The price of one adult ticket is $9 and the price of child ticket is $8
First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108
Consider the price of adult ticket as x and child ticket as y
Then the equation will be
4x+9y = 108
Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets
10x+3y = 114
Here we have to use the elimination method
Multiply the first equation by 10 and second equation by 4
40x+90y = 1080
40x+12y = 456
Subtract the equation 2 from equation 1
90y-12y = 1080-456
78y = 624
y = 624/78
y = $8
Substitute the value of y in any equation
10x+3y =114
10x+3×8 =114
10x +24 =114
10x = 90
x = 90/10
x = $9
Hence, the price of one adult ticket is $9 and the price of child ticket is $8
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Chords WP and KZ intersect at point L in the circle shown.Wz*3x - 22KIL5РWhat is the length of KZ?7.5910O 12
For the cicle with intersecting chords the relation between the length of segments of chords is,
[tex]KL\cdot ZL=WL\cdot PL[/tex]Substitute the values in the equation and solve for x.
[tex]\begin{gathered} 2\cdot(3x-2)=x\cdot5 \\ 6x-4=5x \\ 6x-5x=4 \\ x=4 \end{gathered}[/tex]So value of x is 4.
The equation for the length of chord KZ is,
[tex]\begin{gathered} KZ=KL+LZ \\ =2+3x-2 \\ =3x \end{gathered}[/tex]Substitute the value of x in equation to determine the length of KZ.
[tex]\begin{gathered} KZ=3\cdot4 \\ =12 \end{gathered}[/tex]So answer is 12.
I have question 3 and need to know a b and c
a) Recall that:
[tex]-1\le\cos \theta\le1.[/tex]Therefore:
[tex]\begin{gathered} -1\le\cos (30^{\circ}\times t)\le1, \\ -12\le12\cos (30^{\circ}\times t)\le12, \\ -12+16\le12\cos (30^{\circ}\times t)+16\le12+16, \\ 4\le12\cos (30^{\circ}\times t)+16\le28. \end{gathered}[/tex]Therefore the minimum height of the Ferris wheel above the ground is 4 meters.
b) Recall that to evaluate a function at a given value, we substitute the variable by the given value, then, evaluating the given function at t=3 we get:
[tex]12\cos (30^{\circ}\times3)+16.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 12\cos (90^{\circ})+16, \\ 12\cdot0+16, \\ 0+16, \\ 16. \end{gathered}[/tex]Therefore, the height of the Ferris wheel above the ground after 3 minutes is 16 meters.
(c) Let x be the time in minutes the Ferris wheel takes to complete one full rotation, then we can set the following equation:
[tex]30^{\circ}\times x=360^{\circ}.[/tex]Therefore:
[tex]30x=360.[/tex]Dividing the above equation by 30 we get:
[tex]\begin{gathered} \frac{30x}{30}=\frac{360}{30}, \\ x=12. \end{gathered}[/tex]Answer:
(a) 4 meters.
(b) 16 meters.
(c) 12 minutes.
Decide whether or not the number 46/45 Could represent the probability
Solution
- A probability, by definition, is a fraction that is less than or equal to 1.
- The number 46/45 is a number greater than 1.
- Thus, the number 46/45 CANNOT be a probability
What does the y-intercept mean? What does the x-intercept mean? Explain what each intercept means and then Identify the x-intercept and y-intercept from each equation.A. y=7/2x -2B. x=-3
x intercept = where the function crosses the x axis (x,0)
y intercept = where the function crosses the y-axis (0,y)
A. y=7/2x-2
x intercept , replace y by 0 and solve for x:
0 =7/2x-2
2= 7/2 x
2 / (7/2) = x
x= 4/7
y-intercept, replace x by 0 and solve for y
y= 7/2x-2
y= 7/2 (0) -2
y=-2
B.
x-intercept:
x=-3
y-intercept
0=-3
It doesn't have a y-intercept.
Introduction to Probability
The probability of birthday being in July is 1/12.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a numeric value and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is flipping a fair (impartial) coin. The chance of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Probability of birthday being in July = 1/12 (12 months in a year)
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plssss help!!!! Right triangle RST is drawn below. A square is drawn on to each leg of the triangle, and a square is drawn onto the hypotenuse of the triangle. The area of square A is 25 cm² . The area of square B is 144 cm². Determine the length in centimeters of x, the hypotenuse of the right triangle.O 13 cmO 17 cm O 169 cmO 119 cm
the hypotenuse of the right angled triiangle = x = 13cm (option A)
Explanation:
Area of B = 144cm²
Area of a square = length²
length = √Area of a square
shape of B is a square, hence the length of B:
the length of one of the side of B = √144 = 12cm
Area of A = 25cm²
shape of A is a square
the length of one of the side of A = √25 = 5cm
Triangle is a right angled-triangle
From the diagram, the length of the side of B = opposite = 12cm
The length of the side of A = adjacent = 5cm
The length of the third square marked x = hypotenuse
Using pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
x² = 12² + 5²
x² = 144 + 25
x² = 169
x = √169
x = 13cm
Hence, the hypotenuse of the right angled triiangle = x = 13cm (option A)
when a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted true or false
Question:
When a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted.
Solution:
a smooth curve is by definition a function, so by definition of a function, we have that there is a definite law connecting the two variables (quantities).
Answer: false.
5. Kara earns a 3.5% commission on all sales made by recommendations to the hair salon. If the total amount of sales from referrals by Karo was $3,670, how much did Kara make?
Let's begin by listing out the information given to us:
Commission (C) = 3.5% = 0.035
Total amount of sales (T) = $3,670
To determine how much Kara made, we will find the product of the commission & total amount of sales:
[tex]\begin{gathered} Kara(K)=Commission(C)\cdot TotalAmountOfSales(T) \\ K=C\cdot T=0.035\cdot3670=128.45 \\ K=128.45 \end{gathered}[/tex]We therefore, see that Kara made $128.45 from referrals
find the probability of tossing 5 tails, them 5 heads. on the first 10 tosses of a fair coin
When a coin is tossed, the probability iof getting a head or a tail is 1/2.
The probability of tossing 5 tails = (1/2)^5
The probability of tossing 5 heads = (1/2)^5
The probability of tossing 5 talis and 5 heads = (1/2)^5 X (1/2)^5
= (1/2)^10
8. A plane uses a certain amount of fuel based on the number of miles it travels as shown in thetable.Miles Traveled 0 30 60 90 120Gallons of Fuel0156312468624a. What is the slope of the table, and what does it mean in the situation?b. What is the y-intercept of the table, and what does it mean in the situation?c. Write an equation for the table.
Remember the formua to calculate the slope of a line between to points
[tex]\begin{gathered} A(x_1,y_1) \\ \text{and} \\ B(x_2,y_2) \end{gathered}[/tex]is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So to calculate the slope of the table, let's use the points
A(0 , 0) and B(30 , 156). Thus,
[tex]\begin{gathered} m=\frac{156-0}{30-0}\rightarrow m=\frac{156}{30} \\ m=5.2 \end{gathered}[/tex]You can check that this slope works for any consecutive pair of points of the table, since the data is related with a straight line (constant slope)
To get a better sense of what a slope means, let's think about the original units of measurement of the data. Notice that the units for x data is "Miles traveled" and the units for y data is "Gallons of fuel".
In the formula for slope, we divide y data by x data. Therefore, the whole slope, with units of measurement, would be
[tex]m=5.2\text{ }\frac{\text{Gallons of fuel}}{\text{Mile(s) traveled}}[/tex]Thus, the slope of the table would mean the gallons of fuel consumed per each mile traveled
Now, remember the y-intercept occurs when x = 0.
In this case, the y-intercept would be 0, meaning that the plane didn't use any fuel until it started the journey. Perhaps it was parked and with the engines off.
To come up with an equation for the table, lets use the slope we calculated, point A(0 , 0) and the slope-point form of a line, as following:
[tex]\begin{gathered} y-0=5.2(x-0) \\ \rightarrow y=5.2x \end{gathered}[/tex]Answers:
a)
[tex]m=5.2[/tex]The slope of the table means the gallons of fuel consumed per each mile traveled.
b) The y-intercept is 0. It means the plane didn't use any fuel until it started the journey.
c)
[tex]y=5.2x[/tex]Yea I think and her dad is doing great so
Given the following function:
[tex]tan\text{ }\theta=\frac{10}{y}[/tex]Both θ and y are functions of the time (t)
We will find the derivatives of θ and y with respect of the time (t) as follows:
[tex]sec^2θ*\frac{dθ}{dt}=-\frac{10}{y^2}*\frac{dy}{dt}[/tex]Now, we will find dy/dt when θ = π/6 and dθ/dt = π/12
First, we need to find the value of y when θ = π/6
[tex]\begin{gathered} tan(\frac{\pi}{6})=\frac{10}{y} \\ \frac{1}{\sqrt{3}}=\frac{10}{y} \\ \\ y=10\sqrt{3} \end{gathered}[/tex]so, we will substitute the values to find dy/dt as follows:
[tex]\begin{gathered} sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-\frac{10}{(10\sqrt{3})^2}*\frac{dy}{dt} \\ \\ so,\frac{dy}{dt}=-\frac{(10\sqrt{3})^2}{10}*sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-10.4719755 \end{gathered}[/tex]Rounding to 2 decimal places
So, the answer will be:
[tex]\frac{dy}{dt}=-10.47\text{ feet/hour}[/tex]Solve the inequality a < 5 and write the solution using: Inequality Notation:
Answer:
Step-by-step explanation:
A manufacturing process has a 70% yield, meaning that 70% of the products
Answer:
are acceptable and 30% are defective.
Step-by-step explanation:
Does the least-squares fit line always go through at least one point in the plot?
Not necessarily. The least-squares line is the best fit for all the points in the scatterplot. if it so happens that in order to get close to some point on the plot the line has to go a little further away from some other point, the line will be adjusted to accommodate that.
Hence, the least square line does not always pass through at least one point on the line.
The number of microbes in a tissue sample is given by the functionN (t) = 34.8 + In(1 + 1.2t)where N(t) is the number of microbes (in thousands) in the sample after thours.a.) How many microbes are present initially?b.) How fast are the microbes increasing after 10 hours?
Explanation
[tex]N(t)=34.8+\ln (1+1.2t)[/tex]we have a function where the number of microbes ( N) depends on the time(t)
hence
Step 1
a.) How many microbes are present initially?
to know this, we need replace time I= t = zero, because it was "initially"
so
when t=0
replace.
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(0)=34.8+\ln (1+1.2\cdot0) \\ N(0)=34.8+\ln (1) \\ N(0)=34.8+0 \\ N(0)=34.8 \end{gathered}[/tex]so, initially there were 34.8 microbes
Step 2
b)How fast are the microbes increasing after 10 hours?
to know this, let t=10
so
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(10)=34.8+\ln (1+1.2\cdot10) \\ N(10)=34.8+\ln (1+12) \\ N(10)=34.8+\ln (13) \\ N(10)=34.8+2.56 \\ N(10)=37.36 \end{gathered}[/tex]therefore , after 10 hours the number of microbes is 37.36
I hope this helps you
4. Find the slope of the two points: (-3,-2) & (5, -8)
Enter Numerical value ONLY. NO Decimals
Try Again!
5. Find the slope of the two points: (6, 10) and (-2, 10) *
Enter Numerical value ONLY. NO Decimals
Your answer
This is a required question
Answer:
The slope of (-3, -2) and (5, -8) is -3/4
The slope of (6, 10) and (-2, 10 ) is 0
Step-by-step explanation:
[tex]\frac{-8 - (-2)}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}[/tex]
and
[tex]\frac{10 - 10}{-2 - 6} = \frac{0}{-8} = 0[/tex]
find the missing values in the figure below ( I need help as soon as possible only have 5 minutes available)
You can see in the figure attached that there are two Right triangles.
By definition, Right triangles are those triangles that have an angle that measures 90 degrees.
The larger triangle is the triangle ABC, but you only know the lenght of the side BC, which is:
[tex]BC=15m+2.5m=17.5m[/tex]And for the smaller triangle you only know the side whose lenght is 2.5 meters.
Therefore, since the exercise does not provide any other lenght and it does not provide another angle, you can conclude that the missing values cannot be determine with the given information.
So, the answer is OPTION D.
which of the equation below could be the equation of this parabola
We have a parabola with the vertex at (0,0).
If we write the equation in vertex form, we have:
[tex]\begin{gathered} \text{Vertex}\longrightarrow(h,k) \\ f(x)=a(x-h)^2+k \\ f(x)=a(x-0)^2+0=ax^2 \end{gathered}[/tex]We have to find the value of the parameter a.
As the parabola is concave down, we already know that a<0.
As a<0 and y=a*x^2, the only option that satisfies this condition is y=-1/2*x^2.
Answer: y=-(1/2)*x^2 [Option C]
a) rewrite each equation using function notation f(x) b) find f(3)
Hello there. To solve this question, we'll simply have to isolate y and plug in the value for x.
Given the equation:
4x - 3y = 8
To rewrite it using the notation y = f(x), subtract 4x on both sides and divide the equation by -3
-3y = 8 - 4x
y = - 8/3 + 4x/3
Now, plug in x = 3 in order to find f(3)
f(3) = -8/3 + 4 * 3/3 = -8/3 + 12/3 = 4/3
find the size of each interior angle of a regular hexagon
Answer:
Each interior angle = 180° -60° = 120°
Step-by-step explanation: We know that the three angles in a triangle, add up to 180°, and all the three angles are 60° in an equilateral triangle. The total number of angles of an enclosed space is 180° (n-2) where in is the number of sides.
A hexagon has six sides, so: s= 180° (6-2)
s= 180° x 4
s= 720°
now since in a regular shape, each interior angle is equal. We just divide the total interior angle with a number of sides
6.
720° divided by 6 is equal to 120°
As an incoming college freshman, Tina received a 10-year $15,100 Federal Direct
Unsubsidized Loan with an interest rate of 4.29%. She knows that she can begin making
loan payments 6 months after graduation but interest will accrue from the moment the
funds are credited to his account. How much interest will accrue while she is still in
school and over the 6-month grace period for this freshman year loan?
O $2,813.28
O $2,915.06
O $3,001.32
O $3,102.38
The interest that will accrue while the college freshman is still in school and over the 6-month grace period for this freshman year loan is, approximately, B. $2,915.06.
How is the interest determined?The interest for federal college loans is based on the simple interest formula instead of compounding.
By compounding, we mean that interest is computed on the principal and accumulated interest.
Federal Direct Unsubsidized Loan = $15,100
Number of years for college = 4 years
The number of years before repayment = 4.5 years (4 years + 6 months)
Simple interest for 4.5 years = $2,915.06 ($15,100 x 4.29% x 4.5 years)
On the other hand, one can compute the compounded interest using an online finance calculator.
Compounded Interest:N (# of periods) = 4.5 years
I/Y (Interest per year) = 4.29%
PV (Present Value) = $15,100
PMT (periodic payment) during the 4.5 years = $0
Results:
FV = $18,241.85
Total Interest = $3,141.85
Thus, the interest is Option B.
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Drag each number to the correct location on the statements. Not all numbers will be used. Consider the sequence below. --3, -12, -48, -192, ... Complete the recursively-defined function to describe this sequence. f(1) =...... f(n) = f(n-1) × .....for n = 2, 3, 4... 3, 2, 3, 4, 12, -4
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following sequence:
[tex]-3,-12,-48,-192...[/tex]f(1), is the first term of the sequence, therefore, it would be:
[tex]f(1)=-3[/tex]Now, we calculate the common ratio, just like this:
[tex]\begin{gathered} r=\frac{-192}{-48}=4 \\ \\ r=\frac{-48}{-12}=4 \\ \\ r=\frac{-12}{-3}=4 \end{gathered}[/tex]So the sequence would be:
[tex]f(n)=f(n-1)\cdot4[/tex]Find the ends of the major axisand foci.49x2 + 16y2 = 784Major axis (0,+[? ])
Answer:
Major axis (0, +-14)
Explanation:
The equation of an ellipse with the center in the origin is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]So, to transform the equation into this form, we need to divide both sides by 784 as:
[tex]\begin{gathered} 49x^2+16y^2=784 \\ \frac{49x^2}{784}+\frac{16y^2}{784}=\frac{784}{784} \\ \frac{x^2}{16}+\frac{y^2}{49}=1 \end{gathered}[/tex]It means that a² = 16 and b² = 49. So, a = ±4 and b = ±7
Now, the major axis is 2 times the greater value between a and b. Since the greater value is b = 7, 2 times b is:
Major axis = (0, ±7*2) = (0, ±14)
Find the Standard form of the line that has a slope of -6 and y intercept of 10.
We have to write the standard form, Ax+By=C, of the line that has a slope m = -6 and y-intercept b = 10.
To do that we use that information to write the slope-intercept form of the equation and then rearrange it into standard form.
The slope-intercept for the line is:
[tex]\begin{gathered} y=mx+b \\ y=-6x+10 \end{gathered}[/tex]We can then rearrange it as:
[tex]\begin{gathered} y=-6x+10 \\ 6x+y=10 \end{gathered}[/tex]Answer: 6x + y = 10
Plllssss help Select all equations that are also equivalent to0.6 + 15b + 4= 25.6 ( choose all the ones down below the equal the top)A . 15b+4 = 25.6B .15b+4=25 C. 3(0.6+ 15b +4) = 76.8 D. 15b = 25.6E. 15b= 21
The given equation is
[tex]0.6+15b+4=25.6[/tex]If we subtract 0.6 on each side, we get
[tex]\begin{gathered} 0.6+15b+4-0.6=25.6-0.6 \\ 15b+4=25 \end{gathered}[/tex]Therefore, the given expression is equivalent to B.
If we multiply the given equation with 3, we get
[tex]\begin{gathered} 3\cdot(0.6+15b+4)=25.6\cdot3 \\ 3(0.6+15b+4)=76.8 \end{gathered}[/tex]Therefore, the given expression is equivalent to C.
At last, if we subtract 0.6 and 4 on each side, we get
[tex]\begin{gathered} 0.6+15b+4-0.6-4=25.6-0.6-4 \\ 15b=21 \end{gathered}[/tex]Therefore, the given expression is equivalent to E.
The right answers are B, C, and E.
If there are 78 questions on a test , how many do you have to get correctly to get an 84 % or better on the exam ?
To answer this question, we have to multiply the number of questions times 0.84 (which is 84% written as a decimal):
[tex]78\cdot0.84=65.52\approx66[/tex]Yo have to get 66 questions correctly to get an 84% or better on the exam.
Describe the correlation in the scatter plot below.----------------The scatter plot shows (positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear, or no) correlation because as the plotted values of x increase, the values of y generally (decrease, increase, show no pattern or follow a nonlinear pattern).
A scatter plot shows a positive correlation when the values of y tend to increase as the values of x increases.
From this scatter plot, we can see that as the values of x increase, the values of y also increase. Therefore, this scatter plot shows a positive linear correlation.
An outlier is the the dot which doesn't fit with other dots or is far away from the rest of the dots. Here, we have one outlier.
Therefore, we can say the scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
ANSWER:
The scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
Type the correct answer in each box, у 5 4 3 2. 1 -5 -3 -2 -1 2 3 6 5 -1 -2 3 -4 5 The equation of the line in the graph is y= ghts reserved
Given data:
The first point on the graph is (-1,0).
The second point on the graph is (0, -1).
The expression fo the equation of the line is,
[tex]\begin{gathered} y-0=\frac{-1-0}{0-(-1)}(x-(-1)) \\ y=-(x+1) \\ y=-x-1 \\ \end{gathered}[/tex]Thus, the equation of the line is y=-x-1
I need some kind of tutor really smart on math
To solve this problem we will need a system of equations.
Step 1. Find the first equation.
Using the statement "Emma rented a bike for 4 hours and paid £18", we will call the cost per hour h, and the flat fee f. Thus, the first equation is:
[tex]4h+f=18[/tex]This is because Emma rented the bike for 4 hours but she had to pay a flat fee f, and the total was £18.
Step 2. Find the second equation.
We do the same but now with the statement "Louise rented a bike for 7 hours and paid £25.5". Remember that for our equation, h represents the cost per hour and f the flat fee. The second equation is:
[tex]7h+f=25.5[/tex]Step 3. In summary, our system of equations is:
[tex]\begin{gathered} 7h+f=25.5 \\ 4h+f=18 \end{gathered}[/tex]Step 4. To solve part a. we have to find the cost per hour "h".
To find it, we use the elimination method in our system of equations, which consists of adding or subtracting the equations in order to eliminate one variable.
Since we are interested in finding "h", we can subtract the second equation from the first one, and we get the following:
Applying the subtraction:
And we start subtracting 7h-4h, which results in 3h:
The next subtraction is f-f, which results in 0.
And then, subtract 25.5-18:
The equation we have as a result is:
[tex]3h=7.5[/tex]Which is an equation we can use to solve for the cost per hour h.
Dividing both sides by 3:
[tex]\begin{gathered} h=\frac{7.5}{3} \\ h=2.5 \end{gathered}[/tex]The cost per hour is £2.5
Step 5. To find part b we need to find the rental feed, in our case, this means to find "h".
Using the first equation of the system:
[tex]7h+f=25.5[/tex]And substituting the previous result:
[tex]h=2.5[/tex]We get:
[tex]7(2.5)+f=25.5[/tex]Solving the operations:
[tex]17.5+f=25.5[/tex]And solving for f:
[tex]\begin{gathered} f=25.5-17.5 \\ f=8 \end{gathered}[/tex]the flat fee is £8.
Step 6. To find part c, we consider the cost per hour and the flat fee.
Michael rented the bike for 2 hours.
Since the cost per hour is £2.5, and the flat fee is £8, he will pay:
[tex]2(2.5)+8[/tex]Solving these operations:
[tex]5+8=13[/tex]It will cost £13.
Answer:
a. £2.5
b. £8
c. £13
Find the value of x in this equation.
|2x − 3| − 11 = 0
The value of x in the given equation is 3/2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
WE have been given that equation is |2x − 3| − 11 = 0
First Combine similar terms and use the equality properties to find the variable on one side of the equals sign and the numbers on the other side.
|2x − 3| − 11 = 0
Add 11 to both sides of the equation;
|2x − 3| − 11 + 11= 0 + 11
|2x − 3| = 0
Add 3 to both sides of the equation;
2x - 3 + 3 = 3
2x = 3
Divide both sides by 2;
x = 3/2
Hence, the value of x in the given equation is 3/2.
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