The best way to solve these sorts of problems that involve two factors of unknown quantities but with certain properties is to use equations:
Let's set some variables
h: # of hot dogs solds: # of sodas soldNow based on the information given by the question, let's set up some equations:
vender sold a combined total of 166 sodas and hot dog⇒ [tex]s + h = 166[/tex]
number of hot dogs sold was 54 less than the number of sodas sold⇒ h = s - 54
Now lets put the equation together
s + h = 166 -- equation 1
h = s - 54 -- equation 2
Solve:
Plug the value of h from equation 2 into equation 1
s + (s - 54) = 166
2s - 54 = 166
2s = 220
s = 110 -- equation 3
Plug the value of s from equation 3 into equation 2
h = 110 - 54 = 56
h = 56
Therefore:
number of sodas sold: 110number of hot dogs sold: 56Hope that helps!
What is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree, and enter the number only.
Answer: 13°
Explanation: x = tan^-1 ( 9/40) ≈ 13°
Lela bought 3.3 pounds of nuts they cost $1.79 a pound. How much money did she spend
Answer:
5.907
Step-by-step explanation:
I believe if you multiply 3 times 1.79 you get 5.37 then if you multiply 0.3 times 1.79 you get 0.537. If you combine the 2 you get 5.907. I think this is correct not sure though D:
7(5/14a-5/21)-1/12(3a+6)
[tex]\sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex] or [tex]\sf \dfrac{54a-52}{24}[/tex]
======================================
[tex]\sf \rightarrow 7\left(\dfrac{5}{14}a-\dfrac{5}{21}\right)-\dfrac{1}{12}\left(3a+6\right)[/tex]
use distributive method
[tex]\sf \rightarrow \dfrac{5a}{2}-\dfrac{5}{3}-\dfrac{a}{4}-\dfrac{1}{2}[/tex]
group terms
[tex]\rightarrow \sf \rigtharrow \dfrac{5a}{2}-\dfrac{a}{4}-\dfrac{5}{3}-\dfrac{1}{2}[/tex]
make the denominators same
[tex]\rightarrow \sf \rigtharrow \dfrac{2(5a)}{4}-\dfrac{a}{4}-\dfrac{2(5)}{6}-\dfrac{3(1)}{6}[/tex]
simplify
[tex]\rightarrow \sf \rigtharrow \dfrac{10a-a}{4}-\dfrac{10+3}{6}[/tex]
answer in separate constants
[tex]\rightarrow \sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]
make the denominators same
[tex]\rightarrow \sf \dfrac{6(9a)}{24}-\dfrac{4(13)}{24}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{54a}{24}-\dfrac{52}{24}[/tex]
join both fractions
[tex]\rightarrow \sf \dfrac{54a-52}{24}[/tex]
Answer:
[tex]\boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]
Step-by-step explanation:
[tex]7(\dfrac{5a}{14} - \dfrac{5}{21} ) - \dfrac{(3a + 6)}{12}[/tex]
Step-1: Simplify the distributive property
⇒ [tex]\dfrac{35a}{14} - \dfrac{35}{21} - \dfrac{(3a + 6)}{12}[/tex]
Step-2: Make common denominators
⇒ [tex]\dfrac{35a \times 3}{14 \times 3} - \dfrac{35 \times 2}{21 \times 2} - \dfrac{7 \times (3a + 6)}{12 \times 7}[/tex]
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{7 \times (3a + 6)}{84}[/tex]
Step-3: Simplify the distributive property
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a + 42}{84}[/tex]
Step-4: Rewrite (21a + 42)/84 in a different way
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a}{84} + \dfrac{42}{84}[/tex]
Step-5: Add/Subtract if necessary
⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}}[/tex]
Step-6: Simplify the fractions
⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}} = {\dfrac{9a}{4} - \dfrac{49}{42}} = \boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]
please help me please pleasr please
Answer:
which one's anwer you want
2. length= 65 ft width=24 m area=135 in2
I don’t know what is the least common factor of 18 and 12.
Answer:
the common factors for both are 1,2,3,6
is this correct?
A.yes
B. No
C. Maybe
D. I DUNNO???!!!
Answer:
its yes
Step-by-step explanation:
because it's x 2 I hope this helps
am I right? please only answer if you are positive that you’re correct. thank you!
Answer:
yes you are correct :)))
Give the dimensions of 2 solids with equal surface area and different volume
Two solids with the same surface and different volumes are a cube of side length of 1 unit, and a sphere of radius of 0.69 units.
How to find the two solids?
First, let's define a cube of a side length of 1 unit. The surface of this cube is equal to 6 times the area of one of the faces, or:
S = 6*(1 unit square) = 6 units square.
And the volume is equal to the side length cubed, so we have:
V = (1 unit)^3 = 1 unit cubed.
Now, let's find a sphere with the same surface than our cube. For a sphere of radius R, the surface is:
S = 4*3.14*R^2
Then we must have:
4*3.14*R^2 = 6 units square
R = √(6/(4*3.14)) units = 0.69 units.
And the volume of this sphere is:
V = (4/3)*3.14*R^3 = (4/3)*3.14*(0.69 units)^3 = 1.38 cubic units.
So the sphere has the same surface and more volume.
If you want to learn more about solids, you can read:
https://brainly.com/question/10171109
Determine the perimeter of the figure below:
6 cm
5 1/2
helpppp
Answer:
•SEE BELOW••WHAT IS PERIMETER?
>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE
NOW,LET'S SEE YOUR GIVEN QUESTION.
THE FIGURES 2 SIDES DATA IS GIVEN
•6CM
•5.5CM
THEREFORE : 6 + 5.5
: 11.5 CM
THE PERIMETER OF FIGURE IS 11.5 CM
The first term of an A.P is 3 and the fifth term is 9.Find the number of terms in the progression if the sum of the progression is 81.
Answer:
its A becauss i tryed b and th en i tried A so its a
I need help please give explanation and thank you
50% of the population are within one standard deviation.
O True
O False ???
Answer: False
Step-by-step explanation:
68%
Key Takeaways. The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
Let a represent a non zero rational number and let b represent an irrational number. Which expression could represent a rational number?
The operation between a rational and a irrational number that results in a rational number is a multiplication, hence the expression ab could represent a rational number.
What are rational and irrational numbers?If a number can be represented by a fraction, it is rational, otherwise, it is irrational.
The addition/subtraction of a rational and an irrational numbers is irrational, while the multiplication is rational, hence the expression ab could represent a rational number.
More can be learned about rational numbers at https://brainly.com/question/10814303
A vet is preparing a diet for a group of dogs. Each serving should be no larger than 8
ounces and must contain at least 29 units of Nutrient I and at least 20 units of Nutrient II.
The diet will be prepared from a combination of 2 brands, brand A and brand B. Each ounce
of brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of brand B
contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 3 cents/ounce and B
costs 4 cents/ounce. Determine how many ounces of each brand of dog food should be used
per serving in order to meet the given requirements at a minimum cost.
Find the 18th term in the arithmetic sequence.
2, 8, 14, 20, 26, ...
87
110
104
102
Answer:
104
Step-by-step explanation:
1st term + or - common difference (term -1)
common difference is +6
2 + 6 (18-1)
2 + 6 (17)
2 + 102
104
Tori made a scale drawing of an Italian
restaurant. The restaurant's kitchen is 2
millimeters long in the drawing. The actual
kitchen is 16 meters long. What scale did Tori
use for the drawing?
1 millimeter :
meters
Step-by-step explanation:
2mm : 16m
so to get 1mm you need to divide 16 by 2
16/2 is 8 therefore
1mm : 8m
1 millimeter represents 8 meters in real life
hope that helps :)
how do i solve this?
Answer:
33
Step-by-step explanation:
For 4 triangles area 4*(1/2)*4*3=24
base square area 3*3=9
all together 24+9= 33
can someone please help me with this question???? its an exam study guide and i dont understand it
Josef owns four par value $1,000 bonds from Dowc Beverage Co. Each bond has a market value of 104.561 and gives 9.2% interest. Josef also owns 170 shares of stock in Dowc Beverage Co. Stock in Dowc Beverage Co. has a share price of 26.25 and pays a dividend of $2.38. If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, which aspect of Josef’s investment in Dowc Beverage Co. has a greater percent yield, and how much greater is it?
a.
The stocks have a yield 2.15 percentage points higher than that of the bonds.
b.
The stocks have a yield 0.27 percentage points higher than that of the bonds.
c.
The bonds have a yield 1.35 percentage points higher than that of the stocks.
d.
The bonds have a yield 2.08 percentage points higher than that of the stocks.
Answer:
If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, then the bonds have a yield 1.35 percentage points higher than that of the stocks.
Step-by-step explanation:
Help picture below problem 11
Answer:
Missing Angle = 26⁰ ( corresponding angles )
PLEASE HELP PLEASE PLEASE HELP
Answer:
I believe it is Dissolve.
please help and please leave a legit answer
Answer:
y= -12/x + 3
Step-by-step explanation:
Here's my answer
Why 10^33/2=5*10^32? Explain, pls. :(
Answer:
see below
Step-by-step explanation:
10^33/2
Rewriting the numerator as 10 * 10 ^ 32
10 * 10 ^32
--------------------
2
10/2 = 5
5 * 10 ^32
Therefore
10^33/2=5*10^32
Factor the equation 4x^2-20x+25
Answer:
[tex](2x - 5)^2[/tex]
Step-by-step explanation:
[tex]y = 4x^2 -20x + 25\\\rightarrow (2x - 5)(2x - 5)\\\rightarrow (2x - 5)^2\\\\\text{checking...}\\(2x - 5)^2 = (2x - 5)(2x - 5) = 4x^2 - 10x - 10x + 25 = 4x^2 - 20x + 25[/tex]
Solve for x. Round to the tenths place. Can somebody help
Answer:
12.12
Step-by-step explanation:
7^2+x^2=14^2, as by the Pythagorean theorem.
49+x^2=196,
x^2=147,
square root of 147;
it's close to 144,
thus, 12.12
A rectangular playground measures 5/8 mile long and 1/4 mile wide. What is the area, in square miles, of the playground?
Answer:
5/32 square miles or 0.15625 square miles
Step-by-step explanation:
1/4 miles × 5/8 miles
=5/32 square miles or 0.15625 square miles
Find the domain and range of the function graphed below.
Domain:
Range:
The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
How to find the domain and range of a functionThe domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
Note that point where the circles are shaded shows a closed interval
Learn more on domain and range here: https://brainly.com/question/1942755
BRAINLIEST GIVEN)The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
Enter your answer in the box.
Answer:
238
Step-by-step explanation:
You have to find the area for each box and then you add all of them together
Answer:
238 mm²
Surface area of rectangular prsim = 2(lw + lh + wh)
Here,
length = 11 mm
width = 4 mm
height = 5 mm
area:
2*(4*11+5*11+5*4)238 mm²Select the correct answer. The total cost of a flower bouquet depends on the types of flowers in the arrangement. A bouquet containing 6 roses, 3 lilies, and 2 carnations costs $26.75. A bouquet containing 3 roses, 4 lilies, and 5 carnations costs $25.50. A bouquet containing 1 of each flower costs $6.75. Which system of equations represents this situation, where rrepresents the number of roses, /represents the number of lilies, and c represents the number of carnations?
Answer: Roses 2.70 Lillies 2.45 Carnations 1.60
Step-by-step explanation:
I dont know if its wrong its mostly correct but hope it helps
Two gears are connected and rotating at the same time. The smaller gear completes 2 1/2 rotations every time the larger gear completes 1/4 of a rotation.
How many rotations does the smaller gear complete when the larger gear completes 1 rotation?
A.1/10
B. 5/8
C. 5
D. 10
The small does 2 1/2 for 1/4 of the large. Multiply by 4 to get a full rotation of the large one:
2 1/2 x 4 = 10
answer: D. 10
A pool measuring 10 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1380 square meters, what is the width of the path?
Answer:
112m
Step-by-step explanation:
A = lw
A = 10(26)
A = 260
1380 - 260 = 1120
1120 = 10(w)
1120 / 10 = 112