On a 8.5 x 11 inches (or larger) paper, create a carnival game (for example it could be: throwing a dart at a target, ball through a hoop, ball in cup, etc).
Provide a written description of your game.
Your game must use at least two different geometric shapes.
Label the dimensions of the shapes with the measurements in real life. Draw on the paper using a scale factor.
For example, if the game has a 3 feet diameter, label 3 feet on the image, but draw it to scale, so that the model game is similar to the actual dimensions. If the scale is 1 foot = 2 inches, then 3 feet = 6 inches.
Find the probability of winning your game. Include the calculations to show the probability.
Determine the type of prize a winner would deserve and the cost of playing your game.
The probability of winning the game is 0.065
The description of the gameThe game involves throwing two darts at two targets.
To win the game, the darts must hit anywhere in the following shapes
Rectangle: 5 by 4 inchesCircle: Radius, r = 3 inchesThe probability of winningThe area of the paper is:
Area = 8.5 inches * 11 inches
Area = 93.5 square inches
The area of the rectangle on the paper is:
Area = 5 inches * 4 inches
Area = 20 square inches
The area of the circle on the paper is:
Area = π * (3 inches)²
Area = 28.3 square inches
The probability of landing on both shapes is
P(Both) = 20/93.5 * 28.3/93.5
Evaluate
P(Both) = 0.065
Hence, the probability of winning the game is 0.065
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A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.
Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.
Trigonometric area formula: Area = One-half a b sine (C)
To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin?
16 square centimeters
30 square centimeters
56 square centimeters
60 square centimeters
The napkin covered approximately 56 square centimeters of the plate. The third option is correct.
What is the area of an isosceles triangle?The area of an isosceles triangle can be estimated by using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times a \times b\times sin (C)}[/tex]
From the given information:
The base angle and sides of an Isosceles triangle are equal.The perimeter of the triangle:
P = a + b + c
38 = a + 8 + c
where;
a = c (base sides)So;
38 = 8 + 2a
38 - 8 = 2a
2a = 30
a = c = 15
Similarly, ∠ABC = 30
∠A + ∠B + ∠C = 180 (sum of angles in a triangle)
∠A + 30 + ∠C = 180
∠A = ∠C = x
2x = 180 - 30
2x = 150
x = 150/2
∠A = ∠C = x = 75°
Using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times (15) \times (8) \times sin (75)}[/tex]
= 56 square centimeters.
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Answer: Option C
Step-by-step explanation:
Edge 2020
What is the area of the given figure?
10 in.
O 192 units²
O
92.9 units²
O 101.8 units²
O167.2 units2
O
176.7 units2
6 in.
10 in.
9 in.
[tex]\huge\boxed{192\ \text{in}^2}[/tex]
There are three parts to this figure: a rectangle and two triangles that are congruent.
We'll add together the area for each to get the total area.
We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.
We know that [tex]a^2+b^2=c^2[/tex]. Substitute and solve for [tex]a[/tex]:
[tex]\begin{aligned}a^2+6^2&=10^2\\a^2+36&=100\\a^2+36-36&=100-36\\a^2&=64\\\sqrt{a^2}&=\sqrt{64}\\a&=8\end{aligned}[/tex]
Now, double this to get the total length of the rectangle, which is [tex]16[/tex] inches.
The area of the rectangle is equal to its length times its height:
[tex]16\cdot9=\underline{144}[/tex]
Now, we'll find the area of one of the triangles and double it since they're congruent.
The area of a triangle is one-half of its base times its height, which we then double.
[tex]2\left(\frac{1}{2}\cdot b\cdot h\right)[/tex]
The [tex]2[/tex] and the [tex]\frac{1}{2}[/tex] cancel each other out.
[tex]b\cdot h[/tex]
Substitute and solve:
[tex]8\cdot6=\underline{48}[/tex]
Finally, add the rectangle's area to the two triangles' area.
[tex]144+48=\boxed{192}[/tex]
Solve the equation for x.
6-√4+3x = 2
I think the answered is ×=20
end behavior of f(x)= 10/x^2-7x-30
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
What is the end behavior of a rational function
The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:
[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]
[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]
[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]
[tex]\lim_{x \to \pm \infty} 0[/tex]
0
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
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For the following exercises, solve each inequality and write the solution in interval notation.
31. | 3x − 4 | ≤ 8
Answer:
The solution set in interval form is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].
Step-by-step explanation:
It is given in the question an inequality as [tex]$|3 x-4| \leq 8$[/tex].
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality [tex]$3 x-4 \leq 8$[/tex] and, [tex]$-8 \leq 3 x-4$[/tex].
Step 1 of 2
Solve the inequality [tex]$3 x-4 \leq 8$[/tex]
[tex]$$\begin{aligned}&3 x-4 \leq 8 \\&3 x-4+4 \leq 8+4 \\&3 x \leq 12 \\&x \leq 4\end{aligned}$$[/tex]
Solve the inequality [tex]$-8 \leq 3 x-4$[/tex].
[tex]$$\begin{aligned}&-8+4 \leq 3 x-4+4 \\&-4 \leq 3 x \\&-\frac{4}{3} \leq x \\&x \geq-\frac{4}{3}\end{aligned}$$[/tex]
Step 2 of 2
The common solution from the above two solutions is x less than 4 and [tex]$x \geq-\frac{4}{3}$[/tex]. The solution set in terms of interval is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].
I need help fast please
Answer:
3.4
Step-by-step explanation:
[tex]Interval=\frac{4-2.2}{9}\\Interval=0.2\\therefore :\\ 6 intervals =6(0.2)\\ 6 intervals =1.2\\x=2.2+1.2\\x=3.4[/tex]
rewrite 4 1/2=2
please
The logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]
How to rewrite the expression?The expression is given as:
4^(1/2) = 2
Take the logarithm of both sides
log(4^(1/2)) = log(2)
Apply the change of base rule
1/2log(4) = log(2)
Divide both sides by log(4)
1/2 = log(2)/log(4)
Change the base
[tex]\frac 12 =\log_4(2)[/tex]
Rewrite as:
[tex]\log_4(2) = \frac 12[/tex]
Hence, the logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]
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Express each ratio as a unit rate. Round to the nearest tenth, if necessary.
140 miles on 6 gallons
a.
23.3 mi/gal
c.
0.042 mi/gal
b.
840 mi/gal
d.
13.6 mi/gal
Please select the best answer from the choices provided
A
B
C
D
Answer:
23.3 mpg
Step-by-step explanation:
For the unit rate of miles per gallon (mpg)
140 miles / 6 gallons = 23 1/3 mpg = 23.3 mpg
The required ratio as a unit rate is 23.3 mi/gal, which is determined by dividing the number of miles by the number of gallons.. The correct answer is option (a).
To express each ratio as a unit rate (mi/gal), we need to divide the number of miles by the number of gallons.
The units rate can be calculated as:
Units rate = number of miles / the number of gallons.
Unit rate = 140 miles / 6 gallons
Apply the division operation to get:
Unit rate = 23.3 mi/gal
Thus, the required ratio as a unit rate is 23.3 mi/gal.
Hence, the correct answer is option (a).
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HELP HELO
HELP GELP GELP GELP HLEP
Answer:
A. <T=17, RS= 10
Step-by-step explanation:
These triangles are congruent by AAS congruency. This means that RS and UV will have the same measure and so will <Q and <T. Simply use that info with the measurements given.
Solving for <T:
8y-44 = 5y+7
3y = 51
y = 17
Solving for RS:
7x-2 = 5x+18
2x = 20
x = 10
A population of amoebas in a petri dish will triple in size every hour. At the start of an experiment the population is 800. The function y equals 800 times 3 to the power of x , where x is the number of hours, models the population growth. How many amoebas are in the petri dish after 9 hours?
Answer:
15,746,400
Step-by-step explanation:
This is an example of an exponential function.
1. The function is: [tex]800 * 3^{x}[/tex]
2. We can plug the number of hours into the equation.
3. population = 800 * [tex]3^{9}[/tex]
4. population = 15,746,400
David buys a beanie baby. he later sells it to jessica and loses $3 on the deal. jessica makes a profit of $6 by selling it to bryan for $25. how much did david pay for the beanie baby?
David paid $22 for the beanie baby.
Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.
Let the cost which David pay for the beanie baby be x and y be the price at which Jessica bought the beanie baby
Profit formula :
Profit = Selling price (S.P.) - Cost price (C.P.)
So using the profit formula
$6 = $25 - y
$19 = y
Now using the same equation for David
-$3 = $19 - x
$22 = x.
Thus David paid $22 for the beanie baby.
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Which answer shows y+2x<4x-3, rewritten to isolate y, and its graph
The answer choice which shows y+2x<4x-3, rewritten to isolate y is; y < 2x -3.
What is the rewritten form of the equation in which case y is isolated?From the task content, it follows that the inequality given in the task content is; y+2x<4x-3.
Hence, the variable y can be isolated from the inequality as follows;
y+2x<4x-3
y < 4x -2x -3
y < 2x -3.
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Solve for the remaining angles
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
How to find the missing angles of a triangle
In this question we know the length of the three sides of a triangle, we can find the measure of all angles by using the law of the cosine. So, we know that:
a = 270, b = 442.85, c = 255
Then, by the law of the cosine:
[tex]\cos A = \frac{270^{2}-255^{2}-442.85^{2}}{-2\cdot (442.85)\cdot (255)}[/tex]
A ≈ 33.544°
[tex]\cos B = \frac{442.85^{2}-270^{2}-255^{2}}{-2\cdot (270)\cdot (255)}[/tex]
B ≈ 114.998°
[tex]\cos C = \frac{255^{2}-270^{2}-442.85^{2}}{-2\cdot (270)\cdot (442.85)}[/tex]
C ≈ 31.458°
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
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The graph shows the cube root parent function.
Which statement is true?
A. (0, 0) is the x- and y-intercept of the function.
B. The function has no intercepts.
C. (0, 1) is the x- and y-intercept of the function.
D. (1, 1) is the x- and y-intercept of the function.
Answer:
A)
Step-by-step explanation:
The cube root parent function is [tex]y=x^3[/tex]
When y=0, x=0, hence (0,0) is the x and y-intercept of the function.
Hope I helped!
Which graph represents StartFraction (x minus 2) squared Over 16 EndFraction minus StartFraction (y + 1) squared Over 9 EndFraction less-than-or-equal-to 1?
The attached graph represents the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
How to determine the graph?The inequality is given as:
[tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
The above inequality represents a conic section.
The inequality symbol <= implies that, we make use of a closed line on the graph.
Next, we plot the graph using a graphing tool
See attachment for the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
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Complete question
Which graph represents [tex]\frac{(x - 2)^2}{16} = \frac{(y + 1)^2}{9}[/tex]?
Answer:
C
Step-by-step explanation:
Got it right on Edge
What kind of function is
5x + 19y = 84 ? Thanks
Linear, slope-Intercept form Quadratic
exponential
linear, standard form
Answer:
It's a linear function.
A vector has a magnitude of 8 in the 95 degree direction. what are the horizontal and vertical components?
Is xxx greater than, less than, or equal to 110^\circ110
∘
110, degrees?
The angle z is equal to 110° by vertically opposite angles. Hence, the correct option will be C. z = 110°.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Given;
The one angle is given as 110°.
So, angle z will be equal to 110° by vertically opposite angles.
Hence, the correct option will be C. z = 110°.
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URGENT!!!WORTH 27 POINTS!!!
Doug can download new songs for $1.19 each. Write an equation to show how many songs he can download for $12.00.
A. 12x=1.19
B. 12+x=1.19
C. 1.19+x=12
D. 1.19x=12
Answer:
1.19x = 12
Step-by-step explanation:
To write an equation, we multiply the cost of each song by the number of songs, x
1.19 * x
This is equal to the total amount he is allowed to spend
1.19x = 12
Answer:
D
Step-by-step explanation:
If Doug can download new songs for $1.19 each, then he will be able to download 12 songs.
Find the equation of a line in slope intercept form that is perpendicular to the line y = 2x + 6 through the point (10,4)
The equation of the straight line is y = -1/6(x - 10) + 4
How to determine the line equation?The equation is given as:
y = 2x + 6
Linear equations are represented as:
y = mx + c
Where:
Slope = m
So, we have:
m = 6
The slopes of perpendicular lines are represented as:
n = -1/m
So, we have:
n = -1/6
The equation is then represented as:
y = n(x - x1) + y1
This gives
y = -1/6(x - 10) + 4
Hence, the equation of the straight line is y = -1/6(x - 10) + 4
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Which describes the inverse operations used after the distributive property?
addition then division
subtraction then division
multiplication then subtraction
division then addition
The inverse operations used after the distributive property is B. subtraction then division.
How to illustrate the information?The equation given goes thus:
5(x + 6) = 50.
5x + 30 = 50
5x = 20.
x = 4
Therefore, the inverse operations used after the distributive property is subtraction then division.
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how many real solutions does this system of equations have?
y=x2+1
y=x
A. 1
B. 2
C. 3
D. 0
The system of equations has (d) 0 real solutions
How to determine the number of real solutions?The system of equations is given as:
y = x^2+1
y=x
Substitute y=x in y = x^2+1
x = x^2+1
This gives
x^2 - x + 1 = 0
Calculate the discriminant using:
d = b^2 - 4ac
So, we have:
d = (-1)^2 - 4 * 1 * 1
Evaluate
d = -3
Because the discriminant is negative, the equation has no real solution
Hence, the system of equations has (d) 0 real solutions
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help me please!!!!!!!! 20 points
Answer:
14 in^2
Step-by-step explanation:
Break the figure up into two rectangles (vertical line down the middle). Use the formula area = length x width for the Rectangle A (2 in x 4 in = 8 in^2) and Rectangle B (3 in x 2 in = 6 in^2) Add 8 in^2 and 6 in^2 for a total area of 14 in^2
3 Quick algebra 1 Questions for 50 points!
For (lovetthannah9) or anyone who knows the answer! :)
Answer:
Step-by-step explanation:
6. The rate of change is essentially the slope. But in other words, it's how much the y changes as x increases by 1. If this rate of change is 0, that means the y-value is constant, while the x can be any real number. It can be generally given in the formula: y=b, which comes from simplifying the slope-intercept form: y=(0)x+b = b. You can also derive the same thing for a point-slope form: y-a = 0(x-b)=0 so y=a. In both cases, y is equal to some constant value. So graphing this makes a horizontal line.
7. To define a parallel line, you need the same slope, and a different y-intercept, which is under the assumption that the line has a slope that is definable. If the slope is definable, you'll have the equation: y=mx+b, where m is the same as the other line. Then you plug in the known values as x and y, to solve for b, which is the y-intercept. Now if the line is a vertical line, a parallel line can be defined as: x=a, where a doesn't equal the constant, the other vertical line is equal to. To make it pass through some point (c, d). Then you would simply set x=c, since the x is the only thing that matters, since the y-value is all real numbers, so it will eventually have the y-value d somewhere on the line.
8. To define a perpendicular line, you get the reciprocal of the slope and change the sign. So if the slope is: [tex]\frac{a}{b}[/tex] then it becomes [tex]-\frac{b}{a}[/tex] and vice versa depending on the sign. In this example, let's just say m=a/b, then the perpendicular slope would be -b/a. You can then plug this into the slope-intercept formula: [tex]y=-\frac{b}{a}+c[/tex] where c is the y-intercept. Then you plug in the known point as (x, y) and solve for c, the y-intercept. Now let's say for example that you have a vertical line: x=a. In this case you can see the slope as: [tex]\frac{1}{0}[/tex][tex]\frac{y_2-y_1}{a-a}[/tex]. Of course this isn't definable, but if you take the reciprocal you get something that is: [tex]-\frac{0}{y_2-y_1}[/tex] which will always evaluate to 0. This means you get a horizontal line, since the slope is 0. This means if you have a vertical line, any horizontal line should be perpendicular, which makes sense, since it should form a 90 degree angle when they intersect, because they're straight lines. To make sure that horizontal line passes through the point (b, c), you simply set the y equal to c. So y=c, will pass through (b, c), since the c is constant, and the x can equal anything so somewhere on the line it will intersect (b, c). But let's say we had a horizontal line, the reciprocal can be defined as: [tex]\frac{a-a}{x_2-x_1}[/tex] where a is the y constant. If you take the reciprocal, then you have a-a in the denominator, which gives you an undefined slope, because the perpendicular line to a horizontal line, is a vertical line. To ensure this perpendicular line passes through the point (b, c). You simply set x equal to b. so that x=b.
#6
y=mx+cif m is 0
y=c is the EquationHence line is parallel to x axis
#7
parallel lines have equal slopes
so we can use the point slope form of line to find the equation
y-y_1=m(x-x_1)#2
Same process like no 7 but
slope of perpendicular line is negative reciprocal of given line's slope
y ( x + w ) = c ( x + z )
The formula for x in terms of other terms in the equation is; x = (cz-yw)/(y-c).
What is the formular for x in term of other terms in the equation?According to the task content, it follows that the variable X is to be made the subject of the formula;
Hence, it follows that;
y ( x + w ) = c ( x + z )
yx +yw = cx +cz
x(y-c) = (cz-yw)
x = (cz-yw)/(y-c)
Remarks: The complete question requires that x be made the subject of the formula.
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Substracting 3x2+4x from 7x2+x+9 results in a polynomial. After subtracting 4x2-3x from this polynomial, the difference is ?
Answer:
9
Step-by-step explanation:
So first step is to subtract [tex]3x^2+4x[/tex] from [tex]7x^2+x+9[/tex]. In setting this up you get the following expression
[tex](7x^2+x+9)-(3x^2+4x)[/tex]
Distribute the negative
[tex]7x^2+x+9-3x^2-4x[/tex]
Group like terms
[tex](7x^2-3x^2)+(x-4x)+9[/tex]
Simplify:
[tex]4x^2-3x+9[/tex]
Now subtract [tex]4x^2-3x[/tex]. In setting this up you get the following expression
[tex](4x^2-3x+9)-(4x^2-3x)[/tex]
Distribute the negative:
[tex]4x^2-3x+9-4x^2+3x[/tex]
Group like terms
[tex](4x^2-4x^2) + (-3x+3x) + 9[/tex]
Simplify:
[tex]9[/tex]
Which ordered pairs make the equation true? 3x+2y=−7 Select each correct answer. (3, −8)
(−3, 1)
(−2, −1)
(1, −4)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which ordered pairs make the equation [tex]\bf{3x+2y=-7}[/tex] true? Select all that apply. 3 options are given
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
We can tell which ordered pairs make equations true by plugging in the coordinates.
[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;ONE}[/tex]
[tex]\bf{3(3)+2(-8)=-7}[/tex] | simplify
[tex]\bf{9-16=-7}[/tex] |simplify
[tex]\bf{-7\equiv-7}[/tex] | this one checks
[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;TWO}[/tex]
[tex]\bf{3(-2)+2(-1)=-7}[/tex] | simplify
[tex]\bf{-6-2=-7}[/tex] | simplify
[tex]\bf{-8\neq-7}[/tex] | this one does not check
[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;THREE}[/tex]
[tex]\bf{3(1)+2(-4)=-7}[/tex] | simplify
[tex]\bf{3-8=-7}[/tex] | simplify
[tex]\bf{-5\ne-7}[/tex] | this one does not check
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;First\;Option[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Triangle FIT has been reflected over the y-axis. Which of the following best describes the relationship between the y-axis and the line connecting F to F′?
They share the same midpoints.
They are diameters of concentric circles.
They are perpendicular to each other.
They are parallel and congruent.
The relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.
How to determine the relationship?When a triangle FIT is reflected over the y-axis, the image and the pre-image of the triangle would be at either sides of the y-axis.
This means that the points on the image and the pre-image of the triangle are perpendicular to each other
Hence, the relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.
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Find the gradients of lines A and B.
B
141
12
Hol
8
NO 9 go
6
41
2
-3-2-10
-2
-4
-6
A
2 3 4 5
7x
Let's see
For line A
(2,2)(3,6)Slope
m=6-2/3-2m=4/1m=4For line B
(1,6)(2,4)Slope
m=4-6/2-1m=-2/1m=-2