Let cost of Emma's phone = x
Given that cost of Sophie's phone = 640
Then ratio of their phones cost will be x:640 or x/640
Given that ratio of their phones cost is 7:8 or 7/8
So both ratios will be equal.
[tex]\frac{x}{640}=\frac{7}{8}[/tex]
[tex]x=\frac{7}{8}*640[/tex]
x=560
So the new ratio of the cost of their phones will be 560:640
Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.
So let that decreased amount is k then we will get equation :
[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]
11(560-k)=9(640-k)
6160-11k=5760-9k
6160-5760=11k-9k
400=2k
200=k
Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.
You have a spanish club meeting every fourth day and math club meeting every tenth day. Today you have both meetings. In how many days will you have both meetings on the same day again?
By finding the Least Common Multiple (LCM) of 4 and 10, we can discover that the math club and Spanish club will coincide every 20 days.
Explanation:This query relates to the concept of the Least Common Multiple (LCM). As the math club convenes every 10 days and the Spanish club convenes every 4 days, we need to find when these meetings will coincide again. In other words, we are finding the LCM of 4 and 10. This tells us the least common multiple days that the two clubs meet.
Let's breakdown the calculation:
First, list the prime factors of each number. For 4, that would be 2x2, and for 10, it would be 2x5.Next, take all the unique prime factors and multiply them together. So, 2x2x5 = 20.Therefore, the Spanish club and the math club will meet on the same day every 20 days.
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which of the following numbers is closest to the mean
Hello!
To find the closet number we first need to understand how our data, and how to find the mean.
The mean is known as the average, which we find when we add all of our data up and divide by the number of factors.
In this case, after reading our graph, our data set is equal to:
3,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,8,9,10,11
When all of these numbers are added we get = 120
120 divided by 20 (the total number of factors) is equal to 6!
Which means that the answer to this question is E. 6
Hope this helps.
Based on the calculations, a number which is closest to the mean of this distribution is equal to: E. 6.
What is a mean?
A mean is also known as arithmetic average and it's a ratio of the sum of the total number in a data set to the frequency of the data set.
How to calculate the mean?Mathematically, the mean for this data set would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of data, we have:
F(x) = 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 9 + 10 + 11
F(x) = 120.
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean = [120]/20
Mean = 6.
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the steps to conver 23/4 to a decimal are shown below, which step is the error
The first error is in Step 3 because 4 * 7 = 28, not 26.
The steps to convert 23/4 to a decimal are mentioned, but the error is not specified.
Explanation:The steps to convert 23/4 to a decimal are:
Divide the numerator (23) by the denominator (4).The quotient is 5 with a remainder of 3.Add a decimal point after the quotient (5.)Multiply the remainder (3) by 10.Place the new quotient (7) after the decimal point.Repeat steps 4 and 5 until the remainder is 0.The final decimal is 5.75.The error in the given steps is not mentioned, so it's not clear which step is incorrect. However, if any step is incorrect, it would result in an incorrect decimal conversion.
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In the diagram abc=adb=90, ad=p and dc=q. Use similar triangles to show that x2=pz
plzz anyoneee
Answer:
By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that [tex]x^{2} =pz[/tex]
Step-by-step explanation:
Given that ∠ABC=∠ADC, AD=p and DC=q.
Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles
and given ∠ABC=∠ADB=90°
Hence using AA postulate, ΔABC ≈ ΔADB.
Now we will equate respective side ratios in both triangles.
[tex]\frac{AB}{AC}= \frac{AD}{AB}=\frac{BD}{BC}[/tex]
Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.
[tex]\frac{x}{z}= \frac{p}{x}[/tex]
Cross multiply
[tex]x^{2}=pz[/tex]
Hence proved.
simplify square root of 550
22.360679775 or rounded up to 22.4
Answer:
5 √ 22
Step-by-step explanation:
What is the value of B?
[tex]2x^2-12xy-32y^2=2(x-8y)(x+By)\qquad|\text{use distributive property}\\\\2x^2-12xy-32y^2=(2x-16y)(x+By)\\\\2x^2-12xy-32y^2=(2x)(x)+(2x)(By)+(-16y)(x)+(-16y)(By)\\\\2x^2-12xy-32y^2=2x^2+2Bxy-16xy-16By^2\\\\2x^2-12xy-32y^2=2x^2+(2B-16)xy+(-16By)[/tex]
[tex]\text{therefore:}\\\\2B-16=-12\ \text{and}\ -16B=-32\\\\2B=4\ \text{and}\ B=2\\\\B=2\ \text{and}\ B=2\qquadCORRECT[/tex]
Answer: B = 2Find the greatest Greatest Common Factors of the following Monomials 34a^2b 24a^5b^2
The greatest common factor (GCF) of the monomials [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex]. This is found by determining the GCF of the coefficients and the lowest exponent for each common variable.
To find the GCF of two monomials, we need to find the common factors for the coefficients, and then the lowest exponent for each variable that appears in both terms. The coefficients of the given monomials are 34 and 24. The GCF of these numbers is 2.
Next, look at the variables:
For a, the lowest exponent in both terms is a2
For b, the lowest exponent is just b (since one term is b, and the other is b2)
Therefore, the GCF of [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex].
A bus is driving 122 mph, and stops at a red light that slows him down 22mph. How many mph is he driving??
Answer:
The bus driver is now driving 100 mph after the stop light.
Step-by-step explanation:
If he slowed down 22 mph from 122 you'd subtract. 122-22=120 mph. Hope it helps!
The bus initially driving at 122 mph slows down by 22 mph at a red light, resulting in a current speed of 100 mph. The calculation is 122 mph minus 22 mph.
Calculating the Speed of the Bus
To determine the current speed of the bus, we need to account for the reduction in speed due to the red light.
The bus is initially driving at 122 mph. When it stops at the red light, its speed is reduced by 22 mph.
So, we use the following calculation:
Speed reduction: 22 mph
Therefore, the final speed is:
122 mph - 22 mph = 100 mph
The bus is now driving at 100 mph.
liam is a tyre fitter. it takes him 56 minutes to fit 4 tyres to a van.
a) how long would it take him to fit 12 tyres to 3 vans?
b) if he works for 42 minutes, how many tyres can he fit?
I would first solve how long it takes for 1 tyres to make life easier. Just solve 56 divided by 4, which means that Liam takes 14 minutes to put one tyres into the van. For part a, I don't quite understand the 3 vans part, but you know he 's putting 12 tyres into a van, so multiply 12 by 14 to get 156. Part B gives you time instead of tyres. Solve it practically the same... 42 divided 14 is 3, so he fits 3 tyres in 42 minutes,
Answer:
Part a) [tex]168\ minutes[/tex] or [tex]2\ hours\ 48\ minutes[/tex]
Part b) [tex]3\ tyres[/tex]
Step-by-step explanation:
Part a) Using a proportion
[tex]\frac{56}{4}\frac{minutes}{tyres}=\frac{x}{12}\frac{minutes}{tyres} \\ \\x=12*56/4\\ \\x=168\ minutes[/tex]
[tex]168\ minutes=2.8\ hours=2\ hours\ 48\ minutes[/tex]
Part b) Using a proportion
[tex]\frac{56}{4}\frac{minutes}{tyres}=\frac{42}{x}\frac{minutes}{tyres}\\ \\x=4*42/56\\ \\x=3\ tyres[/tex]
The system of equations below represents the measures of 2 angles created by the diagonal of a rectangle: x + y = 90 y =1/5 What is the measure of the greater angle? ° What is the measure of the smaller angle? °
Answer:
The larger of the two angles is x, which is 75. y is the smaller angle at 15.
Step-by-step explanation:
In order to find these, we can use our solved value for y in the second equation to plug into the first equation. This method is called substitution.
x + y = 90
x + (1/5x) = 90
1.2x = 90
x = 75
Now we can plug that value into either equation to find y
y = 1/5x
y = 1/5(75)
y = 15
Answer:
1.) 75
2.) 15
Step-by-step explanation:
edge 2020 Dec 8
Give one combination of two factors whose product is 0.24, if one of the factors is a whole number greater than 1.
Answer: There are a lot of answers to this product. Some of them include (in the format (w, x), where w is the whole number, and x is the factor you must multiply it by to get 0.24):
(2, 0.12), (3, 0.08), (4, 0.06), (6, 0.04), and so on.
Step-by-step explanation: Well, you could just assign the smallest who number greater than 1 to one of the factors, which is 2. Now you just have to multiply that by another factor to get 0.24. To do this, you could set up an equation like this:
2*x=0.24
Next, you would divide both sides by 2 to cancel out the 2 on the left side of the equation, leaving you with:
x=0.12
There you have it!
Now you can check your work by multiplying 2 and 0.12, and you will get 0.24!
You can do the same thing with other whole numbers, such as 3 and 4, and complete the same process to find the decimal factor that multiplies to 0.24.
There are 16 tables in the school lunch room. Each table can seat 22 students. How many students can be seated at lunch at one time?
16 tables x 22 students = 352 students can be in the lunch room.
Final answer:
The number of students that can be seated at lunch at one time is 352.
Explanation:
To find the number of students that can be seated at lunch at one time, we need to multiply the number of tables by the seating capacity of each table.
Given that there are 16 tables and each table can seat 22 students, we can calculate the total number of students that can be seated at one time by multiplying 16 by 22:
16 tables * 22 students/table = 352 students
Therefore, 352 students can be seated at lunch at one time.
alani wants to buy a $360 bicycle. she is considering two payment options the image shows option A which consists of making an initial down payment then smaller, equal sized weekly payments. option b consists of making 6 equal payments over 6 weeks
for A)
if she has $ for the downpayment of $70
for B)
360-70+290
290/ 5=58
amount paid = 290-58(#month)
a=290-58m
ANSWER
A= -58m+290
A) The factors that Alani should consider before deciding on the option to choose are:
Availability of cash for the initial down paymentInterest rate for each optionTotal cost of each option.B) The amount that Alani would have to pay for the weekly payments is $58.
An equation to model the amount paid for Option A after m months is A = 360 - 70 + mx.
How the equation is derived:Option A:
Total cost = $360
Initial down payment = $70
Number of weekly payments = 5
Weekly payment = $58 (360 - 70)/5
Option B:
Total cost = $360
Weekly payment = $60 ($360/6)
Equation:
Let the weekly payment = x
Let the number of monthly payments = m
Total amount paid after m months (A) = 360 - 70 + mx
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Complete Question:Alani wants to buy a $360 bicycle. She is considering two payment options.
Option A consists of making an initial down payment of $70 and then 5 smaller, equal-sized weekly payments until she has paid a total of $360.
Option B consists of making 6 equal payments over 6 weeks in order to pay a total of $360.
A) What factors should Alani take into consideration before deciding which option to choose?
B) How much would Alani have to pay for each weekly payment with option A? Write an equation to model the amount paid for Option A after m months
an artist enlarged a drawing she made. the original is 3cm wide and 5cm tall .the artist set the copier zoom button to 120% . what is the longer dimension of the new drawing.
For this case we have the following data:
The original dimensions of the drawing are:
Width: 3cm Height: 5cmIf the copier zoom is at 120%, we can find the new dimensions of the drawing by making a rule of three:
Width:
3 ----------> 100%
x ----------> 120%
Where x represents the new width of the drawing:
[tex]x=\frac{(120*3)}{100}\\x=3.6cm[/tex]
Long:
5 ----------> 100%
y ----------> 120%
Where y represents the new long of the drawing:
[tex]y=\frac{(120*5)}{100}\\y=6cm[/tex]
Thus, the new dimensions are 3.6 cm wide and 6 cm long
Answer:
the longer dimension of the new drawing is 6cm
Answer:
the answer is 6 cm
Step-by-step explanation:
Here’s one way you can solve this problem.
A zoom setting of one hundred twenty percent means that the dimensions of the new copy will be one hundred twenty percent of the dimensions of the original drawing.
First, write the scale that expresses the ratio of the original percent to the copy percent, one hundred to one hundred twenty.
Then, let h represent the height of the copy and write the ratio of copy to original as five centimeters to h centimeters.
Next, write a proportion that equates the two ratios. One hundred to one hundred twenty equals five to h.
Then, cross multiply the terms of the proportion. One hundred twenty times five equals one hundred h.
Next, multiply to get six hundred equals one hundred h.
Finally, divide both sides by one hundred to find h. h equals six.
So, the longer dimension of the new drawing is six centimeters, which is one hundred twenty percent of five centimeters.
hope it helps
Kegan wants to buy a new skateboard that will cost $140 so far Keegan has saved $30 toward the purchase of the skateboard to raise the remaining money needed Keegan mothers his neighbors lawn and charges $10 each time he completes the job writing equation to find X the number of times Keegan needs to mow his neighbors lawn to earn enough money how many times of Keegan need to mow his neighbors lawn to have enough money to buy the skateboards
Answer:
Step-by-step explanation:
140-30=110
He charges 10$ every time he mowed someones lawn
So 110/10=11
He would have to mow his neighbors lawn 11 times.
Answer:
Keegan need to mow 11 times to his neighbors lawn to have enough money to buy the skateboards.
Step-by-step explanation:
Consider the provided information.
It is given that Keegan need $140 and Keegan saved $30. Keegan also charges $10 each time he completes the job writing.
Let x the number of times Keegan needs to mow his neighbors lawn to earn enough money.
Thus the required equation is;
[tex]140=30+10x[/tex]
Now solve the equation as shown below:
[tex]140-30=10x[/tex]
[tex]110=10x[/tex]
[tex]\frac{110}{10}=x[/tex]
[tex]x=11[/tex]
Hence, Keegan need to mow 11 times to his neighbors lawn to have enough money to buy the skateboards.
Joanie made 8 bedazzled vests in her sewing class for all her cousins. Give 2 possible combinations of the number of buttons, zippers and sparkly stickers that she used to make the vests. Explain your reasoning
Total number of bedazzled vests made = 8.
We need to find the combinations of the number of buttons, zippers and sparkly stickers that she used to make the vests.
First we need to find all the factors of 8.
Factors of 8 are : 1,2,4,8.
Now we need to find the combinations threes of those factors of 8.
1×2×4 = 8
1×1×8 = 8
2×2×2 = 8.
Therefore, there could be only three combinations of number of buttons, zippers and sparkly stickers that she used to make the vests.
1,2,4
1,2,8 and
2,2,2.
How to solve the equation: |2x+3|>=23
[tex]|2x+3|\geq23\iff2x+3\geq23\ \vee\ 2x+3\leq-23\qquad|\text{subtract 3 from both sides}\\\\2x\geq20\ \vee\ 2x\leq-26\qquad|\text{divide both sides by 2}\\\\x\geq10\ \vee\ x\leq-13[/tex]
A culture of 1.75×10^18 bacteria is in petri dish A. A culture of 6.25×10^15 bacteria is in petri dish B.How many times greater is the number of bacteria in petri dish A than petri dish B?Enter your answer, in standard notation, in the box.
Dividing:- (1.75 * 10^18) / (6.25 * 10^15)
= (1.75 / 6.25) * (10^18 / 10^15)
= 0.28 * 10^3
= 280 Answer
Final answer:
The number of bacteria in petri dish A (1.75×1018) is 280 times greater than the number of bacteria in petri dish B (6.25×1015).
Explanation:
To find out how many times greater the number of bacteria in petri dish A is compared to petri dish B, we divide the number of bacteria in dish A by the number of bacteria in dish B.
Number of bacteria in dish A = 1.75×1018
Number of bacteria in dish B = 6.25×1015
Now, let's divide the two:
(1.75×1018) / (6.25×1015) = (1.75 / 6.25) × 10(18-15)
1.75 divided by 6.25 is 0.28, and 1018 divided by 1015 is 103.
Therefore, 0.28 × 103 = 280. The number of bacteria in petri dish A is 280 times greater than the number of bacteria in petri dish B.
A bike rental shop charges $8 to rent a bicycle (per person), plus $1.75 for every half hour you ride (per person). If the shop charges you and your friend a total of $26.50, how many hours did each of you ride?
So the initial renting fee for you and your friend is $16(8 bucks a piece). Each hour you and your friend will be paying $7 (that's 1.75 for each HALF hour for each of you).
nal answer:
After subtracting the initial rental cost for two bicycles, the remaining amount spent was divided by the cost per half hour to find the total number of half hours ridden. Each person rode for 3 half hours, which equates to 1.5 hours each.
Explanation:
To calculate how many hours each of you rode a rented bicycle at the bike rental shop, let's break down the charges. The shop charges $8 per person to rent a bicycle and $1.75 for every half hour of ride time. Since there were two of you, the initial cost would be 2 × $8 = $16. The total amount spent was $26.50, so subtracting the initial rental cost, we have $26.50 - $16 = $10.50 left for the actual riding time.
The cost of riding time per person is $1.75 per half hour. So, we divide the remaining amount $10.50 by $1.75 to find the total number of half hours both of you rode combined: $10.50 / $1.75 = 6 half hours. Since this is the combined time for both you and your friend, each of you rode for 3 half hours, or 1.5 hours in total.
round 3,458 to the neaerest hundreds
3458=3,458.00
Hoped this worked out well
:) have a nice day
Answer:
3500 is your answer
Step-by-step explanation:
Note the hundreds place value (underlined): 3458.
Look at the number to the right of the underlined number. It is a 5. You round up if the number is 5 or greater.
3458 rounded to the nearest hundred is 3500.
~Senpai
Juan went up 25 feet during a climb on a rock climbing wall. What does 0 represent?
Answer: 25 feet during a climb
Step-by-step explanation:
Which construction is shown in the accompanying diagram
The construction that is shown in the accompanying diagram is the perpendicular bisector of line AB.
What is a perpendicular bisector?
A perpendicular bisector is a line or a line segment that both bisects (cuts in half) another line segment and is perpendicular (forms a right angle) to it. In other words, it is a line that passes through the midpoint of a given line segment and is perpendicular to that segment.
If you have a line segment with endpoints A and B, the perpendicular bisector is the line that passes through the midpoint, in this case (C) of AB and forms a right angle with AB. The perpendicular bisector divides the line segment into two equal parts.
how to solve
/d + 9/ > 3
The solution to the inequality |d + 9| > 3 is d < -12 and d > -6.
Explanation:The question is asking how to solve the absolute value inequality |d + 9| > 3. For this problem, you need to consider two scenarios because an absolute value represents a distance, which can be either positive or negative. For the first scenario, consider the inequality as (d + 9) > 3 which, when simplified, gives us d > -6. For the second scenario, consider the inequality as -(d + 9) > 3, which simplifies to d < -12. That means any value of 'd' that's greater than -6 or less than -12 will satisfy the inequality.
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im thinking of a number. if you add half of this number to a sixth of this number, you will get 12. what is the number?
Let's set the equation and the mysterious number to x:
x/2+2/6=12
Then, times both sides by 12:
6x+2x=144
8x=144
x=18
The number that you are thinking of is 18.
300 out of 500 people went on a trip what PERCENTAGE of people were NOT able to go on the trip...
6 percent because 300/500 equals 0.6.
Well, there are 500 people, but only 300 are coming on the trip. That means that 200 people aren't going on the trip. Therefor, 200/500 is the fraction you would use. Now, just simplify the fraction. 200/100=2, and 500/100=5, so the fraction simplifies down to 2/5. 2/5 equals 40% so 40% of the people were not able to go on the trip.
during one season a total of 453,193 people attended a baseball game teams games what is the value of the digit 5 in the number of people
50,000 or Ten thousands
the value of the digit 5 is 50,000. Think of it as the numbers behind 5 as zeros and you will have the answer.
The equation y-5=6(x+1) is written in point-slope form. What is the equation written in slope-intercept form?y = 6x + 11y = 6x – 1 y = 6x – 4y = 6x + 6
The slope-intercept form: y = mx + b
We have in point-intercept form: y - 5 = 6(x + 1)
Transform:
y - 5 = 6(x + 1) |use distributive property
y - 5 = (6)(x) + (6)(1)
y - 5 = 6x + 6 |add 5 to both sides
y = 6x + 11
The equation of required line in slope intercept form is y= 6x + 11 First option is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c Where m is the slope of the line and c is the y intercept of the line. Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis. If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
[tex]y - 5 = 6(x + 1)\\y - 5 = 6x + 6\\y = 6x + 6 + 5\\y = 6x +11[/tex]
y= 6x + 11 is the equation written in slope intercept form. First option is correct
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You can read 45 pages of your new book in 2 hours. How many pages can you read in 3 hours?
what is -4(2n-3)=12-8n
Step 1. Expand
-8n + 12 = 12 - 8n
Step 2. Cancel -8n on both sides
12 = 12
Step 3. Since both sides equal, there are infinitely many solutions
Answer: Infinitely Many Solutions
which best describes the range of numbers that satisfy the inequality x> 12.4
Let the domain be
i. The set of all natural numbers
ii. The set of all real numbers
i. The set of all natural numbers
Note that the smallest natural number that satisfies this inequality is 13 and there is no biggest natural number which satisfies the inequality.
Hence, the range is {13, 14, 15, ...}
ii. The set of all real numbers
Clearly, the set of all real numbers that satisfies this inequality is the open interval (12.4, ∞).
Answer:
option B :)
Step-by-step explanation: