Students at a sports college choose activities for games.
In Year 7 they chose between rounders and athletics in the ratio 1 : 4.
There are 60 students in Year 7.
Work out how many chose athletics.

Step-by-step explanation:

Which values are part of the solution set based on the result of the inequality?

-4x + 24 < -2x + 2

add 2x to both sides:

-4x + 24 + 2x < -2x + 2 + 2x

-2x + 24 < 2

subtract 24 from both sides:

-2x + 24 - 24 < 2 - 24

-2x  < -22

divide both sides by -2: [remember to flip the sign direction because you are dividing by a negative number]

-2x/-2  > -22/-2

x  > 11

or (11 , ∞)

Answer:

YesTheorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.

A and B are complementary, and C and B are complementary.

The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64

Given,

The equation  x² - 28 = 12x

We need to find the intermediate step in the form (x + a)² =b as a result of completing the square for the given equation

Equation; x² - 28 = 12x

Arrange the equation;

x² - 12x = 28

Take the coefficient of x

k = -12

Divide it by 2

k/2 = -6

Square both sides

(k/2)² = 36

Add 36 to both sides of x² - 12x = 28

x² - 12x + 36 = 28 + 36

(x - 6)² = 64

Therefore,

The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64

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By Pythagoras theorem, The given triangle with sides 37 mm, 39 mm, 56 mm is not a right triangle as the theorem is false in this case.

The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Pythagorean Theorem demonstrates how the side lengths of a right triangle can be calculated from the sum of the areas of three intersecting squares. This theorem is a very helpful tool that serves as the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite.

Here,

We can prove this by Pythagoras theorem,

b²+p²=h²

b=39 mm

p=37 mm

h=56 mm

=39²+37²

=2,890

56²=3,136

As 2890≠3136,

The triangle is not a right triangle. The triangle with sides of 37, 39, and 56 millimeters is not a right triangle according to Pythagoras' theorem because the theorem is incorrect in this case.

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The point on the y-axis is (0,1) such that the distance is minimum.

Let the coordinate of the point W be (0,a)

We know that the distance from any point on the coordinate place is calculated using the distance formula.

Now let us calculate the distance of VW = √[(2-0)²+(3-a)²]

Distance XW = √[(-2-0)²+(-1-a)²]

Now the sum of the distances is given by:

VW + XW

=√[(-2-0)²+(-1-a)²] + √[(2-0)²+(3-a)²]

This can be written in the form of a function in a such that:

f(a) = √a²+2a+5 + √a²-6a+25

Now we will differentiate with respect to a to get the required first degree

f'(a) = [tex]\frac{a+1}{\sqrt{a^2+3a+5}} + \frac{a-3}{\sqrt{a^2-6a+25}}[/tex]

Now at f'(a)=0

we get a=1.

Hence the required point on the y-axis that is at a minimum distance is (0,1) .

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The total number of small boxes is 1.72 and the large boxes is 5.1.

Given;

To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 100 nails in each small box and 450 in each large box. The contractor purchased 3 more tiny boxes—totaling 2500 nails—than large boxes.

To calculate the proportion of small and large boxes that were bought,

Let's assume the small boxes as 's' and the big boxes as '3s'.

∴ s(100) + 3s(450) = 2500

   100s + 1350s = 2500

   1450s = 2500

   s = 2500/1450

   s = 1.72

∴ 3s = 1.72 * 3

       = 5.1

Hence, the total number of small boxes is 1.72 and the number of large boxes is 5.1.

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The number of small boxes purchased is 7 and the number of large boxes purchased is 4 by the contractor.

Let the number of large boxes purchased = x

then the number of small boxes purchased = x + 3

It is also given that,

small box contains = 100 nails

large box contains = 450 nails

According to the question:

450x + 100(x + 3) = 2500

450x + 100x + 300 = 2500

550x = 2500 - 300 = 2200

x = 2200/550

x = 4

and x + 3 = 4 + 3 = 7.

Thus, Let the number of small boxes purchased = 4 and the number of small boxes purchased = 7.

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Using the equation of line, the equation parallel to y=5 and passing through (3,-5) is y+5=0.

In the given question,

We have to find an equation parallel to y=5 and passing through (3,-5).

The equation parallel to y=5.

Point is (3,-5).

We firstly find the slope of y=5

Expressing the equation in the general form

y=0×x+5

On comparing to the y=mx+c, we get slope(m) = 0.

The given point is (3,-5) in which [tex]x_{1}[/tex]=3 and [tex]y_{1}[/tex]= -5

Now finding the equation.

So the Equation of line is

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

Now putting the value

y-(-5)=0(x-3)

Simplifying

y+5=0

Hence, the equation parallel to y=5 and passing through (3,-5) is y+5=0.

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Answer:

4+1.5n=c

9+0.5n=c

5 hours

Step-by-step explanation:

(n) represents the number of hours

(c) represents the total cost

Bike shop A)    $4+$1.5n=c

Bike shop Z)    $9+$0.5n=c

4+1.5n=9+0.5n

n=5                  Both shops would charge the same amount at 5 hours.

Answer: About 7%

Step-by-step explanation:

(Choice A) A Same area only is the correct option about rectangles.

The perimeter and area is calculated using the formula -

Perimeter = 2 (length + breadth)

Area = length × breadth

Now, calculating the perimeter and area of each rectangle

Rectangle with dimensions 5 cm and 4 cm

Perimeter = 2 (5 + 4)

Perimeter = 2 × 9

Perimeter = 18 cm

Area = 5 × 4

Area = 20 cm²

Rectangle with dimensions 2 cm and 10 cm

Perimeter = 2 (2 + 10)

Perimeter = 2 × 12

Perimeter = 24 cm

Area = 2 × 10

Area = 20 cm²

Thus, both the rectangles will have same area.

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Answer:

3x + 5 =3x + 8

Step-by-step explanation:

3x - 3x = 8-5

x = 3

Step-by-step explanation:

we have to soft the ones that have no solutions.

3x + 5 = 3x + 8

5 = 8

that is never true, and therefore there is no solution.

3(x + 5) = 3x + 15

3x + 15 = 3x + 15

that is always true, and it has therefore infinitely many solutions.

2(x + 1) = 2x + 1

2x + 2 = 2x + 1

2 = 1

this is never true, so, there is no solution.

2x + 1 = 2x + 1

this is always true, so this has infinitely many solutions.

The 95% confidence interval estimate of the population mean is between $50,555.51 and $51.444.49.

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = $51,000 ± 1.96 x ($1,200 / √28)

CI = $51,000 ± $444.49

CI = [$50,555.51, $51.444.49]

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Answer:

Q29. ∠CAD = (180° - 92°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)

                    = 44°

Q30. Since triangle ACD is an isosceles triangle,

∴ ∠ACD = ∠CAD = 44°

Q31. ∠ACB = 180° - 44° (adjacent angles on a straight line)

                   = 136°

Q32. ∠ABC = (180 °- 136°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)

                   = 22°

The lower bound for a 95% confidence interval for the proportion of defective iphones from this assembly line is 0.0524.

With the probability of a success of π , and a confidence level of 1-α, we have the following confidence interval of proportions:

π± z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]

z is the z-score having a p-value of 1-α/2.

we have η = 605 and ρ = 0.07

So, α = 0.1 and z is the value of Z that has a pvalue of:

1 - 0.1/2 = 0.95

Z= 1.645

Now the lower limit:

π - z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]

= 0.07-1.645[tex]\sqrt\frac{(0.07*0.93)}{605}[/tex]

= 0.07 - 0.01706

= 0.0524

The lower bound for a 95% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0524

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Answer: b=12x

Step-by-step explanation:

The bakery shipped out b boxes of bagels.

Each box contained 12 bagels

b is the number o boxes

x is the number of bagels in each box

The ordered pair (x,y) obtained from the linear equations is: (-2,-12)

What is Linear Equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason. A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. To discover how a linear equation is stated in its standard form, let's take an example.

The equation is given:

8x-3y=20

5x-y=2

Using the substitution method for solving the linear equations:

From the equation:

5x-y=2;

we can transform this equation as:

⇒-y = 2-5x;

⇒y = 5x-2;

Now substituting the value of y in the other equation: we get;

⇒8x-3(5x-2)=20

⇒8x -15x+6 = 20;

⇒-7x=14;

x = -2;

Now putting the value of x in the equation to get the value of y;

So,

y = 5(-2) -2;

y = -12;

Hence the value of x and y are -2 and -12 respectively;

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Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - 2x - 1 ← equation of line b

The population on the first day of the opening of the mall was 7723.66.

Percentage:

A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Here it is given that there is an increase in the population of the mall by 5%

We have to find the population on the first day.

The population on the 10th day is 12581.

let x be the population on the first day.

Population on the 10th day = x( 1 + 5/100[tex])^{10}[/tex]

12581 = x [tex]1.05^{10}[/tex]

x = 12581/ 1.62889

  = 7723.66

Therefore we get the population on the first day of the mall to be 7723.66.

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Answer: y = 2x - 13

Step-by-step explanation:

y=mx + b

[tex]m= \frac{-7-(-1)}{3-6}[/tex]

   [tex]= \frac{-6}{-3}[/tex]

[tex]m = 2[/tex]

y = 2x + b

(6, -1) <-- use to find "b" by substituting either one of the coordinates

-1 = 2(6) + b

-1 = 12 + b

-13 = b

y = 2x - 13

Answer:

11units (Brainliest?)

Step-by-step explanation:

(20-9)²

(11)²

(cancel squares by square rooting both sides)

11

Answer:

[tex]\frac{7}{b+4}[/tex]

Step-by-step explanation:

[tex]\frac{7}{b^2+5b+4}[/tex] × [tex]\frac{b^2+8b+7}{b+7}[/tex] ← factor quadratics on numerator/ denominator

= [tex]\frac{7}{(b+1)(b+4)}[/tex] × [tex]\frac{(b+1)(b+7)}{b+7}[/tex]

cancel factors (b+ 1) and (b + 7) on numerator/ denominator

= [tex]\frac{7}{b+4}[/tex] × 1

= [tex]\frac{7}{b+4}[/tex]

Correct option is D)

We shall label the figure as shown below:

The simplest parallelograms are ABML, BCNM, COON, DEFO, OFGH, NOHl, MNIJ and LMJK i.e. 8 in number.

The parallelograms composed of two components each are ACNL, BDOM, CEFN, LNIK, MOHJ, NFGI, ABJK, BCLJ, CDHI and DEGH i.e. 10 in number.

The parallelograms composed of three components each are ADOL, BEFM, LOHK and MFGJ i.e. 4 in number.

The parallelograms composed of four components each are AEFL, LFGK, ACIK, BOHJ and CEGI i.e. 5 in number.

The parallelograms composed of six components each are ADHK and BEGJ i.e. 2 in number. AEGK is the only parallelograms composed of eight components.

Total number of parallelograms in the figure =8+10+4+5+2+1=30

Hence, the answer is (D).

Answer:

Option D is correct

Step-by-step explanation:

...

Answer:

x = 7

Step-by-step explanation:

2 (-4x + 2) + 5x - 2 = -19       Distribute 2 to -4x and 2

-8x + 4 + 5x - 2 = -19            Combine like terms

-3x + 2 = -19                          Subtract 2 from both sides

-3x = -21                                To get x by itself, divide -3 on both sides

x = 7

The measure of angle 3 is 22.5°.

Given,

∠1 = (x-18)°

∠2 = (3x+36)°

∠1 + ∠2 = 180°  (Straight Line)

x - 18 + 3x + 36 = 180

            4x + 18 = 180

                   4x = 180 - 18

                   4x = 162

                     x = 162/4

                     x = 40.5

∠3 = ∠1 (Alternate opposite angles)

    = x - 18

    = 40.5 - 18

    = 22.5

Hence, ∠3 is 22.5°.

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Answer: Hello winstead. I'm Walter White

Step-by-step explanation:

Was this an actual question?

The smallest number of rectangles required will be  30.

Given:- The sides of the rectangle are in the ratio of 5:4

let, length=5x

breadth=4x

Area = 20x²

Area of smaller rectangle =2*3

                                           =6cm²

Now, take numbers which are in the ratio of 5:4;

suppose, Case 1=10:8

                 Case2 = 15:12

For Case 1;

number of rectangles needed =10*8/2*3

                                                     =13.3333

This means it is overlapping hence, not possible.

For Case 2;

number of rectangles needed=15*12/2*3

                                                  =30

therefore, the smallest number will be 30.

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Answer:

6√5 - 4√15

Step-by-step explanation:

√5(6 - 4√3) =

Distribute √5

= 6√5 - 4√3√5

= 6√5 - 4√15

According one-way ANOVA, the test is false.

In the given question,

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. We have to check whether this is true or​ false.

We firstly learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given method it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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