Answer:
The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Step-by-step explanation:
Given:
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.
The tax of the first city was 6% and the tax of the second city was 10%.
Total hotel tax paid for two cities with $670.
Now, to find the hotel charge in each city before tax.
Let the hotel charge in first city before tax be [tex]x.[/tex]
And the hotel charge in second city before tax be [tex]y.[/tex]
So, as the hotel charge of the second city was 1500 higher than the first.
Thus,
[tex]y=x-1500[/tex] ........(1)
And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.
6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.
[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]
[tex]0.06x+0.10y=670[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.06x+0.10(x-1500)=670[/tex]
[tex]0.06x+0.10x-150=670[/tex]
[tex]0.16x-150=670[/tex]
Adding both sides by 150 we get:
[tex]0.16x=820[/tex]
Dividing both sides by 0.16 we get:
[tex]x=5125.[/tex]
The hotel charge in first city before tax = $5125.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=x-1500[/tex]
[tex]y=5125-1500[/tex]
[tex]y=3625.[/tex]
The hotel charge in second city before tax = $3625.
Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Can someone help me with the problem in the image
Answer:
PT=57
Step-by-step explanation:
If PT=7x+8 and TQ=9x-6 qnd we have that T is the midpoint of PQ.
Since T is the midpoint of PQ, [tex]PT=TQ[/tex]
We substitute into the equation to get:
[tex]7x+8=9x-6[/tex]
Group the similar terms to get:
[tex]8+6=9x-7x[/tex]
We simplify now to get:
[tex]14=2x[/tex]
Divide through by 2 to get:
[tex]x=7[/tex]
PT=7*7+8=49+8=57
Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?
Answer:
The value of x is 8
Step-by-step explanation:
In the figure below,
The alternate exterior angles are 1 and 2
Alternate Exterior Angles are a pair of angles that lie on the outer side of each of those two lines but on opposite sides of the transversal and they are equal
Also angle 2 and 3 are adjacent and supplementary angle and their sum is equal to 180 degrees
Given that
[tex]\angle 1 = (4x + 28)^{\circ}[/tex]
[tex]\angle 3 = (14x + 8)^{\circ}[/tex]
Now we know that
[tex]\angle 2 + \angle 3 = 180 ^{\circ}[/tex]
[tex]\angle 2 +(14x+8) = 180[/tex]
[tex]\angle 2 = 180 - 14x -8[/tex]
[tex]\angle 2 = 172 - 14x[/tex]
We also know that
[tex]\angle 1 = \angle 2[/tex]
[tex]4x + 28 = 172 -14x[/tex]
[tex]4x + 14x = 172 - 28[/tex]
[tex]18x = 144[/tex]
[tex]x =\frac{144}{18}[/tex]
x = 8
Now
[tex]\angle 1 = (4x+28)^{\circ} = (4(8) +28)^{\circ} = (32 +28)^{\circ} =(60)^{\circ}[/tex]
[tex]\angle 3= (14x+8)^{\circ} = (14(8) +8)^{\circ} = (112 +8)^{\circ} =(120)^{\circ}[/tex]
Answer:
The value of x is 8
Step-by-step explanation:
Mr. Pham has 410,000 in a retirement account that earns 3.85% simple interest each year. Find the amount earned each year by this investment
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$410000\\ r=rate\to 3.85\%\to \frac{3.85}{100}\dotfill &0.0385\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(410000)(0.0385)(1)\implies I=15785[/tex]
Mr. Shively’s TV cabinet is 30 inches tall and 40 inches wide. Best Buy is selling 50 inch, 55 inch, 60 inch, and 65 inch TVs. Of those options, which one should he buy? Explain your answer using mathematics , please explain using Pythagorean theorem.
Answer:
He should buy a 50 inch TV
Step-by-step explanation:
Using Pythagorean theorem the TV cabinet has a diagonal of :
[tex]\sqrt{30^{2} + 40^{2} } = 50[/tex]
Tina has 18 sunflower seeds in 15 Daisy seeds she wants to distribute them equally into pots then planting them with no seeds left over what is the greatest number of pots Tina can use
Answer:11
Step-by-step explanation:
Add 18 and 15 then find the GCF
The maximum number of pots she can make is 15.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, Tina has 18 sunflower seeds and 15 daisy seeds.
Since Tina wants to distribute the sunflower seeds and daisy seeds equally in each pot, each pot must contain at least one daisy seed and one sunflower seed.
Therefore, if, she has 1 daisy seed and 1 sunflower seed in each pot, then she can make 15 pots, as there are only 15 daisy seeds.
Now, there are only 3 sunflower seeds left but she cannot use them to make a pot as there are no daisy seeds.
Hence, the maximum number of pots she can make is 15.
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What’s the fraction of 65% in its simplest form
Answer:
13/20
Step-by-step explanation:
65%=65/100
65/100=13/20
What is the simplified form for (2x^8)*3y^9*2x^4=
Answer:
12x12y9
Step-by-step explanation:
A house is worth 125,000 when it is 2 years old and 135,150 when it is 7 years old. According to this model, how much will the house be worth when it is 16 years old
Final answer:
The house will be worth $153,420 when it is 16 years old, calculated by finding the annual increase in value from the given data and projecting this increase over the relevant time period.
Explanation:
To calculate the worth of the house when it is 16 years old, we need to establish the rate at which the house's value is increasing over time, based on the information given for its value at 2 years and at 7 years. The house is valued at $125,000 when it is 2 years old and $135,150 when it is 7 years old, showing an increase of $10,150 over 5 years.
First, we find the annual increase in value by dividing the total increase by the number of years:
Annual increase = $10,150 / 5 = $2,030.
Next, we predict the value when the house is 16 years old by multiplying the annual increase by the number of years from the starting point (2 years old) to 16 years old:
14 years (from year 2 to year 16) × $2,030 annual increase = $28,420 increase since year 2.
Finally, we add this increase to the original value at year 2:
Projected Value at Year 16 = $125,000 + $28,420 = $153,420.
Hence, according to the model, the house will be worth $153,420 when it is 16 years old.
What is the answer for the equation 8(2x+9)=56
STEPS:
1. Start my distributing the 8 through the parentheses on the left side of the equation. 8 times 2x is 16x and 8 times 9 is 72. So we have 16x + 72 = 56.
2. Next, isolate the x-term by adding 72 to both sides of the equation
and we get 16x = -16.
3. Divide both sides by 16 and x = -1.
Two cards are drawn from a well a shuffled standard deck of match each scenario to its probability
You weren't being specific so I searched up the question.
The correct answer is:
A. 1/169 - The probability of drawing a king followed by a queen with a replacement.
B.1/442 - The probability of drawing a red ace followed by another red ace without replacement.
C.4/442 - The probability of drawing a 3 or 5 followed by 4 or 6, with replacement.
D.1/52 - The probability of drawing a spade followed by a jack of ant color with replacement.
Keep in mind this is not my answer since I got it from somebody else.
Answer:
Refer to the picture bellow
Step-by-step explanation:
83.40 divided by 12
Answer:
3.33 or 10/3
Step-by-step explanation:
simplify by dividing 40/12 by 4:
10/3 or 3.33
The value of the answer on dividing 83.40 by 12 is 6.95, i.e. 83.40 ÷ 12 = 6.95.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
83.40 divided by 12,
The above expression can be written as,
83.40 ÷ 12
Divide the term 83 by 12. You get a quotient of 6 and a reminder of 11 put the dot and then take the value of 4 down, the number will be 114 divided by 12. You will get 9 quotients and 6 as a reminder, Then drop the value 0 and the new number is 60, divide 60 by 12 you will get question 5 and the remainder zero.
Thus, 83.40 ÷ 12 = 6.95.
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The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds.
Age, in months 2 3 4 5 6 7 8
Weight, in pounds 6
Part A: Complete the given table that represents Rex’s current weight, in pounds, as a function of his age, in months
Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points.
Part C: Create a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months.
Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old?
Answer:
A.)
In 2 months, Rex is 6 pounds and in 8 months he's 9lbs (from 2 to 8 is 6 months). So I inferred that to get to 9lbs from 6lbs is to go 0.5 pounds more each month.
B.)
2 = 6
3 = 6.5
4 = 7
5 = 7.5
6 = 8
7 = 8.5
8 = 9
C.) I don't think I can create a linear model here. So I don't think its nessesary.
D.)
If Rex were to grow over the expected 6 months, it would be 45.
What percent of 500,000 equals 250,000?
Answer:
The answer is 50%. 50% of 500,000 is 250,000.
1/2 times 6 minus y equals y
Answer:
I believe the answer to this question is: 3/2 simplified to 1 1/2.
The high temperature in Fairbanks, Alaska was 12.2 degrees, then that night it fell 48.4 degrees. The next morning, it rose 17.1 degrees. What was the temperature in the morning?
Answer:
The temperature next morning was - 19.1 degrees
Step-by-step explanation:
High temperature in Fairbanks, Alaska = 12.2 degrees
Temperature that night = 12.2 - 48.4
Temperature that night = -36.2 degrees
Temperature next morning = -36.2 + 17.1
Temperature next morning = -19.1 degrees
The temperature next morning was - 19.1 degrees
What is the intersection of the sets A= {2,3,4,7} and B= {2,5,7,13}
Answer: { 2 , 7 }
Step-by-step explanation:
The intersection of a set is what the sets have in common. From the given sets , the numbers common to the two are 2 and 7 , so the intersection of the sets will be { 2 , 7 }
what is 0.15151515151 as a fraction
Final answer:
The decimal 0.15151515151 can be written as the simplified fraction 5/33.
Explanation:
To express the decimal number 0.15151515151 as a fraction, we can observe the repeating pattern. The 15 sequence repeats indefinitely, so we can represent it as 15/99. Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which in this case is 3. Therefore, the decimal 0.15151515151 can be written as the simplified fraction 5/33.
Recognizing the recurring pattern in the decimal as 0.15(15), we express it as a fraction, obtaining 15/99. Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3, yields the final result: 5/33. This process highlights the conversion of repeating decimals to fractions.
Jevon has money. Angie has twice as much money as Jevon. Kenny Has five dollars more than Angie. How much more money does each of them have if the sum of their treasure is $80?
Answer:
Money Jevon would be having = $15
Money Angie would be having = $30
Money Kenny would be having = $35
Step-by-step explanation:
Given:
Angie has twice as much money as Jevon
Kenny has $5 more than Angie.
The sum of their treasure = $80
To find how much money does each of them have.
Solution:
Let Jevon has money in dollars = [tex]x[/tex]
Angie having twice as much money as Jevon would have in dollars = [tex]2x[/tex]
Kenny having $5 more than Angie would have in dollars = [tex]2x+5[/tex]
The sum of their money will be given as:
⇒ [tex]x+2x+2x+5[/tex]
Combining like terms.
⇒ [tex]5x+5[/tex]
The sum of their treasure = $80
So, the equation to find [tex]x[/tex] would be given as:
[tex]5x+5=80[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]5x+5-5=80-5[/tex]
[tex]5x=75[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{75}{5}[/tex]
∴ [tex]x=15[/tex]
Thus,
Jevon has = $15
Angie has = [tex]2\times \$15[/tex] = $30
Kenny has = [tex]\$30+\$5[/tex] = $35
what is the mode of 23,95,100,23,100,100
Answer:
The number that occurs most often in a set of numbers
in this case, the number 100 occurs more than any other number in the set. This means that the mode for this set of data is 100.
Answer:
100
Step-by-step explanation:
Mode is the number that appears most often
Hence
In the given set of numbers
The mode is 100
I know there are too many of them but I need help. Giving brainliest
total vol. = 24
If length x base x height = vol. of cuboid
then,
vol. of cuboid = width
base x height
24 / (4 x 2) =
24/8=
3ft
How can we re-write the expression below into “friendlier” terms? 6 ∙ 29
options:
6 ∙ (30 - 1)
6 ∙ (16 + 13)
6 ∙ (19 + 10)
6 ∙ (21 + 8)
Option A: 6 ∙ (30 - 1)
Solution:
Given expression is 6 · 29.
Friendlier term means a number can be expressed using other numbers which are closest to the number.
Option A: 6 ∙ (30 - 1)
30 is closest to 29, so which is the friendlier term to 29.
6 · 29 = 6 ∙ (30 - 1)
Option B: 6 ∙ (16 + 13)
16 and 13 are not closest to 29, which are not the friendlier terms.
Option C: 6 ∙ (19 + 10)
19 and 10 are not closest to 29, which are not the friendlier terms.
Option D: 6 ∙ (21 + 8)
21 and 8 are not closest to 29, which are not the friendlier terms.
Hence Option A: 6 ∙ (30 - 1) is the correct answer.
jess walked for 45 min at 3km/h and then ran for half an hour at xkm/h. at the end of the time she was 6 km from starting point. find the x value?
Hey there! :)
~ They give us some good information in this equation. Let's use it! This can be used to change "45 min" into ".75 hours".
~ Now, let's write an equation; "distance = speed * time."
~ 3(.75) + .5x = 6
~ 2.25 + .5x = 6
~ .5x = 6 - 2.25
~ .5x = 3.75
~ x = 3.75/.5
~ x = 7.5 km/hr
Final answer:
To find Jess's running speed, the total distances she walked and ran are calculated and added to equal the given total distance of 6 km. Solving the equation 6 km = 2.25 km + 0.5x km reveals that Jess ran at 7.5 km/h.
Explanation:
To find the value of x, which represents Jess's running speed, we can use the information provided to set up equations based on the distance formula: distance = speed × time.
Jess walked for 45 minutes at 3 km/h. First, convert 45 minutes to hours by dividing by 60: 45 minutes / 60 minutes/hour = 0.75 hours. The distance walked is:
Distance walked = Speed × Time = 3 km/h × 0.75 hours = 2.25 km.
Next, Jess ran for 30 minutes or 0.5 hours at x km/h. The running distance is:
Distance ran = Speed × Time = x km/h × 0.5 hours = 0.5x km.
According to the question, the total distance from the starting point after both activities is 6 km, so:
Total distance = Distance walked + Distance ran
6 km = 2.25 km + 0.5x km
Now, solve for x:
6 km - 2.25 km = 0.5x
3.75 km = 0.5x
x = 3.75 km / 0.5
x = 7.5 km/h
Therefore, Jess ran at 7.5 km/h.
what is the sum of two numbers is 40 and their difference is 10
Answer:
The two numbers are 25 and 15.
Step-by-step explanation:
Let's find out the two numbers, this way:
x = first number
y = second number
This is the equations system:
x + y = 40
x - y = 10
Solving for x in the first equation:
x + y = 40
x = 40 - y
Solving for y in the second equation:
40 - y - y = 10
40 - 2y = 10
-2y = 10 - 40
-2y = - 30
y = -30/-2 = 15
Solving for x:
x + y = 40
x + 15 = 40
x = 40 - 15
x = 25
The two numbers are 25 and 15.
Ascending Order
18, 1.8, 18, .018
Answer:
.018, 1.8, 18, 18
Step-by-step explanation:
ascending means going from smallest to largest, so you order the numbers from smallest to largest
Answer:
018, 1.8, 18, 18
Step-by-step explanation:
40x+24y-56.
Get to factor the expression
The factored form of given expression is:
[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]
Solution:
Given that we have to factor the given expression
Given expression is:
40x + 24y - 56
We can factor the expression by taking the greatest common factor out
When we find all the factors of two or more numbers, and some factors are the same , then the largest of those common factors is the Greatest Common Factor.
Find G.C.F of 40, 24 and 56
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
Then the greatest common factor is 8
Thus factor out 8 from given expression
[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]
Thus the given expression is factored
Let g(x)=9x−10 and evaluate g(x+h)−g(x)/h
Answer:
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
Step-by-step explanation:
we have
[tex]g(x)=9x-10[/tex]
To find out g(x+h) substitute the variable x by the variable (x+h) in the function g(x)
so
[tex]g(x+h)=9(x+h)-10[/tex]
[tex]g(x+h)=9x+9h-10[/tex]
Evaluate
[tex]\frac{g(x+h)-g(x)}{h}[/tex]
we have
[tex]g(x+h)=9x+9h-10[/tex]
[tex]g(x)=9x-10[/tex]
substitute in the expression
[tex]\frac{9x+9h-10-(9x-10)}{h}[/tex]
[tex]\frac{9x+9h-10-9x+10)}{h}[/tex]
[tex]\frac{9h}{h}[/tex]
[tex]9[/tex]
therefore
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
If 3x/5 = 3/2, then x = ?
Answer:
5/2
Step-by-step explanation:
3x/5=3/2
x=(3/2)/(3/5)
x=(3/2)(5/3)
x=5/2
$12 for 6 bagels; $9 for 24 bagels.
Answer:
What is the question that you are asking?
Step-by-step explanation:
352.83 in expanded notation
We can extend 352.83 and write as (3 x 100) + (5 x 10) + (2 x 1) + (8/10) + (3/100)
Step-by-step explanation:
Considering the given value 352.83 we can expand that step by step as,
(3 x 100) which will give us a value of 300.
Now adding the multiplied answer of (5 x 10) will give us 350.
Next we can also add the multiplied answer of (2 x 1 ) which will further give us 352.
Now adding the divided answer of (8/10) we will get 352.08
Finally adding the divided answer of (3/100) we will get the exact value of 352.83 as mentioned above.
The expanded notation for the number [tex]352.83[/tex] is [tex](3\times 100)+(5\times 10)+(2\times 1)+(8\times \dfrac{1}{10})+(3\times \dfrac{1}{100})[/tex]
A number can always be written in the expanded notation by multiplying the face value with the face notation.
Here, [tex]3[/tex] is at the [tex]100th[/tex] place of the number so, it can be written as [tex]3\times 100[/tex].
Similarly, the digits which are located after the decimal point can be expanded by dividing the face value of the number by [tex]10[/tex] raised to the power of face notation.
Here, [tex]8[/tex] is present just after the decimal point and so, its expanded form is [tex]8\times \dfrac{1}{10}[/tex].
Hence, the expanded notation of [tex]352.83[/tex] is [tex](3\times 100)+(5\times 10)+(2\times 1)+(8\times \dfrac{1}{10})+(3\times \dfrac{1}{100})[/tex].
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Which of the following sequences of transformations is used to obtain figure A’ B’ C’ D’ from figure ABCD?
Answer:
Last one
Step-by-step explanation:
Imagine it as a mirror or like a paper folding in half, then figure out the direction it shifts.