Answers
Answer:
a. The equation is s = [tex]\frac{1}{3}[/tex] w
b. [tex]1\frac{5}{12}[/tex] cups of sugar will be needed to follow the recipe
Step-by-step explanation:
The equation of the direct proportional relation is y = k x, where
x is the inputy is the outputk is the constant of proportionalityWe can find the value of k by using the initial values of x and y
Let us use this rule to solve the question
∵ In the recipe for 1/2 cup of sugar for every 1 1/2 cups of water
→ That means the number of cups of sugar is in proportion to the
number of cups of water
∵ s represents the number of cups of sugar
∵ w represents the number of cups of water
∴ s ∝ w ⇒ (∝ a sign of proportion)
∴ s = k w ⇒ k is the constant of proportionality
∵ s = [tex]\frac{1}{2}[/tex] and w = [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
Substitute the values of s and w in the equation above to find k
∵ [tex]\frac{1}{2}[/tex] = k × [tex]\frac{3}{2}[/tex]
→ Multiply both sides by 2 to cancel the denominators
∴ 1 = 3 k
→ Divide both sides by 3 to find k
∴ [tex]\frac{1}{3}[/tex] = k
∴ The equation is s = [tex]\frac{1}{3}[/tex] w ⇒ a.
→ We need to find the number of sugar cups for 4 1/4 cups of water
∵ w = [tex]4\frac{1}{4}=\frac{17}{4}[/tex]
∵ s = [tex]\frac{1}{3}[/tex] w
→ Substitute w by 5/4
∴ s = [tex]\frac{1}{3}[/tex] × [tex]\frac{17}{4}[/tex]
∴ s = [tex]\frac{17}{12}=1\frac{5}{12}[/tex]
∴ [tex]1\frac{5}{12}[/tex] cups of sugar will be needed to follow the recipe ⇒ b.
Related Questions
Sabine records the daily heights of a random sample of bamboo stalks, in inches. They are: 20, 19, 17, 16, 18, 15, 20, 21 Consider the formulas: A: s squared = StartFraction (x 1 minus x overbar) squared (x 2 minus x overbar) squared ellipsis (x n minus x overbar) squared Over n minus 1. B: s = StartRoot StartFraction (x 1 minus x overbar) squared (x 2 minus x overbar) squared ellipsis (x n minus x overbar) squared Over n minus 1 EndFraction EndRoot. C: Sigma squared = StartFraction (x 1 minus mu) Squared (x 2 minus mu) squared ellipsis (x N minus mu) squared Over N EndFraction. D: Sigma = StartRoot StartFraction (x 1 minus mu) Squared (x 2 minus mu) squared ellipsis (x N minus mu) squared Over N EndFraction EndRoot Which formula should you use for variance? Which formula should you use for standard deviation?.
Answers
The formula Sabine should use for calculating the variance and standard deviation for the random sample of bamboo stalks are,
[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]
[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]
What is variance and standard deviation?The variance of the data is the measure of average level by which every point is differed from the mean.
It can be calculated as,
[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]
The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
It can be calculated as,
[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]
Sabine records the daily heights of a random sample of bamboo stalks, in inches.
They are: 20, 19, 17, 16, 18, 15, 20, 21
For this data Sabine wants to calculate the variance and standard deviation, which can be done using the above formula.
Hence, the formula Sabine should use for variance is,
[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]
The formula should Sabine use for standard deviation,
[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]
Learn more about the variance and standard deviation here;
https://brainly.com/question/15858152
Answer:
First Part: A and B
Second Part: 4.5 and 2.12
Step-by-step explanation:
edge 2022
Explain why 3^-3 = 1/27
Answers
Step-by-step explanation:
Because 3^-3=0.037 and 1/27 also equals 0.037 so they are equivalent thats why.
Wendy asked 40 students on the school football team if they ever injured themselves while playing sports. Fifteen football team members responded “Yes.” Wendy concluded that 375 of the 1,000 students in her school have injured themselves playing sports. Select whether Wendy's conclusion is valid or invalid.
Answers
Answer:
Yes, Wendy's conclusion is valid.
Step-by-step explanation:
40 divided by 15= 2.666666666666667
Therefore, 1000 divided by 2.666666666666667= 374.999999999999953 which can be rounded to 375
SOMEONE HELP ME PLS PLS PLS, I AM BEGGGGINGGGGGGG
Answers
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS
Answers
Answer:
(0, -3)
explanation:
original coordinates of C: (0, -7)If reflected over y axis, there will be additive inverse in x unit
use the formula: (x,y) → (−x, y)
new coordinates: (0, -7)Then if translated vertically, there will be change in y axis:
(0, -7+4) → (0, -3)
Find the value of abc if a = 4, b=-2 and c= -1.
Answers
Answer:
4+2+1=7 Make me brainlist please
what is the value of x
Answers
Answer:
x = 20
Step-by-step explanation:
given a line parallel to a side of a triangle and intersecting the other two sides, then it divides those sides proportionally , that is
[tex]\frac{10}{5x+10}[/tex] = [tex]\frac{11}{121}[/tex] = [tex]\frac{1}{11}[/tex] ( cross- multiply )
5x + 10 = 110 ( subtract 10 from both sides )
5x = 100 ( divide both sides by 5 )
x = 20
The sum of the squares of two consecutive integers is 145. Find the two integers.
Please help asap .
Answers
Answer: The two integers are 8 and 9.
Step-by-step explanation: Let n represent the number.
n^2 + (n + 1)^2 = 145
By foiling, this can be rearranged to:
n^2 + n^2 + 2n + 1 = 145
Subtract 145 from both sides:
2n^2 + 2n - 144 = 0
Divide both sides by 2:
n^2 + n - 72 = 0
Factor the polynomial:
(n + 9)(n - 8) = 0
Solve for n:
n = -9, n = 8
Since they need to be consecutive, make the 9 positive. It will be positive either way because it is being squared.
Now, n = 9 and n = 8.
These are your two integers. Hope this helps!
Write an equation standard form for the line that goes through the following points (-3,-2), (5,3)
Answers
Answer:
Your answer is: y = 5/8x -1/8
Step-by-step explanation:
Hope this helped : )
What is the slope of the line through (2, 9) and (5, 3)
Answers
Answer:
Slope:-2
Step-by-step explanation:
You have to do y-y divided by x-x so 3-9 which equals -6 and 5-2 which equals 3 and then you have -6/3 and simplifying that you get -2.
A student finds the sum of the angle measures in an octagon by multiplying 7 • 180°. What is the student's error?
Answers
The student should compute 6*180 = 1080 because of the formula
S = 180(n-2)
We have n = 8 sides which leads the n-2 part to become n-2 = 8-2 = 6
Which values in this data set are outliers? 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78 Select Outlier or Not Outlier for each value. Value Outlier Not Outlier 20 Outlier – 20 Not Outlier – 20 48 Outlier – 48 Not Outlier – 48 64 Outlier – 64 Not Outlier – 64 78 Outlier – 78 Not Outlier – 78.
Answers
Outlier is a data point that is different from the rest of the data. The outliers in the dataset will be 20 and 78.
What is a Scatter plot?A scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents particular data on both axes.
What is an Outlier?An outlier is a data point that is different from the rest of the data.
If we keenly observe the data set that is given to us, 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78; the range of the data set that is given to us lies mostly between the 48 to 68, therefore, the data point that is the outlier for this data set are 20 and 78.
Hence, the outliers in the dataset will be 20 and 78.
Learn more about Outlier:
https://brainly.com/question/9933184
Answer:
Only 20 is an outlier.
Step-by-step explanation:
Took the test.
what type of number is -4/2
Answers
Answer:
-4 integral and 2 prime number
Can anyone help me find this answer
Answers
Answer:
23.4units
Step-by-step explanation:
√(22)²+(8)²
√484+64
√548
23.4
You use the pythagorean theorem. 64+484=548
548 square root is about 23.41
Why is 2/1 x 1/2 equivalent to 1?
Answers
Answer:
because the when you multiply that the fraction answer is 2/2 or just simply 1
Step-by-step explanation:
2 1 2
— × — = — or 1
1 2 2
pls help!! first correct answer will be awarded brainiest!!!
Answers
Answer: See below
Step-by-step explanation:
Sophie's speed is --> s miles/hour
Yesterday, Sophie biked for --> t hours
Distance = speed * time
Distance = (s miles/hour)(t hours)
Distance = (s)(t)
Therefore, Sophie's route was s*t or st miles long
7
Write the equation of a line that is perpendicular to y = -3 + 6 and that passes through the point
(2,-6).
Answers
Answer:
Perpendicular lines are lines that are at right angles to each other.
For perpendicular lines, the product of their slopes is -1.
[tex]\implies m_2=\dfrac{-1}{m_1}[/tex]
(where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of perpendicular lines)
The slope of the given equation is -3. Therefore, to find the slope of the line that is perpendicular:
[tex]m_2=\dfrac{-1}{-3}=\dfrac13[/tex]
Now we have the slope, we can use the point-slope form of a linear equation with [tex]m=\dfrac13[/tex] and [tex](x_1,y_1)=(2,-6)[/tex] to find the equation of the perpendicular line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-6)=\dfrac13(x-2)[/tex]
[tex]\implies y+6=\dfrac13x-\dfrac23[/tex]
[tex]\implies y=\dfrac13x-\dfrac{20}3[/tex]
A tracksuit top costs £12.75 and matching tracksuit bottoms cost £9.50, how much does the tracksuit cost altogether?
Answers
Step-by-step explanation:
£22.25 pls mark brainliest thanks
Choose the graph of this equation.
Y= -2/3x - 2
Answers
Answer:
c
Step-by-step explanation:
c because
if you use a number such as -4 for x, you do
-3/2*-4 is 12/2 which is 6
6-2 is 4
the coordinate would be (-4,4)
it fits graph c
Simplify the equation
3+7x-(2+9x)
Answers
3 + 7x - (2 + 9x )
3 + 7x - 2 -9x
1-2x
Answer:
1-2x
Step-by-step explanation:
3+7x-(2-9x)
(if there's a minus in front of parenthesis then you have to change the sign in the parenthesis)
3+7x-2-9x(take out from parenthesis)
1-2x(combine/simplify like terms)
$34.97 is what percent of $86.08?
Round your answer to the nearest whole number and include a percent sign (%).
Answers
Answer:
41%
Step-by-step explanation:
PLEASE HELP :)
----How many more miles would you have to travel if you drove down Polk and Fernwood?---- *I found the hypotenuse, 16, I just can't figure out how many more miles it is!*
Answers
Answer:
8 miles.
Step-by-step explanation:
Travelling down Alley street is 20 miles
Travelling along Polk and Fernwood = 12 + 16 = 28 miles.
2. how long does this lease last?
a. month-to-month agreement
b. 12 months
c. 18 months
d. 2 years
Answers
Hope this helps
Please mark as brainliest
can someone help me please?
Answers
Option D is the correct answer
Find the area of the regular figure below:
Answers
Answer:
82.82in^2
Step-by-step explanation:
Solve for t.
16 - 2t =+9+4t
Please solve it out
Answers
Exact form
Y= 7/6
Decimal form
Y=1.16666666
Mixed numbers form
Y=1 1/6
Which geometric term is best described as a straight path between two
points?
A. Point
Ο Ο
B. Line segment
O
C. Angle
O.
D. Vertex
Answers
Answer:
B. Line segment
Step-by-step explanation:
A line segment starts with a point and ends with a point.
Which statement is true about the graph of the equation 2x + y - 5 = 0?
The y-intercept is 5.
O The slope is -1.
The y-intercept is -1.
The slope is 2
Answers
Find the minimum value of the parabola y = x2 – 2x – 3.
Answers
Answer:
- 4
Step-by-step explanation:
the minimum value of the parabola is the value of the y- coordinate of the vertex.
given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² - 2x - 3 ← is in standard form
with a = 1 and b = - 2 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-2}{2}[/tex] = 1
substitute x = 1 into the equation for corresponding y- coordinate
y = 1² - 2(1) - 3 = 1 - 2 - 3 = - 4
then minimum value is - 4
PLEASE HELP,I AM BEING TIMED!!
Measure the angle of 1
Options: 100
90
10
60
Answers
Answer:
angle of 1 will be 60°Step-by-step explanation:
we know vertical opposite angle are equall so angle 1 = 60°