Answer:
[tex][x + 5][2x+ 5][/tex]
Step-by-step explanation:
Given
[tex]2x^2 + 15x + 25[/tex]
Required
Factorize
Expand the x term
[tex]2x^2 + 5x + 10x+ 25[/tex]
Group into 2
[tex][2x^2 + 5x] + [10x+ 25][/tex]
Take the GCF of each group
[tex]x[2x + 5] + 5[2x+ 5][/tex]
Factor out 2x + 5
[tex][x + 5][2x+ 5][/tex]
aulo uses an instrument called a densitometer to check that he has the correct ink colour.
For this print job the acceptable range for the reading on the densitometer is 1.8 ± 10%.
What is the acceptable range for the densitometer reading?
Answer:
The range is from 1.62 to 1.98.
Step-by-step explanation:
We have to solve for the percentage of the particular value if the range of the answer should be +/- 10% of the particular value.
The value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18
Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98
Furthermore, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62
The range will be between these two numbers, so the range is from 1.62 to 1.98.
3.
If 9x = 27, what is the value of x?
Complete the angle addition postulate for the following angle
Answer:
measurement m<GEM+m<MEO=m<GEO
Determine the nature of the roots: 4x2 + 13x + 6 = 0
a. no real solutions
b. cannot be determined
C. a unique real solution
two distinct real solutions d. two distinct real solutions
Answer:
D. is the correct option
Discriminant is greater than zero, so the roots are unequal and real.
Step-by-step explanation:
We use discriminant to find the nature of the roots
discriminant formula is, b^2 - 4ac
13^2 (-4) × 4 × 6 = 169-96
73 >0
if discriminant greater than 0 that means the roots are real and unequal.
Find the distance between the points (3,4) and (–8,4)
Answer:
distance = 11
Step-by-step explanation:
distance = [tex]\sqrt{[3-(-8)]^{2} +(4-4)^{2}}[/tex]
= [tex]\sqrt{11^{2} }[/tex]
= 11
Find an equation for the line with the given properties. Perpendicular to the line 7x - 3y = 68; containing the point (8, -8)
Answer:
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
Step-by-step explanation:
Given that,
A line 7x - 3y = 68 and containing the point (8, -8).
The equation can be written as :
[tex]-3y=68-7x\\\\y=\dfrac{68}{-3}+\dfrac{7x}{3}\\\\y=\dfrac{7x}{3}+(\dfrac{-68}{3})[/tex]
The slope is :7/3
Line is perpendicular so use m = –3/7
[tex]-8=(-\dfrac{3}{7})\times 8+b\\\\-8+\dfrac{3}{7}\times 8=b\\\\b=\dfrac{-32}{7}[/tex]
So, required equation is :
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
What is 233,193 rounded to the nearest thousand
CAN SOMEONE HELP ME ON ANALYZING DOT PLOTS!!!
Answer:
yes
Step-by-step explanation:
but I can't see them here
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 10% fill their tanks (event B). Of those customers using plus, 20% fill their tanks, whereas of those using premium, 30% fill their tanks.
Required:
a. What is the probability that the next customer will request plus gas and fill their tank ?
b. What is the probability that the next customer fills the tank ?
c. If the next customer fills the tank, what is the probability that the regular gas is requested?
Answer:
Remember that for an event with a percentage probability X, the probability is given by:
P = X/100%
a) What is the probability that the next customer will request plus gas and fill their tank ?
We know that 35% of the customers use plus gas, and of these using plus, 20% fill their tank.
So the probability that the next customer uses plus gas is:
p = 35%/100% = 0.35
And the probability that the customer fills the tank (given that the customer uses plus gas) is:
q = 20%/100% = 0.2
The joint probability is just the product between the individual probabilities:
Then the probability that the next customer uses plus gas and fills their tank is:
P = 0.35*0.2 = 0.07
b) What is the probability that the next customer fills the tank?
We know that 20% of the ones that use plus gas (with a probability of 0.35) fill their tank, 10% of these that use regular gas (with a probability of 0.4) and 30% of these that use premium (with a probability of 0.25) fill their tank,
Then the probability is computed in a similar way than above, here the probability is:
P = 0.2*0.35 + 0.1*0.4 + 0.3*0.25 = 0.185
The probability that the next customer fills the tank is 0.185
c) If the next customer fills the tank, what is the probability that the regular gas is requested?
Ok, now we already know that the customer fills the tank.
The probability that a customer uses regular and fills the tank, is
p = 0.1*0.4
The probability that a customer fills the tank is computed above, this is:
P = 0.185
The probability, given that the customer fills the tank, the customer uses regular gas, is equal to the quotient between the probability that the customer fills the tank with regular and the probability that the customer fills the tank, this is:
Probability = p/P = (0.1*0.4)/(0.185) = 0.216
you have to find ABC and I'm not sure how to any help is appreciated
Hello,
Since (BD) bissects angle ABC,
18-x=26-3x
2x=8
x=4
18-x=18-4=14
m angle ABC=14°*2=28°
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
find the x-intercepts y=2x^2 + 5x + 2/x^2-4x+3
Answer:
[tex]{ \tt{y = \frac{2 {x}^{2} + 5x + 2}{ {x}^{2} - 4x + 3 } }} \\ x - intercept : y = 0 \\ { \tt{ \frac{2 {x}^{2} + 5x + 2 }{ {x}^{2} - 4x + 3 } = 0 }} \\ \\ { \tt{2 {x}^{2} + 5x + 2 = 0}} \\ x = \frac{1}{2} \: \: and \: \: x = - 2[/tex]
what’s the answer to this problem please and thank you
Answer:
1.8574 hours
Step-by-step explanation:
Solve for t.
Take the natural log of both sides.
[tex] 3000 = 75000e^{-1.733t} [/tex]
[tex] 1 = 25e^{-1.733t} [/tex]
[tex] \dfrac{1}{25} = e^{-1.733t} [/tex]
[tex] \ln \dfrac{1}{25} = \ln (e^{-1.733t}) [/tex]
[tex] -3.218875 = -1.733t [/tex]
[tex] t = 1.8574[/tex]
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
Step-by-step explanation:
L numbers of hours assigned to Lisa
D numbers of hours assigned to David
S numbers of hours assigned to Sara
Objective Function to minimize:
z = 30*L + 25*D + 18*S
Constraints:
Total time available
L + D + S ≤ 110
Lisa experience
L ≥ 0.4 * ( L + D ) then L ≥ 0.4*L + 0.4*D
0.6*L - 0.4*D ≥ 0
To provide designing experience to Sara
S ≥ 0.15*110 then S ≥ 16.5
Time for Sara
S ≤ 0.25 * ( L + D ) S ≤ 0.25*L + 0.25*D or -0.25*L - 0.25*D + S ≤0
Availability of Lisa
L ≤ 50
The Model is:
z = 30*L + 25*D + 18*S to minimize
Subject to:
L + D + S ≤ 110
0.6*L - 0.4*D ≥ 0
S ≥ 16.5
-0.25*L - 0.25*D + S ≤0
L ≤ 50
L ≥ 0 ; D ≥ 0 , S ≥ 0
After 6 iterations optimal ( minimum ) solution is:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.
Given :
The company estimates that 110 hours will be required to complete the project.Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers.To provide a label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time.The number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers.Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:
z = 30L + 25D + 18S
The constraints are given by:
1) L + D + S [tex]\leq[/tex] 110
2) L [tex]\geq[/tex] 0.4(L + D)
L [tex]\geq[/tex] 0.4L + 0.4D
0.6L - 0.4D [tex]\geq[/tex] 0
3) S [tex]\geq[/tex] 0.15(110)
S [tex]\geq[/tex] 16.5
Now, to minimize 'z' then use:
[tex]\rm -0.25L-0.25D+S\leq 0[/tex]
L [tex]\leq[/tex] 50
L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0
Now, the minimum z is given by:
z = 2079
L = 26, D = 39.6, S = 16.5
For more information, refer to the link given below:
https://brainly.com/question/23017717
Badluckville had been expecting a $50 million investment for a new golf resort, but the contract was cancelled.
Badluckville's mayor estimates that this will cost the city $300 million in total economic activity. What is the mayor's
estimate of the multiplier and marginal propensity to consume?
Answer:
multiplier = 6
marginal propensity to consume = .83
Step-by-step explanation:
/ means divided by
1 .
300,000,000 / 50,000,000 =
multiplier =
6
2.
300,000,000 - 50,000,000 =
250,000,000
250,000,000/300,000,000 =
marginal propensity to consume =
0.83333333333
or
.83
quizlet
marginal propensity to consume is equal to ΔC / ΔY, where ΔC is the change in consumption, and ΔY is the change in income
investopedia
1=5
2=12
3=39
4=148
5=?
Takes a word processor 20 minutes to spell check 6 pages, how long to check 27 pages
9514 1404 393
Answer:
90 minutes
Step-by-step explanation:
Assuming the time is proportional to the number of pages, you have ...
time/pages = 20/6 = T/27
Multiplying by 27 gives ...
T = 27(20/6) = 90
It is expected to take 90 minutes to check 27 pages.
Helpppppp ASAP !!!!!
The graphs below are both quadratic functions. The equation of the red graph is f(x)=x^2 . Which of these is the equation of the blue graph g(x)
Answer:
[tex]{ \bf{c). \: g(x) = {(x - 3)}^{2} }}[/tex]
For an analysis of variance comparing three treatment means, H0 states that all three population means are the same and H1 states that all three population means are different.
A. True
B. False
Answer:
False
Step-by-step explanation:
The analysis of variance may be described as an hypothesis test which is used to make comparison between variables of two or more independent groups. The null hypothesis is always of the notion that there is no difference in the means. While the alternative hypothesis is the opposite, for two independent groups, the alternative hypothesis is that both means are different, or not equal or not the same. However. When we have more than 2 independent groups, then the alternative hypothesis is stated as : 'the means are not all equal'. This means that the means of each group does not all have to be different, but the mean of one group may be different from that of the other groups or the mean of two groups are different from the other groups and so on.
PRACTICE
Find and circle the verb to be in the text about
Sean Canty.
2 a Practice the verb to be.
5 b
2. We are
1.1
.... at home.
in the classroom.
3. My father ............. at work now.
4. My grandmother ....... alive.
5. It ............. Saturday today.
1. What
2
-
3. Whe
4. How
5. Wha
2h
jvdhvfggvvvbbbbbbbbb
Which list shows the following numbers in order from least to greatest: -15, 8, 4, -3, -7,
4, 8, -15, -7, -3
-15, 8, 4, -3, -7.
-15.-7.-3, 4.8
-15.-3, 4, -7.8
A jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint. Each time you draw out an item, you record the outcome and put the item back in the jar before making another draw. What is the probability that you get exactly the following sequence: candy—mintmcandy, in that order?
(a) 0.0300.
(b) 0.0530.
(c) 0.1607.
(d) 1.2143.
Answer:
The correct answer is B.
Step-by-step explanation:
Since a jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint, and each time you draw out an item, you record the outcome and put the item back in the jar before making another draw, to determine what is the probability that you get exactly the sequence candy-mint-candy, in that order, the following calculation should be performed:
4 + 7 + 3 = 14
7/14 x 3/14 x 7/14 = X
0.5 x 0.2142 x 0.5 = X
0.053 = X
Therefore, the probability that the chosen sequence will be obtained is 0.0530, or 5.3%.
Bateman Corporation sold an office building that it used in its business for $800,800. Bateman bought the building 10 years ago for $599,600 and has claimed $201,200 of depreciation expense. What is the amount and character of Bateman's gain or loss?
Answer:
$402.700 capital gain
Step-by-step explanation:
Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test
The null hypothesis is [tex]\mu = 39.09[/tex]
The symbol [tex]\mu[/tex] is the Greek letter mu
The alternate hypothesis is [tex]\mu \ne 39.09[/tex] telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to [tex]\mu \ne 39.09[/tex]
So either mu is 39.09 or it's not 39.09
You can use H0 and H1 to represent the null and alternate hypotheses respectively.
----------------------
Summary:
The two hypotheses are
H0: [tex]\mu = 39.09[/tex]
H1: [tex]\mu \ne 39.09[/tex]
This is a two tailed test.
There is enough grass to feed six cows for three days. How long would the same amount of grass feed nine cows
Answer:
2 days
Step-by-step explanation:
Lets say that in one day, one cow eats 1 block of grass. So, six cows in three days would eat 18 blocks of grass in total. So 18 blocks of grass is how much we have. that means nine cows would eat that much in 2 days.
6. Calculate the area of the octagon in the
figure below.
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement S (to take at least one science course). A poll of 150 sophomore students shows that: 60 completed M, 45 completed S, and 25 completed both M and S
Find the number of students who have completed
(a) At least one of the two requirements
(b) Exactly one of the two requirements
(c) Neither requirement.
all students = 150
M = 60
S = 45
M and S = 25
(a) At least one of the two requirements:
M or S = M + S - (M and S) = 60 + 45 - 25 = 80
(b) Exactly one of the two requirements:
(M or S) - (M and S) = 80 - 25 = 55
(c) Neither requirement:
(all students) - (M or S) = 150 - 80 = 70
I feel like it would be 6/10 but that’s not an answer
Answer:
I think it would be 3/4
Step-by-step explanation:
Which of the following best describes the relationship between angle a and angle bin the image below?
A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting point?
Answer:
The answer is "1035.76 miles"
Explanation:
The aircraft flies at 120 mph for 1.5 hours at a [tex]10^{\circ}[/tex] bearing, then flies at the very same speed at [tex]100^{\circ}[/tex] bearings for 8.5 hours.
However an angle of [tex]100-10 = 90^{\circ}[/tex] between displacements
First shifts[tex]= 1.5 \times 120 = 180\ miles.[/tex]
Second shift [tex]= 8.5\times 120 = 1020\ miles.[/tex]
These two shifts are at [tex]90^{\circ}[/tex] and therefore the final shift is:
[tex]\to \sqrt{180^2+1020^2}=1035.76 \ miles[/tex]
