Answer:x=7
Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5*x-2+x-(9+3*x+10)=0
Step by step solution :
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
3x - 21 = 3 • (x - 7)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : x-7 = 0
Add 7 to both sides of the equation :
x = 7
One solution was found :
x = 7
O is the centre of the circle below.
Use the information below to work out the length of BD to 1 d.p
AC = 22mm
OE = 6mm
The length of BD is 25.06 mm
Define the term Circle identities?The six trigonometric functions of an angle in a right-angled triangle are related by a set of fundamental identities in trigonometry known as the Circle identities.
Given that,
AC = 22 mm and OE = 6 mm
So, AE = AC/2
Then AC = 11 mm
Therefore, OA is a radius then,
By Pythagoras theorem,
OA² = AE² + OE²
AO² = 11² + 6² = 121+36
AO² = 157
AO = √157 = 12.53 ( radius )
Then , BD = 2 * radius = 2 * 12.53 = 25.06 mm
Therefore, the length of BD is 25.06 mm
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i need help , i want to rename my add-in in casio fx-cg50 and/ or change the picture but i dont know how to make that by changing the code
my because he was poor liké kiss
What is the area of the trapezoid?
10 cm
16 cm
Not drawn to scale.
8 cm
8 cm²
62 cm²
84 cm²
125 cm²
7 cm
8 cm
Therefore, the area of the trapezoid is 84cm².
What is trapezoid?A trapezoid (also known as a trapezium) is a four-sided geometric shape with two parallel sides and two non-parallel sides that meet at two endpoints. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the two bases is the height of the trapezoid. The formula for finding the area of a trapezoid is (base1 + base2) x height / 2. The formula for finding the perimeter of a trapezoid is the sum of the lengths of all four sides.
To find the area of a trapezoid, you can use the formula:
[tex]A = (B1 + B2) * h / 2[/tex]
where A is the area of the trapezoid, B1 and B2 are the lengths of the parallel sides (also called bases), and h is the height (the perpendicular distance between the bases).
Using the values, you provided:
[tex]B1 = 8cm\\B2 = 16cm\\h = 7cm[/tex]
Plugging these values into the formula, we get:
[tex]A = (8cm + 16cm) * 7cm / 2[/tex]
[tex]A = 24cm * 7cm / 2[/tex]
[tex]A = 168/2cm^{2}[/tex]
[tex]A = 84cm^{2}[/tex]
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5-6 practice the remainder and factor theorems 5) If f(x) = 3x2 -9x -20, find the value of f(5) using synthetic substitution.
a. 0
b. 10
c. 15
d. -7
6) if f(x) = x3+8x+24, then find f(-2) using synthetic substitution.
a. 12
b. 8
c. 0
d. -6
the value of f(5) is 10, which is option (b) , the value of f(-2) is -12, which is option (d). To find the value of f(5) using synthetic substitution, we first set up the synthetic division table as follows:
5 | 3 -9 -20
|||___
| | |
We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below the second coefficient (-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).
6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:
-2 | 1 0 8 24
|_|||
| | | |
We write the coefficients of the polynomial in the top row of the table and the root (in this case, -2) outside the division symbol. We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).
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The Panthers, Charlotte's professional football team, track their score as a function of the amount of time
passed in a football game. The table below gives the output scores, y, for a given time
Time passed
(in minutes)
0,10,20,30,40,50,60
Points scored
0,10,13,16,23,36,36
If the Panthers gain 7 points for each touchdown and 3 points for each field goal, write a brief story of their scoring in the game based on the function.
The brief storytelling of their scoring in the game based on the function is given below:
The StorytellingIn a thrilling football game, the Carolina Panthers, Charlotte's professional football team, played with fierce determination to score points as the game progressed. Their performance could be tracked through a function that related the time passed in minutes to the number of points scored by the team.
At the 0-minute mark, the game started with both teams at 0 points. The Panthers quickly picked up the pace, and by the 10-minute mark, they managed to score a touchdown followed by a successful extra point attempt, bringing their score to 10 points.
As the clock continued ticking, the Panthers scored a field goal by the 20-minute mark, adding another 3 points to their total, raising the score to 13 points. Ten minutes later, at the 30-minute mark, they secured another field goal, further increasing their lead to 16 points.
The 40-minute mark proved to be a turning point for the Panthers, as they managed to score a touchdown with an extra point, and followed up by another field goal. These successful attempts added 10 points to their score, bringing the total to 23 points.
As the game approached its final stages, the Panthers displayed their best performance yet. By the 50-minute mark, they had scored two touchdowns, each with a successful extra point attempt, adding a whopping 14 points to their score, taking it to 36 points.
However, as the game reached its final 10 minutes, the Panthers were unable to capitalize on any further scoring opportunities. The score remained at 36 points by the end of the 60-minute game.
In summary, throughout the game, the Panthers scored a total of 4 touchdowns with extra points and 4 field goals, amassing a final score of 36 points. Their relentless effort and strategic play led them to a strong performance in the match.
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answer pls a lot of points
Answer:
50.3
Step-by-step explanation:
Area of circle: pi*r ^2
the problem tells us that r =4 and that pi = 3.142
so,
its (4^2) * 3.142 or 50.3 (rounded)
~ lmk if u got Qs
Tina needs to mix 2 gallons of water with one cup of iced tea mix to make the tea. Tina only has a 1 cup measure. How many cups of water does she need to make the iced tea?
A 4 cups
B 8 cups
C 16 cups
D 32 cups
Tina will need 32 cups of water to make the iced tea.
is there evidence of a negative correlation between systolic blood pressure and heart rate? in a sample of 200 patients, we found a sample correlation of -0.057.
There is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate.
There is evidence of a negative correlation between systolic blood pressure and heart rate. In a sample of 200 patients, a sample correlation of -0.057 was found. Correlation is a statistical measure used to assess the degree to which two variables are related to one another. A correlation coefficient ranging from -1 to 1 is used to represent this relationship. A negative correlation exists when two variables move in opposite directions.
It means that as one variable increases, the other variable decreases or vice versa.In the given case, there is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate. Systolic blood pressure is the amount of pressure exerted by blood against the walls of the arteries when the heart pumps. It is the top number in a blood pressure reading.
When your heart beats and pushes blood out, the systolic pressure is created.Heart rate is the number of times your heart beats per minute. It is also known as the pulse rate. It represents the number of times your heart contracts and relaxes with each heartbeat.
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A box contains 30 tins of beans (to the nearest 10).
Find the largest possible amount of tins in the box.
Answer:
Step-by-step explanation:
Answer: 34 tins
If there were 35 tins then this would be rounded up to 40 tins. So 34 is the highest number that will be rounded to 30.
The largest possible amount of tins in the box is 34.
What is Rounding off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
We have,
A box contains 30 tins of beans (to the nearest 10).
Now, we know to round off we need to focus that whether the number is greater than 5 or less than 5.
If greater than 5 than round of to next number otherwise round off to previous number.
Here, the largest number of tins can be 34 because greater than 34 leads to round off 40.
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Let f (x) = -5x + 3 and g(x) = 6x - 2. Find f• g and its domain.
A side of a regular polygon is 11.5cm. If each of
its exterior angles is 18°, calculate the
circumference of the polygon.
Therefore , the solution of the given problem of angles comes out to be the regular polygon has a 230 centimeter circumference.
What does an angle mean?The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.
Here,
All of the edges and angles make up a regular polygon. If a regular polygon's exterior angle is 18 degrees, then the internal angle is:
180 minus the external angle is the interior angle.
180 degrees minus 18 degrees is the interior angle.
Angle inside equals 162 degrees
Sum of internal angles is equal to (n - 2)°, or 180°.
=> (n - 2) × 180 = n × 162
When we simplify and solve for n, we obtain:
=> 180n - 360 = 162n
=> 18n = 360
=> n = 20
The regular polygon in the example has 20 edges.
Given that the length of each side is 11.5 centimeters, the polygon's circumference is as follows:
Circumference is equal to the sum of the lengths of all the edges.
=> Circumference = 20.1 centimeters.
=> 230 centimeters is the circumference.
Consequently, the regular polygon has a 230 centimeter circumference.
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the top face of a phone is a rectangle measuring inches by inches. find the area of the face of the phone.
Thus, the area of the rectangular face of the phone is found to be:
Area = 200 sq. in.
Explain about the features of rectangle?Due to the diversity of shapes seen in geometry, geometry is also referred to as the study of shapes.
A rectangle is a quadrilateral in geometry that has four equal angles, each measuring 90 degrees, and opposing sides that seem to be parallel and equal in length.A polygon is still a two-dimensional shape having straight sides, and a quadrilateral is a polygon with four sides. Combining everything, we can say that a rectangle is still a two-dimensional shape containing four sides, opposite sides that are parallel and equal in length, and four angles that are all 90 degrees.Dimensions of the face of rectangular face of phone:
Length = 20 inches
width = 10 inches
Area = length x width
Area = 20 x 10
Area = 200 sq. in.
Thus, the area of the rectangular face of the phone is found to be:
Area = 200 sq. in.
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Complete question:
The top face of a phone is a rectangle measuring 20 inches by 10 inches. find the area of the face of the phone.
17. A biologist studying ants started on day with a population of 1500 ants. On day 2, there were 3000 ants, and on day 3, there were 4500 ants. The increase in an ant population can be represented using a geometric sequence. What is the ant population on day 5?
Answer:
Step-by-step explanation:
1500
+1500
3000
+1500
4500
+1500
6000
+1500
7500
Answer=7500
A regular hexagon is shown in the picture below. The center point is shown with two line segments drawn from the center to the vertices of the hexagon. The line segment labeled a is the altitude of the triangle that is formed.
Find the lengths of a, b, and c.
The lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are: a = 3, b = 3√3, c = 6√3.
Since the hexagon is regular, all six sides are congruent to each other, and all six angles are congruent to each other. Let's call the length of each side "s".
To find the length of the altitude "a", we can draw a perpendicular bisector from the center of the hexagon to one of the sides. This bisector will bisect the side into two segments of length "s/2", and it will also form a right triangle with "a" as the altitude and "s/2" as one of the legs. Using the Pythagorean theorem, we can solve for "a":
[tex]a^2 + b^2 = 6^2\\a^2 = 6^2 - b^2[/tex]
To find the length of "b", we can draw one of the radii from the center of the hexagon to a vertex. This radius will bisect the angle at the vertex and also bisect the opposite side. This will form two right triangles, each with one leg of length "s/2" and one acute angle of 30 degrees. Using trigonometry, we can solve for "b":
cos(30) = b/6
√3/2 = b/6
b = 3√3
Sin 30 = a/6
1/2 = a/6
a = 3
c = b + b = 3√3 + 3√3 = 6√3
Therefore, the lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are:
a = 3
b = 3√3
c = 6√3
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f(x) x^3 + 3 is the function even odd or neither?
After answering the provided question, we can conclude that Therefore, equation the function [tex]f(x) = x^3 + 3[/tex]is neither even nor odd.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation consists of two sides separated by an algebraic equation (=). For instance, the argument "2x + 3 = 9" states that the sentence "2x + 3" equals the number "9". The purpose of solving equations is to find the value or amounts of the variable(s) that always allow the equation to be true. Equations can just be simple or complicated, regular or nonlinear, and contain one or more variables. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used extensively in mathematics, including algebra, calculus, and geometry.
We must investigate the symmetry features of the function[tex]f(x) = x^3 + 3[/tex] to determine if it is even, odd, or neither.
If f(-x) = f(x) for every x in its domain, a function is even.
If f(-x) = -f(x) for every x in its domain, the function is odd.
If a function meets none of these requirements, it is neither even nor odd.
[tex]f(-x) = (-x)^3 + 3 = -x^3 + 3\\f(x) = x^3 + 3\\f(-x) = -x^3 + 3\\f(x) = x^3 + 3\\f(-x) = -x^3 + 3\\-f(x) = -(x^3 + 3) = -x^3 - 3\\[/tex]
Since f(-x) ≠ -f(x), f(x) is not odd either.
Therefore, the function [tex]f(x) = x^3 + 3[/tex]is neither even nor odd.
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During a sale, a store offered a 30% discount on a stereo system that originally sold for $710. After the sale, the discounted price of the stereo system was marked up by 30%. What was the price of the stereo system after the markup? Round to the nearest cent.
During the sale, the stereo system was sold for 30% less than its original price of $710, so the discount amount was:
0.30 x $710 = $213
Therefore, the sale price of the stereo system was:
$710 - $213 = $497
After the sale, the discounted price of $497 was marked up by 30%. The markup amount is:
0.30 x $497 = $149.10
So the final price of the stereo system after the markup is:
$497 + $149.10 = $646.10
Therefore, the price of the stereo system after the markup is $646.10.
a straight line through a figure from one corner to another is called____
Answer:
a diagonal?
Step-by-step explanation:
simplify the radicals
[tex] \sqrt{ \frac{2}{9} } - 3 \sqrt{ \frac{8}{9} } + \sqrt{ \frac{32}{9} } [/tex]
[tex] \frac{ \sqrt{2} }{3} - 3( \frac{2 \sqrt{2} }{3}) + \frac{4 \sqrt{2} }{3} [/tex]
[tex] \frac{ \sqrt{2} - 6 \sqrt{2} + 4 \sqrt{2} }{3} = - \frac{1}{3} \sqrt{2} [/tex]
10=6+2f
F=
I’m am really confused about this
Answer:
f = 2
Step-by-step explanation:
10 = 6 + 2f
subtract 6 from both sides
4 = 2f
divide both sides by 2
2 = f
pleasee help me fast
Therefore, the expression that can be used to determine YK is (48)tanK that is option D.
What is triangle?A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with straight line segments. Each of these line segments is called a side, and the point where two sides meet is called a vertex. A triangle has three vertices, three sides, and three angles. Triangles can be classified based on the length of their sides and the size of their angles.
Here,
In the right triangle MYK, where MY = 48 units, MK = 73 units, and angle Y = 90 degrees, we can use trigonometric functions to find the length of YK. The trigonometric functions that relate to the sides and angles of a right triangle are:
Sine: sinθ = opposite/hypotenuse
Cosine: cosθ = adjacent/hypotenuse
Tangent: tanθ = opposite/adjacent
To find YK, we need to use the tangent function because we know the opposite and adjacent sides (MY and MK). So, the correct expression to determine YK is: (48)tanK
The other expressions given are:
(73)sinK: This expression would be used to find the opposite side, not YK.
(73)cosK: This expression would be used to find the adjacent side, not YK.
(48)tanM: This expression doesn't relate to the right triangle MYK since there is no angle M in the triangle.
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Increase the number 15/16 by 3/5 of it. Then increase the resulting number by 3/5of it.
PLS HELP
The increased number is 15/16 by 3/5 of is 345/160.
What is a fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
To solve this problem, we need to follow the steps given in the question.
Step 1: Increase the number 15/16 by 3/5 of it.
We can write this mathematically as:
15/16 + (3/5)*(15/16)
Multiplying 15/16 by 3/5, we get:
(15/16)*(3/5) = 45/80
Adding this to 15/16, we get:
15/16 + 45/80 = 375/320 + 225/320 = 600/320
Simplifying this fraction, we get:
600/320 = 75/40 = 15/8
So, the result of the first step is 15/8.
Step 2: Increase the resulting number by 3/5 of it.
We can write this mathematically as:
(15/8) + (3/5)*(15/8)
Multiplying 15/8 by 3/5, we get:
(15/8)*(3/5) = 45/40
Adding this to 15/8, we get:
15/8 + 45/40 = 300/160 + 45/160 = 345/160
Therefore, the final result is 345/160.
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use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.
Use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.Therefore, the estimated amount of metal in the can is 0.001416.
To estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick, we can use differentials.
First, let's calculate the volume of the can. The volume of a cylinder is calculated by the formula
[tex]V = πr^{2} h,[/tex]
where r is the radius of the cylinder, and h is its height.
In this case, the radius is 5 cm and the height is 15 cm, so the volume of the can is
[tex]V = π x (5 cm)^{2} x 15 cm = 707.1 cm^{3}[/tex]
Next, we need to calculate the volume of the metal. The volume of a rectangular prism is
V = l x w x h,
where l is the length, w is the width, and h is the height. In this case, the length and width are both 10 cm, and the height is 0.1 cm, so the volume of the metal is
[tex]V = 10 cm x 10 cm x 0.1 cm = 1 cm^{3}[/tex]
Finally, we can calculate the amount of metal in the can by dividing the volume of the metal by the volume of the can:
[tex]1 cm^{3} / 707.1 cm^{3} = 0.001416.[/tex]
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goran the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on friday there were 8 clients who did plan a and 3 who did plan b. on saturday there were 2 clients who did plan a and 5 who did plan b. goran trained his friday clients for a total of 15 hours and his saturday clients for a total of 8 hours. how long does each of the workout plans last? lengthofeachplanaworkout:hour(s) lengthofeachplanbworkout:hour(s)
On solving the linear equation in two variables, the duration of Plan A workout is 1.5 hours and the duration of Plan B workout is 2 hours.
According to the question, the total hours of Plan A workouts on Friday and Saturday are (8 + 2) = 10,
and the total hours of Plan B workouts are (3 + 5) = 8.
If the duration of Plan A workout is "x" hours, then the duration of Plan B workout is "y" hours.
According to the question, the total hours spent in Plan A workouts is 10, and the total hours spent in Plan B workouts is 8. So, we can write two equations as:
8x + 3y = 1510x + 5y = 8By
solving these equations, we get:
x = 1.5y = 2
Therefore, the duration of Plan A workout is 1.5 hours, and the duration of Plan B workout is 2 hours.
Therefore, the answer is: Duration of Plan A workout is 1.5 hours and that of Plan B workout is 2 hours
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if their first three children have the disease, what is the probability that their fourth child will not
The probability of Bob and Joan's fourth child having sickle cell disease, given that their first three children are healthy, is 6.25%.
When Bob and Joan have children, each child has a 25% chance of inheriting two copies of the sickle cell gene and thus developing the disease, a 50% chance of inheriting one copy of the sickle cell gene and being a carrier like their parents, and a 25% chance of inheriting two copies of the normal gene and not carrying the disease.
To understand this probability calculation mathematically, we can use the laws of probability. We can define the probability of the fourth child inheriting the sickle cell gene as P(s), and the probability of the fourth child inheriting the normal gene as P(n).
Since Bob and Joan are each heterozygous carriers for the sickle cell gene, we know that P(s) = 0.25 (25%), and P(n) = 0.75 (75%). We can use the multiplication rule of probability to calculate the probability of their fourth child inheriting two copies of the sickle cell gene, which is:
P(sickle cell disease) = P(s) x P(s) = 0.25 x 0.25 = 0.0625 or 6.25%
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Complete Question:
Bob and Joan know from a blood test that they are each heterozygous (carriers) for the autosomal recessive gene that causes sickle cell disease. If their first three children are healthy, what is the probability that their fourth child will have the disease?
The marked price of a merchandise is 20% higher than the cost price. After the merchandise is sold at 90% of the marked price, there is still a profit of RM 24. Find the cost price of the merchandise.
Answer:
RM 300
Step-by-step explanation:
Let's assume that the cost price of the merchandise is "C" in RM.
According to the problem, the marked price of the merchandise is 20% higher than the cost price. Therefore, the marked price can be calculated as:
Marked price = Cost price + 20% of Cost price
Marked price = C + 0.2C
Marked price = 1.2C
The merchandise is sold at 90% of the marked price, which means the selling price can be calculated as:
Selling price = 90% of Marked price
Selling price = 0.9 × 1.2C
Selling price = 1.08C
We are given that the profit after selling the merchandise is RM 24. Profit is calculated as the difference between selling price and cost price. Therefore, we can write:
Profit = Selling price - Cost price
24 = 1.08C - C
24 = 0.08C
Solving for C, we get:
C = 24/0.08
C = 300
Therefore, the cost price of the merchandise is RM 300.
Simplify . (fg^2)^4
f= g=
Answer:
f^4 g^8
Step-by-step explanation:
(F^1g^2)^4
Js multiply the exponent by the one outside so 1x4=4
n 2x4=8
so the answer would be f^4 g^8
how do this please urgent
Answer:
D
Step-by-step explanation:
The sin is equal to the opposite of the chord
the average age in a sample of 190 students at city college is 22. as a result of this sample, it can be concluded that the average age of all the students at city college group of answer choices must be more than 22, since the population is always larger than the sample. is around 22. must be less than 22, since the sample is only a part of the population. could not be 22.
The correct answer is that the average age of all the students at City College could not be exactly 22, but it could be close to it. Since the average age of a sample of 190 students at City College is 22, it can be concluded that the average age of all the students at City College could not be exactly 22 because the sample is only a part of the population.
The population is always larger than the sample. Therefore, it cannot be concluded that the average age of all the students at City College must be more than 22 or must be less than 22.In addition, the standard deviation of the sample is needed to determine the exact range of ages for the population.
It is possible that the population has a higher or lower average age than the sample, but without the standard deviation, it is impossible to say for sure.In conclusion, the given statement that the average age of all the students at City College must be more than 22 or must be less than 22, since the population is always larger than the sample, is not accurate. It could not be exactly 22 but could be close to it, depending on the standard deviation of the sample.
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HELPOOOO PLEAAEEEEEEEEEEE
Answer:
A
Step-by-step explanation:
He shouldn't of added the "^1" to c because its changed the value to c^5 in the final step when it should really be c^4
Solve for x,
using the tangent lines.
X
42°
x = [? ]°
Answer:
x = 138°
Step-by-step explanation:
The measure of the angle formed by two tangents drawn from outside point of circle is half the difference of intercepted arcs.
Near arc = 42°
Far arc = 360 - 42 = 318°
[tex]\boxed{\bf x = \dfrac{1}{2}(Far \ arc - near \ arc)}[/tex]
[tex]= \dfrac{1}{2}*(318-42)\\\\= \dfrac{1}{2}*276\\\\= 138^\circ[/tex]