7. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7, find the smallest possible value of m. (3 marks)
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In order to draw a perpendicular bisector you must have ruler , compass and a pencil.

Given nothing and we have to show the steps to draw a perpendicular bisector.

Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.

If we want to make a perpendicular bisector on a line then we have to follow the following steps:

1) First draw a line with the help of ruler on which we want to make perpendicular bisector.

2) Now take a compass and a pencil.

3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.

4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.

5) Now repeat the step 4 from other end.

6) Now draw a line from the point where two arcs intersects on the line.

7) It is the perpendicular bisector of the line.

Hence to draw a perpendicular bisector we require compass, ruler and a pencil.

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The final loss percent is 0.25%.

The gap between the cost price and the selling price is what is referred to as a loss. And the loss percent is the loss as a percentage of the actual cost.

Total CP=Rs. 400

Let the CP of the first watch be Rs. x

So, CP of the second watch=Rs.(400-x)

For the first watch,

Gain Percent=5%

SP = [tex](1+\frac{5}{100})*x[/tex]

SP=105x/100

For the second watch,

Loss Percent=5%

SP=[tex](1-\frac{5}{100})(400-x)[/tex]

SP=95(400-x)/100

As the SP of both the watches is the same.

[tex]\frac{105}{100}x=\frac{95}{100}(400-x)[/tex]

105x=38000-95x

105x+95x=38000

200x=38000

x=38000/200

x=190

CP of the first watch=Rs. 190

CP of the second watch=Rs. (400-190)=Rs. 210

SP of first watch=[tex]\frac{105}{100}*190[/tex] =Rs. 199.50

SP of second watch=[tex]\frac{95}{100}*210[/tex]=Rs. 199.50

Total SP=Rs. 399

Final Loss=Total CP-Total SP

                =Rs.(400-399)

                =Rs. 1

Final Loss Percent=100/400

                              =0.25%

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In general, the greater the between-group variance compared to the within-group variance, the more likely you are to find statistical significance.

Unlike the inside group version, where the focus is on the differences among a population and its implication, the between-organization variant is concerned with finding how the method of corporations differ from each other.

Inside-organization version (on occasion referred to as mistakes organization or error variance) is a time period used in ANOVA tests. It refers to variations because of variations within individual businesses (or ranges). In other words, no longer all of the values within every group (e.g. method) are equal.

With the purpose to examine multiple groups right away, we can study the ANOVA, or analysis of Variance. not like the t-test, it compares the variance within every sample relative to the variance between the samples.

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Answer:

  213°

Step-by-step explanation:

Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...

  Sin = Opposite/Hypotenuse

The sine of the angle at the lighthouse is ...

  sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82

The value of the angle is found using the inverse sine function, called the arcsine function:

  bearing to boat = arcsin(45/82) ≈ 33°

The bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:

  bearing to lighthouse = 33° +180° = 213°

__

Additional comment

The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.

Answer: 1

Step-by-step explanation:

When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]

Option A is correct answer; i.e. 102 homes were sold in 2017.

A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.

Here,

Total Homes sold in 2017 = 850 homes.

Homes sold in Southwest region = 12 % of the total.

                                                      = 0.12 X 850

                                                      = 102.

Thus, option A is correct answer; i.e. 102 homes were sold in 2017.

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Answer:

A

Step-by-step explanation:

So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.

Answer:

A

Step-by-step explanation:

It is absolute value and when it is absolute value, it is positive.

[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]

[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]

[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]

Answer:

k = 20

Step-by-step explanation:

1) Isolate the variable

k - 8 = 12

  +8    +8

2) Solve

k = 12+8

k = 20

Answer:

-5x + 1

Step-by-step explanation:

Hello!

We can find the quotient by factoring the numerator, and cancelling common factors.

The quotient is (-5x + 1).

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{\dfrac{15x^2 - 3x}{-3x}}[/tex]

[tex]\huge\textbf{Simplify the current equation:}[/tex]

[tex]\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}[/tex]

[tex]\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}[/tex]

[tex]\mathbf{= \dfrac{-15x + 3}{3}}[/tex]

[tex]\huge\textbf{Simplify that above:}[/tex]

[tex]\mathbf{= -5x + 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: A=48 squared centimeters

Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)

Answer:

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Step-by-step explanation:

[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]

Make x the subject in (1)

[tex]x=3y+24 \left(3)\right[/tex]

Sub into (2)

[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]

Sub into (3)

[tex]x=-30+24\\\\x=-6[/tex]

Hence

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Answer:

[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]

Step-by-step explanation:

[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]

We multiply equation (1) by -4:

-x+3y=-24 |*(-4)

-x*(-4)+3y*(-4)=-24*-(-4)

4x-12y=96.  (3)        ⇒

[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]

We summarize equations (2) and (3):

[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]

Answer:

Second option 1.6x10^14

Step-by-step explanation:

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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The area of the space under the slide is 2.10 square meters

The diagram in the question is added as an attachment

The vertical distance is represented by h.

So, we have:

sin(70) = h/2

Solve for h

h = 2 * sin(70)

Evaluate

h = 1.88 m

Hence, the vertical distance is 1.88 m

This is calculated using

sin(40) = h/Slide

This gives

sin(40) = 1.88/Slide

Solve for Slide

Slide = 1.88/sin(40)

Evaluate

Slide = 2.92

Hence, the length of the slide is 2.92 m

This is calculated using:

A = 0.5 * h * slide * sin(∅)

Where

∅ = 90 - 40 = 50

So, we have:

A = 0.5 * 1.88 * 2.92 * sin(50)

Evaluate

A = 2.10

Hence, the area of the space under the slide is 2.10 square meters

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Answer:

B

Step-by-step explanation:

since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.

is that 2.11 I think so

Step-by-step explanation:

I don't know explain it to you and

The rate of change of the the given table is: 3/4soda per dollar.

Rate of change = change in total cost / change in number of sodas.

Using (24, 18) and (28, 21), we would have:

Rate of change = (21 - 18)/(28 - 24)

Rate of change = 3/4

Therefore, the rate of change is 3/4soda per dollar.

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Answer:

x = 2 and y = -1

Step-by-step explanation:

that is the solution above

Answer:

x = 2

y == -1

Step-by-step explanation:

     x - 10y = 12 ----------------(I)

   10x + 10y = 10 --------------(II)

We can find the value of 'x' by eliminating 'y'. To eliminate 'y', add equations (I) & (II)

           (I)             x - 10y = 12

          (II)         10x + 10y = 10   {Now add the equations}

                         11x          = 22

                                     x = 22 /11

                                  [tex]\sf \boxed{\bf x = 2}[/tex]

Now, Plugin x = 2 in equation (1)

 10*2 + 10y = 10

   20  + 10y = 10

             10y = 10 - 20

             10y = -10

                 y = -10/10

                [tex]\sf \boxed{\bf y = -1}[/tex]

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Find the slope of the line that passes through the pair of points.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

In this problem we have two points given to us, which are...

... and we should find the slope.

[tex]\bf{We\;will\;use\;the\;Slope-Equation:}\\m=\dfrac{y2-y1}{x2-x1}[/tex]

[tex]\bf{\dfrac{0-6}{7-2}=\dfrac{-6}{5} =-\dfrac{6}{5}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Slope:}[/tex]

                                [tex]\bf{=-\dfrac{6}{5}}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

The minimum sample size needed in the research of systolic blood pressure is 68.

Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.

We have to first find the level of alpha which is known as error.

α=(1-0.9)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05

=0.95 ,so Z=1.645.

now finding the margin of error, which is as under:

[tex]M=z st/\sqrt{n}[/tex]

in which st is standard deviation and the n is sample size of population.

By assuming the standard deviation of 25 mm Hg we get values as under:

n is sample size.

[tex]M=z* st/\sqrt{n}[/tex]

[tex]5=1.645*25/\sqrt{n}[/tex]

[tex]5\sqrt{n}=1.645*25\\[/tex]

dividing both sides by 5

[tex]\sqrt{n}=1.645*5[/tex]

squaring both sides we get

n=67.65.

Hence the sample size needed by the researcher is 68.

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The given question is incomplete as it should includes :

standard deviation= 25mm Hg

Confidence level=90%

Estimation 5 mm Hg of u.

Using linear functions, it is found that the temperatures would be equal after 8 hours.

A linear function is modeled by:

y = mx + b

In which:

Two functions are equal when they intersect. In this problem, both lines pass through point (8,70), that is, they have the same temperature(of 70 degrees) after 8 hours.

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The numbers which are the means of the proportion as given in the task content are in; Choice D; 3 and 20

It follows from the task content that the proportion whose mean is to be evaluated in the task content is; 2/3 = 20/30.

On this note, it follows that the numbers 2 and 30 are the lower and upper extremes of the property and hence, 3 and 20 are the mean of the proportion.

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Answer: If she waits on 13 tables than she should expect to earn $220

Step-by-step explanation:

15*13=195

195+25=220

The value of (g-f)(X) is 2x - 6x³ +6.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x)= 6x³-4, g(x)= 2x+2

Now,

(g-f)(x)= g(x)-f(x)

= 2x+2-( 6x³-4)

=2x+2- 6x³+4

=2x - 6x³ +6

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Answer: 1010

Step-by-step explanation:

[tex]V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}[/tex]