ANSWER
1,440
EXPLANATION
We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.
For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,
[tex]permutations_{boys}=4\cdot3\cdot2=24[/tex]This situation is similar for the girls, but in this case, there are 5 girls in total,
[tex]permutations_{girls}=5\times4\times3=60[/tex]The total ways the six medals can be given is,
[tex]permutations_{boys}\times permutations_{girls}=24\times60=1,440[/tex]Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.
Which of the following polar coordinates would not be located at the point?
Explanation
We are asked to select the option that would not be located at the given point
To do so, let us find the original coordinates of the given polar point
The point is located 6 units away from the origin in a direction of 270 degrees
The equivalent coordinates are
[tex]\begin{gathered} (6,\frac{3\pi}{2}) \\ (6,\frac{-\pi}{2}) \\ (-6,90^0) \end{gathered}[/tex]Thus, we are to eliminate any option that is not equivalent to the above, we are left with
[tex](6,\frac{-3\pi}{2})[/tex]Thus, the answer is option A
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.
I need help on question number 1 I have been stuck on it for a long time
Explanation
Step 1
Vertical angles are formed when two lines intersect each other. Out of the 4 angles that are formed, the angles that are opposite to each other are vertical angles. vertical angles are congruent so
[tex]\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ \end{gathered}[/tex]Step 1
replace the given values
[tex]\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ -2(3x-4)=3(x-3)-1 \end{gathered}[/tex]now, we need to solve for x
a)
[tex]\begin{gathered} -2(3x-4)=3(x-3)-1 \\ \text{apply distributive property} \\ -6x+8=3x-9-1 \\ \text{add like terms} \\ -6x+8=3x-10\rightarrow reason\text{ distributive property} \end{gathered}[/tex]b)subtract 3x in both sides( additioin or subtraction property of equality)
[tex]\begin{gathered} -6x+8=3x-10 \\ subtract\text{ 3x in both sides} \\ -6x+8-3x=3x-10-3x \\ -9x+8=-10 \\ \text{subtract 8 in both sides} \\ -9x+8-8=-10-8 \\ -9x=-18 \\ -9x=-18\rightarrow reason\colon\text{ addition and subtraction property of equality} \end{gathered}[/tex]c) finally, divide both sides by (-9) division property of equality
[tex]\begin{gathered} -9x=-18 \\ \text{divide both side by -9} \\ \frac{-9x}{-9}=\frac{-18}{-9} \\ x=2\rightarrow\text{prove} \end{gathered}[/tex]i hope this helps you
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.
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
(spanish only) (Foto)
Respuesta:
Rectángulo.
Explicación paso a paso:
Cuando un triangulo isósceles (ángulos de la base de igual magnitud) miden 45°, significa que el ángulo que no conocemos será de 90 grados por el teorema de los ángulos internos de un triángulo.
180-(45+45)=90.
Por lo tanto, se forma un triangulo rectángulo, significa que tiene un ángulo recto de 90°.
At a party 15 handshakes took place. Each person shook hands exactly once with each of the other present. How many people were at the party?
2 people => 1 handshake (AB)
3 people => 3 handshakes (AB, BC, AC)
4 people => 6 handshakes (AB, AC, AD, BC, BD, CD)
Do you see a pattern here?
We can write a general formula for this
[tex]handshakes=\frac{n\cdot(n-1)}{2}[/tex]Since we are given that there were 15 handshakes
[tex]15=\frac{n\cdot(n-1)}{2}[/tex][tex]\begin{gathered} 2\cdot15=n\cdot(n-1) \\ 30=n\cdot(n-1) \\ 30=6\cdot(6-1) \\ 30=6\cdot(5) \\ 30=30 \end{gathered}[/tex]This means that n = 6 people were present at the party.
You can substitute n = 6 into the above formula and you will notice that it will give 15 handshakes
[tex]handshakes=\frac{n\cdot(n-1)}{2}=\frac{6\cdot(6-1)}{2}=\frac{6\cdot5}{2}=\frac{30}{2}=15[/tex]proportional relationships, math
The answer is yes, the equation represents a proportional relationship.
The reason is that a proportional relationship is best described as that in which the value of one variable depends on what happens to the other variable. Just like having one more child every year would mean spending more money on education, etc.
In a proportiona; relationship as shown in this question, y is the total cost of a pizza and each x (each topping) would determine how much is y. So requesting for 5 more toppings would result in 1.5 multiplied by 5, and requesting 10 more would result in 1.5 multiplied by 10. So as the amount of toppings (x variable) increases, the total cost (y variable) likewise would increase.
As x increases or decreases, the value of y would likewise increase or decrease. That makes this equation a proportional relationship
Find the area of the shaded region in the figure Type an integer or decimal rounded to the nearest TENTH
Answer:
The area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]Explanation:
Given the figure in the attached image.
The area of the shaded region is the area of the larger circle minus the area of the smaller circle;
[tex]\begin{gathered} A=\frac{\pi D^2}{4}-\frac{\pi d^2}{4} \\ A=\frac{\pi}{4}(D^2-d^2) \end{gathered}[/tex]Given;
[tex]\begin{gathered} D=6 \\ d=3\frac{1}{2} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} A=\frac{\pi}{4}(D^2-d^2) \\ A=\frac{\pi}{4}(6^2-3.5^2) \\ A=\frac{\pi}{4}(23.75) \\ A=18.65\text{ }in^2 \\ A=18.7\text{ }in^2 \end{gathered}[/tex]Therefore, the area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]The polynomial is not written in order how many terms does the polynomial have
Answer:
[tex]\text{This polynomial has 4 terms.}[/tex]Step-by-step explanation:
a TERM is a variable, number, or product of a number and one or more variables with exponents.
Then, ordering the polynomial:
[tex]\begin{gathered} x^3+2x^2+4x-2 \\ \text{This polynomial has 4 terms.} \end{gathered}[/tex]Rabbit's run: distance (meters) time (minutes) way 800 1 900 5 1107.5 20 1524 32.5
Answer:
Notice that:
[tex]\begin{gathered} \frac{800}{1}=800, \\ \frac{900}{5}=180, \\ \frac{1107.5}{20}=\frac{443}{8}, \\ \frac{1524}{32.5}=\frac{3048}{65}. \end{gathered}[/tex]Since all reduced fractions are different, the distance traveled by the rabbit and the time are not proportional.
Solve the inequality a < 5 and write the solution using: Inequality Notation:
Answer:
Step-by-step explanation:
Open the image attached belowProve that:sec n/(tan n + cot n) = sin n
Given:
We are required to prove:
[tex]\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ = sin}\theta[/tex]From the left-hand side:
[tex]\begin{gathered} =\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ } \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}\text{ + }\frac{\cos \theta}{\sin \theta}} \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin ^2\theta+cos^2\theta}{\sin \theta\cos \theta}} \\ \end{gathered}[/tex]From standard trigonometric identity, we have:
[tex]\sin ^2\theta+cos^2\theta\text{ = 1}[/tex]Substituting we have:
[tex]\begin{gathered} =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{1}{\sin \theta\cos \theta}} \\ =\text{ }\frac{\sin \theta\cos \theta}{\cos \theta} \\ =\text{ sin }\theta\text{ (Right-hand side)} \end{gathered}[/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)
Topic 8.2: Solving Using Linear/HELP RN!!!!!Area Scale Factor3. Examine the two similar shapes below. What is the linear scale factor? What is the area scalefactor? What is the area of the smaller shape?3a. Linear scale factor =3b. Area scale factor =Area =99 un.2=3c. Area of small shape =
Solution
Question 3:
- Let the dimension of a shape be x and the dimension of its enlarged or reduced image be y.
- The linear scale factor will be:
[tex]sf_L=\frac{y}{x}[/tex]- If the area of the original shape is Ax and the Area of the enlarged or reduced image is Ay, then, the Area scale factor is:
[tex]sf_A=\frac{A_y}{A_x}=\frac{y^2}{x^2}[/tex]- We have been given the area of the big shape to be 99un² and the dimensions of the big and small shapes are 6 and 2 respectively.
- Based on the explanation given above, we can conclude that:
[tex]\begin{gathered} \text{ If we choose }x\text{ to be 6, then }y\text{ will be 2. And if we choose }x\text{ to be 2, then }y\text{ will be 6} \\ \text{ So we can choose any one.} \\ \\ \text{ For this solution, we will use }x=6,y=2 \end{gathered}[/tex]- Now, solve the question as follows:
[tex]\begin{gathered} \text{ Linear Scale factor:} \\ sf_L=\frac{y}{x}=\frac{2}{6}=\frac{1}{3} \\ \\ \text{ Area Scale factor:} \\ sf_A=\frac{y^2}{x^2}=\frac{2^2}{6^2}=\frac{1}{9} \\ \\ \text{ Also, we know that:} \\ sf_A=\frac{A_y}{A_x}=\frac{y^2}{x^2} \\ \\ \text{ We already know that }\frac{y^2}{x^2}=\frac{1}{9} \\ \\ \therefore\frac{A_y}{A_x}=\frac{1}{9} \\ \\ A_x=99 \\ \\ \frac{A_y}{99}=\frac{1}{9} \\ \\ \therefore A_y=\frac{99}{9} \\ \\ A_y=11un^2 \end{gathered}[/tex]Final Answer
The answers are:
[tex]\begin{gathered} \text{ Linear Scale Factor:} \\ \frac{1}{3} \\ \\ \text{ Area Scale Factor:} \\ \frac{1}{9} \\ \\ \text{ Area of smaller shape:} \\ 11un^2 \end{gathered}[/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.
A manufacturing process has a 70% yield, meaning that 70% of the products
Answer:
are acceptable and 30% are defective.
Step-by-step explanation:
Find the slope and y-intercept for each equation:2. 2x + 9y = 18
Step-by-step explanation:
we need to transform the equation into the slope-intercept form
y = ax + b
a is then the slope, abd b is the y-intercept (the y-value when x = 0).
2x + 9y = 18
9y = -2x + 18
y = -2/9 x + 2
so,
-2/9 is the slope
2 is the y-intercept
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]
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.
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]suppose g(x) = f(x - 3) - 4. I need the graph of g(x) with the graph of f(x)
In order to graph g(x) with the graph of f(x), first we need a translation of 3 units to the right, because of the term f(x - 3)
Then, we need a translation of 4 units down, because of the term -4.
So the movements are: translations of 3 units right and 4 units down.
1
P(7,-3); y=x+2
Write an equation for the line in point-slope form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The equation of line in point-slope form is Y + 3 = 1(X - 7).
What is point-slope form?
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
(Y-Y1)=m(X-X1) is the point-slope form of the equation.
Here the given equation of line is y = x + 2 and the point is (X1, Y1) = (7, -3).
Compare this equation with y = mx + c, which is point slope form of the line.
Where, m is the slope and c is the y - intercept.
So, m = 1 and c = 2.
Now plug m = 1 and (x1, y1) = (7, -3) in the equation (Y-Y1)=m(X-X1),
(Y - (-3)) = 1(X - 7)
Y + 3 = 1(X - 7)
Therefore, the equation for the line y = x + 2 in point - slope form is Y + 3 = 1(X - 7).
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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]
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
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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Help please I’ll give 10 points
The writing of the symbols, <, =, or > in each of the comparison (equality or inequality) statements is as follows:
1. 0.02 > 0.002
2. 0.05 < 0.5
3. 0.74 < 0.84
4. 0.74 > 0.084
5. 1.2 < 1.25
6. 5.130 = 5.13
7. 3.201 > 3.099
8. 0.159 < 1.590
9. 8.269 > 8.268
10. 4.60 > 4.060
11. 302.026 > 300.226
12. 0.237 > 0.223
13. 3.033 < 3.303
14. 9.074 < 9.47
15. 6.129 < 6.19
16. 567.45 > 564.75
17. 78.967 > 7.957
18. 5.346 < 5.4
19. 12.112 < 12.121
20. 26.2 = 26.200
21. 100.32 > 100.232
22) The strategy for solving comparison mathematical statements is to check the place values.
What is a place value?A place value is a numerical value that a digit possesses because of its position in a number.
To find a digit's place value, discover how many places the digit is to the right or left of the decimal point in a number.
Some of the place values before the decimal place include Millions, Hundred Thousands, Ten Thousands, Thousands, Hundreds, Tens, and Units.
After the decimal place, the place values are tenths, hundredths, thousandths, ten thousandths, hundred thousandth, and millionths.
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The Hernandez family and the Cox family each used their sprinklers last summer. The Hernandez family’s sprinkler was used for 15 hours. The fox familys sprinkler was used for 30 hours. There was a combined total output of 1275 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?
ANSWER
The output rate for the Hernandez family was 15 L/hr and for the Fox family was 35 L/hr.
EXPLANATION
To solve this problem, we have to create a system of two simultaneous equations.
Let the output rate of the Hernandez family sprinkler be h.
Let the output rate of the Fox family sprinkler be f.
The product of the rate and the time used is equal to the output:
[tex]\text{Rate}\cdot\text{time}=\text{output}[/tex]We have that the combined total output for both sprinklers is 1275 L, which means that:
[tex]\begin{gathered} (15\cdot h)+(30\cdot f)=1275 \\ \Rightarrow15h+30f=1275 \end{gathered}[/tex]The sum of the two rates is 50 L/hr, which means that:
[tex]h+f=50[/tex]Now, we have a system of two simultaneous equations:
[tex]\begin{gathered} 15h+30f=1275 \\ h+f=50 \end{gathered}[/tex]Solve the equations by substitution.
Make h the subject of the formula in the second equation:
[tex]h=50-f[/tex]Substitute that into the first equation:
[tex]\begin{gathered} 15(50-f)+30f=1275 \\ 750-15f+30f=1275 \\ 750+15f=1275 \\ \Rightarrow15f=1275-750=525 \\ f=\frac{525}{15} \\ f=35\text{ L/hr} \end{gathered}[/tex]Recall that:
[tex]h=50-f[/tex]Therefore, we have that:
[tex]\begin{gathered} h=50-35 \\ h=15\text{ L/hr} \end{gathered}[/tex]Hence, the output rate for the Hernandez family was 15 L/hr and for the Fox family was 35 L/hr.
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
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]