through: (0, -5), slope: 7/3
A candle is 20 in. tall after burning for 3 hours. After 5 hours, it is 19 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.
[tex]\begin{array}{ccll} \stackrel{hours}{t}&\stackrel{height}{h}\\ \cline{1-2} 3&20\\ 5&19 \end{array}[/tex] with those values provided from the table, let's get its equation
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{19}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{19}-\stackrel{y1}{20}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{19 -20}{5 -3} \implies -\cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{-\cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{3}) \implies y-20=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2} \\\\\\ y=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2}+20\implies y=-\cfrac{ 1 }{ 2 }x+\cfrac{43}{2}\implies \LARGE \begin{array}{llll} h=-\cfrac{ 1 }{ 2 }t+\cfrac{43}{2} \end{array}[/tex]
how talll will the candle be after 8 hours? namely when t = 8.
[tex]h=-\cfrac{ 1 }{ 2 }(8)+\cfrac{43}{2}\implies h=-4+\cfrac{43}{2}\implies h=\cfrac{35}{2}\implies \LARGE \begin{array}{llll} h=17\frac{1}{2} \end{array}[/tex]
Try Again
Your answer is incorrect.
Pablo reads a book at a rate of 16 chapters per hour.
How many chapters does he read in 4 hours?
4 chapters
8 08
X
Ś
Answer:
64
Step-by-step explanation:
16 chapters per hour times 4 hours is 64 chapters
in infant's Tylenol, 5 ml contains 160 mg of Acetaminophen. If you child's pediatrician says that your child can take 48 mg of Acetaminophen, how many milliliters (ml) should you give the child?
The amount of milliliters (ml) you should give the child is 1.5 ml
How to determine how many milliliters (ml) you should give the child?The given parameters are:
infant's Tylenol, 5 ml = 160 mg
This can be represented as
5 ml = 160 mg
Let the number of ml to give a child that requires 48 mg be x
So, we have:
5 ml = 160 mg
x = 48 mg
Cross multiply
x * 160 = 48 * 5 ml
Divide both sides by 160
x = 1.5 ml
Hence, the amount of milliliters (ml) you should give the child is 1.5 ml
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Practice
6. Fill in each blank with the correct symbol >,<, or =
(a) 6.5
6.5 x 1
The correct symbol will be (equal to) 6.5 = 6.5
Use the greater than and less than symbols to compare values and expressions. > is the symbol for more than. 6.5 is commonly thought to mean 6.5 "6.5 is the same as 6.5. " "= "is the sign of equality. Two more comparison expressions are "greater than" and "equal to" (less than or equal to).
Two values are equal when the "equals" sign is used to indicate this. (=)
When two values are obviously not equal, the "not equal to" signal is used. (≠)
To show that one value is smaller than another, we use the "less than" sign. (<)
To show that one value is greater than another, we use the "greater than" symbol. (>)
The answer to the left-hand question is 6.5, whereas the answer to the right is 6.5 * 1 is equal to 6.5.
Therefore, 6.5 = 6.5
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Write an equation and
Isolve for x if the area
of the rectangle is 70
square units.
The linear equation for the area is:
40 = 7*(x + 4)
The solution is x = 1.71 = x
How to write and solve the equation?Remember that for a rectangle of length L and width W, the area is:
A = L*W
In this case, we can see that:
W = 7
L = x + 4
A = 70
Replacing that, we can get the linear equation:
40 = 7*(x + 4)
Now we can solve this, we jus need to isolate x.
40/7 = x + 4
40/7 - 4 = x
5.71 - 4 = x
1.71 = x
The solution is x = 1.71 = x
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Simplify (3.7 × 10−9) − (8.2 × 10−8). Write the final answer in scientific notation.
−7.83 × 10−8
−7.83 × 10−9
−4.5 × 101
−4.5 × 10−1
Answer:
The first answer is correct. See the picture below
Step-by-step explanation:
What are
2 sixths in the lowest term
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{6}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{1}{3}[/tex] ← in simplest form
a fraction is in simplest form when no other value but 1 can divide into the numerator/ denominator.
The line with slope of - 2/5 passing through the point (-1,-1)
I'll give brainliest!!!
Answer in the picture !!!
the length of an arc of a circle is 269πcentimeters and the measure of the corresponding central angle is 65∘. what is the length of the circle's radius?
The length of the circle's radius = 744.92 cm
Given the length of arc of a circle, arc length = 269π cm
Central angle of a circle is the angle made between the radius through the arc length at the center of the circle.
The corresponding central angle = 65°
To find the corresponding central angle in radians = 65° x π/180 = 13π/36 radians
We have, arc length of a circle = radius x central angle
Therefore, radius of the circle = arc length / central angle
= 269π /(13π/36)
= 744.92 cm
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kendra reads in modern dog magazine that the average age of dogs currently alive is 4.8 years. to determine if this finding applies to the customers in her pet store, kendra surveys every fifth customer in her store who owns a dog and asks the age of their dog. she collects data for seven weeks and obtains the following averages
Kendra's samples are precise but not accurate.
The results are as follows: 3.7, 3.8, 4.2, 4.1, 3.9, 3.9, and 4.0.Precision refers to how near or far apart the measurements are.The sample is precise since the values are close to each other.The sample mean is the sum of values divided by the number of values.The sample mean is (3.7 + 3.8 + 4.2 + 4.1 + 3.9 + 3.9 + 4.0)/7.The sample mean is 27.6/7.The sample mean is 3.94.Accuracy refers to how close or far a particular collection of measurements is to its real value.But since the sample mean is farther from 4.8, it is not accurate.To learn more about precision, visit :
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Richard wants to paint the top and sides of the block column. What is the surface area he needs to cover?
The Surface area to be painted = 512 ft²
What is the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(w × l + h× l + h × w). Where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
The block column has a shape of rectangular prism. Therefore, the surface area that Richard needs to paint which excludes the bottom of the block = 2(w × l + h× l + h × w) - l × w.
l = 10 fth = 12 ftw = 8 ftPlug in the values
Surface area to be painted = 2(8 × 10 + 12 × 10 + 12 × 8) - 10 × 8
Surface area to be painted = 592 - 80
Surface area to be painted = 512 ft²
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-39 * 99 = ? Solve the question using distributive property.
Step-by-step explanation:
39× 99
= -39×(100 - 1)
= (-39×100) - (-39 × 1)
= -3900 + 39
= -3861
Answer:
-3751
Step-by-step explanation:
you multiple times to the /number
Please Help!!! Quickly as possible will mark brainliest!!
Answer:
(0,5)
Step-by-step explanation:
Let f(x)=|x|-3 write a function g whose graph is a translation 5 units down of the graph of f
If the function is translated 5 units down of the graph of f, the resulting function will be g(x) =. |x|-8
Translation of functionsTranslation is the technique that is used to change the position of a figure on an xy-plane.
For instance, if the function f(x) is translated k units down the graph, the resulting function will be g(x) = f(x) - k
Given the function f(x)=|x|-3, if the function is translated 5 units down of the graph of f, the resulting function will be;
g(x) = f(x) - 5
g(x) = |x|-3 - 5
g(x) =. |x|-8
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line in simplest form is: 1.
How to Find the Slope of a Line?The slope (m) of a line is calculated as:
Slope (m) = rise/run = change in y / change in x.
The horizontal distance across the line is the run, while the vertical distance is the rise.
The blue line shows the rise of the line = 2 units
The red line shows the run of the line = 2 units
Slope (m) = rise/run = 2 units/2 units
Slope (m) = 1
Therefore, the slope of the line in simplest form is: 1.
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In the figure below, m44 = 79°. Find m1, m2, and m 3
The angle of m1, angle of m2 and angle of m3 is 101°, 79° and 101° respectively.
It is given that the angle of m4 is 79°.
To find angles m1, m2 and m3 :
As we know that angle m4 is equal to angle m2 (because they are vertically off opposite angle).
So, angle m2 = 79º
In the same manner the angle of m1will be equal to angle m3.
Now, we can see that in the figure the angles m2 and m1 is lying on one plane, and a plane line makes a angle of 180º
So,
m2+m1 = 180º
79º+m1 = 180º
m1 = 180º-79º
Angle m1 = 101º
And, as we can see that the angles m1 and m3 are vertically of opposite angle.
So, m1= m3= 101º
Hence, angle m1=101º,
angle m2= 79º,
And, angle m3=101º.
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Which of the following pairs consists of equivalent fractions?
Answer:
the second pair
Step-by-step explanation:
the first pair can't be equivalent because to check whether two fractions are equivalent we have to use the criss-cross method so.....
1.3*4=12 and 12*3=36....so not equal
2.6*15=90 and 9*10=90.....it matches:)) so this is the answer
The angle below is the image formed when a figure containing nop is dilated by a scale factor of 2. what is the measure of nop?
The measurement of the actual angle NOP is 56° when it is being dilated by the scale factor of 2 to form the dilated angle NOP as 112° .
We are given the dilated angle as:
∠ NOP = 112°
The scale factor for dilation is given as 2.
Now, we need to find the value of actual angle NOP.
For this, we will divide the dilated angle NOP with the scale factor of dilation.
So, we will get the result as:
Actual ∠ NOP = 112° / 2
Actual ∠ NOP = 56°
Therefore, we get that, the measurement of the actual angle NOP is 56° when it is being dilated by the scale factor of 2 to form the dilated angle NOP as 112° .
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Succotash is made by combining corn with lima beans and costs $1.00 per pound.
If lima beans cost $1.10 per pound and corn costs $.60 per pound, how many pounds of each should be used to make 5 lb of succotash?
Answer:
1 lb corn and 4 lb lima beans
Step-by-step explanation:
Let x = weight of corn.
Let y = weight of lima beans.
x + y = 5
0.6x + 1.1y = 5
x = 5 - y
0.6(5 - y) + 1.1y = 5
3 - 0.6y + 1.1y = 5
0.5y = 2
y = 4
x + y = 5
x + 4 = 5
x = 1
Answer: 1 lb corn and 4 lb lima beans
Approximate when the function is positive, negative, increasing, or decreasing.
From the graph of the function, we have that:
Positive: -1 < x < 1.Negative: x < -1 and x > 1.Increasing: x < 1.Decreasing: x > 1.When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.Hence:
Positive: -1 < x < 1.Negative: x < -1 and x > 1.When a function is increasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.
When a function is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
Hence:
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f(x)=3-2x g(x)=x+1\4 find fg(x) note: 4 is denominator for x+1
Step-by-step explanation:
you can ask questions for clarification
What is the purpose of the list of grievances?
to list the reasons the colonists are abolishing their government
to explain the purpose of natural rights to the king
to declare that the United States of America is a free and independent state
to show that the colonists understand the importance of their actions
The purpose of the list of grievances is to declare that the United States of America is a free and independent state.
The colonists' complaints against King George's treatment of them were listed in the list of grievances. It was essentially a list of justifications for their declaration of independence.
A list of complaints that Thomas Jefferson thought George III, the king of Great Britain, had made against the colonists is included in the Declaration of Independence. The primary justifications for the Colonists' involvement in the American Revolution were described in these grievances. Taxation without representation, or as Thomas Jefferson more elegantly puts it, "for imposing Taxes on us without our Consent," is arguably the most significant of them.
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You believe that water boils at 100 degrees Celsius.
Rate each statement below on a scale from best to worst.
a. Your cousin said that he tested the temperature of boiling water and found that it was 100°C.
b. Most people you know believe that water boils at 100°C.
c. You used a thermometer to measure the temperature at which water boiled. You repeated the experiment 3 times. Each time the thermometer read 100°C.
d. You read an article in a science journal from 50 different labs around the world that have tested the temperature of water and found that it boils at 100°C in every location.
BEST EVIDENCE _____, _____, ______, _____ WORST EVIDENCE
Rating each statement below on a scale from best to worst will be:
1. You read an article in a science journal from 50 different labs around the world that have tested the temperature of water and found that it boils at 100°C in every location.
2. You used a thermometer to measure the temperature at which water boiled. You repeated the experiment 3 times. Each time the thermometer read 100°C.
3. Your cousin said that he tested the temperature of boiling water and found that it was 100°C.
4. Most people you know believe that water boils at 100°C.
How to illustrate the information?It should be noted that the science journal will give the most accurate information. Therefore, it's the best.
It should be noted that the fact that most people you know believe that water boils at 100°C doesn't necessarily mean it's correct. It wasn't tested. Therefore, it's the worst.
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the surface of a solid is 50,682,000 square milliliters. Is the surface area greater than 50 square meters
Answer:
Step-by-step explanation:
One square millimeter converted into square meter equals = 0.0000010 m2 , sq m
1 mm2 , sq mm = 0.0000010 m2 , sq m
Answer:
I think 50,682,000 square milliliters
Step-by-step explanation:
the values listed in the csv filewaitingtimesare waiting times (in minutes) ofcustomers at the bank a, where customers enter a single waiting line that feedsthree teller windows. construct a 95% confidence interval for the populationstandard deviationσ.
The range of the population standard deviation with a 95% confidence level = 0.33 ≤ σ ≤ 0.87.
What does the population mean in terms of standard deviation?A data distribution's spread is measured by standard deviation. It calculates the average separation between each data point. Whether we consider the data to be a population unto itself or a sample of a larger population affects the formula we use to calculate standard deviation.
According to the given data:Sample data, x: {6.5, 6.6, 6.7, 6.8, 7.1, 7.3, 7.4, 7.7, 7.7, 7.7}
Sample size n = 10
Applying chi-square statistics with df=n-1=9-1=8
now 95% confidence interval is given by:
= [tex]\sqrt{\frac{(n-1) S^2}{\chi_{8,0.025}^2}} < \sigma < \sqrt{\frac{(n-1) S^2}{\chi_{8,0.975}^2}}[/tex]
= [tex]\sqrt{\frac{(9-1) * 0.462^2}{17.53}} < \sigma < \sqrt{\frac{(9-1) * 0.462^2}{2.18}}[/tex]
= 0.107 ≤ σ² ≤ 0.757
= 0.33 ≤ σ ≤ 0.87
The range of the population standard deviation with a 95% confidence level = 0.33 ≤ σ ≤ 0.87.
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I understand that the question you are looking for is:
The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Find the sample variance s2 then construct a 95% confidence interval for the population standard deviation σ. Round sample variance to three decimal places. Assume that the population has a normal distribution. Critical values should have three decimal places and confidence interval limits should have two decimal places.
6.5, 6.6, 6.7, 6.8, 7.1, 7.3, 7.4, 7.7, 7.7, 7.7
PLEASE HELP‼️For each direct variation, find the constant of variation. Then find the
value of y when x = -5.
y = -5 when x = 3
Answer: For each direct variation, find the constant of variation. Then find the value of $y$ when $x=-5 .$
$y=-\frac{2}{3}$ when $x=-\frac{1}{3}$
Step-by-step explanation:
Choose a linear function for the line represented by the point-slope equation y - 5= 3(x - 2).
f(x) = 3x + 1
f(x) = 3x - 1
f(x) = 8x + 10
f(x) = 8x - 10
someone help please<3
Answer:
subduction zones <3333