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The factorised form of the given expression as required to be determined in the task content is; p ( p + 1 ) - q (q - 1).

It follows from the task content that the factored form of the given expression is to be determined.

As evident from the task content; the given expression is; p² - q² + p - q.

On this note, by first collecting like terms; we have;

p² + p - q² - q

By factorisation; we have that;

p ( p + 1 ) - q (q - 1)

Ultimately, the factored form of the given expression is; p ( p + 1 ) - q (q - 1).

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Answer:

The answer is 576 inches

Answer:

C

Step-by-step explanation:

\( composite =cuboid + 3d \: triangle \\ = (l \times w \times h) + ( \frac{1}{2} \times b \times h \times w) \\ = (12 \times 5 \times 7) + ( \frac{1}{2} \times (15 - 12) \times 7\times 5) \\ = (12 \times 5 \times 7) + ( \frac{1}{2} \times 3 \times7 \times 5) \\ \)

The correct expression for finding the volume of the composite figure is 7×12×5 + (1/2)×3×7×5.

Correct option is (D).

Any three-dimensional solid's volume is the space it takes up. The shapes of these solids include cube, cuboid, cone, cylinder, and sphere.

As per the given diagram:

The dimensions of the composite figure are given.

Volume of the composite figure

= Volume of the cuboid + Volume of the triangular prism

= l×b×h + (1/2)×base×height×length

From the diagram:

= 12×7×5 + (1/2)×(15 - 12)×7×5

= 12×7×5 + (1/2)×3×7×5

= 7×12×5 + (1/2)×3×7×5

Hence, the correct expression for finding the volume of the composite figure is 7×12×5 + (1/2)×3×7×5.

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Answer:

(3,2)

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

20/25 = 4/5 = 80/100 = 80%

80%

20 ÷ 25 · 100 = 80

Have a luvely day!

Answer:

0,0

Step-by-step explanation:

...

Step-by-step explanation:

Answer:

8/21

Step-by-step explanation:

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

C.)

Step-by-step explanation:

that is exactly the definition of the derivative.

the derivative is the limit of

(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h

with h going to 0.

this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.

Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

627 x 26 equals 16,302 when solved using the standard algorithm.

The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:

627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.

Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.

1254 -- a 6 x 7 partial product

1254 -- a half 6 x 2 product

Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.

1254 x 627

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Answer:

$37.12

Step-by-step explanation:

Total cost = $3.50(350/33) = $37.12

Answer:

about the $37.12

Step-by-step explanation:

→Arrange what we are given and what we need to find out:

With 1 gallon we drive 33 miles for the price of $3.5.

                     We drive 350 miles for the price of $?

→Find how many groups of 33 miles are in 350 miles:

\(\frac{350}{33}\)

→Each one of those groups of 33 miles costs $3.5 so

find the cost of 350 miles

\((\frac{350}{33} )3.5 = \frac{350*3.5}{33} = \frac{1225}{33} = 37.12\)

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Answer:

Step 1 = 9\(\sqrt{3}\)

Step 2 = 4

Step 3 = 25

Step-by-step explanation:

Answer:D x=45° y=10.9√2

Step-by-step explanation:

In a right angle were two sides are equal, two remaining angles add up to 90. So it is 90/2 which is 45°

Y²=10.9²+10.9²

Y=15.41

Or y = 10.9√2

Answer:

-9(m+2)+406-7m)

=-16+388

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

There is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

Step-by-step explanation:

The Analysis of Variance (ANOVA) test is used to determine whether there is any significant difference between the mean of various independent groups.

In this case an ANOVA test is being performed to determine whether the fat percentage of four different ethnic groups are different or not.

The hypothesis can be defined as:

H₀: The fat percentage of four different ethnic groups are same, i.e. μ₁ = μ₂ = μ₃ = μ₄.

Hₐ: The fat percentage of at least one of the four ethnic groups is different, i.e. at least one μ\(_{i}\) is different.

The significance level of the test is, α = 0.05.

The decision rule is:

The p-value of the ANOVA test is computed as, p-value = 0.11.

p-value = 0.11 > α = 0.05.

The null hypothesis was failed to be rejected.

Hence, it can be concluded that there is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

Answer:

x = 6

Step-by-step explanation:

51 = 11b – 15

66 = 11b

b = 6

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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Answer:

A, D, B, C.

Step-by-step explanation:

A probability will range between 0 and 1, 0 meaning that the event is impossible, 1 that the event is certain and 5 meaning it will happen half the time.

Therefore, the correct answer is:

A, D, B, C.

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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Answer:

The missing term is 10

Step-by-step explanation:

2/11=x/55

cross multiply

2*55=11x

x=10

I hope this helps :)

Answer:

10

Step-by-step explanation:

40/4= 10

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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The most appropriate chart to depict US energy consumption would be a pie chart since a pie chart helps to see the composition of different proportions representing total consumption.

Chart A is not appropriate because a line graph is used to depict information to analyze changes over time or over a period. However, to show the energy consumption, the line graph is not an accurate depiction since the type of energy source is a categorical variable.

Chart B is also appropriate because it is a column graph and such type of graphs are used to represent categorical variables. The US energy consumption can be represented well through a column graph as it well depicts the highest consumption source and the lowest consumption source.

Yes more than one kind of display would therefore be acceptable as we can use to show the information through both a pie chart and a column graph.

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