Given
The water park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buses with 354 students. Each van and each bus carried the same number of students.
Answer
Let students in Van be x
And students in bus be y
A/Q
x + 14y = 309 (1)
4x + 14y = 354 (2)
Subtracting (1) and (2)
3x = 45
x = 15
Put in eq (1)
15 + 14 y = 309
14y = 309 - 15
14 y = 294
y = 21
St
152. ) Find all real x such that square root x + 1 = x - Square root x - 1.
Given the equation:
[tex]\sqrt[]{x}+1=x-\sqrt[]{x}-1[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{x}+\sqrt[]{x}=x-1-1 \\ 2\sqrt[]{x}=x-2 \end{gathered}[/tex]Now, we take the square on both sides of the equation:
[tex]\begin{gathered} 4x=x^2-4x+4 \\ 0=x^2-8x+4 \end{gathered}[/tex]Now, using the general solution of quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=-8 \\ c=4 \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot4}}{2\cdot1}=\frac{8\pm\sqrt[]{64-16}}{2} \\ x=\frac{8\pm4\sqrt[]{3}}{2}=4\pm2\sqrt[]{3} \end{gathered}[/tex]But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:
[tex]x=4+2\sqrt[]{3}[/tex]A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone's volume lies inside the cylinder? Express your answer as a common fraction.
The fraction of the cone's volume that lies inside the cylinder would be; V = 44/21 r^4
How to find the volume of a right circular cone?Suppose that the radius of the considered right circular cone is 'r' units.
And let its height be 'h' units. The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Then, its volume is given :
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Let the radius of the cylinder is r
The height of the cylinder is h = 3r
The height of the cone is h = 6r
The fraction of the cone's volume that lies inside the cylinder would be;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 3.14 \times r^3 \times 6r \: \rm unit^3[/tex]
V = 44/21 [tex]r^{4}[/tex]
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Answer:
4/9
Step-by-step explanation:
Answer ASAP please and thank you :)
We can see the pairs (-1, 4) and (1, 4), so the function is not invertible.
Is the function g(x) invertible?
Remember that a function is only invertible if it is one-to-one.
This means that each output can be only mapped from a single input (the outputs are the values of g(x) and the inputs the values of x).
In the table, we can see the pairs (-1, 4) and (1, 4).
So both inputs x = -1 and x = 1 have the same output, this means that the function is not one-to-one, so it is not invertible.
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relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplots
The answer is
[tex]m\text{ }\ne\text{ 0}[/tex]So the first one is the answer.
Because if m = 0 then the function would be a constant function that does not have inverse. and we don't care if b= 0 or not because even if b= 0 or no we just need to know about m.
10 × 1/3
make sure the answer is a fraction and that u explain
1. Ms. Oates is going to plant grass in her backyard. It is 14feet wide and 20.5 feet long. What is the area of thebackyard that will need to be covered with grass?
Area of a rectangle is given by the expression:
[tex]A=\text{base}\times height[/tex]Then:
[tex]\begin{gathered} A=20.5\times14 \\ A=287\text{ square f}eet \end{gathered}[/tex]The area that will need to be covered is 287 square feet.
Write a rule for the given translation.P(-3,6) to P^1(-4,8)
To turn P(-3,6) to P'(-4,8), we have to
•Move 1 unit to the left (from -3 to -4)
•Move 2 units up (from 6, to 8)
TRIGONOMETRY Given a unite circle what is the value for y?
Let's put more details in the given figure:
To find y, we will be using the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{r}^2=x^2+y^2 \\ \end{gathered}[/tex]Where,
r = radius
x = 1/3
y = uknown
We get,
[tex]\text{r}^2=x^2+y^2[/tex][tex]\begin{gathered} y^2\text{ = r}^2\text{ - }x^2 \\ y^{}\text{ = }\sqrt{\text{r}^2\text{ - }x^2} \end{gathered}[/tex][tex]\text{ y = }\sqrt[]{1^2-(\frac{1}{2})^2}\text{ = }\sqrt[]{1\text{ - }\frac{1}{4}}[/tex][tex]\text{ y = }\sqrt[]{\frac{3}{4}}\text{ = }\frac{\sqrt[]{3}}{\sqrt[]{4}}[/tex][tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Therefore, the answer is:
[tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Select the correct answer. What are the zeros of the graphed function? у -6 -5 3 -2 2 3 6 2 3 OA O and 4 OB. 4,-2, and o OC. 0, 2, and 4 OD. -4 and o Reset Next
We have that the next x-intercepts 0,2 and 4, in the graph therefore the zeros of the graph are 0,2 and 4.
The correct choice is C.
10. (01.04 LC)
Your first six-month auto insurance premium was $658.00. Based on your driving record, your renewal premium is $756.70. What percent increase did you see in your premium? (1
12%
15%
28%
35%
There is 15% in the premium.
How take out percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
First six-month auto insurance = $658
Renewal premium = $756
Change in the insurance = $98
percentage of $98 from $658
= 15%
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For how many integers n is 28÷n an interger
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integers: -1.43, 1 3/4, 3.14,.09, and 5,643. 1.
How do you determine an integer's number from a number?
Basic Interest Calculator
Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula. The simplest method for computing interest is using this equation.
The answer to the question "How many integers are there in n?" is n-1.
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A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 360 yards, what are its dimensions?
Answer:
The width is 60 and the length is 120
Step-by-step explanation:
Let l = length
Let w = width
l = 2w
Perimeter
l + l + w + w = 360 Substitute 2w for l
2w + 2w + w + w =360 Combine line terms
6w = 360 Divide both sides by 6
w = 60
If w = 60 then l = 120
Simplify the square root of 25x^4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
[tex]\sqrt{25x^4}[/tex]Step 02:
simplify (radical):
[tex]\sqrt{25x^4}=\sqrt{5^2x^4}=5x^2[/tex]The answer is:
5x²
Rewrite 25% as a fraction in simplest form.
Answer:
1/4
Step-by-step explanation:
hi can you see if I did this estimate right?
Mr Manet need 5 guitars for his 4 grandsons and 1 granddaughter.
Each guitar costs $88,
So the total cost of guitars is $88 x 5 = $440
The best estimate among the choices is Choice B. $450
The estimate should always be higher than the actual cost.
I need help graphing 3x+y=-1I already found the x intercept= -1/3
Here, we want to graph the line
To do this, we need to get the y-intercept and the x-intercept
The general equation form is;
[tex]y\text{ = mx + b}[/tex]M is the slope while b is the y-intercept
Let us write the equation in the standard from;
[tex]y\text{ = -3x-1}[/tex]The y-intercept is -1
So we have the point (0,-1)
To get the x-intercept, set y = 0
[tex]\begin{gathered} 0\text{ = -3x-1} \\ -3x\text{ = 1} \\ x\text{ = -}\frac{1}{3} \end{gathered}[/tex]So, we have the x-intercept as (-1/3,0)
Now, if we join the two points, we have successfully graphed the line
Add and subtract square roots that need simplification Number 186
Hello!
To solve this exercise, we must simplify these square roots until we have the same square root in both numbers (by the factorization process):
[tex]3\sqrt{98}-\sqrt{128}[/tex]First, let's factorize the square root of 98:
So, we know that:
[tex]\begin{gathered} 3\sqrt{98}=3\sqrt{7^2\times2}=3\sqrt[\cancel{2}]{7\cancel{^2}\times2}=3\times7\sqrt{2}=21\sqrt{2} \\ \\ 3\sqrt{98}=21\sqrt{2} \end{gathered}[/tex]Now, let's do the same with the square root of 128:
So:
[tex]\sqrt{128}=\sqrt{2^2\times2^2\times2^2\times2}^1[/tex]Notice that it also could be written as:
[tex]\begin{gathered} \sqrt{128}=\sqrt{2\times2\times2\times2\times2\times2\times2} \\ \text{ or also} \\ \sqrt{128}=\sqrt{2^7} \end{gathered}[/tex]As we are talking about square roots, it will be easier if we group them in pairs of powers of 2, as I did:
[tex]\sqrt[2]{128}=\sqrt[2]{2^2\times2^2\times2^2\times2^1}[/tex]Now, let's analyze it:If the number inside the root has exponent 2, we can cancel this exponent and remove the number inside the root. Then, we can write it outside of the root, look:
[tex]\begin{gathered} \sqrt[2]{128}=\sqrt[2]{2^{\cancel{2}}\times2^{\cancel{2}}\times2^{\cancel{2}}\times2^1} \\ \sqrt[2]{128}=2\times2\times2\sqrt[2]{2^1} \\ \sqrt[2]{128}=8\sqrt[2]{2} \end{gathered}[/tex]Now, let's go back to the exercise:[tex]\begin{gathered} 3\sqrt{98}-\sqrt{128}\text{ is the same as } \\ 21\sqrt{2}-8\sqrt{2} \end{gathered}[/tex]So, we just have to solve it now:
[tex]21\sqrt{2}-8\sqrt{2}=\boxed{13\sqrt{2}}[/tex]Lesson 12.03: Plot Twists Printable Assessment: Plot Twists Plot Twists Show your work. 1. Use the data set provided to create a line plot. Distance of Ski Trails (miles) 1 2 3 2 7 8 4 м 3 - - - - 2 8 1 8 8 -|+ 100 - mlo 2 2 7 8 -100 100-00 글 1 2 2 1 3 8 3 HH 士。 8 2. What is the total number of ski trails? 3. What is the difference in length between the longest ski trail and the shortest ski trail? 7 4. What is the total length of all the ski trails that are 2 miles long? 8 25 5. What is the sum of the lengths of the shortest and longest ski trails? 6. Sam says the longest ski trail is more than three times the length of the shortest ski trail. Eli says it is less than three times the length. Who is correct? Explain.
I need help on my practice sheet. needs to be simplified
then
[tex]\begin{gathered} \frac{x+6}{3x}\times\frac{3(x-6)}{(x+6)(x-6)} \\ \frac{x+6}{3x}\times\frac{3}{x+6} \\ \frac{(x+6)\times3}{3x\times(x+6)} \\ \frac{3}{3x} \\ \frac{1}{x} \end{gathered}[/tex]answer: 1/x
CALCULATO 11 i You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth. 1 2 3 The probability of spinning blue, flipping heads, then spinning a 1 is
Let:
A = Spinning blue
B = flipping heads
C = Spinning a 1
The probality of spinning blue is given by:
[tex]P(A)=\frac{1}{3}[/tex]The probality of flipping heads is:
[tex]P(B)=\frac{1}{2}[/tex]The probality of spinning 1 is given by:
[tex]P(C)=\frac{1}{3}[/tex]Since they are independent events:
[tex]P(A\cap B\cap C)=P(A)\cdot P(B)\cdot P(C)=\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{3}=\frac{1}{18}[/tex]
What is the slope of a line that is perpendicular to the line whose equation is 3x+2y=6?A. −3/2B. −2/3C. 3/2D. 2/3
We would begin by determining the slope of the line given;
[tex]3x+2y=6[/tex]To determine the slope, we would have to express the equation of the line in slope-intercept form as follows;
[tex]y=mx+b[/tex]Therefore, we need to make y the subject of the equation as shown below;
[tex]\begin{gathered} 3x+2y=6 \\ \text{Subtract 3x from both sides of the equation} \\ 2y=6-3x \\ \text{Divide both sides by 2 } \\ \frac{2y}{2}=\frac{6-3x}{2} \\ y=\frac{6}{2}-\frac{3x}{2} \\ y=3-\frac{3}{2}x \end{gathered}[/tex]The equation in slope-intercept form appears as shown above. Note that the slope is given as the coefficient of x.
Note alo that the slope of a line perpendicular to this one would be a "negative inverse" of the one given.
If the slope of this line is
[tex]-\frac{3}{2}[/tex]Then, the inverse would be
[tex]-\frac{2}{3}[/tex]The negative of the inverse therefore is;
[tex]\begin{gathered} (-1)\times-\frac{2}{3} \\ =\frac{2}{3} \end{gathered}[/tex]The answer therefore is option D
The point K lies on the segment JL. Find the coordinates of K so that the ratio of JK to KL is 5 to 4.J(-19,12)K(?,?)L(8,-6)
The Solution:
Step 1:
We shall find the distance between point J an
find the product of 1/1728.
The answer is 12
Because 12x12x12 = 1728
3x - 7 = 3(x - 3) + 2
What are examples of vertical stretch and compression and horizontal stretch and compression?
Examples of vertical stretch and compression and also horizontal stretch/vertical compression are explained below considering x² and
sin(x) function.
What is vertical stretch/vertical compression ?
A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.example : If the graph of x² is is transformed to 2x² Then the function is compressed Vertically.
If the graph of x² is is transformed to x²/2 Then the function is stretch Vertically.
What is horizontal stretch/vertical compression ?
We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively this phenomenon is horizontal stretch and compression.example : If the function y = sin(x) is transformed to y = sin(2x) Then the function is compressed horizontally.
example : If the function y = sin(x) is transformed to y = sin(x/2) Then the function is stretch horizontally.
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Given the points (3, -2) and (4, -1) find the slope
Slope is
[tex]\text{slope}=\frac{y2-y1}{x2-x1}[/tex]Then:
[tex]\text{slope}=\frac{-1-(-2)}{4-3}=\frac{-1+2}{1}=\frac{1}{1}=1[/tex]Answer: slope = 1
Please help me answer this correctly,
anywhere you see x, input the value in the brackets.
eg f(-2) = 2(-2)+8
= -4+8
=4
Answer:
if x= -2
then f(x) = 2×(-2)+8
= -4+8
= 4
if x=0
then f(x)=2×0+8
=0+8
=8
if x=5
then f(x)=2×5+8
=10+8
=18
If $5000 is invested at 9% annual simple interest, how long does it take to be worth $9050?
It takes 9 years to make $9050 from $5000 investment.
Given that, Principal = $5000, rate of interest = 9% and Amount = $9050.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, S.I. = Amount - Principal
= 9050-5000 = $4050
Now, 4050=(5000×9×T)/100
⇒ 4050/450 = T
⇒ T = 9 years
Therefore, it takes 9 years to make $9050 from $5000 investment.
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Find 5 number summary for data given
The 5 number summary of the data given is:
Minimum = 59
Q1 = 66.50
Median = 78
Q3 = 90
Maximum = 99
What is the 5 number summary?A stem and leaf plot is a table that is used to display a dataset. A stem and leaf plot divides a number into a stem and a leaf. The stem is the first digit in a number while the leaf is the second digit in the number.
The minimum is the smallest number in the stem and leaf plot. This is 59. Q1 is the first quartile.
Q1 = 1/4 x (n + 1)
Where n is the total number in the dataset
1/4 x 19 = 4.75 term
(64 + 69) / 2 = 66.50
Q3 is the third quartile.
Q1 = 3/4 x (n + 1)
Where n is the total number in the dataset
3/4 x 19 = 14.25 term = 90
The median is the number that is at the center of the dataset.
Median = 1/2(n + 1)
1/2 x 19 = 8.5 term
(76 + 80) / 2 = 78
The maximum is the largest number in the dataset. This number is 99.
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The length of a rectangle is 6 more than three times the width. If the perimeter of the rectangle is equal to 274 feet then what are the length and width equal to ?(Both of your answers are decimals)The width =The length =
Given data:
The gieven length of the rectangle in erms of width is L=3w.
The perimeter of rectangel is P=274 feet.
The expressio for the perimeter of the rectangle is,
P=2(L+w)
Substitute the given values in the above expression.
274 feet=2(3w+w)
274 feet=8w
w=34.25 feet.
The length of the rectangle is,
L=3(34.25 feet)
=102.75 feet.
Thus, the width is 34.25 feet and lenth of rectangle is 102.75 feet.