3. Olivia ordered 24 cupcakes and a layer cake. The layer cake cost $16 more than one
cupcake, and the total cost of the order was $53.50. What was the price of each cupcake?
a) Define a variable for the cost of one cupcake.
b) Write an expression to represent the cost of a layer cake.
c) Write and solve an equation.
d) Interpret your solution within the context of the problem.
Answer:
$2.14
Step-by-step explanation:
x = price
24x+(x+16) = 53.5
25x+16 = 53.5
25x+53.5
x=53.5/25=2.14
(5b+6)°
(4b-6)°
answer B=
Answer:
B = 10
Step-by-step explanation:
5B + 6 + 4B - 6 = 90
9B + 0 = 90
Therefore, B = 10
3 to the 7th power time 3 to the -4th
Answer:
3 to the 3rd power
Step-by-step explanation:
Leslie gained 5.54 pounds between her third and fourth birthdays. If she weighed 42.48 pounds when on her fourth birthday, how much did she weigh in pounds on her third birthday? Does this mean to add or subtract? Pick the correct operation and solve ONLY that one.
Answer:
We Subtract
Her weight on her third birthday = 36.94 pounds
Step-by-step explanation:
Does this mean to add or subtract? This means we add. The operation we are using is SUBTRACTION
Leslie GAINED 5.54 pounds between her third and fourth birthdays.
This means she added weight
She weighed 42.48 pounds on her Fourth birthday
Hence, Her weight in her third birthday is:
Third birthday + 5.54 pounds = 42.48
$42.48
Third birthday = 42.48 - 5.54
= 36.94 pounds
Her weight on her third birthday = 36.94 pounds.
The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Given :
The ratio of the number of adults to the number of students at a field trip has to be 3:8.
During a current field trip, there are 190 more students on the trip than there are adults.
To Find :
How many students are attending the field trip? How many adults?
Solution :
Let, number of adults are x.
So, number of students are x + 190.
We know :
[tex]\dfrac{x}{x+190}=\dfrac{3}{8}\\\\8x = 3(x+190)\\\\8x -3x = 570\\\\5x = 570\\\\x = 114[/tex]
Number of students are 114 and number of adults are 114+190 = 304.
Hence, this is the required solution.
Simplify the expression.
7/4÷(3/2)
7/4 ÷ (3/2)
=7/4 × (2/3)
=(7×2)/(4×3)
=14/12
=(14÷2)/(12÷2)
=7/6
=1 1/6
12
Mackenzie wants to buy a backpack that cost $60. If the tax rate is 7.5%, how much tax will she
pay?
Answer:
$4.5
Step-by-step explanation:
I'm gonna do my work on paper.
a body of mass 10kg acted upon by a force of 40N for 0.5secs. Find the:(i)impulse on the body. (ii)final speed of the body. (iii)distance covered within the time interval.
Step-by-step explanation:
20n 20394848484848575
The impulse on the body is 20 kg-m/s, the final speed of the body is 2m/s, and the distance covered within the time interval is 0.5m.
What is Force?Force is the strength applied on an object with mass to change its state of motion.
The mass of the body is 10kg.
The force applied on the object is 40N.
The time for which the force is applied is 0.5 sec.
The impulse on the body is calculated by,
Impulse = Force * Time
Impulse = 40 * 0.5
Impulse = 20 kg-m/s
The final speed of the body is given by
v = u + at
Assuming the initial speed = 0
v = at
Acceleration = Force / mass
Acceleration = 40/10
a = 4 m/s²
v = 4 * 0.5
v = 2 m/s
The distance covered within the time interval is given by,
s = ut + (1/2) at²
s = (1/2) at²
s = (1/2) 4 * 0.5 *0.5
s = 0.5 m
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3/5 ÷ 1 1/4. plz help
Answer:
12/25 (0.48 in decimal form)
Step-by-step explanation:
3/5 divided by 1 1/4
Make 1 1/4 an improper fraction:
1 1/4 = 5/4
Now we flip 5/4 (the second fraction) when we divide and then multiply it by the first fraction.
Our equation now:
3/5 x 4/5
After multiplying across, you get 12/25 (0.48 in decimal form).
Hope this helps!
3x²-75=0 find the square root
Answer:
[tex]x=\pm5[/tex]
Step-by-step explanation:
First, add 75 to each side.
[tex]3x^2-75+75=0+75\\3x^2=75[/tex]
Next, divide each side by 3.
[tex]x^2=25[/tex]
Now, you can take the square root.
[tex]x = \pm\sqrt25}[/tex]
[tex]x=\pm 5[/tex]
If sydney answer 15 questions in the first section correctly what is the minimum number of questions she must have answered correctly in the second section
Answer:
8 Is correct on EDGE 2020
Step-by-step explanation:
Just took the test and got it right
The question was incomplete. Below you will find the missing content.
The questions on the first section on a test value 3 points and the questions in the second section carries 5 points. if sydney answer 15 questions in the first section correctly what is the minimum number of questions she must have answered correctly in the second section.And the maximum points she scored is 80.
Answer:
Sydney must have answered at least 8 answers in the second section.
Concept
What is Inequality?
Inequality is a condition which compare algebraic expression using greater than(>), less than(<) symbols. It also shows values greater than equal to(≥), less than equal to(≤) and not equal to(≠) signs to solve the equation.
let x represent the number of correct questions in the first section, and let y represent the number of correct questions in the second question.Therefore the inequality representing her score is 3x + 5y > 80
Solution:
Following the inequality 3x+5y>80, 3x represents sydney's score in the first section which is equal to 3ₓ15 = 45
Now she needs to solve 8 questions in the second section to score
5 ₓ 8 = 40 for the inequality to be maintained.
i.e 3 ₓ 15 + 5 ₓ 8 > 80
45 + 40 > 80
85 > 80
If she solves 7 questions in the second section then the total score will be 45 + 45 ⊅ 80
Therefore sydney answers 8 questions correctly in the second section.
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A) the quantity in column A is larger
B) the quantity in column B is larger
C) the two quantities are equal
D) relationship cannot be determined with the given information
Answer: A
The number of distinctive prime factors in Column A is 60.
The number of distinctive prime factors in Column B is 30.
This number is 1/2 half more prime factors.
There is 30 more prime factors, so the answer is A.
The quantity in column A is larger than column B.
Becky needs to choose a new cell phone plan. She has 2 choices. Carolina Cell offers a monthly fee of $20.79 and $2.00 for each gigabyte of data used. Sanford Cell offers a monthly fee of $22.89 and $1.50 for each gigabyte of data used. What is the amount of gigabytes, to the nearest tenth, when both plans would cost the same?
Answer:
4.2 gigabytes
Step-by-step explanation:
To find the answer, you need to write an equation where the cost of Carolina Cell is equal to the cost of Sanford Cell:
20.79+2x=22.89+1.50x, where x is the number of gigabytes used.
Now, you can solve for x:
2x+1.50x=22.89-20.79
0.5x=2.1
x=2.1/0.5
x=4.2
According to this, the answer is that both plans would cost the same when 4.2 gigabytes are used.
What is the value of x?
A)9.4
B)7
C)-9.4
D)-7
Answer:
we need to see the problem
Step-by-step explanation:
try sending a picture
Hi purple (I think that was your name) please hopefully you see this I was messing around with this app and I logged out I was logged in with my old school email so now it doesn’t work so I had to make this acc it’s my school new school email please send me the pic of the carnival hw again please.
Answer:
I'm sorry but I don't know how to do function notation. I'm so sorry that I couldn't help you with this.
Two lines are parallel. Which of the following statements are true?
Select two answers that apply.
The lines do not intersect.
The lines have the same slope.
The lines intersect and form 4 right angles.
The lines intersect and form two pairs of congruent opposite angles, one acute pair and one obtuse pair.
Answer:
The lines do not intersect. and The lines have the same slope.
Step-by-step explanation:
The two statements that are true for parallel lines are:
The lines do not intersect.
The lines have the same slope.
Here, we have,
given that,
Two lines are parallel.
we have, given options are:
The lines do not intersect.
The lines have the same slope.
The lines intersect and form 4 right angles.
The lines intersect and form two pairs of congruent opposite angles, one acute pair and one obtuse pair.
now, we know that,
Parallel lines never intersect, and their slopes are equal.
The other two statements, that the lines intersect and form 4 right angles or two pairs of congruent opposite angles (one acute pair and one obtuse pair), are characteristics of perpendicular lines, not parallel lines.
so, we get,
The two statements that are true for parallel lines are:
The lines do not intersect.
The lines have the same slope.
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A cubic meter (m³) is ________. a cubic centimeter (cm³).
a.equal to
b.smaller than
c.larger than
d.diferent form
Answer:
It would be larger than
Step-by-step explanation: hope this helps
Solve 5(x + 3) = 3x - 4
Show clear algebraic working,
Answer:
5(x + 3) = 3x - 4
=> (5 * x ) + (5 * 3) = 3x - 4
=> 5x + 15 = 3x - 4
=> 5x = 3x - 4 - 15
=> 5x - 3x = -4 - 15
=> 2x = -19
=> x = -19/2
=> x = -9.5
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Solve for k.
4.5 + 1.5k = 18 - 3k
Answer:
k = 3
Step-by-step explanation:
Given
4.5 + 1.5k = 18 - 3k ( add 3k to both sides )
4.5 + 4.5k = 18 ( subtract 4.5 from both sides )
4.5k = 13.5 ( divide both sides by 4.5 )
k = 3
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
[tex]4.5+1.5k=18-3k[/tex]
Subtract 4.5 to both sides
[tex]15k=13.5-3k[/tex]
Add 3k to both sides
[tex]4.5k=13.5[/tex]
Divide both sides by 4.5 to get k alone
[tex]\frac{4.5k}{4.5} =\frac{13.5}{4.5}[/tex]
[tex]k=3[/tex]
Hope this helps can pls do mark me brainliest:)
4 more then a number squared? expression form
Answer:
4 + x²
Step-by-step explanation:
Given problem:
4 more then a number squared
Problem:
Give the expression form;
Solution:
Let the number x;
So;
4 more than x squared:
4 + x²
X+4y=8 identify the x intercept
Answer: (8, 0)
Step-by-step explanation:
X intercept is when y = 0
[tex]x+4*0=8\\x=8[/tex]
5. 27a3+216b3 ???
tomorrow is the submission :(
Answer:
(3a +6b) (9a² - 18ab + 36b²)
Step-by-step explanation:
27 = 3 * 3 * 3 = 3³
216 = 6 * 6 * 6 = 6³
a³ + b³ = (a + b)(a² - ab + b²)
27a³ + 216b³ = (3a)³ + (6b)³
= (3a + 6b)( (3a)² - 3a*6b + (6b)² )
= (3a +6b) (9a² - 18ab + 36b²)
at the beginning of grade 6 the number of advanced math to the number of regluar math students was 3:8 however after taking placement tests students were moved around chaning the ratio of the number of advanced math students to the number of regluar math students was 4:7 how many student students started in reglaur math and advanced math if there were 92 students in advanced math after the placement test. Please tell me how to do this on a tape diagram
Answer:
There were 69 students in advanced math and 184 students in regular math before the placement tests
Step-by-step explanation:
The correct question
At the beginning of 6th grade, the ratio of the number of advanced math students to the number of regular math students was 3:8. However, after taking placement tests, students were moved around changing the ratio of the number of advanced math students to the number of regular math students to 4:7. How many students started in regular math and advanced math if there were 92 students in advanced math after the placement tests?
Let
x ----> the number of advanced math students
y ----> the number of regular math students
we know that
At the beginning of grade 6
----> equation A
After taking placement tests
----> equation B
----> equation C
Remember that
The total number of students at the beginning of grade 6 is the same that the number of students after taking placement tests
step 1
Find out the total number of students after taking placement tests
we have
----> equation B
----> equation C
substitute the value of x in equation B and solve for y
The total number of students after taking placement tests is
step 2
Find out how many students started in regular math and advanced math
we have that
At the beginning of grade 6
----> equation A
-----> equation D
Solve the system of equations by graphing
The solution is the intersection point both graphs
using a graphing tool
The solution is the point (69,184)
see the attached figure
therefore
There were 69 students in advanced math and 184 students in regular math before the placement tests
Answer:
:o
Step-by-step explanation:
The mean test score of 28 students is 72.
A student joins the class and the mean becomes 71.
Find the test score of the student who joined the class.
Test score =
Answer:
test score of new student = 43
Step-by-step explanation:
28 x 72 = 2016 (total points class scored)
29 x 71 = 2059 (total points class scored after student joined)
2059 - 2016 = 43
The test score of the student who joined the class is 43.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The mean test score of 28 students is 72.
A student joins the class and the mean becomes 71.
We have to find the test score of the student who joined the class.
28 x 72 = 2016
29 x 71 = 2059 (total points class scored after student joined)
The difference between 2016 and 2059 is the test score of new student.
2059 - 2016 = 43
Hence, the test score of the student who joined the class is 43.
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Sylvie and Bono hiked to the 6,288-ft summit of Mount Washington, then hiked to Carter Notch Hut for the night. Carter Notch Hut is located at an elevation of 3,288 ft. A number line going from negative 4000 to positive 4000 in increments of 1000. Which point represents the change of elevation in feet on the hike from the summit to Carter Notch Hut? –4000 –3000 3000 4000
Answer:
- 3000 feets
Step-by-step explanation:
Given that:
Elevation at the summit of Mount Washington = 6288 ft
Elevation of Carter Notch Hut = 3,288 feets
The change of elevation in feets on the hike from summit to Carter Not hut:
Difference in elevation:
Summit at Mount Washington - Carter notch hut
6288 ft - 3288 ft
Change in elevation. = 3000 fts
Since the change decreased from 6288 to 3288, the elevation is downward and hence, negative = - 3000 feets
Answer:
b
Step-by-step explanation:
Last week, Shelly tode her bike a total of 30 miles over a three-day period.
On the second day, she rode the distance she rode on the first day.
On the third day, she rode the distance she rode on the second day.
rts
How many miles did Shelly ride on each day? Select your answers from the drop-down lists.
On the first day, Shelly rode
miles.
On the second day, Shelly rode
miles.
ols
On the third day, Shelly rode
miles.m
Answer:
Step-by-step explanation:
ON THE FIRST DAY, SHELLY RODE 12 MILES
If f(x) = 3x – 7 and g(x) = -x, what is
the value of f(g(2))?
Answer:
C. -19
Step-by-step explanation:
take 2 plug it into g(x)=-x^2 that gives you -4 take that number and plug it into f(x)=3x-7 that gives you -19
Answer:
C) -19
Step-by-step explanation:
Step 1: Define
f(x) = 3x - 7
g(x) = -x²
Step 2: Find g(2)
g(2) = -(2)²
g(2) = -4
Step 3: Find f(g(2)) or f(-4)
f(-2) = 3(-4) - 7
f(-2) = -12 - 7
f(-2) = -19
The formula to convert °F to °C is C = C equals StartFraction 5 Over 9 EndFraction left-parenthesis F minus 32 right-parenthesis.(F – 32).
Convert 50°C to °F.
Answer:
122
Step-by-step explanation:
Find x and y in each figure.
Answer:
[tex]by \:alternate \: interiar \: angle \: \\ (8y + 2) + (25y - 20) = 180 \\ 8y + 2 + 25y - 20 = 180 \\ 33y - 18 = 180 \\ 33y = 180 + 18 \\ 33y = 198 \\ y = 6 \\ \\ now \\ by \: \: linear \: pair \: \\ 10x + 8y + 2 = 180 \\ 10x + 48 + 2 = 180 \\ 10x = 180 - 50 \\ 10x = 130 \\ x = 13[/tex]
so finallyX=13and y=6-------------------------a=24
C=26
What is the length of b?
Answer:
10
Step-by-step explanation:
you use the Pythagorean theorem which you do 24^2 + b^2 = 26^2 you should have 576+b^2=676 then subtract 576 on both sides b^2=100 then sqre root which leaves you with b=10