A group of friends wants to go to the amusement park. They have no more than $150 to spend on parking and admission. Parking is $8, and tickets cost $17.75 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.
Answers
Answer:
12
Step-by-step explanation:
If x be no of people
The inequality is
17.75x+8≤150Solve it.
17.75x≤142x≤8At Max 8 can go
Related Questions
What is the value of x in the equation 1/5 x-2/3y = 30, when y = 15?
Answers
Answer:
The value of x is 200 in the equation 1/5x - 2/3y = 30, when y = 15
Step-by-step explanation:
Given
equation: x - 2/3y = 30
when y = 15
Plug in y:
1/5x - 2/3(15) = 30
1/5x - 10 = 30
add 10 to both sides,
1/5x - 10 + 10 = 30 + 10
1/5x = 40
multiply both sides by 5
1/5x * 5= 40 * 5
x = 200
Answer:
x = 200
Step-by-step explanation:
\(\frac{1x}{5} -\frac{2y}{3} =30\)
Given that, y = 15.
So, to find the value of x you have to replace y with 15 and make the x the subject.
Let us do that now.
\(\frac{1x}{5} -\frac{2*15}{3} =30\\\)
\(\frac{1x}{5} -\frac{30}{3} =30\\\)
\(\frac{1x}{5} =30+ \frac{30}{3}\\\)
\(\frac{1x}{5} =\frac{30}{1} + \frac{30}{3}\\\)
\(\frac{1x}{5} =\frac{30*3}{1*3} + \frac{30}{3}\\\)
\(\frac{1x}{5} =\frac{90}{3} + \frac{30}{3}\\\)
\(\frac{1x}{5} =\frac{120}{3}\)
Use cross multiplication.
\(1x*3=120*5\\3x=600\)
Divide both sides by 3.
x = 200
Question 9f(x)= x? - 10x - 24g(x) = 2x - 24Find (f/g)x
Answers
we have
f(x)= x^2 - 10x - 24
g(x) = 2x - 24
we know that
(f/g)x =f(x)/g(x)
so
substitute
(f/g)x =(x^2 - 10x - 24)/(2x-24)
simplify the expression
we have that
2x-24=2(x-12)
and
x^2 - 10x - 24=(x-12)(x+2)
substitute in the original expression
(f/g)x=(x-12)(x+2)/{2(x-12)}
simplify
(f/g)x=(x+2)/2
2x-24=2x-12(2)
step 1
Factor 2
2x-12(2)=2(x-12)
The staff at an advertising company took a survey of 350 people, each of
whom had visited one of two branches, East and West, of a store. Each
person surveyed was asked whether he or she had purchased a certain
product within the past month. The results of the survey, by location, are
shown in the table.
Answers
7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.
Out of the 168 people who visited the West branch of the store,
98 indicated that they had not purchased the product.
Therefore, the fraction of people who visited the West branch and had not purchased the product is:
98/168
Simplifying this fraction by dividing the numerator and denominator by 14, we get:
7/12
Hence, 7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.
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NEED HELP its math answer quick
Answers
Answer:
31/5 or 6 1/5
Step-by-step explanation:
whats the first term of the expansion of (2x+5)^4
A.2x^2
B. 4x^2
C. 4x^4
D. 2x^4
Answers
The first term of the expansion of (2x+5)^4 is 16x⁴
How to determine the first term of the expansion?From the question, the expression is given as
(2x + 5)^4
The first term of the expansion can be calculated using
First term = 1 * (2x)ⁿ * (5)ⁿ-ⁿ
The values of the variables are
n = 4 --- the exponent
Substitute the known values in the above equation
So, we have the following equation
First term = 1 * (2x)⁴ * (5)⁴⁻⁴
Evaluate
First term = 1 * (2x)⁴ * (5)⁰
Evaluate the product
First term = 16x⁴
Hence, the first term is 16x⁴ and none of the options is correct
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Researchers in the Hopkins Forest (see Problem 7-16 from) also count the number of maple trees (genus
acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots
sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard
deviation of 23.65 trees.
a). If we took the mean of a sample of eight plots, what would be the standard error of the
mean?
b). Using the central limit theorem, what is the probability that the mean of the eight would be
within 1 standard error of the mean?
c). Why might you think that the probability that you calculated in (b) might not be very
accurate?
Answers
a) The standard error of the mean is equal to the standard deviation divided by the square root of the sample size. In this case, the standard error of the mean would be equal to 23.65/sqrt(8) = 6.61.
b) Using the central limit theorem, we can say that the probability that the mean of the eight plots would be within 1 standard error of the mean is approximately equal to 68%. This is because, under the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, in this case, we would expect that 68% of the sample means would be within 1 standard deviation of the population mean.
c) The probability that we calculated in (b) might not be very accurate because the central limit theorem assumes that the underlying population is normally distributed. However, it is not clear from the histogram whether the number of live maples per plot is normally distributed. If the distribution of the number of live maples per plot is not normal, then the central limit theorem would not be applicable and the probability we calculated might not be accurate.
Hence we get the required answer.
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You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answers
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
Suppose you start with one liter of vinegar and repeatedly remove 0.14 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. b. After how many steps does the mixture contain less than 9% vinegar?
Answers
Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and
after 11 steps, the mixture contains less than 9% vinegar.
What is concentration?
Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.
a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:
\(C(1) = C(0) * \frac{1 - 0.14}{1}\)
where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:
C(2) = C(1) * \(\frac{1 - 0.14}{1}\)
Substituting the formula for C(1), we get:
C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)
or, more generally:
\(C(n) = C(0) * (0.86)^n\)
b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:
\(C(0) * (0.86)^n < 0.09\)
Dividing both sides by C(0), we get:
\((0.86)^n < 0.09\)
Taking the natural logarithm of both sides, we get:
n * ln(0.86) < ln(0.09)
Dividing both sides by ln(0.86), we get:
n > ln(0.09) / ln(0.86)
Using a calculator, we get:
n > 10.7
Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.
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Evaluate the following to four decimal places
Sin 23.4 degrees
Answers
Answer: 56554
Step-by-step explanation:
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
Answers
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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The Phillips family had three cats. They needed to split 20 ounces of cat food among 3 cats how much cat food would each cat get?
Answers
Answer:
Below.
Step-by-step explanation:
20 divided by 3.
Because there are 3 cats and 20 ounces of cat food so.
20/3= 6.666667 Ounces of food for each cat.
The water level is a number that indicates whether the level is above or below normal using positive or negative values. After a heavy storm, the water level of a river is −3.7 feet. This level is 1/2 times 2.5 feet more than the previous water level.
What was the previous water level?
A. -18.5
B. -9.9
C. -4.9
D. -4.3
Note: I think it is -4.9. If you have the actual right answer please leave it down below. Thanks.
Answers
Answer:
I also believe it is -4.9 but I may be mistaken
Step-by-step explanation:
Select all of the equations for the line that passes through (5, −2) and (0, 18).
Multiple select question.
A)
y+2=−4(x−5)
B)
x+4y=−12
C)
y−6=−4(x+1)
D)
y=−4x−12
E)
y=−4x+18
F)
4x+y=18
Answers
Answer:
Need more info please
Step-by-step explanation:
Vector u has initial point at (4, 4) and terminal point at (–12, 8). Which are the magnitude and direction of u?
Answers
Let's find the magnitude of each component:
Let:
\(\begin{gathered} (x1,y1)=(4,4) \\ (x2,y2)=(-12,8) \\ \vec{u}=ax+by \\ \mleft\Vert\vec{u}\mright||=\sqrt[]{a^2+b^2} \end{gathered}\)So, let's find a and b:
\(\begin{gathered} a=|x2-x1|=|-12-4|=|-16|=16 \\ b=|y2-y1|=|8-4|=|4|=4 \end{gathered}\)so:
\(\begin{gathered} \Vert\vec{u}||=\sqrt[]{16^2+4^2} \\ \Vert\vec{u}||=\sqrt[]{272} \\ \Vert\vec{u}||\approx16.492 \end{gathered}\)And the direction is:
\(\begin{gathered} \theta=180-\tan ^{-1}(\frac{b}{a}) \\ \theta=180-\tan ^{-1}(\frac{4}{16}) \\ \theta\approx180-\tan ^{-1}(\frac{4}{16})\approx165.963 \end{gathered}\)Answer:
D- ||u|| = 16.492; θ = 165.964°
Step-by-step explanation:
I took the quiz
- 2.7f + 0.9f - 16-6=
Answers
I think( -1.8f -22 )
-2.7f + 0.9f
|
|
-1.8f.
then -16-6
|
|
-22
how many tickets are there when it weighs 135 grams
Answers
Answer:
about like 4-5
Step-by-step explanation:
its 4 or 5
Find the lateral and total surface area round to the nearest hundredth if necessary
Answers
The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.
How to determine the lateral and total surface area of a prismIn this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.
The area formulas for the triangle and the rectangle are, respectively:
Triangle:
A = s · √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
a, b, c - Sides, in feet.s - Semiperimeter, in feet.A - Area, in square feet.Rectangle:
A = w · h
Where:
w - Width, in feeth - Height, in feet.A - Area, in square feet.Now we proceed to determine each surface area:
Lateral surface area:
A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)
A = 1000 ft²
Total surface area:
s = 0.5 · (17 ft + 17 ft + 16 ft)
s = 25 ft
A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²
A = 1120 ft²
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0896. Calculate the atomic mass of copper if copper-63 is 69.17% abundant and copper-65 is30.83% abundant.
Answers
The atomic mass of the copper is
\(63\times69.17\text{ \% + 65}\times30.83\text{ \%}\)solve the above expression
\(63\times\frac{69.17}{100}+65\times\frac{30.83}{100}\)\(63\times\frac{6917}{10000}+65\times\frac{3083}{10000}\)\(46.35+20.03=66.38\)So the atomic weight of the mixture is 66.36 .
The number of hours a student spent studying each week for 9 weeks is shown.
5, 9.5, 3, 12, 6, 8, 4.5, 10, 6.5
What is the value of the range for this set of data?
3
6.5
9
12
Answers
Answer:
Step-by-step explanation:
Range is largest value - smallest value. 12-3=9! EZ
are the triangles similar? explain. please help
Answers
Answer:
The triangles are similar.
Step-by-step explanation:
The reason for this is because they both share two pairs of angles that are the same: 40 degrees and 60 degrees. If these are equal, then that must mean the third angle for both triangles is also the same, making both triangles equal in proportion. Therefore, they must be similar.
Answer:
Yes
Step-by-step explanation:
(i) By AA similarity
Both have two equal angles, 40° and 60°, therefore they can be defined as similar by AA similarity(ii) By SSS similarity
AB/DC = 32/40 = 4/5BC/EF = 24/30 = 4/5AC/DF = 36/45 = 4/5As the ratio of the sides of both triangles are equal, they are defined as similar by SSS similarityMichaela plans on installing heated tile in her kitchen. A diagram of the kitchen floor plan is shown below.
Calculate the area of the floor, to the nearest 10th, to determine how many square metres of tile Michaela will need to buy.
*Hint: Divide the shape into 2! You will need to use trig!
Answers
Check the picture below.
so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".
\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)
Tina was observing the changing heights of a ball as it bounced over time. She graphed the function on this coordinate grid to show f(x), the height of the dropped ball, in feet, after its xth bounce.
Part A: What does the value of f(3) represent in the given context?
A.
After 4 bounces the height of the ball is 3 feet.
B.
After 3 bounces the height of the ball is 4 feet.
C.
After 4 bounces the height of the ball is 4 feet.
D.
After 3 bounces the height of the ball is 3 feet.
Part B: Tina said that a possible range for the given function is y > 0. Based on the given scenario, do you agree or disagree?
A.
I disagree; because the graph has an asymptote at y = 0, the height cannot be 0.
B.
I disagree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.
C.
I agree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.
D.
I agree; because the graph has an asymptote at y = 0, the height cannot be 0
Answers
Answer:
Step-by-step explanation:
Part A:
The value of f(3) represents the height of the ball after its 3rd bounce.
From the graph, we can see that the point corresponding to the 3rd bounce has a height of 4 feet.
Therefore, the correct answer is B. After 3 bounces, the height of the ball is 4 feet.
Part B:
The given function represents the height of the ball after each bounce. Since the ball is bouncing, its height will always be greater than zero.
The graph shows that the function has an asymptote at y = 0, which means that the height of the ball will approach zero as it bounces. However, this does not mean that the ball will never have a height of zero. The ball will eventually stop bouncing and come to rest on the ground, which corresponds to a height of zero.
Therefore, the correct answer is C. We agree that a possible range for the given function is y > 0.
The product of a number and 2 is 3 less than the quotient of a number and 5 .
Answers
Answer:
The sentence you have can be expressed in algebra (using x as 'the number'):
2x + 5 = x / 3. (We add 5 to the left side because that product is less than the right side.)
Now all you have to do is to combine the x terms on one side of equation, putting the constant on the other side of the equation, and solve for x.
or
Let the unknown number that we are solving for be x.
The product of a number and 2 means 2*x
5 less than the quotient of a number and 3 means x/3 - 5.
So,
2*x = x/3 - 5 subtract x/3 from both sides of the equation
2x - x/3 = -5 , now find the least common denominator for the left side of the equation
6x/3 - x/3 = -5
(6x - x)/3 = -5
5x/3 = -5, now multiply both sides of the equation by 3
5x = -15 now divide both sides of the equation by 5
x = - 3. So the number is -3.
Step-by-step explanation:
Building an equation and solving for the number, it is found that the number is \(x = -\frac{3}{2}\)
----------------------
The number can be called x.Product of a number and 2 is \(2x\)3 less than the quotient of a number and 5 is: \(\frac{x}{5} - 3\)Equal, thus:
\(2x = \frac{x}{5} - 3\)
Multiplying everything by 5:
\(10x = x - 15\)
\(9x = -15\)
\(x = -\frac{15}{9}\)
\(x = -\frac{3}{2}\)
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Identify the slope and y-intercept of the line below.
Slope=?
y-intercept=?
Answers
Answer:
Slope- y=1/4x-6
Y intercept= (0,-6)
Hope this helps!
Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box
Answers
Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)
How to determine the key features?Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:
Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).
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What is the slope of the line that passes through the points (0, 7)(0,7) and (8, 7) ?(8,7)? Write your answer in simplest form.
Answers
Answer:
0
Step-by-step explanation:
Use rise over run (y2 - y1) / (x2 - x1)
Plug in the 2 points:
(y2 - y1) / (x2 - x1)
(7 - 7) / (8 - 0)
0/8
= 0
So, the slope is 0.
The slope is 0.
what is slope?The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Given:
(0,7) and (8, 7)
slope = (y2 - y1)/ (x2 -x1)
slope = (7-7) / (8-0)
slope = 0/7
slope= 0
Hence, the slope is 0.
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The temperature inside my refrigerator is about 40 Celsius. That temperature in Kelvin is K.
I place a balloon in my fridge that initially has a temperature of 220 C. This is K.
If the original volume of the balloon is 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? liters. (Round to two decimal places)
Answers
To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.
The law can be expressed mathematically as:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }\)
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow we obtain the data to continue solving:
V₁ = 0.5 LT₁ = 220 °CV₂ = ?T₂ = 40 °CNow, we will convert the temperatures to Kelvin:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }\)
Now we solve for V₂:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }\)
Where:
V₁ is the initial volumeT₁ is the initial temperatureV₂ is the final volumeT₂ is the final temperatureNow, we substitute the values in the formula:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }\)
\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}\)
The final volume of the balloon, when completely cooled in the refrigerator, will be approximately 0.32 liters.Given the following formula, solve for r.
Answers
Which statement can you conclude is true from the given information?
Answers
Answer:
angle IJA is a right angle
What is the remainder when 7842 is divided by 176
Answers
Answer: 5 or 55
Step-by-step explanation:
The remainder is 98 when 7842 is divided by 176 after using the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have two numbers:
7842 and 176
7842 is divided by 176
Mathematically,
= 7842 ÷ 176
We can write the above number expression in the form of a fraction:
= 7842/176
Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The remainder will be:
Quotient = 44
Remainder = 98
Thus, the remainder is 98 when 7842 is divided by 176 after using the arithmetic operation.
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