Noelle bought gifts for her nine nephews and the total cost of these gifts is given. By setting up equations and solving them, we find that she purchased 6 videos and 3 CDs.
Step by Step Solution:
Noelle bought gifts for her nine nephews, which can be either videos costing $14.95 each or CDs costing $16.88 each, and spent a total of $140.34. We need to determine the number of videos and CDs she bought.
Let's denote the number of videos Noelle bought by V and the number of CDs by C. We can set up the following equations based on the given information:
V + C = 9 (as she bought gifts for nine nephews)
14.95V + 16.88C = 140.34 (total amount spent)
To solve these equations, we can use the substitution or elimination method. Let's use substitution:
From equation (1), we get:
C = 9 - V
Substitute this into equation (2):
14.95V + 16.88(9 - V) = 140.34
Expanding and simplifying:
14.95V + 151.92 - 16.88V = 140.34
-1.93V + 151.92 = 140.34
-1.93V = 140.34 - 151.92
-1.93V = -11.58
V = 6
Substitute V = 6 back into C = 9 - V:
C = 3
Therefore, Noelle bought 6 videos and 3 CDs.
a rectangular box has a height of 7 centimeters and a volume of 336 cubic centimeters. The length of the box is three times the width.
Write an equation describing this situation and find the length and width of the box.
The length and width of a box is required.
The equation describing the situation is [tex]V=3W^2H[/tex]
Length of the box is 12 cm and width of the box is 4 cm.
h = The height of the box = 7 cm
V = Volume of the box = [tex]336\ \text{cm}^3[/tex]
Length of the box is three times the width.
[tex]L=3W[/tex]
Volume of a cuboidal box is given by
[tex]V=LWH\\\Rightarrow V=(3W)WH\\\Rightarrow V=3W^2H[/tex]
The equation describing the situation is [tex]V=3W^2H[/tex]
Solving the equation
[tex]W=\sqrt{\dfrac{V}{3H}}\\\Rightarrow W=\sqrt{\dfrac{336}{3\times 7}}\\\Rightarrow W=\sqrt{16}=4[/tex]
[tex]L=3W=3\times 4\\\Rightarrow L=12[/tex]
Length of the box is 12 cm and width of the box is 4 cm.
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Brian needs 10 quarts of Dr. Pepper. He can buy containers with 6 ounces of Dr. Pepper in them. How many containers does he need to buy to have 10 quarts.
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
1 quart = 32 ounces
10 x 32 = 320 ounces needed
320 ÷ 6 = 53.33
Since he can't buy half of a container he would need to purchase 54 containers.
To fulfill a need for 10 quarts of Dr. Pepper using 6-ounce containers, Brian must buy 54 containers, after converting quarts to ounces and dividing by the container size.
Explanation:Brian needs 10 quarts of Dr. Pepper. He is considering buying containers that hold 6 ounces each. To determine how many containers he needs, we must convert quarts to ounces because the volume of the drink given in two different units. There are 32 ounces in 1 quart.
Therefore, 10 quarts is equivalent to 320 ounces (10 quarts x 32 ounces/quart). Since each container holds 6 ounces, Brian needs 320 ÷ 6 containers. Dividing 320 by 6 gives approximately 53.33. Since Brian cannot buy a fraction of a container, he will need to purchase 54 containers of Dr. Pepper to meet his requirement of 10 quarts.
The area of this triangle is
56
c
m
2
and the height is 7 cm. Find the base.
Choose the correct answer from the selection below.
Answer:
Base = 16 cm
Step-by-step explanation:
Area of triangle is given by:
Area of Triangle = [tex]\frac{1}{2}bh[/tex]
Where [tex]b[/tex] is the base and [tex]h[/tex] is the height.
The problem says that area is 56 ([tex]A=56[/tex]) and height is 7 ([tex]h=7[/tex])
Plugging in the values we can solve for base:
[tex]A=\frac{1}{2}bh\\56=\frac{1}{2}b(7)\\56=\frac{7}{2}b\\b=\frac{56}{\frac{7}{2}}=56*\frac{2}{7}=16[/tex]
Hence, the base of the triangle is 16 cm
which of the following are equal to the rational expression below? x^2+x-6/x^2-2x-15
Hello from MrBillDoesMath!
Answer:
(x-2)/(x-5)
Discussion:
Factor the numerator and denominator:
x^2 + x - 6 = (x+3)(x-2)
x^2-2x-15 = (x+3)(x-5)
So
( x^2 + x - 6) / x^2-2x-15 = ( (x+3)(x-2) ) / ( (x+3)(x-5) )
Cancelling the (x+3) term in numerator and denominator gives
(x-2)/(x-5)
Regards,
MrB
(x-2)/(x-5)
A rational expression can have:any number of vertical asymptotes,only 0 or 1 horizontal asymptote,only 0 or 1 oblique (slanted) asymptoteWhat are the steps in solving rational expressions?Solve rational equations.Check for extraneous solutions.Solve application problems involving rational equations.Factor the numerator and denominator:
x^2 + x - 6 = (x+3)(x-2)
x^2-2x-15 = (x+3)(x-5)
So
( x^2 + x - 6) / x^2-2x-15
= ( (x+3)(x-2) ) / ( (x+3)(x-5) )
Cancelling the (x+3) term in numerator and denominator gives
(x-2)/(x-5)
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The perimeter of a rectangular deck is 4 times its width. If the deck's perimeter is 30 feet, what is the deck's area?
Answer:
i think it is 120
Step-by-step explanation:
4 multiplied by 30 is 120
Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
The common difference is –10.
The common difference is 10.
The common ratio is –9.
The common ratio is 9.
Answer:
The common difference would be -10.
Step-by-step explanation: If it were +10 then it would be: 9, 19, 29, 39
If it had a common ratio of -9 then it would be: 9, -81, 729, -6561
It it had a common ratio of 9, then it would be: 9, 81, 729, 6561
Answer:
A
Step-by-step explanation:
Can someone please help me with these
i think it will be B and then the second will be C
Answer:
Step-by-step explanation:
4)
30 is 60% of 50
5)
Amount Saved (Discount): $
350
Sale / Discounted Price: $
650
What food resources can be harvested from the ocean?
Select the three correct answers.
oysters
cranberries
shrimp
fish
(oops sorry for wrong topic dont know how to edit the topic sorry)
Answer: Oysters, Shrimp and Fish
2> -2-c.
how would I graph this?
Answer:
-4< c
Step-by-step explanation:
2> -2-c
Add 2 to each side
2+2> -2+2-c.
4 > -c
Divide each side by -1. Remember that dividing by -1 will flip the inequality.
4/-1 < -c/-1
-4< c
Jessica has driven exactly 90% of the distance to her friends home. Which statement about this trip could be true?
A. Jessica has driven exactly 40 miles out of a total of 360 miles.
B. Jessica has driven exactly 270 miles out of a total of 360 miles
C. Jessica has driven exactly 360 miles out of a total of 400 miles
D. Jessica has driven exactly 396 miles out a total 490 miles
Answer:
The answer is C) Jessica has driven exactly 360 miles out of a total of 400 miles
Step-by-step explanation:
Since 90% is equal to 0.9 of 1
And you need to figure out what statement is true
You would take the largest number from each answer choice and multiply it by 0.9
For Example: In answer choice A), it says Jessica has driven exactly 40 miles out of a total of 360 miles.
So you would multiply 360 by 0.9
Which gives you 324
Which is not 40
Therefore it is wrong
Answer:
c
Step-by-step explanation:
the actual value of the population that the parameter tries to estimate is called the statistic
true or false
this is for data analysis
The statement is false; a parameter is the actual value in the population, while a statistic is the estimate derived from a sample. It's crucial to differentiate between the two when discussing data analysis and inferential statistics.
The statement in question is false. The actual value of the population that the parameter tries to estimate is not called the statistic; it is indeed called a parameter. Parameters are the true values within a population. On the other hand, a statistic is an estimate of a population parameter and is derived from a sample that is intended to be representative of the population.
For instance, consider the population parameter of average corn yield in an area. This parameter is estimated with a sample average, which is the statistic. The sample average serves as a best estimate but is distinct from the true average yield for all farms in the target area, exhibiting variability from sample to sample.
The work of data analysis and inferential statistics involves using sample statistics to make inferences about population parameters. Understanding the difference between the two is crucial, and it involves acknowledging the concept of sampling error that arises due to discrepancies between the parameter and the statistic used to estimate it.
There are three numbers for the combination to the store’s safe. The first number is 14.The other two numbers can be multiplied together to give a product of 24.What are all the possibilities of the other two numbers?Write your answers as multiplication number sentence, and then list all the possible combinations to the safe.
Please somebody help me
Answer:
Corresponding: 1 and 5, 2 and 6, 3 and 7, 4 and 8
Alternate Exterior Angles: 1 and 8, 2 and 7
Alternate Interior Angles: 3 and 6, 4 and 5
Step-by-step explanation:
Searching up the definitions could really help you understand what kinds of angles there are.
Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
The corresponding angles are the ones at the same location at each intersection.
In a school election, Violet received 156 votes. She got 60% of all the votes. How many total votes were cast? Which equation CANNOT be used to answer this question?
a. 0.6 times 156 = x
b. 156 = 0.6x
c. 156/0.6 = x
d. 156/x = 60/100
Answer:
1) Total votes = 260
2) option (a) CANNOT be used to answer this question
================================================
Step-by-step explanation:
Part (A)
let all the votes = x
Violet received 156 votes which equal to 60% of all the votes
∴ 156 = 60% of x
60% = 60/100 = 0.6
∴156 = 0.6 x ⇒ x = 156/0.6 = 260 votes
Part (B) :
options (b), (c) and (d) can be used to answer this question because they will give the same result of part (A)
While option (a) CANNOT be used to answer this question.
Check the following
a. 0.6 times 156 = x ⇒ x = 93.6
b. 156 = 0.6x ⇒ x = 260
c. 156/0.6 = x ⇒ x = 260
d. 156/x = 60/100 ⇒ x = 260
What is the value of h(-2)
Answer:
C
Step-by-step explanation:
Just took the test. Good luck
What is the 15th term of the sequence an =-3n+50
Answer:
a15 = -5
Step-by-step explanation:
Let n=15 for the 15th term
a15 = -3*15 +50
a15 = -45+50
a15 = -5
To find the 15th term of the sequence an = -3n + 50, replace n with 15 in the given formula. The calculation becomes -3(15) +50 which simplifies to -45 + 50, finally giving the result 5. Therefore, the 15th term of the sequence is 5.
Explanation:In mathematics, determining the nth term of a sequence involves applying the sequence formula, and substituting the specific term number, denoted as n, into the formula. For instance, consider the sequence an = -3n + 50. To find the 15th term (a15), one substitutes n = 15 into the formula: a15 = -3(15) + 50. Simplifying, a15 = -45 + 50, resulting in a15 = 5. This process showcases how a specific term in the sequence can be calculated systematically, providing a precise value for the 15th term. The formula an = -3n + 50 encapsulates the underlying pattern, allowing for the determination of any term within the sequence.
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4x-y=6 and 3x+2y=21 Solve by elimination
Answer:
x=3,y=6
Step-by-step explanation:
4x-y =6
3x+2y = 21
To use elimination we will multiply the first equation by 2
2(4x-y) =6*2
8x -2y =12
We will add this equation to the second equation to eliminate y
8x -2y =12
3x+2y = 21
-----------------
11x = 33
Divide each side by 11
11x/11 = 33/11
x =3
We still need to solve for y
3x+2y = 21
Substituting x=3
3*3+2y = 21
9+2y =21
Subtract 9 from each side
9-9+2y = 21-9
2y = 12
2y/2 = 12/2
y =6
Which inequality represents this sentence?
Five plus four is less than ten plus two.
5+4 < 10+2
10+2 < 5+4
5+4 ≤ 10+2
5+4 > 10+2
Answer:
5+4<10+2
Step-by-step explanation:
Two sides of a triangle measure 9 cm and 23 cm. Which could be the measure of the third side of the triangle?
Hello,
Let's be x the length of the 3 side (9,x,23) ==>x>0
Using inequality triangular:
9<x+23==>x>9-23==>x>-14 (done)
x<9+23==>x<32
23<x+9==>x>14
SO 14<x<32
Answer:
[tex]14<x<32[/tex]
Step-by-step explanation:
Let x be the third side of triangle.
We have been given that two sides of a triangle measure 9 cm and 23 cm. We are asked to find the measure of third side of triangle.
We will use triangle inequality theorem to solve our given problem.
Triangle inequality theorem states that sum of two sides of a triangle must be greater than third side of triangle.
Using triangle inequality theorem, we will get:
(1) [tex]x+9>23[/tex]
[tex]x+9-9>23-9[/tex]
[tex]x>14[/tex]
(2) [tex]9+23>x[/tex]
[tex]32>x[/tex]
(3) [tex]x+23>9[/tex]
[tex]x+23-23>9-23[/tex]
[tex]x>-14[/tex] (Not applicable as length cannot be negative).
Therefore, the measure of third side of triangle would be [tex]14<x<32[/tex].
What is the effect on the graph of the function f(x) = |x| when f(x) is changed to f(4x)? A) stretched vertically B) compressed vertically C) stretched horizontally D) compressed horizontally
Answer:
D) compressed horizontally
Step-by-step explanation:
he graph of the function f(x) = |x|
f(x) is changed to f(4x)
When we multiply some number with f(x) outside , then there will be a vertical stretch or compression on the graph
When we multiply some number with x inside f(x), then there will be a horizontal stretch or compression on the graph
Here 4 is multiplied with x inside f(x)
If the number is greater than 0 and less than 1 , then its a horizontal stretch
If the number is greater than 1 then it is a horizontal compression
Here 4 is greater than 1, so there will be a horizontal compression by a factor 1/4
Answer:
the correct answer is c i just got it wrong
Step-by-step explanation:
Gene paid a deposit on a leased car. The deposit earns 2.8 percent simple annual interest. At the end of the year, the interest that is earned is $22.40. What was the amount of the original deposit?
Answer:
it would be 800 because 2.8% of 800 is 22.40 and that is your answer.
hope i helped :)
Answer:
$800.
Step-by-step explanation:
We have been given that Gene's deposit earns 2.8 percent simple annual interest. At the end of the year, the interest that is earned is $22.40. We are asked to find the amount of original deposit.
To find the original amount of deposit, we use simple interest formula:
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Let us convert our given interest rate in decimal form.
[tex]2.8\%=\frac{2.8}{100}=0.028[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\$22.40=P*0.028*1[/tex]
[tex]\$22.40=P*0.028[/tex]
[tex]\frac{\$22.40}{0.028}=\frac{P*0.028}{0.028}[/tex]
[tex]\$800=P[/tex]
Therefore, the amount of original deposit was $800.
A game requires you to roll a dice and flip a coin. How many possible outcomes are there?
Answer:
The total amount of possible outcomes is 12.
Step-by-step explanation:
1.) 1-h
2.) 1-t
3.) 2-h
4.) 2-t
5.) 3-h
6.) 3-t
7.) 4-h
8.) 4-t
9.) 5-h
10.) 5-t
11.) 6-h
12.) 6-t
Hope this helps!! (:
a number x is greater then 25.8 write the word sentence as an inequality
Answer:
x> 25.8
Step-by-step explanation:
A number x is greater then 25.8 write the word sentence as an inequality
x> 25.8
To represent the statement 'a number x is greater than 25.8' as an inequality, we write it as 'x > 25.8'.
The number = x
The number greater than = 25.8
If a number x is greater than 25.8, we can represent this relationship using an inequality symbol.
Based on the meaning of inequality symbols, the correct way to write this statement is:
x > 25.8
This inequality reads as "x is greater than 25.8", thus directly answers the given question by converting the word sentence into a mathematical inequality.
help me understand this please
Basically, geometry screws with your mind. It's tough, but you have to imagine these triangles set up next to each other, or use your finger to trace to the different points, that way you can situate yourself.
So, there are three triangles, ΔCAD, ΔBCD, and ΔBAC. and they're all similar. this would be the answer to your first question. (If you need help finding them, use the methods I mentioned earlier :))
Now, to figure out the proportions, look at which sides are the same (not literally, but size wise. Like, the hypotenuse is always the 2nd longest, the bottom is the longest, and the side is the shortest.
CD and BD go together because #1 the letters go from the top tip of the Δ to the bottom where they meet the bottom side. Now, as for AD, that's the hypotenuse. So, you find another hypotenuse from the other two triangles. (The other two are AC and CB).
the last one heey put that CA and BA are proportionate. CA and BA happen to both be bottoms of Δ's. then they put AC. AC is both a hypotenuse and a bottom, so you have a variety of sides you could go with. (hypotenuses:AD, CD, bottoms:AB, and CB)
I hope this helps!
The area of a rectangular pool deck is 168 ft². The length is 14 ft. What is the width of the pool deck?
Answer:
12 ft
Step-by-step explanation:
First of all, the formula of calculating the area of a rectangle is: w* l = a So, in this equation ? * 14 = 168You then "do the equation backwards": 168/14 = ?You calculate and get 12What is the initial y-value of the linear function whose graph includes the points (-5, 0) and (6, -22)?
The initial y-value (or y-intercept) of the linear function that includes the points (-5, 0) and (6, -22) is -10.
Explanation:The student is asking about the initial y-value of a linear function, which is also known as the y-intercept. This is the value of y when the line crosses the y-axis (where x=0). To find this, we first find the slope of the line using the formula: slope = (y2 - y1) / (x2 - x1) = (-22 - 0) / (6 - (-5)) = -22 / 11 = -2. Then we use the point-slope form of a linear equation to find the y-intercept 'b': y - y1 = m*(x - x1), substituting one of the points and the found slope: 0 - (-2)*(-5) = b gives us b = -10. This implies that the initial y-value of the linear function is -10.
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What is the value of this expression 8/15 divided by
(0.35)
Answer:
1 12/21 or 32/21
Step-by-step explanation:
Okay, it may seem a little complex but you will have to break it down bit by bit. So, if you are dividing a fraction by a decimal I would turn the decimal into a fraction, in this case turn 0.35 into a fraction. You get it? I'm a seventh grader and I get stuck on these too! So, 0.35 as a fraction is 7/20. Next you divide 8/15 by 7/20. Not trying to get you confused but in my math class this is the same thing as multiplying by the reciprocal of the second fraction. So, what is 8/15 divided by 7/20 or 8/15 times 20/7? I will do the multiplying way so lets do the numerators first. 8 times 20 is 160. For the denominators, 15 times 7 is 105. Your final fraction is 160/105. Lastly you have to simplify it. It turns into a mixed number and your final answer is 1 12/21 or simplified is 32/21. Hope this helped! :-)
Final answer:
To find the value of the expression 8/15 divided by 0.35, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction to get the final answer.
Explanation:
To find the value of the expression 8/15 divided by 0.35, we need to divide 8/15 by 0.35.
We can represent 0.35 as a fraction by dividing it by 1. So, 0.35 is equal to 35/100 or 7/20.
Now, let's divide 8/15 by 7/20.
When we divide fractions, we multiply the first fraction by the reciprocal of the second fraction.The reciprocal of 7/20 is 20/7. So, we can rewrite the expression as (8/15) * (20/7).Multiplying these fractions, we get (8 * 20) / (15 * 7).Simplifying further, we have 160/105.Therefore, the value of the expression 8/15 divided by 0.35 is 160/105.
Name a fraction that is equivalent to 1/2.
Answer:
2/4
Step-by-step explanation:
A fraction that is equivalent to [tex]\frac{1}{2}[/tex] is [tex]\frac{14}{28}[/tex]
These fractions have the same value. Although the numerators and denominators of these fractions look different, their fractional values are the same.
3/8 divided by 5 can you plz help me
When you divide a fraction you always multiply the reciprocal of number you divide. So then what you are doing is 3/8*5 which is 15/8.
Hope this helps! <3
Answer:3/4
Step-by-step explanation:
3/8 ÷ 5
How do you graph y=2x-1
Answer:
y is the vertical axis. x is the horizontal axis. Replace any value in x to get your y value. The value you input as x is your x value. God this sounds confusing. I'd graph it for you but i don't know how to do that on Brainly.
Step-by-step explanation:
Step-by-step explanation:
For each value of x you will have a y value
Step 1: Make a Chart with values
X | 1 2 3
Y |
Step 2: Substitute the x values in the y function
y= 2(1) - 1
y=2-1
y=1
Step 3: Fill the Chart with the obtained values
X | 1 2 3
Y | 1
Step 4: Plot the points as coordinates (x, y) i.e (1,1)
Step 5: Connect the points
Step 6: Be happy, you just learn how to plot. You can follow this proccedure for any kind of function.