Answer:
Ben and Alisha will meet at 11:40 a.m.
Step-by-step explanation:
Given: The time at which Ben leaves his house is 7a.m. and the constant speed at which he biked due east is 15mi/hr.
The time at which Alisha leaves her house is 8a.m. and the constant speed at which she biked due west is 10mi/hr.
The distance at which Alisha lives due east of Ben is [tex]$100 \mathrm{mi}$[/tex].
To find: The time at which they meet.
a. Analyze the given data.
b. Define a variable.
c. Form an equation.
d. Solve for the unknown variable.
e. Use addition, subtraction, multiplication, or division properties.
f. Find the required time.
Step 1 of 5
Let t represent the time (in hours) from 12a.m.
We can also assume the houses as being on the number line, where Ben's house is at 0 and Alisha's house is at 100 .
Ben starts biking at 7 a.m. and he moves right (along our imaginary number line) at 15 miles per hour.
So his position at a time t is 15(t-7).
Alisha starts biking at 8a.m. and she moves left at 10 miles per hour.
So her position at a time t is 100-10(t-8).
Step 2 of 5
Ben and Alisha will meet when their positions are equal. Thus equating both the equations, we get
15(t-7)=100-10(t-8)
Using the distributive property,
15t-105=100-10t+80
Step 3 of 5
By the addition and subtraction properties,
We get,
[tex]$$\begin{gathered}15 t+10 t=80+105 \\\Rightarrow 25 t=285\end{gathered}$$[/tex]
Step 4 of 5
By the multiplication and division properties,
[tex]$$\begin{aligned}t &=\frac{285}{25} \\\Rightarrow t &=11.4 \mathrm{~h}\end{aligned}$$[/tex]
Step 5 of 5
Converting the decimal into minutes,
[tex]$0.4 \times 60=24.0 \mathrm{~min}$[/tex]
Thus the required time is 11:24a.m.
HELP?: Concert tickets prices decreased from $125.00 to $75.00. What is the percent of decrease.
Answer:
40%
Step-by-step explanation:
percent change = (new number - old number)/(old number) × 100%
percent change = (75 - 125)/(125) × 100%
percent change = -40%
A negative percent change is a decrease.
Answer: 40%
HELPPPPPP: Roberto wants to buy a $40 gift for his father. He finished one odd job in 4 hrs at $3.75 an hour. He us now working at a job which pays $4.00 an hour. How many hours does he need to work in order to earn the money that he needs?
Answer:
7 hours
Step-by-step explanation:
He already worked 4 hrs at $3.75 an hour.
Meaning he has already accumulated 15 dollars. (4 * 3.75)
$40 - $15 = $25
So if he needs $25 and he makes $4 dollars an hour:
25/4 = 6.25
He needs to work at least 7 full hours to receive 25 dollars to add with the already earned 15 dollars to total 40 dollars.
Answer: 6.25 hours
Step-by-step explanation:
Step 1: find how much he earned from the odd job
3.75 per hour for 4 hours= 3.75x4= $15
Step 2: Write an inequality
4x+15≥40
Breaking it down:
'4x' means $4 per hour for an unknown number of hours, or just "a number of hours". The reason why you put the x next to the number is because to find the total amount of money he made from that job, you'll have to multiply 4 by however many hours he worked.
15 stands for the amount of money he has right now. He finished the job that paid 3.75 an hour, so don't put an x next to the 15.
40 is the amount of money he needs.
the ≥ sign means "greater than or equal to". In other words, to be able to buy the gift, he needs 40 or more dollars. The line underneath means "greater/less than or equal to". Also, the reason why I didn't put the normal greater sign that looks like >, is beacause that would be saying he needs MORE than 40 dollars to buy the gift, which is not a true statment.
Step 2: Solve the inequality
Solving an inequality is no different from solving an algebra equation. You just ignore the ≥ sign.
4x+15≥40
#1: Always do the inverse operation on the left side number first, never the x term. In other words, always start with addition or subtraction:
See how there is a +15. do the operate equation by subtracting 15 from both sides.
4x+15-15 ≥ 40-15
4x≥25
Now divide both sides by 4. This is because 4x stands for "4 multiplied by x" and the opposite of multiplication is division.
4x/4 ≥ 25/4
x≥6.25
Step 4: Checks
Substitute x for 6.25, but write it as en equation.
4x+15=40
4x6.25 +15 = 40
25+15= 40
40=40
Correct ✅
Answer= He needs to work 6.25, or 6 1/4, or 6 hours and 25 minutes, in order to have enough money for the gift.
x+10=1/3(5x+10)
How do you solve this equation?
Answer:
x = 10
Step-by-step explanation:
First, subtract 10 from both sides
Next, Simplify
Then, subtract 5/3x from both sides
After, simplify
Lastly, multiply both sides by 3
Then finally simplify for your final answer of x = 10
Hope this helps! :)
Answer:
x = 10
Step-by-step explanation:
x + 10 = 1/3(5x + 10)
x + 10 = 5/3x + 10/3
3x + 30 = 5x + 10
20 = 2x
10 = x
write the letter of the correct choice in the blank
I got stuck, I need your help and please answer all 4 ques.
thank u
Christina wants to buy some miniature goldfish. She reads that a 9-gallon aquarium is the
right size for 3 miniature goldfish. The graph represents this relationship.
Which points show equivalent ratios that would also be on the graph? Select all that apply.
A. (6,18)
B. (6,12)
C. (4,10)
D. (1,3)
Answer:
A & D
Step-by-step explanation:
If you can fit 3 fish in a 9 gallon tank, that means as a point on a line, that would be at (3, 9).
If you write this as a fraction it's 3/9. Simplifying that, you get 1/3. That means 1 fish needs 3 gallons. If you make hat a point on the line, it's (1,3).
Another equivalent fraction would be 6/18. If you multiply the numerator and denominator by 2, 3/9 becomes 6/18.
B & C are not equivalent fractions.
2 ACTIVITY: Estimating a Whole
Work with a partner. Use a model to estimate the answer to each question.
b. 13 is 25% of what number?
Answer: 52
Step-by-step explanation:
We know that 25 percent is one-fourth, so whatever number divided by 4 equals 13. To do this, we can just multiply 13 by 4 to get our answer, 52.
A urn contains 3 red and 5 black balls. Tom first withdraws a ball from the urn and Mary withdraws a ball from the urn without replacement. They keep withdrawing a ball alternately until a red ball is selected. Find the probability that Tom selects the red ball.
a) 3/8
b) 15/64
c) 31/56
d) 48/64
e) 34/56
Answer:
The answer is B
Step-by-step explanation:
I learned this from my math teacher
please help asap!!! theres multiple answers
Answer: 3rd, 4th, and 5th are correct.
Step-by-step explanation:
We know that the equation 6(t+2) can be simplified to 6*t+6*2, also 6t+12. This causes any statements saying a variable with a certain value applies to one side also applies to the other.
Answer:
- The value of both expressions when t = 3 is 30
- The value of both expressions when t = 7 is 54
- The expressions are equivalent
Step-by-step explanation:
Plug in each value of t into the expressions:
6t + 12, when t = 3 equals 30
6t + 12, when t = 7 equals 54
6(t + 2), when t = 3 equals 30
6(t + 2), when t = 7 equals 54
We have the same answers for both expressions, meaning they are equivalent.
24. SPANISH TEST The double box-and-whisker plot shows the test scores of two Spanish classes taught by the same teacher.
a. Compare the populations using measures of center and variation.
2 ACTIVITY: Estimating a Percents
Work with a partner. Use a model to estimate the answer to each question. d. 50 is what percent of 80?
Answer:
62.5%
Step-by-step explanation:
since percents are just fractions, we have 5/8 and we need to convert it into a percentage. since 100 is not divisible by 8, we can use a trick by multiplying the numerator by 100. we get 500/8 which is 62.5.
0.9(3/2.25-1/8(5/3+1/9))-4/7 / (8/10)
HELP ME PLEASE AND GET 15 POINTS!!
MAKE SURE TO ANSWER ALL 7 QUESTIONS
Tysm
1 ACTIVITY: Estimating a Part
Work with a partner. Use a model to estimate the answer to each question.
c. What number is 40% of 30?
Answer: 12
Step-by-step explanation:
Converting the problem into words, we have
x= 4/10*30
x=12
39. ELECTIONS In an election, the winning candidate receives 60% of the votes. What percent of the votes does the other candidate receive?
Answer:
40%
Step-by-step explanation:
using our lovely knowledge of percents (or per 100s) we can see that 100-60 is 40, which means only 40% of the votes go to the losing candidate
8.3.5 Ana's monthly salary was $2000 in May. In June, she received a 20% raise. In July, she received a 20% pay cut. After the two changes in June and July, what was Ana's monthly salary?
Answer:
After July, Ana's monthly salary was $1920
Step-by-step explanation:
In May, Ana's monthly salary was $2000. During the next month, the salary increased by 20%, or (0.2)(2000)
[tex]2000+(0.2)(2000)=2000+400=2400[/tex]
So, in June, Ana's monthly salary was $2400. During the next month, the salary decreased by 20%, or (0.2)(2000)
[tex]2400-(0.2)(2400)=2400-480=1920[/tex]
Therefore, after the two changes, Ana's monthly salary was $1920
Answer:
Now Ana's monthly salary is 1920$.
Step-by-step explanation:
Given: Ana's salary in may =2000$
in June she received 20% raise
in July she received 20% pay cut.
To find Ana's monthly salary after the two changes in June and July.
we have to first find Ana's salary at the end of June month with 20% raise. and then her salary after the end of July month with the pay cut of 20%.
Step 1 of 2
Ana's salary after June month when she got 20% raise in his salary after May is equal to
[tex]=2000+(20 \% \cdot 2000)$\\ $=2000+\left(\frac{20}{100} \cdot 2000\right)$\\ $=2400 \$$[/tex]
her new salary after May will be 2400$.
Step 2 of 2
now she got a pay cut of 20% on his new salary from July month
so, her salary after that would be equal to
[tex]=2400-(20 \% \cdot 2400)$\\ $=2400-\left(\frac{20}{100} \cdot 2400\right)$\\ $=2400-480$\\ $=1920 \$$[/tex]
HELP: Of 580 students in a high school graduating class 45% are planning to go to college. How many of the graduates are planning to go to college?
Answer:
261 of the graduates are planning to go to college.
Step-by-step explanation:
This is a proportion question.
x 45
___ = ___
580 100
First do 45 x 580 = 26,100
Then divide by 100 to get 261.
Find the area of the shaded region.
Answer:
[tex]18 ft^2[/tex]
Step-by-step explanation:
You could calculate the area of the trapezoid and then subtract the area of the triangle.
Area of a trapezoid:
[tex]A = \frac{a+b}{2}h[/tex]
Plug values in:
[tex]A = \frac{6+12}{2}(6)[/tex]
Add 6 and 12:
[tex]A = \frac{18}{2}(6)[/tex]
Simplify:
[tex]A = 54[/tex]
Area of a triangle:
[tex]A = \frac{1}{2}bh[/tex]
Plug values in:
[tex]A = \frac{1}{2}(6)(12)[/tex]
Simplify:
A = 36
Subtract the area of the triangle from the area of the trapezoid
54 - 36 = 18
You could also calculate the area of the shaded region by assuming that they're congruent meaning the base would be half of 6 which is 3 and the height would be 6 so the area of one would be 1/2 (6)(3) but since they're is 2 you wouldn't need the 1/2 since multiplying by 2 would cancel it out so the area would be (6)(3) = 18
13. Find the equivalent measure.
6.4 km = ________km ________m
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above1.8[/tex]
To turn kilometers, km, into meters, m, multiply the number
of km by 1,000. This comes out as.
[tex]\boldsymbol{\sf{6.4\times1,000=6,400\:Metres}}[/tex]
To convert meters, m, into kilometers, km, divide the number
of m by 1,000. This comes out as
[tex]\boldsymbol{\sf{6,400\div1,000=6.4\:Kilometres}}[/tex]
#learnwithbrainly
[tex]\orange\hspace{300pt}\above2[/tex]
A theatre has 1,450 seats. If 42% of these are balcony seats. How many balcony seats does the theatre have?
Answer:
609
Step-by-step explanation:
All you must do is multiply 1450 by 0.42. That would give you the total.
Answer:
Hello! The answer to your question is 609 seats.
Step-by-step explanation:
To obtain your answer, you have to multiply the percentage of balcony seats by the total number of seats. 42% is converted to 0.42 because 42/100 = 0.42:
0.42 × 1450 = 609 seats
Graph the inequality on a number line. (Section 4.1) 10. x > 5
Answer:
Please see the attached image.
Step-by-step explanation:
If x > 5, it means that the value of x can take on any value that is greater than 5. Therefore, if you draw a number line, you can put a circle on the number 5 and draw an arrow pointing to the right (in the positive direction, representing all the numbers greater than 5). It is important to note that the circle you draw on the number 5 should not be shaded. This is because, according to the problem, while x can be greater than 5, it cannot equal 5. A hollow circle signifies that the value cannot equal the number circled exactly. I hope this answers your question.
50 POINTS!
A used car dealer has the following information for 2 months of sales:
Month 1: 239 cars sold
Month 2: 324 cars sold
Do we have an increase or a decrease in sales and what percentage?
*ANSWER IS NOT 135% INCREASE*
Simplify:
-x + 17 + (-12) + x
Answer: 5
Step-by-step explanation:
Negative x and positive x combined together cancel each other out
(Edge.)
Which number line shows the graph of Negative 2.75 less-than x?
A. A number line going from negative 3 to positive 3. An open circle is at negative 2.75. Everything to the left of the circle is shaded.
B. A number line going from negative 3 to positive 3. An open circle is at negative 2.75. Everything to the right of the circle is shaded.
C. A number line going from negative 3 to positive 3. A closed circle is at negative 2.75. Everything to the left of the circle is shaded.
D. A number line going from negative 3 to positive 3. A closed circle is at negative 2.75. Everything to the right of the circle is shaded.
Answer:
D
Step-by-step explanation:
Can someone help on Question C?
It's - b + a
Because we're going down the arrow on b or the opposite direction of b. Then, up to C where its vector is a as it lies half way on AC with half of the line labelled a. So, the other half must be also a.
Hope this helps!
please help!
-1 1/3 ÷ 2 2/5=
Answer:
[tex]-\frac{5}{9}[/tex]
11. Find the equivalent measure.
4.009 kg = ___________ kg __________ g
Answer:
Step-by-step explanation:
4.009kg × 1000 = 4009g
A box measures 1/6 ft. long, 1/4 ft. wide, and 1/3 ft. high. Find the volume of the box in inches. Do not include units in your answer write as a whole number
Answer:
24
Step-by-step explanation:
We know that the final answer has to be in inches.
To convert ft = in, multiply given ft. by 12.
1/6 = 1/6 * 12 = 2
1/4 = 0.25 * 12 = 3
1/3 = 0.3 * 12 = 4
2*3*4 = 23 cubic in.
24
Step-by-step explanation:
Identify the days when the temperature was 76°F or more.
Answer: Tuesday, Thursday, and Saturday
Step-by-step explanation:
Pretty self-explanatory.
I DO REALLY NEED HELP: An architect is planning a city parking lot. For every 12 commuters, the parking lot will need 5 parking spaces. How many parking spaces will be needed by 132 commuters?
Answer:
55 parking spaces
Step-by-step explanation:
Using unitary method:
For every 12 commuters , 5 spaces are needed.
∴ For 1 commuter:
5 ÷ 12 ⇒ [tex]\frac{5}{12}[/tex] spaces are needed.
∴ For 132 commuters ⇒ [tex]\frac{5}{12}[/tex] × 132 = 55 spaces.
PLEASE ANYONE: Roger worked 9 hours on Friday and 6 hours on Saturday.What is the ratio of the work done on Friday to the total hours worked on both days?