According to the question the area of the smaller rectangle is 0.04 times the area of the larger rectangle.
Explain Area?The surface area of an object is the sum of all the shapes that make up its surface. This kind of rectangle's area is calculated by multiplying its length and breadth.
Given,
To solve this problem, we first need to find the length of the larger rectangle, which we can do using the fact that the two rectangles are similar, meaning their corresponding sides are in proportion.
We can set up a proportion using the widths of the two rectangles:
12 cm / 15 cm = 6000 mm / x
where x is the length of the larger rectangle in millimeters.
We could cross-multiply and simplify to find x's value:
12 cm * x = 15 cm * 6000 mm
x = (15 cm * 6000 mm) / 12 cm
x = 7500 mm
So the length of the larger rectangle is 7500 mm.
To determine the scale factor used to enlarge the smaller rectangle, we can divide the corresponding sides of the two rectangles. Since we know the width of the smaller rectangle is 12 cm and the width of the larger rectangle is 6000 mm (which is equivalent to 60 cm), we can set up the proportion:
12 cm / 60 cm = 1/5
So the scale factor used to enlarge the smaller rectangle is 1/5 or 0.2.
Finally, we can find the relationship between the areas of the two rectangles by using the fact that the ratio of the areas of two similar shapes is equal to the square of the scale factor. In this case, the scale factor is 0.2, so:
Area of smaller rectangle / Area of larger rectangle = (0.2)^2
Area of smaller rectangle / Area of larger rectangle = 0.04
Therefore, the area of the smaller rectangle is 0.04 times the area of the larger rectangle.
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The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted. The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules.
The constant of proportionality for the work done when lifting an object is given as follows:
k = 14.78.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted, hence the equation is given as follows:
W = khm.
The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules, the the constant is given as follows:
150k = 2216.8
k = 2216.8/150
k = 14.78.
Missing InformationThe problem asks for the constant of the proportional relationship.
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If all other quantities remain the? same, how does the indicated change affect the width of a confidence? interval?
(a) Increase in the level of confidence
(b) Increase in the sample size
(c) Increase in the population standard deviation
Increase in the level of confidence and increase in the population standard deviation will increase the width of a confidence interval and increasing the sample size will decrease the width of a confidence interval.
(a) Increasing the level of confidence will increase the width of a confidence interval. This is because a higher level of confidence requires a larger margin of error, which in turn increases the width of the interval.
(b) Increasing the sample size will decrease the width of a confidence interval. This is because a larger sample size leads to a more precise estimate of the population parameter, which reduces the amount of uncertainty and therefore narrows the interval.
(c) Increasing the population standard deviation will increase the width of a confidence interval. This is because a larger standard deviation indicates greater variability in the population, which in turn requires a larger margin of error and therefore widens the interval.
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A(-6,3), B(2,5) and C(0,-5). D is the midpoint of BC. State the coordinates of D
Answer:
D(1,0)
Step-by-step explanation:
to find midpoint add x1 and x2 then divide by 2 same with y
the cost c of a bottle of ketchup was $0.22 in 1966. in 2007, the cost was $1.39. assuming the exponential growth model applies: a. find the exponential growth rate to the nearest tenth of a percent and write the equation. b. find the cost of a bottle of ketchup in 2012.
The exponential growth rate is approximately 3.1% per year, and the equation is C(t) = 0.22 * e^(0.031t). The cost of a bottle of ketchup in 2012 would be approximately $1.72.
To find the exponential growth rate, we use the formula:
r = (ln(P2/P1)) / (t2 - t1)
where P1 is the initial value, P2 is the final value, t1 is the initial time, t2 is the final time, and ln denotes the natural logarithm. Substituting the values we get:
r = (ln(1.39/0.22)) / (2007-1966) = 0.0271 or 2.7% (to the nearest tenth of a percent)
The equation for exponential growth is:
C(t) = C0 * e^(rt)
where C0 is the initial cost and C(t) is the cost at time t. Substituting the values we get:
C(t) = 0.22 * e^(0.0271t)
To find the cost of a bottle of ketchup in 2012, we substitute t = 2012 in the above equation:
C(2012) = 0.22 * e^(0.0271 * 2012) = $1.72 (rounded to the nearest cent)
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A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $350 each, and the desktop computers cost $375 each. How many total computers would someone buy if they get 10 notebooks and 19 desktop computers? How many total computers would someone buy if they get � n notebooks and � d desktop computers? Total computers, 10 notebooks and 19 desktop computers: Total computers, � n notebooks and � d desktop computers:
1) The total number of computers they would buy if they get 10 notebooks and 19 desktop computers is: 54 computers
2) The total number of computers they would buy if they get n notebooks and d desktop computers is: (350/n) + (375/n)
How to solve Algebraic expressions?The parameters given are:
Cost of notebook Computers = $350
Cost of Desktop desktop = $375
Thus, if they get 10 notebooks and 19 desktop computers, then:
Total number of computers is:
(350/10) + (375/19) = 35 + 19
= 54 computers
(375/19) was approximated to 19 because we must use a whole number and not a decimal.
If they buy n notebooks and d desktop computers, then total computers will be:
(350/n) + (375/n)
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Consider parallelogram QRST below.
Use the information given in the figure to find mZR, m/RSQ, and x.
3x
66°
53°
S
12
R
m/R =
m/RSQ =
X =
X
The answers of following questions are given as follows:- m∠R = 114°
m∠RSQ = 13°
TQ = SR = 3x
What is parallelogram?Quadrilateral which is made up of 2 pairs of parallel sides. The opposite sides are parallel and equal in length in a parallelogram.
Since QRST is a parallelogram, opposite angles are congruent. Therefore, we have:
m∠R = m∠T = 180° - m∠QTS = 180° - 66° = 114°
Also, since QRST is a parallelogram, opposite sides are congruent. Therefore, we have:
SR = TQ = 3x
Finally, we can use the fact that the sum of the angles in a triangle is 180° to find m∠RSQ:
m∠RSQ = 180° - m∠QST - m∠T = 180° - 53° - 114° = 13°
Note that we cannot solve for x since we have only one equation and two unknowns.
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Find the frequency with the largest amplitude Find the frequency w for which the particular solution to the differential equation dạy dy 2- + dt2 + 2y = eiwt dt has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. W= number (rtol=0.01, atol=1e-08) ?
The frequency with largest amplitude for the particular solution to the differential equation is w = 0.707 (approximately).
To find the frequency with the largest amplitude, we can assume that the particular solution to the given differential equation is of the form:
y(t) = Aeiwt
Taking the first and second derivatives of y(t), we get:
dy/dt = iwtAeiwt
d2y/dt2 = -w2Aeiwt
Substituting these into the differential equation, we get:
-w2Aeiwt + 2Aeiwt = eiwt
Simplifying, we get:
A = 1 / (1 - 2iw2)
The amplitude of y(t) is given by |A|, which is:
|A| = 1 / |1 - 2iw2|
To find the frequency w for which |A| is largest, we need to minimize the modulus of the denominator of A over all frequencies w. We can do this using numerical optimization methods. So, frequency is 0.707.
Therefore, the frequency with the largest amplitude is w = 0.707 (approximately).
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Tele brushes her teeth 1/6 hour each day use properties of operations to find how many weeks della brushes her teeth One week
Answer:
6.17 hours every week
Step-by-step explanation:
Can someone help me solve this please? I’ll give brainliest!
Answer: If it is pythagorean theorem than it is 10
Step-by-step explanation:
8^2+6^2=100
Squareroot of 100 is 10
A town in the shape of a trapezoid
is shown below. If the population of
the town is 28,000 people, find the
number of people per square mile.
14 mi
12 mi
21 mi
16.6 mi
In Linear equation, 121 the number of people per square mile.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, 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. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
A = (12 + 21) * 14 * 1/2
= 33 * 14 * 1/2
= 231 mi²
28000 ÷ 231 = 121 people
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The function f(x)=x^3 is expanded vertically by a factor of 2, translated down 2 unitsWrite the equation of the transformed function.
To vertically expand a function by a factor of 2, we multiply the function by 2. Thus, the transformed function becomes g(x) = 2f(x) = [tex]2(x^3)[/tex].
To translate a function down 2 units, we subtract 2 from the original function. Thus, the transformed function becomes h(x) = g(x) - 2 = 2[tex](x^3)[/tex] - 2.
So the equation of the transformed function is h(x) = 2[tex](x^3)[/tex] - 2.
Graphically, the transformation of the function f(x) = [tex]x^3[/tex] into h(x) = 2[tex](x^3)[/tex] - 2 means that the graph of h(x) is twice as tall as the graph of f(x) and shifted 2 units downwards. The transformation stretches the function vertically without changing its shape, and then moves it downward by the specified amount.
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A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month
the peanuts had not sold well, so, in order to sell 30 pounds of peanuts, the manager decided to mix the 30 pounds of
peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be
mixed with the peanuts to ensure no change in the revenue?
The manager should mix
pounds of cashews with the peanuts.
Therefore, the manager should not mix any cashews with the peanuts to ensure no change in revenue.
What is revenue?Revenue is the total amount of money a business or organization earns from selling goods or services during a specific period. It is calculated by multiplying the price of each unit sold by the total number of units sold. Revenue represents the income generated by a company's normal business activities and is used to pay for expenses, invest in future growth, and distribute profits to shareholders or owners. It is an important metric for measuring the financial health and performance of a business.
by the question.
Let's assume that x pounds of cashews are mixed with the 30 pounds of peanuts.
The total weight of the mixture would then be 30 + x pounds.
To ensure no change in revenue, the amount earned by selling the peanuts and cashews separately should be equal to the amount earned by selling the mixture.
The revenue earned by selling 30 pounds of peanuts is 30 x $1.50 = $45.
If y pounds of cashews are sold separately, the revenue earned would be y x $4.00 = $4y.
The total revenue earned by selling the peanuts and cashews separately would be $45 + $4y.
When the 30 pounds of peanuts and x pounds of cashews are mixed together and sold for $3.50 per pound, the total revenue earned would be (30 + x) x $3.50 = $105 + $3.50x.
Since the revenues from selling the mixture and selling the peanuts and cashews separately are equal, we can set the equations equal to each other and solve for x:
$45 + $4y = $105 + $3.50x
$3.50x - $4y = -$60
x - 4/7y = -60/7
We still have one unknown variable y, so we need another equation to solve for both x and y.
We know that the total weight of the mixture is 30 + x pounds. If we add y pounds of cashews to the mixture, the total weight becomes:
30 + x + y
We can set this equal to the total weight of the peanuts and cashews sold separately:
30 + y
Solving for y:
30 + x + y = 30 + y
x = 0
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which equations would you use the subtraction property of equality to solve? check all that apply. 5 y
answer 5y - 12 = 8.
In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.
Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27
The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
slope= 1/4
Step-by-step explanation:
On the grid draw the graph of y=2x-3 for values of x from -2 to 4
A graph of the equation y = 2x - 3 is shown in the image attached below.
How to graph the given linear equation?In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given linear equation and then take note of the point that lie on it;
y = 2x - 3
In this scenario and exercise, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.
Based on the graph shown in the image attached below, we can reasonably infer and logically deduce that the domain for this linear equation is -2 < x < 4.
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Work out the perimeter of this quarter circle.
Take n to be 3.142 and write down all the digits given by your calculator.
Radius is 7 cm
Answer:
Step-by-step explanation:
The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.
The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).
So, for a quarter circle with a radius of 7 cm, the length of the arc would be:
(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)
The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:
2r = 2 x 7 = 14 cm
Therefore, the perimeter of the quarter circle would be:
10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)
So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.
A pilot of an airplane flying at 12,000 feet sights a water tower. The angle of depression to the base of the tower is 25°. What is the length of the line of sight from the plane to the tower?
Answer: Let's draw a diagram to visualize the situation:
C (water tower)
/|
/ | 25°
12000 / |
/ |
/ |
/ |
/θ | B (plane)
A |
In this diagram, the pilot of the airplane is located at point B and the water tower is located at point C. The angle of depression from the airplane to the base of the tower is 25°. We are asked to find the length of the line of sight from the airplane to the tower, which is the distance AC.
We can use trigonometry to solve for AC. In particular, we can use the tangent function, which relates the opposite side to the adjacent side of a right triangle:
tan(θ) = opposite / adjacent
In this case, the opposite side is BC (the height of the water tower) and the adjacent side is AB (the distance from the airplane to the base of the tower). We can rearrange the equation to solve for AB:
AB = BC / tan(θ)
We know that BC is the height of the water tower, but we don't have that information. However, we can use the fact that the angle of depression is 25° to find BC. The angle of depression is the angle between the horizontal line (which we can assume is the same as the ground level) and the line of sight from the airplane to the base of the tower. Therefore, the angle between the line of sight and the vertical line (which is perpendicular to the ground) is 90° - 25° = 65°. This means that the triangle ABC is a right triangle, with angle θ = 65°.
Now we can use trigonometry again to find BC, using the sine function:
sin(θ) = opposite / hypotenuse
In this case, the opposite side is BC (the height of the water tower) and the hypotenuse is AC (the line of sight from the airplane to the tower). We can rearrange the equation to solve for BC:
BC = sin(θ) x AC
We know that θ = 65° and sin(θ) ≈ 0.9063 (you can use a calculator to find this value). Substituting these values into the equation gives us:
BC = 0.9063 x AC
Now we can substitute this expression for BC into the equation we derived earlier:
AB = BC / tan(θ) = (0.9063 x AC) / tan(65°)
We can simplify this expression by noting that tan(65°) ≈ 2.1445 (you can use a calculator to find this value). Substituting this value gives us:
AB = (0.9063 x AC) / 2.1445
Multiplying both sides by 2.1445 gives us:
2.1445 x AB = 0.9063 x AC
Dividing both sides by 0.9063 gives us:
AC = (2.1445 x AB) / 0.9063
We know that AB is the altitude of the airplane, which is given as 12,000 feet. Substituting this value gives us:
AC = (2.1445 x 12,000) / 0.9063 ≈ 28,406 feet
Therefore, the length of the line of sight from the airplane to the water tower is approximately 28,406 feet.
Step-by-step explanation:
Set up a system of equation and solve for x and y;Michelle finds some dimes and nickels, total 20 coins in her change purse. She counts $1.40 altogether. How many (x) dimes and (y) nickels does she have?
Therefore , the solution of the given problem of equation comes out to be Michelle has 12 nickels and 8 dime in her coin purse.
What is equation?Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. Consider the information provided by y + 7, when combined with generate y + 7, raising instead produces b + 7 within this situation, as opposed to another technique that could divide 12 into two parts.
Here,
Permit x and y to represent the amount of dimes and nickels, respectively.
Since there are 20 pieces in total, the following is true:
=> x + y = 20 ...(1)
=> 10x + 5y = 140 ...(2)
We can now solve for x in terms of y using equation (1):
=> x = 20 - y
When we enter this formula in place of x in equation (2), we obtain:
=> 10(20 - y) + 5y = 140
By enlarging the parentheses and streamlining, we obtain:
=> 200 - 10y + 5y = 140
Further simplification results in:
=> -5y = -60
When we multiply both parts by -5, we get:
=> y = 12
To find x, we can solve equation (1) by substituting this number of y. The result is:
=> x + 12 = 20
=> x = 8
Michelle has 12 nickels and 8 dime in her coin purse.
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Question content area top
Part 1
A company packages colored wax to make homemade candles in cube-shaped containers. The production line needs to plan sizes of the containers based on the associated costs. Write a cube root function that tells the side lengths of the container, x, in inches for a given cost, C
The cube root function that tells the side lengths of the container, x, in inches for a given cost, C is x = (C^(1/3))^3.
We can use the formula for the volume of a cube, which is V = x^3, where x is the side length of the cube. If the cost of producing one cube-shaped container is C dollars, then the cost of producing one unit of volume is C/V = C/x^3 dollars per cubic inch. Solving for x, we get:
x = (C/V)^(1/3)
Substituting V = x^3, we get:
x = (C/x^3)^(1/3)
Simplifying, we get:
x = (C^(1/3)) / (x^(1/3))
Multiplying both sides by x^(1/3), we get:
x^(2/3) = C^(1/3)
Taking the cube of both sides, we finally get:
x = (C^(1/3))^3
Therefore, the cube root function for a given cost, C, is x = (C^(1/3))^3.
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during a 5 day week, there is a 1/2 chance of rain falling on the first day, and every day thereafter there is a 2/3 chance of the same outcome as the previous day (rain or no rain) and 1/3 chance of opposite outcome. what is the probability that there are at least 3 days of rain?
Answer:
Step-by-step explanation:
Depending on the correlations between the days, the answer can be anywhere from 25% (perfect correlation) to 100% (for example, first four days mutually exclusive).
If you assume the days are independent, which may be what you intended to ask but is not actually a good assumption when it comes to the weather, then the probability is 1 - (1-0.25)^5 = 76%
The issue pertains to probability theory, and specifically the calculation of the likelihood of precipitation on a particular day. We need to find the total probability that it rains at least three out of five days, and this would require enumerating and counting all possible outcomes.
Explanation:This is a problem of probability related to weather forecasts, specifically concerned with the chance of rain. The first day has an independent probability of 1/2 (rain or no rain). Thereafter each day's weather depends on the previous day's. If it rained the day before, there's a 2/3 chance it will rain the next day, and 1/3 chance it won't. If it didn't rain, those chances are reversed.
To get the probability that it rains at least three out of five days, we will think about it in terms of the total possible outcomes and the desired outcomes. The problem can be solved by counting the number of ways that we can have 3, 4 or 5 rainy days out of 5 and then multiplying each by the probability of that particular event.
By following these steps, we will arrive at the total probability, which might require a sophisticated understanding of probability theory.
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please help.!!!!!!!!!!!!!!!!!!!!!!!!!!
The expressions are matched as;
5³· 5³ add the exponents
(4x³)⁵. write as the product of the powers
6⁹ ÷ 6⁵. subtract the exponents
(7²)³. multiply the exponents
What are index forms?Index forms are described as those mathematical models that are used to represent numbers too small or large in more convenient forms.
They are represented as variables or numbers that are being raised to an exponent.
Other names for index forms are;
Scientific notationStandard formsThe rules of the index forms are;
Add the exponents when the bases are similar and being mulitiplied.Subtract the exponents when the bases are similar and being divided.From the information given, we have that;
5³· 5³ multiply the exponents
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pq and qr are 2 sides of a regular 12 sided polygon pr is a diagonal of the polygon work out the size of angle prq you must show ur working
The size of the angle PRQ is 300 degrees.
What is congruent?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
In a regular 12-sided polygon, each interior angle has a measure of:
(12 - 2) × 180° / 12 = 150°
Since PR is diagonal, it divides the 12-sided polygon into two congruent triangles. Therefore, the angle PQR is half of the angle PRQ.
Let x be the measure of angle PRQ. Then we have:
x + 150° + 150° = 180° (sum of angles in triangle PQR)
Simplifying the equation, we get:
x = 180° - 150° - 150° = -120°
However, since x is an angle in a triangle, it must be positive. Therefore, we take the supplement of x, which is:
180° - x = 180° - (-120°) = 300°
Hence, the size of the angle PRQ is 300 degrees.
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# 10: The circle graph below displays the percentage of
students who choose various drinks at a cafeteria. If 110
students chose milk, how many students did not choose
soda?
Percentage of Students Who Chose
Various Drinks
35%
14%
229
2996
Mik
Water
-Tea
Soda
After answering the provided question, we can conclude that As a result, equation 315 kids did not select soda.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
According to the circle graph, 14% of pupils preferred soda. As a result, 100% - 14% = 86% of pupils did not select soda.
We know that 35% of students, or 110 kids, chose milk. Hence we may calculate the fraction of pupils that did not drink soda as follows:
35/100 = 110/x
When we solve for x, we get:
x = (110*100)/35 = 314.29
x = 315
As a result, 315 kids did not select soda.
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1
1
About of a fruit punch is pineapple juice. About of the punch is orange juice. Write and solve an equation to find the
10
fraction of the punch that is pineapple juice or orange juice.
Select the correct equation below, and fill in the answer box to complete your choice.
An equation to find the fraction of punch that is either pineapple juice or orange juice is 1/6 + 1/9 = 5/8.
What is a fraction?In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided about the pineapple juice and orange juice, an equation that can be used for determining the fraction of punch that is either pineapple juice or orange juice is as follows;
Fraction = 1/6 + 1/9
Fraction = 3/18 + 2/18
Fraction = 5/18
In this context, we can reasonably infer and logically deduce that exactly 5/18 of the punch is either pineapple juice or orange juice.
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Complete Question:
About 1/6 of a fruit punch is pineapple juice. About 1/9 of the punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice.
This table shows the average cost of a gallon of gas each year for the past 8 years.
Use the data from the table to create a scatter plot.
Whoever answers this with a screenshot of the answer gets 100 pts + brainliest
The scatter plot for the table shows the average cost of a gallon of gas each year for the past 8 years is attached.
What is a scatter plot and why is it important?A scatter plot is a graphical representation of a collection of data points in a two-dimensional coordinate system. It is important because it allows us to visualize the relationship between two variables and identify any patterns or trends in the data, which can help us to make informed decisions and predictions.
Based on the given data, we can deduce that the average cost of gas remained relatively stable between years 1 to 2, and then increased from years 2 to 5. However, there was a sharp decrease in the average cost of gas in year 6, and it remained constant in years 7 and 8.
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Items 15–16. Refer to the diagram shown.
15. What is m∠EFB?
16. What is AC?
The measure of m∠EFB is 68 degrees and the length of AC is 32 units
Calculating the measure of m∠EFB?From the question, we have the following parameters that can be used in our computation:
The triangle
The sum of angles in a triangle is 180
So, we have
∠EFB = 180 - 90 - 22
∠EFB = 68
Calculating the length of ACBy the congruent theorem, we have
AC = 2 *(6 + 10)
When evaluated, we have
AC = 32
Hence, the length of AC is 32 units
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A supplier must create metal rods that are 18. 1 inches long to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are correct length or an incorrect length?
No, a binomial experiment cannot be used to determine the probability that the rods are the correct length or an incorrect length.
A binomial experiment has the following characteristics:
1. It consists of a fixed number of trials.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent.
4. The probability of success is constant for each trial.
In the case of metal rods, the length can vary continuously, so it is not a binary outcome. Therefore, a binomial experiment cannot be used to determine the probability of the rods being the correct length or an incorrect length. Instead, a probability distribution such as a normal distribution could be used to model the distribution of rod lengths and calculate the probability of a rod being the correct length.
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If p is inversely proportional to the square of q, and p is 9 when q is 5, determine p
when q is equal to 3.
Answer:
p = 125
Step-by-step explanation:
Given p is inversely proportional to q³ then the equation relating them is
p = [tex]\frac{k}{q^3}[/tex] ← k is the constant of proportion
To find k use the condition p = 9 when q is 5, then
9 = [tex]\frac{k}{5^3}[/tex] = [tex]\frac{k}{125}[/tex] ( multiply both sides by 125 )
k = 1125
p = [tex]\frac{1125}{q^3}[/tex] ← equation of proportion
When q = 3, then
p = [tex]\frac{1125}{3^3}[/tex] = [tex]\frac{1125}{9}[/tex] = 125
Mass ( mg)
0 < x < 14
14 ≤ x ≤ 18
18 < x < 20
20 ≤ x ≤ 25
25 ≤ x ≤ 40
Frequency
21
28
17
22
33
The information in this table is being
drawn on a histogram.
What is the smallest integer value that
frequency density axis needs to reach,
in order to plot all of the data?
Answer:
To find the smallest integer value that the frequency density axis needs to reach, we need to first calculate the frequency density for each class interval. The frequency density is calculated by dividing the frequency of each interval by its corresponding class width.
The class widths are:
14 - 0 = 14
18 - 14 = 4
20 - 18 = 2
25 - 20 = 5
40 - 25 = 15
The frequency densities are:
21 / 14 = 1.5
28 / 4 = 7
17 / 2 = 8.5
22 / 5 = 4.4
33 / 15 = 2.2
To plot all of the data, we need to find the maximum frequency density and round it up to the nearest integer. In this case, the maximum frequency density is 8.5, so we need to round it up to 9. Therefore, the smallest integer value that the frequency density axis needs to reach is 9.
For the formula = − , what is the value of x when y = 3 and z = 1?
Answer:
The formula is: x = -y + z
We are given that y = 3 and z = 1. Substituting these values in the formula, we get:
x = -y + z
x = -(3) + 1
x = -3 + 1
x = -2
Therefore, when y = 3 and z = 1, the value of x is -2.
Step-by-step explanation:
The given formula is: x = -y + z
We are given that y = 3 and z = 1.
Substitute the values of y and z into the formula.
x = -y + z
x = -(3) + 1
x = -3 + 1
Simplify the expression.
x = -2
Therefore, when y = 3 and z = 1, the value of x is -2.