What is the slope of the line that passes through the points (10, 3) and
(7,0)? Write your answer in simplest form.

Answer:

1/9^2

Step-by-step explanation:

simplify

9^(7-9)

simplify further

9^-2

simplify even more

1/9^2

Answer:

9^16

Step-by-step explanation:

just took the test

Answer:

No

Step-by-step explanation:

Each x can have only ONE y as its partner. In this relation, -1 has TWO different partners: in one point (-1,-4) the y is -4 and in another point (-1,2) the y is 2. Not a function.

Answer:

B

Step-by-step explanation:

Test statistic is 0.42.

Given

Testing:

h0 : p = 0.74

h1 : p < 0.74

Successes x = 33

Subject n = 43

A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.

It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.

Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]

p = population proportion

n = sample size

z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]

z = 0.42

Hence,

Test statistics is 0.42..

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Answer:

(-6,4)

Step-by-step explanation:

You started at (-4,2)  The first number in the ordered pair moves the number left and right and the second number moved the point up and down.

We are first told to move the point 2 units to the left.  -4 is my left right number.  If I am at -4 and I go to unites to the left, I will be at -6.  My new point is now (-6,2).  Next we are told to go up 2.  The 2 number in my ordered pair tells me that I am 2 above the x axis.  Now I am going to go two more units up.  I am now at 4, so my new ordered pair after the translation is (-6,4)

coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).

What is Translation ?

"Translation" moves points the same distance along lines that are parallel to each other.

Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.

Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points

We are asked to find the coordinates of the points (-4,2) after a translation 2 units left and 2 units up.

We know that translating a point to the left by 'a' units means we need to subtract 'a' units from x-coordinate of the point.

Translation to 2 units left:

(-4,2) → (-4-2, 2)  → (-6, 2)

We know that translating a point to upwards by 'a' units means we need to add 'a' units to y-coordinate of the point.

Translation to 2 units up:

(-6, 2) → (-6, 2+2) → (-6, 4)

Therefore, coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).

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The points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)

Linear equations are equations that have constant average rates of change, slope or gradient

The given parameters are:

Slope = 4

Point = (1, -1)

The slope of 4 means that as x changes by 1, the value of y changes by 4

This means that, we have:

(x + 1, y + 4)

Substitute the known values in the above equation

(1 + 1, -1 + 4)

Evaluate

(2, 3)

Hence, the points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)

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7.1 cm  long is the arc intersected by a central angle .

What is length of an arc?

Given,

Central angle = π / 2

radius = 4.5 cm

we apply formula of length of arc.

length of the arc = angle ×  radius

                              = (π/2) × (4.5 cm)

Now put value of π = 3.14

length of the arc = (3.14 / 2) × (4.5) cm

                            = 7.065 cm ≈ 7.1 cm

Therefore, 7.1 cm  long is the arc intersected by a central angle .

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I believe the slope is negative. If it was positive then it would have been " / "

Answer:

C

Step-by-step explanation:

• A vertical line has an undefined slope

• A horizontal line has a slope of zero

• A line sloping downwards from left to right has a negative slope

• A line sloping upwards from left to right has a positive slope

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

the line here slopes downwards from left to right and has a negative slope

The required equation that represents the line of best fit is y = 2x + 4

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.

Using the following points (4, 12) and (2, 8)

The equation of the line will be in the form y = mx + b

where

m is the slope

b is the y-intercept

Determine the slope

Slope = y2-y1/x2-x1

Slope = 8-12/2-4
Sope = -4/-2
Slope = 2

Determine the y-intercept

Using the coordinate point (2, 8) and m = 2

8 = 2(2) + b

b = 8 - 4

b = 4

Hence the required equation that represents the line of best fit is y = 2x + 4

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The game is not fair as 6 times the expected sum is less than the cost, $43.

In the question, we are asked if the game is fair.

For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,

6E(X) ≥ 43.

The expected sum for the pair, E(X) can be calculated using the formula,

E(X) = ∑x.p(x),

or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,

or, E(X) = 107/18.

Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.

Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.

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Answer:

Step-by-step explanation:

Answer:

(x + 1)² + (y - 3)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 3 ) and r = 4 , then

(x - (- 1) )² + (y - 3)² = 4² , that is

(x + 1)² + (y - 3)² = 16

Answer:

(x+1)^2 + (y-3)^2 = 16

Step-by-step explanation:

The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.  Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2  = (x+1)^2 + (y-3)^2 = 16.

The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

According to the statement

we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.

And we have to find that the yield to maturity on this bond.

So, For this purpose,

The amount given is $911. 10.

Years to maturity = n = 10

Coupon rate = C = 8.25%

Semiannual coupon = $1,000 × (0.0825/2) = $41.25

Yield to maturity = i

Present value of bond = PB = $911.10

Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 9.4%:

= $522.90 + 391.54 ≅ $914.43

The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).

So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

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Solving a system of equations we will see that there are 150 blue marbles in the bag

We know that initially, the ratio of red to blue marbles is 3:5

This means that if there are 8*n marbles in the bag, there are:

Now, when he adds 10 red marbles, the new ratio is 2:3, this means that if now there are 5*m marbles, we have:

Where we will have two relations, so we have a system of equations:

3*n + 10 = 2*m

8*n + 10 = 5*m

With these two we can find the value of n and m.

To do that, we isolate m in the first equation:

m = (3*n + 10)/2

Now we can replace that in the other equation to get:

8*n + 10 = 5* (3*n + 10)/2

Now we can solve this for n:

2*(8*n + 10) = 5*(3n + 10)

16n + 20 = 15n + 50

n = 50 - 20 = 30

n = 30

And the number of blue marbles is:

5*n = 5*30 = 150

There are 150 blue marbles.

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The annual rate of inflation is 35560.86%.

To find the annual rate of inflation:

Now, sub in 4 and 0.099

Therefore, the annual rate of inflation is 35560.86%.

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The correct question is given below:

The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?

If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

Using Pythagoreans theorem formula

a²=b²+c²

Where:

c=16 feet

a=40/2=20 feet

Hence:

20²=b²+16²

b²=20²-16²

b²=400-256

b²=√144

b=12

2b=12×2

2b=24 feet

Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

The complete question is are:

A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?

a. 34 feet

b. 46 feet

c. 24 feet

d. 30 feet

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Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.

By looking at the scatter plot, we can see that as we read from left to right, the number of shoes sold (y variable) decreases.

Then the linear fit must have a negative slope, from that, we can discard options B and C.

Now, we also can see that the line starts almost at y = 70.

If you look at the option D, you can see that the constant term of that line is -70, so we can also discard that option.

Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

As you can see in the quadrilateral ABCD, the two angles measure 90° (as they are tangents to circle c) and one of them is given 124°

we need to find the Angle BAD : let it be x ~

By angle sum property of Quadrilaterals,

[tex]\qquad \sf  \dashrightarrow \: 90 + 90 + 124 + x = 360[/tex]

[tex]\qquad \sf  \dashrightarrow \: x+30 4 = 360[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 360 - 304[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 56 \degree[/tex]

Hence, Angle m A = 56°

Answer: c

Step-by-step explanation:

The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

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If a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes after solving through permutations.

Given that a palindrome is a string of characters the reads the same backwards as it does forwards.

We are required to find the number of 6 letter palindromes.

Permutations is basically finding how many ways in which the some numbers or things can be arranged. It is expressed as [tex]nP_{r}[/tex]=n!/(n-r)!.

If there are 6 letters then in a palindrome 3 alphabets are used here to form a 6 letter word.

=6[tex]P_{3}[/tex]

=6!/(6-3)!

=6*5*4*3!/3!

=120 palindromes.

Hence if a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes.

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Answer:

It is the second picture.

Step-by-step explanation:

The total surface area is 1308 meters square

From the question, we have the following dimensions

Length = 19 m

Width = 16 m

Height = 10 m

The total surface area is then calculated as:

Total surface area = 2 * (Length * Width + Width * Height + Length * Height)

Substitute the known values in the above equation

Total surface area = 2 * (19 * 16 + 16 * 10 + 19 * 10)

Evaluate the expression

Total surface area = 1308

Hence, the total surface area is 1308 meters square

The question is incomplete, and the resources cannot be found online.

So, I used the attached figure to answer the question

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Answer:1,238yd squared

Step-by-step explanation:

The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.

Important assumptions in regression model analysis are

Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.

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Answer:

Angle symbol

Angle ACB

Angle ACE

Angle DCE

t is vertical to s because they share a point and are directly across from each other. vertical angles are congruent. therefore s=113 degrees

t and p are corresponding angles, which means they are congruent. this means p is also 113 degrees.

s and o are corresponding angles, so o is also 113 degrees.

t and u are supplementary. they share a straight line, so they add up to 180. you can find u by subtracting 113 from 180. 180-113= 67, so u is 67 degrees.

u and r are vertical angles, so r is 67 degrees.

r and m are corresponding, as well as u and q. therefore m and q both equal 67 degrees.

hope this helped :)

The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.

The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.

So in the given question, the perimeter of the fence required = 1200 meters.

Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,

Perimeter = 2l + 3w

1200 = 2l + 3w

Thus, let l be equal to 300, we have;

1200 = 2(300) + 3w

1200 - 600 = 3w

w = 200

Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.

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Answer: Look at stwp by step

Step-by-step explanation:

Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2

Answer:

5/3

Step-by-step explanation:

z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67

as most z-tables round the z-scores to hundredths.

not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :

(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67

you did not do anything wrong. that is all ok and valid.

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

In linear algebra, systems of linear equations with a unique solution can be represented by the following expression:

[tex]\vec A \cdot \vec x = \vec B[/tex]      (1)

Where:

The solution of such systems is defined by:

[tex]\vec x = \vec A^{-1}\cdot \vec B[/tex]

[tex]\vec x = \frac{1}{\det(\vec A)}\cdot adj\left(\vec A\right) \cdot \vec B[/tex], where [tex]\det \left(\vec A\right) \ne 0[/tex].

Where:

For the case of [tex]\vec A \in \mathbb{R}_{2\times 2}[/tex], the inverse of [tex]\vec A[/tex] is:

[tex]\vec A^{-1} = \frac{1}{\det \left(\vec A\right)} \cdot \left[\begin{array}{cc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]     (2)

If we know that [tex]\vec A = \left[\begin{array}{cc}3&4\\5&2\end{array}\right][/tex] and [tex]\vec B = \left[\begin{array}{cc}1\\3\end{array}\right][/tex], then the solution of the system of linear equations is:

[tex]\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]

[tex]\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]

[tex]\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right][/tex]

[tex]\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right][/tex]

[tex]\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right][/tex]

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

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The equation that solve for x is as follows;

70 + 60 + x = 180

The equation that can be used to find the measure of angle x can be found as follows:

60 + 70 + y = 180

Therefore,

130 + y = 180

subtract 130 from both sides

130 - 130 + y = 180 - 130

y = 50°

70 + 60 + x = 180

130 + x = 180

x = 180 - 130

x = 50°

x and y are  vertically opposite angles.

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