A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the desert for vacation. How many individuals were surveyed in total? How many people are planning on going to the mountains for their vacation?

Answer:

(14, 6)

Step-by-step explanation:

If you plug in 6 for y you get:

6 = x/2 - 1

Add 1 to both sides:

7 = x/2

Multiply 2 on both sides:

14 = x

The answer is (14, 6)

Answer:

90 euros more

Step-by-step explanation:

Let the number be x

Then,let Ivan's share be 4x and Tanya's share be x

From the given scenario, the equation to represent this would be

4x+x=150 euros

Combine the like terms so that

5x=150 euros

Divide both sides by 5 and simplify

5x/5 and 150/5

so x=30

Ivan's share is 4 times the amount of Tanya's so

4*30=120 euros

So Tanya's share is x=30 euros

Therefore, Ivan gets 90 euros more than Tanya

Answer:

P(4)= 1/6

Step-by-step explanation:

Lots of Love!! <3

Stay Safe! Stay at Home!! =)

Answer:

Step-by-step explanation:

no of sample space, n(s) = 6

no of favorable cases , n(e) = 1

Probability of getting 4,

P(e) = n(e) / n(s)

       = 1 / 6

Answer:

28.26

Step-by-step explanation:

If you find the area by using the eqaution A=pi*raduis*2 you can then divide it by 4

Final answer:

To find the volume of a cylinder with a diameter of 10 inches and height of 8 inches, calculate the radius, then apply the volume formula V = πr²h. In this case, the volume is 628.32 cubic inches.

Explanation:

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height of the cylinder.

First, find the radius by dividing the diameter by 2: radius = diameter / 2 = 10 inches / 2 = 5 inches.

Next, substitute the values into the formula:  V = 3.142 × (5 inches)² × 8 inches = 628.32 cubic inches.

Answer:

Step-by-step explanation:

∠A + ∠B  = 90°  {given they are complementary}

5x+ 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45/5

x = 9

Answer: The mistake caused the perimeter to increase by 4 inches

The mistake caused the area to increase by 13 square inches

Step-by-step explanation: The original dimensions have been given as 5 inches by 7 inches. If this measurement had been correctly used, the perimeter was supposed to be;

Perimeter = 2(L + W)

Perimeter = 2(5 + 7)

Perimeter = 2(12)

Perimeter = 24 inches

Also the area was supposed to be;

Area = L x W

Area = 5 x 7

Area = 35 square inches

However, Sam accidentally printed a photo that is 6 inches by 8 inches, therefore the effect would be as follows;

Perimeter = 2(L + W)

Perimeter = 2(6 + 8)

Perimeter = 2(14)

Perimeter = 28 inches

And the Area would be

Area = L x W

Area = 6 x 8

Area = 48 square inches

From the calculations so far, the mistake would cause the perimeter to increase by 4 inches (28 inches - 24 inches).

Also the area would likewise increase by 13 inches (48 inches - 35 inches).

Answer:

It is translation

3

-5

in brackets

Answer:

We are 99% confident interval for the population proportion of passing test scores between ( 0.5987  and 0.9413 )

Step-by-step explanation:

Given -

n = 40

Population proportion = [tex]\widehat{(p)}[/tex] = [tex]77\%[/tex] = .77

1 - [tex]\widehat{(p)}[/tex] = 1 - .77 =.23

[tex]\alpha[/tex] = 1 - confidence interval = 1 - .99 = .01

[tex]z_{\frac{\alpha}{2}}[/tex] = [tex]z_{\frac{.01}{2}}[/tex] = 2.58

99% confidence interval for the population proportion of passing test scores=

[tex]\widehat{(p)}\pm z_{\frac{\alpha}{2}} \sqrt{\frac{\widehat{(p)} (1 - \widehat{p})}{n}}[/tex]

= [tex].77\pm z_{\frac{.01}{2}} \sqrt{\frac{{(.77)} (.23)}{40}}[/tex]

= [tex].77\pm 0.1713[/tex]

= [tex](.77 + 0.1713 , .77 - 0.1713)[/tex]

= ( 0.5987 , 0.9413 )

Answer:

54/3=18 so Brad is 18 and Corey is 36

36 + 18 = 54

Step-by-step explanation:

If Corey is 2 times older then you divide by that number which is 2 + 1 so you divide by 3.

Hope this helps can I have brainliest

Answer:

Step-by-step explanation:

hello :

the distance between (3,5.25 and (3,-8.75) is :

√((3-3)²+(5.25+8.75)²) ......continu

Answer:

979, 717

Step-by-step explanation:

Given:

The length of arc TS = 40 in

To find:

The length of arc RS.

Solution:

Length of TS = 40 in

θ = 80°

Using arc length formula:

[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]

[tex]$40=2 \times 3.14 \times {r}\left(\frac{80}{360}\right)[/tex]

[tex]$40=6.28 \times {r}\left(\frac{2}{9}\right)[/tex]

[tex]$40=1.39\times r[/tex]

Divide by 1.39 on both sides, we get

[tex]28.7=r[/tex]

Radius = 28.7

Complete angle of circle = 360°

Angle measure of RS = 360° - 60° - 120° - 80°

Angle measure of RS = 100°

Arc length of RS:

[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]

Substitute θ = 100° and r = 28.7

                 [tex]$=2 \times 3.14 \times 28.7 \left(\frac{100}{360}\right)[/tex]

                 = 50 inch

The length of arc Rs is 50 inches.

Answer:  ±7

Step-by-step explanation:

Solution of the expression are,

⇒ ± 7

Mathematical expression is defined as the collection of the number variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √ 49

Now, We can simplify as;

⇒ √49

⇒ √ 7 × 7

⇒ ± 7

Thus, Solution of the expression are,

⇒ ± 7

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Answer: 49929 years ago

Step-by-step explanation:

Radiocarbon dating is a method that provides objective age estimates for carbon-based materials that originated from living organisms

To calculate the time, we will use exponential formula

R% = e^ -kt

Where t = number of years

0.25/100 = e^- 0.00012t

Log both sides with natural logarithm

Ln0.0025 = lne^-0.00012t

-5.9915 = -0.00012t

t = 5.9915/0.00012

t = 49928.9 years

Approximately t = 49929 years

The whale died approximately 49,929 years ago.

To determine how long ago the whale died, we use the fact that its vertebrae contain roughly 0.25% as much carbon-14 as they originally did when the whale was alive. This suggests the carbon-14 has decayed, following its known decay rate.

The carbon-14 decay formula is:

N(t) = N0 × [tex]e^{-kt}[/tex]

where:

Given that N(t)/N0 = 0.0025, we solve for t:

1. Divide both sides by N0:

0.0025 = [tex]e^{(-0.00012 * t)}[/tex]

2. Take the natural logarithm of both sides:

ln(0.0025) = -0.00012 × t

3. Solve for t:

t = ln(0.0025) / -0.00012

t = −5.991464547/−0.00012

Calculating this, we get:

t ≈ 49928.87 ≈ 49,929 years

Therefore, the whale died approximately 49,929 years ago.

Answer:

The are of the spotlight is 14.4m

Step-by-step explanation:

Step one :

To find the area of the spotlight

First let us understand that the shape is a circle since it's a spotlight

Hence we will use the formula for area of a circle which is

A=πr²

Step two :

Given r= 7feet - - - >metre =2.14m

i.e

1foot =0.305m

7feet =xm

Crosss multiplying we have

X=7*0.305=2.14m

π= 3.142

Step three :

Substituting into the formula we have

A=3.412*2.14²

A=3.142*4.58

A=14.4m

Answer:

154 square feet

Step-by-step explanation:

Extracting the key information from the question:-

*** At school play, there's spotlight above centre of floor.

*** This covers a light end area with radius 7 feet.

*** We are required to calculate the area covered by the spotlight.

In other words, we are basically required to calculate the area of a circle because it is almost certain that the area it covers will be a perfect circle. So all we need to do is to put down the formula for calculating the area of a circle.

We already know that the radius here is 7 feet. We will now simply draft this into the formula and we are good to go.

Formula for area of a circle = πr^2. π = 22/7, r = radius = 7 feet.

Then 22/7 × 7 × 7

= 154 feet^2. The area that is covered by the spotlight which is a perfect circle = 154ft^2

The solution to the Quadratic equation [tex]x^2+4x-40=-8[/tex] is -8 & 4. correct option is C.

To solve the quadratic equation x^2+4x-40=-8 using the quadratic formula, we first need to rearrange the equation so that it is in the form [tex]ax^2+bx+c=0.[/tex]

So, the equation becomes [tex]x^2+4x-32=0.[/tex]

Now, we can identify the values of a, b, and c.

In this case, a=1, b=4, and c=-32.

Next, we can substitute these values into the quadratic formula: x = (-b±√([tex]b^2-4ac[/tex]))/(2a).

Using the formula, we can calculate the solutions for x.

After performing the calculations, we find that the solutions are x = -8 and x = 4.

Therefore, the correct answer is option c) -8 & 4.

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Answer:

$299.90

Step-by-step explanation:

Add the $34.56 back to the $265.34

Answer:

Step-by-step explanation:

Purplemath

To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:

Simplify a6 × a5

The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:

MathHelp.com

Simplifying Expressions on MathHelp.com

Simplifying Expressions

a6 × a5 = (a6)(a5)

= (aaaaaa)(aaaaa)

= aaaaaaaaaaa

= a11

Thus:

a6 × a5 = a11

Simplify the following expression:

\mathbf{\color{green}{\dfrac{6^8}{6^5}}}

6

5

6

8

​

The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.

\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}

6⋅6⋅6⋅6⋅6

6⋅6⋅6⋅6⋅6⋅6

​

How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:

= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=

1

6⋅6⋅6

​

=6

3

Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}

t

8

t

10

​

How many extra copies of t do I have, and where are they? I have two extra copies, on top:

\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}

t

8

t

10

​

=

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

​

= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=

1

t⋅t

​

=t

2

Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.

Content Continues Below

Simplify the following expression:

\mathbf{\color{green}{\dfrac{5^3}{5^9}}}

5

9

5

3

​

This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.

How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:

\dfrac{5^3}{5^9} = \dfrac{5 \cdot 5 \cdot 5}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}

5

9

5

3

​

=

5⋅5⋅5⋅5⋅5⋅5⋅5⋅5⋅5

5⋅5⋅5

​

= \dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} = \mathbf{\color{purple}{\dfrac{1}{5^6}}}=

5⋅5⋅5⋅5⋅5⋅5

1

​

=

5

6

1

​

Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for.

Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect.

Let's move on to expressions that are a bit more complex.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{5\mathit{x}^5}{3\mathit{x}^3}}}

3x

3

5x

5

​

I mustn't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers.

And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "\frac{5}{3}

3

5

​

" are not at all the same as the 5 and the 3 in rational expression "\frac{x^5}{x^3}

x

3

x

5

​

". The numerical portion \frac{5}{3}

3

5

​

 stays as it is.

For the variables, I have two extra copies of x on top, so the answer is:

\dfrac{5x^5}{3x^3} = \dfrac{5 \cdot x \cdot x \cdot x \cdot x \cdot x}{3 \cdot x \cdot x \cdot x}

3x

3

5x

5

​

=

3⋅x⋅x⋅x

5⋅x⋅x⋅x⋅x⋅x

​

= \dfrac{5 \cdot x \cdot x}{3}=

3

5⋅x⋅x

​

= \mathbf{\color{purple}{\dfrac{5\mathit{x}^2}{3} = \dfrac{5}{3}\mathit{x}^2}}=

3

5x

2

​

=

3

5

​

x

2

Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.

Simplify (–46x2y3z)0

This is simple enough: anything to the zero power is just 1.

(–46x2y3z)0 = 1

Simplify –(46x2y3z)0

The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:

–(46x2y3z)0 = –1

Final answer:

The expression using only positive exponents is [tex]1/k^3[/tex].

Explanation:

To simplify the expression [tex]k^0 * k^-3[/tex] and write it using , we need to apply the laws of exponents.

The expression can be broken down into two parts.

Therefore,

[tex]k^0 = 1[/tex] (anything raised to the power of 0 is 1).

[tex]k^-3 = 1/k^3[/tex] (negative exponent indicates reciprocal).

Therefore,

[tex]k^0 * k^-3[/tex] [tex]= 1 * 1/k^3[/tex]

[tex]= 1/k^3.[/tex]

Answer:

You mean that if we have two pairs of points, (x1, y1) and (x2, y2)

we can find the slope of the line that conects those two points as:

a = (y2 - y1)/(x2 - x1)

remember that a linear equation has the shape:

y(x) = a*x + b

Now let's prove it:

for our case we have that

y1 = a*x1 + b

y2 = a*x2 + b

we can isolate be in both equtaions and get:

b = y1 - a*x1

b = y2 - a*x2

this means that:

y1 - a*x1 = y2 - a*x2

then:

a*x2 - a*x1 = y2 - y1

a*(x2 - x1) = y2 - y1

a = (y2 - y1)/(x2 - x1)

Which is the thing we wanted to get.

The subtraction of y-values and x-values to find the slope of a line is based on measuring the rate of change of y (rise) per unit change in x (run). This concept is fundamental in determining and understanding the steepness of a line on a graph.

To understand why we subtract y-values and x-values to find the slope, let's look at the formula for the slope of a line, m = (y2 - y1) / (x2 - x1). Here, 'm' represents the slope of the line, the y values (y2 and y1) represent points on the vertical axis, and the x values (x2 and x1) represent points on the horizontal axis.

When we say 'slope', we mean how steep a line is. That steepness is determined by how much y changes (the rise) for a certain amount of change in x (the run). By subtracting y-values and x-values from each other, we are able to accurately measure this change, and therefore calculate the slope of the line.

Graphically, if we consider two points on a straight line, the slope of the line (m) can be seen as how much the line rises (the difference in y-values) for each unit it runs horizontally (the difference in x-values).

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Answer:

7.25h = e

If e = $166.75, h = 23 hours

Step-by-step explanation:

7.25h = e

However many hours he works, he'll earn 7.25 times that number.

If he wants to know how many hours he must work to get the video game system where e = 166.75, we model this with

7.25h = e

7.25h = 166.75

Divide both sides by 7.25.

h = 23 hours

Final answer:

Explanation of the equation relating hours worked to earnings and interpretation of variables.

Explanation:

Equation: e = 7.25h - 166.75

Explanation: The equation that models the relationship between the number of hours worked h and the amount earned e can be represented as e = 7.25h - 166.75. This equation captures the idea that Marvin earns $7.25 per hour and wants to buy a video game system costing $166.75.

Independent and dependent variables: Hours worked (h) is the independent variable, and the amount earned (e) is the dependent variable. The y-intercept is -166.75, and the slope is 7.25, indicating that for each additional hour worked, Marvin earns $7.25.

Answer:

-5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

wHy aM i hErE?!?!

d.

A full warranty will cover any repairs or replacement that the product needs, while a limited warranty will only pay for certain repairs.

A full warranty will cover all necessary repairs or replacements, whereas a limited warranty will only cover specific services. Option D is correct.

A full warranty guarantees the replacement of a damaged product. A comprehensive warranty will cover repairs no matter how many times the product breaks.

The difference between a full warranty and a limited warranty is that a full warranty will cover any repairs or replacements required by the product, but a limited warranty would only cover specified repairs.

Hence, option D is correct.

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Answer:

100 people

Step-by-step explanation:

The new population of the country at the end of the year considering all the conditions will remain at 100.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

As per the given,

The population of the country at the beginning of the year = 100 people.

10 immigrated → 100 + 10 = 110

20 emigrated → 110 - 20 = 90

Birth rate is 15 → 90 + 15 = 105

Death rate is 5 → 105 - 5 = 100

Hence "The new population of the country at the end of the year considering all the conditions will remain at 100".

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The man's age is 57 years old.

To find this answer follow the steps below:

1. Subtract 29 from 200 to get 171.

2. Divide 171 by 3 to get 57.

To check this, use the equation 200 - (57 x 3) = 29.

1. 57 x 3 = 171. 200 - 171 = 29

2. 200 - 171 = 29. 29 = 29.

Thus meaning the man is 57 years old. I hope this helps!

Answer:

57

Step-by-step explanation:

x=age

200-3x=29

x=57

Answer:

8 and 40

Step-by-step explanation:

Both area multiples of 8:

8, 16, 24, 32, 40

40 = 8 × 5

Since 5 is prime, it can only be:

8 and 40

Answer:

Option B.

Step-by-step explanation:

Consider the given geometric series is

[tex]S=20-5+\dfrac{5}{4}-\dfrac{5}{16}+...[/tex]

We need to find the sum of given series.

Here, first term is a=20 and common ratio is

[tex]r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex]

The sum of infinite GP is

[tex]S=\dfrac{a}{1-r}[/tex]

Substitute [tex]a=20\text{ and }r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex].

[tex]S=\dfrac{20}{1-(-\dfrac{1}{4})}[/tex]

[tex]S=\dfrac{20}{\dfrac{5}{4}}[/tex]

[tex]S=\dfrac{20\times 4}{5}[/tex]

[tex]S=16[/tex]

Therefore, the correct option is B.

Answer:

B edge

Step-by-step explanation:

To find out how many different possible ways the coach can choose 5 players from a team of 10, we calculate the combinations using the formula C(10, 5) which results in 252 different possible ways.

To find out how many different possible ways the coach can choose a team of 5 from 10 players, we use combinations. In mathematics, a combination is a selection of items from a larger set, where the order of selection does not matter. This is often denoted as C(n, k) or sometimes nCk, where n represents the total number of items to choose from, in this case, 10 players, and k is the number of items to choose, which here is 5 players.

The formula for a combination is:

C(n, k) = n! / (k!(n-k)!)

where ! denotes factorial, which is the product of all positive integers up to that number.

So for our specific question:

C(10, 5) = 10! / (5!(10-5)!) = 10! / (5!*5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252

Therefore, there are 252 different possible ways the coach can choose a team of 5 players from a pool of 10.

Answer:

4y^2 + 14y + 34

I hope this helps :)

Answer:

C

Step-by-step explanation:

Answer:

C is the correct answer

Step-by-step explanation:

In this question, we are tasked with calculating the angle at standard position which has a cosine value of 1/2

With reference to the cartesian coordinates, there are only two quadrants which has positive valued for Cosine. These are the first quadrant and the last or 4th quadrant. While the first quadrant has angles in the range of 0-90 the fourth quadrant has an angle range from 270-360

Now back to the angle. In the first quadrant, the angle that has cosine value equal to 30 is cos 60. This is same as pi/3 radians

Now the general form of the angle on the fourth quadrant is 360-theta

Thus, since our theta is pi/3, which is 60, that angle on the fourth quadrant having same value as 1/2 is 360-60 = 300

This is same as 5pi/3 radians

So our answers are pi/3 radians and 5pi/3 radians where pi radians is same as 180 degrees