A stratified sample in this case can be selected as follows:
The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.
How are samples classified?The five most common classifications for sampling are listed as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, the groups are given as follows:
Floors overlooking the ocean.Floors overlooking the street.50 rooms will be sampled, hence the number that is sampled from each group is given as follows:
50/2 = 25 rooms from each group.
Missing InformationThe problem asks to describe a stratified sample for this situation.
More can be learned about stratified sampling at https://brainly.com/question/28413252
#SPJ1
Sarah needed to get her computer fixed. she took it to the repair store. the technician at the store worked on the computer for 5.25 hours and charged her $133 for parts. the total was $579.25. which equation could be used to determine cc, the cost of labor per hour?
The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.
Given:
The technician at the store worked on the computer for 5.25 hours and charged her $133 for parts.
Total charged = 579.25
Let x be the charge per hour.
so the equation = 5.25x + 133 = 579.25.
Technician charge = 579.25 - 133 = 446.25
5.25 hours = 446.25
divide by 5.25 on both sides
5.25 hours / 5.25 = 446.25/5.25
1 hour = $85
Therefore The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.
Learn more about the equation and labor cost per hour here:
https://brainly.com/question/4687485
#SPJ1
given that the probability of a family owning a dog is 0.91, and the probability of a family owning a cat and a dog is 0.15, what is the probability of a family owning a cat given that the family owns a dog?
The probability of a family owning a cat given that the family owns a dog is 0.164
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
Here
probability of a family owning a dog is 0.91,
P(dog) = 0.91
probability of a family owning a cat and a dog is 0.15,
P(dog ∩ cat) = 0.15
according to conditional probability
the probability of occurring of B after event A takes place is
P(A|B)=P(A∩B)/P(A)
so, the probability of a family owning a cat given that the family owns a dog is
P(dog | cat) =P(dog∩cat)/P(dog)
= 0.15/0.91
=0.164
To learn more about conditional probability visit:
https://brainly.com/question/29351756
#SPJ4
What is the slope of a line parallel to the line whose equation is 3x+4y=36
Answer:
3/4
Step-by-step explanation:
Get into y=mx+b
Subtract 3x
4y=3x+36
Divide by 4
y=3/4x+9
Parallel= 3/4
Perpendicular= -4/3
The pair of points (−6, y) and (4, 8) lie on a line with a slope of 5/2. Set up and solve for the missing y-value using the slope formula. Show all work to receive credit.
Given the slope of the line and the pair of points, the missing y - value can be found to be - 17
How to find the missing y - value?The slope formula is:
y = Slope(x) + y - intercept
Using the point (4, 8), the y - intercept can be found by the formula:
8 = 5/2 (4) + y - intercept
y - intercept = 8 - 10
y - intercept = -2
The missing y value is therefore:
y = Slope(x) + y - intercept
= -6 (5/2) - 2
= -15 - 2
= - 17
Find out more on the slope formula at https://brainly.com/question/3493733
#SPJ1
Kaitlyn bakes two rectangular cakes to put on top of each other. Each cake is 6 inches wide, 12 inches long and 3 inches high. She removes the cake from the pan to frost it. How many square inches of frosting does she need for both cakes?
Cayaln is making baked goods for a charity bake sale. He places a tray of scones, a tray of muffins, and a tray of cookies in the oven. The scones bake for 25 minutes, the muffins bake for 12minutes, and the cookie bake for 10 minutes. When one tray is done, he removes it and replaces it with another tray of the same item.
How many minutes after Cayaln puts the trays in the oven will he first remove the scones, muffins, and cookie at the same time?
The number of minutes after Cayaln puts the trays in the oven will he first remove the scones, muffins, and cookie at the same time is 300 minutes
What is the number of minutes Cayal removes the scones, muffins, and cookie at the same time?Scones = 25 minutesMuffins = 12 minutesCookie = 10 minutesFind the least common multiple of 25, 12 and 10 minutes
25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 30012 = 12, 24, 36, 48, 60, 72, 84, 96, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 30010 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300The least common multiple of of 25, 12 and 10 minutes is 300 minutes.
Therefore, the number of minutes Cayal removes the scones, muffins, and cookie at the same time is 300 minutes
Read more on least common multiple:
https://brainly.com/question/10749076
#SPJ1
6. Find the distance between each pair of points. Then order each line segment from longest to shortest.
a. A(−6, 1), B(−1, 6)
c. E(2,7), F(4, -2)
e. J(−4, −2), K(1, −5)
b
C(-5, 8), D(5,8)
d. G(7,3), H(7,−1)
f. L(3, -8), M(7, −5)
Using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
What is the distance Formula?The formula for the distance(d) , between two points whose coordinates are (x₁ ,y₁) and (x₂, y₂) is:Distance Formula: d = √[(x₂ - x₁)² - (y₂ - y₁)²]
Now, calculate the distance using the distance formula as follows:
(A) The distance between A and B is:
d = √(-1-(-6))²+(1-6)²)d = √5² + 5²d = √50(B) The distance between C and D is:
d = √[(5 -(-5))²+ (8-(8))²]d = √10² + 0d = 10(C) The distance between E and F is:
d = √[(4-2)²+ ((-2)-7)²]d = √2² + 9²d = √85(D) The distance between G and H is 2.
(E) The distance between J and K is:
d = √ [(1-(-4))² + (-5-(-2))²]d = √5² + 3²d = √34(F) The distance between L and M is:
d = √[(7-3)²= (-5-(-8))²]d = √4² + 3²d = 5Hence, the distance using the distance formula is:
(A) The distance between A and B is √50.(B) The distance between C and D is 10.(C) The distance between E and F is √85.(D) The distance between G and H is 2.(E) The distance between J and K is √34.(F) The distance between L and M is 5.Therefore, using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
Know more about distance here:
https://brainly.com/question/26046491
#SPJ13
an inverted cone is partially filled with water, as shown below. the radius of the inverted cone is 16 mm. the height of the inverted cone is 18 mm. if the volume of the water is increasing at a rate of 548 cubic mm per hour, what is the rate, in mm per hour, at which the height of the water is changing when the height of the water is 2 mm?
The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
Given data,
A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.
The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;
r/h = 16/18
= 8/9
r = 8h/9
The volume of the cone is;
v = [tex]\frac{1}{3}\pi r^2h[/tex]
v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]
v = [tex]\frac{64}{243}\pi h^3[/tex]
Now, differentiating concerning x;
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex] [tex]\frac{64}{243}\pi h^3[/tex]
[tex]\frac{dv}{dt}[/tex]= 64π/243*[tex]\frac{d}{dt}[/tex] h³
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]
We have;
[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm
[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 55.19
[tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.
Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
To learn more about volume click here:
brainly.com/question/1578538
#SPJ4
The Tran family and the Campbell family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 35 L per hour. The water output rate for the Campbell family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1925 L. How long was each sprinkler used?
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The water output rate for the Tran family's sprinkler was 35 L per hour.
The water output rate for the Campbell family's sprinkler was 25 L per hour.
And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.
Now,
Let time in hours for the Tran family's sprinkler = t
And, The time in hours for the Campbell family's sprinkler = 65 - t
So, We can formulate by the given condition,
⇒ 35t + 25 (65 - t) = 1925
Solve for t as;
⇒ 35t + 25 (65 - t) = 1925
⇒ 35t + 1625 - 25t = 1925
⇒ 10t + 1625 = 1925
⇒ 10t = 1925 - 1625
⇒ 10t = 300
⇒ t = 30
Thus, The time in hours for the Tran family's sprinkler = t
= 30 hours
And, The time in hours for the Campbell family's sprinkler = 65 - t
= 65 - 30
= 35 hours.
Therefore, we get;
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Diana recorded the total number of people living in each of the homes of 8 classmates. Which of the following values could be the median of those 8 numbers?
I. 0.0
II. 3.0
III. 4.5
Answer:
The answer is III: 4.5
Step-by-step explanation:
It's not the first option since there has to be more than one person living in those houses. It's not the second since 3 is greater than 0, and median is in order from least to greatest. It's three since it's reasonable and is in order from least to greatest.
you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). which double will occur the least often?
you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). Each double will occur once with the probability of 1/36
The sample space for the event of rolling 2 fair six-sided dice is :
S={ (1, 1),(1, 2),(1,3),(1,4),(1,5),(1,6),(2,1)........., (6,5),(6,6) } , So in total for the outcome, we get a total of 36 pairs, with the probability of getting an event as 1/36, now the situation given to us is the vent of getting a double.So the event space for getting a double while rolling 2 dice is E = { (1, 1),(2, 2),(3,3),(4,4),(5,5),(6,6) } , the outcome will be 6 pairs, so the probability for each double pair to come out when we roll the 2 dice is: 1/36 and the probability of getting the least double from the 6 pairs of double is: 1/6
To know more about probability refer to the link https://brainly.com/question/16722133?referrer=searchResults.
#SPJ4
The equation is y=
Graph of f(x)= |x|
The equation from the given graph is y=-2/3 x²+5.
From the given graph the vertex is (h, k)=(0, 5).
What is quadratic equation of graph?A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
Here, point on the given line from the graph is (3, -1)
Put (x, y)=(3, -1) and (h, k)=(0, 5) in y = a(x - h)² + k, we get
-1=a(3-0)²+5
⇒ 9a=-6
⇒ a=-2/3
Now, y=-2/3(x-0)²+5
y=-2/3 x²+5
Hence, the equation from the given graph is y=-2/3 x²+5.
To learn more about the quadratic function visit:
https://brainly.com/question/27918223.
#SPJ1
when two pipes fill a pool together, they can finish in 4 hours. if one pipe fills half of the pool and then the other takes over and finishes filling the pool, the pool will fill in 9 hours. how long would it take each pipe to fill the pool if it were working alone?
Time taken by pipe 1 to fill the pool is 6 and by pipe 2 is 12.
Here we have to find the time taken by each pipe to fill the pool.
Formula to find the work:
w = r × t
where
w = is the work done
r = is the rate of work done
t = is the time taken to do the work
For pipe 1 working alone to fill 1 pool, the work done is 1
w1 = r1 t1
1 = r1 × t1
t1 = 1/r1
For pipe 2 working alone to fill 1 pool, the work done is 1;
w2 = r2 t2
1 = r2 × t2
t2 = 1/r2
From the question, it would take 9 hours if each pipe took turns filling half the pool. That is;
t1/2 + t2/2 = 9
t1 + t2 = 18
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
w1 + w2 = w
r1t1 + r2t2 = 1
4r1 + 4r2 = 1
r1 + r2 = 1/4
As we know from the above:
r1 = 1/t1 and r2 = 1/t2
So;
1/t1 + 1/t2 = 1/4
(t2 + t1)/ t1 t2 = 1/4
t1 + t2 = 18
So
t1 t2 = 72
The only factors of 72 that satisfy the conditions
t1 + t2 = 18
t1 . t2 = 72
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours.
To know more about the pipe and cistern refer to the link given below:
https://brainly.com/question/1800429
#SPJ4
what does the degree tell you about the zeros of the function of x^3+8x^2+11x-20?
Answer:
Step-by-step explanation:
the degree of the function , also means how many zeros , or roots, There will be.
what condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?
When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:
The data values should be symmetrical in the sample.No outliers should be in sample data .If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.
A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.
Learn more about Sampling distribution at,
https://brainly.com/question/13668062
#SPJ4
DIMENSIONAL ANALYSIS (MATH) GIVING BRAINILIEST!
Q1: What is the speed of a horsefly in feet per second? Round to the nearest hundredth.
Q2: How many times does a dragonfly's wing beat per minute?
Q3: About how many times can a bumble bee travel in one minute?
Answer:
Q1 = 6.45f/s
Q2 = 0.633 times
Q3 = 0.107 miles
Step-by-step explanation:
Q1: Since
4.4 miles = 1 hour
and
1 mile = 5,280 feet
1 hour = 3600 seconds
Then 4.4 miles
= 5,280 feet × 4.4
= 23,232 feet / 3600 seconds
= 6.453f/s
= 6.45f/s
Q2: Wing beat per minute
= 38 ÷ 60
= 0.633 times
Q3: Miles per minute
Since 6.4 miles = 1 hour,
6.4 miles = 1 × 60
6.4 miles = 60 minutes
x miles = 1 minute
= 6.4/60
= 0.107 miles
4 1/3 times 6
NEEDED ASAP
Answer:
26
Step-by-step explanation:
4⅓×6
=13/3 × 6
=26
smash as brainliest
a croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. how many ways are there to choose ) two dozen croissants with at least two of each kind?
There are 6188 ways are there to choose two dozen croissants with at least two of each kind.
A combination is the combination of two or more distinct things. Although it is not necessary to combine things in pairs, the term "combining" comes from the Latin word for "joining together two by two."Combination repetition is permitted.
There are six different varieties of croissants (n = 6), and we must select two dozen croissants (r = 12) with at least two of each type.
In combination, The order does not matter and repetition is allowed.
thus, according to combination,
[tex]C( n+ r - 1,r) = \frac{(n + r - 1 )!}{r! (n-1)!} \\\\C( 6+ 12 - 1,12) = \frac{(6 + 12 - 1 )!}{12! (6-1)!} \\\\ = \frac{17!}{12!5!} \\= 6188[/tex]
thus, there are 6188 ways possible to choose two dozen croissants with at least two of each kind.
Know more about combination here: https://brainly.com/question/11732255
#SPJ4
1. prior to cellular radio, mobile radio and telephone services required: a. a high-power transmitter/receiver b. multiple transmitters/receivers c. only one or two dedicated channels d. that many channels be used, which exceed the frequency capacity
Prior to cellular radio, mobile radio and telephone services required
a. high-power transmitter/receiver.
A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.
Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.
Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.
For more information on Transmitters , visit :
https://brainly.com/question/2084370
#SPJ4
Grace runs a website that has gotten quite popular. However, its popularity seems to have
peaked, and the site is now getting 7% fewer hits each week. If Grace's site got 38,800 hits
this week, how many weekly hits can she expect it to get 7 weeks from.
Answer:
23346
Step-by-step explanation:
You want to know the number of hits on Grace's website 7 weeks from now if she gets 38,800 now and the number decreases 7% per week.
Growth factorThe growth factor per week is ...
growth factor = 1 + growth rate
The growth rate of hits is -7% per week, so this is ...
growth factor = 1 -7% = 0.93
Exponential functionThe exponential function describing the number of hits can be written ...
hits = (initial value)(growth factor)^weeks
hits = 38,800(0.93^weeks)
Then in 7 weeks, the number of hits is expected to be ...
hits = 38,800(0.93^7) ≈ 23,346
Grace can expect to get about 23,346 hits in 7 weeks.
<95141404393>
A triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m. A second
triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m. What must the interior angles of the second triangle
be for the two shapes to be similar?
The interior angles of the second triangle will be 50°, 55°, and 75° respectively.
What are similar triangles?
If the corresponding angles and sides of two triangles are congruent, then the two triangles are said to be similar.
In other words, similar triangles have the same shape but may differ in size.
Given, a triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m.
And, a second triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m.
The corresponding sides of both triangles are 3.1 m, 3.2 m, and 4.0 m with 10.3 m, 10.5 m, and 12.0 m respectively.
Then, the angles of both triangles are also corresponding to each other.
So we get, the interior angles of the second triangle will be 50°, 55°, and 75° respectively.
To learn more about similar triangles
https://brainly.com/question/14285697
#SPJ13
Solve for x.
2/x^2−4 − 1/x+2 = 3/x−2
In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.
What is the equation known as?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.
How to solve this:
2/x^2-4 -1/x+2=3/x-2
collecting like terms
2/x^2-4 -1/x+2 -3/x-2=0
Divides through by:
x^2-42 -1(x-2) -3(x+2)/x^2-4=0
Remove bracket: 2-x+2-3x-6/x^2-4
Lastly, collecting like terms:
2+2-6-x-3x/x^2-4-2-4x/x^2-4
=-2(1+2x)/x^2-4
Read more about Fraction
https://brainly.com/question/29336152
#SPJ1
2: The probability of a $2 winner in a particular state lottery is 1 in 10, the probability of a $5 winner is 1
in 50, and the probability of a $10 winner is 1 in 500.
a) What is the probability of getting either a $2, or $5, or $10 winner?
b) What is the probability of getting a $2 winner?
c) If you buy 50 lottery tickets, what is the probability that you will get at least one $5 winner?
d) If you buy 500 lottery tickets, what is the probability that you will get at least one $10 winner? B
The probability of each event will be
a. 0.122
b. 0.1
c. 0.64
d. 0.63
Probability of a $2 winner is 1 in 10
Probability of a $5 winner is 1 in 50
Probability of a $10 winner is 1 in 500
The formula to find probability is
1. no. of favorable outcomes / total no. of favorable outcomes
OR
2. P(A) = n(A)/n(S)
where
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes
n(S) is the total number of events in the sample space
Now we will use formula to find probability of different events happening
a. To find the probability of getting either a $2, or $5, or $10 winner we
will find probability of $2 , $5 and $10 and add them together.
1/10 + 1/50 + 1/500 = 0.122
b. The probability of getting a $2 winner will be
1/10 = 0.1
c. The probability of getting no $5 winner is (49/50)^50 = 0.36
So the probability of getting $5 winner will be 1 - 0.37 = 0.64
d. The probability of getting no $10 winner is (499/500)^500 = 0.37
And we can take probability of total no. of outcomes as 1.
So the probability of getting $10 winner will be 1 - 0.37 = 0.63
To solve more questions related to probability
https://brainly.com/question/11234923
#SPJ1
The distance (D) that a spring is stretched by a hanging object varies directly as the
weight (W) of the object. If a 6-kg object stretches a spring 29 cm, how far will a 25- kg weight stretch the spring?
Pls help asap! Tysm if u do!
The 25 Kg weight will stretch the spring 120.84 cm .
In the question ,
it is given that
the distance(D) that spring stretches by hanging objects vary directly to the weight(W) of the object .
which means
D ∝ W
to remove the proportionality sign , we write the constant k
So, D = k × W ,
where k is the constant of proportionality
given that 6 Kg weight stretches the spring 29 cm
So,
29 = k * 6
k = 29/6
to find the stretch for 25 Kg weight
D = (29/6)*25
D = 120.84 cm
Therefore ,The 25 Kg weight will stretch the spring 120.84 cm .
Learn more about Distance here
https://brainly.com/question/5056426
#SPJ1
A carton of milk holds 10 cups. a recipe for strawberry milkshake requires 3/4 of a cup of milk. how many recipes could you make with the carton of milk.
An element with a mass of 420 grams decays by 7.5% per minute. To the
nearest minute, how long will it be until there are 210 grams of the element
remaining?
Answer: x= 9
Step-by-step explanation:
I just checked that its right!
Answer:
The correct answer would be 9
Step-by-step explanation:
can someone please solve (iii)
The point on a line that is at an equal distance from either end.
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
What is midpoint ?
The point on a line that is at an equal distance from either end.
Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]
The general formula of the midpoint is
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]
The equation of [tex]AP[/tex] is
[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]
The equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is
where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].
[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
To know more about the midpoint
https://brainly.com/question/28224145
#SPJ1
Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)
The unit rate is
?
Graph the relationship.
The unit rate of change , d with respect to t is = 1.6 .
In the question,
it is given that , the relationship between d and t is proportional
also given that " increase of 5 units in t corresponds to increase of 8 units in d ".
which is represented as 5t = 8d
Divide both sides of the equation 5t = 8d by "5" ,
t = 8/5d
t = 1.6d
next we plot the graph of t = 1.6d
we see that the above equation is a proportional linear equation
and A proportional linear equation is represented as
t = md , Where m represents the unit rate .
So , after comparing , we get
m = 1.6
Therefore , The unit rate of change of d with respect to t is 1.6 .
Learn more about Unit Rate here
https://brainly.com/question/28821706
#SPJ1
Determine the intercepts of the line
x int
y int
Answer:
Y-int = -45, X-int =-11.25
Step-by-step explanation:
Please read this before moving on :)
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.
We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.
Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
1 - Finding the Slope
2 points; (0,-40), (-10,0)
0-(-40)/(-10)-0 = 40/-10 = -4
2 - Y-INTY=MX+B
Y=MX+(-45)
Y=MX-45
Y-int = -45
3 - X-INTY=MX+B
0=(-4)x+-45
45=-4x
X-int =-11.25
Dad fills the car's gas tank when it is about 1/2 empty. Later, he fills the tank when it is about 3/4 empty. He bought a total of 18 1/2 gallons of gas on those two days. How many gallons does the tank hold?
Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
To know more about the mixed fraction, here
https://brainly.com/question/28957298
#SPJ4
