xy + xz is an even integer & x is even and y + xz is an odd integer & either (x-1) is even or (y-z) is even .
1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)
subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.
2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)
subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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select the most appropriate response. what does it mean when sample results are not statistically significant?
The sample results would be somewhat expected if the null hypothesis were true.
The correct option is (b).
Given,
In the question:
The complete question is this:
Select the most appropriate response.
What does it mean when sample results are not statistically significant?
The null hypothesis is true The sample results would be somewhat expected if the null hypothesis were true.The null hypothesis is wrongThe sample results would be unexpected if the null hypothesis were true.The question is based on MCQ's
Now, According to the question:
What does it mean when sample results are not statistically significant?
It means The sample results would be somewhat expected if the null hypothesis were true.
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you have a set of points with a y:x constant ratio of 3:7. what is the equation of the line passing through these points?
The equation of the line passing through these points i.e (7,3 ) and (14,6) is
y = (3/7) x or 3x - 7y = 0 ,
Which is linear equation of two variables.
A linear equation is an algebraic equation of the form y = mx + b , with only one constant and one first-order (linear) term, m is the slope and b is the y-intercept.
We have given that,
the ratio of y and x is y : x = 3 : 7
So the ratio of x and y can be expressed as ,
x : y = 7 : 3 ( reverse order)
So let's consider two points as
(x₁, y₁)=(7 , 3) and (x₂, y₂) = (14 , 6)
The equation of the line passing through these points will be,
( y - y₁ )/ (y₂ - y₁) = (x - x₁)/(x₂ - x₁)
=> (y - 3)/(6-3) = (x - 7)/(14 - 7)
=> (y - 3)/3 = (x - 7)/7
=> 7(y - 3) = 3( x - 7)
=> 7y - 21 = 3x - 21
=> 7y = 3x
=> y = (3/7) x
Hence, y = (3/7) x is required equation of line.
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A line passes through (9,-1) the point and has a slope of 2/3.
Write an equation in slope-intercept form for this line.
Answer:
y = 2/3 x - 7
Step-by-step explanation:
y = mx + b
y = 2/3 x + b
-1 = 2/3 × 9 + b
-1 = 6 + b
b = -7
y = 2/3 x - 7
Answer:
y = 2x-17
Step-by-step explanation:
We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-1 = 2(x-9)
Distribute
y-1=2x-18
Add 1 to each side
y-1+1 = 2x-18+1
y = 2x-17
This is slope intercept form
Step-by-step explanation:
what is the probability you get this question right if you pick a random answer? a.20% b. 80% c. 25% d. 20% e. 50%
Answer: 80%
Step-by-step explanation:
Consider matrix A
135
3 5
A =
2
8 -1 3
What matrix results from -8*4?
A?
Answer:
[tex]\begin{pmatrix}24&-40&-16\\ -64&8&-24\end{pmatrix}[/tex]
Step-by-step explanation:
Each element of the matrix is multiplied by -8
given cos(-x) = 3/4 and tanx= √7/3, find sin(-x)
The trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
cos(-x) =cosx= 3/4
and tanx=
We need to find sin(-x)
tank is ratio of sinx and cosx
We know that tanx=sinx/cosx
√7/3=sinx/3/4
Apply cross multiplication
sinx=√7/3.3/4
sinx=√7/4
sin(-x)=-sinx=-√7/4
Hence, Trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
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when constructing a confidence interval for a population mean from a sample of size 10, the number of degrees of freedom for the critical value is
the Degree of freedom is 9.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
We have given,
Sample size =n=10
Degree of freedom =n-1=10-1=9
Hence the Degree of freedom is 9
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the population of a town increased from 3600 in 2005 to 5650 in 2011. find the absolute and relative (percent) increase.
Absolute increase in population will be 2050
And percentage increase will be 56.94 %
We have given population in 2005 is 3600
And population in 2011 is 5650
So absolute increase in population = 5650-3600 = 2050
We have to find the percentage increase in population
So relative percentage increase in population will be 2050/3600 *100 = 56.94 %
So population will increase by 60 %
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The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
The error of type I is Despite the fact that the median age is 34, we get to the conclusion that it is not. The appropriate response to this question is option C.
A Type I error is rejecting the null hypothesis when it is actually true. It involves making inferences from statistically significant outcomes even though they might have happened by chance or for other reasons.
The probability of error will depend on the significance level (alpha or) that you choose. In order to determine the statistical likelihood of receiving your results, you established that number at the outset of your investigation (p-value).
The usual level of significance is 0.05 or 5%. The likelihood that the null hypothesis is true is only
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golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. the ratio of the length to the width for these rectangles is called the golden ratio. find the value of the golden ratio using a rectangle with a width of 1 unit
golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. The value of this golden ratio = 1/2 (1 + √5) = 1.618
Ratio:
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
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A function has a constant halving time. What type of function does this represent?.
An exponential decay function is one that has a constant time of halving.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Here,
The function which has a constant halving time is in the following form,
A(t)=A₀(¹/²)^(t/h)
Where: A₀ is the initial amount
h is the half life time or the halving time.
t is the time
A(t) the amount that remains at time t
The previous function represents an Exponential decay function.
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digoxin is a drug often prescribed to treat heart ailments. the purpose of a study by parker et al. (a-4) was to examine the interactions of digoxin with common grapefruit juice. in one experiment, subjects took digoxin with water for 2 weeks, followed by a 2-week period during which digoxin was withheld. during the next 2 weeks subjects took digoxin with grapefruit juice. for seven subjects, the average peak plasma digoxin concentration (cmax) when taking water is given in the first column of the following table. the second column contains the percent change in cmax concentration when subjects were taking the digoxin with grapefruit juice [gfj (%) change]. use the cmax level when taking digoxin with water to predict the percent change in cmax concentration when taking digoxin with grapefruit juice.
Cmax (ngl/ml) with Water Change in Cmax with GFJ (%)
2.34 29.5
2.46 40.7
1.87 5.3
3.09 23.3
5.59 -45.1
4.05 -35.3
6.21 -44.6
2.34 29.5
The graph of the change in Cmax is (see in attachments).
Cmax Change in Cmax predicted percentage
2.34 29.5 22.96%
2.46 40.7 20.62%
1.87 5.3 32.14%
3.09 23.3 8.32%
5.59 -45.1 -40.47%
4.05 -35.3 -10.42%
6.21 -44.6 -52.58%
2.34 29.5 22.96%
Graph:
A graph is a logical visual representation of any data in mathematics. The correlation between the variable values is depicted on the graph. A graph is used in graph theory to depict a group of items that are interconnected in some way. In essence, the vertices or nodes of the objects are mathematical notions, and the edges are representations of the connections between the nodes. In mathematics and statistics, many graph types are used to visually display data. The study of points and lines is the focus of the field of graph theory. It is a branch of mathematics with a focus on graph analysis. The mathematical truth is visually illustrated in this image. Relationships are studied using the graph theory.
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I NEED HELP!! IM RUNNING OUT OF TIME!!!
Domain and range of G?
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Write answers as set notation
For the given set G = {(-8, 7), (-9, 0), (3, 7)}, domain is {-8, -9, 3} and range is {7, 0, 7}.
What is domain?Domain is the values of all inputs, In a function f(x), the set of all values of x is called domain
The given set is,
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Since, domain is the set of all values of x,
And range is the set of all values of y
In the given set,
Domain = {-8, -9, 3}
Range = {7, 0, 7}
The domain is {-8, -9, 3} and range is {7, 0, 7}.
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a rhombus has side lengths of 10 and a diagonal measuring 12. what is the length of the other diagonal?
When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.
What is rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.
Here,
The length of side=10 inch
The length of diagonal= 12 inch
Let the length of diagonal be x.
6²+(x/2)²=10²
(x/2)²=64
x/2=8
x=16 inch
The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.
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Which fraction equals a repeating decimal?
A: 18/81
B: 11/88
C: 1/5
D: 5/8
Answer:
A: 18/81
Step-by-step explanation:
A: 18/81 = 0.222222222.....
B: 11/88 = 0.125
C: 1/5 = 0.2
D 5/8 = 0.625
Could you please give me brainiest for this? I just need 1 more to get to the next level. Thanks!
an initial population of 765 quail increases at an annual rate of 16%. write an exponential function to model the quail population. what will the approximate population be after 4 years?
An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
Population growth is seen to increase at an exponential rate. We use the following to model this growth.
y = A₀(1 + r)ⁿ
where
y = value at time
A₀ = original value
r = rate of growth
n = time elapsed
An exponential function that models the quail population is set up like:
y = 765(1+0.16)ⁿ
so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,
y = 765(1+0.16)⁴
y = 765(1.16)⁴
y = 765* 1.81
to get
y = 1384.65 quails after 4 year has elapsed.
Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
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if the speed of the river is s, write an expression for the time it takes to travel 5 kilometers upstream and an expression for the time to travel 10 kilometers downstream
The time taken to travel upstream will be t = 5/(s - r) and the time taken to travel downstream will be equal to t = 10/(s + r).
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
Speed of boat in still water = s
Distance to travel upstream = 5 km and,
Distance to travel downstream = 10 km
Then, the time taken to travel upstream,
t = d/s
t = 5/(s - r)
And, the time is taken to travel downstream.
t = d/s
t = 10/(s + r)
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Find the least common denominator (LCD) of 11/10 and 4/15 .
I think its 30!
Please let me know if its right!
Please answer number 2 I think I answer is A but please explain how you got your answer.
question a 15-foot ladder is leaning against a wall. the top of the ladder is sliding down the wall at a rate of 2 ft/sec. how fast is the bottom of the ladder moving when it is 12 feet away from the wall?
Speed the top of the ladder is sliding down = 1.6ft/sec when it is 12 feet away from the wall
15-foot ladder is leaning against a wall.
the top of the ladder is sliding down the wall at a rate of 2 ft/sec.
how fast is the bottom of the ladder moving when it is 12 feet away
Using equivalent proportion
15 ft -------------------2ft/sec
12 ft-------------------X ft/sec
Hence X = (12 x 2) ÷ 15 =1.6 ft/sec
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The value of y varies exponentially with respect to x and the 1-unit growth factor is 1.7. Which of the following is the best explanation for the meaning of this growth factor?
Whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
Whenever x changes by 1, the value of y becomes 11.7 times as large as its previous value.
Whenever x changes by 1.7, the value of y doubles its previous value.
Whenever x changes by 1.7, the value of y becomes 1 unit larger than its previous value.
Whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.7)ˣ------>equation(1)
1.7=1- unit growth factor.
When ever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.7ˣ⁺¹
y'=1.7ˣ×1.7----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ
y'=(1.7)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
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a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 155.1-cm and a standard deviation of 1.4-cm. for shipment, 30 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is greater than 155.8-cm. p(m > 155.8-cm)
The probability that the average length of a randomly selected bundle of steel rods is 155.8 then P = 0.174 cm
Given sample size 'n' = 30 steel rods
Mean of the Population = 155.1 cm
Standard deviation of the Population = 1.4 cm
Given x⁻ be the random variable of Normal distribution
Let x₁⁻ = 155.8cm
The probability that the average length of a randomly selected bundle of steel rods is 155.8-cm.
P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)
= P(Z <Z₂) - P(Z<Z₁)
= 0.5 +A(1.629) - (0.5 +A(0.7541)
= A(1.629) - A(0.7541)
= 0.4474 - 0.2734
= 0.1
The probability that the average length of a randomly selected bundle of steel rods is 155.8 cm = 0.174
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Which of these tables (if any) represent a proportional relationship?
Answer: none of them
Step-by-step explanation:
they are not equal and dont look right i dont think im sorry if i get it wrong
Convert to standard form:
[tex]y = \frac{5}{12}x - \frac{1}{2}[/tex]
Show work please
Answer: x=12y+6/5
Let's solve for x.
y=5/12x − 1/2
Step 1: Flip the equation.
5/12x + −1/2 =y
Step 2: Add 1/2 to both sides.
5/12x + −1/2 + 1/2 = y + 1/2
5/12x = y + 1/2
Step 3: Divide both sides by 5/12.
5/12x 5/12 = y + 1/2/5/12
x=12y + 6/5
a radioactive substance decays exponentially. a scientist begins with 110 milligrams of a radioactive substance. after 22 hours, 55 mg of the substance remains. how many milligrams will remain after 32 hours?
A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.
Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.
Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.
Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours
Here, radioactive substance decay. exponentially.
[tex]a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}[/tex]
Taking lo both side, we get ln (1/2) = lne²²K
ln (1/2) = k*22
[tex]k=\frac{ln(1/2)}{22}[/tex]
K = -0.03150669
Substance remains after 32 hours,
t=32 hr
[tex]A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)} \\\\[/tex]
A = 110x 0.283578131
A = 31.19359441
A ≈ 31.1936 mg
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one leg of a right triangle has length 17 inches; the hypotenuse is 31.4 inches. what is the length of the other leg of the triangle?
The length of the other leg of the triangle is 26.4 inches.
Here, we are given that one side of a right angled triangle has length 17 inches and the hypotenuse is 31.4 inches.
Now, the Pythagoras theorem states that, in a right angled triangle, the following equation holds-
[tex]hypotenuse^{2} =height^{2} +base^{2}[/tex]
we already know two of these values so we can calculate the 3rd one.
Let the length of the 3rd side be x inches.
then, substituting the values in the Pythagoras equation, we have-
[tex]31.4^{2}[/tex] = [tex]17^{2}+ x^{2}[/tex]
985.96 = 289 + [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 985.96 - 289
[tex]x^{2}[/tex] = 696.96
x = 26.4
Thus, the length of the other leg of the triangle will be 26.4 inches.
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the screenshot is the work that i need help with
Answer:
Step-by-step explanation:
the national center for health statistics has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall? (round to the nearest hundredth of a percent)
If there is a 0.41% chance that an American citizen will die from falling, then the probability that you will not die from a fall is 99.59%
The chances of an American citizen will die from falling = 0.41%
The probability is the ratio of number of favorable outcomes to the total number of outcomes
The equation will be
The probability = Number of favorable outcomes / Total number of outcomes
The probability that you will not die from a fall = 1 - The chances of an American citizen will die from falling
Substitute the values in the equation
The probability that you will not die from a fall = 1 - 0.41
= 99.59%
Therefore, the probability that you will not die from a fall is 99.59%
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i need help on this! i did the first part though
Answer:
Winning jump = 5.474
Her best jump = 4.76
Step-by-step explanation:
4.25×1.12=4.76
4.76×1.15=5.474
Need Urgent help please. Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) = f(1) = f(2) = 0. find the factored form of f.
Answer:
-2
Step-by-step explanation:
8283’a