Allan is a Form I student who drives to school every day. His home is 5 k from the school. Allan left his home for school at 6:30 am on Tuesday morning and arrived at 8:00 am. He remained in school until 4:30 pm since he had afternoon classes that had .

How long did Allan take to get from home to school? You are to give the time in hours, minutes and seconds. (6 marks) Hours Minutes Seconds​

Answer:

Yes

Step-by-step explanation:

For every one x value is equal to one y value, therefore it's a one-to-one function.

Answer:

-5.49

Good Luck!!!

Since it only resolves one of the two inequalities, (1, -5) cannot be a solution to the given system of inequalities.

How are coordinates determined?

We must check that the point (1, -5) fulfils both inequalities in order to determine if it is a solution to the system of inequalities.

y > -6x - 11 is the first inequality. Inputting x = 1 and y = -5 results in:

\(-5 > -6(1) (1) - 11 \s-5 > -6 - 11 \s-5 > -17\)

The first inequality is satisfied at the position (1, -5) since -5 is greater than -17.

y - x - 5 is the second inequality. Inputting x = 1 and y = -5 results in:

\(-5 ≥ -(1) (1) - 5 \s-5 ≥ -6\)

The point (1, -5) does not satisfy the second inequality since -5 is not greater than -6.

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Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map  = 7 cm

Actual distance = Measurement of map \(\times 5\)

Actual distance = 7 \(\times 5\) = 35 km

-------------------

Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

-------------------

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to \(\frac{1}{5}\) cm on scale

30m is equivalent to \(\frac{1}{5} \times 30\) = 6 cm on scale

-------------------

Solution 4.

Angle of elevation of A from B = \(42^\circ\)

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = \(42^\circ\)

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, \(\angle B = 42^\circ\)

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

\(sin\theta = \dfrac{Perpendicular}{Hypotenuse}\)

OR

\(sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m\)

============

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

\(2=0.4x\)

To find x,

\(2=0.4x\)

\(x=\frac{2}{0.4}\)

\(x=5\)

Therefore, Elena plans to run a total distance of 5 miles.

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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The difference quotient for f(x) = 10x² + 4x + 3 is 20x + 10h + 4.

To compute the difference quotient for the given functions, we'll use the formula:

f'(x) = lim(h->0) [f(x+h) - f(x)] / h

(a) For the function f(x) = 1 + 5x:

f(x+h) = 1 + 5(x+h) = 1 + 5x + 5h

Now, we substitute these values into the difference quotient formula:

[f(x+h) - f(x)] / h = [1 + 5x + 5h - (1 + 5x)] / h

= (5h) / h

= 5

Therefore, the difference quotient for f(x) = 1 + 5x is 5.

(b) For the function f(x) = 10x² + 4x + 3:

f(x+h) = 10(x+h)² + 4(x+h) + 3

= 10(x² + 2xh + h²) + 4x + 4h + 3

= 10x² + 20xh + 10h² + 4x + 4h + 3

Now, we substitute these values into the difference quotient formula:

[f(x+h) - f(x)] / h = [10x² + 20xh + 10h² + 4x + 4h + 3 - (10x² + 4x + 3)] / h

= (20xh + 10h² + 4h) / h

= 20x + 10h + 4

Therefore, the difference quotient for f(x) = 10x² + 4x + 3 is 20x + 10h + 4.

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Answer:

it will be (3)

Step-by-step explanation:

since DB is a median

then DB= half AC , AB=BC

then AB=BD

then the two triangles are isosceles

The required m∠BDC is 32° .

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

According to the given question ;

DB is a median;

By the symmetry ;

Then DB = half AC ,

        = AB = BC

Then= AB = BD

In a triangle, a line that connects one corner (or vertices ) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle congruence, is that in an isosceles triangle the median to the base is perpendicular to the base.

Then the two triangles are isosceles.

Means m∠DAB = m∠BDC = 32°

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Hey there! I'm happy to help!

6x=5x+22

Let's move all the variables to the left. We subtract 5x from both sides.

x=22

Have a wonderful day! :D

Answer:

x = 22

I hope this helps!

Answer:

-2

Step-by-step explanation:

you look at the y axis and that is where you start it goes 2 down and 1 to the right

Answer:

C. -2

Step-by-step explanation:

Using the two points on the graph, apply the slope formula.

(y₂ - y₁)/(x₂ - x₁)

The points given are (-3, 3) and (1, -5).

(-5 - 3)/(1 - (-3))

Simplify.

-8/4

Divide.

-2.

To determine the probability that the specification for the clearance is met, we need to assume that the clearance follows a normal distribution. We can then use the standard normal distribution to calculate the probability that a clearance falls within the given specification range.

Assuming a normal distribution, we can use the formula for the standard normal distribution to calculate the probability that a clearance falls within the range of 0.015 to 0.063 mm:

z = (x - μ) / σ

where z is the z-score, x is the value we want to find the probability for, μ is the mean of the distribution (which we assume to be the midpoint of the specification range, i.e., (0.015 + 0.063) / 2 = 0.039 mm), and σ is the standard deviation of the distribution (which we assume to be (0.063 - 0.015) / 6 = 0.008 mm).

Using these values, we can calculate the z-scores for the lower and upper limits of the specification range:

z1 = (0.015 - 0.039) / 0.008 = -3

z2 = (0.063 - 0.039) / 0.008 = +3

We can then look up the area under the standard normal distribution curve between these two z-scores using a standard normal distribution table or a statistical software program. This area represents the probability that a clearance falls within the specification range. The area is approximately 0.9973, or 99.73%.

Therefore, we can say that there is a 99.73% probability that the specification for the clearance is met.

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We can say that the sampling plan leads to non-response bias; because the customers who did not participate in the survey would have provided significantly different answers.

Non-response is a description of non-observation appear in most surveys, that means failure to provide a measurement on one or more research variables for one or more elements chosen for the survey.

Non-response bias happens when participants in the survey are unable or unwilling to respond to a survey question or even the whole survey. Reasons for non-response may vary from person to person. To be considered a disposition of bias, a source of error has to be systematic in nature. Non-response bias is not an anomaly to this rule.

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Answer:

The scale factor would be 1/3

Step-by-step explanation:

Find the scale factor by comparing the heights of the preimage and image.

The height of the image is 4 and the height of the preimage is 12

So the scale factor is 4/12, which can be simplified to 1/3

The product of an irreducible and a unit is always irreducible.

To prove that the product of an irreducible and a unit is irreducible in an integral domain, we must show that it cannot be factored into non-unit factors.
Let's start by defining what we mean by "irreducible" and "unit" in an integral domain.
- An element a in an integral domain is said to be irreducible if it cannot be factored into non-unit factors, i.e., if a = bc for some non-units b and c, then either b or c must be a unit.

- A unit in an integral domain is an element that has a multiplicative inverse, i.e., an element u such that uu^-1 = 1, where 1 is the multiplicative identity of the domain.

Now, let's suppose that we have an irreducible element a and a unit u in an integral domain. We want to show that the product au is also irreducible.

Suppose that au = bc for some non-units b and c. We need to show that either b or c is a unit.

Since u is a unit, we can multiply both sides of the equation by u^-1 to obtain a = (bu^-1)c. Now, since a is irreducible, we know that either bu^-1 or c must be a unit.

If bu^-1 is a unit, then we can multiply both sides by u to obtain b = au^-1. But this means that b is a unit, since a and u are both units and units are closed under multiplication.

On the other hand, if c is a unit, then we can multiply both sides by c^-1 to obtain a(c^-1u) = b. But this means that b is a multiple of a, which contradicts the assumption that b is a non-unit.

Therefore, we have shown that in an integral domain, the product of an irreducible and a unit is always irreducible.

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Answer:

mark me as brainliest

Step-by-step explanation:

okok so first 25 divided by five bc 4+1 in the ratio is five.

then 4 times 5 = 20.

which leaves 25 - 20 = 5. tah-duh!

Answer:

5 is the number of the students who failed

Step-by-step explanation:

4+1=5

25/5=5

4x5= 20 are passed

1x5=5 are failed

hope it helps<33

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.

We can solve this problem in one single step, I'll start off with that.

We can first figure out what it says and make an algebraic equation. We can see what language the question uses and elaborate on that to create our equation.

\(5x-5<6x+2\)

We can use algebra to simplify the equation so that we can solve for it.

\(-5<x+2\\-7<x\\x>-7\)

We can check if this is correct by testing a few numbers from that range, I'll take -5 and 2.

\(5(2)-5<6(2)+2?\\10-5<12+2?\\5<14\)

We've proven that 2 is working.

\(5(-5)-5<5(-5)+2?\\-25-5<-25+2?\\-30<-23\)

We've also proven that -5 works.

We can now say that we've solved the problem, the solution of the problem would be x>-7.

Cheers!

Answer:

\(\boxed {\boxed {\sf 87 \ degrees}}\)

Step-by-step explanation:

The angles in a triangle must add to 180 degrees.

We are given three angles: 2x+6, x, and 3x. Their sum must be 180, so we can create an equation.

\(2x+6+x+3x=180\)

Combine like terms (all terms with an x) on the left side.

\((2x+x+3x)+6=180\)

\(6x+6=180\)

Now solve for x by isolating the variable.

6 is being added and the inverse of addition is subtraction. Subtract 6 from both sides.

\(6x+6-6=180-6\\6x=174\\\)

x is being multiplied by 6. The inverse of multiplication is division. Divide both sides by 6.

\(6x/6=174/6 \\x=29\)

Substitute 29 for x in the angle measures.

The largest angle is 87 degrees.

Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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The critical value of chi-square (χ²) can be estimated using the formula χ²= 1/2(x + √(2x-1))² + (1/2z+2k-1), where k is the degrees of freedom and z is the critical value. In a right-tailed hypothesis test with n=143 and α=0.1, the critical value of χ² is approximately 163.09.

In hypothesis testing, the critical value of chi-square( χ²) is the value beyond which the null hypothesis is rejected. The χ² distribution is used when the population standard deviation is unknown, and the sample size is small. The critical value of χ² depends on the degrees of freedom and the level of significance.

For a right-tailed test with n=143 and α=0.1, the degrees of freedom is k=n-1=142.

Using the given formula, the critical value of χ² is calculated to be approximately 163.09. This means that if the calculated χ² value is greater than 163.09, the null hypothesis is rejected.

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Answer:

2.4x+2.9

Step-by-step explanation:

The probability of rolling a 1, 2, 3, 4, or 5 can be calculated by summing the probabilities associated with each of these outcomes in the given probability distribution. The sum of the probabilities is 11/66 or approximately 0.1667.

b. Calculating the standard deviation of the distribution requires the weights and probabilities of each outcome. By applying the formula for the standard deviation of a discrete probability distribution, the value can be determined in just two lines.

a. The probability of rolling a 1, 2, 3, 4, or 5 can be calculated by summing the probabilities associated with each of these outcomes in the given probability distribution. In this case, the probabilities are 1, 1, 2, 3, and 4 respectively. Add these probabilities together and divide by the total number of outcomes (66 in this case).

b. To calculate the standard deviation of the distribution, you would need to use the weights and probabilities of each outcome. Apply the formula for the standard deviation of a discrete probability distribution.

c. To determine which has better odds, compare the probabilities of getting heads on flipping a coin and rolling a 2 or 3 with two of these dice. Calculate the probability of each event and compare the values. The event with a higher probability has better odds.

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Answer:

7 squares of chocolate

Step-by-step explanation:

14/2 = 7

Answer:

0.5833333.......

Step-by-step explanation:

All you have to do is divide 7 by 12. The fraction 7/12 is equal to 7 ÷ 12.

7 ÷ 12 = 0.583... (repeating 3)

Or if you round, you have 0.58.

Answer:100

Step-by-step explanation:perimeter times apothem divided by two

Answer:

t=2

Step-by-step explanation:

this is the t answer k

Answer:

Use Photo math. It will explain the steps.

Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Each of the following events result in a tax payment, an example of a direct tax is D. Javier owes money to the federal government based on job earnings.

A direct tax is one that is paid by an individual or group of individuals directly to the body that levied it. Taxes on assets, real estate, personal property, and income are a few examples that are all paid by an individual taxpayer directly to the government.

Direct taxes are those that you pay to the government directly. You have paid a direct tax, for instance, if you pay income tax, property tax, or capital gains tax. On the other side, an indirect tax is when you make a purchase and someone else subsequently pays the tax on your behalf through a sales tax.

Therefore, option D is correct.

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