Answer:
0.65%
Step-by-step explanation:
i took the test
The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
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Priya is comparing two functions: (x) = 10 . y? and g(x) = 3 - 2* to find out which
one has greater output values as x gets very large.
She notices that f(1) = 10 and f(2) = 40. However, g(1) = 6 and g(2) = 12. She
concludes that as x continues to grow, the values of f will be greater than the values
of g.
Explain why priyas conclusion is incorrect
Answer:
help me to find Xian pleaseee:( i miss him so much:(
sorry for answering Non sense po i hope u understand me ty po!
period of f(x)=cos(x)+2
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
The mean percent of childhood asthma prevalence in 43 cities is 2.16%. A random sample of 31 of these cities is selected. What is the
probability that the mean childhood asthma prevalence for the sample is greater than 2.6% ? Interpret this probability. Assume that o=1.36%.
The probability is:
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.
What is Probability ?
Probability is the measure of likelihood of an event.
For a Normal Distribution ,
the z-score formula is given by
[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]
Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .
It is the measure of the deviation of the data from its central tendency.
Each z-score has a probability value.
It is given in the question that
Mean of 2.16% = [tex]\rm \mu\\[/tex] = 2.16
Standard deviation of 1.36% means that [tex]\rm \sigma\\[/tex] = 1.36
For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]
s = 1.36/√31
s = 0.2442
Substituting the values
Z = (2.6 -2.16)/0.2442
Z =1.8
the p value from the graph of z and p , 0.9643
To determine value of probability more than X is 1 - 0.9643= 0.0357
the
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.
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0/1
What is the equation of
the line in y=mx+b form?
(Photo)
Answer:
y=-15x+100
Step-by-step explanation:
Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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Q). Express each of the following recurring decimal as a rational numbers . 1) 0.5 2) 0.13 3) 0.341
The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000
What is rational number?A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;
3/4. where,
Numerator = 3Denominator = 4Therefore,
0.5
= 5/10
= 1/2
0.13
= 13/100
0.341
= 341 / 1000
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the diagonal of the rectangular solid with the given measures. (Part of the answer is provided for you.)
l = 18, w = 10, h = 2
Answer:
Step-by-step explanation:
Length=18
Width/Breadth =10
Height=2
The formula for a diagonal face of a cuboid is=√(l²+ b²)
Face diagonal=√(18²+10²)
= 20.59 to 2.d.p
The formula for the body diagonal of a cuboid is=√(l² + b² + h²)
Body diagonal=√(18² + 10² + 2²)
=20.69 to 2.d.p
the multiplication law of exponents says that for any numbers b, n, and m,
b^n.b^m=b^n+m
a. true
b. false
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
Law of indicesIndices are written in term of exponents. Some of the laws of indices;
[tex]a^m\times a^n=a^{m+n}[/tex] (product law of indices)
For the quotient law of indices
[tex]\dfrac{a^m}{a^n} =a^{m-n}[/tex]
According to the given expression, we are to determine if it is true or false
Check:
[tex]b^n.b^m=b^{n+m[/tex]
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
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A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second. the function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t. what is the max height the pumpkins will reach and what time will it reach that height?
The maximum height of the pumpkin is 3 feet
We have given that,
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.
The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.
We have to determine the maximum height.
What is the maxima?
At the point of maxima f'(x)=0
first, find the maxima
Therefore differentiate the given function with respect to t we get,
[tex]h'(t)=-32t+96[/tex]
h'(t)=0
Then we get,
[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]
Therefore the maximum height of the pumpkin is 3 feet.
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If f(x)=3x-2 and g(x)=2x+1,find (f+g)(x)
Answer:
f(x) + g(x) = 3x - 2 + 2x + 1
(f + g)(x) = 5x - 1
what is 15/56 in simplest form
Answer:
15/56
Step-by-step explanation:
15 and 56 have a GCF of 1.
What is the missing probability from the line?
Give your answer as a decimal.
The missing probability from the line in the diagram attached is 0.5.
What is a missing probability from the number line?The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).
The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.
Thus,
Probability from the line = 1/2Probability from the line = 0.5 (decimal)Learn more about missing probability here:
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Pls helpDetermine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of the rectangle, as shown in the image given is calculated as: 48 square units.
What is the Area of a Rectangle?The area of a rectangle = length × width.
Find the length and width of the rectangle:
Length (BC) = 8 unitsWidth (AB) = 6 unitsArea of rectangle ABCD = 8 × 6 = 48 square units.
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In the figure, line p || line q. Find the measure of each angle if m<8 = 115
Answer:
65, 65, 115
Step-by-step explanation:
Attached image
d. If f¹(x+2) =X-1/x+1x not equal to 1 then find f(x) and f¹(4).
I assume by f¹, you actually mean f⁻¹ as in the inverse of f. I also assume you are asked to find f(x) (as in the inverse of f⁻¹) and f⁻¹(4).
Given that
[tex]f^{-1}(x+2) = \dfrac{x-1}{x+1}[/tex]
with x ≠ 1, we can find f⁻¹(x) by replacing x + 2 with x :
[tex]f^{-1}(x + 2) = \dfrac{x-1}{x+1} = \dfrac{(x+2) - 3}{(x + 2) - 1} \implies f^{-1}(x) = \dfrac{x-3}{x-1}[/tex]
Then when x = 4, we have
[tex]f^{-1}(4) = \dfrac{4-3}{4-1} = \dfrac13[/tex]
Of course, we also could have just substituted x = 2 into the definition of f⁻¹(x + 2) :
[tex]f^{-1}(4) = f^{-1}(2+2) = \dfrac{2-1}{2+1} = \dfrac13[/tex]
To find f(x), we fall back to the definition of an inverse function:
[tex]f^{-1}\left(f(x)\right) = x[/tex]
Then by definition of f⁻¹, we have
[tex]f^{-1}\left(f(x)\right) = \dfrac{f(x)-3}{f(x)-1} = x[/tex]
Solve for f :
[tex]f(x) - 3 = x (f(x) - 1)[/tex]
[tex]f(x) - 3 = x f(x) - x[/tex]
[tex]f(x) - x f(x) = 3 - x[/tex]
[tex](1 - x) f(x) = 3-x[/tex]
[tex]f(x) = \dfrac{3-x}{1-x} = \dfrac{x-1}{x-3}[/tex]
Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2
Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]
[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]
Anna and Brian share £24.50
in the ratio 2:5. How much
does each person get?
Which inequality does the graph
represent?
y
−2 O 2 x
2
−2
Answer:
Step-by-step explanation:
find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
Find the product or type
"impossible".
[2 6 -7][5 -2 4]
The value of (26 - 7) and (5 - 24) when they're multiplied will be -399.
How to multiply the values?From the information given, we are told to multiply (26 - 7) and (5 - 24). This goes thus:
= (26 - 7) × (5 - 24)
= 21 × -19
= -399
In this case, value of (26 - 7) and (5 - 24) when they're multiplied will be -399.
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a hypotenuse = 24?
√2, √2, 24
24√2, 24√2, 12
24, 24, 24√2
12√2, 12√2, 24
The sides of the triangle are (d) 12√2, 12√2, 24
How to determine the side lengths?The given parameters are:
Hypotenuse = 24Angle = 45-45-90 degree anglesIn a 45-45-90 degree angle triangle, we have:
Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2
This means that:
Opposite =Adjacent
So, we have:
24 = Adjacent√2
Divide both sides by √2
Adjacent = 24/√2
Evaluate
Adjacent = 12√2
This means that:
Opposite = 12√2
Hence, the sides of the triangle are (d) 12√2, 12√2, 24
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Brad took 5 kicks and made 4 goals: 4/5
Sydney will take 10 shots and she wants to make an equivalent fraction of the goals. How many goals must She make?
4/5 x ?/? = ?/10
Answer: 8/10
Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10
I NEED HELP ASAP Which graph represents the function?
f(x)=√x + 1
Answer:
Step-by-step explanation:
It looks like the best option is 3.
Given the equation,
we can make a table. x as input and y as output to get our points to the graph.
I have used the desmos graph as a reference to confirm the equation by graphing also. The table is also there.
What is the value of x?
2
3
6
7
Answer: 2
Step-by-step explanation:
DE * CE = AE * BE (Two Secants Segment Theorem)
▪︎ DE = 1 + x + 4
▪︎ CE = x + 4
▪︎ AE = 11 + x + 1
▪︎ BE = x + 1
=> (1 + x + 4)(x + 4) = (11 + x + 1)(x + 1)
=> (x + 5)(x+4) = (x + 12)(x + 1)
=> x^2 + 9x + 20 = x^2 + 13x + 12
=> 9x + 20 = 13x + 12
20 - 12 = 13x - 9x
8 = 4x
x = 2
The Algebra Club has decided to rent a convention center for their annual Algebra Gala. The cost for the rental will be split evenly among the attendees, which means that the price per person varies inversely with the number of people attending.
If 25 people attend, the cost will be $30 per person.
How many people would need to attend to get the cost under $20 per person?
A) 28
B) 38
C) 48
D) 58
i need ur help so bad omg
i love you when you call me se
when factoring the following trinomial,you need two numbers that multiply to equal "-24" and add to "-10" choose the two correct numbers
6
-8
-3
4
-6
-4
12
3
8
-2
-12
2
Answer:
-12 and 2
Step-by-step explanation:
-12 × 2 is -24
and
-12 + 2 is -10
What is the area of the shape
The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.
We know the area of the kite = pq/2
Where p and q are the length of the diagonals
p = 10+10 = 20 ft
q = 7+11 = 18 ft
Area = (20×18)/2
Area = 180 square feet
Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.
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4X+8<28
ayudenme por favor
Answer:
x < 5.
Step-by-step explanation:
Creo que esto es correcto. :')