which expression is simplified form of 24/27

Answer:r=14°

Step-by-step explanation:

(5r-5)°+ (8r+3)°=180

(Sum of angles on a straight line =180°)

Collect like terms

5r+8r-5+3=180

13r-2=180

13r=180+2

13r=182

r=182/13

r=14°

For Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

To calculate the sum of money they must deposit, use the compound interest formula.

From the compound interest formula;

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

Given that;

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

P = 20,000 / ( 1 + 0.12/4 )^(4×10)

P = 20,000 / ( 1.03)^40

P = 20,000 / 3.26203779

P = $6,131.14

Therefore, for Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

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The solution to the following mathematical problems are;

Solve using

BODMAS

5² -3⁴ / (2³-5)(6² ÷ 9)

= 25-81 / (8-5)(36÷9)

= -56 / (3)(4)

= -56/12

= - 14/3

20² ÷ {3(5-9)² + 2}

= 400 ÷ {3(-4)² + 2}

= 400 ÷ {3(16) + 2}

= 400 ÷ (48+3)

= 400 ÷ 50

= 8

84/12 + (5-7)² -72 ÷ 6×2

= 7 + (-2)² - 12 × 2

= 7 + (4) - 24

= 11 - 24

= -13

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The amount in the ira's account s = $187,159.62.

How do you interest rate?

Future Value of an Ordinary Annuity

[tex]s = R(( 1 + i)^{n} - 1 ) / i[/tex]

where

S = the future value;

R = the periodic payment;

i = the interest rate per period;

n = the number of periods.

[tex]s = 5000 ( 1 + 0.032)^{25} - 1)/ 0.032[/tex]

[tex]s = 5000((1.032)^{25} - 1 )/0.032[/tex]

[tex]s = 5000( 2.19782157471 - 1)/0.032[/tex]

[tex]s = 5000(1.19782157471)/0.032[/tex]

[tex]s = 5000 * 37.4319242096[/tex]

s = $187,159.62

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This is voluntary response bias. The result overestimates true support for firing the coach.

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Answer:

627

267

276

762

726

and the no. itself, 672

The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The local gym is offering this new promotion:

An enrollment fee of $40 and a monthly fee of $30.

Let m be the total number of months

Total monthly fee = 30m

Total cost(including the enrollment fee of $40) = 40 + 30m

Let the total cost is c:

c = 40 + 30m

If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.

Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

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Step-by-step explanation:

25 as binary number is

11001

1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 1 = 25

25×2 = 50 = 11001 × 2 = 110010

multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.

and so, we see

110P = 110010

P = 010

FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.

so, the problem should have looked like

110P/10 = 11001

110P = 11001×10 = 110010

P = 010

Answer:

01

Step-by-step explanation:

From decimal to binary;

25/2==> 1 (remainder)

12/2===>0

6/2==>0

3/2===>1

1

=11001

Checking the answer;

11001

=1*2^4+1*2^3+0*2*2+0*1+1*2^0

=1*16+1*8+0+0+1*1

=16+8+0+0+2

=25

Answer:

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Step-by-step explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer:

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Step-by-step explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

[tex]5xy-3y+xy[/tex]

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

[tex](5x-3+x)y[/tex]

Simplify this expression to get

[tex](6x-3)y[/tex]

Now just plug the sqrt(2) back in as y and you get the expression

[tex](6x-3)\sqrt{2}[/tex]

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

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Answer:

50 ^^

Step-by-step explanation:

So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7

7x2=14

7x3=21

7x4=28

7x5=35

So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50

need more explaining tell me ^^

Using the normal distribution, we have that the desired information is given as follows:

a) X ~ N(3,1.8).

b) 3 days.

c) Z = 0.5556.

d) 0.33 = 33%.

e) 0.2048 = 20.48%.

f) 5.3 days.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 3, \sigma = 1.8[/tex]

Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.

The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:

Z = (4 - 3)/1.8 = 0.5556.

The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:

Z = (3.8 - 3)/1.8 = 0.44.

Z = 0.44 has a p-value of 0.67.

1 - 0.67 = 0.33.

The probability is of 0.33 = 33%.

The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:

X = 4.2:

Z = (4.2 - 3)/1.8

Z = 0.67.

Z = 0.67 has a p-value of 0.7486.

X = 3.2:

Z = (3.2 - 3)/1.8

Z = 0.11.

Z = 0.11 has a p-value of 0.5438.

0.7486 - 0.5438 = 0.2048 = 20.48%.

The 90th percentile is X when Z = 1.28, hence:

1.28 = (X - 3)/1.8

X - 3 = 1.8 x 1.28

X = 5.3 days.

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Answer:

See below

Step-by-step explanation:

x = largest

x-1   previous

x -2  smallest

sum =   x   +    x-1      +   x-2

sum = 3x -3    

Answer:

J

Step-by-step explanation:

Using the arrangements formula, it is found that:

a) There are 1365 possible outcomes that contain exactly four tails.

b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repetitions, the number of ways is given as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.

Item a:

11 heads and 4 tails, hence:

[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 possible outcomes that contain exactly four tails.

Item b:

The total number is:

[tex]A_{15} = 15! = 1,307,674,400,000[/tex]

With no heads:

[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]

With one head:

[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]

With two heads:

[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]

Hence the number of outcomes with less than three heads is:

1 + 15 + 95 = 111

With at least three heads, the number of outcomes is:

[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]

There are 1,307,674,399,889 possible outcomes that contain at least three heads.

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If they work together, they need 15/8 hours to assemble one shelving unit.

What does work mean in math?

According to tittle, we know worker A can  assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.

If A & B work together , they will spend the same time t to assemble only one shelving .

That means,                  1/5t + 1/3 t = 1                         (equation)

1/5 t is worker A's workload during time t , 1/3 t is worker B workload.

So,   1/5 t + 1/3t = 1  is the answer

     ⇒ 5t + 3t = 15

     ⇒ t = 15/8 hours

If they work together, they need 15/8 hours to assemble one shelving unit.

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Answer:

Letter C is the correct answer or  1/5 t + 1/3t = 1

Answer:Maria

Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.

Answer:

The answer is B, 2.78 hours

Step-by-step explanation:

Answer:

  6 hours 15 minutes, or 6.25 hours

Step-by-step explanation:

We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.

We know that 15 minutes is 1/4 hour, so the proportion can be written ...

  hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)

Multiplying by 250 pages gives ...

  book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour

It will take Hank 6 1/4 hours to read the book.

Answer:

330

Step-by-step explanation:

the change in hirght = 120 - 90 = 30

so 90 + (30 x 8)

= 90+240

= 330//

We can observe

Its a geometric progression having first term 9(3)=27 and common ratio as 1/3

So

The firmula is

Option C

Answer:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the graph, the given points are:

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

 [tex]a_n=ar^{n-1}[/tex]

where:

Rewrite the given points as terms of the sequence:

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

[tex]\implies a_2=9[/tex]

[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]

[tex]\implies \dfrac{1}{3}a=9[/tex]

[tex]\implies a=27[/tex]

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

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For the given functions, the domains are:

1) All real numbers.

2) D: x≥ -3

3) D: set of all real numbers such that x ≠ 0

4) D: 7 ≥ x ≥-7

5)  All real numbers.

For any function, we assume that the domain is the set of all real numbers, and then we remove all the values of x that generate problems (like a denominator equal to zero or something like that).

1) f(x) = x^2 - 4

This is just a quadratic equation, the domain is the set of all real numbers.

2) f(x) = √(x + 3)

Remember that the argument of a square root must be equal to or larger than zero, so here the domain is defined by:

x + 3 ≥ 0

x≥ -3

The domain is:

D: x ≥ -3

3) f(x) = 1/x

We can assume that the domain is the set of all real numbers, but, we can see that when x = 0 the denominator becomes zero, then we need to remove that value from the domain.

Thus, we conclude that the domain is:

D: set of all real numbers such that x ≠ 0

4) f(x) = √(49 - x^2)

Here we must have:

49 - x^2 ≥ 0

49 ≥ x^2

√49  ≥ x ≥-√49

7 ≥ x ≥-7

The domain of this function is:

D:  7 ≥ x ≥-7

5) f(x) = √(x^2 + 1)

Notice that x^2 is always a positive number, then the argument of the above square root is always positive, then the domain of that function is the set of all real numbers.

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Answer:

the triangle is a right angle triangle. I can't see the correct explanation here so I will explain

Step-by-step explanation:

to work out whether triangles are right angle you do :

square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled

i hope this helps . if you need any more help pls ask :)

Answer:

A. 175 m

B. 20 cm

Step-by-step explanation:

[tex]\frac{1 cm}{25 m} =\frac{7 cm}{x m}[/tex]

x = 175 m

[tex]\frac{25 m}{1 cm} = \frac{500 m}{x cm}[/tex]

x = 20 cm

Answer:

No1. 175 m

no2. 20 cm

Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

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Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:

The value of h is the same for all the shape so assume the value of h is 2 units.

The volume of a cylinder is:

= πr²h

First cylinder area:

= 22/7 x 3 x 2

= 56.54867 units

The second cylinder area:

= 22/7 x 6 x 2

= 226.19467 units

The volume of a cone is:

= πr²h/3

First cone volume:

= 22/7 x 3 x 2/3

= 18.84956 units

Second cone volume:

= 22/7 x 6 x 2/3

= 75.39822 units

The order is therefore:

Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units

In conclusion, the shapes with the larger radius of 6 units will have more volume.

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The step which contains the first error in calculation is: B. Step 2 - the sine ratio was applied incorrectly.

The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

Mathematically, the law of sines is given by this equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

For any right-angled triangle, the ratio of the length of its opposite sides to the length of its hypotenuse is generally referred to as sine ratio. Thus, sine ratio is given by this formula:

cos(θ) = Opp/Hyp

Where:

In this context, we can infer and logically deduce that the step which contains the first error in calculation is step 2:

sin(W) = y/XZ; XZsin(W) = y.

In conclusion, the correct step should have been written as follows:

sin(W) = XZ/y; ysin(W) = XZ.

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Answer:

step 2 is incorrect

Step-by-step explanation:

B. Step 2 - the sine ratio was applied incorrectly

Answer:

(a) k = 4
(b) y = - 2x + 9

Step-by-step explanation:

x2-x1, y2-y1  
= 3-2, 3-5

= 1,-2
3,3 + 1,-2 = (4,1)

x=4

Answer:

Step-by-step explanation:

[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]

[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]