The distance from first base to dead center field in a certain baseball stadium is 338 feet.
Explanation:
The distance from first base to dead center field in a certain baseball stadium is 338 feet. Given,The distance from home plate to dead center field in a certain baseball stadium is 407 feet.A baseball diamond is a square with a distance from home plate to first base of 90 feet.
To find,How far is it from first base to dead center field?
Solution:Given that the distance from home plate to dead center field is 407 feet.The baseball diamond is a square with a distance from home plate to first base of 90 feet.Now we have to find the distance from first base to dead center field.We can find the distance by using the Pythagorean theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.Let us consider a right triangle ABC where AB represents the distance from home plate to first base, AC represents the distance from home plate to dead center field, and BC represents the distance from first base to dead center field.
As per the Pythagorean theorem, we have
AC² = AB² + BC²
Putting the values, we have
AC² = (90)² + BC²AC² = 8100 + BC²AC² - BC² = 8100
Taking the square root on both sides, we getAC = √(8100 + BC²)
Now we have AC = 407 ft,AB = 90 ftAC² = AB² + BC²407² = 90² + BC²BC² = 407² - 90²BC² = 165649BC = √165649BC = 407 ft - 90 ft
BC = 338 ft
Therefore, the distance from first base to dead center field in a certain baseball stadium is 338 feet.
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-9>2x what best describes the soltuion to this inequality
The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.
In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.
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Full question:
Which word BEST describes 9(2x+6y)
A Constant
B. Equation
c. Expression
D. Inequality
Work out the area of the rectangle using a calculator and giving your anwser in as a mixed number
The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.
To find the area of the rectangle, we need to multiply its length by its width.
First, we need to convert the mixed numbers to improper fractions:
Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm
Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm
Now, we can multiply the two fractions to get the area of the rectangle:
Area = length × width
= (31/6 cm) × (16/7 cm)
= (31 × 16) / (6 × 7) cm²
= 496/42 cm²
= 248/21 cm²
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:
248/21 cm² = (8 × 31)/ (8 × 3) cm²
= 31/3 cm²
= 10 1/3 cm²
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A box is subject to the forces shown in the diagram below.
5N Up
7.5N Left
7.5N Right
10N Down
Calculate the size and direction of the resultant force on the box.
Show your working.
Resultant force =?
The resultant force on the box, along with it's direction, is given as follows:
5N Down.
How to obtain the resultant force on the box?The resultant force on the box is obtained as the vector sum of all the forces in the box.
The forces are given as follows:
5N Up7.5N Left7.5N Right10N DownThe horizontal forces are the same force in opposite directions, hence the horizontal forces are of zero.
The sum of the vertical forces is given as follows:
5 - 10 = -5N.
As the sum is negative, the direction is in the down direction, hence the resultant force is of -5N down.
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If you start as 2,10 and move 2 units to the left. Where will you end
A coin bank in the shape of a triangular pyramid has a volume of 65 cubic inches. The bank has a height of 9.75 inches. What is the area of the base?
In response to the query, we can state that Therefore, the area of the base of the triangular pyramid is 21 square inches.
what is pyramid?A pyramid is a polygon in mathematics, formed by connecting points referred to as bases and polygonal vertices. For each hace and vertex, a triangle called a face is formed. a cone with a polygonal form. A pyramid with a floor and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The vertex, the intersection of a pyramid's flat tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that connect to the top are formed by the edges of the base.
volume of a triangular pyramid
V = (1/3) * Base Area * Height
65 = (1/3) * Base Area * 9.75
Area = 65 / (1/3) / 9.75
Area = 21
Therefore, the area of the base of the triangular pyramid is 21 square inches.
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A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 5 cm. The spring is then stretched an additional 3 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g = 980 cm/s^2.
Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium position (with the spring stretched 5 cm).
The differential equation with initial conditions describing the motion is F = -k * (s(t) + 5) - 6g and the displacement of the mass from its equilibrium position as a function of time s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
The differential equation for the motion of the mass is given by Newton's Second Law, F = ma:
F = -k * (s(t) + 5) - 6g
where k is the spring constant, s(t) is the displacement from the equilibrium position, and g is the acceleration due to gravity. The initial conditions are s(0) = 3 and s'(0) = 0, since the spring is initially stretched an additional 3 cm and released from rest.
We can rearrange the equation to get:
s''(t) + (k/6) * s(t) = -5k/6 - g
This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:
s(t) = C1 * e^(r1*t) + C2 * e^(r2*t)
where r1 and r2 are the roots of the characteristic equation:
r^2 + (k/6) * r = -5k/6 - g
Using the quadratic formula, we get:
r1,2 = -(k/12) ± √((k/12)^2 + 5k/6 + g)
We can find the values of C1 and C2 by applying the initial conditions:
s(0) = C1 + C2 = 3
s'(0) = C1 * r1 + C2 * r2 = 0
Solving for C1 and C2, we get:
C1 = (3 * r2) / (r2 - r1)
C2 = (3 * r1) / (r1 - r2)
Substituting back into the general solution, we get:
s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
This is the displacement of the mass from its equilibrium position as a function of time.
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please help me i don't understand my homework
Answer:
The final answer is 18-2 = which is 16
Step-by-step explanation:
x =3
y =2
6(3) -2
Then do 18-2
You have to multiply 6 and 3, after that, subtract by 2
Just substitute your value in!
Answer:
16
Step-by-step explanation:
replace x with 3 and y with 2
6x - y =
6 * 3 - 2 =
18 - 2 =
16
Fill in the blanks to make the equations true. (x ....)(x ....)=x^2-4x-32
The first number in a pattern is 1.95.
Each number in the pattern is formed by subtracting 0.15 from the previous number.
What is the third number in this pattern?
1.5 1.65 1.8 2.25
Answer:
1.65
Step-by-step explanation:
The first number is 1.95, to find the rest we must keep subtracting 0.15 from the previous.
1.95-0.15 = 1.8 (second number)
1.8-0.15 = 1.65 (third number)
Above, we find our answer with the 3rd number.
Gauss Jordan elimination method step by step 0. 99x-0. 04y-0. 2z=4
-0. 1x+0. 97y=6
-0. 2x-0. 01y+0. 96z=3
[ 1 -0.0004 -0.00202 | 0.0404 ] [ 0 1 -0.00020828 | 6] this is the Gauss Jordan elimination method step by step of the given linear equation.
The Gauss Jordan elimination method is a systematic way of solving a system of linear equations by performing elementary row operations on an augmented matrix. The augmented matrix is formed by combining the coefficients and constants of the linear equations.
The given system of linear equations can be written in matrix form as:
[ 99 -0.04 -0.2 | 4 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
The goal of the Gauss Jordan elimination method is to transform the augmented matrix into reduced row echelon form, which is a unique form that represents the solution of the system of linear equations.
The following steps outline the Gauss Jordan elimination method to solve the given system of linear equations:
Step 1: Begin with the first column and eliminate the coefficients below the first row by using row operations.
Divide the first row by 99 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.1 times the first row to the second row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.2 times the first row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ 0 -0.00018 0.960396 | 3.00808]
Step 2: Continue with the second column and eliminate the coefficients below the second row by using row operations.
Divide the second row by 0.9704 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 -0.00018 0.960396 | 3.00808]
Add 0.00018 times the second row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 0.0000324 0.96052174| 3.01998]
Step 3: Continue with the third column and eliminate the coefficients above the third row by using row operations.
Divide the third row by 0.96052174 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6]
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6x 10y=-40
Answer:
[tex]\mbox{\large y = -\dfrac{3}{5}x - 4}[/tex]
Step-by-step explanation:
The given equation is
[tex]\mbox{\large 6x + 10y = - 40}[/tex]
The slope-intercept form of the equation of a line is
[tex]y = mx +b[/tex]
where
m = slope
b = y-intercept
Subtract 4x from both sides of [tex]\mbox{\large 6x + 10y = - 40}[/tex]
[tex]6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4[/tex]
2. Which expression below can be simplified to 2x + 11?
A. x + x + 11
B. x + 2 + 11
C. x + 7 + 4
A. x+x+11 is the expression can be best simplified for equation 2x+11
Explain equationA statement that establishes the equivalence of two expressions is known as an equation in mathematics. It has two sides containing expressions on each, each separated by the equals symbol (=).
For example, the equation x + 2 = 5 asserts that the expression on the left side, x + 2, is equal to the expression on the right side, 5. This equation can be solved for the variable x, by subtracting 2 from both sides, to obtain x = 3, which is the value that satisfies the equation.
Given equation 2x+11
2x can be written as x+ x
So, expression can be written as
x+x+11
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The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute.
Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Answer:
Step-by-step explanation:
The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.
By first making the powers of 10 the same,
work out (3 x 10 6) + (5 × 10 7)
Give your answer in standard index form.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(3\times10^6) + (5\times10^7)}\\\mathsf{= (3\times10\times10\times10\times 10\times10\times10) + (5\times 10\times10\times10 \times 10\times10\times10 \times 10)}\\\mathsf{= (3\times 100\times100\times100) + (5\times100\times100\times100\times10)}\\\mathsf{= (3\times10,000\times100) + (5\times10,000\times1,000)}\\\mathsf{= (3\times1,000,000) + (5\times10,000,000)}\\\mathsf{= (3,000,00) + (50,000,000)}\\\mathsf{= 3,000,000 + 50,000,000}\\\mathsf{= 53,000,000}\\\mathsf{= 5.3\times10^7}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{5.3\times10^7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
3. repeated-measures and matched-subjects experiments repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? check all that apply. they both use the same t statistic. the researcher computes difference scores to compute a t statistic. the researcher must compute an estimated standard error for the mean difference score to compute a t statistic. the researcher must compute a pooled variance to compute a t statistic. for a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. how many subjects participated in this study? 64 32 62 31 a matched-subjects experiment produced a t statistic with a df of 17. how many subjects participated in this study? 34 36 18 17
A repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. 32 subjects participated in this study.
A matched-subjects experiment produced a t statistic with a df of 17.
34 subjects participated in this study.
Both a repeated-measures experiment and a matched-subjects experiment share the following characteristics when used to compare two treatment conditions:
1. They both use the same t statistic.
2. The researcher computes difference scores to compute a t statistic.
3. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31.
The number of subjects that participated in this study is 32 because the degrees of freedom (df) for a repeated measures experiment is calculated as (number of subjects - 1),
so 31 + 1 = 32.
A matched-subjects experiment produced a t statistic with a df of 17.
In this case,
the number of subjects that participated in the study is 34 because the degrees of freedom (df) for a matched-subjects experiment is calculated as (number of pairs - 1),
since there are two subjects in each pair, 17 + 1 = 18 pairs, which means 18 * 2 = 34 subjects.
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A popcorn container is in the shape of a square pyramid the container meausers 9 inches high and each side measures 6 inches how many cubic inches does the popcorn container hold?
NEED HELP SO LOST AND CONFUSED PLS HELPP IM NOT A VERY SMART PERSON SO HELPPPP IM LOSIN ME MIND
The popcorn container can hold 432 cubic inches of popcorn.First, we need to find the volume of the popcorn container. The formula for the volume of a square pyramid is:
Volume = (1/3) * base area * height
To find the base area, we need to first find the area of one of the square sides. Since each side measures 6 inches, the area of one square side is:
Area = side length^2 = 6^2 = 36 square inches
Since the popcorn container is a square pyramid, it has four identical square sides, so the total base area is:
Base area = 4 * 36 square inches = 144 square inches
Now we can plug in the values for the base area and height into the formula for volume:
Volume = (1/3) * 144 square inches * 9 inches
Volume = 432 cubic inches
So the popcorn container can hold 432 cubic inches of popcorn.
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a cable company earned 125 million in one year. the next year they earned 312.5 million dollars. estimate how many times bigger their profit was the second year compared to the first year.
Answer: The difference between 125 million dollars and 312.5 million dollars is, 187.5 Million Dollars.
3. The ends of a thermometer on an aquarium are 3
4
inch above the water and 31
2 inches below
the water. What is the length of the thermometer
The length οf the thermοmeter is 16 1/4 inches.
What is thermοmeter ?Any instrument that measures temperature οr a thermal diffusivity is called a thermοmeter (the degree οf hοtness οr cοldness οf an οbject). Twο crucial cοmpοnents make up a thermοmeter:
(1) a temperature sensοr that changes in respοnse tο changes in temperature (fοr example, the mercury-in-glass thermοmeter's bulb οr an infrared thermοmeter's pyrοmetric sensοr);
(2) a way tο translate this change intο a specific number (e.g. the visible scale that is marked οn a mercury-in-glass thermοmeter οr the digital readοut οn an infrared mοdel). In technοlοgy, business, meteοrοlοgy, medicine, and scientific research, thermοmeters are frequently used tο track prοcesses.
Tο find the length οf the thermοmeter, we need tο add the distance abοve the water tο the distance belοw the water.
Distance abοve water: 3/4 inch
Distance belοw water: 31/2 inches
The tοtal length οf the thermοmeter:
3/4 + 31/2 = 6/8 + 124/8 = 130/8 = 16 1/4 inches
Therefοre, the length οf the thermοmeter is 16 1/4 inches.
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What is the value of x?
The value of x in the triangle is 2√3
What are right trianglesRight triangles are triangles with one angle measuring 90 degrees.
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
From the triangle, we have the following equation
x/2 = 6/x
Cross multiiply the equation
So, we have the following representation
x^2 = 12
Take the square roots of both sides
So, the equation becomes
x = 2√3
Hence, the value of x is 2√3
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lines AB and CD are perpendicular to each other. If 3 measures (4x + 3)°, and 4 measures 43°, what is the value of x?
Step-by-step explanation:
4x+3+43=180
46+4x=180
4x=180-46
4x/4=134/4
X=33,5
If two sides of a right triangle are 20 and 25 and the sides form a Pythagorean triple, find the third side.
The third side of the given Pythagorean triple-right-angled triangle is 32.02 units.
As per the formula pertaining to the Pythagorean triple-right-angled triangle, we have the:
h = √{(a)^2+(b)^2} .........(i),
Where, (h) = Third side of a Pythagorean triple-right-angled triangle,
(a) = First side of a Pythagorean triple-right-angled triangle = 20 units
(b) = Second side of a Pythagorean triple-right-angled triangle = 25 units
Substituting the values in equation (i), we get:
h = √{(20)^2+(25)^2} units,
or, h = √(1025) units,
or, h = 32.015 units = rounded off to 32.02 units.
Hence the third side of the given Pythagorean triple-right-angled triangle is 32.02 units.
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Martin is x years old. Jennifer is 3 years younger than Martin. Connor is twice as old as Martin. Write an expression for Jennifer’s age.
Answer: x-3
Step-by-step explanation: if Martin's age is unknown and we have to use x for it, you could only plug in x-3 to figure out Jennifer's age. And if we have to write an expression for Connor's age it would be x*2
martin = x years
jennifer = x - 3
A cylinder has a height of 11 millimeters and a radius of 15 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of this cylinder is equal to 7,771.5 cubic millimeter
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Since the radius of the base is 15 mm and the height of this cylinder is 11 mm, the volume of the cylinder in cubic millimeter can be calculated as follows;
Volume of a cylinder, V = 3.14 × 15² × 11
Volume of a cylinder, V = 3.14 × 2,475
Volume of a cylinder, V = 7,771.5 cubic millimeters.
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Find the area of the entire figure.
the area of the figure will be 15cm²
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
We are given that rajiv wishes to make a cube without lid with cardboard.
the area will be = area of square+area of rhombus
area of square = 3² = 9 cm²
area of rhombus = 2cm * 3cm =6cm²
The total area will be 15cm²
Hence the area of the figure will be 15cm²
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Answer:
watch sean delete this LOL IMAGINE HAVING TO DO THAT BC YOU SUK
the area of the figure will be 15cm²
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
We are given that rajiv wishes to make a cube without lid with cardboard.
the area will be = area of square+area of rhombus
area of square = 3² = 9 cm²
area of rhombus = 2cm * 3cm =6cm²
The total area will be 15cm²
Hence the area of the figure will be 15cm²
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Step-by-step explanation:
100 points please help
Answer:
I really want to help you!
Factored completely:
2x2(−x−2)(x−7)
Step-by-step explanation:
can I get help with this question?
The coordinate of points of the image are:
A' = (-1, 1), B' = (1, 1) and C' = (1, -1)
How to dilate the preimage about the origin?To dilate the preimage about the origin using a scale factor of 1/3, we can use the following formula:
image coordinate = scale factor * preimage coordinate
Substituting the values, we get:
A' = 1/3 * (-3, 3)
A' = (-1, 1)
B' = 1/3 * (3, 3)
B' = (1, 1)
C' = 1/3 * (3, -3)
C' = (1, -1)
Thus, the coordinate of points of the image are A' = (-1, 1), B' = (1, 1) and C' = (1, -1)
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The attorney does not accept legal cases involving litigation that would result in less than a $45,000 fee. The attorney has the opportunity to represent a client who will pay him $175 per hour plus 25% of the settlement. What is the minimum acceptable settlement on a case on which the attorney spent 110 hours?
In linear equation, 103000 is the minimum acceptable settlement on a case on which the attorney spent 110 hours.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let x be the amount settlement.
amount he earn from client = 175 * 110
= 19250
amount he earn from settlement = x * 25/100 = x/4
according to given condition
19250 + x/4 ≥ 45000
x/4 ≥ 45000 - 19250
x/4 ≥ 25750
x ≥ 25750 * 4
x ≥ 103000
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susan is making a blanket. she bought 1/3 pf a yard of material to use for the border for the blanket.susant cut the material into 4 same-size strips. what part of a whole yard is each strip
The fraction of the material that each strip represents is 1/12 of a yard.
Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.
Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.
Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 4 is 1/4, so we can rewrite the expression as:
1/3 ÷ 4 = 1/3 × 1/4
Now we can multiply the fractions:
1/3 × 1/4 = 1/12
Therefore, each strip represents 1/12 of the whole yard of material.
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Simplify the expression \( \sqrt{y^{2}-81} \) as much as possible after substituting \( 9 \sec x \) for \( y \).
The expression√{y²-81} can be simplifies to trigonometry as 9|tanx|.
If an algebraic expression has no like terms and no parenthesis, it is said to be in its simplest form. Use the Distributive Property to add or subtract the coefficients to combine like terms with variables. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
We start by substituting 9 sec x for y:
√{y²-81} = √{(9 sec x)²-81}
= √{81(sec²x) - 81}
= √{81(sec²x-1)}
= 9√{sec²x-1}
Using the trigonometric identity sec²x - 1 = tan²x, we can simplify further:
9√{sec²x-1} = 9√{tan²x}
= 9|tanx|
Therefore, the simplified expression is 9|tanx|.
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I think of a number, treble it and take 6 from my answer. If the result is 18, find the number. My teacher says its 4 I say its eight whats the answer?
Answer: Let's work through the problem step by step:
"Treble it": If we call the unknown number "x", then "trebling" it means multiplying it by 3, so we have 3x.
"Take 6 from my answer": We subtract 6 from 3x, giving us 3x - 6.
"If the result is 18": We set 3x - 6 equal to 18 and solve for x.
So, we have:
3x - 6 = 18
Adding 6 to both sides:
3x = 24
Dividing both sides by 3:
x = 8
Therefore, the answer is 8.
Step-by-step explanation: