Answer:
21 male students
Step-by-step explanation:
For every teacher on the trip, 3 male students and 5 female students are there
If there are 35 female students, we have to divide that by 5 to find the number of teachers
35 divided by 5 is 7
There are seven teachers, so we multiply by 3 to find the number of male students
7 x 3 = 21
There are 21 male students on the school field trip
A baseball team sells snacks at their games to raise money. At their last game, they made 6/7 as much money as they made at their first game. Did they make more money at their first or last game? Explain how you know?
The first game brought in more money than the last game.
What is Fraction?Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.
According to question:
The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.
Therefore, the first game brought in more money than the last game.
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an equilateral triangle has side lengths of 28 m what is the length of its altitude
The length of the altitude of the equilateral triangle with side lengths of 28 meters is 14[tex]\sqrt{3}[/tex] meters.
Define equilateral.
Equilateral is an adjective used to describe a geometric figure, such as a triangle, that has all sides of equal length. In an equilateral triangle, all three sides are of equal length, and all three angles are also equal, measuring 60 degrees each.
To find the altitude of an equilateral triangle, we can use the following formula:
altitude = ([tex]\sqrt{3}[/tex]/2) x side length
Since the side length of the equilateral triangle is 28 meters, we can substitute it in the formula and simplify:
altitude = ([tex]\sqrt{3}[/tex]/2) x 28
= 14[tex]\sqrt{3}[/tex] meters (rounded to two decimal places)
Therefore, the length of the altitude of the equilateral triangle is approximately 14.00 meters.
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What is the contrapositive of the following statement? "If it is not a lion, then it is a cat
The contrapositive of the given statement is "If it is not a cat, then it is a lion."
The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).
The contrapositive takes the form:
"If it is not a cat, then it is a lion."
So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."
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Please help, I can’t figure this out
Answer:
x=15°, ∠A=75°, ∠B=60°, ∠C=45°
Step-by-step explanation:
As we know that sum of the angle of a triangle is 180°
Therefore ∠A+∠B+∠C=180°
5x+4x+3x=180° { ∵ ∠A=5x ∠B=4x ∠C=3x }
⇒ 12x=180°
⇒ x=15°
Hence ∠A=5x=5×15°=75°
∠B=4x=4×15°=60°
and ∠C=3x=3×15°=45°
to verify your answer 75°+60°+45°=180°
I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes? a. S-(red,red), (red,black), (black,red), (black,black) b. S - fred,black) c. S-(0, 1, 2) d. none of the above
The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards
The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).
Sample space S in probability theory denotes the set of all possible outcomes of an experiment.
In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,
These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).
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The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (5, 5).
Answer:
The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (5, 5).
Step-by-step explanation:
To find the bearing of an object located at the point (5, 5) relative to the observer deck at the origin of a coordinate system, we need to find the angle between the positive x-axis and the line connecting the observer deck to the object.
First, we calculate the slope of the line connecting the observer deck at (0, 0) to the object at (5, 5):
slope = (change in y) / (change in x)
= (5 - 0) / (5 - 0)
= 1
Next, we use the inverse tangent function to find the angle whose tangent is equal to the slope:
angle = arctan(slope)
= arctan(1)
= 45°
Therefore, the bearing of the object located at (5, 5) relative to the observer deck at the origin is 45 degrees.
Answer:
45° north of east
Step-by-step explanation:
tan⁻¹(y/x) = tan⁻¹(5/5) = tan⁻¹(1) = 45°
Please answer the question in the photo (will mark Brainliest if available + 20p)
Solution:
we have been asked to graph [tex]f(x)=2^x+1[/tex] and [tex]g(x)=-x+7[/tex] on the same coordinate plane.
Then we have been asked to find the solution to the equation ?
So we will plot the graph and look for their point of intersection, the x-coordinate of the point of intersection will give the value of x.
So from the graph its clear that the point of intersection is (2,5)
Hence the value of x=2.
A line passes through points (3,20) and (8,25). Write a linear function rule in terms of x and y for this line.
To find:-
The equation of line passing through the points (3,20) and (8,25) .Answer:-
To find out the equation of the line , we need to find out the slope first. It can be calculated as ,
[tex]\implies m =\dfrac{\Delta y}{\Delta x }=\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]
And here ,
[tex] y_1[/tex] = 20[tex]y_2[/tex] = 25[tex]x_1 [/tex] = 3[tex]x_2 [/tex] = 8On substituting the respective values, we have;
[tex]\implies m =\dfrac{25-20}{8-3} \\[/tex]
[tex]\implies m=\dfrac{5}{5}\\[/tex]
[tex]\implies m=\boxed{1} \\[/tex]
Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,
[tex]\implies y - y_1 = m(x-x_1) \\[/tex]
Take any of the given two points. Here i am taking (3,20) . So here we have;
[tex] m [/tex] = 1[tex] y_1 [/tex] = 20[tex] x_1[/tex] = 3On substituting the respective values, we have;
[tex]\implies y - 20 = 1(x - 3) \\[/tex]
[tex]\implies y -20 = x - 3 \\[/tex]
[tex]\implies x - 3 - y +20 = 0 \\[/tex]
[tex]\implies \underline{\underline{\green{ x - y +17=0}}}\\[/tex]
Hence the equation of the line in standard form is x - y + 17 = 0 .
and we are done!
A bank statement is shown. Fill in the gaps to complete the sentence below. This bank statement shows a profit / loss of £ Description Sales - Monday Staff wages Sales - Tuesday Supplies - office equipment Sales - Wednesday Rent for office space Customer refund Money in £315.00 £265.00 £190.00 Money out £210.00 £30.00 £450.00 £100.00
The bank statement that is shown in the question shows a loss of £285.00 and calculated by subtracting the total expenses (money out) from the total revenue (money in).
Define profit or loss?Profit or loss is a measure of the financial performance of a business, organization, or individual over a given period of time.
Profit refers to the positive difference between the revenue earned by a business or individual and the expenses incurred during a given period.
A loss occurs when the expenses incurred exceed the revenue earned during a given period.
To calculate the profit or loss, you need to subtract the total expenses (money out) from the total revenue (money in).
In this case, the total revenue is £315.00 + £265.00 + £190.00 = £770.00, and the total expenses are £210.00 + £30.00 + £450.00 + £100.00 = £790.00.
So, the calculation would be:
Total revenue - total expenses = profit/loss
£770.00 - £790.00 = -£20.00
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Can someone just help me on 19, it’s pretty confusing. Just look around at the other questions so it’ll help with answering it.
Answer:
0% (0/40)
Step-by-step explanation:
I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food
cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
Write the percent as a decimal.
95%
Answer:
9.5 decimal
espero y te ayude
a person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1. find the expectation of this game. is the game fair?
A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value
How do we determine the expected value of the game?We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.
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NEED HELP DUE TODAY!!!! GIVE GOOD ANSWERS PLEASE!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.
What is triangle?In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.
Here,
2. This is because the circumference and area of a circle are directly proportional to the radius.
3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.
4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).
A= (-0.87,0.5)
D=(-0.87 + 2, 0.5 - 3)
D=(1.13,-2.5)
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The _____ in which ratio is expressed is important
In mathematics, a ratio is a comparison of two quantities or numbers expressed in terms of division. The order in which the quantities are expressed in a ratio is also important.
Ratios are used in various mathematical applications such as in finance, geometry, and physics. The units or quantities being compared in a ratio are crucial in determining the meaning and significance of the ratio.
For example, if the ratio is expressed as 2:1, it could mean that the first quantity is twice the size of the second quantity, or it could mean that the second quantity is half the size of the first quantity. Therefore, it is important to clearly define the units or quantities being compared to avoid any ambiguity or misunderstanding.
In the example above, if the ratio was expressed as 1:2 instead of 2:1, the meaning of the ratio would be reversed. Therefore, the order of the quantities in a ratio should be consistent with the context in which it is being used. In summary, the units and the order in which the quantities are expressed in a ratio are important in conveying accurate and meaningful information.
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Complete question:
In mathematics, the units or quantities being compared and the order in which they are expressed in a ratio are both important. The _____ in which ratio is expressed is important
A person invests 4500 dollars in a bank. The bank pays 6. 25% interest compounded
semi-annually. To the nearest tenth of a year, how long must the person leave the
money in the bank until it reaches 13300 dollars?
The person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.
Using the formula A=P(1+r/n)⁽ⁿᵗ⁾, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years, we can solve for t.
We have P = 4500, A = 13300, r = 0.0625, n = 2. Plugging these values into the formula and solving for t, we get t ≈ 13.6 years. Therefore, the person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.
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2 Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year, she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?
Answer:
Step-by-step explanation:
Kind of like rema from the song calm down calm down!!
you an find it on youtub
Let θ = 855∘. Complete parts (a), (b), and (c) below. (a) Sketch θ in standard position. (b) Find an angle between 0∘ and 360∘ that is coterminal with θ. (c) Find an angle between −360∘ and 0∘ that is coterminal with θ
Let θ be equal to 855∘. Sketch θ in standard position. θ = 855∘ is in the fourth quadrant of the coordinate plane θ = 855∘
The given angle, θ, is a positive angle. It is measured in the counterclockwise direction from the initial side to the terminal side.Hence, we sketch θ in the standard position with its initial side along the positive x-axis.
Find an angle between 0∘ and 360∘ that is coterminal with θ.
The angle between 0∘ and 360∘ that is coterminal with θ is given by:
θ1 = θ - n × 360∘θ1 = 855∘ - 2 × 360∘θ1 = 855∘ - 720∘θ1 = 135∘
Therefore, an angle between 0∘ and 360∘ that is coterminal with θ is 135∘.Find an angle between −360∘ and 0∘ that is coterminal with θ.
The angle between −360∘ and 0∘ that is coterminal with θ is given by:
θ2 = θ + n × 360∘θ2 = 855∘ + 2 × 360∘θ2 = 855∘ + 720∘θ2 = 1575∘
Therefore, an angle between −360∘ and 0∘ that is coterminal with θ is 1575∘.To learn more about “angle” refer to the https://brainly.com/question/25716982
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Sara’s hair was 25 inches long. Three years later it was 43 inches long. What was the percent increase?
Sara’s hair was 25 inches long. Three years later it was 43 inches long. The percentage increase rounded to the nearest hundredth will be 72.
Percentage:
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate the percentage of a number, we divide the number by the whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".
Calculate the percentage of a total value:
Since percent implies 100, we will split the total portion into 100 parts and then multiply it by b to gather b things per 100 items.
The percentage increase is found as:
[tex]% increase = \frac{change in value}{original value}[/tex][tex]%increase = \frac{change in value}{original value}[/tex][tex]%[/tex]% increase = Change in value/ Original value
⇒ % increase = [tex]\frac{13-25}{25} * 100[/tex]
⇒ % increase = 72
Hence, the percent increase rounded to the nearest hundredth will be 72.
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which of the following is equivalent to 3/8? -0.6, square root of 100, 2/5, -2/3, 0.35217534 ...
The option in the question that is equivalent to 3/8 is 2/5.
How to calculate the equivalent of 3/8We can simplify 3/8 and 2/5 so that they have a common denominator:
3/8 = 3*(5/5)/(85/5) = 15/40
2/5 = 2(8/8)/(5*8/8) = 16/40
Since 15/40 and 16/40 have the same denominator, we can compare their numerators to see which is larger:
15/40 < 16/40
Since 16/40 is larger, we can conclude that 2/5 is greater than 3/8.
Therefore, the option that is equivalent to 3/8 is 2/5.
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What formula is used to find the side lengths?
ANSWER:
The Pythagorean theorem is used to find the hypotenuse of a triangle.
=> AC² = AB² + BC²
In squares, the length of the side can be calculated by finding the square root of the area.
11. Figure EFGH is a parallelogram. Find the length of Line FG.
The length of Line FG is 13.5 inch
Define the term parallelogram?A parallelogram is a four-sided, geometric form in two dimensions. It is a quadrilateral, which means it has four vertices (corners) and four angles.
Area of parallelogram = base × height
As per given diagram, base, GH = 9inch and height, FP = 12inch
So, Area of parallelogram = 9 × 12 = 108 inch²
and also, Area of parallelogram = EQ × FG
put values here, 108 = 8 × FG
FG = 13.5 inch
Therefore, the length of Line FG is 13.5 inch
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if the parametric equations for x and y are both non-constant linear functions of t, then must the curve be a line? if so, give an argument why this must be true. if not, explain and give a counter-example.
If the parametric equations for x and y are both non-constant linear functions of t, then curve must be a line.
A curve (sometimes known as a curved line in ancient texts) is a mathematical entity that is similar to a line but does not have to be straight.
A curve may be conceived of intuitively as the trace left by a moving point. "The [curved] line[a] is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width," Euclid wrote more than 2000 years ago.
Let x = at+b and y = ct+d
Then,
[tex]\frac{x-b}{a}=\frac{y-d}{c}=t xc-bc=ay-adxc-ay+ad-bc=0[/tex]
Which is linear equation in x and y.
Therefore, curve is always a line.
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determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span. a, S = {(1, −1), (2, 1)} b, S = {(1, 1)} c, S = {(0, 2), (1, 4)}
a. S = {(1, -1), (2, 1)}Let's begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0. Because the two vectors are not colinear, they should span R2.|1 -1||2 1| determinant is not 0, therefore S spans R2. No geometric description is required for this example.
b. S = {(1, 1)} The set S contains one vector. A set containing only one vector cannot span a plane because it only spans a line. Therefore, S does not span R2. Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 1).c. S = {(0, 2), (1, 4)} Let's again begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0.|0 2||1 4| determinant is 0, thus S does not span R2. In this scenario, S only spans the line that contains both vectors, which is the line with the equation y = 2x.
Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 2).
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Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is______. A) 0.24 B) 0.34 C) 0.41 D) 0.66
The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.
Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.
Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.
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A computer store sells Ultra Fast brand desktop and laptop computers. They tracked the sales of both kinds of computers over five days. The table shows the sales data. Make a double-line graph of the data.
The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.
What is double-line graph?A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.
To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:
Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.
Label the horizontal axis with the days from Day 1 to Day 5.
Label the vertical axis with the heading "Number of Computers Sold".
Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).
Connect the data points for desktop computer sales with a line.
Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).
Connect the data points for laptop computer sales with a line.
Use a different color or style for the line representing desktop sales and the line representing laptop sales.
Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.
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HURRY PLS
From midnight to 8:00 am, the temperature rose 1. 51. 5°C each hour. If the temperature at midnight was -3−3°C, what was the temperature at 8:00 am?
the temperature at 8:00 am is 9°C This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.
To solve this problem, we need to use the formula for calculating the final temperature based on the initial temperature and the rate of change per hour.
The formula for this is:
Final Temperature = Initial Temperature + (Rate of Change per Hour x Number of Hours)
In this case, the initial temperature is -3°C, the rate of change per hour is 1.5°C, and the number of hours is 8.
Plugging these values into the formula, we get:
Final Temperature = -3 + (1.5 x 8)
Final Temperature = -3 + 12
Final Temperature = 9°C
Therefore, the temperature at 8:00 am is 9°C.
This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.
It's important to note that this problem assumes that the rate of change per hour remains constant throughout the 8 hour period. In reality, the temperature may fluctuate based on various factors, such as wind, cloud cover, and humidity. However, for the purposes of this problem, we can assume that the rate of change per hour remains constant.
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Agent Hunt is transferring classified files from the CIA mainframe into his flash drive. S(t) models the size of the files on the drive (in megabytes) after t seconds. S(t)=5t+45. What was the file size on the drive before the transfer? answer in megabytes
95 Gigabytes 1/3 Every 10 seconds, files are transmitted that are 10 times larger than the transfer rate as a whole. 2 / 3 The graph's slope is 5, according to the slope-intercept version of the equation for S. The unit rate is 5 gigabytes per second, according to this.
We are given the equation:- S(t)= 5t+45
calculate the value of S in 10s, 20s, 30s, ....... and difference in them.
for t= 10:-
S= 5(10)+45= 50+45= 95
for t= 20:-
S= 5(20)+45= 100+45=145
for t= 30:-
S= 5(30)+45= 150+45= 195
The difference:-
195-145= 50 and 145-95= 50
Hence, the file size is 50 MB per 10 seconds or 5 MB per second.
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Jamar delivers sandwiches for a restaurant that charges $9. 50 for each sandwich plus an $8 delivery fee. Jamar has an order that totals $65. Write an equation to describe this situation
Answer:
9.5x + 8 = 65
Step-by-step explanation:
Let x = number of sandwiches.
The cost of x sandwiches is 9.5x.
The delivery fee is $8.
The total cost of an order is the price of the sandwiches, 9.5x plus the delivery fee, 8.
In this case, the total cost is $65.
9.5x + 8 = 65
Answer:
$65
Step-by-step explanation:
X=9.50 because you add the $8 delivery fee to equal 65 in total.
1 0 6
0 1 1
0 0 0
Find the solution(s) to the system, if it exists. State the solution as a point (be sure to use parentheses), use parameter(s) s and t if needed. If the system is inconsistent, then state no solution.
The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
To solve the system of equations:
1x + 0y + 60z = 1
1x + 10y + 0z = 0
0x + 0y + 0z = 0
The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:
From the first equation, we get x = 1 - 60z
From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z
Therefore, the solution to the system can be written as a point in terms of z as:
(x, y, z) = (1 - 60z, -10 + 600z, z)
Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:
(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
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