120 children and 120 adults were admitted to the amusement park if the admission fee collected was $1980.00
The number of children and adults that entered the park can be calculated using linear equations.
Considering x to be the number of adults and y to be the number of children;
As 240 people entered the park, therefore;
x + y = 240
As the fee for children is $3.50 and for adults is $13, therefore;
13x + 3.50y = 1980
Determining the value of y in the first equation;
x + y = 240
y = 240 - x
Putting this value of y in the second equation;
13x + 3.50y = 1980
13x + 3.50(240 - x) = 1980
13x + 840 - 3.50x = 1980
9.5x = 1980 - 840
9.5x = 1140
x = 1140 / 9.5
x = 120
To determine the value of y, we Substitute this value of x in the first equation;
y = 240 - x
y = 240 - 120
y = 120
Hence, 120 children and 120 adults entered the park if the admission fee for children was $3.50 and for adults was $13.00
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if a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
The diameter is decreasing at a rate of - 0.101 cm/min
Given that,
Surface area is decreasing at a rate of [tex]7cm^{2}[/tex]/min,
We know that,
Surface Area of a sphere:
S = 4 π r2
dS/dt = - 7cm2/min
our aim is to find rate of decrease of Diameter:
dD/dt =?
Substitute r in the equation with radius = 1/2*Diameter:
r = 1/2D
Take the derivative of the surface area function with respect to time:
d/dt [S = 4 π (1/2D)2]
d/dt [S = 4 π 1/4*D2]
d/dt [S = π *D2]
dS/dt = 2πD*dD/dt
Solve for dD/dt:
dD/dt = dS/dt / 2πD
Substitute, dS/dt = - 7cm2/min and D = 11 cm
dD/dt = dS/dt / 2πD
dD/dt = - 7cm2/min / 2π*11cm
dD/dt = - 7cm2/min / 22π cm
dD/dt = - 7cm / 22π min
dD/dt = - 0.101 cm/min
Therefore, the diameter is decreasing at a rate of - 0.101 cm/min
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0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm
if a snowball melts so that its surface area decreases at a rate of 7 cm2/min,
find the rate at which the diameter decreases when the diameter is 11 cm.
Surface area: S
radius: r
diameter: e
time: t
[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]
S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e
dS/dt = 7cm^2 / min
de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] / [2pi*11cm]
= 0.101331789 cm/min
Hence , 0.101331789 cm/min is the rate at which the diameter decreases when the diameter is 11 cm
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The fox population in a certain region has a relative growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 20,200 foxes. a) Find an equation that models the population t years after 2000 (t = 0 for 2000). A = b) Use the equation from part (a) to estimate the fox population in the year 2009. Round to the nearest fox. foxes
Answer:
where is the question? plssss so im sorrry but where is the question i don't see a question?
11. (0, 2) and (4, -4)
12. (-2,-4) and (-3, -3)
Answer:
11. -3/2
12. -1
Step-by-step explanation:
To find slope, subtract the y's and put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction. Simplify if you can.
Subtract y's 2 - -4 is
2+4 which is 6, put that on top.
0 - 4 is -4 put it on the bottom.
Slope is 6/-4. Simplified, this is -3/2
The other question, same thing:
y-y over x-x
-4 - -3 / -2 - - 3
= -4+3 / -2 + 3
= -1 / 1
= -1
What's the distance between -9 and 23
Answer:
32 units
Step-by-step explanation:
calculate the distance using the absolute value of the difference.
| - 9 - 23 | = | - 32 | = 32
or
| 23 - (- 9) | = | 23 + 9 | = | 32 | = 32
a/6 -5=9 what’s the answer
Answer:
a = 84
Step-by-step explanation:
[tex]\frac{a}{6} - 5 = 9\\\frac{a}{6}} - \frac{5*6}{6} = \frac{9*6}{6}\\ a - 30 = 54\\ a = 54 + 30\\ a = 84[/tex]
which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?
The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
We know that for any polynomial equation with roots:
[tex]a_{1}, a_{2}, a_{3} ,...[/tex]
with multiplicity:
[tex]m_{1}, m_{2}...[/tex]
the equation for the polynomial is given by:
[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]
If the leading coefficient is negative we may take '-' sign in the starting of the expression.
Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3
Hence, f(x) is given by:
= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]
= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
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The ratio of small dogs to large dogs at the dog show is 4:3. If there are 60 dogs in the
show, how many are large dogs?
Answer:
45 large dogs
Step-by-step explanation:
Step 1:
60 x 3 = 180
180 ÷ 4 = 45
Help guysssssssssssssssssssssssssssssssssssssssssssss
Answer:
i think the answer is 2<x<5
Step-by-step explanation:
Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y=x.
Answer:
3rd Graph = 1st box
2nd Graph = 2nd Box
4th Graph = 3rd Box
Select the algebraic definition for the piecewise function graph.
Y=2x+4
y=4
Y=-2x+8
The answers (C) and (D) are accurate:.
F(x) = 4; 0 = x 2 and F(x) = -2x + 9; 2 = x 4 respectively.
How a piecewise function is defined?A piecewise function's graph has a large number of curve elements. It means that, depending on the value of the input, it has a wide range of definitions. To put it another way, a piecewise function reacts differently to the input.
It follows that:
The image displays the piecewise function:
Observing the piecewise function's graph
Every value in the domain is associated to exactly one value in the range according to the function, which may be thought of as a unique kind of connection with a predefined domain and range.
F(x) = 4; 0< = x < 2
F(x) = -2x + 9; 2 < = x < 4
Thus, F(x) = 4; 0< = x < 2 and F(x) = -2x + 9; 2 < = x < 4 the option (C) and (D) are correct.
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The correct question is:
" 2) Select the algebraic definition for the piecewise function graph.
F(x){_____ 0< = x < 2
{_____ 2 < = x < 4
A. 2x-8
B. 2
C. -2x+8
D. 4
E. 2x-4"
Find the x- and y-intercepts of the graph of x+y=18. State each answer as an integer or an improper fraction in simplest form
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
What is the x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function. The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
For x intercept, y = 0
x + y = 18
x + 0 = 18
x = 18
Hence, the x-intercept is (18, 0)
For y intercept, x = 0
x + y = 18
0 + y = 18
y = 18
Hence, the y-intercept is (0, 18)
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
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Pat and Alex have a combined total of £63.
The ratio of Pat’s money to Alex’s money is 5 : 2
They each spend an equal amount on sweets.
The ratio of Pat’s money to Alex’s money is now 3 : 1
How much did Pat spend on sweets?
Answer:
£4.50
Step-by-step explanation:
ratio of Pat : Alex = 5 : 2 = 5x : 2x ( where x is a multiplier )
then
5x + 2x = 63
7x = 63 ( divide both sides by 7 )
x = £ 9
Pat has 5 × £9 = £45
Alex has 2 × £9 = £18
let the amount they spend on sweets be x , then ratio of money is 3 : 1
so 45 - x : 18 - x = 3 : 1
express the ratio in fractional form and equate proportionally
[tex]\frac{45-x}{18-x}[/tex] = [tex]\frac{3}{1}[/tex] ( cross- multiply )
45 - x = 3(18 - x)
45 - x = 54 - 3x ( add 3x to both sides )
45 + 2x = 54 ( subtract 45 from both sides )
2x = 9 ( divide both sides by 2 )
x = 4.5
Pat spent £4.50 on sweets
Complete all these questions and provide an explanation with complete sentences for full credit.
1) Which muraber is rational? Explain
+
√13
Root 13 is a non-recurring, infinite decimal. Since 13 is not a perfect square, its square root cannot be determined precisely. 13 cannot be expressed as a fraction, which is the definition of a rational number, because it cannot be expressed as a ratio of integers.
An illustration of a rational number?
If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Rational number examples include 1/3, 2/4, 1/5, 9/3, and so on.
Irrational number examples include: Any real number that cannot be expressed as a fraction is considered to be illogical.
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Find a translation that has the same effect as the composition of translations
Translation that has the same effect as the composition of translations is
(x, y)→ ( x+2 , y+7 )
Composition of two reflections can be expressed as translation. Composition of reflections over parallel lines always has the same effect as a translation. Combination of two or more transformations is called composition of translation.
In this case :
As given in the question , 9 units are added from the x-coordinate in the first transformation and then 7 units are subtracted. So, the sum is:
+9-7 = +2
Observe that, in the first transformation, 1 units are added to the y-coordinate and then 6 units are added. The sum is:
+6+1 = +7
Then, the single Translation that has the same effect as the given Composition of translation is calculated to be:
(x, y)→ ( x+2 , y+7 )
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Express in decimal notation. 5.51×10^-4
Step-by-step explanation:
Answer:
= 5.51 × 10⁻⁴
scientific notation
= 5.51e-4
scientific e notation
= 551 × 10⁻⁶
engineering notation
millionth; prefix micro- (u)
= 5.51 × 10⁻⁴
standard form
-4
Order of Magnitude
for scientific and standard forms
= 0.000551
(real number)
= five hundred fifty-one millionths
word form
A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
(d) f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
In the above question it is given that
A project is being created by a group of students by arranging layers.
The first layer is having 4 layers and as we move to the next layers, it is getting 2 times of the number of layers in the first layer.
i,.e f(1) = 4
Number of layers in the second layer = 8 layers
f(2) = 4.2 = 8
Now, we need to find the general arithmetic formula to determine the subsequent n number of layers in the project
As the subsequent layers are getting n times of the first layer, so we'll also find the similar arithmetic formula where addition to the first layer with n times of it is happening
So, after checking all the given options we find, (d) as the appropriate option
f(1) = 4
f(n) = 4 + d(n-1) , n>0
We'll find the number of layers in the 3 layers
Here, n = 3
Putting in the formula, we'll find.
f(3) = 4 + d(3-1)
f(3) = 4 + d(2)
where d(2) = 8 (given)
so, f(3) = 4 + 8 = 12
Hence, f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $80. A season ski pass costs $300. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive then the daily passes?
Answer: I think it's 9 days.
Step-by-step explanation:
you start at (1,7). you move left 1 unit and down 6 unit
The required point on the cartesian plane is (0,1).
What is a cartesian plane?Definition of a Cartesian Plane. The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.
In a graph (1,7) lies in the first quadrant
And if we go 1 unit left then that means that we will be on the y axis
Then if we go down 6 units we will reach at point 1 unit away from the origin on the y axis . This particular point can be represented as (0,1).
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The Earth is approximately 8.0 x 103 miles in diameter, from pole to pole.What number is the distance equivalent to? A- 800 thousand milesB- 80 thousand milesC- 8 thousand milesD- .8 thousand miles
Answer
Option C is correct.
8.0 × 10³ miles = 8 thousand miles.
Explanation
The number given in scientific notation is
8.0 × 10³ miles
= 8.0 × 1000 miles
= 8000 miles
= 8 thousand miles.
Hope this Helps!!!
PLEASE HELP ME SOLVE THESE TWO ANSWERS!!
Answer:
:]
Step-by-step explanation:
x, x+2
Equation: 2x+4=2x+4
All real numbers
b) it is an identity, it has infinite solutions.
The I-70 grade west of Denver has a grade of 5%. The horizontal length of the roadway (run)
is 5.5 miles. What is the change in elevation from the top of the grade to the bottom of the
grade in feet?
The change in the elevation is 0.275 miles.
What is an elevation?An elevation simply means the her that above the sea level. It's used to describe a geographical location.
Thethe change in elevation from the top of the grade to the bottom of the grade in feet will be:
= Percentage of change × Length given
= 5% × 5.5 miles
= 0.05 × 5.5 miles
= 0.275 miles.
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Please help me because I got the answer wrong.
[tex]\cfrac{1}{3}x^2~~ = ~~\cfrac{4}{27}\implies \cfrac{x^2}{3}~~ = ~~\cfrac{4}{27}\implies x^2=\cfrac{(3)4}{27}\implies x^2=\cfrac{12}{27} \implies x=\pm\sqrt{\cfrac{12}{27}} \\\\\\ x=\pm\cfrac{\sqrt{12}}{\sqrt{27}} \implies x=\pm\cfrac{\sqrt{2^2\cdot 3}}{\sqrt{3^2\cdot 3}}\implies x=\pm\cfrac{2\sqrt{3}}{3\sqrt{3}}\implies x=\pm\cfrac{2}{3}[/tex]
Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?
Answer:
390
Step-by-step explanation:
Paul receive about 13 advertisement via email each day. about how many advertisement emails will he receive in 30 days?
13 × 30 = 390
PLS HELP
Lisa needs at least 870 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 200 gigabytes available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs. Lisa is going to use memory cards that each hold 256 gigabytes.
Let C represent the number of memory cards that Lisa buys.
Which inequality describes this scenario?
The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Given that lisa checks and finds that she has 200 gigabytes available on her phone. It is going to use memory cards that each hold 256 gigabytes.
Let consider that C represent the number of memory cards that Lisa buys.
Then the inequality ;
200 + 256C ≥ 870
Hence, The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
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you are traveling 150 miles to your cousins house. You travel at an average rate of 50 miles per hour. How long will it take to get to cousin house?
Answer
It will take 3 hours to get to your cousin's house.
Explanation
Firstky, note that Speed is given as
[tex]\text{Speed =}\frac{Dis\tan ce}{Time}[/tex]For this question, we are told that the distance to your cousin's house is 150 miles.
The speed is an average rate of 50 miles per hour.
We are then asked to calculate how long it will take to get to your cousin's house.
Speed = 50 miles/hour
Distance = 150 miles
Time = ?
[tex]\begin{gathered} \text{Speed = }\frac{Dis\tan ce}{Time} \\ 50=\frac{150}{Time} \\ \text{Cross multiply} \\ 50\times Time=150 \\ \text{Divide both sides by 50} \\ \frac{50\times Time}{50}=\frac{150}{50} \\ \text{Time = 3 hours} \end{gathered}[/tex]Hope this Helps!!!
The picture shows a triangular island:Which expression shows the value of q?s over sin 55 degreess over cos 55 degreesr sin 55°r cos 55°q?
A right triangle is a triangle with a right angle. The opposite side to the right angle is called the hypotenuse and the other sides are the legs. Given an angle in a right triangle, the ratio between the leg adjacent to the angle and the hypotenuse is equal to the cosine of the angle.
Using this relation in our problem, we have the following:
[tex]\cos(55^o)=\frac{s}{q}[/tex]Solving this expression for q, we have:
[tex]\begin{gathered} \cos(55^o)=\frac{s}{q} \\ q\cos(55^o)=s \\ q=\frac{s}{\cos(55^o)} \end{gathered}[/tex]And this is our answer.
[tex]\frac{s}{\cos(55^o)}[/tex]There are 100 students in Year 10.
Each student studies exactly one of French, German, and Spanish.
X girls study French and there are 3X girls in total.
2Y boys study German.
There are 35 students studying Spanish of which Y are boys.
Which of the following is an expression for the total number of students studying German?
The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.
Which expression correctly represents the number of students studying German?It follows from the task content that the number of students studying German be determined from the given information.
Therefore since the total number of students is; 100.
35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).
Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.
Hence, the number of girls who study German is; 2x - (35 - y).
Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).
= 3y + 2x -35.
Ultimately, the total number of students who study German are; 3y + 2x -35.
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can someone help me really quick
Answer:
21
Step-by-step explanation:
63 divided by 3 is 21
210 divided by 10 is 21
What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 1/4x2 - 11?A. The graph of f(x) is horizontally stretched by a factor of 4 andshifted 11 units to the right.B. The graph of f(x) is vertically compressed by a factor of 4 andshifted 11 units down.C. The graph of f(x) is horizontally compressed by a factor of 4 andshifted 11 units down.D. The graph of f(x) is vertically compressed by a factor of 4 andshifted 11 units to the right.SUBMIT
As per transformation of graph, h(x) = 1/4x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted down by 11 units.
To know the effect on the graph
Given, the graph is f(x) = x².
We know that, at the time of horizontally compressing a graph we need to multiply it by a factor of (1/a).
Again, at the time of shifting a graph up we need to add a positive number of (b).
Therefore, a = 4 and b = - 11.
Now, if we horizontally compress f(x) it by a factor of (1/4) then it be (1/4)x².
Again, if we shifted down f(x) by 11 units, then it be (1/4)x² - 11.
Therefore, h(x) = (1/4)x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted 11 units down.
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Which one of them is right?
Answer:
neither of them are right