t = √3/2.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
According to the given figure, we have a right triangle ΔABC which has:
AB = 1/2
BC = √3/2
CA = AB² + BC²
CA = √(1/2)² + (√3/2)²
CA = √1/4 + 3/4
CA = √4/4 = 1
As we know that the trigonometric ratios are as follows:
sin (180°- t) = AB/CA
sin t = (1/2)/1
sin t = 1/2
cos (180°- t) = BC/CA
cos t = (√3/2)/1
cos t = √3/2
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Find the remaining trigonometric functions of 0 if
17
8
CSC 0 =
-
and cos > 0. Answer exactly.
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
COWS
Tt
Lakayja brushed 24 cows in 2 hours. How many can she brush in 15 hours?
Answer: 180
Step-by-step explanation: Hope this helps :D
Answer:
180 Cows
Step-by-step explanation:
24 in 2 = 12/hr
12 cows x 15 hours = 180 cows
Help me with this question……
Answer:
the square root(route?) of four
Step-by-step explanation:
2x2=4, that dot is near two....
WILL GIVE 200 POINTS !!!!> find the x intercept and the y intercept. write each intercept as an ordered pair. y=5x-10
Answer:x intercept (2,0)
Yintercept (0,-10)
Step-by-step explanation:
y=mx+b b= y intercept
To find x you just solve
Y=5x-10
10=5x
2=x
using the midpoint approach calculate the percentage change in price for laundry detergent that decreases from 4.10 to 3.50 as a result quantity demandd increases from 210 to 230
The percentage change in the price is 15.78% decrease.
What is the percentage?
A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.
Here are some percentage examples:
10% is 1/10 of a fraction.20% is equal to a 1/5 portion.25% is equal to 1/4 fractions.Now,
Initial price=4.1
Final price=3.5
Change=3.5-4.1= -0.6 , minus means decrease in price
final value + initial value=7.6
then
percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100
=0.6/3.8*100
=0.1578*100
=15.78%
hence,
The percentage change in the price is 15.78% decrease.
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Divide the following using long division method: 96431÷63
[tex]96431 \div 63 \: longdivision \: method[/tex]
Answer:
So the answer is 1535 with a remainder of 18.
Step-by-step explanation:
63
96431
-----
96431 - 54249 = 42182
-----
42182
4218
-----
420
---
18
---
Find the area of the figure. Round to the nearest tenth, if necessary.
The solution is the area of the figure is 53.17.
What is area of trapezoid?The area of a trapezoid is found using the formula, A = ½ (a + b) h,
where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .
here, we have,
from the given figure we get,
a = 10,
b = 6
h = 8
so, A = 64
again, the cut triangle is a equilateral triangle with side = 5
then, area of triangle = √3/4 * 5^2
= 10.82
so, required area = 53.17
Hence, The solution is the area of the figure is 53.17.
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