Answer:
The dimensions of the old rug are 8 ft by 12 ft
Step-by-step explanation:
Let
x ----> the length of the old rug
y ----> the width of the old rug
we know that
[tex]100\%+50\%=150\%=150\100=1.5[/tex]
so
The dimensions of the old rug multiplied by the factor 1.5 must be equal to the dimensions of the new rug
so
[tex]1.5x=12\\x=8\ ft[/tex]
[tex]1.5y=18\\y=12\ ft[/tex]
therefore
The dimensions of the old rug are 8 ft by 12 ft
91.8% of 648 toy robots on an assembly line will be approved by the quality control inspector. Write and
solve a proportion to find how many robots will be approved.
Answer:
595 will be approved.
Step-by-step explanation:
Multiply 648 by 0.918: the result is 594.9, which should be rounded up to 595.
There are 5 pennies for every 6 quarters in Ahmed's pocket. Could Ahmed have a total of 30 coins in his pocket? Explain
Ahmed cannot have total of 30 coins in his pocket
Solution:
Given that,
There are 5 pennies for every 6 quarters in Ahmed's pocket
We are asked if Ahmed can have a total of 30 coins in his pocket
From given,
5 pennies for every 6 quarters
Therefore, ratio is:
penny : quarter = 5 : 6
Total = 5 + 6 = 11
Then the total number of coins must be multiple of 11
But 30 is not a multiple of 11
Therefore, Ahmed cannot have total of 30 coins in his pocket
No, Ahmed cannot have a total of 30 coins in his pocket.
Explanation:Yes, Ahmed could have a total of 30 coins in his pocket.
To determine how many quarters and pennies Ahmed could have, we can set up a ratio.
The ratio of pennies to quarters is 5:6.
Let the number of quarters be represented by 6x, where x is a positive integer. Then, the number of pennies would be 5x.
To find out if Ahmed could have a total of 30 coins, we need to solve the equation 6x + 5x = 30.
Combining like terms, we obtain 11x = 30. By dividing both sides of the equation by 11, we find that x = 2.7272 (repeating).
Since x must be a positive integer, we can conclude that Ahmed cannot have a total of 30 coins in his pocket.
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Which function is not linear?
tof
Select one:
O a. f(x)=5/x
O b. f(x)=3x4
O c. f(x)=-7x
O d. f(x)=5
Answer:
f(x)=-7x is the only one linear
Step-by-step explanation:
I'm wondering if this is mistake or not with your question, but if you graph each function, all but one graph is linear.
The equation of a straight line is y+10=5x
Answer:
y=5x-10
Step-by-step explanation:
y+10=5x
y=5x-10
If a(x)=2x-4 and b(x) =x+2, which of the following expressions produces a quadratic function?
Answer:
[tex](ab)(x)[/tex]
Step-by-step explanation:
The complete question in the attached figure
we have
[tex]a(x)=2x-4\\b(x)=x+2[/tex]
we know that
(ab)(x) is equal to the product of a(x) and b(x)
so
[tex](ab)(x)=(2x-4)(x+2)[/tex]
Applying distributive property
[tex](ab)(x)=2x(x)+2x(2)-4(x)-4(2)[/tex]
[tex](ab)(x)=2x^2+4x-4x-8[/tex]
[tex](ab)(x)=2x^2-8[/tex]
This is a quadratic equation
The other expressions not produce a quadratic equation
A post it note has an area of A square inches. The width of the post it note is 4 inches.which equation represents X the length of the post it note in inches A X=4/A. B. X=A+2(4) C. X=A/4. D. X=A-2(4)
Answer:
Option C. X=A/4
Step-by-step explanation:
we know that
The area of the rectangular post it note is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]W=4\ in\\L=X\ in[/tex]
substitute
[tex]A=4X[/tex]
solve for x
That means ----> isolate the variable x
Divide by 4 both sides
[tex]X=\frac{A}{4}[/tex]
What is the area of the figure?
Answer:
you have to multiply to get the answer because it's an area not premiter. premiter you at all at once
Answer:
Total area= [tex]28 +25.12= 53.12[/tex] square feet
Step-by-step explanation:
The total area of the 2-D figure= Area of triangle in the fig. + Area of the semicircle in it.
Area of the triangle in the figure [tex]=\frac{1}{2}*Base*Altitude \\\\=\frac{1}{2}*8*7\\\\ =\frac{56}{2} \\\\=28[/tex] square feet
Area of the semicircle=
[tex]\frac{\pi r^2}{2} \\\\\frac{3.14*4*4}{2}\\\\ 3.14*8\\\\25.12square feet[/tex]
Total area= [tex]28 +25.12= 53.12[/tex] square feet
(b) John begins his jogging workout by running faster and faster for about a minute. Once he hits a comfortable pace, he
runs at that pace for several minutes. Then he gradually slows down to a stop over the next few minutes.
Speed
Speed
Speed
Speed
Time
Time
Time
Time
Answer:
What am i supposed to answer?
A sports team is throwing an end-of-season party at the fitness club. The costs associated with the party include a $150 flat fee for the room rental and a $14 per person charge for the Italian buffet. An 18% tip must be added to the cost of the food. Express the total cost for the party as a function of the number of people attending
Answer:
[tex]c(x)=150+16.52x[/tex]
With x being the number of people attending the party, and c(x) the cost in dollars.Explanation:
The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:
[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]
Where x respresents the number of people attending the party.
Convert 18% to its decimal form, which is 0.18 and simplify the equation:
[tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]
Hence, calling the function c(x), it is:
[tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.
The function which representing the total cost of party is [tex]150+16.52x[/tex]
Total cost :Let us consider that number of people who attending part be x.
The room rental amount is $150.
The charge of the Italian buffet for per person = $14
For x number of people [tex]=14x[/tex]
Since, 18% tip added to the cost of the food.
Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]
Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]
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Amy drove to her mothers house, which is 204 miles away. If it took her 3 hours, what was her average speed?
68 m/s was her average speed
Amy's average speed was 68 mph (miles per hour)
Calculating average speedFrom the question, we are to determine what Amy's average speed was
Average speed can be calculated by using the formula,
[tex]Average\ speed =\frac{Distance}{Time}[/tex]
From the given information,
Distance covered = 204 miles
Time = 3 hours
Then
Average speed = [tex]\frac{204}{3}[/tex]
Average speed = 68 mph (miles per hour)
Hence, Amy's average speed was 68 mph (miles per hour)
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16^(3-3r)=256 can someone please help me solve this!! Thanks!!
Answer:
The value of r is 1/3
Step-by-step explanation:
Let's solve for r in the equation:
16 ^(3-3r) = 256
16 ^(3-3r) = 16²
3 - 3r = 2
-3r = 2 - 3
-3r = -1
r = -1/-3
r = 1/3
Let's prove r = 1/3 is correct:
16 ^(3-3r) = 256
16 ^ (3 - (3 * 1/3)) = 256
16 ^ (3 - 1) = 256
16 ² = 256
16 * 16 = 356
We proved that r = 1/3 is correct
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles.
Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Write an algebraic expression to represent the number of large marbles she has.
If Amy has a total of 560 marbles, how many of each size does she have? Show your work.
Answer:
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
i) Let the number of small marbles be x
ii) let the number of medium marbles be y
iii) let the number of large marbles be z
iv) Amy has 5 times as many small marbles as medium marbles therefore we can write 5y = x
v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write
z = 3y + 2
vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560
vii) Therefore from i) we can write x = 5y
viii) using vii) and v) in vi) we can write
x + y + z = 5y + y + 3y + 2 = 560
ix) Therefore 9y = 558 .... therefore y = [tex]\frac{558}{9}[/tex] = 62
x) Therefore from i) we get x = y [tex]\times[/tex] 5 = 62 [tex]\times[/tex] 5 = 310
xi) Therefore z = (3 [tex]\times[/tex] 62) + 2 = 188
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
15 inches increased by 20%
Answer:
18
Step-by-step explanation:
15 + Percentage increase =
15 + (20% × 15) =
15 + 20% × 15 =
(1 + 20%) × 15 =
(100% + 20%) × 15 =
120% × 15 =
120 ÷ 100 × 15 =
120 × 15 ÷ 100 =
1,800 ÷ 100 =
18
A metal worker makes a box from a 15inch by 20inch piece of tin by cutting a square with a side length x out of each corner and folding up the sides
a) write expressions for length width and height of the box
b) write a polynomial for the volume of the box
Answer:
a) Length = (20 - 2x) inches
Width = (15 - 2x) inches
b) Volume = (20 - 2x)(15 - 2x)x cubic inches.
Step-by-step explanation:
A metalworker makes a box from 15 inches by 20 inches piece of tin by cutting a square with a side length x out of each corner and folding up the sides.
a) So, the length of the box will become (20 - 2x) inches.
And, the width of the box will become (15 - 2x) inches.
b) The volume of the box will be = (Length × Width × Height)
= (20 - 2x)(15 - 2x)x cubic inches. (Answer)
one fifth ÷ 4 = ⬜
Luis said the solution is 20.
Matt said the solution is .1/20
Who is correct? Explain your reasoning.
Matt said the solution 1/20 is the correct answer.
Step-by-step explanation:
step 1 :
one fifth ÷ 4 = one part in five equal parts / 4
= (1/5) / 4
The expression can be written as (1/5) / (4/1)
step 2 :
To solve the division of fractions, take reciprocal of the denominator and do multiplication.
The reciprocal of denominator (4/1) is 1/4.
step 3 :
(1/5) / (4/1) = (1/5) [tex]\times[/tex] (1/4)
= 1/20
∴ Matt said the solution is 1/20 is correct.
You deposit $7500 in an account that pays 5.2% interest compounded continuously. Find the balance after 10 years.
Answer:$3900
Step-by-step explanation:
Summer exercises for 0.5 hour on Monday Wednesday and Friday each week. How many hours will she exercise in four weeks
Answer:
She will exercise for 6 hours in four weeks.
Step-by-step explanation:
Summer exercises for 0.5 hour on Monday, 0.5 hour on Wednesday, and 0.5 hour on Friday. There are 3 days where she exercises for 0.5 hour.
3 days X 0.5h = 1.5h each week
For four weeks, multiply the hours each week by 4.
1.5h X 4 weeks = 6h
Therefore Summer will exercise for 6 hours over the course of 4 weeks.
Answer:
6 hours
Step-by-step explanation:
We know that Summer exercises for 0.5 (Or a half) hour every day, three days a week (Monday, Wednesday, Friday). We need to found out how many hours she exercises in 4 weeks.
To solve this we first find out how many hours she exercises in one week. To do so, we set up an equation like this:
(Time exercising) x (# of days exercising) = (Hours spent exercising in one week)
Plug in the given numbers:
0.5 x 3 = 1.5 hours
If we know she exercises 1.5 (Or one and a half) hours in 1 week, we multiply this number by 4 to find out how many hours she exercises in 4 weeks. This can be shown in an equation like this:
1.5 x 4 = 6
So Summer will exercise for 6 hours in 4 weeks.
What is the quotient of the following division problem?
x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol. minus x squared + x to get a remainder of 0 ) 2 x + 2. minus 2 x + 2 to get a remainder of 0 and a quotient of x + 2.
The quotient of x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol is x+2
Step-by-step explanation:
We need to find quotient of x^2+3x+2 divided by x+1
The division is shown in figure attached.
Quotient: x+2
Remainder: 0
The quotient of x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol is x+2
Answer:
x+2
Step-by-step explanation:
An item is regularly placed at $87. Laura bought it on sale for 55% off the regular price. How much did Laura pay?
Answer:
$39.15
Step-by-step explanation:
87 x .55 = 47.85
87-47.85= 39.15
Answer:
$39.15
Step-by-step explanation:
87 x 55%
87 x 0.55 = 47.85
87 - 47.85 = 39.15
You have two fair, six-sides dice. However, the dice have been modified so that instead or 1,2,3,4,5,6 the sides are numbered 1,2,2,2,3,4.
What is the probability the total of the two dice is an even number?
Answer:
.
Step-by-step explanation:
Answer:
5/9.
Step-by-step explanation:
Prob ( first dice = 2 and second = 2) = 1/2 * 1/2 = 1/4
Prob ( first = 2 , second = 4) = 1/2 * 1/6 = 1/12
Prob ( first = 4 and second = 2) = 1/12.
Prob ( first = 3 and second = 1 ) = 1/36
Prob ( first = 1 and second = 3) = 1/36.
Prob ( first = 3 and second = 3) = 1/6 *1/6 = 1/36.
Prob (first = 1 and second = 1 = 1/36.
Prob (first = 4 and second = 4 = 1/36.
Required probability is the sum of these which is:
5/9.
I hope I've thought of all the possible outcomes.
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.
who runs fastest?
Caedin runs fastest (he has the highest speed)
Step-by-step explanation:
The question in this problem is "who runs fastest": this means that the problem is asking us "which runner has the greatest speed?"
The speed of a body is a scalar quantity defined as
[tex]v=\frac{d}{t}[/tex]
where
d is the distance covered by the body
t is the time elapsed
In order to calculate the distance covered by each runner, we have to sum the length of all the pieces of motion, regardless of their direction.
From the graph, we observe that:
- Andy moves from x = 0 to x = 1.25 miles, so the distance covered is d = 1.25 miles. Since the time taken is 10 minutes, his speed is
[tex]v=\frac{1.25}{10}=0.125 mi/min[/tex]
- Berta moves from x = 0.5 miles to x = 1.15 miles, so the distance covered is
d = 1.15 - 0.5 = 0.65 miles
The time taken is 10 minutes, so her speed is
[tex]v=\frac{0.65}{10}=0.065 mi/min[/tex]
- Finally, Caeding moves first from x = 1.5 miles to x = 0, so he covers a distance of
[tex]d_1 = 1.5 mi[/tex]
Then he also moves from x = 0 to x = 1.0 miles, so he covers an additional distance of
[tex]d_2=1.0 mi[/tex]
So the total distance is
[tex]d=d_1+d_2=1.5+1.0=2.5 mi[/tex]
And since the time taken is 10 minutes, the speed is
[tex]v=\frac{2.5}{10}=0.25 mi/min[/tex]
Therefore, Caedin has the highest speed.
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At how many points does the graph of the function below intersect the x-
axis?
y= 16x2 - 8x+1
Apex
Answer:
1
Step-by-step explanation:
Normal Distribution
Using the graph as a reference, select all
statements that are true about a normal distribution
of data.
Normal distributions are symmetrical about
the mean, m.
The total area under the curve is 100.
Ninety-five percent of the data lies within 1
standard deviation of the mean.
The probability that an event is within 1
standard deviation above the mean is 34%.
All data sets are normally distributed
Answer:
1 and 4.
Step-by-step explanation:
i just did it
Consider the line segment shown on the coordinate plane. What are the coordinates of midpoint AB?
A- (-1, 1/2)
B- (1, 1/2)
C - (1, -1)
D-(1,2)
James is considering buying a home priced at $104,000. If the current market
is a buyer's market, which of the following is most likely not the price James
will end up paying for the house?
A. $100,000
B. $106,000
C. $102,000
D. $103,000
Answer:
B. $106,000
Step-by-step explanation:
ILL MARK YOU BRAINLIEST IF YOU ANSWER CORRECTLY
Write in scientific notation: 0.0042
A) 42 x 10^-2
B) 4.2 x 10^-4
C)4.2 x 10^-3
D).42 x 10^-4
---------------------------------------------------
write in standard notation:6.12 x 10^3
A)6120
B)612
C) 61,200
D)61.2
Answer:
Scientific Notation:
4.2 × 10^-3
E-Notation:
4.2e-3
Engineering Notation:
4.2 × 10^-3
Real Number:
0.0042
Step-by-step explanation:
If 2d÷4=5, does 2d÷4+6=5+4
Answer:
3/2d
Step-by-step explanation:
ad 5 and 4 then subtracts 6 from both sides then divide 2 from 3 and get 3/2
Which number is farther from 0: -7 or 5
Answer:
-7
Step-by-step explanation
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.What is the explicit rule for this situation, and how many marbles will be in the 10th row?Drag and drop the answers into the boxes to match the situation.Explicit ruleNumber of marbles in the 10th rowAn = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
The explicit rule for the number of marbles in 10th row is An= 12+ n-1.
Step-by-step explanation:
Total number of rows = 10 rowsThe number of marbles in the 1st row = 12 marblesOne marble is added to each successive rowTherefore, for the remaining 9 rows out 10 rows ⇒ 9 marbles are added.
The number of marbles in the 10th row = 12+9 = 21 marbles.The explicit rule is An = 12 + n-1For n= 10, then
⇒ A10 = 12 + (10-1)
⇒ A10 =12+9 = 21
Answer:
A(n)=11+n
Step-by-step explanation: took test
From 45 ft to 92 ft?
Answer:47
Step-by-step explanation:
Answer:
47 feet
Step-by-step explanation:
92 feet-45 feet= 47 feet
Answer is 47 feet