A quality control technician at a candle factory tested the eight 16-ounce candles, each 3 inches in diameter. These candles came from the same production run. The table shows the decrease in weight of each candle after burning for 3 hours. Candle makers believe that the rate at which the candles burn is constant.
Write an equation that can be used to model the weight,
of such a candle as a function of
, the number of hours burning. Then, explain how the equation can be used to predict the weight of a candle that has burned for 5 hours.
Enter your equation and your explanation in the box provided.
Answer:
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces
Step-by-step explanation:
If the burn rate is believed to be constant, determine the average burn rate for the eight candles as the ratio of weight loss per hour.
ounces lost over three hours
0.5+0.6+0.5÷0.7÷0.7÷0.5÷0.5÷0.6
8
* 0.575
0.575
ounces lost per hour on average
= 0.19
For 0 hours, the weight of each candle is 16 ounces. Therefore, w 16 - 0.19h.
This model can be used to predict the weight of the candle when h, the number of hours of burning, is 5.
W * 16 - 0.19(5)
W = 16 - 0.95
W = 15.05
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces.
Calculating Loan Payments You want to buy a new sports coupe for $69,300, and the finance office at the dealership has quoted you a loan with an APR of 5.6 percent for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
Input area:
Amount borrowed $69,300
APR 5.6%
# of years 4
# of times compounded per year 12
(Output area) Complete the following analysis. Do not hard code values in your calculations. All answers should be positive.
Loan Payment __________
Effective Intrest Rate ____________
The monthly payments will thus be $1,612.81.
The annual effective rate on this loan is 5.78%.
What is the loan payment formulae?We can use the following loan payment formula to determine the loan payment:
Loan Payment = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]
where P = borrowed amount = $69,300
r = yearly interest rate (decimal) = 0.056
n = number of times compounded per year = 12
t = number of years = 4
When we plug in the values, we get:
Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]
= $1,612.81 (to the nearest cent)
The monthly payments will thus be $1,612.81.
We can use the following calculation to obtain the effective annual rate:
Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]
When we plug in the values, we get:
Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%
As a result, the annual effective rate on this loan is 5.78%.
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What is the area of this figure?
20 mi
3 mi
11 mi
7 mi
3 mi
4 mi
3 mil
Write your answer using decimals, if necessary.
square miles
3 mi
The area of the figure composed of two rectangles is 99 mi²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
For the first rectangle:
Area = 11 mile * 5 mile = 55 mi²
For the second rectangle:
Area = 11 mile * 4 mile = 44 mi²
The area of figure = 55 mi² + 44 mi² = 99 mi²
The area of the figure is 99 mi²
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4. Mackenzie's dog can jump 2 1/2 feet off the ground. Jordyn's dog can
jump 1/2 foot off the ground. What is the difference in inches between
2how high Mackenzie's dog can jump and how high Jordyn's dog can
jump? Circle what to do to solve this problem.
The difference in the length of dogs jump is 24 inches.
Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.
We know that, 1 feet = 12 inches
Here, 5/2 feet = 5/2 ×12
= 30 inches
1/2 foot = 1/2 ×12
= 6 inches
Now, difference = 30-6 = 24 inches
Therefore, the difference in the length of dogs jump is 24 inches.
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↑
tructor
Watch the video and then answer the problem given below.
Click here to watch the video.
The circle graph represents a sample of 600 people who were asked which one automobile accessory they would most
prefer to have on a family trip. How many people indicated Bluetooth capability?
people
CEFF
Automobile Accessories for a Family Road Trip
Bluetooth capability 29%
Other 21%
Clear all
Roof rack 8%
Extra cup holders 15%
DVD player 27%
Check answer
Based on the above, about 174 people out of the sample of 600 people indicated Bluetooth capability.
What is the graph about?To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.
Note that:
People who Bluetooth capability =29%
Number of people = Percentage × Total sample size
= 0.29 × 600
= 174
So, 174 individuals shows that the Bluetooth capability is their favored option for the family trip.
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As seen in the diagram below, Dalvin is building a walkway with a width of x x feet to go around a swimming pool that measures 7 feet by 9 feet. If the total area of the pool and the walkway will be 143 square feet, how wide should the walkway be?
Answer: 2
Step-by-step explanation:
(7+2x)(9+2x)= 143 (area= length x width)
63+14x+18x+4x^2=143
4x^2+32x−80=0
x^2+8x−20=0
(x−2)(x+10)=0
x = 2 or -10
Since the length of the walkway can't be negative, the answer is 2.
x^2+7x-9 + 2x-1 what is the polynomial and degree
Answer:
The given expression is a polynomial:
f(x) = x^2 + 7x - 9 + 2x - 1
Combining like terms, we get:
f(x) = x^2 + 9x - 10
The degree of the polynomial is 2, since the highest power of x is 2.
A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample:
If it was obtained from a population with σ = 16
z =
If it was obtained from a population with σ = 32
z =
If it was obtained from a population with σ = 48
z =
c) Population [tex]\sigma = 48[/tex]
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
How to solveAccording to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]
Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
where M = Sample Mean
[tex]\mu[/tex] = Population Mean
[tex]\sigma[/tex] = Population Standard Deviation
n = Sample Size
a) Population [tex]\sigma[/tex] = 16
Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]
Z-score = 4
b) Population [tex]\sigma[/tex] = 32
Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]
Z-score = 2
c) Population [tex]\sigma[/tex]= 48
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
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2x + y = 7
x + y = 1
Answer: x = 6 and y = -5.
Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:
-2(x + y) = -2(1) -> -2x - 2y = -2
Add the resulting equation to the first equation to eliminate the y term:
2x + y = 7
-2x - 2y = -2
0x - y = 5
Solve for y:
-y = 5
y = -5
Substitute y = -5 into either of the original equations and solve for x:
x + y = 1
x + (-5) = 1
x = 6
Therefore, the solution to the system of equations is x = 6 and y = -5.
how do I do 75% of 200
Answer:
150
Step-by-step explanation:
divide the percentage by 100 to make it decimal form,
75/100= .75
The multiple .75 by the total amount to find the 75%,
200 x .75 = 150
Which means 75% of 200 is 150
Use the graph below to answer the question.
Money Spent on Food
dinner
42%
lunch
30%
snacks
10%
breakfast
18%
A shopper spent $100 at the store. How many dollars did the shopper spend on snacks?
A. $10
B. $18
C. $30
D. $42
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 154 yelow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25%, of the offspring peas would be yellow? a. Construct a 90% confidence interval. Express the percentages in decimal form.
Find the sum of 10x² + 7x + 6 and 6x + 5.
Answer:
Submit Answer
M
DELL
10x² + 13x + 11 is the sum of linear equation .
What is a linear equation in mathematics?
The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.
The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.
two equations are 10x² + 7x + 6 and 6x + 5.
now add both equations
= (10x² + 7x + 6 )+ (6x + 5)
= 10x² + 7x + 6 + 6x + 5
= 10x² + 13x + 11
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EASY POINTS!
A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At this rate, in pounds per hour, does the machine make nails? Show your work!
A. 2/3
B. 3/4
C. 1 1/2
D. 3 3/4
The graph of f(x) and table for g(x)= f(kx) are given.- WORTH 40 BRAINLY POINTS PLEASE ANSWER FAST
The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.
x g(x)
−6 8
−3 2
0 0
3 2
6 8
What is the value of k?
k = 3
k is equal to one third
k = 6
k is equal to negative one sixth
The value of k include the following: B. k is equal to one third.
What is the vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function can be modeled by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);
f(x) = a(x - h)² + k
2 = a(1 - 0)² + 0
2 = a
f(x) = 2(x - 0)² + 0
f(x) = 2x²
For the quadratic function g(x), we have;
g(x) = f(kx)
g(x) = 2(kx)²
g(x) = 2k²x²
By using the point (3, 2) from the table, we have:
2 = 2k²3²
1 = k²9
k² = 1/9
k = √(1/9)
k = 1/3 i.e one third.
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In a game of cards you win $1 if you draw a heart (except the ace), $5 if you draw an ace (including the ace of hearts), $10 if you draw the king of spades and $0 for any other card. Let W be the amount you win playing this game, what the probability distribution of W?
There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.
The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:
P(W = $1 ) = 11/52
The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.
P(W = $5) = 1/52
The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.
P(W = $10) = 1/52
The probability of winning $0 is the probability of drawing any other card, which is 39/52.
P(W = $0) = 39/52
This shows a number line. Which point is located at 90 ?
Answer:
incomplete question bru
Choose which sampling technique 1s used. (R) Random (STR) Stratined (CLS) Cluster
(CON) Convenience (SYS) Systematic
1. I ask everyone in my 5th period class who has more than one computer
at home in a study about all of my students for the year.
2. I collect data from every 15th student on my list of the entire school
population.
3. After using a random number table to generate two-digit numbers, I
decide on 10 people to choose from the population.
Answer:
1. CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.
2. SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.
3. R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.
Hope this helps!
Answer:
1. CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.
2. SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.
3. R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.
Hope this helps!
4. Find the product
()
Answer: n^6-25
Step-by-step explanation:
Use the distributive property to obtain: n^6-5n^3+5n^3-25
Simplify: n^6-25
Answer: n^6-25
The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option [tex]n^{6} - 25[/tex].
This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.
In the above question, we have used the following identity:
[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]
In the given question, a = [tex]n^{3}[/tex] and b = 5
So putting values in the identity, we get
[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]
On solving the left side of the equation, we get
[tex]n^{6} - 25[/tex] which is our answer to the given question.
Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.
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Which number line shows the solution set for |h-3| ≤5?
Answer:
Second number line
Step-by-step explanation:
(h-3)^2 <= 25
h^2 - 6h + 9 <= 25
h^2 - 6h - 16 <= 0
(h-8)(h+2) <=0
Using the graph of (x-8)(x+2),
-2 <= h <= 8
Hence, the answer is the second one (as it has shaded circles)
Hope this helps and be sure to mark this as brainliest! :)
What is the perimeter of the parallelogram?
units
Answer:
Step-by-step explanation:
View photo below. This is timed.
Answer: ∠EFB, ∠DFE, and ∠CFB
Step-by-step explanation:
Starting Angle: ∠CFD
Since its in an X formation: ∠EFB, ∠DFE, and ∠CFB would all work.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
1 -E (102/234) *100 =43.6%
2- F
3-C
4-A
18.
Simplify.
y²-6y +11
y-2
Oy-1
Oy³-8y² +23y - 22
none of the answer choices
Oy²-5y +9
O-y²-2y + 10
Answer:
the answer is none of the answer choices
Answer:
the answer is none of the answer choices
SAT/ACT An arc has a central angle of
radians and a length of 6. What is the
circumference of the circle?
A 12T
B 15T
30T
D 36л
Answer: D 36л
Step-by-step explanation:
s = θr
where r is the radius of the circle. given that the arc length is 6, and the central angle is π/3 radians r:
6 = (π/3)r
r = 6/(π/3) = 18/π
the circumference of the circle is given by:
C = 2πr
Substituting r = 18/π, we get:C = 2π(18/π) = 36
Find the weighted mean. Round your answer to the nearest tenth.
The weighted mean of the deliveries each week can be found to be 5. 38 .
How to find the weighted mean ?The weighted mean is a type of mean that takes into account, the weight of the various items in question.
First, find the total frequency :
= 1 + 5 + 4 + 3
= 13
The weighted mean would then be:
= ∑ ( weight of delivery x number of deliveries )
= ( 1 / 13 x 2 ) + ( 5 / 13 x 4 ) + ( 4 / 13 x 6 ) + ( 3 / 13 x 8 )
= 0. 15 + 1. 54 + 1. 84 + 1. 85
= 5. 38
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1
Determine the scale factor used.
one half
2
one fourth
3
Answer:
To determine the scale factor used, we need to find the ratio of corresponding side lengths in both triangles.
Let's compare the length of the first side in both triangles:
x/3.8 = 2/4.8
Cross-multiplying, we get:
4.8x = 7.6
Dividing both sides by 4.8, we get:
x = 1.58
Now, let's compare the length of the second side in both triangles:
2.4/4.2 = 0.57
Finally, let's compare the length of the third side in both triangles:
2.1/4.8 = 0.44
Since the scale factor is the same for all corresponding side lengths, we can take the average of the ratios:
(scale factor) = (1.58/3.8 + 0.57 + 0.44)/3
(scale factor) = 1.01
Therefore, the scale factor used is approximately 1.
Now, find the solution to the system of equations
The solution of equation is (2, 3).
We have,
x= 3y -7.........(1)
y= x + 1.........(2)
Solving equation (1) and (2) we get
y = 3y - 7 + 1
y - 3y = -7 + 1
-2y = -6
y = -6/(-2)
y = 3
and, x = 3(3) - 7
x = 9 - 7
x = 2
Thus, the solution of equation is (2, 3).
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9. data was collected on houses currently for sale. based on a cubic modeling equation, which prediction about this data is the most reliable? a.
a $70k house would have 1,354 square ft
b. a $70k house would have about 1,460 square ft
c. a $400k house would have 492 square ft
d. a $400k house would have 4,328 square ft
10. suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round the answer to the tenth place.
a. 0.8
b. 2.1
c. 54.3
d. 112.8
11. the equation that best models the linearized data for a particular data set is log y= 0.75821x+0.03442. find the approximate value x=4. round your answer to the nearest whole number.
a. 3
b. 25
c. 1,168
d. 62,034
question 9.
Based on a cubic modeling equation, the prediction about this data that is most reliable is a $70k house would have 1,354 square ft.
Option A is correct.
Question 10.
The second coordinate in a scatterplot of the linearized data and rounding the answer to the tenth place is 0.8
Option A is correct.
Question 11.
The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168
Option C is correct.
How do we calculate?The equation is given as
Log y= 0.75821x+0.03442
We substitute x = 4 into the given equation and solve for y:
log y = 0.75821(4) + 0.03442
log y = 3.07286 + 0.03442
log y = 3.10728
We take the antilogarithm of both sides,
y = 10^(3.10728)
y = 1,168.66
Rounding off, the closest answer is option (c) 1,168.
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In the diagram shown, ABC is equilateral. AD is an altitude.
10). ABD = _____.
11). ADB = _____.
12). BAD = _____.
13). CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of ABC
All the correct values are,
⇒ ∠ABD = 60°
⇒ ∠ADB = 90°
⇒ ∠BAD = 30°
⇒ ∠CAD = 30°
⇒ BD = 3
⇒ AD = √27
⇒ The value of area of triangle ABC is, 3√27
Given that;
In the diagram shown, ABC is equilateral. AD is an altitude.
Hence, We get;
All the angles of a equilateral triangle are,
⇒ 60°
Thus, We get;
⇒ ∠ABD = 60°
Since, AD is an altitude.
⇒ ∠ADB = 90°
And,
⇒ ∠BAD = 60 / 2 = 30°
⇒ ∠CAD = 60/2 = 30°
By Pythagoras theorem;
AB² = AD² + BD²
6² = AD² + 3²
36 = AD² + 9
AD² = 27
AD = √27
Thus, The value of area of triangle ABC is,
⇒ 1/2 × AD × BC
⇒ 1/2 × √27 × 6
⇒ 3√27
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