The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.
What are the ratio and proportion?
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given table,
Suppose the number of guest ∝ food prepared.
Take the first data,
12 ∝ 15
12 = k(15)
k = 12/15 = 0.8
Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".
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11. Write the equation of the line in point-slope form with a slope of -2
and passes through the point (2,-9). (YELLOW)
Why is y=mx+b the slope intercept form
Answer:
In the equation of a straight line (when the equation is written as "y = MX + b"), the slope is the number "m" that is multiplied by the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
Answer: The equation defines the relationship between the angle of inclination of the line relative to the x-axis and the point at which the line passes through the y-axis on a graph.
Step-by-step explanation:
Imagine a line, L, that passes through the y-axis of a graph at some point B=(0,b), where the 0 is the x-coordinate of B and b is the y-coordinate of B. In this case, we will use the variable m to represent the slope of the line. Geometrically, the slope of a line is said to be tangent to its angle of inclination, the smaller of the two angles formed by the line L and the x-axis. In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the side opposite of it over the side adjacent to it. This relationship can be illustrated by constructing a right triangle where the hypotenuse is formed by the segment of the line L between the point B and an arbitrary point P somewhere along the line with the coordinates (x,y).
This triangle can be seen in the attached jpg. The side opposite of the angle of inclination is the imaginary vertical line formed between the point P and the x axis and the side adjacent to it is formed by the imaginary horizontal line between the point B and the vertical line from P. The point where these imaginary lines intersect forms the right angle of the triangle. The length of the opposite side, l1, can be expressed as the difference in y between points P and B:
l1 = y-b
Likewise, the length of the adjacent side, l2, can be expressed as the difference in x between points P and B:
l2 = x-0
The tangent of the angle of inclination, labled as [tex]\alpha[/tex] in the picture, can then be expressed as:
tan([tex]\alpha[/tex]) = [tex]\frac{(y-b)}{(x-0)}[/tex]
simplified as:
tan([tex]\alpha[/tex]) = [tex]\frac{y-b}{x}[/tex]
Because we know that slope m = tan([tex]\alpha[/tex]), we can say that
m = [tex]\frac{y-b}{x}[/tex]
solving by algebra for y,
mx + b = y or y = mx + b
in single variable calculus, the slope of a line is described as the rate of change of its y coordinates with respect to the rate of change of its x coordinates, referred to as the derivative of y with respect to x. This relationship is used to describe things like the speed of an object as it relates to the change in the objects position. The important thing to realize here is the connection between the slope, which we expressed as the difference in the y values of two points on a line over the difference in their x values, and the behavior of the coordinates of points as you move along the line.
Hope that helps! If the last bit is confusing, don't worry, as long as you understand why y=mx+b is the slope intercept form you've got the right idea.
Find the slope and the y-intercept of the line.
3x-2y=-6
Write your answers in simplest form.
slope:
3
y-intercept: -6
2
X
08
Undefined
Ś
Step-by-step explanation:
convert equation to y = mx+c:
3x-2y= - 6
3x+6=2y
y=3/2x+6/2
y=3/2x+3
gradient/slope=3/2
y intercept = 3
Please mark as brainliest :))))0
Answer:
Step-by-step explanation:
y = mx + b , where "m" is a slope and "b" is a y-intercept
~~~~~~~~~~~~~~
3x - 2y = - 6
3x - 3x - 2y = - 3x - 6
- 2y = - 3x - 6
[tex]\frac{-2}{-2}[/tex] y = [tex]\frac{-3}{-2}[/tex] x + [tex]\frac{-6}{-2}[/tex]
y = [tex]\frac{3}{2}[/tex] x + 3
Slope: [tex]\frac{3}{2}[/tex]
y-intercept: 3
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Write an equation to determine the number of friends (x) at Jack's party.
Answer:
x = 48/3
when Jack got 50 chocolates and has left 2, then Jack gave away 50-2=48 chocolates. When each friend got 3 chocolates, the number of friends x is equal to 48 divided by 3.
Answer:
x=16 (friends)
Step-by-step explanatn
50/3 = 16.6666
take away the .66666
so 16x3=48
meaning u would have 2 left over
Write your answer as a fraction in simplest form.
Answer:
17/10 (1.7)
Hope this helps!
Slove: -12 divided by 2 3/4
Javon lost 12 pounds in 2 3/4 weeks. On average, how much weight did Javon lose per week?
A biker cycles 9 miles 2/3 of an hour. The distance here varies directly with time. What is the constant of variation (It is the biker's rate.)
The constant of variation of the distance is 13.5 miles
How to determine the constant of variation?From the question, we have the following parameters that can be used in our solution:
Distance cycled = 9 miles
Number of hours = 2/3 of an hour
From the above parameter, we can calculate the constant of variation
The constant of variation is calculated as
Constant of variation = Distance cycled/Number of hours
Substitute the known values in the above equation
So, we have the following equation
Constant of variation = 9/(2/3)
Evaluate the quotient
Constant of variation = 13.5
Hence, the constant of variation is 13.5 miles per hour
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Drag the red and blue dots along the x-axis and y-axis to graph 5x + 7y = 28.
The x-intercept would be 5.6, and the y intercept would be 4, if that helps.
what is the product of 30 x 10 to the power of 5
Answer: 6 zeros
Step-by-step explanation: 30 x 10^5
using P.E.M.D.A.S
you do exponents first
10^5 = 100000
then 100000 x 30 = 3000000
and there is 6 zeros
A cold water pipe can fill a swimming pool in 4 hrs, and a hot water pipe can fill it in 6 hrs. If cold water pipe is turned on and hot water pipe is turned on 3 hrs later, how long will it take for the pool to be filled?
Answer: 3 hours 36 minutes
Step-by-step explanation:
You can find out that the cold pipe fills up the pool by 1/4 every hour from the question. if you turn on the cold pipe for 3 hours, the pool would be filled 3/4 before you turn on the hot water. you also can find out that the hot pipe fills up the pool 1/6 every hour. so the next hour will continue to fill up the pool 5/12 until you turn off the water. you only need to fill up the pool 1/4 more so it will take a total of 3 hours and 36 minutes to fill up.
In a group of 50 people, 20 are vegetarian. If two people are selected at random, what is the expected number of vegetarians?.
In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.
Define mean.In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers. There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.
Given,
In a group of 50 people, 20 are vegetarian. If two people are selected at random,
For proportion,
p = x/n
p = 20/50
p = 0.4
n = 2
Mean:
x = np
x = 2 × 0.4
x = 0.8
In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.
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how do you write x^2+8x+7 in the complete square method? need help asap!!
Answer:
Step-by-step explanation:
Equation
y = x^2 + 8x + 7 Put brackets around the first two terms
y = (x^2 + 8x) + 7 Take 1/2 the linear term's coefficient (8)
8/2 = 4 Put this result inside the brackets and square
y = (x^2 + 8x + 4^2) + 7 Take - 4^2 and add it to the seven.
y = (x^2 + 8x + 16) + 7 - 16 What you did, did not change the eqiuation
Y = (x^2 + 8x + 16) - 9 The first 3 terms make a perfect square
y = (x + 4)^2 - 9
The minimum should be at - 4,-9 Just to make sure it is, I'll graph the original equation. The y intercept should be at 7 and the two x roots should x = + 3 - 4 and x = -3 - 4. or x = -1 and x = - 7
Let's see if this all checks out.
Graph of original equation.
Please help me please , please
Answer:
mAngleT = 60°
mAngleU = 60°
TS = 13cm
SU = 13cm
Step-by-step explanation:
Since two of the sides are the same the two base angles are also the same. One is 60° so the other one is 60° also. But if they are both 60° and all the angles add up to 180° the last one has to be 60° also.
One side is marked 13cm. It is marked congruent to the left side so they are both 13cm.
But we saw from the angles all being the same, that this is actually an equilateral triangle. So all three sides are the same.
Please help me
The probability distribution table describes Eric's movie collection.
What is the probability that a movie chosen at random is a drama or an action movie?
Thriller Drama Comedy Action
The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted. Identify and interpret the key features of the exponential function modeled in terms of this situation.
Of the given options, the correct options are [1], [4], [6], [7].
What is a general equation of a exponential function? What is Asymptote of a curve?The general equation of a exponential function is -
y = aeˣ
It's graph is plotted and attached below.
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the [x] or [y] approaches zero.
Given is the population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year.
We have the graph in the question as shown. Of the given options, the correct options are [1], [4], [6], [7].
Therefore, Of the given options, the correct options are [1], [4], [6], [7].
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A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 6 milliliters of compound
B. If a chemist wants to make 671 milliliters of the drug, how many milliliters of compound A are needed?
If a chemist wants to make 671 milliliters of the drug, then 305 milliliters of compound A are needed.
Given that:
A certain drug is made of compound A and compound B.
There are 5 milliliters of compound A used for every 6 milliliters of compound B.
So, A and B are in the ratio of 5:6.
Let a chemist will use 5x milliliters of compound A and 6x milliliters of compound B to make 671 milliliters of the drug.
So, we equate the total amount and find the value of x.
i.e. 5x + 6x = 671
=> 11x = 671
=> x = 61
Putting the value of x = 61. We get the value of compound A and compound B.
The value of compound A = 5x = 5 x 61 = 305 milliliters.
The value of compound B = 6x = 6 x 61 = 366 milliliters.
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You push yourself on a skateboard with a force of 30N and
accelerate at 0.5m/s². Find the mass of you and the
skateboard together.
The mass of mass of 'you' and the skateboard together will be 60 kg.
According to the question,
We have the following information:
You push yourself on a skateboard with a force of 30N and accelerate at 0.5m/s².
We know that the following formula is used to find the force applied:
Force = mass*acceleration
(More to know: force is denoted by F, mass is denoted by m and acceleration is denoted by a.)
Putting the given values in this formula:
30 = m*0.5
m = 30/0.5
m = 60 kg
Hence, the mass of mass of 'you' and the skateboard together will be 60 kg.
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If i toss a fair coin five times and the outcomes are ttttt, then the probability that tails appears on the next toss is.
The probability that tails appears on the next toss is 0.5
Given,
In the question:
If I toss a fair coin five times and the outcomes are TTTTT,
To find the probability that tails appears on the next toss is.
Now, According to the question:
The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.
A sequence of five fair coin flips has a sample space that contains all potential outcomes. [tex]2^3[/tex] {H, T} is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .
The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH} or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5
Hence, the probability that tails appears on the next toss is 0.5
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Use a graphing calculator to plot each set of points. Which set shows a negative trend? a {(7, 3), (4, 0), (2, −3), (9, 5)}
b {(−1, 9), (2, 4), (−2; 12), (5, 1)}
c {(4, 5), (8, −1), (2, 3), (−4, −2)}
d {(0, 0), (−4, −7), (6, 9), (−2, −3)}
The points that showed a negative trend is
b {(−1, 9), (2, 4), (−2; 12), (5, 1)}How to know a negative trend graphA graph with a negative trend line slope is said to have a negative trend.
The variables are shown to be negatively correlated, meaning that when one increases, the other decreases and vice versa.
An instance of such graphs would be a graph illustrating the relationship between a car's age and value.
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Q36 this is geometry if anyones good at it can someone help me pls
Answer:
Q36 this is geometry if anyones good at it can someone help me pls
a home-improvement store offers a new brand of lawn food that claims to reduce the number of weeds by 30% over a different brand of lawn food. to test the claim, a homeowner plans to use the new brand of lawn food on half of his lawn and the original brand on the other half. the homeowner will count the number of weeds that appear after a month on each half of the lawn. a neighbor explains that there may be confounding variables, such as shade, that might also explain the relationship. which statement best describes the effect of the confounding variables? because of confounding variables, the homeowner should only put the new lawn food on shady spots and the original brand on sunny spots. because shade is a primary cause of weed growth, the brand of lawn food used in shady or sunny spots will not affect the number of weeds. if the half of the lawn with the new lawn food shows fewer weeds after a month, this will prove the new lawn food is better at stopping weed growth. the parts of the lawn that receive the new lawn food may also get more shade than other parts of the lawn, and the shade might also cause fewer weeds.
Answer: D
Step-by-step explanation: The part of the lawn that receive the new lawn food may also get more shade than other parts of the lawn. And the shade might also cause fewer weeds
helpppp................
Answer:
Step-by-step explanation:
Tips: All of the figures are prisms so always add prism to end.
2. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.
3. Hexagonal Prism. Since it is a hexagon with 3d dimensions added to it.
6. Triangular prism. Since it is a triangle with 3d dimensions added to it.
8. Also Triangular prism. Look above.
9. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.
10. Another Rectangular prism.Since it is a rectangle with the 3d dimensions added to it.
Ps. All the answers you created are correct!
What is the slope of the line whose equation is
Oslope = 2
O slope = -9
O
slope = 0
Oslope = -1/2
y = 16?
Answer: slope = 0
Step-by-step explanation:
The equation of straight line can be expressed in the form y = mx + b, which is referred to as slope intercept form.
In this equation, m represents the slope of the line, y is the y-coordinate of an arbitrary point along the line and x is the x-coordinate of the same point, and b is the location where the line intercepts the y-axis of the graph.
if y = 16, then the slope of the line, m, must be 0.
y = mx + b
y = (0)x + b
y = b
In other words, the line described by the equation y = 16 is a horizontal line that passes through the y-axis at the point (0,16).
Cade and Kohl had 55 candy bars to sell . Kohl sold 25 of them of them and Cade sold 20 of them. What fraction of the candy bars do the boys have left to sell
Kylie works as a salesperson at an electronics store and sells phones and phone accessories. Kylie earns a $15 commission for every phone she sells and a $2 commission for every accessory she sells. On a given day, kylie made a total of $352 in commission and sold 6 more accessories than phones. Determine the number of phones sold and the number of accessories sold.
The number of phones sold would be 20
And, the number of accessories sold would be 26.
Used the concept of an equation that states,
An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
Kylie earns a $15 commission for every phone she sells and a $2 commission for every accessory she sells.
And, On a given day, Kylie made a total of $352 in commission and sold 6 more accessories than phones.
Let us assume that,
The number of phones sold = x
And, the number of accessories sold = y
Hence, the equation becomes,
15x + 2y = 352 .. (i)
And, y = x + 6 .. (ii)
Substitute the value of y in (i);
15x + 2y = 352
15x + 2 (x + 6) = 352
15x + 2x + 12 = 352
17x + 12 = 352
17x = 352 - 12
17x = 340
x = 340/17
x = 20
From (ii);
y = x + 6
y = 20 + 6
y = 26
Therefore, The number of phones sold = 20
And, the number of accessories sold = 26
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Visitors to the amusement park must be at least 54 inches tall to ride the roller coaster. How tall might a visitor riding the roller coaster be?
Answer:
Step-by-step explanation:
The visitor might be exactly 54 inches or above 54 inches.
which expression shows how to write(3^4)^2 as a product?
(3⁴)² can be written as 3² × 3⁶.
What is Exponentiation?Exponentiation is the operation of doing multiplication repeatedly and it is written in the form aᵇ.
We have to write the given expression (3⁴)² as product of two numbers.
Now, (3⁴)² = 3⁸
We have the property of exponentiation,
aⁿ × aˣ = a^(n + x)
Thus 3⁸ = 3^(2+6) = 3² × 3⁶
Hence, (3⁴)² can be expressed as 3² × 3⁶.
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what is the confidence interval estimate of the population mean ?
In statistics, a confidence interval defines the possibility that a population parameter will fall between a set of values for a certain proportion of the time. Analysts commonly incorporate confidence zones that encompass 95% or 99% of the expected data. Thus, if a point estimate of 10.00 is derived using a statistical model with a 95% confidence interval of 9.50 - 10.50, there is a 95% chance that the real value falls within that range.
What is the need for Confidence Intervals?
Confidence intervals are one technique to illustrate how "accurate" an estimate is; the higher the 90% confidence interval for a certain estimate, the more the precaution advised when employing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limitations.
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answer the question is decreased or increased by what number
Answer:
Step-by-step explanation:
decrease by 10
Answer:
Step-by-step explanation:
increased by thirty tickets
Based on the graph, which of the following guarantees that an estimate using tangent line approximation will result in an overestimate? point of tangency near x = -2 point of tangency near x = 0 point of tangency near x = 2 point of tangency near x = 4
The value of x at which the tangent line approximation will result in an overestimate is given by:
Point of tangency near x = 0.
When does the tangent line approximation results in an underestimate and when does it results in an overestimate?The possible results for the tangent line approximation are given as follows:
Underestimate: tangent line is below the curve.Overestimate: tangent line is above the curve.The underestimate or underestimate depend on the second derivative of the function, as follows:
Second derivative positive: underestimate.Second derivative negative: overestimate.Hence, regarding the concavity, we have that the definitions are listed as follows:
Concave down: overestimate.Concave up: underestimate.On the graph given by the image at the end of the answer, the concave down point is given as follows:
x = 0.
Hence the correct option is:
Point of tangency near x = 0.
Missing InformationThe graph is given by the image at the end of the answer.
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