Answer:
x= -3 ± [tex]\sqrt{21}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex]+6x=12
We add 9 [[tex](6/2)^{2}[/tex]] to both sides to complete the square as [tex]x^{2}[/tex]+6x+9 = [tex](x+3)^{2}[/tex].
[tex](x+3)^{2}[/tex]=21
Now we take the square root of both sides:
x+3=±[tex]\sqrt{21}[/tex]
x= -3 ± [tex]\sqrt{21}[/tex]
Answer:
x = -3 ± [tex]\sqrt{21}[/tex]
Step-by-step explanation:
[tex]x^2+6x=12[/tex]
[tex](\frac{b}{2} )^{2}[/tex] = 9
[tex]x^2+6x + 9 =12 + 9[/tex]
[tex](x+3)^{2} =21[/tex]
x + 3 = [tex]\sqrt{21}[/tex]
x = -3 ± [tex]\sqrt{21}[/tex]
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
Prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
PLEASE HELP
The function in the table is quadratic:
TRUE
FALSE
Answer:
False
Step-by-step explanation:
Each f(x) increases by 8 therefore this equation is a linear function. If you where to graph it would be a straight line
Hope this helped :)
Answer:
False
Step-by-step explanation:
The slope is the same between all pounts which means the function is linear.
Hope this helps!
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend
Bean Regular DeCaf
Brazilian Natural 75% 40%
Columbian Mild 25% 60%
Romans sells the regular blend for $3.60 per pound and the Decaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Columbian coffee beans that will enable the production of 1000 pounds of Romans Regular coffee and 500 pound of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Columbian Mild that will maximize the total contribution to profit. What is the optimal solution and what is the contribution profit?
Answer:
z(max) = 2996.13 $
x₁ = 968 x₂ = 430 ( quantities of regular and Decaf coffee respectevely)
Total quantity of BN = 898 pounds
Total quantity of CM = 500 pounds
Step-by-step explanation:
Cost of the beans
Brazilian natural = Price market + 10 % = 0.47 + 0.047
BN Cost = 0.517 $/lb
Clombian Mild = Price market + 10 % = 0.62 + 0.062
CM Cost = 0.682 $/lb
Composition of the coffee blend
Regular coffee 0.75 BN + 0.25 CM
De Caf coffee 0.40 BN + 0.60 CM
PRICES
Regular Roman = 3.60 $
Decaf = 4.40 $
Production costs:
Regular Roman = 0.80 $/lb
Decaf = 1.05 $/lb
Packaging costs: 0.25 $/Lb both
Profit = Price - cost
Profit of regular coffee = 3.60 - 0.80 - 0.25 -Cost of bean
for regular coffee cost of BN + CM
BN is : 0.75*BN cost = 0.75*0.517 = 0.38775 and
CM is : 0.25*0.682 = 0.1705
Profit of regular coffee = 1.99175 $
Profit for Decaf coffee = 4.4 - 1.05 - 0.25 - ( 0.517*0.4 + 0.6*0.682)
Profit for Decaf coffee = 4.4 - 1.30 - 0.616
Profit for Decaf coffee = 2.484 $
Let´s call x₁ pounds of regular coffee and x₂ pounds of Decaf coffee then:
Objective Function is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
Availability of beans for 1000 pounds of Regular coffee means:
750 pounds of BN + 250 pounds of CM
Availability of beans for 500 pounds of Decaf coffee means
200 pounds of BN + 300 pounds of CM
Then 750 + 200 = 900 pounds of BN
And 250 + 300 = 550 pounds of CM
Availability of beans for 1000 pounds of Decaf coffee correspond to
0.75 *x₁ + 0.40*x₂ ≤ 900
Availability of beans for 500 pounds of Regular coffee correspond to
0.25*x₁ + 0.60*x₂ ≤ 500
Then the model is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
0.75 *x₁ + 0.40*x₂ ≤ 900
0.25*x₁ + 0.60*x₂ ≤ 500
General constraints x₁ ≥ 0 x₂ ≥ 0 both integers
After 6 iterations optimal solution ( maximum z) is
z(max) = 2996.13 $
x₁ = 968 x₂ = 430
x₁ and x₂ are quantities of Regular and Decaf coffee respectively, to find out quantities of Brazilian Natural and Colombian Mild
we proceed as follows
Regular coffee is : 0.75*968 = 726 pounds of BN
Decaf coffee is : 0.40*430 = 172 pounds of BN
Total quantity of BN = 898 pounds
Regular coffee is : 0.25*968 = 242 pounds of CM
Decaf coffee is : 0.6*430 = 258 pounds of CM
Total quantity of CM = 500 pounds
number of bald eagles in a country a discrete random variable, a continuous random variable, or not a random variable?
Answer:
Discrete random variable.
Step-by-step explanation:
Discrete variable:
Countable numbers(0,1,2,3,...)
Continuous variable:
Can assume decimal values, such as 0.5, 2.5,...
Number of bald eagles:
Number of bald eagles is a countable value, either there a 0, 100, 1000,... so it is a discrete random variable.
Answer:
Discrete random variable.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals
make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
Learn more about exponential equation here
https://brainly.com/question/23729449
#SPJ2
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
Answer:
the operating characteristics have been solved below
Step-by-step explanation:
we have an average of 10 minutes per customers
μ = mean service rate = 60/10 = 6 customers in one hr
the average number of customers that are waiting in line
mean arrival λ = 2.5
μ = 6
[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]
= 6.25/21
= 0.2976
we calculate the average number of customers that are in the system
[tex]L=Lq+\frac{2.5}{6}[/tex]
= 0.2976+0.4167
= 0.7143
we find the average time that a customer spends in waiting
[tex]Wq=\frac{0.2976}{2.5}[/tex]
= 0.1190 hours
when converted to minutes = 0.1190*60 = 7.1424 minutes
[tex]0.1190+\frac{1}{6}[/tex]
=0.2857
probability that arriving customers would wait for the service
= 2.5÷6 = 0.4167
simplify 6 x + 3y /3
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
I need help with this word problem.
Answer:
$3.22 per square feet
Step-by-step explanation:
To solve, I usually set up an equation:
sq ft = 12 1/2 = 1
$ 40.21 x
Then, use cross multiplication.
(12 1/2)x=40.21
Divide both sides by 12 1/2 or 12.5
x = 3.2168
Round to the hundredths place [because we're dealing with money]
$3.22
I hope this helps!
Answer:
3.22 per sq ft
Step-by-step explanation:
Take the total cost and divide by the amount of tiles
40.21 / 12.5
3.2168 per sq ft
Rounding to the nearest cent
3.22 per sq ft
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answer:
The numerical values of the circumference and area of the circle are equal.
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8
Answer:
[tex]x = 77[/tex]
Step-by-step explanation:
Given
[tex]First \to Second[/tex]
[tex]35 \to x[/tex]
[tex]20 \to 44[/tex]
[tex]20 \to 44[/tex]
Required
Find x by SSS
Represent the triangle sides as a ratio
[tex]35 : x = 20 : 44[/tex]
Express as fraction
[tex]\frac{x}{35} = \frac{44}{20}[/tex]
Multiply by 35
[tex]x = \frac{44}{20} * 35[/tex]
[tex]x = \frac{44 * 35}{20}[/tex]
[tex]x = \frac{1540}{20}[/tex]
[tex]x = 77[/tex]
Answer:
ccccccccccccccccccccccccccc
Step-by-step explanation:
Help me plz I can’t figure it out
Answer:
m = 60
Step-by-step explanation:
The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :
- The last one because then a parent would drop their child off earlier
- The first one and the third one because it is too long
What is the equation of the line that is perpendicular to
and has the same y-intercept as the given line?
(0,0)
(5,0)
O y = x+1
O y = x+5
o y = 5x + 1
O y = 5x + 5
-6 -5 -4 -3 -2 -1
23
4 5 6
Mark this and return
Save and Exit
Nyt
Submit
Answer:
y = 5x + 1
Step-by-step explanation:
Given the coordinate points (0,1) and (5,0)
First, get the slope
Slope m =(0-1)/5-0
m = -1/5
Since the required line is perpendicular, then the required slope is;
M = -1/(-1/5)
M = 5
Since 1the y intecept id (0,1) i.e. 1
Required equation is y = mx+b
y = 5x + 1
This gives the required equation
Note that the coordinate (0,1) was used instead os (0,0)
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
Geometry Oddsseseyware
Matthew earns extra money by doing odd jobs for his neighbors. He charges a flat fee of $20 plus $7 per hour for each job. If he earned $90 for a job he did last week, how many hours did he work?
Answer:
10 hours
Step-by-step explanation:
ok so we know he is getting payed $20 + $7 every hour so what i would do is keep the multiply the 7 till you get 70 so thats 7x10=70 and 70+20=90 so he worked for 10 hours last week :) i hope this helps, i tried my best to explain it
Instructions: Solve the following linear
equation
4(n + 5) – 2(5 + 7n) = -70
n =
Answer:
Step-by-step explanation:
4*(n +5) - 2*(5 + 7n) = -70
4*n + 4*5 + 5*(-2) + 7n*(-2) = -70
4n + 20 - 10 - 14n = -70
4n - 14n + 20 - 10 = -70
- 10n + 10 = -70
Subtract 10 from both sides
-10n = -70 - 10
-10n = -80
Divide both sides by (-10)
n = -80/-10
n = 8
Step-by-step explanation:
sjbsbsbeekejebebheebebejekek
What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
angle P and angle Q are complementary. The measure of angle Q is 33.5°. What is the measure of angle P?
Answer:
56.5 degrees
Step-by-step explanation:
Because complementary angles are when their sum is 90, you get the equation:
P + Q = 90
Since Q is 33.5,
P + 33.5 = 90
Subtracting 33.5 from both sides,
P = 56.5
There's a three in the tens
placed
The digit is the ones places is
third multiple of three
It is a two-digit number
Answer:
That number is 39
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
[tex](v+6)^{2}=2v^{2}+14v+12[/tex]
Answer:
v=-6 or 4
Step-by-step explanation:
Answer:
the answer would be 5
Step-by-step explanation:
have to do the question multiply add and divide to find your answer
A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The estimate of the mean viewing time should be within 0.25 hour. The 95% level of confidence is to be used. How many executives should be surveyed? (Use z Distribution Table.)
How many executives should be surveyed? (Round the final answer to the next whole number.)
Answer:
554 executives should be surveyed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 3 hours.
This means that [tex]\sigma = 3[/tex]
The 95% level of confidence is to be used. How many executives should be surveyed?
n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96*3[/tex]
[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]
[tex]n = 553.2[/tex]
Rounding up:
554 executives should be surveyed.
Identify the level of measurement of the data, and explain what is wrong with the given calculation. Ina set of data, alert levels are represented as 1 for low, 2 for medium, and 3 for high. The average mean of the 522 alert levels is 1.3. The data are at the ________ level of measurement. a. Nominalb. Ordinalc. Ratiod. IntervalWhat is wrong with the given calculation?a. Such data should not be used for calculations such as an average.b. One must use a different method to take the average of such datac. The true average is 2.5d. There is nothing wrong with the given calculation.
Answer:
(1) Ordinal
(2) Such data should not be used for calculations such as an average.
Step-by-step explanation:
Given
[tex]1 \to Low[/tex]
[tex]2 \to Medium[/tex]
[tex]3 \to High[/tex]
[tex]Average = 1.3[/tex]
Solving (a): The level of measurement
When observations are presented in ranks such as:
[tex]1 \to Low[/tex]
[tex]2 \to Medium[/tex]
[tex]3 \to High[/tex]
The level of measurement of such observation is ordinal
Solving (b): What is wrong with the computation?
Ordinal level of measurement are not numerical values whose average can be calculated because they are used as ranks.
Hence, (a) is correct
Find the slope of the line that passes through the two points. 4,4 & 4,9
HELPPPPPPP
Answer:
is 22
Step-by-step explanation:
Answer:
It doesn't have a slope?
Step-by-step explanation:
Knowing that the slope equation is y2-y1/x2-x1
9-4 5
----- = ------ = 0
4-4 0
this means that the slope is 0...
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
10-
If(x)
1
х
10
-5
5
10
g(x)
-10
A. g(x) = (– x)2 - 3
B. g(x) = – x2 + 3
c. g(x) = (-x)2 + 3
D. g(x) = -X2 - 3
Answer:
[tex]g(x) = -x^2 + 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
Required
Determine g(x)
First, shift f(x) down by 3 units
The rule is:
[tex]f'(x) = f(x) - 3[/tex]
So:
[tex]f'(x) = x^2 - 3[/tex]
Next, reflect f'(x) across the x-axis to get g(x)
The rule is:
[tex]g(x) = -f(x)[/tex]
So, we have:
[tex]g(x) = -(x^2 - 3)[/tex]
Open bracket
[tex]g(x) = -x^2 + 3[/tex]
Answer:
D
Step-by-step explanation:
I figured out the hard way
Solve this
4 X (10 - 3+2)
Answer:
36
Step-by-step explanation:
10-3=7+2=9
4×9=36
36 is the answer
