Answer:
Part A:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
Number of vanilla wafers packets bought = 6 and
Number of chocolate wafers packets bought = 21
Step-by-step explanation:
Given:
Cost of each packet of vanilla wafer = $4
Cost of each packet of chocolate wafer = $1
Total number of packets bought = 27
Total money spent = $45
Part A:
To write a system of equations for the given situation.
Here, we do not know the number of packets bought for each type of wafer.
We just know that total number of packets bought and the total money spent in buying those packets.
Let us suppose,
Number of packets of vanilla wafers bought = [tex]x[/tex] and
Number of packets of chocolate wafers bought = [tex]y[/tex]
Total number of packets = Number of packets of vanilla wafers bought Plus Number of packets of chocolate wafers bought:
i.e. [tex]x+y=27 ...... (1)[/tex]
Money spent on vanilla wafers packets = [tex]4 \times x[/tex]
Money spent on chocolate wafers packets = [tex]1 \times y[/tex]
Total money spent = [tex]4x+y = 45 ...... (2)[/tex]
So, the system of equations is:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
To find number of packets bought for each flavor = ?
Here, we have two equations and two variables [tex]x[/tex] and [tex]y[/tex].
As, the coefficients of [tex]y[/tex] in both the equations are same.
Let us subtract equation (1) from (2):
[tex]4x+y-x-y=45-27\\\Rightarrow 3x = 18\\\Rightarrow \bold{x =6}[/tex]
By equation (1), putting the value of [tex]x[/tex] and solving for [tex]y[/tex]:
[tex]6+y=27\\\Rightarrow \bold{y =21}[/tex]
So, number of vanilla wafers packets bought = 6 and
number of chocolate wafers packets bought = 21
There are 45 eighth graders and 20 seventh graders in a school club. The president of this club wants 40% of the club’s members to be seventh graders. How many more seventh-graders must join the club in order to meet the president’s wishes? (Assume that the number of eighth-graders remains the same.)
Answer: Please Give Brainliest. Thank You!
10 more
The number of seventh-graders that must join the club in order to meet the president's wishes is 10.
Since there are 45 eighth graders and 20 seventh graders in a school club and the president of this club wants 40% of the club’s members to be seventh graders, we need to find the number of seventh graders that will be added to the school club to make their percentage 40 %.
Let the number of seventh-graders to be added be x.
So, the new number of seventh-graders is 20 + x and the new number of people in the club is 45 + 20 + x = 65 + x
Thus, the percentage of seventh graders in the club is thus
[tex]\frac{20 + x}{65 + x} X 100[/tex] %
Since this percentage equals 40 %, we have that
[tex]\frac{20 + x}{65 + x} X 100[/tex]% = 40 %
[tex]\frac{20 + x}{65 + x} = \frac{40}{100} \\\frac{20 + x}{65 + x} = 0.4[/tex]
Cross-multiplying we have
[tex]20 + x = 0.4(65 + x)[/tex]
Expanding the bracket, we have
[tex]20 + x = 26 + 0.4x[/tex]
Subtracting 20 from both sides we have
[tex]x = 26 - 20 + 0.4x\\x = 6 + 0.4x[/tex]
Subtracting 0.4x from both sides, we have
[tex]x - 0.4x = 6\\0.6x = 6[/tex]
dividing both sides by 0.6, we have
x = 6/0.6
x = 10
So, the number of seventh-graders that must join the club in order to meet the president's wishes is 10.
Learn more about percentages here:
https://brainly.com/question/23127071
Use the figure below to find the measure of angle x.
Answer:
70 degrees
Step-by-step explanation: this is an equilateral triangle. All of its angles are the same.
It cost Lori $14 to go to the movies. She bought popcorn for $3.50 and a soda for $2.50. How much was her ticket?
Answer:
$8.00
Step-by-step explanation:
You need to add 3.50 and 2.50. your answer will be 6.00. If you subtract 6.00 from 14.00 you will get your answer which is 8.00
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was times the weight of the first fish, another was more than times the weight of the first fish, the next was the weight of the first fish, and the last was the weight of the first fish. Bridget's dad caught four fish. The first fish he caught weighed more than times the weight of the first fish caught that day. One fish weighed the weight of the first fish caught that day, one weighed more than times the weight of the first fish caught that day, and the last weighed the weight of the first fish caught that day.
Answer:
Bridget's first fish =f = 5 ounces
Bridget's dad first fish weighs 17 ounces
Step-by-step explanation:
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day. If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.
Solution:
Bridget's fishes:
f ounces
2f ounces
3f+2 ounces
1/2f ounces
3/5f ounces
Total= f +2f + (3f+2) + 1/2f +3/5f
=3f + 3f + 2 + 5f+6f/10
=6f + 2 + 11f/10
=60f+11f/10 +2
=71/10f +2
Bridget's dad fishes
3f+2
4/5f
2f+4
1/2f
Total =(3f+2) + (2f+4) + 4/5f +1/2f
=3f+2+2f+4 + 8f+5f/10
=5f + 6 + 13/10f
= 50f+13f/10 + 6
=63/10f +6
Equate the total weight
71/10f +2=63/10f +6
Collect like terms
71/10f - 63/10f =6-2
71f-63f/10 = 4
8f/10=4
Cross product
8f=40
Divide both sides by 8
f=5
Bridget's first fish =f = 5 ounces
Bridget's dad first fish = 3f +2
=3(5)+2
=15+2
=17 ounces
Bridget's dad first fish weighs 17 ounces
Please help ! First one to give correct answer gets brainliest!
Answer:
(4x+1)²
Step-by-step explanation:
!urgent! PLEASE HELP thanks will give brainliest
Answer:
the first four answers are all correct
*URGENT* Suppose 12 is raised to the second power, like this: 12^2.
Which answers show the inverse operation?
There is more than one correct answer. Select all that apply.
Answer:
12 ^ 1/2 or [tex]\sqrt{12}[/tex]
Step-by-step explanation:
12^2
We want to do the inverse operation, which is the square root
We can write the square root as
^ 1/2 or as [tex]\sqrt{ }[/tex]
So the inverse of squaring 12 is
12 ^ 1/2 or [tex]\sqrt{12}[/tex]
=======================================================
Explanation:
Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write
[tex]\sqrt{x} = x^{1/2}[/tex]
The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.
The more general rule is
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
which says the nth root of x is the same as x^(1/n).
Marcus played 3 different activities this week after school. The time he spent playing is described below. Swam forof an hour Played soccer for 9/10 2/3 2/4 of an hour Jogged forof an hour Which statement correctly compares the times of 2 of his activities?
Answer:
A
Step-by-step explanation:
We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.
Solve for a.
ab+c=d
a= b + c/d
a = b/(c-d)
a = (d - c)/b
Answer:
A=d-c/b
Step-by-step explanation:
Answer:
ab+c=d
Step-by-step explanation:
just took the test
The Cube root of 66 is between which two integers?
Answer:
4 and 5
Step-by-step explanation:
cube root of 66 is 4.041240021
Please Help Answer :(
Answer:
8 ^ 20
Step-by-step explanation:
(8 ^ 10) ^2
We know that a^ b^ c = a^ ( b*c)
8 ^ (10*2)
8 ^ 20
Niko is 3 times as old as Lila. Niko's age is the same as adding Lila's age to the product of 3 and Amber's age. Niko is 45 years old. Kameron's age is equal to 2 times the sum of Amber's age and Lila's age. How old is Kameron? years old
Answer:
Kameron is 50 years old.
Step-by-step explanation:
We can make equations and start filling in what we already know, assuming [tex]n[/tex] is Niko's age, [tex]L[/tex] is Lila's age, [tex]a[/tex] is Amber's age, and [tex]k[/tex] is Kamerons age.
Our first equation:
n = 3L
We know that Niko is 45, so
45 = 3L
Divide both sides by 3:
L = 15
So, Lila is 15 years old.
Another equation:
n = L + 3a
We already know Niko and Lila's age:
45 = 15 + 3a
Subtract 15 from both sides:
30 = 3a
Divide both sides by 3:
a = 10
So Amber is 10 years old.
Another equation:
k = 2(a + L)
We know Amber and Lila's age:
k = 2(10 + 15)
k = 2(25)
k = 50
So Kameron is 50 years old.
Hope this helped!
An NFL kicker will get paid based on the average hang time of his kicks. His average hang time is modeled by the following question: h=-16t^2 +97.6t. How many seconds do his kicks remain in the air on average?
Answer:
6.1 seconds
Step-by-step explanation:
set the equation equal to zero
0 = -16t² + 97.6t
factor out t
t(-16t + 97.6) = 0
-16t =- 97.6
t = 6.1
The NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.
To find the average hang time of the NFL kicker's kicks, we need to determine the time at which the height (h) reaches its maximum value. The maximum height corresponds to the peak hang time.
The equation that models the hang time is given as: h = -16t^2 + 97.6t
This is a quadratic equation in the form: h = at^2 + bt + c
In our case, a = -16, b = 97.6, and c = 0 (since there is no constant term).
The time (t) at which the height (h) reaches its maximum value can be found using the formula: t = -b / 2a
Let's calculate the time (t):
t = -b / 2a
t = -97.6 / (2 * -16)
t = -97.6 / -32
t = 3.05 seconds (rounded to two decimal places)
So, the NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.
To know more about air:
https://brainly.com/question/13700629
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Write the last 4 digits of a telephone number (each digit MUST be different--ex. 5237). List all the 4-digit numbers you can make using those 4 digits.
Answer:
5040
Step-by-step explanation:
All the possible Numbers that can be placed in the last for places =0,1,2,3,4,5,6,7,8,9
If all the digits have be different , then
= 10 x 9 x 8 x 7
= 90 x 56
= 5040 are total no. of 4-digit numbers can be made using those 4 digits.
Simplify this equation -8a-5a
Answer:
-13a
Step-by-step explanation:
Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.
Answer:
-13a
Step-by-step explanation:
These two numbers are already like terms, so you can subtract it easily.
First, don't look at the a.
-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.
Now that we now it equals -13, we can add the variable a back onto the answer. We get -13a.
Determine if the ordered pair (6, 4) is a solution to the inequality
Answer:
[tex]\Large \boxed{\mathrm{Option \ D}}[/tex]
Step-by-step explanation:
(6, 4)
x = 6 and y = 4
y > -1/2x + 7
Plug in the values to check if it is true.
4 > -1/2(6) + 7
4 > -3 + 7
4 > 4
This statement is false.
(6, 4) lies on the line.
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. A deer is 10 miles per hour faster than a bison.
3520/5280 = 2/3 of a mile per minute.
2/3 x 60 minutes per hour = 40 miles per hour.
40-30 = 10
Bison runs 40 miles per hour
The bison runs 10 miles an hour faster than the deer
Answer:
American bison is faster than the white-tailed deer by 10 more miles per hour.
Step-by-step explanation:
In 1 hour there are 60 minutes.
=> 3520 feet = 1 minute
=> 60 minutes = 3520 x 60
=> 211200 feet = 60 minutes
So, 211200 feet can be converted in miles.
=> 1 mile = 5280 feet
=> 211200 feet = x miles
=> x = 211200 / 5280
=> x = 40 miles per hour.
So, a white-tailed deer can run up to 30 miles per hour.
an American bison can run up to 40 miles per hour.
American bison runs 10 more miles per hour than a white-tailed deer.
What is the main difference between simplifying and solving? Which one gives you a value for a variable? How do you know the difference?
Answer:
when you simplify you continue until you get to the simplest form but when you solve you continue until you get an answer. Solving gives you a value for a variable. You mean simplify and get 2x - 10 but when you solve you continue until you get x as 5
Step-by-step explanation:
Answer: ok, so simplifying is when you make something less complex or complicated. Solving means an expression can be used for representating the solutions. for Example, say if you have the equation x+y=2x-1 is solved for the unknown x by the expression x=y+1. solving gives you the value for the variable. you know the difference by when you are simplifying you are trying to make the problem less complicated or less complex. and when you are solving you are trying to find the answer to the problem..
Step-by-step explanation:
(04.01 LC) The science club surveyed 50 students about the number of science courses in which they were enrolled and the time it took them to complete their homework. Classify the random variables from the survey. (2 points) Select one: a. Number of science courses, continuous; time to complete homework, continuous b. Number of science courses, continuous; time to complete homework, discrete c. Number of science courses, discrete; time to complete homework, continuous d. Number of science courses, discrete; time to complete homework, discrete e. Unable to determine from information given
Answer:
The correct option is;
c. Number of science courses, discrete; time to complete homework, continuous
Step-by-step explanation:
There are two types of random variables, discrete random variables and continuous random variables
Discrete random variables are variables that are always re-presentable by a finite countable number, such that discrete random variables can be taken as a count of items count
Therefore, as the number of science courses are fixed and such that a specific number can be ascribed to the courses at any time (except there are changes), is a discrete random variable
A continuous random variable is one whose possible values are infinite and are generally measurements of values of such as weight, height, time, and amount
Therefore, the time to complete the homework is a continuous random variable.
sin theta upon 1 + cos theta + 1 + cos theta upon sin theta is equals to 2 cosec theta prove
Answer:
Step-by-step explanation:
I'll use x instead of theta.
So we have:
sin x / ( 1 + cos x) + (1 +cos x) / sinx
The LCM is sin x(1 + cos x) so we have
sin^2 x + (1 + cos x)^2 / sin x(1 + cos x)
= sin^2 x + cos^2x + 2 cos x + 1 / sin x(1 + cos x)
Now sin^2x + cos^2x = 1 so:
= 2 + 2 cos x / sin x(1 + cos x)
= 2(1+ cos x) / sin x(1 + cos x)
The 1 + cos x is common so we have:
2 / sin x
= 2 cosec x.
A rope 40m long is used to form a rectangle. If the length of the rectangle formed is 4m longer than the width. Calculate the area of the rectangle
Answer:
96 sq. m
Step-by-step explanation:
If the width is x, the length is x + 4 and since perimeter = 2 * (length + width), we can write:
40 = 2(x + x + 4)
40 = 2(2x + 4)
20 = 2x + 4
16 = 2x
x = 8 so x + 4 = 12, therefore the area is 8 * 12 = 96 square meters.
Answer:
96m^2
Step-by-step explanation:
40=2(x+x+4)--> 2(2x+4).
20=2x+4
20-4=2x
16=2x
8=x
8✖️12=96m^2
A pair of parallel lines intersected by a transversal and forms same side interior angles that are in a 5:1 ratio. what are the measures of two same side interior angles?
Answer:
1st side: 150
2nd side: 30
PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
The correct answer is b.
Step-by-step explanation:
if you arrange the data set in ascending order you will have:
x y
-2 [tex]\frac{1}{100}[/tex]
-1 [tex]\frac{1}{10}[/tex]
0 1
1 10
3 1000
Exponential growth is an increase in a specific way of a data set over time. here, as x increases by a +1, y increases with ×10
Try making 100 using:
5,5,5,5,5
?=100
Help ASAP!
Answer:
(5+5+5+5)*5
20*5=100
[tex]5\cdot5\cdot5-5\cdot5=125-25=100[/tex]
Factorise using suitable identities (0.1x-0.2y)^2
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
a = 0.1x
b = 0.2y
(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²
= (0.1)²x² - 0.04xy + (0.2)²y²
= 0.01x² - 0.04xy + 0.04y²
The graphic below shows a protractor, which is used to measure angles. What is the level of accuracy of this measurement tool? its a projractor
Step-by-step explanation:
A protractor is a handheld to use in measuring angles. It is most cases made up of plastic or glass materials, and can accurately measure angles of circles up to 180°.
However, when measuring straight lengths, a ruler or tape has better measuring accuracy than the protector.
12. Write 0.8 as a fraction,
Pls explain in full detail.
Answer:
8/10
Step-by-step explanation:
10x10 is 100 8x10 would be 80 so 80/100=8/10
Answer:
8/10 = 4/5
Step-by-step explanation:
0.8 is 8-10th which means 8 divided by 10
reducing 8/10 to its lowest term since 8 and 10 has 2 as common factor, then
(8=2*4)/(10=2*5)
if 2 cancels out, then you are left with 4/5
Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The table shows the number of winning and losing spaces that could be on the wheel. Based on the ratio, complete the missing values in the table.
The correct answers are Losing 12; Winning 15
Explanation:
The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.
1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.
[tex]\frac{5}{6} = \frac{10}{x}[/tex] - Express the ratios using fractions; use x to show the missing value
[tex]5x = 60[/tex] - Cross multiply to find the value of x
[tex]x = 60 / 5[/tex] - Solve the equation to find x
[tex]x = 12[/tex] - The number of losing is 12 if there are 10 winning spaces
2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.
[tex]\frac{5}{6} = \frac{x}{18}[/tex]
[tex]6x = 90[/tex]
[tex]x = 90 / 6[/tex]
[tex]x =15[/tex] - The number of winning spaces is 15 if there are 18 losing spaces
Answer:
22 and 15 i know because i got it right on khan
Step-by-step explanation:
Please mark mine the brainliest !!
f(x) = x^2. What is g(x)?
The point shown on g(x) is (1,3)
If x = 1 and y = 3, this means x is multiplied by 3 ( 1 x 3 = 3)
This makes g(x) 3x^2
The answer is A.
Please could I have some help? Seven squared equals seven times .........
Answer:
[tex]\large \boxed{\mathrm{seven }}[/tex]
Step-by-step explanation:
[tex]7^2[/tex]
A number squared also means that the number is multiplied by itself twice.
[tex]7^2 =7 \times 7[/tex]
