We have the following table
hour pay
1 12
2 24
3 36
4 ?
It seems that for each hour we work, we end up earning $12. Then, we know that if we work 3 hours we earn 36. So, if we work one more hour (4) we should add 12 to what we earn for working 3 hours. That is
[tex]12+36\text{ = 48 }[/tex]So we aren 48 for working 4 hours.
Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Frozen orange juice:$1.57 for 14 ounces$0.57 for 4 ounces----------------------------Find the unit price of a frozen orange juice which costs $1.57 for 14 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Find the unit price of a frozen orange juice which costs $0.57 for 4 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Which is the better buy?A. $1.57 for 14 ouncesB. $0.57 for 4 ounces
The different sizes of the given brands are
Frozen orange juice:
$1.57 for 14 ounces
$0.57 for 4 ounces
The unit price of a frozen orange juice which costs $1.57 for 14 ounces is
1.57/14 = 0.112
The unit price of a frozen orange juice which costs $0.57 for 4 ounces is
0.57/4 = 0.1425
The better buy is the size that has the lowest cost per ounce. Looking at our calculations, the lowest cost per ounce is $0.112
Therefore, the frozen orange juice which costs $1.57 for 14 ounces is the better buy.
Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9
We have the expression:
[tex]5m+n\text{.}[/tex]We must evaluate the expression for:
• m = 7,
,• n = 9.
Replacing the values of m and n in the expression above, we get:
[tex]5\cdot7+9=35+9=44.[/tex]Answer
44
Hi, can you help me answer this question please, thank you!
From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
I NEED HELP WITH THIS ASAP ILL MARK YOU BRAINLIEST Put each set of numbers from greatest to least
Every number is equivalent to:
[tex]\begin{gathered} 7.18\times10^{-3}=0.00718 \\ \sqrt{\frac{25}{49}}=\frac{5}{7}=0.7143 \\ \frac{7}{10}=0.7 \\ 0.\bar{8}=0.8888 \\ \frac{3}{4}=0.75 \\ 80\text{ \% = 0.8} \end{gathered}[/tex]So, each number from greatest to least is:
[tex]0.\bar{8},80\text{ \%, }\frac{3}{4},\sqrt{\frac{25}{49}},\frac{7}{10},7.18\times10^{-3}[/tex]Solve the following inequality: 6p - 15 < 33
WE are to solve an inequality, so we proceed to isolate the variable "p" on one side of the inequality symbol:
6 p - 15 < 33
we add 15 to both sides:
6 p < 33 + 15
6 p < 48
now divide both sides by 6 (notice that since 6 is a positive number, the division doesn't change the direction of the inequality)
p < 48/6
p < 8
So we need to highlight on the number line, the line that starts at "8" and goes all the way to the left (to minus infinity), and make sure that at the point "8" you draw an "empty" circle to indicate that the number 8 itself is NOT included in your set of solutions.
Write the sequence {15, 31, 47, 63...} as a function A. A(n) = 16(n-1)B. A(n) = 15 + 16nC. A(n) = 15 + 16(n-1)D. 16n
To find the answer, we need to prove for every sequence as:
Answer A.
If n=1 then:
A(1) = 16(1-1) = 16*0 = 0
Since 0 is not in the sequence so, this is not the answer
Answer B.
If n=1 then:
A(1) = 15 + 16*1 = 31
Since 31 is not the first number of the sequence, this is not the answer
Answer D.
If n=1 then:
16n = 16*1 = 16
Since 16 is not in the sequence so, this is not the answer
Answer C.
If n = 1 then:
A(1) = 15 + 16(1-1) = 15
A(2) = 15 + 16(2-1) = 31
A(3) = 15 + 16(3-1) = 47
A(4) = 15 + 16(4-1) = 63
So, the answer is C
Answer: C. A(n) = 15 + 16(n-1)
A boy goes to school by first taking a bus for 1 3/4 km and then by walking 1/3 km. Find the distance of his house from the school.
The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.
To determine the total distance he traveled you have to add both distances:
[tex]1\frac{3}{4}+\frac{1}{3}[/tex]To solve this sum, add the fractions first and then add the result to the whole number:
- Add both fractions:
[tex]\frac{3}{4}+\frac{1}{3}[/tex]To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:
[tex]\frac{3\cdot3}{4\cdot3}+\frac{1\cdot4}{3\cdot4}=\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}=\frac{13}{12}[/tex]The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:
- Solve the division:
[tex]13\div12=1.08\bar{3}[/tex]The mixed number will have the whole number "1".
- To express the decimal value as a fraction, multiply it by 12
[tex]0.08\bar{3}\cdot12=1[/tex]The result is the numerator of the fraction, and the denominator will be 12, so:
[tex]0.08\bar{3}=\frac{1}{12}[/tex]And the resulting mixed number is:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:
[tex]1+1\frac{1}{12}=2\frac{1}{12}[/tex]The distance he traveled from home to school is 2 1/12 km.
Which table shows a proportional relationship between miles traveled and gas used?
Miles Traveled Gas Used
27.3 mi 1.5 gal
49.16 mi 3.8 gal
Miles Traveled Gas Used
120 mi 6.2 gal
180 mi 12.2 gal
Miles Traveled Gas Used
135 mi 7.4 gal
135.5 mi 7.9 gal
Miles Traveled Gas Used
270 mi 15 gal
135 mi 7.5 gal
Answer:
D
Step-by-step explanation:
270mi 15gal
135mi 7.5gal
135/270=0.5
7.5/15=0.5
or
135/7.5=18
270/15=18
Question 11:What is the maximum height of the driver off the diving board
To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)
1. Use the next formula to find the x- coordinate of the vertex
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=-\frac{\frac{24}{9}}{2(-\frac{4}{9})} \\ \\ x=-\frac{\frac{24}{9}}{-\frac{8}{9}}=\frac{-24}{-8}=3 \end{gathered}[/tex]2. Use the value of x above to find y-coordinate in the vertex:
[tex]\begin{gathered} y=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12 \\ \\ y=-\frac{4}{9}(9)+\frac{72}{9}+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}[/tex]Then, the maximum height of the diver is 16 feetWrite a pair of complex numbers whose sum is -4 and whose product is 53
The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.
How to calculate the he value?Let the numbers be represented as a and b.
Therefore a + b = -4 .....i
a × b = 53 ........... ii
From equation I, a = -4 - b
Put this into equation ii
ab = 53
(-4 - b)b = 53
-b² - 4b = 53
Equate to 0
-b² - 4b - 53 = 0
The value can be found using the Almighty formula
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Watch help videoA group of friends wants to go to the amusement park. They have no more than $305to spend on parking and admission. Parking is $19, and tickets cost $26 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.<
p = number of people who can go to amusement park
Amount they want to spend is no more than $305. This means there expenses will be less than or equals to $305.
parking = $19
cost per person = $26
Therefore,
[tex]19+26p\leq305[/tex][tex]\begin{gathered} 26p\leq305-19 \\ 26p\leq286 \\ p\leq\frac{286}{26} \\ p\leq11 \end{gathered}[/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]2 ABC Company has a large piece of equipmentthat cost $85,600 when it was first purchased 6years ago. The current value of the equipment is$30,400. What is the average depreciation of theequipment per year?F. $ 5,800G. $ 9,200H. $15,200J. $27,600K. $42,800
The intial cost of the equipment is C, which is given as 85,600.
The present value is PV, which is given as 30,400.
This simply means the total depreciation over the last 6 years can be derived as;
Depreciation = C - PV
Depreciation = 85600 - 30400
Depreciation = 55200
However, the method of depreciation is not given/specified, and hence the question requires that you calculate the average depreciation per year. That is, the total depreciation would be evenly spread over the 6 year period (which assumes that the depreciation per year is the same figure)
Average depreciation = Total depreciation/6
Average Depreciation = 55200/6
Average Depreciation = 9200
The correct option is option G: $ 9,200
Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden
treats himself to some chocolates. The number of chocolates remaining in the box t
days after Brayden's birthday can be modeled by the equation C = -3t+ 12. What
is the slope of the equation and what is its interpretation in the context of the
problem?
Answer:
Step-by-step explanation:
The slope of the function is -3 which reveals the number of chocolates Brayden eats each night.
Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring. Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.x^{10}-2x^5+1=0Step 1. Identify the quadratic formLet t= Answer. We now have:t^2-2t+1=0Step 2. FactorFactor this and solve for t to get t=Answer Step 3. Solve for xWe have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.x= Answer
Given:
[tex]x^{10}-2x^5+1=0[/tex]Step 1: To identify the quadratic form of the given equation.
[tex]\begin{gathered} x^{10}-2x^5+1=0 \\ (x^5)^2-2x^5+1=0 \\ \text{Put x}^5=t,\text{ it gives} \\ t^2-2t+1=0 \end{gathered}[/tex]So, t = x²
Step 2: Factor the quadratic equation in step 1.
[tex]\begin{gathered} t^2-2t+1=0 \\ t^2-t-t+1=0 \\ t(t-1)-t(t-1)=0 \\ (t-1)(t-1)=0 \end{gathered}[/tex]Thus, the factors of the equation is
[tex](t-1)(t-1)=0[/tex]Step3: solve for x.
[tex]\begin{gathered} (t-1)(t-1)=0 \\ (x^5-1)(x^5-1)=0 \\ \Rightarrow x^5-1=0,x^5-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Answer: x = 1
[tex]4\sqrt[3]{16} /2\sqrt[3]{2}[/tex]
The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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Solve by applying the zero product property.m^2= 27-6m
To apply the zero product property we first need to write all the terms of the equation on side:
[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]Now we need to factorise the expression on the right:
[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:
[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]Therefore, the solutions of the equation are m=-9 and m=3
solve the equation x 1.)132.)13/33.) 104.) none of these choices
Answer:
2. 13/3
Step-by-step explanation:
x will be equal to 13/3.
Given,
5^(2x - 1) = 5^(5x - 14)
We can see that base is the same for both the exponents on each side of the equation.
Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.
And new equation becomes:
(2x - 1) = (5x - 14)
This derives us to another conclusion that if the base of an exponent is equal then,
the powers must be equal too.
(2x - 1) = (5x - 14)
=> 5x - 2x = -1 + 14
=> 3x = 13
which gives us,
=> x = 13/3.
Therefore x = 13/3.
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Convert the following rectangular equation to polar form.Assume a>0 3x^2+3y^2-4x+2y=0
The given equation is,
[tex]3x^2+3y^2-4x+2y=0[/tex]The polar form of the equation can be determined by using the substitution
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]using the substitution,
[tex]\begin{gathered} 3(x^2+y^2)-4x+2y=0 \\ 3(r^2\cos ^2\theta+r^2\sin ^2\theta)-4r\cos \theta+2r\sin \theta=0 \\ 3r^2-4rcos\theta+2r\sin \theta=0 \\ r(3r-4\cos \theta+2\sin \theta)=0 \\ r=0\text{ and }(3r-4\cos \theta+2\sin \theta)=0 \\ (3r-4\cos \theta+2\sin \theta)=0 \end{gathered}[/tex]Thus, the above equation gives the required polar form of the circle.
A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?
Solution:
If x denote the days, the rate unit being Jobs per day is:
[tex]\frac{1}{x}=\frac{1}{9}+\frac{1}{5}[/tex]this is equivalent to
[tex]\frac{1}{x}=\frac{5+9}{45}=\frac{14}{45}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{45}{14}=3.2\text{ days}[/tex]that is just a little more than 3 days.
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 100 randomly selected families to see whether an extended season would be of interest to those that may visit the amusement park.What is the best way to randomly choose these 100 families? Have the owners of the amusement park ask the first 100 people they see.Choose a neighborhood near the amusement park and ask 100 families in this neighborhood.Ask the first 100 families that enter the amusement park on a busy weekend day.Allow a random number generator to come up with 100 families within a 50 radius of the amusement park.
Solution
Option 1:
- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.
Option 2:
- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.
- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.
Option 3:
- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season
If $5000 is invested at 9% annual simple interest, how long does it take to be worth $9050?
It takes 9 years to make $9050 from $5000 investment.
Given that, Principal = $5000, rate of interest = 9% and Amount = $9050.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, S.I. = Amount - Principal
= 9050-5000 = $4050
Now, 4050=(5000×9×T)/100
⇒ 4050/450 = T
⇒ T = 9 years
Therefore, it takes 9 years to make $9050 from $5000 investment.
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hello, while doing the question please don't put A decimal Answer ( ex: 1.5) because my teacher told me that's incorrect, you can add or subtract depending on the question, or check if you need to simplify! Thank you:)
Notice that the unit segment is divided in 8 parts. Then, each mark is equal to 1/8.
The kitten that weighs the most is placed over the 5ft mark. Then, its weight is:
[tex]\frac{5}{8}[/tex]The kitten that weighs the least is placed over the third mark. Then, its weight is:
[tex]\frac{3}{8}[/tex]Substract 3/8 from 5/8 to find the difference on their weights:
[tex]\frac{5}{8}-\frac{3}{8}[/tex]Since both fractions have the same denominator, we can substract their numerators:
[tex]\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{2/2}{8/2}=\frac{1}{4}[/tex]Therefore, the difference in pounds between the heaviest and the lightest kittens, is:
[tex]\frac{1}{4}[/tex]Which expression is undefined? O A. 11 B.- 3 C.6-6) D. -4+0
Answer:
Option C
Step-by-step explanation:
Undefined expression:
Division by 0, or fraction in which the denominator is 0. In this question, this is in option C, since 3/(6-6) = 3/0.
Question 34: Find the polar coordinates that do NOT describe the point on the graph. (Lesson 9.1)
Notice that the polar coordinates of the point on the simplest form are (2,30). Then, the only option that does not match a proper transformation of coordinates is the point (-2,30)
During a tropical storm, the temperature decreased from 84° to 63º. Find the percent decrease in temperature during the storm. (a) 33% (b) 25% (c) 40% (d) 75%
To find the percentage of decrease, first, we divide.
[tex]\frac{63}{84}=0.75[/tex]This means 63° represents 75% of 84°. In other words, the temperature decreased by 25%.
Hence, the answer is B.Solve the inequality and graph the solution on the line provided.
< > M >
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4 -2
0 2 4
Click and drag to plot line.
2x64 -48
6
8
10 12
Answer:
x ≥ 8Step-by-step explanation:
GivenInequality 2x - 64 ≥ - 48Solution2x - 64 ≥ - 482x ≥ 64 - 482x ≥ 16x ≥ 8To graph the solution, plot the point x = 8, make it closed dot, shade the line to the right from this point.
Consider the following equation of a parabola.(y- 7)? = -4(x - 3)Step 1 of 3: Find the focus of the parabola.
Answer
Focus = (2, 7)
Explanation
Given:
The following is the equation of a parabola
[tex](y-7)^2=-4x(x-3)[/tex]What to find:
To find the focus of the parabola.
Step-by-step solution:
The general equation of a parabola can be given as,
[tex](y-k)^2=4p(x-h)[/tex]Comparing the general equation of a parabola with the given equation of a parabola, we have
4p = -4
∴ p = -4/4 = -1
Also,
h = 3
k = 7
Since h ± c = F
We have,
3 - 1 = 2
Therefore, the focus will be (h ± c, k) = (2, 7)
