Table A doesn't represent the constant of proportionality.
Table B doesn't represent the proportional relationship.
How to explain the constant?Treat the values in table as (x,y) values. The result is a linear function
For A, 85/5 = 17 while 79 / 10 = 7.9. This doesn't illustrate a constant.
For B, 1.49/16 and 1.59/20 have different values. In this case, 1.49/16 = 0.093 and 1.59/20 = 0.0795.
Therefore. they don't have a constant of proportionality. This was because the values that were gotten for both A and B aren't equal.
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Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
1. How loud a sound is depending on how far away you are
5 85
10 79
20 73
40 67
b. The fountain drinks at hot dog hut.
16 1.49$
20 1.59$
30 1.89$
problem 2 select all of the equations that represent a proportional relationship. (select all that apply.) the remaining length, , of a -inch rope after inches have been cut off: . the total cost, , after an sales tax is added to an item's price, : . the number of marbles each sister gets, , when marbles are shared equally among four sisters: . the volume, , of a rectangular prism whose height is cm and base is a square with side lengths cm: .
An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.
Equation: y = mx and m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
t/p=1.08
C. Equation: x=m/4
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
m/x=4
D. Equation: V= 12s^2
This equation is NOT proportional because side length is squared, so it is not constant linearly.
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Missy rode her bicycle 16 miles in 1 1/4 hours. What was her average speed in miles per hour
Answer: 12.8 miles per hour
Step-by-step explanation:
divide 16 by 1.25 in order to get your answer
Write the equation of the line in fully simplified slope-intercept form.
Answer:
Step-by-step explanation:
Choose two points on the graph: (-6,-7) and (6,-9)
The straight line equation is: y=mx+b
[tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=\frac{-9-(-7)}{6-(-6)} \\\\m=\frac{-9+7}{6+6} \\\\m=\frac{-2}{12} \\\\m=-\frac{1}{6}\\\\Hence,\ y=-\frac{1}{6}x+b\ \ \ \ \ (1)[/tex]
To determine the coefficient b, take any of the two points,
for example (-6,-7), that is, x=-6 y=-7
Substitute these values into formula (1):
[tex]\displaystyle\\-7=-\frac{1}{6}(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-\frac{1}{6}x-8[/tex]
The height (h), in feet, of a balloon is calculated by using the equation h= 3+ + 2 where t is time, in seconds.What is the height of the balloon after 30 seconds?A. 60 ftB. 66 ftO C. 92 ftO D. 102 ft
Given data:
The given expression for height is h=3t+2.
Substitute 30 for t in the above expression.
[tex]\begin{gathered} h=3(30)+2 \\ =92\text{ ft} \end{gathered}[/tex]Thus, the height of the balloon after 30 seconds is 92 ft, so option (C) is correct.
What are the solutions to the inequality (x-3)(x=5)greater than or equal to 0
The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals
(-∞,3] or [5,∞) that is x ≥5 or x≤3
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
Given inequality (x-3)(x-5) ≥ 0
It generates two cases either case1 is true or case 2.
Case1. (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0
⇒(x-3) ≥0 and (x-5)≥0
⇒ x ≥ 3 and x ≥ 5
⇒ x ∈ [3,∞) and x∈ [5,∞)
⇒ x ∈ [3,∞) ∩[5,∞)
⇒ x ∈ [5,∞)
∴ x is greater than or equal to 5
Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0
⇒(x-3) ≤0 and (x-5)≤0
⇒ x ≤3 and x ≤ 5
⇒ x ∈ (-∞,3] and x∈ (-∞,5]
⇒ x ∈ (-∞,3] ∩ (-∞,5]
⇒ x ∈ (-∞,3]
∴ x is less than or equal to 3
Solution of the given inequality is case 1 or case 2
⇒ x ∈ [5,∞) or x ∈ (-∞,3]
⇒ x x ∈ (-∞,3] ∪ [5,∞)
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5. What is the main doman and range of the roller coaster? (Hint: you should express these as a compound inequality or in interval notation
Answer:
If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section we will investigate methods for determining the domain and range of functions such as these.
Step-by-step explanation:
What is the solution set for -3x + 12 < 4x - 9
A) x > 21
B) x > 3
C) x < -3
D) x < -21
Answer:
C) x < -3
Step-by-step explanation:
-3x +12 < 4x - 9
-3x -4x < -12 - 9
-7x < -21
x > -3
What is the complete factorization of 6x2 + 9x - 6?
A. 3(2x - 1)(x + 2)
B. (3x + 2)(2x - 3)
C. 3(x-2)(2x + 1)
D. 3(x-2)(2x - 1)
Answer: A. 3(2x−1)(x+2)
4. In the graph below, what is the line of reflection for triangle XYZ and triangle X'Y'Z"? (1 point)
the x-axis
Othe y-axis
Ox=2
Oy=2
In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.
Given, the coordinates of the triangle XYZ are:
X = (4,5)
Y = (6,3)
Z = (3,2)
and the coordinates of the triangle X'Y'Z' are:
X' = (0,5)
Y' = (-2,3)
Z' = (1,2)
for image of the triangle XYZ to get reflected and become X'Y'Z',
reflection of axis takes place.
But the images are not identical and symmetrical, so the reflection is not about y axis.
we check for x=2
hence reflection of axis when x=a is :
P(x,y) →x'(2a-x , y)
therefore use the above formula and check the coordinates of the reflected image.
X(4,5) when x=2X(4,5) → X'(2(2)-4 , 5)
x(4,5) → X'(0,5)
Y(6,3) when x=2Y(6,3) → Y'(2(2)-6 , 3)
Y(6,3) → Y'(-2,3)
Z(3,2) when x=2Z(3,2) → Z'(2(2)-3 , 2)
Z(3,2) → Z'(1,2)
hence x=2 is the reflection of triangle XYZ and X'Y'Z'.
Therefore we get the requires answer.
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5y/3 = 30 solve for y simplify your answer as much as possible
Answer: y= 18
Step-by-step explanation:
5y/3 = 30
First step: multiply 3 on both sides
5y/3 * 3 = 30*3
5y = 90
Second step: divide 5 on both sides (isolating variable)
5y/5 = 90/5
y = 18
Answer:
y = 18
Step-by-step explanation:
[tex]\frac{5y}{3}[/tex] = 30 ( multiply both sides by 3 to clear the fraction )
5y = 3 × 30 = 90 ( divide both sides by 5 )
y = 18
The sum of two rational numbers is 4. If one of the numbers is 2/3, then what is the other number
Answer:
10/3
Step-by-step explanation:
Let x be the value of the second rational number. The first rational number is 2/3, and we are told that the sum of these numbers is 4:
x + 2/3 = 4
Therefore:
x + 2/3 = 4
x = 4 - 2/3
x = 12/3 - 2/3
x = (10/3)
can you help me solve part A and B ASAP! THANKYOU
The shape comprises a semicircle, rectangle, and a trapezoid
A) The shape below will illustrate how the side length of the rectangle will be calculated
Part I is the semicircle of diameter
[tex]\begin{gathered} d=8\operatorname{cm} \\ r=\frac{d}{2} \\ r=\frac{8}{2}=4\operatorname{cm} \end{gathered}[/tex]From the diagram above
[tex]AB=r=4\operatorname{cm}[/tex]To find the missing side length of the rectangle , we will use the relation below
[tex]AB+BC+CD=12\operatorname{cm}[/tex]Where.
[tex]\begin{gathered} AB=4\operatorname{cm} \\ CD=3.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} AB+BC+CD=12\operatorname{cm} \\ 4+BC+3.5=12\operatorname{cm} \\ 7.5+BC=12\operatorname{cm} \\ BC=12-7.5 \\ BC=4.5cm \end{gathered}[/tex]The missing side length of the rectangle is = 4.5 cm
Hence,
The rectangle can be represented below as
The formula for the area of the rectangle is
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ \text{where,} \\ \text{length}=8\operatorname{cm} \\ \text{breadth}=4.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ A_{\text{rectangle}}=8\operatorname{cm}\times4.5\operatorname{cm} \\ A_{\text{rectangle}}=36\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Area of the rectangle = 36cm²
B) To calculate the area of the semicircle, we will use the formula below
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ \text{where,} \\ r=4\operatorname{cm} \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ A_{\text{semicircle}}=\frac{\pi\times4^2}{2}=\frac{16\pi}{2}=8\pi \\ A_{\text{semicircle}}=25.13\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the semicircle = 25.13 cm²
To calculate the area of the trapezoid, we will use the formula below
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ \text{where,} \\ a=8\operatorname{cm} \\ b=15\operatorname{cm} \\ h=3.5\operatorname{cm} \end{gathered}[/tex]The diagram below represents the trapezoid
By substituting the values, we will have
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ A_{\text{trapezoid}}=\frac{1}{2}(8\operatorname{cm}+15\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{1}{2}(23\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{80.5\operatorname{cm}}{2} \\ A_{\text{trapezoid}}=40.25\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the trapezoid is = 40.25cm²
To calculate the total area of the shape, we will use the formula below
[tex]\begin{gathered} \text{Total area=} \\ =A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Total area=}A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \\ \text{Total area}=25.13\operatorname{cm}+36\operatorname{cm}+40.25\operatorname{cm}^2 \\ \text{Total area}=101.38\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Total Area of the composite shape = 101.38cm²
2.) The amount of sleep that elementary school children get per night follows a Normal distribution with a
mean of 9.5 hours and a standard deviation of 0.55 hours.
a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep per
night. Sketch the Normal curve and shade the area under the curve that is the answer to the
question.
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
The amount of sleep that elementary school children get per night be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.
the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to
P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)
P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)
P(9≤ X ≤ 10) = 0.6367
P(X > 12) = P(Z>(12 - 9.50)/0.55)
P(X > 12) = P(Z>4.5455
P(X> 12) = 0.000
THere is zero possibility of student to get more than 12 houtrs of sleep
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
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1013 nearest thousand
Answer: The answer is 1013, it is already rounded as much as it can go.
Step-by-step explanation:
Describe the correlation:
r = -.009
strong positive
weak negative
weak positive
moderate negative
The correlation for r = -0.009 is B. weak negative.
What is correlation?The Pearson correlation coefficient (r) is the most commonly used metric for determining a linear relationship. It is a number ranging from -1 to 1 that indicates the strength and direction of a link between two variables. When one variable shifts, the other shifts in the same way.
Positive correlation is graded on a scale of 0.1 to 1.0. Weak positive correlation would be between 0.1 and 0.3, moderate positive correlation between 0.3 and 0.5, and strong positive correlation between 0.5 and 1.0. The stronger the positive correlation, the more probable the equities will move in unison. Having a minus means it's negative correlation.
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Find the measure of B
How do to solve this problem? (The answer is 262 Hz) I don't need to know the question that it is asking. I just want to know how to solve the equation and its answer. I am a grade 10 student if this helps you.
Step-by-step explanation:
Given the formula below
[tex]undefined[/tex]how can i find the angle of elevation of the sun to nearest degree?
SOLUTION
From the diagram at the right of the question, a right-angle has been formed already. So we will use SOHCAHTOA to find angle A. Looking at angle A, the opposite side is 140 ft and the adjacent side is 173 ft.
Using TOA, we have
[tex]\begin{gathered} TOA,tanA=\frac{opposite}{adjacent} \\ tanA=\frac{140}{173} \\ tanA=0.80924855 \\ A=tan^{-1}0.80924855 \\ A=38.98146539 \end{gathered}[/tex]Hence the answer is 39 degrees
Solve for x. Just write the number. Triangle btw
1 + 6x
70°
55°
4z+7 what is the value of z
Answer: it could literally be anything
Step-by-step explanation: if 4*z+7=15 then z=2
please help with this homework
Answer:
a.) x = 5
b.) x = 35/2 = 17.5
Step-by-step explanation:
In both problems, we are trying to solve for x, which means we need to isolate it on one side of the equation.
a.) 5/2 x + 1 = 11
5/2 x = 10
Now to divide by a fraction is the same as multiplying by the reciprocal.
x = 10 * 2/5 = 4
b.) 2/7 x - 3 = 2
2/7 x = 5
To divide by a fraction is the same as multiplying by the reciprocal.
x = 5 * 7/2 = 35/2 = 17.5
Can someone help me in this please
Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
What are supplementary angles?Two angles are considered to be supplementary if their sums total 180 degrees. If two angles in geometry add up to 180 degrees, they are said to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°. When combined, supplementary angles always make a straight angle (180 degrees).So, angles supplementary to ∠3:
∠1 is supplementary to ∠3 (Straight angle)∠2 is supplementary to ∠3 (Inversely opposite angle)∠4 is supplementary to ∠3 (Straight angle)∠5 is supplementary to ∠3 (Adjacent angles)∠6 is supplementary to ∠3 (Alternate angles)∠7 is supplementary to ∠3 (Corresponding angle)(Refer to the image attached below)
Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
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Solve for b.49 = b 2b = = 1or
√49 = +/- 7
√16 = +/- 4 as you calculated
Congrats, you did it!
What is the value of X in the equation 1/5x - 2/3y = 30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
a) Simplify both sides of the equation.
1/5x - 2/3(15) = 30
1/5x + -10 = 30
1/5x - 10 = 30
b) Add 10 to both sides.
1/5x - 10 + 10 = 30 + 10
1/5x = 40
c) Multiply both sides by 5.
5 * (1/5x) = (5) * (40)
x = 200
the ratio of bots to girls in a school is nine : ten. what does this ratio mean. if there are 300 girls at the school, how many total students are at the school.
The number of the total students that are at the school is 570 if the ratio of boys to girls in a school is nine: ten and there are 300 girls at the school.
What is the ratio formula?The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
Given that a and b are separate amounts for two quantities, the combined total quantity is denoted as (a + b).
How are these ratio difficulties solved?Three steps are necessary to determine the ratio of three numbers:
Step 1: Add the ratio's numbers together to determine the total number of pieces.
Step 2: By dividing the given sum by the total number of parts, determine the value of each component in the ratio.
Step 3: Divide the original ratio by the sum of each component's values.
The ratio is given as 9:10 as boys to girls.
Number of girls = 300
Thus, girls will be 10x and boys will be 9x
then 10x = 300
⇒x = 30
Then we can calculate the number of boys as
9x = 9*30
=270
Thus, the total number of students in the school
= exact number of girls + exact number of boys
= 300 + 270
= 570
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We an equivalent agression for 40+8(n-3)
Answer:
8n+16
Explanation:
Given the expressions:
[tex]40+8\left(n-3\right)[/tex]First, distribute 8 over the terms in the bracket:
[tex]\begin{gathered} =40+8(n)+8(-3) \\ =40+8n-24 \end{gathered}[/tex]Finally, collect like terms and simplify:
[tex]\begin{gathered} =40-24+8n \\ =16+8n \end{gathered}[/tex]An equivalent expression is 8n+16.
Evaluate express your answer in exact simplest form9P4=
The formula for Permutation is,
[tex]^nP_r=\frac{n!}{\left(n-r\right)!}[/tex]The expression given is,
[tex]^9P_4[/tex]Given:
[tex]n=9,r=4[/tex]Plug in n = 9, r = 4
[tex]\frac{9!}{\left(9-4\right)!}[/tex]Simplify
[tex]\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}=9\times8\times7\times6=3024[/tex]Hence, the answer is 3,024.
PLEASE HELP URGENT!!!!
Answer:
Step-by-step explanation:
answer is the first one: square root property of equality
BTS zzz
Answer:
Reflexive property of equality
Step-by-step explanation:
look at the image
What’s 12:28 reduced
Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.
Step-by-step explanation: I hope this helps!
HELP HELP HELP What is the x-intercept of the line with this equation −5x+15y=15 ?
<3
Answer: (-3, 0)
Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.
0 = 1+1/3x
-1 = 1/3x
-3 = x
Answer:
x = - 3
Step-by-step explanation:
To get the x intercept, y has to be equal to 0.
- 5·x + 15·y = 15
- 5·x + 15·0 = 15
- 5·x = 15
x = 15/(- 5)
x = - 3