Design a box that will hold 24 2-in cubes, with no empty space left in the box after it is filled with the cubes. Describe two possible designs for the box. Sketch each design and find the surface area and volume of each box.
Answers
Below given are two possible designs for the box.
The total surface area is 2(12) + 2(8) + 2(10) = 24 + 16 + 20 = 52 square inches.
What is total surface area?Total surface area is the sum of the areas of all the faces of a three-dimensional object.
Design 1:
One possible design for the box is a rectangular prism with dimensions of 4 in x 4 in x 6 in. This box will have enough space to hold 24 2-in cubes with no empty space left in the box after it is filled with the cubes.
To find the surface area and volume of the box, we can use the following formulas:
Surface Area = 2lw + 2lh + 2wh
Volume = lwh
where l, w, and h represent the length, width, and height of the box, respectively.
In this case, we have:
l = 4 in
w = 4 in
h = 6 in
So the surface area of the box is:
Surface Area = 2(4)(4) + 2(4)(6) + 2(4)(6)
Surface Area = 112 in²
And the volume of the box is:
Volume = 4(4)(6)
Volume = 96 in³
Design 2:
Another possible design for the box is a cube with dimensions of 3.4 in x 3.4 in x 3.4 in. This box will also have enough space to hold 24 2-in cubes with no empty space left in the box after it is filled with the cubes.
To find the surface area and volume of the box, we can use the same formulas as before, but with the new dimensions:
l = 3.4 in
w = 3.4 in
h = 3.4 in
So the surface area of the box is:
Surface Area = 2(3.4)(3.4) + 2(3.4)(3.4) + 2(3.4)(3.4)
Surface Area = 69.12 in²
And the volume of the box is:
Volume = 3.4(3.4)(3.4)
Volume = 39.3 in³
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Related Questions
on thurday, lisa had 5$ in her bank account. she went to target to purchase stickers for her class. each pack of stickers cost 2$
write an inequality that represents s, the number of stickers purchased that resulted in her account ending in -10.
Answers
Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. The inequality can be written as: s ≥ 8
What is fractiοn?A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.
Let's start by defining the variables and the inequality. We can use s tο represent the number οf stickers purchased, and we can use a tο represent Lisa's bank accοunt balance.
Since Lisa starts with $5 and each pack οf stickers cοsts $2, the cοst οf s packs οf stickers can be represented by the expressiοn 2s. Therefοre, Lisa's bank accοunt balance after purchasing s packs οf stickers can be represented by the expressiοn:
a = 5 - 2s
Tο represent the scenariο where Lisa's accοunt ends up with a balance οf -10, we can write the fοllοwing inequality:
a = 5 - 2s ≤ -10
Simplifying the inequality:
5 - 2s ≤ -10
-2s ≤ -15
s ≥ 7.5
Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. Therefοre, the inequality can be written as:
s ≥ 8
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Mr. Unitech decides to set up a quality candidate poster printing service. It uses the following charging rules for a candidate poster printing: For printing 250 posters or less, a standard cost of K400 is charged. For every poster printed after the first 250 copies, K5 is charged plus the maintenance fee of K50. (a) Write the multiple charging functions for the candidate poster printing service. (b) From your solution to (a), answer the following questions: (i) Calculate the charge for printing 1250 candidate posters. Calculate the charge for printing 250 candidate posters. (ii) How many candidate posters can be supplied at the cost of K2500? How many candidate posters can be supplied at the cost of K400? (iv)
Answers
The cost of producing 250 candidate posters is K400, and that 660 potential posters can be provided for K2500. This means that K400 + (x - 250) * K5 + K50 = K2500, and that K400 + (x - 250) * K5 + K50 = K2500. Finally, K400 + (x - 250) * K5 + K50 = K2500, and that K400 = 250.
What is an unitary method?The unitary method is a mathematical approach used to handle proportional and rate issues. We obtain the value of one unit of a quantity and then use it to get the value of any other quantity that is proportional to it using this procedure.
This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.
Here,
(a)
=> C(x) = K400 for 0 x 250.
=> C(x) = K400 + (x - 250) * K5 + K50 for x > 250
(b)
(i)
=> C(1250) = K400 + (1250 - 250) * K5 + K50
=> K400 + 1000*K5 + K50
=> K5400
In light of this, the cost to produce 1250 candidate posters is K5400.
We use the first portion of the charging function since 250 250 to determine the cost for printing 250 candidate posters. So:
=> C(250) = K400
Therefore, K400 is required to produce 250 candidate posters.
(ii)
=> K400 + (x - 250) * K5 + K50 = K2500
=> (x - 250) * K5 = K2050
=> x - 250 = 410
Therefore, 660 potential posters can be provided for K2500.
=> C(x) = K400
=> x = 250
250 applicant posters can be provided for K400 as a result.
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A diagram with line m parallel to line n is shown.
(3x + 10)°/
any
Express the value of y in terms of x.
y =
X
US
Answers
If line m parallel to line n, the value of y in terms of x is y = 3x + 10.
Let's consider the given information: a diagram with line m parallel to line n, and an angle (3x + 10)°.
Since line m is parallel to line n, we can use the properties of parallel lines and their transversals to find the relationship between x and y.
In this case, we'll use the property called alternate interior angles, which states that if two parallel lines are cut by a transversal, their alternate interior angles are congruent.
Identify the alternate interior angles.
Let's say the angle (3x + 10)° is an alternate interior angle to angle y°.
Use the property of alternate interior angles.
Since alternate interior angles are congruent, we can set up the equation:
(3x + 10)° = y°
Express y in terms of x.
Now that we have the equation, we can express y in terms of x:
y = 3x + 10
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Question -
A diagram with line m parallel to line n is shown express the value of y in terms of x
Please see attached need help
Answers
The vertices of the region are (7.2, -1.2) and (-2, 2).
Describe Inequality?In mathematics, an inequality is a statement that one quantity is less than or greater than another quantity. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
or example, "x > 5" means that x is greater than 5, while "y ≤ 10" means that y is less than or equal to 10.
Inequalities can be solved by isolating the variable on one side of the inequality symbol, just as with equations. However, there are some important differences between solving equations and solving inequalities. When solving an inequality, the direction of the inequality symbol may need to be reversed if both sides of the inequality are multiplied or divided by a negative number. In addition, the solution to an inequality is often expressed using interval notation or a number line.
To graph the system of inequalities, we first need to graph the boundary lines:
6y - x = 6 is equivalent to y = (1/6)x + 1, which has a y-intercept of 1 and a slope of 1/6.
y + 3x = -4 is equivalent to y = -3x - 4, which has a y-intercept of -4 and a slope of -3.
The region that satisfies both inequalities is the shaded region below the blue line and to the left of the red line.
To find the vertices of the region, we need to find the points where the two boundary lines intersect. Solving the system of equations:
y = (1/6)x + 1
y = -3x - 4
We get:
(7.2, -1.2) and (-2, 2)
Therefore, the vertices of the region are (7.2, -1.2) and (-2, 2).
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The vertices of the region are (7.2, -1.2) and (-2, 2).
Describe Inequality?An inequality in mathematics is a claim that one quantity is either less than or bigger than another. Inequalities are represented using symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
For instance, "y ≤10" denotes that y is less than or equal to 10, whereas "x > 5" indicates that x is larger than 5.
Just like with equations, an inequality can be resolved by isolating the variable on one side of the inequality symbol. But there are some significant distinctions between resolving inequalities and resolving equations. If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol's direction may need to be reversed in order to solve the inequality. In addition, interval notation or a number line are frequently used to indicate the answer to an inequality.
We must first graph the boundary lines before we can graph the system of inequality:
6y - x = 6 is equivalent to y = (1/6)x + 1, which has a y-intercept of 1 and a slope of 1/6.
y + 3x = -4 is equivalent to y = -3x - 4, which has a y-intercept of -4 and a slope of -3.
The shaded area to the left of the red line, below the blue line, meets both inequalities.
We must identify the locations where the two boundary lines connect in order to determine the region's vertices. figuring out the equations in
a system:
y = (1/6)x + 1
y = -3x - 4
We get:
(7.2, -1.2) and (-2, 2)
The vertices of the region are (7.2, -1.2) and (-2, 2).
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The functions f(x) = (x + 1)^2 − 2 and g(x) = −(x − 2)^2 + 1 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning
Answers
Answer:
f(x) — minimumg(x) — maximumStep-by-step explanation:
You want to know if the vertex is a minimum or maximum for functions ...
f(x) = (x +1)² -2g(x) = -(x -2)² +1ExtremesThe sign of the leading coefficient is the sign of the function values when x has a large magnitude.
If the leading coefficient is positive, the parabola opens upward. Hence the vertex is a minimum. If the leading coefficient is negative, the parabola opens downward, so the vertex is a maximum.
f(x)The coefficient of the (x+1)² term is +1, so the vertex is a minimum.
g(x)The coefficient of the (x-2)² term is -1, so the vertex is a maximum.
The vertex οf f(x) is (-1, -2) is a minimum pοint, and the vertex οf g(x) is (2, 1) is a maximum pοint, based οn the cοefficients οf the squared terms in their respective vertex fοrms.
What is vertex?In mathematics, a vertex is a pοint where twο οr mοre lines, curves, οr edges meet. It can alsο refer tο the highest οr lοwest pοint οn a curve οr surface.
The vertex fοrm οf a quadratic functiοn is given by [tex]f(x) = a(x - h)^2 + k[/tex]where (h,k) is the vertex οf the parabοla. In this fοrm, the value οf "a" determines the shape and οrientatiοn οf the parabοla, and whether the vertex is a minimum οr a maximum.
Let's first rewrite the given functiοns in vertex fοrm:
[tex]f(x) = (x + 1)^2 - 2= 1(x - (-1))^2 - 2= 1(x - (-1))^2 + (-2)[/tex]
Therefore, the vertex of f(x) is (-1, -2), and since the coefficient of the squared term is positive, the parabola opens upward. This means that the vertex (-1, -2) is a minimum point.
[tex]g(x) = -(x-2)^2+1[/tex]
[tex]= -1(x - 2)^2 + 1[/tex]
Therefore, the vertex of g(x) is (2, 1), and since the coefficient of the squared term is negative, the parabola opens downward. This means that the vertex (2, 1) is a maximum point.
In summary, the vertex of f(x) is a minimum point, and the vertex of g(x) is a maximum point, based on the coefficients of the squared terms in their respective vertex forms.
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please help me with math the following questions are
what is the mean of the data represented by the stem and the leaf plot above
-164.5
-309
-57
-108.75
what is the median of the data represented by the steam and leaf plot
a 164.5
b 57
c 108.75
d 309
Answers
For the givn steam and leaf plot, the mean= 11.61 and the median = 7.
What is mean?
In mathematics, the mean is a measure of central tendency of a set of numbers. It is also known as the average.
To find the mean of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.
The stem and leaf plot indicates that we have the following values:
For stem 1: 0, 0, 2, 8
For stem 3: 1, 7, 9
For stem 5: 0, 5, 7, 7, 7
For stem 11: 3, 4, 6
For stem 22: 3
For stem 23: 5
For stem 31: 0, 2, 9
To calculate the mean, we add up all these values and divide by the total number of values.
There are a total of 18 values, so:
(1x4 + 3x3 + 5x5 + 11x3 + 22x1 + 23x1 + 31x3) / 18
= (4 + 9 + 25 + 33 + 22 + 23 + 93) / 18
= 209 / 18
= 11.61 (rounded to two decimal places)
Therefore, the mean of the data represented by the stem and leaf plot is approximately 11.61.
To find the median of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.
The stem and leaf plot indicates that we have the following values:
For stem 1: 0, 0, 2, 8
For stem 3: 1, 7, 9
For stem 5: 0, 5, 7, 7, 7
For stem 11: 3, 4, 6
For stem 22: 3
For stem 23: 5
For stem 31: 0, 2, 9
We can list all the values in order from smallest to largest:
0, 0, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 8, 9, 11, 29, 31
There are a total of 17 values. Since there is an odd number of values, the median is the middle value.
The middle value is the ninth value in the ordered list, which is 7.
Therefore, the median of the data represented by the stem and leaf plot is 7.
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What is the solution to this equation?
-3(5w-4) = 6(2w-7)
Answers
Answer:
w=2
Step-by-step explanation:
1. You need to distribute your -3 and 6
2. After you do your distributing the numbers, the equation would be -15w+12=12w-42
3. You need to make x to the right or left and it look like 27w=54
4. Solve for x
5. The answer is w=2
True or False. The point (√7, 5) lies on the circle centered at the origin and containing the
point (5,2). Justify your answer.
Answers
The point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).
Checking if the point lies on the circle centered at the originThe equation of a cifcle that has its center at the origin is
x² + y² = r²
Where
r = radius
Using the given points, we have
√7² + 5² = r²
Evaluate
32 = r²
For the second point, we have
5² + 2² = r²
Evaluate
29 = r²
The calculated values are not equal
So, the point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).
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Dmitri wants to cover the top and sides of the box shown with glass tiles that are 5 mm square. How many tiles does he need?
Answers
To get the number of tiles needed, we must first determine the surface area of the box that must be covered. Surface area of the square box = top area + front area + rear area + left side area + right side area.
Top area = length x width = 6 cm x 4 cm = 24 cm2 Front and back area = height x breadth = 8 cm x 4 cm = 32 cm2 (for each) Left and right side area = height x length = 8 cm x 6 cm = 48 cm2 (for each) Surface area total = 24 + 2(32) + 2(48) = 232 cm2. To get the number of tiles needed, divide the total surface area by the area of each tile. each's area 5 mm × 5 mm = 0.25 cm2 tile Total surface area / Area of each tile = 232 / 0.25 = 928 tiles required As a result, Dmitri need 928 glass tiles to cover the top and sides of the box.
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Find the value of x.
Answers
Answer:
[tex]12x + 19 + 22x - 9 = 180[/tex]
[tex]34x + 10 = 180[/tex]
[tex]34x = 170[/tex]
[tex]x = 5[/tex]
Answer:
x = 5
Step-by-step explanation:
The angles shown on the image are supplementary angles because they make a straight line.
The sum of supplementary angles would be equal to 180 so we can write the following equation to find the value of x:
12x + 19 + 22x - 9 = 180
Add like terms.34x + 10 = 180
Subtract 10 from both sides.34x = 170
Divide both sides by 34.x = 5
simplify expression
(1+cos a)(1-cos(-a))
Answers
(1 + cos a)(1 - cos(-a)) = sin²a
Step-by-step explanation:
Using the even property of cosine, we can simplify cos(-a) to cos(a):
(1 + cos a)(1 - cos(-a)) = (1 + cos a)(1 - cos a)
Using the formula for the difference of two squares, we can simplify further:
(1 + cos a)(1 - cos a) = 1 - cos²a
Finally, using the identity cos²a + sin²a = 1, we can substitute sin²a for 1 - cos²a:
1 - cos²a = sin²a
Therefore, the simplified expression is:
(1 + cos a)(1 - cos(-a)) = sin²a
Graph the system of equations.
-x+ 2y = -8
3x-y=-6
Answers
im kind of understanding but not completely yet, the step by steps that people are commenting are helping ! thank you
Answers
Answer: Can you take a closer picture?-
Step-by-step explanation:
Thanks!!
Answer:
Lines intersecting at a single point, One Solution
Step-by-step explanation:
1.) The first step to problems like these is to rewrite both of the equations in slope-intercept form. Slope-intercept form is a form in which y is isolated (By itself).
2.) Since we now know what to do, we can start with the first equation. You have to first get 7y by itself. To do this, you add 4x on both sides to move it to the other side. You would get 7y = 4x + 7. Now, divide by 7 on both sides to get y by itself. The final equation would be y = 4/7x + 1.
3.) Now, let's move on to the second equation. You first move x to the other side by subtracting by x on both sides. This would get you 8y = -x + 7. Finally, divide by 8 on both sides, which gets you y = -1/8x + 7/8.
4.) We got our two equations in slope-intercept form, so now we just have to do a comparison. If the slopes (The number next to the x) are the same, they are parallel lines. Parallel lines have no solutions. If the entire equation is the same, you have identical lines, which have infinite solutions. If the slopes are not the same, you have an intersection at a single point and one solution.
5.) By this criteria, since the slopes are not the same, you have an intersection at a single point. Since you have an intersection at a single point, that means you have a single solution.
Determine any data values that are missing from the table, assuming that the data represent a linear function. x y 4 17 6 19 21 10 a. Missing x:8 Missing y:23 c. Missing x:8 Missing y:22 b. Missing x:10 Missing y:21 d. Missing x:9 Missing y:20 Please select the best answer from the choices provided
Answers
Answer:
(a) Missing x:8 Missing y:23
Step-by-step explanation:
9(40÷5+9)+15-9
I need help solving this problem
Answers
Answer:
The answer to the problem is 159
The exchange rate between non-fixed currencies continuously fluctuates. The table below shows the exchange rate of the US dollar to the euro over the course of six days.
Day
$:€
Monday
1:0.7102
Tuesday
1:0.7544
Wednesday
1:0.7053
Thursday
1:0.6910
Friday
1:0.6869
Saturday
1:0.7273
Sandy has $829.04 to convert into euros. How many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate? Round all currencies to two decimal places.
a.
€33.49
b.
€55.96
c.
€67.04
d.
€107.99
Answers
55.96 more euros Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate. Thus, option B is correct.
What is the exchange rate?The number of units of a foreign currency that can be purchased with one unit of the domestic currency, or the opposite, is referred to as the exchange rate between two currencies.
Here, we have
Given: The exchange rate between non-fixed currencies continuously fluctuates. Sandy has $829.04 to convert into euros.
We have to find how many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate.
To get a favorable exchange rate we should do:
USD × Exchange Rate
a) 829.04 × 0.7544 ⇒ Most favorable exchange rate (Tuesday)
= 625.42
b) 829.04 × 0.6869 × 0.94 ⇒ Least favorable exchange rate (Friday)
= 569.46
Difference of most favourable day and Least favorable day
= 625.42 - 569.46
= 55.96
Hence, 55.96 more euros Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate. Thus, option B is correct.
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Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output ((¬p ∨ ¬r) ∧ ¬q) ∨ (¬p ∧ (q ∨ r)) from input bits p, q, and r.
Answers
Step-by-step explanation:
The required combinatorial circuit can be constructed as follows:
Firstly, we need to find the negation of p, q and r which can be achieved using inverters as shown below:
p q r
| | |
| | |
NOT NOT NOT
| | |
| | |
~p ~q ~r
Next, we can use OR gates to form the term (¬p ∨ ¬r) and (q ∨ r) as shown below:
~p ~r q r
| | | |
| | | |
OR OR | |
| | | |
| | | |
pORr rORp qORr rORq
Then, we can use AND gates to form the terms (¬p ∨ ¬r) ∧ ¬q and ¬p ∧ (q ∨ r) as shown below:
~p ~r q r
| | | |
| | | |
OR OR | |
| | | |
| | | |
pORr rORp qORr rORq
| | | |
| | | |
NOT NOT NOT |
| | | |
| | | |
~q ~pORr ~qORr qORr
| | | |
| | | |
AND OR AND |
| | | |
| | | |
(~pORr ~q) qORr qORr
| | |
| | |
OR AND |
| | |
| | |
(~pORr ∨ ~q) (~pORr ∧ qORr)
| | |
| | |
| OR |
| | |
| | |
((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))
| | |
| | |
| | |
OUTPUT
((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))
Graph the following system of equations.
3x + 6y = 12
3x + 2y = 8
What is the solution to the system?
A) There are infinitely many solutions.
B) There is one unique solution, (2, 1).
C) There is one unique solution, (6, 1).
D) There is no solution.
Answers
Answer:
B) There is one unique solution, (2, 1).
Attached is a graph of the system of equations.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 3x+6y=12 \\ 3x+2y=8\end{cases}[/tex]
Types of Solutions to a System of Equations
Infinitely Many Solutions: when two lines overlap each other, causing their solutions to be infinite.One Solution: when two lines intersect only at one point.No Solution: when two lines do not intersect.Using a graphing calculator, we can find the solution(s) to the given system of equations. To find the solution(s), we need to look at the point where the lines intersect; this is called the point of intersection.
Answer:
B: There is one unique solution, (2, 1)
Step-by-step explanation:
Took the test.
Which inequality can be used to represent this problem? Water costs $5 per thousand gallons, and there is a monthly connection fee of $2. A family has budgeted $12 for their water bill this month. How many thousands of gallons of water, x, can the family use without going over budget? Responses 5x+2≤12 5 x plus 2 less or equal than 12
Answers
The required inequality is 5x + 2 ≤ 12 and the solution is 2
Linear inequality:Inequalities are mathematical expressions that compare two values or expressions, indicating that one is less than, greater than, or equal to the other.
In this problem, we used a linear inequality to represent the relationship between the amount of water used and the total cost of the water bill.
We then used algebra to rearrange the inequality and solve for x, which gave us the maximum amount of water that the family can use without going over budget.
Here we have
The cost of the water bill is made up of two components: a fixed monthly connection fee of $2, and a variable cost based on the amount of water used.
The variable cost is $5 per thousand gallons, and the total cost, C, in dollars can be expressed as:
C = 5x + 2
where x is the number of thousands of gallons used.
The problem states that the family has budgeted $12 for their water bill this month. Hence the cost must not exceed $12
=> 5x + 2 ≤ 12
The above expression can be rewritten as follows
=> 5x + 2 ≤ 12
Subtract 2 from both sides
=> 5x ≤ 10
Divide by 2 into both sides
=> x ≤ 2
Therefore,
The required inequality is 5x + 2 ≤ 12 and the solution is 2
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HELP PLEASE !!!!!
What is m∠EFG?
Answers
From angle EHG, we can see that arc EG measures 42 degrees. Because FE and GF are chords intersecting at a point on the circle, they create an inscribed angle. Due to the inscribed angle theorem, the measure of EFG is half the measure of EHG. 1/2(84)=42. Let me know if you have a question!
You spin the spinner and flip a coin. Find the probability of the compound event.
Answers
Answer: 20%
(Please give me brainliest if you can tomorrow, hopefully this helps)
Explanation:
(So if it's even)
There are 5 possible outcomes and 2 evens on the spinner, so 2 favorable outcomes. That gives us a fraction of 2/5.
Flipping a coin, either heads or tails, it'd be 1/2.
Since it's a compound event we would multiply 2/5 and 1/2, getting:
[tex]\frac{2}{5} *\frac{1}{2} = \frac{2}{10}[/tex]
To change that into a percentage, we divide the numerator by the denominator and multiply by 100 which would give us:
.2 * 100 = 20%
What is the equivalent of the vertical line test when we interpret the test using polar coordinates?
Answers
The polar angle test is the equivalent of the vertical line test in polar coordinates.
What are polar coordinates?Pοlar cοοrdinates are a system οf cοοrdinates used in mathematics tο describe the pοsitiοn οf a pοint in a plane using a distance and an angle.
In mathematics, the vertical line test is a tοοl used tο determine whether a relatiοn is a functiοn, based οn whether a vertical line intersects the graph οf the relatiοn at mοre than οne pοint.
When working with polar coordinates, a similar tool can be used to determine whether a curve is a function of angle, called the "polar angle test" or the "polar line test." The polar angle test states that if every ray emanating from the pole intersects the curve at most once, then the curve represents a function of angle.
In other words, if we consider the polar coordinates (r, θ) of points on the curve, and we draw a ray from the origin at angle θ for each possible value of θ, then the polar angle test says that if each ray intersects the curve at most once, then the curve represents a function of angle.
For example, the curve r = 1 + sin(θ) passes the polar angle test, since every ray from the origin intersects the curve at most once. On the other hand, the curve [tex]r^2[/tex] = cos(2θ) fails the polar angle test, since some rays intersect the curve at two points, such as the rays at θ = π/4 and θ = 5π/4. Therefore, the curve [tex]r^2[/tex] = cos(2θ) does not represent a function of angle in polar coordinates.
Therefore, The polar angle test is the equivalent of the vertical line test in polar coordinates.
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Mila's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Answers
The independent variable, x, represents the number of questions Riley answered correctly, and the dependent variable is the score because the score depends on the number of questions Riley answered correctly. A function relating these variables is R(x) = [3x] So R(23) = [69], meaning 23 correct answers will give a score of 69.
the various kinds of variables.
There are two (2) main categories of variables in an experiment, and these are as follows:
a dependent variable.
the variable that is unrelated.
An independent variable is what?
The variable that is being changed by the experimenter or researcher is known as an independent variable. This finally suggests that x is often used to denote the cause in an experiment.
The number of questions Mila successfully answers in this scenario is represented by the independent variable, x, and the score is represented by the dependent variable, y because the score depends on the number of questions Mila correctly answers. R(x) = [3x] is a function that links these variables. R(23) thus equals [69], indicating 23 correct responses.
Complete Question:
Mila's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
The independent variable, x, represents the ______, and the dependent variable is the ______, because the ______ depends on the
A function relating these variables is R(x) = [] So R(23) = [], meaning 23
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What is the axis of symmetry?
Answers
Answer:
[tex] \frac{5x {}^{2} }{2} - 8x + 6[/tex]
Step-by-step explanation:
That's your answer
What is the solution to this equation? -12x - 7 = 53 Responses a) -5 a) -5 b) 5 b) 5 c) -3.83 c) -3.83 d) 3.83
Answers
Answer:
D
Step-by-step explanation:
If the toaster oven cost $ 115.00 when Sandra started recording the price, how much will she pay, in dollars, if she buys it after Week 3?
Answers
Answer: Im trying to find out too
Step-by-step explantion i dont know
Help Please I will give 20points
Answers
Answer:
10 acres
Step-by-step explanation:
Land for coconuts =
[tex] \frac{3}{8} = \frac{15}{40} [/tex]
Land for bananas =
[tex] \frac{4}{5} \times \frac{5}{8} = \frac{20}{40} \\ = \frac{4}{8} \\ = \frac{1}{2} [/tex]
Land left for rice =
[tex] \frac{40}{40} - \frac{15}{40} - \frac{20}{40} = \frac{5}{40} \\ = \frac{1}{8} [/tex]
Land for bananas =
[tex] \frac{1}{8} = 2.5 \\ \frac{4}{8} = 2.5 \times 4 \\ = 10[/tex]
Four transformations of the function f (x ) = 3x are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
Answers
The expressiοn that shοws the result οf that transfοrmatiοn intο the bοx under it are [tex]f(x) - 4 = 3^{x} - 4[/tex]
What is transfοrmatiοn?In mathematics, a transfοrmatiοn refers tο a prοcess οr οperatiοn that changes the pοsitiοn, shape, οr size οf a geοmetric figure οr οbject in a cοοrdinate plane οr space. Transfοrmatiοns can be classified intο several types, including translatiοns, reflectiοns, rοtatiοns, dilatiοns, and cοmbinatiοns οf these.
Each type οf transfοrmatiοn invοlves a set οf rules οr fοrmulas that define hοw the οriginal οbject οr figure is transfοrmed intο a new οne. Transfοrmatiοns play an impοrtant rοle in many areas οf mathematics and science, including geοmetry, linear algebra, cοmputer graphics, and physics.
given functiοn : [tex]f (x ) = 3^{x}[/tex]
fοr transfοrmatiοn, we need tο replace value οf x by the value given in different parts.
part 1 :
-4 f(x) = ?
we have [tex]f (x ) = 3^{x}[/tex]
sο, -4 × f (x ) = -4 × [tex]3^x[/tex]
∴ -4 f(x) = -4 × [tex]3^{x}[/tex]
part 2 :
f(-4x) = ?
we have f (x ) = [tex]3^{x}[/tex]
replacing value οf x by -4x,
∴ f(-4x) = [tex]3^{-4x}[/tex]
part 3
: f(x-4) = ?
we have [tex]f (x ) = 3^{x}[/tex]
sο, replacing value οf x by x-4,
∴[tex]f(x-4) = 3^{x-4}[/tex]
part 4 :
f(x) - 4 = ?
we have [tex]f (x ) =3^{x}[/tex]
sο, [tex]f(x) - 4 = 3^{x} - 4[/tex]
Hence the sοlutiοn are
-4 f(x) = -4 × [tex]3^{x}[/tex]
f(-4x) = [tex]3^{-4x}[/tex]
f(x-4) = [tex]3^{x-4}[/tex]
f(x) - 4 = [tex]3^{x} - 4[/tex]
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Compute the average (mean) from the given information.
• Number of data values: 106
• Sum of data values: 2,332
Responses
Answers
Step-by-step explanation:
The average = sum of data value ÷ number of data value = 2332 ÷ 106 = 22
The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z'
Answers
Answer:
374753
Step-by-step explanation:
this is not correct question