ALGEBRA Suppose M is the midpoint of FG. Use the given information to find the
missing measure or value.
MG =7x - 15, FG = 33, x= ?

Answer:

C. it is not a function

Step-by-step explanation:

It fails the horizontal and vertical line test.

To pass the horizontal line test [injective]: must not hit a horizontal line passing through more than once.

To pass the vertical line test [function]: must not hit a vertical line passing through more than once.

The actual value is 8.42 x 7.24 = 59.6576.

as an estimate she has rounded the values up to the nearest whole number ;

i.e. 8.42 ≅ 9 and 7.24 ≅ 8

to obtain 9 x 8 to get 72.

What is rounded value?

Making a number simpler while maintaining a value that is close to what it was is known as rounding.

Although less accurate, the outcome is simpler to utilize.

For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is. However, 76 rises to 80.

What is whole number?

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

What is natural number?

Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.

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Answer:

Step-by-step explanation:

And we have:

Also we have:

or substitute as above given:

Answer:

ST+TU=SU

ST=TU

SU/2=ST=TU

5x-2=3x-4

2x=-2

x=-1

ST=5x-2=5(-1)-2=-5-2=-7 --->|ST|=7

TU=3x-4=3(-1)-4=-3-4=-7 --->|TU|=7

ST+TU=SU ---> 7+7=14

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The statement "All seasons had the same level of variability in game scores" must be false.

To determine which statement must be true based on the mean game scores and standard deviations of four seasons of a football team, we need to analyze the data provided.

Given:

Season 2005: Mean = 193.5, Standard Deviation = 0

Season 2006: Mean = 212.8, Standard Deviation = 0

Season 2007: Mean = 121.0, Standard Deviation = 0

Season 2008: Mean = 94.0, Standard Deviation = 0

From the given data, we observe that all the standard deviations are zero. This indicates that there is no variation or spread in the game scores within each season. However, it is highly unlikely for a football team to have zero variation in game scores across multiple seasons.

Therefore, the statement "All seasons had the same level of variability in game scores" must be false.

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Answer:

-------------------

Use two points on the line:

Find the slope using slope equation:

Find the y-intercept using the point-slope equation and one of the points, (1, 6):

Convert it into slope-intercept form:

Answer:

x = 7

Step-by-step explanation:

given f(x) = 3x - 1 and f(x) = 20, then equate the right sides to find x

3x - 1 = 20 ( add 1 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer: x = 7

Step-by-step explanation:

f (x) = 20 eq_i

f (x) = 3x - 1 eq_ii

eq_i = eq_ii

20 = 3x - 1

3x = 20 + 1

x = 21 ÷ 3

x = 7 answer

hope that helps...

(a) The of constant c is: 1/15.

(b) The of constant c is: 1/10.

(c) The of constant c is: 1/36.

(d) The of constant c is: 1/2.

(a) We need to find the value of c such that f(x, y) satisfies the following properties:

f(x, y) >= 0 for all x and y

\(\sigma_x \sigma_y f(x, y) = 1\), where the sums are taken over all possible values of x and y

Given f(x, y) = c(x + 2y), x = 1, 2, y = 1, 2, 3, we have:

\(\sigma_x \sigma_y f(x, y) = c(\sigma_x(x) + 2\sigma_y(y))\)

= c((1+2+1)+(2+4+3))

= 15c

To satisfy property (2), we need:

15c = 1

Therefore, c = 1/15, and f(x, y) = (x+2y)/15 is the joint probability mass functions (pmf) for X and Y.

(b) We have f(x, y) = c(x + y), x = 1, 2, 3, y = 1, ..., x. Using the same reasoning as in part (a), we have:

\(\sigma_x \sigma_y f(x, y) = c(\sigma_x(x) + \sigma_x(x-1) + \sigma_x(x-2))\)

= c(6+3+1)

= 10c

To satisfy property (2), we need:

10c = 1

Therefore, c = 1/10, and f(x, y) = (x+y)/10 is the joint pmf for X and Y.

(c) We have f(x, y) = c, where x and y are integers such that 9 <= x+y <= 18, 0 <= y <= 5. Using the same reasoning as in parts (a) and (b), we have:

\(\sigma_x \sigma_y f(x, y) = \sigma_x \sigma_y c\)

\(= c \sigma_x \sigma_y 1\)

= c (6)(6)

= 36c

To satisfy property (2), we need:

36c = 1

Therefore, c = 1/36, and f(x, y) = 1/36 is the joint pmf for X and Y.

(d) We have \(f(x, y) = c(1/4)^x (1/3)^y, x = 1, 2, ..., y = 1, 2, ....\) Using the same reasoning as in parts (a), (b), and (c), we have:

\(\sigma_x \sigma_y f(x, y) = c \sigma_x ((1/4)^x) \sigma_y ((1/3)^y)\)

= c (1/(1-(1/4))) (1/(1-(1/3)))

= c(4/3)(3/2)

= 2c

To satisfy property (2), we need:

2c = 1

Therefore, c = 1/2, and \(f(x, y) = (1/2)(1/4)^x (1/3)^y\)is the joint pmf for X and Y.

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Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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The balance in the account after 11 years with continuous compounding at a 2% interest rate will be approximately $498.40.

To find the balance in an account when $400 is deposited for 11 years at an interest rate of 2% compounded continuously, you'll need to use the formula for continuous compound interest:

A = P * e^(rt)

where:
- A is the final account balance
- P is the principal (initial deposit), which is $400
- e is the base of the natural logarithm (approximately 2.718)
- r is the interest rate, which is 2% or 0.02 in decimal form
- t is the time in years, which is 11 years

Now, plug in the values into the formula:

A = 400 * e^(0.02 * 11)

A ≈ 400 * e^0.22

To find the value of e^0.22, you can use a calculator with an exponent function:

e^0.22 ≈ 1.246

Now, multiply this value by the principal:

A ≈ 400 * 1.246

A ≈ 498.4

So, the balance in the account after 11 years with continuous compounding at a 2% interest rate will be approximately $498.40.

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Answer:

He can wrap 6 gifts using the spool of ribbon

Step-by-step explanation:

Here, we want to know the number of gifts of the same dimension that Franklin can wrap using the spool of ribbon

Per gift 1.25m of ribbon is needed

Now in the spool, there is 25 feet of ribbon

1 m = 3 feet

x m = 25 feet

x = 25/3 meter

so the number of gifts of the same dimension he can wrap using the spool of ribbon will be;

25/3/1.25 = 25/3.75 = 6.67

Since he cannot wrap a gift fractionally, the number of gifts he can wrap is thus 6

The rate of change of the radius is 2.75 ft/min

Given

Rate of sand falling on conical pile = 8 ft³/min

Height of pile = 3 times the radius

Radius = 5.5 ft

We can calculate the rate of change of the radius by using the formula for the volume of a cone.

The volume of a cone is given by V = (1/3)πr²h, where r is the radius of the cone and h is the height of the cone.

We can rewrite this equation as 3V = πr²h.

We know that the height of the pile is always 3 times the radius, so we can substitute h = 3r into the equation and get  3V = 3πr³

We know the volume and the rate of sand falling on the pile, so we can substitute V = 8 ft³/min and solve for r.

3(8 ft³/min) = 3πr³

3πr³ = 24 ft³/min

r³ = 8 ft³/min/3π

r = \((8 ft³/min/3π)^(1/3)\)

Now that we know the radius, we can use the slope formula to calculate the rate of change of the radius.

The slope formula is given by m = (y2 - y1)/(x2 - x1).

In this case, x1 = 5.5 ft, x2 = 5.51 ft, y1 = \((8 ft³/min/3π)^(1/3)\), and y2 = \(((8 + 1) ft³/min/3π)^(1/3)\). So,

\(m = ((( 8 + 1 ) ft³/min/3π)^(1/3) - (8 ft³/min/3π)^(1/3))/ (5.51 ft - 5.5 ft)\)m = 2.75 ft/min

Therefore, the rate of change of the radius is 2.75 ft/min.

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Answer:

x = 0.5

Step-by-step explanation:

The given expression is :

4(x+2) = 10

Using commutative property at LHS.

4x+8 = 10

Subtract 8 from both sides.

4x+8-8 = 10-8

4x = 2

x = (1/2) = 0.5

So, the value of x is equal to 0.5 instead of 0. Hence, the given expression cannot be equal to 0.

Answer:

$3.42

Step-by-step explanation:

the cost = 11.4 × 0.30 = $ 3.42

The point-slope form of the line with slope 3/4 that passes through the point (-8,7) is y = (3/4)x + 13.

To find the point-slope form of a line, we need to know the slope of the line and one point that the line passes through. In this case, we are given that the slope is 3/4 and the line passes through the point (-8,7).

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1,y1) is the point the line passes through and m is the slope of the line.

Substituting in the given values, we get:

y - 7 = (3/4)(x - (-8))

Simplifying this equation, we have:

y - 7 = (3/4)x + 6

Adding 7 to both sides, we get:

y = (3/4)x + 13

Therefore, the point-slope form of the line with slope 3/4 that passes through the point (-8,7) is y = (3/4)x + 13.

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Answer:  6,048

Step-by-step explanation:

15,000-8,952=6,048

Answer:

4/£

6048

Step-by-step explanation:

just subtract 8952 from 15,000

Given:

The expression is:

\(13+23+12+7\)

To find:

The value of the given expression by using Commutative and Associative properties of numbers.

Solution:

We have,

\(13+23+12+7\)

Applying parenthesis and brackets, we get

\(=[13+(23+12)]+7\)

\(=[13+(12+23)]+7\)             [Commutative properties of numbers]

\(=[(13+12)+23]+7\)             [Associative properties of numbers]

\(=(25+23)+7\)

Using Associative properties of numbers, we get

\(=25+(23+7)\)               [Associative properties of numbers]

\(=25+30\)

\(=55\)

Therefore, the value of the given expression 55.

Answer:

This is a translation considering that it moved and, didnt change size or form.

Step-by-step explanation:

Answer:

\(\approx 6^\circ\)

Step-by-step explanation:

Given that:

Little Gull Island Lighthouse shines a light from a height of 91 feet above the sea level.

The angle of depression is unknown.

Distance of the point at sea surface from the base of lighthouse is 865 ft.

This situation can be modeled or can be represented as the figure attached in  the answer area.

The situation can be represented by a right angled \(\triangle ABC\) in which we are given the base and the height of the triangle.

And we have to find the value of \(\angle BAD \ or \ \angle C\) (Because they are the internal vertically opposite angles).

Using tangent ratio:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tanC = \dfrac{AC}{BC}\\\Rightarrow tanC = \dfrac{91}{865}\\\Rightarrow tanC = 0.105\\\Rightarrow \angle C \approx 6^\circ\)

Therefore, the angle of depression is: \(\approx 6^\circ\)

The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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The population of organism A grows by a factor of approximately 2.47 (i.e., 24.70/10) in the first five days. We can express this as an exponential expression as follows:\(2.47 = 1.2^5\)

we need to use the formula for exponential growth which is given by:\(Nt = N_{0}\)×\((1 + r)^t\)

where Nt is the population size at time t, \(N_{0}\) is the initial population size, r is the rate of growth, and t is the time interval.

Using this formula, we can calculate the population growth of organism A in the first five days.

Let's assume that the initial population size of organism A is \(N_{0} = 10\) and the rate of growth is r = 0.2 (which means that the population increases by 20% per day).

Then, we can calculate the population size at day 5 using the formula:  \(N_{5} =N_{0}\) × \((1 + r)^5 N_{5} = 10\) × \((1 + 0.2)^5 N_{5} = 10\) × \(1.2^5 N_{5}\) ≈\(24.70\)

Therefore, the population of organism A grows by a factor of approximately 2.47 (i.e., 24.70/10) in the first five days.

We can express this as an exponential expression as follows:\(2.47 = 1.2^5\)

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The radius of the tire given the inches travelled in 100 revolution is 12 inches.

A tire has the shape of a circle. A circle is a bounded object which points from its center is equidistant to its circumference. One revolution is equal to the circumference of the tire. The circumference of a circle is the distance round the circle.

Circumference of a circle = 2πr

Where:

Circumference = total distance / number of revolutions

7540 / 100 = 75.40 inches

75.40 inches = 22/7 x r x 2

75.40 = 44/7 x r

r = 75.40 x 7/44 = 12 inches

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Answer:

Conclusion:

Step-by-step explanation:

Given

We know that the diagonals of a parallelogram bisect each other.

Therefore,

Given RT = x and TP = 5x-28, so

x = 5x-28

5x = x+28

5x-x = 28

4x = 28

divide boh sides by 4

4x/4 = 28/4

x = 7

Thus, the value of x = 7

Similarly,

QT = TS

Given QT = 5y and TS = 2y+12, so

5y = 2y+12

5y-2y = 12

3y = 12

divide both sides by 3

3y/3 = 12/3

y = 4

Thus, the value of y = 4

Conclusion:

Given the fraction,

The required mixed number is,

The situation described, where Joe overheard 5 girls talking about their love for princess movies and then concluded that all girls love princess movies, is an example of a hasty generalization.

A hasty generalization occurs when a person makes a broad assumption or generalization based on a small or limited sample size. In this case, Joe is assuming that all girls share the same interest in princess movies based on the opinion of only 5 girls.

It is important to recognize that not all girls have the same preferences and interests, and it would be more accurate to gather a larger and more diverse sample before making such a conclusion.Making hasty generalizations can lead to inaccurate or unfair judgments.

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Answer:

Step-by-step explanation:

x + 5 =0 & x + 12 =0

:- x = -5 & -12

Answer:

-7<=t<=-4

Step-by-step explanation:

from negative seven to negative four there is no decreasing, only increasing.

Answer: Choice C) \(4 \le t \le 8\)

======================================================

Explanation:

The point (4,5) is on the blue curve, and so is (8,9)

Draw a straight line through these points. This line has positive slope because it moves upward as we move from left to right, so there's a positive average rate of change from t = 4 to t = 8. Generally the curve goes upward as we move from t = 4 to t = 8.

Use the slope formula to compute the average rate of change if needed. It appears your professor doesn't want the actual numeric value, but just wants to know which interval corresponds to a positive average rate of change.

\(208012.5\)

Step-by-step explanation:

\( \sqrt{645 \times 645} \)

\( = \sqrt{416025} \)

\( = 208012.5\)

Answer:

√{645×645}=√645²=±645 is your answer

if the linear correlation between two variables is​ negative,  correlation between two variables corresponds to a negative slope in the regression line.

If the linear correlation between two variables is negative, it indicates that there is a negative relationship between the variables. In other words, as one variable increases, the other variable tends to decrease.

In terms of the slope of the regression line, when the correlation is negative, the slope of the regression line will also be negative. This means that for every unit increase in the independent variable, the dependent variable is expected to decrease by the value of the slope.

The slope of the regression line represents the change in the dependent variable for a one-unit change in the independent variable. In the case of a negative correlation, the slope will be negative to reflect the negative relationship between the variables.

Therefore, a negative correlation between two variables corresponds to a negative slope in the regression line.

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