Simplify the following expression. 5/2 + 11/60


A. 31/60


B. 3/5


C. 2/9


D. 37/60

Answer:

The answer is 7/20

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

This is an isosceles triangle.  Two angles (D and F) are equal because the sides opposite them are equal (or vice versa).

Thus, side DE = side EF, or

12x - 8 = 4x + 16

Combining like terms:  8x = 24

Thus, x = 24/8 = 3

x = 3

Answer:

The total T can be described as

\(T = (B+(B*.15))+1\)

Answer:

it is IH - 110 ft

Step-by-step explanation:

The plane height is down 110 feet from its initial height.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Let x be the initial height of the plane.

Then according to question;

if drop down means height in negative term and rise up means height in the positive term.

Then,

the height is

= x -300-180+240+130

= x-110

Therefore, down 110 feet is the height of the plane now relative to its initial height.

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Answer:

D

Step-by-step explanation:

Step-by-step explanation:

f(x) = 2^x (this is exponential function)

f(x) = 8

the equation is :

2^x = 8

2^x = 2³

cross out 2

so, we get : x= 3

The conversion is given below.

x is 3.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = \(2^x\)

f(x) = strength and x is the length.

Now,

Strength = 8

So,

8 = \(2^x\)

Taking logs on both sides.

log 8 = x log 2

x = log 8 / log 2

x = log (8/2)

x = log 4

x = log \(2^2\)

x = 2 log 2

or

2 x 2 x 2 = 2³ = 8

So,

8 = 2³

x = 3

Thus,

x = 3.

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Answer:

I think B

Step-by-step explanation:

because their age group is 20-25 more of a constant age group

compared to 20-30

Hi

Your question would be better with  "  Could you help me please ? " at the end. Quite sure your mum told you that some time in the past.

I will show you how to solve but you will do the calculus. Math is all about rules, methods and training.  If you dont practice, you will never progress.

rule  :  you must know by heart your remarkable identities.

Here we have  :   ( 4x-3)² - (2x+5)² = 0

It 's of the  form  A² -B² =  ( A+B) ( A-B)  

here A is  :   4x-3   and  B is  2x+5  

Now let's apply rule  :   ( 4x-3)² - (2x+5)² =  ( (4x-3) +( 2x+5) )  ( (4x-3) - (2x+5)

                                                                  =    ( 4x-3 +2x+5 )  ( 4x-3 -2x-5 )

                                                                  =     ( 6x +2)  ( 2x-8)  

so :  ( 4x-3)² - (2x+5)² =  ( 6x +2)  ( 2x-8)  

so  ( 4x-3)² - (2x+5)²  = 0   means  :  ( 6x +2)  ( 2x-8)    = 0

Rule A*B = 0 if A = 0  or B = 0

A  is  6x+2     and B = 2x-8

So I let you now work  :  

You have to solve :   6x+2 = 0

and   2x-8 = 0

Solutions of this two calculus will be the solutions of  ( 4x-3)² - (2x+5)²  = 0  

Have fun !                                    

30% percent of the students passed both Mathematics and English.

A rate, number, or amount in each hundred is known as a percentage

Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.

We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.

We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.

where the number in each section represents the number of students who passed the respective exam.

To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:

percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%

= (28 + 2) / 40 × 100%

= 30%

Therefore, 30% of the students passed both Mathematics and English.

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Answer:

this is actually about derivatives,

the answer would be simply 10x-6

The distance is the same that was covered.

Distance is speed multiplied by time.

Mr O takes 30 minutes and Mr Gordon takes 1 hour.

So the speed of Mr O is given by:

Convert the speed in meter per second.

The speed of mr G is:

So the difference between the speeds is:

So Mr O is 2.9167 m/s faster than Mr Gordon.

Answer:

The answer is true.

Step-by-step explanation:

Because we are working on negative integers and if a negative number is leaning more to the right on a number line it is bigger.

Check the picture below.

Answer:

AB/AD = AD/AC

Step-by-step explanation:

From the triangle given, we can get the required expression to calculate CD using the altitude theorem as shown:

AB/CB = CB/DB (Hypotenuse/Adjacent side using the similar triangle ABC and CDB)

AB/AC = AC/AD (Hypotenuse/Opposite side using the similar triangle ABC and ACD)

BD/CD = CD/AD (Adjacent/Opposite side using the similar triangle BCD and ACD)

Hence the odd one out will be option C AB/AD = AD/AC (since there is no altitude CD in the expression)

Answer:

AB/AD = AD/AC

Step-by-step explanation:

Had it on my quiz

After 5 years of compounding interest at a rate of 4% per year, your balance will be approximately $349.65.

To calculate the balance after 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (balance)

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the principal amount (P) is $300, the annual interest rate (r) is 4% (or 0.04 as a decimal), and the time period (t) is 5 years. The interest is compounded annually, so the number of times interest is compounded per year (n) is 1.

Plugging these values into the formula, we have:

A = 300(1 + 0.04/1)^(1*5)

A = 300(1 + 0.04)^5

A = 300(1.04)^5

A ≈ 349.65

Therefore, after 5 years of compounding interest at a rate of 4% per year, your balance would be approximately $349.65.

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A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.

A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).

The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.

However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.

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Answer:

I did the problem but it won't show sorry

Answer:

all real numbers

Step-by-step explanation:

the domain will always be all real numbers

The probability (in percentage) that a score will fall between a -3z and +2 z scores is 97.59%.

Assuming a standard normal distribution, the probability that a score falls between -3z and +2z can be calculated as the difference between the cumulative probabilities of +2z and -3z.

Using a standard normal distribution table or calculator, we find that the cumulative probability of +2z is approximately 0.9772, and the cumulative probability of -3z is approximately 0.0013.

Therefore, the probability that a score falls between -3z and +2z is:

0.9772 - 0.0013 = 0.9759

Converting to a percentage, we get:

0.9759 x 100% ≈ 97.59%

So the probability that a score falls between -3z and +2z is approximately 97.59%.

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Answer:

87.375

Step-by-step explanation:

Answer:

699/8 or 87.375

Step-by-step explanation:

Assuming 12 5/8+ 12 3/4+ 12 7/8+ 13+ 13 1/8 are mixed numbers.

The equation for the line with a slope of 1/2 and a y-intercept of (0, 6) in slope-intercept form is y = (1/2)x + 6. slope-intercept form,This equation represents a line with a positive slope that rises at a rate of 1/2 unit for every 1 unit increase in x, starting from the point (0, 6).

Given that the slope is 1/2 and the y-intercept is (0, 6), we can substitute these values into the slope-intercept form.
So, the equation becomes y = (1/2)x + 6. This equation represents a line with a positive slope that rises at a rate of 1/2 unit for every 1 unit increase in x, starting from the point (0, 6). The equation for the line with a slope of 1/2 and a y-intercept of (0, 6) in slope-intercept form is y = (1/2)x + 6.

Given that the slope is 1/2 and the y-intercept is (0, 6), we can substitute these values into the slope-intercept form. So, the equation becomes y = (1/2)x + 6. This means that for every unit increase in x, y increases by half a unit, and the line intersects the y-axis at the point (0, 6).

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A book cost $2.00.

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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The polygon which on rotated gives the given cylinder is a rectangle with dimensions 10 inches × 9 inches.

Given a cylinder with the diameter of the base 18 inches and the height of the cylinder 10 inches.

This cylinder is formed by rotating some polygon around YZ.

The polygon must be a rectangle which has the height or the length equal to the height of the cylinder.

So length = 10 inches

The width of the rectangle will be half of the diameter.

Width = 18/2 = 9 inches

Hence the rotated polygon is a rectangle with length 10 inches and width 9 inches.

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Answer:

x=70

z=20

y=30

Step-by-step explanation:

first find x: the sum of straight angle is 180

x+110=180

x=180-110=70

now find z: the sum of the angles of triangle is 180:

x=70, right angle=90

z+70+90=180

find y:

y+110+40=180

y=180-150=30

z=180-160=20

Answer:

x=70 degrees, y= 30 degrees, z=20 degrees

Step-by-step explanation:

110+x=180 => straight angle def.

180-110+40=y => def. of angles in triangle

x( 70 degrees) +90+z=180, z= 20 => angles in triangle

If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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Answer:

200% and  M is 100% of N.

Step-by-step explanation:

Answer:

1)200%

2)100m/n

Step-by-step explanation:

2/1=2

2*100=200%

m/n*100= 100m/n

Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: \((x,y)\rightarrow(x+5,y-2)\).

Apply the rule to point 'B':

\(\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}\)

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation: