What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)? y 3 = −4(x 4) y 3 = â€"one-fourth(x 4) y 3 = one-fourth(x 4) y 3 = 4(x 4)

The coordinates of the midpoint M for the line segment AB are (-1/2, -2).

As per the stated values;

Th end points of the line segment AB are given as;

A(−5, 1) = (x1, y1)

B(4,−5) = (x2, y2)

The formula for the evaluation of the coordinates of the mid point is-

Mid point - M(x, y)

x = (x1 + x2)/ 2

x = (-5 + 4) /2

x = -1/2

y = (y1 + y2)/2

y = (1 - 5)/2

y = -2

Thus, the coordinates of the midpoint M for the line segment AB are (-1/2, -2).

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The three consecutive even integers are -2, 0 and 2.

Let the three consecutive even integers be x, x+2 and x+4.

Since the product of the first two is taken, the result is four less than the square of the third one. This will be:

x(x + 2) = (x + 4)² - 4

x² + 2x = x² + 8x + 16 - 4

x² + 2x = x² + 8x + 12

Collect like terms

x² - x² + 2x - 8x - 12

-6x - 12 = 0

-6x = 12.

Divide

x = -12/6

x = -2

x + 2 = -2 + 2 = 0

x + 4 = -2 + 4 = 2

They're -2, 0, and 2.

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Answer:

The number is -36 or x = -36

Step-by-step explanation:

2x + 16 = -56
       2x = -72
         x = -36

The rate at which the height of the water changes when the water is 1m deep is; dh/dt = 1.5m/min

We are given;

width; w = 3m

Height; h = 4m

Length of trough; L = 10m

According to similar triangle property; w =3/4h

volume of water; V = 1/2×w×h×L = 1/2 × 3/4h × h × 10 = 15/4 h²

Differentiate using chain rule for both sides with respect to t gives;

dV/dt = (1/2)(15/2)h(dh/dt).

Now, we are given dV/dt = 5m³/min and we want to find the rate at which the height of water changes when the water is 1 m deep.

Thus;

5 = ×dh/dt

At h = 1m; 5 = 15(1)/2 × dh/dt

⇒ dh/dt = 2/3

dh/dt = 1.5 m / min

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Answer:

264,600

Step-by-step explanation:

249 ÷ 83 = 3

88,200 ×3 = 264,600

0.10 > 0.05 is value of p - value of the data .

What does P stand for?

If we use 10% p - value cutoff = 0.10

then as 0.10 > 0.05

reject the null / data is consistent with the alternative hypothesis .

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10 + 10i

Apply Multiplicative Distribution Law: 12i - 9 x i^2 - 2i - i^2

Rewrite by definition: i^2 = -1:12i - 9 x (-1) -2i - (-1)

Remove the parentheses: 12i + 9 - 2i + 1

Combine like terms: 10 + 10i

Answer 10 + 10i

Answer:

10 + 10i

Step-by-step explanation:

Given expression:

[tex]3i(4 - 3i) - i (2 + i)[/tex]

Expand:

[tex]\implies 12i-9i^2-2i-i^2[/tex]

[tex]\implies 12i-2i-9i^2-i^2[/tex]

[tex]\implies 10i-10i^2[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies 10i-10(-1)[/tex]

Simplify:

[tex]\implies 10i+10[/tex]

Rewrite in standard complex form  a + bi:

[tex]\implies 10+10i[/tex]

The amount of money that Amelia would spend on five bags of cat food is $22.5.

Amelia needs to buy some cat food. At the nearest store, three bags of cat food cost $13.50. We need to find out the amount of money that Amelia would spend on five bags of cat food.

Let the amount of money that Amelia would spend on 5 bags of cat food be represented by the variable M. We will use the unitary method. First of all, we will calculate the cost of one bag of cat food.

C = $13.50/3

C = $4.5

Now we need to find out the cost of five bags of cat food.

M = $4.5×5

M = $22.5

Hence, the amount of money that Amelia would spend on five bags of cat food is $22.5.

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Answer:

  15 feet

Step-by-step explanation:

Given an 8' object casts a 10' shadow, you want to know the length of the shadow of a 12' object.

The shadow length is proportional to the object length:

  shadow/object = 10'/8' = s/12'

Multiplying by 12', we have ...

  s = (12')(10/8) = 15'

The shadow of a tree 12 feet tall will be 15 feet long.

The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

Given that,

The points (-7,9).

We have to find the image of the point after a rotation of 90° counterclockwise.

Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.

Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.

(x,y)→(y,-x)

(-7,9)→(9,7)

Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

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well, looking at the picture we can see the blue rectangle is a 4x6 whilst the larger containing rectangle is a 14x15, well, we can simply get the area of the larger one and subtract the area of the smaller one.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{white~rectangle}{(14)(15)}~~ - ~~\stackrel{blue~rectangle}{(4)(6)}}\implies 210-24\implies \text{\LARGE 186}[/tex]

The maximum the company can expect for returned items is  $4190.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The average daily profit of an electronics store is $27,235.

The company estimates that 15% is lost each day to returns.

∴ The amount of return is (15/100)×27135.

= 0.15×27125.

= $4068.

Now this has an error of ± 3%, therefore the maximum the company can expect for returned items is {(100 + 3)/100}×100

= 1.03×4068.

= $4190.

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The graph the system of linear equations on a coordinate plane is added as an attachment

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y=4/3x+4

3y=-2x-6

Rewrite the equations in the system of equations as follows:

So, we have the following representation

y = 4/3x + 4

3y = -2x - 6

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (-3, 0)

This means that the solution to the system of equations is (-3, 0)

See attachment for the graph of the system of equations

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Answer:

22

Step-by-step explanation:

Answer: Around 40 pages

Step-by-step explanation: Im not sure if this is the answer but from what I can do this would be the answer

Answer:

she will read 22 pages :)

Step-by-step explanation:

The solution to the linear system of equation is x = 3, y = 5, and z = -0.5

A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together

The system of linear equation is presented as follows;

2·x - 3·y + 6·z = -12...(1)

5·x + 2·y - 8·z = 29...(2)

7·x + 6·y + 4·z = 49...(3)

Multiplying equation (1) by 5 and equation (2) by 2, we get;

5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)

2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)

Subtract equation (4) from equation (5), to get;

10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118

19·y - 46·z = 118...(6)

Multiplying equation (1) by 7 and equation (3) by 2, we get;

7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)

2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)

Subtracting equation (7) from equation (8), we get;

14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182

33·y - 34·z = 182...(9)

Multiplying equation (6) by 33 and equation (9) by 19, we get;

627·y - 1,518·z = 3,894...(10)

627·y - 646·z = 3,458...(11)

Subtracting equation (10) from equation (11), we get;

627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436

872·z = -436

z = -436 ÷ 872 = -0.5

z = -0.5

From equation (6), we have;

19·y - 46·z = 118

19·y - 46 × (-0.5) = 118

19·y - 46 × (-0.5) = 118

19·y = 118  + 46 × (-0.5) = 95

y = 95 ÷ 19 = 5

y = 5

From equation (1), we get;

2·x - 3·y + 6·z = -12

2·x - 3 × 5 + 6 × (-0.5) = -12

2·x = -12 + 3 × 5 - 6 × (-0.5) = 6

x = 6 ÷ 2 = 3

x = 3

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Answer:

The range is 9.

Step-by-step explanation:

The range of a data set is the difference between the maximum and the minimum values.

Let's begin by putting the set of values in order from lowest to highest.

12, 14, 15, 16, 17, 17, 21

The lowest value is 12, and the highest value is 21.

Let's subtract the minimum value from the maximum value to determine the range:

21 - 12 = 9

Hope this helps :)

Answer:

Step-by-step explanation:

Put them in order (lowest to highest)

so,

12, 14, 15, 16, 17, 17, 21

to find the range : highest - lowest

21 - 12 which is 9

Thanks

Answer:

area of rhombus=1/2*36*22.5

=405cm^2

Step-by-step explanation:

Answer:

That doesn't even make any sense you can't simplify or solve for anything if there isn't the right equation???????

Step-by-step explanation:

0.1875 is  the probability of having a daughter .

Describe probability using an example?

Let X = No. of sons

n = 5 and p = 0.5, because probability of having son and daughter is same.

X follows Binomial distribution with parameter n and p. Then its pmf is,

P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5

Now,

P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125

Probability of haveing at least four sons

P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875

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If a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter

The hypotenuse of the right triangle = 10 centimeter

The measure of angle = 40  degree

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

Substitute the values in the equation

sin 40 = Opposite side / 10

Opposite side = 10 × sin 40

= 6.43 centimeter

Similarly

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos 40 = Adjacent side / 10

Adjacent side = 10 × cos40

= 7.66 centimeter

Hence, if a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter

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According to the integer N,

a) The smallest possible value of N is 6.5 if N >= 6.5

b) The largest possible value of N is -2 if N < - 3

c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.

Integer

Integer refers a collection of whole numbers and negative numbers.

Given,

Here we have the integer N.

And we need to find the following:

a. the smallest possible value of N if N >= 6.5

b. the largest possible of N if N < -3

c. the possible values of N if N >= -2 and N <2.

Part a). smallest possible value of N if N >= 6.5

Here the smallest number is 6.5 because other value are greater than this one.

Part b). the largest possible of N if N < -3

The largest possible number is -2, because the other values on N are less than -2.

Part c). the possible values of N if N >= -2 and N <2.

Here the possible values between these are {-2, -1, 0, 1}.

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The percentage of people that have a blood glucose level between 100 and 125 is 21.945%

From the question, the given parameters about the distribution are

Mean value of the set of data = 85

Standard deviation value of the set of data = 25

The actual data values = 100 and 125

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

For x = 100, we have:

Substitute the given parameters in the above equation

z = (100 - 85)/25 = 0.6

For x = 125, we have:

Substitute the given parameters in the above equation

z = (125 - 85)/25 = 1.6

The percentage between 100 and 125 is then calculated as:

P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)

From the z table of probabilities, we have;

P(100 < x < 125) = 0.9452 - 0.72575

This gives

P(100 < x < 125) = 0.21945

Express as percentage

P(100 < x < 125) = 21.945%

Hence, the percentage is 21.945%

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The quadratic function f(x) = -3(x + 2)²  + 1is represented in the graph below

When graphing parabolas, we want to include certain special points in the graph. The y-intercept is the point where the graph intersects the y-axis. The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of the graph. Lastly, the line of symmetry (also called the axis of symmetry) is the vertical line through the vertex, about which the parabola is symmetric.

In the function given;

f(x) = -3(x + 2)² + 1

vertex of the function = (-2, 1)

Axis of symmetry =

This can be graphed using a graphing calculator;

Kindly find the attached image

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Extend the compass from point T to little more than the midpoint of ST in such a way the arc drawn touches the point R. Similar is to be done from point S. Draw a line through the cut made by the 2 arcs at R.

The value of y = 110.

What is slope intercept form?

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

Rise of the water = 11

run = 1 min

slope m = 11/1 = 11.

The slope intercept form is

y = mx +b

after substituting the values, we get

m = 11,

x = 10and y = ?

y = 10 (11)

y = 110.

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The rate of the passenger train is 60mph.

We know that,

Speed = Distance / Time

Time = Distance / Speed

s = speed of passenger train

speed of freight train = (s - 20)

T = 240 / s

T = 160 / (s-20)

240 / s = 160 / (s-20)

240(s - 20)/s(s - 20) = 160s/s(s - 20)

240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0

240(s - 20) - 160s = 0s(s - 20)

240s - 4800 - 160s = 0

80s - 4800 = 0

80s = 4800

Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.

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The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.

The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.

Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.

Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.

The mean of the size of processor chips= μ =1 cm

The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ

Mean of sampling distribution x  = mean of the size of the processor chips μ

⇒ x = μ

   x = 1 cm

The mean of this sampling distribution is 1 cm.

The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.

The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm

Let 'x' be the standard deviation of random samples X of the size of processor chips.

Number of random multiple samples of processor chips, n =35

The standard deviation of this sampling distribution can be calculated by using the below formula;

x = σ/[tex]\sqrt{n}[/tex]

Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;

x = 0.2/√35

x = 0.033 cm

The standard deviation of this sampling distribution is 0.033 cm.

The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.

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The values of x and y if the mean and median are equal are:

x = 7

y = 8.

The mean is the total sum of the values in a data set divided by the number of values of the data set.

The median of a data set is the center value when the data distribution is ordered.

Given the ordered data set as, 4, 6, x, y, and 10.

The center value is x. Therefore, the median of the data set is x.

The mean of the data = (4 + 6 + x + y + 10)/5

The mean of the data = (20 + x + y)/5

The mean and the median are equal, therefore:

(20 + x + y)/5 = x

20 + x + y = 5x

20 + y = 5x - x

20 + y = 4x

The value of x cannot be less than 6, if x = 7, we woud have:

20 + y = 4(7)

20 + y = 28

y = 28 - 20

y = 8

The values of x = 7, y = 8.

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