Answer:
Step-by-step explanation:
hello
last step is not good
from
(x+9)(x-1) = 0 we can write
<=> x+9 = 0 or x-1=0
<=> x = -9 or x = 1
so the solutions are -9 and 1
hope this helps
There are 11 seats in a vehicle. How many ways can 11 people be seated if only 2 can drive
Answer:
They can be seater in 7,257,600 ways
Step-by-step explanation:
Arrangment formula:
Number of ways that n elements can be arranged, that is, distributed in n places is:
[tex]A_{n} = n![/tex]
In this question:
11 seats(driver and other 10).
Only 2 people can drive.
So
The driver can be 2 people.
The other 10 people are arranged in 10 positions.
[tex]T = 2A_{10} = 2*10! = 7257600[/tex]
They can be seater in 7,257,600 ways
PLEASE HELP. FINAL TEST QUESTION!!!!
Devon is having difficulty determining if the relation given in an input-output table is a function. Explain why he is correct or incorrect.
Step-by-step explanation:
input x , output y
if x= x1 then y=y1 and y1 is the only value then it is a function
if we get multiple values of y then it is not a function
Write an expression involving integers for each statement a) moving 4 steps left, then moving 9 steps right b) on 3 separate occasions, Shari lost 2 pencils can someone answer me in separate parts A and part B
Answer:
(a)[tex]-4+9[/tex]
(b)[tex]-2 \times 3[/tex]
Step-by-step explanation:
Part A
Moving 4 steps left, then moving 9 steps right
When you move left, we indicate with a negative sign while a move right is indicated with a positive sign.
Moving 4 steps left = -4
Moving 9 steps right = +9
Therefore, an expression for the statement is:[tex]-4+9[/tex]
Part B
When you lose or owe in word problems, it is usually indicated using a negative sign.
Therefore, the statement Shari lost 2 pencils can be represented with the integer: -2
Since Shari lost 2 pencils on 3 occasions, we simply have:
[tex]-2 \times 3[/tex]
What is the area of the triangle?
18 cm x 24cm x 30cm
Answer:
The area of triangle = 12,960
Step-by-step explanation:
:)
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ)=6cosθ+3sin2θ g
Answer:
The critical value of [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]
Step-by-step explanation:
The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:
First derivative
[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]
[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]
The procedure to determine the critical number of the given function are described briefly:
1) First derivative is equalised to zero.
2) The resultant equation is solved.
Then,
[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]
Whose roots are:
[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]
The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:
[tex]\theta \approx \sin^{-1} 0.281[/tex]
There are two subsets of solutions:
[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]
A 30% cranberry juice drink is mixed with a 100% cranberry juice drink. The function f(x)=(6)(1.0)+x(0.3)6+x models the concentration of cranberry juice in the drink after x gallons of the 30% drink are added to 6 gallons of pure juice. What will be the concentration of cranberry juice in the drink if 2 gallons of 30% drink are added? Give the answer as a percent.
Answer:
82.5%
Step-by-step explanation:
It helps to start with the correct formula:
f(x) = ((6)(1.0) +x(0.3))/(6 +x) . . . . parentheses are required
Then f(2) is ...
f(2) = (6 +.3(2))/(6+2) = 6.6/8
f(2) = 82.5%
2{ 3[9 + 4(7 -5) - 4]}
Answer:
2{3[9+4(7-5)-4]}
2{3[9+4(2)-4]}
2{3[13(2)-4]}
2{3[26-4]}
2{3[22]}
2{66}
132
Step-by-step explanation:
F =9/5 C + 32 A) constants B) units C) variables D) numbers
Answer:
a) 32
b) none?
c) C & F
D) 9/5, 32?
Step-by-step explanation:
What is the quotient of 2 1/9÷3 4/5
Answer:
[tex] \frac{5}{9} [/tex]
Step-by-step explanation:
[tex]2 \frac{1}{9} \div 3 \frac{4}{5} \\ \\ = \frac{2 \times 9 + 1}{9} \div \frac{3 \times 5 + 4}{5} \\ \\ = \frac{18 + 1}{9} \div \frac{15 + 4}{5}\\ \\ = \frac{19}{9} \div \frac{19}{5}\\ \\ = \frac{19}{9} \times \frac{5}{19} \\ \\ = \frac{5}{9} [/tex]
A small regional carrier accepted 19 reservations for a particular flight with 17 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance, independently of each other. (Report answers accurate to 4 decimal places.)
1. Find the probability that overbooking occurs.
2. Find the probability that the flight has empty seats.
Answer:
(a) The probability of overbooking is 0.2135.
(b) The probability that the flight has empty seats is 0.4625.
Step-by-step explanation:
Let the random variable X represent the number of passengers showing up for the flight.
It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.
Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.
Number of reservations = 19
Regular customers = 14
Seats available = 17 - 14 = 3
Remaining reservations, n = 19 - 14 = 5
P (A remaining passenger will arrive), p = 0.52
The random variable X thus follows a Binomial distribution with parameters n = 5 and p = 0.52.
(1)
Compute the probability of overbooking as follows:
P (Overbooking occurs) = P(More than 3 shows up for the flight)
[tex]=P(X>3)\\\\={5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}\\\\=0.175478784+0.0380204032\\\\=0.2134991872\\\\\approx 0.2135[/tex]
Thus, the probability of overbooking is 0.2135.
(2)
Compute the probability that the flight has empty seats as follows:
P (The flight has empty seats) = P (Less than 3 shows up for the flight)
[tex]=P(X<3)\\\\1-P(X\geq 3)\\\\=1-[{5\choose 3}(0.52)^{3}(1-0.52)^{5-3}+{5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}]\\\\=1-[0.323960832+0.175478784+0.0380204032]\\\\=0.4625399808\\\\\approx 0.4625[/tex]
Thus, the probability that the flight has empty seats is 0.4625.
Sameer chose 12 different toppings for his frozen yogurt sundae, which was Three-fourths of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below.
Three-fourths = StartFraction x over 12 EndFraction. Three-fourths (12) = StartFraction x over 12 EndFraction (12). 9 = x.
Which best describes the error that Sameer made?
Sameer did not use the correct equation to model the given information.
Sameer should have multiplied both sides of the equation by Four-thirds instead of by 12.
The product of Three-fourths(12) is not equal to 9.
The product of Four-thirds and StartFraction 1 over 12 EndFraction should have been the value of x.
Answer: B. Sameer did not use the correct equation
Step-by-step explanation:
12 IS three-fourths OF x
IS: equals
OF: multiplication
[tex]12=\dfrac{3}{4}x[/tex]
48 = 3x
16 = x
Answer:
it's b in Edg
Step-by-step explanation:
which point is a solution to the inequality shown in the graph? (3,2) (-3,-6)
The point that is a solution to the inequality shown in the graph is:
A. (0,5).
Which points are solutions to the inequality?The points that are on the region shaded in blue are solutions to the inequality.
(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
Suppose IQ scores were obtained for 20 randomly selected sets of siblings . The 20 pairs of measurements yield x overbar equals98.26, y overbar equals99, requals 0.911, P-valueequals 0.000, and ModifyingAbove y with caret equals negative 5.9 plus 1.07 x , where x represents the IQ score of the older child . Find the best predicted value of ModifyingAbove y with caret given that the older child has an IQ of 102 ? Use a significance level of 0.05 g
Answer:
The answer to the best prediction is 115.04
Step-by-step explanation:
We have to:
x = 102
They also tell us that:
y = 5.9 + 1.07 * x
If we replace we have:
y = 5.9 + 1.07 * (102)
y = 115.04
Therefore, the best predicted value of ModifyingAbove and with caret given that the older child has an IQ of 102 is 115.04
What is the product of the polynomials below?
(8x2 - 4x-8)(2x2+3x+2)
A. 16x4+16X9 - 12x2 - 32x – 16
B. 16x4 + 16x2 - 12x2 - 16x-6
C. 16x4 +16X - 12x2 - 32x-6
D. 16x4 +16x2 - 12x2 - 16x-16
Answer:
16x⁴+16x³-32x-16. None of the options are correctStep-by-step explanation:
Given the polynomial function (8x² - 4x-8)(2x²+3x+2). To take the product of both quadratic polynomial, we will need to simply open up the bracket as shown;
= 8x²(2x²+3x+2) - 4x(2x²+3x+2) - 8(2x²+3x+2)
= (16x⁴+24x³+16x²) -(8x³+12x²+8x)-(16x²+24x+16)
Open up the parenthesis
= 16x⁴+24x³+16x² - 8x³-12x²-8x- 16x²-24x-16
Collect the like terms
= 16x⁴+24x³- 8x³+16x² - 16x²-8x-24x-16
= 16x⁴+16x³-32x-16
ANSWER ASAP! PLEASE HELP!
Geena decided to solve the quadratic x2 + 6x = 8. Which of the following steps is where Geena made her first mistake? x2 + 6x = 8 Step 1: x2 + 6x + 8 = 0 Step 2: (x + 4)(x + 2) = 8 Step 3: x = -4 and x = -2
Answer:
Step 2: (x + 4)(x + 2) = 8
Step-by-step explanation:
x2 + 6x + 8 = 0
x2 + 4x + 2x + 8 = 0
x(x + 4) + 2(x + 4) = 0
(x + 2)(x + 4) = 0
Find the smallest perimeter and the dimensions for a rectangle with an area of 2525 in. squared g
Answer:
5 in x 5 in
Step-by-step explanation:
The area of the rectangle is given by:
[tex]A=x*y=25\\y=\frac{25}{x}[/tex]
Where x and y are the length and width of the rectangle.
The perimeter is:
[tex]P=2x+2y\\P=2x+2*\frac{25}{x}\\ P=2x+\frac{50}{x}[/tex]
The value of x for which the derivate of the perimeter function is zero is the length that yields the smallest perimeter:
[tex]P=2x+\frac{50}{x} \\\\P'=2-\frac{50}{x^2} =0\\2x^2=50\\x=5\ in[/tex]
The value of y is:
[tex]y=\frac{25}{5}\\y=5\ in[/tex]
Therefore, the dimensions that yield the smallest perimeter are 5 in x 5 in.
patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into small boxes. There were 45 cupcakes in 3 big boxes and 8 small boxes altogether.
a) How many cupcakes dud Patricia bake?
b) She sold all the small boxes and collected $189. How much did she sell each small box for?
Answer:
The answer is given below
Step-by-step explanation:
a)
Let us assume Patricia baked x number of cakes. She put half of the cupcakes (i.e x/2) equally into 6 big boxes.
6 big boxes contained [tex]\frac{x}{2}[/tex] cakes, therefore 1 big box would contain [tex]\frac{x}{2}/6=\frac{x}{12}[/tex] cakes.
Let us assume she put the other half into 14 small boxes, therefore each small box would contain [tex]\frac{x}{2}/14=\frac{x}{28}[/tex] cakes.
There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. That is:[tex]3(\frac{x}{12} )+8(\frac{x}{28})=45\\ 84x+96x=15120\\180x=15120\\x=84[/tex]
Therefore Patricia baked 84 cup cakes
b)
She sold all the small boxes and collected $189, i.e she sold 14 small box for $189. Each small box = $189/14 = $13.5
Find the volume of each cone.
Answer:
The volume of the cone is 94.25 in³.
Step-by-step explanation:
The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in. The volume of a cone is given by:
[tex]V = \frac{\pi*r^2*h}{3}\\V = \frac{\pi*(3)^2*10}{3}\\V = 94.25 \text{ in}^3[/tex]
The volume of the cone is 94.25 in³.
A committee has ten members. There are two members that currently serve as the board's chairman and vice chairman. Each member is equally likely to serve in any of the positions. Two members are randomly selected and assigned to be the new chairman and vice chairman. What is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and reassigning them to their current positions?
Answer:
1/90 = 1.11%
Step-by-step explanation:
We have that the number of ways of total selections and assignments possible is a permutation.
We know that permutations are defined like this:
nPr = n! / (n-r)!
In our case n = 10 and r = 2, replacing:
10P2 = 10! / (10 - 2)! = 10! / 8!
10P2 = 90
In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,
Probability would come being the following:
P = 1/90 = 1.11%
Factor completely
2n^2+ 5n + 2
Answer:
(2n+1)(n+2)
Step-by-step explanation:
Use basic factor pairs, then figure out the two 2s in the factor pairs add with the one to be five. Then just make the answer above.
Which is the graph of x - y = 1?
Answer:
This question is very simple,
Ok first you will need to find the x and y intercepts by letting y=0 and x=0
First let x=0
so, 0-y=1
y=-1
let y=0
x-0=1
x=1
now we know
x-intercept=(1,0)
y-intercept=(0-1)
Hence, find the graph that has the two corresponding points and that would be the graph you are looking for.
Step-by-step explanation:
Select the correct answer. The function h(x) = 31x2 + 77x + 41 can also be written as which of the following? A. h(x) + 41 = 31x2 + 77x B. y + 41 = 31x2 + 77x C. y = 31x2 + 77x + 41 D. y = 31x2 + 77x − 41
Answer:
[tex]y=31x^2+77x+41[/tex]
which agrees with option C in your list of possible answers.
Step-by-step explanation:
Since normally functions are represented on the x-y plane, it is common to replace h(x) with the "y" variable of the vertical axis where its values will be represented (plotted). Then the expression can be also written as follows:
[tex]h(x)=31x^2+77x+41\\y=31x^2+77x+41[/tex]
You buy six pens for $2.99 each, and sales tax is 10%. How much change should you receive from a clerk if you give her a $20 bill?
Answer:
$2.06
Step-by-step explanation:
$2.99 x 6 = $17.94
$20.00 - $17.94 = $2.06
Hope this helps
Answer: $0.26
Step-by-step explanation:
Cost of 6 pens
= 2.99 x 6
= 17.94
Add sales tax at 10%,
= 17.94 x 1.1
= 19.74
Change due to me
= 20 - 19.74
= 0.26
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A coin mint has a specification that a particular coin has a mean weight of 2.5 g. A sample of 35 coins was collected. Those coins have a mean weight of 2.49546 g and a standard deviation of 0.01839 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the coins appear to conform to the specifications of the coin mint?
Answer:
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean is signficantly different from 2.5 g.
We can not conclude that the sample is drawn from a population with mean different from 2.5 g. This does not confirm that the sample is drawn from a population with mean 2.5 g (we can not confirm the null hypothesis, even if it is failed to be rejected).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean is signficantly different from 2.5 g.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2.5\\\\H_a:\mu\neq 2.5[/tex]
The significance level is 0.05.
The sample has a size n=35.
The sample mean is M=2.49546.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.01839.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.01839}{\sqrt{35}}=0.0031[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.49546-2.5}{0.0031}=\dfrac{0}{0.0031}=-1.4605[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=35-1=34[/tex]
This test is a two-tailed test, with 34 degrees of freedom and t=-1.4605, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-1.4605)=0.1533[/tex]
As the P-value (0.1533) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean is signficantly different from 2.5 g.
What is the value of x in the figure below? In this diagram, triangle ABD- triangle CAD .
Answer:
D
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AD}{CD}[/tex] = [tex]\frac{BD}{AD}[/tex] , substitute values
[tex]\frac{x}{13}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
x² = 39 ( take the square root of both sides )
x = [tex]\sqrt{39}[/tex] → D
The value of x in the figure showing triangles ABD & triangle CAD is;
x = √39
From the given figure showing the triangles, we can say that there are 2 congruent triangles. This is because we are told that ΔABD ≅ ΔCAD and the symbol ≅ means congruent.Now, corresponding sides of 2 congruent triangles usually have same ratio.
Using this concept of congruent triangles, to write the ratio of corresponding sides, we have;BD/AD = AD/DC
Thus; 3/x = x/13
cross multiply to get;
x² = 13 × 3
x² = 39
take square roots of both sides to get;
x = √39
Read more at; https://brainly.com/question/3304327
Solve the equation 3x-13y = 2 for y.
Answer:
y= 3/13x + 2/13
Step-by-step explanation:
3x-13y=2
Subtract 3x from both side
-13y=-3x-2
Divide by -13
y= 3/13x + 2/13
Answer:
[tex]y = \frac{2-3x}{-13}[/tex]
Step-by-step explanation:
=> 3x-13y = 2
Subtract 3x to both sides
=> -13y = 2-3x
Dividing both sides by -13
=> [tex]y = \frac{2-3x}{-13}[/tex]
what is x2 + 2x + 9 = 0
Answer:
x has no real solution
Step-by-step explanation:
Our equation is qudratic equation so the method we will follow to solve it is using the dicriminant :
Let Δ be the dicriminant a=1b=2c=9 Δ= 2²-4*1*9 =4-36=-32 we notice that Δ≤0⇒x has no real solutionWhich angles are pairs of alternate exterior angles
Answer:
when a straight line cuts two or more parallel lines then the angles forming on the side of transversal line exteriorly opposite to eachother is called exterior alternative angle.
for eg if AB //CD and EF is a transversal line meeting the parallel lines at G abd H then the exterior alternative angle are angle EGB = angle CHF and angle AGE=angle DHF are two pairs of exterior alternative angle .
hope its helpful to uh !!!!!!
What is the volume of a cubed shaped box with edges 6 cm. in length?
Answer:
216 cm³
Step-by-step explanation:
The volume of a cube is denoted by V = s³, where s is the side length.
Here, the side length is 6 centimetres, so plug this into the formula to find V:
V = s³
V = 6³ = 6 * 6 * 6 = 216
The answer is thus 216 cm³.
~ an aesthetics lover
Answer:
216
Step-by-step explanation:
6³ = 216