The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.
What is null hypothesis ?
The null hypothesis is a statement that there is no statistical significance between the results of an experiment and a certain theoretical prediction or postulate. It is usually denoted by H0 and it is a statement of "no effect" or "no difference".
The null hypothesis is that the mean mpg of the vans is equal to the manufacturer's rating of 28.228.2 mpg, and the alternative hypothesis is that the mean mpg of the vans is less than the manufacturer's rating.
We can use the t-test statistic to determine the probability of observing a sample mean as extreme or more extreme than the one computed from the data, assuming that the null hypothesis is true.
The t-test statistic is: (sample mean - population mean) / (standard deviation/sqrt(sample size)) = (28.028.0 - 28.228.2) / (2.62.6 / sqrt(2727)) = -3.34
The p-value is the probability of observing a t-value as extreme or more extreme than -3.34, assuming that the null hypothesis is true. With a sample size of 2727, we can use a t-distribution table to find that the p-value is less than 0.01.
The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.
To learn more about null hypothesis visit : brainly.com/question/28920252
#SPJ4
What is they system of inequalities associated with the following graph?
Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.
Step-by-step explanation:
f(x) = (3)*
9(x) = ²* - 3
Which statement about f(x) and its translation, g(x), is
true?
O The range of g(x) is. {y ly>0} and the range of f(x)
is {yly > -3}.
The range of g(x) is, {y ly> 3} and the range
of f(x) is {yly> 0}.
O The asymptote of g(x) is the asymptote
of f(x) shifted three units down.
O The asymptote of g(x) is the asymptote
of f(x) shifted three units up.
The true statement is:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = [tex](2/5)^x[/tex]
and, g(x) == [tex](2/5)^x[/tex] - 3
Now, Using translation the '-3' in g(x) shows the Vertical Translation down by 3 units.
Hence, The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Learn more about Function here:
https://brainly.com/question/12431044
#SPJ1
What is an example of one solution?
A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need.
One possible solution to the problem of food insecurity is to start a food pantry. A food pantry is a place where people can donate non-perishable food items for those in need. These items can include canned goods, boxed goods, and non-perishable items. People can then come to the pantry and take what they need. This helps to ensure that people in the community have access to the food they need.
A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need. People can come to the pantry and take what they need, providing access to food for those in the community.
learn more about solution here
https://brainly.com/question/30109489
#SPJ4
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y^2 + 5y - 750 = 0
y(y + 5) = 750
750 - y(y - 5) = 0
Step-by-step explanation:
students majoring in psychology surveyed 200 of their fellow students about their dreams. the results of the survey are shown in the venn diagram. let b be the event that the participant dreams in black and white and let c be the event that the participant dreams in color. a venn diagram titled student dreams. one circle is labeled b, 4, the other circle is labeled c, 10, the shared area is labeled 12, and the outside area is labeled 174. what is the probability that a randomly selected participant dreams in black and white or color? 0.06 0.07 0.13 0.26
The probability that a randomly selected participant dreams in black and white or color is 0.01
The probability that a randomly selected participant dreams in black and white or color is the sum of the probabilities of the individual events (dreaming in black and white or dreaming in color) and the probability of the intersection of the two events (dreaming in both black and white and color).
The probability of dreaming in black and white is the number of participants who dream in black and white divided by the total number of participants surveyed:
P(b) = 4/200
The probability of dreaming in color is the number of participants who dream in color divided by the total number of participants surveyed:
P(c) = 10/200
The probability of dreaming in both black and white and color is the number of participants who dream in both black and white and color divided by the total number of participants surveyed:
P(b ∩ c) = 12/200
The probability of dreaming in black and white or color is the sum of the individual probabilities and the intersection probability:
P(b ∪ c) = P(b) + P(c) - P(b ∩ c) = 4/200 + 10/200 - 12/200 = 2/200 = 1/100
The probability that a randomly selected participant dreams in black and white or color is 1/100.
To learn more about probability visit: brainly.com/question/30034780
#SPJ4
B C= 16 c m, and is the diameter of the circle,A B CDis a rectangle, a section A B is 12 taller thanB C.
Determine the areaSfor the given figure!
In the calculations, it is assumed thatπ≈ 3!
Area of a semicircle S1 =
Area of the figure S =
We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.
Determine the area ?We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.
The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.
The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
To learn more about area refer
https://brainly.com/question/29301914
#SPJ1
All changes saved
1. A store offers a discount of 40% off any one regular-price item. The price paid after this discount is represented by s(2). Employees also receive 10% off any purchases; the price paid after this discount is
represented by e(z). Which of the following represents the composite function of applying the employee discount first, and the store discount second?
Oe(s(z)=0.04z
Oe(s(z))=0.54z
Os(e(z))=0.54z
Os(e(z)) = 0.04z
A function that depends on another function is referred to as a composite function.
What is composite function?A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. For instance, f(g(x)) is the composite function created when x in f is replaced with g(x) (x). You can interpret f(g(x)) as "f of g of x." Replace the rightmost function with the middle function, then this with the leftmost function to find a composite function made up of three functions. For instance, if g(x)=x2, f(x)=3x+1, and h(x)=1/x, h(g(f(x))=1/(3x+1)2 is the result.Let's say the price of an item is $1
Scenario #1 - 40% off $1 = 40 cents OFF
The discounted price = 60 cents
Now the 10% off of 60 cents
60-6 = 54 cents.
Scenario #2 - 10% of $1
The discounted price = 10 cents
100(cents) - 10 = 90 cents
Now the 40% off of 90 cents
90-36 = 54 cents
Let's try another value to confirm
Let's say the price of an item is $2
Scenario #1 - 40% off $2 = 80 cents OFF
200-80= 120 = $1.20
Now the 10% off of $1.20
120-12= 108 = $1.08
Scenario #2 - 10% off $2 = 20 cents OFF
200-20 = 180= 1.80
Now the 40% off of $1.80
180-72 = 108 = 1.08
The complete question is,
A store offers a discount of 40 off any one regular-priced item. employees also get 10% off any purchases. in which order should the discounts apply so that the employee pays the least amount?
A. Employee discount then store discount
B. They are both the same
C. Store discount then employee discount
To learn more about composite function refer to:
https://brainly.com/question/10687170
#SPJ1
(1.1: geometry) suppose we want to express the point (2,3) in r2 as the solution space of a system of linear equations. (a) what is the smallest number of equations you would need? write down such a system. (b) can you add one more equation to the system in (a) so that the new system still has the unique solution (2,3)? (c) what is the maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3)? (d) is there a general form for the equations in (c)?
(a) A system of two equations, x=2 and y=3, is needed to express (2,3) in R2. (b) No, only two equations can express (2,3) in R2. (c) The maximum number of distinct equations that can be added is three. (d) Yes, the general form for the equations is x-2=0, y-3=0, and z=0.
(a) The smallest number of equations you would need is two. The system of linear equations would be:
x + 2y = 6
2x + 4y = 12
(b) Yes, you can add one more equation to the system in (a) so that the new system still has the unique solution (2,3). The equation would be:
3x + 6y = 18
(c) The maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3) is three. The equations would be:
x + 2y = 6
2x + 4y = 12
3x + 6y = 18
(d) Yes, there is a general form for the equations in (c). The general form is:
ax + by = c, where a, b, and c are constants.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 366.67 b 373.33 с 333.33 d 350 e 379.15
For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33
What is keyboard navigation to select an answer?By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.
The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.
This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.
For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33
To learn more about keyboard visit:
brainly.com/question/24921064
#SPJ4
Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.
By using the properties of real numbers the given expression can be written as -8y.
What is solving an expression?
Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.
Given:
The given expression is, [tex]\frac{4}{3}(-6y)[/tex]
According to the distributive property of real numbers, if a, b, c are three real numbers the,
a(bc) = (ab)c
Using the associative property of multiplication, the given expression can be written as,
[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]
Hence, by using the properties of real numbers the given expression can be written as -8y.
To know more about solving an expression, click on the link
https://brainly.com/question/723406
#SPJ4
what does the value of the sample correlation coefficient indicate about the relationship between the admit rate () and the -yr grad. rate ()?
The sample correlation coefficient, is represented as r, measures the strength of correlation and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.
The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.
A positive correlation tells us that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.
So, the value of the sample correlation coefficient between the rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as correlated and how strong is this correlation occurs.
To know more about correlation coefficient, , click here:
brainly.com/question/15577278
#SPJ4
x • 2/5 = 4 what is X standing for?
[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]
Answer: X stands for 10
Step-by-step explanation:
If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4
To convert a fraction to a decimal, you simply divide the numerator by the denominator.
the screamers are coached by coach yells at. the screamers have $12$ players, but two of them, bob and yogi, refuse to play together. how many starting lineups (of $5$ players) can coach yells lot make, if the starting lineup can't contain both bob and yogi? (the order of the $5$ players in the lineup does not matter; that is, two lineups are the same if they consist of the same $5$ players.)
The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.
What is starting lineups?An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.
Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.
⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!
⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)
⇒ ¹⁰C₄ = 210
Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.
⇒ ¹⁰C₄ = 210
Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.
⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!
⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)
⇒ ¹⁰C₅ = 252
To get the total number of starting lineups, we add the number of lineups in each of the cases:
Case 1 + Case 2 + Case 3
= 210 + 210 + 252 = 672
The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.
To learn more about starting lineups visit:
brainly.com/question/28140396
#SPJ4
a pulley on a dock is 5 feet above the water level. a rope on the pulley is attached to a boat in the water. the rope is being pulled in at a rate of 3 ft/sec. find the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon, when the boat is 12 feet from the dock. please give an exact simplified answer.
The rate of change of the angle of elevation is -2π/3 radians/second.
We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.
The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.
Using the tangent ratio, we can calculate the angle of elevation:
tan(θ) = opp/hyp = 5/12
θ = arctan(5/12) = 0.927 rad
Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:
rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second
Learn more about rate here
https://brainly.com/question/13481529
#SPJ4
solve the given initial-value problem. d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0
The solution to the given initial-value problem is x(t) = c1(e-ωt - eωt) = 2c1 sin ωt
The given initial-value problem is a second-order differential equation: d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0
First, we can solve the homogeneous equation d2x dt2 + ω2x = 0 using the method of characteristic equation. The characteristic equation is r2 + ω2 = 0, which has two solutions r1 = -ω, r2 = ω.
The general solution to the homogeneous equation can be expressed as:
x(t) = c1e-ωt + c2eωt
Next, we can solve the non-homogeneous equation d2x dt2 + ω2x = f0 sin ωt. Since the right-hand side of the non-homogeneous equation has a sinusoidal form, we can use the method of variation of parameters to solve it.
The particular solution can be expressed as:
x(t) = A sin ωt + B cos ωt
By substituting the initial conditions, we can get:
A = 0, B = 0
Therefore, the solution to the given initial-value problem is:
x(t) = c1e-ωt + c2eωt
The constant c1 and c2 can be determined by the initial conditions:
x(0) = c1 + c2 = 0
x'(0) = -ωc1 + ωc2 = 0
Therefore, c1 = -c2 and c1 + c2 = 0.
Hence, the solution to the given initial-value problem is:
x(t) = c1(e-ωt - eωt) = 2c1 sin ωt
Learn more about initial-value problem here:
https://brainly.com/question/8736446
#SPJ4
Fwam and his children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $4.50 and each brownie costs $1.75. Fwam has a total of $50 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b.
The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.
What is inequality?The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.
How to write the inequality in this situation?1. List the variables
b = cupcakes
c = brownies
4.50 = price of the cupcakes
1.75 = price of the brownies
50 = total money
2. Relate the variables
1.75b + 4.50c ≤50
Each product should be multiplied by its price
The total money can be equal to or less than 50 (≤)
The products should be added
Learn more about inequality in: https://brainly.com/question/20383699
#SPJ1
How do you know if two ratios are proportional?
Answer: Ratios are proportional if they represent the same relationship.
Step-by-step explanation:
One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
What is the topic in Grade 7 math?
Grade 7 maths includes integers, shapes, and symmetry etc. that is incorporated with the earlier study of previous grades.
Grade 7 math covers many topics, including: number sense and operations, geometry, data analysis, probability and statistics, expressions and equations, and problem solving. Number sense and operations involves understanding the properties of integers, rational numbers, and real numbers, and how to use them in operations and equations. Geometry focuses on understanding the properties of shapes and angles, and how to measure, construct, and classify them. Data analysis involves collecting, organizing, and interpreting data, as well as understanding the concept of probability. Expressions and equations involves solving equations and manipulating algebraic expressions. Finally, problem solving involves using the knowledge from all of the topics to solve real-world problems. Grade 7 math builds on the fundamentals learned in earlier grades, and is essential for success in math classes in the future.
Learn more about integers here:
https://brainly.com/question/490943
#SPJ4
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer:
Sin A / A = Sin B / B Law of Sines
Sin 73 / X = Sin 59 / 18 Application of Law of Sines
X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1
Car rental company A charges a set fee of $75 for the week plus an additional $0.07 per mile driven. Car rental company B shares a set fee of $100 for the week plus an additional $0.03 per mile driven. When would the two car companies cost you the same amount of money?
Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.
What is an equation?An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.
Equations use the equation symbol (=) to depict the equality of the expressions.
Company A Company B
Fixed rental charge $75 $100
Rental charge per mile $0.07 $0.03
Let the number of miles driven = m
Equations:Total cost of Company A's rental = 75 + 0.07m
Total cost of Company B's rental = 100 + 0.03m
For the cost to be the same, 75 + 0.07m = 100 + 0.03m.
Solving for m:
75 + 0.07m = 100 + 0.03m
0.07m - 0.03m = 100 - 75
0.04m = 25
m = 625
Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
The total area of the two triangles is _____ square inches.Numerical Answers Expected!Answer for Blank 1:
The total area of the two triangles is 28 square inches.
Step 1: Calculate the area of the first triangle.
The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.
Area of a triangle = (1/2) * Base * Height
Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.
Step 2: Calculate the area of the second triangle.
The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.
Area of a triangle = (1/2) * Base * Height
Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.
Step 3: Add the areas of the two triangles.
Total area = 6 + 8 = 14 square inches.
Learn more about area here
https://brainly.com/question/13194650
#SPJ4
Q1.Which of following is not a polynomial?
a)x^3+√3x+5 b)x^3+√2x+6 c)x^2-3x+2 d)(x-1) (x+1)
Q2. If x/y + y/x= -1 (x,y isn't zero), then value of x^3-y^3
a)1 b)-1 c)0 d)1/2
Q3.One of factors of (25x^2-1)+(1+5x^2) is-
a)5+x b)5-x c)5x-1 d)10x
To make the polynomial monic, divide even by leading term first.
Then, in order to create an equation even without linear element, replace x = y a12 for the supplied values of x2 + a1x + a0.
A monic polynomial is what?A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.
x3=y3 and y2=x2+xy+y2.
Finding a common denominator allows us to determine that x2 + y2 + xy=1 if xy+yx=1.
By multiplying by xy:
x2+y2=−xy
move every term to the left:
x2+xy+y2=0
Consequently, x3y3=(xy)(x2+xy+y2)=(xy)
x/y+y/x+1=0
=>(x²+y²+xy)/xy=0/1
=>x²+xy+ y²=0——(1)
Now, Since,x³-y³=(x-y)(x²+xy+y²)
=>x³ -y³=(x-y)(0). [from equation (1)]
=>x³ -y³=0,Ans.
To know more about the polynomial monic visit:
https://brainly.com/question/30117170
#SPJ4
Carol has three times as many 10 dollar bills as 5 dollar bills. she has a total of $350.
how many five dollar bills does carol have? how many 10 dollar bills?
A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = cos t . At time t = 0, its position Is x = 3.
(a) Find the velocity and position functions for the particle.
(b) Find the values of t for which the particle is at rest.
a) The velocity and position functions are given as follows:
Velocity: v(t) = sin(t).Position: s(t) = -cos(t) + 3.b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...
How to obtain the functions?The acceleration function for this problem is defined as follows:
a(t) = cos(t).
The velocity function is the integral of the acceleration function, hence it is given as follows:
v(t) = sin(t).
(as the integral of cos(t) is sin(t).)
The particle will be at rest when:
v(t) = 0.
Hence:
sin(t) = 0
t = arcsin(0)
t = kπ, k = ± 1, ± 2, ± 3, ...
The position function is the integral of the velocity function, hence it is given as follows:
s(t) = -cos(t) + 3.
As:
The integral of the sine function is the negative cosine function.The initial position of 3 represents the constant of integration.More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
Factorise : 2 5 x x 19x 42 3 2 − − +
Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).
What is factorization?Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.
The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.
In this case one rational zero is x=2.
This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)
That is:
2x³-5x²-19x+42/ x-2
= 2x² - x - 21, this means that
2x³-5x²-19x+42 = (2x² - x - 21) * (x-2)
From the above, our constants are given as:
a = 2, b = -1 and c = 21
Multiply the constant terms by the leading coefficient.
a *x = -42
Find out two number that multiply to a*c = -42 and add b = -1
Next we identify all pairs of numbers with a product of -42. They are:
-1 * 42-2 * 21-3 * 14-6*71 *-422 * -213 * -146 * -7Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.
Next, replace the middle term -1x with 6x-7x to get:
(2x² −x−21) * (x-2) =(2x² +6x−7x−21) * (x-2)
If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).
Learn more about Factorization:
https://brainly.com/question/25829061
#SPJ1
Full Question:
Factorise 2x³-5x²-19x+42
The dimensions for a rectangular prism are x+5 for the length, x+1 for the width, and x for the height. What is the volume of the prism?
The volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.
Rectangular Prism:
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here.
The Volume of a Rectangular Prism Formula is,
The volume of a Rectangular Prism (V) = l × b × h
Where,
“b” is the base length of the rectangular prism
“l” is the base width of the rectangular prism
“h” is the height of the rectangular prism
The formula for the volume of a rectangular prism is length x width x height. So, the volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.
To learn more about rectangular prism, refer to the link:brainly.com/question/21308574
#SPJ4
a survey company that wants to know the views of the average person sends an agent to a shopping mall to interview anyone who is available. the people who are interviewed constitute a
The people who are interviewed constitute a convenience sample.
If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.
In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.
To know more on convenience sample
https://brainly.com/question/1413932
#SPJ4
MARKING BRAINLIEST! please help asap
Answer: the answer is negative 5
Step-by-step explanation:
when serenity goes bowling, her scores are normally distributed with a mean of 195 and a standard deviation of 14. what is the probability that the next game serenity bowls, her score will be between 183 and 218, to the nearest thousandth?
The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
Given that,
Mean = 195
Standard deviation = 14
Thus, the probability between 183 and 218 is the ρ value of z when x = 195
Subtracting by the ρ value of z when x = 183
so, x = 218
z = 218-195/14 = 1.64
when x = 183
z = 183-195/14= -0.85
Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886
Now, 0.94950 - 0.21886 = 0.73064
Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
To know more about probability visit: brainly.com/question/30034780
#SPJ4
Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:
I WILL MARK IT BRAINLIEST
If Last year, Christine had $20,000 to invest. The amount that she invest in each account is First account $16,000 and Second account: $4,000.
How to find the amount invested ?Let x represent the amount Christine invested in an account that paid 8% interest
Let y represent the amount Christine invested in an account that paid 10% interest
x + y = 20,000
.8x + .010y = 1920
Multiply each sides of this equation by 100 to remove the decimal points.
8x + 10y = 192,000
8(20,000-y) + 10y = 192,000
160,000 - 8y + 10y = 192,000
2y = 32,000
y = 32,000/2
y = $16,000
So,
x = 20,000 - 16,000
x = $4000
Therefore the First account is $16,000 and Second account is $4,000.
Learn more about amount invested here:https://brainly.com/question/25300925
#SPJ1
