Answer:
Part a) [tex]y=0.05x+1.50[/tex]
Part b) [tex]y=0.50x+0.50[/tex]
Part c) The graph in the attached figure
Part d) see the explanation
Step-by-step explanation:
The complete question is
A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.
Part a) Write a linear function for the price of tea at restaurant
Part b) Write a linear function for the price of tea at gas station store
Part c) Graph both equations
Part c) Compare the lines in terms of slope and y-intercept
Let
y -----> the price of tea in dollars
x -----> the number of refills
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value (value of y when the value o x is equal to zero)
Part a)
At restaurant
we have that
The slope or unit rate is equal to
[tex]m=\$0.05\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$1.50[/tex]
substitute
[tex]y=0.05x+1.50[/tex]
Part b)
At gas station store
we have that
The slope or unit rate is equal to
[tex]m=\$0.50\ per\ refill[/tex]
The initial value or y-intercept is equal to
[tex]b=\$0.50[/tex]
substitute
[tex]y=0.50x+0.50[/tex]
Part c) Graph both equations
we know that
The easiest way to graph a line is with two points
Find the intercepts of the line
At restaurant
[tex]y=0.05x+1.50[/tex]
The y-intercept is the point (0,1.50)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=0.05x+1.50[/tex]
[tex]x=-30[/tex]
The x-intercept is the point (-30,0)
Plot the points and join to graph the line
see the attached figure
At gas station store
[tex]y=0.50x+0.50[/tex]
The y-intercept is the point (0,0.50)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=0.50x+0.50[/tex]
[tex]x=-1[/tex]
The x-intercept is the point (-1,0)
Plot the points and join to graph the line
see the attached figure
Part c) Compare the lines in terms of slope and y-intercept
The slope or unit rate at the restaurant is less than the slope at the gas station store
[tex]\$0.05\ per\ refill < \$0.50\ per\ refill[/tex]
The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store
[tex]\$1.50 > \$0.50[/tex]
What is the third quartile of this data set? 14, 18, 20, 21, 25, 32, 38, 42, 48
Answer: the answer is 40
please help wit all questions! leave work below! if you do this , it will give you 40 points!!
Answer:
13. ft per minute is 150. ft per hour is 9,000.
work:
300÷ 2 = 150150 times 60 min.14. x ÷ y = feet per minute.
it is this because the time divided by the depth will equal the time that it took.
15. it would be more reasonable to use feet by minute, because of the accuracy of the answers. with measuring it using feet per hour, your answers will be less precise.
16. the distance will double because the proportional relationship says that the distance is 3 km away if thunder is 9 secs apart from lightning.
will answer next question later
If I graduated highschool in 2017 what year was I in 5th grade
Answer:
the year 2010
Step-by-step explanation:
since the end of high school is 12th grade, you have to numbers. 12, and 5.
subtract 5 from 12 and you get seven. subtract seven from 2017, and you get 2010
You were in 5th grade in the year 2010.
Explanation:To determine what year you were in 5th grade, you can subtract 7 from the year you graduated high school. In this case, if you graduated in 2017, you subtract 7to get 2010. Therefore, you were in 5th grade in the year 2010.
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5(1+4r)- 8(4-r) simplify
Answer: =28r−27
Step-by-step explanation:
Answer:
= 25r - 32-r
Step-by-step explanation:
5(1+4r)-8(4-r)
= 5 x 5r - 32-r
= 25r - 32-r
If r was 2, (example),
= 25 x 2 - 32 - 2
= 50 - 30
= 20
Joe measured 1/2 cup of water. Mary measured 3/4 cup, and Ron measured 3/8 cup. How can the least amount of water be completed to the greatest amount
Answer:
3/8, 1/2, 3/4.
Step-by-step explanation:
Now I believe this is asking to set the fractions from least to greatest, but ignore this if im wrong. If so, the answer would be 3/8, 1/2, 3/4. 3/8 is less than 4/8, which is the halfway point for the 8ths, 1/2 is half of a whole, and 3/4 is more than 2/4, the half for 4ths.
svetlanas hair is 4 centimeters long her hair grows 1.5 centimeters per month. Svetlana wants her hair to be less than 16 centimeters long.
Answer:
I guess the question is when her hair will be almost 16cm long.
So she needs to grow hair almost 12 cm of hair. Because 16-4=12
To grow 12cm hair she needs 8 months (12/1.5=8)
So Svetlana needs to cut her hair before 8th month.
47. A medication is supplied in a 400-mg scored tablet. A physician prescribes 200 mg every 6 hours for
14 days. How many tablets will be dispensed for the entire course of therapy?
A. 7
B. 14
C. 28
D. 56
28 tablets will be required for course of therapy.
One tablet is of 400-mg and prescription is for 200 mg for every 6 hours for 14 days. total number of tablets to be find out.
Arithmetic operation are Addition, subtraction, division, and multiply in order to achieve mathematical solution of the statement.
Here, tablet for a day = 200-mg/400-mg x 24 hr/6 hr
= 1/2 x 4
= 2 Tablets a day
Now, for number of tablets for 14 days course,
= 14 x 2
= 28 Tables in 14 days
Thus, 28 tablets will be required for course of therapy.
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on a farm there are 3 sheep for every 1 horse. if y = the number of sheep, and X = the number of horses, which graph models the relationship?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x ----> the number of horses
y ---> the number of sheep
In this problem the relationship between the variables, x, and y, represent a proportional variation.
Remember that, if the linear equation represent a proportional variation then it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
we have
For x=1, y=3
Find the value of the constant of proportionality k
[tex]k=\frac{3}{1}=3\ \frac{sheeps}{horse}[/tex]
substitute
[tex]y=3x[/tex]
using a graph tool
The graph in the attached figure
Ryaan goes skydiving and falls at a constant rate toward the ground. The equation y = -32x + 14,000 represents the situation where y is the height of Ryaan in feet above the ground and x is the seconds since she jumped. Which statement describes the situation?
a)From a starting position of 32 feet above the ground, she is descending at 14,000 feet per second.
b)From a starting position of 14,000 feet above the ground, she is ascending at 32 feet per second.
c)From a starting position of 14,000 feet above the ground, she is descending at 32 feet per second.
d)From a starting position of 32 feet above the ground, she is ascending at 14,000 feet per second.
Answer:
c
Step-by-step explanation:
You answered 21 out of 25 questions correctly on a test. Did you reach your goal of at least
80%
Answer:
Yes.
Step-by-step explanation:
21/25=84/100=84%
Answer:
Yes
Step-by-step explanation:
If you got all off it that means you have 100 and to make it more simpler you are removing 4 points for every question that you failed so if you got 21 questions right then you have 84%
Please answer for brainiest
Which of the following is the probability against drawing a 7 from a standard deck of 52 cards on the first try?
97%
89%
92%
77%
Answer:
92%
Step-by-step explanation:
there are 4 cards of "7"
52-4=48
48÷52×100=92.307...%
There are 11 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible
There are 165 different subcommittees possible.
Explanation:To calculate the number of different subcommittees possible, we can use the combination formula. The number of different subcommittees is equal to the number of ways to choose 3 members out of 11. This can be calculated using the formula C(n, r) = n! / (r! (n - r)!), where n is the total number of members and r is the number of members in the subcommittee.
Plugging in the values, we have C(11, 3) = 11! / (3! (11 - 3)!) = 165. Therefore, there are 165 different subcommittees possible.
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Need help with this problem.
Answer:
18
Step-by-step explanation:
To find this we must divide 45 by 20 which gives the answer of 2.25. As we know this we now must multiply that by 8 resulting in to 18.
Therefore the answer is 18
Nathaniel is saving money to buy a new graphics card for his computer that
costs $260.
If he is saving $18 a month and already has $134, in how many
more months will he have enough money for the graphics card?
Answer:
7 months
Step-by-step explanation:
260=134+18m
126=18m
7=m
Answer: 7 months.
$18 × 7 months = $126
$134 + $126 = $260
The width of a rectangle is 5 units less than the length. The area of the rectangle is 6 units. What is the width, in units, of the rectangle?
Answer:
The width of rectangle is 1 unit.
Step-by-step explanation:
Given:
The area of rectangle is 6 units and its width is 5 units less than the length.
So, to find the width of rectangle.
Let the length be [tex]x[/tex] and the width be [tex]x-5[/tex].
Now, to find the width we put the formula of area of rectangle:
Area = length × width
[tex]6= x\times (x-5)[/tex]
[tex]6=x^{2}-5x[/tex]
[tex]0=x^{2}-5x-6[/tex]
[tex]0=x^{2}-6x+x-6[/tex]
[tex]0=x(x-6)+1(x-6)[/tex]
[tex]0=(x-6)(x+1)[/tex]
On solving equation we get:
[tex]x-6=0, x+1=0[/tex]
Therefore, we take the value x=6 as it is positive value:
[tex]x-6=0[/tex]
[tex]x=6[/tex]
So, the width of rectangle:
Width = [tex]x-5[/tex]
= [tex]6-5[/tex]
= [tex]1[/tex]
Therefore, the width of rectangle is 1 unit.
If there was 10 pine trees & 2 ash trees how many more pine trees were there? Answer is 8 but need to know how to show the work??
Answer:
The number of pine tress more than the number of ash trees is 8 .
Step-by-step explanation:
Given as
The number of pine trees = 10
The number of ash trees = 2
Let The number of pine tree more than that of ash tress = x
So, The number of ash trees + x = 10
Or, 2 + x = 10
I.e x = 10 - 2
∴ x = 8
So, The pine trees is 8 more than the ash trees
Hence The number of pine tress more than the number of ash trees is 8 . Answer
please help :) thanks :)
Answer:
1. 5417.412
2. 401.13
Step-by-step explanation:
1. First, rewrite
[tex]5\times 10^3+4\times 10^2+1\times 10^1+7\times 10^0+4\times \dfrac{1}{10^1}+1\times \dfrac{1}{10^2}+2\times \dfrac{1}{10^3}[/tex]
as
[tex]5\times 1000+4\times 100+1\times 10+7\times 1+4\times 0.1+1\times 0.01+2\times 0.001[/tex]
So, this is
[tex]5000+400+10+7+0.4+0.01+0.002\\ \\=5417.412[/tex]
2. First, rewrite
[tex]4\times 10^2+1\times 1 \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]
as
[tex]4\times 10^2+1\times 1 +1\times \dfrac{1}{10^1}+3\times \dfrac{1}{10^2}[/tex]
This is
[tex]4\times 100+1\times 1+1\times 0.1+3\times 0.01[/tex]
So, this is
[tex]400+1+0.1+0.03\\ \\=401.13[/tex]
Which of the following is an example of an expression?
7x - 8y + 11z = 22
11z = 22
7x = 22
7x - 8y + 11z
Answer:
7x-8y+11z
Step-by-step explanation:
Because this is the only one that doesn't have an equal sign. Therefore, this is an example of an expression, not a equation. All of the other answer choices have an equal sign, they're equations.
PLEASE ANSWER ASAP!!! SHOW ALL THE STEPS.
Solve the system of equations using elimination. Make sure to show all work and find the value of both x and y
1.
x - 3y = 7
3x + 3y = 9
2.
8x+ 3y = 1
4x + 2y = 0
Answer:
For the first question [tex]x = 4\\ y = -1[/tex] and
For the second question [tex]x = 0.5\\ y = -1[/tex]
Step-by-step explanation:
Given:
1.
x - 3y = 7
3x + 3y = 9
2.
8x+ 3y = 1
4x + 2y = 0
Elimination method :
In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.
Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.
For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get
[tex](x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4[/tex]
Now substitute X equal to 4 in equation x -3y = 7 we get
[tex]4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\[/tex]
This way we have x is equal to 4 and y is equal to -1 for question number 1.
For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get
[tex]8x + 4y = 0\\[/tex]
Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get
[tex](8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1[/tex]
Now substitute y equal to -1 in equation 8x +3y = 1 we get
[tex]8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\[/tex]
This way we have x is equal to 0.5 and y is equal to -1 for question number 2.
For a scientific Experiment, A physicist must make sure that the temperature of a metal at 0°C gets to no colder than -80°C. the physicist changes the metals temperature at a steady rate of -4°C per hour. Let t represent the temperature in degrees Celsius. Write an inequality. use the fact that the rate of change in temperature times the number of hours equals the final temperature.
Answer:
- 4 h ≥ - 80
Step-by-step explanation:
The temperature of the metal is 0°C and the gets to no colder than - 80°C.
If the temperature is decreasing at the rate of - 4°C per hour, then the temperature after h hours will be t = 0 + (- 4) h which will not be less than - 80°C.
So the inequality that models the situation is 0 + (- 4) h ≥ - 80
⇒ - 4 h ≥ - 80 (Answer)
Final answer:
The inequality to ensure that the temperature of the metal does not fall below -80°C as it drops steadily at -4°C/hour is 0 - 4h ">= -80. This represents the highest number of hours (h) the physicist can allow before the temperature reaches the limit.
Explanation:
The student has asked to write an inequality based on a physicist's experiment where a metal's temperature decreases at a steady rate of -4°C per hour and should not get colder than -80°C. Starting at 0°C, the relationship between time (in hours) and temperature can be represented mathematically.
To express this as an inequality, we can set up a relationship where the temperature (t) after a certain number of hours (h) is no less than -80°C. Since the temperature is decreasing at -4°C per hour, we can write the inequality as:
t ≥ -80
Where t = 0 + (-4 × h), and h represents the number of hours passed.
Substituting the expression for t into the inequality:
0 - 4h ≥ -80
This inequality tells us that regardless of how many hours go by at this rate, the temperature of the metal should remain higher than -80°C.
Students were surveyed about their wither break plans.Of the people that stated they were going skiing, 25% did not actually go.How many students actually went skiing?
Answer:
The number of students who actually went for the skiing is 0.75 times the total number of students .
Step-by-step explanation:
Given as :
Students were surveyed about their wither break plans
The percentage of students who did not go for skiing = 25 %
So, The percentage of students who did not go for skiing =100 % - 25 % = 75%
Let The total number of students = x
So, The number of students actually went for the skiing = 75% of the total number of students
I.e The number of students actually went for the skiing = [tex]\frac{75}{100}[/tex]× x
Or, The number of students actually went for the skiing = 0.75× x
∴ The number of students actually went for the skiing = 0.75 x
Hence The number of students who actually went for the skiing is 0.75 times the total number of students . Answer
For the last five months, Vivian borrowed ($35 from her brother to pay for her gym
membership. Vivian just received a raise and wants to repay the money she borrowed from
her brother. Vivian can only afford to repay $25 each month to her brother. How many
months will it take Vivian to repay her brother the money she borrowed?
Answer:7 months
Step-by-step explanation:
$35 x 5 months = $175
175 / 25 = 7
Answer:
7 months
Step-by-step explanation:
Question 5
Find the sum of the following geometric series.
8+1.6+0.32+0.064 + ...
good morning,
Answer:
10×(1-0.2ⁿ)
Step-by-step explanation:
1.6/8=0.2
0.32/1.6=0.2
0.064/0.32=0.2
let S represent the sum of n term then S=8×[(1-0.2ⁿ)/(1-0.2)] = 10×(1-0.2ⁿ).
:)
Final answer:
To find the sum of a geometric series, use the formula for the partial sum by identifying the first term and common ratio.
Explanation:
A geometric series is represented by the formula a + ax + ax² + ax³ + ... with a as the first term and x as the common ratio. The sum of the first N terms of a geometric series can be found using the formula of the partial sum.
In the given series 8+1.6+0.32+0.064+..., the first term a = 8 and the common ratio x = 0.2. To find the sum, you can use the formula for the sum of a geometric series: S = a / (1 - x).
Substitute a = 8, x = 0.2 into the sum formula: S = 8 / (1 - 0.2) = 8 / 0.8 = 10. Therefore, the sum of the given geometric series is 10.
Alexandra has 127 flowers. She puts
the same number of flowers in each
of her vases. How many flowers will
be left over?
How many vases are there?
The number of flowers in each vase is 31 and the number of flowers left over is 3.
Given that, Alexandra has 127 flowers and 4 vases.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here,
The same number of flowers in each of her vases =Total number of flower/Number of vases
= 127/4
Now, 4|127|31
124
_______
3
Number of flowers left over =3
Therefore, the number of flowers in each vase is 31 and the number of flowers left over is 3.
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"Your question is incomplete, probably the complete question/missing part is:"
Alexandra has 127 flowers and 4 vases. She puts the same number of flowers in each of her vases. How many flowers will be left over?
Jenna bought 5 reams of paper at the store for a total of $21 . The tax on her purchase was $1 . Write a equation and solve to find the price of each ream of paper
Answer:
The equation needed is [tex]\textrm{Cost of 1 ream of paper} = \frac{20}{5} [/tex]
The cost per ream of paper = $4
Step-by-step explanation:
Here, the cost of 5 reams of paper = $ 21
The tax on her purchase = $1
So, the actual cost of 5 reams of paper = Total Cost paid - Tax amount
= $ 21 - $ 1 = $20
So, the actual cost of 5 reams of the paper is $20.
Now, to find out the cost of 1 ream of paper:
[tex]\textrm{Cost of 1 ream of paper} = \frac{\textrm{Total amount paid for 5 reams}}{\textrm{ 5}} \\= \frac{20}{5} = 4[/tex]
= $4
Hence, the cost of each ream of paper = $ 4.
The diagonal length of a rectangular playing field is 76 feet, and its width is 48 feet. How long is the playing field?
The length of playing field is 58.9 feet
Solution:
Given that, the diagonal length of a rectangular playing field is 76 feet,
And its width is 48 feet.
To find: length of playing field
Now, we know that, diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse.
So, now, in a right angled triangle we can use pythagorean theorem to find the length
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition, In a right angled triangle ABC we get
[tex]c^2 = a^2 + b^2[/tex]
Where "c" is the length of hypotenuse
"a" is the length of one leg of right angled triangle
"b" is the length of other leg of right angled triangle
[tex]\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}[/tex]
[tex]\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}[/tex]
Hence, the length of the rectangular field is 58.9 feet
Answer:The answer is 3,472
Step-by-step explanation:
I GOT THIS CORRECT TRUST ME!! :)
Let x y be a real number. If x * y = x (x-y) then What is the value of 2 * (7 * 1)?
The value of [tex]2 \times(7 \times 1)[/tex] is -80
Solution:Given that x y is a real number
Also given that [tex]x \times y = x(x - y)[/tex]
We are asked to find the value of [tex]2 \times (7 \times 1)[/tex]
To solve it we have to first solve terms in brackets.
[tex]\begin{array}{l}{\text {So, } 7 \times 1=7(7-1) \quad[\text {from given rule }]} \\\\ {\rightarrow 7 \times 1=7 \times 6} \\\\ {\rightarrow 7 \times 1=42} \\\\ {\text {Now, the required expression is modified as } 2 \times 42} \\\\ {\text {Then, } 2 \times 42=2(2-42)=2(-40)=-80} \\\\ {\text {Hence, the value of } 2 \times(7 \times 1)=-80}\end{array}[/tex]
What is the sum of interior degrees for a 13-gon?
How many degrees in each angle for a regular 13-gon?
What is the sum of interior degrees for a 23-gon?
How many degrees in each angle for a regular 23-gon?
What is the sum of interior angles for a triangle?
What is the sum of interior angles for a quadrilateral?
What is one difference, and one similarity between a Square and a Rhombus?
Answer:
1980°
152.3°
3780°
164.35°
180°
360°
Step-by-step explanation:
The sum of all the interior angles of a polygon is given by (n - 2)180° where n is the number of sides.
So, the sum of all interior angles of a 13-gon is (13 - 2) 180° = 1980° (Answer)
As the 13-gon is regular, so each angles will be same. Assume each angle is x°.
So, 13x = 1980, ⇒ x = 152.3° (Answer)
Now, the sum of all interior angles for a 23-gon will be (23 - 2) 180° = 3780° (Answer)
Again,as the 23-gon is regular, so each angles will be same. Assume each angle is x°.
So, 23x = 3780, ⇒ x = 164.35° (Answer)
The sum of all the interior angles of a triangle is 180° (Answer)
The sum of all the interior angles of a quadrilateral is 360° (Answer)
The similarity between a square and a rhombus is all the sides of both are same and the difference, between a square and a rhombus is that a square has every angle 90°, but the rhombus has no angle equal to 90°. (Answer)
An construction company poured a cylindrical shaped concrete column 15 feet long with a radius of 3 feet. How much concrete did it take to make the column, in terms of π?
Answer:
[tex]135\pi\ ft^3[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder (concrete column) is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=3\ ft\\h=15\ ft[/tex]
substitute
[tex]V=\pi (3)^{2}(15)[/tex]
[tex]V=135\pi\ ft^3[/tex]
which of the following is equivalent to the expression 5^3*5^-5 there are 3 /A-5^-2, B- 1 /5^2 C- 5^2, D- 1 5^-2, E- 1 /25
Answer:
e-1/25
Step-by-step explanation: