what is 2x-6 >-16 and 3x-10 8
Answer: 2x-6>-16 = -5
Step-by-step explanation:
add 6 to -16, you get -10.
divide 2x by 10, you get -5
The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 4,700 students who would like to take a course, and there are 58 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed, accommodate all of the students, and give one teaching assignment to each professor?
Answer:
The number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
Step-by-step explanation:
[tex]x[/tex] = Number of sections in Ancient history
[tex]y[/tex] = Number of sections in Medieval history
[tex]z[/tex] = Number of sections in Modern history
The number of sections that are allowed is 45 so
[tex]x+y+z=45[/tex]
The number of students in each section is 4700 where 100 of them take ancient history 50 of them take medieval history and 200 take modern history so
[tex]100x+50y+200z=4700[/tex]
The number of professors is 58 where Ancient and Medieval History need only 1 professor per section and Modern History sections are taught by a team of 2 professors, so
[tex]x+y+2z=58[/tex]
Solving the first and last equations by subtracting them we get
[tex]-z=-13\\\Rightarrow z=13[/tex]
Substituting this value in the second equation and first equation we get
[tex]100x+50y+2600=4700\\\Rightarrow 100x+50y=2100\\\Rightarrow 2x+y=42[/tex]
[tex]x+y+13=45\\\Rightarrow x+y=32[/tex]
Solving these equations by subtracting them we get
[tex]x=10[/tex]
[tex]x+y=32\\\Rightarrow y=32-10=22[/tex]
So, [tex]x=10, y=22, z=13[/tex]
Hence, the number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
Please help I don't understand!!!!!!
Answer:
X-3
Step-by-step explanation:
The graph shifted 3 units to the left so you subtract from the x value.
How do I write the equation of hyperbola in standard form with center (0,0),endpoints of the transverse axis (±6,0) and length of latus rectum is 16?
Answer:
Length of latusrectum =9=
a
2b
2
⇒b
2
=
2
9a
..... (i)
and e=
4
5
∵1+
a
2
b
2
=
16
25
∴1+
2a
2
9a
=
16
25
[from Eq. (i)]
⇒
2a
9
=
16
9
⇒a=8
On putting the value of a in Eq. (i), we get
b
2
=
2
9×8
=36⇒b=6
∴ Equation of hyperbola is
8
2
x
2
−
6
2
y
2
=1⇒
64
x
2
−
36
y
2
=1
Bits are items of ________.
A. Biannual data
B. Bimodel data
C. Binary data
D. Binomial data
Answer:
C. Binary Data
Step-by-step explanation:
Andrew is showing his work in simplifying (−5.7 + 2.2) − 1.1.
Step 1: (2.2 − 5.7) − 1.1
Step 2: 2.2 − (5.7 + 1.1)
Step 3: 2.2 − (6.8)
Step 4: −4.6
Which statement is true?
In step 1, Andrew used the commutative property.
In step 2, Andrew used the distributive property.
In step 3, Andrew used the associative property.
In step 4, Andrew's answer is incorrect.
Step 2 i believe im not sure tho.
Three less than the product of a number and two
A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt." How many batches are represented by the diagram? mustard seeds (tsp) chili powder (tsp) salt (tsp)
you need to put a picture again
sorry i cant answer because it doesnt show diagram
Solve for y.
2y − 2 = 8
y =
Answer:
y=5
Step-by-step explanation: 8+2=10 so 10/2=5
Describe your thinking and the steps taken when developing an
algebraic representation for the sum of the first t terms of a
linear sequence.
Let's see what to do buddy...
_________________________________
Step (1)
Suppose we want to find the sum of numbers from 1 to n.
To do this, we use the following method.
By writing the sum of numbers from 1 to n
, Then we write the sum of numbers n to 1 below it, see :
[tex]s = 1 + 2 + 3 + ... + n[/tex]
[tex]s = n + (n - 1) + (n - 2) + ... + 1 \\ [/tex]
Now we add the sentences of the above two phrases, peer to peer like this :
[tex]1 + n = n + 1 \\ [/tex]
[tex]2 + n - 1 = n + 1[/tex]
[tex]3 + n - 2 = n + 1[/tex]
And the others.....
So we have :
[tex]2s = ( n + 1) + (n + 1) + ... + (n + 1) \\ [/tex]
We had n numbers to sum so we have :
[tex]2s = n \times (n + 1)[/tex]
Divided the sides of the equation by 2
[tex]s = \frac{n \times (n + 1)}{2} \\ [/tex]
Remember this step I will use it again.
_________________________________
Step (2)
What does the linear sequence mean ?
The linear sequence is the sequence which any terms created by the sum of previous term with constant.
I name that constant value d.
According to above :
[tex]t(2) = t(1) + d[/tex]
And
[tex]t(3) = t(2) + d [/tex]
[tex]t(3) = t(1) + d + d[/tex]
[tex]t(3) = t(1) + 2d[/tex]
I have a question ;
[tex]3 - 1 = 2[/tex]
Is it correct ?
If it is correct we have :
[tex]t(3) = t(1) + (3 - 1)d[/tex]
WOW we found a thing ;
Put n instead of 3 :
[tex]t(n) = t(1) + (n - 1)d[/tex]
_________________________________
Step (3)
Stop right here.
Let's go to find the sum of the n first terms of the linear sequence.
Do you remember what did we do in step(1) ? Of course you do.
Let's do it again.
[tex]s = t(1) + t(2) + t(3) + ... + t(n) \\ [/tex]
[tex]s = t(n) + t(n - 1) + t(n - 2) + ... + t(2) + t(1) \\ [/tex]
According to the thing what we found in step(2) we have :
[tex]s = t(1) + ( \: t(1) + d \: ) + ( \: t(1) + 2d \: ) + ... + ( \: t(1) + (n - 1)d \: ) \\ [/tex]
[tex]s = ( \: t(1) + (n - 1)d \: ) + ( \: t(1) + (n - 2)d \: ) + ... + t(1) \\ [/tex]
Sum the two above equation's terms like this:
[tex]t(1) + t(1) + (n - 1)d = 2t(1) + (n - 1)d \\ [/tex]
And
[tex]t(1) + d +t(1) + (n - 2)d = 2t(1) + d(n - 2 + 1) = 2t(1) + (n - 1)d \\ [/tex]
And the others like this.
We had n terms so we sumed n terms.
So we have :
[tex]2s = n \times ( \: 2t(1) + (n - 1)d \: )[/tex]
Divided the sides of the equation by 2
[tex]s(n) = \frac{n}{2} \times ( \: 2t(1) + (n - 1)d \: ) \\ [/tex]
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Which type of parent function is graphed on the coordinate plane?
Answer:
f(x)=∛x
Step-by-step explanation:
Suzi starts her hike at 200 feet below sea level. When she reaches the end of the hike, she is
still below sea level at -190 feet. What was the change in elevation from the beginning of
Suzi's hike to the end of the hike?
3.8.10) Inclusions are defects in poured metal caused by contamitants. The number of (large) inclusions in cast iron follows a Poisson distribution with a mean of 2 per cubic millimeter. Deter mine the following:
(a) Probability of at least one inclusion in a cubic millimeter.
(b) Probability of at least 3 inclusions in 4.0 cubic millimeters.
(c) Volume of material to inspect such that the probability of at least one inclusion is 0.98
(d) Determine the mean inclusion per cubic millimeter such that the probability of at least one inclusion is 0.98.
Answer:
a) P(X>=1) = 0,7293 or P(X>=1) = 72,93 %
b) P(X>=3) = 0,5686 or P(X>=3) = 56,86 %
c) y = 0,8494 mm³
d) λ = 1,69897 inc per mm³
Step-by-step explanation:
a) P(X>=1) = 1 - P(X=0)
P(X = 0) = λ⁰ * e∧⁻λ / 0! where λ = 2 in/mm³
P(X = 0) = e∧-2 ⇒ P(X = 0) = 0,2706
Then
P(X>=1) = 1 - 0,2706
P(X>=1) = 0,7293 or P(X>=1) = 72,93 %
b) 3 inc. in 4 mm³ = 2*4/3 λ = 2,67 inc. per mm³
P(X>=3) = 1 - P(X=1 ) - P(X=2)
P(X=1) = λ¹ * e∧-λ / 1! ⇒ P(X=1) = 2,67 *e∧- 2,67/1
P(X=1) = 0,1846
P(X=2) = λ² * e∧-λ / 2! ⇒ P(X=2) = (2,67)² * e ∧ - 2,67/2
P(X=2) = 7,1289* 0,06925/2 ⇒ P(X=2) = 0,2468
Then
P(X>=3) = 1 - 0,1846 - 0,2468
P(X>=3) = 0,5686 or P(X>=3) = 56,86 %
c) P(X>=1) = 0,98
and λ = 2*y where y is the quantity of material
P(X=0) = 1 - P(X>=1)
P(X=0) = 1 - 0,98 P(X=0) = 0,02
0,02 = (2*y)⁰ * e ∧ -2*y /0!
0,02 = 1 * e ∧ -2*y
Taking log on both sides of the equation
log (0,02) = -2*y - 1,69897 = - 2*y
y = 0,8494 mm³
d) P(X >=1 ) = 1 - P( X = 0)
0,98 = 1 - P( X = 0)
P( X = 0) = 0,02
0,02 = λ⁰ * e ∧ - λ / 0!
0,02 = e ∧ -λ
Taking log on both sides of the equation we get:
log ( 0,02 ) = - λ
- 1,69897 = - λ
λ = 1,69897 inc. per mm³
A sports club tests its players for steroid usage with a test that gives a positive reading 93% of the time when administered to a steroid user and gives a negative reading 96% of the time when administered to a player who does not use steroids. It is known that 8% of the players are steroid users. Draw a probability tree diagram for the given problem.
What is the probability that a player does not use steroids, given that the person had a positive reading on the test? Round your answer to four decimal places.
Answer:
P(no steroid user / positive reading on test) = 0.3309
Step-by-step explanation:
Computation:
Bayes' Theorem:
P(A / B) = P(A and B) / P(B)
P(no steroid user / positive reading on test) = P(no steroid user and positive) / P(positive)
P(no steroid user / positive reading on test) = (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)
P(no steroid user / positive reading on test) = 0.3309
The probability that a player does not use steroids, given that the person had a positive reading on the test is 0.3309.
Calculation of the probability:Since A sports club tests its players for steroid usage with a test that gives a positive reading 93% of the time when administered to a steroid user and gives a negative reading 96% of the time when administered to a player who does not use steroids. It is known that 8% of the players are steroid users.
So, here the probability should be
P(no steroid user / positive reading on test) = (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)
= 0.3309
Hence, The probability that a player does not use steroids, given that the person had a positive reading on the test is 0.3309.
Learn more about probability here: https://brainly.com/question/24442276
(-12,8), (9,1)
What is the point-slope form of the equation of the line?
Answer:
y-y1 = m (x-x1)
where
m is the slope
and (x1,y1) is one of the points given.
You have been given 2 points (-12,8) and (9,1). You can call one of them (x1,y1) and the other (x2,y2). It doesn't matter which one is which.
But before we go further, we need to determine the slope.
We can do this from the points as well.
y2-y1
m = ---------
x2-x1
Let's say
(x1,y1) = (-12,8)
(x2,y2) = (9,1)
This gives us a slope of
y2-y1 1-8 -7 -1
m = --------- = ---------- = ---- = ---
x2-x1 9-(-12) 21 3
Now that we have everything we need
y-8 = (-1/3)[x-(-12)]
Distribute the -1/3
y-8 = (-1/3)x -4
If we add 8 to both sides we have the equation in the slope intercept form (y=mx+b)
y = (-1/3)x + 4
A ball is thrown into the air with an initial velocity of 22 meters per second.
The quadratic function ℎ() = −4.9
2 + 22 + 5.5 represents the height of
the ball above the ground, in meters, with respect to time , in seconds.
Part A: Determine ℎ(3) and explain what it represents.
Answer:
27.4 metres
Step-by-step explanation:
Um, your question is missing the x's. I'm going to assume, -4.9x^2+22x+5.5
= -4.9(3)^2+22(3)+5.5
= 27.4
At 3 seconds the ball is 27.4 metres above the ground.
Greg ran 12 miles a day on 18 different days last month. How many miles did he run?
Answer:
216
Step-by-step explanation:
12*18=216
hope this helps :3
if it did pls mark brainliest
I need help plz mark brainliest
Answer:
Yes, No, No, Yes
Step-by-step explanation:
Answer:
A.) No
B.) No
C.) No
D.) Yes
Step-by-step explanation:
I just did it a month ago.
Find the value of x in the following ratio 3:15=x:30
b) x :9 =4=36
-3-(3-10)
can someone help me find the answer to this integer problem plz
question likh kar bhej dijiye
11.
April is going to the bakery to purchase donuts and cinnamon rolls for the office personnel. She must purchase at least 30 items. She has collected only $30, so total cost must be no more than $30. If d represents donuts that cost $0.75 each and r represents cinnamon rolls that cost $1.25 each, which system of inequalities can be used to represent the region for the number of donuts and cinnamon rolls April could purchase?
A.d + r ≥ 30
0.75d + 1.25r ≤ 30
B. d + r ≥ 30
1.25d + 0.75r ≤ 30
C. d + r ≤ 30
0.75d + 1.25r ≥ 30
D. d + r ≤ 30
1.25d + 0.75r ≥ 30
Please answer quickly :)
The system of inequalities that can be used to represent the region for the number of donuts and cinnamon rolls April could purchase is $0.75d + $1.25r ≤ $30
April cannot spend more than $30. Thus, the inequality sign that would be used is ≤ (the less than or equal to sign).
April wants to purchases two items, cinnamon rolls and donuts. The donuts cost $0.75 per dollar and cinnamon rolls cost $1.25 per dollar.
The total amount April can spend on donuts = $0.75 x d = $0.75d
The total amount April can spend on cinnamon rolls = $1.25 x r = $1.25r
The sum of $0.75d and $1.25r has to be less than $30
This can be represented with this inequality: $0.75d + $1.25r ≤ $30
A similar question was solved here: https://brainly.com/question/18649886?referrer=searchResults
The juice dispenser in the cafeteria holds 21 1/4 pints of juice. The glasses in the cafeteria only hold 1/4 of a pint of juice. How many full glasses can be served at breakfast?
Answer:
85 can
Step-by-step explanation:
21 x 4 = 84
Then you add one more because there is still 1/4 of a pint left and each cup can hold that much too.
what is the reciprocal of 8
Answer:
0.125
Step-by-step explanation:
to get the reciprocal of a number we divide the number by 1
in this case it would be 1 divide by 8
1/8 = 0.125
1 meter is equal to 37.3701 inches. What is 37.3701 inches rounded to the nearest tenth?
Answer:
37.4
Step-by-step explanation:
the number places after the column go as followed ; tenth, hundredths, thousandths, ten thousandths
Running 7/4 miles in 11 minutes how many miles per minutes
Answer:
it is either 10 or 6.67 minutes per hour
Step-by-step explanation:
if you ran 3 miles basically in 30 minutes :30 minutes divided 3 miles = 10 minutes per mile pace or 6.67 minutes per hour
The ratio of the number of Andy's seashells to the number of seashells Ben has is 4:9. Andy has 100 seashells. How many does Ben have?
Answer:
Ben has 225
Step-by-step explanation:
100 ÷ 4 = 25
25 × 9 = 225
Use the Distributive Property to expand the expression -(u-v)
Answer:
(U+V) is the answer to the solution
convert 3250 ml to L
Answer:
3250 milliliters transfers into 3.25 liters.
The slope of the line passing through the points (2,3) and (4, y) is
3/2. What is the value of y?
Answer:
6
Step-by-step explanation:
y2-y1 y-3 =3 what -3 =3? 6 :)
x2-x1 4-2 = 2
slope is 3/2
A transportation engineer uses the formula, R = 1600/15+127e, to determine the minimum radius of curvature (R) in meters, for a roadway with a 40 km/hr design speed and a maximum superelevation rate (e). What is the maximum superelevation rate recommended if the radius of curvature is 350 meters? Answer as a decimal, rounded to two decimal places.
Answer:
The value is [tex] e = 1.92 [/tex]
Step-by-step explanation:
From the question we are told that
The formula for radius of curvature is [tex]R = \frac{1600}{15} +127e[/tex]
The design speed of the roadway is [tex]v = 40 \ km/hr[/tex]
The value of radius of curvature considered R = 350 m
From the equation given e is the superelevation rate
Now making the subject of the formula
[tex] e = \frac{R}{127} - \frac{1600}{1905} [/tex]
At R= 350
[tex] e = \frac{350 }{127} - \frac{1600}{1905} [/tex]
[tex] e = 1.92 [/tex]
Here, we are required to determine the maximum superelevation rate, e (rounded to 2 decimal places) recommended if the radius of curvature, R is 350 meters.
The answer is e = 1.92 (rounded to 2 decimal places).
First, from the information given, the minimum radius of curvature, R is related to the maximum superelevation rate, e by the formular;
R = (1600/15) + (127e)
Therefore, to evaluate the value of e for R = 350, we have;
350 - (1600/15) = 127e.
350 - (1600/15) = 127e.350 - 106.667 = 127e
Therefore, 243.333 = 127e.
Therefore, e = 1.9160meters
As a result, The maximum superelevation rate, e recommended if the radius of curvature, R is 350 meters is:
e = 1.92 (rounded to 2 decimal places).Read more:
https://brainly.com/question/21140562