Answer:
24 gallons
Step-by-step explanation:
To answer this question let's call "a" the capacity of the tank in gallons.
Initially it is one third of its capacity, but when 4 gallons are added, it is half full.
This statement can be written as an equation in the following way:
[tex]\frac{1}{3}a+4=\frac{1}{2}a\\[/tex] (1)
This equation represents the given conditions, therefore solving it we can clear "a" the capacity of the tank in gallons
Solving the equation we have:
[tex]\frac{1}{3}a-\frac{1}{2}a =-4\\a (\frac{1}{3}-\frac{1}{2}) = -4\\a (-\frac{1}{6}) = -4\\a (\frac{1}{6}) = 4\\a = 24\\[/tex]
Therefore the capacity of the tank is 24 gallons.
We can check this result by verifying if it meets the given conditions. The half of 24 is 12. Therefore, if we divide 24 at 3 and then add 4, we should get half the capacity of the tank, that is, 12 gallons.
[tex]\frac{24}{3} = 8\\8 + 4 = 12[/tex]
12 is half the capacity of the tank, then equation (1) is met and the result is checked
Kevin has $25 . MP3 downloads cost $0.75 each . How many songs can he download and still have $13 left to spend
He can download at most 16 songs to leave $13 for himself to spend.
Use the equation $25-$0.75(x)=$13
The cost to rent a hall for alysa’s sweet sixteen birthday party is $300. Her mom said she must keep the party cost to no more than $5.00 a person. She watched her mom write an expression on her notes that is listen below. What does the variable represent in this expression. 300+200/x
In the expression 300 + 200/x for Alysa's party, the variable 'x' stands for the number of attendees to ensure the party cost stays within the $5.00 per person limit.
In the expression 300 + 200/x, the variable x represents the number of people attending Alysa's sweet sixteen birthday party.
Alysa's mom has set a maximum cost of $5.00 per person, and the total cost for renting the hall is $300, which is a fixed cost. To ensure the party cost does not exceed $5.00 per person, the cost per person is calculated by dividing the additional $200 by the number of attendees (x).
Distribute and simplify the radicals below
2√3*(2√+√3)
Given expression: [tex]2\sqrt{3} *(\sqrt{2}+ \sqrt{3})[/tex].
We need to distribute and simplify.
We have 2√3 in front of paranthesis.
We need to distribute 2√3 over paranthesis.
2√3*(√2+√3) would give : 2√3 * √2 + 2√3 * √3.
We need to multiply radical numbers inside radicals and outside number by outside number.
On simplifying, we get
2√6 + 2 * 3 = 2√6 + 6.
Therefore, final answer is 6+2√6.
Answer:
6+2√6
Step-by-step explanation:
D on edg
Multi-step: Glen finds the sum of (3 3/10 + 4 1/3) + 2 1/2 and Ana finds the sum of (4 1/3 + 3 3/10) + 2 1/10. What is the total sum if their answers?
Step-by-step explanation:
This is what I could do please
Can you list these least to greatest? It doesn’t have to be in the same form
8. -1.6, -7/8, 0.9, 6/5, 5/2
9. -16/3, -1.3, -2/3, 0.5, 5/9
find the prime factorizations foor the following numbers 36 and 84
15 points! Thanks so much!
answer is C 1410.01 mark as brainliest
you make dog collars and anticipate selling all of them at a craft fair you spent $85 for materials and hope to make a $90 profit how much should you charge for each collar
To cover costs and achieve a $90 profit, each collar should be sold for $175 divided by the number made.
To determine the selling price for each dog collar, we need to consider both the cost of materials and the desired profit.
1. **Calculate total cost**:
- Cost of materials: $85
- Desired profit: $90
Total cost = Cost of materials + Desired profit
= $85 + $90
= $175
2. **Determine number of collars**:
Since you anticipate selling all the collars, the total profit should cover the cost of materials and the desired profit.
3. **Calculate selling price per collar**:
Divide the total cost by the number of collars to determine the selling price for each collar.
[tex]\[ \text{Selling price per collar} = \frac{\text{Total cost}}{\text{Number of collars}} \][/tex]
Substitute the values:
[tex]\[ \text{Selling price per collar} = \frac{\$175}{\text{Number of collars}} \][/tex]
Without knowing the exact number of collars, we can't determine the exact selling price per collar. However, if you know the number of collars you're making, you can use this formula to find the selling price for each collar.
what is the y intercept of -10x -1/2 y = 5 ?
y-intercept is when x = 0 or the b-value when in the form y = mx + b
-10x - [tex]\frac{1}{2}y[/tex] = 5
-10(0) - [tex]\frac{1}{2}y[/tex] = 5
[tex]\frac{-1}{2}y[/tex] = 5
[tex]-2(\frac{-1}{2}y)[/tex] = -2(5)
y = -10
Answer: (0, -10)
-10x - [tex]\frac{1}{2}y[/tex] = 5
+10x +10x
[tex]\frac{-1}{2}y[/tex] = 10x + 5
[tex]-2(\frac{-1}{2}y)[/tex] = -2(10x + 5)
y = -20x - 10
b = -10
Hey can anyone help me? I just need help with the bottom table.
The question asks how many hours each person worked, and how much they earned, or basically they're asking for the right two columns to be filled in. (Total hours = how many hours each person worked, and Total pay = how much they earned)
Now let's recall the information which is given.If we look at the table, we can see we're given information for each person, Sue, Bob, and Chris. We're given their rate per hour, and the numbers of hour they worked for each day.
Now that we've looked at that, we can connect the information we're given and what the question is asking.The two things we are looking to calculate can correspond with a part of information we're given:
Total Hours <-> hours worked each day: we can see these connect as the total hours work (I'm assuming) are weekly, and to calculate the total hours worked we can look the hours worked for each day as days make up weeks. Therefore, if you just add the number of hours worked on Monday, Tuesday, Wednesday, Thursday, and Friday together, you get the total hours worked in the week.Total Pay <-> rate per hour and total hours: the total amount of pay can be calculated once we know the rate per hour and the total hours. The rate per hour is based off of the hours, it's how much is earned every hour, and the total hours include the total amount of hours worked. Therefore, if you multiply the two together you'll get the total pay. (Multiplying is essentially adding a number, another number of times, in this case it's adding the pay rate, the total hours amount of times.)Now that we know how they're connected, and therefore how to solve the equation, we can complete the calculations.Find the total hours worked for each person:
Sue: Monday: 3.5 hours, Tuesday: 10.5 hours, Wednesday: 5.25 hours, Thursday: 6 hours, Friday: 12 hours. 3.5 + 10.5 + 5.25 + 6 + 12 = 37.25 total hours workedBob: Monday: 5 hours, Tuesday: 3.5 hours, Wednesday: 7.75 hours, Thursday: 5.5 hours, Friday: 10.25 hours. 5 + 3.5 + 7.75 + 5.5 + 10.25 = 32 hours total workedChris: Monday: 6.5 hours, Tuesday: 7.25 hours, Wednesday: 9.5 hours, Thursday: 3.5 hours, Friday: 3.5 hours. 6.5 + 7.25 + 9.5 + 3.5 + 3.5 = 30.25 hours totalWe have now calculated the total hours for each person. You can therefore fill in the column of total hours, starting from the top, with 37.25 hours, then 32 hours, and finally 30.25 hours.
The final step is to calculate the total pay for each person.As I stated earlier, the only thing needed to do to find the total pay is to multiply the total hours my the rate per hour.
Sue: $16.50 per hour, 37.25 hours. 16.50 * 37.25 = $614.625, rounds up to $614.623Bob: $11.25 per hour, 32 hours. 11.25 * 32 = $360 dollarsChris: $14.50 per hour, 30.25 hours. 14.5 * 30.25 = 438.625, rounds up to $438.63Now we have all our solutions. For the total hours column, top to bottom: 37.25 hours, 32 hours, 30.25 hours. For the total pay column, top to bottom: $614.623, $360, $438.63Hope this helped!Which of the following mathematical statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 7 − 6 = 1 D. 42 ÷ 6 = 7
Answer:
B: 7 x 6 = 42 and the only reason that B is the answer is because a quotient is the word used for a answer when you multiply c:
Step-by-step explanation:
What is the value of the expression? −26−(6)2 Enter your answer in the box.
Is it −26−(6)^2? If so
−26−(6)^2
= -26 - 36
= - 62
If −26−(6)2 (means 6 times 2) then
= -26 - 12
= -38
A costume designer has 36 bat buttons and 18 black cat buttons she must use to create costumes. In her costumes, she used both bat and cat buttons. what is the largest number of costumes she can make?
A costume designer has 36 bat buttons and 18 black cat buttons she must use to create costumes
To find the largest number of costumes we take GCF
GCF gives the largest and greatest number of grouping
WE find GCF of 36 and 18
1, 2, 3, 6, 9, 18 are the factors of 18
1, 2, 3, 4, 6, 9, 12, 18, 36 are the factors of 36
Greatest common factor GCF is 18
So , 18 is the largest number of costumes she can make.
Solve each system by elimination. Show ALL work!!!
3) -7x-7y=-14
2x-4y=16
Solution:
Work:
The attempt to solve the provided system of equations by elimination encountered a misunderstanding in the manipulation of the equations. A straightforward correction highlighted the importance of accurately aligning coefficients before attempting to eliminate a variable, underscoring the necessity of precise calculations in solving such problems.
Explanation:To solve the given system of equations by elimination, we start with the system:
-7x - 7y = -142x - 4y = 16Our goal is to eliminate one of the variables, either x or y. To do this efficiently, we aim to make the coefficients of either x or y the same or exact opposites. In this case, we can easily adjust the second equation to align the coefficients of y by multiplying the entire equation by a suitable number.
Multiply the first equation by 1 (effectively keeping it the same) and the second equation by 7/4 to align the y coefficients:
-7x - 7y = -14(7/2)x - 7y = 28However, there seems to be a misunderstanding in the calculation or transcription of the equations provided. Instead, let's correct the approach based on the equations listed in the inquiry.
Looking at the original system provided:
-7x - 7y = -142x - 4y = 16We see an opportunity to simplify the first equation by dividing everything by -7:
x + y = 22x - 4y = 16Now, to proceed with elimination effectively, aligning coefficients or a straightforward substitution should be re-evaluated, given the error in initial steps noted. Let's correct it:
Notice the instructional error in application; hence, a direct solution via the provided method is not feasible without the correct system alignment or revised equations. When solving similar problems, getting coefficients to align through multiplication or division is key before adding or subtracting equations to eliminate a variable.
Elimination becomes difficult with inaccurate steps, so it's crucial to double-check each phase of your work.
Assignment: Show Me the Sets Investigation
Karen got a bit confused in math class today when Mrs. Hudson was talking about the different subsets for classifying real numbers.
Create a visual representation of the relationships between subsets of the real number system and explain the relationships in words. Provide a real number that matches each description.
Draw a diagram to represent the relationships between subsets of the real number system. Include a sample number in each subset.
Explain the relationships in words. Use the sample numbers in your diagram and describe the classification. For example, 1/2 is a rational number, but it is not a whole number, natural number, or an integer.
Answer: Consider a power set [tex]\mathbb{R}[/tex] of real numbers.
The subsets of the power set are as follows:-
1. Natural number([tex]\mathbb{N}[/tex])={1,2,3,4,5,....}
2.Whole numbers[tex]\mathbb{W}[/tex]={0,1,2,3,4,......}
3.Integers([tex]\mathbb{I}[/tex])={.......-3,-2,-1,0,1,2,3,....}
4.Rational numbers([tex]\mathbb{Q}[/tex])=It contains all of the above subsets and fractions (where denominator ≠ 0) ,terminating and repeating decimals.
5.Irrational numbers=It contains numbers which cannot be expressed as the ratio of integers, and they are non-repeating, non-terminating decimals.
for the school play, 40 rows of chairs are set up. there are 22 chairs in each row. how many chairs are there in all?
Multiply the rows by the number of chairs 40×22= 880
plz answer most point
its D or the 4th answer
What is thw radius of a circle given by the equation x^2+y^2-2x+8y-47=0
x^2 + y^2 - 2x + 8y - 47 = 0
x^2 + y^2 - 2x + 8y = 47
(x^2 - 2x) + (y^2 + 8y) = 47
(x^2 - 2(1)x) + (y^2 + 2(4)y) = 47
(x^2 - 2(1)x + 1^2) + (y^2 + 2(4)y + 4^2) = 47 + 1^2 + 4^2
(x - 1)^2 + (y + 4)^2 = 64 = 8^2
r=8
American Indians staged an occupation in 1969?
(options listed below)
to protest the lack of educational opportunities.
to end poverty on American Indian reservations.
to raise awareness about unfair treatment.
to convince the government to protect their lands.
The occupation staged by American Indians in 1969 was in order to to raise awareness about unfair treatment.
American Indians in 1969:
Occupied Alcatraz from 1969 to 1971.The reason they did this was to draw attention to the injustices they were subjected to and the unfair treatment of American Indian tribes by the U.S. government. This led to the federal government giving more land to them.
In conclusion, option C is correct.
Find out more about this Native American protests at https://brainly.com/question/1318181.
A flying disc has a diameter of 9 inches. What is the circumference of the disc in inches? Round to the nearest tenth.
formula= 2(3.14)r
2(3.14)4.5
2(14.13)
28.26
A flying disc is assumed to be in the shape of a circle. Since we know it is in the shape of a circle, we can use the formula for circumference of a circle.
The formula for circumference of a circle is d * pi, where d represents the diameter of the circle and pi is the representation of 3.14.
Finding the circumference.You can find the circumference of a circle by multiplying the diameter by pi, and since the question gives us the diameter of the flying disc we can substitute in 9 inches for the diameter to solve for the circumference.
diameter * pi
(9 inches) * ([tex]\pi[/tex]) = 28.2743...
Answer to the question.The question wants the final answer to be rounded to the nearest tenth, so rounding 28.2743... to the nearest tenth would make it into 28.27.
The answer to this problem is the circumference of the disc is 28.27 inches.
a customer bought 8.5 pounds of apples from a local produce market. how many ounces of apples did the customer buy?
A:112
B:128
C:120
D:136
please show work
To convert pounds to ounces, you can use the conversion factor of 1 pound = 16 ounces. Therefore, 8.5 pounds of apples equates to 136 ounces. The correct answer is D: 136.
Explanation:The subject of this question is mathematics. Specifically, it revolves around the concept of units conversion. To convert from pounds to ounces, we use the conversion factor that 1 pound is equivalent to 16 ounces.
Given in the question, the customer bought 8.5 pounds of apples. To find out how many ounces this translates to, we need to multiply 8.5 by 16.
The calculation is as follows:
8.5 pounds * 16 ounces/pound = 136 ounces
So, the customer bought 136 ounces of apples. Therefore, the correct answer is D: 136.
Learn more about units conversion here:https://brainly.com/question/19420601
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two cars traveled equal distances in different amounts of time. car A traveled the distance in 2 hours , and car B traveled the distance in 1.5 hours. car B traveled 15 mph faster than car be what is the speed of car B
The answer is 90 I believe
Answer:
60 mph
Step-by-step explanation:
Let distance travelled by both the cars equal to d.
Also assume speed of Car A as x and speed of Car B as y
Then using distance formula,
d = 2x
Similarly for car B, d = 1.5 y
Also given that
speed of car B = speed of car A +15
y =x+15
Hence we have 2 x = 1.5 y Or x =0.75 y
Substitute in y =x+15 : y =0.75y+15
0.25y = 15
y = 15/0.25 = 60 mph
Speed of car B = 60 mph
which function in the vertex form is equivalent to f(x)=x^2+6x+3
Answer:
B. f(x) = (x + 3)2 − 6
Step-by-step explanation:
Answer:
[tex]f(x)=(x+3)^2-6[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=x^2+6x+3[/tex]. We are asked to find the function equivalent to our given function in vertex form.
To convert our given function in vertex form, we need to complete the square for our given function as:
Add and subtract [tex](\frac{b}{2})^2[/tex] from equation:
[tex](\frac{b}{2})^2=(\frac{6}{2})^=3^2=9[/tex]
[tex]f(x)=(x^2+6x+9)+3-9[/tex]
[tex]f(x)=(x^2+2\cdot 3x+3^2)-6[/tex]
[tex]f(x)=(x+3)^2-6[/tex]
Therefore, the [tex]f(x)=(x+3)^2-6[/tex] is equivalent to our given function in vertex form.
Brenda finish 1/3 of a friendship bracelet 1/2 of an hour at this rate how many bracelets can she finish in 1 hour
Brenda is able to complete 2/3 of a friendship bracelet in one hour, based on the rate given in the question.
Explanation:This question deals with rate and time, key concepts in Mathematics. Brenda can finish 1/3 of a bracelet in 1/2 hour, which means she completes 2/3 of a bracelet in one hour. Let me explain why.
We start with the given rate: 1/3 bracelets per 1/2 hour. To find out how many bracelets Brenda can complete in 1 hour, we simply multiply this rate by 2 (as 1 hour is equivalent to two 1/2 hours). Therefore, Brenda can complete (1/3 bracelet/1/2 hour) x 2 = 2/3 of a bracelet in one hour.
Learn more about Rate of Work here:https://brainly.com/question/14305692
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Find AB if BC = 4, BD = 5, and AD = 2.
show your work.
Solving this system of equations without a CAS: $4=a+c$, $5=d+ac+b$, $4=ad+bc$, $4=bd$ 2
Let $A,B,C,D$ be the vertices of a four sided polygon taken in anti clockwise. Given $|AB|=|BC|=3,|AD|=|CD|=4,|BD|=5$ , Find $|AC|$ 1
Find $ad - bc$ if $ac = 18$ and $bd = 50$ 2
Which of the pairs of activities is an example of using the commutative property?
A) washing the car and waxing the car
B) washing your clothes and drying your clothes
C) putting on your socks and putting on your shoes
D) adding sprite and orange juice to a punch mixture
The commutative property is illustrated by option D, where adding sprite and orange juice to a punch mixture shows that the order in which the ingredients are mixed does not affect the final product.
The commutative property primarily relates to mathematical operations like addition and multiplication, where changing the order of the numbers does not change the result. For example, in addition, 4 + 5 is the same as 5 + 4. Applying this concept to the options provided, the pair that is an example of the commutative property is adding sprite and orange juice to a punch mixture (Option D). Whether you add sprite to the orange juice or orange juice to the sprite, the resulting punch mixture remains the same.
What is 5458258525 times (868)
The correct answer is 4737768399700 Hope this helps!
it equals 7.7377684
Tommy is taking inventory in a warehouse. He’s counting tennis shoes. There are 43 pairs of women’s tennis shoes and 39 pairs of men’s tennis shoes. How many pairs of tennis shoes are there in all?
72?76?80?82?
43+39=82
hope this helps!
Answer:
43 + 39 = 82
Step-by-step explanation:
amount of mens shoes plus amount of womens shoes
Enter the number that belongs in the green box.
The number that belongs in the green box is 2.
Explanation:Based on the information provided, which relates to probability and the use of a calculator, we can assume the question pertains to Mathematics, likely within a Middle School curriculum where basic probability and calculator skills are taught.
When dealing with shuffled cards or marbles in a bag, one typically calculates probabilities or expected outcomes
There are a total of eight cards: five green cards and three yellow cards.
Since the cards are well shuffled, the probability of drawing a green card is 5/8.
The probability of drawing a yellow card, in this case, would be 3/8.
Since the green cards are marked with the numbers 1, 2, 3, and 4, the number that belongs in the green box would be 2.
Final answer:
To find the number in the green box, calculate the ratio of green cards to total cards.
Explanation:
The number that belongs in the green box can be found by calculating the ratio of green cards to total cards. In this case, there are 5 green cards out of 8 total cards. To find the number that belongs in the green box, we can use the formula:
Number in green box = green cards / total cards
Number in green box = 5 / 8
Using a calculator or simplifying the fraction, we find that the number in the green box is 5/8 or approximately 0.625.
what is the value of x to the nearest tenth the figure is not you scale x=2.1 x=3.4 x=9.6 x=13.1
Answer:
the answer is x = 9.6
Step-by-step explanation:
Answer:
the answer is
C - X=9.6
Step-by-step explanation: