A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.
Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).
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Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
[tex]-3a=-3(3,2)\text{ = (-9,-6)}[/tex]Also, vector b = (-5, 6), then;
[tex]2b=2(-5,6)=(-10,12)[/tex]Then, -3a + 2b = (-9, -6) + (-10, 12)
[tex]\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}[/tex]The answer is (-19,6)
14. A function is defined by the
equation y = x² + 3x + 1. Which
statements are true? Select all
that apply.
O The equation in vertex form is y =
5
(x + ²³2) ²
I
A LOT
4
O The equation in vertex form is y = (x + ²)² − ³/
-
O The graph of the function has a minimum of y =
O The domain of the function is all real numbers
-² at x = -²
The correct statements regarding the quadratic function y = x² + 3x + 1 are given as follows:
A. The equation written in vertex-form is: (x + 3/2)² - 5/4.C. The graph of the function has a minimum of y = -5/4 at x = -3/2.D. The domain of the function is all real values.How to analyze the quadratic function?The quadratic function in this problem is defined as follows:
y = x² + 3x + 1.
Hence the coefficients are given as follows:
a = 1, b = 3, c = 1.
The x-coordinate of the vertex is given as follows:
x = -b/2a = -3/2.
The y-coordinate of the vertex is then given as follows:
y = (-3/2)² + 3(-3/2) + 1
y = 9/4 - 9/2 + 1
y = 9/4 - 18/4 + 4/4
y = -5/4.
Hence the vertex-form definition of the quadratic equation is given as follows:
y = (x + 3/2)² - 5/4.
Due to the positive leading coefficient, the vertex means that the function has a minimum of y = -5/4 at x = -3/2.
The domain of the function is all real values, as the quadratic function has no constraints such as a fraction or an even root.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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The rental price of a dacha was $9000. At the end of each month
the price is increased by 6%.
a) Find the price of the house after 1 month.
b) Find the price of the house after 3 months.
c) Find the price of the house after 10 months
a) The price (amount) of the house after 1 month = $9540
b) The price (amount) of the house after 3 months = $10719.14
c) The price (amount) of the house after 10 months = $16117.629
a ) How to find the rental price of the house after 1 month ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 1
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]
The rental price of the house after 1 month = $9540
b ) How to find the rental price of the house after 3 months ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 3
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]
The rental price of the house after 3 months = $10719.14
c ) How to find the rental price of the house after 10 months ?
The rental price of a dacha =Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 10
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]
The rental price of the house after 10 months = $16117.629
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Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the
day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19,
22, 25}
Which equation represents the growth of the puppy?
Select one:
O
O
y = x + 3
y = 3x + 10
y = 10x + 3
y = x + 10
Equation (B) "y = 3x + 10" represents the growth of the puppy.
What are equations?An equation is a mathematical formula where the "equal to" sign appears between two expressions having the same value. Like 3x plus 5 equals 15, for example. Different types of equations exist, such as linear, quadratic, cubic, and others. The three primary forms of linear equations are the slope-intercept form, standard form, and point-slope form.So, the equation that represents the situation:
The weight increase is: (10, 13, 16, 19, 22, 25)We can observe that every time, there is a rise of 3lbs of weight.Now, let 10 be a constant as the weight is starting from 10 lbs.And 'x' be the number of time Salomon tracks the weight.Then:
y = 3x + 10For example, Salomon checks the weight for the 6th time then:
y = 3x + 10y = 3(5) + 10y = 15 + 10y = 25So, the equation is correct.
Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.
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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}
Which equation represents the growth of the puppy? Select one:
A. y = x + 3
B. y = 3x + 10
C. y = 10x + 3
D. y = x + 10
Is the following relation a function? {(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
25 points
No, the given relation is not a function. An association between items of two sets—the domain and the codomain—is known as a binary relation.
What is a function ?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A binary connection in mathematics links elements of one set, referred to as the domain, with elements of another set, referred to as the codomain. A new set of ordered pairs made up of elements from sets X and Y and x in X is known as a binary relation across these sets.
Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, functions represented the idealised relationship between two changing quantities.
Consider the given relation
{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
We need to check whether the given relation is function or not.
A relation is a function if there exist a unique value of y for each value of x.
In the given relation, for x=0.3 there exist more than one value of y.
y=0.6 at x=0.3
y=0.7 at x=0.3
For one input there exist more than one output. Therefore, the given relation is not a function.
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Jayden had $8 last week. He now has $11. what is the percent of change?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
initial money = $8
final money = $11
percent of change = ?
Step 02:
percent of change
percent of change = ( final money - initial money ) / initial money * 100
= ( 11 - 8 ) / 8 * 100
= 3/8 * 100
= 0.375 * 100 = 37.5 %
The answer is:
The percent of change is 37.5 %
Assuming a direct proportion between the distance and time, how far would they travel in 5 hours?
A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
a container of milk contains 8 cups of milk. if paul sets aside $1\frac{2}{5}$ cups of milk for use in a recipe and divides the rest evenly among his three children, how much milk should each child receive? express your answer as a mixed number.
Each child will receive the 1.1 cup of milk.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;
8 - [tex]1\frac{2}{5}[/tex] = 8 - 7/5
= 40- 7/5
= 33/5
= 6.6
The the rest cups of milk = 6.6
Then the rest evenly among his three children 6.6/3 = 1.1
Hence, Each child will receive the 1.1 cup of milk.
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a researcher obtains a list of all prisons in the u.s. she draws a random sample of 75 of the prisons on this list. she then obtains a list of all inmates from the warden at each of the 75 prisons and interviews a random sample of 30 inmates at each prison. this is a:
The researcher draws a random sample using a Multistage cluster sample
At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.
In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.
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f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
Answer: 19
Step-by-step explanation:
[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]
23 - x < 23(1 + 7x)
What does x equal???
[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]
without given any restriction x is all the numbers greater than 0.
NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
what percentage grade should a road have if the angle of elevation of the road is 44 degrees? (the percentage grade is defined as the change in the altitude of the road over a 100100 -foot horizontal distance. for example a 5%5% grade means that the road rises 55 feet for every 100100 feet of horizontal distance.)
For a 44° elevation angle, the grade will be 96%.
Given that,
if the angle of elevation of the road is 44 degrees,
The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)
A tangent ?
One of the six basic trigonometric functions is tangent, denoted as tan().
The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.
[tex]tan \alpha = sin\alpha /cos \alpha[/tex]
The tangent of the angle is the ratio of rise to run.
tan(angle) = grade
tan(44°) ≈ 0.96 = 96%
Therefore, The grade will be 96% for an angle of elevation of 44°.
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please help me understand...
Answer:
A
Step-by-step explanation:
It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).
These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.
There is a negative correlation between the number of years in college and earnings.
Please select the best answer from the choices provided
Or T
F
Answer:
F (false)
Step-by-step explanation:
i hope this helps! Have a good day! c:
The lines represented by the equations
12
y
−
4
x
=
84
12y−4x=84 and
y
=
−
3
x
+
8
y=−3x+8 are
The two linear equations are perpendicular.
What are the lines?
Here we have the two linear equations:
12y - 4x = 84
y = -3x + 8
If we write both of them in the slope-intercept form (as the second one) we will get:
12y - 4x = 84
12y = 4x + 84
y = (4x + 84)/12
y = (1/3)*x + 7
Now, if we take the product of the slopes of the two lines, we get:
p = -3*(1/3) = -1
when this product is -1, the lines are perpendicular, so that is the relation between our lines.
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haresh is writing a coordinate proof involving an isosceles triangle. haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis. what coordinates should he assign to this third vertex of the isoceles triangle?
The third vertex of the isosceles triangle is (a/2, b).
Let one vertex of the triangle lies on the base of the x-axis as 'a' which is written as (a,0)
Similarly, the other vertex of the triangle lies on the base of the y-axis as 'b' which is written as (0,b)
Let other vertex be at origin (0, 0)
An isosceles triangle is a triangle that has at least two sides of equal length.
Hence, the vertex of the triangle is (a/2, b).
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Simplify the expression, 2√54x8 - 4√24x8
Answer:
[tex]-2\sqrt{} 6x^{8}[/tex]
Step-by-step explanation:
Which of the following rational functions is graphed below?
Answer: A.
Step-by-step explanation:
1. The function is even (symmetric about the y-axis)
2. The function F(x) is positive
[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]
[tex]a(a-9)=0[/tex] yyyyyyyyyyyyyyy
Answer:
a = 0 , a = 9
Step-by-step explanation:
a(a - 9) = 0
equate each factor to zero and solve for a
a = 0
a - 9 = 0 ⇒ a = 9
Need an explanation why it’s 46.4
(Please help I need this asap)
Answer:
9 + 7 + 7.2 = 23.2
23.2 x 2 = 46.4
Step-by-step explanation:
4. Your test scores for the semester are 87, 84, and 85. Can you raise your test average to 90with your next test?DefineEquation:Answer:can i have help on 4, 5 and 6?
5.
The sum of three consecutive integers is 228. You can write this situation, in an algebraic way, as follow:
x + (x + 1) + (x + 2) = 228
where the lower number is x, and the largest number is (x + 2).
You solve the previous equation for x:
x + (x + 1) + (x + 2) = 228 eliminate prenthesis
x + x + 1 + x + 2 = 228 sum similar terms
3x + 3 = 228 rest 3 both sides
3x = 228 - 3
3x = 225 divide by 3
x = 225/3
x = 75
Then, the lower number is 75, and the largest one is (75+2) = 77
Please help! Consider the following diagram where the regular polygon ABCDE has center at M, polygon DEHGF is irregular, and point D is on CF.Which of the following statements are correct? Select all that apply.
Solution:
From the given diagram;
The statements that are correct about the given diagram are
b)
[tex]m\angle EDC=108\degree\text{ \lparen Interior angle of a regular pentagon\rparen}[/tex]d) The sum of exterior angles of a polygon is 360°,
Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°
e)
[tex]m\angle ABM=m\angle DCM[/tex]Find the measures of angle B (questions 1-6)
Answer:
1)
b = 42° (corresponding angles, parallel lines)
2)
b + 31 + 90 = 180 (sum of angles on a straight line=180)
b = 59°
3)
b + 34 = 180 (sum of angles on a straight line=180)
b = 146°
4)
b + 30 + 90 = 180 (sum of angles on a straight line=180)
b = 60°
5)
b + 35 + 90 = 180 (sum of angles on a straight line=180)
b = 55°
6)
b = 58° (alternate angles, parallel lines)
"Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?" Please help meee
Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?
Let
x ------> students enrolled last year
we have that
100%+10%=110%=110/100=1.10
so
528=1.10x
solve for x
x=528/1.10
x=480
answer is 480 studentshi I circled the answer but I just need to figure out how to do it
Let's begin by listing out the information given to us:
216^(-2n) = (1/6)^(3n+2)
6 is a factor of 216: 216 = 6³
1/6 = 6^(-1)
⇒ 6^(-2*3n) = 6^[(-1*(3n+2)]
⇒ 6^(-6n) = 6^(-3n-2)
Since both sides are in the same base, we equate the exponents. We have:
-6n = -3n - 2
Add "6n" from both sides, we have:
-6n + 6n = -3n + 6n - 2 ⇒ 0 = 3n - 2
⇒ 3n = 2
A bag contains:• 3 red marbles• 2 2 orange marbles• 1 yellow marble• 4 green marblesA marble is drawn from the bag and replaced 150times. How many times can you predict that a greenmarble or yellow marble will be drawn?
The probability of getting a green of a yellow marble can be determined like this:
Probability = (yellow marbles + green marbles) / total number of marbles
Probability = (1 + 4) / 10
Probability = 5 / 10
Probability = 1/2
By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:
Number of predictions = 150 × 1/2
Number of predictions = 75
Then, the answer is 75 times
Answer:
75 times.
Step-by-step explanation:
There are a total of 10 marbles in the bag.
Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.
In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.
Probability a yellow marble is drawn (in 1 draw) = 1/10.
In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.
So, the number of times for a green or yellow marble
= 60+15= 75.
a 2.0 kg box is at rest on a table, The static friction coefficient μs between the box and table is 0.40, and the kinetic friction coefficient μk is 0.2
Then, a 25N horizontal force is applied to the box.
What is the best estimate of the magnitude of the box's acceleration?
The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².
How to determine the box's acceleration?In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.
Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:
F = μkN = μk(mg)
Where:
μk is the coefficient of kinetic frictional force.N is the normal force.m is the mass.g is the acceleration due to gravity.Substituting the given parameters into the formula, we have;
F = 0.20 × 2.0 × 9.81
F = 3.924 Newton.
By applying Newton's second law of motion, the net force is given by:
∑Fx = Applied force - kinetic frictional force = ma
Acceleration, a = [Applied force - kinetic frictional force]/m
Acceleration, a = [25 - 3.924]/2
Acceleration, a = 21.076/2
Acceleration, a = 10.538 ≈ 11 m/s²
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Ans
Find the Tem 90 is in the
Ap-10₁-8,-6,-4
Answer:
a₉₀ = 168
Step-by-step explanation:
there is a common difference between consecutive terms, that is
- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 10 and d = 2 , then
a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168
the population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. assume the variable is normally distributed. (a) find the probability the cholesterol content for a single egg is between 210 and 220. (b) find the probability the average cholesterol content for 25 eggs is between 210 and 220. (c) find the third quartile for the average cholesterol content for 25 eggs. (d) if we are told the average for 25 eggs is less than 220 mg, what is the probability the average is less than 210 mg?
Using the normal distribution, the probabilities are given as follows:
a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.
b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.
c) Third quartile for the average of 25 eggs: 213 milligrams.
d) Less than 220 if less than 210: 0.1011 = 10.11%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for the cholesterol levels are given as follows:
[tex]\mu = 215, \sigma = 15[/tex]
For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (220 - 215)/15
Z = 0.33
Z = 0.33 has a p-value of 0.6293.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210- 215)/15
Z = -0.33
Z = -0.33 has a p-value of 0.3707.
Hence the probability is:
0.6293 - 0.3707 = 0.2586.
For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:
n = 25, s = 15/sqrt(25) = 3.
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (220 - 215)/3
Z = 1.33
Z = 1.33 has a p-value of 0.9082.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210 - 215)/15
Z = -1.33
Z = -1.33 has a p-value of 0.0918.
Then the probability is:
0.9082 - 0.0918 = 0.8164 = 81.64%.
The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 215)/3
X - 215 = -0.675 x 3
X = 213.
The conditional probability in item d is calculated as follows:
P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.
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-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
The result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
The equation is
(-2/3)w - 4/5 = -3/2
Here we have to rearrange the terms and combine the like terms.
Mover 4/5 to the right hand side of the equation
(-2/3)w = -3/2 + 4/5
(-2/3)w = -7/10
Move the number (-2/3) to the right hand side of the equation
x = -7/10 ÷ (-2/3)
To make it multiplication, take the reciprocal of the the second number
x = -7/10 × (-3/2)
Multiply the numbers
x = 21/20
Hence, the result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20
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