Using front end estimation, the solutions to the given problems are;
1) 25.72
2) 137.521
3) 17.1
How to use front end estimation?
Front-end estimation is defined as a particular way of rounding numbers to estimate sums and differences.
The procedure for using front- end estimation, is to add or subtract only the numbers in the greatest place value. Thereafter, we add the decimals rounded to the nearest tenth.
1) 32.47 - 6.75
First of all, let's deal with the whole numbers part;
32 - 6 = 26
Next is to deal with the decimal part to get;
0.47 is approximately 0.5 while 0.75 is approximately 0.8. Thus;
0.5 - 0.8 = - 0.3
Thus, we have;
26 + (-0.3) = 25.70
Therefore, our given solution can be written as; 25.72
2) 118.234 + 19.287
First of all, let's deal with the whole numbers part;
118 + 19 = 137
Next is to deal with the decimal part to get;
0.234 is approximately 0.2 while 0.287 is approximately 0.3. Thus;
0.2 + 0.3 =0.5
Thus, we have;
137 + 0.5 = 137.5
Therefore, our given solution can be written as; 137.521
C) 17.9 - 0.8
First of all, let's deal with the whole numbers part;
17 - 0 = 17
Next is to deal with the decimal part to get;
0.9 - 0.8 = 0.1
Thus, we have;
17 + 0.1 = 17.1
Therefore, our given solution can be written as; 17.1
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isosceles triangle abc has a perimeter of 96 centimeters. the base of the triangle is line segment a c and measures 24 centimeters.
The measure of the line segment AB is 36cm .
In the question ,
it is given that ,
The triangle ABC is a isosceles triangle ,
that means side AB = side BC ,
and the length of base AC = 24 cm .
given the perimeter of the triangle is 96 cm .
So ,
AB + BC + AC = 96
AB + AB + AC = 96 .....because AB = BC
2AB + AC = 96
Substituting the value of AC = 24 cm
2AB + 24 = 96
Subtracting 24 from both the sides , we get
2AB = 96 - 24
2AB = 72
Dividing both sides by 2 ,
we get ,
AB = 72/2 = 36 .
Therefore , The measure of the line segment AB is 36cm .
The given question is incomplete , the complete question is
Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is Line segment A C and measures 24 centimeters.
What is the measure of Line segment AB ?
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4. The first three terms of an infinite geometric sequence are m- 1,6, m + 8.
(a)write down two expressions for r.
(b) the find two possible values of m.
(c) Hence, find two possible values of (r)
For the given infinite geometric sequence,
(a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
What are Geometric Series?
A geometric sequence's finite or infinite terms are added together to form a geometric series. The geometric series that corresponds to the geometric sequence a, [tex]a,ar, ar^{2} ,..., ar^{n-1} ,...[/tex] is [tex]a+ar+ar^{2}+...+ar^{n-1} +...[/tex] Clearly, "series" means "sum." The phrase "geometric series" refers specifically to the total of words with a common ratio between every adjacent pair of them. Finite and infinite geometric series are both possible.What is the Common Ratio of an Infinite Geometric Sequence?
The common ratio (r) of a geometric sequence or series is defined as the ratio between the two consecutive terms of it.The common ratio of an infinite geometric sequence, [tex]a_{0} , a_{1} ,a_{2} ,a_{3} ,...[/tex] is given as [tex]r=\frac{a_{1} }{a_{0} } =\frac{a_{2}}{1}[/tex]In the question, the first three terms of an infinite geometric sequence are given as, m-1, 6, m+8
[tex]\implies a_{0} =m-1, a_{1}=6,[/tex] and [tex]a_{2}=m+8[/tex]
So, the common ratio is calculated as,
[tex]r=\frac{6}{m-1}=\frac{m+8}{6}[/tex]
Here, there are two expressions,
[tex]r=\frac{6}{m-1}[/tex] ------(1), and [tex]r= \frac{m+8}{6}[/tex] ------(2)
Simplifying (1), we get
[tex]r(m-1)=6[/tex] -----(3)
Simplifying (2), we get
[tex]6r=m+8\\\implies r= \frac{m}{6}+\frac{8}{6}[/tex] ------(4)
Now, substituting the values of (4) in (3), we get
[tex](\frac{m}{6}+\frac{8}{6})(m-1)=6\\\implies \frac{m^{2} }{6}-\frac{m}{6} +\frac{2m}{3}-\frac{2}{3} =6\\\implies m^{2}+3m-4=36\\[/tex]
Solving further, we get
[tex]\implies m^{2}+3m-40=0\\\implies m=5, m=-8[/tex]
So, when [tex]m=5, r=\frac{6}{5-1}=\frac{3}{2}[/tex]
Also, when [tex]m=-8, r=\frac{6}{-8-1}=-\frac{2}{3}[/tex]
Therefore, (a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
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Determine the equation of the polynomial, f(x), of minimum degree whose graph is shown above. Write your answer in factored form.
f(x)=____
Answer:
[tex]f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]
Step-by-step explanation:
The root -2 has a multiplicity of 2, and corresponds to a factor of [tex](x+2)^2[/tex].
The root 1 has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].
The root 3 has a multiplicity of 1, and corresponds to a factor of [tex](x-3)[/tex].
So, [tex]f(x)=a(x+2)^2(x-1)(x-3)[/tex].
Since [tex]f(0)=10[/tex],
[tex]10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]
Solve the system of linear equations by graphing.
X = -3
y = -8
Answer:
X = -3, y = -8
Please see the link to view the Graph:
Find the measure of all three interior angles and exterior angles
Check the picture below.
Answer:
Exterior angle: 86°
Base angle: 43°
Base angle: 43°
Third angle: 94°
Step-by-step explanation:
First we'll find x, then calculate all the angles.
There is a mark on two of the sides of the triangle. Two sides are the same. This is an isosceles triangle. So that means the base angles are the same also. One is marked 5x - 12, so the other base angle is also 5x - 12.
The marked exterior angle has a special relationship with the two remote interior angles.
If you add the two remote interior angles it equals the exterior angle.
8x-2 = 5x-12 + 5x-12
Combine like terms.
8x - 2 = 10x - 24
Subtract 8x.
-2 = 2x - 24
Add 24.
22 = 2x
Divide by 2.
11 = x
Now we can find all the angles.
The exterior angle is 8x - 2
= 8(11) - 2
= 88 - 2
= 86°
Base angle is 5x - 12
= 5(11) - 12
= 55 - 12
= 43°
The last angle in the triangle is a linear pair with the exterior angle. Or (Also,) the three angles in the triangle add up to 180°.
Angle+43°+43°=180°
Angle + 86 = 180
Angle = 94°
Find the prime factorization of
the number 68.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [×]
Enter the number that belongs in the green box.
The prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the prime factorization of the number 68
Prime factorization is a process of writing all numbers as a product of primes.
The prime factorization of 68 is 2×2×17
The prime factors of 68 are 2 and 17.
The least prime number is 2 and greatest prime number is 17.
Hence the prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.
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answer this attachment pls its upside down btw
The strategies that would eliminate a variable to help solve the system of equations are
B. Multiply the first equation by -2 and add it to the second equation
C. Multiply the first equation by 1/3 and add it to the second equation
D. Multiply the second equation by 3 and add it to the first equation
Determining strategies that would help solve system of equations by eliminationFrom the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.
The given system of equations is
12x + 5y = 7
-4x + 10y = -7
To eliminate y,
Multiply the first equation by -2 and add it to the second equation
-2 × [12x + 5y = 7]
-24x - 10y = -14
Now add to the second equation
-24x - 10y = -14
+ (-4x + 10y = -7
-----------------------------
-28x = -21
To eliminate x
Multiply the first equation by 1/3 and add it to the second equation
1/3 × [12x + 5y = 7
4x + 5/3y = 7/3
Now, add it to the second equation
4x + 5/3y = 7/3
+ (-4x + 10y = -7
------------------------------
5/3y + 10y = 7/3 + (-7)
Also, to eliminate x
Multiply the second equation by 3 and add it to the first equation
3 × [-4x + 10y = -7
-12x + 30y = -21
Now, add to the first equation
-12x + 30y = -21
+ (12x + 5y = 7
----------------------------
35y = -14
Hence, the required strategies are the ones explained above.
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Please write a linear equation that has m=-4 and has an x-intercept of (5,0)!
Answer:
If you use y = mx + b, your equation would be y = -4x + 20
Step-by-step explanation:
M is always the slope, and to find the x-intercept, you just set y = 0 and in this case it would be 0 = -4x + 20. If you subtract 20 from both sides you get -20 = -4x and to find x, you just divide by -4 and get -20/-4, which equals 5. You're welcome :)
We need to determine the value of the y-intercept for this equation. Let's start by finding all other information about the x-intercept.
If the x-intercept is x = 5, f(5) = 0. So, now let's solve for b.
f(5) = -4(5) + b
0 = -4(5) + b
0 = -20 + b
0 + 20 = -20 + 20 + b
b = 20
We have m and b now, so:
y = -4x + 20
Identify the variation as a direct, inverse, joint, or combined.
xy/z=c
The given equation is a combined variation.
We have been given an equation is
[tex]\frac{xy}{z}[/tex]
This is an equation in which we have three variables and one constant.
This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.
So, Direct and inverse options are discarded.
So, either It can be joint or combined
In joint variation both the variables are directly proportional
Hence, given equation is not joint because if we rewrite the equation we will get [tex]y = \frac{cz}{x}[/tex] both the variables are not directly proportional.
In combined, one variable is directly proportional and the other one is inversely proportional.
From [tex]y = \frac{cz}{x}[/tex] we can see that z is directly proportional and x is inversely proportional.
Hence the answer is, the given equation is combined variation.
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yvaries directly as x
and y=30 when x=5,find
a) K b) equation
need help po i need it right now po complete answer po
Rewrite each expression without using absolute value bars.
|3r-15| if r<5
Rewriting the expression |3r-15| without using absolute value bars gives
3r < 15 for r < 5
How to write the expression without using the absolute value barsAbsolute value do not give negative values it gives only the positive value
The given expression is |3r-15|
|3r - 15| < 0
|3r| < |-15|
3r < 15
If r < 5 then say 4
|3r - 15|
|3 * 4 - 15|
|12 - 15|
|-3| = 3
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Here is a function, double numbers (int x), what data type will this function return?.
The function will return the data type double.
Simply put, a function is a "chunk" of code that you can reuse repeatedly rather than having to write it out several times. Programmers can divide a problem into smaller, more manageable chunks, each of which can carry out a specific task, using functions.
Function declaration type will be as follows in general,
return type function name(argument 1, argument 2,...)
In the given question the declaration is double numbers (int x).
The return type is double, the name of the function is numbers and it has one argument which in an integer.
Hence, the return type of the function is double.
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Find the slope and the y-intercept of the line.
y=4x-7
Answer:
slope: 4
Y intercept: -7
Step-by-step explanation:
slope intercept form is y=Mx+b
m- slope
b- y intercept
Looking at this equation where m is 4 is so the slope is 4
And where b is -7 is so the y intercept is -7
Hopes this helps please mark brainliest
The price of a car
including VAT at 20%
is £14400.
Work out the original
price before VAT:
Let's call the price before the VAT "x".
Then x plus that 20% VAT totals 14400.
The VAT is calculated as 20% of the original price, so 20% of x or 0.20x.
This gives us x + 0.20x = 14400.
Simplifying, we get 1.2x = 14400.
Dividing by 1.2 on both sides, we get x = 14400/1.2 = 12000.
Answer:
£18000
Step-by-step explanation:
[tex]x[/tex] x 80/100=14400
80x=1440000
x=1440000/80
x=£18000
The perimeter of a rectangle is 68 cm. If the diagonal 26
is 26 cm, find the dimensions of the rectangle.
The dimensions of the rectangle are either 10cm x 24cm or
24cm x 10cm having perimeter 68 cm.
What is Pythagorean theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
A rectangle has 4 angles measure of each is 90°.
A diagonal of rectangle divides it into two right angled triangles.
Pythagorean theorem can be applied on these triangles to get the desired values.
According to the given question:
Let the length and breadth of rectangle be x and y .
Perimeter: 2x + 2y = 68 (Given)
Using Pythagorean theorem diagonal: [tex]x^2+y^2=26^2[/tex]
Using perimeter, x + y = 34
∴ x = 34 - y
Substituting this is the equation for diagonal
[tex](34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0[/tex]
Therefore dimensions of rectangle are either 10cm x 24cm or
24cm x 10cm.
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how to solve this and answer
After simplifying the equation, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.
From the given question,
Let that chemist used x, y, z liters of 20%, 35% and 80% solution respectively.
Then according to the given information,
x+y+z=54..........(1)
As we know that in x liters having 20% acid, in y liters having 35% acid, in z liters having 80% acid and in total mixture having 50% acid.
So the equation should be
x ×20%+y×35%+z×80%=54×50%
On simplifying we get
20x+35y+80z=2700
4x+7y+16z=540...............(2)
As given that the number of 80% solution used in 2 times the number of liters of 35% solution used.
So z=2y
Now putting the value of z in equation (1)
x+y+2y=54
x+3y=54
Subtract 3y on both side
x+3y−3y=54−3y
x=54−3y
Now putting the value of x and z in equation (2)
4(54−3y)+7y+16×2y=540
Simplifying
216−12y+7y+32y=540
216+27y=540
Subtract 216 on both side
216+27y−216=540−216
27y=324
Divide by 27 on both side
27/27 y=324/27
y=12
Now putting the value of y in x=54−3y to find the value of x
x=54−3×12
x=54−36
x=18
Now putting the value of y in z=2y to find the value of z
z=2×12
z=24
Hence, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.
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an article summarizes a report of law enforcement agencies regarding the use of social media to screen applicants for employment. the report was based on a survey of 731 law enforcement agencies. one question on the survey asked if the agency routinely reviewed applicants' social media activity during background checks. for purposes of this exercise, suppose that the 731 agencies were selected at random, and that you want to use the survey data to decide if there is convincing evidence that more than 25% of law enforcement agencies review applicants' social media activity as part of routine background checks.
a) The sampling proportion's mean value is 0.25. 0.016 is the standard deviation. The form resembles a bell.
b) There is a 10% possibility of getting this number, p=0.27 or more, given a sample proportion, so I wouldn't be surprised.
c) Since there is no chance that the sample fraction of 0.31 will occur, I would be shocked if it did.
Given,
a) The null hypothesis proportion would be the middle of the sampling distribution (p-0.25). So, p=0.25 is the sampling proportion's mean value.
This would be the standard deviation:
σp = √(p (1 - p) / n) = √(0.25 × 0.75/731) = 0.016
The distribution would resemble a binomial distribution, hence the form would be bell-shaped.
b) By calculating the z-value and checking for its probability in the standard normal distribution, we may determine the likelihood of a value p=0.27 in this distribution.
z = (p - π) / σp = (0.27 - 0.25) / 0.016 = 0.02/0.016 = 1.25
p(z > 1.25) = 0.106
There is a 10% probability of achieving this value, p=0.27 or more, for a sample proportion, so I wouldn't be surprised.
c) We repeat the calculation for p=0.31
z = (p - π) / σp = (0.31 - 0.25) / 0.016 = 0.06/0.016 = 5
p(z > 5) = 0.000
I would be astonished to see that value because the probability of this sample fraction occurring at p=0.31 is zero.
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given a vector/array with values 5, 10, 15, 20, 25, what are the fewest number of swaps needed to reverse the list? group of answer choices 2 3 4 5
The minimum number of swaps required to flip the list is 2.
Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.
Given an array with values 5, 10, 15, 20,25
swap reverses the array:
25, 10, 15, 20, 5
25, 20, 15, 10, 5
So, for reversing the number of swaps required list is 2 ..
This may be the smallest variation possible.
Hence, the minimum exchange required to achieve list reversal is two.
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Can anyone help me :( how you calculate the area of an L shaped room
The area of an L-shaped room is calculated by cutting off the Leg of the L and finding the area of the rectangles separately.
Area of the floor space occupied by an objected which is measured in unit squares.
A rectangle is an object which is bounded by four sides, four vertices
The area (A) of a rectangle is;
A=Length x Width
The Area of the L-shaped room is calculated by
A = Area of the Vertical rectangle + Area of the Leg
A = LW + lw
where
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2. Carmen, Memo, Poncho y Jocelyn están en
una carrera de bicicletas. Carmen lleva 3/5
del trayecto, Memo 4/7, Poncho 3/4 y
Jocelyn 1/2, ¿quién lleva más recorrido?
Poncho ha recorrido más trayecto de la carrera de bicicletas, con una fracción de 3/4 del recorrido.
Problema de comparación de fracciones:
Carmen lleva: 3/5 del trayecto
Memo: 4/7
Poncho: 3/4
Jocelyn: 1/2
Una forma de comparar las fracciones es usando un mismo denominador, esto es posible con el Mínimo Común Múltiplo (MCM):
MCM(2,4,5,7) = 2² · 5 · 7 = 140
Fracciones con mismo denominador:
3/5 = (3 · 7 · 4)/(5 · 7 · 4) = 84/140
4/7 = (4 · 5 · 4)/(7 · 5 · 4) = 80/140
3/4 = (3 · 5 · 7)/(4 · 5 · 7) = 105/140
1/2 = (1 · 2 · 5 · 7)/(2 · 2 · 5 · 7) = 70/140
Comparando:
70/140 < 80/140 < 84/140 < 105/140
1/2 < 4/7 < 3/5 < 3/4
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A new pair of Jordans are going to drop in a couple weeks and you know you just have to have them. It looks like the/il
be expensive, so you decide to start babysitting your cousin to make the money. You already have $42 saved up and
you will make $6 for every hour of babysitting. The shoes will cost at least $90.
a) What’s the initial cost
Answer:
incomplete question..please complete the question to get the answer. there are some missing details
A spherical balloon has a 8-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon.
c. What is the radius of the half-inflated balloon?
The volume of the fully inflated balloon is 267.95 cubic inches, the volume of half-inflated balloon is 133.97 cubic inches and it's radius is 3.17in
Volume of a SphereThe volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
The formula of a sphere is given as
v = 4/3πr³
But diameter = 2 * radius
radius = diameter / 2
radius = 8/2
radius = 4in
The volume of the fully inflated balloon will be
v = 4/3πr³
v = 4/3 * 3.14 * 4³
v = 267.95in³
The volume of the fully inflated balloon is 267.95in³
b) The volume of the half-inflated balloon will half the size of the current volume
v = 267.95in³ / 2 = 133.97in³
c) v = 4/3πr³
133.97 = 4/3 * 3.14 * r³
r = 3.17in
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PLEASE HELP!!!
for points
Complete each row of the table.
The Hiking club will be 0.6.
The completion for the row of the table will be:
Grade 7
Dance club: 0.25
Hiking club: 0.75
Total : 1
Grade 8:
Dance club: 0.40
Hiking club: 0.60
Total : 1
How to calculate the values?
The dance club for grade 7 will be calculated as:
= Number of dancers / Total number
= 5/20
= 0.25
The hiking club will be:
= 15/20
= 0.75
The dance club for grade 8 will be calculated as:
= Number of dancers / Total number
= 20/50
= 0.4
The hiking club will be:
= 30/50
= 0.6
Hence, The Hiking club will be 0.6.
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Fully factorise this expression
Answer:
3k(7k + 4)
Step-by-step explanation:
1. Find the GCF of all terms in the polynomial
2. Express each term as a product of the GCF and another factor.
3. Use distributive property to factor out GCF
If h(x) = 3x² – 5x – 2, find h(2)
Answer:
h(2) = 0
Step-by-step explanation:
1) 2 * 2 = 4
2) 4 * 3 = 12
3) 5 * 2 = 10
4) 12 - 10 - 2 = 0
Exercise 4Consider the piecewise linear function
(-(x + 2)
2
4x-10
f(x)=
-4≤x≤2
2
(a) Complete the table and graph the function
f(x)
x
(b) State the function's domain and range.
Domain:
Range:
Exercise 4 I need this asap
a) The graph of f(x) is as shown below.
b)
The domain of f(x) is: [-4, 4]
The range of function f(x) is [-2, 6]
In this question we have been given a piecewise function [tex]f(x)=\left \{ {{\frac{-(x+2)}{2} ~~~-4\leq x\leq 2} \atop {4x-10}~~~~2 < x\leq 4} \right.[/tex]
We need to graph the given function.
The table of (x, f(x)) values is as shown below.
x f(x)
-2 0
-4 1
0 -1
2 -2
2.5 0
3.5 4
4 6
The graph of f(x) is as shown below.
The domain of f(x) is: [-4, 4]
The range of function f(x) is [-2, 6]
Therefore, for given piecewise function,
a) The graph of f(x) is as shown below.
b)
The domain of f(x) is: [-4, 4]
The range of function f(x) is [-2, 6]
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Quick! Evaluate (-2 2/5)^2 !
Answer:5.76
Step-by-step explanation:
-2 2/5=-2.4
(-2.4)^2=5.76
PLEASE SOMEONE HELP I DONT GET THIS!!!!!
Check the picture below.
if the segment AD is an angle bisector, that means it makes two twin angles, and let's also keep in mind that the side AG is shared by both triangles, so is not shorter or longer for either, is the same for both, which means Andrea rules!!!
Convert the following equations from standard form to slope intercept form. -2x+3y=-6
Converting the given equations from standard form to slope intercept form gives
standard form -2x + 3y = -6 slope intercept y = 2x/3 - 2How to Convert the equations from standard form to slope interceptInformation given in the question include
-2x+3y=-6
Standard form of linear equations is of the form Ax + By = C
The slope intercept form is y = mx + c
rearranging the equation
-2x + 3y = -6
3y = 2x - 6
y = 2x/3 - 2
The equation of the line in slope intercept form is y = 2x/3 - 2
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help please and thankyou6
In triangle ABC, the value of angle A is 60°.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the triangle ABC,
b=5cm, c=10cm
And by using Pythagoreans theorem,
a²=c²-b²
a²=10²-5²
a²=75
Use cosine rule to determine the angle A,
cosA=b²+c²-a²/2bc
cosA=25+100-75/2×5×10
cosA=50/100
cosA=1/2
cosA=cos60
⇒A=60°
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