Explanation
We are asked to find the change in the water level per hour for Patrick's swimming
We have to use the formula
[tex]change\text{ in water level per hour=}\frac{Volume\text{ of water}}{Time\text{ taken to drain}}[/tex]Thus
[tex]change\text{ in water level per hour=}\frac{9644.6}{8}=1205.575\text{ gallons per hour}[/tex]Note: The rate will be negative because we are draining
Therefore, the change in water level will be -1205.58 gallons per hour
The figure shows a person estimating the height of a tree by looking at thetop of the tree with a mirror. Assuming that both the person and the tree formright angles with the ground, which of the following proportions can be usedto estimate the height of the tree?6 ft3 ft7 fthft
SOLUTIONS
Using the rule of SOHCAHTOA:
The height of the tree compared to the height of the boy is tangent:
[tex]tan\theta=\frac{opp}{adj}[/tex]For the small triangle:
[tex]tan\theta=\frac{6}{3}.........(1)[/tex]For the Big triangle:
[tex]tan\theta=\frac{h}{7}..........(11)[/tex]Equating (1) and (11
[tex]\begin{gathered} \frac{6}{3}=\frac{h}{7} \\ \frac{6}{h}=\frac{3}{7} \end{gathered}[/tex]Hence the correct answer = Option A
What is the perimeter of the figure2x + 3 inchesX- 6 inches
Perimeter of the figure = 6x - 6
Explanation:Perimeter = 2(length + width)
length = 2x + 3 inches
width = x- 6 inches
Perimeter = 2(2x + 3 + x- 6)
collect like terms in the bracket:
= 2(2x +x + 3 - 6)
= 2(3x - 3)
Expand the bracket:
Perimeter = 2 × 3x + 2× -3
Perimeter of the figure = 6x - 6
The lines represented by the equations y = 1/2x-8 and 2y+4x=10
The first equation is in slope-intercept form but the second equation is not. Therefore, our first step is to bring 2y+4x=10 into slope-intercept form.
Subtracting 4x from both sides gives
[tex]2y=10-4x[/tex]finally, dividing both sides by 2 gives
[tex]y=-2x+5[/tex]Now, that we have the equation in slope-intercept form, let us compare their slopes to see how they relate to each other.
The lines are perpendicular if the slope of one line is negative of the reciprocal of the other.
Now, -2 is negative of the reciprocal of 1/2. Meaning if you take the reciprocal 1/2, then multiply it by -1 you will end up with -2.
Since the slope of a negative reciprocal of each other, the lines are perpendicular.
what does ☆ equal if the symbols below represents digits 0-9?
First, let's start from the sixth equation.
Since the parallelogram divided by the circle is equal the parallelogram, it means the circle has a value of 1.
Then, from the 7th equation, the pentagon minus the arrow is equal the pentagon, it means the arrow is equal 0.
From the 8th equation, the two curved arrows summed are equal 10, so the curved arrow is equal 5.
From the 2nd and 4th equations we can find that the triangle is equal 2.
Using the value of the pentagon from the 4th equation in the 3rd one, we have that 3 * moon is equal parallelogram, so the only option is:
moon = 3, pentagon = 6, parallelogram = 9.
From the 1st equation, the square is equal 8.
Finally, from the 5th equation, the arrow with circle is equal 7.
So we have:
pentagon = 6
parallelogram = 9
moon = 3
triangle = 2
arrow = 0
curved arrow = 5
arrow with circle = 7
circle = 1
square = 8
So the star is the missing algarism: 4
The number of needles in each packet are 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7,and 8. Find the range of the given data.
Given that
The number of needles in the packet is 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8
And we have to find the range of this data.
Explanation -
To find the range first we will arrange the numbers in the order as
1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 7, 8
Now we will subtract the lowest number from the highest to get the range.
So
nge = 8 - 1 = 7
Final answer -
Hence the range is 7, So the final answer is 7.solve for x[tex] \frac{x + 3}{2} + \frac{2x}{7} = 7[/tex]just need some help with this
Here, we are to calculate for the value of x.
We start by finding the Lowest common multiples of both fractions. The lowest common multiple of both fractions is 14
Now, we can multiply each of the terms in the question by 14. Thus, we have;
14(x + 3)/2 + 14(2x/7) = (7 * 14)
7(x + 3) + 2(2x) = 98
Opening the brackets, we have;
7x + 21 + 4x = 98
Collect like terms;
7x + 4x = 98 - 21
11x = 77
x = 77/11
x = 7
Options for all the three boxes are:neither student, Becky and Laura
The parent cosine function is given to be:
[tex]f(x)=\cos (x)[/tex]The graph of this function is shown below:
Laura's Function:
Laura's function is given to be horizontally compressed by a factor of 1/3 and reflected over the x-axis.
The rule for horizontal compression by a factor of 1/a is given to be:
[tex]f(x)\Rightarrow f(\frac{1}{a}\cdot x)[/tex]and the rule for reflection over the x-axis is given to be:
[tex]f(x)\Rightarrow-f(x)[/tex]Therefore, Laura's function will be:
[tex]f(x)=-\cos (3x)[/tex]The graph of the function will be:
Becky's Function:
Becky's function is given to be:
[tex]f\mleft(x\mright)=3\cos \mleft(x-\pi\mright)[/tex]The graph is given to be:
ANSWERS:
BECKY's GRAPH is the FIRST GRAPH
The SECOND GRAPH belongs to NEITHER
LAURA's GRAPH is the THIRD GRAPH
find the correct area
we have that the area of the semicircle is 100,530964915 m^2
[tex]\begin{gathered} A\text{ = }\frac{\pi r^2}{2} \\ =\text{ }\frac{\pi(8m)^2}{2}=\text{ }32\pi m^2 \\ =\text{ }100,530964915m^2 \end{gathered}[/tex]Now we need to find the area of the triangle, we now that the area of the non rectangle triangle is 96 m^2
[tex]\begin{gathered} A\text{ = }\frac{b\cdot h}{2}\text{ = }\frac{16m\cdot\text{ 12m}}{2} \\ =\text{ }\frac{192m^2}{2}=96m^2 \end{gathered}[/tex]So the area of the figure is 196,530964915, the answer is 196.5 m^2.
Simplify each expression using Product to a Power Property a. (9a)^2 b. ( 3x)^2
1) Let's simplify those expressions making use of exponents rules:
[tex](9a)^2=81a^2[/tex]Note that the exponent outside the parenthesis is 'distributed' over each term inside.
2) Similarly for the second expression we can state that:
[tex](3x)^2=9x^2[/tex]Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 1: Problem
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 2: Concept
Word problem on subtraction
Step 3: Method
Audrey total earning = $528
Money spent on new bike = $125.7
Money spent on new clothes = $85.09
Money left = 528 - 125.7 - 85.09
= $317.21
Step 4: Final answer
Audrey money left = $317.21
Jose is riding his bicycle. He rides for 14.4 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride?hours:
Given:-
Jose rides 14.4 kilometers at a speed of 9 kilometers.
To find:-
The amount of hours he ride.
The formula used to find the time is,
[tex]time=\frac{Dis\tan ce}{speed}[/tex]Subsituting the value we get,
[tex]\begin{gathered} t=\frac{14.4}{9} \\ t=1.6 \end{gathered}[/tex]So the amount of hours jose rides is 1.6 hours.
Mrs. Walsh assigned 16 worksheets each month, how many did she assign over 4 montns?
Data Input
Mrs. Walsh assigned 16 worksheets each month
Procedure
To calculate the number of worksheets we need to multiply the number of months by the number of worksheets per month
Total = 16*4 = 64 Worksheets
I need help with this
Ok, so
We have the following expression:
We're going to multiply all terms inside the bracket by "-x", and we obtain:
So, the answer is B.
a crate is 24cm by 18cm by 15cm. it has to be packed with boxes that are 8cm by 6cm by 5cm. what is the largest number of boxes that can fit in the crate.
please help its level 2
show answer and working out.
The maximum no. of small boxes that can fit is 27 boxes.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2( lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A crate is 24cm by 18cm by 15cm and it has to be packed with boxes that are 8cm by 6cm by 5cm.
Now, the maximum no of small boxes that can fit is the volume of the larger box divided by the volume of the sampler box which is,
= (24×18×15)/(8×6×5).
= 3×3×3.
= 27 boxes.
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if 5 pounds of apples cost 5.50,then what is the cost of 1 pound of apples
The cost of 1 pound of apple is 1.10
Here, we want to calculate the cost of 1 pound of apples given the cost of 5 pounds
From the question;
5 pounds = 5.5
1 pound = x
Thus, we have that;
[tex]\begin{gathered} 5\text{ }\times\text{ x = 1 }\times\text{ 5.5} \\ \\ 5x\text{ = 5.5} \\ \\ x\text{ = }\frac{5.5}{5} \\ \\ x\text{ = 1.1} \end{gathered}[/tex]A builder is buying boxes of nails. She has $187 to spend and each box of nails costs $4. How many boxes of nails can the builder buy?42503746
To find How many boxes of nails can the builder buy divide the total she has into the cost of each box:
Then, she can buy 46 boxes of nailsHelp with number one a and b is both parts of number one
Design A. The garden is 9 ft by 12 ft.
Design B. The garden is a circle of radius 5 ft
Area of garden A:
[tex]A_A=9\times12=108[/tex]Area of garden B:
[tex]A_B=\pi\left(5\right)^2=25\pi\approx78.54[/tex]The areas are:
Design A = 108 square ft
Design B ≈ 78.54 square ft
Note: The area of garden B can also be expressed in exact form as 25π square ft
The following dataset represents the dollar amounts of donations collected at the entrance to a free museum during onehour:5, 10,5,5, 15, 1, 10, 10,5,600,5Is the mean a reasonably good measure of central tendency for this dataset? What if the outlier were removed fromconsideration?
Given the data set :
5, 10, 5, 5, 15, 1, 10, 10,5, 600, 5
As seen most of th data is between 1 and 15 except one data is 600
so, 600 represents an outlier for the data
so, the answer is option 4
The function h is defined below.xh (x) =2+5x-- 142x- 81Find all values of × that are NOT in the domain of h.If there is more than one value, separate them with commas.
We want to find the value of x that is not in the domain of the function;
[tex]h(x)=\frac{x^2+5x-14}{x^2-81}[/tex]The value of x that will make h undefined is the value that makes the denominator zero.
Therefore;
[tex]\begin{gathered} x^2-81=0 \\ x^2=81 \\ x=\pm9_{} \end{gathered}[/tex]Therefore, the values not in the domain is +9 and -9
The composition of rigid motions T(10,- 27 OT(-24,4, describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north. block(s) north, and then it drives 3 block(s) west and 4 block(s) north. First the limousine drives 2 block(s) east and (Type whole numbers.)
The problem describes two operations of translation on the car. The first operation says that the car translated "10" units on the x-coordinate and "-2" units on the y-coordinate.
When translations are performed on the "x-coordinate" if they are positive, the function is moved to the left and if they are negative the function is moved to the right. When translations are performed on the "y-coordinate" if they are positive the function is moved up and if negative, the function is moved down.
Since the first translation on the x-axis was positive, then the car moved to the left 10 units, which would be "10 blocks" on the west direction. The translation on the y-coordinate was negative, so the function moved down. The car moved "2 blocks" on the south direction.
The second translation is (-24, 4). The translation on the x-axis is negative so the car is moved 24 units to the east direction. The translation on the y-axis is positve so the car is moved 4 units on the north direction.
The final answer is:
First the limousine drives 10 blocks west and 2 blocks south and then it drives 24 blocks east and 4 blocks north.
Solve for t and graph the solution.|t+ 4| < 2
The solution to the inequality is (-6, -2). The graph of the solution is attached below.
We are given an inequality. The inequality consists of a variable "t" and it also uses the modulus function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The inequality is |t + 4| < 2. We can solve the inequality by expanding the modulus operator. The inequality becomes -2 < (t + 4) < 2. Now we will subtract 4 from all the sides in the inequality. The inequality is solved as -6 < t < -2. The interval notation for the solution is (-6, -2). The graph is attached below.
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how do you dilate with a scale factor of -1/2Coordinates (-2,8)
Multiply the coordinates by the scale factor.
(-2,8) = (-2x-1/2, 8x-1/2) = (1,-4)
selecting among the numbers 1 through 8 and repeating none of them, fill in the boxes below to make the sum as close as possible to one but not equal to one
We need ti fill in the boxes below, selecting among the numbers 1 through 8 and repeating none of them to make the sum as close as possible to 1 but not equal to 1.
First fraction could be 1/2
Now, the second fraction should be closer to 1/2 to make the sum as close as possible to 1, but not equal to 1.
We know that 3/6 = 1/2
So, 3/7 would be closer to 1/2
Therefore, the boxes could be filled as;
[tex]\frac{1}{2}+\frac{3}{7}[/tex]..
1990, the cost of tuition at a large Midwestern university was $101 per credit hour. In 2005, tuition had risen to $236 per credit hour.
Solution:
According to the problem, the linear equation would be:
[tex]C(X)=101+9(x-1990)[/tex]now, if x=2013, the tuition will be:
[tex]C(2013)=101+9(2013-1990)=101+9(23)[/tex]this is equivalent to
[tex]C(2013)=101+9(23)=308[/tex]The diameters of ball bearings are distributed normally. The mean diameter is 125 mm and the standard deviation is 3 mm. Find the probability that the diameter of a selected bearing is greater than 127 mm. Round your answer to four decimal places.
Explanation
Given that the mean diameter is 125 mm and the standard deviation is 3 mm. We can find the probability that the diameter of a selected bearing is greater than 127 mm below.
We will first find the z score of the given value.
[tex]z=\frac{x-\mu}{\sigma}=\frac{127-125}{3}=\frac{2}{3}=0.66667[/tex]Using the z score calculator,
[tex]P\left(x>127\right)=0.2525[/tex]Answer: 0.2525
question will be in picture
Consider the guven system of equations,
[tex]\begin{gathered} x-y=-1 \\ 2x+y=4 \end{gathered}[/tex]It is asked to find the correct graph which represent the solution of this system.
Logic: Find the solution and see which graph gives the same solution.
Add the equations,
[tex]\begin{gathered} (x-y)+(2x+y)=-1+4 \\ 3x+3 \\ x=1 \end{gathered}[/tex]Substitute this value in the first equation,
[tex]\begin{gathered} 1-y=-1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]Thus, the given system has a unique solution (1,2).
Now, observe that only the graph given in option (c) shows the line intersecting at point (1,2).
Therefore, option (c) is the correct choice.
a tree that is 20 feet tall casts a shadow 30 feet long. a girl standing next to the tree has a shadow 9 feet long. how tall is the girl?
The shadow of the three is proportional to the shadow of the girl, then we can use a rule of three:
if x is the height of the girl: 20 is to 30 is the same as x is to 9
This can be written as:
[tex]\frac{20}{30}=\frac{x}{9}\Longrightarrow x=\frac{9\cdot20}{30}=\text{ 6}[/tex]Answer:
The girl is 6 feet tall
A survey wanted to determine if there was a relationship between the number of joggers who used a local park for exercise and the temperature outside. The data in the table display their findings.Use graphing technology to create a scatter plot of the data.What is the slope of the line of best fit and what does it mean in this context? Is it realistic?
Step 1
In order to find the slope of the line of the best fit, we must graph the points given.
Step 2
From the image above we can conclude that the equation of the line is;
[tex]y=0.410045x-2.8757[/tex]The slope is, therefore;
[tex]0.410045[/tex]The Slope (or Gradient) we call m, represents the change in y-value per unit change in x-value. In the case of this survey, the slope represents the increase in the number of joggers per degree rise in temperature.
From the calculated slope, there are about 0.4 more joggers for every degree rise in temperature. Using whole numbers to represent this, we can multiply the slope by 5:
[tex]0.4\times5=2[/tex]Therefore, there are 2 more joggers for every 5°F increase in temperature.
Sam is building a model of an antique car. The scale of his model to the actual1car is 1:10. His model is 15 1/2 inches long. How long is the actual car?215The length of the actual car isinches.
The car is 10 times the size of the model.
So, we have to multiply the length of the model by 10.
15 1/2 x 10 =
(15x2+1)/2 x 10=
31/2 x10 =310/2 = 155
The length of the actual car is 155 inches
Please help me and explain how to find the result
A family consumes 1.2kg of rice a day
If the family have 30ky of rice
Let the number of days be x
The minimum number of days required for the amount of rice remaining not to be more than 6kg can be expressed below as
[tex]30-1.2x\le6[/tex]Solve for x by collecting like terms
[tex]\begin{gathered} 30-1.2x\le6 \\ 30-6\le1.2x \\ 24\le1.2x \\ 1.2x\ge24 \\ \text{Divide both sides by 1.2} \\ \frac{1.2x}{1.2}\ge\frac{24}{1.2} \\ x\ge20\text{ days} \end{gathered}[/tex]Hence, the minimum number of days required for the amount of rice remaining not to be more than 6kg is 20 days