The total number of books in the library are 75.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What will be the equation for given scenario?Let the total number of books in the library be x.
The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]
Collect the like terms,
[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]
On solving the equation for x we get x=75.
Therefore, the total number of books in the library are 75.
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Find the value of x
A 41
B 44
C 46
D 36
Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018? a. 70% b. -27% c. -17% d. -75%
Using linear function concepts, it is found that the industry’s percent change from 2008 to 2018 will be of:
b. -27%
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
The industry had 63.1 thousand jobs in 2008, hence b = 63.1.This number is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018, hence m = -1.7.Thus, the function is:
y = -1.7x + 63.1.
In 2018, which is 10 years after 2008, the value of the function is:
y(10) = -1.7(10) + 63.1 = 46.1.
The percent change is given by the change divided by the initial value, hence:
(46.1 - 63.1)/63.1 = -27%
Hence option b is correct.
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The correct answer is b. -27%.
To solve this problem, we need to find the number of jobs in 2018 and then calculate the percent change from 2008 to 2018.
Given information:
- Number of jobs in 2008: 63.1 thousand
- Average annual rate of decline: 1.7 thousand jobs per year
- Time period: 2008 to 2018 (10 years)
Step 1: Find the total decline in jobs from 2008 to 2018.
Total decline in jobs = Average annual rate of decline × Number of years
Total decline in jobs = 1.7 thousand × 10 years = 17 thousand jobs
Step 2: Find the number of jobs in 2018.
Number of jobs in 2018 = Number of jobs in 2008 - Total decline in jobs
Number of jobs in 2018 = 63.1 thousand - 17 thousand = 46.1 thousand jobs
Step 3: Calculate the percent change from 2008 to 2018.
Percent change = (Change in value / Original value) × 100%
Percent change = ((46.1 - 63.1) / 63.1) × 100%
Percent change = (-17 / 63.1) × 100%
Percent change ≈ -27%
Therefore, the industry's percent change from 2008 to 2018 is approximately -27%.
Number of jobs in 2018 = [tex]46.1\text{ thousand} \\[/tex]
Percent change from 2008 to 2018 = [tex]-27\%[/tex]
what is the area of a circle with a radius of 7 inches
Answer is provided in the image attached.
486 is what percent of 900
simplify the expression by using a double angle formula
cos^2 4theta-sin^2 4theta
A sofa is on sale for 26% off. The sale price is $629 . What is the regular price?
D=6.3cm what is the circumference and area of the circle
Question help a robotic rover on mars finds a spherical rock with a diameter of 1313 centimeters. the rover picks up the rock and lifts it 1515 centimeters straight up. the rock has a specific gravity of 5.255.25. the gravitational acceleration on mars is 3.73.7 meters per second squared. if the robot's lifting arm has an efficiency of 3535% and required 1212 seconds to raise the rock 1515 centimeters, how much power (in watts) did the arm use?
If 5 workers can pave 10 driveways in 30 days, how many days would it take 20 workers to pave 38 driveways?
Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. (remember, m is a factor of n if m divides n evenly.)
Below is the solution of assign true to is_prime if n has no factors other than 1 and itself.
Further explanationPython is an interpreted, high-level, general-purpose programming language. Python is created by Guido van Rossum and first released in 1991. Its design philosophy emphasizes code readability. Python is a more productive language than Java because it is an interpretive language which is accompanied by elegant syntax and it makes an excellent choice for scripting and rapid application development in many areas. Python is a general-purpose, versatile and popular because it is concise and easy to read, and it is also a good language to have in any programmer’s stack as it can be used for everything such as web development, software development, data science applications.
Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. And remember, m is a factor of n if m divides n evenly. So:
if n == 2:
is_prime = True
elif n % 2 == 0:
is_prime = False
else:
is_prime = True
for m in range (3, int(n**0.5)+1, 2):
if n % m == 0:
is_prime = False
Learn moreLearn more about python https://brainly.com/question/4331067Learn more about python IDLE or similar environment https://brainly.com/question/6280029Learn more about python function https://brainly.com/question/9806744Answer details
Grade: 9
Subject: mathematics
Chapter: python
Keywords: python, integer, factors, python IDLE, is_prime
A basket contains five apples and seven peaches. Four of the apples and two of the peaches are rotten. You randomly pick a piece of fruit. It is fresh or it is an apple. Find the probability of this occuring.
Answer:[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Given
5 apples and 7 peaches out of which 4 apples and 2 peaches is rotten
i.e. 1 apple and 5 peaches is fresh
probability of fresh fruit is =[tex]\frac{6}{12}[/tex]
probability of apple =[tex]\frac{5}{12}[/tex]
Probability of both =[tex]\frac{1}{12}[/tex]
Probability of fresh or an apple is=[tex] \frac{6}{12}+\frac{5}{12}-\frac{1}{12}[/tex]
=[tex]\frac{5}{6}[/tex]
Help Please question in the file.
py+7=6y+q
what is the answer for this question (linear equations with unknown coefficients)?
Answer:
The required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]py+7=6y+q[/tex]
We need to simplify the equation and convert it into a linear equation with unknown coefficients.
Subtract 6y from both sides.
[tex]py - 6y + 7 = q[/tex]
Subtract 7 from both sides.
[tex]py - 6y = q - 7[/tex]
Take y common from left side.
[tex]y(p-6) = q-7[/tex]
Divide both sides by p-6.
[tex]y =\frac{(q-7)}{(p-6)}[/tex]
Hence, the required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].
Three times a number added to seven is 22
3x+7=22
3x=15
x=5
the number is 5
It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level
To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, approximately 187 samples are needed.
Explanation:To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, we need to determine the required sample size. In this case, we can use the formula for sample size determination, which is:
n = (Z^2 * σ^2) / E^2
Where:
n is the required sample sizeZ is the Z-score associated with the desired confidence level (99% corresponds to a Z-score of approximately 2.58)σ^2 is the variance of the GPAs (given as 1.44)E is the desired margin of error (0.25)Plugging in the values, we get:
n = (2.58^2 * 1.44) / 0.25^2
n ≈ 186.43
Therefore, we need a sample size of approximately 187 to estimate the mean GPA within a margin of error of 0.25 at a 99% confidence level.
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palace help me solve these two equations 14, 15
John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.
Breanna works in the mall and her hours increase during busy shopping times of the year. Breanna has a plan to save $25 each week for 5 weeks, and then increase that amount by $20 for the next 7 weeks during the busy time, then go back to $25 per week. If Breanna’s plan is to save $540, how many weeks total will she need to save?
a.
11 weeks
b.
16 weeks
c.
22 weeks
d.
23 weeks
Answer:
Number of weeks Breanna saves are 16 weeks .
Option (b) is correct .
Step-by-step explanation:
As given
Breanna works in the mall and her hours increase during busy shopping times of the year.
Breanna has a plan to save $25 each week for 5 weeks.
Thus
Breanna saves in first 5 weeks = Amount saves per weeks in next 5 weeks × Number of weeks .
= $25 × 5
= $ 125
Increase that amount by $20 for the next 7 weeks during the busy time.
Thus
Amount saves per weeks for next 7 weeks = Amount saves per weeks in first 5 weeks + Increase in amount .
= $25 +$ 20
= $ 45
Breanna saves in next 7 weeks = Amount saves per week× Number of weeks .
Put all the values in the above
= $45 × 7
= $ 315
As given
Breanna saves $25 per week.
If Breanna’s plan is to save $540 .
Let us assume last weeks in which Breanna saves $25 per weeks be x .
Breanna saves in last x weeks = Amount saves for next x weeks × Number of weeks .
= 25 × x
= 25x
Equation becomes
Breanna saves in first 5 weeks + Breanna saves in next 7 weeks + Breanna saves in last x weeks = Total saving amount .
125 + 315 + 25x = 540
440 + 25x = 540
25x = 540 - 440
25x = 100
[tex]x = \frac{100}{25}[/tex]
x = 4 weeks
Thus
Total number of weeks Breanna saves = 5 weeks + 7 weeks + 4 weeks
= 16 weeks
Therefore the number of weeks Breanna saves are 16 weeks .
Option (b) is correct .
What are the X intercepts of a parabola with vertex (6,27) and y intercept of (0,-81)?
The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test? Show your work. A. List the two equations B. Find each type of question
solve for y 6y-8=3y-2
6y-8 =3y-2
subtract 3y from both sides
3y-8 = -2
add 8 to both sides
3y=6
y=6/3 =2
y = 2
To make the two triangles below similar, what would the values of x and y have to be?
What is the solution to the equation 0.8m − 4 = −0.8m?
Describe the relationship between the similarity ratio of two triangles and the ratio of their areas.
In a certain company, 74 employees were hired in the last 5 years. If
this represents 43% of the current number of employees, then how
many current employees does the company have?
- list the steps please & thank you!
To find the total number of employees in the company, set up and solve the equation, 0.43 * X = 74. Solving this provides approximately 172 employees
Explanation:In order to answer this question, we need to use the concept of percentages. Here are the steps:
Since we know 74 employees represent 43% of all employees, we set up the equation: 0.43 * X = 74, where X is the total number of employees in the company. Solving the equation for X leads us to the answer. We divide both sides of the equation by 0.43, which gives us X = 74/0.43. Calculating the right side of the equation, we find X is approximately 172, so there are approximately 172 employees in the company. Learn more about Percentages here:https://brainly.com/question/29306119
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today there are 3,659 thousand elementary and secondary teachers employed in a certain country. this number is expected to increase to 3,856 thousand by next decade. what is the percent increase?
Suppose that an individual has a body fat percentage of 17.9% and weighs 132 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)
A pizza parlor sold 38 1/8 pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
38*8 = 304
304 + 1 =305 slices were sold
Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. How many spare tires of this same variety must carried so that a trip of 15,000 miles can just be completed.