The art teacher has 36 small sticks and 60 pipe cleaners for art projects. He wants to make kits for all the students using all the sticks and pipe cleaners. All the kits must be alike. He wants to make as many kits as possible. What is the greatest number of kits he can make.
A) 8 kits
B) 9 kits
C) 12 kits
D) 36 kits
Answer:
The greatest number of kits he can make is 12 kits
Step-by-step explanation:
The greatest common divisor or GCD is called the greatest number that divides exactly two or more numbers at the same time.
The greatest common divisor is usually expressed as GCD(a,b), where a and b are numbers.
Being the divisor of a number is the value that divides the number into exact parts, that is, that the remainder is zero, one way to calculate the GCD is to determine all the divisors of each number, and from these point out the common divisors, of which the major divisor will be the GCD of those numbers. In this case:
Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
The common divisors of 36 and 60 are 1, 2, 3, 4, 6 and 12, of which the greatest is 12. So GCD(36,60)=12
Another way to calculate the GCD is through prime factorization, which always starts with the smallest divisible number of the number being analyzed. In this case:
The decomposition of 36 is: 2*2*3*3 = 2²*3²
The decomposition of 60 is: 2*2*3*5= 2²*3*5
Now the common factors with the lowest exponent are chosen and multiplied. The result obtained is the GCD. In this case, the common factors of 36 and 60 are: 2² and 3 and their multiplication gives: 2²*3= 12. So GCD(36,60)=12
The greatest number of kits he can make is 12 kits
The temperature inside the lab refrigerator is at most 35 Fahrenheit used to represent the temperature in fahrenheit of the refrigerator
Complete question is;
Write inequalities to represent the situations below. The temperature inside the lab refrigerator is no more than 45 °F. Use t to represent the temperature (in °F) of the refrigerator.
Answer:
t ≤ 45 °F
Step-by-step explanation:
We are told to use t to represent the temperature (in °F) of the refrigerator.
We are also told that the temperature inside the lab refrigerator is no more than 45 °F.
For the temperature inside the refrigerator to be no more than 45 °F, it means the temperature should be either less than or equal to 45 °F
Thus means that t is less than or equal to 45 °F.
Thus, it can be represented in terms of inequality as;
t ≤ 45 °F
Answer:
t ≤ 35
Step-by-step explanation:
I took the test, it was right! :)
A set contains five consecutive even integers . The least even integer in the 5 points set has a value of 14. Write all the elements of the set.
Answer:
14, 16, 18, 20, 22
Step-by-step explanation:
14 is the smallest of 5 consecutive integers.
The next larger even integer is 16, then 18, then 20, then 22.
Answer: 14, 16, 18, 20, 22
There are a total of 55 people at a birthday party. There are three times as many kids at the party as parents, and there are five fewer grandparents than parents. Use the guess and check method to find out how many kids are at the birthday party?
Answer:
165
Step-by-step explanation:
Answer:
27
Answer:
Answer:
What’s the answer Evaluate 2^4
Answer:
[tex]16[/tex]
Step-by-step explanation:
[tex]2^4[/tex]
To solve, you're gonna have to multiply 4 times.
[tex]2*2*2*2[/tex]
[tex](2*4)(2*4)[/tex]
Since [tex]4*2[/tex] is [tex]8[/tex] , you will have to multiply [tex]8[/tex] by [tex]2[/tex].
[tex]8*2=16[/tex]
Your answer is [tex]16[/tex].
Hope this helps!
Out of 270 racers who started the marathon, 247 completed the race, 14 gave up, and 9 were disqualified. What percentage did not complete the marathon?
Answer:
8.5%
Step-by-step explanation:
Total number of racers = 270
From the question, we have two categories who did not complete the race.
a. 14 that gave up
b. 9 that were disqualified
Total number of those who didn't complete race = 14 +9 = 23
To get the percentage of this group in the marathon:
= (23/270)*100
= 0.0851 *100
= 8.5percent
Is sqrt -5 rational, irrational or imaginary?
Answer:
Imaginary
Step-by-step explanation:
[tex] \sqrt{ - 5} \: is \: imaginary[/tex]
The sale price of a spring break vacation package was $209.99 the travel agent said by booking early you saved $20.00. Find the percent decrease in price
Answer:
[tex]\%\ decrease = 9.52\%[/tex]
Step-by-step explanation:
Given
[tex]Sales\ Price = \$209.99[/tex]
[tex]Saved = \$20.00[/tex]
Required
Determine the %decrease
First, we need to determine the amount paid
[tex]Amount = Sales\ Price - Amount\ Saved[/tex]
[tex]Amount = \$209.99 - \$20.00[/tex]
[tex]Amount = \$189.99[/tex]
The percentage decrease is the calculated as follows:
[tex]\%\ decrease = -100\% * \frac{Final - Initial}{Initial}[/tex]
In this case;
[tex]Initial = Sales\ Price = \$209.99[/tex]
[tex]Final = Amount\ Paid = \$189.99[/tex]
So; we have:
[tex]\%\ decrease = -100\% * \frac{189.99 - 209.99}{209.99}[/tex]
[tex]\%\ decrease = -100\% * \frac{-20}{209.99}[/tex]
[tex]\%\ decrease = 100\% * \frac{20}{209.99}[/tex]
[tex]\%\ decrease = \frac{2000\%}{209.99}[/tex]
[tex]\%\ decrease = 9.52426306015\%[/tex]
[tex]\%\ decrease = 9.52\%[/tex] (Approximated)
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.4 years, and standard deviation of 0.6 years. The 4% of items with the shortest lifespan will last less than how many years?
Answer:
7.35 years
Step-by-step explanation:
Given that :
mean = 8.4
standard deviation = 0.6
From the negative z tables, the corresponding data for 0.04 = -1.75
So, using the z-score formula:
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]-1.75 = \dfrac{x - 8.4}{0.6}[/tex]
-1.75 × 0.6 = x - 8.4
- 1.05 = x - 8.4
x = -1.05 + 8.4
x = 7.35 years
the shortest lifespan will last less than 7.35 years
∴ the longest 4% will have lifespans longer than x = 8.4 + 1.75(0.6)
= 9.45 years
Which is the interquartile range for the city that has the greater variability in temperature?
Answer:
D. 40
Step-by-step explanation:
The greater the interquartile range of a data set, the greater the variability.
Interquartile range = third quarter (Q3) - first quartile (Q1)
Interquartile range of City A = 70 - 40 = 30
Interquartile range of City B = 80 - 40 = 40.
City B has a greater interquartile range than city A, therefore, City B has the greater variability in temperature, with an interquartile range of 40.
please answer thank you!
Answer:
Maya messed up on Step 1, David messed up on Step 2
Step-by-step explanation:
Maya:
Step 1 should distribute to 5x - 15 = 12
David:
Step 2 should be 3x - 2x = -2 - 3 after you combine like terms
Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella has $15 to spend and must buy at least 19 apples and mangos altogether. If Gabriella decided to buy 13 mangos, determine the maximum number of apples that she could buy. If there are no possible solutions, submit an empty answer.
Answer:
She can buy a maximum of 8 apples.
Step-by-step explanation:
Let x represent the number of apples that she wants to buy.
The grocery store sells apples for $1 each and mangos for $0.50 each.
If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as
x + 13 × 0.5 = x + 6.5
If she buy at least 19 apples, it means that
x + 13 ≥ 19
x ≥ 19 - 13
x ≥ 6
Gabriella has $15 to spend. It means that
x + 6.5 ≤ 15
x ≤ 15 - 6.5
x ≤ 8.5
Therefore, the maximum number of apples that she can buy is 8
Answer:She would only be able to buy 8 more apples
Step-by-step explanation:
First you multiply 13 by .50 and you get 6.50
Next you subtract 6.50 from 15 and get 8.50
After that you see 1 dollar per apple so she can only get 8 apples for 8 dollars.
Therefore, she can only buy 8 more apples.
Extra:She can buy an extra mango with the leftover .50cent
An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 80 of these tires, the braking distance has a mean of 77 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value.
Answer:
The calculated value t = 3.032 > 1.9904 at 5% level of significance
Step-by-step explanation:
Step(i):-
Given mean of the population 'μ'=75 feet
Given mean of the sample(x⁻) = 77
Given standard deviation of the sample(S) = 5.9
Given sample size 'n' =80
Step(ii):-
Test statistic
[tex]t=\frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t=\frac{77-75}{\frac{5.9}{\sqrt{80} } }[/tex]
t = 3.032
Degrees of freedom ν=n-1 = 80-1 =79
tabulated value = 1.9904 at 5% level of significance
The calculated value t = 3.032
Final answer:-
The calculated value t = 3.032 > 1.9904 at 5% level of significance
John is walking around a circular track with a radius of 50 ft. If he walks the equivalent of 140 degrees, find the total distance he has walked around the track to the nearest Foot.
Answer: 122 ft
Step-by-step explanation:
s = r Ф (Ф must be in radians)
Given: r = 50
Ф = 140°
[tex]\dfrac{\pi}{180^o}=\dfrac{x}{140^o}[/tex]
[tex]\dfrac{140^o\pi}{180^o}=x[/tex]
[tex]\dfrac{7\pi}{9}=x[/tex]
[tex]s=50\bigg(\dfrac{7\pi}{9}\bigg)\\\\\\.\quad =\dfrac{350\pi}{9}\\\\\\.\quad =122\ ft[/tex]
what is the value of the expression below when y=5? y^2-3y+6
Answer:
y = 5
y^2 - 3y + 6
= 5^2 - 3(5) + 6
= 25 - 15 + 6
= 10 + 6
= 16
Answer the descriptions
x - intercepts (zeros)
y-intercept
increasing interval
decreasing interval
constant interval
Maximum
Minimum
Domain
Range
Answer:
x-int: (-1.5, 0) and (3.5, 0)
y-int: (0, 3)
Increasing Interval: [-2, 1)
Decreasing Interval: (1, 4]
Constant Interval: [-4, -2)
Maximum: (1, 5)
Minimum: (4, -1) or (-4, -1) or (-2, -1) or (-3, -1)
Domain: [-4, 4]
Range: [-1, 5]
Step-by-step explanation:
x-intercepts are where the function f(x) crosses the x-axis when y = 0.
y-intercepts are where the function f(x) crosses the y-axis when x = 0.
Increasing interval is the set of x-values in which the graph f(x) increases in y-value.
Decreasing interval is the set of x-values in which the graph f(x) decreases in y-value.
Constant interval is the set of x-values in which the graph f(x) y-values stay constant.
Maximum is the largest y-value function f(x) can output.
Minimum is the smallest y-value function f(x) can output.
Domain is the set of x-values that can be inputted into function f(x).
Range is the set of y-values that can be outputted from function f(x).
Carissa counts by 5s from 32 to 62. Which number does carissa count?
Answer:
32, 37, 42, 47, 52, 57, 62.
Step-by-step explanation:
It is given that Carissa counts by 5s from 32 to 62.
It means, we have to add 5 in the number to get the next number.
Add 5 in 32.
[tex]32+5=37[/tex]
Now, add 5 in 37.
[tex]37+5=42[/tex]
Similarly, continue the process.
[tex]42+5=47[/tex]
[tex]47+5=52[/tex]
[tex]52+5=57[/tex]
[tex]57+5=62[/tex]
Therefore, the numbers counted by carissa are 32, 37, 42, 47, 52, 57, 62.
Answer:
It is 47
Step-by-step explanation:
Find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y = - x + 4, y = 4x - 2
Answer:
[tex]x = 1.2[/tex]
See Attachment for Graph
Step-by-step explanation:
Given
[tex]y = -x + 4[/tex]
[tex]y = 4x - 2[/tex]
Required
Determine the point of intersection
To do this, we simply equate both expressions of y
i.e.
[tex]-x + 4 = 4x - 2[/tex]
Solve for x
[tex]-x - 4x = - 2 - 4[/tex]
[tex]-5x = -6[/tex]
Divide through by -5
[tex]x = \frac{-6}{-5}[/tex]
[tex]x = \frac{6}{5}[/tex]
[tex]x = 1.2[/tex]
Hence, the point of intersection is 1.2
Find the slope intercept form for the equation of the line which passes through the point (-5,4) and the origin
Answer:
Step-by-step explanation:
(-5, 4) and (0, 0)
(0 - 4)/(0 + 5) = -4/5
y - 4 = -4/5(x + 5)
y - 4 = -4/5x - 4
y = -4/5x
What's 10+10-5+10+5
Answer:
the answer is 30
Step-by-step explanation:
10+10=20-5=15+10=25+5=30
Answer:
30!
Step-by-step explanation:
( 125 ) - 1/3 can be written as :
a) 5
b) -5
c) 1/5
d) None of these
Answer:125-1/3 can be written as : none of these
Sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581, what were the sales (in $) last month?
Answer:
Step-by-step explanation:
(103,581) • (%110)
= (103,581) • (1.10)
= $113,939.1
The sales (in $) last month were $115,090 if the sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
Let suppose x be the sales last month:
(x - 103581)/x = 0.1
x - 103581 = 0.1x
x - 0.1x = 103581
0.9x = 103581
x = 103581/0.9
x = $115,090
Thus, the sales (in $) last month were $115,090 if the sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.
Learn more about the percentage here:
brainly.com/question/8011401
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What is the slope of the line represented by the equation y = - 1/2x + 1/4
Answer:
The slope is -1/2
Step-by-step explanation:
-1/2 is a negative slope. Down 1 to the right 2
QUESTION 4!! MATH PLS HELP ASAP
Answer:
Step-by-step explanation:
There is a relationship between the degree of the polynomial and the number of times its graphed curved changes direction> this change is called turning point which is a point where the graph changes from increasing to decreasing or from decreasing to increasing
A polynomial of n degree will have n-1 turning points
ex: f(x)=x³+3x²+x+1
degree of polynomial is 3, it has 2 turning points (3-1)
Solve for the specified variable.
(c+d)
Solve Q=
for d.
2
Answer:
2Q -c = d
Step-by-step explanation:
Q= ( c+d)/2
Multiply each side by 2
2Q = ( c+d)/2 *2
2Q = ( c+d)
Subtract c from each side
2Q - c = c+d-c
2Q -c = d
Steps to solve:
Q = (c+d)/2
~Simplify
Q = 1/2c + 1/2d
~Subtract 1/2c to both sides
Q - 1/2c = 1/2d
~Divide 1/2 to both sides
d = 2q - c
Best of Luck!
what is an algebraic word phrase for 49 + M
Answer:
slader
Step-by-step explanation:
ion 1(Multiple Choice Worth 2 points)
Find the area of the triangle with the given measurements. Round the solution
B = 107°, a = 10 cm, c = 22 cm
O 32.16 cm2
O 110 cm2
O 105.19 cm2
210.39 cm2
Answer:
105.19.
Step-by-step explanation:
Area = 1/2 ac sin B
= 1/2 * 10 * 22 * sin 107
= 105.19..
5. While still in the hospital, the doctor writes an order for an antibiotic at 300mg/kg daily. You are nervous now because the nurse was wrong before. If you weigh 123 lb, determine how many milligrams you should be given.
The correct answer is 16737 mg
Explanation:
The first step to solve this problem is to convert the weight to kilograms because the dosage of the antibiotic is given in milligrams per kilo. This can be done by multiplying the pounds by 0.453 considering each pound is equal to 0.453 kilos. The process is shown below:
123 lb x 0.453 = 55.791 kg
Now, simply multiply the kilos by the recommended dose:
55.791 kg x 300 mg/kg = 16737 mg
Also, this can be converted to grams by dividing the number into 1000 (1000 mg = 1 g)
16737mg ÷ 1000 = 16.737 grames
Is 0.485 greater than 0.5
Answer:
no
Step-by-step explanation:
Answer:
No 0.485 is less than 0.5
0.485 < 0.50
I will give the brainiest
Tim has 74 socks, all in pairs. He has 1 more pair of white socks than black socks. How many
individual socks of each color does he have?
black socks
white socks
Answers:
36 individual black socks
38 individual white socks
Check: 36+38 = 74 total individual socks
====================================================
Work Shown:
b = number of pairs of black socks
w = number of pairs of white socks
w = b+1 since he has 1 more pair of white socks compared to black socks
2b = number of individual black socks
2w = number of individual white socks
2b+2w = total number of individual socks
2b+2w = 74
2b+2(b+1) = 74 .... plug in w = b+1
2b+2b+2 = 74 ... distribute
4b+2 = 74
4b = 74-2 .... subtracting 2 from both sides
4b = 72
b = 72/4 ... dividing both sides by 4
b = 18 is the number of pairs of black socks he has
2b = 2*18 = 36 is the number of individual black socks he has
w = b+1 = 18+1 = 19 is the number of pairs of white socks he has
2w = 2*19 = 38 is the number of individual white socks he has
2b+2w = 36+38 = 74 individual socks overall