Manny says he should multiply the first equation in the system of equations below by 3 and the second equation by 2, then add to eliminate x. Is there a more efficient way to solve this system? Explain your answer.
−2x+y=15
3x+4y=−12
A. No, there isn't a more efficient way to solve this system.
B. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate y, then solve for x.
C. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate x, then solve for y.
D. Yes, a more efficient way is to multiply the first equation by 4
add to eliminate y, then solve for x.

Answer:

Use SAS postulate

Step-by-step explanation:

In triangles LAT and SAT,
AT = AT (common side)
ang. LAT = ang. SAT (given, as angle is bisected)
SA = LA (from figure)
Hence, the triangles are congruent

Equation used to represent the amount of interest that was paid​ is S.I = 900 × 0.11 × 0.5 and the amount is $49.5.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest amount can be calculated using the formula,

S.I = Prt

Here P is the principal amount, r is the rate of interest and t is the time in years.

Given a loan of $900 at a rate of 11% with paid off in 6 months.

P = $900,

r = 11% = 0.11 and

t = 6 months = 0.5 year

S.I = 900 × 0.11 × 0.5

    = 49.5

Hence the amount of simple interest is $49.5.

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Time it will take to reach the same location driving at an average speed of 50 miles per hour,  4.4 hour

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Given that,

The time it takes to travel to a location varies inversely to the speed traveled,

Time = 4 hours

Average speed = 55 miles per hour

If average speed  = 50 miles per hour

then time = ?

First, it is required to calculate distance covered,

Distance = Time × Speed

               =  4 x 55

               = 220 miles

Now, when average speed is 50 miles per hour,

Distance = Time × Speed

Speed   = Distance/Time

             = 220/50

             = 4.4 hour

Thus, the required time is 4.4 hour

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Answer:

The answer would be C: not every input maps to an output.

An ordered pair which is a solution of the linear system of equations include the following: A. (-3, -1/2)

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = 1/2 x + 1     ......equation 1.

y = 3x/2 + 4     ......equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant III and it is given by the ordered pair (-3, -1/2).

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The larger the p-value, the more likely it is that the null hypothesis that the population coefficient is equal to 0 is true regarding p-value.

In a linear regression model, p-values are associated with the estimated coefficients and provide information about the statistical significance of each predictor variable. The null hypothesis for each predictor is that the population coefficient for that predictor is equal to 0, meaning that it has no effect on the response variable.

The p-value is the probability of observing the estimated coefficient given the null hypothesis is true. If the p-value is small, it means that the observed coefficient is unlikely to be due to chance, If the p-value is large, it means that the observed coefficient could easily be due to chance and we cannot reject the null hypothesis.

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Two puppy's Max and Ruby will have equal weight after 6 weeks

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

Two puppy's

Max, currently weighs 5 pounds and is expected to gain 1 pound per week,

Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week

The number of weeks when both will have equal weight = ?

Suppose, it number of weeks = n

It can be solved by using concept of arithmetic sequence,

a₁ = 5 pounds

d₁ = 1 pound per week

Tₙ = 5 + 1xn = 5 + n

a₂ = 8 pounds

d₂ = 0.5 pounds per week

Tₙ = 8 + 0.5xn = 8 + 0.5n

Both should be equal,

5 + n = 8 + 0.5n

0.5n  = 8 - 5

n  = 6

Hence, after 6 weeks they will have same weight

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The scalar projection of vector b onto vector a is 57/289 and the vector projection of vector b onto vector a is (0.38, 0.92).

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

The scalar projection of vector b onto vector a is given by:

(b . a) / ||a||^2

= (3 * -8 + 5 * 15) / ( -8^2 + 15^2)

= 165 / 289

= (57/289)

The vector projection of vector b onto vector a is given by:

proj(b onto a) = (b . a) / ||a||^2 * (a / ||a||)

= (57/289) * (-8/√(-8^2 + 15^2), 15/√(-8^2 + 15^2))

= (0.38, 0.92)

Note: sqrt(-8^2 + 15^2) = sqrt(289) = 17

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Answer:

A) 2/5

B) 4/15

Step-by-step explanation:

A)

adults : students

1          :  10

year 10 : year 11

1            : 4

fraction of all the people on the trip are year 11 students =

4   : 10

4 / 10

2 / 5

B)

adults : children

2         : 3 _____________(1)

boys    : girls

5         : 2 _____________(2)

multiplying ratio (1) with 5

adults : children

10 : 15

multiplying ratio (2) with 2

boys : girls

10     :  4

fraction of all the people in the cinema are girls

4  : 15

4 / 15

Answer:

What is the question?

Step-by-step explanation:

Peter is right and Nadia is wrong.

Equivalent fractions are fractions that represent the same value, even though they look different.

Given is that Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.

{ 1 } -

3/4 = (3 x 2)/(4 x 2) = 6/8

Peter is right.

Now -

3/4 = 6/8

So it could not represent two different quantities. So, Nadia is wrong.

{ 2 } -

3/4 = 6/8 = 9/12 = 12/15

These all represent the same quantity. Division of all the expressions will result in same value.

Therefore, Peter is right and Nadia is wrong.

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Rotation clockwise  about the origin 90 degrees , then reflect over the x axis

A transformation is a mapping or a function that changes the position, size, or shape of an object or image. In mathematics, transformations can refer to a variety of operations such as

The transformation involved in the image is 90 degrees counterclockwise rotation and reflection over the x axis.

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Answer:

The writer should give equal attention and value to opposing views, including using evidence. This helps to strengthen the argument by acknowledging and refuting counterarguments. It also demonstrates to the reader that the writer has considered multiple perspectives and is able to effectively argue their position. By giving equal attention to opposing views, the writer shows that their argument is well-reasoned and credible.

Step-by-step explanation:

When making an argument, it's important to consider and address any opposing views that exist. Giving equal attention to opposing views means acknowledging the validity of these views and providing evidence to refute them. This helps to strengthen the argument by showing that the writer has considered multiple perspectives and has a solid understanding of the issue at hand. It also demonstrates to the reader that the argument is well-reasoned, credible, and based on evidence.

On the other hand, ignoring opposing views, or attacking those who believe in them, weakens the argument and undermines the writer's credibility. If a counterargument is not addressed, the reader may assume that the writer is not aware of it or cannot effectively defend their position. By giving equal attention to opposing views and refuting them with evidence, the writer is able to make a stronger argument and persuade the reader of their point of view.

Answer:

The writer should use facts that can be verified to address and disprove opposing viewpoints.

Step-by-step explanation:

Hope it helps long time no seen

Answer:

C

Step-by-step explanation:

if you put the point value in the equation you get

-4 - (-2×7) = n

-4 + 14 = n

10 = n

The quadratic regression equation for the data-set in this problem is given as follows:

y = 0.96x² - 5.77x + 1.38.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points are given as follows:

(-1,8), (5,-4), (7,8), (2,-6).

Inserting these points into a calculator, the regression equation is given as follows:

y = 0.96x² - 5.77x + 1.38.

Meaning that the second option is the correct option.

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The segment drawn from the apex to the edge of the circular base is 24.19 units.​

From the question, we have the following parameters that can be used in our computation:

Volume = 72π

Diameter = 6

The volume of a cone is

V = 1/3πr^2h

Where

r = 6/2 = 3

So, we have

1/3π * 3^2h = 72π

This gives

3h = 72

Divide by 3

h = 24

The slant height is then calculated as

l = √(h² + r²)

So, we have

l = √(24² + 3²)

Evaluate

l = 24.19

Hence, the slant height is 24.19 units

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The required percentage of regular grade gasoline are;

a) 34%

b) 95.5%

c)4.5%

(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.

$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.

Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.

Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.

(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.

$3.85$ is $1.5$ standard deviations above the mean.

Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.

Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.

(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.

Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.

Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.

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Answer:

AnCr+AnCr - 1 = n!/(n - r)!r! + n/(n - r + 1)!(r -

|1)! = n!(n - r+ 1)/(n -r+ 1)!r! + n!r/(n - r + 1)!r!

F n!/(n - r+ 1)!r!(n - r+1 +r) = (n +.

Answer:

Figure 1 is vertical, through the cone's topmost point

Figure 2 is horizontal

Figure 3 is diagonal

Explanation:

The easiest way to think about this is that you have a cone-shaped cake and you are cutting it.

The frequency table using the six classes have been done below

Class interval Frequency

20 - 35 2

36 - 50 0

51 - 65 2

66 - 80 5

81 - 95 5

96 - 110 5

Note: The class intervals were created as follows: 20-35, 36-50, 51-65, 66-80, 81-95, and 96-110. The frequency is the number of data values that fall into each class interval.

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Out of the following, the statement Excel can add only linear trendlines to data in a scatter chart is  true  regarding   trendlines in scatter chart in excel.This means that the trendline in Excel will be a straight line that will best fit the data points in the scatter chart.

It will not be able to fit any other type of trendline, such as a polynomial or exponential trendline. Additionally, Excel cannot output the R Square value for a trendline in Excel for scatter charts of 3 or more variables. This is because the R Square value is a statistical measure that can only be calculated for linear regression models.

Finally, for simple linear regression models, the trendline in Excel will give the same equation as the data analysis toolpak regression tool. This means that the equation of the trendline in Excel will be the same as the equation of the regression line calculated by the data analysis.

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The solution is Option B.

The angle ∠AEC is a right angle by definition of perpendicular bisector

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as AB

Let the second line be represented as CD

Now , AB is perpendicular to the line CD

where , the measure of ∠CEB = 90°

And , angles on a straight line has a sum of 180°

So , the measure of ∠AEC is a right angle by perpendicular bisector theorem

Hence , the measure of the perpendicular angle ∠AEC is 90°

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Answer: Definition of Perpendicular Bisector

Step-by-step explanation:

Took the test!

Answer:

To determine whether the ball will eventually reach a pocket, we need to determine if the ball will collide with any other balls or obstacles on the way to its target. If there are no obstacles, and the ball has enough force and the correct trajectory, it will reach the target pocket.

To show the path of the ball, we can draw a straight line connecting the starting position and the target pocket. This line represents the trajectory of the ball if it is not obstructed by any other balls or obstacles.

In conclusion, without any obstacles in the way, if Montana hits the ball with enough force and the correct trajectory, the ball will reach the target pocket. It is important to consider any potential obstacles or interference when planning a shot in billiards.

The volume of the cylinder is given by the equation V = 8,167.14 yards³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the equation will be

The height of the cylinder h = 9 yards

The diameter of the cylinder d = 34 yards

So , the radius of the cylinder r = d/2 = 17 yards

And , Volume of Cylinder = πr²h

Substituting the values in the equation , we get

Volume of Cylinder = ( 3.14 ) x ( 17 )² x 9

On simplifying the equation , we get

Volume of Cylinder = ( 3.14 ) x 2,601

Volume of Cylinder = 8,167.14 yards³

Hence , the volume of cylinder is 8,167.14 yards³

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The longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

The longest a blender can last and still be in the lowest 6% of life spans is calculated by using the inverse normal distribution formula. This formula is P(X ≤ x) = 1 - P(X > x). The X is the longest a blender can last and P(X ≤ x) is 6%. First, we need to calculate the z-score for 6%. This can be done by P(X ≤ x) = 0.06 and using the z-score formula z = (x - μ) / σ , where μ is the mean and σ is the standard deviation. Substituting the values into the equation, we get z = 0.06 = (x - 8.2) / 0.8. Solving for x gives us x = 7.96. Therefore, the longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

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The equation y = e^-4 can be evaluated using a graphing calculator by plugging in -4 for x and finding the corresponding y-value.

On a graphing calculator, this is usually done by setting the calculator to the "y=" mode and entering the equation y = e^x. Then, by entering -4 as the value of x, the corresponding y-value can be found.

The result would be y = e^-4 = 0.0183. To four decimal places, this value is 0.0183.

The range of the function shown in the graph below is [-6, ∞].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

The y-coordinate value is the range of the function.

We see that,

The y-coordinate value is from -6 to ∞.

So,

Range = [-6, ∞].

Thus,

The range of the function is [-6, ∞].

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The expanded form of 8! is 8×7×6×5×4×3×2×1.

A whole number's factorial is the result of multiplying the integer by each natural number below it.

The sign '!' can be used to indicate a factorial symbolically.

Therefore, 'n factorial' is denoted by the number n and is the product of n up to whole numbers below n except zero.

Given, A factorial number 8!.

Therefore, 8! = 8×7×6×5×4×3×2×1.

The product of all whole numbers below 8 and except zero.

We use factorials in permutation and combination also.

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The account with simple interest will have a smaller balance than the account with compound interest because compound interest is interest paid both on the original investment and on all interest that has been added to the original investment. (option F)

An account that earns a simple interest grows at a linear rate while an account that earns a compound interest grows at an exponential rate.

Let us assume the following:

Amount invested = $1000

Interest rate = 5%

Number of years = 5 years

Future value of the account that earns a simple interest in 5 years = amount invested + simple interest

Simple interest = amount invested x time x interest rate

$1000 x 0.05 x 5 = $250

Future value in 5 years = $1000 + $250 = $1250

Future value of the account that earns a compound interest :

Future value = amount invested x (1 + interest rate)^number of years

= 1000 x (1 + 0.05)^5

= 1000 x 1.05^5

= 1,276.28

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Scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

The evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus comes from the application of the quantum mechanical model. The quantum mechanical model states that the energy of an electron is quantized, meaning it can only occupy discrete energy levels rather than any random energy level in between. This is expressed mathematically through the equation E n = nhf, which states that the energy of an electron is equal to the product of Plank's constant (h) and the frequency (f) of the electron's orbit multiplied by the quantum number (n). This equation demonstrates that electrons can only occupy certain energy levels and not any random energy level. Therefore, scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

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