The break-even point is 54,000 units given the cost function and revenue function.
The break-even point is the moment at which a product's sales revenue equals its production costs. There is currently neither a gain nor a loss.
This problem's cost function is C(x) = 0.75x + 63,180, where x is the total number of created units. R(x) = 1.92x, where x is the quantity of units sold, is the revenue function.
We must set the revenue equal to the expense in order to determine the break-even point:
R(x) = C(x) (x)
1.92x = 0.75x + 63,180
1.17x = 63,180
x = 54,000
Thus, 54,000 units are needed to break even.
This means that the money earned will be equivalent to the cost of creating the product if the company produces and sells 54,000 units of it. The corporation will make money on any units sold over this threshold while losing money on any units sold below it.
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Determine the values of the parameter s for which the system has a unique solution, and describe the solution.
5sx1 + 9x2 = -3
5x1 + sx2 = 4
The solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero
Determine the values of the parameter s?The values of the parameter s
for which the system has a unique solution are s ≠ -45/8. Let's understand how to find the solution and the values of s:
Given equation of the system is,5x1s + 9x2 = -3 ...(1)
5x1 + sx2 = 4 ...(2)
Now, let's solve the given system of equations using the elimination method:
Multiply equation (2) by 5, we get:25x1 + 5sx2 = 20 ...(3)
Now, we'll subtract equation (1) from equation (3) as:
25x1 + 5sx2 = 20- (5x1s + 9x2 = -3)20x1 + 5sx2 = 23 ... (4)
Let's divide equation (4) by 5s, we get:
4x1 + x2/s = 23/5s ... (5)
Multiply equation (2) by 9 and subtract equation (1) from it. We get:40x2 + 9sx2 = 39
Simplifying the above equation, we get:(49s+360)x2 = 39 ... (6)
Now, we have two equations:(5) 4x1 + x2/s = 23/5s(6) (49s+360)
x2 = 39The given system of equations will have a unique solution only if x2 ≠ 0. So, let's consider the value of x2.If x2 ≠ 0, then from equation (6)
we get,49s+360 ≠ 0 or s ≠ -360/49
This means that s ≠ -360/49 is necessary for the given system to have a unique solution.
Now, let's solve the equation (5):4x1 + x2/s = 23/5s
If we multiply both sides of the equation (5)
by s, we get:
4sx1 + x2 = 23/5If x2 ≠ 0, then we can solve this equation for x1 as:
x1 = (23/5s - x2)/4s
Therefore, the solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero value.
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Two groups of friends went to the local movie theater. The first group bought four large buckets of
popcorn and five boxes of candy and spent $42.75. The second group spent $25.50 on two boxes of
candy and three large buckets of popcorn.
How much would one large popcorn and one box of candy cost?
One large bucket of popcorn costs $6 and one box of candy costs $3.75.
To solve this problemLet's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :
Equation 1: 4p + 5c = 42.75 (first group's purchase)
Equation 2: 3p + 2c = 25.50 (second group's purchase)
We can use any method to solve these equations, such as substitution or elimination.
Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":
8p + 10c = 85.50 (multiplying Equation 1 by 2)
-15p - 10c = -127.50 (multiplying Equation 2 by -5)
Adding the two equations, we get :
-7p = -42
p = 6
Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:
4(6) + 5c = 42.75
24 + 5c = 42.75
5c = 18.75
c = 3.75
Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.
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PLS help and explain A quadratic function intersects the z-axis at the points (-4, 0) and (2, 0),and passes through the point (-6,-8). Select the equivalent equations for the quadratic function.
Oy=-0.52²-z+4
y=-0.52²+2-4
Oy=(z-4)(1-0.52)
Oy=(z+4)(1-0.5z)
Oy=-0.5(2-2)(=+4)
O y=-0.5(z+2)(z-4)
Previous
Pause Test
Nex
Therefore , the solution of the given problem of function comes out to be Oy=-0.5z²+z+4.
What is function?On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
We must make use of the data provided in the challenge in order to identify the quadratic function.
=> f(z) = a(z + 4)(z - 2)
where an is a constant we need to figure out.
We can use the position (-6, -8), which is where the function passes through, to determine the value of a:
=> -8 = a(-6 + 4)(-6 - 2)
=> -8 = a(-2)(-8)
=> -8 = 16a
=> a = -1/2
Inputting this number of an into the quadratic function equation yields the following results:
=> f(z) = -1/2(z + 4)(z - 2)
By extending this phrase, we get:
=> f(z) = -1/2(z² - 2z - 8)
Further simplification results in:
=> f(z) = -0.5z² + z + 4
The quadratic function's corresponding equation is thus:
=> Oy=-0.5z²+z+4
The following is the appropriate decision from the options provided:
=> Oy=-0.5z²+z+4
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Please help
What was the balance before the ATM withdrawal on June 5?
Answer: 586.20
Step-by-step explanation:
you add the balance on june 5th with the amount withdrawed to get the past balance
A superhero action figure has volume 1700 cubic centimeters. The figure is dilated to create a store display.
The volume of the dilated figure is 25,500 cubic centimeters
What was the approximate scale factor of the dilation? (Round your answer to the nearest tenth, one decimal place ex. 4.2)
Therefore , the solution of the given problem of surface area comes out to be scale factor of the dilation is 15.0, rounded to one decimal point.
What does an area actually mean?By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.
Here,
By dividing the volume of the dilated figure by the volume of the initial figure, we can determine the scale factor of the dilation:
volume of dilated figure / volume of initial figure is the scale factor.
Scale factor:
=> 25,500/1700 cm3
=> 15 scale factor
The approximate scale factor of the dilation is 15.0, rounded to one decimal point.
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Maia was baking cupcakes for a party. She mixed 4 drops of red food coloring for every 6 drops of yellow food coloring to dye her icing orange. Circle the ratios of food coloring drops that would create the same orange color and justify your choices.
2 red to 3 yellow 40 yellow to 100 red 44 red to 66 yellow 24 red to 26 yellow 28 red to 42 yellow
The ratios that would create the same orange color as Maia's ratio of [tex]2:3[/tex] are [tex]2[/tex] red to [tex]3[/tex] yellow, [tex]44[/tex] red to [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.
What are the ratios?The ratio of 4 drops of red food coloring to 6 drops of yellow food coloring can be simplified to 2:3 by dividing both numbers by 2. This means that for every 2 drops of red food coloring, Maia used 3 drops of yellow food coloring to create orange icing.
Let's evaluate each of the given ratios:
2 red to 3 yellow: This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
40 yellow to 100 red: We can simplify this ratio by dividing both numbers by 20, giving us 2 yellow to 5 red. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.
44 red to 66 yellow: We can simplify this ratio by dividing both numbers by 22, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
24 red to 26 yellow: We can simplify this ratio by dividing both numbers by 2, giving us 12 red to 13 yellow. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.
28 red to 42 yellow: We can simplify this ratio by dividing both numbers by 14, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
Therefore, the ratios that would create the same orange color as Maia's ratio of [tex]2:3[/tex] are [tex]2[/tex] red to [tex]3[/tex] yellow, [tex]44[/tex] red to [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.
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John worked 35 hours at a rate of $11.50. What is his gross pay this week?
What is |x-13|+18=-4?
Answer:
No solution
Step-by-step explanation:
Solve for x
[tex]|x-13|+18=-4[/tex]
Subtract 18 on both sides
[tex]|x-13|=-22[/tex]
There is no solution to this problem. Absolute value cannot be less then 0.
The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 80,000 citizens answered the question, how many chose Fish or Snakes?
fish 12%
dogs 25%
birds 22%
cats 23%
snakes 10%
hamsters 8%
17,600 citizens chose Fish or Snakes.
What is circle graph?
A circle graph, also known as a pie chart, is a type of data visualization used to represent data in a circular format. It is called a pie chart because the graph resembles a pie, which is divided into slices or sectors, where each sector represents a portion of the whole data set. The size of each slice is proportional to the corresponding value it represents in the data set. The circle graph is often used to show relative sizes of different categories or portions of a whole. It is a popular way to display data in business, statistics, and other fields.
According to the given information, the percentage of citizens who chose Fish or Snakes is 12% + 10% = 22%.
It is also given total number of citizens are 80,000.
To find the number of citizens who chose Fish or Snakes, we can first calculate 22% of 80,000,
[tex]22\% \: of \: 80000 \\ = \frac{22}{100} \times 80000 \\ = 0.22 \times 80,000 \\ = 17,600[/tex]
Therefore, 17,600 citizens chose Fish or Snakes.
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QUICK !
A rectangle has a length that is 2 units longer than the width, w.
Complete the equation representing the area of the rectangle, in square units.
A= ( )( )
Options: w-2, w, w+2, 2w, 2w+2, 2w+4.
The equation representing the area of the rectangle with width w is A = w² + 2w.
We have a rectangle with a length that is 2 units longer than the width w. Let's refer to the rectangle's length as L. Then we have:
[tex]L = w + 2[/tex]
The product of a rectangle's length and breadth determines its area A. So, to find an equation representing the area of the rectangle, we need to multiply the length L by the width w. Substituting L with the expression we got from the problem statement, we get:
A = L × w
A = (w + 2) × w
A = w² + 2w
This is the final equation representing the area of the rectangle in terms of its width w
This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 2, and the constant term is 0. We can use this equation to find the area of the rectangle for any given width w.
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6.4 a bus arrives every 10 minutes at a bus stop. it is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. what is the probability that the individual waits more than 7 minutes? what is the probability that the individual waits between 2 and 7 minutes?
The probability that the individual waits more than 7 minutes is 0.3 or 30%. The probability that the individual waits between 2 and 7 minutes is 0.5 or 50%.
Let X be the waiting time for a particular individual at the bus stop. As per the given information, X follows a continuous uniform distribution with parameters a=0 and b=10 (as the bus arrives every 10 minutes).
The probability that the individual waits more than 7 minutes can be calculated as follows:
P(X > 7) = (b-7)/(b-a) = (10-7)/(10-0) = 3/10 = 0.3
Similarly, the probability that the individual waits between 2 and 7 minutes can be calculated as follows:
P(2 < X < 7) = (7-2)/(10-0) = 5/10 = 0.5
In summary, the probability that the individual waits more than 7 minutes is 0.3 and the probability that the individual waits between 2 and 7 minutes is 0.5. This means that there is a higher chance that the individual waits between 2 and 7 minutes than waiting for more than 7 minutes.
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The image of the point ( 6 , − 9 ) (6,−9) under a translation is ( 11 , − 4 ) (11,−4). Find the coordinates of the image of the point ( − 3 , − 2 ) (−3,−2) under the same translation
The translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation: (-3+5, -2+5) = (2, 3)
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
Let's denote the translation vector as (a, b), then the image of point (x, y) under the translation is given by (x+a, y+b).
We know that the image of point (6, -9) under the translation is (11, -4), so we can write:
(6+a, -9+b) = (11, -4)
Solving this system of equations for a and b, we get:
a = 5 and b = 5
Therefore, the translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation:
(-3+5, -2+5) = (2, 3)
So the image of point (-3, -2) under the given translation is (2, 3).
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What additional information is needed to prove Triangle ACE is congruent to Triangle BDE using the ASA postulate?
To prove Triangle ACE is congruent to Triangle BDE using the ASA postulate, we need either ∠A ≅ ∠B or ∠C ≅ ∠D.
To prove two triangle congruent by angle side angle postulate, these triangle must have two sides equal or one angle from these two must be equal and identical to each other.
What are congruent triangle?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.
The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. There are basically four congruence rules that proves if two triangles are congruent.
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the ability of a study to detect a difference if one actually exists is called what? group of answer choices beta alpha significance power
The ability of a study to detect a difference if one actually exists is called option (d) power
Power in statistics is the probability of correctly rejecting a false null hypothesis. In other words, it is the ability of a statistical test to detect a difference or effect if one actually exists in the population being studied. A study with high power has a low probability of a Type II error (failing to reject a false null hypothesis) and a high probability of correctly detecting a true difference or effect.
Power is affected by several factors, including sample size, effect size, level of significance (alpha), and variability of the data. Researchers often aim for a power of at least 80% to ensure that their study has a reasonable chance of detecting a meaningful effect.
Therefore, the correct option is (d) power
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In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the length of DC
Thus, the arc length of DC for the given central angle of circle is found as: 16.74 units.
Explain about the arc length:Arc Length Formula: Assume a circle with radius r. If a circle's arc of length s subtends a central angle theta (measured in radians), the formula is as follows: r X theta = s.
Radian Measure: The centre angle must only be expressed in radian measure with in arc length formula above.A novel method of calculating angles in circles is suggested using arc length. Angles can also be measured in radians instead of the previous method of measuring all angles in degrees. The angle of one radian results in an arc whose length is equal to the radius.For the given circle:
Radius r = 8 units.angle APD = 60 degrees.Thus,
∠APD + ∠DPC = 180° (angle sum property of triangle)
60 + ∠DPC = 180°
∠DPC = 180° - 60°
∠DPC = 120°
Using the formula for the arc length:
Arc length = Ф/360 * 2*π*r
Arc length DC = 120/360 * 2*3.14*8
Arc length DC = 16.74 units
Thus, the arc length of DC for the given central angle of circle is found as: 16.74 units.
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Complete question:
In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the arc length of DC.
The figure is attached.
An airline has a new plane with 120 seats and a new route from panama city, FL to New York city, NY. The function F(x) models the profit the airline makes, where x is the cost per seat. The table of values for function f(x) is shown
The correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.
What is Correlation Coefficient?The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient.
To calculate the correlation coefficient between x and f(x), we need to calculate several quantities first:
mean of x:
[tex]$\overline{x}[/tex] = {50+35+60+65+70+75+80}{7} = {435}/{7}
= 62.14
mean of f(x):
[tex]$\overline{f(x)}[/tex]= {1,272 + 1,884.5 + 2,322 + 2,584.5 + 2,672 + 2,584.5 + 2,322}/{7}
= 2,112.86
and, standard deviation of x:
[tex]$s_x[/tex]=[tex]\sqrt{\frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n-1}}[/tex]
= [tex]= \sqrt{\frac{(50-62.14)^2 + (35-62.14)^2 + (60-62.14)^2 + (65-62.14)^2 + (70-62.14)^2 + (75-62.14)^2 + (80-62.14)^2}{6}} \\\approx 17.27$[/tex]
and, standard deviation of f(x):
[tex]$s_{f(x)} = \sqrt{\frac{\sum_{i=1}^n (f(x_i) - \overline{f(x)})^2}{n-1}}[/tex]
= (1,272-2,112.86)² + (1,884.5-2,112.86)² + (2,322-2,112.86)² + (2,584.5-2,112.86)² + (2,672-2,112.86)²+ (2,584.5-2,112.86)² + (2,322-2,112.86)²}/ 6
= 385.09
Now, covariance of x and f(x):
[tex]$cov(x,f(x)) = \frac{\sum_{i=1}^n (x_i - \overline{x})(f(x_i) - \overline{f(x)})}{n-1}[/tex]
= {(50-62.14)(1,272-2,112.86) + (35-62.14)(1,884.5-2,112.86) + (60-62.14)(2,322-2,112.86) + (65-62.14)(2,584.5-2,112.86) + (70-62.14)(2,672-2,112.86) + (75-62.14)(2,584.5-2,112.86) + (80-62.14)(2,322-2,112.86)} / 6
= 762.36
Using these values, we can calculate the correlation coefficient:
[tex]$r = \frac{cov(x,f(x))}{s_x s_{f(x)}} = \frac{762.36}{17.27 \cdot 385.09} \approx 0.39$[/tex]
Therefore, the correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.
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rcumference of Circles Extra Practice Question 1 of 22 Question 1 4 3 cm > □ Find the circumference of the bottle cap. Use 3.14 for T. Round to the nearest hundredth if necessary.
The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.
What is the circumference of the circle?The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.
The diameter of the circle is given, D = 3cm
Therefore the radius of the circle, r = D/2 = 3/2 cm
Circumference of circle = 2[tex]\pi[/tex]r
= 2 * 3.14 * 3/2
= 3.14 * 3
= 9.42 cm
Therefore the circumference of the bottle cap is 9.42 cm.
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Pls help, its easy I just dont want to do it.
Step-by-step explanation:
The green triangle :
The angle x is 65°
this is because both the sides are equal so when the other angle is 65° angle x is also 65°
The blue triangle :
The angle x is 25°
this is because both the sides are equal so when the other angle is 25° angle x is also 25°
The red triangle :
The angle x is 45°
this is because both the sides are equal so when the other angle is 45° angle x is also 45°
solve please help!!!!
The value of angle V which is ∠V is calculated as: 64.01°
How to use trigonometric ratios?The trigonometric ratios are used to find the angles and lengths of a right angle triangle.
Some of the trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
The parameters given are:
∠W = 90°
UW = 39
WV = 80
VU = 89
Thus, using trigonometric ratios, we have:
∠V = tan⁻¹(80/39)
∠V = 64.01°
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Find m < b
Find m < c
The answer of the given figure is ∠B = 72° and ∠C = 108°
What do you understand by the term Corresponding Angle?In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.
More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.
According to question
∠CFE = 72°
In given diagram
DC ║ EF ║ AB and CB is transversal
∴ ∠CFE + ∠BFE = 180° ( Linear pair )
72° + ∠BFE = 180°
∠BFE = 180 - 72
∠BFE = 108°
∵∠DCF = ∠BFE ( Corresponding equal angle )
∠DCF = 108°
∠C = 108°
∠CFE = ∠B ( Corresponding equal angle )
72° = ∠B
∴∠B = 72°
Hence, the ∠B = 72° and ∠C = 108°
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A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
Answer:
A line graph, because it would show the association or relationship between two variables
Step-by-step explanation:
Pls help and explain
Answer: A (0.5)
Step-by-step explanation:
Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.
Write a formula for the nth term of the arithmetic sequence with the third term 7 and the common difference -2
So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference -2 is aₙ = 13 - 2n.
An arithmetic sequence's nth term is represented by the formula:
aₙ = a₁ + (n-1)d
In this case, we are given that the third term is 7, so we can use this information to find a₁:
a₃ = a₁ + (3-1)(-2)
7 = a₁ - 4
a₁ = 11
Now we have a₁ and d, so we can write the formula for the nth term:
aₙ = 11 + (n-1)(-2)
Simplifying this expression, we get:
aₙ = 13 - 2n
So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference is
-2 is aₙ = 13 - 2n.
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5.
Each table represents a proportional relationship. For each table:
Fill in the missing parts of the table.
Draw a circle around the constant of proportionality.
a.
b.
X
2
7
1
y
10
15
a.(Constant of proportionality: 5)
b.(Constant of proportionality: 5)
Hi! I'm happy to help you with your question. Let's analyze each table and fill in the missing parts.
a.
X | 2
Y | 10
To find the constant of proportionality, divide Y by X:
10 / 2 = 5 (Constant of proportionality)
Now, let's fill in the missing parts for X=7 and X=1 using the constant of proportionality:
For X=7:
Y = 5 * 7 = 35
For X=1:
Y = 5 * 1 = 5
So, the completed table for (a) is:
X | 2 | 7 | 1
Y | 10 | 35 | 5
(Constant of proportionality: 5)
b.
X | 1
Y | 15
To find the constant of proportionality, divide Y by X:
15 / 1 = 15 (Constant of proportionality)
As there are no other values in table (b), we can't fill in any more parts. The constant of proportionality is 15.
Your answer:
a.
X | 2 | 7 | 1
Y | 10 | 35 | 5
b.
X | 1
Y | 15
(Constant of proportionality: 15)
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In one part of the world, the number of a certain species of forest wildflowers is expected to grow according to the
function f graphed below. In another area of the world, the same species is expected to grow according to the the
function g represented by the data in the table. The values for x in each function represent time, in decades.
what function has the greater initial value
in a third area, the number of flowering plants is expected to grow according to the following description the initial count is 1500 and for each decade moving forward the count will increase by 200. Will this model be linear or exponential what is the model that relates the number of plants h to the number of decades x
Answer:
f(x) has the greater initial value.
linear; h(x) = 200x + 1500
Step-by-step explanation:
f(0) = 1000
g(0) = 750
Therefore, f(x) has the greater initial value.
In the third area, the model is linear and the function would be:
h(x) = 200x + 1500
¿Cuál será el fenotipo de un individuo I a
English please I don't unless
I need to know the missing angle if u can help I’ll give u a lot of points if u keep helping me
Answer:
?=45 degrees
Step-by-step explanation:
All of the angles are congruent.
So the equation is:45+90+?=180
?=45 degrees
Answer: 45 degrees
Step-by-step explanation:
The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 105 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of a the tower to be 29.2°. Find the length of the tower to the nearest meter.
the tower leans 5.6° from the vertical, so we can draw a line perpendicular to the ground from the top of the tower to find the height. Let's call the height "h". the length of the tower is approximately [tex]57 meters[/tex] (rounded to the nearest meter).
What is the angle of elevation?We know that the angle of elevation from the tourist to the top of the tower is [tex]29.2^\circ[/tex] , so we can label that angle as 29.2°. We also know that the angle between the perpendicular line and the ground is 5.6°, so we can label that angle as 5.6°.
Using trigonometry, we can find the value of h:
[tex]tan(29.2^\circ) = h/105[/tex]
[tex]h = 105^\circ tan(29.2^\circ)[/tex]
[tex]h \approx 55.05[/tex]
So the height of the tower is approximately [tex]55.05[/tex] meters.
To find the length of the tower, we can use the Pythagorean theorem:
[tex]h^2 + x^2 = (105/cos(5.6^\circ))^2[/tex]
[tex]x^2 = (105/cos(5.6^\circ))^2 - h^2[/tex]
[tex]x \approx 56.67[/tex]
So the length of the tower is approximately [tex]56.67[/tex] meters.
Therefore, the length of the tower is approximately [tex]57[/tex] meters (rounded to the nearest meter).
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The area of the trapezoid is 42square kilometers. What is the trapezoid's height, h?
the height of the trapezoid is 8.4 kilometers. To find the height, h, of a trapezoid when given the area, A, we need to use the formula:
A = ([tex]b_{1} + b_{2}[/tex])h/2
where b1 and b2 are the lengths of the two parallel bases of the trapezoid.
Given that the area of the trapezoid is 42 square kilometers, we can write:
42 = ([tex]b_{1} + b_{2}[/tex])h/2
We can simplify this equation by multiplying both sides by 2:
84 = ([tex]b_{1} + b_{2}[/tex]) h
Now we need to find the values of b1 and b2. Unfortunately, the problem does not provide us with these values. Without them, we cannot find the exact value of h. However, we can provide an example to show how to solve the problem if we have the values of b1 and b2.
Let's say that b1 = 4 km and b2 = 6 km. We can substitute these values into the equation:
84 = (4 + 6)h
Simplifying:
84 = 10h
Dividing both sides by 10:
h = 8.4 km
So, in this example, the height of the trapezoid is 8.4 kilometers.
In general, to find the height of a trapezoid when given the area, we need to know the values of both bases. Once we have those values, we can use the formula above to solve for the height. If we are not given the values of the bases, we cannot find the exact value of the height.
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a laboratory scale is known to have a standard deviation of 0.005 in repeated weightings. scale readings in repeated weightings are normally distributed, with the mean of all possible measurements equal to the true weight of the specimen. a specimen weighted 4 times on this scale. the average weight is 4.53 grams. suppose that we needed a 95% confidence interval for this specimen using this data. what would the margin of error be?
The margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
To find the margin of error for a 95% confidence interval, we need to determine the standard error of the mean. The standard error of the mean formula can be written as:
SE = σ/√n
where:
SE = standard error of the mean,
σ = the standard deviation of the population
n = the sample size.
the standard deviation of the laboratory = 0.005
sample size = 4.
calculating the standard error of the mean:
SE = 0.005/√4
= 0.0025
Next, we need to find the critical value for a 95% confidence interval. the sample size is small (n < 30), then we need to use a t-distribution.
Critical value = 3.182.
The formula for calculating the margin of error is:
ME = t*SE
where :
ME = margin of error
t = critical value = 3.182.
SE = standard error of the mean = 0.0025
By substuting the values, we get:
ME = t*SE
= 3.182*0.0025
= 0.008 grams
Therefore, the margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
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