Answer:
240 tickets sold
Step-by-step explanation:
first, you would set up the proportion by writing [tex]\frac{228}{95} =\frac{x}{100}[/tex]
with "x" being the number of seats that needs to be sold
then, you would cross multiply
and you get
[tex]95x=228*100[/tex] next, you simplify to get the inequality [tex]95x=22800[/tex]
then divide both sides by 95
[tex]x=240[/tex]
so 240 tickets to fill all the seats
hope this helps ;)
Graph y=−4/7x+1.
Use the line tool and select two points on the line to graph the line.
To graph the line y=−4/7x+1, we can use the slope-intercept form of a linear equation, y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -4/7 and the y-intercept is 1.
To plot the line, we can select two points on the line and connect them with a straight line. One easy way to do this is to set x=0 and solve for y to find the y-intercept, which is (0,1). Then, we can set y=0 and solve for x to find another point on the line. This gives us (-7/4,0).
Once we have these two points, we can use a straight edge or ruler to draw a line through them to represent the graph of the equation. It should be a downward-sloping line that intercepts the y-axis at (0,1).
Alternatively, we can use a graphing calculator or an online graphing tool to plot the line more accurately. This will allow us to see more clearly the shape and direction of the line, as well as any other important features such as intercepts, slopes, and points of intersection with other lines.
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4.27 L = mL, 0.35 L = mL, 0.06 L, 9.05 L mL? im sorry its for my important exam coming up and if i dont pass my homework i wont be able to do the exam and my teacher said i would fail my grade if it happens
volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL.
How to convert the volumes from liters (L) to milliliters (mL)?Knowing the relationship between the two units will make converting between litres and millilitres simple. Both litres and millilitres are measurements of a liquid's volume.
The basic measure of liquid capacity is the litre. The liquid volume can also be measured in millilitres, centilitres, and kilolitres. All of these units have different values from one another.
Similar to millilitres, litres also denote volume, however one litre is equivalent to one thousand millilitres (1 L = 1000 mL).
To convert the given volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL. Here are the conversions:
4.27 L = 4.27 x 1000 mL = 4270 mL
0.35 L = 0.35 x 1000 mL = 350 mL
0.06 L = 0.06 x 1000 mL = 60 mL
9.05 L = 9.05 x 1000 mL = 9050 mL
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Find the area of the red-shaded region (arc ED). Round your answer to the nearest
hundredths.
Answer:
Step-by-step explanation:
It should be 177.88
Through (3,3) perpendicular to y=-3/4x+5
y = (-4/3)x + 1 this line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.
What is the standard equation of a line?y = (3/4)x + 5
Compare with the standard form of equation y = mx +c
3/4 is the slope.
The negative reciprocal of the slope is used to obtain a perpendicular slope.
-4/3 is the perpendicular slope.
Let's rewrite the equation: y = (-4/3)x + b
Remember that b is the line's y-intercept base. If the line must pass straight through the point (3, -3), we must determine the location of the base.
To accomplish this, we just enter our point into the formula and solve for our base.
-3 = (-4/3)(3) + b
Now calculate b: b = (-4/3)(3) + 3
b = -4 + 3 b = 1
You now get the final equation: y = (-4/3)x + 1 now that you have the base.
This line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.
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Complete question:
write an equation passing through the point that is perpendicular to(3,-3); y= 3/4 x+5
Help me shoe work on this question please
The line /TV/ that we have been asked to find from the information is the question is obtained as 7.
What is the sine rule?The sine rule, also known as the law of sines, is a trigonometric formula used to find an unknown side or angle in a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle.
We know that the missing angle U is obtained from;
180 - (58.3 + 80)
= 41.7°
Then;
8.9/Sin 58.3 = /TV//Sin 41.7
/TV/ = 8.9 Sin 41.7/Sin 58.3
/TV/ = 5.9/0.85
= 7
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Solve for x in the equation 2x + 3 > 11
Hi !
[tex]2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4[/tex]
Have a nice day ;)
Answer:
x > 4
Isolate the variable by dividing each side by the factors that don't contain the variable
the angle of elevation to an airplane viewed from the control tower at an airport is 7. the tower is 200 feet high and the pilot reports that the altitude is 5200 feet. how far away from the control tower on a straight line is an airplane?
The distance between control room to airplane is 41027.5 feet.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here This distance (d) from tower will be the hypotenuse of a right triangle.
The altitude is the side opposite the angle at the tower
The tower is 200' high, therefore, the altitude above the tower.
=> 5200 - 200 = 5000 feet.
Now using sine ratio then,
=> Sin 7° = AC/BC
=> BC = AC/sin 7°
=> BC = 5000/sin 7°
=> BC = d = 41027.5 feet.
Hence the distance between control room to airplane is 41027.5 feet.
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Jesus necesita una tapa para un frasco.El perimetro del frasco es 21.98 cm ¿cuanto mide el radio de la tapa?
por favor ocupo ayuda
The radius of the lid would be 3. 5 cm.
How to find the radius ?To estimate the radius of the lid, we must first determine the circumference of the jar, which is equal to the jar's perimeter. The specified circumference is 21.98 cm.
The circumference is:
C = 2πr
We can solve for circumference as:
21. 98 = 2 πr
r = 21. 98 / ( 2 π )
r = 21. 98 / (2 x 3. 1416 )
r = 21. 98 / 6. 2832
r = 3. 5 cm
In conclusion, the radius of the lid is approximately 3.5 cm.
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What is the procedure for quickly stopping a car with ABS
Answer:
Press down the brake firmly and smoothly. ...
Don't brake and swerve the car at the same time. ...
Avoid using your transmission for quick stops. ...
Focus on where you want to go, not what you want to avoid.
regarded as likely, probable, or certain.
Probable and certain both speak about something that may (or may not) happen in the future, but probable and possible speak about future possibilities in different ways.
What is Probable?‘Probable’ is high up on the scale of probability. If something is probable, then there is a high chance that something will happen. We can imagine that ‘probable’ is around 80% and up on the scale of probability.
If something is possible, it doesn’t mean it’s probable. However, if something is probable then it’s possible too. And if this confuses you then you’re probably in the right place.
Probable and certain are both on a scale of probability. Probability is the level of possibility or chance that something will happen or will be true in the present or future.
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In the hawk-dove game, at what value of c do doves and hawkshave equal payoffs when hawks are extremely rare?0.501There is no such value.
This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
The mathematical field of game theory helps shed light on how it emerges. Game theory is “the study of mathematical models of strategic interaction among rational decision-makers” (according to Wikipedia).
Game theory applies to “games” as varied as economics, politics, chess, and tic-tac-toe. In each case, there are some rules, some “players” or “agents”, and a set of strategies available to them.
Each player has a concept of “utility” – a “currency” they seek to individually maximize through the strategies they play.
The currency of evolution is the concept of fitness.
That is, the chance of being represented in the next generation. Genes and traits which increase the odds of survival to reproductive age are more likely to be passed on to future generations. Therefore, they confer a greater fitness to the individual which "hosts” them.
The evolutionary game theory takes the concepts from game theory and applies them in an evolutionary context.
In the hawk-dove game, at what value of c do doves and hawks have equal payoffs when hawks are extremely rare? The answer is that there is no such value. This is because when hawks are extremely rare, their payoff is higher than that of doves regardless of the value of c. Therefore, there is no point at which their payoffs will be equal.
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a survey was given to 318 students at east river high school asking what their grade point average (gpa) was. which is the best graphical representation to display the data?
The best graphical representation to display the data on the GPA of 318 students at East River High School would be a histogram.
What is a histogram?A histogram is a graphical representation of data that groups data into bins or intervals and displays the frequency of occurrences of data within each bin. In this case, the bins would represent GPA ranges, and the frequency would represent the number of students falling within each GPA range.
A histogram is a good choice for displaying this data because it allows the viewer to see the distribution of GPA scores across the student population. It provides a visual representation of how many students fall within certain GPA ranges and can help identify trends in the data.
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f(x)= lx+3l-7
What will the function be if it has been:
1. Reflected across the x-axis
2. Translated left 4 units
3. Translated down 3 units
Please type answer with no spaces. The absolute value key should be located directly above the "Enter/Return" key on your keyboard.
The function after each transformation is given as follows:
1. Reflected across the x-axis: f(x) = -|x + 3| + 7.
2. Translated left 4 units: f(x) = |x + 7| - 7.
3. Translated down 3 units: f(x) = |x + 3| - 10
How to define the functions?The function for this problem is defined as follows:
f(x) = |x + 3| - 7.
When the function is reflected across the x-axis, we have that the entire function is multiplied by -1, hence:
f(x) = -(|x + 3| - 7)
f(x) = -|x + 3| + 7.
When the function is translated left 4 units, we have that x -> x + 4, hence:
f(x) = |x + 4 + 3| - 7
f(x) = |x + 7| - 7.
When the function is translated down 3 units, we have that f(x) -> f(x) - 3, hence:
f(x) = |x + 3| - 7 - 3
f(x) = |x + 3| - 10
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10 yd
T
12 yd
5 yd
Name of figure: ___\\
Volume:
Answer:
name of figure : pyramid
volume : 200yds.
Step-by-step explanation:
The formula for volume of a pyramid is 1/3(lwh), in this case, it would be 1/3(12x5x10). 12x5x10 is 600, and 1/3 of 600 is 200. Therefore, the volume is 200yds.
IM VERY SORRY IF THIS DIDN'T MAKE SENSE!
A survey was dispersed throughout the county in order to gather information comparing the amount of money spent on groceries and the percentage of that money spent on fruits and vegetables.
Which of the following methods could be used to represent the data?
Dot plot
Box plot
Line plot
Histogram
Line graph
Scatter plot
Stem-and-Leaf plot
A scatter plot or a line graph could be used to represent the relationship between the two variables.
What is scatter plot?A scatter plot is a graph in which each data point is represented by a dot on the graph. In this case, the data points would represent the amount of money spent on groceries and the percentage of that money spent on fruits and vegetables. Each data point would be plotted based on its corresponding values for the two variables, with the horizontal axis representing the amount of money spent on groceries and the vertical axis representing the percentage of that money spent on fruits and vegetables. The scatter plot would allow us to see if there is any relationship between the two variables, such as whether people who spend more on groceries tend to spend a higher percentage of that money on fruits and vegetables.
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Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
For the given data correct option is option a.) The range is the best measure of variability, and it equals 8.
How to find the measure of variability?The dots on the line plot reflect the quantity of roses purchased every day at a grocery shop based on the supplied data. The dots are scattered horizontally, with some dots above specific numbers.
1, 2, 6, 7, 8, and 9 have dots above them , thus,
for given problem,
[tex]\text{Number of Rose Bouquets: 1, 2, 6, 7, 8, 9}[/tex]
[tex]\text{The range is the difference between the highest and lowest values:}[/tex]
[tex]Range = \text{Highest value} - \text{ Lowest value}\\Range = 9 - 1\\Range = 8[/tex]
The Interquartile Range (IQR) is a measure of variability that considers the difference between the data set's 25th and 75th percentiles (Q3).
The median (Q2) would be towards these digits since there are dots above numbers 6, 7, and 8. As a result, using the information provided, the IQR cannot be computed precisely.
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URGENT PLEASE ANSWER!!! I INCLUDED THE GRAPH!
Graph the line y = 4/3x + 1.
Use the line tool and select two points on the line.
Answer:
I put the equation on math-way and it gave me this:
Answer:
Starting at (0, 1), go up 4 units, then right 3 units. You will end at (3, 5). Plot that point, and then draw a line that goes through the two points.
Round your answer to the nearest tenth, and type it in the blank without units.
Answer:
Set your calculator to degree mode.
sin(72°) = x/25
x = 25sin(72°) = about 23.8 feet
Two boys share 35notebooks in the radio of 2:5. How many notebooks does each get?
When two boys share 35notebooks in the ratio of 2:5, each boy will get these numbers of notebooks:
Boy A = 10Boy B = 25.What is the ratio?The ratio refers to the relative or comparative size of one value, quantity, or number compared to another.
Ratios are depicted as proportional values using fractions, decimals, percentages, or the standard ratio form (:).
Ratios give the equivalent values of quantities that are compared.
The total number of notebooks to share between two boys = 35
The sharing ratio = 2:5
The sum of ratios = 7 (2 + 5)
The share of Boy A = 10 (²/₂ x 35)
The share of Boy B = 25 (⁵/₇ x 35)
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How many teaspoons are there in 6 milliliters?
Hint: 1mL≈0.2tsp
Round your answer to the nearest tenth.
Answer:
1.2 tsp
Step-by-step explanation:
6x0.2=1.2
There are 6 mL,and if each mL is 0.2tsp, then you have to multiply.
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15(Multiple Choice Worth 2 points)
Answer:Answer: A. tennis=17 , soccer= 12, baseball=27, basketball=44
BAR GRAPH make sure its not a histogram!!
Step-by-step explanation:
just took the test
if the median of 127 numbers is 35, which of the following must be true? i) at least 64 of the numbers are greater than or equal to 35 ii) at least 64 of the numbers are smaller than 35 iii) at most 64 numbers are greater than or equal to 35
Answer:
Option i) At least 64 of the numbers are greater than or equal to 35 must be true
Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.
Sally invested some money into a savings account that earns 7. 2%
annual simple interest. At the end of 9 years, she earned $745. 20 in
interest. How much money did she put into the account initially?
Round to the nearest dollar
According to simple interest, Sally initially put $1,150 into the savings account.
To solve this problem, we need to use the formula for simple interest, which is:
Simple Interest = Principal x Rate x Time
We know that the interest earned is $745.20, the rate is 7.2%, and the time is 9 years. We can plug these values into the formula and solve for the principal:
$745.20 = Principal x 0.072 x 9
$745.20 = 0.648 x Principal
Principal = $1,150
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please help me I've been stumped on this problem
The Results:
a) The measure of ∠BDC = 67°
b) The measure of arc DAC = 46°
How to measure angles?a) The measure of ∠BDC
Since DC ⊥ AB, ∠DCB is a right angle, which means it measures 90°. Also, given that m∠DCB = 23, we can use the fact that the angles in a triangle sum to 180° to find ∠DBC.
∠DBC + ∠DCB + ∠B = 180 (angles in a triangle sum to 180)
∠DBC + 90 + 23 = 180 (substituting values)
∠DBC = 180 - 90 - 23 = 67°.
Thus, the measure of ∠BDC = 67°
b) The measure of arc DAC:
Since AB = AC, it implies that ∠ABC = ∠ACB (angles opposite to equal sides of an isosceles triangle are equal). Therefore, ∠ACB is also 23°.
Now, since ∠ACB is an inscribed angle that intercepts the arc DAC, the measure of the arc DAC is twice the measure of ∠ACB.
Arc DAC = 2 × ∠ACB = 2 × 23 = 46°.
Therefore, the measure of arc DAC is 46°.
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Stein Corp. reported the following information for 2013 and 2014.Accounts payable, December 31, 2013 $ 51,000Accounts payable, December 31, 2014 46,000Purchases--2014 467,000How much cash was paid for merchandise purchases during 2014?A. $421,000B. $462,000C. $467,000D. $472,000
The total amount of cash paid by Stein Corp. for merchandise during the interval of 2014 is $462,000, under the condition that accounts payable, for December 31, 2013 is $ 51,000 and accounts payable, for December 31, 2014 is $46,000
Purchases-2014 is $467,000.
In order to evaluate the cash paid for merchandise purchases during 2014, it is crucial to calculate the change in accounts payable from December 31, 2013 to December 31, 2014 and summation of purchases made during 2014.
Accounts payable change
= Accounts payable at December 31, 2014 - Accounts payable at December 31, 2013
= $46,000 - $51,000
= -$5,000
This explains that accounts payable decreased by $5,000 from December 31, 2013 to December 31, 2014.
Cash paid for merchandise purchases in 2014
= Purchases during 2014 + Change in accounts payable
= $467,000 - $5,000
= $462,000
The total amount of cash paid by Stein Corp. for merchandise during the interval of 2014 is $462,000, under the condition that accounts payable, for December 31, 2013 is $ 51,000 and accounts payable, for December 31, 2014 is $46,000
Purchases-2014 is $467,000.
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a band just recorded a new album with 13 tracks. the shortest song on the album is 1 minute and 14 seconds. The longest song is 5 minutes and 54 seconds. What is a reasonable estimate for the total time of the album?
To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.
What is a reasonable estimate for the total time of the album?The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.
The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.
Therefore, the average time per song is:
(74 + 354) / 2 = 214 seconds
And the total time of the album is approximately:
13 songs x 214 seconds/song = 2,782 seconds
Converting this to minutes and seconds, we get:
2,782 seconds = 46 minutes and 22 seconds
So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.
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Use separation of variables to solve the initial value problem. Indicate the domain over which the solution is valid.
dy/dx=10x^9y and y=4 when x=0
The solution to the initial value problem is [tex]y = 4e^{(5x^{10})[/tex]. The domain of the function is all real numbers.
What is first-order ordinary differential equations?Ordinary differential equations of the first order only take into account the dependent variable y's first derivative with regard to the independent variable x. They could be written as follows:
f(x,y) = dy/dx
where the supplied function of both x and y is f(x,y). There are numerous methods for solving first-order ordinary differential equations, which are crucial in many branches of science and engineering. One such method is variable separation. Other methods include Bernoulli equations, integrating components, and precise equations.
The given differential function is:
[tex]dy/dx = 10x{^9}y[/tex]
Separating the variables we have:
dy/y = 10x^9 dx
Now, integrating on both sides:
[tex]]int dy/y = \int 10x^9 dx\\ln (y) = 5x^{10} + C[/tex]
Solving for y:
[tex]y = ke^{(5x^{10})[/tex]
Now, for the initial values y = 4 and x = 0 we have:
[tex]4 = ke^{(0)}[/tex]
k = 4
Hence, the solution to the initial value problem is [tex]y = 4e^{(5x^{10})}[/tex].
The domain of the function is all real numbers.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Question 9
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs
Interpreting the histogramThe histogram is not given and the data represented on the histogram are not properly presented
This means that the histogram cannot be interpreted
Predicting the number of hotdogsHere, we have
Ketchup = 63
Mustard = 27
Chili = 60
So, we have
Mustard = 27/(63 + 27 + 60) * 5000
Evaluate
Mustard = 900
This means that 900 people prefer mustard
The graphical representation of a datasetGiven that
Data = Milligrams of Vitamin C from 100 different gummy vitamins sold
This data can be represented using a box plot because the five-summary data can be easily identified from the dataset
From the five-summary, the median can be derived
The graphical representation of a datasetIn this case, the graph to use is a circle graph
This is so because the circle graph would show the proportion of the student's preferences
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18 Two vans leave a campground at the
same time. One is traveling north at a
speed that is 10 miles per hour faster
than the other, which is traveling south.
After 2.5 hours, the vans are 255 miles
apart. What is the speed in miles per hour
of the van traveling south?
F 56
G 46
H 66
J 36
The speed of the van traveling south is 46 miles per hour. The correct option is (G) 46.
To solve this problemLet's call the speed of the van traveling south "x" in miles per hour. Then, the speed of the van traveling north is "x + 10" miles per hour.
We know that the vans have been traveling for 2.5 hours, and that they are 255 miles apart. This means that the total distance traveled by both vans is 255 miles:
Distance traveled by the van traveling south + Distance traveled by the van traveling north = 255 miles
Using the formula distance = speed × time, we can express the distances traveled by each van in terms of their speeds and the time they traveled:
Distance traveled by the van traveling south = x × 2.5 = 2.5x
Distance traveled by the van traveling north = (x + 10) × 2.5 = 2.5x + 25
Substituting these expressions into the equation above, we get:
2.5x + 2.5x + 25 = 255
Simplifying this equation, we get
5x + 25 = 255
Subtracting 25 from both sides, we get:
5x = 230
Dividing both sides by 5, we get:
x = 46
Therefore, the speed of the van traveling south is 46 miles per hour. Answer: (G) 46.
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Alyssa received a leadership patch, as shown below, when she was elected Student Body President.
The patch is in the shape of a right triangle where the top section and the whole patch form similar triangles.
If x = 55 mm, z = 80 mm, and the tangent of the bottom angle, where the star is located, is equal to , what is the length of w?
A. 32 mm
B. 48 mm
C. 55 mm
D. 40 mm
The length of the side w is 55mm. Option C
How to determine the valueNote that the different trigonometric identities are;
sinetangentcosinesecantcosecantcotangentFrom the triangle shown, we have;
x = 45mm
z = 80mm
We also have tangent where the star is located is 1
Then,
tan θ = 1
find the tangent inverse of the values
θ = 45 degrees
As given in the diagram, the diagrams are similar
So both angles are 45 degrees
However, we can deduce that since the angles are equal, then, the sides are equal
x = w = 55mm
w = 55mmm
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