By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 300 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 86 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 566 mg of cholesterol. How much cholesterol is in each item?
Answer:
cholesterol in egg= 273 mg
cholesterol in cupcake = 18 mg
cholesterol in slice of pizza = 9 mg
Step-by-step explanation:
Given data:
1 egg , 1 cupcake , 1 slice of pizza = 300mg
3 cupcakes , 4 slices of pizza = 90mg
2 eggs , 1 cupcake = 564mg
Let egg be x , let cupcake be y and let pizza be y
x + y + z = 300 (equation 1)
0x + 3y + 4z = 90 (equation 2)
2x + y + 0z = 564 (equation 3)
Using equation 1 and equation 2
x + y + z = 300 (Multiply equation by 3)
0x + 3y + 4z = 90
3x + 3y +3z =900
0x +3y +4z = 90 (Subtracting the equations)
3x - z = 810 (equation 4)
Using equation 2 and equation 3
0x + 3y + 4z = 90
2x + y + 0z = 564 (Multiply equation by 3)
0x + 3y + 4z = 90
6x +3y + 0z = 1692 (Subtracting the equations)
-6x +4z =-1602 (equation 5)
Solving equation 4 and equation 5
3x - z = 810 therefore z =3x -810
Substituting z into equation 5
-6x +4(3x - 810) =-1602
-6x + 12x - 3240 = -1602
6x = -1602+3240
6x = 1638
x = 273
Substituting x into z = 3x - 810
z = 3(273) - 810
z = 819-810
z = 9
Using equation 1 to find y
x + y + z = 300
273 + y + 9 = 300
282 + y = 300
y = 300-282
y = 18
Find the following for the function f(x) = x/x^2+1
(a) f(0)
(e) – f(x)
(b) f(9)
(f) f(x + 1)
(c) f(-9)
(g) f(3x)
(d) f(-x)
(h) f(x + h)
Step-by-step explanation:
step 1. f(0) = 0/(0^2 + 1) = 0/1 = 0
step 2. -f(x) = -x/(x^2 + 1)
step 3. f(9) = 9/(9^2 + 1) = 9/82.
A function is defined as a relation between a set of inputs having one output each. The values can be written as shown below.
What is function explain?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given function is f(x) = [tex]\frac{x}{x^{2} +1}[/tex], therefore, the values can be found by as shown below. Therefore, we can write,
(a) f(0) = 0/0+1 = 0
(e) – f(x) = - [ x / (x²+1)]
(b) f(9) = 9/(81 + 1) = 9/82
(f) f(x + 1) = (x + 1)/(x² + 2x + 2)
(c) f(-9) = - 9/(81 + 1 ) = -9/82
(g) f(3x) = 3x/(9x² + 1)
(d) f(-x) = -x/(x² + 1)
(h) f(x + h) = (x + h) / [(x+h)²+1]
For more about Function here:
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277
If =
then the value of cos 0 =-
1
Part A:
What is another angle, 8, that has the same value as cos
277
if 0 < < 2?
Part B:
Name two angles that have the opposite value of cos
277
if 0 < < 27.
At the bakery where you work, loaves of bread are supposed to weigh 1 pound, with a standard deviation of 0.13 pounds. You believe that the new personnel are producing loaves that are heavier than 1 pound. As supervisor of Quality Control, you want to test your hypotheses at the 5% level of significance. You weigh 20 loaves and obtain a mean weight of 1.05 pounds.
1. Identify the population and parameter of interest. State your null and alternative hypotheses.
2. Identify the statistical procedure you should use. Then state and verify the conditions required for using this procedure.
3. Calculate the test statistic and the P-value. Illustrate using the graph provided.
a. .50
b. -3.0
c. 3.0
d. -.50
4. State your conclusions clearly in complete sentences.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
H0 : μ = 1
H1 : μ > 1
Sample size, n = 20 ; xbar = 1.05; Standard deviation, s = 0.13
Test statistic;
t because sample size is < 30
(xbar - μ) ÷ (s/sqrt(n))
(1.05 - 1) ÷ (0.13 / sqrt(20))
0.05 ÷ 0.0290688
= 1.7200572
Using a p value calculator :
With alpha = 0.05 ; df = n - 1 = 20 - 1 = 19
P value = 0.05084
P value > alpha
We fail to reject H0
There is not sufficient evidence to support that the new personnel are producing loaves that are heavier than 1 pound
A movie theater sends out a coupon for 20% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket.
Answer:
y = 0.8x
Step-by-step explanation:
y = x-0.2x
y=x(1-0.2)
y=x(0.8)
hence y = 0.8x
Please help me with this Math question...
Answer:
A) length = 9cm, width = 4 cm
Step-by-step explanation:
The key word "times" refers to multiplication, so if you're trying to find dimensions at 1/4 times its original size, you need to multiply the original dimensions by 1/4.
l = 36
new l = 36 (1/4)
= 36/4
= 9 cm
w = 16
new w = 16 (1/4)
= 16/4
= 4 cm
I need an answer ASAP thank you
Answer: i think its
Step-by-step explanation: carrot
Aaron went to watch The Avengers at the movie theater. He noticed that 60% of the movie extras during one of the scenes were teachers from his school. He recognized 24 teachers from his school. How many movie extras were there all together?
Answer:
40 extras
Step-by-step explanation:
24 is 60% I would divide 24 by 6 to get 10% 24/6 is 4. 4*10 is 40. There were 40 extra's all together.
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. Let I(t) denote the number of infected individuals. Suppose that the total population is 3000, the proportionality constant is 0.0001, and that 1% of the population is infected at time t-0, write down the intial value problem and the solution I(t)
dI/dt I(0) = _______
I(t) = _______
Answer:
Step-by-step explanation:
See attached file for answer .
A 22 foot ladder leans against a building. The distance between the bottom of the ladder and the base of the building is 9 feet.
No random answers pls
Answer:
the building is 13 feet tall
Answer: the equation to find h is 9^2+h^2 is about 20.1 feet
Step-by-step explanation: ima be honest I’m not sure but that’s what I got
Find the value of x and y.
20
12
у
X =
y =
9514 1404 393
Answer:
x = 35∠BCA = 29°Step-by-step explanation:
In order to determine the value of x, the measure of angle BCA must be known. If we assume the figure is a kite, then ...
∠CDB = ∠CBD = 61°
∠CBD +∠BCA = 90°
So, the measure of angle BCA is ...
∠BCA = 90° -∠CBD = 90° -61°
∠BCA = 29°
__
Now we can find x from ...
29° = (-6 +x)°
29 +6 = x = 35
Find the distance between the points C(-6,5) and D( -3,1).
The distance between the two points is
Answer:
5 units
Step-by-step explanation:
Distance between 2 points
[tex] = \sqrt{(y1 - y2)^{2} + (x1 - x2)^{2} } \\ = \sqrt{(5 - 1)^{2} + ( - 6 + 3)^{2} } \\ = \sqrt{ {4}^{2} + ( - 3)^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} \\ = 5 \: units[/tex]
What does F v stand for
What single decimal multiplier would you use to decrease by 3% followed by a 4% increase?
Answer:
The single decimal multiplier is 26%.
Step-by-step explanation:
Since we have given that
You use to increase by 5% followed by 20% increase.
So, the single decimal multiplier would be
Hence, the single decimal multiplier is 26%.
What is the answer to 4(x + 3) < 7x - 3x - 11
Answer:
THE ANS IS 0<-23
Step-by-step explanation:
4(X+3)< 7x-3x-11
4x+12< 4x-11
4x will be cancelled,
So we get,
4x-4x< -11-12
0 < -23
Thank YOU AND PLZ MARK AS BRAINLY AND GIVE RATING ALSO
What is 12 divided by 8
Answer:
1.5
Step-by-step explanation:
Answer:
1.5 is the answer
hope it helps!
Solve the inequality.
m + 3 < 5
Please help with this
Answer:
Step-by-step explanation:
m+3 < 5
Isolate the m by subtracting 3
m+3 - 3 < 5 - 3
m < 2
An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.5 and P(B) = 0.3. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. Since the events are independent, then A′ and B′ are not independent. Since the events are independent, then A′ and B′ are independent. Since the events are not independent, then A′ and B′ are mutually exclusive. Since the events are independent, then A′ and B′ are mutually exclusive. (b) What is the probability that at least one of the two projects will be successful? (c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful? (Round your answer to three decimal places.)
Answer:
0.7 ; 0.65 ; 0.115
Step-by-step explanation:
Step-by-step explanation:
P(A) = 0.5 ; P(B) = 0.3
P(not successful) = P(B') = 1 - 0.3 = 0.7 ; P(A') = 1 - 0.5 = 0.5
1.)
Both events are independent events, hence the outcome of one does not depend on the other. That is the failure of the Asian project has nothing to do with the European project.
Probability that European project isn't successful;
P(B') = 1 - P(B) = 1 - 0.3 = 0.7
2.)
Probability that atleast one of the 2 projects is successful :
P(AUB) = P(A) + P(B) - P(AnB)
P(AnB) = P(A) * P(B) = 0.5 * 0.3 = 0.15
P(AUB) = 0.5 + 0.3 - 0.15 = 0.65
3.)
Probability that only the Asian project is successful, given that atleast one of the two projects is successful :
[P(A) - P(AnB)] ÷ P(AuB)
[0.5 * 0.15] ÷ 0.65
= 0.075 ÷ 0.65
= 0.1153846
= 0.115
Find the value of x and state the converse! Plz help if you can
Work out the value of angle x.
Х
110 degree
Answer:
40 degrees
Step-by-step explanation:
the bottom angles are 70 each because you can find one of them by subtracting 110 from 180 (110 is an exterior angle to one of the bottom sides). The other is also 70 because the triangle is an isosceles. Then, subtract 70*2 from 180 to get 40 degrees for x (the remaining side).
Please help I’m giving brainliest!
=================================================
Explanation:
Label the center point of the circle as point G.
Also, label the top and bottom tangent points as H and J respectively. This means that H is on line segment ED, while J is on line segment EF.
The given arc measure of 100 degrees directly leads to the central angle HGJ to be 100 degrees.
Focus on quadrilateral EHGJ. It has two right angles at points H and J since they are tangent points. Angle G of this quadrilateral was found to be 100. Let's find angle E
E+H+G+J = 360 ..... any four angles of a quadrilateral add to 360
E+90+100+90 = 360
E+280 = 360
E = 360-280
E = 80
Or as a shortcut, we can note that angles E and G must add to 180, since H+J = 90+90 = 180, making up half of 360.
So, E+G = 180 leads to E+100 = 180 which solves to E = 80.
Once we know that E = 80, this leads to angle DEF to be 80 degrees.
This is an inscribed angle that subtends arc DF. By the inscribed angle theorem, we double the inscribed angle value to get the arc measure
arc DF = 2*(inscribed angle DEF)
arc DF = 2*(80)
arc DF = 160 degrees
22 - 5x + 4 = 0 ?
What is the value of the greater root of the above equation
Answer:
[tex] - 5x = - 22 - 4 \\ \\ - 5x = - 26 \\ x = 5.2 \\ \: \\ [/tex]
which graph is linear and non linear and why?
prove that sin x + cos x the whole square is equal to 1 + sin 2x
THE ANS IS 1+sin2x
Step-by-step explanation:
This result follows almost directly from the following:
The number of kilograms of water in a human body varies directly as the mass of the body A 96kg person contains 64kg of water.How many kilograms of water is in a 60 kg person
Answer: There are 40 kg of water in a 60 kg person.
Step-by-step explanation:
What will be the winning numbers for Mega Millions on 12 February 2021?
In circle C, IL is a diameter, ∠ICR = (3x + 5)°, and angle∠RCL = (x – 1)°.
find X and (arc) ILR
The measure of arc ILR is 223 degrees
Circle geometryThe sum of angle on a straight line is 180 degrees
Given the following parameter
∠ICR = (3x + 5)°, and
∠RCL = (x – 1)°.
Taking the sum:
3x + 5 + x - 1 = 180
4x + 4 = 180
4x = 176
x = 176/4
x = 44
arc ILR = 180 + arcRL
arc ILR = 180 + 44 - 1
arc ILR = 223 degrees
Hence the measure of arc ILR is 223 degrees
Learn more on circle geometry here; https://brainly.com/question/24375372
in a basket of carrots 12% of them are rotten if 42 carrots are rotten how many carrots are in the basket
Answer:
356 hope this is correct :)
Step-by-step explanation:
I WILL GIVE BRAINLIEST BUT HELP ME ON THIS ONE PLEASE
Answer:
th correct center is in B
Give the slope and the y-intercept of the line y = x – 4.
Make sure the y-intercept is written as a coordinate.
Given:
The equation of a line is
[tex]y=x-4[/tex]
To find:
The slope and y-intercept of the line.
Solution:
We have,
[tex]y=x-4[/tex] ...(i)
The slope intercept form of a line is
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=1,b=-4[/tex]
Slope of the line = 1
y-intercept of the line = -4
The coordinate form of y-intercept is (0,b). So, the y-intercept of the given line is (0,-4).
Therefore, the slope of the line is 1 and the y-intercept is (0,-4).