A truck is delivering goods to a supermarket in Sharjah.
The shopkeeper has run out of cornflakes and he
needs 37 large cartons. One carton contains 22 boxes
of cornflakes. Find at average dimensions of one large
box of cornflakes.
(a) What will be the dimensions of one carton of
cornflakes presuming they are packed in so there
no empty space.
(b) What volume would the truck need to be to deliver
the 37 cartons to the shop in one delivery?

Answer:

164 Cakes

Step-by-step explanation:

382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.

Thus, the value of x and y for the given right angled triangle are found as:   x = 8 and y = 2√3.

The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the

a² + b² = c².

For the larger triangle, applying Pythagorean theorem:

4² + (4√3)² = x²

x² = 16 + 16*3

x² = 16 + 48

x² = 64

x = 8

Then, x - 6 = 8 - 6 = 2

Now applying Pythagorean theorem for smaller triangle:

y² + (x - 6)² = 4²

y² =  4² - 2²

y² =  16 - 4

y² =  12

y² =  √12

y = 2√3

Thus, the value of x and y for the given right angled triangle are found as:   x = 8 and y = 2√3.

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Consequently, 1 pound weighs more than 19 ounces.

What additional weight units are there?

The weight can also be expressed in terms of grams, kilograms, pounds, and tons.

Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.

The weight unit known as an ounce is 1/16th of a pound.

A ton weighs 2000 pounds.

16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.

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There are two solutions for given system of equations: (5, 35) and (-4, 8).

A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.

Typical approaches for resolving equation systems include:

Given system of equations is,

[tex]y=x^2+2x[/tex]..................(1)

[tex]y=3x+20[/tex]..................(2)

Solving equations algebraically,

Equating the formulas for 'y' in both equations:

[tex]x^2 + 2x = 3x + 20[/tex]

Rearranging the equation :

[tex]x^2 - x - 20 = 0[/tex]

Here, we got a quadratic equation,Solving for values of x,

[tex](x - 5)(x + 4) = 0[/tex]

[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]

For values of 'y', putting values of x in equation (1),

for x = 5,

[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]

Thus, (5, 35) is one of the solution.

for x= -4,

[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]

Thus, (-4, 8) is other solution.

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Lynn is hesitant to allow Greta to drop off the potato salad at 10am .

Greta could make the potato salad the night before and keep it in the refrigerator to solve the problem she and Lynn were having. She could then transport the potato salad at a safe temperature in a cooler filled with ice packs on the day of the picnic.

She could ask Lynn to store the potato salad in a cooler or refrigerator until the picnic starts when she gets to the park. Along these lines, the potato salad will be protected to eat and won't represent a gamble of food contamination.

The mayonnaise in Greta's potato salad will spoil, leading to the growth of bacteria that could result in foodborne illness, if it is left outside in the sun until the picnic begins at 2 p.m. The potato salad may cause nausea, vomiting, diarrhea, and stomach cramps in those who consume it.

Because food safety guidelines state that perishable foods, like potato salad, should not be kept at room temperature for more than two hours, Lynn is hesitant to let Greta drop off the potato salad at 10 a.m.

If the potato salad is left out in the sun from 10 a.m. to 2 p.m., bacteria can grow on it, and eating it could make you sick.

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The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.

The total number of ways to develop the complex would be 665, 280 ways.

To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.

Using combinations, we have:

Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)

Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)

Now, we find the probability:

Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members

Probability = (C(28, 6) x C(12, 4)) / C(40, 10)

Probability = 0.3633

To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:

The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:

P(11, 5) = 11! / (11 - 5)!

Total ways to develop the complex = 12 x P(11, 5)

= 12 x 55440 = 665,280 ways

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The calculated value of the limit of (ln x)^3 / x^2 as x approaches infinity is 0.

To apply L'Hopital's rule, we need to take the derivative of the numerator and denominator separately with respect to x.

We can apply this rule repeatedly until we get a determinate form.

lim x → ∞ [(ln x)^3 / x^2]

Taking the derivative of the numerator:

= 3(ln x)^2 (1/x)

Taking the derivative of the denominator:

= 2x

Applying L'Hopital's rule again by taking the derivative of the numerator and denominator:

= lim x → ∞ [6(ln x) / x]

Taking the derivative of the numerator:

= 6/x

Taking the derivative of the denominator:

= 1

Applying L'Hopital's rule one last time:

= lim x → ∞ 6 / x^2

= 0

Therefore, the limit of (ln x)^3 / x^2 as x approaches infinity is 0.

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Answer:

8√2 cm

Step-by-step explanation:

In a case whereby Shandra is giving a snack bag to each of her 4 friends. She puts 4 pear slices in each bag the number of pear slices that are there in all is 16 pear slices.

The calculation can be done in a simple way, If Shandra puts 4 pear slices in each of the 4 snack bags, then the total number of pear slices will be:

4 friends x 4 pear slices per bag = 16 pear slices

Therefore, there are 16 pear slices in all.

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The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.

Let's first calculate the total number of ways to choose 4 lightbulbs from 24:

24 choose 4 = (24!)/(4! * 20!) = 10,626

Probability that all 4 lightbulbs in the sample are defective:

There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:

4 choose 4 = 1

So, the probability that all 4 lightbulbs in the sample are defective is:

1/10,626 = 1/5313

Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.

Probability that none of the 4 lightbulbs in the sample are defective:

There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:

20 choose 4 = (20!)/(4! * 16!) = 4,845

So, the probability that none of the 4 lightbulbs in the sample are defective is:

4,845/10,626 = 805/1763

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Answer:

Step-by-step explanation:

We first have to find cos 275 and sin 275 and then put them into the formula:

cos 275 = .0872

sin 275 = -.9962

Therefore,

24(.0872 - .9962i) distributes to

2.1 - 23.9i

Answer:

To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.

First, we will take the derivative of both sides of the equation with respect to x:

d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]

Next, we will differentiate each term on the left side of the equation:

cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx

We can simplify this equation by moving all the terms involving dy/dx to the left side:

cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]

Now we can solve for dy/dx by isolating it on one side of the equation:

dy/dx [2 - sin(y)] = cos(x) - 2xy^2

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

The area of the remaining portion of the sheet is -4x² + 12x + 6.

Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.

Therefore, the area of the remaining portion can be found as follows:

area of the rectangle = 3(4x + 2)

area of the rectangle = 12x + 6

Therefore,

area of each square cut out = x²

area of the 4 square cut out = 4x²

Therefore,

area of the remaining portion = 12x + 6 - 4x²

area of the remaining portion = -4x² + 12x + 6

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The percentage of adults who preferred soccer or basketball is 25%.

The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.

From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.

Thus,

11% + 14% = 25%

Hence, the percentage of adults who preferred soccer or basketball is 25%.

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Answer:

8.36

Step-by-step explanation:

67 - 1

8. 82

= 2747 - 4

328

=2743

328

= 8.36

Answer:

Step-by-step explanation:

in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

Let's start by setting up an equation based on the given information.

Let Leah's current age be represented by "x". Then, we know that:

x = 3(x-4)

Expanding the right side of the equation:

x = 3x - 12

Bringing the "x" term to the left side and simplifying:

2x = 12

x = 6

So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:

6 + y = 2(6 - 4 + y)

Simplifying:

6 + y = 2(2 + y)

6 + y = 4 + 2y

2 = y

So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

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The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

In the given question,

There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH)

We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:

P(HHT) = (1/2) * (1/2) * (1/2) = 1/8

P(HTH) = (1/2) * (1/2) * (1/2) = 1/8

P(THH) = (1/2) * (1/2) * (1/2) = 1/8

So, the probability of getting exactly one tail is:

P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8

Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.

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Answer:

Step-by-step explanation:

we can't say because we don't have a couple of coordinates

Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.

The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:

y = –38x + 922.

Therefore, the answer is y = –38x + 922.

Step-by-step explanation:

.............................

With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.

What is Compound interest?

Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.

Now,

Using the given formula:

N = (-log(1 - i * A / P)) / (log(1 + i))

where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250

N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))

N = (-log(1 - 175)) / (log(1.0025))

N = (-log(0.9883)) / (0.0025)

N = 376.48

Rounding up to the nearest whole number, it will take 377 months to pay off the loan.

Therefore, it will take approximately 31 years and 5 months to pay off the loan.

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Answer:

The symbols used to represent the negation of a statement are “~” or “¬”. For example, the given sentence is “If you don’t look both ways before crossing the street, then you will get hit by a car." Then, the negation of the given statement is “that u won't get hit”. Thus, if the given statement is true, then the negation of the given statement is false.

The fraction of the panel, that is left after cutting out the hole is [tex]\frac{11}{12}[/tex]

The area of a rectangle equals the product of its 2 sides. The area of a triangle is equal to half of the product of the base and height.. If we choose one of the sides as the base, then for area calculation,  for height we have to use the height of the opposite vertex from this base. To find it, we have to drop a perpendicular from the opposite vertex onto the base. The area of a parallelogram is the product of the length of the base and the perpendicular distance between the two parallel sides of the parallelogram. Area of a trapezium = half of the product of the distance between the parallel sides and the sum of the length of the parallel sides. Area of a circle is [tex]\pi r^2[/tex], in which r is the radius of the given circle. Sometimes the plane figure maynot be a standard shape. In that case we have to divide the figure into suitably many parts such that, each part is a standard figure whose area we can calculate. Also sometimes we can represent an area as the difference of the area of two standard figures. In that case to find the area we have to take the difference of the areas of the two standard figures.

In our question. Initial area of the panel is (3)(2) = 6 square ft.

Area of the cutout = (1)([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{2}[/tex] square ft.

Using the formula, fraction left = [tex]\frac{6 - \frac{1}{2}}{6} = 1 - \frac{1}{12} = \frac{11}{12}[/tex]

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Required fraction left is 11/12 square feet.

What is area of rectangle?

A rectangle is a geometric shape that has four sides and four right angles. It is a type of quadrilateral and is characterized by its two pairs of parallel sides. The opposite sides of a rectangle are congruent, which means they have the same length, and the adjacent sides are perpendicular to each other.

The area of a rectangle is the total amount of space inside the rectangle and is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is Area = length x width

For example, if a rectangle has a length of 6 units and a width of 4 units, the area can be calculated as:

Area = 6 units x 4 units = 24 square units

The area of the panel is 3 feet x 2 feet = 6 square feet

The area of the hole is 1 foot x 1/2 foot = 1/2 square feet

Therefore, the area left is 6 square feet - 1/2 square feet = 11/2 square feet

The fraction left is (11/2 square feet) / (6 square feet) = 11/12

Therefore, the required correct option is C.

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Answer:

The answer is the Blue car

Step-by-step explanation:

let Red car be x

let blue car be y

x=120km---->1hr

y=130km----->1hr

Average speed =distance(km)/time(hr)=km/hr

let A be average speed

A(x)=120/1=120km/hr

A(y)=130/1=130km/hr

therefore,

the blue car has the greatest average speed

Answer:

8x+26

Step-by-step explanation:

distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.

8x + 26

multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.

Therefore , the solution of the given problem of angles comes out to be  the three propositions  m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.

The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.

Here,

Regarding the illustrated diagram, the appropriate statements are:

=> m∠3 + m∠4 + m∠5 = 180°

This is accurate since every triangle's internal angles add up to 180°.

=>  m∠5 + m∠6 = 180°

This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.

=>  m∠2 + m∠3 = m∠6

This is accurate because, based on the information provided,

the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.

Therefore, the three propositions  m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.

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From the data in the table, we can conclude that when x = 4, then the residual will equal -1.

To determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.

So, Residual = Gven value - Predicted value.

When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.

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Answer:

The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.

Step-by-step explanation:

In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.

If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.