To find the area of the trapezoid we need to find the height of the trapezoid.
TrapezoidA trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Area of TrapezoidThe area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.
\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of the\ parallel\ Sides)
The area of the trapezoid is 54 units².
Given to us :ABCD is a trapezoid
AD=10, BC = 8,
CK is the altitude altitude
Area of ∆ACD = 30
Area of ∆ACD,In ∆ACD,
\begin{gathered}\rm { Area\ \triangle ACD = \dfrac{1}{2}\times base\times height\\\\\ \end{gathered}
Substituting the values,
30 = 1/2 * AD × CK
30 = 1/2 * 10 × CK
(30 * 2)/10 = CK
CK = 6 units
Area of Trapezoid ABCD\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of\ the\ parallell Sides)
Area ABCD = \( \frac{1}{2} \times ck \times (ad + bc)\)
Area ABCD = \( \frac{1}{2} \times 6 \times (10 + 8)\)
Area ABCD = \( \frac{1}{2} \times 6 \times (18)\)
Area ABCD = 54 units²
Hence, the area of the trapezoid is 54 units².
what is the process of displaying large quantities of data in a meaningful way called?
The process of displaying the large quantities of data in a meaningful way is called Data Visualization .
The Data Visulalization involves presenting data in a graphical or pictorial format to help people understand and analyze the data more easily.
The goal of data visualization is to make complex data sets more accessible, understandable, and actionable by presenting them in a clear and visually appealing way.
The Common types of data visualization include bar charts, line graphs, scatter plots, heat maps, and infographics, among others.
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Help! My teacher never taught me this and gave it to me for what ever reason. Questions 6-11. (Middle school)
Answer:
6. 12cm
7. 11.2 cm
8. 92 degrees
9. 53 degrees
10. 37.5 cm
11. $ 693.12
Step-by-step explanation:
For questions 6-9 the triangle is congurent which means both their angles will be equal.
For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5
So for Q. 6 we can multiply side PQ by 1.5.
For Q.7 divide CA by 1.5.
For Q. 10 we can do cross multiplication:
5/4 = x/30
= 150= 4x
= 37.5=x
For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)
So the shorter side is 30.4 cm.
Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.
Then to figure out the money we multiply again and we get $693.12.
The perimeter of a square is 80 minus 64 y units. Which expression can be used to show the side length of one side of the square?
The perimeter of a square is 80 minus 64 y units. Which expression can be used to show the side length of one side of the square?
Answer · 1 vote
Perimeter of the square80-64yA square has 4 sides, so divide the perimeter by 4:(80-64y) / 480 divided by 4 is 2064y divided by 4 is 16yOne side of the ..
Answer:
Its C
Step-by-step explanation:
took the test
Points A, R and G are points of tangency. Find the perimeter of ∆NET below.
Answer:
\(\small\mathfrak\red{here \: is \: your \: solution..} \\ \\ we \: know \: that \: tangent \\ from \: a \: same point \: are \: equal \\ \\ tr = 9 | an = 7 | eg = 5 \\ \\ tr = ta | an = gn | eg = re \\ \\ ta = 9 | gn =7 | re = 5 \\ \\ hence \: perimeter \: = 2(9 + 7 + 5) \\ \\ perimeter = 42 \: \\ \\ \huge\mathfrak\purple{hope \: it \: helps...}\)
Steven pay 10% tax on a purchase of $40 to what's the dollar amount of the tax and total dollar amount Steven paid on the number line
Answer:
$4, and $44
Step-by-step explanation:
10% of 40 = $4
40+4=$44
just mark 4 , 44 on number line
Answer: $44.00
Step-by-step explanation: The dollar amount of the taxes are $4.00 and the total amount he paid was$44.00
You are at the grocery store choosing between bananas and walnuts. You know that the price of walnuts is $2 per pound and the price of bananas is $1 per pound, and your satisfaction from consuming is given by the following utility function: U=W .5
B .5
a. What is your marginal rate of substitution of walnuts for bananas? b. Using the Lagrangian approach, find your optimal consumption bundle. What is your total utility at this level? c. If the price of bananas doubles to $2 per pound, how much income must you have to maintain the same level of utility?
a. MRS = √(W/B)
b. Optimal bundle and total utility.
c. Adjusted income for constant utility.
a. The marginal rate of substitution (MRS) of walnuts for bananas is the rate at which you are willing to give up walnuts in exchange for one additional pound of bananas while keeping the utility constant. In this case, the MRS is equal to the ratio of the marginal utility of walnuts to the marginal utility of bananas. Since the utility function is U = √(W * B), the MRS can be calculated as MRS = √(W/B).
b. Using the Lagrangian approach, we can set up the following optimization problem: maximize U = √(W * B) subject to the constraint 2W + B = I, where W represents the pounds of walnuts, B represents the pounds of bananas, and I represents income. By solving the Lagrangian equation and the constraint, we can find the optimal consumption bundle and income level.
c. If the price of bananas doubles to $2 per pound, we need to determine the income required to maintain the same level of utility. With the new price, the constraint becomes 2W + 2B = I. By solving the Lagrangian equation again and substituting the new constraint, we can find the income level required to maintain the same level of utility.
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What value of x is in the solution set of the inequality 9 2x 1 9x 18?.
The value of x in the solution set of the inequality 9(2x+1) < 9x-18 is
x <-3.
Given inequality:
9(2x+1) < 9x-18
simplifying
9*2x + 9*1 < 9x - 18
18*x + 9 < 9x - 18
18x + 9 < 9x - 18
combining the like terms
18x - 9x + 9 < -18
9x + 9 < -18
combining the constants
9x < -18-9
9x < -27
divide by 9 on both sides
9x/9 < -27/9
x < -27/9
x < -3
Therefore the value of x in the solution set of the inequality 9(2x+1) < 9x-18 is x <-3.
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7th garde math question pt 2 pls answer a s a p i ready grade f level
Answer:
45
Step-by-step explanation:
3² · (12-2) ÷ 2
= 9 · (10) ÷ 2
= 90 ÷ 2
= 45
So, the answer is 45
Answer: 135
Step-by-step explanation: use a calculator/online calculator
Which figure is missing in the pattern?
Answer:
B
Step-by-step explanation:
The pattern is square numbers so
1, 4, 9, 16, 25
Find an equation in slope-intercept form for the line with slope -3/4 and y-intercept=0? will give BRAINLIEST
Answer:
Step-by-step explanation:
See the solution process below:
Explanation:
The slope-intercept form of a linear equation is: y =mx+b
Where m is the slope and b
is the y-intercept value.
We are given the slope in the problem so we can substitute
−5/6 for m in the formula.
And,
(0,6)
is the y-intercept so we can substitute
6
for
b
in the formula giving:
y
=
−
5
6
x
+
6
Answer:
y=-3/4x
Step-by-step explanation:
y=mx+b
If the y-intercept is 0 then the b in y=mx+b is 0.
the slope is -3/4 so mx is going to be -3/4x.
Oh please help!! urgent it’s due in 10 minutes and I don’t get this one please help!
Answer:
it growth
negative infinity to positive
-7, positive infinity
y inter = -6
horizontal asym = -7
Step-by-step explanation:
1. Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a
12.4-mile bike ride, and a 3.1-mile run.
a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her average
swimming speed in miles per minute?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which fraction is equal to 12%
Answer:
3/25
Step-by-step explanation:
Simplify the fraction by using common factors of numerator and denominator. Now, 12% can be written as 12/100.
Samir is raising money for a school trip by selling candy bars and bags of chips. The
price of each candy bar is $1 and the price of each bag of chips is $2. Yesterday Samir
made $32 from selling a total of 20 candy bars and bags of chips. Graphically solve a
system of equations in order to determine the number of candy bars sold, x, and the
number of bags of chips sold, y.
The number of candy bars sold, x, is equal to 8 candy bars.
The number of bags of chips sold, y, is equal to 12 chips.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the number of bags of chips sold and the number of candy bars sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable y represent the number of bags of chips sold.Let the variable x represent the number of candy bars sold.Since the price of each candy bar is $1 and the price of each bag of chips is $2, and he made $32 from selling a total of 20 candy bars and bags of chips, a system of linear equations to describe this situation can be written as follows;
x + y = 20
x + 2y = 32
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use common logarithms to solve for x in terms of y. (enter your answers as a comma-separated list.)
Hence, x in terms of y is x = log(y) / log(5) found using the common logarithms.
To solve the given problem with common logarithms and find x in terms of y, let's start with the provided information that is to use common logarithms.
Let us begin with a common logarithm defined as a logarithm to the base 10.
Therefore, we use the common logarithmic function of both sides of the given equation,
y = 5^x.
As a result, we get:log(y) = log(5^x)
We know that the power property of logarithms states that logb (a^c) = c * logb (a), where b is the base, a is a positive number, and c is a real number.
Using this property, we can rewrite the right-hand side of the above equation as:x log(5)
Now, we have:log(y) = x log(5)
To get the value of x in terms of y, divide both sides of the above equation by log(5).
We obtain the following:log(y) / log(5) = x
Therefore, x = log(y) / log(5).
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19. find the moments of inertia ix, iy, i0 for the lamina of exercise 5.
To find the moments of inertia ix, iy, and i0 for the lamina of exercise 5, we need to first determine the coordinates of its center of mass. Once we have the center of mass coordinates, we can use the parallel axis theorem and perpendicular axis theorem to calculate the moments of inertia.
Assuming we have the coordinates (x,y) of each point mass of the lamina and its corresponding mass m, we can use the following formulas to find the center of mass:
x_cm = (Σmx) / M
y_cm = (Σmy) / M
where M is the total mass of the lamina.
Once we have the center of mass coordinates, we can use the following formulas to find the moments of inertia:
ix = Σm(y-y_cm)^2
iy = Σm(x-x_cm)^2
i0 = ix + iy
where ix and iy are the moments of inertia about the x and y axes, respectively, and i0 is the moment of inertia about an axis passing through the center of mass perpendicular to the plane of the lamina.
Note that we can use the parallel axis theorem to find the moments of inertia about any axis parallel to the x or y axis, and we can use the perpendicular axis theorem to find the moment of inertia about any axis perpendicular to the plane of the lamina.
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Whats 4/5 of 20 help ALMSOT done
Answer:
16
Step-by-step explanation:
(4/5)*20=16
4 x 20 =80
5 x 1 =5
80/5=16
5/5=1
16/1=16
16 ur answer
the null hypothesis is always a statement about what?
The null hypothesis is always a statement about the population parameter or the absence of a relationship or difference between variables in a statistical hypothesis test. It is typically denoted as "H0" and assumes no effect or no difference exists.
The null hypothesis can take different forms depending on the specific research question. For example, in a study comparing the mean scores of two groups, the null hypothesis might state that the means are equal. In a correlation study, the null hypothesis could assert that there is no correlation between variables.
The null hypothesis acts as a baseline for comparison in hypothesis testing. Researchers aim to gather evidence against the null hypothesis to support an alternative hypothesis. Statistical analysis helps determine the likelihood of observing the obtained data if the null hypothesis were true.
By specifying a null hypothesis, researchers can objectively evaluate the evidence and draw conclusions about the relationship or difference they are investigating.
In summary, the null hypothesis is a statement about the population parameter or lack of relationship/difference, which serves as a reference point for hypothesis testing. It helps researchers assess evidence and draw conclusions based on statistical analysis.
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If f(x) = x to the 2nd power+ 2x - 10, what is f(-2)?
Answer:
Step-by-step explanation:
f(-2)= x^2+2x-10= (-2)^2+2(-2)-10= 4-4-10= 0-10 = -10
to compute χ2, the entries in the contingency table should be _________.
To compute the chi-square (χ2) statistic for a contingency table, the entries in the table should be non-negative whole numbers and should represent counts or frequencies.
The entries should indicate the number of observations falling into each category or combination of categories. It is important to note that the χ2 test is a statistical test used to analyze the association between categorical variables, and it requires the data to be in the form of a contingency table with appropriate counts or frequencies.
The χ2 test is commonly used to examine the relationship between two categorical variables. The contingency table is a table that summarizes the observed frequencies or counts for each combination of categories of the variables. The entries in the contingency table should fulfill certain requirements to ensure the validity of the χ2 test. Firstly, the entries in the table should be non-negative whole numbers, as they represent counts or frequencies of occurrences. Negative values or non-integer values are not meaningful in this context.
Secondly, the entries should reflect the number of observations falling into each category or combination of categories. Each cell in the table represents the count or frequency of observations falling into a specific combination of categories. By ensuring that the entries in the contingency table satisfy these criteria, we can accurately compute the χ2 statistic and perform the appropriate statistical analysis to assess the association between categorical variables.
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Calculate the slope of the line:
(-3,-4)
3(run)
(0,4)
8(rise)
The slope of the line with a rise of 8 and a run of 3 is 8/3 OR 2 2/3
Calculating the slope of a lineFrom the question, we are to calculate the slope of the line
Using the formula for the slope of a line,
Slope = (y₂ - y₁) / (x₂ - x₁)
x₁ = -3
x₂ = 0
y₁ = -4
y₂ = 4
Slope = (4 - (-4)) / (0 - (-3))
Slope = (4 + 4) / (0 + 3)
Slope = 8 / 3
Slope = 2 2/3
Also,
Slope can be calculated by using the formula
Slope = Rise / Run
Slope = 8 / 3
Slope = 2 2/3
Hence,
The slope of the line is 8/3 OR 2 2/3
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find the product. give your answer as a simplified fraction. 5/6×5=?
To solve:
\(\frac{5}{6}\cdot5\)We multiply the denominator by 5:
\(\frac{5\cdot5}{6}=\frac{25}{6}\)To write it as a simplified fraction, we can note that 4 * 6 = 24
Then:
\(\frac{25}{6}=4\frac{1}{6}\)
The set of all real numbers x that satisfies -3
Answer:
\(567 { {yx6 { {x}^{2} }^{?} }^{?} }^{2} \times \frac{?}{?} 6 {x156346x { \frac{6y9yx9 { { \sqrt[ \sqrt{6x9 = x { \div x \times - { + x2x2 {?}^{2} }^{2} }^{2} } ]{?} }^{?} }^{2} \times \frac{?}{?} }{?} }^{?} \times \frac{?}{?} }^{2} \)
Step-by-step explanation:
copy that in your paper good luck to you
Answer:
It's False
Step-by-step explanation:
both signs are < not ≤, which means they are not included. [ ] means the number is included, but ( ) means they are not.
Basically:
( ) = > <
[ ] = ≥ ≤
In the equation y = $7.20x + $790, "y" represents Select one: A. variable costs/unit. B. total fixed costs. C. total costs. D. none of the above
In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.
The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.
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Use the function shown in the table to answer the questions below .
Answer:
a) -6
b) 3
c) Y = -6x + 3
Step-by-step explanation:
Pick two points and find rise/run = slope
rise y1 - y2 = 9 - 3 = 6
run x1 - x2 = -1 - 0 = -1
slope = 6 / -1 = -6
The y intercept is where x = 0 which is given in the table (0,3) so
y intercept = 3
Point slope form is y = mx + b , so
y = -6x + 3
a number r divided by 82
Answer:
574 is a number that can be divided by 82
What is the end behavior of the function shown in the graph above?
A
As x approaches 0, y approaches 15.
As x approaches 25, y approaches 0.
B
As x approaches∞, y approaches 0.
As x approaches −∞, y approaches ∞.
C
As x approaches 0, y approaches ∞.
As x approaches ∞, y approaches −∞.
D
As x approaches ∞, y approaches 0.
As x approaches ∞, y approaches ∞.
Answer:
B
Step-by-step explanation:
how do you solve 2/10 = 4/n + 5
Answer:
n=5/6
Step-by-step explanation:
multiply both sides by n
get
(2/10)n =4 +5n
5n-(2/10)n=4
4.8n=4
n=5/6
on an american roulette table, there are 38 squares that correspond to 38 slots in the roulette wheel. you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead? 0.64 0.36 0.50 none of the above.
The probability of coming out ahead after 30 spins is about 0.0732
The probability of winning on a single spin by betting on red (or black) is 18/38, which is approximately 0.4737.
Assuming each spin is independent of the others, the probability of winning exactly 15 times out of 30 is given by the binomial distribution with n=30 and p=0.4737. This can be calculated using the formula
P(X = k) = (n choose k) × \(p^k\) × \((1-p)^{n-k}\)
where X is the random variable representing the number of times we win in 30 spins, k is the number of times we win, "choose" denotes the binomial coefficient, and ^ denotes exponentiation.
Using a calculator or software that can calculate binomial probabilities, we find that
P(X = 15) = (30 choose 15) × 0.4737¹⁵ × 0.5263¹⁵ ≈ 0.0971
This means that the probability of winning exactly 15 times out of 30 is about 0.0971, or approximately 9.71%.
To find the probability of coming out ahead (winning more than you bet) after 30 spins, we need to consider all the possible outcomes. If we win exactly 15 times, we break even (winning 15 dollars and losing 15 dollars). If we win more than 15 times, we come out ahead. If we win less than 15 times, we come out behind.
The probability of winning more than 15 times can be calculated by adding up the probabilities of winning 16 times, 17 times, and so on, up to 30 times. This can be expressed as
P(X > 15) = P(X = 16) + P(X = 17) + ... + P(X = 30)
Using the same binomial distribution formula as before, we can calculate each term in this sum and add them up:
P(X > 15) ≈ 0.0732
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The give question is incomplete, the complete question is:
On an American roulette table, there are 38 squares that correspond to 38 slots in the roulette wheel. you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead?
Lila planted a tree in her backyard. She made a graph to show the tree growth over 5 years.
1) What does the slope mean in real life in the context of the problem?
2) What does the y-intercept mean in real life in the context of the problem?
Answer in complete sentences.
Answer:
1. Growth rate of tree 3 ft per year, 2. Beginning height of tree 5 feet, rise/run = 3/1 = 3
Step-by-step explanation:
The solution is
1) The slope of the graph m = 3 represents the growth of the tree per year
2) The y-intercept means the initial height of the tree , when x = 0
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( 3 , 14 )
Let the second point be Q = Q ( 1 , 8 )
Now , the slope of the two points on the line is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 14 - 8 ) / ( 3 - 1 )
Slope m = 6/2
Slope m = 3
Therefore , the slope is 3 feet per year
b)
The y intercept is calculated from the equation of line , when x = 0
So , the equation of line is given as
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 14 = 3 ( x - 3 )
On simplifying the equation , we get
y - 14 = 3x - 9
Adding 14 on both sides of the equation , we get
y = 3x + 5
Now , when x = 0
y = 3 ( 0 ) + 5
y = 5 feet
From the graph we can see that , at 0 years the initial height of the tree is also 5 feet
Therefore , the y intercept is 5 feet
Hence , The slope of the equation is 3 and y intercept is 5
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