Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
The name of the assignment is 5-1 Writing Equations In Slope Intercept Form
Answer:
✅[tex] R = 4c [/tex]
Step-by-step explanation:
The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as [tex] y = mx + b [/tex].
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like:
[tex] R = mc + b [/tex]
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{88 - 60}{22 - 15} = \frac{28}{7} = 4 [/tex]
To find b, substitute c = 15, R = 60 and m = 4, into [tex] R = mc + b [/tex].
[tex] 60 = 4(15) + b [/tex]
[tex] 60 = 60 + b [/tex]
[tex] 0 = b [/tex]
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into [tex] R = mc + b [/tex] to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
[tex] R = 4c + 0 [/tex]
✅[tex] R = 4c [/tex]
PLS HELP I WILL MARK BRAINLIEST SINCE YOIR WRITING FOR ME
Answer:
-0.5. -0.5 is to the right of -1.5
Refer to the accompanying data set and construct a % confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results. Click the icon to view the pulse rates for adult females and adult males. Construct a % confidence interval of the mean pulse rate for adult females. nothing bpm nothing bpm (Round to one decimal place as needed.) Construct a % confidence interval of the mean pulse rate for adult males. nothing bpm nothing bpm (Round to one decimal place as needed.) Compare the results.
A. The confidence intervals overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
B. The confidence intervals overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.
C. The confidence intervals do not overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.
D. The confidence intervals do not overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval of mean pulse rate for adult female is [tex]71.98 < \mu < 79.88 [/tex]
The 95% confidence interval of mean pulse rate for adult male is [tex]62.89 < \mu < 70.57 [/tex]
The correct option is C
Step-by-step explanation:
Generally the sample mean for Male pulse rate is mathematically represented as
[tex]\= x_1 = \frac{\sum x_i }{n}[/tex]
= > [tex]\= x_1 = \frac{81 + 74 + \cdots + 59 }{40 }[/tex]
= > [tex]\= x_1 = 66.73[/tex]
Generally the standard deviation for male pulse rate is mathematically represented as
[tex]\sigma_1 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]
=> [tex]\sigma_1 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (74 - 66.73 )^2+ \cdot + (59 - 66.73 )^2 }{40-1 } }[/tex]
=> [tex]\sigma_1 = 12.24[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma_1 }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{12.4 }{\sqrt{40} }[/tex]
=> [tex]E =3.84 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x_1 -E < \mu < \=x_1 +E[/tex]
=> [tex]66.73 -3.84 < \mu < 66.73 +3.84 [/tex]
=> [tex]62.89 < \mu < 70.57 [/tex]
Generally the sample mean for Female pulse rate is mathematically represented as
[tex]\= x_2 = \frac{\sum x_i }{n}[/tex]
= > [tex]\= x_2 = \frac{81 + 94 + \cdots + 73 }{40 }[/tex]
= > [tex]\= x_2 = 75.93[/tex]
Generally the standard deviation for Female pulse rate is mathematically represented as
[tex]\sigma_2 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]
=> [tex]\sigma_2 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (94 - 66.73 )^2+ \cdot + (73 - 66.73 )^2 }{40 } }[/tex]
=> [tex]\sigma_2 = 12.73[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma_2 }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{12.73 }{\sqrt{40} }[/tex]
=> [tex]E =3.95 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x_2 -E < \mu < \=x_2 +E[/tex]
=> [tex]75.93 -3.95 < \mu < 75.93 + 3.95 [/tex]
=> [tex]71.98 < \mu < 79.88 [/tex]
Please help I will mark the brainiest answer please
Answer:
Part A 40
Part B 90
part C show your work
please mark brainliest i need it
Hope helps
All of the following ordered pairs satisfy the function rule y = -2 x - 1 except _____.
(2, -5)
(-1, -3)
(-2, 3)
(0, -1)
Answer:
(-1, -3)
Step-by-step explanation:
The length of a rectangle is 97 meters and the width is 14 meters. Find the area. Give your answer without units.
Provide your answer below:
The area of a rectangle is the product of length and width thus the area will be 1358 square meters.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of the rectangle = 2( length + width).
It is known that,
Area of rectangle = length × width.
Area = 97 x 14 = 1358 sqare meters
Hence "The area of a rectangle is the product of length and width thus the area will be 1358 square meters".
For more about rectangles,
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Complete the area model. Find the product of 2.3 x 1.5
The product of 2.3 × 1.5 from the area model is 3.45
The product of two numbers implies the multiplication of the two numbers. Here, the two numbers to be multiplied together are decimal numbers.
Using the long multiplication method.
2.3
× 1.5
1 1 5
+ 2 3
3 . 4 5
So, what we did basically is to first multiply the two numbers normally and then, decide how many decimal places are the two numbers which two.
Therefore, the product of 2.3 × 1.5 from the area model is 3.45
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A pool that is being drained contained 18,000 gallons of water. After 2 hours, 12, 500
Gallons of water remain. Write an equation in all 3 forms to model this situation,
HELLPPP PLLEASEEEE!!!!!
Answer:
y-18,000=2,750(x-0) --> point-slope
y=2,750x+18,000 --> slope-intercept
-2,750x + y = 18,000 --> standard
Step-by-step explanation:
Linear Modeling
Some situations can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The pool being drained contained initially 18,000 gallons of water. If we set the variable x as the time in hours and y as the remaining gallons of water in the pool, this first point is (0;18,000).
We are also aware that after 2 hours 12,500 gallons of water remain. This gives us the second point as (2;12,500).
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let's find the equation of the line with the 2 points:
[tex]\displaystyle y-18,000=\frac{18,000-12,500}{2-0}(x-0)[/tex]
Calculating:
[tex]\displaystyle y-18,000=\frac{5,500}{2}(x-0)[/tex]
[tex]y-18,000=2,750(x-0)[/tex]
The equation above is the point-slope form of the line
Simplifying and adding 18,000:
[tex]y=2,750x+18,000[/tex]
The equation above is the slope-intercept form of the line
Moving all the variables to the left side:
[tex]-2,750x + y = 18,000[/tex]
The equation above is the standard form of the line
Answer:
y-18,000=2,750(x-0) --> point-slope
y=2,750x+18,000 --> slope-intercept
-2,750x + y = 18,000 --> standard
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:45 mins.
Step-by-step explanation: half of 30 is 15 (one box = 15) and 15 times 3 is 45
Hey how you doing? Hope everyone is doing great! I have a quick question for math, How do you find the unit rate in slopes and graphs?
Answer:
Divide the numerator and denominator of the given rate by the denominator of the given rate.
Step-by-step explanation:
How does trig on the coordinate plane differ from trig with triangles?
Answer:
Trig ratios on coordinates can be negative or positive in value
But
Trig ratios on triangles can only be positive
Step-by-step explanation:
The difference is that, the length of sides used in trig on the coordinates is not absolute
What this mean is that it is dependent on the axes that we are and thus might take up a negative or positive value for trig on coordinates
What we are saying is that while trig on triangle can be positive only, trigonometric ratios on coordinates can be negative or positive
A football Waze proximately 0.42 kg. The physical education teacher needs to purchase a dozen footballs. What will be the total weight, in kilograms, of the footballs to calculate shipping and handling?
A total of six and x is less than 20
Answer:
x+6<20
x<14
Step-by-step explanation:
Answer:
20-6+x
Step-by-step explanation:
you would add six and x and then subtract it from twenty becouse less than means to subract
WILL MARK BRAINLIEST!! PLEASE HELP ME
a. If sea level is represented by 0, then something below sea level would be a value of something less than zero, a negative number. Because the Challenger Deep is 35,814 feet below sea level, it will be represented by -35,814.
b. Trieste is trying to reach the bottom of the challenger deep, which is y, and descending the ocean at -3 feet per second. So the equation would be like this
-35,814 = -3x
We are just looking for x. Notice how both number values are negative so the time it would take Trieste to reach the bottom would be a positive value.
-35,814 divided by -3 = 11938, so it would take 11938 seconds to reach the bottom.
c. y and x would be used in the same context as it would just now. Except that Trieste is coming up to the surface, so the depth of the Challenger Deep is positive.
35814 = k * 11938
k = 3, the amount of time it took to reach the surface in hours.
Hope this helps!
Examine the equation. 4(x – 3) = 4x – 12 Which of the following is true? (Check all that apply.) It is a true statement. Any input will result in an equivalent equation. It is equivalent to an equation of the form a = a. It has no solution. Only one input will result in a true statement.
Answer:
A, B, and C.
Step-by-step explanation:
We have the equation:
[tex]4(x-3)=4x-12[/tex]
Let’s distribute the left. This yields:
[tex]4x-12=4x-12[/tex]
Let’s add 12 to both sides:
[tex]4x=4x[/tex]
And subtract 4x from both sides:
[tex]0=0[/tex]
We get the true statement 0=0.
Hence, A is correct.
Because it is a true statement, any input will yield an equivalent output.
Hence, B is also correct.
We also have the form a=a, where a is 0.
Hence, C is also correct.
Therefore, our correct answers are A, B, and C.
Answer:
It is a true statement.
Any input will result in an equivalent equation.
It is equivalent to an equation of the form a = a.
The average monthly cost of basic cable TV was $9.73 in 1985 and has increased by about $1.35 each year since then. Let t be the number of years since 1985.
1. Use function notation to write an equation giving the monthly cost of basic cable TV as a function of t.
f(t)=____t+____
2. Using the function from above what is the average monthly cost of basic cable TV for this year?
3. Using the function from 1, what year was the average monthly cost of basic cable TV $23.23?
Answer:
$50.23
Step-by-step explanation:
f(t)=1.35(t)+9.73
First I found out how many years are after 1985 so you would do 2020-1985 which equals 30.
I plug it in for t.
f(t)=1.35(30)+9.73
Then you multiply 1.35 and 30 which would leave us with.
f(t)=40.5+9.73
Add them and you get $50.23
can you plz help me with this
Answer:
Step-by-step explanation:
im traade =23423423423
Answer correctly and I will mark you brainless ❤️
PLEASE HELP URGENT WILL GOVE BRAINLIEST
^ABC is similar to ^EDC shown below.
Which equation could be used to determine x, the
length of CD?
Answer:
last one 12/8 = 9/X
Step-by-step explanation:
according to the rule of similarity in triangles
The equation that can be used to find the length of CD is 9/x = 12/8.
Where x is CD.
Option D is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
ΔABC ≅ ΔEDC
We can write:
BC/BA = CD/DE
9/12 = x/8
9/x = 12/8
Thus,
The equation 9/x = 12/8 can be used to find x.
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Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]2 \times \frac{1}{2} hour = 1hour \\ [/tex]
Thus ;
[tex]2 \times \frac{5}{12} \: \: miles = \frac{10}{12} \: \: miles = \frac{5}{6} \: \: miles \\ [/tex]
,♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
I think the answer is 5/6
The mean lifetime of a tire is 48 months with a standard deviation of 77 months. If 147 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.83 months?
Answer:
0.55199
Step-by-step explanation:
When we have a random number of samples, We solve using z score formula
z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation
n is random number of samples
z = 0.83/77/√147
z = 0.13069
Probabilty value from Z-Table:
P(x<48.83) = 0.55199
The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199
Sarah is training for a bike race. She rides her bike 5 3/4 miles in 1/3 hour. What is Sarah’s rate in miles per hour. Express your answer as a mixed number
Answer:no
Step-by-step explanation:
Answer:
17 [tex]\frac{1}{4}[/tex]
A newborn giraffe weighs about 65 kilograms. How much does it weigh in grams?
Answer:
65,000 grams
Step-by-step explanation:
1 kilogram = 1,000 grams
The giraffe weighs 65,000 grams.
The value of 100 pennies is ___% of the value of a dollar
Answer:
The type of coins =pennies has = 100 pennies.
servant has a total number of 100 coins
The sum of the percentage and pennies = $100
Let us represent the number of nickels as which is _% = 55.4
The number of pennies as y
Step-by-step explanation:
(Ill mark brainliest if u help me! :D)
Solve five and four tenths times two.
A) ten and four twentieths
B) ten and eight twentieths
C) ten and four tenths
D) ten and eight tenths
(Here is an image if needed) :
Answer:
10 4/10
Step-by-step explanation:
multiply it together
Maggie has a 2-gallon pitcher of lemonade. How many liters of lemonade did she make?
I'LL GIVE BRAINLIEST!
Answer:
2 gallons converted to liters is 7.57 or 8 liters rounded
6 ones 453 thousandths + 4 hundredths =
Answer:
your answer is 463
Step-by-step explanation:
Hope this help you
have a great thanksgiving
What is the constant of proportionality in the equation y = 5/9x
Answer: 5/9
This is assuming the equation is y = (5/9)x
Note it is in the form y = kx with k = 5/9 as the constant of proportionality.
Solve the equations:
2^(3x−4) = −2
Answer:
x=NaN your welcome hehe