The different ways of solving percent increase or percent decrease problems has been described below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.
Another method is by multiplier method
Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then 1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease
For the first method
Suppose the number is n and it is increased by p%
Required result is
[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]
For the second method
Suppose the number is n and it is increased by p%
Here n is taken as 1 and p% is converted to decimal
then 1 and p% in decimal form is added
we get (1 + 0._p)
Now the result is obtained is multiplied by n
Required result is
n(1 + 0._p)
[tex]n(1 + \frac{p}{100})[/tex]
In this way the two methods are related
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18. Write three valid congruency statements given the triangles below.
The three valid congruency statements are; Triangle PQR = Triangle STU
What are congruent angles?Angles who are of same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of same measure, then
[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
Congruence statement states that a statement used in geometry that simply says that two objects are congruent, or has the same shape and size.
Also, we can make congruence statements in words or in symbols. Using symbols we use the congruence symbol i,e ≅ to indicate that two objects are congruent.
In the given triangles;
Angle T = Angle Q
QR = ST
TU = PQ
Triangle PQR = Triangle STU reason=ASA
Therefore, the three valid congruency statements are;
Triangle PQR = Triangle STU
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Rewrite x^3+8x^2+11x-20 as a product of linear factors. Explain how you found the factors.
The linear factors of the given cubic polynomial are (x-1)(x+4)(x+5).
What are linear factors?The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials.
Given a cubic polynomial, x³+8x²+11x-20
x³+8x²+11x-20 = (x-1)(x²+9x+20)
= (x-1)(x²+4x+5x+20)
= (x-1){x(x+4)+5(x+4)}
= (x-1)(x+4)(x+5)
Hence, The linear factors of the given cubic polynomial are (x-1)(x+4)(x+5).
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You are painting a room that is 18 ft long, 14 ft wide and
8 ft high. Find the area of the four walls that you are going to paint.
Answer:
do the answer is 532 ft.
u should be careful not to count the area of the ceiling and the floor of the room!
Answer:
512 ft²-------------------------
Perimeter of the room:
P = 2(18 + 14) = 2(32) = 64 ftArea of the four walls:
A = Ph = 64*8 = 512 ft²What is an equation of the line that passes through the points (-2, -7) and
(-1, -3)?
m= (6- 3)/ (-5 -1)
2x - y + 11= 0
Which ordered pairs is a solution to 5x+3y>12 Question 2 options: (3, 9) (-5, 5) (3, -6) (-2, -5) (2, 8) (-6, 0)
The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)
How to determine the ordered pair of the solution?From the question, we have the following inequality that can be used in our computation:
5x + 3y > 12
Solving further, we need to collect the like terms
So, the expression becomes
3y > 12 - 5x
Next, we divide through the inequality by 3
So, we have the following representation
y > 12/3 - 5/3x
Evaluate
The equation becomes
y > 4 - 5/3x
At this point, we assume any value for x and then solve for y
Assume that the value of x is 3
So, we have the following representation
y > 4 - 5/3 * 3
Evaluate the products
y > -1
A value greater than -1 is 0
So, we have
x = 3 and y = 0
Express as ordered pairs
(x, y) = (3, 0)
Hence, the ordered pair of the solution is (3, 0)
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Nick bought a new car.
Each year the car depreciates in
value by 12%.
Work out the number of years it takes for the car to half in value.
Solve:
2000(2000^2000)
(A) 2000^2001
(B) 4000^2000
(C) 2000^4000
(D) 4,000,000^2000
(E) 2000^4,000,000
PLEASE ANSWER ASAP!!!
Answer:
They all come out to be infinity
Sarah has 21.50 to go grocery shopping. On her way to the store, she donates 3.00 to a canvasser for a charity. IF mangoes cost 2.25 at the store that day, how many mangoes can she purchase if she uses up all of her remaining money
Sarah can purchase 8 mangoes with all her remaining money
How to find the number of mangoes she can purchase using her remaining money?Given that:
Sarah has 21.50 to go grocery shopping
She donates 3.00 to a canvasser for a charity (that is subtraction).
Thus, the remaining money = 21.50 - 3.00 = 18.50
If mangoes cost 2.25. In order to know how many mangoes she can purchase if she uses up all of her remaining money, you have to divide the remaining money (18.50) by the cost of the mangoes (2.25). Thus:
Number mangoes = remaining money /cost of mangoes
Number mangoes = 18.50 / 2.25 = 8
Therefore, she can purchase 8 mangoes if she uses up all of her remaining money
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There are approximately 420 national parks in the United States. A survey
showed that 85% of the national parks allow overnight camping. Based on
this information, how many national parks allow overnight camping?
Answer:
357 national parks
Step-by-step explanation:
420x85/100
420x17/20
21x17=
357
raina swam 8 kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometer per hour. how fast would raina swim if there were no current?
The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.
Given that,
In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.
Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)
16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)
(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8
8 * Raina's velocity = 24
Raina's velocity = 3 kilometers per hour
As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.
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Lines m and n are parallel and are intersected by transversal p.
Which angle corresponds with angle 2?
3
5
6
8
The angle which corresponds with angle 2 given that; lines m and n are parallel and are intersected by transversal p is; angle 6.
What are corresponding angles?Corresponding angles by definition are any pair of angles each of which happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.
Therefore, it follows from the definition above that the angle which is corresponding to Angle 2 as required in the task content is; angle 6.
This follows from the fact that angles 2 and 6; each happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.
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A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
function f(x)=100/x-5 represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function f(x)=1/x
transformed to create the graph of the function f(x)=100/x-5?
Answer:
The parent graph has been dilated by a scale factor of 100 and has been moved to the right by 5 units
Step-by-step explanation:
The change made to f(x) = 1/x to f(x) = 100/x is a dilation by a scale factor of 100(the function has been multiplied by 100) .
The transformation of function f(x) = 100/x to f(x) = 100/x-5 is moving o the right 5 units (whenever a constant, let's call it "c", is being subtracted from the x when graphing, it means the graph has moved "c" units to the right, and vice versa--if "c" was added to x, then the graph would be moved "c" units to the left.).
TL;DR: f(x-c) means c units to the right, f(x+c) means c units to the left. f(x)*c means a dilation of c units.
Find d, the distance across the lake.
If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 3.
The probability is
The probability that the sum of the dice is 9 is, 4/33.
What is dice?
Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.
Let two fair dice are rolled.
So the possible number of outcomes are,
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4,6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
There are total 36 outcomes.
There are 33 outcomes with sum greater than 3.
The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).
Hence, the probability that the sum of the dice is 9 is, 4/33.
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Double points. Please help!
A survey of the worlds nation in 2004 shows a strong positive correlation between percentage of the country using cell phones and life expectancy and years at birth
1. No This survey does not mean that cell phones are good for your health.
2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.
What is meant by a strong correlation?When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.
A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.
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complete question
A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.
a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no
b. What might best explain the strong correlation (as a lurking variable)?
Select one:
_____ Percent of young people
____ General economic conditions of the country
____ Percent of pop. living in cities
Can someone please help me this is due tomorrow!
Answer:
I can use the given (algebraic expression) 24c+12 to find the total cost of the order
The expression has two (terms). They are 24c and 12
In 24c the number 24 is the (coefficient) and the letter c is the (variable).
The term 24c represents a (product)
To find the total cost of the order I can (evaluate) the given expression
I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression
24c+12
24(6)+12
144+12
156
The total cost is 156
Hope this helps :)
3 quarts of blueberries for every 4 quarts of strawberries how many quarts of strawberries do they need for 9 quarts of blueberries?
f(-10) = 4, ƒ(8) = -5
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
3² × 3 = 3² Find the value of x.
The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
According to the question,
We have the following information:
3² × [tex]3^{x}[/tex] = 3²
We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.
Now, we have the following expression:
2+x = 2
x = 2-2
x = 0
Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
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how to solve/fhfhfhfhfhfhf
Answer:
b
Step-by-step explanation:
the right side base angle and 80° are vertically opposite angles and are congruent, both 80°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
123° is an exterior angle of the triangle , then
x + 80 = 123 ( subtract 80 from both sides )
x = 43
calculate the %cw for a sample of 1040 steel that has an original diameter of 12 mm and a final diameter of 10 mm.
The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA
Given original diameter do = 12 mm
Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²
Deformed diameter d =10mm
Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²
Degree of cold work %CW = (Ao - Ad/Ao)X 100
=(113. 097 - 78. 54/113.097) x 100
= 30.56%
% CW is 30.56 %
Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.
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a column contains phone numbers such as (801)-555-1234. what function should you use to extract the last four digits?
RIGHT function should be used to extract the last four digits from a column containing phone numbers.
The Excel TEXT functions section includes the RIGHT Function[1]. A predetermined number of characters from the end of a provided text string will be returned by the function.
The RIGHT function can be helpful in the financial analysis if we want to extract characters from a text string's right side. It is typically used in conjunction with functions like VALUE, SUM, COUNT, DATE, DAY, etc.
Formula is=RIGHT(text,[num chars])
The following arguments are used by the RIGHT function:
Text is the original text string (mandatory argument).
The number of characters to be returned from the end of the provided text is specified by the optional argument Num chars. It specifies how many characters will be taken, beginning on the right side of the text. If the argument is omitted, the value of 1 by default is used.
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I don’t know the answer to this can you please help me
Answer:
The answer is 24 I think
Step-by-step explanation:
just multipy the numbers
a javalina rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. there are 580 feet of fencing available to complete the job. what is the largest possible total area of the 5 pens?
When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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A group of students are at a library.
6 of them leave. 7 students are left. Which part-part-whole
model shows how many students were at the library to start?
The total number of students at library using part part whole model is 13.
What is part part whole model ?
The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.
Here Number of student who leave library = 6
Number of students who stay at library = 7
Here we have to take Number of student who leave library as one part and Number of students who stay at library as another part . Then
Total number of students at library at start = 6+7 = 13.
The part part whole model like,
=> Total = 13
Part=6 Part=7
Hence the Total number of students is 13.
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Find the vertex of the parabola y=2(x-1)2+4.
Answer:
(1, 4)
Step-by-step explanation:
You want the vertex of the parabola y=2(x-1)²+4.
Vertex formThe vertex form of the equation for a parabola is ...
y = a(x -h)² +k . . . . . . 'a' is the scale factor; (h, k) is the vertex
Comparing the given equation to the vertex form, we see that ...
a = 2
h = 1
k = 4
Then the coordinates of the vertex are (h, k) = (1, 4).
How to find a in this equation?
Answer:
Step-by-step explanation:
5) f(1)= 2x^3-3x^2-2x+a=-4
2^3- 3^2-2+a= -4
a=-1
6)b= 42
The angles of elevation of the top of a tower with respect to points A and B are 30° and 75°respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.
The height of the tower is 87.4870 feet
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The body of the calculation is contained in the attached file.
In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet
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The rectangular frame is made from 5 straight pieces of metal.
The weight of metal is 1.5kg per metre.
Work out the total weight of the metal in the frame.
Answer:
weight = 57 Kg
Step-by-step explanation:
We require to find the length of the diagonal (d) piece of metal
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )
d = [tex]\sqrt{100}[/tex] = 10
the length of the 5 pieces is then
8 + 8 + 6 + 6 + 10 = 38 m
the total weight of the 5 pieces is then
weight = 38 × 1.5 Kg = 57 Kg
