On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y = 7x - 17
at x= 0
y = -17
and m = -17
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find the area of the region enclosed by one loop of the curve. r = sin(6θ)
Area of the region enclosed by one loop of the curve is pi/288.
To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:
A = 1/2 * ∫(r^2)dθ
We can use this formula with the equation for r given:
A = 1/2 * ∫(sin^2(6θ))dθ
This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))
Thus,
A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ
This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).
Therefore, the area enclosed by one loop of the curve is
A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6
A = (1/48)(sin(2pi) + pi/6)
= (1/48)(0 + pi/6)
= pi/288
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2. The value of a machine depreciates by 5% every year. It is given that the initial value of the machine is RM100 000.
(a) Express its value, in RM, after n years.
(b) Hence, find its value after 10 years to the nearest ringgit.
Answer:
Step-by-step explanation:
Depreciation means wearing and tearing in the value of an asset over the years
(a) Given:
p = initial value of an asset
i% = depreciation per year
n = number of years
Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]
Value of machine after n years = p-d
(b) Given:
p = RM100000
i% = 5
n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]
Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608
Value of machine after 10 years to nearest ringgit = RM40123
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume=46.41+0.45(Advertising Expenditures) If the company has a target sales volume of $200,000 how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
The sales manager should allocate approximately 341311.111 for advertising in the budget.
What is advertising expenditure?Generally, Advertising expenditure refers to the amount of money that a company or organization spends on promoting their products or services through various forms of advertising media, such as television, radio, print, and online.
This can include costs for creating and producing advertisements, as well as fees for placing them on different platforms. Advertising expenditure can also be referred to as "advertising budget" or "advertising spend."
To find the advertising expenditure needed to reach a target sales volume of $200,000, we can use the equation provided: Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
We can set the target sales volume as the left-hand side of the equation and solve for the advertising expenditure:
200,000 = 46.41 + 0.45(Advertising Expenditures)
Subtracting 46.41 from both sides:
153,590 = 0.45(Advertising Expenditures)
To find the Advertising Expenditures, divide 153,590 by 0.45:
Advertising Expenditures = 341311.111
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Matt wants to contrast girls and boys views about leadership. He selects a random sample of 100 students from Northeastern High School in Maine and administers a standardized leadership survey. Scores range from 5 to 20. Matt's research design could best be classified as a(n):
On solving the provided question, we can say that random samples range from 5 to 20. Matt's research design could best be classified as a(n): students at Northeastern High School
what is random sample?selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.
Scores range from 5 to 20. Matt's research design could best be classified as a(n): students at Northeastern High School
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3 times one number minus a second is 8 and the sum of the numbers is 12
Answer: 3x-y=8
Step-by-step explanation:
Jose has $34 to spend at the Texas State Fair. If the entrance ticket costs $12, then how much money does jose have to spend on food and games?
ONE-STEP EQUATIONS APPLICATION II 6TH MATH
WITH EQUATION!
Answer:
22
Step-by-step explanation:
34-12=22 you just basically subtract 34 and 12 and it gives you 22 but theres the equation too
URGENT!! 50 POINTS!!! based on the linear table of ordered pairs, what is the y intercept?
Answer:
y- intercept = 0
Step-by-step explanation:
the linear function can be expressed in slope- intercept form, that is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁ , y₁ ) = (4, - 4) and (x₂, y₂ ) = (- 2, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-(-4)}{-2-4}[/tex] = [tex]\frac{2+4}{-6}[/tex] = [tex]\frac{6}{-6}[/tex] = - 1
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - x + 0, that is
y = - x ← is the linear function defining the ordered pairs in the table
In an isosceles triangle ABC with AC = BC, point M is on the side BC , and point N is on the segment MC. It is known that MN=AM, and m∠BAM=m∠NAC. Find m∠MAC
The measure of angle MAC is 90°.
What is means of isosceles triangle?
An isosceles triangle is a type of triangle where two of its sides are congruent, or have the same length. This means that if you draw a line down the center of an isosceles triangle, it will split the triangle in half and both halves will have the same side lengths.
In an isosceles triangle, the angles opposite the congruent sides are congruent. Therefore, in triangle ABC, m∠BAM = m∠CAB = m∠NAC.
Since angle BAM and angle NAC are congruent, and they are both supplementary to angle MAC, it follows that angle MAC is congruent to itself.
Therefore, m∠MAC = m∠MAC = 180 - m∠BAM = 180 - m∠NAC.
Since m∠BAM = m∠NAC, we can conclude that
m∠MAC = 180 - m∠NAC = 90°
Hence, the measure of angle MAC is 90°.
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(PLS HELP) (I NEED IT NOW OR I'LL TURN IT IN LATE!!)
Stephan is planning a hiking trip at Kings Canyon National Park. He plans to hike 14 miles every 2 days. If he hikes 42 miles, how many days will he hike?
Answer:
he will hike approximately 6 days
What would the approximate amperage setting be if a welder were set to the high range (150 to 350 amps) and the fine adjustment knob were painting at 5 on a 10 point scale
On solving the provided question, we can say that the approximate amperage setting be if a welder were set to the high range would be 350 amps.
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.
here,
the approximate amperage setting be if a welder were set to the high range would be 350 amps
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Evaluate 5c+cd5c+cd5, c, plus, c, d when c=\dfrac15c=
5
1
c, equals, start fraction, 1, divided by, 5, end fraction and d=15d=15
Answer:
the value is 4
Step-by-step explanation:
It takes 3 hours to drive 180 miles. How long will it take to drive 330 miles?
Answer:
5.5
Step-by-step explanation:
180/3 =60 (60/1 hr)
330/60 =5.5
Can a polynomial have no zero?
A quadratic polynomial does not cross the x axis at any point since it has no zeros.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
x^2 - 2x + 5 when compared with the standard form of the quadratic equation, a = 1, b=- 2, c=5
Value of the discriminant =b^2 - 4 ac
= (-2)2 - 4(1) (5)= 4 - 20
= - 15
The value of the discriminant is negative i.e less than zero.
Hence, the quadratic equation x^2 - 2x + 5 has no real zeroes.
Since a quadratic polynomial may only have two real roots, the number of times the graph will cross the x-axis at most is two, and at least zero when there are no roots in the equation.
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Solve for 2 |v+2|-41=-9
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution"
Answer:
[tex]v=-18,14[/tex]
Step-by-step explanation:
[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]
This year’s favorite to win the frog jumping event is Newton. The objective is to take the longest jumps and stop as close as possible to 120 steps. Pythagoras and Fermat are Newton’s toughest competition. ● Newton takes 4 jumps and falls short of the mark by 4 steps. ● Pythagoras takes 5 jumps and overshoots the mark by 5 steps. ● Fermat hits the mark exactly after 6 jumps. How long, in steps, is each frog’s jump?
The length of jump by Pythagoras = 25 units
The length of jump by Newton = 29 units
The length of jump by Fermat = 20 units
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the length of the jump by Pythagoras be P
Let the length of the jump by Newton be N
Let the length of the jump by Fermat be F
Now , the equation will be
The total number of steps = 120 steps
The number of jumps by Pythagoras = 5 jumps
The number of steps overshoot by Pythagoras = 5 steps
So , P ( 5 ) - 5 = 120 be equation (1)
On simplifying the equation , we get
Adding 5 on both sides of the equation , we get
5P = 125
Divide by 5 on both sides of the equation , we get
P = 25 units
The number of jumps by Newton = 4 jumps
The number of steps fell short by Newton = 4 steps
So , N ( 4 ) + 4 = 120 be equation (2)
On simplifying the equation , we get
Subtracting 4 on both sides of the equation , we get
4N = 116
Divide by 4 on both sides of the equation , we get
N = 29 units
The number of jumps by Fermat = 6 jumps
So , F ( 6 ) = 120 be equation (2)
On simplifying the equation , we get
Divide by 6 on both sides of the equation , we get
F = 20 units
Therefore , the value of P , N and F are 25 , 29 and 20 units respectively
Hence , the length of each jump is 25 , 29 and 20 units
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Using the clues below, what is the value of the bigger number?
Clue 1: The sum of two numbers is ten.
Clue 2: The difference of the numbers is two.
Answer:
6
Step-by-step explanation:
Call the bigger number a, smaller b
a + b = 10
b + 2 = a
a + b + 2 = a + a = 2a = 12
a = 12 : 2
a = 6
Can someone please help me with this I'm not great with math.
The width of a rectangle is unknown. The length of the rectangle is two more units than its width.
Write a simplified algebraic expression for the area of the rectangle in terms of width (w).
Write your answer in descending order with no spaces. Use w as your variable and use ^ infront of exponents
The algebraic expression for area of rectangle in terms of width(w) is w^2+2w.
What is algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
The expressions are mainly of 4 types that includes:
Monomial Expression: These expressions have only one term.Binomial Expression: These expressions have two terms.Trinomial Expression: These expressions have three terms.Polynomial Expression: These expressions have many terms.Let the width be w.
So, length of rectangle will be w+2
Now, area of rectangle is length*width
Area= (w+2)*w
= w^2+2w
Hence, a simplified algebraic expression for the area of the rectangle in terms of width (w) is w^2+2w.
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carmen has 92 kilograms of clay. she has 5 students in her art class. how much clay does each student get
Answer:
18.4 kg of clay
Step-by-step explanation:
92 kg for 5 students
=> 92 : 5 = 18,4 kg for 1 student
Answer: 18.4 kg
Step-by-step explanation:
DATA :
total mass of clay = 92 kg
total students = 5
how much clay does each student get?
SOLUTION:
assuming that each student got equal amount of clay, we are simply going to divide ⇒92 by 5.
⇒92 ÷ 5
⇒18.4 kg ANSWER
hope that helps...
Select the correct answer.
Use the quadratic formula to solve the equation below.
x ( x + 16) = -64
Answer:
x = -8 (10
Step-by-step explanation:
x (x + 16) = -64
-8(10 + 16) = -64
-80 + 16 = -64
-64 = -64
There were 9 pieces of paper. Some of them were cut into 3 pieces. As a result, there
are now 15 pieces of paper. How many pieces of paper were cut?
6=3
6÷3
2 is the required answer for this question
What is m∠B?
A. 67
B. 54
C. 57
D. 150
The measure of angle B is, 67°.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Interior angles are,
⇒ ∠ C = 83°
⇒ ∠ B = 6x + 7
An exterior angle is,
⇒ ∠ A = 15x
Now, We know that;
The sum of two interior angles in a triangle is equal to the exterior angle in a triangle.
⇒ 83° + 6x + 7 = 15x
⇒ 90 = 15x - 6x
⇒ 90 = 9x
⇒ x = 10
Thus, The measure of B is,
⇒ m ∠B = 6x + 7
= 6×10 + 7
= 60 + 7
= 67
⇒ m ∠B = 67
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There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them how many kids own their instruments how many kids rent their instruments and what percentage of kids rent their instruments?
Answer: 80% rent or 72 students
Step-by-step explanation:
20 percent of 90 is 18
So 18 kids own instruments
100-20=80%
So 80% of kids do rent instruments
Or
18x4= 72 kids rent
2/3(6x-1/6) + 3x simplify the expression
Answer:
[tex]21x \: - \frac{1}{3} \\ 3[/tex]
In AJLP. m/JMP = (3x −6)°, JK = 3y-2, and LK = 5y-8. Find LK if PK is a median.
LK=
On solving the provided question, we can say that - the value ox in the following angle = 3x = 84 => x = 28
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
here
angle JMP = 3x-6 - 90
3x = 84
x = 28
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According to the direct instruction, what is the recommended amount of servings for milk or milk products per day?
a.5 cups
b.3 cups
c.1 cup
Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.
What are dairy products ?Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).
The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.
Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.
A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .
After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.
Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.
Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.
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Please help here’s an image
On solving the provided question we can say that - the domain of the function f(x) = [tex]sinx(e^{-x})[/tex] will be = ( [tex]\frac{-\pi }{2} , \frac{\pi }{4}[/tex] )
what is domain?The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.
so, we have
f(x) = [tex]sinx(e^{-x})[/tex]
the domain = ( [tex]\frac{-\pi }{2} , \frac{\pi }{4}[/tex] )
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On a negatively skewed curve, which is true?
The answer is On a negatively skewed curve ,The mean is lower than the median, which is lower than the mode
What is Negatively skewed curve?When a distribution is negatively skewed in statistics, more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
A longer or fatter tail on the left side of the distribution is referred to as negative skew, whereas a longer or fatter tail on the right is referred to as positive skew. The direction or weight of the distribution is indicated by these two skews.
The distribution's mean, median, and mode are referred to as its central tendency. The fact that the usually skewed data's mean, median, and mode are all equal illustrates how equally distributed wealth and income are, as well as the importance of government initiatives and economic growth.Because the negative side is so weighted, the distributions have a large gap. The data, for instance, includes income distributionin negatively skewed distribution, data shows the unequal distribution, the central tendency shows as under:Mode > Median > Mean.
Examples of negatively skewed curveUniversity exams. The tests are the same, yet a small fraction of students receive zero, average, or high percentage scores, indicating a negative skewed distribution of the data.The human Life cycle ,As many people live ordinary lives, some live very short lives, and some live very long lives in terms of age, the human life cycle is another illustration of a negatively skewed distribution.What causes a negatively skewed distribution?When the long tail is on the distribution's left side, the distribution is said to be left skewed. They are also referred to as negatively skewed by statisticians. Probabilities taper off more slowly for decreasing values, which causes this circumstance.
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can somebody please help me with this
The scale factor of the image is 1/4 or 0.25.
What is scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
To solve this question, use the coordinates of WX and W'X' as points of reference.
From the diagram, it can be obtained that -
W(-8,8) and X(8,0)
W'(-2,2) and X'(2,0)
First, calculate distance for WX -
Distance formula is -
d = √(x2-x1)^2+(y2-y1)^2
Distance for WX -
d1 = √(8+8)^2+(0-8)^2
d1 = √(16)^2+(-8)^2
d1 = √256+64
d1 = √320
d1 = 17.88
Distance for W'X' -
d2 = √(2+2)^2+(0-2)^2
d2 = √(4)^2+(-2)^2
d2 = √16+4
d2 = √20
The scale factor is then calculated using -
Scale = W'X'/WX
Scale = d2/d1
Substitute values of d1 and d2 -
Scale =√20/√320
Scale = √(20/320)
Scale = √1/16
Scale = 1/4
Therefore, the scale value is 0.25.
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Imagine you have a wood block that is 4 cm wide, 4 cm long, and 8 cm high. It
weights 200 grams.
What is the volume of the block? Be sure to include the units.
Then, imagine that you are cutting the block into 2 exactly equal halves. What is the
volume of one of the pieces (including the units)? How does its volume compare to
that of the original block?
The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.
How to find the volume of the block?The volume of a rectangular block is gotten from the formula;
Volume = length * width * height
Now, we are given;
Width = 4 cm
Length = 4 cm
Height = 8 cm
Thus;
Volume of block = 4 * 4 * 8
= 128 cm³
Now, if you are cutting the block into 2 exactly equal halves, then you can say that;
New length = 4/2 = 2cm
Thus;
Volume of cut block = 2 * 4 * 8
= 64 cm²
This is concluded to be half of the original block.
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two electric irons were sold at Rs.1050 each. If one was sold at a loss of Rs.300 and the other at a profit of Rs.450, what was the total cost price? Find the profit or loss
Answer:
Step-by-step explanation:
Selling price of two irons is Rs.1050 each.
Loss on one iron = Rs.300
Profit on second iron = Rs.450
We know that ,
Cost price = Selling price + loss ,when loss is given
and cost price = Selling price - profit ,when profit is given.
therefore, cost price of first iron = 1050 + 300 =1350 rupees
cost price of second iron = 1050 - 450 = 600 rupees
total cost price = 1350 + 600 = 1950 rupees
total selling price = 1050 + 1050 = 2100 rupees
since total cost price < selling price
so, there is a profit of 2100 - 1950 = 150 rupees.