You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.
C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.
D.
There is not enough information
Answer:
Hello again! Fellow Connexus user? Because I just had this on my Honors Algebra 1 test today. Anyways the answer is: A. x + y = 126 and 2.25x + 1.50y = 225.75; 49 Hot Dogs and 77 Sodas.
Step By Step Explanation:
To verify just use the substitution method to solve the equations x+y=126 and 2.25x + 1.50y = 225.75 then you'll get your x (Number of Hotdogs) and y (Number of Sodas)
Hope this helps!
The required equations are use to solve this problem;
[tex]x + y =126[/tex]
[tex]2.25x + 1.50y = 223.75[/tex]
There are x = 49 hot dogs, and y = 77 sodas were sold.
Given that,
Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
You sold a total of 126 hot dogs and sodas combined.
We have to determine,
What equations did you use to solve this.
And How many hot dogs were sold and how many sodas were sold.
According to the question,
Let, The x represent the number of hot dogs,
And y represent the number of sodas.
Then,
You sold a total of 126 hot dogs and sodas combined.
Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.
[tex]x + y =126[/tex]
And Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
Then,
Cost of each hot dogs + cost of each soda = total earning end of the night
[tex]2.25x + 1.50y = 223.75[/tex]
On solving both the equation,
[tex]x + y = 126\\\\x = 126-y[/tex]
Substitute the value of x in the equation 2,
[tex]=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77[/tex]
Then,
Substitute the value of y in the equation 1,
[tex]x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49[/tex]
Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.
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danny is offering 36$ for 4 hours of swimming lessons. Martin in offering 54$ for 3 hours of swimming lessons. whose offer is better
Answer:
Danny's offer is cheaper
Step-by-step explanation:
Danny is offering 36$ for 4 hours meaning you would do 36÷4=9 (9$ per hour)
Martin is offering 54$ for 3 hours so 54÷3=18 (18$ per hour)
Or the faster way of finding why is Danny is offering more hours for cheaper
Hope this helps
Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes? Find the z-table here. 6.68% 10.56% 89.44% 93.32%
Answer:
mean = 4.5
SD = 1.2
Z value = (3-4.5)/1.2 = - 1.25
Percentage based on z value = 1 - pnorm(1.25) = 0.1056498 = 10.56498%
The response times under 3 minutes is 10.56%
What is Normal Distribution?'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
mean = 4.5
SD = 1.2
Z value = [tex]\frac{3 - 4.5}{1.2}[/tex] = - 1.25
Percentage based on z value = 1 - pnorm(1.25)
= 0.1056498
= 10.56498%
Hence, we can conclude that the response time of fire station under 3 minutes is 10.56%.
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Help me pls :D Make the equations match with the number
Answer:
18 + s = 33 (drag to 15)
27 = 9 × s (drag to 3)
40 - s = 23 (drag to 17)
5 × s = 35 (drag to 7)
18/s = 3 (drag to 6)
m/5 = 10 (drag to 50)
m + 14 = 18 - m (drag to 2)
m + m + 12 = 22 (drag to 5)
n + 7 = 18 (drag to 11)
n-9 = 22 (drag to 31)
A student writes down four random numbers: -20, 55, 10, -15. A second students adds one number to the set, making the average 11. What number did the second student add to the set?
Answer:
-19
Step-by-step explanation:
-20 + 55 + 10 + -15 = 30
30 - 11 = 19
-19
-) Which is a valid velocity reading for an object? O 45 m/s O 45 m/s north 23 O O m/s south O 0 m/s ok Save and Exit Next Mark this and return
Answer:
Step-by-step explanation:
0 can't have a direction. It does not move. It has no speed component. Therefore 0 m/s south is not the answer.
45 m/s has no direction stated. It is just a speed, not a velocity.
45 m/s north is a velocity. It has both speed and direction.
List all the factors of 19. Tell whether 19 is prime or composite.
Answer:
19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)
Step-by-step explanation:
simply the problem pls answer quick
[tex]\\ \sf\Rrightarrow 1\dfrac{2}{5}m-\dfrac{3}{5}(\dfrac{2}{3}m+1)[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{7}{5}m-\dfrac{3}{5}(\dfrac{2m+3}{3})[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{7m}{5}-\dfrac{6m+9}{15}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{21m-6m-9}{15}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{15m-9}{15}[/tex]
[tex]\\ \sf\Rrightarrow m-\dfrac{3}{5}[/tex]
The simplified form of the expression is m - 3/5
Given the expression 1 2/5 m - 3/5 (2/5m + 1)
We need to simplify the term. Expand the bracket to have:
1 2/5 m - 3/5 (2/3m + 1)
1 2/5 m -2/5 m - 3/5
7/5 m - 2/5 m - 3/5
(7m-2m)/5 - 3/5
5m/5 - 3/5
m - 3/5
Hence the simplified form of the expression is m - 3/5
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Pls HELP meeee. My child needs some real help I I wish I would’ve took those college lessons.
Answer:
75%
Step-by-step explanation:
100/64*48=75%
Which of the following satisfy x ≥ 4.1? Select all that apply.
x = 4
x = 3.5
x = 4.5
x = 4.1
Answer:
x = 4.5
x = 4.1
Step-by-step explanation:
Can someone help me?
Answer:
just make something that is eqivalant to 4= or 14=
Step-by-step explanation:
2/3 divided by 10
PLEASE answer
Answer:
1/15
Step-by-step explanation:
2/3 x 1/10 = 2/30 or 1/15
Answer:
1/15
Step-by-step explanation:
7 x [(7 + 7) = 7
Help plz
Answer:
[tex] \frac{1}{14} [/tex]
Step-by-step explanation:
7 x (7+7)=7
7x [(14)]=7
x=
[tex] x = \frac{1}{14} [/tex]
Brainliest if correct What kind of coin is coin B And coin C
Answer:
coin B
Better Date 2000 American Silver Eagle 1 Troy Oz .999 Fine Silver BU Unc
Coin C
1923 United Kingdom Great Britain GEORGE V Silver Florin 2 Shillings Coin i63027
you can get those coins from ebay
Which statement is true about the value of 1-5/?
O It is the distance that -5 is from 0 on the number line.
O It is the distance that -5 is from 5 on the number line.
O It is less than 5.
0 It is greater than 5.
Answer:
O It is less than 5.
Step-by-Step
OK so, first u check if it has a negative. It does, so its at the left of 0. SO you know its less than.
?/5 =8/10 type the missing number that makes this fraction equal
Answer:
4/5 = 8/10
Step-by-step explanation:
x/5 = 8/10
x = 8/10 × 5
x = 4
Please Help - Suppose f(t)=6t−8−−−−√.
(a) Find the derivative of f.
f′(t) =
-3/(sqrt(t-8)(t-8))
(b) Find an equation for the tangent line to the graph of y=f(t) at the point (t,y)=(33,6/5).
Tangent line: y =
[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]
(b)
[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]
Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units
down on the parent function f(x)=x^2
Answer: The graph for x cubed has a steep incline levels for a little before another steep incline
explanation: Since choice B is the only one that looks like this the answer is B
What is this in simplest form?
Ax+2y=10 through the point (4,3)
Answer:
can you give more context to the question and I will answer it in the comments? thanks!
Answer:
Slope-intercept form y=10x-37
Point slope form y-3=10(x-4)
Step-by-step explanation:
Find the sum of 12.351 and 0.5362
Find the sum of 12.351 and 0.5362
Answer:-12.351 + 0.5362 = 12.8872
212 + 115 × 6 + 968 HELP ME please!
Answer:
1870
Step-by-step explanation:
Answer : 1,870
Step - by - step explanation :
When there is multiple math signs in a problem you use PEMDAS . . .
Parentheses, Exponents, Multiplication and Division ( from the left side to right ), Addition and Subtraction ( from the left side to right )
212 + 115 x 6 + 968 --> 212 + 690 + 968
212 + 690 + 968 --> 902 + 968
902 + 968 --> 1,870
Use logarithms to solve the equation 5^x = 3^(2x-1), giving your answer correct to 3 significant figures.
[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]
The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):
Take the natural logarithm (ln) of both sides:
ln(5^x) = ln(3²ˣ⁻¹)
Apply the logarithm rule: ln(a^b) = b * ln(a):
x * ln(5) = (2x - 1) * ln(3)
Expand the equation:
x * ln(5) = 2x * ln(3) - ln(3)
Move the terms with "x" to one side of the equation:
x * ln(5) - 2x * ln(3) = -ln(3)
Factor out "x" from the left side:
x * (ln(5) - 2 * ln(3)) = -ln(3)
Solve for "x":
x = -ln(3) / (ln(5) - 2 * ln(3))
Now, we can calculate the value of "x" using a calculator:
ln(3) ≈ 1.099
ln(5) ≈ 1.609
x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864
Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
Learn more about natural logarithm from the link given below.
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Help
This is a a or b question
Answer:
A. (A) Yes
B. (A) Yes
C. (B) No
Step-by-step explanation:
A is Categorical because it is not based on numbers.
B is Categorical because it is not based on numbers.
C is Not Categorical because it is based on numbers.
Of 92 adults selected randomly from one town, 61 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Group of answer choices 0.582 < p < 0.744 0.548 < p < 0.778 0.536 < p < 0.790 0.566 < p < 0.760
A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
The formula for calculating the confidence interval is expressed as;
[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]
p is the proportion = 61/92 = 0.66n is the sample size = 92z is the z-score at 90% = 1.645Substitute the given parameters into the formula to have:
[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]
Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
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What is the volume of the following cylinder?
150.72 in. 3
301.44 in. 3
75.36 in. 3
602.88 in. 3
Answer:
150.72 in³
Step-by-step explanation:
We know that
Radius = Diameter/2
Radius = 8/2
Radius = 4 in
Now,
Volume of cylinder = πr²h
=> 3.14 × (4)² × 3
=> 3.14 × 16 × 3
=> 150.72 in³
Answer:
The correct answer is option 150.72 in³.
Step-by-step explanation:
Given :
✧ Diameter of cylinder = 8 in.✧ Height of cylinder = 3 in.To Find :
✧ Volume of cylinderUsing Formula :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\pink{V = \pi{r}^{2}h}}}}}}[/tex]
»» r = Radius »» D = Diameter »» V = Volume »» h = heightSolution :
Firstly, finding the radius of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{8}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = 4 \: in}}}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 4 \: in}}}}}}[/tex]
Hence, the radius of cylinder is 4 in.
[tex]\rule{300}{1.5}[/tex]
Now, finding the volume of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4)}^{2} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4 \times 4)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(16)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314}{100} \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 16 \times 3}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 48}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{15072}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of cylinder is 150.72 in³.
[tex]\rule{300}{1.5}[/tex]
Quadratic functions 30pt
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2
Slope of line segment
= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)
= \frac{4 + 8}{5 + 7}=5+74+8
= \frac{12}{12}=1212
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)
Midpoint of line segment
= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)
= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Which of the following is the decimal counterpart of the binary number 10012? a. 9 b. 10 c. 11 d. 12
Answer:
maybe it's 12 but i don't know...
Enter the number that belongs in the green box
Answer:
8
Step-by-step explanation:
The diagonals of a parallelogram divide each other into two equal parts.
A’= _ , _
B’= _ , _
C’= _ , _
Answer:
if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)
