2. Find the number of ways in which 9 different computer games can be shared out between Wendy, Jim and Hannah so that each person receives an odd number of computer games.

Answer:

First option: 37°, 11°,  132°

Step-by-step explanation:

The sum of the three interior angles of a triangle must add up to 180°

Only the first option 37°, 11° and 132° add up to 180°
37 + 11 + 132 = 48 + 132 = 180°

You don't need to add up all the other sets of angles completely. Just look at the units place

Option 2, units sum = 4 + 6 + 1 =11; does not end in a 0, ends in 1

Option 3: units sum = 1 + 0 + 2; does not end in a 0, ends in 3

Option 4: units sum = 0 + 1 + 5 ends in a 6

Answer:

To solve the problem, Sarah used the equation:

Left-handed people = (11/100) * Total people

Step 1: Plug in the total number of people (30) into the equation.

Left-handed people = (11/100) * 30

Step 2: Simplify the right side of the equation.

Left-handed people = (11/100) * 30

Left-handed people = 3.3

Step 3: Round the answer to the nearest whole number.

Left-handed people = 3

So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.

Answer:ez

Step-by-step explanation: blah blah blah blah

The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

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

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence we consider that:

[tex]\pi = 0.5[/tex]

The minimum sample size is obtained as n when M = 0.05, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:

B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.  

by bodmas

((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

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Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.

If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.

Option A: (2, 1)

Substituting x = 2 and y = 1 into the equation, we get:

1 = 4 * 2 - 7

1 = 8 - 7

1 = 1

Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.

Option B: (4, 9)

Substituting x = 4 and y = 9 into the equation, we get:

9 = 4 * 4 - 7

9 = 16 - 7

9 = 9

Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.

Option C: Both (2, 10) and (4, 9)

Substituting x = 2 and y = 10 into the equation, we get:

10 = 4 * 2 - 7

10 = 8 - 7

10 = 3

Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.

So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).

Step-by-step explanation:

Answer:

[tex]x^{2}-4x-12[/tex]

Step-by-step explanation:

(x+2)(x-6)

STEP 1 - USE FOIL

(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):

Forward

Outside

Inside

Last

(x+2)(x-6) becomes this when you FOIL it:

[tex](x^{2} )(-6x)(2x)(-12)[/tex]

STEP 2 - COMBINE ALL THE TERMS

[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's  in it.

STEP 3 - WRITE THE SOLUTION

All in all, the final solution, once you put everything together, is:

[tex]x^{2} -4x-12[/tex]

A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.

When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.

Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.

However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.

Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.

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The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.

To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.

Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g

Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.

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The system using substitution has its solution to be (-1.8, -1.2)

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

3x-2y=3

y=6+4x

By susbstitution, we have the following equation

3x - 12 - 8x = 3

Evaluate the like terms

so, we have the following representation

-5x = 9

Divide by 5

x = -1.8

So, we have

y= 6 + 4 * -1.8

Evaluate

y = -1.2

Hence, the value of y is -1.2

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The total number of cupcakes packed is 846 cupcakes.

percentage, a relative value indicating hundredth parts of any quantity.

Let's first find out the number of boxes of each size:

40% of 60 boxes = 24 boxes are medium

35% of 60 boxes = 21 boxes are small

The remaining 60 - 24 - 21 = 15 boxes are large

Now we can calculate the total number of cupcakes packed:

24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes

21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes

15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes

Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.

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The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,

We need to find ∠ 1

Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,

Therefore,

3x-10 = 2x+5

x = 15

Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,

Therefore,

∠ 1 = 2(15)+5

∠ 1 = 35°

Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

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The figure was not given so the figure is attached.

The cost of a pair of pants is $17.

And the cost of a shirt is $31.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The total cost of 5 shirts and 3 pairs of pants is $206.

The total cost of a shirt and a pair of pants is $48.

Let y be the cost of a pair of pants and x be the cost of a shirt.

That means,

we have the system of equations,

x + y = 48   {equation 1}

5x + 3y = 206   {equation 2}

Multiply 5 to the equation 1 and then subtract equation 2 to equation 1,

we get,

2y = 34

y = 17

And x = 48 - 17 = 31.

Hence, $17 is the cost of a pair of pants.

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(i) none of these ailments, 26

(ii) arthritis but neither of the other two ailments, 17

(iii) exactly one of these ailments, 102

(iv) arteriosclerosis and loss of hearing but not arthritis, 16

We can use a Venn diagram to solve this problem.

Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:

A = 70

B = 60

C = 80

A ∩ B = 35

A ∩ C = 33

B ∩ C = 31

A ∩ B ∩ C = 15

Using these values, we can find the answers to the questions:

(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:

n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)

                      = 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)

                      = 26

Therefore, 26 senior citizens had none of these ailments.

(ii) The number of senior citizens with arthritis but neither of the other two ailments is:

n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15

                                                                   = 17

Therefore, 17 senior citizens had arthritis but neither of the other two ailments.

(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:

n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102

Therefore, 102 senior citizens had exactly one of these ailments.

(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:

n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16

Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.

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The area of the region between line y =3x -6 and line y=-2x+8 and

the x-axis with the help of integration will be 2.88 sq units.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

As given in image

Area of the region will be  =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.

=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x)  from x=2.8 to 4.

=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2

=2.88 sq units.

Hence,

           The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.

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Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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Answer:R(d)=0.30d+75

Step-by-step explanation:

Note:  This equation, as requested, only shows the cost of

rental on a daily basis.  In order to solve for more than 1

day the equation should be:  Cost = .3r+ 100d or something

similar... with r representing miles driven, d representing

total number of days for the rental.

Time for working for history is 50 minutes.

First we need to multiply to make the fractions have equal denominators so we can add/subtract.

Science: 1/3 x 4/4=4/12

Math: 1/4 x 3/3=3/12

Now we can find the time she spent on history (I assume this is what you are looking for)

Total time-math time-science time=history time

12/12-4/12-3/12

=5/12

Macy spent 5/12 of her time working on history.

so totak fo 2 hours she spent 5/12 time to work on history

so 2 hours*5/`12 = 5/6 hours = 50 minutes

Q- Macy spent 2 hours working on homework she spent 1/4 of that time working on math he spent 1/3 of her time working on science find time for working for history.

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Answer:

[tex]x = \frac{17}{3} = 5\frac23 = 5.\overline6[/tex].

Step-by-step explanation:

No idea what your question is, but [tex]x = \frac{17}{3} = {5\frac23} = 5.\overline{6}[/tex].

The surface area of the given cylinder is 602.88 square centimeters.

The surface area of the cylinder is: A = 2πr(r+h)

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

The cylinder with a height of 10 cm and a radius of 6 cm.

⇒ A = 2πr(r+h)

Here h = 10 cm and r = 6 cm

Substitute the known values in the above formula,

⇒ A = 2(3.14)(6)(6+10)

⇒ A = (12.56)(6)(16)

Apply the multiplication operation, and we get

⇒ A = 602.88

Therefore, the surface area of the given cylinder is 602.88 cm².

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The two states will never have the same median house value.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The intercepts are given by the values of each home in 1950, thus:

The slopes are given by the average change over the 50 years, hence:

As the number of years must be positive, Delaware starts with the higher income and has a higher yearly increase, the two states will never have the same median house value.

Solving 35500 + 1416x = 55000 + 1508x, we would end up with a negative value of x.

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Given one point and a slope:

To graph the line plot the given point first.

Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:

Next, plot the second point (-2, - 9).

Now connect the two pints and extend either side. This is the line you need.

Volume of the composite shape is =  114 ft³

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.

Now, According to the question:

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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Answer:

68

Step-by-step explanation:

-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3]  Start in the center and work your way out.

-2[-4 + 3(2 - 32 + 8 -3) - 3]

-2[-4 + 3(-30 + 8 - 3) -3]

-2[-4 + 3(-22 -3) -3]

-2[-4 + 3(-25)-3]

-2[-4 -27 -3}

-2[-31 - 3]

-2(-34)

68

Answer:

We can write an inequality to represent the weight that the truck can carry:

Weight of Refrigerators + Weight of Pianos <= 6500

Let x be the number of refrigerators and y be the number of pianos. Then we can write:

300x + 475y <= 6500

To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:

300 * 10 + 475 * 9 <= 6500

3000 + 4275 <= 6500

7275 <= 6500

Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.

Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.

Answer:

7275lb

Step-by-step explanation:

Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:

Weight = 300R + 475P

The weight must be less than or equal to 6500lb, so we have the inequality:

300R + 475P <= 6500

To graph this inequality, we can first rewrite it in slope-intercept form:

475P <= 6500 - 300R

P <= (6500 - 300R) / 475

Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).

The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.

As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:

Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275

This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.

The volume of the triangular prism is 433.013cm^3.

Triangular prism formulas

volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

We are given that;

Base area of prism = 10cm

Breadth of prism= 10cm

Height of prism = 10cm

Now,

To find the volume of triangular prism

Volume = base area × length of the prism

=10x43.3013cm

=433.013

Therefore, the volume of prism will be 433.013cm^3

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The total surface area is π[(4/3)x]² + π(4/3)x². The base area is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

substituting:

SA = π[(4/3)x]² + π(4/3)x(x)

SA = π[(4/3)x]² + π(4/3)x²

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

The base area is greater than the lateral area.

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Answer: Sure, I can help you with that!

Let's assume that the height of the cylinder is h and its radius is r. The volume of the cylinder can be calculated using the formula:

V = πr^2h

Similarly, let's assume that the length, width and height of the cuboid are l, w and h respectively. The volume of the cuboid can be calculated using the formula:

V = lwh

As the volume of the cylinder and the cuboid are the same, we can set the two expressions equal to each other:

πr^2h = lwh

Now, let's assume that the radius of the cylinder is equal to the length of the cuboid (r = l). This means that:

πl^2h = lwh

Solving for h, we get:

h = (πl^2)/w

Finally, substituting the value of h back into the original equation:

πr^2h = πl^2h = lwh

πr^2 = lwh/w = lw

r^2 = lw

r = sqrt(lw)

So, the value of x (the radius of the cylinder) can be found by knowing the length (l) and width (w) of the cuboid. To two decimal places, x = sqrt(lw).

Step-by-step explanation: