Alexander is taking part in a race. For the first 180 m he runs at 3 m/s. The remaining 240 m of the race takes him 100 seconds. What is Alexander's average speed, in m/s, over the whole race? If your answer is a decimal, give it to 2 d.p.​

The area of the triangle is same as the area of the rectangle in the third figure with length 4 mm an width 3 mm.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Area of a triangle = [tex]\frac{1}{2}[/tex] b h, where b is the base and h is the height.

Here for triangle, b = 6 mm and h = 4 mm

Area of triangle =  [tex]\frac{1}{2}[/tex] × 6 × 4 = 12 mm²

Area of a rectangle = l × b, where l is length and b is width.

For first figure,

Area = 6 × 3.5 = 21 mm²

For second figure,

Area = 4 × 2.5 = 10 mm²

For third figure,

Area = 4 × 3 = 12 mm²

For fourth figure,

Area = 6 × 4 = 24 mm²

Hence the rectangle in the third figure has the same area as the triangle.

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A scatterplot is a type of data display that shows the relationship between two numerical variables.

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.

On the graph, each individual in the data is represented by a point. Whether or not a straight line graph passes through the origin, it is formally referred to be linear, and the relationship between the two variables is referred to as a linear relationship. Similar to this, a curved graph's depiction of a connection is referred to as non-linear.

Three main characteristics of bar graphs are: A bar diagram makes it simple to quickly compare sets of data between several groupings.

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Answer:  [tex]a_n = 2n+5[/tex]

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

Work Shown:

[tex]a_n = a_1 + d(n-1)\\\\a_n = 7 + 2(n-1)\\\\a_n = 7 + 2n-2\\\\a_n = 2n+5\\\\[/tex]

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

Explanation:

We plug in [tex]a_1 = 7 \ \text{ and } \ d = 2[/tex] as they represent the first term and common difference in that order. The common difference is 2 because the number of chairs increases by 2 each time you move up a row.

To verify that answer, let's plug in the value n = 1

[tex]a_n = 2n+5\\\\a_1 = 2(1)+5\\\\a_1 = 2+5\\\\a_1 = 7\\\\[/tex]

Which matches with the first term being 7. I'll let you verify other terms.

Answer:

32

Step-by-step explanation:

2x2x2x2x2

4x2x2x2

8x2x2

16x2

32

The scale factor of the perimeter of polygon ABCD to JKLM is 2/3

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

Given:

Polygon ABCD is similar to polygon JKLM. AB = 8, BC = 6, CD = 4. DA = 8, and JK = 12.

scale factor of sides = AB/JK = 8/12 = 2/3

BC/KL = 2/3

6/KL = 2/3

KL = 9

CD/LM = 2/3

4/LM = 2/3

LM = 6

DA/MJ = 2/3

8/MJ = 2/3

MJ = 12

perimeter of polygon ABCD = AB + BC + CD + DA

perimeter of polygon ABCD = 8 + 6 + 4 + 8 = 26 units

perimeter of polygon JKLM = JK + KL + LM + MJ

perimeter of polygon JKLM = 12 + 9 + 6 + 12 = 39

scale factor of the perimeter of polygon ABCD to JKLM = perimeter of polygon ABCD / perimeter of polygon JKLM

scale factor of the perimeter of polygon ABCD to JKLM = 26/39 = 2/3

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If A is the scale image of B, the value of x is 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

A is a scale image of B.

This means,

12.5/10 = x/16

x = (12.5 x 16) / 10

x =  200/10

x = 20

Thus,

The value of x is 20.

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Answer:

6.45kg

Step-by-step explanation:

there are 1000g in one kilogram

250g/1000g=0.25kg

4.2kg+2.25kg=6.45kg

Answer:

6.45kg

Step-by-step explanation:

First, let us convert all the values into grams.

Weight of a watermelon ⇒ 4.2 kg

Multiply by 1000 to convert it to grams.

Weight of a watermelon ⇒ 4200 g

Weight of a pumpkin ⇒ 2kg 250g

First, multiply 2kg by 1000 to convert it to grams and add it to 250 grams.

Weight of a pumpkin

⇒ ( 2 × 1000 ) + 250

⇒ 2000 + 250

⇒ 2250 g

Total Weight  :

To get the total weight, add the weights of the watermelon and pumpkin in grams.

Total weight ⇒ 4200g + 2250g

                     ⇒ 6450g

Now to convert the answer into kilograms, divide the answer by 1000.

⇒ 6450/1000 = 6.45kg

The slope-intercept form of the equation is b = -0.0016a + 210 and the boiling point at 2300ft is 206.32°F

A linear function is an equation that describes a straight line when graphed. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. Linear functions are used to model relationships between two variables, such as the cost of a product and its quantity.

In this problem, we can model the boiling point in form of a linear equation.

The data given;

The slope can be calculated as;

m = y₂ - y₁ / x₂ - x₁

m = 202.8 - 197.04 / 4500 - 8100

m = -0.0016

Using this in the slope-intercept form of a linear function, we can find the y-intercept.

y = mx + c

Taking one point;

202.8 = -0.0016(4500) + c

c = 210

The linear equation can be written as

b = -0.0016a + 210

b) The boiling point at 2300ft

b = -0.0016(2300) + 210

b = 206.32°F

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The probability that the student plays a sport and is involved in theatre is 82%*20%=16.4% which is approximately equal to 14%.

The probability that the student plays a sport and is involved in theatre can be calculated using the following formula:

P(A∩B)=P(A)*P(B|A)

Where P(A) is the probability of playing a sport (70%) and P(B|A) is the probability of being involved in theatre given that the student plays a sport (20%).

Therefore, P(A∩B)=0.7*0.2=0.14

This means that the probability that the student plays a sport and is involved in theatre is 14%. This can also be calculated by subtracting the probability of not playing a sport or being involved in theatre (18%) from 100%. That is, 100%-18%=82%. Since 20% of the 82% are involved in theatre, the probability that the student plays a sport and is involved in theatre is 82%*20%=16.4% which is approximately equal to 14%.

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Answer:

Mode

Step-by-step explanation:

Answer:

[tex]x^4[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(\sqrt[3]{x^2}\right)^6[/tex]

[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \left((x^2)^\frac{1}{3}}\right)^6[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(x^\frac{2}{3}\right)^6[/tex]

[tex]\implies x^\frac{12}{3}[/tex]

Simplify the exponent:

[tex]\implies x^4[/tex]

The function is y=3x-16 and the rate of change is 3 when a  table of values that models a linear function.

Given that,

We have a table of values that models a linear function.

We have to find the rate of change of the function.

We know that,

x     |       y

-3   |      -25

1     |     -13

3    |      -7

8    |      8
So,

The equation of the function is

y=mx+b

Taking two points

(1,-13) and (3,-7)

m = -7+13/3-1 = 6/2 = 3

Now,

-7= 3(3)+b

b=-7-9

b= -16

So, y= 3x-16

Therefore, The function is y=3x-16 and the rate of change is 3 when a  table of values that models a linear function.

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£270 will be allocated to the first person and £135 will be allocated to the second person.

Ratio is a mathematical expression that is used to compare two or more quantities in relation to each other. It is usually expressed as a fraction or a decimal. Ratios are used to compare values, trends, and proportions. Ratios are essential for understanding the relationship between numbers and for making informed decisions. Ratios are often used in business, finance, economics, and other areas to measure performance and risk.

This is calculated by multiplying the total amount of £405 by the ratio 2:3.
The first person's ratio is 2 out of 5 and the second person's ratio is 3 out of 5.

Therefore, 2/5 of £405 is £270 and 3/5 of £405 is £135.

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The normal of a function is a line that is perpendicular to the tangent line at a particular point on the curve.

The normal of a function can be used to find the equation of the tangent line to the curve at a particular point. This is done by finding the slope of the normal and the coordinates of the point of tangency, and then using these values to write the equation of the line in slope-intercept form (y = mx + b).

For example, consider the curve y = x^2. If we want to find the equation of the tangent line to this curve at the point (2,4), we can take the derivative of y = x^2, which is y' = 2x. Setting x equal to 2, we find that the slope of the tangent line at (2,4) is 4.

The normal to this curve at (2,4) is perpendicular to the tangent line, so its slope is the negative reciprocal of the slope of the tangent line, or -1/4. We can then use the coordinates of the point of tangency (2,4) and the slope of the normal (-1/4) to find the equation of the normal: y - 4 = -1/4(x - 2), which simplifies to y = -x/4 + 2.

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Answer:

2.7 rounding; exact = 2.76923076918

Step-by-step explanation:

26 divided by 12, multiplied by 6.

Answer:

Hey there! To answer this question, we need to determine the rate at which the snow was falling, and then use that rate to calculate how much snow fell during school hours.

We know that 12 inches of snow fell in 26 hours, so the rate at which the snow was falling is 12 inches / 26 hours = 0.46 inches/hour.

If we want to find out how much snow fell during school hours, which is approximately 6 hours, we can use the following formula:

Snowfall during school hours = rate of snowfall * time

Plugging in the values, we get:

Snowfall during school hours = 0.46 inches/hour * 6 hours = 2.76 inches

So if 12 inches of snow fell in 26 hours at a rate of 0.46 inches/hour, we can estimate that approximately 2.76 inches of snow fell during school hours.

I hope this helps! Let me know if you have any other questions.

Answer:

Down below

Step-by-step explanation:

1 case = 4.35

3.5 cases bought total

4.35 * 3.5 = 15.225

Hope this helps! :)

[tex]\begin{array}{ccll} pages&minutes\\ \cline{1-2} 57 & 60\\ 95& m \end{array} \implies \cfrac{57}{95}~~=~~\cfrac{60}{m} \\\\\\ \cfrac{ 3 }{ 5 } ~~=~~ \cfrac{ 60 }{ m }\implies 3m=300\implies m=\cfrac{300}{3}\implies m=100[/tex]

Answer:

The graph of the function y = sqrt(x + 1) - 2 is a transformation of the graph of the parent function y = sqrt(x). The parent function y = sqrt(x) is the square root function in its simplest form, with no transformation applied to it.

The transformation y = sqrt(x + 1) - 2 affects the parent function in the following ways:

The function inside the square root sign (x + 1) is shifted one unit to the right, meaning that the graph is shifted one unit to the right.

The function is then shifted two units downward, meaning that the graph is shifted two units downward.

As a result, the graph of y = sqrt(x + 1) - 2 is the same as the graph of y = sqrt(x), but shifted one unit to the right and two units downward.

Both of the functions has the same vertex point which is (-1,-2) and the domain is x>=-1 and the range is y>=-2.

It also shares the same shape as the parent function, an upward opening parabola with vertex at the origin.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Awnser: 3 to 1

Answer:

3:1

Step-by-step explanation:

12 inches in a foot

12 divided by 4 is 3 hope this helps:)

Triangle ABD is an equilateral triangle because all three angles in the triangle are equal to 60°.

An equilateral triangle is a triangle in which all three sides as well as all three angles in the triangle are equal.

The three angles in an equilateral triangle are all equal to 60°.

Considering the given triangle;

angle DCB = 30°

angle CBD = 30° ( base angles of an isosceles triangle)

angle BDC = 120° ( sum of angles in a triangle)

angle ADB = 60° ( sum of angles in a straight line)

angle ABD = 60° (90° - 30°)

angle BAD = 60° (sum of angles in a triangle)

Hence, ABD is an equilateral triangle.

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V(t) = 30 * e^(-0.012t) is the value of the car after t years.

The value of the car 2 years from now will be approximately $29,300.

Let's call the original value of the car V0, and the decay factor k. The exponential model representing the value of the car after t years is given by:

V(t) = V0 * e^(-kt)

To find the value of the car after 3 years, we can plug in t=3 into the equation:

V(3) = V0 * e^(-k*3) = 18

We can rearrange the equation to solve for the decay factor k:

k = -ln(V(3)/V0)/3

Plugging in the known values, we get:

k = -ln(18/V0)/3

Since the value of the car has decreased by 40%, V0 = 18 / (1 - 0.4) = 30. Therefore, k = -ln(18/30)/3 = -0.012.

Therefore, the exponential model representing the value of the car after t years is:

V(t) = 30 * e^(-0.012t)

V(2) = 30 * e^(-0.012*2) = 30 * e^(-0.024) = 30 * 0.977 = 29.3

This model represents the value of the car in thousands of dollars.

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According to the decreasing exponential value, the exponential function for the given situation is written as [tex]E(t) = 30 \times e^{-0.012t}[/tex] and the value of the car 2 years from now will be approximately $29,300.

Here we have given that  a new xar 3 years ago. Its value has decreased exponentially by 40 percent since I got it and it's now worth $18,000

Here let us consider that the original value of the car E0, and the decay factor k.

Then the exponential model representing the value of the car after t years is written as

=> [tex]E(t) = E0 \times e^{-kt}[/tex]

Here we need to find the value of the car after 3 years, then we have to  plug in t=3 into the equation, then we get,

[tex]E(3) = E0 \times e^{-k\times3}= 18[/tex]

Now, we have to rearrange the equation to solve for the decay factor k, then we get the value as,

=> k = [-ln(E(3)/E0)]/3

Now, we have to put the values on the equation then we get

=> k = [-ln(18/V0)]/3

Here we know that the value of the car has decreased by 40%,

Therefore, it can be written as,

=> E0 = 18 / (1 - 0.4) = 30.

Therefore, the value of

=> k = -ln(18/30)/3 = -0.012.

Now the exponential model representing the value of the car after t years is calculated as

[tex]E(t) = 30 \times e^{-0.012t}[/tex]

Apply the value of t as 2, then we get the value of E(T) as,

=> [tex]E(t) = 30 \times e^{-0.012\times 2}[/tex]

=> E(T) = 29.2

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Answer:

B

Step-by-step explanation:

6 is being multiplied by a quantity greater than 1, meaning the product will be more than 6.

The expression equivalent to the given expression is [tex]-5 \frac{1}{4}x - \frac{1}{2}[/tex], hence the correct option is D.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder.

To covert a fraction into mixed fraction:

By denominator, divide the numerator. Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.

In the given expression solve the brackets and seperate the like terms as follows:

[tex]-\frac{1}{2}(-\frac{3}{2}x + 6x + 1 ) - 3x\\ \\\frac{3}{4}x - 3x - \frac{1}{2} - 3x\\ \\ \frac{3}{4}x - 6x - \frac{1}{2}\\\\-\frac{21}{4}x - \frac{1}{2}[/tex]

Convert the fraction into mixed fraction by dividing the numerator and denominator:

[tex]-\frac{21}{4}x - \frac{1}{2} \\ \\-5 \frac{1}{4}x - \frac{1}{2}[/tex]

Hence, the expression equivalent to the given expression is option D.

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Tori's loss from the stock will be $28.29 and her rate of return will be -84.75%.

While a high share price discourages trading in the company's stock, it advertises its stellar performance to existing and potential investors.

A high share price also discourages corporate takeovers, assuring the jobs of senior management. Existing investors can realize some quick gains by selling their shares at high profits.

Since Tori bought one share of Macy's stock on Nov 1, 2016, for $33.38 and she sold it and the closing price for that day was $5.09, her loss will be;

= $5.09 - $33.38

= -$28.29

Her rate of return will be:

= -28.29/33.38 × 100

= -84.75%

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A 90% confidence interval for the true mean loan amount is (e) (23,984 +1.64513,879/√(1280), 23,984 -1.64513,879/√(1280))

To calculate a 90% confidence interval for the true mean loan amount, you can use the following steps:

        margin of error = critical value × standard deviation / √(sample size)

       (point estimate - margin of error, point estimate + margin of error)

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Answer:

Step-by-step explanation:

Use the distance formula of coordinate geometry.

Mark all the coordinates.

(-5, 5) , (-1, 7) , (4, -3) , (0, -5)

We need to find the length and width of the rectangle.

Lets pick, (4, -3) and (0, -5).

Distance formula,

√((x₁ - x₂)² + (y₁ - y₂)²)

or, √((4 + 0)² + (-3 + 5)² = √20 = 2√5 (width)

Again, we can take (-5, 5) and (0, -5)

√(25 + 100) = √125 = 5√5 (length)

Area of rectangle is length x width or 2√5 x 5√5 = 10 x 5 = 50 units²

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Answer:

Step-by-step explanation:

27 years old

The inequality that is graphed on the coordinate plane is D. y ≥ -2x − 1.

An equation has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

An inequality shows the non equal comparison of two or more numbers and variables. From the graph, a dotted intersects x-axis at unit 0.5 (0.5, 0) and Y-axis at unit -1 (0, -1).

Using the points (0.5, 0) and (0, -1), hence:y - 0 = [(-1 - 0)/(0 - 0.5)](x - 0.5)y = 2x - 1.

Since the line graph is dotted and it is shaded to the left, hence it is the inequality y ≥ -2x − 1.

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Answer:

Step-by-ste…….explanation:

The shaded portion of CUA'UB'  is given in the attached figure.

A set is a collection of well defined objects

The given sets are A , B , C and the universal set U.

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Now we need to share the portion of CU(AnB)'

(AnB)'=A'UB' from the propertys

CUA'UB'

A'=U-A

B'=U-B

So the shaded portion of CUA'UB'  is given in the attached figure.

Hence, the shaded portion of CUA'UB'  is given in the attached figure.

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