Answer:
13. 5/8
14. 16/24
15. 15/35
Answers:
13. 5/8
\(\frac{5}{8} \neq \frac{2}{3}\)
14. 16/24
\(\frac{16}{24} \neq \frac{3}{4}\)
15. 15/35
\(\frac{15}{35} \neq \frac{2}{7}\)
Nate runs 8 miles each week. Write an expression for the number of miles he runs in n weeks. Find the number of miles Nate runs in 5 weeks.
Total miles = number of miles per week x number of weeks:
Total = 8n
For 5 weeks, replace n with 5:
Total = 8(5) = 8 x 5 = 40 miles
Answer:
8x, 40 miles
Step-by-step explanation:
He runs 8 miles each week.
8 miles x week
8 x week
To replace week, use a variable, commonly x.
8x
For 5 weeks, plug in the numbers.
x = 5
8 x 5 = 40
40 miles
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Find the sum of 3 and -3
Answer
The sum of 3 and -3 = 0
Explanation
The sum of two numbers is the addition of both numbers.
Hence, the sum of 3 and -3 is written mathematically as
3 + (-3)
But we should also know that adding a negative number is the same as just subtracting that number
3 + (-3)
= 3 - 3
= 0
Hope this Helps!!!
How do you find the maximum or minimum value of a quadratic polynomial?
Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches. Use 3. 14 for pi and round to the nearest tenth
The volume of the cone with height of 9 inches and a diameter of 12 inches is approximately 339.3 cubic inches.
To find the volume of a cone, we need to use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
Since the diameter of the cone is given as 12 inches, we can find the radius as half of the diameter, which is 6 inches. The height of the cone is given as 9 inches.
Now, we can substitute the values of r and h in the formula to get the volume as follows
V = (1/3)πr^2h
= (1/3)×3.14×6^2×9
= 339.12 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the given cone is approximately 339.1 cubic inches.
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use the following information to write an equation in terms of x. then solve the equation and find rs and st. rs
The equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.
To find rs and st, we need to write an equation in terms of x using the given information and then solve for x.
Let's suppose that rs and st are two line segments, and x represents the length of rs. To find the lengths of rs and st, we can set up an equation based on the given information.
From the problem, we know that the length of st is three times the length of rs. This can be expressed as:
st = 3 * rs
Additionally, the total length of rs and st is 32 units. Mathematically, this can be represented as:
rs + st = 32
Now, we can substitute the value of st from the first equation into the second equation:
rs + 3 * rs = 32
Simplifying this equation, we have:
4 * rs = 32
To solve for rs, we divide both sides of the equation by 4:
rs = 32 / 4
rs = 8
Hence, we have found that rs is equal to 8 units.
To find the length of st, we can substitute the value of rs into the first equation:
st = 3 * rs
st = 3 * 8
st = 24
Therefore, the length of st is 24 units.
In summary, the equation in terms of x (rs) is rs + 3 * rs = 32. By solving this equation, we found that rs = 8 and st = 24.
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if λ 5 is a factor of the characteristic polynomial of a , then 5 is an eigenvalue of a .
If λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.
Given that λ = 5 is a factor of the characteristic polynomial of matrix A, we need to determine whether 5 is an eigenvalue of A or not. Definition of Characteristic Polynomial:
A matrix A is a linear transformation whose characteristic polynomial is given by;
p(x) = \text{det}(xI - A)
Definition of Eigenvalue:
Let A be a square matrix of order n and let λ be a scalar.
Then, λ is called an eigenvalue of A if there exists a non-zero vector x, such that
A \bold{x} = \lambda \bold{x}
For some non-zero vectors x is known as the eigenvector.
Now, let's prove if 5 is an eigenvalue of A, or not.
According to the question, λ = 5 is a factor of the characteristic polynomial of A.Therefore, p(5) = 0.
\Rightarrow \text{det}(5I - A) = 0
Consider the eigenvector x corresponding to the eigenvalue λ = 5;
\Rightarrow (A-5I)x = 0$$$$\Rightarrow A\bold{x} - 5\bold{x} = 0
\Rightarrow A\bold{x} = 5\bold{x}
Since A satisfies the equation for eigenvalue and eigenvector, 5 is an eigenvalue of matrix A.
Therefore, if λ = 5 is a factor of the characteristic polynomial of matrix A, then 5 is an eigenvalue of A.
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This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?
Answer:
send the complete question . there are some missing signs .
The sum of two numbers is 52 and the difference is 18. What are the numbers?
Answer:
17 and 35
Step-by-step explanation:
x + y = 52
x − y = 18
Add the equations together:
2x = 70
x = 35
Substitute into either equation:
y = 17
Please help I don't understand this!
Answer:
5
Step-by-step explanation:
you have to look at the temperature in the picture and look at how it slopes down and predict.
The ratio ? Describes the part to whole relationship for boys
In a case whereby Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.
The ratio of the part-to-whole relationship for boys is 14/31.the ratio of the part-to-whole relationship for girls is 17/31.How can the ratio be described?From the question we were told that there are 14 boys in the class wehereby there the whole class has 31 students
Then we can conclude that te ratio of the part-to-whole relationship for boys= 14/31.
From the question, there are 17 girls in the class, then we can conclude that the ratio of the part-to-whole relationship for girls = 17/31.
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complete question:
Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.
The ratio
describes the part-to-whole relationship for boys.
The ratio
describes the part-to-whole relationship for girls.
be smart help me please i’m bout to throw a fit
Answer:
I would say 1/4 of a chance
pleasseeee helppppppp
what is the nth term rule of the linear sequence below 15, 7, -1, -9, -17
Answer:
8n+7
Step-by-step explanation:
what are the relationships of numerator and denominator coefficients with r, l, and c values of a circuit?
The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.
In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.
For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.
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2.6 sq. cm X 3.1 cm
Answer 8.06 X 10-8 M*4
Step-by-step explanation: No Explanation Just Answer srry could think of a way to say it.
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S '(x)= 175 - x^2, where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) = x^2 +11x. a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
a) To maximize its net savings, the company should use the new machine for 7 years. b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar). c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).
Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.
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there are 30 students in a class 1-10 of the students say red is their favorite color How many students like red
Answer: 3
Step-by-step explanation: if there are 30 students and 1 out of 10 like red then it’s 3 because there are 3 groups of ten in 30 so 3 out of 3 will like red
Answer:
3
Step-by-step explanation:
let x = # of students who like red
x/30 = 1/10 cross multiply to solve for x
10x = 30
x = 30/10 = 3
Compare the graph h(x)=1/4x^2 to the graph of f(x) = x2.
Answer:
h(x) is the image after f(x) is horizontally stretched by a scale factor of 4
Step-by-step explanation:
Given
\(h(x) = \frac{1}{4}x^2\)
\(f(x) = x^2\)
Required
Compare h(x) to f(x)
We have:
\(h(x) = \frac{1}{4}x^2\)
Substitute \(f(x) = x^2\)
\(h(x) = \frac{1}{4}f(x)\)
This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)
1. The medical assistant took the oral temperature of 42 patients on Monday, 37
patients on Tuesday, 65 patients on Wednesday, was off work on Thursday, and 56
patients on Friday. How many total thermometer probe covers were utilized by this
medical assistant this week at the clinic when taking patient temperatures?
2. The teenage patient grew % inch from January to March, ½ inch from March to May,
2 inches from May to September, and 1 % inches from September to December.
How many total inches did this patient grow this year?
3. An infant was born weighing 8 pounds and gained 2 pounds by his one-month
check-up, 2 pounds by his three-month check-up, and 4 more pounds by his
six-month check-up. How many pounds did this infant weigh by his 6-month
check-up appointment?
4. If 3 teaspoons = 0.5 fluid ounce and there are 4 ounces in a bottle of children's
Tylenol, how many 1-teaspoon doses are there in a bottle?
Answer:
1. The medical assistant utilized a total of 200 thermometer probe covers this week at the clinic when taking patient temperatures.
2. The teenage patient grew a total of 5 7/8 inches this year.
3. The infant weighed 14 pounds by his 6-month check-up appointment.
4. There are 24 1-teaspoon doses in a bottle of children's Tylenol.
Step-by-step explanation:
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Which of the following correctly uses absolute value to show the distance between −70 and 13? (5 points)
−70 − 13| = |−83| = −83 units
|−70 − 13| = |−83| = 83 units
|−70 + 13| = |−57| = 57 units
|−70 + 13| = |−57| = −57 units
Answer:
|−70 − 15| = |−85| = 85 units - B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
First of all, distance cannot be negative so you eliminate answers A and D immediately.
Now to find the distance between a negative number and a positive number, you either have to take the absolute value of the negative number (to turn it positive) and add it to the positive or take the absolute value of the positive number subtracted by the negative number.
Basically, you're doing this because it compensates for the distance between the negative number and 0.
The only answer choice that is consistent with these terms is B.
Subtract.
6/11-2/11=
I need some help what’s the answer:(
4 = 2 (-2 - a) + a
Find A and please explain how to do it
The required value of variable "a" would be -8 which is determined by the distributive property of multiplication,
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The equation is below which is given in the question,
4 = 2(-2 - a) + a
Apply the distributive property of multiplication,
4 = 2 × -2 - a × 2 + a
4 = - 4 - 2a + a
Rearrange the likewise terms and apply the arithmetic operation,
- 2a + a = 4 + 4
- a = 8
Multiply by the (-) sign on both sides to get the answer,
a = -8
Hence, the required value of variable "a" is -8.
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a company had 80 employees whose salaries are summarized in the frequency distribution below. find the standard deviation.
The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.
The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).
By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.
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Put decimals in order from smallest to largest and then find the median?
Answer:
0.11,0.4,0.42,0.5,0.8. The median would be 0.446
When you are finding a percent of a number or price, you need to convert the percent to a
Answer:
When you are finding a percent of a number or price, you need to convert the percent to a decimal.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
A cylinder and cone have the same height and radius. The height of each is 5 cm, and the radius is 2 cm.
Calculate the approximate volume of the cylinder. Use 3.14 for pi. Do not include units.
Answer:
12rhehrhehrhjnehrhrhehrhehehrrhrjejejej
Answer:
Step-by-step explanation:
Use 3.14 for the pi DO NOT INCLUDE UNITS
A bag contains blue, red, and green marbles. Paola draws a
marble from the bag, records its color, and puts the mar-
ble back into the bag. Then, she repeats the process. The
table shows the results of her experiment.
Color
Blue
Red
Green
Number of
Times Drawn
14
30
6
Based on the results, which is the best prediction of how many times
Paola will draw a red or blue marble in 500 trials?
Answer:
500 × P(blue marble) = 500 × 14/50 = 140
500 × P(red marble) = 500 × 30/50 = 300
Based on the results, the best number of predictions Paola will draw a red marble or a blue marble is 440 times in 500 trials.
is a fraction a term? If it's not a term, why is it that we can apply the distributive property to it? the distributive property only works for either terms, or addition and subtraction. a fraction is technically division, so why does it work? Please help!!!!!
No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.
A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.
The distributive property states that for any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c).
When working with fractions, we can apply the distributive property as follows:
Let's consider the expression: a × (b/c).
We can rewrite this as: (a × b)/c.
Now, let's distribute the 'a' to 'b' and 'c':
(a × b)/c = (a/c) × b.
In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.
Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.
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Carolyn is looking into two companies for a new cell phone plan.
•Megacell charges $14. 80 per month plus 10 cents per minute for every minute over 200
•Fun Fone charges $18. 50 per month plus 8 cents per minutes for every minute over 200
What system of equations represents these relationships, where y is the cost for x, minutes over 200?
A. Megacell: y=0. 1+14. 8x
Fun Fone: y=0. 08+18. 5x
B. Megacell: y=10+14. 8x
Fun Fone: y=8+18. 5x
C. Megacell: y=14. 8+0. 1x
Fun Fone: y=18. 5+0. 08x
D. Megacell: y=14. 8+10x
Fun Fone: y=18. 5+8X
The correct system of equations that represents the cost relationships for the two cell phone plans is option(a) Megacell: y = 0.1x + 14.8 and Fun Fone: y = 0.08x + 18.5.
Let's break down the given information for the two cell phone plans:
Megacell charges $14.80 per month plus 10 cents per minute for every minute over 200. This means that the cost (y) for using x minutes over 200 can be represented by the equation y = 0.1x + 14.8. The $14.80 represents the fixed monthly charge, and the 10 cents per minute over 200 is added to the total cost.
Fun Fone charges $18.50 per month plus 8 cents per minute for every minute over 200. This means that the cost (y) for using x minutes over 200 can be represented by the equation y = 0.08x + 18.5. The $18.50 represents the fixed monthly charge, and the 8 cents per minute over 200 is added to the total cost.
Therefore, the correct system of equations that represents these cost relationships is Megacell: y = 0.1x + 14.8 and Fun Fone: y = 0.08x + 18.5, which corresponds to option A.
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Two consecutive odd numbers are doubled resulting with a sum of 160. What are the two odd numbers? can someone please answer this I need help now
Given:
Two consecutive odd numbers are doubled resulting with a sum of 160.
To find:
The two odd numbers.
Solution:
Let the two consecutive odd numbers are x and x+2.
Double of the two consecutive odd numbers are 2x and 2(x+2).
Two consecutive odd numbers are doubled resulting with a sum of 160, so
\(2x+2(x+2)=160\)
\(2x+2x+4=160\)
\(4x=160-4\)
\(4x=156\)
Divide both sides by 4.
\(x=\dfrac{156}{4}\)
\(x=39\)
Now,
First odd number = 39
Second odd number = 39+2=41
Therefore, the two consecutive odd numbers are 39 and 41.