The expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
We need to expand the expression (y² - 3y³ + x⁻¹) (2m⁰ + y⁻²)
The distributive property allows to multiply a sum by multiplying each term separately and then add all of the products together.
y²(2m⁰ + y⁻²) - 3y³(2m⁰ + y⁻²) + x⁻¹(2m⁰ + y⁻²)
2(1)y² + y²⁻² - 3y³2(1) - 3y³⁻² + x⁻¹2(1) + x⁻¹y⁻²
2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
Therefore, the expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
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a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?
The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
This given test is a test for single sample proportion
The test hypothesis are:
[tex]H_{o} :p=0.20[/tex], null hypothesis
[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis
The test statistic fallows a standard normal distribution and is given by:
[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]
p=0.20
X=47 plants
Sample size, n=500
x, is the sample mean:
x=X/n=47/500
x=0.094
So, test statistic is calculated as:
[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]
Z=-5.93
From the z-table, the p-value associated with Z=-5.93 is approximately 0
The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level
In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim
So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
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If f(x) = 4x5 - x - 3, then what is the remainder when f(x) is divided by x - 3?
The remainder of the division of the given polynomial by (x - 3) is 966.
From the question, we have
f(x) = 4x^5 - x - 3
The remainder of the division is the f(x) at x= 3
f(3) = 4*3^5 - 3 - 3
=972-6
=966
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Between which two integers does the square root of 92 lie?
The square root of 92 lies between 9 and 10.
According to the question,
We have the following information:
Square root of 92
Now, we have to find the two integers between which its square root lie.
So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.
Perfect squares are given below:
1 = 1
2 = 4
3 = 9
4 = 16
5 = 25
6 = 36
7 = 49
8 = 64
9 = 81
10 = 100
Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.
Hence, the square root of 92 lies between 9 and 10.
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The diagram shows a circular disc with radius 6cm in the centre of the disk there is a circular hole with radius 0.5cm
The area of the shaded portion of the circular disc is 112.255 cm².
What is the area of the shaded portion?A circle is a bounded object in which points from its center to its circumference is equidistant.
The area of the shaded portion is the difference between the area of the circular disc and the area of the circular hole.
Area of a circle = πr²
Where :
π = pi = 3.14
R = radius
Area of the circular disc = 3.14 x 6²
Area of the circular disc = 3.14 x 36
Area of the circular disc = 113.04 cm²
Area of the circular hole = 3.14 x 0.5²
Area of the circular hole = 3.14 x 0.25
Area of the circular hole = 0.785 cm²
Area of the shaded portion = area of the circular disc - area of the circular hole
Area of the shaded portion = 113.04 cm² - 0.785 cm²
Area of the shaded portion = 112.255 cm²
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If a interior angle of regular polygon equal 174. 5 how many ide doe a polygon have
Answer:
Each interior angle of a regular polygon is 174°
To find The number of sides of the polygon.
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)
Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.
So, the exterior angle of the given regular polygon :
= (Sum of an interior angle and an exterior angle) - (An interior angle)
= 180° - 174°
= 6°
Let, the number of sides of the regular polygon = n
Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)
So, the exterior angle of the given regular polygon :
= (360°/n)
By, comparing the two values of an exterior angle of the given regular polygon, we get :
360/n = 6
n × 6 = 360
n = 360/6
n = 60
Number of sides of the regular polygon = n = 60
(This will be considered the final result.)
Hence, the number of sides of the regular polygon is 60.
100 PIONTS, FOR ANSWERING 10 Q'S
1. A zoo is keeping track of the weight of a baby elephant. The table shows the weight for the first, second, third, and fourth weeks. Which graph could represent the data shown in the table?
Week Weight
1 138
2 159
3 175
4 185
2. The table shows the amount of money made by a summer blockbuster in each of the first four weeks of its theater release. Which graph could represent the data shown in the table?
A two column table is shown. The first column is titled 'Week' and contains the values 1, 2, 3, and 4 from top to botom. The second column is titled 'Money in dollars' and contains the values 19,600,000, 7,800,000, 3,100,000, and 1,300,000 from top to bottom. (1 point)
3. In the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form?
4. The table shows the relationship between the number of players on a team and the minutes each player gets to play.
Players Minutes
7 35
8 30
9 25
10 20
Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or nonlinear? (1 point)
increasing; linear
increasing; nonlinear
decreasing; linear
decreasing; nonlinear
5. The ordered pairs left parenthesis 1 comma 1 right parenthesis, left parenthesis 2 comma 16 right parenthesis, left parenthesis 3 comma 81 right parenthesis, left parenthesis 4 comma 256 right parenthesis, and left parenthesis 5 comma 625 right parenthesis represent a function. What is a rule that represents this function? (1 point)
y equals 4 superscript x baseline
y equals 4 x
y equals x superscript 4 baseline
y equals x plus 4
6. Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase. Write a function rule for the cost of n sodas. How much would 10 sodas cost? (1 point)
C(n) = 0.5n – 0.75; $4.25
C(n) = 0.75n – 0.5; $7.00
C(n) = 0.5n – 0.5; $4.50
C(n) = 0.75n; $7.50
7. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
{(–2, –4), (–1, –4), (3, –4), (6, –4)} (1 point)
8. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
left-brace left-parenthesis negative 8 comma negative 6 right-parenthesis comma left-parenthesis negative 5 comma 2 right-parenthesis comma left-parenthesis negative 8 comma 1 right-parenthesis comma left-parenthesis 7 comma 3 right-parenthesis right-brace (1 point)
A relation is shown.The numbers negative 6, 1, 2, and 3 are shown in one oval. The numbers negative 8, negative 5, and 7 are shown in another oval. An arrow points from the negative 6 to the negative 8. An arrow points from the 1 to the negative 8. An arrow points from the 2 to the negative 5. And an arrow points from the 3 to the 7. Text at the bottom of the image reads The relation is not a function.
A mapping diagram is shown with two ovals.
The first oval contains the numbers negative 8, negative 5, and 7. The second oval contains the numbers negative 6, 1, 2, and 3.
Arrows point from negative 8 in the first oval to both negative 6 and 1 in the second oval.
An arrow points from negative 5 in the first oval to 2 in the second oval.
An arrow points from 7 in the first oval to 3 in the second oval.
Below the mapping diagram, text reads: The relation is a function.
9. The function b(n) = 12n represents the number of baseballs b(n) that are needed for n games. How many baseballs are needed for 15 games? (1 point)
27 baseballs
150 baseballs
180 baseballs
200 baseballs
10. Tell whether the sequence is arithmetic. If it is, what is the common difference?
2, 7, 13, 20, . . . (1 point)
yes; 5
yes; 6
yes; 2
no
The cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00
Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase
Let n-----> the number of sodas
C(n) -----> the total cost
we know that
The total cost is equal to the number of sodas multiplied by the cost of one soda minus $0.50 of the coupon
so
C(n) = 0.75n – 0.5
For n=10 sodas
substitute the value of n in the equation
C(10) = 0.75(10) – 0.5
7.5 - 0.5
= 7
Therefore, the cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00
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3. What linear equation models the relationship between the values in each table?
a)
P
t
0
11
1 2 3
16
21
26
b)
C
r
1
-2.1
2
-0.6
3
0.9
4
2.4
The linear equations that can satisfy the values given in tabular form are
t = 5d +11 c = [tex]\frac{2}{3}[/tex] r + 2.4How to form line equation using values given in tabular form?
A line equation is of the form y = mx + b where x and y are the coordinate values, m is the slope of the line and b is the y intercept.
Follow these steps to find the line equation:
Write the standard form of the line equation according to the variables given.Find the value of slope m by the formula [tex]m = \frac{y - y'}{x - x'}[/tex] where (x, y) and (x',y') are the given values.Find the value of y-intercept by substituting value of y,x and m in standard form.According to the given data:
Table I)
Standard form: t = md + b
Slope: m = [tex]\frac{16 - 11}{1 - 0}[/tex] = 5
y-intercept: t = 5d + b
Substituting (d, t) = (1, 16) as given in the table
16 = 5x(1) + b
∴ b = 11
Hence linear equation in terms of d and t is t = 5d +11
Similarly, for Table II)
Standard form: c = mr + b
Slope: m = [tex]\frac{2 - 1}{-0.6 + 2.1}[/tex] = [tex]\frac{2}{3}[/tex]
y-intercept: c = (2/3)r + b
Substituting (r, c) = (-2.1, 1) as given in the table
1 = 2/3 x (-2.1) + b
∴ b = 2.4
Hence linear equation in terms of r and c is c = [tex]\frac{2}{3}[/tex] r + 2.4
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What is the angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow?
O
The angle of elevation is
(Simplify your answer. Type an integer. Round to the nearest degree.)
***
The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127
What is the angle of elevation ?At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."
The "tangent" trig function includes the following variables:
Tan = (opposite side) (elevation angle) (adjacent side).
In this case, tan (angle of elevation) equals opposing side / adj opposing side.
is used for
radians, or tan (angle of elevation)
= 47/14 = 3.3571
3.3571 is equal to 73.4127 degree.
The angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow 73.4127 degree
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each of 14 mothers-to-be received 3d ultrasound scans, which showed that 7 of them will give birth to girls. assuming that simultaneous births do not happen (i.e., babies are born one after another), what is the probability that the first two babies that are born happen to be boys? g
Probability that first two babies born are boys is 0.23
Number of Mothers to be received ultrasound = 14
Number of mother giving birth to girl = 7
Number of mother giving birth to boy = 14 - 7 = 7
P(giving birth to girl) = P(G) = 7 / 14 = 0.5
P(giving birth to boy) = P(B) = 7 / 14 = 0.5
Probability that the first two babies that are born happen to be boys =
favorable outcome / total outcome
here, favorable outcome = ⁷C₂
Total outcome = ¹⁴C₂
Required probability = ⁷C₂ / ¹⁴C₂
= (7×6 / 2×1) / (14×13 / 2×1)
= 7×6/14×13
= 42 / 182
=0.23
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what is 6,000 lb/day = ____ t/wk?
Answer: 21 tons/wk
Step-by-step explanation:
6000 lb/day = 3 tons/day
3 t/day * 7 = 21 t/wk
rohit studies 5⅖ hrs daily. He devotes 1¼ hrs of his time for English abd 1½ hrs for Mathematics. How much time does he devote for other subjects
Answer:3 1/2 hours
Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2
a cone is constructed by cutting a sector from a circular sheet of metal with radius 20. the cut sheet is then folded up and welded (see figure). find the radius and height of the cone with maximum volume that can be formed in this way.
The radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].
How to find volume of the cone?
Given
metal radius = R = 20
cone base radius = r
cone height = h
First, we can use Pythagoras theorem
R^2 = r^2 + h^2
r^2 = R^2 - h^2
r^2 = 400 - h^2
Then, we use volume of cone formula
V = 1/3[tex]\pi[/tex] * r^2 * h
V = 1/3[tex]\pi[/tex] * (400 - h^2) * h
V = 1/3[tex]\pi[/tex] * 400h - h^3
To get maximum volume of cone, V'(h) must be 0. So,
1/3[tex]\pi[/tex] * 400 - 3h^2 = 0
400 - 3h^2 = 0
3h^2 = 400
h^2 = 400/3
h = [tex]\frac{20}{\sqrt{3}}[/tex] or 11.55
Next, we find the r with substitution method. So,
r^2 = 400 - ([tex]\frac{20}{\sqrt{3}}[/tex] )^2
r^2 = 400 - [tex]\frac{400}{3}[/tex]
r^2 = [tex]\frac{800}{3}[/tex]
r = [tex]\frac{20\sqrt{2}}{\sqrt{3}}[/tex] or 16.33
Now, we can get maximum volume of cone.
V = 1/3[tex]\pi[/tex] * 16.33^2 * 11.55
V = 1,026.67[tex]\pi[/tex]
Thus, the radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].
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On a math quiz, Tatiana earns 5 points for each question she answers correctly. She wrote this
equation to find how many points she earns (p) based on how many questions she answers
correctly (g):
p = 5q
Identify the dependent and independent variables.
Points earned (p)
Questions correct (g)
Dependent variable Independent variable
Answer:
For points earned (p), the button should be on the left, and for questions correct (q), its on the right.
Step-by-step explanation:
me not know how to speak English!
In the given equation p = 5q, p is the dependent variable and g is the independent variable.
Given that Tatiana earns 5 points for each question she answers.
So, the equation is p = 5q
The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.
The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.
From the above explanation, we can conclude that p is dependent variable and q is independent variable.
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(
−
8
x
2
−
5
x
+
8
)
−
(
−
6
x
2
+
3
x
−
3
)
(−8x
2
−5x+8)−(−6x
2
+3x−3)
The simplified expression representing (−8x²−5x+8)−(−6x²+3x−3) is given as follows:
14x² - 8x + 11.
How to simplify the expression?The expression for this problem is presented as follows:
(−8x²−5x+8) − (−6x²+3x−3).
The first step towards simplifying the expression is removing the negative signal from the expression, inverting the signal of each term inside the second parenthesis, hence:
(−8x²−5x+8) − (−6x²+3x−3) = 8x² - 5x + 8 + 6x² - 3x + 3.
(the first parenthesis can be removed with no changes as there is not any signal in front of it).
Then the like terms, which are the terms with the same variable and same exponent, are added, adding the coefficients and keeping the variables and exponents, as follows:
8x² and 6x²: 8x² + 6x² = 14x².-5x and -3x: -5x - 3x = -8x.8 and 3: 8 + 3 = 11.The simplified expression is obtained by these three additions of the like terms above, hence:
14x² - 8x + 11.
Missing InformationThe problem is incomplete, and it asks for us to simplify the given expression.
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The question is in the picture please help
The perimeter of the shaded region is 135 in.
Given, a triangle ABC in which K, L & M are the mid-points of the sides AB, BC, AC.
Also, the perimeter of the triangle ABC is 108 in.
Now, using the mid-point theorem, we get
KL = 1/2(AC)
LM = 1/2(AB)
KM = 1/2(BC)
Now, the perimeter of the shaded region is,
Perimeter of 3 small triangles + Perimeter of triangle KLM
Perimeter of 3 small triangles = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4)
Perimeter of triangle KLM = AB/2 + BC/2 + AC/2
Perimeter of the shaded region = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/2 + BC/2 + AC/2)
Perimeter of the shaded region = 5/4(AB + BC + AC)
As, we know that AB + BC + AC = 108 in
Perimeter of the shaded region = 5/4×108
Perimeter of the shaded region = 135 in
Hence, the perimeter of the shaded region is 135 in.
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Greg mow and rakes lawn to earn extra money He makes 45 for every lawn he mows and an extra 15 for raking his goal is to earn at least 250 per week
The inequality is 45m + 14 n ≥ 250.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
He makes 45 for every lawn he mows
and an extra 15 for raking
His goal earning= at least 250 per week
let the number of lawn he mow is m and the number of lawn rakes is n.
Then the inequality is
45m + 14 n ≥ 250
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PLEASE CAN SOMEONE HELP ME WITH THIS?! I DO NOT WANT TO FAIL MATH
1(3x+9)/3 = -3x + 11, 3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space respectively
How to solve an algebraic equation?
Given: the algebraic equation, 4(3x+9)/12 = -3x + 11
4(3x+9)/12 = -3x + 11
Divide the Right-Hand Side (RHS) by 4 to get:
1(3x+9)/3 = -3x + 11
Then, on the RHS divide 3x and 9 separately by 3:
3x/3 + 9/3 = -3x + 11
x + 3 = -3x + 11
Take -3x to the Left and take 3 to the right (Note that, this will change their signs):
x + 3 + 3x = 11
x+3x = 11-3
Add/subtract like terms:
4x = 8
Divide both sides by 4:
x = 8/4
x = 2
Therefore, 1(3x+9)/3 = -3x + 11, 3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space accordingly. The solution of the equation is x =2
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Change the following problem to an addition problem.
-5-4
Answer:-9
Step-by-step explanation:
-(5+4)
-(9)
select all of the following statements that are true
1. if 6 > 10, then 8 x 3 = 24
2. 6 + 3 = 9 and 4 x 4 = 16
3. if 6 x 3 = 18 then 4+8=20
4. 5x3=15 or 7+5 = 20
The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .
In the question ,
four statements are given ,
we need to find which statement is true ,
Option(1) ,
if 6 > 10, then 8 x 3 = 24
we know , that 10 > 6 , but it is given that 6 > 10 ,
hence the statement is false .
Option(2)
6 + 3 = 9 and 4 x 4 = 16
we know , that 6+3=9 and 4×4=16
so , the statement is true .
Option(3)
if 6 x 3 = 18 then 4+8=20
we know , that 4+8 = 12 , but it is given that 4+8=20
So , the statement is false ,
Option(4)
5x3=15 or 7+5 = 20
we know , that 7+5 = 12 , but it is given that 7+5=20
So , the statement is false .
Therefore , The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .
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What is x in the equation 2x+6=8
X= 1
First you subtract 6 from both sides to get
2x=2
Then you divide by 2 to get 1
x=1
find the growth or decay rate: y=2.5(0.72)^x
Answer: decay
Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers
the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]
Find the nth term of this quadratic sequence
2, 8, 18, 32, 50
Answer:
it is 20
Step-by-step explanation:
use the formula
hope i helped
what happens to the probability of rejecting the null hypothesis as the obtained statistic decreases
if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases
1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.
2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.
3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.
4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.
if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases and hence 1- [tex]\alpha[/tex] increases which are called the rejection of test sample increases
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the group gives 50% of the money they raised to youth programs. this year the team gave $3,100 to youth programs
Using the percentage of money the group gave out to the youth program, the amount of money the group raised is 6200 dollars.
How to find the amount the group raised?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
The group gives 50% of the money they raised to youth programs. This year the team gave $3,100 to youth programs.
Therefore, the amount of money the group raised can be calculated as follows:
let
x = amount of money raised by the group
Hence,
50% of x = 3100
50 / 100 × x = 3100
50x / 100 = 3100
cross multiply
50x = 3100 × 100
50x = 310000
divide both sides by 50
50x / 50 = 310000 / 50
x = 6200
Therefore, the group raised 6200 dollars this year.
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in a survey of 1000 adult americans, 44.5% indicated that they were somewhat interested or very interested in having web access in their cars. suppose that the marketing manager of a car manufacturer claims that the 44.5% is based only on a sample and that 44.5% is close to half, so there is no reason to believe that the proportion of all adult americans who want car web access is less than 0.50. is the marketing manager correct in his claim? provide statistical evidence to support your answer. for purposes of this exercise, assume that the sample can be considered as representative of adult americans. test the relevant hypotheses using
Answer: No, the marketing manager was not correct in his claim.
We are given that in a survey of 1005 adult Americans, 46.6% indicated that they were somewhat interested or very interested in having web access in their cars.
Suppose that the marketing manager of a car manufacturer claims that the 46.6% is based only on a sample and that 46.6% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50.
Let p = population proportion of all adult Americans who want car web access.
SO, Null Hypothesis, : p 50% {means that the proportion of all adult Americans who want car web access is more than or equal to 0.50}
Alternate Hypothesis, : p < 50% {means that the proportion of all adult Americans who want car web access is less than 0.50}
The test statistics that will be used here are One-sample z-proportion statistics;
T.S. = ~ N(0,1)
where = sample proportion of Americans who indicated that they were somewhat interested or very interested in having web access in their cars = 46.6%
n = sample of Americans = 1005
So, test statistics =
= -2.161
Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives the critical value of -1.6449 for the left-tailed test. Since our test statistics are less than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Step-by-step explanation:
find the common difference d to make 5 comma space x comma space y comma space 32 as a part of an arithmetic sequence.
The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.
It is given that the arithmetic sequence is
5, x, y, 32
We know that for any arithmetic sequence the term aₙ is
aₙ = a + (n - 1)d
where,
a = first term
n = order of the value in the sequence
Since x is the second term
x = 5 + (2 - 1)d
or, x = 5 + d
Similarly,
y = 5 + 2d
32 = 5 + 3d
or, 3d = 27
or, d = 9
Hence, x = 14
y = 5 + 18
= 23
Hence, the common difference is 9
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Graph the function f(x)=-2 \log _{4}(x+8) on the axes below. You must plot the asymptote and any two points with integer coordinates.
Answer:
Asymptote: x= -8
Two points: (-7,0) and (-6,-1)
Step-by-step explanation:
1. Convert log form to exponential form.
y = -2log_4(x+8)
-y/2=log_4(x+8)
4^(-y/2)=x+8
x=4^(-y/2)-8
Note: from here, you can choose to find the inverse of the graph, solve f(x)^-1, and then revert the x and y coordinates to find the f(x) (but I won't be going over that because the question is not asking for the inverse).
2. Make a table by plugging in points.
At this point, all you need to do is to plug in y-values into the equation: x=4^(-y/2)-8
If we plug in y as 0, we get x as -7, and plug in y as -1, we get x as -6, so (-7,0) and (-6,-1) will be your two points.
3. Find the asymptote
An asymptote is a line in which the log function will approach infinitely close to, but never touch. Same deal, we can try to plug in more numbers into our graph -- y as 1 and we will get x as -15/2 (-7.5); y as 3 and we will get x as -63/8 (-7.875); y as 5 and we will get x as-255/32 (-7.96875). At this point, it's pretty clear that our graph is approaching -8. Hence, x= -8
We use vertical asymptote (x=) when graphing log and we use horizontal asymptote (y=) when graphing exponential.
The vertical asymptote is x = -8.
One point on the graph is (-7, 0).
Another point on the graph is (-6, -1).
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To graph the function [tex]f(x) =-2 \log _{4}(x+8),[/tex]
we need to first find the vertical asymptote, which is the value of x that makes the argument of the logarithm equal to zero.
x + 8 = 0
x = -8
So the vertical asymptote is x = -8.
Next, we can choose two integer values of x and find their corresponding values of f(x).
Let's choose x = -7 and x = -6.
When x = -7:
[tex]f(-7) = -2 \log _{4}(-7+8) = -2 \log _{4}(1) = 0[/tex]
So one point on the graph is (-7, 0).
When x = -6:
[tex]f(-6) = -2 \log _{4}(-6+8) = -2 \log _{4}(2) = -2(1/2) = -1[/tex]
So another point on the graph is (-6, -1).
Now we can plot the points and draw the vertical asymptote at x = -8.
Thus,
The vertical asymptote is x = -8.
One point on the graph is (-7, 0).
Another point on the graph is (-6, -1).
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Question 4 (3 points)
Use a graphing calculuator, like desmos, to graph the function, then use the graph to determine the number of turning points, global
maximums and minimums, and local maximums and minimums that are not global.
h(x) = x²(x − 3)(x + 2) (x - 2)
-
Turning Points: 4
Local Maximum(2):
Local Minimum(s):
Blank 1: 4
Blank 2:
Blank 3:
From the graph the turning points are 4 i.e. (-1.467,17.765), (0,0), (1.251,6.665), (2.616,-7.472), global maximum is (-1.467,17.765), global minimum is (2.616,-7.472), local maximum is (0,0) and local maximum is (1.251,6.665).
In the given function, we have to graph the function, then use the graph to determine the number of turning points, global maximums and minimums, and local maximums and minimums that are not global.
The given function is h(x) = x^2(x − 3)(x + 2) (x - 2).
The graph of the given function is below:
As we know that
A local minimum or maximum is represented by each turning point. A turning point may occasionally be the peak or trough of the entire graph. In these situations, we argue that a global maximum or global minimum marks the turning moment.
The output at the greatest or lowest point of the function is referred to as a global maximum or global minimum.
So the terning point of the given function is 4 i.e. (-1.467,17.765), (0,0), (1.251,6.665), (2.616,-7.472).
Global Maximum = (-1.467,17.765)
Global Minimum = (2.616,-7.472)
Local Maximum = (0,0)
Local Maximum = (1.251,6.665)
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write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question
Answer: y=-0.5x-1
Step-by-step explanation:
y=mx+b
Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4) (8,-5)
Hence we use the formula for finding the slope m:
[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]
We substitute the value of (-10,4) into equation (1):
[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]
Hence, y=-0.5x-1
What are the coordinates of the point on the directed line segment from (-9, -10)
to (1,5) that partitions the segment into a ratio of 2 to 3?
The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
The end points of the line segment = (-9, -10) and (1, 5)
The partition ratio = 2 : 3
According to the partition rule
The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]
A = 2
B = 3
Substitute the values in the equation
The x coordinate of the point = -9 + [2(1--9) / 2+3]
= -9 + [2×10 / 5]
= -9 + [20/5]
= -9 + 4
= -5
Similarly,
The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]
= -10+[2(5--10)/2+3]
= -10+[2×15/5]
= -10+[30/5]
= -10 + 6
= -4
Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
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