Answers
Given a table represents a relation between x and y
As shown, the change of (x) and (y) vary with a constant rate
So, the table represents a linear function
The general equation will be: y = m * x + b
where (m) is the slope, (b) is the value of y when (x=0)
So, from the table, when x = 0 , y = 25
The slope will be as follows:
[tex]m=\frac{30-25}{1-0}=\frac{5}{1}=5[/tex]So, the equation will be:
[tex]y=5x+25[/tex]When the input = 200, x = 200
So, substitute with (x) to find the output (y)
[tex]y=5\cdot200+25=1000+25=1025[/tex]So, the answer will be:
For an input 200, the output is 1025
===================================================
Another method to solve using the arithmetic sequence.
As shown in the table consider (x) represents the number of terms
So, (y) will be an arithmetic sequence
The first term = a = 30
The common difference = d = 35 - 30 = 5
the general rule of the arithmetic sequence is:
[tex]y_{}=a+d(x-1)[/tex]substitute with (a) and (d)
[tex]y=30+5(x-1)[/tex]When x = 200
[tex]y=30+5(200-1)=30+5\cdot199=1025[/tex]So, for an input 200, the output = 1025
Related Questions
what is the slope of a line that passes through (1,3) and (-7,-5)
Answers
Suppose line g is the line with equation y=x. Given A(8,−5), B(7,3), and C(−1,−7), what are the coordinates of the vertices of △A′B′C′ for the reflection?
Answers
The point (x,y) on the reflection about y = x axis changes to,
[tex]A(x,y)\rightarrow A^{\prime}(y,x)[/tex]Determine the coordinates of the vertices of triangle after reflection.
[tex](6,3)\rightarrow(3,6)[/tex][tex](8,-3)\rightarrow(-3,8)[/tex][tex](-2,-6)\rightarrow(-6,-2)[/tex]So vertices of triangle after reflection is,
(3,6), (-3,8) and (-6,-2)
A probability experiment consists of rolling a 6-sided die, numbered 1 to 6. Find the probability of the event below.
rolling a number less than 6
Answers
According to the solving the Probability of the event below is as:
= 0.8333
What is probability?Probability is the possibility that an event will occur given all the potential outcomes. A decision-maker considers the likelihood of a result to be important. Decisions will be made better as potential outcomes are better understood.
The purpose of probability:Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.
According to the given data:The probability of rolling a number less than 6.
There are six sides to the die with numbers on each side of (1, 2, 3, 4, 5, 6)
There is a total of six numbers and five ae below six in value.
So,
P(X < 6) = 5/6
= 0.8333
According to the solving the Probability of the event below is as:
= 0.8333
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HELP PLS
Do anybody know answer to these problomes?
Answers
you can do this easily by BODMAS Frist open small bracket and slove it then open curly bracket and solve it at last open third bracket and open it then solve
Remember you should always open divide first then multiply then add and then subtract
Practice it is easy.
Step-by-step explanation:
[tex]28 \div (1 + 2 \times (19 - 16))[/tex]
[tex]28 \div (1 + 2 \times 3) [/tex]
[tex]28 \div (1 + 6)[/tex]
[tex]28 \div 7[/tex]
[tex]4[/tex]
3. Compare the numbers 5/9 and 0.5^- Use the symbols <, >, or =.
Answers
So 5/9 is equal to 0.5- so the right answer is
[tex]\frac{5}{9}=0.\bar{5}[/tex]the little line on the top of the number means that this number will be repeated Infinitely is like 0.555555555...
Evaluate the expression when y=4 and x=6 so what is x+8y
Answers
6 + 8(4) ---> 6 + 32 = 38
So, the answer is 38.
What do you put in each box
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The equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.
The given expressions are 8(t+8) and 8t+8.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Now, 8(t+8)
Using distributive property a(b+c)=ab+ac, simplify 8(t+8)
That is, 8t+64
Take common factor in 8t+8 is 4(2t+2) and 8t+8=4t+8+4t
Therefore, the equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.
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-109-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 Which of the following inequalities is represented by the number line?
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The inequality is x > -3
The second choice is the correct answer.
Complete the sentence
Percent means per _______.
Answers
Answer:
Percent means parts per hundred.
Step-by-step explanation:
Percent comes from the Latin phrase per centum which means per hundred. The % symbol is used to represent percent.
Example: 54/100 is equal to 54%.
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hello this is all 1 math problem together may I get help with the solve and check .
Answers
The given expression is,
[tex]7n+14=-21[/tex]So bringing "14" to the other side of the euals,
[tex]\begin{gathered} 7n=-21-14 \\ =-35 \end{gathered}[/tex]On division,
[tex]\begin{gathered} 7n=-35 \\ n=-\frac{35}{7}=-5 \end{gathered}[/tex]Now, let us substitute -5 for n,
[tex]7\times(-5)=-35[/tex]Hence checked.
Coupon A: $25 rebate on $96 shoes coupon B; 40% off of $96 shoes
Answers
Answer: Coupon B is more profitable
(-7) -4 evaluate expression
Answers
Answer:
28
Step-by-step explanation:
To evaluate this expression, multiply the two numbers.
-7x-4=28
28 is not negative because a negative times a negative is positive.
Hope this helps! :D
The vertices of a figure are F(1, 2), G(3,5),and H(3, 2). Rotate the figure 180° about the origin. Find the coordinates of the image.
Answers
The coordinates of the vertices after the image is rotated about origin will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
What is rotation of figure?
A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
Given are the vertices of a figure as → F(1, 2), G(3,5) and H(3, 2).
Since, it is not given in which direction the figure is rotated, we will consider it to be rotated in anti - clockwise direction about the origin. When we rotate a coordinate point by 180 degrees in counterclockwise direction about the origin, then the point A(x ,y) becomes A'(-x ,-y).
The new coordinates will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
Therefore, the coordinates of the vertices after the image is rotated about origin will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
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The graph of a function g is shown below.
Find g (0)
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. simplify using order of operations. Show all of your work and one operation at a time to receive all possible points. 90 divided by [10 plus (3^2-4)]
Please help!
Answers
the equation you summited is
90÷10+3²-4
Answer:
the answer to the question is 14
Step-by-step explanation:
90÷10+3²-4
Follow the PEMDAS order of operations
3²=9
90÷10+9-4
Multiply and divide from left to right
90÷10=9
9+9-4
Add and subtract from left to right
9+9=18
18-4=14
So the answer to your question is 14
A printing service charges a set-up fee of $14.50 for each order and 15 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given by the following function.
C (x) = 0.15x + 14.50
What is the total cost for an order of 30 copies?
Answers
Answer: $19
Step-by-step explanation:
Since we want 30 copies, let x=30.
[tex]C(30)=0.15(30)+14.50=19[/tex]
I need help with this the question reads before the pandemic Corning planned to make 75 millions vials in 2021 due to the vaccine demand Corning will make d times as many vials write an expression to find how many vials Corning will make in 2021
Answers
The solution:
The question says Corning planned to make 75,000,000 vials in 2021.
But due to the demand for the vaccine, Corning decided to make d times as many vials.
We are asked to write an expression to find the number of vials Corning will make in 2021.
So, the required expression is:
[tex]75000000\times d=75000000d\text{ vials}[/tex]Therefore, the correct answer is 75000000d vials.
When your grandmother got out of the hospital, she was so excited that she gave you some money. You decided to go to Canada where the exchange rate is 1.06 Canadian dollars to $1 US dollar as of November 2015. You have $10,000 to take with you. How many Canadian dollars do you have to spend? (Show all work using dimension analysis, round to nearest cent if necessary)
Answers
Answer:
10,600 Canadian dollars
Step-by-step explanation:
[tex] \frac{1.06}{1} = \frac{x}{10000} [/tex]
[tex]x = 10000(1.06) = 10600[/tex]
Use a calculator to find the natural logarithm, base e. In 0.0746 In 0.0746
Answers
By using a calculator,
ln 0.0746 = - 2.596
No correlation means that as the x-values increase, the y-values O a have no effect Ob increase Ос decrease
Answers
we know that
If there is no correlation between x and y, that just means that there's no relationship, connection, or interdependence between the two variables
No correlation means that as the x-values increase, the y-values have no effect
the answer is the option A
The midpoint of AB is (2,7) and point A is located at (5,-3).
What are the coordinates of point B?
Answers
The coordinates of point B =(5,10)
what is coordinates?
Coordinates are a set of values which helps to show the exact position of a point in the coordinates plane.
step - by - step explanation
5-2 = 3
2-3= -1 = the x coordinate of B
-7-3= -10
-7-10 = -13 = the y coordinate of B
(-1, -13) is the point B
A is 3 to the right of the midpoint ,so B is 5 to the left to the midpoint
A is 10 up from the midpoint so B is 10 down from the midpoint.
so the coordinates of point B is (5,10)
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ASAP FREE PONTS! HELP! The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
Answers
The height of the water balloon at 15 seconds based on the potential rupturing effect of the balloon's initial gravitational potential energy on the membrane of the balloon upon impact with the ground and that addition forces are not added, is at the ground level or zero feet.
What is gravitational potential energy?Gravitational potential energy is the energy possessed by a body by virtue of its elevation above ground level.
The points on the path of the water balloon thrown from the building's roof are;
(0, 4), (2, 7), (7, 5), (6, 4), (9, 1), (9.5, 0)
The location of the water balloon, 9.5 seconds after it is thrown off the roof is therefore at the point, h(9.5) = 0 feet, which can be taken as the ground level or base of the building.
According to Newton's third law of motion, which is a physics or natural law, and which states that all bodies remain at rest or continue perpetually in a straight line unless acted upon by a force.
Given that no additional force is specified after the water balloon is thrown from the building, and that a water balloon can be treated as a large drop of water, where the elastic balloon membrane, represents the surface tension holding the large droplet together, we have that the energy of impact of collision of the balloon when it lands, which is obtained from the initial gravitational potential energy of the water balloon, can potentially rupture the membrane, such that the water is spilled and remains on the floor, well after 9.5 seconds, such that at 15 seconds, the height of the balloon remains at ground level.
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A number is multiplied by 6, and that product is added to 3. The sun is equal to the product of 3 and 11
Answers
Answer:
x = 5
Step-by-step explanation:
3 + x * 6 = 3 * 11
3 + 6x = 33
6x = 30
x = 5
Sabastian Company has 10,000 shares of $100 par, 2% cumulative preferred stock and 50,000 shares of $50 par common stock. The following amounts were distributed as dividends: Year Amount Year 1 $10,000 Year 2 30,000 Year 3 45,000 Determine the dividends per share for preferred and common stock for each year. If required, round your answers to two decimal places. If your answer is zero, please enter "0".
Answers
The dividends per share for preferred and common stock for each year is year 1 $20,000, $10,000; year 2 $30,000, $0 year 3 $30,000, $15,000.
How to determine the Preferred and common stock?Year 1
Preference Shares = Number of shares × Par value ×%
Preference Shares = 10,000 ×100 × 2%
Preference Shares = $20,000
Common Shareholders:
Common Shareholders = $20,000 - $10,000
Common Shareholders = $10,000
Year 2
Preference Shares = $30,000
Common Shareholders = $0
Year 3
Preference Shares = $20,000 + ($20,000 - $10,000)
Preference Shares = $20,000 + $10,000
Preference Shares = $30,000
Common Shareholders:
Common Shareholders = $45,000 - $30,000
Common Shareholders = $15,000
Therefore year 1 has the amount of $20,000 as preferred stock and $10,000 as common stock.
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Are there more buildings that have 10-19 bricks or buildings that have 50-59 bricks ?
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We can see from the graph that there are 10 buildings that have 10-19 bricks and 2 buildings that have 50-59 bricks. So there are more buildings with 10-19 bricks in the neighborhood.
Answer: 10-19 bricks
3/4x = 24/3 × fraction ? x = ___ × 4/3× = fraction × 4/3x = ___ or 2 2/3
Answers
Given that 3/4x = 2
[tex]\begin{gathered} \frac{3}{4}x\text{ = 2} \\ \text{This can be written as} \\ \frac{3\cdot\text{ x}}{4}\text{ = 2} \\ \frac{3x}{4}\text{ = 2} \\ \text{Cross multiply} \\ 3x\text{ = 2 x }4 \\ 3x\text{ = }8 \\ x\text{ = }\frac{8}{3}\cdot\text{ }\frac{1}{1} \\ \text{x = }\frac{8}{3} \\ x\text{ = 2}\frac{2}{3} \end{gathered}[/tex][tex]undefined[/tex]x=0,0.5,1,3,3.5,4,5y= 63,72,75,81,84,90,93calculate the correlation coefficient, r.round answer to the 3 decimal places
Answers
In order to find the correlation coefficient r, we can use the formula:
[tex]r=\frac{7\sum ^{}_{}(xy)-\sum ^{}_{}x\sum ^{}_{}y}{\sqrt[]{\lbrack7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2\rbrack\cdot\lbrack7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2\rbrack}}[/tex]where the sum must be taken upon all 7 values of x and y.
So, let's find each term and then use them in the formula:
[tex]\begin{gathered} 7\sum ^{}_{}(xy)=7(0\cdot63+0.5\cdot72+1\cdot75+3\cdot81+3.5\cdot84+4\cdot90+5\cdot93) \\ =7\cdot1473=10311 \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x\sum ^{}_{}y=(0+0.5+1+3+3.5+4+5)\cdot(63+72+75+81+84+90+93) \\ =17\cdot558=9486 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2 \\ 7\cdot(0^{2^{}}+0.5^2+1^2+3^2+3.5^2+4^2+5^2)-(0+0.5+1+3+3.5+4+5)^2 \\ 7\cdot63.5-17^2 \\ 444.5-289 \\ 155.5 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2 \\ 7\cdot(63^2+72^2+75^2+81^2+84^2+90^2+93^2)-(63+72+75+81+84+90+93)^2 \\ 7\cdot45144-558^2 \\ 316008-311364 \\ 4644 \end{gathered}[/tex]Now, we need to use them in the formula to find r:
[tex]r=\frac{10311-9486}{\sqrt[]{155.5\cdot4644}}=\frac{825}{\sqrt[]{722142}}\cong0.9708[/tex]Finally, round the answer to the 3 decimal places, we find
r = 0.971
The length of a rectangle is 2 cm longer than its width.
If the perimeter of the rectangle is 44 cm, find its area.
Answers
Answer:
perimeter = 2(b x L)
p° 2(2+20)
= 22X2 =44cm
area = B x W
a = 20x 2 =40 cm²
Specifically, I need the surface are which can be found by using this formula: S= Ph+2B
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The surface area of a prism of heigh H and base of sides a, b, and c is:
A = PH + 2B
Where P = a + b + c is the perimeter of the base and B is its area.
We can see in the figure a prism of height H = 14 in, base sides of 10 in, 10 in, and 12 in. The height of the base is also given as h = 8 in.
Calculate the perimeter of the base:
P = 10 in + 10 in + 12 in = 32 in
The area of the base is:
[tex]B=\frac{12\text{ in }\cdot8\text{ in}}{2}=48\text{ }in^2[/tex]Calculate the surface area:
[tex]\begin{gathered} A=PH+2B \\ A=32\text{ in }\cdot\text{14 in}+2\cdot48\text{ }in^2 \\ A=448\text{ }in^2+96\text{ i}n^2 \\ A=544\text{ }in^2 \end{gathered}[/tex]The area is 544 square inches
What is the slope-intercept equation of the line below?y-intercept = (0, 3)5slope =4
Answers
Step-by-step explanation:
the slope-intercept form is
y = ax + b
a is the slope, b is the y- intercept (the y-value when x = 0).
so, the equation is
y = -5/4 x + 3