The vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).
What is the quadratic functiοn?A quadratic functiοn is a functiοn οf the fοrm where a, b, and c are cοnstants, and a is nοt equal tο 0. It is a type οf pοlynοmial functiοn that can be graphed as a parabοla, which is a symmetric curve that οpens either upwards οr dοwnwards.
Given the table οf pοints fοr the cοntinuοus quadratic functiοn h(x), we can find the vertex and range οf the functiοn. Since the functiοn is quadratic and cοntinuοus, it can be represented in the standard fοrm [tex]$f(x)=a(x-h)^{2}+k,$[/tex], where (h, k) is the vertex οf the parabοla.
Tο find the vertex, we can use the fact that the x-cοοrdinate οf the vertex is given by -b/2a, where a and b are the cοefficients οf the quadratic term and the linear term, respectively. In this case, a = 1 (since the functiοn is cοntinuοus and quadratic), and b can be fοund using any twο pοints οn the parabοla:
[tex]\rm b=(h(x_2)-h(x_1))/(x_2-x1)=(4-7)/(-2+1)=3$[/tex]
Therefοre, the x-cοοrdinate οf the vertex is x = -b/2a = -3/2. Tο find the y-cοοrdinate οf the vertex, we can evaluate the functiοn at this value οf x:
[tex]$\rm h(-3/2)=(1)(-3/2-h)^{2}+k$[/tex]
Tο sοlve fοr k, we can use οne οf the pοints οn the parabοla, say (-6, 12):
[tex]$12=(1)(-6-h)^{2}+k\,$[/tex]
Expanding and simplifying, we get:
[tex]$12=(h-6)^{2}+k$[/tex]
Substituting -3/2 fοr h, we get:
[tex]$\begin{array}{l}{{12=(-(3/2)-6)^{2}+k}}\\\\ {{12=81/4+k}}\\\\ {{k=-21/4}}\end{array}$[/tex]
Therefοre, the vertex οf the parabοla is at the pοint (-3/2, -21/4).
Tο find the range οf the functiοn, we can lοοk at the shape οf the parabοla. Since the cοefficient οf the quadratic term is pοsitive, the parabοla οpens upwards, and the vertex is the lοwest pοint οn the graph. Therefοre, the range οf the functiοn is all real numbers greater than οr equal tο the y-cοοrdinate οf the vertex, which is -21/4. In interval nοtatiοn, we can write the range as (-21/4, infinity).
Hence, the vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).
To learn more about the quadratic functions, visit:
brainly.com/question/1214333
#SPJ1
ala Manufacturing purchases land for $445,000 as part of its plans to build a new plant. The
Ompany pays $37,600 to tear down an old building on the lot and $55,583 to fill and level
me lot. It also pays construction costs of $1,402,600 for the new building and $88,536 for
ghting and paving a parking area.
repare a single journal entry to record these costs incurred by Cala, all of which are paid in
ash.
View transaction list
No
A
View journal entry worksheet
Transaction
1
No Transaction Recorded
General Journal
D
Note that the journal for the above transaction is attached accordingly.
What is the explanation for the above journal?The journal entry records the purchase of land for $445,000, demolition expense of $37,600, land improvement cost of $55,583, building construction cost of $1,402,600 and lighting and paving cost of $88,536, all paid in cash.
Therefore, the amounts are debited to their respective accounts and credited to cash.
The total credit amount is equal to the total debit amount, ensuring the accounting equation remains in balance.
Learn more about journals;
https://brainly.com/question/27159868?
#SPJ1
SIxty meters of rope is used to make three sides of a rectangular camping area with a long wall used as the other side. The length of each side of the rectangle is a natural number. WHat is the largest area that can be enclosed by the rope and the wall?
Using the area formula for rectangle, the largest area that can be enclosed by rope and wall = 450m².
Define a rectangle?A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are many rectangular objects all around us. The two characteristics that distinguish each rectangle are its length and its breadth. A rectangle's longer and shorter sides are its width and length, respectively.
Here in the question,
The rope used here is 60m.
Now 60m of rope is forming 3 sides of the rectangle.
The adjacent sides cannot be equal to each other as it is a rectangle.
So, the sides of the rectangle can be given as such so that area will be maximum:
length = 30m
width = 15m
So, the rope includes one length and 2 widths of the rectangle.
As such (60m = 30m + 15m + 15m).
Now, area of the rectangle =
l × w
= 30 × 5
= 450m²
Therefore, the largest area that can be enclosed by rope and wall = 450m².
To know more about rectangles, visit:
https://brainly.com/question/29123947
#SPJ1
Which statement best describes the function h(t) = 210 - 15t?
O h is the function name; h(t) is the input, or independent variable: and t is the output, or dependent variable.
Ohis the function name: t is the input, or independent variable; and h(t) is the output, or dependent variable.
• t is the function name: h(t) is the input, or independent variable: and h is the output, or dependent variable.
O t is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.
Answer:
h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
Step-by-step explanation:
It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.
we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads.
What is meter?
A meter is a unit of length in the International System of Units (SI). It is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. The symbol for meter is "m".
To determine which option is less expensive, we need to compare the cost of laying pipes along the rural roads to the cost of laying pipes through the field.
Let's assume that we need to lay a water pipe that is 100 meters long. If we choose to lay the pipe along the rural roads, the cost would be:
Cost = length of pipe x cost per meter = 100 x $3.00 = $300.00
If we choose to lay the pipe through the field, the cost would be:
Cost = length of pipe x cost per meter = 100 x $4.50 = $450.00
Therefore, laying the pipe along the rural roads would be less expensive in this case, with a cost of $300.00 compared to $450.00 for laying the pipe through the field.
In general, we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads. Conversely, if the cost per meter of laying pipes through the field is less than the cost per meter of laying pipes along the rural roads, then it would be less expensive to lay the pipes through the field.
To know more about meter visit:
https://brainly.com/question/1578784
#SPJ1
Full question:
It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.
One side of the triangle is 1 inch less than three times the length of the altitude to that side. Write a polynomial that represents the area of this triangle.
By answering the presented question, we may conclude that the answer of the triangle [tex]A = (3/2)h^2 - (1/2)h\\[/tex] => [tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
x = 3h - 1
A = (1/2)bh
A = (1/2)xh
A = (1/2)(3h - 1)h
[tex]A = (3/2)h^2 - (1/2)h\\[/tex]
[tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open,
pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds
per minute. Find the concentration (pounds per gallon) of sugar in the tank after 10 minutes.
Answer:
the concentration of sugar in the tank after 10 minutes is approximately 0.056 pounds per gallon.
Step-by-step explanation:
Let's first calculate the amount of sugar that will be added to the tank during the 10 minutes:Amount of sugar added = rate of sugar * time = 2 pounds/minute * 10 minutes = 20 poundsThe initial amount of water in the tank is 300 gallons, and 20 gallons per minute are being added, so after 10 minutes, the amount of water in the tank will be:Amount of water in the tank = initial amount of water + rate of water * time = 300 gallons + 20 gallons/minute * 10 minutes = 500 gallonsTherefore, after 10 minutes, the total volume of the mixture in the tank will be 500 gallons, and the total amount of sugar in the tank will be 8 + 20 = 28 pounds.To find the concentration of sugar in the tank, we divide the total amount of sugar by the total volume of the mixture:Concentration of sugar = total amount of sugar / total volume of mixture = 28 pounds / 500 gallons ≈ 0.056 pounds per gallon
We can use the formula:
concentration = (total sugar added in pounds) / (total water in gallons)
First, we need to find out how much sugar is added in 10 minutes. Since sugar is being added at a rate of 2 pounds per minute , in 10 minutes, we will have:
total sugar added = 2 pounds/minute * 10 minutes = 20 pounds
Next, we need to find out how much water is in the tank after 10 minutes. Since water is being added at a rate of 20 gallons per minute , in 10 minutes, we will have:
total water added = 20 gallons/minute * 10 minutes = 200 gallons
Therefore, the total amount of water in the tank after 10 minutes is:
total water = 300 gallons (initial water) + 200 gallons (water added) = 500 gallons
Finally, we can calculate the concentration of sugar in the tank by plugging in the values:
concentration = total sugar added / total water
concentration = 20 pounds / 500 gallons
concentration = 0.04 pounds/gallon
Therefore, after 10 minutes, the concentration of sugar in the tank is 0.04 pounds per gallon.
Amadou and Olivia are making fruit salads for a picnic. Amadou mixes 9 cups of melon and 10 cups of apple and Olivia mixes 2 cups of melon and 3 cups of apple. Use Amadou and Olivia’s percent of apple to determine whose fruit salad will taste more appley.
Given that 60% of Olivia's fruit salad is made up of apples as opposed to Amadou's fruit salad's 52.63%, Olivia's fruit salad will have a more apple-forward flavor based on percent.
The amount of apples in each fruit salad needs to be compared in order to determine which salad will taste more apple-like.
There are 19 cups of fruit in Amadou's fruit salad, of which 10 cups are apples. By dividing the total number of cups of fruit by the number of cups of apples, and multiplying the result by 100, we can get the proportion of apples in Amadou's salad:
Apple's percent of Amadou's fruit salad is equal to (10/19) x 100, or 52.63%.
There are 5 cups of fruit in Olivia's fruit salad, of which 3 cups are apples. We can use the same formula to determine how much apple is in Olivia's salad:
Olivia's fruit salad contains 60% apples, or (3/5) x 100.
As a result, Olivia's fruit salad will taste more apple-like because apples make up 60% of it as opposed to only 52.63% of Amadou's fruit salad.
It is important to keep in mind that the maturity, sweetness, and freshness of the fruits used, as well as other elements like the dressing and presentation, may all affect how the fruit salad tastes.
Learn more about percent here:
https://brainly.com/question/28670903
#SPJ1
Find the 36th term.
5, 12, 19, 26, 33, ...
36th term = [?
1st term + common difference(desired term - 1)
Enter
Help Resourc
Answer: 250
Step-by-step explanation: because i got it right
Help I give points pls
Answer:
-12
Step-by-step explanation:
g(x)=3x,h(x)= x²-4
(g•h)(0)=g(h(0))
=g(0²-4)
=g(-4)
=3×(-4)
=-12
A Ferris Wheel is 60 meters in diameter and rotates once every four minutes. The center axle of the Ferris Wheel is 40 meters. from the ground. Write at least 2 mathematical models that represent the motion of the passenger on this Ferris wheel.
y = acos bx +c
y=-25 cos
C. where X = 2.3 min
Another mathematical representation of how a rider on this Ferris wheel might move is :y = cos(0.25x) + 40
What more uses does trigonometry have?Trigonometry is widely used in many fields, including physics, engineering, architecture, surveying, oceanography, and more. Here are several examples:
In astronomy and physics, trigonometry is used to compute the motions of moving objects, gauge the separations between planets and stars, and examine waves. Trigonometry is used in architecture and engineering to determine angles and distances for building structures like bridges and buildings.
In surveying, trigonometry is a tool used to determine angles and separations between points on the surface of the ground.
.
The function y = a cos(bx) + c, where an is the function's amplitude, b is its frequency, and c is its vertical shift, can be used to mimic the height of a rider on a Ferris wheel.
Given that the Ferris wheel's diameter in this instance is 60 meters, its radius is 30 metres. The Ferris wheel's center axle is 40 metres off the ground. This indicates that a rider is 70 metres above the earth when they are at the top of the Ferris wheel (30 + 40). A rider is 10 metres above the ground when they reach the bottom of the Ferris wheel. (40 - 30).
We can determine that the Ferris wheel's period is four minutes because it rotates once every four minutes. The following formula can be used to get our function's frequency:
f = 1/T, 1/4, and 0.25 Hz
Therefore, our function has a frequency of 0.25 Hz.
The vertical shift of our function is equivalent to 50% of the difference between a Ferris wheel passenger's maximum and minimum heights:
, c = (a_max + a_min) /2
c = (70 + 10) /2
c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
For example, c = (a_max + a_min) / 2 c = (70 + 10) / 2 c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
A=(a_max - a_min) / 2 A=(70 - 10) / 2 A=30
Therefore, our function has an amplitude of 30.
When you combine everything, you get:
Y equals a cos(0.25x) + 40
y = -25 cos(C), where C is the time in minutes since the motion started at position, is another potential mathematical model that could describe this motion. (0,-25).
To know more about trigonometry visit:
brainly.com/question/22986150
#SPJ1
Calculate the area of the shaded region below
Answer:
Step-by-step explanation:
According to the given situation,
the area of figure A= l*b
=4m * 5m
=20m²
As the measures of the figure A and B is same,
the area of figure B = the area of figure A=20m²
the length of the side C and D are = 16m-8m-4m=4m
the area of figure C = l * b
=4m*5m
=20m²
As the measures of the figure C and D is same,
the area of figure D = the area of figure C=20m²
Area of the figure E=l * b
=8m * 13m
=104m²
∴ the area of the shaded region is =184m²
If y = x² - 2x + 3, find the value(s) of x when y = 3.
Answer:
x = 0 , x = 2
Step-by-step explanation:
y = x² - 2x + 3 ← substitute y = 3
3 = x² - 2x + 3 ( subtract 3 from both sides )
0 = x² - 2x ← factor out x from each term on the right side
0 = x(x - 2)
equate each factor to zero and solve for x
x = 0
x - 2 = 0 ⇒ x = 2
Find the value of x in the matrix equation.
[-8-14 -2x]-([-19 17 -1]+[14 13 -2])-[-3 -44 -9]
a. x = -5.7
C.
b. x=-17.7
X=7
d. x = 6
Answer:
the answer is x=6
Step-by-step explanation:
how to find the surface area of 12 ft 14 ft 20 ft 16 ft
The surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.
What is surface area?
The area is the space occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
To find the surface area of a rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft, we need to calculate the area of each face and then add them together.
First, let's calculate the area of the top and bottom faces, which are both rectangles with dimensions of 12 ft by 20 ft:
Area of top and bottom faces = 2 x (12 ft x 20 ft) = 480 square feet
Next, let's calculate the area of the front and back faces, which are both rectangles with dimensions of 12 ft by 14 ft:
Area of front and back faces = 2 x (12 ft x 14 ft) = 336 square feet
Finally, let's calculate the area of the left and right faces, which are both rectangles with dimensions of 14 ft by 20 ft:
Area of left and right faces = 2 x (14 ft x 20 ft) = 560 square feet
To find the total surface area, we add up the area of all six faces:
Total surface area = Area of top and bottom faces + Area of front and back faces + Area of left and right faces
Total surface area = 480 sq ft + 336 sq ft + 560 sq ft = 1376 sq ft
Therefore, the surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.
Learn more about surface area on:
https://brainly.com/question/20771646
#SPJ1
my subscription is not showing what i pain for
Answer:
Try restarting your computer or using a different web browser
Step-by-step explanation:
The probability that Gerald makes a three-point shot in basketball is
20
%
20%20, percent. For practice, Gerald will regularly shoot a series of these shots until he succeeds at one. He's curious how many shots it will typically take him to get his first successful shot.
He simulated
40
4040 trials of three-point shots where each shot had a
0.2
0.20, point, 2 probability of being successful, and in each trial, he counted how many shots it took to get the first successful shot. Here are his results:
A dot plot for number of shots taken has a scale from 0 to 16. The number of dots for each is as follows. 0, 0. 1, 9. 2, 6. 3, 5. 4, 4. 5, 4. 6, 2. 7, 2. 8, 0. 9, 1. 10, 1. 11, 1. 12, 2. 13, 1. 14, 0. 15, 1. 16, 1.
Use his results to estimate the probability that it takes
10
1010 or fewer shots to get his first successful shot.
Give your answer as either a fraction or a decimal.
�
(
10
or fewer shots
)
≈
P(10 or fewer shots)≈P, left parenthesis, 10, start text, space, o, r, space, f, e, w, e, r, space, s, h, o, t, s, end text, right parenthesis, approximately equals
The estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
What is probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.
From the given dot plot, we can see that the number of dots for each value up to 10 shots are:
0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33
Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 33/40
This can also be written as a decimal:
P(10 or fewer shots) ≈ 0.825
Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
To know more about probability visit:
https://brainly.com/question/13604758
#SPJ1
John's rock collection contains 15 igneous rocks, 9 sedimentary rocks, and 12 metamorphic rocks. If he randomly chooses a rock from his collection, what is the probability it is a sedimentary rock?
There is a 0.25 percent chance of choosing a sedimentary rock from John's collection based on laws of probability.
We must apply the following formula to determine the likelihood of choosing a sedimentary rock from John's collection:
Probability is calculated as the ratio of favourable outcomes to all other possible outcomes.
The best result in this situation is choosing a sedimentary rock, and the total number of outcomes is equal to the entire number of rocks in John's collection, which is:
Igneous rocks, sedimentary rocks, and metamorphic rocks together make up the total quantity of rocks.
a total of 15 + 9 + 12 stone.
There are 36 rocks in all.
As a result, the likelihood of choosing a sedimentary rock is:
Number of sedimentary rocks divided by the total number of rocks is the likelihood of choosing a sedimentary rock.
picking a sedimentary rock has a 9/36 probability.
25% or 0.25 of the time will a sedimentary rock be chosen.
So, there is a 0.25 percent, or 25%, chance that you will choose a sedimentary rock from John's collection. This indicates that 25% of all the rocks in John's collection are sedimentary rocks, and if one were to choose a rock at random from his collection, there is a one in four chance that they would be sedimentary rocks.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ1
5.2, 5.2, 4.7, 5.4, 3.9, 3.5, 4.1, 4.2, 5.4, 4.7, 4.8, 4.2, 4.6, 5.1, 3.8, 3.9, 4.6, 5.1, 3.6,
4.6, 4.3, 3.4, 4.9, 4.2, 4.0
A manufacturer of pencils randomly selects 25 pencils and measures their length (in
inches). Their data is shown. Create a frequency distribution with 6 classes and a
class width of 0.4 inches. What is the shape of the frequency histogram?
A The histogram is bimodal.
B The histogram is roughly symmetrical.
C histogram is skewed right.
D The histogram is uniform.
E The histogram is skewed left.
Since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The range οf the data is the difference between the maximum and minimum values:
Maximum value: 5.4
Minimum value: 3.4
Range: 5.4 - 3.4 = 2.0
Next, we divide the range by the desired number οf classes tο find the class width:
Class width = 2.0 / 6 = 0.3333 (rοunded tο 0.4)
Based οn the given data, we can expect the histοgram tο be apprοximately bell-shaped, with a peak arοund the middle classes (4.0-4.8) and fewer pencils in the extreme classes (3.4-3.8 and 5.4-5.8).
Hοwever, since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
Learn more about frequency distribution, by the following link
https://brainly.com/question/16698786
#SPJ1
In a village, 80% of people are Hindus and 2% are Muslims. If 36 people do not follow these two religions, by drawing a Venn diagram find the number of the Hindu.
Explanation:
Assuming the two religions are mutually exclusive, this would mean 80%+2% = 82% of people are either Hindu or Muslim (but not both).
The remaining 100% - 82% = 18% of people are neither religion mentioned.
x = number of people in the village
18% of x = 36
0.18x = 36
x = 36/0.18
x = 3600/18
x = 200
Then,
80% of x = 0.80*x = 0.80*200 = 160 people are Hindu
The Venn diagram is shown below.
A new car is purchased for $33, 000 and over time its value depreciates by one half
every 4 years. How long, to the nearest tenth of a year, would it take for the value of
the car to be $9, 300?
The value of the car is $30675.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: A new car is purchased for $33, 000 and over time its value depreciates by one-half every 4 years.
We have to find the value of the car to be $9, 300.
Then the value of the car is given by the linear equation. Then the line is passing through (0, $33,000) and (4, $9,300). Then we have
Let y be the value of the car and x be the number of years. Then we have
y - 33000 = (-9300/4)(x-0)
y + 2325x = 33000
Then the value of the car of a year after it was purchased, to the nearest hundred dollars will be
y + 2325(1) = 33000
y = 33000 - 2325
y = 30675
Hence, the value of the car is $30675.
To learn more about the linear equation from the given link
https://brainly.com/question/28732353
#SPJ1
please help me with this math question i’ll give you brainlist
a- y=-1.2x+30
b- y=2x+20
c- y=0.48x+11
d- y=0.71+22
Option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.
What is correlation coefficient?A statistical metric called a correlation coefficient shows the degree and direction of the association between two variables. Its value falls between -1 and 1, with -1 being a perfect negative correlation, 0 denoting no connection, and 1 denoting a perfect positive correlation. If there is a positive correlation, it implies that as one variable rises, the other variable likewise tends to rise, and if there is a negative correlation, it means that as one variable rises, the other variable tends to fall. The letter r is frequently used to represent the correlation coefficient.
Comparing the scatter plot with the given equations we observe that the slope of option b and d are very large as compared to the given distribution.
Observing from the given graph, the y-intercept of the best fit line will be nearly less than 20.
Thus, option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.
Learn more about correlation coefficient here:
https://brainly.com/question/15577278
#SPJ1
Can someone please help me with this problem involving Proofs involving similarity in right triangles.
The statement and reason to complete the proof that TU² = TV · TW include the following:
Statement Reason_____
TU² = TV · TW cross product.
What is the Tangent Secant Theorem?In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.
By applying the Tangent Secant Theorem to the given triangles after the definition of similarity step, we would cross-multiply as follows:
TU/TW = TV/TU definition of similarity
TU(TU) = TV(TW) cross product.
TU² = TV · TW cross product.
Read more on Tangent Secant Theorem here: https://brainly.com/question/26826991
#SPJ1
Ximena decides to estimate the volume of an apple by modeling it as a sphere. She measures its diameter as 11.9 cm. Find the apple's volume in cubic centimeters. Round your answer to the nearest tenth if necessary
The volume of the apple is approximately 832.2 cubic centimeters.
What is volume of sphere?The following equation determines a sphere's volume:
V = (4/3)πr³
When V denotes the sphere's volume, r denotes its radius, and denotes the mathematical constant pi (approximately 3.14). By seeing the sphere as an unlimited number of little cylinders piled on top of one another, the formula may be created. Each cylinder has a height equal to the sphere's shell thickness and a radius equal to the sphere's radius.
The volume of a sphere:
V = (4/3)πr³
Here, r = d/2 = 11.9 cm / 2 = 5.95 cm
Substituting the values we have:
V = (4/3)π(5.95 cm)³ ≈ 832.2 cm³
Therefore, the volume of the apple is approximately 832.2 cubic centimeters.
Learn more about volume of sphere here:
https://brainly.com/question/21623450
#SPJ1
Write the standard form of each equation. Then graph the equation.
x^2+y^2+6x-8y+18=0
The standard form of the equation is (x + 3)² + (y - 4)² = 2.
What is standard form of equation?A linear equation with two variables has the conventional form Ax + By = C, where A, B, and C are constants and where A and B are not equal to zero. The general form of a linear equation is another name for this format. When the line is plotted on the Cartesian plane, the constant term C and coefficient A in this form indicate the line's y-intercept and slope, respectively. When solving systems of linear equations and graphing linear equations, the standard form is helpful.
Complete the squares for the given equation: x² + y²+ 6x - 8y + 18=0.
Starting with the x terms, we add (b/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 18 = 9
For y terms by adding (c/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 16 = -2
The standard form is:
(x + 3)² + (y - 4)² = 2
Hence, the standard form of the equation is (x + 3)² + (y - 4)² = 2.
Learn more about equation here:
https://brainly.com/question/12452575
#SPJ1
A normal distribution has a mean of 16 and a standard deviation of 5. Use the 68-95-99.7 rule to find the percentage of values in the distribution between 16 and 21.
What is the percentage of values in a normal distribution between 16 and 21 with a mean of 16 and a standard deviation of 5, according to the 68-95-99.7 rule is approximately 68%.
How to calculate the percentage of values in a normal distribution?
According to the 68-95-99.7 rule, approximately 68% of the values in a normal distribution are within one standard deviation of the mean, approximately 95% are within two standard deviations of the mean, and approximately 99.7% are within three standard deviations of the mean.
In this case, we want to find the percentage of values in the distribution between 16 and 21.
The range from 16 to 21 is one standard deviation above the mean, since the mean is 16 and the standard deviation is 5. Therefore, approximately 68% of the values in the distribution will fall between 16 and 21.
So, the answer is approximately 68%.
To learn more about standard deviation, visit: https://brainly.com/question/475676
#SPJ1
Yolanda hiked each day for a week. The first day she hiked mile, the second day she hiked mile, and the third day she hiked 1 mile. By how much did she increase the distance she hiked each day?
the distance she hiked each day, we need to calculate the difference between the distance she hiked on consecutive days. Yolanda increased the distance she hiked by 1 mile each day.
What is the total distance?To find the increase in the distance Yolanda hiked each day, we need to calculate the difference between the distance she hiked on each consecutive day.
The distance Yolanda hiked each day for the first three days can be represented as:
Day 1: d miles
Day 2: [tex]d + 1[/tex] miles
Day 3: [tex]d + 2[/tex] miles
The increase in distance from day 1 to day 2 is [tex](d + 1) - d = 1[/tex] mile.
The increase in distance from day 2 to day 3 is [tex](d + 2) - (d + 1) = 1[/tex] mile.
Therefore, Yolanda increased the distance she hiked by 1 mile each day.
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ9
I will give brainlyest to whoever answers this its in a pic because I'm to lazy to type it
Blank #1: 6
Blank #2: 2
which one of these numbers is the largest?
5/4, 1.3, 10/9, 1.6
Answer:
1.6
Step-by-step explanation:
it is this one trust me
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
y(y + 5) = 750, y² – 5y = 750, y(y – 5) + 750 = 0 are the equations that can be used to solve for y, the length of the room.
What is area?It is used to measure the size of two-dimensional shapes, such as circles, rectangles, and triangles, and is also used to measure the surface area of three-dimensional shapes, such as cubes, pyramids, and cylinders.
Option 1: y(y + 5) = 750
This equation can be used to solve for y, the length of the room. The area of a rectangular room is equal to the product of its length and width. Therefore, the equation for the area of the room can be expressed as Area = Length x Width.
Substituting y for Length and y+5 for Width, yields Area = y(y+5). Rearranging this equation to solve for y, yields y(y+5) = 750.
Option 2: y² – 5y = 750
This equation can be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.
Rearranging this equation yields Area = y² – 5y. Substituting this equation with the given area of 750, yields y² – 5y = 750.
Option 3: y(y – 5) + 750 = 0
This equation can also be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.
Rearranging this equation yields Area = y(y – 5).
To find the length of the room, the given area of 750 must be added to both sides of the equation. This yields y(y – 5) + 750 = 0.
For more questions related to circles
https://brainly.com/question/26594685
#SPJ1
смотрите на фото
я его прикрепил ниже