the running time in 1500-metre run for us olympics athletes is best modeled according to the normal distribution with a mean of 4.1 minutes (that is, 4 minutes and 6 seconds) and a standard deviation of 0.45 minutes (or equivalently, 27 seconds). what is the cut-off time (in minutes and seconds) for the 6% slowest runners?

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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What method are you required to use to solve this given expression? Are you simply dividing, or it is a specific method of division? If you could lmk, I'd be more than happy to assist you asap. Thanks!

Angles can be measured in degrees and radians

The measure of angle XYZ is 34 degrees

From the question, the measure of arc XY is 68 degrees

The measure of angle XYZ is then calculated as:

Angle XYZ = 0.5 * Arc XY

This gives

Angle XYZ = 0.5 * 68

Evaluate the product

Angle XYZ = 34

Hence, the measure of angle XYZ is 34 degrees

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Answer:

the answer for first question is $112.

the answer for second question is 16 trips.

Step-by-step explanation:

Hope it helps you!!

Step-by-step explanation:

a) 224-14(8)=224-112=112dollars

b) 112 divided by 14=8trips

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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The total money she repays to the bank is $1297.2.

Given,

Amanda takes out a loan of $1,200 from a bank.

The bank charges 5.4% interest a year.

She borrows the money for 1.5 years.

We need to find the total amount she repays to the bank after 1.5 years.

we have,

Loan amount = $1200

Bank interest rate per year = 5.4%

So,

The interest amount per year:

= 1200 X (5.4/100)
= $64.8

If,

1 year = $64.8

1/2 year = 1/2 x 64.8

1/2 year = $32.4

In 1.5 years the interest amount will be:

1.5 years = 1 year + half-year

               = $64.8 + $32.4

               = $97.2

The total money she needs to pay to the bank after 1.5 years is:

= loan amount + 1.5 interest amount

= $1200 + $97.2

= $1297.2

Thus if she borrows the $1200 for 1.5 years with a yearly interest of 5.4%, she needs to repay $1297.2.

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The measure of the angle of the straight line is equal to the 180 degree. the measure of the \(\angle HLI\) is equal to the \(\angle ILM\) which is 30 degrees. Thus the option 4 is the correct option.

The measures of the angle KLH is 120 degrees.

The image is attached below for the given problem.

The measure of the angle of the straight line is equal to the 180 degree.

The line KLM is a straight line thus the angle of the line KLM is equal to the 180 degrees.

The value of the angle ILH is 30 degrees given in the figure.

The value of the angle KLH is given in the question which is equal to the 120 degrees. Thus,

\(\angle KLM=\angle ILM +\angle KLH + \angle ILH\)

Take the angle KLH and the angle ILH on the other side,

\(\angle ILM=\angle KLM -\angle KLH - \angle ILH\)

\(\angle ILM=180-120-30\)

\(\angle ILM=30\)

Thus the measure of the \(\angle ILM\) is 30 degrees.

As the measure of the \(\angle HLI\) is equal to the \(\angle ILM\) which is 30 degrees. Thus the option 4 is the correct option.

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Answer:

Answer: D. m<HLI = m<ILM

Step-by-step explanation:

Ed2022

The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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Based on table shown above, we have that: A. Yes, the table describe a function.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Based on table shown above, we have the following parameters:

Input value       Output value

2001                         30

2002                        60

2003                        30

2004                        50

2005                        40

In conclusion, we can reasonably infer and logically deduce that this table is a function because it has the different input values (x-values) for different or the same output values (y-values).

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Same question here answered by me with proper explanation.Visit the link below for your ans

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Maria received 999 votes out of a total of 25, which means that 999/25 = 39.96% of the class voted for her. Therefore, approximately 40% of the class voted for Maria.

To find the percentage of the class that voted for Maria, we need to first find the total number of students who voted:

Total number of students who voted = number who voted for Benjamin + number who voted for Sahil + number who voted for Maria

= 444 + 1212 + 999

= 2655

Now we can calculate the percentage of the class that voted for Maria:

Percentage of class that voted for Maria = (number who voted for Maria / total number of students who voted) x 100%

= (999 / 2655) x 100%

= 37.6%

Therefore, 37.6% of the class voted for Maria, approximately 40% of the class voted for Maria.

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Answer:

remember that the circumference of a circle is 2πR

so the answer is 157.08

Answer: 3200

Step-by-step explanation:

First, we know that 48 % is 0.48 in decimal number so we will make this equation:

0.48 times the total of children = the boys that are in the summer camp

0.48 times X=1536

To isolate the x we can divide 1536/0.48 = 3200

So the 48% of 3200= 1536

Because 0.48 * 3200=1536

Answer:3200

Step-by-step explanation: basically u gotta divide 1536 by 48 to get one percent of the kids. this is equal to 32. After you get this you gotta multiply by 100 to get the final answer which is 3200.

Answer:

Rectangle

Step-by-step explanation:

It's a rectangle because opposite sides are parallel as you can see , it has 4 right angles , and it has 4 sides .. it's not a square because in a square all sides are equal

3u-1/2u or 3u-0,5u or 3u-u/2

Answer:

Step-by-step explanation:

y = -2x +2

y - 3 = -2(x -3)

y - 3 = -2x + 6

y = -2x + 9

Answer:

7.74 feet (approximate is 8 feet)

Step-by-step explanation:

Radius of the circle is r = 6/2 = 3

Area of the circle is A = π x 3^2 = 9π = 28.26

Area of the square = 6^2 = 36

Remaining board area = 36 - 28.26 = 7.74

Hope this helps! <3

The predicate in the conditional statement checks whether the value of variable "a" is less than or equal to 1. However, it does not directly determine if "a" is of type double.

In this specific case, let's break down the code:

1. The expression `(2 + 1) / 2` is evaluated first. Since both 2 and 1 are integers, the division operation `/` results in a floating-point value, specifically 1.5.

2. The result of the expression is then assigned to variable "a" with the statement `a = (2 + 1) / 2`. The value of "a" becomes 1.5.

3. The conditional statement `if (a <= 1)` is evaluated. The comparison `1.5 <= 1` is false because 1.5 is greater than 1.

Therefore, the predicate result for the variable "a" to be a double primitive type in this case is false.

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The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Step-by-step explanation:

Turn the standard form equation into a slope-intercept form equation using algebra.

Slope-intercept form: \(y=mx+b\)

Key:

Subtract each side by 3x:

\(8y=-3x+5\)

Divide each side by 8:

\(y=-\frac{3}{8} x+\frac{5}{8}\)

-3/8 is in the position of m, the slope.

The slope is -3/8.

The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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Answer:

cat is 6 pumpkin is 12 pot is 14 so 6+14-12=8

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

15i-18=12

15i= 12+18

15i= 30

I= 30/15= 2

Step-by-step explanation:

Expressions are collection of algebric equetion and equal sighn and used for expresion of mankind problems like items, money and other mankind problem.

to know length by using degree but most of the time for the archtechture. soon

The perimeter of a right triangle with hypotenuse 30cm and one of the legs 18cm is 72 cm.

The given sides of the right triangle are :

                 Hypotenuse (H) = 30cm

                  Perpendicular/leg (P) = 18cm

The formula of the perimeter of right triangle is = sum of its side.

For that we will first find out the value of base. For that we will use Pythagoras theorem which states that the square of the hypotenuse is equal to the sum of squares of the other two side. Numerically,  

                               H^2 = B^2 + P^2

Now putting the required values in the above formula we get

                              (30)^2 = B^2 + (18)^2

                               B^2 = 900 – 324

                                B^2 = 576

                                  B = √576

                                  B = 24cm

Thus the value of base is 24cm

Hence the perimeter of the triangle = H + B + P

                                                                 = 30 + 18 + 24cm

                                                                 = 72cm

Therefore the perimeter is 72cm

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Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

22

Step-by-step explanation:

Use a proportion.

30/15 = 44/x

30x = 15 × 44

2x = 44

x = 22

Answer:

22

Step-by-step explanation:

30 miles/ 15 sessions of tract practice

Per practice Jack is running a total of 2 miles.

So 44 miles/2 miles

22 sessions of track practice

If the vertex of a parabola is ​(- 10, 7), The equation for the axis of​ symmetry

is y = - 10.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know, The graph of a quadratic function ax² + bx + c = 0 is a parabola.

The vertex of a parabola consists of the roots of the quadratic equation.

Given,  The vertex of a parabola is ​ (-10, 7).

We know, The axis of symmetry is a dotted vertical line that bisects the parabola.

Therefore, The equation for the line of symmetry is y = - 10.

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Answer:

x = 20

y = 25

Step-by-step explanation:

Vertical angles are always congruent, that is a theorem.

Set the vertical pairs equal to each other.

182 - 4x = 5x + 2

The lowest of the two coefficients is 4x, so that will be added to both sides.

4x + 5x = 9x

Simplify

9x + 2 = 182

Subtract both sides by 2

9x = 180

Divide by 9

180/9 = 20

x = 20

Plug in the 20 to get the angle measure.

182 - 80 = 102

the vertical pairs are 102 degrees

There is another theorem that sets the two angles outside as congruent.

So set 4y + 2 = 102

Subtract 2

100

Divide 4, which equals 25

y = 25