Answer:
168cmsqured
Step-by-step explanation:
as for me,15 acts as the lower part of the trapezium while 13 acts as the upper part of the trapezium .so since I know the measurements of the both sides I can easily calculate the area use using the formula indicated in the image.hope it helps
This table shows some values of an exponential function.
What is the function?
The exponential function of the table is y = 0.75(2)^x
How to determine the exponential function?From the table, we have the following points
(x,y) = (0,0.75) and (1,1.5)
An exponential function is represented as:
y = ab^x
At (0,0.75), we have:
0.75 = ab^0
a = 0.75
Substitute a = 0.75 in y = ab^x
y = 0.75b^x
At (1,1.5), we have:
1.5 = 0.75b^1
Evaluate
1.5 = 0.75b
Divide both sides by 0.75
b =2
Substitute b =2 in y = 0.75b^x
y = 0.75(2)^x
Hence, the exponential function is y = 0.75(2)^x
Read more about exponential function at:
https://brainly.com/question/11464095
#SPJ1
Is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The distribution of the values obtained from a simple random sample of size n from the same population is incorrect.
What is sampling distribution?The sampling distribution of a statistic of size n is the distribution of the values obtained from a simple random sample of size n from the same population.
The sampling distribution is the process of getting a sample through simple random techniques from the sample population.
So, it is incorrect that the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
Learn more about sampling distribution here:
https://brainly.com/question/3663642
#SPJ1
R FIVE Given that k = 3n+2/n+1 write 'n' in terms of 'k'
[tex]~~~~~~k = \dfrac{3n+2}{n+1}\\\\\implies k(n+1) = 3n+2\\\\\implies kn+k=3n+2\\\\\implies kn -3n= 2-k\\\\\implies n(k-3) = 2-k\\\\\implies n = \dfrac{2-k}{k-3}\\\\\implies n = -\dfrac{k-2}{k-3}~~~~~~~~;[k\neq 3][/tex]
What is the Domain and Range of the function f(x)[tex]\sqrt{x-7} +9[/tex]?
For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}
How to get the domain and range?
Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:
x - 7 ≥ 0.
Solving for x we get:
x ≥ 0 + 7
Then the domain is:
x ≥ 7
To get the range, we evaluate in the minimum of the domain:
f(7) = √(7 - 7) + 9 = 9
Then the range is the set of all values larger than 9, because the function is increasing.
So the range is R: y ≥ 9.
If you want to learn more about domain and range:
https://brainly.com/question/10197594
#SPJ1
If a male student is selected at random, what is the probability the student is a freshman?
The probability that the student selected at random is a freshman is; 29%
How to find the Probability?
From the given table;
Total number of male students = 4 + 6 + 2 + 2 = 14
Number of freshmen students = 4 students
Thus;
Probability that the student selected at random is a freshman is;
P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%
Read more about Probability at; https://brainly.com/question/251701
#SPJ1
Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?
x squared over 4 plus y squared over 1 equals 1
x squared over 1 plus y squared over 2 equals 1
x squared over 1 minus y squared over 4 equals 1
x squared over 1 minus y squared over 2 equals 1
The answer will be x squared over 4 plus y squared over 8 equals 1.
What is an ellipse?An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.
The general equation of the ellipse is given as;
(x²/a²) + (y²/b²) = 1
The coordinates of a foci are: (±c, 0) where;
c² = b² - a²
However, we know that equation of directrix is; x = ±a/e
Now, Directrix is given ±4
Thus, a/e = 4
a = 4e
We also know that c = ae from ellipse foci coordinates.
Thus, ae = 2
since ae = 2, then (4e)e = 2
4e² = 2
e² = 2/4
e = 1/2
Thus;
a = 4 × 1/2
a = 2
Since c² = b² - a²;
2² = b² - 2²
4 = b² - 4
b² = 8
From (x²/a²) + (y²/b²) = 1, we can put our values to get;
x²/4 + y²/8 = 1
Hence the answer will be x squared over 4 plus y squared over 8 equals 1.
To know more about an ellipse follow
https://brainly.com/question/16904744
#SPJ1
Find the first 3 iterates of the function f(x) = 0.80x when x^0= 150
Based on the calculations, the first three (3) iterations of the given function are 120, 96 and 76.8.
How to find the first three iterations?In this exercise, you're required to find the first three (3) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:
First iteration:
f(x) = 0.80x
f(x₀) = 0.80x₀
f(150) = 0.80 × 150
f(150) = 120.
Second iteration:
f(x) = 0.80x
f(x₁) = 0.80x₁
f(120) = 0.80 × 120
f(120) = 96.
Third iteration:
f(x) = 0.80x
f(x₂) = 0.80x₂
f(96) = 0.80 × 96
f(120) = 76.8.
Read more on iteration here: https://brainly.com/question/14828536
#SPJ1
Solve for x:
2x² - 2x+5=0
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
How to solve a quadratic function by the quadratic formula
Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (1)
Where a, b, c are the coefficients of the quadratic function.
In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:
[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]
x₁ = 0.5 + i 1.5
[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]
x₂ = 0.5 - i 1.5
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
To learn more on quadratic functions: https://brainly.com/question/5975436
#SPJ1
What is the probability that the top-three finishers in the contest will all be seniors?
Type in the correct answer in each box. Use numerals instead of words. If necessary, round your answers to the nearest tenth.
There are __ different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is __%.
CONTEXT: Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Using the combination formula, it is found that:
There are 364 different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is 15.38%.
The order in which the players are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In total, three students are taken from a set of 14, hence:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
Including only seniors, it would be three students from a set of 8, hence:
[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]
Hence the probability is given by:
p = 56/364 = 0.1538 = 15.38%.
More can be learned about the combination formula at https://brainly.com/question/25821700
#SPJ1
[100 POINTS] What is the measure of the arc from A to B that does not pass through C?
(Fill in the blanks)
Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
What is the Inscribed Angle Theorem?Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
Learn more about the inscribed angle theorem on:
https://brainly.com/question/3538263
#SPJ1
Molly's jump rope is 6 1/3 feet long. Gail's jump rope is 4 2/3 feet long. How much longer is Molly's jump rope? NOT MUTLIPLE CHOICE IM SO SORRY PLS FORGIVE ME
Answer:
Molly's jump rope is 1 2/3 feet longer than Gail's jump rope.
Step-by-step explanation:
To get this answer, you would have to subtract 6 1/3 - 4 2/3 to find the difference between the two lengths.
To solve this subtraction problem: Start by doing 6 - 4 to get 2, because when the fraction parts are like that, start with whole numbers. Then, solve the fraction parts. 1/3 - 2/3 is -1/3 (you can go to negatives)! Lastly, combine the whole number and fraction parts. 2 - 1/3, because the negative symbol changes to a minus symbol, which will get you 1 2/3.
Hope this helped!
What similarity statement can you write relating the three triangles in the diagram?
Answer:
They are both right-angled triangles.
Step-by-step explanation:
help heelp help help help
Need Help with this..
Answer:
119 4/7
Step-by-step explanation:
Add up all the sides
Hi Student!
Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is. Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.
In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.
Create an expression
[tex]\textsf{Perimeter = side_{1}}[/tex][tex]\textsf{Perimeter = side1 + side2 + side3 + side4 + side5 + side6 + side7}[/tex]Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape. However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.
Combine the whole numbers
[tex]\textsf{Perimeter = }35\frac{3}{7} + 10\frac{1}{7} + 10\frac{1}{7} + 12\frac{2}{7} + 12\frac{2}{7} + 15\frac{3}{14} + 24\frac{1}{14}[/tex][tex]\textsf{Perimeter = }(35 + 10 + 10+12+12+15+24)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex]Combine those with a common denominator
[tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7}) + (\frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3+1+1+2+2}{7}) + (\frac{3+1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{9}{7}) + (\frac{4}{14})[/tex]Covert to mixed fraction and simplify
[tex]\textsf{Perimeter = }(118)+(1\frac{2}{7}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{2}{7}) + (\frac{4}{14})[/tex]Find common denominator and combine
[tex]\textsf{Perimeter = }(119)+(\frac{2*2}{7*2}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}+\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4+4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{8}{14})[/tex]Simplify the expression
[tex]\textsf{Perimeter = }(119)+(\frac{8/2}{14/2})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{7})[/tex][tex]\textsf{Perimeter = }119\frac{4}{7}[/tex]Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.
Simplify the following expressions
2x-2y+5z-2x-y+3z
Answer:
-3y+8z
Step-by-step explanation:
2x-2y+5z-2x-y+3z
you don't need to change their signs just place them accordingly
2x-2x-2y-y+5z+3z
-3y+8z
-2h - 8 = 4h - 3(2h + 12)
A rocket is launched from a height of 3m with an initial velocity of 15 m/s at what time will the rocket be 13m from the ground? first person to answer gets brainliest
How many modes does the following data set have?
2, 2, 3, 3, 3, 4, 4, 4, 4, 11, 11, 11, 25, 25, 25, 25, 26, 26, 26
A. 2
B. 6
C. 4
D. 1
SUBT
Rotate the triangle 180° about the cross.
A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b
If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.
Learn more about Triangle:
https://brainly.com/question/2773823
#SPJ1
According to the Centers for Disease Control and Prevention (CDC) , 47% of adults in the United States have hypertension. In a random sample of 500 U.S adults, find the probability that sample the proportion of adults with hypertension is greater than 0.5.
The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
How to determine the probability?The given parameters are:
p = 47%
Sample size, n =500
The standard deviation is calculated as:
[tex]\sigma = \sqrt{np(1 - p)[/tex]
So, we have:
[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]
Evaluate
σ = 11.16
The number of adults with hypertension is calculated as:
x = 500 * 0.5 = 250
And the mean is:
μ = 500 * 0.47 = 235
Start by calculating the z-score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{250 - 235}{11.16}[/tex]
Evaluate
z = 1.34
The probability is then calculated as:
P(z >1.34) = ??
From z table of probabilities, we have:
P(z >1.34) = 0.090
Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
Read more about probability at:
https://brainly.com/question/251701
#SPJ4
Which of the following expressions are equivalent to
4-3
?
4-8
U
ful foo
45
DONE
Answer: The correct answers are the first and the fourth one.
Step-by-step explanation:
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
(32)4
3-3
3243 2-1
(34)²
3-3 2-3 63 24 35
(40)2
(23)
1
112122
2
23.3
The simplified value is shown below:
What is exponents and powers?Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.
First,
3²*4³*[tex]2^{-1}[/tex]/(3*4)²
=9*64/144*2
= 576/288
=2
Second,
(3*2)^4 *[tex]3^{-3}[/tex]/2³*3
=1296/8*81
=1296/648
=2
Third,
[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]
= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
=1
Fourth,
[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]
= 1/2
Learn more about exponents and powers here:
https://brainly.com/question/15722035
#SPJ1
Work out the perimeter of the shaded shape.
4m
19m
14m
8m
The diagram is not drawn to scale.
Answer:
45m
Step-by-step explanation:
4m+19m+14m+8m=45m
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
Step 1: –c = ax2 + bx
Answer:
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
[tex] \: first the formula of quadratic equation \: = - b ≠ \: \sqrt{ \frac{ \: {b }^{2} - 4ac}{ \: 2a} } [/tex]
let's begin to solve this equation,,,
[tex]ax² + bx + c = 0 \\
ax² + bx + c =0 \\ {x}^{2} + \frac{b}{a} \: + \frac{ {b}^{2} }{2a} = \frac{b2}{a} - \frac{c}{a}
\\ x + \frac{ {b}^{2} }{2a} = - \frac{ {b}^{2} }{2a} - \frac{c}{a} [/tex]
MORE BASIC INFORMATIONan equation having the maximum power of the variable equal to is called the quadratic equation the general form of quadratic equation is ax² + bx +c =0 where a,b,c are real numbers a ≠0 x is variable •
a quadratic equation can be solved by two method by factorization and by formula
by factorization a quadratic equation can be solved by factorization only when the product AC can be divided into two such part that it had the sum of the difference of the two part is equal to b
[tex]by the formula of quadratic equation can be solved by \ - } [/tex]
[tex]x = \frac{ - b \sqrt{ {b}^{2} - 4ac } }{2a } \\ root \: of \: equation \: {ax}^{2} + bx + c = 0 \\ - b - \sqrt{ \frac{ {b}^{2} - 4ac}{2a} } [/tex]
Write the slope-intercept form of the equation of the line through the given points.
through: (0, 2) and (-1,-5)
Answer:
y = 7x +2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )
m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = 7x + 2 ← equation of line
2x+2y
3x+3y
=5
=7
How many solutions does the system of equations above have?
The system of equations have one solution
How to determine the number of solutions?The equations are given as:
2x + 2y = 5
3x + 3y = 7
The above equations are distinct linear equations.
This means that they would have one point of intersection, if plotted on a graph
Hence, the system of equations have one solution
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
In the triangle below, which of the following best describes AD?
B
D
O A. Median
OB. Altitude
OC. Perpendicular bisector
A
38
38
Answer:
A. median
explain i just aced the test rn
Answer:
Angle bisector
Step-by-step explanation:
The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.
Victoria is putting down fertilizer in her garden. For every 25 square feet of garden, she needs one pound of fertilizer.
Let p represent the number of pounds of fertilizer.
Let g represent the area, in square feet, of garden she covers.
Which correctly names the independent and dependent variables?
independent variable: number of pounds of fertilizer; dependent variable: number of square feet of garden covered
independent variable: brand of fertilizer; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of people it takes to fertilize the garden
The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.
Let
p = number of pounds of fertilizer.g = area, in square feet, of garden she coversWhat is dependent and independent variable?Dependent variable are variables which takes its value based on other values in an equation.
Independent variable are variables which takes its value outside an equation.
Learn more about dependent variable:
https://brainly.com/question/82796
#SPJ1
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 100 points
packs of collectible cards claim that 1 out of 3 packs contains a rare card. margie bought 7 packs and only received a rare card in 1 of the packs.
margie runs a simulation of 100 trials. in the simulation, she used a random number generator to select 7 digits from 1 to 3 with 1 representing a pack with a rare card and 2 and 3 representing a pack without a rare card. the frequency of the number of packs with rare cards in each trial of 7 samples in the simulation is represented by this table.
what is the best conclusion for margie to make based on the data?
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
Answer:
My guess would be b or d
Step-by-step explanation:
I don't under stand what is wrong.
Answer:
In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.
The full correct process is:
(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15
= 4m - 6m + 9 + 15
= -2m + 24