Answer:
-1/2 ≤ x ≤ 1/2 or x∈ [- 1/2, 1/2]Step-by-step explanation:
|16x| ≤ 8|16x/16| ≤ 8/16|x| ≤ 1/2x ≤ 1/2 or x ≥ - 1/2Combination of two inequalities above:
-1/2 ≤ x ≤ 1/2Or interval notation:
x∈ [- 1/2, 1/2]first 120 km of the road the car is moving at speed rate of 90 kilo meter per hour. next one hour and 15 minute the car is moving at speed rate of 64 kilo meter per hour. what need to be the speed rate for the rest of the road so that speed rate of the whole trip would be 80 kilo meter per hour if 1/8 of the is left?
Using the relation between velocity, distance and time, it is found that a rate of 102 km/h is needed for the rest of the trip to achieve the desired rate for the entire trip.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first 120 km, the rate is of 90 km/h, hence the parameters are given as follows:
d = 120, v = 90.
Hence the time is given by:
90 = 120/t1
t1 = 120/90
t1 = 1.33 hours.
For the second part of the trip, the parameters are given as follows:
t = 1.25, v = 64.
The time is 1.25 hours because 15 minutes is one fourth(15/60) = 0.25 of an hour.
Hence the distance found as follows is:
64 = d/1.25
d = 1.25 x 64
d = 80
The distance for the first two parts is given by:
120 + 80 = 200 km.
This is equivalent to 7/8 of the trip, hence the total distance is:
7/8d = 200
d = 200 x 8/7
d = 228.57 km.
For a rate of 80 km, we have that the time has to be of:
80 = 228.57/t
t = 228.57/80
t = 2.86 hours.
The time of the first two parts is:
1.33 + 1.25 = 2.58 hours.
2.86 - 2.58 = 0.28 hours.
Hence the last 228.57 - 200 = 28.57 km have to be traveled in 0.28 hours, for a rate of:
v = 28.57/0.28 = 102 km/h.
A rate of 102 km/h is needed for the rest of the trip to achieve the desired rate for the entire trip.
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Alguém pode me ajudar
Answer:
x≤1
Step-by-step explanation:
1. It cost Luke $9.12 to send 114 text messages. How
much does each text cost to send?
In the 1988 football season, John Elway earned $2,543,666. If he played 15 games that season, what was his average salary per game? Round to the nearest dollar.
Answer:
169,578$
Step-by-step explanation:
If you divide 2 million 5 hundred and 43 thousand 6 hundred and 66 by 15, the answer you would get would be 169,577.733333 (digit 3 goes on and on), but the question says we would need to round it to the nearest dollar. Therefore, the answer is 169,578$!!!
Identify the vertices and foci of each. Then sketch the graph.
Answer:(0,4)
Step-by-step explanation:
A gym charges members $25 for a registration fee, and then $32 per month. You became a member some time ago, and
now you have paid a total of $281 to the gym. How many months have passed since you joined the gym?
months have passed since you joined the gym.
Answer:
It has been 8 months since I joined the gym.
Step-by-step explanation:
1. Subtract the registration fee from the total (which would be $281 - $25 = $256)
2. divide that total by $32 and you will get the total number of months you've gone to the gym. ( which would be $256 ÷ $32 = 8)
3. check your work
6. A dash polynomial cannot be factored by using only integers.true or False
Han tiene 4 tazas de jugo de naranja para poner en frascos. Si pone ½ taza de jugo en cada frasco, ¿cuántos frascos puede llenar?
Han llenaría 8 tazas con jugo de naranja porque si tomas la mitad de 1 taza de jugo de naranja puedes hacer 2 tazas ahora haz eso 4 veces y obtendrás 8 tazas de jugo de naranja
An airline charges an extra fee
for a checked bag that weighs more than 50 pounds.
Your bag weighs 44.9 pounds. You have a 2.5-pound
hair dryer, a 1.3-pound souvenir, and a 3.6-pound pair
of boots. Which items can you add to the bag without
paying the extra fee?
The items that you can add with not breaking the weight limit are:
The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.
Which items can you add to the bag without paying the extra fee?
The maximum weight allowed is 50 pounds, and you already have 44.9 pounds, then the weight you can add is:
50lb - 44.9lb = 5.1lb
Now, the items that you have are:
2.5 lb hair dryer.
1.3 lb souvenir.
3.6 lb pair of boots.
The only things that you can't add together are the hair dryer and the boots, because the weight adds up to:
2.5lb + 3.6lb = 6.1lb
Which is more than the 5.1lb left that you have.
Obviuously, you can't take the 3 items.
Then you can add:
The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.
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Tracy is training to lower her mile time. She completed 4 practice runs and lost a total of 1 minute off her personal record for her mile time. What does (−1)÷4=−0.25 represent in the context of the problem?
a.She lost 1 minute off her mile time.
b.She lost an average of 0.25 of a minute off her mile time.
c.She gained 0.25 minutes on her mile time.
d.She lost 4 minutes off her mile time.
Answer:
hi can we talk for a while I'm a little alone
How can you use the
Product of Powers, Power of a Product, and
Power of a Power Laws to evaluate and write
equivalent numerical expressions with whole-
number exponents?
Answer:
An equivalent numerical expression with whole-
number exponent using these laws can be written as:
1) 2² × 2³ = 2^5 => using product of Powers
2) 2² × 3² = (2×3)² = 6² => using power of a Product
3) (2²)³ = 2^6 => using power of a power
Step-by-step explanation:
First of all, let us understand some terms like;
1) Exponentiation: It is the mathematical process of raising one integer to the power of another. The base is the first integer, while the exponent is the second.
2) Power: A power is a phrase that depicts the same component being multiplied repeatedly.
3) Exponent: The number of times the base is used as a factor is represented by the exponent.
Now, let us understand the 7 Laws of Exponents;
1) a^m × a^n = a^(m+n) => Product With the Same Bases
2) a^m / a^n = a^(m-n) => Quotient with Same Bases
3) (a^m)^n = a^(m×n) => Power Raised to a Power
4) a^n × b^n = (ab)^n => Product to a Power
5) a^n / b^n = (a/b)^n => Quotient to a Power
6) a^0 = 1 => Zero Power
7) a^(-m) = 1/a^m => Negative Exponent Rule
Furthermore, an equivalent numerical expression with whole-
number exponent using these laws can be written as:
1) 2² × 2³ = 2^5 => using product of Powers
2) 2² × 3² = (2×3)² = 6² => using power of a Product
3) (2²)³ = 2^6 => using power of a power
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You can get 1 cookie for 42 cents or 8 cookies for $3.44. Which is the better deal? How do you know?
Answer:
The better deal is 1 cookie for 42 cents
Step-by-step explanation:
We need to find the price of 1 cookie when the cookies are 8 for 3.44
Divide the total price by the number of cookies
3.44/8
.43
We can get 1 cookie for 42 cents or 1 cookie for 43 cents
The better deal is 1 cookie for 42 cents because it is less money.
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm. Use function notation to respond to each item below. Represent the area (in square cm) of a circle that has a radius of 3.4 cm.
The area of the given circle is 36.298 cm square.
Here, we are given that f is the function that determines the area of a circle (in square cm) that has a radius of r cm.
The area of a circle is given the the formula as follows-
area of a circle = πr^2
⇒ f(r) = πr^2
The value of π is approximately 3.14
⇒ f(r) = 3.14r^2
Now, we are given that the radius of a circle is 3.4 cm.
Thus, its area will be-
f(3.4) = 3.14 × 3.4 × 3.4
= 3.14 × 11.56
= 36.298
Thus, the area of the given circle comes out to be 36.298 cm square.
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Find the equation of the line that contains point (1,6) with a slope of -1/4. Write the answer in slope-intercept form.
Answer:
Step-by-step explanation:
Write equation in point slope form:
y - y1 = m(x - x1), where m is slope and (x1,y1) is a point on the line
Here m = 1/4 and (x1,y1) = (0,-6)
y--6 = 1/4(x - 0)
y+6 = 1/4x
in slope-intercept form
y = 1/4x - 6
to find x-intercept, substitute 0 for y and solve for x
to find y-intercept, substitute 0 for x and solve for y
0.95x = 0.55x + 60
Step 1, 2, 3 written out
0.95X -0.55X+10-62 ... Step 1: Find Roots solution. X=-4. X = 3. Step 2: Graph ... Write the Domain and Range of the function. Positive.
Can you please help with this
for the two given fractions 3/4 and 1/6 we have:
sum = 11/12product = 1/8quotient = 9/2How to work with fractions?Here we have two fractions, 3/4 and 1/6, and we want to find the sum, product, and quotient between them.
First let's do the sum:
3/4 + 1/6
We just need to find a common denominator, which can be 12, so we can rewrite it as:
9/12 + 2/12 = 11/12
The sum of the two fractions is 11/12
Now the product, it is, we multiply denominator with denominator and numerator with numerator, we will get:
(3/4)*(1/6) = (3*1)/(4*6) = 3/24 = 1/8
The product between the two fractions is equal to 1/8.
Finally, the quotient, this is:
The product between the first numerator and second denominator, and between the first denominator and second numerator, so the quotient becomes:
(3/4)/(1/6) = (3/4)*(6/1) = (3*6)/(4*1) = 18/4 = 9/2
Then we conclude that for the two given fractions 3/4 and 1/6 we have:
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Determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation.
−6x+6x−6=2−5
Answer:
(c) inconsistent equation
Step-by-step explanation:
You want to know if the equation -6x+6x-6=2-5 is an identity, conditional, or inconsistent.
SimplifiedThe simplified equation, after combining like terms, is ...
-6 = -3
This is an "inconsistent" equation, always false.
How many even 2 digit positive integers can be written using the numbers 2,4,5,8
Answer:
12
Step-by-step explanation:
Suppose i want a 2 digit number and i specifically want it to be even okay, and it can only contain the numbers, 245 and 8 point well in order for it to be even the end would have to be 248 right. An even number. The last digit is divisible by 2 or it even so, there's 3 possibilities here. My question is: can my numbers repeat there's nothing that says my numbers can't repeat so: im gonna some they can so i could use 2 twice, 4 twice and so on and so for, but i can only use 5 once and there's 5 other possibilities here. So 4 possibilities for the first digit 3 possibilities for the second. I'M gonna multiply these together: 4 times 3 there's a total of 122 digit numbers.
Which of the following points are located 3 units from (-4,-2) ? Select all that apply.
The points that are located 3 units from (-4,-2) are (-1, 2), (-7, 2), (-4, -1) and (-4, 5)
How to determine which of the points is located 3 units from (-4,-2)?The point is given as
Point = (-4, 2)
The distance is given as
Distance = 5
The points that are located 3 units from (-4,-2) are calculated using
Points = (x ± 3, y) and (x, y ± 3)
So, we have
Points = (-4 ± 3, 2) and (-4, 2 ± 3)
Expand
Points = (-4 + 3, 2), (-4 - 3, 2), (-4, 2 - 3) and (-4, 2 + 3)
Evaluate the sum and the difference
Points = (-1, 2), (-7, 2), (-4, -1) and (-4, 5)
Hence, the points that are located 3 units from (-4,-2) are (-1, 2), (-7, 2), (-4, -1) and (-4, 5)
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The gestation period of humans (266 days) is _____ percent longer than the gestation period of dogs (65days).
The gestation period of humans is 309.23% percent longer than the gestation period of dogs.
What is the percentage?
Percentage is the fraction out of an amount that is expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %. In order to convert a number to percentage, express the number as a fraction and multiply by 100.
Percent of gestation period = (difference in the gestation period of dogs and humans / gestation period of humans) x 100
[(266 - 65) / 56] x 100
(210 / 65) x 100 = 309.23%
A second method :[ (gestation period of humans / gestation period of dogs) - 1] x 100
[(266 / 65) - 1] x 100 = 309.23%
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10y^2+12y=7y
how do i factor this, whats the two x’s
SHOW ME HOW TO FACTOR IT
45 POINTS
The two values of y after factorizing the given quadratic equation are 0, -0.5
The given equation is quadratic as the order of the equation is 2. In a quadratic equation with a single variable, the variable will have two different values which satisfy the equation. These values of the variable can be real and different, real and equal, or imaginary.
So, there will be two values of y.
Consider the given equation,
10y^2 + 12y = 7y
10y^2 +12y - 7y = 0
10y^2 + 5y = 0
Since the coefficients of y and y^2 are both multiples of 5,
5*(2y^2 + y) = 0
2y^2 + y = 0
Taking y as a common factor,
y*(2y+1) = 0
Now, we get two cases,
y = 0 or 2y + 1 = 0 => y = -(1/2) = -0.5
Therefore, y = 0 or y = -0.5
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Donna makes $9.75 per hour at her job. Kaylee makes $4 per hour at her job, and she receives a $0.25 raise each month. Which inequality could be used to find the number of months it will take for Kaylee to earn at least as much as Donna per hour?
Avery is renting a car and needs to compare the prices of the two car rental companies. Hertz charges $42 per day and an additional $32 in service charges. Enterprise charges $46 per day and an additional $24 in service changes.
Part A: Write an equations for EACH company that represents the total charges for renting a car for a certain number of days. For both questions (one for Hertz and one for Enterprise), define the variable used.
Part B: Use the equations you made in Part A. Which company charges more for renting a car for 6 days? Show your work and justify your answer.
Part C: If Avery decides to rent the car for only 4 days, which company is less expensive? How much money will Avery save? Show your work and explain your reasoning.
The total cost functions are:
total charges for Hertz=32+42x
total charges for Enterprise=24+46x
What does the total rental cost of each company entails?
The total rental cost of each company consists the fixed service charges and the daily charge which can be multiplied by the total of number of days of rental to determine total charges overall.
Hertz:
total charges=32+42x
when x=6 days
total charges=32+(42*6)
total charges=$284
Enterprise:
total charges=24+46x
when x=6 days
total charges=24+(46*6)
total charges=$300
Renting for 4 days:
total charges(Hertz)=32+(42*4)
total charges(Hertz)=$200
total charges(Enterprise)=24+(46*4)
total charges(Enterprise)=$208
savings=$208-$200
savings=$8
The company that charges less when Avery decides to rent car for only 4 days is Hertz and Avery can $8 as result of choosing Hertz
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A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $13, and tickets cost $39 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.
Few friends want to visit the amusement park. They can only spend a total of $325 on parking and entrance. Tickets are $39 per person, tax included, and parking is $13. Create and resolve an inequality that may be used to calculate p, the maximum number of visitors to the theme park.
the maximum number of visitors to the theme park p=14.
Given that few friends want to visit the amusement park .
They are limited to spending $325 for parking and admission.
Tickets are $39 per person, tax included, and parking is $13.
We have to find the the maximum number of visitors to the amusement park p.
We can write as $13+$39p[tex]\leq[/tex]$325
$39p[tex]\leq[/tex]$325-$13
p[tex]\leq[/tex]14
Therefore, the maximum number of visitors to the amusement park p=14.
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Micaela and Elisa each improved their yards by planting rose
bushes and geraniums. They bought their supplies from the
same store.
Micaela spent $122 on 14 rose bushes and 8 geraniums.
Elisa spent $120 on 12 rose bushes and 12 geraniums.
What is the cost of one geranium?
• $1
• $7
• $3
• $5
Answer:
One geranium is $3
Step-by-step explanation:
Let r = roses and g = geraniums
14r + 8g = 122
12r + 12g = 120
Multiply first equation by -3 and the second by 2 (we are trying to get terms that cancel when we add the two equations)
-42r - 24g = -366
+24r + 24g = 240
Add
18r = 126
r = 7, so one rose is $7
Put this into either of the original equations
14(7) + 8g = 122
98 +8g = 122
8g = 24
g = 3, so one geranium is $3
(78 - x) + ( 84 - 3x)
Hey there!
(78 - x) + (84 - 3x)
= 78 - x + 84 - 3x
= 78 - 1x + 84 - 3x
= (78 + 84) - (1x - 3x)
= (78 + 84) - (x - 3x)
= (1x - 3x) + (78 + 84)
= (x - 3x) + (78 + 84)
= x - 3x + 78 + 84
= -4x + 162
Therefore, your answer should be:
-4x + 162
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The ratio of tiger to elephants in a circus is 1 to 3. If there are a total of 48 tigers and elephants in the circus, then how many tigers and elephants are there?
Answer:
There are 12 tigers and 36 elephants.
Step-by-step explanation:
If the ratio of tigers to elephants is 1 to 3, that means that the total would be 4,
so 1/4 of the total would be tigers and 3/4 of the total would be elephands.
1/4 x 48 is 12
and
3/4 of 48 = 36
The maximum load in a freight elevator is 1500 lb let W equal the weight in the elevator write an inequality to describe the allowable weight in the elevator
The inequality to represent the given situation is W≤1500.
Given that, the maximum load in a freight elevator is 1500 lb let W equal the weight in the elevator.
We need to write an inequality to describe the allowable weight in the elevator.
What is inequality?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Now, W≤1500
Therefore, the inequality to represent the given situation is W≤1500.
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Pete Ross read in a Wall Street Journal article that the cost of parts and labor to make an Apple iPhone 4S were as follows:
Help please
Answer: $466.
Step-by-step explanation:
Add all the numbers in the graph together, you get 194.
Now, subtract 194 from 660, you get 466. That's how much profit the company makes.
The required generated profit on iPhone 4s is given as $466.2.
What is the cost price and selling price?The cost price is defined as the is the price of producing something while the selling price is the amount that the buyer pays.
Here,
As of the mentioned data,
Cost of making an iPhone = $193.8
The selling price of the iPhone = $660
Profit is meant how much money is generated from the product besides the product cost price.
Profit = selling price - cost price
Profit= 660 - 193.9
Profit = $466.2
Thus, the required generated profit on iPhone 4s is given as $466.2.
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Benjamin has papayas and pears in a ratio of 50:94. How many pears does he have if he has 25 papayas? On the double number line below, fill in the given values, then use multiplication or division to find the missing value. delta math
If Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.
What is the ratio?The ratio is the numerical relationship that one variable has when compared with another.
The ratio has the same meaning as proportion.
Ratios are represented in percentages, decimals, fractions, or with the ratio sign (:).
How is the number determined?Another way to calculate it is to examine the ratio against the number of papayas he has.
Benjamin has 25 papayas, which is half of 50 (25/50). This means he has half of the pears, which is 47 (94/2).
Data and Calculations:Papayas = 25
The ratio of papayas to pears = 50:94
For every 50 papayas Benjamin has, he has 94 pears.
The number of pears he has = 47 (25/50 x 94)
Thus, if Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.
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