a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,
[tex]\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}[/tex]Therefore, the answer to the first question is $58.
b) Substitute 5 for p and 7 for d in the expression above; therefore,
[tex]T=6p+4d[/tex]The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.
The table represents the amount of money in a bank account each month. Month Balance ($) 1 2,215.25 2 2,089.75 3 1,964.25 4 1,838.75 5 1,713.25 What type of function represents the bank account as a function of time? Justify your answer.
The form of function that represents the bank account as a function of time is a linear function.
How to determine the type of function?The table of values is given as illustrated:
Month Balance ($)
1 2,215.25
2 2,089.75
3 1,964.25
4 1,838.75
5 1,713.25
From the above table of values, we can see that the balance in the bank account reduces each month by $125.5
So, we have
Difference = 1,838.75 - 1713.25 =125.5
Difference = 1,964.25 - 1,838.75 =125.5
Difference = 2,089.75 - 1,964.25 =125.5
Difference = 2,215.25 - 2,089.75 =125.5
This shows a linear function.
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Which of the following equations could you solve by first adding six and then dividing by negative three?
3x - 6 = -9
6 - 3x = -9
-3x - 6 = -9
x/-3 + 6 = -9
Answer:
-3x-6=-9
Step-by-step explanation:
[tex]-3x-6=-9[/tex]
[tex]+6[/tex] [tex]+6[/tex]
[tex]-3x = -3[/tex]
[tex]-3x/-3 = -3/-3[/tex]
[tex]x=1[/tex]
During the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week. During a rainy stretch in the summer, his grass grew a total of 8 inches in 4 weeks.
Based on the growth rate of Mr. Salina's grass per week in the summer, and in spring, the relationship is not proportional.
How are relationships proportional?When relationships are said to be proportional, it means that they increase or decrease by the same rate.
In the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week.
In the rainy stretch of summer, this rate goes to:
= Total number of inches / Number of weeks
= 8 / 4
= 2 inches per week
This means that the relationship is not proportional and one rate is higher than the other.
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I just finished my other 2 questions and I need help with this one now, I don't understand the letters really. please help
So, c(x) = 8.25x + 1500
the marginal cost doubles so, (8.25 x) will be 2 * (8.25x )
And the fixed cost decreased by 30%
so, 1500 will be (1 - 30%) of 1500
so, (1 - 30%) of 1500 = 70% of 1500 = 0.7 * 1500 = 1050
So, k(x) = 2 * (8.25x) + 1050
K(x) = 16.5 x + 1050
There are 3 consecutive even integers that sum to 186. What is the value of the greatest integer?
Answer:
The 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.
Explanation:
If the numbers are consecutive even numbers, it means that the next number will be 2 more than the previous one.
Let the 1st number be x, then other 2 consective numbers will be x + 2 and x + 4.
We're told that the sum of the 3 consecutive even numbers is equal to 186, our equation can then be written as shown below;
[tex]x+(x+2)+(x+4)=186[/tex]Let's go ahead and collect like terms and solve for x;
[tex]\begin{gathered} 3x+6=186 \\ 3x=186-6 \\ 3x=180 \\ x=\frac{180}{3} \\ \therefore x=60 \end{gathered}[/tex]So our 1st number is 60.
Let's go ahead and find the other 2 numbers;
1st number: x + 2 = 60 + 2 = 62
2nd number: x + 4 = 60 + 4 = 64
So the 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.
Sheldon is painting a wall in his house and is using a paint roller.The paint roller had a radius of 1 inch and a height of 8 inches.How many square inches of space Sheldon paint with one revolution of paint roller?Round to nearest tenths
The information we have about the paint roller:
Radius: r=1in
Height: h=8in
To find the answer to how many square inches of space he can paint with one revolution, it is useful to visualize the surface area of a cylinder:
The circles are the top and bottom of the cylinder, and the rectangle is the body of the cylinder (the paint roller). The area of this rectangle is the area that the paint roller will paint with one revolution.
Calculate the area of the rectangle:
To find the area, first, we need to find the length "L":
This length L is equal to the circumference of the circle defined as follows:
[tex]L=2\pi r[/tex]So to find L we substitute r=1in and pi=3.1416:
[tex]\begin{gathered} L=2(3.14216)(1\text{ in)} \\ L=6.2832in \end{gathered}[/tex]And finally, to find the area of the rectangle and thus, the area that the paint roller covers with one revolution, we multiply the length by the height:
[tex]A=h\times L[/tex]Where "A" is area.
Substituting h and L:
[tex]\begin{gathered} A=8in\times6.2832in \\ A=50.2656in^2 \end{gathered}[/tex]Rounding our answer to the nearest tenths:
[tex]50.2656\approx50.3[/tex]Answer: 50.3 square inches
How many and what type of solution(s) does the equation have?6p2 = 8p + 32 rational solutions1 rational solutionNo real solutions2 irrational solutions
We are going to solve the question using the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{(b^2}-4ac)}{2a} \\ \text{where the quadratic equation is ax}^2+bx+c=0 \end{gathered}[/tex]The quadratic equation given is
[tex]\begin{gathered} 6p^2=8p+3 \\ 6p^2-8p-3=0 \\ \text{where a=6} \\ b=-8 \\ c=-3 \end{gathered}[/tex]By substitution we will have,
[tex]\begin{gathered} p=\frac{-(-8)\pm\sqrt[]{(-8)^2}-(4\times6\times-3)}{2\times6} \\ p=\frac{8\pm\sqrt[]{64+72}}{12} \\ p=\frac{8\pm\sqrt[]{136}}{12} \\ p=\frac{8\pm\sqrt[]{4\times34}}{12} \\ p=\frac{8\pm2\sqrt[]{34}}{12} \\ p=\frac{2(4\pm\sqrt[]{34)}}{12} \\ p=\frac{4\pm\sqrt[]{34}}{6} \\ p=\frac{4+\sqrt[]{34}}{6}\text{ or p=}\frac{4-\sqrt[]{34}}{6} \end{gathered}[/tex]Therefore,
With the roots gotten from the quadratic equation, we can therefore deduce that the solutions to the equation 6p²=8p+3 will give 2 irrational roots.
The correct answer is OPTION D
if (11,13) is an ordered pair of the function F(x), which of the following is an ordered pair of the inverse of F(x)
Given:
There are given that the ordered pair is:
[tex](11,13)[/tex]Explanation:
According to the question:
We need to find the inverse of the given ordered pair.
Then,
To find the inverse of the given relation, we need to switch the x and y-coordinates.
Then,
The inverse is:
[tex](11,13)\rightarrow(13,11)[/tex]Final answer:
Hence, the correct option is C.
Give the digits in the ones place and the hundredths place.
12.86
Please help ASAP
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 3". Let B be the event "the outcome is a divisor of 4". Are A and B independent events? Outcome Probability 1 0.09 2 0.41 3 0.06 4. 0.1 5 0.34 no yes
A is the event - the outcome is a divisor of 3
B is the event - the outcome is a divis
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables. What is the relationship between the number of students to tables? (Do not reduce the ratios to their lowest terms.)
Answer: 8/1 = 6/48
Step-by-step explanation: um thats the answer bye
The relationship between the number of students to tables or the ratio of students to number of tables is 8 to 1.
According to question,
We have the following information:
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables.
Now, we will find the relationship between the number of students and the number of tables or in simple words, ratio.
So, we have:
8 students = 1 table
48 students = 6 tables
It can be rewritten by dividing both the sides by 6 as 8 students to 1 table.
It means that there are 8 students for 1 table.
Hence, the relationship between the number of students to the number of tables is 8 to 1.
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find the ranges of values for which x²-5+6<0
Answer:
The range of values of x for which the function is < 0 is:
2<x<3.
Step-by-step explanation:
x²-5x+6<0
First find the critical points:
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0.
x = 2, 3.
The critical points are 2 and 3.
Make a table of values:
x x<2 2<x<3 x >3
x -2 < 0 >0 >0
x -3 <0 <0 >0
(x - 2)(x - 3) >0 <0 >0
Matthew filled two 20 oz. water bottles before he left home. At the end of the day, he has less than 8 oz. left. Write an inequality to determine how much water, z, Matthew drank.
Given data:
The expression for the inequality is,
[tex]\begin{gathered} 2(20)-z<8 \\ 40-z<8 \end{gathered}[/tex]Thus, the second inequality is correct.
im not sure the steps to this math problem, from step one to step three
The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]Please see the picture below,PART BUse the real zeros to factor f
Explanation:
The polynomial is given below as
[tex]f(x)=x^4+2x^3-7x^2-8x+12[/tex]Given in the question above the real zeros are gotten below as
[tex]x=-3,-2,1,2[/tex]Concept:
To figure out the factor form of the polynoimial, we will equate each zero to x below as
[tex]\begin{gathered} x=c \\ (x-c) \end{gathered}[/tex]Therefore,
The factored form of the polynomial will be
[tex]\begin{gathered} f(x)=x^{4}+2x^{3}-7x^{2}-8x+12 \\ x=-3,x=-2,x=1,x=2 \\ f(x)=(x+3)(x+2)(x-1)(x-2) \end{gathered}[/tex]Hence,
Using the real zeros of f(x) , the factored form of the polynomial is
[tex]\Rightarrow f(x)=(x+3)(x+2)(x-1)(x-2)[/tex]Hello this is a multi step question and I am struggling to help my son with this. It is 1 of 3 so hoping to get guidance with this first one to be able to know how to apply it to the others in his activities. Thank you as I know this is multiple steps and time consuming. The help is greatly appreciated as a parent.
In the first part of this problem, we must compute some statistic variables of two distributions:
0. the mean value,
,1. the median,
,2. the standard deviation.
,3. the interquartile range.
1. The mean of a data set is the sum of all the data divided by the count n:
[tex]\mu=\frac{x_1+x_2+\cdots+x_n}{n}\text{.}[/tex]2. The median is the data value separating the upper half of a data set from the lower half, it is computed following these steps:
• arrange data values from lowest to the highest value,
,• the median is the data value in the middle of the set
,• if there are 2 data values in the middle the median is the mean of those 2 values.
3. The standard deviation for a sample data set is given by the following formula:
[tex]\sigma=\sqrt[]{\frac{(x_1-\mu)^2+(_{}x_2-\mu)^2+\cdots+(x_n-\mu)^2}{n-1}_{}}\text{.}[/tex]4. The interquartile range (IQR) is given by:
[tex]\text{IQR}=Q_3-Q_1\text{.}[/tex]Where Q_1 and Q_3 are the first and third quartiles. The lowest quartile (Q1) covers the smallest quarter of values in your dataset.
--------------
Using the definitions above, we compute the mean, the median and the standard deviation for the samples taken by Manuel and Gretchen.
Manuel's sample
• Sample = {3, 6, 8, 11, 12, 8, 6, 3, 10, 5, 14, 9, 7, 10, 8}
,• Count = 15
1. Mean
Using the formula above, we get:
[tex]\mu=\frac{120}{5}=8.[/tex]2. Median
We order the data set:
[tex]3,3,5,6,6,7,8,(8),8,9,10,10,11,12,14.[/tex]From the ordered data set, we see that the central number 8 divides the data set into two equal parts.
So the median of this sample is:
[tex]\bar{x}=8.[/tex]3. Standard deviation
Using the formula above, we get:
[tex]\sigma=\sqrt[]{\frac{138}{15-1}}\cong3.14.[/tex]4. Interquartile range
Dividing the data sample into quartiles, we have:
[tex]3,3,5,6|6,7,8|8|8,9,10|10,11,12,14.[/tex]We have:
• Q_1 = 6,
,• Q_3 = 10.
So the interquartile range is:
[tex]\text{IQR }=Q_3-Q_1=10-6=4.[/tex]Gretchen's sample
• Sample = {22, 4, 7, 8, 12, 15, 10, 7, 9, 6, 13, 3, 8, 10, 10}
,• Count = 15
1. Mean
[tex]\mu=\frac{144}{15}=9.6.[/tex]2. Median
We order the data set:
[tex]3,4,6,7,7,8,8,(9),10,10,10,12,13,15,22.[/tex]From the ordered data set, we see that the central number 8 divides the data set into two equal parts.
So the median of this sample is:
[tex]\bar{x}=9.[/tex]3. Standard deviation
[tex]\sigma=\sqrt[]{\frac{307.6}{15-1}}\cong4.69.[/tex]4. Interquartile range
Dividing the data sample into quartiles, we have:
[tex]3,4,6,7|7,8,8|9|10,10,10|12,13,15,22.[/tex]We have:
• Q_1 = 7,
,• Q_3 = 12.
So the interquartile range is:
[tex]\text{IQR }=Q_3-Q_1=12-7=5.[/tex]Answers
Manuel's sample
0. Mean = 8
,1. Median = 8
,2. Standard deviation ≅ 3.14
,3. Interquartile range = 4
Gretchen's sample
0. Mean = 9.6
,1. Median = 9
,2. Standard deviation ≅ 4.69
,3. Interquartile range = 5
Equipment was purchased for $50,000. The equipment is expected to be used 15,000 hours over its useful life and has a residual value of $10,000. In the first two years of operation, the equipment was used for 2,700 hours and 3,300 hours, respectively. Using the activity-based method, what is the equipment’s accumulated depreciation at the end of the second year?
The equipment’s accumulated depreciation at the end of the second year is $16,000.
What is the accumulated depreciation?Depreciation is the process used in expensing the cost of an asset. The activity based method allocates the depreciation expense using the number of hours the asset was used. Accumulated depreciation is the sum of the depreciation over a period of time.
Depreciation expense using the activity based method = (cost of the asset - residual value) x (number of hours used in a year / total number of hours)
Depreciation expense in year 1 = ($50,000 - $10,000) x (2,700 / 15,000)
$40,000 x 0.18 = $7,200
Depreciation expense in year 2 = ($50,000 - $10,000) x (3,300 / 15,000)
$40,000 x 0.22 = $8,800
Accumulated depreciation = $8,800 + $7,200 = $16,000
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Find a if (10-a )×2 +(2a×2)+(4a+7)=48
First step: Simplify everything
[tex]2(10-a) + 4a + 4a+7 = 48[/tex]
Next: Distribute required values
[tex]20-2a+4a+4a+7=48[/tex]
Next: Time to add like terms
[tex]6a = 21[/tex]
Final Step: Divide 6 on both sides to isolate variable
[tex]a = \frac{21}{6}[/tex]
Thus, the value "a" = [tex]\frac{21}{6}[/tex]
Hope this helps :)
The radius of a circle is 8 inches. What is the area?Give the exact answer in simplest form. _____ square inches. (pi, fraction)
Given:
Radius of circle is 8 inches.
The objective is to find the area of the circle.
The formula to find the area of the circle is,
[tex]\begin{gathered} A=\pi r^2 \\ =\pi\times8\times8 \\ =64\pi \\ =201in^2 \end{gathered}[/tex]Hence, the area of the circle is 201 square inches.
Make an estimate. Then divide using partial-quotients division. Write your remainder as a fraction and pls make it make sense
Notice that 812 is close to 810 and 17 is closer to 15 than to 20; thus, a possible estimate is
[tex]\frac{810}{15}=54[/tex]However, 800/20 is a more straightforward approximation. Both can be used since you are not being asked for a specific approximation.
Partial-quotients division
Thus, the answer is quotient equal to 47 and remainder equal to 13/17.
Cobalt-60 has a half-life of about 5 years. After 20 years, how many grams of a2,076 gram sample will remain? Round to the hundredths place, if answer doesn'thave a tenths place then use a zero so the answer does.
Solution:
The formula for half-life is given below as
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{\frac{t1}{2}}}[/tex]Where the given values are
[tex]\begin{gathered} N_0=2076g \\ t=20years \\ t^{\frac{1}{2}}=5years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} N(t)=N_{0}(\frac{1}{2})^{\frac{t}{\frac{t\times1}{2}}} \\ N(t)=2076\times(\frac{1}{2})^{\frac{20}{5}} \\ N(t)=2076\times(\frac{1}{2})^4 \\ N(t)=\frac{2076}{16} \\ N(t)=129.75g \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow129.75g[/tex]Expand and simplify 3(3x - 4) - 2(2x - 1)
Answer:
5x-10
Step-by-step explanation:
expand to 9x-12-4x+2
collect like terms.
5x-10
Sq root of z +3 + Sq root of Z -2 = 5
I dont know how to complete this please help.
A' ∩ C U B in roster form is {3, 7, 8, 9}
What is A' ∩ C U B?To write a set in a roster form, the elements in the set are written in a row within curly brackets.
The following are set symbols and their meaning:
• U = union = it means all the elements in two or more sets.
• ∩ = intersection = it means elements that are common to two or more sets.
• ' = complement = it means elements that are not in the set but in the universal set.
A' = {3, 6, 7, 8, 9}
C U B = {2, 3, 4, 5, 7, 8, 9}
A' ∩ C U B = {3, 7, 8, 9}
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Question 5 Fill in the table. First Integer Next Integers Give four consecutive odd integers: The simplified sum of the second and forth integers are Question Help: Message instructor Submit Question
The four consecutive odd integers
If the first integer is given to be x
Then the next three are:
x + 2, x+ 4 and x+ 6
The sum of the second and forth integers :
x+2 + x+ 6 = 2x + 8
Hence, the sum of the second and forth integers are: 2x+8
one box of strawberries cost $5 what equation can be used to calculate the most number of boxes a person can buy with $30
Answer
The maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.
Explanation
One box of strawberries cost 5 dollars.
If one buys x boxes of strawberries, the cost would be (5x) dollars.
So, if one has 30 dollars, we want to find the maximum number of boxes that the person can buy, that is, the maximum value of x
5x ≤ 30
Divide both sides by 5
(5x/5) ≤ (30/5)
x ≤ 6
The number of boxes that one can buy is less than or equal to 6.
Hence, the maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.
Hope this Helps!!!
Assume your salary is $24,000 per year and $50 for each computer you sell. What function represents your total pay for one year? Be sure to indicate any domain restrictions.
Let x represent the total amount of computers you sell in one year.
Since you get $50 for each computer, then, you would get 50x for x computers.
Additionally, your base salary is $24,000. Then, add 50x and 24,000 to find your total salary in a year.
If f(x) is a function that represents your salary depending on the amount of computers you sell, then:
[tex]f(x)=50x+24000[/tex]Notice that the amount of computers that you sell cannot be a negative number. Then, you must take into account the following restriction:
[tex]x\ge0[/tex]Therefore, the answer is:
[tex]f(x)=50x+24000\text{ for }x\ge0[/tex]Pls help me with this I will give brainless thank u <3
15.sum,neg
16.sum,neg
17.diff,neg
18.sum,neg
19.sum,pos
20.neg
21.pos
22.neg
23.pos
24.neg
solve by using quadratic formula25c^2 + 40c + 16= 0
Recall that the quadratic formula states that the solutions to the equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Therefore the solutions to the given equation are:
[tex]c=\frac{-40\pm\sqrt{40^2-4(25)(16)}}{2(25)}.[/tex]Simplifying the above result we get:
[tex]c=\frac{-40\pm\sqrt{1600-1600}}{2(25)}=\frac{-40}{50}=-\frac{4}{5}[/tex]Answer: The given equation has only one solution:
[tex]-\frac{4}{5}.[/tex]U Last Saturday V. Tomo los restaurant sold 85 cheese pizzes and 54peperon p2205 Wechple was cut into elchihs, how many peces ofpedid hosilinona nlgh?2Adeleydiverlor the realanddeliverpiznes ot 5-13 ke arrivedback at therestaurant 6 45. How many manutes wesheoulding p2205 ?3 Tomola hoz 158 ounces domaSouce The uses 9 aunces of louce bonepi? how many plazos canhe moke with mesouce behet?41 Au months ago the restaurar had 2 258pizobe in their warehouse Today they have749 boxen led. How many pizza bazea haether
Answer : The amount of boxes of pizzas used is 2009 boxes
A few months ago, the company has 2, 758 boxes of pizzas in the warehouse
Today, they have 749 boxes of pizzas in the warehouse
To calculate the amount left
The amount used = 2758 - 749
The amount of boxes used = 2009 boxes