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 82 mg of cholesterol. By eating 2 eggs and 1​ cupcake, a child consumes 568 mg of cholesterol. How much cholesterol is in each​ item?

∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.

∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.

∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.

∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.

∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.

∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.

Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.

Right Angles Theorem states that two right angles(90° angles) are congruent to each other.

Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.

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The total cost paid by the senior citizen for 3 days = $50

The function representing the total cost of the annual pass is:

f(x) = 20x + 80

A senior citizen pays $20 less than half of this price for x days

The total cost paid by the senior citizen = [tex]\frac{f(x)}{2} -20[/tex]

The total cost paid by the senior citizen =[tex]\frac{20x+80}{2} -20[/tex]

Simplify the resulting expression:

The total cost paid by the senior citizen =10x + 40 - 20

The total cost paid by the senior citizen = 10x + 20

x represents the number of days

Substitute x = 3 into the resulting equation

The total cost paid by the senior citizen for 3 days  =10(3)+20

The total cost paid by the senior citizen for 3 days = $50

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So probability that kayla rolls an even number on the red cube and a multiple of 3 on the blue cube is 16.66 ≈ 16%

Given that we have red number cube and blue number cube so as we all know that Probability is the ratio of the favourable number of outcomes to the total number of outcomes is known as Probability.

First, find the possible outcomes.

Kalya has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6

So, possible outcomes =6×6 =36

Let, S be the sample space.

Then, ⁿ(s) =36

Let, E = the event of getting an even number on the red cube and a multiple of  on the blue cube.

E = (2,3),(2,6),(4,3),(6,3),(6,6)

Then,  ⁿ(E)=6

Let, P  is the probability of the event .

So, P(E)= [tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex] = 16.67 percent or 16[tex]\frac{2}{3}[/tex]  %

Thus, the probability Kayla rolls an even number on the red cube and a multiple of  on the blue cube is 16.66 percent.

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Answer:

16%

Step-by-step explanation:

The time it would take Shirley to mow the lawn alone is 3 hours

From the information given;

Let Shirley's working hours be x

Let Pam's working hours be y

We have  that;

Shirley and Pam work 6 hours together, this is expressed as;

x + y = 6

Given that Pam work 3 hours alone, we have;

y = 3

Substitute the value of y as 3 in the equation

x + 3 = 6

x = 6 - 3

x = 3

Thus, the time it would take Shirley to mow the lawn alone is 3 hours

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Answer:

B and D

Step-by-step explanation:

The wording in the answer choices make a huge difference. It is possible implies that there is a possibility

A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}

B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output

C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)

E is false. The x, y coordinates have been interchanged in this answer choice

The true statements are B and D.

The wording in the answer choices make a huge difference.

It is possible implies that there is a possibility

A. 4 is in the range of g.

A is false.

The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7.

Here, whatever the value of x, the y value is always 7.

This represents a horizontal line passing through y = 7.

So the range is just a single number {7}

B. For a value a, it is possible that g (a) = 4.

B can be true.

It is possible but not a certainty that f(a) = 4 for some value of a.

For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output.

C. For a value y, it is possible that g (4) = y.

C is false.

A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D. The point (4,7) is on the graph of y = g (x).

D is true.

Since at x =4, y = g(x) = 7, this corresponds to a point on the graph.

The point will be (x=4, y =7) or (4,7)

E. The point (7, 4) is on the graph y = g(x).

False. The statement doesn't provide any information about g(7), and we cannot determine whether the point (7, 4) lies on the graph of the function y = g(x) based solely on the given information.

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Three rational numbers between

1/3 and 1/5 are 4/15, 3/10, and 7/30

Given:The two numbers are 1/3 and 1/5

To find:The rational number between two numbers

Solution:Now, to find the rational number, add the numbers and divide their sum by 2.

(i) First rational number between

1/3, 1/5 = 1/3+1/5=8/5

Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15

The series becomes, 1/3, 4/15, 1/5

(ii) Second rational number

= 4/15+1/5 = 7/15

Divide

7/15 by 2 ------> 7/15 x 1/2 = 7/30

Hope this helps!

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

A = -6 and B = 65

From the question, we are to express the given expression in the form (x + A)^2+B by completing the square

The given expression is

x² -12x + 101

Using the completing the square method

x² -12x + 101

Divide the coefficient of x by 2 and then square it

The coefficient of x is -12

Dividing by 2, we get

-12/2 = -6

Squaring

(-6)²

Now, add and subtract this value from the expression

x² -12x + (-6)² + 101 - (-6)²

Then, we can write that

(x - 6)² + 101 - (-6)²

(x - 6)² + 101 - 36

(x - 6)² + 65

Thus,

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

By comparison,

A = -6

and

B = 65

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Answer:

3452

Step-by-step explanation:

Simplify the expression, and add/muiltiply where necessary.

Answer:

17.7 m

Step-by-step explanation:

57 m / 30 m/s = time in the air = 1.9 s

vertical drop for 1.9 s

 vertical d = 1/2 a t^2 = 17. 7 m

It is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.

We are given a relation:

{(9 / 2, 1 / 4),(4 1 / 2, -4),(0, 5 / 6)}

We can also write it as:

{(9 / 2, 1 / 4),(9 / 2, -4),(0, 5 / 6)}

The domain of the relation will be:

Domain = { 9 / 2 , 0}

The range of the relation will be:

Range = {1 / 4, -4, 6}

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, this relation is not a function because:

The input 9 / 2 has 2 outputs as 1 / 4 and -4 which is not possible in a function.

Therefore, we get that it is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.

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After solving for x in the constructed equation, 97100 bushels were harvested last year.

What is an equation?

Constructing equation to determine no. of bushels.

Bales from the previous year = x + 0.45 x

= 140795 1.45 x

= 140795 X

= 97100 bales

After solving for x in the constructed equation, 97100 bushels were harvested last year.

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Answer:97100

Step-by-step explanation:

∑ Hey, shadowwolf9764 ⊃

Answer:

1.52545155993

Round if needed: 1.53

Step-by-step explanation:

Given:

[tex]\frac{0.128\div 3.2+0.86}{\frac{5}{6}\cdot 1.2+0.8}+\frac{\left(1\:\frac{32}{63}-\frac{13}{21}\cdot 3.6\right)}{0.505\cdot \frac{2}{5}-0.002}[/tex]

Solution:

Convert Mixed Number to a improper fraction:

[tex]1\frac{32}{63}=\frac{95}{63}[/tex]

Now we have;

[tex]=\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}+\frac{95}{63}[/tex]

Solving the first part:

[tex]\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}=\frac{0.128}{7.308}[/tex]

Then we have;

[tex]=\frac{0.128}{7.308}+\frac{95}{63}[/tex]

Least common factor: 460.404

[tex]=\frac{8.064}{460.404}+\frac{694.26}{460.404}[/tex]

Now using this formula: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]

[tex]=\frac{8.064+694.26}{460.404}[/tex]

Adding the numbers:

[tex]=\frac{702.324}{460.404}[/tex]

Next divide the numbers:

[tex]1.52545155993[/tex]

Hence, the answer is:

[tex]1.52545155993[/tex]

Round if needed:

[tex]1.53[/tex]

xcookiex12

9/4/2022

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Answer:

give me those points boy=o >:)

Step-by-step explanation:

While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function

f

(

x

)

=

b

x

by a constant

|

a

|

>

0

. For example, if we begin by graphing the parent function

f

(

x

)

=

2

x

, we can then graph the stretch, using

a

=

3

, to get

g

(

x

)

=

3

(

2

)

x

and the compression, using

a

=

1

3

, to get

h

(

x

)

=

1

3

(

2

)

x

.

Answer:

Step-by-step explanation:4

Step-by-step explanation:

We do the ones that are in parenthesis first. Find out the exponent. 2 to the power of two is 4. 3-4=-1. Then we would add 5. 5+-1 would result of 4.

convert 81°into radian

81°=(81×pie/180)=9pie/20 pie=22/7

now,

radius=arc length/θ in radian

then 69/(9pie/20)

=48.79

The final answer for 2211₃ to convert into base 10 is 76₁₀.

Given 2211₃

Expand the number as below

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

To convert base 3 to base 10 we need to expand form numbers as

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

         = 2 * 27 + 2 * 9 + 1 * 3 + 1 * 1

         = 54 + 18 + 9 + 1

         = 76₁₀

Therefore, the Correct answer for 2211₃ to convert into base 10 is 76₁₀

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The Average return rate for the investment will be 3.2%.

The Return Rate can be defined as a profit that is made on investment .

In the Question

let the investment be "x" .

25% stocks in Company A have return rate of 6%.

Investment in Company A = (25% of x)

Return is 6% of investment = (25% of x) + 6% of (25% of x)

Return from company A= (25% of x)(1+0.06)     ...as 25%=0.25 & 6%=0.06

                                        = 0.25*x*(1.06)     ...(i)

40% stocks in Company B have return rate of 2.5%.

Investment in Company B = (40% of x)

Return is 2.5% of investment = (40% of x) + 2.5% of (40% of x)

Return from company A = (40% of x)(1+0.025)         ...

                                        = 0.40*x*(1.025)     ...(ii)

Stocks in Company C = 100 - 25 - 40 = 35%

35% stocks in Company C have return rate of 2%.

Investment in Company C = (35% of x)

Return is 2.5% of investment = (35% of x) + 2% of (35% of x)

Return from company C = (35% of x)(1+0.02)         ...

                                        = 0.35*x*(1.02)     ...(iii)

Total Return = Return from Company A + Return from Company B + Return from Company C .

From equation (i) ,(ii) and (iii) we get

Total Return = 0.25*x*(1.06) + 0.40*x*(1.025) + 0.35*x*(1.02)

= 0.265x + 0.41x + 0.357x

= 1.032x

The Average rate of return  = [tex]\frac{return- investment }{investment } \times100[/tex]

Substituting the value we get,

= (1.032x - x ) / x  *100

= 0.032x /x  * 100

= 0.032*100

= 3.2%

Therefore , the Average return rate for the investment will be 3.2%.  

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Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

Answer:

0.01775

Step-by-step explanation:

Answer: x = [tex]\frac{-31}{23}[/tex], y = [tex]\frac{-9}{23}[/tex], z = [tex]\frac{-83}{23}[/tex]

Step-by-step explanation :Solving system of equations

Given the following system of equation below

 - 4x + 2y + z =1 .......(1)

x − y + 3x =  −5 ........(2)

3x + y − 4z = 10.........(3)

first we solve eq 1 and eq 3:

we get, -13x + 9y = 14 ..........(4)

Now we solve eq 2 and eq 4 and get value of x and y:

we get,  x = [tex]\frac{-31}{23}[/tex] and y = [tex]\frac{-9}{23}[/tex]

finally we put value of x and y in eq 1 and get the value of z:

-4(-31/23) + 2(-9/23) + z = 1

106/23 + z = 1

z = 1 - 106/23

z =[tex]\frac{-83}{23}[/tex]

Hence the solution of equation is ([tex]\frac{-31}{23}[/tex], [tex]\frac{-9}{23}[/tex], [tex]\frac{-83}{23}[/tex])

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Answer: -2.25

Step-by-step explanation:-2.25 because it is closer to 0

Answer:

(i)

Step-by-step explanation:

express the ratio as a fraction, that is

4 : 5 = [tex]\frac{4}{5}[/tex]

to convert the fraction to a percentage multiply it by 100%

[tex]\frac{4}{5}[/tex] × 100% = 4 × 20% = 80%

Answer:

126

Step-by-step explanation:

A number is divisible by 3 if its sum of digits is divisible by 3 (you can do it over and over again until it's one digit!).

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

A number is divisible by 6 if it is divisible by 2 and by 3.

A number is divisible by 9 if its sum of digits is divisible by 9 (you can do it over and over again until it's one digit!).

So we need a number with last digit 0, 2, 4, 6, or 8 (because it's divisible by 6 hence by 2) and with a sum of digits divisible by 9 (because if it's divisible by 9 it's also divisible by 3).

130 is not divisible by 9, so the first digits must be 12X.

to get a number divisible by 9, we need to add a digit D so that 1+2+D is divisible by 9.

9 - 1 - 2 = 6

126 is divisible by 9 because it's sum of digits is 9. It's also divisible by 6, because it is divisible by 3 and its last digit is 6.

The average change is 3 degrees per hour.

To calculate the average of any data we have to divide the change by the time taken for that change.

let us suppose there is a data 4,5,6,7 and 8.

Average of the data will be the sum of data divided by the number of terms.

Average=[tex]\frac{4+5+6+7+8}{5}[/tex]

            =[tex]\frac{30}{5}[/tex]

            = 6

So now we will calculate the average change in temperature per hour,

Given that there is a fall of 12 degrees in 4 hours.

Average change per hour=[tex]\frac{12}{4}[/tex]

                                        = 3 degrees per hour

So, the required change is 3 degrees per hour.

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The sequence is an AP with a = 11 and d = - 4 , 6th term is - 9 and formula is a + ( n - 1 ) d .

First Term = 11

Second Term = 7

Third Te3rm = 3

Fourth Term = - 1

Fifth Term = - 5

a ) Sequence is 11 , 7 , 3 , - 1 , - 5

b ) a + ( n - 1 ) d

    11 + ( 6 - 1 ) ( - 4 )

     11 + 5 ( - 4 )

 11 - 20 = - 9

c )    a + ( n - 1 ) d

where a is the first term , n is the tem no . and d is the common difference of an AP .

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Answer:

24y^2

Step-by-step explanation:

4y x 6y =

24y ^2

24y to the second power