The equation to model the situation given in the question is (x+3)(x+6) = 148.
Let's assume that the original length and width of the square flower garden were "x". When Harrison expanded the garden, the new length became "x+3" and the new width became "x+6".
The area of a rectangle is given by the formula A = L × W, where A is the area, L is the length, and W is the width. Therefore, the area of the expanded rectangular flower garden is:
A = (x+3)(x+6)
We know that the area of the expanded rectangular flower garden is 148 square feet. So we can set up an equation:
(x+3)(x+6) = 148
{When we solve this equation using the quadratic formula we get x values:
x ≈ 8.2 and x ≈ -17.2 but we know x is the side of the garden so it cannot be negative, therefore, x = 8.2 unit}
This is the equation that models the situation described in the problem.
Therefore, the equation to model this situation is (x+3)(x+6) = 148.
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Which are the coordinates of the vertex of F(x)=x^2-2x-3
Therefore , the solution of the given problem of coordinates comes out to be (1, -4) are the coordinates of the vertex of the function F(x) = x² - 2x - 3.
What does coordinate plane actually mean?When used in connection with particular other algebraic components on this place, such as Euclidean space, a parameter can reliably detect placement using a number of qualities or coordinates. Coordinates, which appear as collections of numbers when traversing in reflected space, can be utilised to identify particular places or things. Using the two y & x measurements, one can find something over both sides.
Here,
The formula x = -b/2a can be used to determine the vertex of a quadratic function with the form
F(x) = ax² + bx + c. A and B are equal in the given function
=> F(x) = x² - 2x - 3.
With these values entered into the formula, we obtain:
=> x = -b/2a x = -(-2)/(2*1)
=> x = 2/2 x = 1
Consequently, the vertex's x-coordinate is 1.
Now, we can enter the value of x into the following function, F(x), to determine the vertex's y-coordinate:
=> F(1) = 1² - 2(1) - 3
=> F(1) = 1 - 2 - 3
=> F(1) = -4
Therefore, the vertex's y-coordinate is -4.
As a result, (1, -4) are the coordinates of the vertex of the function
=> F(x) = x² - 2x - 3.
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Expand:3(×+2y)+4(2×-y)
Answer:
11x + 2y
Step-by-step explanation:
Expand the equation:
3(x + 2y) + 4(2x - y)
Multiply 3, by x & by 2y:
3(x + 2y) ===> 3x + 6y
Then, multiply 4, by 2x & by -y:
4(2x - y) ===> 8x - 4y
Finally, you add/subtract the two results from the parenthesis:
3x + 6y + 8x - 4y ===> 11x + 2y
Your final expanded result will be: 11x + 2y.
an urn contains 14 balls, seven of which are red. the selection of a red ball is desired and is therefore considered to be a success. if a person draws three balls from the urn, what is the probability of two successes?
We get a probability of 3/8 or 0.375.
How to find the probability of two successes?To find the probability of two successes (i.e., drawing two red balls) out of three draws from an urn containing 14 balls (7 of which are red), we can use the binomial probability formula:
[tex]P(X = 2) = (n\ choose\ x) * p^x * (1-p)^{(n-x)[/tex]
where
n is the total number of draws (3 in this case),
x is the number of successes (2 in this case),
p is the probability of a success on any given draw (7/14 or 1/2 in this case),
and (n choose x) is the number of ways to choose x items out of n items.
Plugging in the values, we get:
[tex]P(X = 2) = (3\ choose\ 2) * (1/2)^2 * (1/2)^{(3-2)} = 3/8[/tex]
Therefore, the probability of getting two red balls out of three draws is 3/8 or 0.375.
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For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.
What is equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal is usually to solve for the value of the variable that makes the equation true.
In the given question,
The equations in which 8 is a solution are:
x - 4 = 8 (which simplifies to x = 12)
2x = 16 (which simplifies to x = 8)
x/2 = 16 (which simplifies to x = 32)
x/8 = 1 (which simplifies to x = 8)
Therefore, the correct answers are:
x - 4 = 8
2x = 16
x/2 = 16
x/8 = 1.
The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.
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x² - 16x + 64 = 0 is the equation whose solution is 8.
How to check for which equations is 8 a solution?
To check if 8 is a solution for each equation, we substitute x = 8 into each equation and see if the equation is true or not.
x + 6 = 8 + 6 = 14
and
2x + 2 = 2(8) + 2 = 18, which is not equal to the value of (x+6).
Therefore, 8 is not a solution to this equation.
4x - 4 = 4(8) - 4 = 28,
and
10 - 2x = 10 - 2(8) = -6, which is not equal to 28.
Therefore, 8 is not a solution to this equation.
2x - 4 = 2×8-4 = 12
and
3x-24 = 3×8-24 = 0 which is not equal to 12. Therefore, 8 is not a solution to this equation.
Now,
x² - 16x + 64 = 0 (which can be factored as (x-8)² = 0)
x = 8 (which is always true)
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Correct question is "For which equations is 8 a solution? Select the correct answers from the following,
1) x + 6 = 2 x + 2
2) 10 - 2x = 4 x - 4
3) 2 x-4 = 3 x - 24
4) x² - 16x + 64 = 0
an analysis of future events performed by the probability of those events and the potential outcomes is called
An analysis of future events performed by the probability of those events and the potential outcomes is called probabilistic analysis.
Probabilistic analysis involves using mathematical models and statistical techniques to estimate the likelihood of different outcomes, given a set of assumptions and inputs. It is commonly used in risk management, financial analysis, and project management to evaluate the potential impact of different scenarios and make informed decisions. By quantifying the probabilities of different outcomes, probabilistic analysis helps decision-makers identify the best course of action and manage uncertainty and risk.
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2. A small box in the shape of a cube for packaging has a volume of 216 cubic inches.
(a) For a medium box, the length, width, and height are all tripled. What is the ratio of the sides, area of the bases, and volumes of the boxes? Show your work.
(b) What is the volume of a medium box? Show your work.
(b) The volume of the medium box is 5832 cubic inches.
What is ratio?In mathematics, a ratio is a comparison of two quantities or numbers. It is expressed as the quotient of one number divided by another, and is often written as "a:b" or "a/b". Ratios are used to compare the sizes of two or more quantities, and they can be used to solve problems involving proportions and percentages.
For example, if a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, this means that for every 2 cups of flour used, 1 cup of sugar should be used as well. Similarly, if a company has a debt-to-equity ratio of 2:1, this means that for every $2 of debt, the company has $1 of equity.
(a) Let x be the length of the sides of the original box. Then the volume of the box is x^3 = 216, so x = 6.
When the length, width, and height are all tripled, the new side length of the medium box is 3x = 18.
The ratio of the sides of the medium box to the original box is 18:6, or simplified, 3:1.
The area of the base of the original box is. [tex]x^2 = 6^2 = 36[/tex]square inches.
The area of the base of the medium box is. [tex](3x)^2 = 18^2 = 324[/tex] square inches.
The ratio of the 5832 of the bases of the medium box to the original box is 324:36, or simplified, 9:1.
The volume of the medium box is. [tex](3x)^3 = 18^3 = 5832[/tex]cubic inches.
The ratio of the volumes of the medium box to the original box is 5832:216, or simplified, 27:1.
(b) The volume of the medium box is 5832 cubic inches.
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In mathematics What is 35% of 10.l
Answer:
3.535
Step-by-step explanation:
35% is the same as .35
therefore, you can multiply 10.1 by .35 to get 3.535
Alfonso said that the perimeter of this
triangle is 66 centimeters. What was his error?
Required error is the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.
What is perimeter of a triangle?
The perimeter of a triangle is the total length of the three sides of the triangle. It is a fundamental geometric concept that is important in many applications, including architecture, engineering, and construction.
To calculate the perimeter of a triangle, you simply add up the lengths of its three sides. This is expressed by the following formula,
Perimeter = side a + side b + side c
where "a," "b," and "c" are the lengths of the three sides of the triangle.
Here Alfonso's error is that he added the three side lengths incorrectly. The correct way to find the perimeter of a triangle is to add up all three sides.
In this case, the three side lengths are 22 cm, 11 cm, and 27 cm. Adding them up, we get,
22 cm + 11 cm + 27 cm = 60 cm
Therefore, the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.
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Correct question is " There is a triangle whose sides are 22 cm, 11 cm and 27 cm.
Alfonso said that the perimeter of this
triangle is 66 centimeters. What was his error?"
in an analysis testing differences between an experimental and a control group on the dependent variable, a p-value of 0.07 means there is a
A control group on the dependent variable, P-value is higher than the usual cutoff of 0.05 for rejecting the null hypothesis that there is no difference between the groups, this is frequently regarded as evidence that the difference between the groups is not statistically significant.
In an analysis testing difference between an experimental and a control group on the dependent variable, a p-value of 0.07 means that there is a 7% chance of obtaining a difference as large or larger than the observed difference between the two groups, assuming that there is no true difference between the groups in the population.
Interpreted as evidence that the difference between the groups is not statistically significant, since the p-value is greater than the conventional threshold of 0.05 for rejecting the null hypothesis of no difference between the groups.
Statistical significance does not necessarily imply practical significance, and there may still be a meaningful difference between the groups that is not detected by the statistical test.
Additionally, the interpretation of a p-value depends on the study design, sample size, and other factors, and should be considered in conjunction with other information about the study.
True difference between the groups in the population, a p-value of 0.07 indicates that there is a 7% chance of finding a difference as large or larger than the observed difference between the two groups in an analysis testing the difference between an experimental and a control group on the dependent variable.
P-value is higher than the usual cutoff of 0.05 for rejecting the null hypothesis that there is no difference between the groups, this is frequently regarded as evidence that the difference between the groups is not statistically significant.
It's crucial to remember that statistical significance does not always imply practical relevance.
There could still be a significant difference between the groups that is not shown by statistical analysis.
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in a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was
We can be 90% confident that the true mean additional tax owed in the population of audited estate tax returns falls between $3044.92 and $3875.08.
To construct a 90% confidence interval for the mean additional tax owed in a random sample of 100 audited estate tax returns, we need to use a t-distribution because the population standard deviation is not known. The formula for the confidence interval is:
CI = x' ± t*(s/√n)
Where x' is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with (n-1) degrees of freedom and a 90% confidence level.
The t-value for a 90% confidence level with 99 degrees of freedom (n-1=100-1=99) is 1.660.
Substituting the values given in the problem, we get:
CI = 3460 ± 1.660*(2520/√100)
CI = 3460 ± 415.08
CI = (3044.92, 3875.08)
This means that if we were to repeat this sampling process many times, 90% of the time the true mean would be captured by the confidence interval.
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Complete question is:
In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3460 with a standard deviation of $2520
Construct and interpret a 90% confidence interval for the mean additional.
Which of the following choices describes the function?
an exponential function that is decreasing.
a quadratic function that is increasing then decreasing.
a quadratic function that is decreasing then increasing.
None of these choices are correct.
Answer: The function that is an exponential function that is decreasing is described as:
an exponential function that is decreasing.
A quadratic function that is increasing then decreasing would have a U-shaped graph, and a quadratic function that is decreasing then increasing would have an inverted U-shaped graph. However, neither of these options describes an exponential function that is decreasing.
Therefore, the correct choice is: an exponential function that is decreasing.
Step-by-step explanation:
the scores of the top quartile of students in a math class were 95, 86, 87, 91, 94, and 87 on the last test. what is the average score of these top students?
90 is the average score of these top students.
What is the average in mathematics?
Mean is defined as the average equal to the ratio of the total number of values in a particular set to the total number of values in the set.
The average in mathematics is the average of a data set obtained by adding all the numbers and dividing the sum of the numbers by the number of numbers. For example, using the following dataset:
8, 9, 5, 6, 7, 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7, so the average is 7.
the average score of these top students = 95 + 86 + 87 + 91 + 94 + 87/6
= 540/6 = 90
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help. the picture is attached below, when i search it up it’s trying to solve it.
The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 when x = 4 is 0
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = 0
What is a mathematical expression?A mathematical expression comprises, variables, and or numbers, which could include indices, joined together by mathematical operators.
The value of the expression -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 can be found by plugging in x = 4 into the expression as follows;
Where; x = 4
-0.4·(3·x - 2) + (2·x + 4)/3 = -0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = -0.4 × (12 - 2) + (8 + 4)/3
-0.4 × (12 - 2) + (8 + 4)/3 = -0.4 × 10 + 12/3 = -4 + 4 = 0
Therefore;
The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 is zero
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9. Find the sum of the expressions
(-4.25x + 9) and (8x - 2.2). Select all
of the statements that are true.
The coefficient of x is 3.75.
The coefficient of x is 4.75.
The constant is 11.2.
The constant is 6.8.
The sum is 3.75x + 6.8.
The sum is 4.75x + 11.2.
The sum of the expression is 3.5x+6.8.
Given that are two expressions, we need to find the sum of the expressions,
The expression is a mathematical statement which is constructed by putting arithmetical operations, variables and numbers together.
So, finding the sum.
(-4.25x + 9) and (8x - 2.2)
Putting the sign of addition,
= (-4.25x + 9) + (8x - 2.2)
Opening the brackets,
= -4.5x + 9 + 8x - 2.2
Combining the like terms.
= 8x-4.5x + 9-2.2
Operating the like terms,
= 3.5x+6.8
Hence, the sum of the expression is 3.5x+6.8.
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A parallelogram has the following vertices, A(2,3), B(2,8), C(7,8), and D(7,3). What type of parallelogram is this?
This parallelogram is a rhombus.
Using the characteristics of parallelograms, we can establish what kind of parallelogram this is. In addition to having opposite sides that are parallel and congruent, parallelograms also have opposite angles that are congruent.
The distance formula can be used to get the length of each side of the parallelogram first.
A = 5, B = 5, C = 5, D = 5, etc.
As all the sides are identical in length, we know that this object is a rhombus.
The slopes of the lines comprising the opposing sides of the parallelogram can also be determined in a different way:
AB's slope is (8-3)/(2-2) = undefined.
CD's slope is (3-8)/(7-7) = undefined.
BC has a slope of 0 (8-8)/(7-2)
AD slope is equal to 0 (3-3)/(7-2)
The slopes of opposing sides can be seen to be both undefinable or zero, suggesting that they are parallel. Moreover, this is a rhombus because the opposing sides are the same length.
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Akira and Desmond order eggs for $4. 45, pancakes for $4. 05, and 2 mugs of cocoa for $1. 10 each. The tax is $0. 85. How much change should they get from $15. 00?
Answer:
$3.45
Step-by-step explanation:
A small juice company spends $1200 per day on business expenses plus $1. 10 per bottle of juice them make. They charge $2. 50 for each bottle of juice they produce. How many bottles of juice must the company sell in a day for the company to break-even?
The company must produce and sell at least 857 bottles of juice in a day to break-even, given the given expenses and selling price per bottle.
Let's denote the number of bottles of juice sold in a day as "x".
The total cost of production and business expenses :
Total cost = Business expenses + (Cost per bottle of juice) x (Number of bottles produced and sold)
Total cost = $1200 + $1.10x
The revenue generated from selling "x" bottles :
Revenue = (Selling price per bottle of juice) x (Number of bottles produced and sold)
Revenue = $2.50x
The company will break-even when revenue equals total cost, so we can set two expressions equal to each:
[tex]\\$2.50x = $1200 + $1.10x\\$2.50x - $1.10x = $1200\\$1.40x = $1200\\x = $1200 / $1.40\\[/tex]
x ≈ 857
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Mrs. Hanson is filling containers in her bakery with flour. How much flour will fit into two of the containers?
The flour will fit into two of the container is 144 inches.
What is the volume of cuboids?
A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
Here, we have
Given: Mrs. Hanson is filling containers in her bakery with flour.
we have to find how much flour will fit into two of the containers.
Volume of cuboid = length × breadth × height
Length = 6 inches
Breadth = 3 inches
Height = 8 inches
The flour will fit into two of the containers = length × breadth × height
= 6 ×3 × 8
= 144 inches
Hence, The flour will fit into two of the container 144 inches.
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What is the solution to 9/x+81 > 45?
Answer:
I dont know the answer to be honest..
JUST KIDDING.. ill answer this step by step lol
To solve the inequality 9/x + 81 > 45, we can follow these steps:
Step 1: Subtract 81 from both sides of the inequality to isolate the fraction on the left-hand side:
9/x + 81 - 81 > 45 - 81
9/x > -36
Step 2: Take the reciprocal of both sides of the inequality to eliminate the fraction:
1 / (9/x) < 1 / (-36)
x/9 < -1/36
Step 3: Multiply both sides of the inequality by 9 to get rid of the fraction in the numerator:
9 * (x/9) < 9 * (-1/36)
x < -1/4
So, the solution to the inequality 9/x + 81 > 45 is x < -1/4. This means that x must be less than -1/4 for the inequality to be true.
suppose the monetary policy curve is given by r = 0 0.5π , and the is curve is e y = 19 − r. find the expression for the aggregate demand curve
e y = e y is the expression for the aggregate demand curve the level of result is defined exclusively by the equilibrium state in the goods market and is autonomous of the monetary policy curve.
Monetary policy curve = r = 0 0.5π
IS curve e y = 19 − r
To calculate the aggregate demand curve, we need to converge the IS curve and the monetary policy curve. By substituting the monetary policy curve into the IS curve:
e y = 19 − r
e y = 19 − 0.5π
π = 38 - 2e y
Substituting this expression for π into the monetary policy curve:
r = 0.5π = 19 - e y
e y = 19 - r
e y = 19 - (19 - e y)
e y = e y
The aggregate demand curve is simply equated as:
e y = e y
Therefore we can conclude the expression for the aggregate demand curve as e y = e y.
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To find the expression for the aggregate demand curve, we will first solve for the equilibrium interest rate (r) and output level (y) using the given monetary policy curve and IS curve.
Step 1: Express r from the monetary policy curve
r = 0.5π
Step 2: Substitute the value of r in the IS curve
y = 19 - r
y = 19 - 0.5π
Step 3: Rearrange the equation to express the aggregate demand curve
y = 19 - 0.5π
The aggregate demand curve is represented by the equation y = 19 - 0.5π.
EXPLAINATION
To find the expression for the aggregate demand curve, we can use the equation:
Aggregate Demand = C + I + G + NX
Where:
C = Consumption
I = Investment
G = Government Spending
NX = Net Exports
We can express the Consumption and Investment components as functions of output (Y) and the interest rate (r):
C = a + bY - c(r)
I = d - e(r)
Where:
a, b, c, d, and e are constants.
Now, we can substitute the expressions for Consumption and Investment into the Aggregate Demand equation:
Aggregate Demand = a + bY - c(r) + d - e(r) + G + NX
Next, we can use the IS-LM model to solve for output (Y) in terms of the interest rate (r). From the given IS curve, we have:
Y = 19 - r
Now, we can substitute this expression into the Aggregate Demand equation:
Aggregate Demand = a + b(19-r) - c(r) + d - e(r) + G + NX
Simplifying this expression, we get:
Aggregate Demand = (a + 19b + d + G + NX) - (b + c + e)r
Thus, the expression for the Aggregate Demand curve is:
AD = (a + 19b + d + G + NX) - (b + c + e)r
Where: a, b, c, d, e, G, and NX are constants.
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KKIC
8. The area of a circle can be found using the formula A = (pi)r^2. Find the area of the circle with a radius of 3xy^3.
The area of circle is with radius 3xy³ is 9πx²y⁶.
What is area?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2.
Define radius of a circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius. Circumference of circle = 2π (Radius)
area of circle=πr²
=π×(3xy³)²
=9πx²y⁶
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The sum of first two angles is 120 degree and that of last two angles is 130 degree. Find all the angles in degrees.
The four angles are: A = 110 degrees, B = 10 degrees, C = 120 degrees, D = 120 degrees
What are angles ?Angles are geometric shapes created when two lines, rays, or line segments cross at a single point.
The two lines or line segments that make up the angle are referred to as the sides or arms of the angle, and this shared point is known as the vertex of the angle.
The amount of rotation required to shift one side to overlap with the opposite side determines the magnitude of an angle.
Angles are commonly expressed in degrees, with 360 degrees representing a full rotation around a point.
Acute angles (less than 90 degrees),
right angles (exactly 90 degrees),
obtuse angles (more than 90 degrees but less than 180 degrees), and straight angles (exactly 180 degrees) are some frequent forms of angles.
What are degrees ?
Angles are measured in degrees, a unit of measurement. 1/360th of a full revolution around a point is equivalent to one degree (1°).
Two perpendicular lines can be used to create a right angle, which has a 90 degree angle.
A straight angle, created by a straight line, has a degree value of 180.
Angles, rotations, and slopes are frequently measured in degrees in the fields of mathematics, physics, engineering, and several others.
The freezing point of water is 0 degrees Celsius (or 32 degrees Fahrenheit), whereas the boiling point is 100 degrees Celsius. In daily life, degrees are frequently used to express temperatures. (or 212 degrees Fahrenheit).
According to question :-
Let the four angles be A, B, C, and D. We know that:
A + B + C + D = 360 (the sum of all angles in a quadrilateral is 360 degrees)
We also know that:
A + B = 120 (the sum of the first two angles is 120 degrees)
C + D = 130 (the sum of the last two angles is 130 degrees)
We can use these equations to solve for the individual angles. First, we can rearrange the equation A + B = 120 to get:
A = 120 - B
Similarly, we can rearrange the equation C + D = 130 to get:
D = 130 - C
Substituting these expressions for A and D in terms of B and C into the equation A + B + C + D = 360, we get:
(120 - B) + B + C + (130 - C) = 360
Simplifying, we get:
250 - B + C = 360
Subtracting 250 from both sides, we get:
C - B = 110
Now we have two equations with two unknowns:
C + B = 130 (from the equation C + D = 130)
C - B = 110
We can add these equations to eliminate B and get:
2C = 240
Dividing by 2, we get:
C = 120
Substituting this value for C into either of the equations above, we get:
B = 10
Now we can use the equation A + B = 120 to find A:
A + 10 = 120
A = 110
Finally, we can use the equation A + B + C + D = 360 to find D:
110 + 10 + 120 + D = 360
D = 120
Therefore, the four angles are:
A = 110 degrees
B = 10 degrees
C = 120 degrees
D = 120 degrees
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Please help, I’ve given up on trigonometry
Answer:
6.02
Step-by-step explanation:
sin 37=x/10
x/10=sin 37
x=10(sin 37)
x=6.02
Write an expression in terms of m and p that represents tan(R).
Answer: tan(R) = m/p
Step-by-step explanation: In the right triangle shown in the diagram, we know that the tangent of angle R is equal to the length of the opposite side (m) divided by the length of the adjacent side (p).
Therefore, an expression in terms of m and p that represents tan(R) would be tan(R) = m/p
9) all of the following are required of a binomial distribution except: a) each trial has exactly two outcomes. b) the number of trials is fixed. c) all trials have the same probability of success. d) there must be at least 30 trials.
d) there must be at least 30 trials.
1. In a survey, it was found that the ratio of the people who liked modern songs and folk songs is 8:9, out of which 50 people like both songs, 40 liked folk songs only and 80 liked none of the songs.i) Represent the above information in a Venn - diagram. ii) How many people like folk song? iii) How many people like Modern song? iv) Find the number of people in the survey.
According to the information, the number of people who likes folk song is 90, and the number of people who likes modern song 80. So, the total number of people in the survey is 250.
How to calculate how many people like folk song?Let the number of people who like modern songs be 8x, and the number of people who like folk songs be 9x.
From the given information, we know that:
50 people like both modern and folk songs
40 people like only folk songs
The total number of people who like at least one type of song is (8 + 9)x - 50 = 17x - 50
80 people like none of the songs
Therefore, we can write the following equation:
(8x + 9x) - 50 - 40 + 80 = 17x
Simplifying this equation, we get:
17x - 10 = 17x
Thus, x = 10.
So, the number of people who like folk songs is 9x = 9(10) = 90.
How to calculate how many people like modern song?Similarly, the number of people who like modern songs is 8x = 8(10) = 80.
How to calculate the number of people in the survey?The total number of people in the survey is the sum of the number of people who like modern songs, the number of people who like folk songs, and the number of people who like none of the songs.
So, the total number of people in the survey is:
80 + 90 + 80 = 250.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
The correct answer is: Fast Chicken, because it has a smaller median.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.
Based on the information provided, the drive-thru restaurant with less wait time is Fast Chicken, as it has a smaller median wait time of 12.5 minutes compared to the median wait time of 12 minutes for Super Fast Food. The mean wait time is not given, and even if it were, the median is a better measure of central tendency to compare in this scenario, as the box plots suggest some potential outliers.
Therefore, the correct answer is: Fast Chicken, because it has a smaller median.
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‼️WILL MARK BRAINLIEST‼️
Part A:
The correct answers are:
The data set is numerical data
The data in this set can be quantified in the form of numbers.
The set has an outlier
An outlier is an extreme value that differs from the rest of the set. The outlier in this set is 5.
A box plot is an appropriate data display for this data
A box plot is great for showing distribution of data. A circle chart would not be good for this set because circle charts are better for part-to-whole data.
Part B:
A: Students in his class have between 5 to 950 photos stored on their cell phones.
The text at the top explains that this data was gathered from students in Shamar's class, and the data ranges from 5 to 950.
Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.
A line has points A, C, B.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the
property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.
what is the effect of the interaction of the number of pages and cover type on cost? (round your answers to four decimal places.)
To determine the effect of the interaction of the number of pages and cover type on cost, a statistical analysis would need to be performed using data on the number of pages, cover type, and cost. The analysis would likely involve running a regression model that includes both the number of pages and cover type as predictor variables, as well as an interaction term between the two.
To answer your question, the effect of the interaction between the number of pages and cover type on the cost can be determined through a step-by-step process:
1. Identify the base cost of each cover type (e.g., hardcover, paperback, etc.).
2. Determine the cost per additional page for each cover type.
3. Calculate the cost for a specific number of pages and cover type by adding the base cost and the cost of additional pages.
For example:
- Base cost for hardcover: $5.00
- Base cost for paperback: $3.00
- Cost per additional page for hardcover: $0.10
- Cost per additional page for paperback: $0.05
Now, let's say you want to find the cost of a 100-page hardcover book:
1. Start with the base cost of a hardcover: $5.00
2. Multiply the number of pages (100) by the cost per additional page for hardcover ($0.10): 100 * $0.10 = $10.00
3. Add the base cost and the cost of additional pages: $5.00 + $10.00 = $15.00
So, the cost of a 100-page hardcover book is $15.00.
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