The little monsters solved 15 problems in March's Math meet
Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.
In March's math meet, they solved 2/3 of the problems.
In total, the little monsters solved 13 of 30 problems over both math meets.
Let, the number of problems in November be n,
and the number of problems in March be m
According to the question,
n + m = 30 as, the total problems be 30
Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems
n + m = 30 ... (1)
n/5 + 2m/3 = 13 ... (2)
On simplifying Eq (2) becomes
3n + 10m = 195 ... (2)
On multiplying Eq (1) by 3, we get
3n + 3m = 90
3n + 10m = 195
On subtracting, we get
- 7m = - 105
m = 105/7
m = 15
So, the problems asked in March's Math meet be 15.
Hence, 15 problems were asked at March's Math meet.
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Dario bakes a lasagna containing $\frac 23$ pound of parmesan cheese, $1\frac 34$ pounds of ricotta cheese, and $1\frac 13$ pounds of mozzarella cheese.
Dario cuts the lasagna into several equal slices, each containing exactly $\frac 14$ pound of cheese. How many slices are there?
Dario cuts the lasagna into 15 equal slices.
Given,
Quantity of Parmesan cheese = 2/3 pounds
Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds
Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds
The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds
We have to find the number of slices of cheese.
Here,
Total quantity of cheese;
2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds
Number of slices = total cheese / quantity of cheese in pieces
= (15/4) / (1/4) = 15 slices
That is,
Dario cuts the lasagna into 15 equal slices.
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Convert the following. Round to 1 decimal.
0. 57 miles2 converted into feet2
0.57 mi² = 15,890,688 ft² after converting square miles in square foot.
Define the meaning of unit conversion?A unit conversion is the expression of the same feature in an another unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles into kilometers, feet, or indeed any length measurement. Measurements are frequently stated in one set of units, including feet, but require different units, such like chains. A conversion factor seems to be a numerical equation that allows for the equal exchange of feet and chains.The given conversion in question is-
0.57 mi² = __ ft²
We know that
1 mi² = 27,878,400 ft²
Then, multiply both sides by 0.57
1 x 0.57 mi² = 27,878,400 x 0.57 ft²
0.57 mi² = 15,890,688 ft²
Thus, the conversion of 0.57 mi² = 15,890,688 ft².
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a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).
What is Random Sample?A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:
Convenient: Sample taken from a pool that is easily accessible.
Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.
Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.
Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.
Now, finding the sample proportion,
[tex]p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8[/tex]
The confidence level is given as,
[tex]C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ][/tex]
The value of [tex]z(\frac{\alpha}{2})[/tex] is 1.96
Putting the values, we get
[tex]C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)[/tex]
Therefore, the 95% confidence interval is (0.782,0.818).
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The given question is incomplete. Here is the complete question.
a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
a) 0.782 to 0.818
b) 0.754 to 0.799
c) 0.690 to 0.713
d) 0.799 to 0.951
There are some sweets in a jar
The sweets are red or orange or blue or yellow.
Hannah is going to take at random a counter from the bag.
The table shows cach of the probabilities that the counter will be blue or will be yellow.
Colour
Probability
red
orange
blue
0.5
yellow
0.2
There are 20 blue sweets in the jar.
The probability that the sweet Hannah takes will be red is twice the probability that the
sweet will be orange.
(a) Work out the number of red sweets in the jar.
the mom
the number of Red sweets=14
Let the probability of getting a red sweet be = P(R)
Let the probability of getting a Blue sweet be = P(B)
Let the probability of getting an orange sweet be = P(O)
Let the probability of getting a yellow sweet be = P(Y)
Let the number of Red sweets be represented as = n(R)
Let the number of Yellow sweets be represented as = n(Y)
Let the number of Orange sweets be represented as = n(O)
Let the number of Blue sweets be represented as = n(B)
Let the total number of sweets in the jar be represented as = n(T)
P(B) = 0.5
P(E) = 0.2
P(R) = 2 x P(O)
The formula of probability =
Number of the Sweets of a color/Total number of sweets in the jar
then,
P(B)=n(B)/ n(T)
P(B)=0.5 (Given in question)
n(B)=20 (Given in question)
So,
0.5 = 20/n(T)
5/10 = 20/n(T)
5/10 x 1/20 = 1/n(T)
cross multiplying
n(T)=10/5 x 20
dividing 10 by 5 =2
n(T) = 2 x 20
n(T) = 40
P(Y)=0.2 (Given in question)
Applying the formula of probability
P(Y) = n(Y)/n(T)
putting values
0.2=n(Y)/40
2/10=n(Y)/40
2/10 x 40 =n(Y)
Dividing 40 by 10 = 4
n(Y)= 2 x 4
n(Y)= 8
P(R)=2P(O)
Applying the formula of probability
n(R)/n(T)=2n(O)/n(T)
Cancelling out n(T) with n(T)
So,
n(R)=2 x n(O) -(i)
n(T) = n(O)+n(R)+n(B)+n(Y)
putting values
40=n(O)+n(R)+20+8
40=n(O)+n(R)+28
40-18=n(O)+n(R)
From -(i)
22=2n(O)+n(O)
22=3n(O)
n(O)=22/3
Since,
n(R)=2xn(O)
n(R)=2x22/3
n(R)=44/3
n(R)=14.6
the number of Red sweets=14.6
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Write the coordinates of the vertices after a translation 3 units right and 12 units down
Step-by-step explanation:
3 units right = x + 3
12 units down = y - 12
E = (-5, 4) -> E' (-2, -8)
F = (-5, 9) -> F' (-2, -3)
G = (1, 9) -> G' (4, -3)
H = (1, 4) -> G' (4, -8)
An equation and the steps to solve it are shown
below:
1
2x - 4 (12x+4)= 3
Step 1: 2x + 3x + 1 = 3
Step 2: 5x+1=3
Step 3: 5x+1-1=3-1
Step 4: 5x = 2
In which step was the error made and why? (1 point)
The error was made in the Step 1 as Distributive property of multiplication was not used correctly .
In the question ,
it is given that
the equation is 2x -(1/4)(12x+4)= 3
Step 1 : by using the distributive property of multiplication ,
we get
2x - (1/4)*12x -(1/4)*4 = 3
2x - 3x - 1 = 3
So , after the first step the equation should be 2x - 3x - 1 = 3
we see that the Distributive property of multiplication , was not used properly as the negative sign was not distributed to both the terms .
So , Step 1 is wrong.
Step 2 : Adding like terms
we get ,
-x - 1 = 3
Step 3 : Adding 1 to both the sides ,
we get
-x - 1 [tex]+[/tex] 1 = 3 + 1
Step 4:
-x = 4
x = -4
Therefore ,The error was made in the Step 1 as Distributive property of multiplication was not used correctly .
The given question is incomplete , the complete question is
An equation and the steps to solve it are shown below:
2x -(1/4)(12x+4)= 3
Step 1: 2x + 3x + 1 = 3
Step 2: 5x+1=3
Step 3: 5x+1-1=3-1
Step 4: 5x = 2
In which step was the error made and why?
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.
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On a coordinate plane, a line goes through (0, 3) and (3, negative 1). A point is at (negative 3, 2).
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answer:
Step-by-step explanation:
The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.
Unit 4 congruent triangles
Answer: 9/3
Step-by-step explanation: the trriangles proportion is three and 9/3=3
Walnut Creek Inc. is going to do a revers stock split with a 3:4 ratio. The current price per share is $234.75 and the current number of outstanding shares is 38,750,000. What is the post-split number of shares?
The post-split market capitalization of Walnut Creek Inc. is $12995089.
Given that, Walnut Creek Inc. is going to do a revers stock split with a 3:4 ratio. The current price per share is $234.75 and the current number of outstanding shares is 38,750,000.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, 3+4 = 7
Now, 1/7 × 38,750,000
= 5535714 .29 shares
So, capitalization is 5535714 × 234.75
= $12995089
Therefore, The post-split market capitalization of Walnut Creek Inc. is $12995089.
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ksiodhhhwdaaaaaaaaaaoidjooaaaaaaaaaaaaaaaaaaa
Answer:
vyfyxfrr6c*"8&"; hxh6 byhd,tf7zg5gzyfe55eE4E45w522
Step-by-step explanation:
6dyxg9yyfz6t bztrfr 4.Sabina the tortoise is an 56,123 way of Policy for recharge of the angles and tricks of Policy in order for me and I have a wonderful experience and a
2x^3 + 2
________
x + 3
In long division of polynomials
Answer:
2x^2
__________
x+3 | 3
2x + 2
3
- 2 x - 3
_________
R = - 1
is 8.75x linear or non-linear
Find the degree of the equation to determine if linear.
Linear
Pls help and answer all questions I will give brainly for whoever answers are correct!.
Answer:
x=-5/2
Step-by-step explanation:
x=-5/2
Answer:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
Step-by-step explanation:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
Use point-slope form to write the equation of a line that passes through the point
(1,-5) with slope-1.
The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Given:
(1,-5) with slope m = -1
The standard slope intercept form is y = mx + c.
substitute m = -1 and (1,-5)
-5 = -1(1) + c
-5 = -1 + c
c = -4.
y = mx + c
y = -1(x) + (-4)
y = -x - 4.
Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
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At Sascha's Salad Bar, customers make their own salads and pay by the ounce. Jenny paid $6.16 for a 22-ounce salad. Seth spent $7.28 on a salad. How much did his salad weigh?
The weight of the salad at the cost of $7.28 will be 31.9 ounces.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at Sascha's Salad Bar, customers make their own salads and pay by ounce. Jenny paid $6.16 for a 22-ounce salad. Seth spent $7.28 on a salad.
$6.16 ⇒ 22 ounces
$1 ⇒ 22 / $6.16
$7.28 ⇒ ( 22 x 7.28 ) / $6.16
$7.18 ⇒ 31.9 ounces
Therefore, the weight of the salad at the cost of $7.28 will be 31.9 ounces.
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Solve:-
[tex]\bf 7(5a - 4) - 1 = 14 - 8[/tex]
Answer:
a = 1
Step-by-step explanation:
Given equation,
→ 7(5a - 4) - 1 = 14 - 8
Now the value of a will be,
→ 7(5a - 4) - 1 = 14 - 8
→ 35a - 28 - 1 = 6
→ 35a - 29 = 6
→ 35a = 6 + 29
→ a = 35/35
→ [ a = 1 ]
Hence, the value of a is 1.
Can someone please help me with the following problems
The day which has the least change in temperature is Wednesday.
The two consecutive days which showed a drop in temperature is Wednesday and Thursday.The graph which was easier to read is table graph.Table graph illustrate the data because it clearly shows the data representation.How to read and explain graph?The day which has the least change in temperature can be calculated by finding the change in temperature:
Monday = High temperature - low temperature
= 82° - 58°
= 24°
Tuesday = High temperature - low temperature
= 85° - 60°
= 25°
Wednesday = High temperature - low temperature
= 77° - 62°
= 15°
Thursday = High temperature - low temperature
= 68° - 50°
= 18°
Friday = High temperature - low temperature
= 75° - 48°
= 27°
Saturday = High temperature - low temperature
= 70° - 52°
= 22°
Sunday = High temperature - low temperature
= 84° - 56°
= 28°
The day which has the least change in temperature is Wednesday
Which two consecutive days which showed a drop in temperature: Wednesday and Thursday with 77° and 68° respectively.
Unlike line graph, table graph is the graph that is easier to read.
Therefore, the graph which best illustrate the graph is table graph because it represent the data in a clearer way.
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standard automobile license plates in a country display 3 numbers, followed by 2 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetitions of letters and numbers are allowed.) there are different standard plates possible in this system.
The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
Define the term permutation?The number of potential arrangements for a given set is assessed mathematical terms, but this procedure is referred to as permutation. The arrangement's order is essential when using permutations.For the stated data;
Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.
There are total 9 digits (0 - 9).
There are total 26 letter (A - Z)
Repetitions of letters and numbers given allowed.
Thus, numbers and the letters ca be arranged as;
1st place = 9 ways.
2nd place = 9 ways.
3nd place = 9 ways.
4th place = 26 ways.
6th place = 26 ways.
7th place = 9 ways.
8th place = 9 ways.
Total ways = 9×9×9×26×26×9×9
Total ways = 39917124
Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
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Type the correct answer in each box. Use numerals instead of words.
The surface area of a square pyramid is 96 square feet. The height is two-thirds of the length of the base edge.
What is the length of the base edge?
The length of the base edge of the pyramid is …
feet.
The length of the base edge of the given square pyramid is 3.67 feet.
What is the Surface Area?
The sum of all an item's faces makes up the surface area of a three-dimensional object. When wrapping, painting, and finally creating things to get the finest possible design, we apply the idea of surface areas of various items in real life.
What is a Square Pyramid?
In geometry, a pyramid with a square base and four lateral sides is referred to as a square pyramid.A polyhedron with a base and three or more triangle faces that meet above the base is called a pyramid (the apex). A pentahedron is a three-dimensional structure with a total of five faces, such as a square pyramid. The Great Pyramid of Giza is one of the most well-known examples of a pyramid like this in real life.Steps to Calculate the Base Edge Length of Square Pyramid
The formula for surface area of square pyramid is given by, [tex]SA=a^{2} +2a\sqrt{\frac{a^{2} }{4}+h^{2} }[/tex], -----(1)
where [tex]a[/tex] is the length of the base edge and [tex]h[/tex] is the square pyramid height.
In the question, it is given that the surface area of the square pyramid is 96 square feet.
The height of the square pyramid is two-thirds of the base edge length.
[tex]\implies h=\frac{2a}{3}[/tex] ------(2)
Now substituting the given values in (1), we get
[tex]96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+(\frac{2a}{3} )^{2} }\\\implies 96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+\frac{4a^{2} }{9} }[/tex]
Simplifying, we get
[tex]96=a^{2} +2a\times 0.834a^{2} \\\implies 96=a^{2} +1.668a^{3} \\\implies 1.668a^{3}+a^{2} -96=0[/tex]
Finally, we get the value of [tex]a=3.67[/tex] feet.
Therefore, the base edge length of the given square pyramid is 3.67 feet.
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Grace runs a website that has gotten quite popular. However, its popularity seems to have
peaked, and the site is now getting 7% fewer hits each week. If Grace's site got 38,800 hits
this week, how many weekly hits can she expect it to get 7 weeks from.
Answer:
23346
Step-by-step explanation:
You want to know the number of hits on Grace's website 7 weeks from now if she gets 38,800 now and the number decreases 7% per week.
Growth factorThe growth factor per week is ...
growth factor = 1 + growth rate
The growth rate of hits is -7% per week, so this is ...
growth factor = 1 -7% = 0.93
Exponential functionThe exponential function describing the number of hits can be written ...
hits = (initial value)(growth factor)^weeks
hits = 38,800(0.93^weeks)
Then in 7 weeks, the number of hits is expected to be ...
hits = 38,800(0.93^7) ≈ 23,346
Grace can expect to get about 23,346 hits in 7 weeks.
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Tom is applying for a visa.
He has to pay £2,300 for the visa as well as a 7% charge on the visa price for an on-the-day service.
If Tom has 1 year to save, how much money should he save per month to be able to cover his costs?
Round your answer to the nearest £10.
Pls help me ! for this question
Answer:
f = 3cm g = 16cm
Step-by-step explanation:
Area of ABCE = 60cm²
Area of ABCD = 48cm²
60 - 48 = 12
Area of ADE = 12cm²
A to D = 3cm
f = 3cm
g = 16cm
or Line p has an equation of y= – 8x+6. Line q, which is perpendicular to line p, includes the point (2, – 2). What is the equation of line q?
Answer:
y = 1/8 x - 9/2
Step-by-step explanation:
slope of line q = 1/8
y-(-2)= 1/8(x-2)
y+2 = 1/8 x - 1/4
y = 1/8 x - 1/4 - 2
y = 1/8 x + (-1-8)/2
y = 1/8 x -9/2
Add 7w-12 and -15w+60
Show your work
Answer:
Step-by-step explanation: 7w-12+(-15w+60)= 7w-12-15w-60= -8w-72
-8w-72 is the answer or -8(w+9) if you take out a -8
The required simplified solution of the sum of the expressions is -8w + 48
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To add 7w-12 and -15w+60
According to the question,
= 7w - 12 - 15w + 60
= 7w - 15w + 60 - 12
= -8w + 48
Thus, the required simplified solution of the sum of the expressions is -8w + 48
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Seamus buys £600 of shares in a new Company. One week later the value of the shares has Increased by 15%. find the value of the shares one week after Seamus bought them. 600/100x 15 =90 90+600=690 Is this a righ answer ?cause i am not so sure if i did it right
Answer:
yes, you did it right!
Step-by-step explanation:
You firsth calculate how much 15% of £600 are.
You did it exactly right. It's £90.
And to work out rhe value of the shares one week later, you add the £90 to the £600.
What causes an echo?
rarefaction
reflection
refraction
Answer:
Reflection
Step-by-step explanation:
Reflection is like looking at yourself through a mirror, so it would be the same for sound.
Tell me if this is correct.!
Answer:
Reflection
Step-by-step explanation:
i took this quiz
Compare the following fraction 8/14 and 4/7
Answer:
These fractions are equivalent, with 4/7 being the simplest form of both.
Step-by-step explanation:
8/14 can be simplified to 4/7 also by dividing both sides by two :)
What is the area of the figure at the right 6 in.
7.5 in.
Please HELP
Answer:
B.
Step-by-step explanation:
52% of all americans are home owners. if 41 americans are randomly selected, find the probability that a. exactly 19 of them are are home owners. b. at most 24 of them are are home owners. c. at least 23 of them are home owners. d. between 19 and 27 (including 19 and 27) of them are home owners.
With the help of permutanions and combinations we can conclude the answer.
What is permutations and combinations?By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.Here is a detailed explanation of permutation and combination, along with their distinctions.acc to our question-
a= total americans -41 probability of 19 of them is house owner= 41C19b= total americans -41 probability of 24 of them is house owner41C24Hence ,permutanions and combinations concept helped us to reach our solution.
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