least common denominator of 7/2 and1/2​

135 as a product of its prime factors is written as  3 × 3 x 3 x 5

The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.

In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.

From the information given, we have the value as;

135

The prime factors are  3 × 3 x 3 x 5

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Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

The partial products of 3706 × 4 is ( 3000 × 4 ) + ( 706 × 4 ).

Calculating the product of two or more numbers is the procedure known as multiplication in mathematics. When two integers are multiplied together in mathematics, the result is a product or an expression that describes the factors to be multiplied.

The decimal numeral system is widely used to express both integer and non-integer numbers. The way of representing numbers in the decimal system is known as decimal notation.

The given product is 3706 × 4 and can be written as:-

3706 × 4 = [ 3000 + 706 ] × 4

3706 × 4 = ( 3000 × 4 ) + ( 706 × 4 )

Therefore, the partial products of the given expression is ( 3000 x 4 ) + ( 706 x 4 ).

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Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

\((x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )\)

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

\(t_{(16 , 0.05)} = 2.1199\)

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

\((x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )\)

\((12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )\)

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)

Answer:

Therefore, the earliest time to take the next pill is after 10.85 hours and the latest time is before 15.14 hours have passed.

Step-by-step explanation:

The concentration of the drug in your system after ingesting 100.0 mg can be calculated using the formula:

C = D / V

where C is the concentration, D is the dose, and V is the volume of distribution (assumed to be constant).

At the initial time, t = 0, the concentration is:

C(0) = 100.0 mg / V

After one half-life, t = 16 hours, the concentration is:

C(16) = C(0) / 2 = 50.0 mg / V

After two half-lives, t = 32 hours, the concentration is:

C(32) = C(16) / 2 = 25.0 mg / V

After three half-lives, t = 48 hours, the concentration is:

C(48) = C(32) / 2 = 12.5 mg / V

To find the earliest and latest times to take the next 100.0 mg pill, we need to calculate the concentration at those times and make sure it stays between 20.0 mg and 140.0 mg.

Let's first find the earliest time at which the concentration drops below 20.0 mg.

20.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 20.0 = 2.5

x/16 = log2(2.5)

x = 16*log2(2.5) = 16*0.678 = 10.85

So the earliest time to take the next pill is after 10.85 hours.

Now let's find the latest time at which the concentration goes above 140.0 mg.

140.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 140.0 = 0.3571

x/16 = log2(0.3571)

x = 16*log2(0.3571) = -15.14

So the latest time to take the next pill is before 15.14 hours have passed.

Answer:

sorry

Step-by-step explanation:

Answer:

M<3 is 49 degrees, M<4 is 131 degrees  

Step-by-step explanation:  

This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees  

First, we know that M<1 and M<2 added together is 180. We know M<1 is 11x-38 and M<2 is 19x+8, so then, we have:

(11x-38) + (19x+8) = 180

30x - 30 = 180

30x = 210

x = 7

Now, we plug in 7 for x to find M<1 and M<2.

M<1 is (11x-28), so it would be 49 degrees.

M<2 is (19x+8), so it would be 131 degrees (or just do 180-49).

Now, we can find M<3 and M<4 easily. M<3 and M<2 are supplementary, so 131 + M<3 must equal 180. Thus, M<3 is 49.

M<4 and M<1 are supplementary, so 49 + M<4 must equal 180. Thus, M<3 is 131.

AN EASIER WAY TO FIND M<3 AND M<4:

Vertical angles are angles directly opposite each other, created by two intersecting lines. A pair of vertical angles holds the same degree measurements. In this problem, M<2 and M<4 are a pair of vertical angles, and M<3 and M<1 are a pair. Thus, M<2 and M<4 must are the same degree and M<3 and M<1 must are the same degree. Thus, if M<2 is 131, M<4 is 131 degrees as well. If M<1 is 49 degrees, M<3 is 49 degrees as well.  

Answer:

805

Step-by-step explanation:

It's kinda hard to explain but first you would convert 23% to a decimal. To do that, move the decimal 2 places to the left, resulting in 0.23. Then multiply 3500 by 0.23 to get your answer.

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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Answer:

Step-by-step explanation:

4

4

3

1

Answer:

about 3.42

Step-by-step explanation:

multiply 8*3 = 24

24/7=3.42...

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

Answer: 12.56

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-5 x 7 = -35

-12 x 0 = 0

-35 x 0 = 0

I hope this helped!

Answer:

F

Step-by-step explanation:

x-9=15 will equal to 24 so x=24

if Allison is 15 but she is 9 years younger then Pam, Pam is x, so all you have to do is count up from 15, so 15+9 which equals 24 Pam is 24 making F the right choice

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

a(n)=1+(n-1)(-3)

Step-by-step explanation:

Notice there's a common difference of d=-3.

If we use the formula a(n)=a1+(n-1)d to find the nth term given the first term and the common difference, we will see that the function that describes the arithmetic sequence as a(n)=1+(n-1)(-3)

Answer:

1.25

Step-by-step explanation:

1.5 divided by 1.2 is 1.25

Hope this helps☺️

Answer:

1.25

Step-by-step explanation:

1.5 / 1.2 = 15/12 = 5/4 = 1 1/4 = 1.25

Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

Answer:

First multiply 112,500 times 3 (because of the 3 cars) answer should be $337,500

Then do the percentage (7%) $23,625

I believe that 23625 is the answerrr

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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apply absolute value formula(thats what i call it)

|5-6i|=

\(\sqrt{5^2+\left(-6\right)^2}\)=

\(\sqrt{61}\)

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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Answer:

Step-by-step explanation:

u cant explain it

Answer:

x = 5

Step-by-step explanation:

assuming you mean the slope of the line id undefined and passes through (5, 0 )

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (5, 0 ) with x- coordinate 5 , then

x = 5 ← equation of line

Answer

what is 50 divided by 20 is 2.5

Step-by-step explanation:

Answer:

5/2 (in fraction) or 2.5 (in decimal)

Step-by-step explanation:

50 = 5*10

20 = 2*10

50 divided by 20,

50/20

= 5/2 (in fraction)

(or)

= 2.5 (in decimal)

The formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) can be proven using the trigonometric identities.

Starting with the definition of cosecant:

cosec (A + B) = 1/sin (A + B)

Using the sum-to-product identity:

sin (A + B) = sinA cosB + cosA sinB

Substituting this expression into the definition of cosecant:

cosec (A + B) = 1 / (sinA cosB + cosA sinB)

Using the difference-to-product identity:

sinA - sinB = 2sin((A - B)/2)cos((A + B)/2)

Dividing both numerator and denominator by 2sin((A - B)/2)cos((A + B)/2), we get:

cosec (A + B) = (sinA cosB - cosA sinB) ÷ (sinA + sinB)(sinA - sinB)

Therefore, the formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) has been proven.

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Answer:

5/9 of the marbles are red

Step-by-step explanation:

Of the 45 marbles, 20 are black, and the other 25 are red. So 25/45, or 5/9, of the marbles are red.