Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(12,-5) 7x-3y=-5

Answer:

V= 2596.125 cm squared

SA= 1187.5 cm squared

Answer:

Step-by-step explanation:

\(V=xyz\\ \\ V=21.5(11.5)10.5=2596.125cm^3\\ \\ A=2xy+2xz+2yz\\ \\ A=2(xy+xz+yz)\\ \\ A=2(21.5(11.5)+21.5(10.5)+11.5(10.5))\\ \\ A=2(247.5+225.75+120.75)\\ \\ A=2(594)\\ \\ A=1188cm^2\)

Answer:

33.

Step-by-step explanation:

75%   x

100   44

x = (44 * 75 ) / 100 = 33.

a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

Answer:

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

Given is a quadratic equation:

A quadratic equation has no real solutions if its discriminant is negative.

The discriminant of ax² + bx + c is:

Apply to given equation:

Find the value of n when D < 0:

Answer:

\(-\dfrac{1}{2}\)

Step-by-step explanation:

Slope Formula

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}\)

Where (x₁, y₁) and (x₂, y₂) are points on the line.

Given points:

Substitute the given points into the formula and solve for m:

\(\implies \textsf{slope}\:(m)=\dfrac{1-3}{12-8}=\dfrac{-2}{4}=-\dfrac{1}{2}\)

Therefore, the slope of the line for the path of the track is -¹/₂.

The coordinates of the point R: (0, 3.4)

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line

Slope PQ 5–0/ 2–6 = 5 /-4

equation of PQ y =-5/4 x +c ;

this passing through 2,5

5 =-5/4*2 +c ; C = 5 -5/2 =5/2

y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;

equation of PQ =5x +4y-10 =0 ;

slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5

equation of PR y = mx +c this passes through [2,5]

5 = 4/5*2 +C so C = 5- 8/5 =17/5

y =4 x /5 +17/5 so coordinates of R = [0, 3.4]

Hence, the coordinates of the point R: (0, 3.4)

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Answer:

\(4x {}^{2} - 36 \\ = (2x + 6)(2x - 6) \\ hence \: option \: b \: is \: correct\)

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

\(\displaystyle m=\frac{2}{25}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (200, 14)

Point (225, 16)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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7π/12 lies in the second quadrant, so we expect cos(7π/12) to be negative.

Recall that

\(\cos^2x=\dfrac{1+\cos(2x)}2\)

which tells us

\(\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1+\cos\left(\frac{7\pi}6\right)}2}\)

Now,

\(\cos\left(\dfrac{7\pi}6\right)=-\cos\left(\dfrac\pi6\right)=-\dfrac{\sqrt3}2\)

and so

\(\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1-\frac{\sqrt3}2}2}=\boxed{-\dfrac{\sqrt{2-\sqrt3}}2}\)

The percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio is 55.56%.

Time spent using the internet = 4 hours

Time spent doing chores = 4 hours

The time spent listening to the radio = 10 hours

The total time spent during the week is 4 + 4 + 10 = 18 hours

The percentage of this total time that is spent listening to the radio is:

(10 hours / 18 hours) x 100% =55.56%

This is basic arithmetic operations and is used in calculation of numbers.

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a. FPCF for this sample is FPCF = √(199/24) = 2.89.

b. The population cannot be considered effectively infinite, so the answer is no.

When the sample size is significant compared to the size of the community, the Finite Population Correction Factor, also known as the FPC factor, is applied. The population in most cases is so vast that typical sample sizes are insufficient to raise concerns about the need for the FPC.

The recommendation is to use the FPC when the sample size to population size ratio is higher than 5%. The FPCF must be used, for instance, if the population number is 300 and the sample size is 30, which results in a ratio of 10%.

a. To calculate the FPCF (finite population correction factor) for this sample, we can use the formula:

FPCF = √(N/n)

where N is the population size, and n is the sample size.

In this case, N = 199 (the number of blood samples in the racks), and n = 24 (the number of samples selected every seventh blood sample).

FPCF = √(199/24) = 2.89 (rounded to two decimal places)

b. To determine whether the population should be considered effectively infinite, we need to compare the sample size to the population size. A general rule of thumb is that the population can be considered effectively infinite if the sample size is less than 5-10% of the population size.

In this case, the sample size is 24, which is approximately 12% of the population size of 199. Therefore, the population cannot be considered effectively infinite, and the FPCF should be applied to adjust for the finite population size.

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Answer:

The data given is  

    235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500

  The sample size is  n =  16

   The population is  \(\mu  =  \$201,800\)

  The sample mean is mathematically represented as

             \(\= x =\frac{\sum x_i}{n}\)

=>  \(\= x  =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}\)

=>    \(\= x  = 218653.125\)

Generally the sample standard deviation is mathematically represented as

     \(s =  \sqrt{\frac{\sum (x_i - \= x)^2}{n} }\)

=>   \(s =  \sqrt{\frac{ (235,000 -  218653.125)^2+ (271,900 -  218653.125)^2 + \cdots +  (245,500 -  218653.125)^2}{16} }\)

=>   \(s =  23946.896 \)

The null hypothesis is  \(H_o : \mu =  \$201,800\)

The alternatively hypothesis is  \(H_o : \mu >  \$201,800 \)

Generally the test statistics is mathematically represented as

     \(t =  \frac{\= x  - \mu }{ \frac{s}{\sqrt{n} } }\)

=>  \(t =  \frac{218653.125  - 201800 }{ \frac{23946.896 }{\sqrt{16} } }\)

=>  \(t =  2.82\)

Generally the degree of freedom is mathematically represented as

     \(df =  n - 1\)

=>   \(df =  16 - 1\)

=>   \(df =  15\)

Generally the probability of  \(t =  2.82\) at a degree of freedom of  \(df =  15\) from the t - distribution table  is  

     \(p-value  = P( t >2.82 ) =0.00646356\)

The

From the values obtained we see that \(p-value  < \alpha\)

The decision rule is  

   Reject the null hypothesis

The conclusion is

 There is sufficient evidence to conclude that the real estate company's  projection is true

Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution

Type I  Error

 The type 1 error occur when the null hypothesis is wrongfully rejected

  The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still  $201,800

   Type II  Error

 The  type 11 error occur when the null hypothesis is wrongfully  accepted(i.e wrongfully failed to reject the null hypothesis)

    The consequence in this case is that the company will assume that the average selling price  is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased

   Given that resource is scare the management of the company will want a  smaller  significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources

generally the critical value  of  \(\frac{\alpha }{2}\) from the normal distribution table is    

     \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

   \(E  =Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }\)

=>\(E  =1.96*  \frac{23946.896}{\sqrt{16} }\)

=>\(E  = 11733.96\)

Generally the 95% confidence interval is  mathematically represented as

     \(218653.125 - 11733.96  < \mu  <  218653.125 + 11733.96\)

=>  \(206919.165  < \mu  <  230387.085\)  

Generally there is 95% confidence that the actual average selling price is within this interval  

Step-by-step explanation:

Answer: 7725.5775

Step-by-step explanation:

d=27

r=d/2=27/2=13.5

the volume of the spherical balloon= 3.14*r^3

                                                       = 3.14*(13.5)^3

                                                       = 7725.5775

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The answer is b

it satisfies all the given x,y values

when x=0

its give y=-3

when x=-1

it gives y=-3

so it satisfies the condition'

so the answer is B

Solution:

Given:

The data;

Question 1:

To get the mean:

The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.

Therefore, the mean is 12.5

Question 2:

To get the median:

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest)

If there is an even number of data, the median is the average of the middle two numbers.

The data indicates an even number of data. There are 6 numbers in the set.

Hence, the median is the mean of the middle two numbers.

Therefore, the median is 12.5

Question 3:

To find the mode:

The mode of a set of numbers is the number that occurs the most. Hence, the mode of a set of numbers is the number with the highest frequency.

If a set of data has two modes, the data is said to be bimodal.

Therefore, the modes are 10 and 15.

Question 4:

The range is the difference between the highest and lowest values in a set of numbers.

Therefore, the range is 5.

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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The equation of line passes through the points (-3, -1) and (5, -1) will be;

⇒ y = - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-3, -1) and (5, -1).

Now,

Since, The equation of line passes through the points (-3, -1) and (5, -1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-1)) / (5 - (-3))

m = 0/8

m = 0

Thus, The equation of line with slope 0 is,

⇒ y - (-1)= 0 (x - (-3))

⇒ y + 1 = 0

⇒ y = - 1

Therefore, The equation of line passes through the points (-3, -1) and       (5, -1) in slope intercept form is,

⇒ y = - 1

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Answer:

The expected number of defective batteries to be pulled out is 0.9, which rounded to the nearest integer gives a total of 1, that is, 1 of the 3 batteries is expected to be defective.

Step-by-step explanation:

Given that a box contains 3 defective batteries and 7 good ones, and I reach in and pull out three batteries, to determine what is the expected number of defective batteries, the following calculation must be performed:

3 + 7 = 100

3 = X

10 = 100

3 = X

3 x 100/10 = X

300/10 = X

30 = X

3 x 3/10 = X

0.9 = X

Therefore, the expected number of defective batteries to be pulled out is 0.9, which rounded to the nearest integer gives a total of 1, that is, 1 of the 3 batteries is expected to be defective.

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

Y = 20x so the answer is 20

Step-by-step explanation:

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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Answer:

a...

associative property

Step-by-step explanation:

trust me

Answer:

it is A.

Step-by-step explanation:

hope this helps!

The area of the shaded region in each of the shapes are:

10) 16.324 ft²

11) 114.546 cm²

10) The formula for the area of a circle is:

A = πr²

where:

r is radius

Thus;

A_c = π * 4²

A_c = 50.265 ft²

Area of a hexagon inscribed in a circle is:

A_h = ((3√3)/2) * r²

A_h = ((3√3)/2) * 4²

A_h = 33.941 ft²

Area of shaded region = 50.265 ft² - 33.941 ft²

= 16.324 ft²

11) Area of a hexagon with side length has the formula:

A_h = 2(1 + √2)a²

where a is the length of one side. Thus:

A_h = 2(1 + √2) * 9²

A_h = 391.103 cm²

The interior angle of a regular octagon is 135°.

Using sine rule, we can find the length of the square:

9/sin 22.5 = x/sin 135

x = 16.63 cm

Area of square = 16.63 * 16.63

= 276.557 cm²

Area of shaded region = 391.103 - 276.557

Area of shaded region = 114.546 cm²

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The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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Answer:

∠\(ACD=60\)° or B

Step-by-step explanation:

\(110+120+70= 300\)

\(360-300=60\)

Answer:

B 60

Step-by-step explanation:

Do not let all the extra triangles on the outside trip you out. The shape is a trapezoid which total should equal 360. Add all the angles up and subtract from 360 to get 60

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