total price of made dolls:
n×£8.50
=170×£8.50
=£1445
total cost:
C= 5n+432
C = 5×170+432
C= £1282
profit=price-cost
p= £1445-£1282
= £165
A carpenter has a board that is 8 feet long. He cuts off 2 pieces. One piece is 3 1/2 feet long and the other is 2 1/3 feet long. How much of the board is left? IM SO SORRY THIS QUESTION ISN’T MULTIPLE CHOICE PLS FORGIVE ME
Answer:
2 1/6
Step-by-step explanation:
The answer is 2 1/6 because you should start by adding 3 1/2 + 2 1/3. This equals 5 5/6 feet. You should then subtract 8 - 5 5/6 because you are figuring out how much is left. When you subtract 8 - 5 5/6, you get 2 1/6. So 2 1/6 feet of the board is left.
Hope this helps!
Use synthetic division to evaluate (3x2 − 6x + 3) ÷ (x − 1). 3x − 9 3x2 − 3x 3x − 3 3x2 − 6
Answer:
[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
Answer:
3x-3
Step-by-step explanation:
use synthetic division
Hello. Im stuck on this question. It says find 25% of 70. And I got 17.5 but it says it is wrong Could anyone help
Question: what is 25% of 70
= 17.50 or 25%
why the question “How many colors are there in the United States flag?” is NOT a statistical question.
Answer:
3
Step-by-step explanation:
blue, white, and red colors
Help me please
calculate the value of x in the polygon
Answer:
122.5 degrees
Step-by-step explanation:
A six sided polygon's interior angles sum to
(n-2)(180) = (6-2) (180) = 720 degrees
then x + x + x + x+10 + 130 + 90 = 720
4x = 490 so x = 122.5 degrees
9=-7x+7x^2 Helppp please
Answer:
x= 0.21428571428 or x=0.2
Step-by-step explanation:
-7x+7x^2=9 1. simplify 7x^2
-7x+ 7x(7x)=9 2. combine like terms
-7x+49x=9 3. combine like terms
42x=9 4. /42 on both sides
x= 0.21428571428 or x=0.2
Factor 4x² - 121 a) (2x + 11) (2x + 11) b) (2x - 11) (2x - 11) (2x + 11) (2x - 11) d) (4x + 11) (4x - 11)
Answer:
(2x-11)(2x+11)
Step-by-step explanation:
2x-11 × 2x+11 yields
4x^2 + 22x -22x +121
22x subtracts itself and final result is
4x^2 -121
Three numbers have the sum of 112. The first number is twice the second and the third number us twice the first. What is the smallest of the 3 numbers?
Answer:
x = 16
Step-by-step explanation:
Let the second number be x.
The first number = 2x
The third number = 2×2x = 4x
2x + x + 4x = 112
7x = 112
x = 112/7
x = 16
Do you know the answer to this
Answer:
[tex] 4x^2y\sqrt[4]{3y} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{768x^8y^5} = [/tex]
[tex] = \sqrt[4]{256 \times 3(x^2)^4y^4y} [/tex]
[tex] = \sqrt[4]{4^4 \times 3(x^2)^4y^4y} [/tex]
[tex] = 4x^2y\sqrt[4]{3y} [/tex]
simplify the expression
4x(x + 1) (3x − 8) (x + 4)
Answer:
4×(x+1)(3x-8)(x+4)= (4x²+4)(3x-8)(x+4)= (12x³-32x²+12x²-32)(x+4)= (12x³-20x²-32)(x+4)= 12x⁴+48x³-20x³-80x²-32x²-128x= 12x⁴+28x³-112x²-128x
Find the height of the trapezoid.
Answer:
height = 7
Step-by-step explanation:
[tex]2\cdot\frac{42}{8.7 + 3.3} = 7[/tex]
[((a ^ 2 - 25b ^ 2) ^ 3 + (25b ^ 2 - 9c ^ 2) ^ 3 + (9c ^ 2 - a ^ 2) ^ 3)/((a - 5b) ^ 3 + (5b - 3c) ^ 3 + (3c - a) ^ 3)]
The factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
To answer the question, w e need to know what factorization is
What is factorization?Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.
So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have
[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Factorizing out the denominator, we have
= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Cancelling out the denominator, we have
= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
So, the factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
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Point QQQ is located at (-4, 6)(−4,6)left parenthesis, minus, 4, comma, 6, right parenthesis. Point RRR is located at (8, 6)(8,6)left parenthesis, 8, comma, 6, right parenthesis.
What is the distance from point QQQ to point RRR?
=========================================================
Explanation:
Points Q and R have the same y coordinate of 6.
This means they're on the same horizontal level and we can form a number line through these points. Think of Q and R being on the x axis.
Going from -4 to 8 is a distance of 12 units because either
-4-8 = -12 which flips to +12 or 12
8-(-4) = 8+4 = 12
Effectively I used absolute value for the first part to go from -12 to 12. Distance cannot be negative.
Alternatively, you can count out the number of horizontal spaces from -4 to 8 and you should count out 12 units.
--------------------------------
If you need to use the distance formula, then this is what the steps may look like:
[tex]Q = (x_1,y_1) = (-4,6) \text{ and } R = (x_2, y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-8)^2 + (6-6)^2}\\\\d = \sqrt{(-12)^2 + (0)^2}\\\\d = \sqrt{144 + 0}\\\\d = \sqrt{144}\\\\d = 12\\\\[/tex]
In my opinion, the distance formula is overkill because we can simply apply subtraction or count out the number of spaces. It's up to you which you prefer you like better. Of course be sure to follow all instructions your teacher mentions.
If the two points weren't on the same horizontal level, then we would have no choice and have to use the distance formula. Or you could use the pythagorean theorem which is effectively what the distance formula is derived from.
(4-x)/(x^2-5x+4)+(2)/(x-1)=1
show all steps please!!
Answer:
[tex]x = 2, 4[/tex]
Step-by-step explanation:
Given :
[tex]\frac{4-x}{x^{2} -5x+4} + \frac{2}{x-1} =1[/tex]
=============================================================
Factorize the denominator of the first term :
⇒ x² - 5x + 4
⇒ x² - x - 4x + 4
⇒ x(x - 1) - 4(x - 1)
⇒ (x - 4)(x - 1)
============================================================
Hence, the equation now is :
[tex]\frac{4-x}{(x-1)(x-4)} + \frac{2}{x-1} =1[/tex]
============================================================
Multiply the second term by (x - 4) in the numerator and denominator :
[tex]\frac{4-x}{(x-1)(x-4)} + \frac{2(x-4)}{x-1(x-4)} =1[/tex]
============================================================
Combine the numerator of both terms and bring the denominator to the other side :
[tex]\frac{4-x+2(x-4)}{(x-1)(x-4)} = 1[/tex]
[tex]4 - x+2x-8 = x^{2} - 5x + 4[/tex]
[tex]x - 4 = x^{2} - 5x + 4[/tex]
[tex]x^{2} -5x-x+4+4=0[/tex]
[tex]x^{2} -6x+8=0[/tex]
[tex](x-4)(x-2)=0[/tex]
[tex]x = 2, 4[/tex]
please help because I don’t know!!
Answer:
Step-by-step explanation:
Comment
There was a flat fee of 10 dollars
Each 1/4 hour brought in 3,75
The total charge was 55 dollars.
Equation
Charge = 10 + 4*3.75*x as an hourly rate,
Solution
55 = 10 + 4*3.75x Combine
55 = 10 + 15x Subtract 10 from both sides
55-10= 10-10 + 15x
45 = 15x Divide by 15
45/15 = 15x/15
x = 3 hours
Answer 3 hours
What is the value of x in the equation?
Answer:
What is the value of x in the equation?
Step-by-step explanation:
Question 9 of 9
Which of the expressions are equivalent to the one below? Check all that
apply.
(15.3)-20
A. (3.15)-20
B. 20-(3.15)
C. 6 (15-20)
D. (3-20) (15-20)
- Write the inequality that shows how much money you can spend on the booth.
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if you have $1000 and need to buy 10 chairs worth $5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:
x + 10(5) ≤ 1000
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.
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What is the equation of a line that passes through (-6,2) and has a slope of -(1)/(2)?
Answer:
y= -1/2x+5
Step-by-step explanation:
A rectangular piece of material with sides 150 cm and 100 cm is used to make a circular table cloth. the diameter of the completed cloth must be 0.9 m and 5 cm is provided for the hem. how much material is wasted?
The material wasted is 7915.375 sq cm.
What is area of rectangle?The product of its length and breadth.
Area = length* breadth
Given:
length= 150 ac, breadth = 100 cm
d= 0.9m 5cm
r= 47.5 cm
Area of rectangle,
= l * b
= 150*100
= 15000 sq. cm
Area of Circular cloth,
= πr²
=3.14*47.5*47.5
=7084.625 sq cm.
Hence, the wasted material is = 15000-7084.625
= 7915.375 sq cm
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Fawzia has an action figure collection of 500 action figures. She keeps 58% of the action figures on her wall. How many action figures does she keep on her wall?
Answer:
290
Step-by-step explanation:
Formula :
Number of action figures on wall = Total number of figures × % of figures on wall
=============================================================
Given :
⇒ Total number of action figures = 500
⇒ % of action figures on wall = 58%
=============================================================
Solving :
⇒ Action figures on wall = 500 × 58%
⇒ Action figures on wall = 500 × 58/100 (all % are ratios of 100%)
⇒ Action figures on wall = 5 × 58
⇒ Action figures on wall = 290
Total action figures
58% of 5000.58(500)2.9(100)290action figuresDone!
X is a normally distributed random variable with mean 46 and standard deviation 22.
What is the probability that X is between 2 and 90?
A. .99
B. .95
C. .85
D. .65
Answer:
B. 0.95
Step-by-step explanation:
The probability that the value of the random variable is in the given range is the area under the normal probability distribution curve over that range. The value of this area is conveniently provided by any number of calculators, apps, or spreadsheets. It can also be determined using the "empirical rule" that tells you the probability over certain normalized ranges.
__
normalized rangeA standard normal probability density function (PDF) has a mean of 0 and a standard deviation of 1. The range in this problem can be normalized to some number of standard deviations above or below the mean. The mean is given as 46, and the standard deviation is given as 22.
In this problem, the lower limit of the range is ...
z = (2 -46)/22 = -2
standard deviations from the mean.
Similarly, the upper limit is ...
z = (90 -46)/22 = +2
standard deviations from the mean.
empirical ruleThe empirical rule tells us that 95% of the area of the PDF lies between -2 and +2 standard deviations from the mean.
P(2 < X < 90) ≈ 0.95
_____
Additional comment
The empirical rule for other ranges is ...
± 1 standard deviation: 68%
±2 standard deviations: 95%
±3 standard deviations: 99.7%
A rectangular piece of iron has sides with lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3 m. what is the volume of the piece of iron? 6.96 × 10–7 m3 6.96 × 107 m3 6.96 × 10–18 m3
The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m
What is volume?Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.
It is represented in cubic units.
How to determine the volume of a rectangleFormula:
Volume, V = length × breadth × height
Given the values;
7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m
Multiply all the lengths
Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3
= 69.6 × 10^-8
= 6. 96 × 10^ -7 m
Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m
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Answer:
A
Step-by-step explanation:
trust
Which of the following best describes ZAOR?
R
142⁰
A
A major arc is an arc that is greater than 180 degrees.
A minor arc is an arc less than 180 degrees.
An acute angle is an angle less than 90 degrees.
What is the central angle?
A central angle is an angle created in the center of a circle with 2 sides being the radius.
Thus, we can see in the figure that we are talking about the angle so we can eliminate the major arc and minor arc.
Now, we clearly see that the angle is greater than 90 degrees so it cannot be an acute angle.
The correct answer is the central angle as it goes with the definition.
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Slope of (-9,-2) and (-9,-6)
Answer:
Slope is undefined.
Step-by-step explanation:
Find the volume of this rectangular pyramid.
length =5cm
width =6cm
hight =7cm
PLEASE HURRY
What is the equation of a line parallel to y=(3)/(4)x-5 and passes through (12,-2)?
A parallel line has the same slope as the original line. So in this case the slope of the line is also 3/4. Now how do we know if it intersects the point? We need to adjust the y intercept.
Currently, we know the equation of the line is y= 3/4 x + b, where b is the thing we are looking for. We also have a point, which supplies the x and y. Plug that in and solve for b
-2 = (3/4)*(12) + b
You'll get b= -11
So the equation of the parallel line intersecting the point given is y= 3/4x -11.
I am assuming that the slope is 3/4 based on the way you formatted the original equation, but it's the same steps if the slope is different.
Which equation represents a population of 300 animals that increases at an annual rate of 23% ?
Answer:
300+(300 + 0.23x)
Step-by-step explanation:
I'm not sure what you are asking but this is the only equation I can get
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
A correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
What is a circle?A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.
The general form of the equation of a circle is given as:-
( x - h )² + ( y - k )² = r²
By comparing the given equation we can see the following results:-
x² + (y – 3)² = 36
( x - ( 0 ))² + ( y - 3 )² = 6²
We can see that the coordinate of the center are ( 0, 3 ) and the radius is 6 so the diameter is 12.
Therefore the correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
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Answer:
A and E (first and last, ending in "=36")
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
Step-by-step explanation:
just took the quiz
Find the least common multiple of 35 and 21
Answer:
105
Multiples of 35:
35, 70, 105, 140, 175
Multiples of 21:
21, 42, 63, 84, 105, 126, 147
Answer:
105
Step-by-step explanation:
Given the following question:
We are given two numbers and we are trying to find the least common multiple (LCM) of the two. In order to find the LCM we have to find the GCM or the greatest common multiple.
[tex]35\div7=5[/tex]
[tex]21\div7=3[/tex]
[tex]GCM=7[/tex]
Now that we have the GCM we multiply 35, and 21 then divide it by the GCM.
[tex]35\times21=735[/tex]
[tex]735\div7=105[/tex]
[tex]LCM=105[/tex]
The least common multiple is "105."
Hope this helps.