Answer:
Step-by-step explanation:
temperature is heated half an hour
19°c+71°c=90°c
{since its increased by 71°c}
90°c-[2°c*30]=30°c
so the final temperature is 30°cgeorge and jenna each completed a 12 miles run. this graph shows the total distance in miles that genna ran over time
In the first hour of their run, Jenna ran 1 mile more than George.
Given graph shows the data on Jenna's running status.
It shows that Jenna ran 12 miles in 2 hours of time.
Jenna's running status in the first one hour = 12/2 = 6 miles.
Given that George ran at a constant of 5 miles per hour.
To find out how many miles will Jenna ran more than George in the first one hour = 6 -5 = 1 mile.
From the above analysis, we can conclude that the Jenna will run 6 miles in the first one hour and George will run 5 miles in the first one hour. So, Jenna will run 1 mile more than George.
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Given question is not having enough information, the complete question is attached below,
Find the vertex and the axis of symmetry of the parabola given by the equation.
y = −x2 + 16x − 65
The axis of symmetry of the parabola is 8.
The vertex of the parabola is (8, -1).
How to find the vertex and the axis of symmetry of a parabola?The vertex of a parabola in standard form, y = ax² + bx + c, is given by:
Vertex, (h, k) = (-b/2a, c - b²/4a)
For y = -x² + 16x − 65:
a = -1, b = 16 and c = -65
-b/2a = -16/2(-1)
-b/2a = 8
c - b²/4a = -65 - (16)²/4(-1)
c - b²/4a = -65 + 64
c - b²/4a = -1
Vertex, (h, k) = (8, -1)
For a parabola in standard form, y = ax² + bx + c, the axis of symmetry of the parabola is given by:
x = -b/2a
For y = -x² + 16x − 65:
a = -1 and b = 16
Thus, the axis of symmetry of the parabola is:
x = -16/2(-1)
x = 8
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3
Please help
Question in image
Answer:
A. 12
Step-by-step explanation:
You want to know the length of tangent PQ, given that secant QS has segments QR = 8 and RS = 10. Points P, R, and S are on the circle. Point Q is external to the circle.
Secant relationThe relevant relation is ...
PQ² = QR·QS
x² = (8)(8+10) = 144
x = √144 = 12
The value of x is 12.
<95141404393>
Esports the Titian determined that the probability of a certain rugby team winning its next match is 11/23. Find the odds of the next match
The odds of the next match from the probability of 11/23 is 11 : 12
Finding the odds of the next matchFrom the question, we have the following parameters that can be used in our computation:
Probability = 11/23
For a probability represented as a/b, the odds is
Odds = a : b - a
In this case
a = 11 and b = 23
Using the above as a guide, we have the following:
Odds = 11 : 23 - 11
Evaluate the difference
So, we have
Odds = 11 : 12
Hence, the value of the odds is 11 : 12
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Plot the numbers -1 1/2 and 2 3/4 on the number line below.
Answer:
Step-by-step explanation:
ok, so for the -1 1/2 your going to find the -1 point on the left of 0. Then from there you will count to the second small point (or small line intersecting through the number line) to the right of -1. It will be this one right here
Now for the second number 2 3/4 you will find the 2 point, to the right from 0. Now count three small points to the left to get the 3/4 part. It will be right here.
Hope this helps!!
PLEASE HELP!! WILL GIVE BRAINLEST AND 100 POINTS FOR CORRECT ANSWER ONLY !!
(Enlarge photo)
Answer:B
Step-by-step explanation:the triangle has 3 sides
What is mHI?
mHI
I
=
H
O
120°
120°
J
The calculated value of the measure of the arc HI is 55 degrees
Calculating the measure of the arc HIFrom the question, we have the following parameters that can be used in our computation:
The circle
The sum of angles at a point is 360
So, we have
∠HAI + 60 + 100 + 145 = 360
When the like terms are evaluated, we have
∠HAI = 55
The angle subtended by the arc equals the angle at the center
This means that
mHI = ∠HAI
By substitution, we have
mHI = 55 degrees
Hence, the arc HI is 55 degrees
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Determine the value(s) for which the rational expression −6a−10−5a−8 is undefined. If there's more than one value, list them separated by a comma, e.g. a=2,3.
Since the rational expression is incorrectly constructed, I am unable to determine what it actually means.
I'll attempt to respond to this in a general approach so that you may try to apply it to the specific issue.
Let's say that this is our expression of reason:
[tex]\frac{-6a-10}{-5a-8}[/tex]
There is no undefined value because the numerator is -12d and this component is unaffected by any value of d.
-5a-8 is the denominator.
Any rational expression that has a denominator equal to zero is now undefined. (we can not divide by zero)
Thus, a value that is undefined will be when
-5a-8 = 0
d = 8/5
This means that the number d = 8/5 is invalid because it would cause the denominator to be equal to 0.
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Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to at least 4 decimal places.
539=13^r+9
The solution for r is:
r = ln(539)/ln(13) - 9
And an estimation is:
r = -6.5478
How to solve the exponential equation?Remember the rule for logarithms of powers:
ln(x^n) = n*ln(x)
Now let's look at our equation, here we have:
539 = 13^(r + 9)
We want to solve this equation for r, to do so, we can apply the natural logarithm in both sides:
ln(539) = ln( 13^(r + 9))
Using the rule we can rewrite this as:
ln(539)= (r + 9)*ln(13)
Now just solve the equation for r:
r = ln(539)/ln(13) - 9
And an approximate solution is:
r = -6.5478
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6. Social Security numbers are of the form XYZ - MN - ABCD.
a. The first three digits XYZ are referred to as the area number. The number is associated
with where you registered for your social security card. X is a number 1 - 7. Y and Z can
be any number 0 - 9. Also the area code 666 has never been used. How many area code
numbers are possible?
b. The middle two digits MN are referred to as the group number. The group number can
be any number from 01 to 99 (it cannot be 00). The last 4 digits ABCD are the serial
number. The serial number can be any from 0001 to 9999 (it cannot be 0000).
Additionally, the social security number 123-45-6789 is only used in advertisements.
How many social security numbers are possible?
a) The number of possible area code numbers is: 69,299. b) the number of possible social security numbers is: 68,665,031,401
How to determine the How many area code numbers are possiblea. The first three digits can be any number from 001 to 999, except for 666. Since X can be any number from 1 to 7, there are 7 choices for X. For Y and Z, there are 10 choices each (0-9). Therefore, the number of possible area code numbers is:
(7 choices for X) x (10 choices for Y) x (10 choices for Z) - 1 (for 666) = 69,299
b. The middle two digits can be any number from 01 to 99, which gives 99 choices. The last 4 digits can be any number from 0001 to 9999, which gives 9999 - 1 (for 0000) = 9998 choices. Therefore, the number of possible social security numbers is:
(69,299 choices for the area number) x (99 choices for the group number) x (9998 choices for the serial number) - 1 (for 123-45-6789) = 68,665,031,401
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The frequency table that summarizes the data by the biologist and the additional plants is c. third table.
How to find the frequency table?From the data by the biologist and the additional plants, we see that there are 11 plants with flowers and 7 with caterpillars.
The number of flowering plants with caterpillars is 6 plants. Those without flowers would then be:
= 11 - 6
= 5 plants
This is shown by the second frequency table.
In conclusion, the correct frequency table showing the data by the biologist is the second frequency table.
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Write about plane of contact , pole and polar plane ?
Explain all briefly!
The concepts of plane of contact, pole, and polar plane are related to the study of conic sections in geometry.
Plane of Contact:
The plane of contact is a plane that passes through the points of intersection of a cone and a plane. In other words, when a plane intersects a cone, the points where the plane and cone touch determine a plane of contact. This plane is important in determining the properties of the conic section that is formed by the intersection.
Pole:
The pole is a point that is used to define a polar plane. It is a point that is not on the plane and is located on the axis of the cone. When a plane passes through the pole, it intersects the cone in a conic section. The pole is a useful concept in determining the properties of the conic section.
Polar Plane:
The polar plane is a plane that passes through the pole and is perpendicular to the plane of contact. It is the plane that contains the polar axis, which is the axis of the cone passing through the pole. The polar plane is important in determining the properties of the conic section that is formed by the intersection of the cone and the plane of contact.
In summary, the plane of contact, pole, and polar plane are all concepts that are used in the study of conic sections. The plane of contact is a plane that passes through the points of intersection of a cone and a plane. The pole is a point on the axis of the cone that is used to define a polar plane. The polar plane is a plane that passes through the pole and is perpendicular to the plane of contact. These concepts are important in determining the properties of conic sections and are used in various applications, including optics, astronomy, and engineering.
Answer:
Step-by-step explanation:
Sure! Let's start with the plane of contact.
Plane of Contact:
The plane of contact is a term commonly used in geometry and physics. When two objects come into contact with each other, their surfaces touch at a particular area. This area of contact is known as the plane of contact. It is a two-dimensional surface that represents the point of contact between the two objects.
Imagine two books placed on a table. The area where the bottom surface of each book touches the table is the plane of contact. It is like a flat sheet that separates the objects and defines the region where they interact with each other.
Pole and Polar Plane:
The concepts of pole and polar plane are closely related to the plane of contact. Let's explore them:
Pole:
In geometry, the pole is a point that represents the point of contact between a line and a plane. When a line is in contact with a plane, the point of contact is called the pole. It is the specific point where the line intersects the plane.
For example, if you have a line placed on a tabletop, the point where the line touches the surface is its pole.
Polar Plane:
The polar plane is the plane that contains all the lines passing through a specific point called the pole. In other words, the polar plane is a plane that is perpendicular to the line at its pole.
Continuing with the previous example, if you have a line touching the tabletop at a certain point, the polar plane would be a plane that is perpendicular to the line at that point. It includes all the lines passing through that point.
The pole and polar plane are connected in such a way that every line passing through the pole lies on the polar plane, and the polar plane contains the pole.
In summary, the plane of contact represents the area where two objects touch each other, while the pole represents the point of contact between a line and a plane. The polar plane is a plane that contains all the lines passing through the pole.
Hope it helps!!
Classify the following triangle as right or not. Explain why it is or is not.
24
27
15
42 SING A chef makes batches of dumpling wrappers for shrimp dumplings. She uses 2 cups of flour for each batch and a total of an additional § cup of flour to keep the dough from sticking. She uses 21 cups of flour to make n batches of dumpling wrappers. How many batches of dumpling wrappers does the chef make?
The chef makes 11 batches of dumpling wrappers.
What is dumpling wrapper?
Dumpling wrappers are thin pieces of dough that are used to wrap around fillings to make dumplings. They are a staple in many Asian cuisines, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.
Let's assume that the chef makes "n" batches of dumpling wrappers.
For each batch of dumpling wrappers, the chef uses 2 cups of flour.
So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.
In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.
According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21
To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.
So, the equation becomes 2n + 0.25 = 21
Subtracting 0.25 from both sides,
2n = 20.75
Dividing both sides by 2,
n = 10.375
Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.
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The chef makes 11 batches of dumpling wrappers.
What is dumpling wrapper?
Dumpling wrappers are thin pieces of dough that are used to wrap around fillings to make dumplings. They are a staple in many Asian cuisines, including Chinese, Japanese, Korean, and Thai. The dough is typically made with flour, water, and salt, and is rolled out into thin circles or squares. The size and thickness of the wrappers can vary depending on the type of dumpling being made and the regional cuisine. Dumpling wrappers can be used to make a variety of dumplings, such as pork and cabbage dumplings, shrimp dumplings, potstickers, and gyoza.
Let's assume that the chef makes "n" batches of dumpling wrappers.
For each batch of dumpling wrappers, the chef uses 2 cups of flour.
So, the total amount of flour used for making "n" batches of dumpling wrappers is 2n cups of flour.
In addition to the 2 cups of flour for each batch, the chef also uses an additional § cup of flour to keep the dough from sticking. So, the total amount of flour used for "n" batches is 2n + § cups of flour.
According to the problem statement, the chef uses a total of 21 cups of flour to make "n" batches of dumpling wrappers. So, we can set up the following equation 2n + § = 21
To solve for "n," we need to first convert the § cup of flour to a decimal. § is equivalent to 0.25 cups of flour.
So, the equation becomes 2n + 0.25 = 21
Subtracting 0.25 from both sides,
2n = 20.75
Dividing both sides by 2,
n = 10.375
Since we can't have a fraction of a batch, we can round up to the nearest whole number. Therefore, the chef makes 11 batches of dumpling wrappers.
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A net of a square pyramid is shown below.
What is the surface area, in square centimeters, of the pyramid?
Answer:
Option (B) 86.7 is the correct answer.
Step-by-step explanation :
Dividing the given diagram in 5 parts :
Firstly finding the area of one right angle triangle :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}[/tex]
↠ b (base) = 5.1 cm↠ h (height) = 5.95 cmsubstituting all the given values in the formula :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 5.1 \times 5.95}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1 \times 5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{30.345}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725\: {cm}^{2}}[/tex]
Hence, the area of right angle triangle is 15.1725 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Here we have 4 right angle triangle with equal base and height and we have already find the area of one right angle triangle. So, the area of 4 triangle will be :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725 \: {cm}^{2}}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 15.1725 \times 4}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 60.69 \: {cm}^{2}}[/tex]
Hence, the area of 4 right angle triangles is 60.69 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, we have to find the area of square
[tex]\longrightarrow\sf{Area_{(Square)} = {a}^{2}}[/tex]
↠ a (side) = 5.1 cmSubstituting the given value in the formula :
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1)}^{2}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1 \times 5.1)}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = 26.01 \: {cm}^{2}}[/tex]
Hence, the area of square is 26.01 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the total area :
[tex]{\sf{\implies{Total \: Area = Area_{(\triangle)} + Area_{(Square)}}}}[/tex]
↠ Area of triangle = 60.69 cm²↠ Area of square = 26.01 cm².[tex]{\sf{\implies{Total \: Area = 60.69 + 26.01}}}[/tex]
[tex]{\sf{\implies{Total \: Area = 86.7 \: {cm}^{2}}}}[/tex]
Hence, the total area of given diagram is 86.7 cm².
———————————————Answer:
Option (B) 86.7 is the correct answer.
Step-by-step explanation :
Dividing the given diagram in 5 parts :
Firstly finding the area of one right angle triangle :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}[/tex]
↠ b (base) = 5.1 cm↠ h (height) = 5.95 cmsubstituting all the given values in the formula :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 5.1 \times 5.95}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1 \times 5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{30.345}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725\: {cm}^{2}}[/tex]
Hence, the area of right angle triangle is 15.1725 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Here we have 4 right angle triangle with equal base and height and we have already find the area of one right angle triangle. So, the area of 4 triangle will be :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725 \: {cm}^{2}}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 15.1725 \times 4}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 60.69 \: {cm}^{2}}[/tex]
Hence, the area of 4 right angle triangles is 60.69 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, we have to find the area of square
[tex]\longrightarrow\sf{Area_{(Square)} = {a}^{2}}[/tex]
↠ a (side) = 5.1 cmSubstituting the given value in the formula :
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1)}^{2}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1 \times 5.1)}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = 26.01 \: {cm}^{2}}[/tex]
Hence, the area of square is 26.01 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the total area :
[tex]{\sf{\implies{Total \: Area = Area_{(\triangle)} + Area_{(Square)}}}}[/tex]
↠ Area of triangle = 60.69 cm²↠ Area of square = 26.01 cm².[tex]{\sf{\implies{Total \: Area = 60.69 + 26.01}}}[/tex]
[tex]{\sf{\implies{Total \: Area = 86.7 \: {cm}^{2}}}}[/tex]
Hence, the total area of given diagram is 86.7 cm².
———————————————HELP PLEASEE!!!
Whoever answers right gets brainliest!!
The average rate of change of the given function between the two given values is: 0.82
How to find the average rate of change of a function?The Average Rate of Change of a function is one that is defined as the average rate at which one quantity is changing with respect to another thing changing. Thus, an average rate of change function is basically a process that helps to calculate the amount of change in one item divided by the corresponding amount of change in another.
It is given by the formula:
f'(x) = [f(b) - f(a)]/(b - a)
We are given the function:
f(x) = √(3x - 11)
Thus from x1 = 4 to x2 = 6, we will have:
f(4) = √(3*4 - 11) = 1
f(6) = √(3*6 - 11) = √7
Thus:
f'(x) = ((√7) - 1)/(6 - 4)
f'(x) = 0.82
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Mai is jogging from her house to school. Her school is 2 5/6 miles from her house. She has gone 1 3/5 miles so far. How many miles does Mai still have to jog? Write your answer as a mixed number in simplest form.
Step-by-step explanation:
[tex]2 \times \frac{5}{6} = \frac{17}{6} [/tex]
[tex]1 \times \frac{3}{5} = \frac{8}{5} [/tex]
[tex] \frac{17}{6} - \frac{8}{5} [/tex]
[tex] \frac{17}{6} \times 5 = \frac{85}{30} [/tex]
[tex] \frac{8}{5} \times 6 = \frac{48}{30} [/tex]
[tex] \frac{85}{30} - \frac{48}{30} = \frac{37}{30} [/tex]
[tex]37 \div 30 = 7 \times \frac{1}{30} [/tex]
so 7 1/30
What is the meaning of "Since the angle from axis j to axis i is [tex]\pi (i-j)/n[/tex], it follows that [tex]s _{i}\circ s_{j}=r_{i-j}[/tex]?
This statement describes the relationship between symmetries and rotations
Explaining the meaning of the statement as statedIn this context, "axis i" and "axis j" refer to two different coordinate axes, and "n" is the total number of axes. The notation "s_i" represents a reflection transformation across axis i, and "r_k" represents a rotation transformation that rotates the entire coordinate system by an angle of 2πk/n, where k is an integer between 0 and n-1.
The statement "Since the angle from axis j to axis i is π(i-j)/n, it follows that s_i ∘ s_j = r_{i-j}" means that if we reflect the coordinate system across axis i, and then reflect it again across axis j, the resulting transformation is equivalent to rotating the entire coordinate system by an angle of 2π(i-j)/n. In other words, the composition of the two reflections is equivalent to a single rotation.
This relationship is important in the study of group theory and symmetry, where it is used to understand the properties of groups of transformations that preserve the symmetry of an object or system.
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5. a. A box contains 20 pens of which m are red. If 5 more pens of which 3 are red are added, the probability of selecting two red pens at random without replacement is 7/20 Find the value of m. b. The first four consecutive terms of a linear sequence are x,y, (2x + 1), (2y-3). i. Show that S4= 3(x+y) - 2. ii. Find the fifth term, U5
a. There are 4 red pens in the box.
b i. Simplifying, we get:
S₄ = 3(x + y) - 2
ii. The fifth term is 4y - 2x + 1.
What is probability?The chance of an event occurring is called the probability of the event happening. It tells us how likely it is for an event to happen; it does not tell us what is going to happen. There is an even chance of an event happening (happen/not happen).
a. Let the number of non-red pens be n, then we have m + n = 20. Also, after adding 5 more pens, we have m + 3 red pens and n + 2 non-red pens. The probability of selecting two red pens at random without replacement from these 25 pens is given by:
(m + 3)/(20 + 5) * (m + 2)/(20 + 4) = 7/20
Simplifying this equation, we get:
(m + 3)(m + 2) = 14 * 5
Expanding the left side and simplifying, we get:
m² + 5m - 36 = 0
Factoring this equation, we get:
(m + 9)(m - 4) = 0
Since m cannot be negative, we have:
m = 4
Therefore, there are 4 red pens in the box.
b. i. The sum of the first n terms of an arithmetic sequence can be given by:
Sₙ = n/2[2a + (n - 1)d]
where a is the first term, d is the common difference, and n is the number of terms. Using this formula, we can find S₄ as follows:
S₄ = 4/2[x + y + (2x + 1) + (2y - 3)]
= 2(3x + 3y - 1)
= 6(x + y) - 6 - 2
Simplifying, we get:
S₄ = 3(x + y) - 2
ii. The common difference of the sequence is given by:
d = y - x
Therefore, the fifth term can be expressed as:
U₅ = (2x + 1) + 4d
= (2x + 1) + 4(y - x)
= 4y - 2x + 1
Therefore, the fifth term is 4y - 2x + 1.
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a. There are 4 red pens in the box.
b i. Simplifying, we get:
S₄ = 3(x + y) - 2
ii. The fifth term is 4y - 2x + 1.
What is probability?The chance of an event occurring is called the probability of the event happening. It tells us how likely it is for an event to happen; it does not tell us what is going to happen. There is an even chance of an event happening (happen/not happen).
a. Let the number of non-red pens be n, then we have m + n = 20. Also, after adding 5 more pens, we have m + 3 red pens and n + 2 non-red pens. The probability of selecting two red pens at random without replacement from these 25 pens is given by:
(m + 3)/(20 + 5) * (m + 2)/(20 + 4) = 7/20
Simplifying this equation, we get:
(m + 3)(m + 2) = 14 * 5
Expanding the left side and simplifying, we get:
m² + 5m - 36 = 0
Factoring this equation, we get:
(m + 9)(m - 4) = 0
Since m cannot be negative, we have:
m = 4
Therefore, there are 4 red pens in the box.
b. i. The sum of the first n terms of an arithmetic sequence can be given by:
Sₙ = n/2[2a + (n - 1)d]
where a is the first term, d is the common difference, and n is the number of terms. Using this formula, we can find S₄ as follows:
S₄ = 4/2[x + y + (2x + 1) + (2y - 3)]
= 2(3x + 3y - 1)
= 6(x + y) - 6 - 2
Simplifying, we get:
S₄ = 3(x + y) - 2
ii. The common difference of the sequence is given by:
d = y - x
Therefore, the fifth term can be expressed as:
U₅ = (2x + 1) + 4d
= (2x + 1) + 4(y - x)
= 4y - 2x + 1
Therefore, the fifth term is 4y - 2x + 1.
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A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 3.8 in. The survey also found that men's heights are normally distributed with mean 67.3 in. and standard deviation 3.8 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 64 in. Complete parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement is ?
The percentage of men who meet the height requirement is 19.09%. This result suggests that a relatively small proportion of men meet the height requirements for the characters at the amusement park.
To find the percentage of men who meet the height requirement, we need to calculate the probability that a randomly selected man has a height between 56 and 64 inches.
Using the z-score formula, we can standardize the height range as follows:
z = (64 - 67.3) / 3.8 = -0.87
z = (56 - 67.3) / 3.8 = -3.00
Using a standard normal distribution table, we can find that the area to the left of z = -0.87 is 0.1922 and the area to the left of z = -3.00 is 0.0013.
Therefore, the percentage of men meeting the height requirement is:
P(-0.87 < Z < -3.00) = P(Z < -0.87) - P(Z < -3.00) = 0.1922 - 0.0013 = 0.1909 or 19.09%.
It suggests that the park may be employing more women than men as characters, as the mean height for women is below the maximum height requirement.
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2/9 ÷2/8_____ reduce the answer to the lowest terms
Calculate the height of the pole
Step-by-step explanation:
See image
Change 14,277 s to h, min, and s.
Answer:
3hours 237 minutes 5700 seconds
PLEASE SOMEONE HELPP!!!!
i know that answer Is −12
8
1
but i need explain! 100points, plus 5 Stars+ brainliest
[tex] - 3 \frac{3}{4} - x = -6 \frac{1}{6} [/tex]
THIS IS MATH FOR 7TH GRADE!!
Answer:
[tex]x=2\frac{5}{12}[/tex]
Step-by-step explanation:
Given equation:
[tex]-3\frac{3}{4}-x=-6\frac{1}{6}[/tex]
Begin by adding x to both sides of the equation:
[tex]-3\frac{3}{4}-x+x=-6\frac{1}{6}+x[/tex]
[tex]-3\frac{3}{4}=-6\frac{1}{6}+x[/tex]
Add -6¹/₆ to both sides of the equation:
[tex]-3\frac{3}{4}+6\frac{1}{6}=-6\frac{1}{6}+x+6\frac{1}{6}[/tex]
[tex]-3\frac{3}{4}+6\frac{1}{6}=x[/tex]
Swap sides:
[tex]x=6\frac{1}{6}-3\frac{3}{4}[/tex]
Rewrite the mixed numbers as improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]x=\dfrac{6 \times6+1}{6}-\dfrac{3 \times 4+3}{4}[/tex]
[tex]x=\dfrac{36+1}{6}-\dfrac{12+3}{4}[/tex]
[tex]x=\dfrac{37}{6}-\dfrac{15}{4}[/tex]
When subtracting fractions, we must ensure that they have the same denominator. To do this, find the least common multiple (LCM) of the two denominators.
As 6 and 4 are factors of 12, then 12 is the LCM.
Rewrite the fractions as their equivalent fractions (with a denominator of 12) by multiplying the numerator and denominator by the same number.
[tex]x=\dfrac{37\times 2}{6\times 2}-\dfrac{15\times3}{4\times3}[/tex]
[tex]x=\dfrac{74}{12}-\dfrac{45}{12}[/tex]
Now the fractions all have the same denominator, we can simply subtract the numerators:
[tex]x=\dfrac{74-45}{12}[/tex]
[tex]x=\dfrac{29}{12}[/tex]
Finally, convert the improper fraction into a mixed number:
[tex]x=\dfrac{24+5}{12}[/tex]
[tex]x=\dfrac{24}{12}+\dfrac{5}{12}[/tex]
[tex]x=2+\dfrac{5}{12}[/tex]
[tex]x=2\frac{5}{12}[/tex]
PLS HELP!! suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round the answer to the tenth place.
a. 0.8
b. 2.1
c. 54.3
d. 112.8
Answer:
D
Step-by-step explanation:
i think its D because next to x the y coordinate is 112.8
Find the value of x, y, and z in the parallelogram below.
The values of x , y and z in the parallelogram are 12, -20 and -33 respectively
How to find the angles of a parallelogram?A parallelogram is a quadrilateral with opposite side equal to each other and opposite sides parallel to each other.
The opposite angles of parallelogram are equal . Consecutive angles in a parallelogram are supplementary .
Therefore,
-4y + 5 = 85
-4y = 85 - 5
-4y = 80
divide both sides by -4
y = 80 / -4
y = - 20
Therefore, let's find x and z as follows:
8x - 1 + 85 = 180
8x = 180 - 84
8x = 96
divide both sides by 8
x = 96 / 8
x = 12
Let's find z
- 3z - 4 + 85 = 180
-3z = 180 - 81
-3z = 99
divide both sides by -3
z = 99 / -3
z = -33
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Please help me im struggling with my test
The y-intercept is (0, 10) and the values of x that make sense are x > 0
The graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 10(2)^x
The graph is added as an attachment
The y-interceptThis is the point of intersection with the y-axis
From the graph, it is (0, 10)
The values of x that make senseThese are the values whose corresponding y values are not negative
In other words, the values are x > 0
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In January, the amount of snowfall was 5 2/3 feet. In February, the amount of snowfall was 3 1/5 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
To add these fractions, we need a common denominator. The smallest common multiple of 3 and 5 is 15.
Converting 2/3 to fifteenths:
2/3 = 10/15
Converting 1/5 to fifteenths:
1/5 = 3/15
Now, we can add:
5 10/15 + 3 3/15 = 8 13/15
Therefore, the amount of snowfall in the two months combined was 8 13/15 feet.
Juan catches 80% of the passes thrown to him in football. If the quarterback throws to him 15 times during a game, what is the probability he will catch atleast 10 of them?
the probability that Juan will catch at least 10 passes out of 15 is approximately 0.9951, or about 99.51%.
We may utilise the binomial distribution formula to resolve this issue:
P(X ≥ 10) = 1 - P(X < 10)
where P(X 10) is the likelihood that Juan catches fewer than 10 passes and X is the total number of passes he catches.
By applying the binomial distribution formula, we may determine P(X 10):
P(X < 10) = Σ(k=0 to 9) [(15 select k)×(0.8)k×(0.2)×(15-k)]
where (15 select k) is the binomial coefficient and (0.8)k×(0.2)(15-k) is the probability of catching k passes and missing (15-k) passes, and (15 choose k) is the number of possibilities to choose k items out of 15.
P(X 10) can be calculated using a calculator or a spreadsheet and is roughly equal to 0.0049.
P(X 10) is therefore equal to 1 - P(X 10) 1 - 0.0049 0.9951.
So the probability that Juan will catch at least 10 passes out of 15 is approximately 0.9951, or about 99.51%.
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Planes T and X are parallel. Plane T contains line a. Plane X contains line b.
Planes T and X are parallel. Plane T contains line a and plane X contains line b.
Which best explains the relationship between lines a and b?