Answer:
We can use change of base rule
A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for 2450. she sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. if her profit on the entire transaction was 855, find the cost price of a basket of pawpaw and the selling price of 100 baskets of mangoes.
The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.
How to calculate the price?Based on the information given, the equations to solve the question will be:
30p + 100m = 2450 .... i
1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii
30p + 100m = 2450
12p + 30m = 855
Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.
Therefore, the cost of 100 basket of mangoes will be:
= 12.5 × 100
= 1250
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A cylindrical barrel of water has a base radius of 30 cm and is 110 cm high.
a) Find it’s volume in cm³.
b) Find it’s capacity in litres
( Hint is 1 cm³= 1 ml )
c) Find the number of bottles of water that can be filled from the barrel if each bottle holds 0.73 litres.
The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
We have:
The radius of the cylindrical barrel r = 30 cm
Height of the cylindrical barrel h = 110 cm
Volume:
[tex]\rm V = \pi (30)^2 (110)[/tex]
V = 311017.67 cubic cm
The volume of litres:
V = 311.017 cubic ml (1 liter = 1000 cubic cm)
Number of bottles = 311.017 /0.73= 426 bottles
Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
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what's a frustum and what's the formula of the Almighty Formula
Answer:
the portion of a solid that lies between one or two parallel planes cutting it
Step-by-step explanation:
Calculate the area of the Parallelogram.
I will mark as brainliest, Please help quick!
Answer:
A = 42 cm²
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 6 and h = 7 , then
A = 6 × 7 = 42 cm²
Solve for x. The triangles are similar.
Answer:
[tex]\fbox {D. 10}[/tex]
Step-by-step explanation:
As the triangles are similar :
45/55 = (12x - 3)/143
9/11 = (12x - 3)/143
9 x 13 = 12x - 3
12x = 117 + 3
12x = 120
x = 10
Answer:
D. 10
Step-by-step explanation:
We can use similar triangles to solve this question. ΔRSE ≅ ΔFGE by SAS. We can set up this similarity equations: [tex]\frac{SE}{GE} = \frac{RE}{FE}[/tex] . Plugging in the numbers from the diagram, we get [tex]\frac{45}{12x-3} = \frac{55}{143}[/tex] . Using cross multiplication, we get the following equation:
[tex]45 * 143 = 55 *(12x-3)\\ 6435 = 660x - 165\\6600 = 660x\\x = 10[/tex]
Our final answer is D. 10
Write an equation for each translation of y=|x|
13 units down
y-13= |x|
y=1x1-13
y=1-13x1
y=1x1+13
The answer is y=|x|-13.
Answer:
y=|x|-13
Step-by-step explanation:
Here is a sketch of y=x^2 +bx+c
Answer:
Step-by-step explanation:
Which expression is represented by the diagram?
-6 - (-1)
-6 - 1
-5 - (-1)
-5 -1
Answer:
C
Step-by-step explanation:
Answer:
Please review the question. I don't see a diagram. And the "expressions" are just numbers.
Step-by-step explanation:
The expressions aren't really expressions. There are no variables (x or y).
-6 - (-1) is -5
-6 - 1 is -7
-5 - (-1) is -4
-5 -1 is -6
We don't know if these are values of x or y, so the diagram could only be a series of dots on a number line.
Consider the following graph.
Which statement best describes Cheryl's commute?
A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes
The statement best describes Cheryl's computer is option C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
If we know that the function crosses the x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Let's assume the graph of Cheryl's commute was like the one below.
We can see that she started at 0 mph.
One minute later, she was up to 65 mph, so she had accelerated (increased her speed).
At 6.5 min (5.5 min later) her speed was still 65 mph therefore, she was driving at a constant speed.
Over the next 2.5 min, her speed dropped to 45 mph, therefore she was decelerating.
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What is the equation of the line that passes through the point (1,4) and has a slope of 4
Answer:
y = 4x
Step-by-step explanation:
Equation of line in point -y intercept form:
[tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]
[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]
y - 4 = 4(x -1)
y - 4 = 4*x - 4*1
y - 4 = 4x - 4
Add 4 to both sides
y = 4x - 4 + 4
y =4x
can anybody help me?
f(-2) = 2(-2)² - 8(-2) + 6 = 30
f(-1) = 2(-1)² - 8(-1) + 6 = 16
f(0) = 2(0)² - 8(0) + 6 = 6
f(1) = 2(1)² - 8(1) + 6 = 0
f(2) = 2(2)² - 8(2) + 6 = -2
NEED HELP ASAPP PLEASE!!
Each step of the proof are:
a || b∠1 ≅ ∠5∠1 ≅ ∠5∠5 ≅ ∠7∠5 ≅ ∠7∠1 ≅ ∠7∠1 ≅ ∠7How to complete the proof?The given parameter is:
Lines a and b are parallel.
This is represented as; a || b
Corresponding angles are equal.
∠1 and ∠5 are corresponding angles.
So, we have: ∠1 ≅ ∠5
Also, they are congruent.
So, we have ∠1 ≅ ∠5
Vertical angles are equal.
∠5 and ∠7 are vertical angles.
So, we have: ∠5 ≅ ∠7
Also, they are congruent.
So, we have ∠5 ≅ ∠7
According to the transitive property;
If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7
Hence, it has been proved that ∠1 ≅ ∠7
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give me da answer.........................................................................
Answer:
Ok ya sure I would love to. :)
Step-by-step explanation:
Oh wait….
*Crickets chirping*
By the distributive law 49 x 17 + 49 x 3=
Answer:
49(17 + 3)
Step-by-step explanation:
The Distributive Law says [tex]a(b+c)=ab+ac[/tex]. But it can be used in the other direction, [tex]ab+ac=a(b+c)[/tex]. That way, you look at ab and ac to find the common factor a. What's playing the role of a in the expression 49 x 17 + 49 x 3? It's 49, the factor that shows up twice. That's the factor that can be taken outside the parentheses.
49 x 17 + 49 x 3 = 49(17 + 3)
This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
O A. x² +2²=100
OB. x+y=10
O C. x¹0 + 10 = 100
O D. x² + y² = 10
a
5
10
Answer:
[tex] {x}^{2} + {y}^{2} = 100[/tex]
The equation of the circle is x² + y² = 100.
Option A is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
The circle's equation is:
x² + y² = r²
where r is the length of the radius.
In this case, r = 10, so the equation becomes:
x² + y² = 10²
Simplifying:
x² + y² = 100
Therefore,
The equation of the circle is x² + y² = 100.
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1. If x³ +3x²-4=0 has x=-2 as a root (zero), find the other two roots.
Answer:
1 and -2 (has a multiplicity of 2)
Step-by-step explanation:
so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division
-2 | 1 3 0 -4
-2 -2 4
1 1 -2 0
(x+2)(x²+x-2)
Now you can factor the quadratic into
(x+2)(x-1)
x+2 = 0
x = - 2
x-1 =0
x = 1
Describe the shape of the distribution for the following and justify your answer:
a. The distance people travel to work on a typical day - The horizontal axis is the distance traveled in a person's daily commute. The vertical axis is frequency (number of people with that distance for their daily commute). Shape of distribution:
uniform
symmetric
skewed left
skewed right
Justification:
b. Number of hours of sleep for each night of the week (weekdays only) - The horizontal axis is the day of the week (Monday to Friday) and the vertical axis is the amount of sleep in hours for that night. Shape of distribution:
symmetric
skewed left
skewed right
uniform
Justification:
c. Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. Shape of distribution:
skewed left
symmetric
skewed right
uniform
Justification:
d. Scores on the Graduate Requirement Exam - This is a standardized test for people entering graduate school. The horizontal axis would be the person's total score. The vertical axis would be frequency (number of people with that score). The population would be all GRE test takers for a given year. Shape of distribution:
skewed left
symmetric
skewed right
uniform
Justification:
As the travelling distance to work increases, number of such people decreases. Therefore this distribution shape will be skewed right.
How to depict the shape?On each weekday, the number of sleeping hours generally remains the same. So the shape of the distribution will be uniform.
In general, most people will have their first heart attack at a higher age. So the shape of the distribution will be skewed left.
Scores of GRE will have a normal distribution in general. So the shape of the distribution will be symmetric.
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A six-sided die is thrown three times. What is the probability of getting a prime number on all three rolls?
Answer:
3/216
Step-by-step explanation:
The sample space for this experiment is 6^3 which is 216
there are three prime numbers on die
namely 2 , 3 and 5
so the probability of getting a prime number on all three roles would be
(3/6)^3
PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answer: 55[tex]m^{2}[/tex]
Step-by-step explanation:
First find the area of the trapezoid: [tex]\frac{b1 +b2}{2}[/tex](h) : (base 1 + base 2) ÷ 2 x height
base 1 is 5m and we know the other base is parallel to the base of the rectangle so base 2 is 9m.
Since the total height is 7 m and the height of the rectangle is 5 m, subtract to get the height of the trapezoid: 7m - 5m = 2m
put the three values into the equation and solve:
(5m + 9m) ÷ 2 x 2m
(14m) ÷ 2 x 2m
7m x 2m
14[tex]m^{2}[/tex]
Find area of the rectangle which is just base x height
Which is 9m x 5m = 45[tex]m^{2}[/tex]
To find the total area, add the area of the trapezoid and the area of the rectangle. 14[tex]m^{2}[/tex] + 45[tex]m^{2}[/tex] = 55[tex]m^{2}[/tex]
Hope this helps
Please helppppppp????
The volume of the spherical ball will be 4 · π · 3² · 10⁶ cubic cm. Then the correct option is A.
The complete question is attached below.
What is the volume of the sphere?Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The radius of the sphere is 3·10² cm.
Then the volume of the spherical ball will be
V = 4/3 πr³
V = 4/3 π(3 x 10²)³
V = 4/3 · π · 3³ · 10⁶
V = 4 · π · 3² · 10⁶ cubic cm
Then the correct option is A.
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Does someone mind helping out with this ?
Write the fraction as a decimal.
six tenths
0.6
0.06
6.0
1.6
Answer:
[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]
Step-by-step explanation:
[tex]0.6=\dfrac{6}{10}[/tex]
one digit after the decimal point - one zero in the denominator
[tex]0.06=\dfrac{6}{100}[/tex]
two digits after the decimal point - two zeros in the denominator
[tex]6.0=6[/tex]
[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]
f(x) = 3x + 6, find the ordered pair when x = -1.
(-1,-3)
(-1,3)
(-1,-9)
(-1,9)
Answer:
(-1 ; 3)
Step-by-step explanation:
when they say find the ordered pair they simply mean find the corresponding y value when x = -1
* where you see x substitute-1 *
f(-1) = 3(-1) + 6
=3
Find the surface area of a hexagonal prism if the length of each side of the hexagonal base is 4 cm and the height is 7 cm.
The surface area of a hexagonal prism willl be 251.13844 cm².
What is the surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
A=6ah+3√3a²
A=6×4×7+3√3×4²
A≈251.13844
Hence the surface area of a hexagonal prism willl be 251.13844 cm².
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Fluffy the bunny ate 1/2 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1/3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
Answer:
1/6
Step-by-step explanation:
the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6
What is the point slope form of an equation of the line through the points (-2, 6) and (3, -2)
[tex] \frac{1 }{4 } \times \frac{3}{4} \div \frac{10}{3} [/tex]
What is the answer to the above equation?
Answer:
Step-by-step explanation:
Solution
This (after combining the top 2 fractions, is a 4 tier fraction.
1/4*3/4 = 3/16
So the question now becomes 3/16 ÷ 10/3
The rule for such a question is invert (turn up side down) the second fraction and multiply.
3/16 * 3/10 Combine
(3*3)/(16* 10)
9 / 160
0.05625
[tex]\bf{\dfrac{1}{4}\times\dfrac{3}{4}\div\dfrac{10}{3} }[/tex]
Multiply 1/4 by 3/4 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\bf{\dfrac{1\times3}{4\times4}\div\dfrac{10}{3} \ \ \to \ \ \ Multiply.}[/tex]
Do the multiplications in the fraction 1 × 3 / 4 × 4.
[tex]\bf{\dfrac{3}{16}\div\dfrac{10}{3} }[/tex]
Divide 3/16 by 10/3 by multiplying 3/16 by the reciprocal of 10/3.
[tex]\bf{\dfrac{3}{16}\times\left(\dfrac{3}{10}\right) }[/tex]
Multiply 3/16 by 3/10 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\bf{\dfrac{3\times3}{16\times10 } \ \ \to \ \ \ Multiply }[/tex]
Do the multiplications in the fraction 3 × 3 / 16 × 10
[tex]\bf{\dfrac{9}{160} \ \ \to \ \ Answer }[/tex]
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
HELP PLEASE GIVING BRIANLEST
Answer:
Maybe the answer will be C. P (A and B )
Ans: C
Explanation:
I think it is option c , P(A and B)
as this is the only option which has the value of 80, which we got from the table
[tex]\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}[/tex]
The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
How to solve the equation?The equation is given as:
[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]
Start by taking the LCM
[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]
Expand the denominator
[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]
Cancel out the common factor
4x(x - 2) - 5x(x - 1)= 2
Expand
[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]
Evaluate the like terms
[tex]-x^2 - 3x = 2[/tex]
Rewrite as:
[tex]x^2 + 3x + 2 = 0\\[/tex]
Expand
[tex]x^2 + 2x + x + 2 = 0[/tex]
Factorize
x(x + 2) + 1(x + 2) = 0
Factor out x + 2
(x + 1)(x + 2) = 0
Solve for x
x = -1 or x = -2
Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
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Let a be a matrix with 4 columns. What are the possible values for rank(a)?
The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?
The possible values for rank A = 2
What is a vector space?A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.
From the information given:
If v,w be the vectors in a [tex]\mathbb{R}[/tex]where;
A = matrix with 4 columns v, w, 2v+w, v-w, which are non-independent vectors.However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).
We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.
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