Step-by-step explanation:
college level ? what teacher puts such a question in on college level ? and you can't answer this ?
that is middle school basics.
what is going on ?
x can have in the defined interval the integer values
2, 3, 4, 5, 6
there, that was all to it ...
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was5%, and the tax in the second city was 6%. The total hotel tax paid for the two cities was $552.50. How much was the hotel charge in each city before tax?Note that the ALEKS graphing calculator can be used to make computations easier.
SOLUTION
Let us represent the hotel charge with different variables x and y:
Let the hotel charge before tax in the first city be x
Let the hotel charge before tax in the second city be y
Now, let us represent the word problem in equation form:
First, we were told that the charge before tax in the second city is $500 more than the charge before tax in the first city, this can be represented thus:
[tex]y=x+500\ldots\text{.eqn 1}[/tex]Going forward in the question, we were told the tax for the first city (x) is 5%(0.05), and the tax for the second city is 6%(0.06). The total tax from both cities is $552.5, this expression can be written mathematically as:
[tex]0.05x+0.06y=552.5\ldots\ldots\text{eqn 2}[/tex]Now, by solving equation 1 and equation 2 simultaneously, we will obtain the hotel charge in each city before tax. (that is the value of x and y).
[tex]\begin{gathered} y=x+500 \\ 0.05x+0.06y=552.5 \\ \end{gathered}[/tex]Using, the substitution method of solving simultaneous equation, we will solve further:
[tex]\begin{gathered} \text{substitute equation 1 into equation 2} \\ 0.05x+0.06(x+500)=552.5 \\ 0.05x+0.06x+30=552.5 \\ 0.11x+30=552.5 \end{gathered}[/tex][tex]\begin{gathered} 0.11x=552.5-30 \\ 0.11x=522.5 \\ x=\frac{522.5}{0.11} \\ x=4750 \end{gathered}[/tex]The hotel charge before tax in the first city is $4750.
Now, substitute the value of x into equation 1 to get the value of y (hotel charge before tax in the second city)
[tex]\begin{gathered} y=x+500 \\ x=4750 \\ y=4750+500 \\ y=5250 \end{gathered}[/tex]The hotel charge before tax in the second city is $5250.
Lines PQ and Rs are parallel. Find y. P(2, -5); Q(5, 6); R(3, -1); S(6, y)y = ?
To answer this question it is necessary to find the equation of the given lines
Find the equation for PQ. To do it, find the slope of the equation:
[tex]m=\frac{6-(-5)}{5-2}=\frac{11}{3}[/tex]Now, use the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-6=\frac{11}{3}(x-5) \\ y=\frac{11}{3}x-\frac{55}{3}+6 \\ y=\frac{11}{3}x-\frac{37}{3} \end{gathered}[/tex]Parallel lines have the same slope, it means PQ and RS have the same slope, then RS has a slope of 11/3
Use the point slope formula to find the equation of the line RS:
[tex]\begin{gathered} y-(-1)=\frac{11}{3}(x-3) \\ y+1=\frac{11}{3}x-11 \\ y=\frac{11}{3}x-12 \end{gathered}[/tex]Now, use this equation to find y when x is 6 (which corresponds to point S):
[tex]\begin{gathered} y=\frac{11}{3}x-12 \\ y=\frac{11}{3}(6)-12 \\ y=22-12 \\ y=10 \end{gathered}[/tex]y has a value of 10.
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]Daylyn wants to win headphones . In addition to his grandmother and uncle, some friends of his agree that each one will give him a $5 donation . Some other friends agree that each one will pay him $0.25 for every correct answer. The number of friends who donate $ 5 to Daylyn is 3 times the number who pays him for correct answers. Write and solve an equation to find the number of friends who must pay him $0.25 for each correct answer in order for Daylyn to meet his goal
Let
x ------> number of friends of his agree that each one will give him a $5 donation
y -----> the number of friends who must pay him $0.25 for each correct answer
so
to win headphones-------> $350
we have that
x=3y -------> equation A
5x+0.25y=350 -------> equation B
substitute equation A in equation B
5(3y)+0.25y=350
solve for y
15y+o.25y=350
15.25y=350
y=22.95
therefore
the answer is 23 friends who must pay him $0.25 for each correct answeryesenia knits 21 centimeters of a scarf every week. what Is yesenia's unit rate (cm per day)for her knitting?After 18 days of knitting, how many centimeters long will the scarf be?write an equation and solve.
Answer:
3cm per day
54cm long
Explanation
Let x be yesenia's unit rate
If yesenia knits 21 centimeters of a scarf every week, then;
21 cm = 1 week (7 days)
To determine the amount for her knitting in a day, we can write;
x = 1 day
Divide both expressions
21/x = 7/1
Cross multiply
7 * x = 21
7x = 21
x = 21/7
x = 3
hence yesenia's unit rate is 3cm per day
- Recall that;
21 cm = 1 week (7 days)
Let y be the length of the scaf sfter 18 days, To get the length of the scarf, we can write;
y = 18days
Divide both resulting expressions;
21/y = 7/18
7y = 21 * 18
y = 3 * 18
y = 54cm
Hence the scarf will be 54cm longy
Finding the time given an exponential function with base e that models a real-world situation
We are solving for the value of t if C(t) = 19. We can rewrite the equation into
[tex]19=5+17e^{-0.038t}[/tex]Solving for t, we have
[tex]\begin{gathered} 17e^{-0.038t}=19-5 \\ 17e^{-0.038t}=14 \\ e^{-0.038t}=\frac{14}{17} \\ -0.038t=\ln \frac{14}{17} \\ -0.038t=-0.1941 \\ t=\frac{-0.1941}{-0.038} \\ t\approx5.1 \end{gathered}[/tex]The bottled water will achieve a temperature of 19 degrees C after 5.1 minutes.
Answer: 5.1 min
Create an equation that models the table below. Use the variables in the table for your equation. Write your equation with 'S' isolated.
The table show piszzas (P) on the left column and the slices of Pepperonin (S) on the right column.
To determine the equation models first check the ratio S/P to determine whether they are proportinal or not.
[tex]\begin{gathered} \frac{36}{3}=12 \\ \frac{96}{8}=12 \\ \frac{228}{19}=12 \end{gathered}[/tex]Now as the ratios are constant it mean the variation is linear and the relationship is proportional.
Thus the model equation can be determine as,
[tex]\begin{gathered} \frac{S}{P}=12 \\ S=12P \end{gathered}[/tex]Thus, the above equation gives the required model equation.
What is x in x/4=1.8/5
Answer:
x = 1.44
Step-by-step explanation:
Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x
(x/4) x 4 = 1.8/5 x 4
x = 1.44
In the equation y = 2x, y represents the perimeter of a square.What does x represent?Ahalf the length of each sideBthe length of each sideСtwice the length of each sideDtwice the number of sides
Given:
An equation that represents the perimeter of a square:
[tex]y=2x[/tex]To find:
What x represents.
Solution:
It is known that the perimeter of the square is equal to four times the side of the square.
Let the side of the square be s. So,
[tex]\begin{gathered} y=P \\ 2x=4s \\ x=\frac{4s}{2} \\ x=2s \end{gathered}[/tex]Therefore, x represents twice the length of each side.
The flow of water from a faucet can fill a 4-gallon container in 28 seconds Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction. The faucet fills the container at rate of——gallon per second
The flow of water can fill a 4-gallon container in 28 seconds.
Given:
Number of gallons = 4
Time = 28 seconds
Hence, the ratio of gallons to seconds will be 4 : 28
[tex]\begin{gathered} As\text{ a rate in gallons per second = }\frac{\text{number of gallons}}{time\text{ taken}} \\ As\text{ a rate in gallons per second = }\frac{4}{28}=\frac{1}{7} \\ As\text{ a reduced fraction, the rate in gallons per second is }\frac{1}{7}\text{gallons per second} \end{gathered}[/tex]Therefore, the faucet fills the container at the rate of 1/7 gallon per second
A circle has a circumference of 10 inches. Find its approximate radius, diameter and area
Answer:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Explanation:
The circumference of a circle can be calculated as:
[tex]C=2\pi r[/tex]Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:
[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]Then, the radius is 1.59 in.
Now, the diameter is twice the radius, so the diameter is equal to:
Diameter = 2 x r = 2 x 1.59 in = 3.18 in
On the other hand, the area can be calculated as:
[tex]A=\pi\cdot r^2[/tex]So, replacing r = 1.59 in, we get:
[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]Therefore, the answer are:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
How to fill out an income summary
Answer: Pick a Reporting Period. ...
Generate a Trial Balance Report. ...
Calculate Your Revenue. ...
Determine the Cost of Goods Sold. ...
Calculate the Gross Margin. ...
Include Operating Expenses. ...
Calculate Your Income. ...
Include Income Taxes.
Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportionate relationship.
Proportional Relationship
When two variables' ratios are equivalent, proportional relationships between them emerge. The fact that one variable is consistently equal to the constant value of the other in a proportional connection is another way to think of them. This constant is known as the "constant of proportionality."
Ratio
In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of apples to mangos in a bowl of fruit would be nine to six if there were nine apples and six mangos. Apples make up 9:15 of the entire fruit, whereas Mangos make up 6:9 of the total fruit.
Option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," illustrates a proportional relationship because the ratio is correct
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Two students measured a box in class. They used a digital scale and found that the mass was 400 grams. They then measured the box found the length is 2cm, the width is 2cm, and the height is 1cm. What is the density of the object
Explanation
Step 1
the density of an object is given by:
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ \end{gathered}[/tex]Let
mass: 400 grams
length's box=2 cm
width´s box= 2 cm
height's box= 1 cm
Step 2
find the volume of the box
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{replacing} \\ \text{Volume= 2 cm }\cdot\text{ 2 cm }\cdot\text{ 1 cm} \\ \text{Volume}=\text{ 4 cubic cm} \end{gathered}[/tex]Step 3
finally, replace the values of mass and volume in the density equation
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ density=\frac{400\text{ grm}}{4cm^3} \\ \text{density}=100\frac{gr}{cm^3} \end{gathered}[/tex]I hope this helps you
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
We use z score formula to calculate :
z = (x-μ)/σ
where,
z = standard score
x = observed value
μ = mean of students height
σ = standard deviation of students height
x = 63 inches
μ = 70 inches
σ = 3 inches
For x shorter than 63 inches we calculate
Z = (x - μ)/σ
then put the given values in above equation.
= (63 - 70)/3
= -2.33333
Probability value is :
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
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Refer to the diagram below to prove that the exterior angle equals the
To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:
1.- the inner angles of a triangle add up 180 degrees
2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3+\measuredangle4=180^{\circ} \\ \Rightarrow \\ \measuredangle1+\measuredangle2+\measuredangle3=\measuredangle3+\measuredangle4 \\ \Rightarrow \\ \measuredangle1+\measuredangle2=\measuredangle4 \end{gathered}[/tex]Answer:
They are linear pair and therefore supplementary.
Triangle sum theorem.
Substitution.
Subtraction property of equality.
simplify 12 times y to the 6th power times z to the 4th power divided by 6 times y times z to the 6th power
The simplified expression of the given expression is 2y^5 z^{-2}
What is expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
Given expression, [tex]\frac{12y^6 z^4}{6 yz^6}[/tex]
Simplifying and we get
[tex]\frac{12y^6 z^4}{6 yz^6}\\=2y^{6-1} z^{4-6}\\=2y^5 z^{-2}[/tex]
Therefore, the simplified expression of the given expression is 2y^5 z^{-2}
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In the diagram, m/ACB = 55°.
E
What is mZECD?
90°
O 55°
180°
D
O 125°
C
B
80
Answer:
55°
Step-by-step explanation:
Angle ACB and angle ECD are alternate exterior angles and alternate angles have same angle measurements:
If angle ACB = 55°
then angle ECD is also = 55°
Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.(-2,4).(1, -2)
The vertex form of a parabola is given by:
[tex]x=a(y-k)^2+h[/tex]Where the vertex is:
[tex]\begin{gathered} V(h,k)=(-2,4) \\ so\colon \\ x=a(y-4)^2-2 \\ x=a(y-4)^2-2 \end{gathered}[/tex]for (1,-2):
[tex]\begin{gathered} 1=a(-2-4)^2-2 \\ 1=a(-6)^2-2 \\ 1=36a-2 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ 36a=1+2 \\ 36a=3 \\ a=\frac{3}{36} \\ a=\frac{1}{12} \\ \end{gathered}[/tex]therefore:
[tex]x=\frac{1}{12}(y-4)^2-2[/tex]a company loses $5,400 as the result of manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss. How much each owner paid?
Explanation:
If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:
[tex]8x=5,400[/tex]Solving for x:
[tex]x=\frac{5,400}{8}=675[/tex]Answer:
Each owner has to pay $675
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
Theo sales person makes $350 each week plus an additional $28 per sale. Theo wants his paycheck to be at least $550 each week. Solve the inequality and choose the best answer to the scenario.
Let f(t) = 3 + 2, g(x) = -x^2?, andhe) = (x - 2)/5. Find the indicated value:24. h (g(5))
The Solution to Question 24:
Given the function below:
[tex]\begin{gathered} g(x)=-x^2 \\ h(x)=\frac{x-2}{5} \end{gathered}[/tex]We are asked to find the value of h(g(5)).
Step 1:
We shall find g(5) by substituting 5 for x in g(x).
[tex]g(5)=-5^2=-25[/tex]So that:
[tex]h(g(5))=h(-25)[/tex]Similarly, we shall find h(-25) by substituting -25 for x in h(x).
[tex]h(-25)=\frac{-25-2}{5}=\frac{-27}{5}[/tex]Therefore, the correct answer is
[tex]\frac{-27}{5}[/tex]Determine the period
I hate acellus
Answer:
my answer i got is y=2x+9
Answer:
5
Step-by-step explanation:
They are asking for the Period. The Period goes from one peak to the next (or from any point to the next matching point). To me it looks like that value is 5 for this graph.
Please Help!!!!! NOT FOR QUIZ!!!!!!!!
The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation , the correct option is (c) .
In the question ,
it is given that
the equation of the line is y [tex]=[/tex] -3x + 4 ,
we have to plot the line in the coordinate plane .
we plot the line ,w e need at least two points .
for the first point ,
for x = 0 , we have
y = -3(0) + 4
y= 0 + 4
y = 4
the first point is (0,4)
for the second point
for y = 0 , we have
0 = -3x + 4
-3x = -4
x = 4/3
the second point is (4/3 , 0)
so , from the graph plotted below , we can see that the line y [tex]=[/tex] -3x+4 shows the set of all solutions to the equations .
Therefore , The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation .
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factor out 2x^4 = 9x^2
Solution
Step 1
Rearrange the equation
[tex]2x^{4\text{ }}-9x^2=0[/tex]Step 2
factorise the equation
[tex]x^2(2x^2-9)=0[/tex]Hence by factorization, the answer is
x^2(2x^2 - 9) = 0
m(25+2)(x-7)(4%-8)"y =
From the figure we can obtain 2 equations:
[tex](2y+2)+(4x-8)=180[/tex]and
[tex](9x-7)+(4x-8)=180[/tex]first lets simplify both equations:
for the first;
[tex]2y+4x=186[/tex]and for the second one:
[tex]9x+4x=195\Rightarrow13x=195\Rightarrow x=\frac{195}{13}=15[/tex]Now we have that x=15 and we can substitute x for 15 in the first equation to find y:
[tex]2y+4(15)=186\Rightarrow2y=126\Rightarrow y=63[/tex]so the final answe is: x=15 and y=63
4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance ittravels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another80 feet. The distances traveled each second form an arithmetic sequence:16, 48, 80,...Part 1: How far does the stone fall during the 5th second? Find and use the explicitformula.a. What is the first term of the sequence?b. What is d, the common difference?c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, wheref(1) represents the first term.d. Use the explicit formula to find the distance the stone travels in the 5th second.Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds. Time (s) 1 2 3 4 5 6 7 Distance (ft) 16 48 80 | | 144 | | | | Part ||| : Use the table from part 2 to answer the questions a. The values in the table form a(n)___ sequence and the term numbers are shownb. The term values are shown in the in the____row, and the term numbers are shown in the ___ row. c. This sequence is associated with a(n)___function d. The domain of the function is the set of time values:___
The formula for determining the nth term of an arithmetic sequence is expressed as
f(n) = f(1) + (n - 1)d
Where
f(1) represents the first term
d represents the common difference
n represents the number of terms
From the information given,
f(1) = 16
d = 48 - 16 = 80 - 48 = 32
a) The first term of the sequence is 16
b) the common difference is 32
c) The explicit is
f(n) = 16 + 32(n - 1)
d) To find the distance the stone travels in the 5th second, it means that n = 5
Thus
f(5) = 16 + 32(5 - 1)
f(5) = 16 + 32 * 4
f(5) = 144
the distance the stone travels in the 5th second is 144 feet
a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
