Answer:
1/36 or 0.0277... or approximately a 3% chance of rolling a sum greater than 11 (i.e., a sum of 12)
Step-by-step explanation:
Create a 6 x 6 grid on a piece of graph paper. Number the 6 columns 1-6 at the top (for the value of the first die) and number the rows 1-6 on the side (for the value of the second die). You must imagine that you are rolling one die then the other (rather than how people "normally" roll both simultaneously). In the 36 empty boxes in your grid below the column numbers and to the right of the row numbers, put the sums of rolling the die at the top of the column + its corresponding die from the row (for example, use your fingers to match column number 4, say, with row 4 to get a sum of 8). When you've filled out the grid, you will see that a sum of 2 and sum of 12 have the same probability (there's only one way to get a sum of 2 or sum of 12, either 1 + 1 or 6 + 6). But there are many more ways, for example, to get a sum of 7
Thomas buys a case of bottled water .A case contains 36 bottles of water and $4.69.Thomas would sell each bottle of water for $0.75 at a school event How much profit ,in dollars ,will Thomas earn if he sells all the bottles of water ?
Answer:
The profit will be [tex]\$22.31[/tex]
Step-by-step explanation:
we know that
To find the profit subtract the cost of the case of bottled water from the sell of all the bottles of water
Let
x-----> the profit
[tex]x=36*0.75-4.69=\$22.31[/tex]
Which of the following is unnecessary when multiplying these polynomials?
(2x∧3 + 2x∧2 - 3x)(9x∧2-4x+5)
A.
use the distributive property
B.
use the multiplication property of exponents
C.
combine like terms
D.
find the GCF
Answer:
Find the GCF
Step-by-step explanation:
When multiplying the following polynomials:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5)
1. First we need to use the distributive property:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 2x^3 * 9x^2 - 2x^3 * 4x + 2x^3 * 5 + 2x^2 * 9x^2 - 2x^2 * 4x + 2x^2 * 5 - 3x * 9x^2 + 3x * 4x - 3x * 5.
2. Second, we need to use the multiplication property of exponents:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 - 8x^4 + 10x^3 + 18x^4 - 8x^3 + 10x^2 - 27x^3 + 12x^2 - 15x.
3. We need to combine like terms:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 +10x^4 -25x^3 + 22x^2 - 15x.
We don't need to find the GCF.
A polygon is convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon.If this statement is true, then which of the following statements must also be true?A.A segment connecting any two vertices of a polygon never passes through the exterior of a polygon if and only if the polygon is not convex.B.A polygon is not convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon.C.A polygon is convex if and only if a segment connecting any two vertices never passes through the interior of the polygon.D.A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon.
Answer:
D
Explanation:
A is the same thing as the statement, only that it says if the polygon is convex. Same thing for B. C could've worked if it said exterior instead of interior. D is basically the converse of the statement.
A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D
What is the difference between a convex polygon and a concave polygon?Each interior angle of a convex polygon is less than 180° while in the case of the concave polygon at least one angle is more than 180°.
In the diagram attached,
We can see in the case of a convex polygon if we join any two vertices, a line segment joining two vertices never passes through the exterior or interior of the polygon.
In the case of a concave polygon, at least a line segment joining two vertices passes through the exterior of a polygon.
Therefore, A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D
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Residuals
A residual is the difference between the actual value and the predicted value.
Suppose the regression line modeling ticket sales is y = –5.9x + 170.85, where x represents ticket price and y represents attendance.
1. What is the predicted attendance when the ticket price is $5? _________
2. The actual attendance was 160 when the ticket price was $5.
Find the residual: _________ – _________ = _________
Answer:
1. predicted attendance: 141.35
2. residual: 18.65
Step-by-step explanation:
1. Predicted attendance is ...
y = -5.9·5 +170.85 = 141.35
__
2. As the problem statement tells you, ...
actual value - predicted value = residual
160 - 141.35 = 18.65 . . . the residual
What is the total weight, in pounds, of 100 sharks that each weigh 5.015× 10 (to the 3rd power) pounds
Answer:
12612837.8375
Step-by-step explanation:
first you have to multiply 5.015 x 10 and you get 50.15 the put that to the power of 3 and then multiply the total by 100.
In circle P, which arc is a semicircle?
Please help! Asap! Ty in advanced
Answer:
d. arc BCE
Step-by-step explanation:
BE is a diameter which means it cuts the circle in half therefore arc BCE is a semicircle
Which of the following expressions is equal to ?
Answer:
Second choice
Find the measure of the leg of a 45-45-90 right triangle given the hypotenuse is 4√2 .
A.) 2
B.) 2√2
C.) 8
D.) 4√2
E.) 4
Answer:
e). 4
Step-by-step explanation:
45-45-90
x-x-xsquare root of 2
Final answer:
The measure of the leg of a 45-45-90 right triangle with a hypotenuse of 4√2 is 4 units.
Explanation:
The question asks for the measure of the leg of a 45-45-90 right triangle given that the hypotenuse is 4√2. In a 45-45-90 right triangle, both legs are of equal length and the hypotenuse is √2 times the length of a leg. Using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a2 + b2), we can find the length of a leg when the hypotenuse is known.
Let the length of each leg be 'a'. Since the hypotenuse is 4√2, the equation according to the Pythagorean Theorem would be a2 + a2 = (4√2)2. This simplifies to 2a2 = 32, so a2 = 16, and thus a = √16. Therefore, each leg measures 4 units.
help please thank you.
first answer choice is yes or no.
other answer choices are: 3 4 5 6
Hello there! Here are your answers:
Does Kerri's dot plot match the data in the tally table? No.
Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.
The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):
5 - classmates spent 3 hours at the park
3 - classmates spent 4 hours at the park
6- classmates spent 5 hours at the park
4 - classmates spent 6 hours at the park
I hope this was helpful and let me know if you need more help! :) Have a great day! :)
Answer:
the other guy is right
Step-by-step explanation:
-~- boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii laggy
A guide climbs a mountain at the rate of 30 minutes for every 50 feet. How many hours will it take the guide to climb 750 feet
Answer: 7.5 hours
Step-by-step explanation:
750/50=15 to see how many times he climbed 15 feet
15 times 30=450 (total minutes)
450/60=7.5 hours
Answer:7.5
Step-by-step explanation:
450/60
What is the solution of log((3x + 4))4096 = 4? ( the 3x+4 is like an exponent but lower
[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3x+4}(4096)=4\implies \stackrel{\textit{exponential form}}{(3x+4)^4=4096}\implies (3x+4)^4=2^{12} \\\\\\ \stackrel{~\hfill \textit{same exponents, the bases must be the same}}{(3x+4)^4=2^{3\cdot 4}\implies (3x+4)^4=(2^3)^4}\implies 3x+4=2^3\implies 3x+4=8 \\\\\\ 3x=4\implies x=\cfrac{4}{3}[/tex]
The head librarian at a public library releases a report. The report states that visitors to the library want the library to open one hour earlier on Saturdays. The report was based on a survey of the first 50 visitors to the library on a recent Saturday. Participants were asked the question, "Do you think the library should open one hour earlier on Saturdays?"
Select ALL statements that correctly evaluate the report.
Answer:
Step-by-step explanation:
The question is not biased. It doesn't push the participants to answer one way or another.
However, the sample is biased. It does not represent the population.
The first and fourth options are correct.
Match the equations of ellipses to their equivalent equations in standard form.
Answer:
# The general form of x²/3² + (y - 2)²/2² = 1 is 4x² - 36y + 9y² = 0
# The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0
# The general form of x²/6² + (y + 4)²/4² = 1 is 16x² + 288y + 36y² = 0
# The general form of (x - 3)²/3² + y²/5² = 1 is 25x² - 150x + 9y² = 0
Step-by-step explanation:
* Lets revise the general form and the standard form of the ellipse
- The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0
- The standard form is (x - h)²/a² + (y - k)²/b² = 1
* Lets solve the problem
# x²/3² + (y - 2)²/2² = 1
∵ x²/9 + (y - 2)²/4 = 1 ⇒ multiply both sides by 9 × 4 (36)
∴ 4x² + 9(y - 2)² = 36 ⇒ open the bracket power 2
∴ 4x² + 9(y² - 4y + 4) = 36 ⇒ multiply the bracket by 9
∴ 4x² + 9y² - 36y + 36 = 36 ⇒ subtract 36 from both sides
∴ 4x² - 36y + 9y² = 0
* The general form of x²/3² + (y - 2)²/2² = 1 is 4x² + 9y² - 36y = 0
# (x + 7)²/7² + y²/6² = 1
∵ (x + 7)²/49 + y²/36 = 1 ⇒ multiply both sides by 49 × 36 (1764)
∴ 36(x + 7)² + 49y² = 1764 ⇒ open the bracket power 2
∴ 36(x² + 14x + 49) + 49y² = 1764 ⇒ multiply the bracket by 36
∴ 36x² + 504x + 1764 + 49y² = 1764 ⇒ subtract 1764 from both sides
∴ 36x² + 504x + 49y² = 0
* The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0
# x²/6² + (y + 4)²/4² = 1
∵ x²/36 + (y + 4)²/16 = 1 ⇒ multiply both sides by 36 × 16 (576)
∴ 16x² + 36(y + 4)² = 576 ⇒ open the bracket power 2
∴ 16x² + 36(y² + 8y + 16) = 576 ⇒ multiply the bracket by 36
∴ 16x² + 36y² + 288y + 576 = 576 ⇒ subtract 576 from both sides
∴ 16x² + 288y + 36y² = 0
* The general form of x²/6² + (y + 4)²/4² = 1 is 16x² + 288y + 36y² = 0
# (x - 3)²/3² + y²/5² = 1
∵ (x - 3)²/9 + y²/25 = 1 ⇒ multiply both sides by 9 × 25 (225)
∴ 25(x - 3)² + 9y² = 225 ⇒ open the bracket power 2
∴ 25(x² - 6x + 9) + 9y² = 225 ⇒ multiply the bracket by 25
∴ 25x² - 150x + 225 + 9y² = 225 ⇒ subtract 225 from both sides
∴ 25x² - 150x + 9y² = 0
* The general form of (x - 3)²/3² + y²/5² = 1 is 25x² - 150x + 9y² = 0
Answer:In Plato this is the correct answer
Step-by-step explanation:
I legit hate Word problems they are so stupid, so if anyone can help me that would be great, thank you
Suppose that a man standing at the edge of a cliff near the North Rim of the Grand Canyon is looking downward towards a campground inside the canyon. The elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The man's range finder indicates that his line of sight distance to the campground is 3044 ft.
What is the angle of depression of the man's line of sight to the campground?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
To find the angle of depression, we can use trigonometry. The elevation of the North Rim and the campground, along with the line of sight distance, can be used to calculate the angle using the tangent function.
Explanation:To find the angle of depression of the man's line of sight to the campground, we can use trigonometry. The angle of depression is the angle between the line of sight and a horizontal line. In this case, the elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The line of sight distance to the campground is 3044 ft.
We can use the tangent function to find the angle of depression. Tangent(theta) = opposite/adjacent. The opposite side is the difference in elevation between the North Rim and the campground (5389 ft - 2405 ft) and the adjacent side is the line of sight distance (3044 ft). So, tangent(theta) = (5389 ft - 2405 ft) / 3044 ft.
Using a scientific calculator, we can find the value of theta by taking the inverse tangent (or arctan) of the ratio: theta = arctan((5389 ft - 2405 ft) / 3044 ft). The answer is approximately 57.38 degrees.
Membership to a national running club is shown in the table which answer describes the average rate of change from year 3 to year 5?
Membership increased by an average of 6,600 people per year from year 3 to year 5
Membership decreased by an average of 6,600 people per year from year 3 to year 5
Membership decreased by an average of 13,200 people per year from year 3 to year 5
Membership increased by an average of 13,200 people per year from year 3 to year 5
Answer:
"Membership decreased by an average of 6,600 people per year from year 3 to year 5"
Step-by-step explanation:
To get average rate of change from year 3 to year 5, we need to divide the change from year 3 to 5 by 2 (because from year 3 to 5 is 2 years).
THe change is:
83.6 - 96.8 = -13.2
We divide by 2 to get per year average rate of change:
-13.2 / 2 = -6.6
In thousands, that is 6600 decrease.
2nd answer choice is right.
30pts BRAINLIEST please help? teach me how to do it as well, thankyou!
look up a video on the internet and it will show you
A snack food company packs 5 cookies in each box. Let b represent the number of boxes and c represent the total number of cookies.
Answer:
5*B=C
Step-by-step explanation:
Five cookies times the number of boxes will give you the total number of cookies
Two rectangles have the same width. One is 12 units long and the other is 8 units long. The area of the first rectangle is 320 square units more than the area of the second rectangle. Find the width of each rectangle.
Answer:
80
Step-by-step explanation:
let w = the width of the rectangles
then
12w = the area of one rectangle
8w = the area of other
:
12w - 8w = 320
4w = 320
w = 320/4
w = 80 units wide
;
:
Check
12 * 80 = 960
8 * 80 = 640
--------------
difference: 320
We know that both rectangles have the same width, which is 80 units.
How to find the width of each rectangle?
We know that both rectangles have the same width, so we can say that both have the width W.
One of the rectangles has a length of 12 units, and the other of 8 units, so the areas are:
A = 12*W
A' = 8*W
And the largest area is 320 square units more than the other area, so we have:
12*W = 8*W + 320
Solving for W we get:
12*W - 8*W = 320
4*W = 320
W = 320/4 = 80
Then the width of each rectangle is 80 units.
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Billy needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the total area of the two triangles that need to be painted? Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 9 cm, and its base is 3 cm.
The area of a triangle is half the multiplication of the base and the height.
So, if the smaller triangle has height 6 cm and base 2 cm, its are is
[tex]\dfrac{6\times 2}{2}=6[/tex]
Similarly, if the height of the larger triangle is 9 cm, and its base is 3 cm, its area is
[tex]\dfrac{9\times 3}{2}=\dfrac{27}{2}[/tex]
So, the total area is
[tex]6+\dfrac{27}{2} = \dfrac{12}{2}+\dfrac{27}{2}=\dfrac{39}{2}[/tex]
The total area of the two triangles that need to be painted is 19.5 cm².
Explanation:The total area of the two triangles that need to be painted can be found by adding the area of the smaller triangle and the area of the larger triangle. The formula to calculate the area of a triangle is:
Area = (base * height) / 2
For the smaller triangle, the base is 2 cm and the height is 6 cm. Substituting these values into the formula, we get:
Area of smaller triangle = (2 cm * 6 cm) / 2 = 6 cm²
For the larger triangle, the base is 3 cm and the height is 9 cm. Substituting these values into the formula, we get:
Area of larger triangle = (3 cm * 9 cm) / 2 = 13.5 cm²
To find the total area, we add the areas of the two triangles:
Total area = area of smaller triangle + area of larger triangle = 6 cm² + 13.5 cm² = 19.5 cm²
Please help me out please!!!!!!!! :)
Answer:
12.3
Step-by-step explanation:
cos(35) = y/15
y = 15 * cos(35) = 12.3
Answer:
y = 12.3 cm
Step-by-step explanation:
Since the triangle is right with hypotenuse 15, use the cosine ratio to solve for y, that is
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]
Multiply both sides by 15
15 × cos35° = y, hence
y ≈ 12.3
Someone please help??
Answer:
the correct answer would be c, g(x)=2^x+2
Step-by-step explanation:
We can eliminate the first and the last option because the line is going upwards, not downwards(it would if it was negative or had the negative sign in front). We can cross out the second option because if it was 2^x+3, then it would be crossing (0,4) on the y-axis. Therefore the correct option is C, since it crosses right at (0,3).
hope this helps :)
The ratio of cups of orange juice concentrate to cups of water in punch is 1:3 if James made 32 cups of punch how many cups of orange juice did he need
Answer:
We have 8 cups of orange juice
Step-by-step explanation:
orange juice: water: total
1 : 3 : 4
Multiply everything by x
1x 3x 4x
We have 32 cups total
4x = 32
Divide each sice by 4
4x/4 = 32/4
x = 8
We have 8 cups of orange juice
3*8 = 24
We have 24 cups of water
The ratio of orange juice to water in the punch is 1:3, which means that for every single cup of orange juice, there are 3 cups of water. To find out how many cups of orange juice were used to make 32 cups of punch, we find out what 1 part out of the total 4 parts is, which is 32 ÷ 4 = 8. Therefore, James used 8 cups of orange juice for the punch.
Explanation:The subject of the question is Mathematics and it pertains to the concept of ratios in particular. The ratio of orange juice concentrate to water is given as 1:3. This means that for every 1 cup of orange juice, James uses 3 cups of water. So, the total parts in the punch are 1 (for orange juice) + 3 (for water) = 4 parts.
However, James made 32 cups of punch. Hence, to find out how many cups of orange juice he used, we need to find out what 1 part out of the total 4 parts is. To do this, you divide the total punch made (32 cups) by the number of total parts (4).
Therefore, 32 cups divided by 4 equals 8 cups. Hence, James used 8 cups of orange juice to make the punch.
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The number of instructions N performed per second by a computer varies directly as the speed S of the computer's internal processor. A processor with a speed of 20 megahertz can perform 1 comma 600 comma 000 instructions per second.
a) Find an equation of variation.
b) How many instructions per second will the same processor perform if it is running at a speed of 180 megahertz?
Answer:
a)
The equation of variation is;
N = 80000*S
b)
14400000
Step-by-step explanation:
We are informed that the number of instructions N performed per second by a computer varies directly as the speed S of the computer's internal processor. This means that N and S are directly proportional;
N∝S
Introducing a constant of proportionality, k;
N=k*S
We shall find the value of k by using the information given;
N = 1600000
S = 20
k = 1600000/20
= 80000
a)
The equation of variation is thus;
N = 80000*S
b)
We are required to find N when S = 180
Using the equation of variation obtained above;
N = 80000 (180)
= 14400000
Re-write this question to make it a statistical question:
How old am I?
it means that you must write "How old am I" into a statistical question
A statistical question is a question asked with the goal of collecting data. You could rewrite the question so that it says something like, “How old were you when..” That way the responses will vary and you would be able to graph and compare them.
The statistical question of the given statement is How old were you then.
The following tells about the statistical question:A statistical question is one that can be answered by collecting data and for which there will be variability in that data.For example, there will likely be variability in the data collected to answer the question, "How much do the animals at Fancy Farm weigh?" but not to answer, "What color hat is Sara wearing?"A statistical question is a question that can be answered by gathering data and a question for which we expect to have variation in the data we collect.Hence, the statistical question of the given statement is How old were you then.
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Mrs. Paulson bought chicken wire to enclose a rectangular garden. She is restricted to a width of no more than 30 feet. She would like to use at most 180 feet of chicken wire. This situation can be represented by a system of inequalities, where x = the width of the chicken wire and y = the length of the chicken wire. Identify two possible combinations for the width and length of the chicken wire in order to make her a rectangular garden. Create a system of linear inequalities.
Answer:
Let l = length and w = width of the rectangular garden
=> w < 30
and 2(l + w) ≤ 180
=> l + w ≤ 90
=> 0 < w < 30 and 60 ≤ l < 90.
Step-by-step explanation:
What is the value of B?
Answer: 120
Step-by-step explanation:
what is the midpoint of the line segment with endpoints (3, 2, 2, 5) and (1, 6, -4.5)?
A. (4.8, -1)
B. (2.4, -2)
C. (4.8, -2)
D. (2.4, -1)
Answer:
D. (2.4, -1).
Step-by-step explanation:
The midpoint of the line segment with endpoints (x1,y1) and (x2,y2) is
[(x1+x2) / 2 , (y1+y1)/2 ].
So here we have : [ (3.2+1.6)/ 2 (2.5 - 4.5)/2)
= (2.4, -1) answer.
The midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).
To find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂), you can use the midpoint formula:
Midpoint (M) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
For the given endpoints (3.2, 2.5) and (1.6, -4.5), we can calculate the midpoint as follows:
Midpoint (M) = ((3.2 + 1.6) / 2, (2.5 + (-4.5)) / 2)
= (4.8 / 2, -2 / 2)
= (2.4, -1)
Therefore, the midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).
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hat is the surface area of sphere with diameter 23 ft? 529π ft2 184π ft2 46π ft2 2,116π ft2\
Answer:
The surface area of the sphere is [tex]529\pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=23/2=11.5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]SA=4\pi (11.5)^{2}[/tex]
[tex]SA=529\pi\ ft^{2}[/tex]
A rectangular lot is 275 feet deep, and it contains 2\3 of an acre. what is the length of the lot
Answer:
The length of the lot is [tex]105.6\ ft[/tex]
Step-by-step explanation:
Remember that
[tex]1\ acre=43,560\ ft^{2}[/tex]
In this problem the area of the lot is equal to
[tex]\frac{2}{3} (43,560)=29,040\ ft^{2}[/tex]
Let
x-----> the length of the lot
y ----> the deep of the lot
The area of the lot is
[tex]A=xy[/tex]
we have
[tex]A=29,040\ ft^{2}[/tex]
[tex]y=275\ ft[/tex]
substitute and solve for x
[tex]29,040=x(275)[/tex]
[tex]x=29,040/(275)=105.6\ ft[/tex]
Please help me out please
Answer:
(a, 0)
Step-by-step explanation:
As S is on the x-axis, its y-coordinate will be zero.
And since this is a right trapezoid, ∠QPS and ∠PSR are right angles, so S and R will have the same x-coordinate, which is a.
Therefore, the coordinate of Point S is (a, 0)