Answer:
An equation to represent the given geometric sequence would be [tex]a(x)=5*3^{x-1}[/tex], and a(8) of the geometric sequence will be 10,935.
Step-by-step explanation:
In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.
We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be [tex]a(n)=5*3^{n-1}[/tex]. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.
Lastly, we can use the equation [tex]a(n)=5*3^{n-1}[/tex] to find the 8th term of the sequence by replacing n with 8. So [tex]a(x)=5*3^{n-1}[/tex] would become [tex]a(8)=5*3^{8-1}[/tex], and you will get [tex]a(8)=5*3^{8-1}[/tex] ⇒ [tex]a(8)=5*3^{7}[/tex] ⇒ [tex]a(8)=5*2187[/tex] ⇒ [tex]a(8)=10,935[/tex]. Therefore, the equation for the nth term of the geometric sequence would be [tex]a(n)=5*3^{n-1}[/tex], and the 8th term of the sequence is 10,935.
Have a great day! Feel free to let me know if you have any more questions :)
Given the following segment lengths, find the length of segment AB.
AC : 10
EC : 16
ED :4
Show all your work
2.5 is the length of segment AB.
What is line segment ?
A line segment in geometry has two unique points on the line that define its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.
In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.
BD ║ AE
Δ CBD ≈ ΔCAE by AA similarity corresponding sides are proportional .
CB/CA = CD/DE ⇒ CB/10 = EC - ED/16
CB/10 = 16 - 4/16 ⇒ CB/10 = 12/16
CB = 12 * 10/16 = 7.5
AB= AC - CB = 10 - 7.5
AB = 2.5
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Will give brainliest
Answer:
Below
Step-by-step explanation:
f(x) = x^2+ 6x -5 Use Quadratic Formula with a = 1 b = 6 c = -5
to find :
x = - 3 ± [tex]\sqrt{17}[/tex]
3 5 fraction fill up 6 bowls =
The fraction of the box she puts in each bowl is, 1/10
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
To find the fraction of the box that Evangeline puts in each bowl, we need to divide the total amount of nuts in the box by the number of bowls.
The amount of nuts she has is 3/5 of a box.
To find the amount of nuts in each bowl, we need to divide 3/5 by 6:
(3/5) ÷ 6
To divide by a fraction, we can multiply by its reciprocal:
= (3/5) ÷ (6/1)
= (3/5) x (1/6)
Multiplying across, we get:
= (3/5) x (1/6)
= 3/30
= 1/10
Therefore, Evangeline puts 1/10 of the box in each bowl.
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The complete question:
Evangeline has 3/5 of a box of nuts. She uses it to fill 6 bowls. What fraction of the box does she put in each bowl.
Paul gross weekly salary is $456 what is the maximum monthly rent he can afford?
Answer:
A metal disk 12cm in diameter and 5cm thick is melted down and cast into a cylindrical bar of diameter 5cm . How long is the bar
What is t statistic table ?
The t statistic table is the t-test table is used to evaluate proportions combined with z-scores.
In Statistics, a t-test, can be expressed similarly as a statistical hypothesis test where the test statistic maintains a student’s t-distribution, if the null hypothesis is set. Hence, we know we can use the t-test table here.
The t-test table is used to evaluate proportions combined with z-scores. This table is used to find the ratio for t-statistics. The t-distribution table displays the probability of t-values from a given value. The acquired probability is the t-curve area between the t-distribution ordinates, i.e., the given value and infinity.
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I NEED HELP ASAP!!!
Answer:
x = 30
Step-by-step explanation:
ΔABC is a right-angled triangle where:
∠C = 90°
Sum of interior angles in any triangle = 180°
Therefore:
x° + 2x° + 90°= 180°
3x° + 90° = 180°
3x° = 180° - 90°
3x° = 90°
x = [tex]\frac{90}{3}[/tex]
∴Value of x = 30
Answer:
[tex]x[/tex] is equal to [tex]30\textdegree[/tex]
Step-by-step explanation:
The sum of the interior angles in a triangle is 180 degrees. This is because a triangle is a polygon with three sides and three angles, and the sum of the angles in any polygon can be found by using the formula:
sum of interior angles = (n - 2) x 180 degrees
Note: n is the number of sides.
A triangle has 3 sides. So substituting 3 in for n gives us
(3 - 2) x 180 degrees = 180 degrees
So the sum of the interior angles in a triangle is always 180 degrees.
In this example we can say that [tex]\angle A +\angle B+ \angle C=180\textdegree[/tex]
We are given a right triangle. A right angle is equal to 90 degrees.
We can conclude that
[tex]x+2x+90=180[/tex]
Lets solve for [tex]x[/tex].
Subtract 90 from both sides.
[tex]x+2x=180-90[/tex]
[tex]x+2x=90[/tex]
Add [tex]x[/tex] and [tex]2x[/tex].
[tex]3x=90[/tex]
Divide both sides by 3.
[tex]x=\frac{90}{3}[/tex]
[tex]x=30[/tex]
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Explain why you can write the product (26) 23• (26) 15as the single power (26) 38 .
The reason [tex]26^{23[/tex] x [tex]26^{15[/tex] can be written as [tex]26^{38[/tex] because both have same base and power get added.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
We have [tex]26^{23[/tex] x [tex]26^{15[/tex]
Now, using the property of exponents and power if the base of number same and in relation of multiplication then the power get added.
So, [tex]26^{23[/tex] x [tex]26^{15[/tex]
= [tex]26^{23 + 15[/tex]
and, 23+ 15 = 38
= [tex]26^{38[/tex]
So, the exponent can written with power of 38 as the power gets added.
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YOU GUYS I’M BEGGING YOU
A ball is dropped from a height of 64 feet. It
rebounds three-fourths of the height from which it falls every time it hits the ground. Write a function that models the height the ball
reaches after each time it hits the ground.
Answer:
This is a standard problem if GP (Geometric Progression) as the height of the ball is getting reduced by 25% every-time it touches the ground.
Step-by-step explanation:
how do you graph 3x+2y=12 on a graph? i need to graph y=5x-7 and 3x+2y=12 to see where they intersect.
The solution of the system of equations is equal to (2, 3).
What is a point of intersection?In Mathematics, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (2, 3).
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How can i learned maths hardly?
Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.
Some tips that may help you learn maths quickly and efficientlyStart with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.
Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.
Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.
Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.
Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.
Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.
Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.
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What is 56 prime factors?
The prime factorization of 56 is the process of breaking 56 down into its prime factors. The prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
One way to calculate the prime factorization of 56 is to use a factor tree. To begin, find two numbers that multiply together to equal 56. The two factors that multiply together to equal 56 are 8 and 7. Since 8 and 7 are both prime numbers, they can be written as the prime factors of 56: 56 = 8 x 7.In mathematical terms, the prime factorization of 56 can be expressed as 56 = 2 x 2 x 2 x 7, where 2 is multiplied by itself three times and then multiplied by 7. This is because 56 can also be written as 2 x 2 x 2 x 7, which is the same as 8 x 7.The prime factorization of 56 can also be expressed as the product of the prime exponents: 56 = 2^3 x 7^1. Here, 2 is raised to the third power, and 7 is raised to the first power. This expression is equivalent to 8 x 7.In summary, the prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
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Four of the following statements are correct descriptions of a Normal curve. Which one is NOT a characteristic of a Normal curve?
A. It is symmetric.
B. Its spread increases as its mean increases.
C. It is bell-shaped.
D. Its mean is equal to its median.
E. It is single-peaked (unimodal).
(D) Its mean is equal to its median is NOT a characteristic of a Normal curve.
While it is true that the mean and median are equal in a symmetrical distribution like the Normal curve, not all distributions with equal mean and median are symmetrical and Normal.
In a Normal distribution, the mean, median, and mode are equal and located at the center of the bell-shaped curve. However, in a skewed distribution, the mean and median may still be equal but the distribution will not be symmetrical or bell-shaped.
The most important continuous probability distribution in probability theory and statistics is known as the Normal Distribution, commonly known as the Gaussian Distribution.
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3(x+5)<5(-x+18)
??????
Answer:
Step-by-step explanation:
3(x+5)<5(-x+18)
3x+3x5<5(-x)+5x8
3x+15<-5x+40
3x-(-5x)<40-15
3x+5x<25
8x<25
x<25/8
Sally is near the end of a three year lease on a car with an original MSRP of $38,000. Her leasing company claims that the car is now worth only $28,500. Which percentage represents the residual value of Sally’s leased car?a.25%b.33%c.67%d.75%
The residual value of Sally's leased car is 75%.
So, the answer is d. 75%.
To find the residual value of Sally's leased car, we can divide the value claimed by the leasing company by the original MSRP and multiply by 100 to express the answer as a percentage.
MSRP stands for Manufacturer's Suggested Retail Price. It is the price recommended by the manufacturer of a product for its retail sale.
Residual value refers to the estimated value of an asset at the end of its lease or at a specified future date. It is used in the context of lease financing or depreciation calculations and is usually expressed as a percentage of the original value of the asset. In the context of a car lease, the residual value refers to the estimated value of the car at the end of the lease term.
The residual value is:
= $28,500 / $38,000 * 100
= 75%
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proportionality constant between 3.56 and 13.35?
5 and 18.75
6.12 and 22.95
(finish the chart )
what pounds to cost
(constant)?
The constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.
What is the Constant of Proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables.
The proportionality constant, k, is often used.
So, the Constant of Proportionality is as follows:
C = y/x
Now, insert values as follows:
C = y/x
C = 13.35/3.56
C = 3.75
Therefore, the constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.
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Correct question:
Proportionality constant between 3.56 and 13.35?
A B C D E F G H I J K L M N O P Q R S T U V W X Y AND Z NOW I KNOW MY ABCS NEXT TIME WONT YOU SING WITH MEEEEEEEEE
_____________ is multiplying the numerator of the first fraction times the denominator of the second and multiplying the denominator of the first times the numerator of the second.
Answer:
Step-by-step explanation: umm i'm a middle schooler so i tried i'm sorry.
Step 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________ What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answer: The final step in solving the inequality -2(5 - 4x) < 6x - 4 would be to isolate x on one side of the inequality. In the previous step (-6 < -2x), we have -2x on one side of the inequality and -6 on the other. To isolate x, we divide both sides of the inequality by -2:
-6 ÷ -2 < -2x ÷ -2
Since dividing by a negative number reverses the inequality direction, we get:
3 > x
So, the final solution to the inequality -2(5 - 4x) < 6x - 4 is x > 3. This means that all values of x that are greater than 3 satisfy the inequality.
Step-by-step explanation:
y=3x-8
3x+2y=2 GRAPH
Answer:(x,y)=(8/3+y/3,-3-y/2
Step-by-step explanation:
y=3x-8 3x+2y=2 next simplify
8/3+y/3 -x-2/3y=-2/3 multiply both sides by -1/3
x=8/3+y/3 -x-2/3y=-2/3 eliminate at least 1 variable
y=-3-y/2
ordered pair to the solution 0=0 & 2=2
Pls help me I am struggling and neither me or my mom can figure it out
Mark has a bag containing a mixture of 30 green and white
marbles. Without looking, he guesses that half of the marbles in
the bag are green. He randomly selected 1 marble from the bag,
recorded the color, and returned the marble to the bag. After 15
trials, Mark has drawn 10 green marbles and 5 white marbles.
Which of the conclusions below is best supported by his data?
The best conclusion is:
The bag contains more green Marbles than white marbles.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The bag contains 10 green marbles and 20 white marbles.
The bag contains an equal amount of each color.
The bag contains more green than white marbles.
After 15 trials, Mark has drawn 10 green marbles and 5 white marbles
So, the Probability of Total green Marbles
= (10/15) x 30
= 20
Probability of Total White Marbles
= (5/15) x 30
= 10
So, The bag contains more green Marbles than white marbles.
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The punnett square shows the possible genotype combinations of two parents who are heterozygous for a particular trait. What is the probability of the parents having a child who is homozygous dominant for this trait? 0% 25% 50% 75%.
The probability of the parents having a child who is homozygous dominant for this trait is 25%
In the given question, there is a particular character that has two alleles Y dominant allele and y recessive allele. Both parents are heterozygous for the trait that is encoded as Yy cross with Yy.
Cross between: Yy X YyIf both parents carry only one copy of a recessive gene, the likelihood of a child having the recessive trait is one in four.Offspring are produced: YY: 2Yy: yyHomozygous would be represented for dominant - YYThere is one YY out of 4 offspring(1/4)x100 = 25%
Thus, the correct probability would be 25%
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Bodin Company manufactures finger splints for kids who get tendonitis from playing video games. The firm had the following inventories at the beginning and end of the month of January. Jan 1 Jan 31 Finished goods$125,000 $117,000 Work in process 233,000 251,000 Raw material 133,000 124,000 The following additional data pertain to January operations. Raw material purchased$190,000 Direct labor 350,000 Actual manufacturing overhead 170,000 Actual selling and administrative expenses 110,000 The company applies manufacturing overhead at the rate of 60 percent of direct-labor cost. Any overapplied or underapplied manufacturing overhead is accumulated until the end of the year. Compute the company's prime cost for January.
The company's prime cost for January is 556000.
As per the data given:
Bodin Company manufactures finger splints for kids who get tendonitis from playing video games.
The firm had the following inventories at the beginning and end of the month of January.
January 1 January 31
Finished goods---------$125,000----------------$117,000Work in process--------$233,000---------------$251,000Raw material-------------$133,000----------------$124,000The following additional data pertain to January operations.
Raw material purchased------------------------------------$190,000Direct labor------------------------------------------------------350,000 Actual manufacturing overhead--------------------------170,000Actual selling and administrative expenses----------110,000Here we have compute the company's prime cost for January.
First add Raw materials, January 1 with Raw materials purchased and then subtract Raw materials, January 31 from this sum and then later add up the Direct labor to the result.
The final result will be the prime cost for January
Raw materials, January 1_______133000(+) Raw materials purchased____190000(-) Raw materials, January 31____117000Raw materials used___________206000(+) Direct labor______________ 350000Prime cost__________________556000Therefore the prime cost is 556000.
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Micro economics, I will give brainliest if you get this correct
Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources
Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.
Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.
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Kayla rolls a die 84 times. How many times can she expect to roll a 3?
A. 14
B. 21
C. 12
D. 18
Answer:
[tex]\huge\boxed{\sf 14\ times}[/tex]
Step-by-step explanation:
Formula:[tex]\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}[/tex]
Solution:If we roll a die 1 time, the probability of obtaining a 3 is:
= 1 / 6
Because a die has total 6 faces, out of which 3 is only 1.
But, if we roll it 84 times, it becomes:
= [tex]\displaystyle \frac{1}{6} \times 84[/tex]
= 84/6
= 14 times[tex]\rule[225]{225}{2}[/tex]
Speedy Auto Repairs uses a job-order costing system. The company's direct materials consist of replacement parts installed in customer vehicles, and its direct labor consists of the mechanics' hourly wages. Speedy's overhead costs include various items, such as the shop manager's salary, depreciation of equipment, utilities, insurance and magazine subscriptions and refreshments for the waiting room.
The company applies all of its overhead costs to jobs based on direct labor-hours. At the beginning of the year, it made the following estimates:
Direct labor-hours required to support estimated output $12,000
Fixed overhead cost $114,000
Variable overhead cost per direct labor-hour $1.00
Required:
1. Compute the predetermined overhead rate.
2. During the year, Mr. Wilkes brought in his vehicle to replace his brakes, spark plugs, and tires. The following information was available with respect to his job:
Direct materials $626
Direct labor cost $292
Direct labor hours used 4
Compute Mr. Wilkes' total job cost.
3. If Speedy establishes its selling prices using a markup percentage of 40% of its total job cost, then how much would it have charged Mr. Wilkes?
(1) The predetermined overhead rate is $10.50 per direct labor-hour.
(2) Mr. Wilkes' total job cost is $960.
(3) Speedy Auto Repairs would have charged Mr. Wilkes $1344 for the job.
1) To compute the predetermined overhead rate, we need to add the fixed and variable overhead costs, and then divide by the estimated direct labor-hours:
$114,000 + ($1.00 * 12,000) = $126,000
Predetermined overhead rate = $126,000 / 12,000 = $10.50 per direct labor-hour
2) To find Mr. Wilkes' total job cost, we need to add up the costs of the direct materials and direct labor, and then apply the predetermined overhead rate to the direct labor hours used:
Direct materials cost: $626
Direct labor cost: $292
Total direct costs: $626 + $292 = $918
Overhead cost: $10.50 * 4 = $42
Total job cost: $918 + $42 = $960
3) To find the selling price, we need to add a markup of 40% of the total job cost:
Total job cost: $960
Markup: 40% * $960 = $384
Selling price: $960 + $384 = $1344
So, Speedy Auto Repairs would have charged Mr. Wilkes $1344 for the job.
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(-2 -2) and y=8/3x-5 in slope intercept form
The equation of a line perpendicular to line y = 8/3x-5 in slope-intercept form that contains point (-2, -2) is y = -3x/8 - 11/4.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
8/3 × m₂ = -1
m₂ = -3/8.
At data point (-2, -2), a linear equation of this line can be calculated in point-slope form as follows:
y - (-2) = -3/8(x - (-2))
y + 2 = -3/8(x + 2)
y = -3x/8 - 3/4 - 2
y = -3x/8 - 11/4
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Solve and show your work.
The garden has 3 times as
many cabbages as carrots. If
there are 36 cabbages, how
many carrots are there? [easy points]
Answer:
12 carrots
Step-by-step explanation:
If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much. The answer would be 12 carrots.
36/3=12
What is 62kg in pounds ?
62kg is equivalent to approximately 136.7 pounds and both are unit of measurement of weight.
The conversion factor from kilograms to pounds is 2.20462. To convert kilograms to pounds, you simply multiply the weight in kilograms by this conversion factor.
Therefore, to convert 62kg to pounds, we can multiply 62 by 2.20462, which gives us approximately 136.7 pounds.
It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.
When traveling or communicating with people from different countries, it's important to be able to convert between different units of measurement.
Online converters or calculators can be useful tools to quickly and accurately convert between kilograms and pounds, or other units of measurement, as needed.
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PLEASE HELP!! WILL MARK YOU BRAINLIEST!!! LOTS OF LOVE!!! ♡♡
1) Mika can eat 21 hot dogs in 6 minutes. She wants to know how many minutes
it would take her to eat 35hot dogs if she can keep up the same pace.
How many minutes would it take her to eat 35 hot dogs?
Answer:
10 minutes
Step-by-step explanation:
21/6 will give us how much hot dogs in 1 minute
You then get 3.5 hot dogs per minute.
For 35 hot dogs do 35/3.5 which gives us the amount of time it wil take for Mika to eat 35 hot dogs
Dave spent $6 on a pack of 3 test tubes. Which shows the money spent per test tube?
An expression which shows the money spent per test tube is u = 6/3.
How to determine the unit price?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the unit price, we would determine the unit rate for one pack of 3 test tubes by using the following mathematical expression;
Unit price = Cost of test tubes/Number of test tubes
Substituting the given parameters into the unit price formula, we have the following;
Unit price = $6/3
Unit price = $2.
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