[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -8 +2}{2}~~~ ,~~~ \cfrac{ 5 -6}{2} \right) \implies \left(\cfrac{ -6 }{2}~~~ ,~~~ \cfrac{ -1 }{2} \right)\implies \left(-3~~,~~-\cfrac{1}{2} \right)[/tex]
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have what property?
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
What are equal intervals?Equal intervals denote that the variations between numbers (units) are the same anywhere on the scale (e.g., the difference between 4 and 5 is the same as the difference between 76 and 77). The difference between two successive categories is equal in an equal interval. Temperature measured in Fahrenheit, for example, has equal intervals; that is, the difference between 30 and 31 degrees is one degree, and the difference between 100 and 101 degrees is one degree.When the relationship between a scale's unit of measurement (strength) and a consequence (pounds lifted) can be described by the linear equation y = a bx, the scale is said to possess an equal intervals property.Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
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If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, measure of angle 1 = 133 degrees, find the measures of angle 2 and angle 3
If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, The measure of ∠2 = 47° and ∠3 = 133°.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are supplementary angles as the total of these two angles is 180°. The sum of complimentary angles is 90 degrees.
Given,
the measure of angle 1 = 133°
As, ∠1 + ∠2 are supplementary angles,
⇒ ∠1 + ∠2 = 180° ......(1)
∠2 + ∠3 are supplementary angles,
⇒ ∠2 + ∠3 = 180° .......(2)
From (1),
⇒ 133° + ∠2 = 180°
⇒ ∠2 = 47°
From (2),
47° + ∠3 = 180°
∠3 = 133°
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Find the equation of the line.
Use exact numbers.
y=
#+
DIG DEEPER The diagram shows the elevation changes between checkpoints on a trail.
A drawing shows the change in elevation between checkpoints on a mountain trail. From a point labeled start, the trail moves down to a point which is labeled negative 174 feet from the starting point. The trail then moves upward up to a point labeled 350 feet above the previous point. Next, the trail moves down to a point which is labeled negative 180 feet below the previous point. Then the trail moves up to a point labeled 282 feet above the previous point labeled end.
The trail begins at an elevation of 8136 feet. What is the elevation at the end of the trail?
The elevation is
feet.
Skip to navigation
Using operations with integers, it is found that the elevation at the end of the trail is of 8,414 feet.
How to find the elevation at the end of the trail?We initially take the initial elevation, and then:
We add positive points labeled on the graph.We subtract negative points labeled on the graph.Thus, operations of sum and subtraction with integers are used to find the final elevation.
From the listed points on the problem, the operations are given as follows:
-174, 350, -180, +282.
The trail begins at an elevation of 8136 feet, hence the final point can be found as follows:
8136 - 174 + 350 - 180 + 282 = 8414 feet.
The elevation at the end of the trail is of 8,414 feet.
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Samir just got hired for a new job and will make $50,000 in his first year. Samir was told that he can expect to get raises of $2,500 every year going forward. How much money in salary would Samir make in his 29th year working at this job?
122.500$
First hello I hope you are doing. The first step is to multiply 2.500 with 29 and the result is 72.500$ . Then you add the 50.000$ to 72.500$ which is the raise and you have the result which is 122.500$
I hope I helped you
8x+5=hx-8
find h
why does this only have one answer
Answer:
it's supposed to have 2 answers Because we are looking for h and x (we have two "unknown") so therefore we are gonna get two answer.if you don't mind let's solve it:8x+5=hx-8
collect like terms (values that are alike in one place)
8x-hx = -8-5
8x-hx = -13
8x -hx+13 =0
factorize
x(8-h) + 13 =0
we can't do nothing to it anymore I think
Hope this helpsace that workGood luck ✅Solve the quadratic equation by completing the square.
x²+12x+33=0
[tex]x^2 + 12x=-33 \\ \\ x^2 + 12x+36=3 \\ \\ \boxed{(x+6)^2=3} \\ \\ x+6=\pm \sqrt{3} \\ \\ \boxed{x=-6 \pm \sqrt{3}}[/tex]
The function f(x) is given by the set of ordered pairs.
{(8, –3), (0, 4), (1, –5), (2, –1), (–6, 10)}
Which is true regarding the function?
A bed has a sale price of £257.40
This is a saving of 22% on the original price.
What was the original price of the bed?
The original price of the bed was £330.
Calculating priceFrom the question, we are to determine the original price of the bed.
Let the original price of the bed be x
From the given information,
The current sale price of the bed is £257.40, and this price is a saving of 22% on the original price
Then,
We can write that
x - 22% of x = £257.40
Thus,
x - 0.22x = £257.40
0.78x = £257.40
x = £257.40/0.78
x = £330
Hence, the original price of the bed was £330.
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Answer:330
Step-by-step explanation:
easy way to do this:
1. ok so you know 100%=x and 100-22=73 so that means that 73%=2570.40
2. so write them with the known above the unknown: 100%=x
78%=2457.40
3. no cross multiply like this [tex]\frac{100X257.40}{78}[/tex] imagine the multiplication sign is the X here( the app didn't let me change that?)
4. the solution equals 330 which the answer
5. YOU DID IT!!
Given m∠ADC= 118°, find m∠ADB.
118=11x-7+5x-3
118=16x-10
128=16x
8=x
11x-7=adb
88-7=adb
81 degrees
Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets for $20. The venue has the capacity to hold
400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise $5,000 for her school:
How many Pre-sale Tickets tickets must she sell to make her goal?
A)400
B)300
C)250
D)100
The number of presales tickets can be obtained as 300. The correct option is (B).
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
Since, total number of people are 400.
Suppose the number of pre-sales tickets be x.
Then, the number of at door tickets is given as 400 - x.
As per the question, the following equation can be written for total money raised as,
⇒ 10x + 20(400 - x) = 5000
⇒ 10x = 3000
⇒ x = 300
Hence, the number of pre-sales tickets is given as 300.
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Answer: The answer would be 100.
Step-by-step explanation:
Frank was born in 1933 and died in 1946 at the age of 57. How can this be?
Answer:
Frank was born in 1933 and died in 1946 at the age of 57. 1933 and 1946 are not years but just room or ward numbers.
EXPLANATION:
The numerical 1933 and 1946 do not signify the year of birth or death. No where in the question is the word 'years' mentioned. Thus 1933 signifies either the room number or the ward number of the hospital Frank was born in.
Similarly 1946 is the room or ward number where Frank died. Hence his age is irrelevant with respect to 1933 and 1946. His related age of 57 thus has nothing to do with them.
Answer:
The numerical 1933 and 1946 do not signify the year of birth or death. Nowhere in the question is the word ‘years’ mentioned. Thus 1933 signifies either the room number or the ward number of the hospital Frank was born in.
Step-by-step explanation:
What is an explicit formula for the sequence 0,3,8,15,24,...? What is the 20th term?
Answer:
the most logical answer is
n^2-1
20th term is then 399
Step-by-step explanation:
The rule behind the sequence could be anything, but it is very likely that we're supposed to notice that the terms are all squares minus 1
0 = 1*1 - 1
3 = 2*2 - 1
8 = 3*3 - 1
15 = 4*4 - 1
24 = 5*5 - 1
So we expect that the explicit formula is n^2-1 and the 20th term is 399
Please help due soon.
Answer should be l=p-w/2, or c.
Calculate the length of ac to 1 decimal place below
Answer:
18.11
Step-by-step explanation:
Look at the file I attached
I marked a new point E for explanation purposes.
to find out the length of AC, we need to find out the length of CD and the length of CD = length of BE.
To find out the length of BE, we need to know AE, and
AE is AD - BC
AE = 11 - 4
AE = 7
Now we have AE
Use the Pythagoras theorem to calculate BE
AE² + BE² = AB²
7² + BE² = 16²
16² - 7² = BE²
207 = BE²
√207 = BE
Since BE = CD
The length of CD is √207
Now use the Pythagoras theorem again
AD² + CD² = AC²
11² + (√207)² = AC²
121 + 207 = AC²
328 = AC²
√328 = AC
AC = 18.11
22 ml of rboh is titrated with 35 ml of 0.9 m hf. what is the concentration of the base?
22 ml of rboh is titrated with 35 ml of 0.9 m hf. The concentration of the base is 1.43M.
What is titration?Titration is a method of chemical analysis in which the amount of a sample's ingredient is determined by adding an exact known amount of a different substance to the measured sample in which the desired constituent interacts in a specific, known proportion. Titrating reagent, or titrant, is often added to a standard solution (i.e., a solution of known concentration) using a burette, which is essentially a long, graduated measurement tube with a stopcock and a delivery tube at its bottom end. When the equivalence point is achieved, the addition is terminated.
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Please help and show how you did it!!
Answer
EAD= EBC true.
Step-by-step explanation:
Both triangles are equal. The line between AE and EB show the lines are equal. In turn this makes the sides AD and BC equal. DC are the same length as AE and EB. In short, all sides are equal so the triangles are the same.
Including a 5% sales tax, an inn charges $189 per night. Find the inn's nightly cost before the tax is added.
The inn's nightly cost before tax is added is
Answer:
180
Step-by-step explanation:
Nightly cost = x
x × 5% = Sales Tax
Total Cost : Percentage
189 : 105%
x : 100%
Cross multiply:
189 × 100% = 105% × x
189 = 1.05x
189 ÷ 1.05 = x
x = 180
The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. what is the z-score of an appliance that stopped working at 64 months?
The z-score of an appliance that failed after 64 months is 2.
What is mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.To find the z-score:
The given parameters are:
Mean, [tex]\mu[/tex] = 48 monthsStandard deviation, [tex]\sigma[/tex] = 8 monthsThe z-score is then computed as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]We have the following for an appliance that stopped working after 64 months:
x = 64So, the equation becomes:
z = 64 - 48/8Compare and contrast the differences:
z = 16/8Calculate the quotient:
z = 2Therefore, the z-score of an appliance that failed after 64 months is 2.
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A family is comparing different car seats. one car seat is designed for a child up to and including 30 lb. another car seat is designed for a child between 15 lb and 40 lb. a third car seat is designed for a child between 30 lb and 85 lb, inclusive. model those ranges with compound inequalities. which car seats are appropriate for a 32-ib child?
The Second and third car seats are appropriate for a 32-ib child
The first car :
The range 30 ≤x< 32
So it is not possible for a car seat appropriate for a 32-ib child.
The second car:
The range 15<x <40
So it is possible for a car seat appropriate for a 32-ib child.
The third car:
The range 30< x< 85
So it is also possible.
Hence the second and the third ranged car is possible for a 32-ib child.
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Solve #5, which algebraic proof is it
If angle 1 = 30° and angle 1 and angle 2 are equal, then angle 2 = 30°. This illustrates vertically opposite angles.
What are vertically opposite angles?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.
A pair of angles that are vertically opposed to one another are always equal. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.
In this case, the angles are vertically opposite angles.
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A box of 8 crayons costs $0.96. How much does each crayon cost? At the unit price, how much would a box of 30 crayons cost.
Answer:
the price of 30 crayons is 3.6$.
Step-by-step explanation:
Given that
price of 8 crayons is 0.96$
so the price of 1 crayon is
0.96÷8=0.12$
now we have to find the cost of 30
crayons
we know that price of 1 crayon is 0.12$
so the price of 30 crayons is
0.12$×30= 3.6$.
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Answer:Given the cost of a box of 8 crayons, the cost of each crayon is 0.12. a box containing 30 cryaons will cost 3.6
Step-by-step explanation: Given that ,
box of 8 crayons cost=0.96 cost of each crayon=? cost of each 30 crayon box=? first, we determine the cost of abox with 30 crayons . 8 crayons cost 0.96. 1crayon cost x. x=0.96÷8=0.12 Next we determine the cost of abox with 30 crayons . 1 cryaon cost 0.12 30 crayons cost y y=30×0.12 y=3.6
Brad's father asked an engineer to survey the field behind their house. He wanted to plant some orange and
tangerine trees there. According to the survey, the field is 32 feet long and 6 yards wide. What is the perimeter
of the yard in feet?
Joann works in a publicity office at the state university. she is paid $ 13.00 an hour for the first 35 hours she works each week and $ 19.50 an hour for every hour after that. if she makes $ 572.00 one week, how many hours did she work?
Joann worked for 64 hours in week.
Let the number of hours she work be x. The payment for first 35 hours will be added with the multiple of number of extra hours and payment for the same.
Forming the equation according above mentioned statement :
13 + 19.5x = 572
Solving the equation to find the number of hours worked by Joann
Shifting 13 to Right Hand Side of the equation
19.5x = 572 - 13
Performing subtraction on Right Hand Side of the equation
19.5x = 559
Shifting 19.5 to Right Hand Side of the equation at denominator
x = 559 ÷ 19.5
x = 28.67 hours
Rounding off the number of hours, we get the value = 29
So, Joann worked for 29 extra hours. To find the total number of hours she worked, we will simply add her working hours.
Total number of hours Joann worked = 35 hours + extra hours
Total number of hours Joann worked = 35 + 29
Total number of hours Joann worked = 64 hours
Hence, Joann worked for 64 hours in week.
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Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' y'-4x-4y=e^-t x' y' 2x y=e^4t
It looks like the system of ODEs is
[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]
Differentiate both sides of both equations with respect to [tex]t[/tex].
[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]
Eliminating the exponential terms, we have
[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]
[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]
Now we can eliminate [tex]y[/tex] and it derivatives.
[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]
Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is
[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]
Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives
[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]
The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is
[tex]y(t) = C_3 e^{-t}[/tex]
Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form
[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]
Substituting into the ODE gives
[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]
so that the general solution is
[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]
A student believes there is a correlation between the number of texts sent during class and GPA. The student collected data and found that the line of fit can be modeled by the equation ŷ = 3.6 − 0.3x.
Identify and interpret the slope in this scenario.
The slope is −0.3. Starting at 3.6, the GPA will increase by 0.3 for every text sent in class.
The slope is −0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.
The slope is 3.6. Starting at 0.3, the GPA will increase by 3.6 for every text sent in class.
The slope is 3.6. Starting at 0.3, the GP will decrease by 3.6 for every text sent in class.
Using linear function concepts, the correct option is given by:
The slope is −0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the function is:
y = 3.6 - 0.3x.
The function has a initial GPA of 3.6(student who sends 0 texts), then for each text the student sends, the GPA falls by 0.3(slope of -0.3), hence the correct option is:
The slope is −0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.
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The real estate agent's base salary is $21,000. They also receive 5% commission on total sales. How much in total sales do they have to make in order to earn $70,000 in one year?
======================================================
Work Shown:
x = amount of sales
0.05x = five percent of sales to represent commission earned
21,000+0.05x = add on the base salary to get total salary
21,000+0.05x = 70,000
0.05x = 70,000-21,000
0.05x = 49,000
x = (49,000)/(0.05)
x = 980,000
----------
Check:
If the real estate agent sold $980,000 worth of property, then s/he earned 5% of 980,000 = 0.05*980,000 = 49,000 dollars in commission.
The total salary for the year is 21,000+49,000 = 70,000 dollars. The answer is confirmed.
Revenue management methodology was originally developed for the banking industry. group of answer choices
a. true
b. false
The statement 'Revenue management methodology was originally developed for the banking industry.' is False.
The revenue Management is an analytics technique.
This technique is used to predict consumer behavior at the micro-level, which is ultimately useful in optimizing the product availability and pricing and maximize revenue growth.
This methodology is used by companies in certain industries, particularly those with fixed costs and capacity and products or services that expire.
It is the operational procedures and practices that maximize revenues without creating additional products or services.
Therefore, The statement 'Revenue management methodology was originally developed for the banking industry.' is False.
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In exercises 19 and 20, find the indicated angle measure. (See photo)
Answer:
See below to complete
Step-by-step explanation:
ABC = 37 +21 °
LMN = 85 +23 °
Of the books in a personal library, 3/5 are fiction. Of these books, 6/7 are paperback. What fraction of the books in the library are fiction and paperbacks?
The fraction of the books in the library that are fiction and paperbacks is 18/35
How to calculate the fraction ?
3/5 of the books in the library are fiction
6/7 of the books are paperback
Therefore the fraction of the books that are fictions and paperbacks can be calculated as follows
3/5 × 6/7
= 18/35
Hence 18/35 of the books are fiction and paperbacks
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