Gretchen can make 5 pillows with the fabric she has.
Define fractionA fraction is a numerical quantity that represents a part of a whole. It consists of two numbers separated by a line, with the number on top called the numerator and the number on the bottom called the denominator
1 5/8 yards of fabric = 13/8 yards of fabric
8 1/4 yards of fabric = 33/4 yards of fabric
Number of pillows = (Total fabric) ÷ (Fabric per pillow)
Number of pillows = (33/4 yards of fabric) ÷ (13/8 yards of fabric per pillow)
Number of pillows = (33/4 yards of fabric) × (8/13 pillows per yard of fabric)
Number of pillows =5.076≈5
Hence, the greatest number of pillows she can make is 5, which corresponds to option (a) in the multiple choice list.
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Rewrite in simplest radical form
Answer:
sqrt(x)
Step-by-step explanation:
1/ ( x^(-3/6))
We can simplify the fraction
1/ ( x^(-1/2))
A negative exponent means that since it is in the denominator, it goes to the numerator. It still keeps the exponent.
x^ (1/2)
sqrt(x)
Solve. Give your answer in scientific notation. (3.4x10^2)x(2x10^3)
A.1.4x10^-1
B.6.8x10^5
C.5.4x10^5
D.6.8x10^6
Plz answer
Final answer:
The multiplication of (3.4x10²) and (2x10³) results in 6.8x10⁵ after multiplying the coefficients and adding the exponents. Therefore, the correct answer is option (B).
Explanation:
Considering, the question it has asked to solve the following arithmetic operation in scientific notation: (3.4x10²)x(2x10³).
To solve this the following steps can be used :
we multiply the coefficients (3.4 and 2) and then add the exponents (2 and 3).
Multiplication of coefficients: 3.4 * 2 = 6.8
Addition of exponents: 2 + 3 = 5
Combining both parts: 6.8 x 10^5
The correct answer in scientific notation is therefore 6.8x10⁵, which corresponds with option B.
What is the result of factoring out the GCF from the expression (24 + 36)?
A. 12 × (12 + 18)
B. 12 × (2 + 3)
C. 6 × (8 + 12)
D. 12 × (4 + 6)
24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
GCF(24, 36) = 2 · 2 · 3 = 12
24 = 12 · 2
36 = 12 ·3
24 + 36 = 12 × 2 + 12 × 3 = 12 × (2 + 3)
Answer: B.The result of factoring out the Greatest Common Factor (GCF) from the expression (24 + 36) is 12 × (2 + 3).
Explanation:To factor out the Greatest Common Factor (GCF) from the expression (24 + 36), we first need to determine the largest number that divides evenly into both 24 and 36. The GCF of 24 and 36 is 12. We divide each term by the GCF to factor out it from the expression:
24 ÷ 12 = 2
36 ÷ 12 = 3
Thus the expression factored out by the GCF is 12 × (2 + 3).
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Using the slope formula, find the slope of the line through the given points.
(-8, -5) and (9, -5)
Simplify
Answer:
0
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
= (-5--5)/ (9--8)
= (-5+5)/(9+8)
= 0/17
=0
The slope it 0
This is a horizontal line because the y value doesn't change. If the y value doesn't change, the slope it zero.
Express as a fraction or a mixed number.
0.15%
Answer:
15/100
Step-by-step explanation:
If the the number as a decimal is in the hundredths place you put the number over 100
5/6 + (-1/2)value of sum
Answer:
it's 1/3
Step-by-step explanation:
5/6+(-1/2)
5/6-1/2
LCM= 6
(5-3)/6
2/6
1/3
Simplify 7x +42/ x2+13x +42
[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{x^2+7x+6x+42}=\dfrac{7(x+6)}{x(x+7)+6(x+7)}\\\\=\dfrac{7(x+6)}{(x+7)(x+6)}=\boxed{\dfrac{7}{x+7}}[/tex]
Your answer should be 2(10x^3+21x^2+21) over X^2 2(10x^3+21x^2+21)/X^2 unless the / was a fraction symbol and not a division symbol then your answer would be 7 over x+7 7/x+7
James has a model helicopter. The model is 8 inches long and 7 inches wide. The actual helicopter is 56 inches long. What is the helicopters actual width, if we assume the models proportions are accurate?
A: 40 inches
B: 49 inches
C: 56 inches
D: 60 inches
Answer:
49 inches
Step-by-step explanation:
Write and solve an equation of ratios, as follows:
7 inches x
-------------- = -----------------
8 inches 56 inches
Then (8 ")x = (7 ")(56 "), and
x = 392/8 inches = 49 inches.
The actual width of the helicopter is 49 inches.
The actual width is found to be 49 inches, which corresponds to answer choice B.
The question is asking us to determine the actual width of a helicopter given its scale model dimensions and the actual length. To solve the problem, we use the concept of ratios or proportions. The scale model is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long.
We set up a proportion to find the actual width:
Model length : Actual length = Model width : Actual width8 inches : 56 inches = 7 inches : x inchesTo solve for x, we cross multiply:
8 * x = 56 * 7
x = (56 * 7) / 8
x = 392 / 8
x = 49 inches
Therefore, the correct answer is B: 49 inches, which is the actual width of the real helicopter.
find the common ratio for this geometric sequence 8, 2, 1/2, 1/8, 1/32
Answer:
Multiply 1/4 ; dividing 4
Step-by-step explanation:
Note that in each number going from left to right, it decreases by dividing 4 each time (or multiplying 1/4)
8/4 = 2 ; 2/4 = 1/2 ; (1/2)/(4) = 1/8 ; etc.
(8)(1/4) = 2 ; (2)(1/4) = 1/2 ; etc.
~
Answer: 1/4
Step-by-step explanation:
All geometric figures,shapes,and solids can be named using sets of
Answer:
All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.
Step-by-step explanation:
Julie had $2000 in her savings account, but then she purchased a plane ticket for spring break, decreasing her savings account by 14%. How much was her plane ticket? How much money was left in the account after she bought it?
Step-by-step explanation:
A function f(x) is graphed.
What is the slope of the function? M= 1,2,3,4
What is the y-intercept of the function? B= -2,-1,1,2
Which equation represents the graph of the function y=-x+2 , y=x+2 , y=2x+1 , y=-2x+1
Answer:
Point-Slope form: The equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex] ......[1]
where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.
From the given graph:
Consider two points i.e,
[tex](0, 1)[/tex] and (-0.5, 0)
Calculate slope:
Formula for slope is given by;
[tex]\text{Slope}(m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we have;
[tex]m = \frac{0-1}{-0.5-0} = \frac{-1}{-0.5} = \frac{10}{5} =2[/tex]
Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;
[tex]y-1 = 2(x-0)[/tex]
y-1 = 2x
Add 1 to both sides we get;
y = 2x+1
On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;
slope(m) = 2
y-intercept(b) = 1
therefore, the slope of the function:
m = 2
y-intercept(b) = 1
and the equation represents the graph: y = 2x+1
Answer:
2
1
y = 2x + 1
Step-by-step explanation:
Please help
Evaluate - 8×|12|
Answer:
-96 or 96
Step-by-step explanation:
this is because the distance from zero is twelve, so it could be -12 or 12, plug both into the problem and then solve.
the absolute value |x| of a real number x is the non-negative value of x without regard to its sign.
|x| = x for x ≥ 0.
|x| = -x for x < 0.
Examples:
|2| = 2
|-5| = -(-5) = 5
If is -8 × |12| = -8 × 12 = -96
If is 8 × |12| = 8 × 12 = 96
the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family included the sales tax when calculating the tip, what percent tip did the family leave?
Answer:
20% tip
Step-by-step explanation:
Dinner: $48.00
Tax: 0.05($48.00) = $2.40
Total (final) bill before tip: $50.40
Tip: $10.08
Percentage tip was then $10.08 (100%) / $50.40 = 20%
The family left a 20% tip.
If x = 1 is a zero of the polynomial x3 – 7x + 6, find the other two zeroes.
Answer:
x = - 3, x = 2
Step-by-step explanation:
Since x = 1 is a zero then (x - 1) is a factor of the polynomial
dividing x³ - 7x + 6 ÷ (x - 1)
= (x - 1)(x² + x - 6)
= (x - 1)(x + 3)(x - 2)
equating (x + 3)(x - 2) = 0 gives the other zeros
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per year Which function models the average annual cost of owning a small dog for x years?
Answer:
Average cost per year = 400 + 180/x
Step-by-step explanation:
Using the formula y=mx+b
We know that b is the y intercept or initial value. That would be the start up costs
m is the slope on costs each time x increases, that would be 400 per year
Costs = 400x + 180
To find the average cost per year, we need to divide by x
Average cost per year = (400x + 180)/x
= 400 + 180/x
Answer:
answer to this question is f(x) = (180 + 400x)/x
An investor invested a total of $3 comma 500 in two mutual funds. One fund earned a 4% profit while the other earned a 2% profit. If the investor's total profit was $110, how much was invested in each mutual fund
Answer:
$2000 invested in first fund
$1500 invested in second fund
Step-by-step explanation:
An investor invested a total of $3,500 in two mutual funds.
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let y be the amount invested in second fund
second fund earned a =2% profit (2%= 0.02)
So interest is 0.02y for second fund
An investor invested a total of $3,500 in two mutual funds.
So x+y = 3500----> equation 1
y= 3500-x
the investor's total profit was $110
0.04x + 0.02y = 110----> equation 2
Plug in 3500 -x for y
0.04x + 0.02(3500-x) = 110
0.04x + 70 - 0.02x = 110
0.02x + 70 = 110
Subtract 70 onboth sides
0.02x = 40
Divide both sides by 0.02
x= 2000
y= 3500-x
so y= 3500 - 2000 = 1500
$2000 invested in first fund
$1500 invested in second fund
Need help with 21-22, 27-34 plz
x-y<3
Do I need to flip the sign?
Which quantity is proportional to 35⁄80? Check all that are true. 3⁄5 14⁄36 26⁄52 21⁄48 7⁄16
Hey there!
"Which quantity is proportional to [tex]\frac{35}{80}[/tex]?"
The easier way, I figured out how to solve this particular problem is simplify the fraction to decimal
[tex]\frac{35}{80}[/tex] [tex]= 0.4375[/tex]
[tex]\frac{3}{5}[/tex] [tex]= 0.60[/tex] so, this one isn't your answer[tex]\frac{14}{36}[/tex][tex]=0.288889[/tex] so this one isn't your answer [tex]\frac{26}{52}[/tex][tex]=0.50[/tex] so this one isn't your answer[tex]\frac{21}{48}[/tex][tex]=[/tex][tex]=0.4375[/tex] this one is your answer [tex]\frac{7}{16}[/tex][tex]= 0.4375[/tex] so this one is your answer[tex]\boxed{Answer: \frac{21}{48} AND \frac{7}{16}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Answer:
3/5 no
14/36 no
26/52 no
21/48 yes
7/16 yes
Step-by-step explanation:
Compute the amount of interest earned in the following simple interest problem. A deposit of 1,295 at 7% for 180 days=____. (note: use 365 days in a year
The interest earned is approximately $50.06.
To calculate the amount of interest earned in a simple interest problem, we can use the formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{\text{Total days in a year}} \][/tex]
Given:
- Principal (P) = $1,295
- Rate (R) = 7% or 0.07
- Time (T) = 180 days
- Total days in a year = 365 days
Plugging these values into the formula:
[tex]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} \approx 1295 \times 0.07 \times 0.493150685 \]\[ \text{Interest} \approx 50.05958904 \][/tex]
A computer is normally $550 but is discounted to $385 which precent of the original price does mark pay
Answer:
70%
Step-by-step explanation:
We assume, that the number 550 is 100% - because it's the output value of the task.
We assume, that x is the value we are looking for.
If 100% equals 550, so we can write it down as 100%=550.
We know, that x% equals 385 of the output value, so we can write it down as x%=385.
Now we have two simple equations:
1) 100%=550
2) x%=385
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=550/385
Now we just have to solve the simple equation, and we will get the solution we are looking for.
Solution for 385 is what percent of 550
100%/x%=550/385
(100/x)*x=(550/385)*x - we multiply both sides of the equation by x
100=1.4285714285714*x - we divide both sides of the equation by (1.4285714285714) to get x
100/1.4285714285714=x
70=x
x=70
-10-|1+4b|=-19
Y = 0
Answer:
b=2 or b=-2.5
Step-by-step explanation:
We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.
[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]
We now have the absolute value isolated. We will set it equal to both 9 and -9.
[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]
and
[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}= -2.5[/tex]
A 3-ounce package of pistachios cost $5.99 what is the unit rate???!
Answer: 1.996666666666667
Step-by-step explanation:
3ounces divided by 5.99
Answer:If you round 5.99 it would be 6.00 and then dived 3 and 6.00 its going to be 1.5 because you have to split it up
Step-by-step explanation:
Karonlina flips a coin 60 times. how many times would you expect it's to land heads up?
Answer:
30 times
Step-by-step explanation:
There's a 50% chance that they will get heads.
60 divided by 2 is 30
50% of 60 is 30
Answer:
We expect 30 heads.
Step-by-step explanation:
There are 2 sides to a coin, heads and tails. They are equally likely. So the probably of getting a heads is 1/2
If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.
number of heads = 60 * 1/2
= 30
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? Be sure to show your work using the equation above.
Answer:
17.922
Step-by-step explanation:
first you plug it in
y=0.860(17) + 3.302
then u simplify
y=14.62+3.302
then add them
y=17.922
Answer:
17.922 inches long
Step-by-step explanation:
y=0.860x + 3.302
y= 0.860(17) + 3.302
y= 14.62 + 3.302
y= 17.922
Hope it helps!!
Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?
Could I have an equation for the problem.
Thank you so Much!
Answer:
Twenty Pounds
Step-by-step explanation:
Equation #1:
30lbs x Mix Price = (Lollipop Lbs x 0.95) + (Caramel Lbs X 1.10)
Equation #2:
Lollipops Lbs + Caramel Lbs = 30 Lbs
Rearrange expressions to solve for different variables
EQ1: Caramel Lbs = (30 - .95 Lollipop Lbs)/ 1.10 NOTE: (mix price = 1.00)
EQ2: Lollipop Lbs = 30 - Caramel Lbs
Substitute formula 1 into formula 2
Lollipop Lbs = 30 - [(30 - .95 Lollipop Lbs)/1.10]
Distribute divisor
Lollipop Lbs = 30 - 27.2727 + .8636 Lollipop Lbs
Collect terms
Lollipop Lbs = 2.7273 + .8636 Lollipop Lbs
Remove .8336 Lollipops from both sides of the equation
.1364 Lollipop Lbs = 2.7273
Divide both sides by .1364 (Answer is 19.9949 which rounds to 20)
Lollipop Lbs = 20
PROOF:
30 = (20 x 0.95) + (10 x 1.10)
30 = 19 + 11
30 = 30 TRUE!
To determine the number of pounds of lollipops in the mixture, we can set up an equation with the total weight of the mixture and the weight of the lollipops. Solving the equation, we find that there are 15 pounds of lollipops in the mixture.
Explanation:
To solve this problem, we can set up an equation using the given information.
Let x represent the number of pounds of lollipops in the mixture.
Since Rachel has a total of 30 pounds of the mixture, we can write the equation: x + (30 - x) = 30
Simplifying the equation, we have: 2x = 30
Dividing both sides by 2, we find that x = 15.
Therefore, there are 15 pounds of lollipops in the mixture.
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Multiply: (3x + 7)(5x2 − 3x + 6)
Answer:
15x^3+26x^2-3x+42
Step-by-step explanation:
The multiplication is 15x³ +26x² - 3x + 42.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The multiplication (3x + 7)(5x²-3x+6) is as shown:
(3x + 7)(5x²-3x+6)
= 15x³ - 9x² + 18x +35x²- 21x +42
= 15x³ +26x² - 3x + 42
Hence, the multiplication is 15x³ +26x² - 3x + 42.
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What is equal to 19.04 divided 5.6
Answer: 19.04 divided by 5.6 is 3.4
Step-by-step explanation:
Simplify
[tex]\frac{(3 + i)}{(5 + 2i)} [/tex]
Answer:
17-i
--------
29
Step-by-step explanation:
To simply fractions with complex numbers, we have to multiply by the complex conjugate of the denominator.
The denominator is 5+2i, so the complex conjuate is 5-2i
3+i 5-2i
------ * ---------------
5+2i 5-2i
Simplifying the numerator
(3+i) * (5-2i) = 3*5 + 5i -3*2i -2i^2 = 15 +5i -6i -2(-1) = 15-i+2 = 17-i
Simplifying the denominator
(5+2i) (5-2i) = 25 -10i + 10i -4i^2 = 25 -4(-1) = 29
17-i
--------
29
Answer:
- [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]
Step-by-step explanation:
to simplify the fraction ewe require to rationalise the denominator.
This is done by multiplying the numerator/ denominator by the conjugate of the denominator.
the conjugate of 5 + 2i is 5 - 2i, hence
= [tex]\frac{(3+i)(5-2i)}{(5+2i)(5-2i)}[/tex]
= [tex]\frac{15-i-2i^2}{25-4i^2}[/tex]
[ i² = ([tex]\sqrt{-1}[/tex])² = - 1 ]
= [tex]\frac{-i+17}{29}[/tex] = - [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]