The formulas that represent the linear function in this problem are given as follows:
y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).f(x) = 2x/3 + 4/3.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The line has a slope of 2/3, hence:
y = 2x/3 + b.
When x = 1, y = 2, hence the intercept b is obtained as follows:
2/3 + b = 2
b = 6/3 - 2/3
b = 4/3.
Hence the slope-intercept equation of the line is given as follows:
f(x) = 2x/3 + 4/3.
The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:
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find the surface area
Answer:
The surface area of the hexagonal pyramid is 313.13 square inches.
Step-by-step explanation:
Hexagonal pyramid,
Surface Area = Area of hexagon base + areas of six triangles
b = 6
h = 12.2 (height of the triangle)
A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]
A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]
A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]
A = 93.53 + 219.6
A = 313.13 square inches
A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 centimeters to 40 centimeters is 9000 joules.
To determine the work done in stretching the spring from 10 centimeters to 40 centimeters, we need to understand the relationship between force, displacement, and work.
In this case, we are given that a force of 450 newtons stretches the spring by 30 centimeters.
We can use this information to calculate the spring constant (k) using Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement it undergoes.
Hooke's Law: F = kx
Where:
F is the force applied,
k is the spring constant, and
x is the displacement of the spring.
We can rearrange the equation to solve for k:
k = F / x
k = 450 N / 30 cm
k = 15 N/cm
Now that we have the spring constant, we can calculate the work done in stretching the spring from 10 cm to 40 cm using the formula for work:
Work [tex]= (1/2)k(x2^2 - x1^2)[/tex]
Where:
k is the spring constant,
x1 is the initial displacement, and
x2 is the final displacement.
Plugging in the values:
Work [tex]= (1/2)(15 N/cm)(40 cm^2 - 10 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work = 9000 N·cm or 9000 joules (since 1 N·cm = 1 joule)
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NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Consecutive Interior Angles.
They are on the same side of a line that cuts through two other lines.
Solve 5(2x – 3) = x – 15 + 9x for x. Question 7 options: A) Infinitely many solutions B) –18∕5 C) 0 D) –12∕5
Step-by-step explanation:
5(2x – 3) = x – 15 + 9x
10x - 15 = x - 15 + 9x
10x - 9x - x = -15 + 15
0 = 0
Answer = A) Infinity many solutions
b) 9 mm 6 mm 7 mm surface area for this question
The surface area of the rectangular prism is 318 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
9 mm by 6 mm by 7 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (9 * 6 + 9 * 7 + 6 *7)
Evaluate
Area = 318
Hence, the area is 318 square mm
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Question
The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?
2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
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does anyone have answers to Practice: Unit Rates for Ratios with Fractions Level G iready and the quiz? I will give a lot of points and brainliest answer
While direct answers to iReady tasks are not provided, guidance for tackling problems involving unit rates and ratios with fractions was presented. The concept to calculate the unit rate involves dividing the first quantity by the second quantity. One should work towards solving these problems independently to reinforce the learning.
Explanation:I'm sorry, but I cannot provide direct answers to your iReady task; it would not be fair or beneficial to your learning. However, I can guide you in how to tackle problems involving unit rates and ratios with fractions. With a unit rate, you're finding a ratio that compares a quantity to one unit of another quantity. The method typically involves dividing the first quantity by the second one.
For example, if you have a problem that says '6 cookies cost $1.50, what is the unit rate?', you would solve it by dividing 1.50 (the cost) by 6 (the number of cookies) to find the unit cost of a single cookie. This gives you a unit rate of $0.25 per cookie. If your questions on iReady involve complex fractions or operations, follow the same concept but use the relevant operation (multiplication, division, etc.). Practice moving toward solving these problems independently to improve your understanding of the concept.
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A native wolf species has been reintroduced into a national forest. Originally, 46 wolves were transplanted. Assuming that the population is growing exponentially at a rate of 5.6%, how long will it take for the population to reach 150 wolves? Round your answer to the first decimal place.
Can u help me please fill in the square
The equation of the circle is (x + 4)² + (y - 1)² = 81
Given is an equation of a circle we need to convert it in standard form,
x² + y² + 8x - 2y = 64,
To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.
The standard form of a circle equation is:
(x - h)² + (y - k)² = r²
where (h, k) represents the center of the circle, and r represents the radius.
Let's convert the given equation to standard form step by step:
x² + y² + 8x - 2y = 64
Rearrange the equation to group the x-terms and y-terms:
x² + 8x + y² - 2y = 64
Now, complete the square for the x-terms.
Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:
x² + 8x + 16 + y² - 2y = 64 + 16
Simplify:
(x + 4)² + y² - 2y = 80
Complete the square for the y-terms.
Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:
(x + 4)² + y² - 2y + 1 = 80 + 1
Simplify:
(x + 4)² + (y - 1)² = 81
Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.
Hence the equation of the circle is (x + 4)² + (y - 1)² = 81
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According to the synthetic division below, which of the following statements are true? -4/3 7 20
According to the synthetic division below, the true statements are as follows:
B. The number 4 is a root of F(x) = 3x2-13x+4.
D. (3x2 - 13x+4) - (x - 4) = (3x - 1)
F. (x-4) is a factor of 3x2.13x+ 4.
How to determine the true statementsSynthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:
1. F(x) = 3x² - 13x +4.
(x-4) (3x-1)
So, x = 4 or 1/3
4 is an actual root of the function.
2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)
3. 3x² - 13x + 4 = (x-4) (3x-1)
So, since all these expressions are true, they meet the requirements for the synthetic division.
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Complete Question:
According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.
A missile is moving 1810 m/s at a 20.0° angle. It needs to hit a target 19,500 m away in a 32.0° direction in 9.20 s. What is the magnitude of the acceleration that the engine must produce?
Answer:
Aprox: 465.4 ms/2
Step-by-step explanation:
To find the magnitude of the acceleration the engine must produce, we'll break down the missile's motion into its horizontal and vertical components.
Given:
Initial velocity (V₀) = 1810 m/s
Launch angle (θ) = 20.0°
Target distance (d) = 19,500 m
Target direction (φ) = 32.0°
Time of flight (t) = 9.20 s
First, let's find the horizontal and vertical components of the missile's initial velocity (V₀x and V₀y).
V₀x = V₀ * cos(θ)
V₀y = V₀ * sin(θ)
V₀x = 1810 m/s * cos(20.0°) ≈ 1712.4 m/s
V₀y = 1810 m/s * sin(20.0°) ≈ 618.8 m/s
Now, let's find the horizontal and vertical displacements (dx and dy) of the missile using the time of flight (t) and the target distance (d).
dx = d * cos(φ)
dy = d * sin(φ)
dx = 19,500 m * cos(32.0°) ≈ 16,402.8 m
dy = 19,500 m * sin(32.0°) ≈ 10,236.8 m
Next, let's calculate the acceleration needed in the x-direction (ax) and y-direction (ay) to cover the horizontal and vertical displacements in the given time.
ax = (2 * dx) / t²
ay = (2 * dy) / t²
ax = (2 * 16,402.8 m) / (9.20 s)² ≈ 391.7 m/s²
ay = (2 * 10,236.8 m) / (9.20 s)² ≈ 257.7 m/s²
Finally, to find the magnitude of the acceleration, we can use the Pythagorean theorem:
acceleration magnitude (a) = √(ax² + ay²)
a = √(391.7 m/s²)² + (257.7 m/s²)² ≈ 465.4 m/s²
Therefore, the magnitude of the acceleration that the engine must produce is approximately 465.4 m/s².
1-56.
The owner of Universal Widgets has two teams of employees and
wants to know which team is working the "best." The assistant
manager gathered data for the number of widgets made per team
member on various days. He presented the data to the owner as
two boxplots, shown at right. The owner is confused.
a. Help the owner decide which team is working the "best"
by comparing center, shape, spread, and outliers.
b. Which team had a smaller standard deviation? Explain.
200
150
100
30
Team I
93°
65°
m
X
finding the angle of x
The measure of angle C is,
⇒ x = 22°
We have to given that,
In a triangle ABC,
Angle A = 65 degree,
Angle B = 93 degree.
Now, Let us assume that,
Measure of angle C = x
Hence, We get;
⇒ ∠A + ∠B + ∠C = 180°
Substitute all the values,
⇒ 65 + 93 + x = 180
⇒ 158 + x = 180
⇒ x = 180 - 158
⇒ x = 22
Therefore, The measure of angle C is,
⇒ x = 22°
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Complete question is,
In Triangle ABC, Angle A = 65 degree, B=93 degree. Find Angle C?
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
J
ہے
Answer:
(a) x-intercept = -2
(b) y-intercept = 4
What is the area of a rectangle whose width is n feet and who’s length is 2 feet more than 3 times it’s width in terms of n?
Answer: The length of the rectangle is given as "2 feet more than 3 times its width."
Let's break it down step by step:
The width of the rectangle is n feet.Three times the width is 3n.Two feet more than 3 times the width is 3n + 2.
The formula for the area of a rectangle is length multiplied by width. So, in terms of n, the area of the rectangle would be:
Area = Length × Width
= (3n + 2) × n
= 3n^2 + 2n
Therefore, the area of the rectangle, in terms of n, is 3n^2 + 2n.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The surface area of each solid is listed below:
Case A: A = 584.988 ft²
Case B: A = 320π in²
How to determine the surface area of a solidIn this problem we must determine the surface area of each of two solids, that is, the sum of the areas of all faces, whose area formulas are introduced below:
Square
A = l²
Where l is the side length.
Triangle
A = 0.5 · w · h
Where:
w - Widthh - HeightCircle
A = π · r²
Where r is the radius.
Lateral side of a cylinder
A = 2π · r · h
Where h is the height of the cylinder.
Now we proceed to determine the surface area of each solid:
Case A:
A = (14 ft)² + 4 · 0.5 · (14 ft) · √[(7 ft)² + (12 ft)²]
A = 584.988 ft²
Case B:
A = 2π · (8 in)² + 2π · (8 in) · (12 in)
A = 320π in²
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A girl is on a bridge 38.9 m high. She throws a rock straight down at -12.5 m/s. How long does it the rock to hit the ground
Answer:
3.14 seconds
Step-by-step explanation:
the region in the first quadrant enclosed by the curves y=0, x=2, x=5 and y=1/sqrt(1+x) is rotated about the x-axis. The volume of the solid generated is A. πIn(2) B. πIn(3/4) C. πIn(10) D. πIn(5) E. πIn(4/3)
The volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and [tex]y=1/\sqrt(1+x)[/tex] about the x-axis is πln(2),
(option A).
To find the volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and[tex]y=1/\sqrt(1+x)[/tex] about the x-axis, we need to use the formula for the volume of a solid of revolution.
The formula is ∫[a,b] [tex]π(f(x))^2dx[/tex], where a and b are the limits of integration and f(x) is the function that describes the distance between the axis of revolution and the curve being rotated.
In this case, we need to use the function f(x) = 1/sqrt(1+x), since this function describes the distance between the x-axis and the curve being rotated. The limits of integration are from x=2 to x=5, since these are the values of x that define the region being rotated.
Using the formula, we can set up the integral as follows:
[tex]∫[2,5] π(1/\sqrt(1+x))^2dx[/tex]
= π∫[2,5] 1/(1+x) dx
= π[ln(1+x)]|[2,5]
= π[ln(6) - ln(3)]
= πln(2) (option-A)
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Susan borrowed $18,500 at 5.00% p.a. from her parents to start a business. In 4 months, she repaid $5,300 towards the loan, and in 10 months she repaid $3,800. How much would she have to repay her parents at the end of 13 months to clear the outstanding balance? Use the declining balance method to calculate the last payment.
Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
To calculate the outstanding balance at the end of 13 months, we need to use the declining balance method. This method involves applying the interest rate to the remaining balance after each repayment.
First, let's calculate the interest for the first 4 months. The interest for this period can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the principal is $18,500, the rate is 5.00% per year (or 0.05), and the time is 4 months (or 4/12 years). Thus, the interest for the first 4 months is $18,500 × 0.05 × (4/12) = $308.33.
Next, we subtract the repayment made after 4 months ($5,300) from the outstanding balance ($18,500) and add the interest for the first 4 months ($308.33). This gives us a new outstanding balance of $18,500 - $5,300 + $308.33 = $13,508.33.
Now, let's calculate the interest for the period between 4 and 10 months. The principal remains the same ($13,508.33), the rate is still 5.00% per year (or 0.05), and the time is 6 months (or 6/12 years). Therefore, the interest for this period is $13,508.33 × 0.05 × (6/12) = $337.71.
Subtracting the repayment made after 10 months ($3,800) from the outstanding balance ($13,508.33) and adding the interest for the period gives us a new outstanding balance of $13,508.33 - $3,800 + $337.71 = $10,045.04.
Finally, to determine the last payment required to clear the outstanding balance at the end of 13 months, we subtract the new outstanding balance ($10,045.04) from the principal ($18,500). The last payment is therefore $18,500 - $10,045.04 = $8,454.96.
Therefore, Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
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HELPP PLEASEE I REALLY NEEED THIS 7 cm
What is the volume of the figure?
3 cm
5 cm
Answer:
Volume = 105 cm³
Step-by-step explanation:
Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)
Volume = 7 × 5 × 3
Volume = 35 × 3
Volume = 105 cm³
In a laboratory experiment, the population of bacteria in a petri dish started off at
4900 and is growing exponentially at 8% per hour. Write a function to represent the
population of bacteria after t hours, where the rate of change per minute can be
found from a constant in the function. Round all coefficients in the function to four
decimal places. Also, determine the percentage rate of change per minute, to the
nearest hundredth of a percent.
1. The function representing the population of bacteria after t minutes is P(t) = 4900× [tex]e^{(0.08(t/60)}[/tex]
2. The percentage rate of change per minute is approximately 0.13%.
How did we find the function and percentage rate?
The general form of an exponential growth function ⇒ P(t) = P0 ×[tex]e^{(rt)}[/tex]
P(t) is the population at time t,
P0 is the initial population,⇒4900
r is the growth rate ⇒ 8%
t is the time.
Therefore, our function in terms of hours (t) becomes:
P(t) = 4900 × [tex]e^{(0.08t)}[/tex]
To find per minute, there are 60 minutes in an hour,
∴ t becomes t/60
P(t) = 4900× [tex]e^{(0.08(t/60))}[/tex]
We know the rate of change per hour is 8%, so the rate of change per minute will be 8% divided by 60, which is
[tex]e^{(0.08/60)-1}[/tex] × 100 = 0.13%.
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hat amount did she get back? (h) Ujeli had 11 pencils. She kept 3 pencils for herself and divided the remaining pencil equal among 4 of her friends. How many pencils did she give to each of them?
Answer:
2
Step-by-step explanation:
Ujeli had 11 pencils and she kept 3 so 11-3 = 8
so that means that the remaining pencil were dived by 4 (8÷2) = 2
Robert is baking a cake. He
needs 5 cups of milk, but notices that
his measuring device is only marked in
pints.
How many pints of milk will Robert
need?
what is greatest common factor of -x^2+6x-19
The greatest common factor of -x^2 + 6x - 19 is 1.
To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.
First, let's examine the polynomial and see if we can factor it further:
[tex]-x^2 + 6x - 19[/tex]
The polynomial does not appear to have any common factors among its terms.
It cannot be factored using simple integer factors.
In this case, we can say that the GCF of the given polynomial is 1.
It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.
It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.
However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.
But in this case, the polynomial does not exhibit any common factors beyond 1.
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Which of the following exponential regression equations best fits the data shown below?
(-4,0.05), (-3, 0.20), (-2, 0.75)
The exponential regression equation is y = 11.37 * 3.87ˣ
How to determine the exponential regression equationFrom the question, we have the following parameters that can be used in our computation:
(-4,0.05), (-3, 0.20), (-2, 0.75)
To calculate the exponential regression equation that best fits the data shown, we use a graphing tool
An exponential function is represented as
y = abˣ
From the graphing tool, we have
a = 11.37
b = 3.87
substitute the known values in the above equation, so, we have the following representation
y = 11.37 * 3.87ˣ
Hence, the exponential regression equation is y = 11.37 * 3.87ˣ
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77th term of the sequence 16,19,22,25
The 77th term of the given Sequence is 244.
The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.
The formula for the nth term of an arithmetic progression is:
_ = _1 + ( − 1),
where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.
In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:
_77 = 16 + (77 − 1) × 3.
_77 = 16 + 76 × 3.
_77 = 16 + 228.
_77 = 244.
Therefore, the 77th term of the given sequence is 244.
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The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favourite exhibit was either dinosaurs, or planets, express your answer as a decimal.
Butterfly: 12
Dinosaurs: 25
Planets: 17
Trains: 6
The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.
How do we find the relative frequency?To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.
The total number of students surveyed is 12 + 25 + 17 + 6 = 60.
The number of students who chose dinosaurs or planets is 25 + 17 = 42.
Therefore, the relative frequency will then be 42 / 60 = 0.7.
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Cold Beans wants to make a blend of their two best coffees, Guatemalan and Jamaican coffee. The pound of Guatemalan Coffee costs $11/lb and the other one costs $5/lb. If they want the cost of a 6 pound bag of blend to be $8/lb, how much Guatemalan coffee should they use per pound of the blend?
For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.
Given information:
Cost of Guatemalan coffee = $11/lb
Cost of the other coffee = $5/lb
Desired cost of the blend = $8/lb
Total weight of the blend = 6 pounds
To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:
[tex](x \times 11 + (6 - x) \times 5) / 6 = 8[/tex]
In this equation, [tex](x \times 11)[/tex] represents the cost of the Guatemalan coffee in the blend, and[tex]((6 - x) \times 5)[/tex] represents the cost of the other coffee in the blend.
The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.
Now, let's solve the equation for x:
(11x + 30 - 5x) / 6 = 8
6x + 30 = 48
6x = 48 - 30
6x = 18
x = 18/6
x = 3
Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.
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Write a system of linear equations for the graph below. really need lots of help with this!
i also need the y's
Answer:
friend with this information you cannot know the answer you have to say everything says about that mathematical problem
A statue that is 25 feet tall casts a shadow that is 16 feet long. A cement pose next to the statue is 4 feet tall. find the length of the cement post’s statue.
The length of the cement post's statue is 6.25 feet.
How to calculate the length of the cement post's statue?We shall use Mathematical operators to compute the length of the cement post's statue.
(Height of the statue) / (Length of the shadow) = (Height of the cement post's statue) / (Height of the cement post)
Given:
Height of the statue = 25 feet
Length of the shadow = 16 feet
Height of the cement post = 4 feet
Let x = length of the cement post's statue
25 feet / 16 feet = x / 4 feet
To find x, we cross-multiply:
25 * 4 = 16 * x
100 = 16 * x
To isolate x, we divide both sides of the equation by 16 feet:
100 / 16 = x
x ≈ 6.25 feet
Therefore, the length of the cement post's statue is 6.25 feet.
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