A spinner divided into three equal sections marked A A and Z is spun 570 times approximately how many times will it be expected to land on an A
If a spinner divided into three equal sections marked A A and Z is spun 570 times . The number of times it will be expected to land on an A is 380 times.
How to find the Expected number of time ?Since the spinner has three equal sections in which two of them are marked A. The probability of landing on an A in a single spin will be 2/3 while the probability of landing on Z will be 1/3.
So,
Expected number of time E(A) =Number of spins x Probability of landing on A
Expected number of time E(A) = 570 x (2/3)
Expected number of time E(A) = 380
Therefore the Expected number of time E(A) is 380 times.
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Two cars are traveling in the same direction. The first car is going 45 mi/h and the second car is going 60 mi/h. The first car left 2 hours before the second car. How many hours will it take for the second car to travel the same distance as the first car
The time taken for the second car to travel the same distance as the first car is 6 hours.
What is the time of motion of the second car?
The time taken for the second car to travel the same distance as the first car is calculated as follows;
let the time taken for the second car to travel the same distance = t
distance traveled by second car = 60t
the time taken for the first car = t + 2
distance traveled by the first car = 45(t + 2)
Since both distance are equal, we will have the following equations;
60t = 45 (t + 2)
60t = 45t + 90
15t = 90
t = 90/15
t = 6
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
1+2i, 1+√5
The other zeros are
(Use a comma to separate answers.)
Answer:
The other zeros are:
1 - 2i, 1 - √5
Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
The volume of the cylinder is 8,038.4 ft3
How to calculate the volume of the cylinder?The height(H) is 10ft
The diameter is 32 ft
The formula for calculating the volume of a cylinder is
πr²h
Radius= 32/2
= 16
Volume= 3.14 × 16² × 10
= 3.14 × 256 × 10
= 8,038.4
Hence the volume of the cylinder is 8,038.4 ft3
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NASA launches a rocket at
t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t^2+43t+339
.
(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)
The rocket splashes down after
seconds._______
(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)
The rocket peaks at _____
meters above sea-level._____
Answer:
(A)
[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]
[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]
[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]
The rocket splashes down after 13.79 seconds.
(B) h'(t) = -9.8t + 43 = 0
t = 43/9.8 = 215/49 = 4.39 seconds
h(4.39) = 433.34 meters
At t = 4.39 seconds, the rocket peaks at
433.34 meters above sea level.
A business manufactures and sell laptops.Each laptop is sold for R14000.the fixed monthly cost is R32000 and it cost R9000 to manufacture each laptop.let L be number of laptops manufactured and sold per monthly
The total cost equation can be written as:
Total Cost = 32000 + 9000L
What is total cost?
Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.
The total cost equation can be expressed as:
Total Cost = Fixed Cost + Variable Cost
where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.
In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.
If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:
Total Cost = 32000 + 9000L
This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.
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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?
Electronics store reduced price of tv From $900 to $837
The percentage decrease of the TV from $900 to $837 is 7%
Percentage decreaseOriginal price of TV = $900New price of TV = $837Percentage decrease = Difference in price / original price × 100
[tex]=\dfrac{(900-837)}{900} \times 100[/tex]
[tex]=\dfrac{63}{900} \times 100[/tex]
[tex]= 0.07 \times 100[/tex]
[tex]= 7\%[/tex]
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Complete question-
An electronics store reduced the price of a TV from $900 to $837. What was the percent of decrease?
To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
The given scenario is Biased, since those who chose to respond may be systematically different than those who chose not to respond. So, the correct answer is C).
The sampling method is biased, since those who chose to respond may be systematically different than those who chose not to respond. This is known as non-response bias, where the opinions and characteristics of those who choose not to respond to the survey may differ from those who choose to respond.
Additionally, only one higher education institution per state was selected, which may not be representative of all institutions within the state. Therefore, the sample may not accurately reflect the population of students in the United States who pay for their higher education. So, the correct option is C).
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--The given question is incomplete, the complete question is given
" To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
Is the sampling method biased or unbiased and why?
Unbiased, since a random sample was selected
Unbiased, since a large sample was selected
Biased, since those who chose to respond may be systematically different than those who chose not to respond
Biased, since all higher education institutions are represented
Unbiased, since a questionnaire was used
Biased, since every state will be represented in the sample"--
what is twenty-five divided bye four?
Answer: The answer is 6.25
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
Let
sin A = − 24/25
with A in QIII and find the following.
sin 2A
Answer:
sin(2A) = 2sin(A)cos(A)
To find cos(A), we can use the Pythagorean theorem:
sin^2(A) + cos^2(A) = 1
cos^2(A) = 1 - sin^2(A)
cos(A) = -√(1 - sin^2(A)) (since A is in QIII, cos(A) is negative)
cos(A) = -√(1 - (-24/25)^2) = -7/25
Now we can substitute into the double angle formula:
sin(2A) = 2sin(A)cos(A)
sin(2A) = 2(-24/25)(-7/25)
sin(2A) = 336/625
Therefore, sin(2A) = 336/625.
The sides of a square are increased
by a scale factor of 3. The area of
the larger square is what percent of
the area of the smaller square?
So the area of the larger square is 900% of the area of the smaller square.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.
Here,
If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.
Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:
A' = (3s)²
= 9s²
The ratio of the area of the new square to the area of the original square is:
A' / A = (9s²) / (s²)
= 9
Multiplying by 100% to convert to a percentage, we get:
A' / A = 900%
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Imagine that two friends, Lola and Joni, each buy an iPod touch for $400, and pay with a credit card. When this happens, the credit card company pays Apple, and the friends become indebted to the credit card company. For every year they don't pay back the debt, the company charges them interest: a percentage of what they owe. The interest rate is called an annual percentage rate (APR), while the amount owed is called a balance.
Calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is calculated once per year.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%:
Joni 36%
In reality, credit card companies don't charge interest every year, they charge interest every month. To determine the monthly interest rate, divide the APR by 12.
Lola has an annual rate of 6%. So Lola has a monthly rate of
0.5%
Joni has an annual rate of 36%. So Joni B has a monthly rate of:
3%
Given that both Lola and Joni charge $400 initially calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is compounded monthly.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%
Joni 36%
Do you think it matters how often credit card companies charge interest? Explain.
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 10 years, how much would the $400 iPod end up costing in total (with monthly compounding)?
Lola's total cost (balance after 10 years): $
Joni's total cost (balance after 10 years): $
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
How to solveAmount = P = 340
Amy's interest rate = ra = 6% = 0.06
Mackenzie's interest rate = rm = 30% = 0.3
Amount is compounded yearly.
Amount at the end of the year is calulated as
Pn= P(1+r)
We will use Excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.40 382.02 404.95 482.30
Mackenzie 30% 340.00 442.00 574.60 746.98 1641.12
Amy has an annual rate of 6%. So Amy has a monthly rate of 6 /12 = 0.5% = 0.005
Mackenzie has an annual rate of 30%. So Mackenzie has a monthly rate of 30/12 = 2.5% = 0.025
Pn= P(1+r)
Here will be replaced by a number of months and r is relaced by monthly interest rate
We can modified this formula as
12n
Pn= P(1+)
Where n and r is same as in first part of question.
We will use excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.97 383.23 406.87 486.90
Mackenzie 30% 340.00 457.26 614.97 827.06 2011.86
From the above two tables, it is clear that it does matter how the company charges interest. When compounded monthly, the amount will more as compared to when compounded yearly. So,
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 12 years, we can add one more column to calculate for n = 12.
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
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What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
The equation of a parabola with a vertical axis and vertex (h, k) is given by:
(x - h)² = 4p(y - k)
How to explain the equationIn the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
If the vertex is at the origin (h=0, k=0), then the equation simplifies to:
x² = 4py
where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
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lmop are the angles LN is the diagonal the sides are missing
All four angles of the rhombus are 20, 160, 20, and 160 degrees.
What is meant by diagonal of an angle ?Diagonals are the parts of a shape, in geometry, a diagonal is a line that join two vertices of a polygon or a solid shape , whose vertices are not on the same edge. In general, a diagonal is called as a sloping line or the slant line, that connects to the vertices of a shape.
According to question a rhombus , all four sides are congruent and opposite angles are equal. Let's call the rhombus ABCD, where AB, BC, CD, and DA are the four sides, and AC and BD are the diagonals.
If one of the angles formed by diagonals and adjacent sides is 20 degrees, let's say that angle is ABD. We can draw a line from point A to point C, which will divide the rhombus into two congruent triangles, ABC and ACD.
Since triangle ABC is isosceles, with sides AB = BC, angles ABC and BCA are equal. Similarly, in triangle ACD, angles ACD and CDA are equal.
∴ angles ABD and CDA are adjacent angles formed by intersecting lines, they must add up to 180 degrees. Therefore, angle CDA is 160 degrees.
If triangles ABC and ACD are congruent, angle CAD is also 20 degrees.
Now we can use the fact that opposite angles in a rhombus are equal. Angles BCD and ABD are opposite angles, so angle BCD is also 20 degrees. Similarly, angles BAC and ADC are opposite angles, so angle BAC is also 160 degrees.
Therefore, all four angles of the rhombus are 20, 160, 20, and 160 degrees.
Complete question If one of the angles formed by diagonals and adjacent sides. of Is 20, all four angles of the a rhombus are.
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35. The equation v=20Vt + 273 relates the speed v, in m/s, to the air
temperature t in Celsius degrees.
a. Find the temperature when the speed of sound is 340 m/s.
b. Find the temperature when the speed of sound is 320 m/s.
a. The temperature is about 3.35 degrees Celsius at 340 m/s, the speed of sound.
b. The temperature is about 2.35 degrees Celsius at 320 m/s, or the speed of sound.
Describe Speed?Speed is a scalar physical quantity that quantifies the rate of motion of an object. It is described as the distance that an object covers in a specific period of time. Meters per second (m/s) is the SI unit for measuring speed.
The speed formula is as follows:
Speed = distance / time
Depending on the purpose, speed can also be stated in different units, such as kilometres per hour (km/h), miles per hour (mph), or feet per second (ft/s).
The concept of speed, which is used to describe how objects move, is important to physics. It plays a significant role in a variety of fields of science, engineering, and technology, including sports, aircraft, and transportation. For the purpose of analysing and forecasting the behaviour of physical systems, it is essential to comprehend the idea of speed.
a. We can change v = 340 into the equation and solve for t to determine the temperature when the speed of sound is 340 m/s:
v = 20Vt + 273
340 = 20Vt + 273
67 = 20Vt
t = 67/20
Therefore, the temperature is about 3.35 degrees Celsius when the sound travels at 340 m/s.
b. We may once more enter v = 320 into the equation and solve for t to determine the temperature when the speed of sound is 320 m/s:
v = 20Vt + 273
320 = 20Vt + 273
47 = 20Vt
t = 47/20
As a result, the temperature is roughly 2.35 degrees Celsius at 320 m/s, the speed of sound.
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How many triangles exist with the given side lengths?
3in , 4in , 2in
Step-by-step explanation:
Only ONE .....there are three sides to a triangle and you supplied 3 sides.
What is the midpoint of the line segment with the given endpoints (4,6) (3,-3)
Help it’s urgent
The coordinates of the midpoints of the given line segment is:
(3.5, 1.5)
How to find the midpoints of a line segment?The midpoint of a line segment is simply referred to as the center of that specific line segment.
Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.
The coordinates of the endpoints of the line are:
(4,6) and (3,-3)
The formula to find the coordinates of the midpoint of the line is:
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Thus, we have:
(x, y) = (4 + 3)/2, (6 - 3)/2
= (3.5, 1.5)
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-1/2x<18 pls help figure
Answer:
-36
Step-by-step explanation:
-1/2x<18
multiply each term by LCM=2
-1/2x×2<18×2
the 2on the left hand side will cancel each other leaving
-x <36
divide both sides by -1
-x/-1>36/-1
(note the equality sign changes because following the laws when you divide by a negative number the sign will change
X>-36
Answer:
Step-by-step explanation:
x>-36 is the anwser brainlist whould be aprecited and verifed
Jade is constructing wooden figures for a park.
She is making six of them and fitting them
together to form part of a stage. What is the total
volume of all of the parts? Show your work.
10 ft
3 ft
4 ft
It is to be noted that the volume of all the wooden figures will come to.
Why is this so?Each wooden figure as shown in the image is
L = 4ft
W = 4ft
H = 10ft
Where L = Length, w= Width and H = height.
The volume of a cuboid is L x W x H
So we have
4 x 4 x 10
Since there are six of the figures, we restate the expression as:
6 x 4 x 4 x 10
= 960 Ft³
Thus, volume of all of the parts is 960 Ft³
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
Write an equation of a circle with the given center and radius. center (3,4) and radius 6
(x-3)^2+(y-4)^2=36
(x-3)^2+(y-4)^2=6
(x+3)^2+(y-4)^2=36
(x+3)^2+(y-4)^2=6
Answer:
[tex] {(x - 3)}^{2} + {(y - 4)}^{2} = 36[/tex]
a baseball stadium keeps track of how many hot dogs each customer orders. the data is organized into the frequency table below. what os the relative frequency of customers ordering five hot dogs?
a.) about 5%
b.) about 7%
c.) about 8%
d.) about 14%
The relative frequency of customers ordering five hot dogs is 7%, option B is correct.
To find the relative frequency of customers ordering five hot dogs, we need to divide the frequency of customers who ordered five hot dogs by the total number of customers.
The total number of customers is the sum of the frequencies in the table:
Total frequency = 90 + 45 + 18 + 18 + 14 + 13 = 198
The frequency of customers ordering five hot dogs is 14, so the relative frequency is:
Relative frequency of customers ordering five hot dogs = (frequency of customers ordering five hot dogs) / (total frequency) = 14 / 198 = 0.0707
To express this as a percentage, we can multiply by 100:
Relative frequency of customers ordering five hot dogs = 0.0707 * 100% = 7.07%
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Several trusses are needed to build the frame of the shed roof. Each roof truss is 16 inches apart, as measured from the centers of the beam widths.
The roof could be constructed so that the ridgeline of the roof is parallel to the longest dimension of the shed (first picture below) or it could be constructed so that the ridgeline of the roof is parallel to the shortest dimension of the shed (second picture below).
The number of roof trusses that would be needed for the longest length is 2
Calculating the number of roof trusses that would be neededThe longest lengths from the question are given
Longest lengths = 28 and 22
Next, we expand the lengths of the roof trusses
This is to calculate the greatest common factor (GCF) of the lengths
So, we have
28 = 2 * 2 * 7
22 = 2 * 11
Multiplying the common factors gives the GCF
So, we have
GCF = 2
This means that the number of roof trusses that would be needed for the longest length is 2
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A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.When time, t = 0, the initial value can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]
C(0) = 18(1)
C(0) = 18 degrees Celsius.
When time, t = 0 = 20, the temperature can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]
C(20) = 2.73 degrees Celsius.
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Complete Question:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
[tex]C(t)=18(0.91)^{t}[/tex]
Find the initial temperature of the soda and its temperature after 20 minutes?
State the domain, the range, and the intervals over which the graphically defined function is increasing, decreasing, or constant.
The domain will be (-∞, ∞). The range will be (-1, 1]. The function will be increasing during the intervals (0, π/2) and (3π/2, 2π), and will be decreasing at the interval (π/2, 3π/2). It will be constant only at x=0 and not at any interval.
We are given a graph in the question and we have to determine its domain, range, and the intervals over which the defined function is increasing, decreasing, and constant. If we observe this graph, we can see that this is a sin(x) graph.
The domain of this graph will be from -[tex]\infty[/tex] to [tex]\infty[/tex] as we can see in the graph that it is a repeating pattern. The range for this graph will lie between -1 and 1 as it is a sin x graph. The sin x graph increases at the intervals (0, π/2) and (3π/2, 2π) and decreases at the interval (π/2, 3π/2). As we can see from the graph, it is constant only at a point where x = 0 and there is no interval at which this graph is constant.
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Explain how you know what a fraction was multiplied by when the product is greater than a factor.
When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.
Why is this true of fractions ?Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.
By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.
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Ava uses a total of 72 bead. without dividing, how can you know if she made an even number of bracelets?
To check if the total number of beads used in each bracelet is even, we need to find out if the sum of the digits in the number 72 is even or odd.
How to know number of bracelets madeIf Ava made an even number of bracelets using the 72 beads, then the total number of beads used in each bracelet must be an even number.
One way to check if the total number of beads used in each bracelet is even is to find out if the sum of the digits in the number 72 is even or odd. If the sum of the digits is even, then it is possible that Ava made an even number of bracelets. If the sum of the digits is odd, then it is not possible that Ava made an even number of bracelets.
The sum of the digits in 72 is 7 + 2 = 9, which is an odd number. Therefore, it is not possible for Ava to have made an even number of bracelets using the 72 beads, without dividing the beads.
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n/4.4 =7 Pls Help nowwwwwwwwwwwwwwwwwwwww
Answer:
n=7
Step-by-step explanation:
[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]
reasoning.
19. Challenge: Find the lengths of BC, DE, and FG in the diagram
below.
A
1
30°
B
0.5
C
D
E
-1.5√3
F
G
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.
What are trigonometric functions?Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.
This can be solved by using trigonometric functions.
First we need to find the length of FA to solve the question further.
FA = 1.5+ FD
AG = FA cos 30
AG = 1.5 √3
AG = 1.5 FD √3/2 = 1.5√3 (as cos 30 = √3/2)
DF = 1.5
Thus, FA = AB+BD+FD
FA = 1 + 0.5 + 1.5
So, the length of FA is 3.
Now, for the triangle, ΔABC
as ∠BAC= 30
BC = AB/2
= 0.5
This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.
For ΔADE,
as ∠DAE= 30, and AD= 1.5
DE= AD/2
= 0.75
For ΔGAF,
as ∠GAF= 30, and FA= 3
FG = FA/2
= 1.5
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.
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The distance between Town P and Town Q is 237.5 Km. At 11.30 a.m a van travels from
Town P to Town Q at an average speed of 35 km/h. At the same time, a car travels from
Town Q to Town P along the same route at an average speed of 60 km/h.
a)At what time will the vehicles meet on the way?
b) How far will each vehicle have travelled when they meet?
Answer:
So when the two vehicles meet, the van has travelled 87.5 km and the car has travelled 150 km.
Step-by-step explanation:
(a) Let's call the time it takes for the two vehicles to meet "t". We know that the distance between the two towns is 237.5 km, and the combined speed of the two vehicles is 35 km/h + 60 km/h = 95 km/h. Using the formula distance = speed × time:
237.5 = 95t
Solving for t:
t = 237.5/95
t ≈ 2.5 hours
So the two vehicles will meet on the way 2.5 hours after 11.30 a.m., which is at 2.00 p.m.
(b) To find how far each vehicle has traveled when they meet, we can use the formula distance = speed × time again. The van travels at 35 km/h for 2.5 hours, so it travels:
distance = speed × time = 35 km/h × 2.5 hours = 87.5 km
The car travels at 60 km/h for 2.5 hours, so it travels:
distance = speed × time = 60 km/h × 2.5 hours = 150 km
So when the two vehicles meet, the van has traveled 87.5 km and the car has traveled 150 km.
What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.