Answer:
The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.
Step-by-step explanation:
Suppose we have a function y = f(x). The zeros, which are the values of x for which y = 0, are also called the x-intercepts of the function.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
I will write the function as a function of x, just exchanging a for x.
[tex]f(x) = x^{2} + 5x + 6[/tex]
[tex]\bigtriangleup = 5^{2} - 4*1*6 = 1[/tex]
[tex]x_{1} = \frac{-5 + \sqrt{1}}{2*1} = -2[/tex]
[tex]x_{2} = \frac{-5 - \sqrt{1}}{2*1} = -3[/tex]
The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.
evaluate the limit of tan 4x/ 4tan3x
Answer:
1/3
Step-by-step explanation:
The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.
[tex]\displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}[/tex]
Simplify the expression sin 2x+ sin x + cos2x - 1.
Answer:
Sin(2x)+sin(x)+cos(2x)-1
Step-by-step explanation:
What type of angels are <1 and <4?
The scale of the drawing shows that 1” = 10 feet. If the drawing
shows the height of the building as 6 inches, how tall is the
actual building?
Answer:
60 foot
Step-by-step explanation:
Just multiply by 10?
Awnser in the lowest terms 5 years 6 months + 8 years 9 months
Answer:
14 years 3 months.
Step-by-step explanation:
5 + 8 = 13 years
6 + 9 = 15 months = 1 year 3 months.
Total = 14 years 3 months.
Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. Their parents must have a basement! A random sample of 125 young adults in this age group was selected. What is the probability that between 13 and 17 of these young adults lived with their parents? Hint: use 14.2% to determine the standard error and the p-bar would be the 13/125 and the 17/125.
Answer:
38.76% probability that between 13 and 17 of these young adults lived with their parents
Step-by-step explanation:
I am going to use the normal approxiation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]p = 0.142, n = 125[/tex]
So
[tex]\mu = E(X) = np = 125*0.142 = 17.75[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.142*0.858} = 3.9025[/tex]
What is the probability that between 13 and 17 of these young adults lived with their parents?
Using continuity correction, this is [tex]P(13 - 0.5 \leq X \leq 17 + 0.5) = P(12.5 \leq 17.5)[/tex], which is the pvalue of Z when X = 17.5 subtracted by the pvalue of Z when X = 12.5. So
X = 17.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 17.75}{3.9025}[/tex]
[tex]Z = -0.06[/tex]
[tex]Z = -0.06[/tex] has a pvalue of 0.4761
X = 12.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 17.75}{3.9025}[/tex]
[tex]Z = -1.35[/tex]
[tex]Z = -1.35[/tex] has a pvalue of 0.0885
0.4761 - 0.0885 = 0.3876
38.76% probability that between 13 and 17 of these young adults lived with their parents
A scientist needs 10mL of a 17% acid solution for an experiment. The lab has available a 20% solution and a 10% solution. How many milliliters of the 20% solution and how many milliliters of the 10% solution should the scientist mix to make the 15% solution?
On moving day, Jorge needs to rent a truck. The length of the cargo space is 12 ft, and the height is 1 ft less than the width. The brochure indicates that the truck can hold 504 ft3. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.
Answer:
12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft
Step-by-step explanation:
Given that truck can hold = 504 [tex]ft^{3}[/tex] i.e.
Volume, V = 504 [tex]ft^{3}[/tex]
Length of cargo space = 12 ft
Let width of cargo space = w ft
As per question statement:
Let height of cargo space = (w-1) ft
To find: The Dimensions of Cargo Space
Formula for Volume of Cargo Space:
V = Length [tex]\times[/tex] Width [tex]\times[/tex] Height
Putting the given values and conditions:
504 = 12 [tex]\times[/tex] [tex]w \times (w-1)[/tex]
[tex]\Rightarrow w(w-1) = \dfrac{504}{12}\\\Rightarrow w^{2} -w = 42\\\Rightarrow w^{2} -w - 42=0\\\Rightarrow w^{2} -7w +6w -42 =0\\\Rightarrow w(w -7) +6(w -7) =0\\\Rightarrow (w -7)(w+6) = 0\\\Rightarrow w =7, -6[/tex]
Dimensions can not be negative, so width, w = 7 ft
Height = (w-1) = 7-1 = 6 ft
So, the dimensions are 12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft.
what is the quotient of 2/3 and 2/g ?
What value of y satisfies the system of equations {9x+2y=24y=6x+19? Enter your answer as the correct value for y, like this: 42
Answer:
Step-by-step explanation:
9x + 2y = 24 (A)
y = 6x + 19 ------ > y - 6x = 19 * (-2) -------> -2y + 6x = -38 (B)
(A) + (B)
15x = -14
x = -14/15
y = 6 * (-14/15) + 19 = -28/5 + 19 = 67/5
Answer:
A. 9x + 2y = 24
i got +2 is that the correct answer
Answer:
Option (1)
Step-by-step explanation:
Quadratic equation is given as,
2x² + 8 = 0
Let the function is,
f(x) = 2x² + 8
f(x) = 2(x - 0)² + 8
Now we will prepare the table for every input value,
x -2 -1 0 1 2
y 16 10 8 10 16
By plotting these points we get a parabola having vertex at (0, 8).
Graph of the given function doesn't touches or intersects the x-axis.
And we know if a graph has no x-intercept, function graphed will have no real solution.
Therefore, function f(x) will have no real solutions.
Option (1) will be the answer.
Kim and Dan sold 160 homes together. Kim sold 4 times more than Dan. How many homes did Kim sell?
Paper and Pencil Construction: Construct a Line Perpendicular to a Given Line through a Point on the Line
Step-by-step explanation:
wait a person was about to report it sorry ;/
had to take it off
Para ir a visitar a los abuelos Paula y Mario se ponen de acuerdo en que Paula vaya cada 5 días y Mario cada 6 días. Si coincidieron el 24 de diciembre,
a) ¿Cuándo volvieron a coincidir?
b) ¿Cuántas visitas habrá hecho cada uno?
Answer:
a) January 24(24 de Enero)
b) Paula will have made 5 visits(Paula habrá hecho 5 visitas). Mario will have made 4 visits(Mario habrá hecho 4 visitas).
Step-by-step explanation:
When two events, A and B, happen every x and y days, respectively, they will happen on the same day in each lcm(x,y) days. lcm(x,y) is the lesser common multiple of x and y which is not 0.
In this question:
Paula each 5 days
Mario each 6 days
Multiples of 5: {0, 5, 10, 15, 20,25,30, ...}
Multiples of 6: {0, 6, 12, 18, 24, 30, ...}
a) ¿Cuándo volvieron a coincidir?
lcm(5,6) = 30
30 days from December 24, which is January 24(24 de Enero).
b) ¿Cuántas visitas habrá hecho cada uno?
Paula visits each 5 days.
30 is 6th non-zero multiple of 5. This means that on January 24 will be her 6th visit. So she will have made 5 visits.
30 is the 5th non-zero multiple of 6. This means that on January 24 will be her 5th visit. So he will have made 4 visits.
what is the center of the circle with a diameter having endpoints
Answer:
(0.5, 2)
Step-by-step explanation:
Since the y coordinates are the same, the distance is between the x values
4 - -3
4+3 = 7
The distance is 7
1/2 the distance would be the center
7/2 = 3.5
Add this to the left coordinate
The x coordinate of the center is -3 + 3.5 = .5
The y coordinate is 2
Calculate the standard score of the given X value, X=28.3, where μ=26.3 and σ=28.1 and indicate on the curve where z will be located. Round the standard score to two decimal places.
Answer:
Standard score z=0.07
Step-by-step explanation:
The z-score, or standard score, represents an equivalent value for X but in the standard normal distribution, where μ=0 and σ=1.
For X=28.3 in a normal distribution with μ=26.3 and σ=28.1, the standard score can be calculated as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{28.3-26.3}{28.1}=\dfrac{2}{28.1}=0.07[/tex]
This value is 0.07 standard deviations right to the mean.
In the picture attached, we have located the z-score.
Error Analysis A math test asks the students to solve the inequality X-2<16, and then graph the
solutions. Mason said the solutions are x < 14 and graphed the solutions as shown below. Solve
the inequality and graph the solutions. What error might Mason have made?
What are the solutions?
Answer:
The solution is X<18
Step-by-step explanation:
When Mason was solving the inequality he subtracted two from the equation instead of adding two to solve for x.
X-2<16
X<18
Answer:
x < 18Step-by-step explanation:
x - 2 < 16
We eliminate 2 to isolate the variable, x by adding 2 to both sides. -2 + 2 = 0.
x < 18
We can test this because 17 is less than 18. Pretend x = 17
17 < 18✅
Mason subtracted 2, instead of adding 2.
In order to graph this, put an open circle at 18, and the arrow should point to the left.
Hope this helps ;D
Find the value of x and y in the parallelogram below.
Answer:
x = 18°
y = 6
Step-by-step explanation:
in a parallelogram:
Any two opposite sides are congruent
and any two opposites angles are congruent:
then
y + 4 = 10
and 3x = 54
then
y = 6
and x = 54/3 = 18
Answer:
x= 18 , y = 6
Step-by-step explanation:
A parallelogram has two opposite sides equal and parallel hence;
y + 4 = 10
y = 10 -4 = 6
Similarly
54 = 3x( opposite angle of a parallelogram are the same because it's congruent)
3x = 54
x = 54/ 3 = 18°
To be congruent means to have the same shape, size and form but can be flipped.
For a given rectangle, the length= 3x +2 and the width = 5. What is the area of the rectangle?
Answer:
15x+10
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW
Fill in the given values and simplify.
A = (3x+2)(5)
A = 15x +10
The area of the rectangle is 15x+10.
Answer:
[tex]15x + 10[/tex]
Step-by-step explanation:
[tex]area = length \times width \\ = 3x + 2 \times 5 \\ = 5(3x + 2) \\ = 15x + 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
According to a study conducted by the Toronto-based social media analytics firm Sysomos, of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January ). Suppose we randomly select tweets.a. What is the expected number of these tweets with no reaction (to the nearest whole number)
a) What is the expected number of these tweets with no reaction?
b) What are the variance and standard deviation for the number of these tweets with no reaction?
Answer:
a) E(X) = 71
b) V(X) = 20.59
Sigma = 4.538
Step-by-step explanation:
The question is incomplete:
According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015).
Suppose we randomly select 100 tweets.
a) What is the expected number of these tweets with no reaction?
b) What are the variance and standard deviation for the number of these tweets with no reaction?
This can be modeled with the binomial distribution, with sample size n=100 and p=0.71, as the probability of no reaction for each individual tweet.
The expected number of these tweets with no reaction can be calcualted as the mean of the binomial random variable with these parameters:
[tex]E(X)=n\cdot p=100\cdot 0.71=71[/tex]
The variance for the number of these tweets with no reaction can be calculated as the variance of the binomial distribution:
[tex]V(X)=np(1-p)=100\cdot0.71\cdot0.29=20.59[/tex]
Then, the standard deviation becomes:
[tex]\sigma=\sqrt{V(X}=\sqrt{20.59}=4.538[/tex]
Calculate the slope between the two points: (7, –4), (7, 8)
Answer:
undefined
Step-by-step explanation:
We can find the slope by using the formula
m = (y2-y1)/(x2-x1)
m = (8 - -4)/97-7)
= (8+4)/(7-7)
= 12/0
We cannot divide by 0 so the slope is undefined
A retail store had sales of $45000 in April and $56000 in May. The store employs eight full time workers who work 40 hours per week. In April the store also had seven part time workers at 10 hours per week, and in may the store had 9 part time workers at 15 hours per week. Using sales dollars as the measure for output, what is the percentage of change in productivity from April to May?
The percentage of change in productivity from April to May is found to be 6.66%.
Productivity ChangeWhat is meant by change in productivity?A change in labour productivity reflects an output change that cannot be accounted for by a change in the number of hours worked. The development of technology over time might lead to an increase in output per hour enhanced employee skills.
Step by step solutionStep 1: Productivity for month of AprilWe must first determine the number of man hours worked in April in order to compute the percentage change in productivity:
8 employs worked for 40 hours along with 7 employs worked for 10 hours in a week( total 4 weeks in April).
Input of April is,
= 8×40 + 7×10×4
= 1560 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 45000/1560
= 28.846
Step 2: Productivity for month of May8 employs worked for 40 hours along with 9 employs worked for 15 hours in a week( total 4 weeks in April).
Input of May is,
= 8×40 + 9×15×4
= 1820 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 56000/1820
= 30.769
Step 3: Calculate the total productivityFinding the difference between productivity in each month and dividing by April's productivity percentage yields the percent change in productivity:
= [tex]\frac{30769-28.846}{28.846}[/tex]×[tex]100[/tex]
= 6.66 %
Therefore, the productivity from April to May increased by 6.66%.
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The six faces of a cube are painted black. The cube is then cut into [tex]5^3 = 125[/tex] smaller cubes, all the same size. One of the small cubes is chosen at random and rolled. What is the probability that when it lands, the face on the top is black?
Answer:
The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
Step-by-step explanation:
We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.
We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.
This probability is equal to the proportion of black area in the total area of the cube.
We can define the side of the original cube as A=5a, being a the side of the small cubes.
The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:
[tex]S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2[/tex]
The total area of the 125 small cubes is:
[tex]S=125(6a^2)=750a^2[/tex]
Then, the ratio of black surface to the total surface is:
[tex]s_b/s=(150a^2)/(750a^2)=0.2[/tex]
Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
There are 454 grams in a pound. Convert 330 grams to ounces.
Answer:
11.62 ounces
Step-by-step explanation:
Given m \| nm∥n, find the value of x. m n t (4x-18)° (3x-8)
Answer:
12x2
Step-by-step explanation:
A standard deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck without replacement. Let A=first card red and B=second card red. Are A and B independent? Explain why or why not.
They aren't independent since the probability uses all the cards in the deck
So at the first deal we have the chance of 26/52 of getting a red card, at the second deal we have the chance of a 25/51 of getting another red card, so they aren't independent
1 point
Bob is flying his kite while standing in his yard and the kite is flying over
his friends house. He know the string is 75 ft long and the angle the string
where he is holding it makes a 35° angle with the ground. How far is Bob
from his friends house?
43 ft
61 ft
75 ft
35 ft
Answer:
Ground distance of Bob from his friends house = 61 ft (Approx)
Step-by-step explanation:
Given:
Length of string = 75 ft
Angle with the ground = 35°
Find:
Ground distance of Bob from his friends house.
Computation:
Using trigonometric application:
⇒ Cos [tex]\theta[/tex] = Base / Hypotenuse
⇒ Cos 35° = Base / 75
⇒ 0.819 = Base / 75
⇒ Base = 61.425 ft
Ground distance of Bob from his friends house = 61 ft (Approx)
In a restaurant 40% of the customers choose Chinese food while 65% opt for Pakistani food .if the restaurant is visited by 260 people then how many opt for both in quarter ? Ans is 39 please give the working ?
Answer:
13 ppl choose both
Step-by-step explanation:
Hello,
In a restaurant 40% of the customers choose Chinese food
while 65% opt for Pakistani food.
if the restaurant is visited by 260 people then how many opt for both ?
There are 260 people we need to compute
40% of 260 = 40*260/100 = 104 to know the customers choosing Chinese food
65% of 260 = 65 * 260/100 = 169 to know the customers choosing Pakistani food
There are ppl choosing both Chinese and Pakistani, let s note x
we can say that 104 + 169 -x = 260
so x = 273-260=13
in conclusion, 104-13=91 ppl choose Chinese food only
169-13=159 ppl choose Pakistani food only
13 ppl choose both
in total there are 91 + 159 + 13 = 260
hope this helps
The number of people who opt for both Chinese and Pakistani food is 13.
We have,
Let's denote the number of people who choose Chinese food as "C" and the number of people who choose Pakistani food as "P".
We are given that 40% of the customers choose Chinese food, which means
C = 40% of 260.
C = 0.4 * 260
C = 104
Similarly, we are given that 65% of the customers opt for Pakistani food, which means
P = 65% of 260.
P = 0.65 * 260
P = 169
Now, we need to determine the number of people who opt for both Chinese and Pakistani food.
To find this, we can use the principle of inclusion-exclusion.
The total number of people who opt for both is given by:
Total = C + P - Both
We know that the total number of customers is 260, so:
260 = 104 + 169 - Both
Rearranging the equation to solve for Both:
Both = 104 + 169 - 260
Both = 273 - 260
Both = 13
Therefore,
The number of people who opt for both Chinese and Pakistani food is 13.
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1. Joy bought jewelry at a crafts fair. She bought a necklace for $8 and
some bracelets for $5 each. She spent $23 in all. Write and solve equation
that can be used to find the number of bracelets she bought
Answer:
5y + 8 < 23 and y < 3
2c - 3 = 9
Step-by-step explanation:
She bought a jewelry at a craft fair . The necklace is $8 and the bracelet is $5 each. Her total expenses is $23.
She bought a single necklace. The number of bracelet she bought is unknown but each of the bracelet she bought is $5 each. The number of bracelet she bought can be represented below.
Let
y = number of bracelet bought
Therefore, the cost of the total number of bracelet will be 5y
Recall the total expenses is $23
5y + 8 < 23 and y < 3
if you insert the value of y in the following inequalities the resulting value should be less than 23 so the value of y should be less than 3.
2. 2c - 3 = 9
A 100-gallon barrel, initially half-full of oil, develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at time t. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. The mathematical model is:___________.
(a) =kA, A(0) = 0
(b) A = ktA, A(O) = 50
(c) A tA, A(0) = 100
(d) A = két +A), A
(e) = 50 None of the above.
Answer:
the mathematical model is : [tex]-\frac{1}{A}= kt - \frac{1}{50}[/tex]
Step-by-step explanation:
Given that:
Let A(t) to be the amount of oil in the barrel at time t.
However; Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel.
Then,
[tex]\frac{dA}{dt} \ \alpha \ A^2[/tex]
[tex]\frac{dA}{dt}= KA^2[/tex]
Initially the 100 -gallon barrel is half-full of oil
So, A(0) = 100/2 = 50
[tex]\frac{dA}{dt}= KA^2 \ \ \ \ \ \ :A(0)=50[/tex]
The variable is now being separated as:
[tex]\frac{dA}{A^2}=kdl[/tex]
Taking integral of both sides; we have:
[tex]\int\limits\frac{dA}{A^2}=\int\limits \ kdt[/tex]
[tex]-\frac{1}{A}= kt +C[/tex]
However; since A(0) = 50; Then
t = 0 ; A =50 in the above equation
[tex]-\frac{1}{50}= 0 +C[/tex]
[tex]C = - \frac{1}{50}[/tex]
Thus; the mathematical model is : [tex]-\frac{1}{A}= kt - \frac{1}{50}[/tex]
