ERADES
4
Declan is training to take part in a 10 km race.
He runs the same distance every day for 30 days. A
For the first 20 days, his mean running time was 56.2 minutes.
His mean running time for all 30 days was 54.4 minutes.
Work out Declan's mean running time for the last 10 days of his training.
unning time for first 20

Answer:24

Step-by-step explanation: 4(4÷2 + 4) = 24/1 = 24

Spelled result in words is twenty-four.

Divide: 4 / 2 = 2

Add: the result of step No. 1 + 4 = 2 + 4 = 6

Multiple: 4 * the result of step No. 2 = 4 * 6 = 24

This calculator adds two fractions. When fractions have the same denominators calculator simply adds the numerators and place the result over the common denominator. Then simplify the result to the lowest terms or a mixed number.

Answer:

24

Step-by-step explanation:

We have to solve this according to BODMAS Theorem.

That is,

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Let us solve it now.

4 ( 4 ÷ 2 + 4 )

4 ( 2 + 4 )

4 × 6

24

The area of a rectangle with given length and width is 2t³+15t²+19t+6 square units.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, length of a rectangle =t²+7t+6 and width of rectangle =2t+1.

Here, area of a rectangle = (t²+7t+6)×(2t+1)

= t²(2t+1)+7t(2t+1)+6(2t+1)

= 2t³+t²+14t²+7t+12t+6

= 2t³+15t²+19t+6 square units

Therefore, area of a rectangle is 2t³+15t²+19t+6 square units.

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Answer:

To find the mass in grams, multiply the number of kilograms by the unit rate, 1000 grams per kilogram.

Explanation:

For every kilogram, there are 1000 grams. So, if you have 12 kilograms, you have 12,000 grams.

The radius of a circle is 5 feet, 23.55 feet is the length of an arc.

The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc.

The arc length formula may be used to get a circle's arc length from its radius and central angle.

The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. An arc's angle at any given location is the angle created by the two line segments connecting that point to the arc's endpoints.

Given that,

radius (r) = 5 feet

angle (θ) = 3π/2

Now as we know,

Arc length = radius x subtended angle in radians

or, Arc length = 5 feet x (3π/2 radians)

or, Arc length = 15π/2

or, Arc length = 23.55 feet

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The measures of the angles are m ∠ 1 = 68°, m ∠ 2 = 126° and m ∠ 3 = 54°

Parallel lines are those straight lines that are always the same distance apart from each other. Parallel lines never meet, no matter how much they are extended.

Given is a figure, in which, lines d, e and lines f, g are parallel and h is a transversal.

In figure, (refer to figure attached)

ABC is a triangle,

Therefore, according to angle sum property of a triangle,

m ∠ 1 + 58° + 54° = 180°

m ∠ 1 = 180° - 112°

m ∠ 1 = 68°

Since, f║g

m ∠ 2 + 54° = 180° (consecutive angles between parallel line are supplementary)

m ∠ 2 = 126°

Similarly, d║e

m ∠ 2 + m ∠ 3 = 180°

m ∠ 3 = 180° - 126°

m ∠ 3 = 54°

Hence, The measures of the angles are m ∠ 1 = 68°, m ∠ 2 = 126° and m ∠ 3 = 54°

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the mean

the mean is the average, having an outlier will make the average significantly higher or lower than accurate.

TRUE: The given condition is correct that m ≤ 10 and m > 4.

For the given statement;

m ≤ 10 and m > 4, the number for the value of m be;

m = 5, 6, 7, 8, 9, 10.

Thus, the given condition is correct that m ≤ 10 and m > 4.

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Answer:

B

Step-by-step explanation:

To eliminate one of the variables from a system of equations, we can multiply one or both equations by constants and then add the equations together. In this case, the correct method to use is to multiply the first equation by 3 and the second equation by 4, and then add the equations together. This will eliminate the y-variable from the system of equations. Thus, the correct answer is option B: multiply the first equation by 3 and the second equation by 4, and then add the equations together.

The correct is option B (i.e.Multiply the first equation by 3 and the second

the equation by 4. Then add the equations.)

multiplying the first equation by 3 and the second equation by 4:

12x - 18y = 54

12x + 16y = 20

subtracting the first equation from the second equation:

     ( 12x - 18y = 54) - (12x + 16y = 20)

                     -2y = -34

                         y = 17

substituting y = 17 in the first equation:

4x - 6(17) = 18

4x = 106

x = 26.5

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The value of x if The measure of the angle is = 5x + 4, The measure of the angle is = 146, The lines are parallel, is 6.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Given:

The measure of the angle is = 5x + 4

The measure of the angle is = 146

The lines are parallel,

Calculate the value of x as shown below,

5x + 4 = 180 - 146  (Parallel line theorem, corresponding angle, and supplementary angles)

5x = 34 - 4

x = 30 / 5

x = 6

Thus, the value of x is 6.

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Answer:

26

Step-by-step explanation:

Mr Ford has 78 cattle

so Mrs Metcalf has 78/3 = 26

Answer:

26

Explanation:

No of cattle Mr. Ford has= 78

Then, no of cattle Mrs. Metcalf will have:

= 78/3

=26

The function that can be represented by this graph is defined as follows:

f(x) = 2x³ + x - 3.

The function is defined looking at the features of the graph.

The first feature which we look at is the y-intercept, as the graph of the function crosses the y-axis at y = -3, hence the function can be defined as follows:

f(x) = ax^n + x - 3.

The function has an inflection point, as it has a change in it's concavity, thus the function has a second derivative of the first degree, meaning that the function is of the third degree, that is:

n = 3.

The x-intercept is when the function crosses the x-axis, meaning that when x = 1, y = 0, then the leading coefficient a is obtained as follows:

0 = a + 1 - 3

a = 2.

Which means that the function rule can be given by:

f(x) = 2x³ + x - 3.

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The simplified form of inequality -3x - 1 ≥ 20 is x ≤ -7.

The correct option is option (A).

A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.

The given inequality is,

-3x - 1 ≥ 20.

To find the right number line from the options

Solve the inequality,

Add 1 to both the sides,

-3x -1 + 1 ≥ 20 + 1

-3x ≥ 21

-x ≥ 21 / 3

-x ≥ 7

x ≤ -7

The value of x are less than or equal to -7. Implies that, in number line graph close circle.

The number line in option (A), is correct option.

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In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. ,m∠2 = 40°.

An unending, one-dimensional figure with no breadth is a straight line. It consists of an infinite number of points connected on either side of a point. A straight line has a 180° measurement.

In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. Alternatively said, it divides two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

The graphic XYQ is the straight line, m∠3 = 40°, and m∠4 = 25°. YZ is the angle bisector of ∠s.

m∠2 =  40°  the reason is YZ is the angle bisector of ∠s

∠s = m∠2  + m∠3  

m∠2  = m∠3

therefore m∠2 =  40°

m∠1  + m∠2 +  m∠3  + m∠4 = 180° the reason is XYQ is the straight line.

substitution of all values

m∠1  + 40° +  25° + 40° = 180°

m∠1  + 105° = 180°

m∠1 =  75°  (straight line, substitution of all values )

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Answer: 99.

If you take 275 and subtract it by 176, it should be 99, if I’m correct.

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex .

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There are 90000 palindromes 10-digit numbers.

In this question we need to find the number of 10-digit integers are there which are palindromes.

We know that a palindrome is a number that reads the same forward and backward.

The numbers that remain same even if they are reversed.

For exa., 131, 5225

We can observe that for even digit palindromes first half should be equal second half in reversed order.

we can generalize it as variables:

abcdeedcba, for a not equal to 0

So if we know how many 5-digit numbers are there, all we have to do is reverse it and we will have our 10-digit palindrome number.

There are 10 digits in total (0 - 9)

Since the first digit cannot be zero we excluded it from our choice hence we have 1–9 i.e 9 choices for first place(hundred's place)

The second, third, fourth and fifth digit has all 10 choices.

So, in total there are 9 x 10 x 10 x 10 x 10= 90000 five digit numbers.

Therefore, the total 10-digit numbers which are palindromes =  90000

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Answer:

try 1239128981441231241

Step-by-step explanation:

myra

the points of AA'B'C' is A'(4,0)  B'(5,-1)  C'(7,-2)

Solution:

x, y = 0

(x + 2, y - 3) = 0

x + 2 = 0

x = -2

y - 3 = 0

y = 3

AABC

A(2,3)  B(3,2)  C(5,1)

A: (2,3) → (2+2,3-3) = (4,0)

B: (3,2) → (3+2,2-3) = (5,-1)

C: (5,1) → (5+2,1-3) = (7,-2)

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The percentage of change is 10.17%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given are the two measures 3.25 centimetres and 2.95 centimetres

The percentage change, of a quantity, is the ratio of the difference in the quantity to its initial value multiplied by 100.

Therefore, The percentage of change = [(3.25-2.95)/3.25]x100

= 0.3/3.25x100

= 10.17%

Hence, the percentage change = 10.17%

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Answer:

Step-by-step explanatihelpson:

is c hope it

Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.

In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.

In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:

Measure of angle Y = 38.25°

Measure of angle Z = 74.3°

Therefore:

The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z

Substitute

The measure of the exterior angle to angle X = 38.25° + 74.3°

The measure of the exterior angle to angle X = 112.55°

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The transformation describing the function is a translation 5 units to the right.

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects".

Given that, a function f(x) = x² translated to g(x) = (x-5)²

We know,

h(x) = A(x - h)² + k

Where

A represent the vertical stretch (by factor of A)

h represent the horizontal shift (positive = Right, negative = Left)

k represent the vertical shift (positive = Up, negative = Down)

f(x) = x²

g(x) = (x - +5)²

Where,  positive shows to  the right.

Hence, the translation is 5 units to the right.

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Given restriction is an example of Time-of-day restrictions

The correct answer is an option (C)

In this question we have been given a friend tells you that tellers

are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday through Saturday.

We need to identify the type of restriction in this example.

We know that time-of-day restrictions are the restrictions that often used to limit the hours during which a user is allowed to log into or access a system.

This type of restrictions helps prevent unauthorized access outside that user's normal working hours .

Therefore, given restriction present in this example: Time-of-day restrictions

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The complete question is:

A friend of yours who works in the IT department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday

through Saturday. What is this restriction an example of?

A. User auditing

B. Least privilege

C. Time-of-day restrictions

D. Account verification

Layla can make the box up to 5centimeter long.

       V = l x w x h

Here it is given that,

volume= 45cm³

width= 3cm

height=3cm

volume = width × height × length

45cm³=3cm×3cm×length

45cm³=9cm²×length

length=45cm³÷9cm²

          =5cm.

Hence, Layla can make the box up to 5centimeter long.

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Answer: The barrel can only hold less than 42 gallons of water, which means w<42.

Answer: -7/1

Step-by-step explanation: When graphing both points and drawing a line through it, count how many times it goes up or down and then count how many times it goes left or right.

When she subtracts 4 from both side of the equation, then she gets the value of x is 0.

Expressions means the idea of expressing numbers using letters or alphabets without specifying their actual values, the expression is the statement consisting variable, numbers, and arithmetical operation.

Given that, Karissa begins to solve the equation,

1/2(x-14)+11 = 1/2x-(x-14)

1/2x-1/2(14)+11 = -1/2x-x+4

1/2x-7+11 = -1/2x+4

1/2x+4 = -1/2x+4

1/2x+1/2x = 4-4

x = 0

Hence, When she subtracts 4 from both sides, then x = 0

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I Agree With The Other Person

After 2.5 hours cars be 237.5 miles apart.

What is distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.

First to write equation for each car

[tex]d_1=r_1t_1 (east bound)\\d_2 = r_2t_2 (west bound)[/tex]

They both start at the same time, and I will stop them both when they are 165 mi apart.

So, [tex]t_1=t_2[/tex] call just t.

⇒

[tex]d_1 = r_1t\\d_2=r_2t[/tex]

[tex]t = \frac{d_1}{r_1} \\t= \frac{d_2}{r_2}[/tex]

⇒

[tex]\frac{d_1}{r_1} = \frac{d_2}{r_2} \\d_1r_2 = d_2r_1[/tex]            ..(1)

We also know that

[tex]d_1 + d_2 = 237.5[/tex]

[tex]d_2 = 237.5 - d_1[/tex]

[tex]r_1 = 55, r_2 = 40[/tex]

So, equation (1) becomes,

[tex]40d_1 = 55d_2[/tex]

Plug the value of [tex]d_2[/tex].

[tex]40d_1 = 55(237.5 - d_1)\\40d_1 = 13,062.5 - 55d_1\\40d_1 + 55d_1 = 13062.5\\95d_1 = 13062.5\\d_1 = 137.5[/tex]

[tex]d_1 = 137.5 mi[/tex]

Now,

[tex]t = \frac{d_1}{r_1} = \frac{137.5}{55} = 2.5[/tex]

Hence, after 2.5 hours cars be 237.5 miles apart.

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The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

The given data set is 14, 13, 13.5, 16, 14, 15.5, 14.5.

Order of data is 13, 13.5, 14, 14, 14.5, 15.5, 16.

Here, minimum is 13

Maximum is 16

Median is 14

Lower quartile range(Q1) is 13.5

Upper quartile range(Q3) is 15.5

Therefore, the box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

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Answer:137

Step-by-step explanation: