The total charges of both companies is the same at 24 months.
The equation of the scenariosWe have:
Company one:
Set up fee - $20Service plan-$25/monthPhone payment-$40/monthThis means that:
y = 20 + 25x + 40x
y = 20 + 65x
Company two:
Set up fee-$30New phone-$700Service plan-$35/monthThis means that:
y = 30 + 700 + 35x
y = 730 + 35x
The graph of both companiesSee attachment
The point of intersectionOn the attached graph, the point of intersection is at
(x, y) = (24, 1558)
This means that the total charges of both companies is the same at 24 months.
The better dealOn the long run, phone company two has a better deal.
On the short run, phone company one has a better deal.
Because the function have lesser values after the point of intersection.
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Find (−7z−4)−(−3z+1) .
Answer:
\( \sf \: -4z - 5 \)
Step-by-step explanation:
Given expression,
→ (-7z - 4) - (-3z + 1)
Let's simplify the expression,
→ (-7z - 4) - (-3z + 1)
→ -7z - 4 + 3z - 1
→ (-7z + 3z) + (-4 - 1)
→ (-4z) + (-5)
→ -4z - 5
Hence, the answer is -4z - 5.
If a ball is thrown in the air with a velocity 40 ft/s, its height in feet t seconds lateris given by y = 40t -16t2.
(a) Find the average velocity for the timeperiod beginning when t = 2 and lasting 0.5 second.
1
ft/s
(b) Find the average velocity for the time period beginning whent = 2 and lasting 0.1 second.
2
ft/s
(c) Find the average velocity for the time period beginning whent = 2 and lasting 0.05 second.
3
ft/s
(d) Find the average velocity for the time period beginning whent = 2 and lasting 0.01 second.
4
ft/s
(e) Estimate the instantaneous velocity when t = 2.
5
ft/s
a) The average velocity of a) is -14 ft/s.
b) The average velocity of b) is 100 ft/s.
c) The average velocity of c) is 180 ft/s.
d) The average velocity of d) is 840 ft/s.
e) The instantaneous velocity when t = 2 is -24 ft/s.
(a) If the height of the ball thrown in the air is given by y = 40t -16t2,
the average velocity can be calculated for the time period beginning
when t = 2 and lasting 0.5 second using the given formula:
Average velocity = [y(2 + 0.5) - y(2)] / 0.5= [y(2.5) - y(2)] / 0.5
Now, substituting t = 2.5 and t = 2, we get,
Average velocity = [40(2.5) - 16(2.5)2] - [40(2) - 16(2)2] / 0.5
= [25 - 32] / 0.5
= -14 ft/s
Therefore, the average velocity is -14 ft/s.
(b) If the height of the ball thrown in the air is given by y = 40t -16t2,
the average velocity can be calculated for the time period beginning
when t = 2 and lasting 0.1 second using the given formula:
Average velocity = [y(2 + 0.1) - y(2)] / 0.1= [y(2.1) - y(2)] / 0.1
Now, substituting t = 2.1 and t = 2, we get,
Average velocity = [40(2.1) - 16(2.1)2] - [40(2) - 16(2)2] / 0.1
= [42 - 32] / 0.1
= 100 ft/s
Therefore, the average velocity is 100 ft/s.
(c) If the height of the ball thrown in the air is given by y = 40t -16t2,
the average velocity can be calculated for the time period beginning
when t = 2 and lasting 0.05 second using the given formula:
Average velocity = [y(2 + 0.05) - y(2)] / 0.05= [y(2.05) - y(2)] / 0.05
Now, substituting t = 2.05 and t = 2, we get,
Average velocity = [40(2.05) - 16(2.05)2] - [40(2) - 16(2)2] / 0.05
= [41 - 32] / 0.05
= 180 ft/s
Therefore, the average velocity is 180 ft/s.
(d) If the height of the ball thrown in the air is given by y = 40t -16t2,
the average velocity can be calculated for the time period beginning
when t = 2 and lasting 0.01 second using the given formula:
Average velocity = [y(2 + 0.01) - y(2)] / 0.01
= [y(2.01) - y(2)] / 0.01
Now, substituting t = 2.01 and t = 2, we get,
Average velocity = [40(2.01) - 16(2.01)2] - [40(2) - 16(2)2] / 0.01
= [40.4 - 32] / 0.01
= 840 ft/s
Therefore, the average velocity is 840 ft/s.
(e) The instantaneous velocity can be estimated when t = 2 by finding the derivative of the function y = 40t -16t2 with respect to time t.
The derivative of y is given by:
y' = 40 - 32tAt t = 2,
y' = 40 - 32(2) = -24 ft/s
Therefore, the instantaneous velocity when t = 2 is -24 ft/s.
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Let the random variable H represent the height of a woman in the population. P(H<60) represents the probability, of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model for the normal model.
Answer:
Hello your question in incomplete attached below is the complete question
answer : 0.03
Step-by-step explanation:
H represents the height of women
Determine P ( H < 60 ) using either discrete or normal model
using discrete model
P ( H < 60 ) = ∑ relative frequencies of women with height < 60 inches
= 0.01 + 0.02 = 0.03
4 kg metal to 500g of plastic simplest ratio
Answer: 8:1
Step-by-step explanation:
To find the simplest ratio of 4 kg of metal to 500g of plastic, we need to convert both quantities to the same unit of measurement. Let's convert 4 kg to grams:
4 kg = 4000 gNow we have 4000 g of metal and 500 g of plastic. To simplify the ratio, we can divide both quantities by their greatest common factor (GCF), which is 500:
4000 g ÷ 500 = 8500 g ÷ 500 = 1Therefore, the simplest ratio of 4 kg of metal to 500g of plastic is 8:1.
________________________________________________________
The total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.
Solution and Explanation:The total weight of metal and plastic is:
\(\large\rm{4\: kg + 0.5\: kg = 4.5\: kg}\)The simplest ratio of metal to plastic is found by dividing both quantities by their greatest common factor.
The greatest common factor of 4 kg and 0.5 kg is 0.5 kg. Dividing both quantities by 0.5 kg gives:
\(\large\rm{Metal:Plastic = 8:1}\)\(\therefore\) The simplest ratio of metal to plastic is 8:1.
To check, we can verify that:
\(\large\rm{\dfrac{8}{9} \cdot 4.5\: kg \approx 4\: kg}\) (for metal)\(\large\rm{\dfrac{1}{9} \cdot 4.5\: kg \approx 0.5\: kg}\) (for plastic)So the total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.
\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)
Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with the adjacent marble(s). Also, each marble is in contact all around the funnel wall. The smallest marble has a radius of 8, and the largest marble has a radius of 18. What is the radius of the middle marble
The radius of the middle marble is 12. To find the radius of the middle marble, we can use the concept of similar triangles and proportions.
Let's denote the radii of the marbles as follows:
r1 = radius of the smallest marble (8)
r2 = radius of the middle marble (unknown)
r3 = radius of the largest marble (18)
Since each marble is in contact with the adjacent marble(s) and with the funnel wall, we can consider the three marbles (smallest, middle, and largest) as forming a triangle within the funnel.
By observing the arrangement of the marbles, we can see that this triangle is similar to a triangle formed by connecting the centers of the marbles.
Now, let's focus on the ratio of the radii of the marbles in the two triangles:
r1 : r2 : r3
We know that r1 = 8 and r3 = 18. To find r2, we can set up the proportion:
r1 / r2 = r2 / r3
Substituting the known values:
8 / r2 = r2 / 18
Cross-multiplying:
(r2)^2 = 8 * 18
Simplifying:
(r2)^2 = 144
Taking the square root of both sides:
r2 = √144
r2 = 12
Therefore, the radius of the middle marble is 12.
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solve for x
A)8
B)9
C)-9
D)-8
Answer:
C) -9
Step-by-step explanation:
x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.
2(x + 19) = x + 29
2x + 38 = x + 29
x + 38 = 29
x = -9
there are 20 marbles in a bag. 35% of the marbles are blue. how many marbles are blue?
Answer:
7 marbles are blue.
Answer:
7
Step-by-step explanation:
20 divided by 100 times 35!
8. Find the value of x.
m_1 = x + 10
mZ2 = 3x + 18
12
Answer is it 46x 12 im confused im not in this stage yet
Step-by-step explanation:
Question 10, please help
10/10
Optiοn C represents a prοpοrtiοnal relatiοnship . The values οf all the given values are prοpοrtiοnal tο each οther i.e, 1/3.
What is prοpοrtiοnal relatiοnship?A prοpοrtiοnal relatiοnship is a mathematical relatiοnship between twο variables where the ratiο οf the twο variables is cοnstant. In οther wοrds, if we have twο variables x and y, they are said tο have a prοpοrtiοnal relatiοnship if the ratiο οf x tο y is always the same, regardless οf the values οf x and y.
This can be expressed mathematically as:
x/y = k
where k is a cοnstant called the prοpοrtiοnality cοnstant. This means that as x increases, y will increase prοpοrtiοnally, and as x decreases, y will decrease prοpοrtiοnally.
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Chef Johnson used 4 1/2 cups of flour to make 4 fruitcakes. How many cups of flour are
needed for 1 fruitcake?
Answer:
Is should be 1 1/8. cups of flour to make one fruitcake.
Glokk8x - The Album 8x out on all platforms
how do u sovle Find x .
Two non-congruent parallelograms. The width and length of one parallelogram are marked 4 centimeters and 6 centimeters respectively. The width and length of the other parallelogram are marked 6 centimeters and x respectively.
The length of the second parallelogram is 2 cm.
What are parallelograms ?
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. It has two pairs of parallel sides and opposite angles are equal. Some common properties of parallelograms include:
According to the question:
To solve for x, we need to use the fact that opposite sides of a parallelogram are equal in length.
For the first parallelogram, we know that the width is 4 cm and the length is 6 cm. Therefore, the opposite side lengths are also 4 cm and 6 cm.
For the second parallelogram, we know that the width is 6 cm. Since the opposite sides are equal in length, the length of the parallelogram must be x cm.
So, we have:
Width of first parallelogram = Width of second parallelogram
4 cm = 6 cm
Length of first parallelogram = Length of second parallelogram
6 cm = x cm
Simplifying the first equation, we get:
2 cm = x
Therefore, the length of the second parallelogram is 2 cm.
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Find the length of side x to the nearest tenth.
30°
5
60⁰
X
Answer: x = 4.3
Step-by-step explanation:
You can use sine:
sin(60) = x/5 ; x = 5(sin(60)) ; x = 4.3
Hope this helps!
What is the vertex form of the equation? y = – x 2 + 12 x – 4 show steps of how you solved please
The vertex form of the equation is in the form of y = a(x-h)^2 + k.
Step 1: Use the formula below to solve for a.
a = -1/4 * (4 - 12) = -1
Step 2: Use the formula below to solve for h.
h = -b/(2a) = 12/(2(-1)) = -6
Step 3: Use the formula below to solve for k.
k = f(h) = -(-6)^2 + 12(-6) - 4 = 36
Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.
In mathematics, what is the vertex?A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.
What is the vertex location?Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.
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2.) the acosta family went out to dinner. the price of the meal was $79.85. if the tip was 15%. how much money did the acosta family pay for the meal, including tip
the acosta family went out to dinner. the price of the meal was $79.85. if the tip was 15%.The Acosta family paid $91.83 for the meal, including the 15% tip.
To calculate the total amount paid, we need to add the original price of the meal to the tip amount. The price of the meal was $79.85, and the tip was 15% of that amount. To find the tip, we multiply $79.85 by 0.15 (or 15% expressed as a decimal), which equals $11.98. Adding the tip of $11.98 to the original price, the total amount paid is $91.83.
In more detail, a 15% tip means that 15% of the meal price is added as an extra amount to the bill. To calculate the tip, we multiply the meal price ($79.85) by 0.15 (or 15% as a decimal), resulting in $11.98. This represents the additional amount the Acosta family paid for the tip. To find the total amount paid, we add the tip amount to the original meal price: $79.85 + $11.98 = $91.83. Therefore, the Acosta family paid $91.83 for the meal, including the tip.
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make w the subject of the formula s = w/a
Answer:
w = sa
Step-by-step explanation:
Given
s = \(\frac{w}{a}\) ( multiply both sides by a to clear the fraction )
sa = w
PLEASE ANSWER ASAP And don't be a scam The average diameter of a car wheel is 25 inches. How far will the car travel if the wheel rotates 1 time? Round your answer to the nearest inch.
A. 39 inches
B. 491 inches
C. 157 inches
D. 79 inches
Answer:
D. 79 inches.
Step-by-step explanation:
That would be the circumference of the wheel
= π * diameter
= 78.54 inches
easy points just answer correctly
Give the values of b, h, and k for the function f(x) = log_5 (x - 4) – 1 .
b = 5, h = -4, and k = 1
b = 5, h = 4, and k = 1
b = 5, h = 4, and k = -1
b = 5, h = -4, and k = -1
Answer:
D. b = 5, h = - 4, k = - 1Step-by-step explanation:
Translated of logarithmic function:
\(f(x) = log_b (x + h) + k\) where b is base, h - horizontal shift, k - vertical shiftAccording to given function the values are:
b = 5, h = - 4, k = - 1Correct choice is D
General equation
log_b(x+h)-kHere our equation
log_5(x-4)-1So
b=5h=-4k=1Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 45 bacteria are present o begin with the total number present after a days is f(x) = 45 - 64* Find the total number present after 1, 2 and 3 days. There will be bacteria present after 1 day, after 2 days and after 3 days.
A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
The problem can be solved using the exponential growth model.
In the given problem, the formula for the growth model is given, that is:
f(x) = 45 (64)^(x)
Where:
f(x) = total number of bacteria present after x days
To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.
f(1) = 45 (64)¹ = 2,880
f(2) = 45 (64)² = 184,320
f(3) = 45 (64)³ = 11,796,480
Hence,
after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
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It’s due today. PLEASE
Answer: y=3.33x+20
Step-by-step explanation:
Slope intercept form- y=mx+c
m=slope
c=y-intercept
Slope-
y2-y1/x2-x1
30-20/3-0
10/3
m=3.333333
Y-intercept= 20
So,
y=3.33x+20
Hope this helps! :)
134 x 0.01 what is it
-27<7x-13<8 Please help do not understand
Answer:
-2<x<3
Step-by-step explanation:
A plane flies 810 miles from Franklin to Centerville with a bearing of 75° Then it flies 648 miles from Centerville to Rosemount with a bearing of 32°. Draw a figure that visually represents the situation. Then find the straight-line distance and bearing from Franklin to Rosemount.
Navigation A plane flies 810 miles from Franklin to Centerville with a bearing of 75∘. Then it flies 648 miles from Centerville to Rosemount with a bearing of 32∘. 63.7° is the straight-line distance and bearing from Franklin to Rosemount.
The scenario of the plane travelling from Franklin to Centerville and subsequently from Centerville to Rosemount is depicted in the figure below.
From Franklin to Centerville, the bearing is 75°, and from Centerville to Rosemount, the bearing is 32°. The hypotenuse of the triangle created by these two legs of travel is the straight-line distance from Franklin to Rosemount, which can be computed using the Pythagorean theorem as √(810² + 648²) = 1040 miles.
The angle between the two legs, which can be determined using the Law of Cosines as cos⁻¹((810²+648²-1040²)/(2×810×648)) = 63.7°, is the bearing from Franklin to Rosemount.
Complete Question:
Navigation A plane flies 810 miles from Franklin to Centerville with a bearing of 75∘. Then it flies 648 miles from Centerville to Rosemount with a bearing of 32∘. Find the straight-line distance and bearing from Franklin to Rosemount.
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Adina is starting a band and wants to buy a guitar and amplifier. The cost of the guitar is g(m) = 680 + 10m where m is time in months. The amplifier cost is represented by the function a(m) = 450 - 5m. Adina hopes to have enough money saved up to buy both items in 4 months. How much will she need?
The cost of the amplifier=$26.33
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Step 1: Derive expression for amplifier cost and guitar cost
guitar cost=g
amplifier cost=a, but since its costs 1.54 more than 1.26 times the cost of the guitar, a=(1.26×g)+1.54=1.26 g+1.54
amplifier cost=a=1.26 g+1.54
Step 2: Derive the expression for the total cost of guitar and amplifier
Total cost of guitar and amplifier=Cost of guitar+cost of amplifier
where;
Cost of guitar=g
Cost of amplifier=1.26g+1.54
Total cost of guitar and amplifier=46
replacing;
46=g+1.26g+1.54
46=2.26g+1.54
2.26g=46-1.54
2.26g=44.46
g=44.46/2.26
g=19.67
a=(1.26×19.67)+1.54=26.33
The cost of the amplifier=$26.33
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Find the 22nd term of the arithmetic sequence whose common difference is d=4 and whose first term is a, = 3
Answer:
Step-by-step explanation:
t22 = a + (n- 1)d
t22 = 3 + 21*4
t22 = 3 + 84
t22 = 87
question 3
pls help me as soon as possible
i'm being timed i only have a hour
The measure of arc FE in the figure is 100 degrees
How to determine the measure of arc FEFrom the question, we have the following parameters that can be used in our computation:
The circle and the intersecting chords
The value of arc FE represented by x is then calculated as
80 = 1/2(x + 60)
Cross multiply the equation
This gives
x + 60 = 160
Subtract 60 from both sides
x = 100
Hence, the measure of x is 100 degrees
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Kareem will run at least 31 miles this week. So far, he has run 13 miles. What are the possible numbers of additional miles he will run?
Use for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Answer:
\(t\geq 18\)
Step-by-step explanation:
A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying.A. operation.B. smart.C. super cool.
Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.
The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.
The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.
Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.
Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.
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Find the equation that intersects the x-axis at point (3, 0) and
intersects the y-axis at
point (0, 5). Then sketch the diagram.
The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.
To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).
Using the slope formula: m = (y2 - y1) / (x2 - x1)
Substituting the values (0 - 5) / (3 - 0) = -5 / 3
So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).
Using the point (0, 5):
5 = (-5/3) * 0 + b
5 = b
The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:
y = (-5/3)x + 5
To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.
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What is the correct factorization of:
x? - 11x + 18
9514 1404 393
Answer:
x² -11x +18 = (x -9)(x -2)
Step-by-step explanation:
The x-coefficient is the sum of the constants in the binomial factors; the constant term is their product. It usually works well to look for factors of the constant that have the right sum. Here, both must be negative.
18 = (-1)(-18) = (-2)(-9) = (-3)(-6)
The factors -2 and -9 have a sum of -11, so those are the binomial constants of interest. The factorization is ...
x² -11x +18 = (x -9)(x -2)
hello! help please ?
Answer:
d
Step-by-step explanation:
the graph of using step by step
Answer:
x = 9.32
Step-by-step explanation:
use the angles strategy