Leila wanted to order her IFTAR meal from La Gondola, Al Khobar. The menu stated that their pasta is a blend of wheat and corn. La Gondola does not disclose the percentage of each ingredient in the blend but we know that the wheat in the blend contains 5% protein, and the corn in the blend contains 10% protein. Overall, each 57 gram serving of pasta contains 4 grams of protein.
Leila told her sister that there was more wheat than corn in the pasta. Use multiple representations to justify if this is a true statement. (You may use DESMOS for graphing. You must also put in the algebraic solution and a table.)
Answers
Step-by-step explanation:
Let the amount of wheat is x and amount of corn is y.
The total amount of pasta is
x + y = 57Amount of protein in same pasta is
5% of x + 10% of y = 4or
0.05x + 0.1y = 4The graphical solution is attached
x = 34, y = 23It is easy to solve the system by substitution
y = 57 - x0.05x + 0.1(57 - x) = 40.05x + 5.7 - 0.1x = 40.1x - 0.05x = 5.7 - 40.05x = 1.7x = 1.7/0.05x = 34Then the value of y is
y = 57 - 34 = 23As we see x > y, so Leila is right
The above problem is solved using Multiple Representations. Multiple representations are used to achieve a deeper comprehension of concepts related to the same operation.
How do we evaluate the veracity of Leila's assertion?We can arrive at whether the statement is true or false by solving for the value of Y using the graphical method. Where Y is the amount of wheat and X is the amount of corn.
Our function is given as follows:
X + Y= 57. ..........1
Recall that the total amount of pasta is 57 grams
Recall as well that the total amount of protein in the pasta is given as:
0.05x + 0.1y= 4grams.......2
By inputting equations 1 and 2 into the Desmos Graph, we have x to be equal to = 34, and y = 23. (please see the attached image).
Recall that Leila's assertion was that there is more corn in the Pasta. Since x is the amount of corn, then Leila's assertion is True that: x>y.
The algebraic solution is arrived at using substitution.
Rewriting equation (1), we have
y = 57 - x .......................(3)
Let us substitute y into equation (2) above. That gives us:
0.05x + 0.1(57 - x) = 4.........................(4)
Expanding the brackets, we obtain
0.05x + 5.7 - 0.1x = 4
Collecting like terms, we can rewrite the quation as:
0.1x - 0.05x = 5.7 - 4
0.05x = 1.7
Rewriting the equation such that it is subject to x, we have
x = 1.7/0.05
x = 34
If from the above, x = 34, inputting that into equation (3) above, we have
y = 57 - 34; Therefore,
y = 23
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Related Questions
find the equation of the tangent to the circle whose equation is given below at the point (1,2)
(x-3)^2 + (y+2)^2 = 20
give answer in form ax+by+c=0 where abc are integers
Answers
Answer:
[tex]x-2y+3=0[/tex]
Step-by-step explanation:
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the centre, and r is the radius)
Given equation: [tex](x-3)^2+(y+2)^2=20[/tex]
Therefore, the centre is (3, -2) and the radius is √20
To find the equation of the tangent
The tangent of a circle is perpendicular to the radius at the point.
Therefore, first find the gradient (slope) of the line that passes through the centre of the circle and the given point.
[tex]\textsf{let}\:(x_1,y_1)=(1,2)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(3,-2)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{3-1}=-2[/tex]
If two lines are perpendicular to each other, the product of their gradients will be -1.
Therefore, the gradient of the tangent is:
[tex]m_t \cdot-2=-1\implies m_t=\dfrac12[/tex]
Now use the point-slope formula of a linear equation to find the equation of the tangent:
[tex]\implies y-y_1=m_t(x-x_1)[/tex]
[tex]\implies y-2=\dfrac12(x-1)[/tex]
[tex]\implies 2y-4=x-1[/tex]
[tex]\implies x-2y+3=0[/tex]
How many congruent faces does the square pyramid below have?
A.
5
B.
6
C.
4
D.
2
Answers
Answer:
C. 4
Step-by-step explanation:
Each side of the Square pyramid is congruent
Answer: c which is 4 sides
Step-by-step explanation: the square pyramid has 4 sides which are having equal sides so they are congruent . Hope it helps . Please give brainliest .
help me find Find AB
Answers
The reason is b/c there is a pattern. 1st is since 11.5+7.2=18.7 than you would add 7.2 to 18.7 than you would get 25.9. Also another way is subtracting 18.7-11.5=7.2.
Ps: Jisoo is my bias wby???
Blackpink in your area
The distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
We have,
The length along a line or line segment between two points on the line or line segment.
The coordinates of A are (-18, -18)
coordinates of B are (20, 0)
coordinates of C are (-12, 16)
The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²
Distance AB=√(20-(-18))²+(0-18)²
=√(20+18))²+(0-18)²=√38²+18²
AB=√1444+324
=√1768
=42.04 units
Distance BC=√(-12-20)²+(16)²
=√(-32)²+(16)²=√1024+256
=√1280
=35.77
Distance CA=√(-12-(-18))²+(16+18)²
=√(6)²+(34)²
=√36+1156=34.5
Hence, the distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
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complete question:
PLease help me find the distance between AB BC and CA please help
Help me out please simple
Answers
A straight line is 180 degrees in measure
The straight line is made up of three angles
--> angle 1
--> angle 2
--> angle with a little square on it
(angle with a little square means it is 90 degrees in measure)
Let's set up an equation
[tex]angle1 + angle2 + 90 = 180\\angle1 + 87 + 90 = 180\\angle1 = 3[/tex]
Thus angle 1 is 3 degrees or the second choice
Hope that helps!
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN=13x-9 and MP=4x+5
Answers
Answer:
x = 3.25 Each diagonal = 34.25. Step-by-step explanation: LMNP is a rectangle and it has diagonals LN and MP. Now, given that LN = 13x - 8 and MP = 9x + 5 Now, we know that the two diagonals of a rectangle are of the same length. So, LN = MP ⇒ 13x - 8 = 9x + 5 ⇒ 4x = 13 ⇒ x = 3.25 (Answer) Therefore, the each diagonal is of (13 × 3.25 - 8) = 35.25 length. (Answer)
Read more at Answer.Ya.Guru – https://answer-ya.com/questions/4694576-lmnp-is-a-rectangle-find-the-value-of-x-and-the-length-of-each.html
Step-by-step explanation:
Answer:
Can you provide an Attachment?
Step-by-step explanation:
^^
A circle has an area between 100-150 square inches,what are some possible lengths for a diameter of this circle
Answers
Answer:
it would range between 11.28379... to 13.819765...
Step-by-step explanation:
the circle's area formula is pi * radius^2
so you make to equation, plugging the 100 and 150 into the circle's area
you get square root of (100/pi) which gets 11.28379... for the area of 100
you do the same with 150 to get square root of (150/pi) which gets 13.819765...
those are the diameter of the circle since the diameter is double the radius which i already multiplied afterwards. so if you need the radius divide the number ive given you
Critical Thinking: I am a 7-digit number. All my digits are non-zero and distinct, My ones digit is four times the tens digit. • The sum of the ones and tens digits is equal to the sum of the lakhs and ten lakhs digits. • The sum of the ten thousands and thousands digits is equal to the double of the hundreds digit. • The ten lakhs digit is greater than the lakhs digit , and the ten thousands digit is greater than the thousands digit. Find which number I am.
Answers
Answer:
3286714
Step-by-step explanation:
Let the digits of the number be :
ABCDEFGOur given conditions :
G = 4F [ones digit is four times the tens digit]G + F = B + A [sum of the ones and tens digits is equal to the sum of the lakhs and ten lakhs digits]C + D = 2E [sum of the ten thousands and thousands digits is equal to the double of the hundreds digit]A > B and C > D [ten lakhs digit is greater than the lakhs digit , and the ten thousands digit is greater than the thousands digit]Solving :
Condition 1 : G is either 1 or 2 and F is either 4 or 8For now, let G be 1 and F be 4 Now G + F = A + BThen A + B = 5 [but not 1 + 4] ⇒ A can be 3 and B can be 2Now C + D = 2E and our remaining numbers are 5,6,7,8,9C and D can be 8 and 6, then their mean would be 7, which is ESolution :
So, the number is :
ABCDEFG3286714Which expression is approximately equal to 5 5/8 x 4 5/6?
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5 \dfrac{5}{8}\times 4\dfrac{5}{6}}\\\\\mathsf{= \dfrac{5\times6+5}{8}\times\dfrac{4\times6+5}{6}}\\\\\mathsf{= \dfrac{45}{8}\times \dfrac{29}{6}}\\\\\mathsf{= \dfrac{45\times29}{8\times6}}\\\\\mathsf{= \dfrac{1,305}{48}}\\\\\mathsf{= \dfrac{1,305\div3}{48\div3}}\\\\\mathsf{= \dfrac{435}{16}\approx 27 \dfrac{3}{16}}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{27\dfrac{3}{16}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
NEED AN ANSWER NOW! WILL GIVE YOU BRAINLIEST!!
I can't figure out what's the answer, I'm clueless.
Answers
Answer:
10
Step-by-step explanation:
On the chart, it says "Number of hostel rooms: 10". The rest of the data is useless and is just there to confuse you.
Just add them all together
3+5+8+6+2+1
What is a major difference between parallel lines and perpendicular lines?
Answers
Answer:
Parallel lines never intersect. Perpendicular lines are lines that intersect.
Step-by-step explanation:
Hope this helps.
Answer:
Perpendicular lines meet at a 90 degree angle while parallel lines will never touch
Step-by-step explanation:
find the second derivative of the parametric equation x(t)=sin t and y(t)=cos t
Answers
Presumably you mean the second derivative of y with respect to x, d²y/dx².
Compute the first derivative. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Differentiate the two parametric equations with respect to t :
[tex]x = \sin(t) \implies \dfrac{dx}{dt} = \cos(t)[/tex]
[tex]y = \cos(t) \implies \dfrac{dy}{dt} = -\sin(t)[/tex]
Then the first derivative is
[tex]\dfrac{dy}{dx} = \dfrac{-\sin(t)}{\cos(t)} = -\tan(t)[/tex]
Now, dy/dx is a function of t, so we can denote it by, say, dy/dx = f(t). Then by the chain rule, the second derivative will be
[tex]\dfrac{d^2y}{dx^2} = \dfrac{df}{dx} = \dfrac{df}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{df}{dt}}{\frac{dx}{dt}}[/tex]
Differentiating f(t) :
[tex]f(t) = -\tan(t) \implies \dfrac{df}{dt} = -\sec^2(t)[/tex]
Then the second derivative is
[tex]\dfrac{d^2y}{dx^2} = \dfrac{-\sec^2(t)}{\cos(t)} = \boxed{-\sec^3(t)}[/tex]
and since y = cos(t), we can go on to say
[tex]\dfrac{d^2y}{dx^2} = -\dfrac1{y^3}[/tex]
Please hurry
What is the surface area of this figure? Enter your answer in the box.
Answers
Answer:
692ft3
Step-by-step explanation:
Surface area of the rectangular prism;
SA = lw(2) + wh(2) + hl(2)
SA = 15(5)(2) + 5(8)(2) + 8(15)(2)
SA = 150 + 80 + 240 =
SA = 470ft3
Surface area of the triangular prism
SA = (S1 + S2 + S3) l + bh
SA = (9 + 9 + 11) 5 + 11(7)
SA = (29) 5 + 11(7)
SA = 145 + 77
SA = 222ft3
Add both the SA's
470ft + 222ft = 692ft3
Mr. Turner has two Algebra 1 classes. With one class, he lectured and the students took notes. In the other class, the students worked in small groups to solve math problems. After the first test, Mr. Turner recorded the student grades to determine if his different styles of teaching might have impacted student learning.
Class 1: 80, 81, 81, 75, 70, 72, 74, 76, 77, 77, 77, 79, 84, 88, 90, 86, 80, 80, 78, 82
Class 2: 70, 90, 88, 89, 86, 86, 86, 86, 84, 82, 77, 79, 84, 84, 84, 86, 87, 88, 88, 88
1. Analyze his student grades by filling in the table below. Which class do you think was the lecture and which was the
small group? Why?
Answers
Q1 Q2 IQR Mean Median MAD
Class 1 76.25 81.75 5.5 79.35 79.50 3.12
Class 2 84 88 4 84.60 86 3.85
What is Q1, Q3, IQR, Mean, Median and the MAD?The first step is to arrange the grades in the classes in ascending order.
Class 1: 70, 72, 74, 75, 76, 77, 77,77, 78, 79, 80, 80, 80, 81, 81, 82, 84, 86, 88, 90
Class 2: 70, 77, 79, 82, 84, 84, 84, 84, 86, 86, 86, 86, 86, 87, 88, 88, 88, 88, 89, 90
Q1 for class 1= 1/4(n + 1) = 21/4 = 5.25 = 76.25
Q2 for class 2 = 1/4(n + 1) = 5.25 = 84
Q3 for class 1= 3/4(n + 1) = 15.75 = 81.75
Q3 for class 2 = 3/4(n + 1) = 15.75 = 88
IQR for class 1 = Q3 - Q1 = 81.75 - 76.25 = 5.50
IQR for class 2 = Q3 - Q1 = 88 - 84 = 4
Mean for class 1 = sum of grades / total number of grades = 1587 / 20 = 79.35
Mean for class 2 = sum of grades / total number of grades= 1692 / 20 = 84.6
Median for class 1 = (n + 1) / 2 = 21/2 = 10.5 = 79.50
Median for class 1 = (n + 1) / 2 = 21/2 = 10.5 = 86
MAD = [tex]\frac{1}{n}[/tex]∑ l x - m(x) l
Where: n = number of observations
x = number in the data set
m = mean
Mean absolute deviation for class 1 = 62. 3/ 20 = 3.12
Mean absolute deviation for class 2. = 77/ 20 = 3.85
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A plant nursery receives shipments of soil in containers as shown below
( a picture of a cube that has 3 numbers - The heigh = 1 1/4 the base =2 . The width= 1 1/2
Part a- what is the volume of the soil in each container in cubic yards
(I put my answer as 3 3/4 which is right I think )
Part b - if a cubic yard of soil weighs 2000 pounds of soil does each container hold?
***I need help with part b pls
Answers
The volume of the three-dimensional figure is 3.75 yd³, and it can hold 7500 pounds of soil
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
The volume of the three dimensional shape is:
Volume = length * width * height = 1 1/4 * 1 1/2 * 2 = 3.75 yd³
1 yd³ = 2000 pounds
3.75 yd³ = 2000 pounds * 3.75 yd³ = 7500 pounds
The volume of the three-dimensional figure is 3.75 yd³, and it can hold 7500 pounds of soil
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{2x+3y=−7, 7x+9y=−14
Answer as an ordered pair (x,y).
Answers
Answer:
Step-by-step explanation:
2x + 3y = -7
7x + 9y = -14
-3(2x+3y= -7) = -6x - 9y = 21
-6x - 9y = 21
7x + 9y = -14
add columns (y values cancel)
1x + 0y = 7
x = 7
plug 7 into the x value in either equation to find y
2(7) + 3y = -7
14 + 3y = -7
3y = -21
y = -7
(x,y) = (7,-7)
1. Select the three rational numbers.
A. 5/1
B. 7/0
C. -0.02
D. 4.17(the 7 repeats)
E. 3.14 (pi)
F. 3.14 (pi squared)
Answers
Answer:
A. 5/1
C. -0.02
D. 4.177777....
Step-by-step explanation:
Rational numbers can be written as a ratio of numbers, such as 5/1. As decimals, the numbers either
*** "terminate" the decimal has a certain number of digits and then stops, such -0.02, this can be written as a ratio -2/100 which is -1/50
OR
*** "repeats" , such as 4.17777... which can also be written as a ratio, 4.1777... = 188/45
7/0 is undefined and the pi numbers are irrational, the digits of the decimal do not repeat and do not ever end, therefore NOT rational.
9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint : convert data in cm.)
Answers
Answer:
1 Shirt and 185cm remaining cloth
Step-by-step explanation:
2m and 15cm = 215cm
40m = 400cm
400/215=1.860465116
A shirt cant be in decimal so we remove the decimals, and take the as the answer. For the decimals, they are the remaining cloth.. to calculate the amount of remaining cloth we do:
1.860465116-1
=860465116
215*860465116=185cm
Use the order of operations to find the value of the expression. 12
÷
2
×
3
−
(
7
−
5
) HELP KME OUT
Answers
Answer:
16
Step-by-step explanation:
12 divided by 2 x 3 - (7 - 5)
6 x 3 - 2
18 - 2
16
Answer:
answer 16
Step-by-step explanation:
12 ÷ 2 x 3 - ( 7 - 5 ) is it right?
---------------------------------------------
Solving from left to right
12 ÷ 2 x 3 - ( 7 - 5 )
6 x 3 - (+2)
18 - 2
16
Solve the system of equations.
−4x+3y=−2y=x−1
Answers
Step-by-step explanation:
Is this helpful to you
support me
List three numbers that are less than -7
Answers
Answer:
Step-by-step explanation: first one way that you can answer this question is to use a numberline, so you start at zero and go to the left of the numberline and the numbers behind -7 would be -8,-9, and or ,-10 they are all less than negative seven
Write an exponential expression with 5 as the base and 8 as the exponent?
Answers
Answer:
y=[tex]5^{8}[/tex]
Step-by-step explanation:
An exponential equation is in the form y=[tex]a^{x}[/tex] where a is the base and x is the exponent.
If 5 is the base then it would replace a, and if it 8 was the exponent it will replace x.
Consider the principle
N{A ∪ B} = N{A} + N{B} − N{A ∩ B}.
An interview of 50 women in a residential subdivision reveals that 22 are gardeners while 31 are avid readers. How many are both gardeners and avid readers?
Answers
3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation:[tex]31+22-50[/tex]
____________________________________________
Calculate
[tex]53-50[/tex]
____________________________________________
Calculate the sum or difference
[tex]3[/tex]
I hope this helps you
:)
What is the solution to the equation?
Answers
Answer: Your answer is X=-63
Hope this helps!
Please help me with this thanks! God bless you
Answers
5. The sports store sold three times as many basketballs as footballs last month. If they sold
140 fewer footballs than basketballs, how many of each type of ball did they sell last
month?
Answers
Answer:
basketballs = 210 footballs = 70
Step-by-step explanation:
footballs =b
basketballs= 3b
if there ate 140 fewer footballs than basketballs it means that the difference between basketballs and footballs sold is 140
hence 3b - b = 140
2b= 140
b= 70
hence footballs are 70
while basketballs are 70×3 = 210
A=bh (b=8, h=5) what does A equal to evaluate this problem using the equation below
Answers
Answer:
40
Step-by-step explanation:
Factor completely
X^6-125y^6
Answers
solve for x ~
[tex]46x - 23x = 2[/tex]
thankyou ~
Answers
Answer: x = 2/23
Step-by-step explanation:
[tex]46x-23x=2[/tex]
[tex]\mathrm{Add\:like\:terms:}\:46x-23x=23x[/tex]
[tex]23x=2[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}23[/tex]
[tex]\frac{23x}{23}=\frac{2}{23}[/tex]
[tex]$$Simplify[/tex]
[tex]\bold{x=\frac{2}{23}}[/tex]
Answer:
x = 2/23Step-by-step explanation:
Inthis question we are given with one equation that is 46x - 23x = 2 and we have asked to find the value of x or solve for x .
So , from here we are solving :
[tex] \longmapsto \: 46x - 23x = 2[/tex]
Step 1 : Taking 23x common at left hand side :
[tex] \longmapsto \: 23x(2 - 1) = 2[/tex]
Step 2 : Subtracting 1 with 2 :
[tex] \longmapsto \:23x = 2[/tex]
Step 3 : Transposing 23 to right hand side :
[tex] \longmapsto \: \red{ \boxed{x = \frac{2}{23} }}[/tex]
Therefore, value of x is 2/23Verifying the answer :
We are verifying our answer by substituting the value of x in the given equation .
[tex] \longmapsto \: 46(\frac{2}{23}) - 23( \frac{2}{23} ) = 2[/tex]
Now , calculating :
[tex] \longmapsto \: \cancel{46}(\frac{2}{ \cancel{23}}) - \cancel{23}( \frac{2}{ \cancel{23}} ) = 2[/tex]
[tex] \longmapsto \: 4 - 2 = 2[/tex]
[tex] \longmapsto \: 2 = 2[/tex]
[tex] \longmapsto \: L.H.S = R.H.S[/tex]
[tex] \longmapsto \: Hence, \: Verified . \: [/tex]
Therefore , our value for x is correct .#Keep LearningSelect the two values of x that are roots of this equation.
x² + 34-3=0
. A. X=
-3+2/3
2
B. X=
-3-3
N
I X =
C. x.-3+27
=
1/21
2
O
D. *= -3-V21
=
2
Answers
Answer:
A. x=3 2.3
B . x=8
C. x=i do not know.
D. x=26
Step-by-step explanation:
A. -3+2/3=2
-3+2/3=-2 1/3
-2 1/3+3 2/3.=2
B. -3-3n=1
-3-3=-6n
-6n+8=1
C i do not understand.
D. -3-v21=2
21√5
Decimal Form:
1.0796532
or -24=2
-24+26=2
For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why. (Select all that apply.)
(a) H0: ? = 15, Ha: ? = 15
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(b) H0: p = 0.5, Ha: p > 0.6
This pair complies.This pair does not comply because p is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(c) H0: ? = 121, Ha: ? < 121
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(d) H0: ? = 123, Ha: ? = 125
This pair complies.This pair does not comply because ? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
(e) H0: p? = 0.2, Ha: p? ? 0.2
This pair complies.This pair does not comply because p? is not a population characteristic.This pair does not comply because both hypotheses use an equal sign.This pair does not comply because the two hypotheses use different numbers.
Answers
It can be inferred that H0: ? = 15, Ha: ? = 15 doesn't comply because both hypothesis use an equal sign.
How to illustrate the hypothesis?From the information, H0: p = 0.5, Ha: p > 0.6 doesn't comply because the two hypothesis use different numbers.
Furthermore, H0: ? = 121, Ha: ? < 121 shows that the pair complies. Also, H0: ? = 123, Ha: ? = 125 doesn't comply as they use the equal sign and different numbers.
Lastly, H0: p? = 0.2, Ha: p? ? 0.2 doesn't comply because p is not a population characteristic.
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