Final answer:
The simplified product of the square root of 8 and the square root of 98 is determined by multiplying the numbers under the square roots to get √784, which is a perfect square. Hence, the product simplifies to 28.
Explanation:
To find the simplified product of the square root of 8 and the square root of 98, we can use the property of square roots that allows us to multiply the numbers under the radicals first, before taking the square root of the resultant product. This is a form of simplifying square roots when dealing with exponentials.
Firstly, multiply the numbers inside the square roots:
√8 × √98 = √(8 × 98)
Calculate the product:
8 × 98 = 784
Now we have:
√8 × √98 = √784
By squaring of exponentials, we know that the square root of a perfect square is the base number:
√784 = 28 (since 28 × 28 = 784)
Therefore, the simplified product is 28.
The simplified product of the square root of 8 and the square root of 98 is 28, achieved by using the property of radicals and simplifying the exponents within the radical.
Explanation:To find the simplified product of the square root of 8 and the square root of 98, we can use the property of radicals where the product of two radicals can be combined into one radical, such that √(a) * √(b) = √(ab). To simplify further, we factor each number into its prime factors: 8 = 2³ and 98 = 2 * 7². We then combine the radicals: √(8) * √(98) = √(2³) * √(2 * 7²) = √(2´ * 7²).
Based on the properties of exponents and radicals, we can take the square roots of exponentials by finding which factors have exponents that are multiples of 2. In our case, we have 2´, which simplifies as 2², and 7², which is already a perfect square. Thus, √(2´ * 7²) simplifies to 2² * 7 = 4 * 7 = 28. So the simplified product of √(8) * √(98) is 28.
What is the mode of the given data set? 65, 45, 79, 56, 63, 45, 71, 69, 65, 53, 45
Whenever you see ______ it is a blank spot where I need to fill in information.
An employee at a state park has 43 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 4 rows.
Complete the description of two different ways she can arrange the photos.
She can arrange the photos as
______ rows of 10 photos and 1 row of ______
photos or arrange the photos as ______
rows of 8 photos and 1 row of ______
photos.
Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1400. What was the rate charged per hour by mechanic if the sum of the two rates was $130 per hour
Yesterday, Dustin biked 4 1/2 miles, jogged 2 3/4 miles, and swam 3 1/8 miles. How many miles did he travel while exercising?
Your answer would be 10 3/8 miles
Niona needs $50 to go on a school trip. She sells necklaces for $15 each and bracelets for $5 each. If she raises the money by selling half as many necklaces as bracelets, how many necklaces and bracelets does she sell? Write a system of linear equations that represent this problem.
To solve the problem, create a system of linear equations representing the sale of necklaces and bracelets. The two equations will be 15n + 5b = 50 and n = 0.5b, which describe the total funds raised and the relationship between the number of necklaces and bracelets sold.
Explanation:Niona is trying to raise $50 for her school trip by selling necklaces and bracelets. We need to establish a system of linear equations to represent the problem. Let's define n as the number of necklaces and b as the number of bracelets. According to the problem, Niona sells necklaces for $15 each and bracelets for $5 each, and she sells half as many necklaces as bracelets.
Therefore, we can write the first equation based on the total amount of money raised:
15n + 5b = 50
And the second equation based on the relationship between the number of necklaces and bracelets:
n = 0.5b
Solving this system will give us the number of necklaces and bracelets Niona needs to sell to raise $50 for her trip.
Out of 28 students in a class, 7 have blue eyes. What is the probability a student picked at random from the class does NOT have blue eyes?
A) 1/4
B) 3/4
C) 1/7
D) 6/7
A person needs to pay TK. 500 to by pencils and TK. X for any additinal unit of pencil.If the cumstomer pays a total of TK. 4700 for 1200 pencils what is the value of X?
Answer:
3.50
Step-by-step explanation:
First we take the 500 fee for purchasing pencils off of the total:
4700-500 = 4200
This means we pay 4200 for 1200 pencils; dividing this will tell us the amount per pencil, x:
4200/1200 = 42/12 = 21/6 = 7/2 = 3.5
Thus we pay 3.50 per pencil.
The value of X for any additional pencil is gotten as;
X = 3.5
We are told that base amount for pencils is TK. 500 and amount per pencil is TK. X.
This means formula for total cost for n number of pencils is;
C(n) = 500 + Xn
We are told that a customer pays TK. 4700 for 1200 pencils. Thus;
C(n) = TK. 4700
n = 1200 pencils
Therefore;
4700 = 500 + 1200X
1200X = 4700 - 500
1200X = 4200
X = 4200/1200
X = TK. 3.5 per pencil
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Solve and graph on number line.
a-1 > -9
How many inches are equal to 10 centimeters? Remember, 2.54 cm = 1 in. Round your answer to the nearest hundredth. Do not include units in your answer.
Answer:
10 centimeters = 3.94 .Step-by-step explanation:
We are given 2.54 cm = 1 in.
We need to convert 10 centimeters into inches.
We have 2.54 cm = 1 in.
On dividing both sides by 2.54, we get
[tex]\frac{2.54}{2.54}cm = \frac{1}{2.54} in[/tex]
1cm=[tex]\frac{1}{2.54}[/tex] in.
In order to find the number of inches in 10 centimeters, we need to multiply [tex]\frac{1}{2.54}[/tex] by 10.
On multiplying [tex]\frac{1}{2.54}[/tex] by 10, we get
=[tex]10\times \frac{1}{2.54}[/tex]=3.94.
Therefore,
10 centimeters = 3.94.10 centimeters is approximately equal to 3.94 inches when converted using the conversion factor of 1 inch equals 2.54 centimeters.
The student is asking for conversion of a length measurement from centimeters to inches. Given that 1 inch equals 2.54 centimeters, you can convert 10 centimeters to inches by dividing by the conversion factor. Here's the calculation:
Identify the conversion factor: 2.54 centimeters per inch.
Divide the number of centimeters by the conversion factor: 10 cm \/ 2.54 cm/in = approximately 3.94 inches.
Therefore, 10 centimeters is approximately equal to 3.94 inches when rounded to the nearest hundredth.
How can i find the missing angle of this shape?
What is the outlier in the following set?
28,31,40,26,38,65,39,35,30
The lock on a safe requires a three-digit code to open it. The three digits must each be a number from 0-9 (10 possible numbers). Each number cannot be used more than once in the code. How many codes could there be?
A.1,000
B.720
C.30
D.120
This problem can be solved through permutation in mathematics. Without repetition, with 10 possible digits (0-9), there are 10 choices for the first digit, 9 for the second, and 8 for the third. The total number of 3-digit codes is 10*9*8 = 720.
Explanation:The subject of this question is combinations in mathematics. To solve it, you have to calculate the number of ways you can arrange 3 digits from 0-9 (10 digits), when each digit can only be used once.
This problem is a type of permutation (an ordering or arrangement of objects), specifically a permutation without repetition. With 10 possible digits (0-9), there are 10 choices you can make for the first digit. After the first digit is chosen, there are 9 digits left for the second place, and 8 digits left for the third place.
Therefore, the total number of possible 3 digit codes is calculated as follows: 10*9*8 = 720. Hence, "option B is the correct answer".
Learn more about Permutations here:
https://brainly.com/question/23283166
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Anna calculated the area of parallelogram with a base of 72
5
m and a height of 2 m. Her work is shown here.
Answer:
a , c
Step-by-step explanation:
on edge 2021
What expression is equal to -1/3(2x+15)-3
Giving 10 points! Please help!
Which of the following expresses 12 + 42 by using the GCF of the two numbers? (3 points)
A. 3(9 + 14)
B. 3(4 + 38)
C. 6(2 + 7)
D. 6(6 + 36)
Which figures are familiar?
You are given the following list of values: 5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9 Which values are outliers?
A rectangular horseshoe pit is 53 inches long and 32 inches wide.
What is the area of the horseshoe pit?
ASAP plzzzz help I need answerssss
a day care center charges a $75 enrollment fee plus $100 per week which of the following represents the cost of sending a child to daycare for 14 weeks?
Answer:
cost of sending a child to daycare for 14 weeks is $1475
Step-by-step explanation:
a day care center charges a $75 enrollment fee plus $100 per week
LEt x be the number of weeks
cost of sending a child to day care = 100x + 75
To find the cost for 14 weeks, we plug in 14 for x
cost = 100(14) + 75= 1400+75 = 1475
cost of sending a child to daycare for 14 weeks is $1475
Write a problem that involves finding the unknown measure of a side of a rectangle include the solution?
WILL GIVE BRAINLIEST: Which of the following are solutions to the equation below
x^2+3x-18=0
A 9
B 3
C -3
D 6
E 18
F -6
Sara got 98, 100, 65, 78, 98, 46, 100, 100, 45, and 50 on her reading test. Lee got 97, 67, 89, 99, 100, 45, 79, 89, 58, and 67 on his reading test. What is the mean of Sara's reading test? What is the mean of Lee's reading test? please help with both questions.
Answer:
Saras Mean on her reading test is 78
Lee's Mean on his reading test is 79
Step-by-step explanation:
You add grades for Sara's test together and then you will divide by the= number of graded test there were and you will get 78.
You add Lee's Grades for the test together and divide by the number of graded test there were and you will get 79.
The mean of Sara's reading test scores is 78, and the mean of Lee's reading test scores is 79.
To find the mean (average) score of Sara's and Lee's reading tests, we need to add up all of the scores and then divide by the number of scores.
Let's start with Sara's scores:
Sara's scores: 98, 100, 65, 78, 98, 46, 100, 100, 45, and 50.
Add up Sara's scores:98 + 100 + 65 + 78 + 98 + 46 + 100 + 100 + 45 + 50 = 780
Divide the total by the number of scores (which is 10):Mean of Sara’s scores = 780/10 =78
Now, let's calculate the mean for Lee's scores:
Lee's scores: 97, 67, 89, 99, 100, 45, 79, 89, 58, and 67.
Add up Lee's scores:97 + 67 + 89 + 99 + 100 + 45 + 79 + 89 + 58 + 67 = 790
Divide the total by the number of scores (which is 10):Mean of Lee’s scores = 790/10 = 79
So, the mean of Sara's reading test scores is 78, and the mean of Lee's reading test scores is 79.
At a ballroom dancing lesson there were twenty-three students. Deena danced with six boys, Chloe with seven, Moira with eight and so on for all the girls up to the last girl, Anna, who danced with all the boys. How many boys were at the lesson?
First girl, Deena danced with 6 boys.
Second girl, Chloe danced with 7 boys.
Third girl, Moira danced with 8 boys.
And so last girl, Anna danced with all boys, given is an arithmetic series as 6, 7, 8, ........, a+(n-1)d.
Let's assume number of girls are 'n'.
Last term of a.p. series would be number of boys = a+(n-1)d.
Here a=6 and d=1, so number of boys = 6+(n-1)*1 = 5+n.
Given there were 23 students.
So total students = number of girls + number of boys
23 = n + (5+n)
23 = 2n + 5
2n = 23-5 = 18
n = 9.
Hence, there were 9 girls and 14 boys.
What's the answer to this? Also if you could explain that would be great but you don't have to! (I picked that answer by accident :/)
what is the value of the missing number in the sequence
4,12,36,__,324,972,2916
area of a square when 1 side is 44cm
If f(x) = x2 and g(x) = 1 over 2x + 3 , find g(f(-1)).
What is the sample space when a coin is tossed twice?
Answer:
HH, HT, TT, TH
Step-by-step explanation:
Your welcome.
USA testprep squad waz good
What is the difference in the sum of the exterior angles measures of a rectangular nonagon and a rectangular dodecagon?
The sum of the exterior angles of any polygon is 360 degrees, thus the difference between the sums of the exterior angles of a nonagon and a dodecagon is 0 degrees.
The question asks about the difference in the sum of the exterior angle measures of a nonagon and a dodecagon. The key concept here is that for any polygon, the sum of the exterior angles is always 360 degrees, regardless of the number of sides.
Therefore, the sum of the exterior angles of both a nonagon (9-sided polygon) and a dodecagon (12-sided polygon) would be 360 degrees each. Consequently, the difference in their sums would be 0 degrees.