Dylan is making a party favorites for his dylan is making party favors for his birthday party he has 32 pencils and 56 lollipops and he must use all the pencils and lollipops for his birthday favorites if dylan creates the greatest number of identical packages possible how many parties favors can he make how many pencils and lollipops are there in each party package
He can make 8 party package and each package consists 4 pencils and 7 lollipops with 32 pencils and 56 lollipops .
To determine the greatest number of identical packages possible we have to determine the highest common factor of two given no. , 32 and 56
Let's determine the factors of the 32 and 56 ,
32 = 2 × 16 = 2 × 2 × 2 × 2 × 2
56 = 2 × 2 × 2 × 7
So , common factors are 2 , 2 ,2
Now , The HCF is , 2 × 2 × 2 = 8
So , total combination is 8 and in each combination , there is 4 pencils ( 32 / 8 = 4 )and 7 ( 56/8 = 7 ) lollipops .
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Andy and his friend sam were walking along the road together. andy had a big bag of marbles. unfortunately the bottom of the bag split and all the marbles spilled out. poor andy! one third of the marbles rolled down the slope too quickly for andy to pick them up. one sixth of all the marbles disappeared into the rain-water drain. andy and sam picked up all they could but half of the marbles that remained nearby were picked up by other children who ran off with them. andy counted all the marbles he and sam had rescued. he gave one third of these to sam for helping him pick them up. andy put his remaining marbles into his pocket. there were 14 of them. how many marbles were there in andy's bag before the bottom split?
The total number of marbles that were there in Andy's bag before the bottom split are 84 marbles.
Let, the total number of marbles Andy have in the bad in beginning = x
One third of the marbles rolled down the slope too quickly for Andy to pick them up. So we can write,
Total number of marbles Andy have now = x - (x/3)
One sixth of all the marbles disappeared into the rain-water drain. So, So we can write,
Total number of marbles Andy have now = x - (x/3) - (x/6) = (x/2)
Half of the marbles that remained nearby were picked up by other children who ran off with them. So, we can write
Total number of marbles Andy have now = (x/2) - (x/4) = (x/4)
Andy gave one third of these to Sam for helping him pick them up. So,
Total number of marbles Andy have now = (x/4) - (x/12) = (x/6)
Now, we have given that Andy have 14 marbles in the end in his pocket. On comparing it with above equation, we get
(x/6) = 14
⇒ x = 84
The total number of marbles that were there in Andy's bag before the bottom split are 84 marbles.
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1, .25 blank , -1.25, blank complete each arithmetic sequence
The complete arithmetic sequence is 1, .25, -0.5, -1.25, -2
How to complete the arithmetic sequence?The arithmetic sequence is given as:
1, .25, blank, -1.25, blank
Replace the blanks in the arithmetic sequence with x and y
So, we have:
1, .25, x, -1.25, y
An arithmetic sequence has a common difference (d)
The common difference is calculated using
d = T2 - T1
So, we have
d = 0.25 - 1
d = x - 0.25
d = y + 1.25
Substitute d = x - 0.25 in d = 0.25 - 1
x - 0.25 = 0.25 - 1
This gives
x = 0.25 + 0.25 - 1
Evaluate the sum
x = -0.5
Substitute d = 0.25 - 1 in d = y + 1.25
0.25 - 1 = y + 1.25
This gives
y = 0.25 - 1 - 1.25
Evaluate
y = -2
Hence, the complete arithmetic sequence is 1, .25, -0.5, -1.25, -2
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what is the answer of 20 plus 12
Answer:
32
Step-by-step explanation:
58 divided by 5,350 (working out please!)
When we divide 58 by 5,350, the value is 0.108411.
How to compute the value?The information is that we should divide 58 by 5,350.
It should be noted that we cab reduce to the lowrst term before dividing. This will be:
= 58/5350
= 29/2675
Therefore, we can then convert the value to decimal and this will be:
= 29/2675
= 0.108411
The division is 0.108411.
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#3 D
MODELING REAL LIFE You consider buying a phone from one of two cell phone carriers. The table shows the total costs
(in dollars) of the phone and service for different numbers of months at Carrier A. The total cost y (in dollars) of the phone
and x months of service at Carrier B is represented by the equation y = 55x + 300. Which carrier has the lower initial fee?
Answer:
Step-by-step explanation:
The carrier that has the lower initial fee is carrier B
How to determine which carrier has the lower initial fee?For carrier B, we have the following equation
y = 55x + 300
Set x = 0 to determine the initial fee
y = 55 x 0 + 300
Evaluate
y = 300 ---- the initial fee of carrier B
For carrier A, we have the following points on the table
(x, y) = (3, 500), (6, 650)
The slope of the points is calculated using
m = (y2 - y1)/(x2 - x1)
This gives
m = (650 - 500)/(6 - 3)
Evaluate
m = 50
Let the initial fee of carrier B y
So, we have the following points
(x, y) = (0, y), (6, 650)
The slope of the points is calculated using
m = (y2 - y1)/(x2 - x1)
This gives
m = (650 - y)/(6 - 0)
Evaluate
m = (650 - y)/6
Substitute m = 50 in m = (650 - y)/6
50 = (650 - y)/6
This gives
300 = 650 - y
Solve for y
y = 350
So, we have:
y = 300 ---- the initial fee of carrier B
y = 350 ---- the initial fee of carrier A
300 is less than 350
Hence, the carrier that has the lower initial fee is carrier B
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Simplificación the -49/88
We can't simplify -49/88 any further because it's already reduced to the least common factor in the numerator and denominator.
We'll leave it as it is;
-49/88
[tex]--------------------------------[/tex]
No podemos simplificar más -49/88 porque ya está reducido al mínimo común divisor en el numerador y el denominador.
Lo dejaremos como está;
-49/88
if C = 5/9(f-32)find the value of f when c=30
The answer for this equation would be f = 86
URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
Answer:
1. l
2. h
3. j
4. k
Step-by-step explanation:
Looks right to me :)
PLEASE WHAT IS THE LIMIT HELP IM SOBBING CRYING THANKS
Answer:
Step-by-step explanation:
Click this link to see the answer pls. I cannot explain it on this little square box.
i swear, just click it.
https://giphy.com/gifs/trolli-basketball-weirdly-awesome-sour-brite-slam-STcNf6rLHyMA8
Find the rate of change between the following points. (-1, -4) (3, 1)
Answer:
Step-by-step explanation:
rghhgrwfgethyrtegrgrfrgtgrgrtt4gt
i need help ! pls ive been having a hard time with it ive looked at it 100 times
Answer:
6.4 (or round to 6 for one digit)
Step-by-step explanation:
Look up "distance between two points formula"
Answer: MN≈6.4
Step-by-step explanation:
[tex]M(-3,-1)\ \ \ \ N(2,3)\\[/tex]
[tex]\boxed {MN=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex]x_1=-3\ \ \ \ x_2=2\ \ \ \ y_1=-1\ \ \ \ y_2=3\\MN=\sqrt{(2-(-3))^2+(3-(-1))^2}\\ MN=\sqrt{(2+3)^2+(3+1)^2}\\ MN=\sqrt{5^2+4^2}\\ MN=\sqrt{25+16} \\MN=\sqrt{41} \\MN\approx6.4[/tex]
I need help with this ASAP
Solution : Straight line question : y= 2x-3
Straight Line:
A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
Slope:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Use the slope and one of the points to solve for the y-intercept (b).
One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line
1)Point (3,3) (4,5)
slope: (5-3)/(4-3) = 2/1 = 2
Y= mx+c
y -3 = 2(x-3)
y-3= 2x-6
y= 2x-6+3
y= 2x-3
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How to find the nth term in the sequence
3,6,9,12
The n th term of the series is 3n where n is the term of reference
As we can see that there is constant difference in the terms
12-9=3
9-6=3
6-3=3
We are made sure that it is the arithmetic progression
Common difference is the difference that is constantly subtracted or added to each term after the first term
Thus the common difference 'd' is 3 as per the calculations above
Now the first term is 3
We know that any N th term of arithmetic progression is given by the formula
Tn= a+ (n-1)*d
where a is the first term of the progression and n is the term of reference and d is the common difference
a=3
d=3
Therefore, nth term of the series is = Tn= 3 + (n-1) *3
Tn= 3+3n-3
Tn = 3n
Hence the n th term of the series is 3n where n is the term of reference
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The variable y varies directly with the variable x.
If the value of x is 14, what is the value of y?
Given that the variable y varies directly with the variable x. If the value of x is 14, the value of y will be 21.
If the value of x is 14, what is the value of y?Proportional relationships are relationships between two variables where their ratios are equivalent.
A direct variation is expressed;
a ∝ b then a = kb
Where k is the proportionality constant.
Given the data in the question
a = 10b = 15k = ?First, we determine the proportionality constant.
a = kb
15 = k × 10
k = 15/10
k = 3/2
Now, if the value of x is 14, then the value of y will be;
a = kb
y = kx
y = (3/2) × 14
y = ( 3 × 14 )/2
y = 42/2
y = 21
Given that the variable y varies directly with the variable x. If the value of x is 14, the value of y will be 21.
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Answer:
Value of y is 21, when x is 14.
Step-by-step explanation:
Now we have to,
→ find the value of y when x is 14.
Forming the formula,
→ k × 2 = x
→ k × 3 = y
Let's complete the given table,
→ k × 2 = x, k × 3 = y
→ 1 × 2 = 2, 1 × 3 = 3
→ 2 × 2 = 4, 2 × 3 = 6
→ 3 × 2 = 6, 3 × 3 = 9
→ 4 × 2 = 8, 4 × 3 = 12
→ 5 × 2 = 10, 5 × 3 = 15
→ 6 × 2 = 12, 6 × 3 = 18
→ 7 × 2 = 14, 7 × 3 = 21
Then the table will look like,
|| x || y |||| 2 || 3 |||| 10 || 15 |||| 14 || 21 ||Hence, y is 21 when x is 14.
Nicole cleans six of the ten windows in her house. Her mom said she needs to wash 3/5 of the windows. Has Nicole cleaned enough windows? Explain your answer.
Answer:
Yes she has cleaned enough windows.
Step-by-step explanation:
If you simplify 6/10 you get 3/5
determine whether the following statements are true and give an explanation or counterexample. a. all polynomials are rational functions but not all rational functions are polynomials.
The given statement: " all polynomials are rational functions but not all rational functions are polynomials." is true; its counterexample will be: Not all polynomials are rational functions but all rational functions are polynomials.
What is a polynomial?Polynomial refers to an algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variable (s).
Now,
A polynomial of degree n has at most n real zeros. The degree of a polynomial function determines the end behavior of its graph. A rational function is a function of the form: [tex]f(x)=\frac{P(x)}{Q(x)}, Q(x) \neq 0[/tex] and P(x) and Q(x) are both polynomials.A function that cannot be written in the form of a polynomial is not a rational function.Further,
A counterexample refers to an idea or a statement that contradicts an idea or a theory.Basically, we can infer that it is the negation of a statement.For the given statement, the negation would be given as: Not all polynomials are rational functions but all rational functions are polynomials.Hence, The given statement: " all polynomials are rational functions but not all rational functions are polynomials." is true; its counterexample will be: Not all polynomials are rational functions but all rational functions are polynomials.
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The vertex of this parabola is at (4,-3). When the x-value is 5, the y-value is -6. What is the coefficient of the squared term in the parabola’s equation?
In parabola , the coefficient of the squared expression is -3..
What on a graph is a parabola?
Drawing a parabola for the quadratic function f(x) = ax2 + bx + c results in a U-shaped curve. When an is smaller than zero, the parabola's graph is downward (or opens downward). When the value of an is greater than 0, the parabola's graph ascends (or opens up).Parabola equation with a vertex at (h, k) is given by y = a(x - h)^2 + k
For the give parabola, y = a(x - 4)^2 - 3
y = a(x^2 - 8x + 16) - 3
At (5, -6)
-6 = a((5)^2 - 8(5) + 16) - 3 = a(25 - 40 + 16) - 3 = a - 3
a = -6 + 3 = -3
Therefore, the coefficient of the squared expression is -3..
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A customer wanted to purchase a video game and realized that they were short $3.96 to be able to pay. Which value is the opposite of being short $3.96?
Using the absolute value function, the value that is the opposite of being short $3.96 is: x + 3.96.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, that is, |2| = |-2| = 2.
For this problem, the number is of $3.96, that is:
|x| = 3.96.
Hence:
Short of $3.96 means that x = -3.96.The opposite is the other solution, of x = 3.96.More can be learned about the absolute value function at https://brainly.com/question/24734454
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Answer:
Impressive explanation
Exactly what I needed
I double checked this and it's fine
Better than from a teacher!
Step-by-step explanation:
Impressive explanation
Exactly what I needed
I double checked this and it's fine
Better than from a teacher!
Help me please, I need to pass this class
Answer:
Step-by-step explanation:
20
Answer: KL IS 3 + 9 THEN 5 MINUS NINE
Step-by-step explanation: FIND KL
Write the first six terms of the arithmetic sequence with the first term, a1, and common difference, d.
a1 = 2, d=3
Answer:
2.5.8.11.14.17
Step-by-step explanation:
Start from 2 and add 3 every time
PLEASE SHOW WORK
HELP
Answer:
82 + 0.6h = 85 and h = 5
Step-by-step explanation:
hours = h
82 + 0.6h = 85
85 - 82 = 0.6h
3 = 0.6h
3/0.6 = h
h = 5
The diameter of the most popular brand of flying disc used in disc golf measures between 8 and 10 inches. Find the range of possible circumferences and areas for these flying discs to the nearest tenth.
The range of possible circumferences and areas for these flying discs are 25. 24 inches to 31. 42 inches and 50. 27 square inches and 78. 55 square inches respectively.
How to determine the circumferenceThe formula for circumference of a circle is expressed as;
Circumference = πd
Where;
π takes the value 3. 142d is the diameterCircumference for diameter of 8 inches
Circumference = 3. 142 × 8 = 25. 14 inches
Area = 1/ 4 πd² = 1/ 4 × 3. 142 × 8²
Area = 50. 27 square inches
Circumference for diameter of 10 inches
Circumference = 3. 142 × 10
Circumference = 31. 42 inches
Area = 1/ 4 × 3. 142 × 10²
Area = 78. 55 square inches
Thus, the range of possible circumferences and areas for these flying discs are 25. 24 inches to 31. 42 inches and 50. 27 square inches and 78. 55 square inches respectively.
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what property of the median does this illustrate? a. it does not illustrate any property of the median. b. it illustrates the non-resistance of the median. c. it illustrates the resistance of the median. d. it illustrates that the median divides the bottom 50% of the data from the top 50%.
Answer: C. It illustrates the resistance of the median.
A set of 10 scores has ss = 90. if the scores are a sample, the sample variance is ____, and if the scores are a population, the population variance is ____.
If the scores are a sample, the sample variance is 10, and if the scores are a population, the population variance is 9.
A set of 10 scores has SS = 90.
The formula in getting the population variance is
σ² = SS / N
where SS is the sum of squared deviation and N is the number of population.
Therefore, the population variance is
σ² = 90 / 10
σ² = 9
The formula in getting the sample variance is
σ² = SS /( n - 1)
where SS is the sum of squared deviation and n is the number of samples.
Therefore, the sample variance is
σ² = 90/ (10 - 1)
σ² = 90 / 9
σ² = 10
Therefore, if the scores are a sample, the sample variance is 10, and if the scores are a population, the population variance is 9.
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solve the inequality -5x - 7 less than 28
Step-by-step explanation:
Determine the area of square 1
Answer:
x > - 7
Step-by-step explanation:
- 5x - 7 < 28 ( add 7 to both sides )
- 5x < 35
divide both sides by - 5 , reversing the symbol as a result of dividing by a negative quantity.
x > - 7
Which of these tables represents a function? A table has values of X and Y. Row 2: X negative 1 and Y 15. Row 3: X negative 2 and Y 6. Row 4: X 0 and Y 15. Row 5: X 4 and Y 6. W. A table has values of X and Y. Row 2: X 0 and Y 4. Row 3: X 6 and Y 15. Row 4: X 0 and Y 6. Row 5: X negative 2 and Y negative 1. X. A table has values of X and Y. Row 2: X 4 and Y 0. Row 3: X negative 1 and Y negative 2. Row 4: X 6 and Y negative 2. Row 5: X 6 and Y 15. Y. A table has values of X and Y. Row 2: X 6 and Y negative 2. Row 3: X 4 and Y 0. Row 4: X 15 and Y negative 1. Row 5: X 4 and Y 3. Z. A. W B. X C. Y D. Z
Answer:
A. E negitive
Step-by-step explanation:
Answer: x is alys a step behind y so you can make ech difrints by moltapling to ech step
Step-by-step explanation:
Type the correct answer In each box. Spell all words correctly, and use numerals Instead of words for numbers. If necessary, use / for the
fraction bar(s).
IS What is the mean of the given distribution, and which type of skew does it exhibit?
(4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}
The mean of the distribution Is
and it exhibits a
skew.
The solution is Mean = 3.25 for the given distribution's mean and its type of skew.
What in mathematics is Mean?A list of values, such as measurements or numbers, is used to calculate it by dividing the total number of values in the list by the total number of values in the list. Add up each value in the set to determine the mean. Next, divide the total by the number of values.
based on the facts provided;
Step 1: Presented data:
4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2
Step 2:
Sum of the numbers
= 4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2
= 52
Sum of the numbers = 52
Number of terms = 16
Step 3:
Mean=sum of the number/number of term
=52/16
= 3.25
Mean = 3.25
Mean of the distribution is 3.25.
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A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.
x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0
If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
a
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
b
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.
c
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.
d
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.
The end behavior of g(x) is;Option A: As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
What is the End behavior of the Polynomial?
The Factor Theorem states that a function with leading coefficient a and zeros x1, x2, x3,....,xn is defined by;
g(x) = a(x - x1)(x - x2).....(x - xn)
In the given table;
f(x) = 0 for x = -4 and 12. Thus, the zeros are x1 = -4 and x2 = 12
Then the definition is;
g(x) = a(x + 4)(x - 12)
g(x) = a(x² - 8x - 48)
The end behavior is the limit of g(x) as x goes to infinity, thus:
limₓ→ ∞ g(x) = limₓ→ ∞ax² = a * ∞
Since the leading coefficient a is negative, then;
a * ∞ = - ∞
Thus, the end behavior of g(x) is; As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
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10. Circle the irrational number in the list below.
√196
7.27
5/9
√15