Answer:
Step-by-step explanation:
Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.
Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.
Part 1: Writing Expressions
Q1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.
25(10j + 18 + 5j)
Your expression is good.
Q2. Translate the new algebraic expression you created in Question 1 to a verbal expression.
Skuttle offered to pay his sister Izzy $25 for every four leaf clover she finds in the woods. Izzy finds 18 clovers but decides to get Roxy’s help. Izzy finds clovers twice as fast as Roxy but they will over all make more money together.
Your verbal expression is good. It refrects your chosen equation.
Part 2: Writing Equivalent Expressions
Q3. Use your knowledge of the mathematical properties to create two equivalent algebraic expressions for the algebraic expression you created in Question 1. Explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.
Using commutative property of addition, the expression in question 1 can be rewritten as follows:
25(10j + 18 + 5j) = 25(10j + 5j + 18)
Using distributive property of multiplication over addition, the expression in question 1 can also be rewritten as follows:
25(10j + 18 + 5j) = 250j + 450 + 125j
Q 4. Use substitution to prove your algebraic expressions are equivalent. You may substitute any number for the variables you choose. Show all your work for complete credit.
Now we can subsitute, say 7 for j.
For the first expression, we have:
25(10j + 5j + 18) = 25(10(7) + 5(7) + 18)
= 25(70 + 35 + 18) = 25(123) = 3,075.
For the second expression, we have:
250j + 450 + 125j = 250(7) + 450 + 125(7) = 1,750 + 450 + 875 = 3,075.
Thus, we can see that both expressions are equivalent.
Part 3: Finish the Story
Q5. Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?
Sarah found 3 + 7 = 10 shark teeth.
John found 10 / 2 = 5 shark teeth.
The total money they earned is $5 x 15 = $75.
1) an expression that looks similar would be (could be anything)
4(5j+8+4j)
2) It would become:
four times the sum of five times a number, eight, and four times the same number
3) equivalents would be 4(9j+8)
or:
4(5j)+4(8)+4(4j)
4) say J=1 for simplicity
4(9+8)
=4x17
=68
next one would be:
4x5+4x8+4x4
=20+32+16
=68
ok, this is correct.
5) Sarah found 10 shark teeth for $50. John found 5 shark teeth for $25. They got $75 from their neighbor in total.
Step-by-step explanation:
Find the level of measurement (nominal, ordinal, interval, or ratio) and type quantitative or qualitative) for the following variable.
a. End-of-year stock classification (high yield, medium yield, or low yield)
b. Length (in feet) of a roll of plastic wrap advertised to be 30 feet long.
c. Temperature (in degrees Celsius)
d. Duration (in minutes) of a call to a customer support line
Answer:
a. Nominal and qualitative.
b. Ratio and quantitative.
c. Interval and quantitative.
d. Interval and quantitative.
Step-by-step explanation:
A level of measurement can be defined as a classification which is used to illustrate the attributes of the values assigned to variables. There are four (4) basic levels of measurement for a variable and these are;
1. Interval: data can be arranged in an ordering scheme and subtracting its differences is meaningful. Examples are year, temperature, time etc.
2. Ratio: data can be arranged in an ordering scheme and subtracting its differences is meaningful with respect to the value of true zero. Examples are height, price, weight, distance etc.
3. Ordinal: data can be arranged in an ordering scheme but subtracting its differences is meaningless or impossible. Examples are happy, sad etc.
4. Nominal: is characterized by data that are non-numerical, comprises of categories, labels or names and can't be arranged in an ordering scheme.
In this scenario, the level of measurement and data type are listed below;
a. End-of-year stock classification (high yield, medium yield, or low yield): the level of measurement is nominal because they are categorized. Also, the type of data is qualitative because it describes the quality of the stock and it's non-numerical in nature.
b. Length (in feet) of a roll of plastic wrap advertised to be 30 feet long: the level of measurement is a ratio because they can be arranged in order. Also, it's a quantitative data because it is numerical in nature.
c. Temperature (in degrees Celsius): the level of measurement is an interval because they can be arranged in order and the difference in value is meaningful. Also, the type of data is quantitative because it is numerical in nature.
d. Duration (in minutes) of a call to a customer support line: the level of measurement is an interval because they can be arranged in order and the difference in value is meaningful. Also, the type of data is quantitative because it is numerical in nature.
how many solutions does this graph have?
Answer:
one solution
Step-by-step explanation:
It will cross the x-axis one time
Use the given information below to determine the value of x.
A. 121
B. 180
C. 59
D. 62
HELP PLEASE like I really need help
Solve the equation x^2 - 16x+ 54 = 0 by completing the square.
Fill in the values of a and b to complete the solutions.
Answer:
[tex]x = 8\±\sqrt{10[/tex]
[tex]a =8[/tex] [tex]b = 10[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 16x + 54 = 0[/tex]
Required
Complete the square
[tex]x^2 - 16x + 54 = 0[/tex]
Subtract 54 from both sides
[tex]x^2 - 16x + 54 -54= 0-54[/tex]
[tex]x^2 - 16x = -54[/tex]
--------------------------------------------------
Take half of - 16
[tex](-16/2) = -8[/tex]
Square the result
[tex](-8)^2 = 64[/tex]
Add the squared result to both sides of the equation
--------------------------------------------------
So, we have:
[tex]x^2 - 16x +64= -54+64[/tex]
[tex]x^2 - 16x +64= 10[/tex]
Expand
[tex]x^2 - 8x - 8x + 64 = 10[/tex]
Factorize
[tex]x(x - 8) - 8(x - 8) = 10[/tex]
Factor out x - 8
[tex](x - 8)(x - 8) = 10[/tex]
[tex](x - 8)^2 = 10[/tex]
Take square roots
[tex]x - 8 = \±\sqrt{10[/tex]
Solve for x
[tex]x = 8\±\sqrt{10[/tex]
We have:
[tex]x = a - \sqrt{b}[/tex]
[tex]x = a + \sqrt{b}[/tex]
By comparing the above with: [tex]x = 8\±\sqrt{10[/tex]
Answer:
Step-by-step explanation:
Help pls show work if needed
Answer: The mode is 12
Step-by-step explanation: It is the most common number in the data set.
Leia, Chewy, Han Solo, and Luke have to cross a bridge. They only have one flashlight, and the bridge can only hold two people at a time. They each take a different length of time to get across the bridge. At any time, a group of two can only move as fast as the group's slowest person. The times that it takes each person to cross the bridge are:
Chewy -- ten minutes
Han Solo -- five minutes
Leia -- two minutes
Luke -- two minutes
How can the four get across the bridge the fastest?
Answer:
luke and han solo
Step-by-step explanation:
because han solo have the most mins and luke is one of thr 2 mins and that added is 7min
please what is the interquartile range ?
Answer:
3.
Step-by-step explanation:
15 - 12 = 3.
The ends of the box are the lower and upper quartiles.
The difference upper - lower = the interquartile range.
11. Explain how to evaluate the expression 9 +(45 x 2) = 10.
The Answer Is 18
Order Of Operation laws says that you must do the parentheses first, 45x2.
45x2=90
The next thing you must do is divide 90 by 10 since division is before addition.
90/10=9
Now combine like terms.
9+9=18
A student wants to report on the number of movies her friends watch each week. The collected data are below: 2 14 1 2 0 1 0 2 Which measure of center is most appropriate for this situation and what is its value? (4 points) a Median, 1.5 b Median; 3 c Mean, 1.5 d Mean; 3
Answer:
The best measure of center for a set of data is the median value.
To find the median list the values from
Smallest to largest:
0, 0, 1, 1, 2,2, 2, 14
Since there is an even number of values, find the middle two numbers, add them together and divide by 2:
1+2 = 3
3/2 = 1.5
The answer is median 1.5
Step-by-step explanation:
plz brain list
Need help with this problem!!
Answer:
Area:
4 x 4 = 16
Finding area of semi circle:
4 is your diameter so half of it is your radius which is 2 since half of 4 is 2!
2^2<---your radius being squared = 4
4(radius squared) x 3.14(pi) = 12.56
12.56 divided by 2 since its a semi circle is = 6.28
6.28 + 16 = 22.28 is your area
Perimeter is:
4 + 4 + 4 (all sides of a square are equal therefore one or two given lengths will be all the sides) = 12
Circumference:
Radius is 2,
2(you just always have to multiply this number when finding circumference) x 3.14(pi) x 2(radius), 2 x 3.14 x 2 = 12.56
12.56 divided by 2 = 6.28
6.28 + 12 = 18.28 is your perimeter.
Just a refresh:
Circumference Formula:
2(always use this number when finding circumference) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x radius
Area of a Circle Formula:
Radius squared x pi(3.14 or 22/7 whatever they tell you to use for pi)
Another thing you should remember:
Whenever it gives you 1/4 of a circle or 1/3 or a semi circle or any fraction, REMEMBER TO DIVIDE BY THAT DENOMINATOR TO WHAT YOU GET FROM EITHER CIRCUMFERENCE OR AREA OF A CIRCLE!
50 POINTS. A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t)= -16t^2 + 64t + 4, where t is measured in seconds and h is the height in feet. What domain makes sense for this function
Answer:
The domain that makes sense for this function is all values greater than or equal to 0.
Step-by-step explanation:
A ball is thrown into the air from a height of 4 feet at time t = 0. It is modeled by the function:
[tex]h(t)=-16t^2+64t+4[/tex]
The domain of the function is time t. The range of the function is the ball's height in the air h.
Since time is our domain, we must restrict our domain to values equal to or greater than 0 since time cannot be negative.
Therefore, the domain that makes sense for this function is all values greater than or equal to 0.
In interval notation, this is:
[tex][0, \infty)[/tex]
And as an inequality:
[tex]t\geq 0[/tex]
What is (5b + 3x)(5d-3b)
Jena has a small jewelry box in the shape of a cube with side lengths of two inches. How much greater is the volume of her large jewelry box with the dimensions 7 inches, 5 inches, and 4 inches?
Plz help no links please
Answer:
216 cubic inches
Jena's large jewelry box is 132 inches³ bigger than her small cube jewelry box.
What is a cube?
A cube is a three dimensional figure. All of it's sides are equal in length and all the planes of it are perfect square.
Given, length of the each side of Jena's small jewelry box = 2 inches.
Therefore, the volume of the small jewelry box is = 2³ inches³ = 8 inches³.
Again, length of the each side of Jena's small jewelry box are 7 inches, 5 inches, and 4 inches.
Therefore, the volume of the small jewelry box is = (7 × 5 × 4) inches³ = 140 inches³.
Hence, the difference = (140 - 8) inches³ = 132 inches³.
Learn more about cube here: https://brainly.com/question/21270685
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A popular internet subscription service for movies, TV series, and documentaries conducts a survey in which it randomly samples 1,000 of its customers. The survey asks the customers which way they use their streaming service the most: (1) watching movies, (2) watching TV series, or (3) watching documentaries. They also ask the level of satisfaction with the service they most often use (on a scale of 0 to 10 with 0 very poor and 10 excellent). Is there statistical evidence for this internet subscription service that the mean satisfaction differs between customers who watch movies, TV series, or documentaries the most?
(a) State the hypothesis for conducting ANOVA. What were the assumptions on which the ANOVA was based?
(b) What F test statistic is needed to reject the null hypothesis at the signficance level 0.05?
(c) Suppose the test statistic is observed at F 0.46 and the p-value equals 0.63. State your conclusion in the context of this problem using the significance level .01.
Hello :D help pls? Thanks
What is the area of this partial circle if the radius is 8 inches long? Leave your answer in terms of pi.
Answer:201.06
Step-by-step explanation:
HELP ME IN MATH PLEASE IM FAILING :( NO FAKE ANSWERS PLS :)
The area of a parallelogram has the following formula: A=bh
Plug-in the given numbers.
Base=14cm
Height=13cm
A=bh
A=14 x 13
A=182
Therefore, the area of the figure is 182cm2
Answer: 182 square centimeters
Step-by-step explanation:
The formula for finding the area of a parrallelogram is A = bh. If the top measurement is 14 cm, then the bottom measurement is also 14 cm. The height is 13 cm.
A = (14) (13)
A = 182 cm^2
harrison bought a 10 foot ramp to load his dirt bike into the back of his truck. the ramp hooks to the 3 foot high tailgate. how far away from the tailgate doe the ramp sit in the ground?
Answer:
9.54 feet
Step-by-step explanation:
Using Pythagoras rule :
Length of ramp = 10 feets = hypotenus
Hypotenus² = opposite² - adjacent²
d² = 10² - 3²
d² = 100 - 9
d² = 91
d = √91
d = 9.5393920
d = 9.54 feets
If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D. what is the perimeter of
A'B'CD?
A)
30 units
B)
60 units
90 units
D)
120 units
Convert 22 days to weeks and days.
22 days=
Convert 454 minutes to hours and minutes.
454 minutes =
Convert 4 years and 4 months to months.
4 years and 4 months =
Convert 12 pounds and 13 ounces to ounces.
12 pounds and 13 ounces=
Answer:
22 days = 3 weeks and 1 day
454 minutes = 7 hours and 34 minutes
4 years and 4 months = 148 months
12 pounds and 13 ounces = 205 ounces
The complex plane is also known as what?
Find the area of the circle when the circumference is 26 in
Answer:
"None of the answers are correct."
Step-by-step explanation:
The formula for Area given the circumference is A = [tex]\frac{C^{2} }{4\pi }[/tex]
[tex]\frac{26^{2} }{4\pi } = 53.79437[/tex]
So none of the above are correct
HELP ME PLEASEEEEEEEEEEEE
Answer:
C) (-4,2)
Step-by-step explanation:
It would be in quadrant II, so (-4,2)
HELP LOL!!
What is the independent variable?
Amplitude
Frequency
Tension
Density
Speed
6. What is the dependent variable?
Amplitude
Frequency
Tension
Density
Speed
7. What are the constants? (Choose 3)
Amplitude
Frequency
Tension
Density
Speed
Please help me please
Answer:
Option D
Step-by-step explanation:
→ Simplify the option
3 × 3 × 2 × 2 = 36
→ Simplify the other part
3 × 2 × 2 = 12
URGENT!! PLS HELP 16 students are competing an art contest in how many different ways can students finish first second and third
A bakery offers a sale price of $2.80 for 3 muffins. What is the price per dozen?
Answer: 11.2$
Step-by-step explanation:
A recipe calls for 21 scoops of sugar. each scoop is 2.5 oz. how many scoops do you need if each scoop holds 3.5 oz of sugar ?
Answer:
we need 6 scoops of sugar
I will give you Brainiest if you are right.
Answer:
Students 1 & 4
Step-by-step explanation:
An expression has NO equal sign, EQUATIONS have equals.
2 & 3 have equals which makes then equations.
~R3V0
ANSWER FAST
.Give the value of a.
a - 15 = 21
Answer:
a=36
Step-by-step explanation:
a - 15 = 21
+15 +15
a = 36