Hello there. To solve this question, we'll have to simply subtract and divide the numbers to find how many students were in each bus.
Knowing that for this field trip, 17 from 367 students went by cars, we know that 350 went by bus.
If there were 10 buses and we assume that all the buses transports the same amount of students, to find this amount, we just divide:
350/10 = 35
Therefore, 35 students were in each bus for this field trip.
The table below represents the status of different animals.Mammal Bird Reptile Amphibian TotalEndangered 59 75 14TotalThreatened 12 15 32 9371 90 461215168219What is the approximate probability that a selected animal will be a reptile and endangered?
Solution
Animals that are reptiles and endangered = 14
Total animals = 219
[tex]\begin{gathered} Probability\text{ of a selected animal will be reptile and endagered } \\ =\frac{14}{219} \\ =0.0639 \\ =0.06\text{ \lparen 2 decimal places\rparen} \end{gathered}[/tex]Anna is using a 6 1/2 pound bag of salt to Pour on snow. After using the salt 2/5 of the bag remains. How many pounds of salt did Anna use to pour on snow
If after using the salt, 2/5 of the salt remains, it means that Anna used 3/5 of the salt in the bag.
A bag contains 6 1/2 pounds of salt, convert this to a fractional number:
[tex]6\frac{1}{2}=6+\frac{1}{2}=\frac{13}{2}[/tex]To find how many pounds of salt she used, multiply 3/5 by the total amount of salt in the bag, this is:
[tex]\frac{3}{5}\cdot\frac{13}{2}=\frac{39}{10}[/tex]She used 39/10 pounds of salt.
how do i isolate F in the equation C= 5 over 9 (F - 32)
According to the given data we have the following:
[tex]C=\frac{5}{9}(f-32)[/tex]In order to isolate F in the equation we would make the following:
First we would have the following property:
[tex]\frac{a}{b}=\frac{m}{n}=a\cdot n=b\cdot m[/tex]Therefore 9C=5f-160
9C+160=5f
So:
[tex]\begin{gathered} \frac{9C\text{ + 160}}{5}=f \\ \frac{9}{5}C+32=f \end{gathered}[/tex]At a sale this week, a suit is being sold for $174.80. This is a 62% discount from the original price.What is the original price?
Let x be the original price then we can set up the following equation:
[tex]\begin{gathered} x(1-0.62)=174.80 \\ \text{solving for x we get} \\ x=\frac{174.80}{(1-0.62)}=\frac{174.80}{0.38}=460 \end{gathered}[/tex]Answer: $460.
Using the graph of the function g(x) = log2 (x – 2), what are the x-intercept and asymptote of g(x)?A. The x-intercept is –3, and the asymptote is located at x = 4.B. The x-intercept is –2, and the asymptote is located at y = 3.C. The x-intercept 3, and the asymptote is located at x = 2.D. The x-intercept is 4, and the asymptote is located at y = 2.
Solution
step 1
Step 2
X Intercepts = 3
or (3, 0)
Step 3
Vertical asymptote = 2
Final answer
C. The x-intercept 3, and the asymptote is located at x = 2.
Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.Donna also drove at a constant rate. This table shows the number of miles she had driven in different numbers of hours.How do the unit rates compare?Select from the drop-down menus to correctly complete the statement.Miguel has a Choose... greater or less unit rate of change than Donna because Choose... 48 mph or 53 mph or 424 mph or 432 mph is greater than Choose... 48 mph or 53 mph or 424 mph or 432 mph
As Miguel drove a total of 424 miles in 8 hours, at a constant rate, then the unit rate of change can be calculated as:
[tex]M=\frac{424miles}{8hours}=53\text{ miles/hour}[/tex]Now, Donna also drove at a constant rate, and we have a table of values, by dividing the miles driven in the corresponding time, the unit rate of change is:
[tex]D=\frac{144miles}{3hours}=\frac{288miles}{6hours}=\frac{432miles}{9hours}=48\text{ miles/hour}[/tex]As can be seen, Miguel has a greater unit rate of change than Donna because 53 mph is greater than 48 mph.
identify the distances in the other two polygons that correspond to DB and AC
You have to determine the distance of the diagonals of the polygons.
Asuming each square of the grid corresponds to one unit, to determine said distances you have to count the squares.
For the second polygon the diagonals are HF= 6 and GE= 9
For the third polygon the diagonals are LJ=2 and KI= 3
5. If AKLJ - AVWU, find the value of x.
The triangles are similar according to the question. Therefore, the following ratio can be formed
[tex]\begin{gathered} \frac{25}{20}=\frac{4x-23}{2x+2} \\ \text{cross multiply} \\ 25(2x+2)=20(4x-23) \\ 50x+50=80x-460 \\ 50x-80x=-460-50 \\ -30x=-510 \\ x=\frac{-510}{-30} \\ x=17 \end{gathered}[/tex]in a survey of 800 college students 800, it is found that:274 are majoring in english,156 are majoring in mathematics and422 are majoring in at least one of english and mathematics.A. How many of the 800 are majoring in both english and mathematics?B. how many are majoring in mathematics only?
A. There are 17 students that are majoring in both english and mathematics
B. There are 139 students that are majoring in mathematics only
Explanation:Given that 274 are majoring in english, n(E) = 274
156 are majoring in mathematics, n(M) = 156
422 are majoring in at least one of english and mathematics, n(E U M) = 422
We have:
A. The number of students that are majoring in both english and mathematics is obtained as follows:
[tex]\begin{gathered} n(E\cap M)=n(E)+n(M)-n(E\cup M) \\ \\ =274+165-422 \\ \\ =17 \end{gathered}[/tex]B. The number of students that are majoring in mathematics only is obtained as follows:
[tex]\begin{gathered} n(M\text{ only\rparen=}n(M)-n(M\cap E) \\ \\ =156-17 \\ =139 \end{gathered}[/tex]Baby McKenna wants to arrange 10 blocks in a row. How many different arrangements can she make?
3,628,800
1) Note that in these arrangements, according to the text the order of the blocks does not matter.
2) When this kind of thing happens we call this is a Permutation, in which the blocks may present in any order, that is not relevant
3) We can calculate it like this:
[tex]P_{10}=10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3,628,800[/tex]Thus, there are 3,628,800 different ways to arrange those 10 blocks
richard can break up a fight in 12 minutes, harold can break up a fight in 5 minutes how long will it take them to solve it together pls help
SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Time for Richard to break up a fight =12 minutes } \\ \text{Time for harold to break up a fight =5 minutes } \end{gathered}[/tex]Let the time at which both of them work be
[tex]R[/tex]Then
The individual rate will be
[tex]\begin{gathered} \text{Richard}=\frac{1}{12} \\ \text{And } \\ \text{Harold}=\frac{1}{5} \end{gathered}[/tex]Then
[tex]\frac{1}{12}+\frac{1}{5}=\frac{1}{R}[/tex]Simplifying fraction, we have
[tex]\begin{gathered} \frac{5+12}{60}=\frac{1}{R} \\ \text{Then} \\ \frac{17}{60}=\frac{1}{R} \end{gathered}[/tex]Hence
[tex]\begin{gathered} R=\frac{60}{17} \\ R=3.53 \end{gathered}[/tex]Therefore
It will take both of them 3.53 minutes to solve it together
The harris family and the carter family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 25 L per hour. The water output rate for the Carter family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1075 L. How long was each sprinkler used?
Let Harris family used their sprinkler for x hours and Carter family used their sprinkler for y hours.
Then the equation for total time of sprinkler use is,
[tex]\begin{gathered} x+y=55 \\ y=55-x \end{gathered}[/tex]Determine the equation for total water output from both the sprinkler.
[tex]\begin{gathered} 25x+15y=1075 \\ 5x+3y=215 \end{gathered}[/tex]Substitute 55-x for y in the equation to eliminate the y terms.
[tex]\begin{gathered} 5x+3(55-x)=215 \\ 5x+165-3x=215 \\ 2x=50 \\ x=25 \end{gathered}[/tex]Substitute 25 for x in the equation y=55-x to obtain the value of y.
[tex]\begin{gathered} y=55-25 \\ =30 \end{gathered}[/tex]So Harris family used sprinkler for 25 hours and Carter family used sprinkler for 30 hours.
use the graph of y=-x/3 -1 determine which of the ordered pairs of the solution to the equation select all correct answers
Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
Find the output global maximum and global minimum values of the function f(x) = x^3- 9x^2 - 32x + 10(A) Interval = -5, 0Global maximum = (B) Interval = 0,9 Global minimum = (C) Interval =-5, 9.Global maximum =Global minimum =
Given the function f:
We want to find its output global maximum and global minimum values.
To do this, we need to find the deritative of the function first:
Now, we're going to set it equal to zero:
Finally, replace the values x=-5, x=0, and the solutions of the previous equation in the original function. The highest value will be the maximum and the lowest value will be the minimum:
The output global maximum at the interval -5,0 is 34.43.
A. Identify the two points located on the graph and explain what they represent in the context of this situation. B. Approximately how much money will sheryl earn if she works 9 hours?
Graphs
The amount of money Sheryl makes is modeled in the graph shown.
A.
There are two points located on the graph.
The first point is at (0, 0) and represents the condition where Sheryl has not worked (0 hours) and has not earned a dollar ($0). This means she only gets paid per hour worked.
The other point at (1, 13) (approximately) represents the fact that Sheryl earned $13 for an hour worked.
B.
The graph does not show Shery's earnings for 9 hours, but we can use the result in part A to find that out.
If she makes $13 in an hour worked, then she should earn $13 * 9 = $117 for 9 hours of work.
Find the percent increase for the given original and new quantities in parts a through c.a. Original quantity: 100 New quantity: 106b. Original quantity: 10 New quantity: 16c. Original quantity: 50 New quantity: 56
We can find the percent of increase by means of this formula:
Increase in percent = 100 * (new quantity - original quantity) /original quantity
By replacing the given values into the above formula, we get:
a.
Increase in percent = 100 * (106 - 100) / 100 = 100 * 6 / 100 = 600/100 = 6
Then, the percent of increase equals 6%
b.
Increase in percent = 100 * (16 - 10) / 100 = 100 * 6 / 10 = 600/10 = 60
Then, the percent of increase equals 60%
c.
Increase in percent = 100 * (56- 50) / 50 = 100 * 6 / 50 = 600/50 = 12
Then, the percent of increase equals 12%
Find the product of (x - 3) (x - 11)
The expression is given as
[tex](x-3)(x-11)[/tex]ExplanationTo determine the product of the expression.
[tex]\begin{gathered} (x-3)(x-11)=x^2-11x-3x+33 \\ x^2-11x-3x+33=x^2-14x+33 \end{gathered}[/tex]AnswerHence the product of the expression is
[tex]x^2-14x+33[/tex]I have a practice question that I need answered and explained
Answer:
32(x-1)²/33 +12(y-1/2)²/11 = 1
Explanation:
The equation of the ellipse is:
8x² + 9y² - 16x - 9y + 2 = 0
First, let's rewrite the expression as:
(8x² - 16x) + (9y² - 9y) + 2 = 0
(8x² - 16x) + (9y² - 9y) + 2 - 2 = 0 - 2
(8x² - 16x) + (9y² - 9y) = -2
Now, we need to complete the squares, so we will add 8 and 9/4 to both sides to get:
(8x² - 16x + 8) + (9y² - 9y + 9/4) = -2 + 8 + 9/4
8(x² - 2x + 1) + 9(y² - y + 1/4) = 33/4
8(x - 1)² + 9(y - 1/2)² = 33/4
Finally, multiply by 4 and divide by 33 to get:
4(8)(x-1)² + 4(9)(y - 1/2)² = 4(33/4)
32(x-1)² +36(y-1/2)² = 33
32(x-1)²/33 +36(y-1/2)²/33 = 33/33
32(x-1)²/33 +12(y-1/2)²/11 = 1
Therefore, the answer is:
32(x-1)²/33 +12(y-1/2)²/11 = 1
HELP PLEASE In the table above, what is the constant of proportionality for width tolength?
The back of Toms property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 120 feet of fencing available, what is the maximum possible area of the pasture?
Suppose that the sides of the rectangle have lengths x and y, and that the measure of the side parallel to the creek is y, as shown in the drawing below
The total length of the fence, according to the drawing, is:
[tex]2x+y[/tex]Since there is 120 feet of fencing available, then:
[tex]\begin{gathered} 2x+y=120 \\ \Rightarrow y=120-2x \end{gathered}[/tex]On the other hand, the area A of the pasture, is equal to the base 120-2x times the height x:
[tex]\begin{gathered} A=x(120-2x) \\ =2x(60-x) \end{gathered}[/tex]Find the maximum value of the 2nd degree polynomial for A. Since A has roots at x=0 and x=60, the maximum value is found at x=(60+0)/2=30.
Then, the maximum possible area of the pasture can be found by plugging in x
Please Help. Functions and Relations. A power company calculates a persons monthly bill from the number of kilowatt- hours (kWh), x, used. how much is the bill for a person who used 600 kWh in a month?
ANSWER:
B. $80
EXPLANATION:
[tex]b(x)=\begin{cases}0.15x,{x\leq400} \\ 0.10(x-400)+60,x>400{}\end{cases}[/tex]We'll use the below function to determine how much is the bill for a person who uses 600 kWh in a month;
[tex]\begin{gathered} b(x)=0.10(x-400)+60 \\ b(600)=0.10(600-400)+60 \\ =0.10(200)+60 \\ =20+60 \\ =\text{\$}80 \end{gathered}[/tex]So the bill is $80
Step 1 of 2: Reduce the rational expression to its lowest terms 3x - 9/3 - xStep 2 of 2: Find the restricted values of X, if any, for the given rational expression.
Step 2.
There are not restricted values because because it's possible to simplify the expression and there is not a denominator.
Which equation can be used to find the area of the figure below? 10 16 FA = (598)+(168) GO A=()+(108) HOA = (1+ (6 - 8) 3 A = (6 - 8)+(108) Bducano
The given figure is the combination of a triangle and rectangle.
In the given
How would you do this type of problem and what would the increasing and decreasing interval be
y-intercept is the point in the y-axis that the graph intersects.
From the figure, the graph intersects at point (0, 3)
The y- intercept is (0, 3)
x-intercept is the point in the x-axis that the graph intersects.
Since the graph does not intersects the x-axis, the x-intercept does not exist
Vertex is a point on the graph that is a maximum or a minimum.
The vertex of the graph which is the lowest point as shown in the figure is at point (1, 2)
And this is a minima, since it is the lowest point.
Domain is the set of x-values that exist in the graph, the graph is going infinitely to the left and to the right, therefore the domain is (-∞, ∞)
Range is the set of y-values that exist in the graph, the y values starts from the vertex which is the lowest point at (1, 2) going upward.
So the range is all real numbers greater than or equal to 2. [2, ∞)
End behavior is the behavior of the function at large positive and negative values of x.
when x goes positive infinity, f(x) goes to positive infinity
As x ⇒ ∞, f(x) ⇒ ∞
when x goes negative infinity, f(x) goes to negative infinity
As x ⇒ -∞, f(x) ⇒ -∞
Decreasing interval occurs when the graph is going down, and increasing interval occurs when the graph is going up.
Decreasing interval will be (-∞, 1]
Increasing interval will be [1, ∞)
The data shows the number of customers Joe's diner serve during lunchtime hours for the past 12 days22,25,50,58,28,24,25,51,43,32,49,38
The dataset consists on the points:
{22,25,50,58,28,24,25,51,43,32,49,38}
Sorting the numbers from lowest to highest:
{22,24,25,25,28,32,38,43,49,50,51,58}
There are 12 numbers, thus the median is the mean of the data 6 and 7:
M = (32+38)/2 = 35
The first point is 22, the last point is 58
The only box plot that follows all the conditions is A, where the median is at 35
Answer: A
if B D equals b c b d equals 5x - 26 BC equals 2x + 1 and a C equals 43 find a b
Given the information
BD=BC
where
BD= 5x-26
BC=2x+1
then
[tex]5x-26=2x+1[/tex][tex]5x-2x=1+26[/tex][tex]3x=27[/tex][tex]x=\frac{27}{3}=9[/tex]Since
AB= AC-BC
where
BC=2x+1
BC= 2(9)+1 = 19
AC=43
[tex]AB=43-19=24[/tex]which square root is a whole number ?
Let's find the square root of all to find which is a whole number
√254 = 15.937
√255 =15.967
√256 =16
Hence √256 is a whole number
The correct option is C.
Find the value of the expression below.log4 3 + log4 8 - log4 6A.1B.3C.0D.2
Given:
[tex]log_43+log_48-log_46[/tex]To Determine: The value of the given expression
Solution
Let us apply the logarithm rule below
[tex]\begin{gathered} logA+logB=log(A\times B) \\ So \\ log_43+log_48=log_4(3\times8)=log_424 \\ log_43+log_48-log_46=log_424-log_46 \end{gathered}[/tex]Applying the rule below again
[tex]\begin{gathered} logA-logB=log(A\div B) \\ So, \\ log_424-log_46=log_4(24\div6)=log_44 \end{gathered}[/tex]And finally applying the rule below
[tex]\begin{gathered} log_aa=1 \\ Then \\ log_44=1 \end{gathered}[/tex]Hence, the solution of the given expression is 1, OPTION A
2. Write an expression for the perimeter of a rectangle with a length of(3x2 + x + 2) and a width of (-22 – 5x + 1).O 4248x 7.60 4224x + 34x28x + 6O 2x24x + 3
You have that the perimeter of the rectangle is given by the following formula:
[tex]P=2l\text{ + 2w}[/tex]l: length of the rectangle
w: width of the rectangle
[tex]\begin{gathered} l=3x^2+x+2 \\ w=-x^2-5x+1 \end{gathered}[/tex]Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:
[tex]\begin{gathered} P=2(3x^2+x+2)+2(-x^2-5x+1) \\ P=2(3x^2)+2(x)+2(2)+2(-x^2)+2(-5x)+2(1) \\ P=6x^2+2x+4-2x^2-10x+2 \\ P=4x^2-8x+6 \end{gathered}[/tex]Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6
If a cylinder has a height of 7 inches and avolume of 2,908.33 ins, find its diameter.
Remember that the formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]We know that:
[tex]r=\frac{D}{2}[/tex]Thereby,
[tex]V=\pi r^2h\rightarrow V=\pi(\frac{D}{2})^2h\rightarrow V=\frac{\pi D^2h}{4}[/tex]Solving for D,
[tex]\begin{gathered} V=\frac{\pi D^2h}{4}\rightarrow4V=\pi D^2h\rightarrow\frac{4V}{\pi h}=D^2 \\ \rightarrow D=\sqrt[]{\frac{4V}{\pi h}} \end{gathered}[/tex]Using the data given,
[tex]\begin{gathered} D=\sqrt[]{\frac{4V}{\pi h}} \\ \\ \Rightarrow D=23 \end{gathered}[/tex]We get that the diameter of the cylinder is 23"