The correct answer is option (B) [tex]\frac{5}{8}x - 6\frac{1}{2}[/tex] when [tex]\frac{5}{8}x +1\frac{1}{3}[/tex] is subtracted from [tex]1\frac{1}{4} x -5\frac{1}{6}[/tex] . Both values are in mixed fraction.
Define mixed fraction ?
A mixed fraction is a mathematical expression that represents a whole number and a fraction together. It is also called a mixed number. In a mixed fraction, the whole number is written first, followed by a space and then the fraction. The fraction represents a part of the whole number, with the numerator (top number) indicating the number of parts and the denominator (bottom number) indicating the total number of parts.
To subtract [tex]\frac{5}{8}x +1\frac{1}{3}[/tex] from [tex]1\frac{1}{4} x -5\frac{1}{6}[/tex] , we can simplify both terms to have a common denominator. The common denominator is 24. Then we have
[tex]1\frac{1}{4}x - 5\frac{1}{6} - \left(\frac{5}{8}x + 1\frac{1}{3}\right)[/tex]
[tex]= \frac{5}{4}\cdot\frac{6}{6}x - \frac{31}{6}\cdot\frac{4}{4} - \frac{15}{24}x - \frac{32}{24}[/tex]
[tex]= \frac{30}{24}x - \frac{124}{24} - \frac{15}{24}x - \frac{32}{24}[/tex]
[tex]= \frac{15}{24}x - \frac{156}{24}[/tex]
[tex]= \frac{5}{8}x - \frac{13}{2}[/tex]
[tex]= \frac{5}{8}x - 6\frac{1}{2}[/tex]
Therefore, the correct answer is option B [tex]\frac{5}{8}x - 6\frac{1}{2}[/tex] .
To learn more about denominator visit the link :
https://brainly.com/question/7067665
#SPJ1
What is the value of 3(3+3n) when n=4?
Answer: 23
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
3(3+3×4)
3(3+12)
3(15)
3×15
45
A televevision costs #5 400. A 12.5% discount is given for cash. What is the cash price?
Malcolm started with a board that was 62/3 feet long. He then cut off a section that was 3 1/2 feet long. How much of the board is left?
A. 3 1/4 feet
B. 4 feet
C. 3 1/6 feet
D. 9 3/5 feet
Only for I Brainly Expert
The board is 3 1/6 feet left. The correct option is C.
To find out how much of the board is left, we need to subtract the length of the section that was cut off from the original length of the board:
6 2/3 - 3 1/2
To subtract these two mixed numbers, we need to find a common denominator. The smallest common denominator of 3 and 2 is 6:
Next, we can simplify the fractions,
62/3 - 3 1/2
= 20/3 - 7/2
= (40 - 21)/6
= 19/6
= 3 1/6 feet.
Therefore, the answer is C. 3 1/6 feet.
To learn more about fractions;
https://brainly.com/question/10354322
#SPJ1
Unit 8: Right Triangles & Trigonometry. Homework 6: Law of Sines. NO LINKS OR FILES I WILL REPORT!!!!
Thanks!
1.) The missing side of the triangle given above would be = 7.4
How to calculate the value of the missing side of the triangle?To calculate the value of the missing side of the triangle, the sine rule is used.
That is;
a/sinA = b/sinB
Where;
a = 5
A = 29°
b = ?
B = 46°
That is;
5/sin29° = b/sin46°
make b the subject of formula;
b = 5×0.719339800/0.484809620
b = 3.596699/0.484809620
b = 7.4
Learn more about triangle here:
https://brainly.com/question/28470545
#SPJ1
Rewrite the following equation of a circle in general form: (x-7)^2+(y+8)^2=64
Answer:
(a) x² +y² -14x +16y +49 = 0
Step-by-step explanation:
You want the equation (x -7)² +(y +8)² = 64 written in general form.
General formIn general form, the terms are written in lexicographical order of decreasing degree, and the right side of the equation is 0.
ApplicationWe know the square of a binomial is ...
(a +b)² = a² +2ab +b²
so we can write down the squares of the binomials:
x² -14x +49 +y² +16x +64 = 64
Rearranging and subtracting 64 from both sides, we have ...
x² +y² -14x +16y +49 = 0
Tom's bedroom door is 8 feet tall and 4 feet wide. A new door would cost $5.00 per square foot. How much would a new bedroom door cost in total?
The area of the door is 8 feet x 4 feet = 32 square feet.
So a new door would cost 32 square feet x $5.00 per square foot = 160.00
Ivanna spent 24$ on fruit at the grocery store. She spent a total of 60% at the store. What percentage of the total did she spend on fruit?
Plsssss answer quick need this NOWWWWWW
Answer: 204
Step-by-step explanation:
Area of Triangle= 1/2 b h b=6 h=18-10=8
=1/2 *6*8 =24
Area of rectangle = Lw L=18 w=10
=18*10
=180
Now add the 2 areas together
=180+24 = 204
I need help answering this question off of study island explain how you got it….
Answer:
D. 36 units
Step-by-step explanation:
You want the perimeter of the given isosceles triangle.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths of a right triangle. An altitude of an isosceles triangle divides it into two congruent right triangles. We can use this fact to find the lengths of the sides of the triangle that are not aligned with the grid.
By counting grid squares, or by finding the difference of coordinates, we can determine the lengths of the sides of each right triangle to be 12 units (horizontally) and 5 units (vertically). Then the slant length s is ...
s² = 12² + 5²
s² = 144 +25 = 169
s = √169 = 13
PerimeterThe two congruent side lengths of the red triangle are 13 units each, and its "base" is 10 units. The perimeter is the sum of these lengths:
P = 13 +13 +10 = 36 . . . . units
__
Additional comment
The integer side lengths of the right triangle can be written as a triple: {5, 12, 13}. This is known as a "Pythagorean triple." Perhaps the most famous of these is {3, 4, 5}. Others you will encounter in algebra, trig, and geometry problems are {7, 24, 25}, {8, 15, 17}.
It can be time-saving to learn to recognize such ratios of side lengths, so you don't have to go through the whole Pythagorean theorem calculation when you want to find a missing side.
You can also find the perimeter of the given triangle by considering the red sides of the right triangle: 5 + 13 = 18. They match corresponding lengths on the other half of the red triangle, so its perimeter is 2×18 = 36.
A rectangular aquarium fish tank is 10.2 meters long, 5.8 meters wide, and 3.5 meters deep. What is the volume of the fish tank if the top 1/3 is just air
The volume of the water in the fish tank is 135.27 cubic meters if the top 1/3 of the tank is just air.
To find the volume of the fish tank containing water, we need to find the volume of the fish tank and then subtract the volume that is occupied by the air i.e 1/3 of the volume of the tank.
So, the volume of the fish tank is :
=length x width x depth of the tank
=10.2 meters x 5.8 meters x 3.5 meters
= 203.94 cubic meters
Now we need to find the volume of the air that is occupied by the fish tank which is :
=1/3x the volume of the fish tank
=1/3x203.94 cubic meters
=68.67 cubic meters
The volume of the fish tank containing just water is:
=volume of the fish tank - the volume of the air occupied
= 203.94 cubic meters - 68.67 cubic meters
=135.27 cubic meters
Learn more about Volume at:
https://brainly.com/question/1972490
The line shown below are perpendicular. if the green line has a slope of 3/4 what is the slope of the redline
Answer:
-4/3
Step-by-step explanation:
If the green line has a slope of 3/4, then the slope of the red line, which is perpendicular to the green line, is -4/3. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the other line.
Write log3(X)+2log(y) into a single logarithm
The simplified expression of the logarithm is log3(Xy²).
The expression given to you is log3(X) + 2log(y). To simplify this expression, you need to use the properties of logarithms. One of the properties of logarithms states that the sum of the logarithms of two numbers is equal to the logarithm of their product. Another property of logarithms states that the logarithm of a number raised to a power is equal to the product of the exponent and the logarithm of the number.
Using these properties, you can rewrite the expression as follows:
log3(X) + 2log(y) = log3(X) + log(y²) (since 2log(y) = log(y²))
Now, using the property that the sum of the logarithms of two numbers is equal to the logarithm of their product, you can further simplify the expression:
log3(X) + log(y²) = log3(Xy²)
To know more about logarithm here
https://brainly.com/question/30085872
#SPJ4
Kevin is going to keep some pigs in the field.
Each pig needs an area of 36 square metres.
Work out the greatest number of pigs Kevin can keep in the field
the greatest number of pigs Kevin can keep in the field is 4.
How to solve the question?
To determine the maximum number of pigs that Kevin can keep in his field, we need to divide the total area of the field by the area required by each pig.
If we let x represent the maximum number of pigs that can be kept in the field, then we can write the equation:
36x ≤ A
where A is the total area of the field in square meters.
To solve for x, we can divide both sides of the inequality by 36:
x ≤ A/36
This means that the maximum number of pigs that can be kept in the field is equal to the total area of the field divided by 36.
For example, if the field has an area of 144 square meters, then the maximum number of pigs that can be kept in the field is:
x ≤ 144/36 = 4
Therefore, the greatest number of pigs Kevin can keep in the field is 4.
It is important to note that the above calculation assumes that each pig will have exactly 36 square meters of space. In reality, the actual amount of space required per pig may vary depending on factors such as breed, age, and weight. Additionally, it is important to consider other factors such as food, water, and shelter when determining the number of pigs that can be kept in a field.
To know more about Area visit :-
https://brainly.com/question/25292087
#SPJ1
the ideal way to organize electronically the raw data for a study is to:____.
The ideal way to organize electronically the raw data for a study is to use a database management system (DBMS). A DBMS allows the researcher to store, manipulate, and retrieve data in a structured and organized manner. This enables the researcher to easily analyze the data and draw meaningful conclusions from it.
Additionally, a DBMS ensures data accuracy, consistency, and security. Overall, using a DBMS is the most efficient and effective way to manage raw data for a study.
This allows for efficient organization, storage, and retrieval of the data, making it easier to analyze and interpret the results. Additionally, employing proper data cleaning techniques and establishing a clear metadata structure can enhance the overall organization and accessibility of the study's raw data.
To learn more about DBMS : brainly.com/question/28813705
#SPJ11
A store owner discounted some DVD players from $64 to $32. What percentage is the
discount?
Write your answer using a percent sign (%).
Answer:
Step-by-step explanation:
To find the percentage discount, we need to find the amount of discount first.
Discount = Original Price - Discounted Price
Discount = $64 - $32 = $32
The percentage discount is then:
Percentage Discount = (Discount / Original Price) x 100%
Percentage Discount = (32 / 64) x 100%
Percentage Discount = 0.5 x 100%
Percentage Discount = 50%
Therefore, the discount is 50%.
Answer: it's 50%.
$64 - $32 = $32
(32 / 64) x 100%
0.5 x 100%
50%.
so it's 50%
can i please have brainliest i really need it
the mean output of a certain type of amplifier is 495 watts with a variance of 100 . if 85 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.9 watts? round your answer to four decimal places.
The probability is given by -0.004 , that the mean of the sample would differ from the population mean by less than 0.9 watts.
What is normal probability distribution?Normal distribution also known as the Gaussian probability, is a probability distribution that is symmetric about the mean, showing that data bear the mean are more frequent in occurrence than data far from the mean.
In a set with mean μ and standard deviation (which is the square root of the variance) σ , the z score of a measure X is given by:
Z =X-μ/σ
we have given μ = 495
σ =root(100), n = 85
This is the p-value of Z when X = 495 +1.7 =496.7 subtracted by the p-value of Z when X = 495 - 1.7 = 493.3
When X = 496.7
Z =X-μ/10
Z = 496.7 -495/10
Z = 0.447 p-value = 0.447
When X = 493.3
Z =X-μ/σ
Z = 493.3- 495/10
=- 0.443 p-value
0.443 - 0.447= -0.004
Hence the probability is -0.004.
Learn more about probability here :-
https://brainly.com/question/30034780
#SPJ4
At a flea market, used computer
games are sold at the prices shown
in the table below.
Number of Games Price ($)
2 9.00
5 22.50
7 31.50
Do the number of games and price
form a proportional relationship?
Explain.
The ratios are all equal to 0.22, we can conclude that the number of games and price do form a proportional relationship.
What is a proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
To determine if the number of games and price form a proportional relationship, we need to check if the ratio between the number of games and price is the same for all the data points given in the table.
Let's calculate the ratios for each data point:
For 2 games at $9.00: 2/9 = 0.22
For 5 games at $22.50: 5/22.50 = 0.22
For 7 games at $31.50: 7/31.50 = 0.22
Since the ratios are all equal to 0.22, we can conclude that the number of games and price do form a proportional relationship.
Specifically, the ratio between the number of games and price is a constant value of 0.22, which means that if we double the number of games, the price will also double, and if we triple the number of games, the price will triple, and so on. Therefore, we can say that the relationship between the number of games and price is proportional.
To know more about proportional relationship
visit:
https://brainly.com/question/29765554
#SPJ1
A pizza restaurant is located in a town with a population density of 1000 people per square mile. What delivery radius will allow the pizza restaurant to deliver to approximately 20,000
people?
A 2.2 milles
B 2.5 miles
C 4.5 miles
D. 6.4 miles
The delivery radius which will allow the pizza restaurant to deliver to approximately 20,000 people is: B: 2. 5 miles
How to find population density?Population density can be defined as the number of individuals within a species in a specific geographic area.
The formula for population density is expressed as;
Population density = Number of people/Land area
We are given the parameters as:
Number of people = 20000
Population density = 1000
Land area = 20000/ 1000
Land area = 20 square miles
Area of a circle is: πr²
Substitute the value of area in the formula to get:
20 = 3. 142 × r²
r² = 20/ 3. 142
r² = 6. 37
r = √6. 37
r = 2. 5 miles
Thus, the delivery radius which will allow the pizza restaurant to deliver to approximately 20,000 people is 2. 5 miles
Read more about Population Density at: https://brainly.com/question/13902749
#SPJ1
Solve (2x-5)^1/3=3
Your anwser should be 16
SHOW WORK
Answer:
16
Step-by-step explanation:
(2x-5)^(1/3) = 3, we can start by cubing both sides of the equation to get rid of the cube root. This gives us (2x-5)^(1/3)^3 = 3^3, which simplifies to 2x-5 = 27. Solving for x, we get x = (27+5)/2 = 16. So, the solution to the equation (2x-5)^(1/3) = 3 is x = 16.
y = 3/8x -1
x=8
help me out pls
help out w this pls
Answer:
x = -6
y = -1
Step-by-step explanation:
Hope this helps! :)
Graph the given data set and describe what kind of model best describes the data. Then write a function that models
the data.
X y
-2,-1
-1,-2
0,-1
1,2
2,7
The data appears to follow a quadratic curve, and a quadratic model would best describe the data. The quadratic function that models the data is y = 2x^2 - x - 1.
To graph the given data set, we can plot the points on a coordinate plane as follows:
|
8 |
7 | ●
6 |
5 |
4 |
3 |
2 | ●
1 | ●
0 | ●
-1 | ●
-2 | ●
|_____________
-2 -1 0 1 2
From the graph, we can see that the data appears to follow a quadratic curve. Therefore, a quadratic model would best describe the data.
To write a quadratic function that models the data, we can use the standard form of a quadratic equation:
y = ax^2 + bx + c
where a, b, and c are constants to be determined.
To find the values of a, b, and c, we can use the data points and solve the resulting system of equations
-1 = 4a - 2b + c
-2 = a - 2b + c
-1 = c
2 = 4a + 2b + c
7 = 4a + 8b + c
Solving the system of equations, we get:
a = 2
b = -1
c = -1
Therefore, the function that models the data is:
y = 2x^2 - x - 1
The manufacturer of a popular brand of markers is planning to release a new color. To determine which color to add, it mailed out surveys to 5,000 of its customers regarding the general color family they prefer. The returned results are shown in this pie chart.
A Pie Chart with four sections representing the color preferences Blues, Greens, Yellows, and Pinks
Based on the results, one member of the management team says they should choose the new color from the blue family of colors since a majority of people prefer those colors.
Another member doesn’t agree and thinks they should do more research. Which statements would support her request?
The percentage obtained from the pie chart for different colors are Blue =29%, Green = 25%, Yellow = 24%, & Pink = 22%.
As per the results of the survey, Blue color received 29% votes so it must be chosen as the new color for receiving majority votes but as the other three colors also received almost similar percentage of votes. So, the manufacturer must do more research in order to reach on any conclusion.
#SPJ1
what does 6 1/5+ (-7 3/5) equal?
Answer:
-1.4
Step-by-step explanation:
just add the two numbers together
a manufacturer of automobile transmissions uses three different processes. management ordered a study of the production costs to see if there is a difference among the three processes. a summary of the findings is shown next. process 1 process 2 process 3 total process totals ($100s) 137 108 107 352 sample size 10 10 10 30 sum of squares 1,893 1,188 1,175 4,256 in an anova table, what are the total degrees of freedom? multiple choice 30 29 27 28
The total degrees of freedom is option (b) 29
Degrees of freedom refer to the number of values in a calculation that are free to vary. In the context of ANOVA, degrees of freedom represent the number of independent pieces of information that are available for estimating the population variance.
To find the total degrees of freedom in an ANOVA table, you need to add up the degrees of freedom for the different sources of variation. In this case, there are three sources of variation: between groups (processes), within groups (error), and total.
The total degrees of freedom is equal to the total sample size minus one
Total degrees of freedom = n - 1 = 30 - 1 = 29
Therefore, the correct option (b) 29
Learn more about degrees of freedom here
brainly.com/question/31178740
#SPJ4
I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)
a) The probability of picking a red marble first and a yellow marble second is 6/25. So, correct option is A.
b) The probability of spinning a 5 two times in a row is 1/64. So, correct option is c.
a) To calculate the probability of picking a red marble first, replacing it, and then picking a yellow marble, we need to multiply the probabilities of each event.
The probability of picking a red marble first is 2/5, since there are 2 red marbles out of a total of 5 marbles. Since we replace the red marble, the probability of picking a yellow marble on the second draw is also 3/5, since there are still 3 blue marbles and 2 red marbles in the jar.
Therefore, the probability of picking a red marble first and a yellow marble second is:
(2/5) x (3/5) = 6/25
So the correct answer is option a) 6/25.
b) The probability of spinning a 5 on a single spin of the spinner is 1/8, since there is only one 5 out of 8 possible outcomes.
To find the probability of spinning a 5 two times in a row, we need to multiply the probability of spinning a 5 on the first spin by the probability of spinning a 5 on the second spin. Since the spins are independent events, we can use the multiplication rule of probability.
Therefore, the probability of spinning a 5 two times in a row is:
(1/8) x (1/8) = 1/64
So the correct answer is option (c) 1/64.
To learn more about probability click on,
https://brainly.com/question/21616475
#SPJ1
Rewriting multiplication of a sum or difference as an addition or subtraction problem is known as ______.
Rewriting multiplication of a sum or difference as an addition or subtraction problem is known as the distributive property.
The distributive property allows you to break down a multiplication problem involving a sum or difference into separate addition or subtraction problems. Here's a step-by-step explanation:
Step:1. Identify the sum or difference within the multiplication problem. For example, in the problem (a + b) * c, the sum is (a + b).
Step:2. Apply the distributive property by multiplying each term inside the parentheses by the outside term. In our example, this would be: a * c + b * c.
Step:3. The result is the rewritten problem as an addition or subtraction problem. In this case, it is a * c + b * c.
Learn more about distributive property here, https://brainly.com/question/4077386
#SPJ11
Nicole deposited $4000 into an account with a 4% annual interest rate compounded quarterly assuming that no withdrawals are made how long will it take for the investment to grow to $4288?
It will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.
What is an investment?
An investment is the purchase of an asset or item with the goal of generating income or appreciation in value over time. Investments can include a wide range of assets such as stocks, bonds, real estate, commodities, and more. The aim of investing is typically to grow wealth over the long term, although some investments may be made with a shorter-term goal in mind, such as generating income or protecting against inflation.
To solve this problem, we can use the formula for compound interest:
A = P[tex](1 + r/n)^{(nt)}[/tex]
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, t is the time in years.
We can rearrange this formula to solve for t:
t = (1/n) × log(A/P) / log(1 + r/n)
where log denotes the natural logarithm.
In this problem, P = $4000, r = 0.04 (4% as a decimal), n = 4 (compounded quarterly), and A = $4288. Plugging in these values, we get:
t = (1/4) × log(4288/4000) / log(1 + 0.04/4)
t = (1/4) × log(1.072) / log(1.01)
t ≈ 10.18 quarters
Therefore, it will take approximately 10.18 quarters for the investment to grow to $4288. To convert this to years, we divide by 4 (since there are 4 quarters in a year):
t ≈ 2.55 years
So, it will take approximately 2.55 years for the investment to grow to $4288, assuming no withdrawals are made.
To know more about compound interest, visit:
https://brainly.com/question/30572027
#SPJ1
Complete question is: Nicole deposited $4000 into an account with a 4% annual interest rate compounded quarterly assuming that no withdrawals are made 2.55 years will it take for the investment to grow to $4288.
Myra likes blueberry yogurt, but cherry yogurt is her favorite. Yesterday, she bought 3 cartons of cherry yogurt for every 2 cartons of blueberry yogurt. If Myra bought 3 more cartons of cherry yogurt than blueberry yogurt yesterday, how many cartons of cherry yogurt did she buy?
Answer:
Step-by-step explanation:
6 blueberry 9 cherry
the ration is 2:3 and when you multiply both number by three, the ratio is 6:9. 9 is 3 greater than 6, so Myra bought 6 blueberry cartons and 9 cherry cartons.
A baseball has a radius of 1.75 inches. How much material is needed to cover the
baseball? Round your answer to the nearest tenth, if needed.
Answer:
9.7 in²
Step-by-step explanation:
We Know
A baseball has a radius of 1.75 inches.
How much material is needed to cover the baseball?
They basically ask us to find the area of the circle.
Area of circle = r² · π
r = 1.75 inches
π = 3.14
We Take
1.75² · 3.14 = 9.61625 in²
So, you need about 9.7 in² material to cover the baseball.