a)Table is completed below.
b)The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
What is proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Given.
The proportion is: according to the first row of the proportional relationship
y = kx
28 = k*20
k = 28/20 = 1.4
the following is the function:
y = 1.4x
a) Fill in the following table:
Weight and distance (in centimeters) (newtons)
20 | 28
55 | 55*1.4 = 77
140/1.4 = 100 | 140
1 | 1*1.4 = 1.4
b) The scale should take the coefficient 1.4 into account, therefore the x-axis scale will be 100 with 1-cm intervals and the y-axis scale will be 140 with 1.4-newton intervals.
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a population of watermelons in a farmer’s field has unknown population mean weight , but the population standard deviation weight is known to be about
95% confidence interval for the true population mean watermelon weight. is (69.94, 72.06)
Confidence Interval formula = Mean ± z × Standard deviation/√n
Mean = 71 ounces
Standard deviation = 2.8 ounces
z score = 95% confidence interval = 1.96
Confidence Interval = 71 ± 1.96 × 2.8/√27
= 71 ± 1.96 × 0.5388602512
= 71 ± 1.0561660924
71 - 1.0561660924
= 69.943833908 ounces
Approximately = 69.94 ounces
71 + 1.0561660924
= 72.0561660924 ounces
Approximately = 72.06 ounces
95% Confidence Interval = (69.94, 72.06).
the complete question is
You measure 27 watermelons' weights, and find they have a mean weight of 71 ounces. Assume the population standard deviation is 2.8 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight.
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what congruence short cut do I use
By ASA or SAS the triangles can be proves congruent.
What is Congruence of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.
As, from the given figure we can find some equal parts.
First we have two triangles named KOE and LOB
Now, in both triangles
EO = OB ( given)
<KOE =< LOB (Vertically opposite angle)
Now, we have one side and one angle congruent.
There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.
So, either KO = OL or
<LBO = <OKE.
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A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answer:
25 kg
Step-by-step explanation:
The sum of the weights of the small and large sacks is 65 kg. The larger sack weighs 15 kg more. You want the weight of the smaller sack.
SetupLet w represent the weight of the sand in the small sack. Then (w+15) is the weight of the sand in the larger sack. The total weight is 65 kg, so we have ...
w +(w+15) = 65
SolutionSubtracting 15 from both sides gives ...
2w = 50
w = 25
The weight of the sand in the small sack is 25 kg.
A floor plan of an apartment has a rectangular living room. Its length is 10 centimeters and its width is 4 centimeters. The scale of the floor plan diagram is 2 centimeters for every 1 meter. What is the actual area of the apartment's living room?
The actual area of the apartment's living room is 10 [tex]m^{2}[/tex]
Given
Room is in the shape of a rectangle
Length of the room (L)= 10 cm
Width of the room (W) = 4 cm
Also the scale of floor plan is 2 cm for every 1 meter
Initially the are of the living room = area of rectangle
Area of the rectangle = length × width
= 10 × 40
= 40 [tex]cm^{2}[/tex]
To find actual floor area we need to scale the dimensions
Since 2cm = 1 m
10cm = 5m and 4 cm = 2m
Now calculating the actual area
Area = length × width
= 5×2
=10 [tex]m^{2}[/tex]
Hence the actual area of the living room is 10 [tex]m^{2}[/tex]
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In Barangay San Jose, it was found that the population double every 10 years. If in the year 1995, the population was 7824, what will be the population in the year 2015?
The population in the year 2015 is 31296.
In 1995 the population was 7824. It was found that the population gets double every 10 years.
We have to find the population in the year 2015.
Rate = 200% = 2
Time =( 2015 - 1995) / 10
= 20/10
= 2
The population in 2015 = population in 1995 ×[tex]rate^{time}[/tex]
= 7824 × [tex]2^{2}[/tex]
= 7824 × 4
= 31296
Therefore the population in the year 2015 is 31296.
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Do number 12 and 13 please thank you!!
12. The statement ' x+3 = 9' is true sometimes.
How is this explained?
Let x= 6,
6 + 3 = 9 (true)
Let x= 5 ,
5 + 3 = 8 (not true)
13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.
How is this explained?
Let us consider some numbers,
a) 1
The multiplicative inverse of 1 = 1
Thus, multiplicative inverse of this number is not less than the original number.
b) 2 (greater than 1)
The multiplicative inverse of 2 = 1/2
multiplicative inverse of this number is less than the original number.
c) 8/7 (greater than 1)
The multiplicative inverse of 8/7 = 7/8
Here, multiplicative inverse of this number is less than the original number.
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A ticket to see your favorite baseball team costs 37.26$. That price decreases by 0.28$ for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 37 games. What is the price of a ticket after the team loses 37 games?
Equation: (C Stands for Cost and L stands for losses)
37.26 C-0.28 L
The total change in the cost of a ticket is dollars.
The equation that represents the given situation is required.The cost of the ticket after L losses is a. Initial cost of the ticket = $49.64Price decrease per game lost = $0.41Number of games lost = LMoney lost after L losses is So, the cost of the ticket after L losses would be the initial cost of the ticket minus the money lost after L losses.The cost of the ticket after L losses is a.
George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during the 51 blinks?
How much do 6 dresses cost if 2 dresses cost $44?
3. Sandra signed up for Workout Jazz during the
spring special. Which equation represents
the proportional relationship?
The proportional relationship that models this situation is given by:
y = 16.99x, 0 ≤ x ≤ 12.
What is a direct proportional relationship?In a direct proportional relationship, the output variable y is found as the multiplication as the multiplication of the constant k by the input variable x, according to the following rule:
y = kx
In the context of this problem, the input variable and the output variable are given as follows:
x: number of months.y: total cost of the plan during x months.The monthly cost for the first 12 months is of $16.99, hence the constant is given as follows:
k = 16.99.
Considering the given domain, the relationship is modeled by the following equation:
y = 16.99x, 0 ≤ x ≤ 12.
What is the missing information?The missing information is that for the first 12 months, the monthly cost of the plan is of $16.99.
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For a project in her Geometry class, Mila uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.45 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.2 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
The goalpost is 15.13 meters tall which is labeled as X in the figure which has been attached below.
She walks 13.45 meters away from the goalpost, then places a mirror flat on the ground with an X in the center. She next walks 1.2 meters to the opposite side of the mirror, where she can easily see the top of the goalpost depicted in the X. Her partner determines that the distance between her eyes and the ground is 1.35 meters.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
As per the given information, the figure has been attached below.
Set up the proportional and solve for x
1.2 : 13.45 = 1.35 : x
⇒ 1.2 / 13.45 = 1.35 / x
Cross multiplication, and we get
⇒ 1.2x = 1.35 × 13.45
Divided by 1.2 into both sides of the above equation,
⇒ x = (1.35 × 13.45) / 1.2
⇒ x = 15.13
Therefore, the goalpost is 15.13 meters tall.
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Eugene is deciding between two payment plans when purchasing a new car. If Eugene chooses payment plan A, he will pay $429.47 a month for 36 months for the car. If Eugene chooses payment plan B, he will pay $340.89 a month for 48 months for the car. How much money will Eugene save on the car overall if he chooses payment plan A?
Eugene will save $901.8 on the car overall if he chooses payment plan A.
Eugene has to buy a new car, and there are two payment plans from which he has to decide which to opt for.The two plans are, namely, plan A and plan B.In plan A, he has to pay an amount of $429.47 a month for 36 months for the car.In plan B, he has to pay an amount of $340.89 a month for 48 months for the car.The total amount to be paid if he chooses plan A is 36*429.47 = $15,460.92.The total amount to be paid if he chooses plan B is 48*340.89 = $16,362.72.We can see that plan A is better than plan B.The amount saved by Eugene by selecting plan A is represented in the equation below:$16,362.72 - $15,460.92 = $901.8To learn more about equations, visit :
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The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers
The number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
What is an integer ?
Integer is the collection of whole numbers and negative numbers. It does not include the fractional part.
It is given that square root of a decimal number is 9.2371 and we have to find out that the number lies between which 2 integers.
We know that the integer 9 is less than 9.2371 , so the square of 9 will be :
9² = 81
And
The square of next integer 10 is equal to 100.
The square of 9.2371 will be equal to :
= (9.2371)²
= 85.32
So , the number is 85.32 and it lies between 2 integers which are 81 and 100.
Therefore , the number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.
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Solve this problem!!! PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1.264×10^-5
Step-by-step explanation:
If you are allowed to use a calculator, it will totally do this question for you. Check mode for Sci Not or use the ^ or EE button.
If no calculator allowed, factor out the 10^-6 and add the numbers. Change back to Scientific Notation and fix the first number. It has to have one digit to the left of the decimal. Adjust the exponent to account for changing 12.64 to 1.264 See image.
Which function produces a range of {−11,−5,1,4,10} given a domain of {−2,0,1,3,5}?
theres a pic to help u understand more
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Plug domain into each function and see if it matches any values in the range.
is 15 feet above sea level negative or positive or a zero
Answer:
Positive
Step-by-step explanation:
Below sea level would be negative and at sea level would be zero.
PLEASE HELP IM BEGGING
Answer:
y= 3/2 x + -4
Step-by-step explanation:
-4 Is the y intercept (the vertical axis)
the 3/2 is the rise over run of the line (how many up over how many across). It's positive because of the slope up to the right.
the first one please help!!
The y-intercept of f(x) is equal to the y-intercept of g(x).
Y-intercept explained ?the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.
How can I find the y-intercept?Finding the value of y at x=0 will help you locate the y-intercept on a graph. The graph's intersection with the y-axis occurs here.
What is the slope's y-intercept?When the slope of the line being studied is known, and the provided point is also the y - intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B is used in the equation to indicate the y value of the y intercept point.
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Point Q has coordinates (5,6). If you rotate Q 90° about the origin, (0,0), what are the coordinates of Q′
The coordinates of the image after 90° about the origin is (6, -5)
What is a 90 degrees rotation?A 90 degrees rotation denoted by R(90, 0) is a rotation that has the same effect as the 270 degrees counterclockwise of a figure.
How to determine the image of the rotation?The coordinate of the point is given as
(5, 6)
The rotation is given as 90° about the origin
So, we have
(x, y) => (y, -x)
Substitute (5, 6) in (x, y) => (y, -x)
So, we have
(5, 6) => (6, -5)
Hence, the coordinates of the image is (6, -5)
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Something's Strange about this little problem..
99 + 2 = ?
Answer:
the answer is 101 !!!
There's isn't nothing strange your just over thinking it!
x³-10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working out
The value of x is approximately 5.4 when x^3 -10x = 100
How to solve the equation?
The equation is given as:
x^3 -10x = 100
Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100
After several attempts, we have:
x = 5.4 (approximately)
Substitute 5.4 for x in x^3 -10x = 100
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100This means that x is approximately 5.4 when x^3 -10x = 100
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a fruit salad contains pineapples, apples. bananas, and oranges. It contains twice as many bananas as apples, 10 times as many oranges as pineapples, and the same number of apples as oranges. Jeff made this fruit salad using 1 pineapple. How many of each of the other fruits did he use
Using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas
Number of pineapples = 1 pineapple
Number oranges equal to the 10 times the number of pineapples
We have to multiply number of pineapples by 10
Number of oranges = 1×10
= 10 oranges
Number of oranges equal to the number of apples
Number of apples = 10 apples
Number of bananas equal to the twice the number of apples
Number of bananas = 2×10
= 20 bananas
Hence, using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas
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Which could be the first step in solving the equation represented by the model below? XX X X Add 4 negative unit tiles to both sides. Add 4 negative unit tiles to the left side, and add 6 negative unit tiles to the right side. Add 4 positive unit tiles to both sides. Add 6 negative unit tiles to the left side, and add 4 negative unit tiles to the right side.
The most appropriate choice for linear equation will be given by -
First option is the correct option
Adding 4 units negative tiles to both sides.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expression by an equal to sign.
A one degree equation is called linear equation.
Here,
The equation is 3x + 4 = 2x + 6
For the second option,
If we have to add 4 units negative tiles to left side, we will also have to add 4 units negative tiles to right side.
Second option is wrong
For the third option
We have to add four units negative tiles to both sides, not 4 units positive tiles.
For the fourth option
Adding 6 units negative tiles to left side and 4 units negative tiles to right side will not eliminate any of 6 or 4.
So the first option is correct.
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Complete Question
The diagram has been attached below
What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.
the answer in scientific notation rounding to 2 decimal places is given by 68490.98
What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.
6.849 *(10)^4=6.849* 10000=68490
2.329*(10)^-2= 0.02329
according to the question
6.849 times ten to the fourth power minus 2.329 times ten to the negative second power
therefore 68490-0.02329
=68489.9767
round to 2 decimal
the answer in scientific notation rounding to 2 decimal places is given by 68490.98
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Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Answer choses
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.
The student that raised the least amount based on the information is student C.
How to illustrate the information?For student A, the equation illustrated is y = 14x and this represents the amount of money raised (y) for walking (x) miles.
For student B, $42 is raised after walking 3 miles. The amount raised per mile will be:
= $42 / 3
= $14 per mile
For C, The miles walked 6 and 9 and the money raised $72 and $108. This shows that the amount is:
= $72 / 6
= $12 per mile.
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Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Who raised the least amount
Answer:
The student that raised the least amount based on the information is student C.
Step-by-step explanation:
Select the EXAMPLE(S) that demonstrate financial honesty.
1.Cooper includes all truthful information when he completes an application for a checking account.
2. Brianna writes a check knowing that she has the funds in her checking account to cover it.
3. Allison makes a large purchase with store credit without knowing how she will pay for it.
4. Greg discloses all the fees in the sales contracts for the products he sells in his store
(multiple choice) help please
Answer: 1, 2, and 4
Step-by-step explanation:
1. Cooper included ALL truthful information.
2. Brianna KNOWS she has the funds.
3. Allison makes a large purchase WITHOUT knowing how she will pay.
4. Greg discloses ALL fees.
Help me please someone this is very confusing to me.
Answer:
7
Step-by-step explanation:
slope = rise/run = (difference in y)/(difference in x)
First, we find a difference in y.
Subtract any two values of y.
For example: 35 - 14 = 21
Now we find the corresponding difference in x.
Now subtract the x values corresponding to those y values in the same order.
-1 in x corresponds to 35 in y.
-4 in x corresponds to 14 in y.
That means your difference in x is the subtraction -1 - (-4) = -1 + 4 = 3
The difference in y is 21.
The difference in x is 3.
slope = (difference in y)/(difference in x) = 21/3 = 7
Answer: 7
Pls help!
if you have to work it out pls work it out my teacher will be mad if no work!
Answer:
1st one: 50%, 0.5, 1/2
2nd one: 25%, 0.25, 1/4
3rd one: 18%, 0.18, 9/50
4th one: 10%, 0.1, 1/10
5th one: 20%, 0.2, 1/5
Step-by-step explanation:
Hope this helps!
Micah is planning a road trip. He estimates that he will drive a total of of 7 hours. He wants to stop for gas after ⅓ of the total time has passed. How long will he drive before he stops for gas? Express your answer as a mixed number.
Answer:
After 2 1/3 hours.
Step-by-step explanation:
For this you have to calculate how much hours is 1/3 of 7 hours. The word 'of' implies a multiplication function.
1/3 * 7 = 7/3 = 2 1/3
Pls help me how did I get the question wrong
Answer:
see explanation
Step-by-step explanation:
the equation of a line (linear equation) has slope- intercept form
y = mx + c ( m is the slope (gradient)) and c the y- intercept )
y = 12 + 2x or y = 2x + 12 ← is in slope- intercept form
with gradient m = 2
--------------------------------------------------------
the only graphs in linear form are
y = [tex]\frac{1}{2}[/tex] x and y = 12 - x
the other 2 have an x² term which indicates they are quadratic