Answer:
5
To find the first term
T(1)=(1×2)+3
=2+3
=5
What is the factored form of the polynomial?
x2 + 9x +20
A. (x - 4)(x - 5)
B.(x-2)(x - 10)
C.(x + 4)(x+5)
D.(x + 2)(x + 10)
Answer:
C. (x + 4)(x + 5).
Step-by-step explanation:
We need 2 numbers whose product is + 20 and whose sum is + 9.
They are + 5 and + 4 , so
x2 + 9x +20
= (x + 4)(x + 5).
What type of angels are <1 and <4?
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
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]
If f(x)=2x squared + 1 and g(x)=x squared-7 find (f-g)(x)
Answer:
[tex]x^2+8[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+1 \\\\g(x)=x^2-7 \\\\(f-g)(x)= (2x^2+1)-(x^2-7)=x^2+8[/tex]
Hope this helps!
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.
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]
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)
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%.
To know more about how to find percentage change, here
https://brainly.com/question/809966
#SPJ2
The percentage charged each month on purchases charged to the credit card
account is called the__?
A) periodic rate
B) new balance
C) unpaid balance
D) minimum payment
Answer:
A) periodic rate
Step-by-step explanation:
Because a percentage that is charged or added to the credit card we assume that it is an interest rate, they also tell us that it is charged every month, that is, it has a known collection frequency, which means that it is Newspaper.
therefore, the answer in this case is A) periodic rate since it complies with the premise of the statement
There are 454 grams in a pound. Convert 330 grams to ounces.
Answer:
11.62 ounces
Step-by-step explanation:
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 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
What’s the surface area of this shape?
Answer:
210 in²
Step-by-step explanation:
6*2.5+6*6*2+(8+6)*2.5+10*2.5+1/2*6*8*2+6*2.5= 210 in²
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
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.
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.
The equation for the trend line for the scatterplot shown below is y = 5x + 24. What does the slope mean in the context of this problem?
A). The total amount of dollars earned is about $64
B). If no hours are worked, $24 is made
C). For each hour worked the dollars earned increases by $5
D). A total of $80 was earned
Please help
Answer:
C) For each hour worked the dollars earned increases by $5
Step-by-step explanation:
I don't have the context of the problem.
However, we do know that in math, when we have an equation of the form [tex]y=mx+b[/tex], the slope m represents the rate of change. This means, how much one quantity changes in regards to other quantity (from the options I can assume that we are talking about amount earned and hours worked).
Thus, in this case we have [tex]m=5[/tex] and this tells us how much the payment increase in terms of hours worked. Thus, we can say that for each work we work the payment increases by $5.
Thus, the correct answer is c) For each hour worked the dollars earned increases by $5
The numerator of a
fraction is 1 more than
twice its denominator. If 4
is added to both the
numerator and the
denominator, the fraction
pos
inve
reduces to 3. Find the
denominator.
Answer:
-7
Step-by-step explanation:
The numerator of a fraction is 1 more than twice its denominator.
Let the denominator=x
Therefore, the numerator=2x+1
The fraction is: [tex]\dfrac{2x+1}{x}[/tex]
If 4 is added to both the numerator and the denominator, the fraction reduces to 3.
Therefore:
[tex]\dfrac{2x+1+4}{x+4} =3[/tex]
First, we solve for x
[tex]\dfrac{2x+5}{x+4} =3[/tex]
Cross multiply
2x+5=3(x+4)
Open the bracket on the right-hand side
2x+5=3x+12
Collect like terms
3x-2x=5-12
x=-7
Therefore, the denominator of the fraction, x=-7
What makes things concurrent?
Answer:
When the are intercepted by other lines (math)
Existing, happening at the same time (definition)
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
Kim and Dan sold 160 homes together. Kim sold 4 times more than Dan. How many homes did Kim sell?
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?
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.
Tamera and Adelina are throwing a birthday party for their friend.
Tamera invited 5 fewer friends than Adelina. Together they invited 47 guests.
How many guests did each girl invite?
Answer: Tamera invited 21 guests while Adelina invited 26 guest.
Step-by-step explanation:
x + (x-5) = 47
x + x -5 = 47
2x -5 =47
+5 +5
2x= 52
x= 26
26 -5 = 21
N. Section 2.2
Find the difference. Write the difference in lowest terms.
8 1/3 - 5=
Answer:
3 1/3
Step-by-step explanation:
8-5=3=3 1/3.
hope u understand
Which expression(s) are greater than 0? Select all that apply.
Answer:
1234567891011121314151617181920
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.
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 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