To convert an area from inches to centimeters, conversion factor should be 15.24 square centimeters.
To convert an area from inches to centimeters, we use the conversion factor of 2.54 cm per inch.
This means that for every inch, there are 2.54 centimeters. In order to find the area in centimeters, we first need to find the area in inches, and then multiply it by 2.54.
To find the area, we use the formula
=> area = length x width.
Let's say the length of a rectangle is 2 inches and the width is 3 inches. The area of this rectangle would be 6 square inches
=> (2 x 3 = 6).
To convert this area to square centimeters, we multiply the area in inches by 2.54.
So,
=> 6 square inches x 2.54 = 15.24 square centimeters.
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the lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are $4$, $5$, $6$, $8$, $9$, and $10$ centimeters. what is the number of centimeters in the length of a side of this hexagon? express your answer as a common fraction in simplest radical form.
The number of centimeters in the length of a side of this hexagon is 14√3/3 centimeters.
The lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are 4, 5, 6, 8, 9 and 10 centimeters.
Finding the side of this hexagon using the Pythagorean Theorem
Let the side of the hexagon is s.
So according to theorem
s^2 = (s/2)^2 + 7^2
Now solving
s^2 = s^2/4 + 49
Subtract 49 on both side, we get
s^2 - 49 = s^2/4
Multiply by 4 on both side, we get
4s^2 - 196 = s^2
Subtract s^2 + 196 on both side, we get
3s^2 = 196
Divide by 3 on both side, we get
s^2 = 196/3
Taking square root on both side, we get
s = 14/√3
Multiply and divide by √3
s = 14√3/3
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assume that you purchase a box of cereals every week and that each box contains a coupon. there are n different types of coupons in total (all of them equally likely to be in a box) and your goal is to collect all of them. what is the probability that you collect all n coupons in exactly n weeks?
This probability is approximately [tex]\frac{1}{e}[/tex], which is around 0.37, that we collect all n coupons in exactly n weeks.
The probability of collecting all n coupons in exactly n weeks is very low, as it is dependent on getting a unique coupon every week for n weeks. This is known as the "Coupon Collector's Problem".
The probability can be calculated using the formula:
[tex](1/n) * (1 - (1 - \frac{1}{n})^n)[/tex]This formula can be broken down as follows:
1/n represents the probability of getting the first unique coupon in the first week, it's 1/n because there are n different types of coupons and all of them are equally likely to be in a box.
[tex](1 - (1 - \frac{1}{n})^n)[/tex]represents the probability of getting the remaining n-1 unique coupons in the next n-1 weeks.[tex](1 - \frac{1}{n} )[/tex] represents the probability of not getting a unique coupon in any given week. And raising it to the power of n gives the probability of not getting a unique coupon in n weeks.So, by subtracting this probability of not getting a unique coupon in n weeks from 1, we get the probability of getting at least one unique coupon in n weeks.
Finally, by multiplying the probability of getting the first unique coupon [tex]\frac{1}{n}[/tex] with the probability of getting at least one unique coupon in the next n-1 weeks, we get the overall probability of collecting all n coupons in exactly n weeks.
Therefore, the probability is approximately [tex]\frac{1}{e}[/tex], which is around 0.37, this is a very low probability, and in practice it would take a much longer time to collect all n coupons.
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can someone help me? and also write the answer down so i can copy it please thank you
Answer:
You run at a faster rate. The rate is 19 feet per second or about 5.7912 meters per second.
Step-by-step explanation:
The expression representing the friend says the friend is running at a speed of 14 feet per second with a head start of 50 feet. The table show that you run at a speed of 38 feet per 2 seconds otherwise said as 19 feet per second.
19 > 14, so you run faster.
Find the mean of the values. Round to two decimal places.
79, 83, 54, 77, 98 61, 88
Answer:
77.14
Step-by-step explanation:
To find the mean(average) we add all the values and divide the sum by the number of values. Here, we are given 7 total values.
The sum of these values = 79 + 83 + 54 + 77 + 98 + 61 + 88 = 540
Because there are 7 total values we divide the sum by 7 to get the mean
So mean = 540 / 7 = 77.14 (rounded to two decimal places)
A cylindrical rod measures 4 inches long and the circumference of one of its bases is 12π inches. the rod is cut into two equally-sized pieces and then all surfaces are painted. what is the area that is painted? use π≈3.14.
The total surface area painted is 644.16 square inches.
Let the radius of the cylindrical rod be r. The circumference of the base is given as 12π, which can be converted to the diameter as:
diameter = circumference / π = 12π / π = 12 inches.
So, the radius of the cylindrical rod is half of that. That is 6 inches.
The area of one base of the cylindrical rod can be calculated as π [tex]r^2[/tex], which is:
π * [tex]6^2[/tex] = 3.14 * 36 = 113.04 square inches.
The surface area of one-half of the cylindrical rod can be calculated by:
2 * π * r * l + 2 * π * [tex]r^2[/tex], where l is the length of the rod.
Since the length of the rod is 4 inches, the surface area of one-half of the cylindrical rod can be calculated by:
2 * π * 6 * 4 + 2 * 113.04 = 96 + 226.08 = 322.08 square inches.
Given that two equally sized pieces are cut, the total surface area painted would be 2 * 322.08 = 644.16 square inches.
Therefore, the total surface area painted is 644.16 square inches.
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use the conversion factor along with the symmetry of the circle to complete the degree or radian measure of the missing angles. give the answer in exact, simplified form.
The conversion factor along with the symmetry of the circle to complete the degree or radian measure of the missing trigonometric angles = 90° = 90° × (π/180°) = π/2.
A degree, which is referred to as the degree of arc or arc degree, is the unit of measuring a plane angle. It is denoted by the symbol (°). 360° is the angle measure for a complete rotation. A complete rotation is denoted by the angle measuring 360° and the instrument used to measure an angle in degrees is known as the protractor.
Radian is another unit of measuring an angle in geometry. One radian is the angle that is formed at the center of a circle by an arc whose length is equal to the radius 'r' of the circle. One complete counterclockwise rotation is equal to 2π in radians. The below-given image shows the measure of one radian as 57.296°. Also, a right angle is expressed as π/2 radians, and a straight angle is expressed as π radians.
We can compare the measure of angles for a complete rotation in radian and degrees as,
360 Degrees = 2π Radians
180 Degrees = π Radians
In order to convert degrees to radians manually, we use the formula: Radians = Degrees × (π/180°). We can follow the steps given below to calculate the measure of an angle given in degrees to radians.
We know, 1°= (π)/180 radians. So, to convert the angle given in degrees to radians we multiply it with π/180°.
Angle in Radians = Angle in Degrees × π/180°.
Simplify the values and express the answer in radians.
Example: Convert 90 degrees to radians.
Solution: 90° = 90° × (π/180°) = π/2.
Therefore,
The conversion factor along with the symmetry of the circle to complete the degree or radian measure of the missing trigonometric angles = 90° = 90° × (π/180°) = π/2.
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640 word it take him 4 minute how long would it take to read 800 at the ame peed
The person will read 800 words in 5 minutes if he does so at the same speed.
The current average speed of the person will be given by the formula -
Average speed = number of words read ÷ total time taken
Keep the values in formula
Average speed of the person = 640/4
Performing division on Right Hand Side of the equation
Average speed of the person = 160
Now, using the same formula to find the time.
Total time required = 800/160
Performing division on Right Hand Side of the equation
Total time required = 5
Thus, it will take him 5 minutes to read.
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Help plsssssssssssssssssss
Answer: Its c
Step-by-step explanation: -2 - 6 is -8
explain the dangers of utilizing only a subset of the performance equation as a performance metric. use examples if necessary.
the dangers of utilizing only a subset of the performance equation as a performance metric
SUBSET ARE
Clock rate of P1 = 4 GHz
Clock rate of P2 = 3 GHz
Average CPI of P1 = 0.9
Number of Instructions = 5.0E9 = 5 × 10^9
Clock rate of P2 = 3 GHz
Average CPI of P2 = 0.75
Number of Instructions = 1.0E9 = 10^9
To find: If the computer with largest clock rate has the largest performance?
As given in the question, clock rate of P1 = 4 GHz which is greater than clock rate of P2 = 3 GHz
According to the performance equation:
CPU Time = instruction count * average cycles per instruction/ clock rate
CPU Time = I * CPI / clock rate
Where instruction count refers to the number of instructions.
It is not true that computer with the largest clock rate as having the largest performance.
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What method proves this two triangles congruent?
SOMEONE HELP ME 40 POINTS! A central angle measuring 90° Intercepts an arc In a circle whose radlus is 8.
What Is length of the arc of the circle formed by this central angle? Round the length of the arc to the nearest hundredth
of unit.
Answer:
12.56 units------------------------
The 90° arc is representing the quarter of circle.
Its length is the quarter of the circumference of circle with radius of 8.
The arc length is:
C/4 = 2πr/4 = 2*3.14*8/4 = 12.56what is the difference between k means clustering and hierarchical clustering?
K-means clustering is an iterative algorithm that partitions a data set into k clusters, where k is predefined.
It works by first randomly selecting k points as cluster centers, also known as centroids. All points are then assigned to the nearest cluster center based on a distance metric, such as Euclidean distance. This process is repeated until the centroids no longer move, which is when the clusters have stabilized. The formula for calculating the distance between two points is d = sqrt((x1-x2)^2 + (y1-y2)^2).
Hierarchical clustering is a type of clustering algorithm that builds a hierarchy of clusters. It starts by assigning each point to its own cluster, then combines the two closest clusters and repeats the process. The calculation used to determine the distance between two clusters is the distance between their two closest points, also known as the single linkage method. The formula for calculating the distance between two clusters is d = min(d1, d2, ..., dn), where d1, d2, ..., dn are the distances between the two closest points in the two clusters.
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special right triangle
The missing length of the triangle be 7.93725.
What is meant by Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, [tex]$c^2=a^2+b^2$$[/tex], are equal to the total of the squares on the legs.
Remember that in every right triangle, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the two legs side (the two sides that meet at a right angle).
With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares.
By using Pythagorean Theorem is:
[tex]$c^2=a^2+b^2$$[/tex]
where c exists the hypotenuse and a and b exists the sides.
[tex]$\sqrt{\left(12^2-9^2\right)}=7.93725$$[/tex]
Therefore, the correct answer is 7.93725.
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a plane takes 6 hours to fly from san francisco to new york, and 5 hours to return back. the plane's airspeed is 880 miles per hour, from new york to san francisco. what is the speed of the wind
The speed of wind is 73.335 miles per hour. The distance between San Francisco and New York remains constant and we a considering wind speed is also constant.
It is known that,
The relation between distance , speed
the distance travelled = speed × time
Put the values of given data in above formula.
Then 880×5= 4400 miles
the distance between NY to SF = 4400 miles.
Speed at which the plane was travelling from SF to NY = 4400/6 =733.33 miles per hour.
Differences in the speed is caused by the relative wind speed, which equals (880-733.33)/2 = 146.67/2 =73.335 miles per hour
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Write down the percentage multiplier to find 67% of an amount.
Answer:
To find 67% of an amount, we use the percentage multiplier of 0.67.
This is because 67% can be expressed as 67/100, and when we divide a number by 100, we are essentially moving the decimal point two places to the left. So, 67/100 can also be written as 0.67.
Therefore, the percentage multiplier to find 67% of an amount is 0.67.
marie needs 380 quarts of soil to fill her vegetable planter. a bag of soil contains 64 quarts and costs $9.50. how much will it cost marie to fill the planter with soil
The cost Marie to fill the planter with soil to fill her vegetable planter is $57.
A bag of soil has 64 quarts and is costing 9.50
And required soil is 380 quarts so,
380 → X
64 → 9.50
By using cross multiplication method,
64 × X = 380 × 9.50
X = 3610/64
X = 56.4
X ≈ $57
Cross multiplying is the process of multiplying the denominator of the second fraction by the numerator of the first fraction, which is on one side of the equals to symbol. In a similar way, the denominator of the first fraction is multiplied by the numerator of the second fraction. The butterfly method, also referred to as cross-multiplication, has another name.
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I really need help with this question . Please and thank you
Answer:
8.5m
Step-by-step explanation:
7. What is the equation of a quadratic function P with rational
coefficients that has a zero of 3 + i?
The equation of a quadratic function P with rational coefficients that has a zero of (3 + i) is p(x) = x² - 6x + 10.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The complex number value is given as (3 + i)
Since, x = (3 + i) is a complex zero of p(x), then -
It is known that , the complex zeros occur in pair.
So, x=(3 - i) is also a complex zero of the quadratic function of p(x).
So, {x − (3 + i)} and {x − (3 - i)} are the factors of p(x).
Substitute the values to form a quadratic function -
p(x) = {x − (3 + i)}{x − (3 - i)}
Open the brackets and evaluate -
p(x) = (x - 3 + i)(x - 3 - i)
Use the arithmetic operation of multiplication -
p(x) = x(x - 3 - i) - 3(x - 3 - i) + i(x - 3 - i)
p(x) = x² - 3x - ix - 3x + 9 + 3i + ix - 3i - i²
Collect all the like terms -
p(x) = x² - 3x - 3x - ix + ix + 9 + 3i - 3i - i²
p(x) = x² - 6x + 9 - i²
Substitute the value of i² = -1 into the equation -
p(x) = x² - 6x + 9 - (-1)
p(x) = x² - 6x + 9 + 1
p(x) = x² - 6x + 10
Therefore, the quadratic function is x² - 6x + 10.
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PLS HELPPP!!!!! A student is running a 5 km race he runs 1 km every three minutes select a function that describes his distance from the finish line after X minutes
Answer:
Step-by-step explanation:
multiply 5km by 3 minutes he would have run the 5km in 1 5 minutes
Which of the following is not true about continuous random variables? (Points : 5) The entire area under each of the curves equals 1.Some may be described by uniform distributions or exponential distributions.They can only be integer values.The area under each of the curves represents probabilities.They have an infinite set of values.
The statement "They can only be integer values" is not true about continuous random variables.
Continuous random variables can take any value within a certain range, not just integers. They are characterized by a probability density function (pdf) that describes the distribution of the variable over a range of values. The pdf is a continuous curve, not a set of discrete points.
The other statements about continuous random variables are true: the entire area under each of the curves does equal 1, some may be described by uniform distributions or exponential distributions, the area under each of the curves represents probabilities, and they have an infinite set of values.
Therefore, The statement "They can only be integer values" is not true about continuous random variables.
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Consider the two functions below
Function A:
A hiker starts tracking her climb 4/5 mile from the trailhead and climbs at a rate of 2 miles per hour.
(FUNCTION B IN PHOTO)
Select all true statements about function A and function B.
The true statements are Function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
We have to first find the linear equations of the functions.
Given for function A,
Let x be the number of hours.
Function A can be represented as f(x) = 4/5 + 2x
Equation in slope intercept form is y = mx + c, where m is the slope and c is the intercept along Y axis.
Y intercept is the point of the line where it touches the Y axis. x coordinate will be zero here.
x intercept is the point of the line where it touches the X axis. y coordinate will be zero here.
y = 2x + (4/5), in slope intercept form.
Here 2 is the slope and 4/5 is the y intercept.
When y = 0, 2x + (4/5) = 0, then x = -2/5
x intercept = -2/5
For function B,
we have when x = 0, f(x) = y = 2/3
y intercept = 2/3
Slope = [(2/3) - (-25/3)] / [0 - -3]
= [27/3] / 3
= 9 / 3
= 3
Equation in slope intercept form of function B is,
y = 3x + 2/3
When y = 0, 3x + 2/3 = 0, then x = -2/9
x intercept = -2/9
So function B has greater slope as slope is 3 for B and 2 for A.
Function A has greater y intercept as y intercept for A is 4/5 and for B is 2/3.
Function B has greater x intercept as x intercept is -2/9 for B and -2/5 for A.
Hence the correct options are function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.
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a law firm is going to designate associates and partners to a big new case. the daily rate charged to the client for each associate is $500 and the daily rate for each partner is $1400. the law firm designated 3 times as many associates as partners to the case and was able to charge the client $5800 per day for these lawyers’ services. Determine the number of associates assigned to the case and the number of patented assigned to the case.
Answer:
there was 6 associates assigned to the case and 2 partners
Step-by-step explanation:
what i did was did 1400 times 2 and 500 times 6. then i did 6 divided by 3 which gave me 2. So there are 3 times more associates.
Hope this helped
Isabelle invests $4350 at 7.6%/a compounded quarterly. How long will it take for her investment to grow to$10 000?
it will take Isabelle about 10.33 years for her investment to grow to $10,000.
To calculate the time it takes for Isabelle's investment to grow to $10,000, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A is the amount of money at the end of t years, P is the initial amount (4350), r is the interest rate per year (7.6%), n is the number of times compounded per year (4, since it's compounded quarterly), and t is the number of years.
We can rearrange the formula to solve for t:
t = (log(A/P)) / (log(1 + r/n))
Plugging in the values, we get:
t = (log($10,000 / $4350)) / (log(1 + 7.6% / 4))
Using a calculator, t = approximately 10.33 years.
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Im sorry guys just need this and I should get an A is the answer A,B,C, or D thanks much gratitude
Answer:
C
Step-by-step explanation:
For the second graph
the equation should be:
y = 1/2 x^2
Which makes the graph true.
You can try plug numbers into x to check your answer.
I need to find the slope of each line and show my work for it
Answer:
3) m = -3/2
4) m = 3/2
5) m = 5/3
6) m = 7/3
7) m = -3
8) m = 7/3
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
3/ ( -4, 0) ( -2, -3)
The y decrease by 3, and the x increase by 2, so the slope is
m = -3/2
4/ (2,0) (0, -3)
The y decrease by 3, and the x decrease by 2, so the slope is
m = -3/-2 = 3/2
5/ (-1,2) (-4, -3)
The y decrease by 5, and the x decrease by 3, so the slope is
m = -5/-3 = 5/3
6/ (4,3) (1, -4)
The y decrease by 7, and the x decrease by 3, so the slope is
m = -7/-3 = 7/3
7/ (1,2) (3, -4)
The y decrease by 6, and the x increase by 2, so the slope is
m = -6/2 = -3
8/ (0,3) (-3, -4)
The y decrease by 7, and the x decrease by 3, so the slope is
m = -7/-3 = 7/3
∫9cosxdx= 9sin(x) c. ∫(n 2)πnπ 9cosxdx= 9sin(n*pi 2pi)-9sin(npi) , where n is an arbitray integer.
9sin is the integral of 9cosx (x). 9sin(n*/2) - 9sin(n) is the integral of (n2)* to n* in the expression for 9cosx.
A fundamental trigonometric integration is the integral of 9cosx. The trigonometric substitution formula and the integral of cosx formula, sin, can both be used to calculate this integral (x). This indicates that 9sin is the integral of 9cosx (x).The integral of 9cosx from (n2)* to n* is a little more challenging. The trigonometric substitution formula and the integral of cosx formula can both be used to solve this integral. Sin is the integral of cosx (x). The integral of (n2)* to (n*) of 9cosx is therefore 9sin(n*/2) - 9sin(n). Accordingly, the integral of the function from n* to n* is equal to the difference between the integrals of the functions from 0 to n* and from 0 to n*.
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in a hypertensive study, nurses took the blood pressure readings of 250 participants. to determine the accuracy of their readings, they wanted to test the sensitivity of their instruments. if the number of true positives is 40, and the total number of participants with disease (true positives plus false negatives) is 55, the sensitivity of the instrument is . group of answer choices
The sensitivity of the instrument can be calculated as the ratio of true positives (40) to the total number of participants with disease (55) is 73%.
Sensitivity, also known as the true positive rate or recall, is a measure of the accuracy of a diagnostic test or medical screening tool in detecting positive cases. In medical research, sensitivity is an important aspect to evaluate the performance of a diagnostic test.
In a hypertensive study, if a participant has a blood pressure reading above a certain threshold, they are diagnosed as having hypertension (a positive case). Sensitivity is calculated as the proportion of true positive cases (those with hypertension and correctly diagnosed) to the total number of actual positive cases (those with hypertension, both correctly and incorrectly diagnosed).
The formula for sensitivity is:
sensitivity = true positive / (true positive + false negative)
In the example given, the number of true positives is 40 and the total number of participants with disease (true positives plus false negatives) is 55. So, the sensitivity of the instrument is:
sensitivity = 40 / 55 = 0.73 or 73%
This means that out of all the participants with hypertension, the instrument correctly diagnosed 73% of them.
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A website has 900,000 members. The number y of members increases by 8% each year.
a. Write an exponential function that represents the website membership after t years.
b. How many members will there be after 5 years? Round your answer to the nearest ten thousand.
a. y=
b. about (blank) members
1,156,530 members were in attendance in 2016. You can round it to $1,160,000.
What is an exponential function?The exponential function is represented mathematically by the formula F(x)=exp or e(x). Unless otherwise specified, the phrase generally refers to a real variable's positive-valued function, though it can also be applied to complex numbers and other mathematical objects like matrices and Lie algebras.One of mathematics's most crucial functions is the exponential function (though it would have to admit that the linear function ranks even higher in importance). As the independent variable in an exponential function, the exponent is used. F(x)=2x is a straightforward illustration.Functions that take the form f(x) = axe are referred to as exponential functions. where an is a constant and x is a variable.
500,000 people are registered members of the website as of 2010.
Y members grew by 15% annually.
Members and year have an exponential relationship that is
y = 500,000(1.15)^t
Then in 2016 the number of members present are given by,
y = 500,000(1.15)^6 = 1,156,530.
Hence, 1,156,530 members present in 2016. It can rounded to 1,160,000.
The complete question is:
A website 500,000 members in 2010. The number y of members increases by 15% each year. Write an exponential growth function that represents the website membership t years after 2010. How many members will there be in 2016? Round your answer to the nearest ten thousands
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Which expression is equivalent to 7.5(22 + 1.2s)?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Original equation:}[/tex]
[tex]\mathsf{7.5(22 + 1.2s)}[/tex]
[tex]\huge\textbf{DISTRIBUTE 7.5 within the}\\\\\huge\textbf{parentheses:}[/tex]
[tex]\mathsf{7.5(22 + 1.2s)}[/tex]
[tex]\mathsf{= 7.5(22) + 7.5(1.2s)}[/tex]
[tex]\mathsf{= 165 + 9s}[/tex]
[tex]\mathsf{= 9s + 165}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{9s + 165}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Melanie and noah are baking a birthday cake for franceca. The recipe call for 3/4 meauring cup and noah ha a 1/8 meauring cup. Which cup hould they ue
They should use 6 cup of Noah's measuring cup
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Recipe call = 3/4Noah's cup = 1/8Number of cup = ?Calculating the number of cup the should use:
Number of cup = Recipe call / Noah's cup
Number of cup = (3/4) / (1/8)
Number of cup = 3*8 / 4*1
Number of cup = 24/4
Number of cup = 6
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Correctly written question:
Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?
