At summer camp, 60 students are divided in two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.


Outcome Frequency
Swimming 26
Hiking 34


Compare the probabilities and determine which statement is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 34 over 60.
The theoretical probability of swimming, P(swimming), is 26 over 34, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is 26 over 60, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 26 over 60

The equation is given as y = 4x - 3 , where the slope is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The value of term 1 = 1 square

The value of term 2 = 5 suqres

The value of term 3 = 9 squares

So , the increment in the number of squares is 4

Let the first point be P ( 1 , 1 )

Let the second point be Q ( 2 , 5 )

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 1 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 1 = 4 ( x - 1 )

On simplifying the equation , we get

y - 1 = 4x - 4

Adding 1 on both sides of the equation , we get

y = 4x - 3

Therefore , the value of y is 4x - 3

when x = 1 . y = 4 - 3 = 1

when x = 2 , y = 4 ( 2 ) - 3 = 8 - 3 = 5

Hence , the equation of line is y = 4x - 3

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Based on the following given inequality; the symbol will be reversed when the variable is isolated

The condition for the symbol of an inequality to be reversed is;

if the variable is isolated and a negative number is used to divide.

The symbols of inequality are;

Greater than >

Less than <

Greater than or equal to ≥

Less than or equal to ≤

Equal to=

–10.5 < 3a

a < -10.5/3

a > -3.5

Yes

b6 ≤ 7

b ≤ 7/6

b ≤ 1.17

No

–4.5c > 9

c > 9/-4.5

c < -2

Yes

–215 ≤ –52d

d ≤ -215 / -52

d ≤ 4.14

No

Hence, the symbol will be reversed when the variable is isolated if the result of the division is negative.

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Answer: If Ken brought 8 liters of water for everyone to share and they drank 5 liters of it, then the remaining amount of water they have is 8 - 5 = 3 liters.

Step-by-step explanation:

The students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: Given, Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5.

We have to find the error made by the students.

5 less than a number n = n - 5

5 less than a number n divided by 3 = (n - 5)/3

Correct expression = (n - 5)/3

Expression written by student = (n/3) - 5

Therefore, the students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

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What’s the Error? A Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5. What error did the they make?

The perimeter of the triangle is 16+8√2 feet.

The perimeter of any two-dimensional figure is defined as the distance around the figure. The formula for a closed shape figure's perimeter is typically equal to the length of the figure's outer line.

The perimeter of a triangle will therefore be equal to the sum of its three sides. Consequently, if a triangle has sides a, b, and c,

Here, a= 8 feet

b=  8 feet

c= 8√2 (length of a leg * √2= 8*√2)

Perimeter= Sum of all three sides of the triangle

Perimeter = a + b + c

Perimeter= 8+ 8 +8√2

Perimeter=  16+8√2 feet.

16+8√2 feet is the perimeter of the triangular garden.

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If the sample met these conditions, then it is possible to construct a confidence interval for the proportion of all homes in the city that have a television.

In order to construct a confidence interval, the sample must meet the following conditions:

The sample must be randomly selected from the population, large enough to ensure a normal distribution, and the population must be normally distributed. If these conditions are met, then a confidence interval can be constructed to provide an estimate of the proportion of homes that have a television.

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The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

From the first equation, we can solve for y:

y = x + 3

Substitute y = x + 3 into the second equation:

3x - 3(x + 3) = 9

Simplify the right side:

3x - 3x - 9 = 9

-9 = 9 (inconsistent)

Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.

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The possible value of angle X, to the nearest degree is 78°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔXYZ, x = 300 cm, z = 290 cm and ∠Z=109°.

Here, sinX/x=sinZ/z

sinX/300 = sin109°/290

sinX/300 = 0.9455/290

sinX/300 = 0.00326

sinX=0.00326×300

sinX=0.978

∠X=78°

Therefore, the possible value of ∠X, to the nearest degree is 78°.

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Answer:

x = 12

y = 11

Step-by-step explanation:

It's a parallelogram, so opposite sides are equal.

4x + 10 = 58

4x = 58 - 10 = 48

x = 48/4 = 12

10y - 6 = 104

10y = 104 + 6 = 110

y = 110/10 = 11

200 number of students brought their lunch to school on Thursday.

A Percentage is a number or ratio that can be expressed as a fraction of 100.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage formula = (Value/Total Value) × 100

P% of Number = X

where X is the required percentage.

If we remove the % sign, we need to express the above formula

P/100 × Number = X

Given:

Total number of students in school = 800

25% students bring their lunch every day.

25% of 800

= [tex]\frac{25}{100} \times 800[/tex]

= 25 × 8

= 200

200 students bring their lunch to school on Thursday.

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a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.

a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:

Area = length x width = 925 cm x 485 cm = [tex]448,625 cm^2[/tex]

Area in square meters =[tex]448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2[/tex]

b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:

Area in square meters rounded up = ceil(44.8625) = [tex]45 m^2[/tex]

The cost of the flooring is $56 per square meter, so Tina pays:

Total cost = [tex]45 m^2 * $56/m^2 = $2520[/tex]

To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:

Number of square meters =[tex]$2520 / $56/m^2 = 45 m^2[/tex]

Total cost = [tex]45 m^2 x $56/m^2 = $2520[/tex] (same as the original answer)

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Answer:

The surface area of the label is 28 squared inches.

Step-by-step explanation:

The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.

The lateral surface area of a cuboid is given by 2(length+breadth)×height.

Now, lateral surface area of juice box = 2(2+1.5)×4

= 2×3.5×4

= 28 squared inches

Answer:

28 square inches

Step-by-step explanation:

         The label covers the lateral surface area of the box.

  l = 2 in ;  w = 1.5 in ; h = 4 in

    [tex]\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}[/tex]

                                                                      [tex]\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2[/tex]

The diameter of the circle is 22 / 12 units

To find the diameter of the figure, we need to rewrite this in standard form of a equation of a circle.

3x² + 3y² - 7x - 6y - 3 ;

This will be written in (h, k) form which is

3x² + 3y² - 7x - 6y - 3

The coordinate of the center is at (7/6, 1)

The radius of the circle is 11/6 and we can find the diameter of the circle by;

diameter of circle = 2 * radius of circle

diameter = 2 * 11 / 6

diameter = 22 / 12

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Answer:

56in.²

Step-by-step explanation:

the given figure can be divided into three parts .

( see attachment)

Finding area of I

Area = 7*4

Area = 28 in.²

Area of II

Area = 5 * (7-3) = 5*4

Area = 20 in.²

Area of III

area = 1/2 * 4*4

area = 8in.²

Total area [ 28 + 20 +8] in.² = 56in.²

Answer:

(1 +a + b)(1 - a -b)

Step-by-step explanation:

1 - 2ab - (a² +b²) = 1 - 2ab - a² - b²

                           = 1 - (2ab + a² + b²)

                           = 1 - (a + b)²

                           = 1² - (a +b)²    

Identity: x² - y² = (x + y)(x - y)

                          = (1 + (a+b))(1- [a +b] )

                          = (1 +a + b)(1 - a -b)

The value of h(x) = 0 gives x=5.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the b. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

h(x) = -x + 5

So, for h(x)= 0 we have

-x + 5= 0

now, solving for x

-x = -5

x= 5

Thus, the value of x is 5.

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Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.

(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.

(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.

Answer:

Both C and D are equations for the two given points.

Step-by-step explanation:

A. Y+2=0.5(x-3)  NO

 (-3,-5):  -5+2 = 0.5(-3-3);   -3 = 0.5(-6);   -3 = -3  YES

 (3,2):     2+2 = 0.5(3-3):   4 = 0.5(0);   4 = 0   NO

B. Y-5=0.5(x-3)  NO

(-3,-5):  -5-5=0.5(-3-3);  -10 = -3   NO

(3,-2):  -2-5=0.5(3-3);   -7 = 0       NO

C. Y+5=0.5(x+3)   YES

(-3,-5):  -5+5=0.5(-3+3);  0 = 0    YES

(3,-2):   -2+5=0.5(3+3);  3 = 3      YES

D. Y=0.5x-3.5   YES

(-3,-5):  -5 = 0.5(-3)-3.5;  -5 = -5 YES

(3,-2):  -2 = 0.5(3)-3.5;  -2 = 1.5 - 3.5   YES

The volume of the composite shape is

Volume is a measure of three-dimensional space.

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

The shape above shows two cuboid joined together.

volume of the base cuboid = lbh

= 6×3×1 = 18ft³

Volume of the second cuboid = lbh

= 4×3×8 = 96 ft³

volume of the composite shape = 18ft³ + 96ft³

= 114 ft³

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Graph the Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1.

The preimage's point corresponds to the image's points in the following way:

P(-6, 2) → P'(6, 2)

Q(-2, -1) → Q' (2, -1)

R(-2, -3) → R'(2, -3)

S(-6, -6) → S'(6, -6)

                                       (x,y)→(−x,y)

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

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S=B+15

15 more than blouse (b)

S representing skirts

Sally has 20 water bottles he gives 10 to jerry, then final count of water bottles that Sally has is 10.

What is the addition?

The addition is the process of adding two or more numbers together to get their sum. Addition in math is a primary arithmetic operation, used for calculating the total of two or more numbers. For example, 7 + 7 = 14.

We have given,

sally has 20 water bottles he gives 10 to jerry how many does sally have left?

Sally originally had 20 water bottles.

When she gives 10 water bottles to Jerry, she will have 20 - 10 = 10 water bottles left.

Therefore, the final count of water bottles that Sally has is 10.

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Since the corresponding sides are not proportional, we can say that the triangles are not similar

In similar triangles, corresponding sides are always in the same ratio.

Given are two triangles ΔWUV and ΔXZY.

It is given that -

VW = 60     ZY = 48     YX = 40     VU = 50     UW = 40     XZ = 32

For the triangles to be similar, the corresponding sides will be proportional.

WU/XZ = UV/ZY = WV/XY

40/32 = 50/48 = 60/40

1.25 ≠ 1.044 ≠ 1.5

The corresponding sides are not proportional.

Therefore, since the corresponding sides are not proportional, we can say that the triangles are not similar.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -1}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -1 }{2}=1\implies x-1=2\implies \boxed{x=3} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=3\implies y+5=6\implies \boxed{y=1}[/tex]

Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

Answer:

Step-by-step explanation:

The percent change in the price is  -6.67

The percentage change will be given by the formula:

Percent change = 100%*(new price - old price)/old price

We know that:

old price = 15 pounds.

new price = 14 pounds

Replacing that we will get:

percent change = 100%*(14 - 15)/15 = -6.67%

The price is 6.67% smaller.

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