Answer:34
Step-by-step explanation:
Which table matches the data in the graph?
Math Test Raw Scores
Points
2288 2288 2 2 2 2
120
110
100
90
80
70
50
40
30
20
10
X
y
X
0 2 4 6 8 10 12 14 16 18 20 22 24
Correct answers
Y
X
y
X
y
(5,30)
(12, 72)
1
2
1
3
5
120
1
6
(20, 120)
(18. 108)
24
4
2
10
12
108
3
18
3
6
3
12
18
72
5
30
4
8
4
13
20
30
7
42
A table that matches the data in the graph include the following:
Correct answers Points
0 0
5 30
12 72
18 108
20 120
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be represented by the following mathematical equation:
y = kx
Where:
k is the constant of proportionality.y represent the points.x represent the correct answers.Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:
Constant of proportionality, k = y/x = t/d
Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20
Constant of proportionality, k = 6.
Therefore, the required equation is given by;
y = kx
y = 6x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the sum of the interior angles of a 16-sided polygon. 2,880° 2,160° 2,700° 2,520°
Answer: Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘
Step-by-step explanation:
Answer:
D) 2520°------------------------
To find the sum of the interior angles of a 16-sided polygon, you can use the formula:
S(n) = (n - 2) × 180° , where n is the number of sides of the polygon.In our case, n = 16.
Substitute the value of n into the formula:
S(16) = (16 - 2) × 180° = (14) × 180° = 2520°The matching choice is D.
A construction crew is lengthening a road. The road started with a length of 56 miles, and the crew is adding
3 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has
worked. Write an equation relating L to D. Then use this equation to find the total length of the road after
the crew has worked 36 days.
Using A linear equation, It ia found that:
• The equation is: L = 56 + 3d
Where D is representing the number of day crew has worked and L presenting the total length of the road. So let's solve this.
Step by step Explanation:
= L = 56 + 3d
= L = 56 + 3(36)
= L = 54 + 108
= L = 162
Write an inequality for the shaded region shown in the figure.
The inequality for the shaded region shown in the figure is; y ≥ x^2 - 1
We can see that the shaded region seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)
Then:
y ≥ ax^2 + bx + c
where ax^2 + bx + c is the general quadratic equation.
Now to find the equation for the parabola:
f(x) = ax^2 + bx + c
We also can see that the vertex of the parabola is at the point (0, -1)
This means
f(0) = -1 = a0^2 + b0 + c
-1 = c
c = -1
Then:
f(x) = ax^2 + bx - 1
Now we can see at the graph again, to see that the zeros of the parabola are at +1 and -1
Which means that:
f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1
f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1
Then we have two equations:
a + b - 1 = 0
a - b - 1 = 0
b = 0
these equations become:
a - 1 = 0
a - 1 = 0
Then solving for a, a = 1
Then the quadratic equation is:
f(x) = 1*x^2 + 0*x - 1
f(x) = x^2 - 1
And the inequality is y ≥ x^2 - 1
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1. explain what is meant by decision variables, objective function and constraints in linear programming.
Decision variables are the unknown quantities that need to be determined in a linear programming problem.
The objective function is a mathematical expression that needs to be maximized or minimized. It represents the goal or objective of the problem. Constraints are the restrictions or limitations that need to be satisfied in a linear programming problem. These constraints limit the feasible region of the problem and provide boundaries for the decision variables. Linear programming involves finding the optimal solution by maximizing or minimizing the objective function, subject to the constraints. The solution must satisfy all the constraints and provide the best possible value for the objective function.
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Find the volume of the pyramid with a base of 7 meters by 9 meters and a height of 13 meters.
Answer:
The volume of a pyramid can be calculated using the formula:
V = (1/3) * base area * height
where "base area" is the area of the base of the pyramid.
In this case, the base of the pyramid has a length of 9 meters and a width of 7 meters, so its area is:
base area = length * width = 9 m * 7 m = 63 m^2
The height of the pyramid is 13 meters.
Now we can calculate the volume:
V = (1/3) * base area * height
= (1/3) * 63 m^2 * 13 m
= 273 m^3
Therefore, the volume of the pyramid is 273 cubic meters.
a 5lb force acting in the direction of (5,-3) moves an object just over 12 ft from point (0,6) to (7,-4). find the work done to move the object to the nearest foot-lb.
a. 11ft lb
b. 34ft lb
c. 56ft lb
d. 61ft lb
ANSWER FIRST GETS BRAINLIEST
Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team. She assigns a students to each team.
What is the probability that Tally is on the red team? Enter your answer as a simplified fraction. Use the / key to represent the fraction bar.
The probability that Tally is on the red team would be 1/4
Probability means a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team.
Therefore, the probability that Tally is on the red team will be;
P(E) = Number of favorable outcomes / total number of outcomes
P(E) = Number of teams / total number of students
P(E) = 4/16
P(E) = 1/4
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when analyzing a resultant vector, what equation allows you to find the magnitude of the vector? What allows you to find the direction?
When analyzing a resultant vector, the equation to find the magnitude of the vector is the Pythagorean theorem. This equation states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of its components.
To find the direction of the resultant vector, the trigonometric function of inverse tangent or arctan can be used. This involves taking the inverse tangent of the vertical component divided by the horizontal component, which gives the angle of the vector with respect to the positive x-axis.
Alternatively, the direction can also be found using the trigonometric functions of sine and cosine by dividing the vertical and horizontal components of the vector by its magnitude.
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helppp with this geometry problem pleasee
pls answer
worth 20 points!!!!
Step-by-step explanation:
Circumference of a circle is found by:
Circ = pi * d
= pi * 9.7 cm = 30.5 cm
sam wants a wall purple and the mixture says to use 1:3 of blue paint to red paint. if she uses 2 tins of blue paint,how many tins of red paint will she use?
Answer:
6 tins of red paint
Step-by-step explanation:
blue = 1, red = 3 so:
from 1 to 2 tins of blue, you multiply 1 x 2 = 2 tins. Now we have to multiply by 2 on the other side
So: 3 x 2 = 6 tins of red
In ratios, multiplying or dividing has to be applied to both sides
1 : 3 becomes 2: 6
Evan bought a pair of shoes online for $67. He used a coupon code to get a 20% discount. The website also applied a 10% processing fee to the price after the discount. How much was the processing fee? Round to the nearest cent.
After discount the cost is $53.6 and the processing fee is $5.36
The discount reduces the price of the shoes by 20%, which means Evan only has to pay 80% of the original price.
To find the price after the discount
we multiply the original price by 0.8:
Price after discount = 0.8 × $67 = $53.60
Next, the website applies a 10% processing fee to this discounted price. To find the processing fee, we can multiply the discounted price by 0.1:
Processing fee = 0.1 × $53.60
= $5.36
Hence, the processing fee is $5.36 and after discount the cost is $53.6
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PLEASE HELP ME! I DON'T UNDERSTAND HOW TO SOLVE THIS!!
If the volume is 64π how would i solve this equation for r?
V=4/3πr^3
Step-by-step explanation:
V = 4/3 pi r^3
64 pi = 4/3 pi r^3 divide both sides of the equation by pi :
64 = 4/3 r^3 multiply both sides by 3/4
3/4 * 64 = r^3 simplify a bit
48 = r^3 take cube root of both sides
r = 3.63 units
four identical glasses are shown below. one glass is empty, and the other three glasses are 1/4 full, 1/2 full and 4/5 full of water, respectively. if the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled
If the water were redistributed equally among the 4 glasses, the fractional part of each glass that would be filled include the following: K. 31/80.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided above, the division can be calculated as follows;
Fraction = (1/4 + 1/2 + 4/5) ÷ 4
Fraction = 31/20 ÷ 4
Next, we would multiply the fraction 31/20 by the reciprocal of 4 as follows;
Fraction = 31/20 × 1/4
Fraction = 31/80
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
let u d 2 4 5 6 7 3 5 , and let w be the set of all x in r 3 such that u ? x d 0. what theorem in chapter 4 can be used to show that w is a subspace of r 3 ? describe w in geometric language.
Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.
To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.
A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:
For any vectors a, b ∈ S, their addition a + b ∈ S.
For any vector a ∈ S and any scalar k, the product ka ∈ S.
Now, let's define a vector m = v - e.
Observe that for any y in S, we have:
m • y = (v - e) • y = (v • y) - (e • y) = 0.
This implies that y is orthogonal to the vector m.
Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.
As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.
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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).
What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.
Yoshi has 22$ in his wallet and makes 5$ per hour
Answer:
Number of Hours | Money
0 hrs — 22$ (+0$)
1 hrs — 27$ (+5$)
2 hrs — 32$ (+5$)
3 hrs — 37$ (+5$)
(he would gain 15$ after 3 hours of baby sitting)
Step-by-step explanation:
Y = 5x + 22
5x is the amount being added each time, 22 is the y-intercept of the slope; the slope is going at a linear rate of 5 per hour.
jack and jane each spend $ 2 4 $24 on snacks. jack decides to buy bags of chips, and jane buys granola bars. each bag of chips costs $ 1 $1 less than a granola bar, and jack buys 2 2 more items than jane buys. how many bags of chips does jack buy?
If each bag of chips costs $1 less than a granola bar, and jack buys 2 more items than jane buys, Jack buys 15 bags of chips
Let's assume that Jack buys x bags of chips and Jane buys y granola bars. We know that they each spend $24 on snacks, so we can set up the following equation:
x*(price of one bag of chips) + y*(price of one granola bar) = $24
We also know that each bag of chips costs $1 less than a granola bar, so we can write:
(price of one bag of chips) = (price of one granola bar) - $1
Substituting this into the first equation, we get:
x*((price of one granola bar) - $1) + y*(price of one granola bar) = $24
Expanding and simplifying, we get:
x*(price of one granola bar) + y*(price of one granola bar) - x = $24
We also know that Jack buys 2 more items than Jane, so we can write:
x = y + 2
Substituting this into the previous equation, we get:
(y + 2)(price of one granola bar) + y(price of one granola bar) - (y + 2) = $24
Simplifying, we get:
2*(price of one granola bar) + y = $26
We can now solve for y:
(price of one granola bar) = ($26 - y)/2
Substituting this back into the equation for x, we get:
x = y + 2
x = (26 - y)/2 + 2
Simplifying, we get:
x = (28 - y)/2
We know that x and y must be whole numbers, so we can test different values of y until we find one that makes x a whole number. Starting with y = 2, we get:
(price of one granola bar) = ($26 - 2)/2 = $12
2*(price of one granola bar) + y = $26
2*($12) + 2 = $26
Therefore, Jack buys 15 bags of chips (x = (28 - y)/2 = (28 - 2)/2 = 15) and Jane buys 13 granola bars (y = 2).
In summary, Jack and Jane each spend $24 on snacks. Jack buys bags of chips and Jane buys granola bars. Each bag of chips costs $1 less than a granola bar, and Jack buys 2 more items than Jane buys. We can solve for the number of bags of chips Jack buys by setting up and solving equations based on these facts. We find that Jack buys 15 bags of chips.
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ventajas y desventajas del modelo atómico de rutherford
The Rutherford model of the atom is known to be a term that is also seen as planetary model. It was said to have been proposed by Ernest Rutherford in 1911. It was a vital improvement over previous models, but it had some few limitations.
What is Rutherford model of the atom?Below are some advantages and disadvantages of the Rutherford model:
In terms of Advantages:
The Rutherford model was said to be one that was first model that introduced the concept of the nucleus.The Rutherford model aids man to explain the reason most of the alpha particles passed straight through the gold foil, while a few were deflected.In terms of Disadvantages:
The Rutherford model was unable to tell the ways of electrons.The Rutherford model was said to have assumed that the positive charge in the nucleus was one that is uniformly distributed and this was notLearn more about Rutherford model from
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See text below
advantages and disadvantages of the rutherford model of the atom
Gary borrowed $12,500 to buy a new equipment for his restaurant. He signed a 292-day promissory note an interest rate of 4%. Find the maturity value of the promissory note, round to the nearest cent. Use ordinary interest, which is based on a 360-day year 
Answer:
The formula for ordinary interest is:
I = P * r * t
where:
I = the interest
P = the principal
r = the interest rate per year
t = the time in years
In this case, the principal is $12,500, the interest rate is 4%, and the time is 292/360 years (since there are 360 days in a year according to the problem statement). Therefore, we have:
t = 292/360 = 0.811111111
I = 12500 * 0.04 * 0.811111111 = 405.5555555
To find the maturity value, we add the interest to the principal:
M = P + I = 12500 + 405.5555555 = 12905.56
Therefore, the maturity value of the promissory note is $12,905.56 rounded to the nearest cent.
during winter, the average temperature inside your room is 70 degrees with standard deviation of 2 degrees. what is an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees?
For a sample of room temperature during winter, an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees is equals to the 0.25.
For a sample of temperature during winter, Average temperature of room
= 70 degree
Standard deviations = 2 degrees
We have to determine upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees. According to chebyehev's theorem, [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex].
here , σ = 2 , μ = 70, kσ = 4
=> k = 2
So, the required upper bound of probability is [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex]
≤ [tex]\frac{ 1 }{2²} [/tex]
≤ [tex]\frac{ 1 }{4} [/tex]
= 0.25
Hence, required upper bound value is 0.25.
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define the following terms:independent eventsdependent eventsmutually exclusive eventsexhaustive
Independent events- events that do not affect each other's probability of occurring. Dependent events- events where the occurrence of one event affects the probability of the other event happening. Mutually exclusive events- events that cannot occur at the same time. Exhaustive events- events that cover all possible outcomes.
1. Independent events: Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of another event. In other words, the outcome of one event has no impact on the outcome of the other event.
2. Dependent events: Dependent events are events in which the occurrence of one event does affect the probability of the occurrence of another event. The outcome of one event is influenced by the outcome of the other event.
3. Mutually exclusive events: Mutually exclusive events are events that cannot occur at the same time. The occurrence of one event means the other event cannot occur. For example, flipping a coin and getting both heads and tails at the same time is a mutually exclusive event, as it is impossible for both to happen simultaneously.
4. Exhaustive events: Exhaustive events are a set of events that include all possible outcomes in a given situation. They are complete and cover every possibility, leaving no room for additional outcomes. For example, when flipping a coin, the set of exhaustive events includes both heads and tails, as there are no other possible outcomes.
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which type of error occurs when certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame? a. type i error b. sampling frame error c. statistical error d. list error
The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.
The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.
There are 4 types of sampling error
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Calculator This figure shows A ABC. BD is the angle bisector of ZABC. What is AD? Enter your answer, as a decimal, in the box. units A 4.5 B D 5 4
Using similar side theorem and taking the ratios of similar sides, the value of AD is 3.6 units
What is similar side theorem?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
In this problem, we can use the similar side theorem by taking ratios of similar sides.
4.5 / 5 = AD / 4
Cross multiply both sides
AD = (4.5 * 4) / 5
AD = 18/5
AD = 3.6
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Rowan thinks of a number. His number is a factor of both 18 and 30. His number is odd. What is the largest possible number he could be thinking of?
The largest possible number that he could be thinking of is given as follows:
3.
How to obtain the number?A number a is said to be a factor of another number b when the divisibility of b by a has a remainder of zero, that is, it is an exact division.
The factors of 18 are given as follows:
{1, 2, 3, 6, 9}.
The factors of 30 are given as follows:
{1, 2, 3, 5, 6, 10, 15, 30}
The number is odd, hence the largest possible number is of 3.
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An exponential function in the form y=20(b)^x contains the points (0,20) and (1,10). What is the value of b?
Step-by-step explanation:
When x = 0 y = 20 Plug in:
20 = 20 b^0
20 = 20 true , but we didn't find 'b'
when x = 1 y = 10 Plug in:
10 = 20 * b^1
10 = 20 b
b = 1/2
Find the hypotenuse length
The requried measure of the hypotenuse of the given right triangle is 37.
The hypotenuse of the right angle triangle can be evaluated by Pythagoras' theorem, which states that the sum of squares of the legs of a right triangle is equal to the square of the third side.
Hypotensue² = 12²+35²
Hypotensue = √1369 = 37
Thus, the requried measure of the hypotenuse of the given right triangle is 37.
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PLEASE HELP IM GOING T0O FAIL THIS :(
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
The measure of variability that the Charity should use is B. The IQR of 13 is the most accurate to use, since the data is skewed.
Why is the IQR best ?Adopting the IQR gives a better picture of the standard donations, since it is less responsive to outliers and unbalanced data than the range. The charity must take advantage of the Interquartile Range (IQR) for an exact depiction of the data, as it is less impressionable to outliers and skewed data.
The IQR would be:
= Q3 - Q1
Q1 from the data is:
= (6 + 8) / 2 = 7
Q3 is :
(20 + 20) / 2 = 20
The IQR is:
= 20 - 7
= 13
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Write the equation of the conic satisfying the given conditions.
focus at the pole, e=d
=,directrix rsin0 = -2
The equation about the conic is r = 6/(4|sinθ| - 3cosθ).
We have,
Since the focus is at the pole, the conic is a polar equation with the form
r = e d / (1 - e cosθ), where d is the distance from the pole to the directrix and e is the eccentricity.
In this case,
e = 3/4 and the directrix is r sinθ = -2.
We can rewrite the equation of the directrix in Cartesian coordinates as
y = -2/sinθ.
Now we can use the formula for the distance from a point (x, y) to a line Ax + By + C = 0, which is:
d = |Ax + By + C| / sqrt(A^2 + B^2)
In our case,
The equation of the directrix is y + 2/sinθ = 0, which we can rewrite as
y = -2/sinθ.
The coefficients of x and y are both 0 and the constant term is 2/sinθ, so
A = 0, B = 1, and C = -2/sinθ.
Substituting into the formula.
d = |-2/sinθ| / √(0² + 1²)
d = 2/|sinθ|
Now we can write the equation of the conic as:
r = e d / (1 - e cosθ) = (3/4) (2/|sinθ|) / (1 - (3/4) cosθ)
Simplifying.
r = 6/(4|sinθ| - 3cosθ)
This is the polar equation of the conic with focus at the pole and directrix r sinθ = -2, and eccentricity e = 3/4.
Thus,
The equation about the conic is r = 6/(4|sinθ| - 3cosθ).
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given that 3 feet equal 1 yard how many yards equal 7 feet
Answer: 2.333
Step-by-step explanation:
Since 3 feet equal 1 yard, we can divide 7 feet by 3 to get the equivalent distance in yards:
7 feet ÷ 3 feet/yard = 2.333 yards (rounded to 3 decimal places)
Therefore, 7 feet is equivalent to approximately 2.333 yards.
hope this help mark me brainst
