The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet " ⇒ D
Step-by-step explanation:
The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function T(a) = −0.0018 a + 212, where
a is the altitude measured in feetT(a) is the boiling point of water in degreeThe form of the linear function is f(x) = mx + b, where m is slope (the rate of change), and b is the y-intercept (the value of f(x) at x = 0)
By comparing between the form of the function and the given function
∴ m = -0.0018 ⇒ degrees per foot
∵ The sign of the slope is negative
∵ The slope = Δf(x)/Δx
- That means T(a) is decreasing function
∴ The boiling point is decreases when the altitude increasing
∵ -0.0018 = [tex]-\frac{18}{10,000}[/tex] degrees per feet
∴ The boiling point decreases by 18 degrees as the altitude
increases by 10,000 feet or the boiling point decreases by 1.8
degrees as the altitude increases by 1,000 feet
The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet "
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The meaning of slope is best described by the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet. The option (D) is correct.
To understand the meaning of the slope in the given function[tex]\( T(a) = -0.0018a + 212 \)[/tex], where [tex]\( T \)[/tex] represents the boiling point of water in degrees and [tex]\( a \)[/tex] represents the altitude in feet, we need to analyze the slope of the function.
The slope of the function is given by the coefficient of [tex]\( a \)[/tex], which is [tex]\( -0.0018 \)[/tex]. This slope tells us how the boiling point of water changes with altitude. To interpret the slope in terms of degrees per foot:
A slope of [tex]\( -0.0018 \)[/tex] means that for every 1 foot increase in altitude, the boiling point decreases by 0.0018 degrees.
To find out how much the boiling point changes over an increase of 1,000 feet in altitude, we multiply the slope by 1,000:
[tex]\( \text{Change in boiling point} = \text{slope} \times \text{change in altitude} \)[/tex]
[tex]\( \text{Change in boiling point} = -0.0018 \times 1000 \)[/tex]
[tex]\( \text{Change in boiling point} = -1.8 \)[/tex]
Therefore, the correct interpretation of the slope is that the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet, which corresponds to option D.
The complete question is:
The boiling point of water, T (measured in degrees), at altitude a (measured in feet) is modeled by the function T(a)=-0.0018a+212. In terms of altitude and temperature, which statement describes the meaning of the slope?
A. The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.
B. The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.
C. The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.
D. The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.
A little towns population is growing at an annual rate of 7.5%, annually. What is it’s growth rate per 3 years? Per 5 years? Round to the nearest tenth of a percent.
Answer:
A) The increase population of town after 3 years is 1.2 times initial population
B) The increase population of town after 5 years is 1.4 times initial population .
Step-by-step explanation:
Given as :
The rate of growth of population of a town = r = 7.5%
Let The initial population of town = p
A ) Let The increase population of town after 3 years = P
The time period = n = 3 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 3 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]
Or, P = p × [tex](1.075)^{3}[/tex]
Or, P = p × 1.242
So, The increase population of town after 3 years = P = 1.2 times initial population
Hence,The increase population of town after 3 years is 1.2 times initial population . Answer
B ) Let The increase population of town after 5 years = P'
The time period = n = 5 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]
Or, P' = p × [tex](1.075)^{5}[/tex]
Or, P' = p × 1.4356
So, The increase population of town after 5 years = P' = 1.4 times initial population
Hence,The increase population of town after 5 years is 1.4 times initial population . Answer
Someone please help!
Answer:
See explanation
Step-by-step explanation:
1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.
2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.
3. Angles 2 and 7 are congruent (see 1)
Angles 2 and 10 are congruent (see 2)
Hence, angles 7 and 10 are congruent by transitive property.
A waiter received a $15.25 tip. If the check totaled $25, what percentage was received?
Answer:
61%
Step-by-step explanation:
15.25/25
=0.61
Multiply it by 100 and you will get the answer
Whole row form: 15.25/25*100
61 percentage was received.
Hope that helps! :)
Answer: He received 61%
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Tip (t) : $15.25 Total amount (T): $25To, find the percentage (p):
p = t/T x 100
Replacing with the values given:
p = (15.25/25)x100
p= 0.61 x 100=61%
He received 61%
Feel free to ask for more if needed or if you did not understand something.
What’s equivalent to 25x + 35y
Answer:5x+7y
Step-by-step explanation:
Your welcome
What is the domain for the piece of the function represented by f(x) = x + 1? x < –1 –1 ≤ x ≤ 1 1 ≤ x < 2 x > 1
Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.
Answer:
x > 1 is the domain of the f(x) = x + 1.
Step-by-step explanation:
A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.
So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.
For example,
Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.
For example, for x > 1
For x = 2, f(x) = 3. So, the graph must pass through of P(2, 3)For x = 3, f(x) = 4. So, the graph must pass through of P(3, 4)For x = 4, f(x) = 5. So, the graph must pass through of P(4, 5)and so on.
So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.
So, x > 1 is the domain of the f(x) = x + 1.
Keywords: domain, function
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Answer:
"D" X > 1
Step-by-step explanation:
HOPE THIS HELPS!!!
Vivi is a drummer for a band. She burns 756756756 calories while drumming for 333 hours. She burns the same number of calories each hour.
How many calories does Vivi burn per hour?
burned: 756 calories
hours: 3
same number of calories each hour
-> to find this, we must split the number of calories evenly among the hours
steps
756/3
= 252 calories per hour
Answer:
252
Step-by-step explanation: 756/3
NEED NEED HELP! !!!!
Nati randomly selected 10 girls and 10 boys from her 7th grade class and recorded their heights in inches. The results are shown. Girls: 61, 58, 63, 57, 58, 59, 62, 60, 64, 56 Boys: 58, 55, 63, 60, 58, 65, 60, 57, 63, 62 A. Find the mean and median of the girls’ heights. Show your work.
Answer:
Mean= 59.8 and median = 59.5
Step-by-step explanation:
Mean = Summation of values/ No. of Values
Mean of Girls' height= 61+58+63+57+58+59+62+64+60+56/10
Mean= 598/10= 59.8
Arranged Data = { 56, 57,58,58,59, 60, 61,62,63,64}
As the number of observations is even so the 5th and 6th value will be added and divided by 2
59+60/2= 59.5
Median = 59.5
mike scored a 125 at a semi final diving competition season. He scored a 95 at this final season. what is the percent decrease?
Answer:
24%
Step-by-step explanation:
Formula:
x new price - old price
--------- = ---------------------------------
100% old price
X/28=2/10 I need help solving for X
Answer:
x = 28/5
Step-by-step explanation:
Step 1: Cross-multiply
x / 28 = 2/10
x*(10)=(2)*(28)
10x=56
Step 2: Divide both sides by 10.
10x / 10 = 56/10
x = 28/5
The given ratios can be solved to obtain x as 5.6.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given expression is x/28 = 2/10.
In order to find the equality of two ratios, the cross products of their numerators and denominators are equal which is given as,
10x = 2 × 28
⇒ x = 56/10
⇒ x = 5.6
Hence, the value of x is given as 5.6.
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There were 9 beluga whales, 3 bowhead whsles, and 2 narwhales. Each whale travels 6 miles. How many miles did the whale trvael?
84 miles I would think
Explanation:
14 whales in all, each travelled 6 miles.
14x6=84
Hope I helped :)
What is a rational number equivalent to ——
3.12
Answer:
[tex]\frac{78}{25}[/tex]
Step-by-step explanation:
A rational number has the form
[tex]\frac{a}{b}[/tex] ← where a and b are integers
3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus
3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form
please help I need to get this done today
Answer:
18) If ∠1 = 124° , then ∠4 = 56°.
19) if ∠2 = 48°, then ∠3 = 132°.
20) if ∠4 = 55°, then ∠2 = 55°.
21) if ∠6 = 120° , then ∠8= 120°.
22) if ∠7 = 50.5 , then ∠6= 50.5°.
23) if ∠3 = 118.7°, then ∠2= 61.3°
Step-by-step explanation:
Given two parallel lines a and b.
And other line, which is called transversal line cuts these two parallel lines to make 8 angles.
Now,
18) Given, ∠1 = 124°
Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .
⇒∠1 + ∠4 = 180°
⇒∠a = 180° - 124° = 56°.
19) ∠2 = 48°.
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠2 + ∠3 = 180°.
⇒ ∠3 = 180° - 48° = 132°.
20) ∠4 = 55°
Alternate angles made by transversal line with parallel lines are equal .
⇒∠2 = ∠4 = 55°.
21) ∠6 = 120°
As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.
now, also opposite angles are equal
⇒ ∠3 = ∠8 = 120°.
22) ∠7 = 50.5
As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.
now, also opposite angles are equal
⇒ ∠2 = ∠6 = 50.5°.
23) ∠3 = 118.7°
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠3 + ∠2 = 180°.
⇒ ∠2 = 180° - 118.7° = 61.3°
What is the point (5, -3) after a rotation of 90 degrees counterclockwise
Answer:
It would be (3,5)
Step-by-step explanation:
On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.
which formula can be used to find an ?
Answer:
Step-by-step explanation:
an = 6n - 13
If n = 10 , a10 = 6*10 - 13 = 60-13 = 47
If n = 11 , a11 = 6*11 - 13 = 66-13 = 53
If n = 12 , a12 = 6*12 - 13 = 72-13 = 59
The formula to find the nth term of the sequence an, is a(n) = -13 + 6n
How to determine the formula to find an ?From the question, we have the following parameters that can be used in our computation:
a(10) = 47
a(11) = 53
a(12) = 59
a(13) = 65
The nth term of an arithmetic sequence can be represented as
a(n) = a(1) + (n - 1) * d
Where,
common difference,
d = 6
So, we have
a(n) = a(1) + (n - 1) * 6
Using the 12th term, we have
a(1) + (12 - 1) * 6 = 59
a(1) = 59 - 66
a(1) = -7
So,, we have
a(n) = -7 + (n - 1) * 6
Expand
a(n) = -13 + 6n
Hence, the formula to find an is a(n) = -13 + 6n
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The scatterplot represents the total fee
for miles traveled on a toll road.
The line of best fit for the data is
y = 0.043x + 0.324.
Use the line of best fit to predict the toll
when 100 miles are driven.
Answer:
[tex]4.624[/tex]
Step-by-step explanation:
[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]
A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells
Caramels: $10.28
Milk Chocolate: $13.85
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Step-by-step explanation:
Given,
Cost of one pound of Caramels = $10.28
Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]
Cost of one pound of chocolate milk = $13.85
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]
Difference = 24.24 - 17.99 = $6.25
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Keywords: difference, multiplication
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Final answer:
The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.
Explanation:
To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:
Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99
Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24
Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:
Cost difference = $24.24 - $17.99 = $6.25
So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.
Six more than five times a number is the same as nine less than twice the number. Find the number.
Answer:
x = -5
Step-by-step explanation:
let the number be x
"five times a number" : 5x
"Six more than five times a number" : 5x + 6
"twice the number" = 2x
"Six more than five times a number = 2x - 9
"Six more than five times a number" = "Six more than five times a number
5x + 6 = 2x - 9
5x - 2x = -9 -6
3x = -15
x = -15 / 3
x = -5
The buyer for a chain of stores purchased lawn ornaments in bulk, paying $23 each. The stores will sell each lawn ornament for $37.08. What is the mark-up percentage?
Answer:
The markup percentage is 61.2
Step-by-step explanation:
Given as :
The cost price of each ornaments = $23
The sell price of each ornament = $37.08
Let The markup percentage = x
Now, According to question
Markup percentage = [tex]\dfrac{s.p - c.p}{c.p}[/tex] × 100
Or, x% = [tex]\dfrac{37.08 - 23}{23}[/tex]
Or, x% = [tex]\dfrac{14.08}{23}[/tex]
Or, x% = 0.612
∴ x = 0.612 × 100
I.e x = 61.2
So, The The markup percentage = x = 61.2
Hence, The markup percentage is 61.2 Answer
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sale price (original price minus discount) of those televisions, y, as a function of the regular price of the TV, x.
25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).
To find the sale price you would multiply the regular price by 75%:
The equation would be y = 0.75x
Two-thirds of a number added to itself is 20. What is the number?
Answer:
12
Step-by-step explanation:
2/3 x + x = 20
2/3 x + 3/3x = 20
5/3 x = 20 ... times 3/5 both sides
x = 12
check: 2/3 x 12 + 12 = 8 + 12 = 20
Round 8923 to the thousands
Answer:
9000
Step-by-step explanation:
When you are rounding to the thousands, if the hundreds place is 500 or greater you have to round up in the thousands place.
That would mean 8923 rounded to the thousands place would equal 9000
Hope This Helps!
Answer:
9000
Step-by-step explanation:
To round a number to the nearest thousand, you look at the number in the hundreds place.
If the number in the hundreds place is
greater than 5, you add 1 to the number in the thousands place less than 5, you keep the number in the thousands place exactly 5 with only zeros following it, you round the number in the thousands place to the nearest even numberHere's how to round 8923 to the nearest thousand.
The digit in the thousands place is the 8. The number in the hundreds place (8) is greater than 5. Add 1 to the digit in the thousands place.The rounded number is 9000.
the midpoint is AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.
To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).
Explanation:The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.
Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:
[(x + 7) / 2, (y + -9) / 2] = (3, -2)
Simplifying the equation, we get:
(x + 7) / 2 = 3
(y - 9) / 2 = -2
Multiplying both sides by 2, we have:
x + 7 = 6
y - 9 = -4
Subtracting 7 from both sides, we get:
x = -1
Subtracting -9 from both sides, we get:
y = 5
Therefore, the coordinates of the other endpoint are B(-1, 5).
3.3(x – 8) - x = 1.2
Answer:
3.3 x - (3.3*8) - x = 1.2
2.3 x - (3.3*8) = 1.2
2.3 x - 26.4 = 1.2
2.3 x - 26.4 + 26.4 = 1.2 + 26.4
2.3 x = 27.6
2.3 x / 2.3 = 27.6 / 2.3
x = 12
5/6 ÷2/7 divide the fraction
Answer:
35/ 12
Step-by-step explanation:
5/6 divided by 2/7
= 5/6 x 7/2
= 35/ 12
please help me I need it.
Deon needs 50g of shugger to make 15 biscuits.
she also needs three times as much flour as sugar
two times as much butter as sugar
Deon is going to make 60 biscuits
work out the amount of flour she needs.
Answer:
200g of sugar, 600g of flour, 400g of butter
Step-by-step explanation:
50g sugar = 15 biscuits
3 x 50g = flour --) 150g = flour
2 x 50g = butter --) 100g = butter
60/15 = 4; 4 times as much
4 x 50g = 200g of sugar
4 x 150g = 600g of flour
4 x 100g = 400g of butter
The amount of flour she needed is 600g.
Given that,
Deon needs 50g of shugger to make 15 biscuits. she also needs three times as much flour as sugar two times as much butter as sugar. Deon is going to make 60 biscuits.Based on the above information, the calculation is as follows:
50g sugar = 15 biscuits
[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]
And.
[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]
Now
[tex]= 60\div15[/tex]
= 4 times
Therefore, the amount of floor should be
[tex]= 150 \times 4[/tex]
= 600 grams.
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What is the y-intercept of the function f(x) = -3x
Ο
Ο
on who wire on
Ο
Ο
Answer:
see the explanation
Step-by-step explanation:
we know that
The y-intercept is the value of the function when the value of x is equal to zero. Also is called the initial value of the function
I will analyze two cases
Part 1) we have
[tex]f(x)=-3x[/tex]
so
For x=0
substitute
[tex]f(0)=-3(0)=0[/tex]
therefore
The y-intercept is the point (0,0)
Part 2) we have
[tex]f(x)=-3^x[/tex]
so
For x=0
substitute
[tex]f(0)=-3^0=-1[/tex]
therefore
The y-intercept is the point (0,-1)
Emily has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emily has.
Answer:
The number of dimes is 14 and the number of quarters is 7.
Step-by-step explanation:
Given:
Emily has $3.15 worth of dimes and quarters.
She has twice as many dimes as quarters.
Now, to determine the number of dimes and the number of quarters.
Let the number of quarters be [tex]x.[/tex]
And the number of dimes be [tex]2x.[/tex]
So, the total worth of dimes and quarters = $3.15.
Now, to get the number of dimes and quarters:
According to question:
[tex]0.10(2x)+0.25x=3.15[/tex]
[tex]0.20x+0.25x=3.15[/tex]
[tex]0.45x=3.15[/tex]
Dividing both sides by 0.45 we get:
[tex]x=7.[/tex]
Thus, the number of quarters = 7.
So, the number of dimes = [tex]2x=2\times 7=14.[/tex]
Therefore, the number of dimes is 14 and the number of quarters is 7.
Solve for x
Y= 0.39(8x+30)
Answer:
[tex]\large\boxed{x=\dfrac{50y-585}{156}}[/tex]
Step-by-step explanation:
[tex]y=0.39(8x+30)\qquad\text{use the distributive propety}\\\\y=(0.39)(8x)+(0.39)(30)\\\\y=3.12x+11.7\qquad\text{multiply both sides by 100}\\\\100y=312x+1170\qquad\text{subtract 1170 from both sides}\\\\100y-1170=312x\qquad\text{divide both sides by 312}\\\\\dfrac{100y-1170}{312}=x\\\\x=\dfrac{100y:2-1170:2}{312:2}\\\\x=\dfrac{50y-585}{156}[/tex]
Solve for X
12.8 = 8x