A restaurant noted what type of food its customers purchased last week. Here are the results:

Burger

Fries

15%

55%

10%

20%

In this sample, are the events "burger" and "fries" mutually exclusive?

Final answer:

To find two consecutive odd integers where the sum of the smaller integer and twice the larger is 43, we use the equation n + 2(n + 2) = 43, which simplifies to n = 13, identifying the smaller integer as 13.

Explanation:

The student is asking for an equation to solve for two consecutive odd integers such that when the smaller is added to twice the larger, their sum is equal to 43. Let's define the smaller integer as n, and since they are consecutive odd integers, the next integer would be n + 2. The equation that represents this situation is:

n + 2(n + 2) = 43

This equation can be simplified:

n + 2n + 4 = 43

Combining like terms, we get:

3n + 4 = 43

To solve for n, subtract 4 from both sides:

3n = 39

Then, divide by 3:

n = 13

Therefore, the smaller integer is 13.

Answer:

3293 ft to nearest tenth = side

Step-by-step explanation:

To find altitude this is the same in trigonometry as finding the side and we use calculation below in finding the hypotenuse which is same term as side for the angle of depression just to double check that height (altitude is less than slope in calculation).

sin (32) = 0.9271838546

3600/0.9271838546 = 3882.725074

= 3883 ft to nearest tenth. = slope

Then cos (32)x3882.725074 = 3292.737608

= 3293 ft to nearest tenth = side

The plane flying with an angle of depression of 32 degrees to a small fire below has an altitude of 2250 ft.

The situation forms a right angle triangle.

A right angle triangle has one of its angles as 90 degrees. The sides can be found using trigonometric ratios.

Therefore, the horizontal distance from the kurt's plane to the fire is the adjacent side of the right triangle.

The altitude of the plane is the opposite side of the triangle.

Hence,

tan 32 = opposite / adjacent

tan 32° = h / 3600

cross multiply

h = 3600 tan 32°

h = 3600 × 0.6248693519

h = 2249.52966687

h = 2250 ft

Therefore, the approximate altitude of the plane is 2250 ft.

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I think this is the answer + working out

x= Tori's age

y= her grandmother's age

x+y=72

5x=y

5x-y=0

x+y=72

+(5x-y=0)

6x=72

72 divided by 6=

x=12

So Tori is 12...

We substitute 12 for x into the first equation...

12+y=72

Bring 12 to the other side

y=72-12

y=60

Her grandmother is 60 and Tori is 12.

Answer:

x = 2 and x = -2

Step-by-step explanation:

The quadratic formula of a quadratic of the form ax² + bx + c is:

x = [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or x = [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Here, our equation is: 3x² - 18 = -6. Let's move all the terms to one side:

3x² - 12 = 0

a = 3 and c = -12. Notice that since there's no x term, b = 0.

Plug these into the quadratic formula:

x = [tex]\frac{0+\sqrt{0^2-4*3*(-12)} }{2*3}=\frac{\sqrt{144} }{6}=12/6=2[/tex]  

or

x = [tex]\frac{0-\sqrt{0^2-4*3*(-12)} }{2*3}=\frac{-\sqrt{144} }{6}=-12/6=-2[/tex]

So, x = 2 and x = -2.

Answer: x = -2, x = 2

Step-by-step explanation:

The quadratic formula:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\AND\\\\x = \frac{-b-\sqrt{b^2-4ac} }{2a} \\[/tex]

You can find the variables a, b, and c in the standard form of a quadratic equation:

[tex]f(x)=ax^2 + bx+c[/tex]

Your equation:

[tex]f(x)=3x^2 + 0x -12[/tex]

The variables are:

a = 3

b = 0

c = -12

Substitute those for the variables in the quadratic formula:

[tex]x=\frac{-0+\sqrt{0-(4*3*-12)}}{2(3)} \\\\AND\\\\x=\frac{-0-\sqrt{0-(4*3*-12)}}{2(3)} \\[/tex]

You can simplify this to get:

[tex]x=\frac{-\sqrt{144}}{6} \\[/tex]

(or positive square root of 144.)

The square root of 144 is 12, and 12/6 = 2.

The x-values are -2 and 2.

the answer is 24in its easy

Answer:

24"

Step-by-step explanation:

Volume= length*width*height

4*3= 12

12*2= 24

Final answer:

To find the volume of a gift box, multiply its length, width, and height. For a box with dimensions 4x3x2 inches, the volume is 24 cubic inches.

Explanation:

Volume formula: Volume = length x width x height

Given dimensions: Length = 4 inches, Width = 3 inches, Height = 2 inches

Calculation: Volume = 4 inches x 3 inches x 2 inches = 24 cubic inches

Answer:

225% increase

Step-by-step explanation:

Since the number went up from 24 to 78 this is an increase

To find out how much

(78- 24)/24 =2.25 * 100% =225% increase

The percent of change from 24 songs to 78 songs is a 225% increase.

To identify the percent of change from 24 songs to 78 songs, follow these steps:

Therefore, the percent of change from 24 songs to 78 songs is a 225% increase.

Answer:

1,5/5=279,3

Step-by-step explanation:

Answer:

It is an arithmetic sequence.

Step-by-step explanation:

64 - 7 = 57

121 - 64 = 57

178 - 121 = 57

We have a common difference of 57, so it is arithmetic.

The explicit formula for the nth term

= 7  +57(n - 1).

Answer:

B y = − 3 ( x + 1 ) ^2 + 8

Step-by-step explanation:

Hope it helps.

Answer:

╱▔▔▔▔▔▔▔▔▔▔▔▏  

┈╱╭▏╮╭┻┻╮╭┻┻╮╭▏  

▕╮╰▏╯┃╭╮┃┃╭╮┃╰▏  

▕╯┈▏┈┗┻┻┛┗┻┻┻╮▏  

▕╭╮▏╮┈┈┈┈┏━━━╯▏

▕╰╯▏╯╰┳┳┳┳┳┳╯╭▏  

▕┈╭▏╭╮┃┗┛┗┛┃┈╰▏  

▕┈╰▏╰╯╰━━━━╯┈┈▏

Step-by-step explanation:

Answer:

a) 1.892a

b.) 5.1x - 1.49y

1.) X = 0.36

2.) Y = 4.347

Car B went faster by 1.25 times

Step-by-step explanation:

a)2.15a+0.03∙(3.4a−12a)

Open the bracket

2.15a + 0.102a - 0.36a

2.252a - 0.36a

1.892a

b)3.27x+1.28y+1.83x−2.77y

Rearranged the algebraic expression above

3.27x + 1.83x + 1.28y - 2.77y

5.1x - 1.49y

1)22.5x−4.6=3.5

Collect the like term

22.5x = 8.1

X = 0.36

2)y÷2.3+5.69=7.58

Y/2.3 = 7.58 - 5.69

Y = 2.3 × 1.89

Y = 4.347

WORD PROBLEM: Car A went 60 km in 5/6 hours while car B went 54 km in 2/3 hours.

Which car was faster?

That's speed

Speed = distance/time

Speed A = 60 ÷ 5/6 = 72 km/h

Speed B = 54 ÷ 2/3 = 81 km/h

How many times faster? 

5/6 ÷2/3

5/6 × 3/2

15/12

1.25 seconds faster

Answer:

5 power 2 is the answer

Step-by-step explanation:

Answer:

c

or

P (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25)

Step-by-step explanation:

Step-by-step explanation:

The equation of the given graph for the function g(x) is [tex]f(x) = x^4 - x^2 -2[/tex]. so option D is correct. The graph of f(x) is shifted down by a factor of 2 on the y-axis.

The given graph  [tex]f(x)=x^4 -x^2[/tex] is shifted downwards on the y-axis.

And named g(x)

The shift in the y-axis is by 2 units

So,

g(x) = f(x) - 2

      = [tex]x^4-x^2-2[/tex]

Therefore, the equation of the given graph when shifted is [tex]g(x)=x^4-x^2-2[/tex]

Learn more about transformations on graphs here:

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Answer:

Rational

Step-by-step explanation:

2.2360679.  A rational number is a number that terminate or can be written as a fraction.  In this case, the number can be written as 22,360,679/10,000,000.  

The number 2.2360679 is a rational number because it can be expressed as the fraction 22360679/10000000. Rational numbers can be written as fractions with integer numerators and denominators (where the denominator is not zero) or terminates.

The number 2.2360679 is a rational number. A rational number can be expressed as a fraction, where both numerator and denominator are integers and the denominator is not zero. In this case, 2.2360679 can be written as an approximate fraction rounded to seven decimal places: 22360679/10000000.

On the other hand, an irrational number cannot be expressed as an integer fraction. It continues indefinitely without repeating, such as the number pi. Therefore, 2.2360679 is not an irrational number as it doesn't meet this criterion.

Learn more about Rational here:

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Answer:

2 books per month.

Step-by-step explanation:

For this, you will simply need to divide the total number of books by the amount of months.

10÷5= 2 books per month.

Natalie read two books for five months.

Divide.

Ten books divided by 5 months.

Find the answer. You get 2.

10 ÷ 5 = 2.

So, her rate of reading books per month was 2.

Hope this helps!

Answer:

26% of people from city B work less than 20 hours

Answer:

26%

Step-by-step explanation:

Look at the row for city B, first column is for "less than 20"

Answer:

a) 1/32 = 0.0313

b) 21.2058 cm

c) 19.635 ft2

Step-by-step explanation:

We have a total of 8 different areas in the circle.

a) The yellow area are 2 parts of a total of 8, so the probability is 2/8 = 1/4

The number 4 is one area of a total of 8, so the probability is 1/8

So the probability of landing on a yellow and then a 4 is (1/4)*(1/8) = 1/32 = 0.0313

b) The blue area is 3 parts over 8, so we can solve this using rule of three:

Total circunference -> pi*d = 18pi cm

3/8 of the circunference -> x

x = (3/8) * 18pi = 21.2058 cm

c) The purple sections are 2 parts over 8, so following the same logic as letter b), we have:

Total area -> pi*r^2 = 25pi ft2

2/8 of the area -> x

x = (2/8) * 25pi = 19.635 ft2

Answer:

10

1 + 100 = 101

101 is between 10 and 11

10.04987

Step-by-step explanation:

Answer:

-2034

Step-by-step explanation:

make me brainliest please

The rate of appreciation of the ring is approximately 6.52% per year.

How to find the rate of appreciation

We shall use the formula for simple interest to find the rate of appreciation:

Rate of appreciation = (Final value - Initial value / Initial value * Number of years) * 100

Given:

Final value = $1875

Initial value = $750

Number of years = 2024 - 2001 = 23 years

Let us plug the values into the formula:

Rate of appreciation = ($1875 - $750 / $750 * 23) *100

Rate of appreciation = $1,125/1,7250 * 100

Rate of appreciation ≈ 0.0652 * 100

Rate of appreciation ≈ 6.52%

Hence, the rate of appreciation of the ring is ≈ 6.52% per year.

The rate of appreciation is 150%.

To find the rate of appreciation, we'll use the formula for simple interest:

[tex]\[ \text{Simple Interest} = \frac{{\text{Final Value} - \text{Initial Value}}}{{\text{Initial Value}}}\times 100 \][/tex]

Given:

Initial value (purchase price) = $750

Final value (appraised price) = $1875

Substitute these values into the formula:

[tex]\[ \text{Simple Interest} = \frac{{1875 - 750}}{{750}} \times 100 \][/tex]

[tex]\[ = \frac{{1125}}{{750}} \times 100 \][/tex]

[tex]\[ = 1.5 \times 100 \][/tex]

[tex]\[ = 150\% \][/tex]

So, the rate of appreciation is 150%.

Answer:

20%

Step-by-step explanation:

If you want to buy the car again, it means that they are satisfied. 700/3500=7/35=1/5

1/5=20%.

20% of the people were satisfied.

Answer:

x

y

−

2

2

−

1

0.5

0

0

1

0.5

2

2

Step-by-step explanation:

Answer:

If the value of x increases by 1, the value of y will double.

Step-by-step explanation:

i just took the thingy

Answer:

9cm3

Step-by-step explanation:

6 x 4 x 3/8=9cm3

Answer:

9 cm³

Step-by-step explanation:

V = l x w x h

= 6 x 4 x 3/8

= 24 x 3/8

= 9 cm³

Step-by-step explanation:

[tex]300 = 3 \times {10}^{2} \\ 47300 = 4.73 \times {10}^{4} \\ 24 = 2.4 \times {10}^{1} \\ 14565 = 1.4565 \times {10}^{4} \\ 7001 = 7.001 \times {10}^{3} \\ 19050000 = 1.905 \times {10}^{7} \\ [/tex]

Answer: StartFraction n Over 4 EndFraction minus 9 + 3

n/4-9 +3

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given.

The quotient of a number means the result of the division of 2 numbers.

In this case the numbers are: a number (n) and 4 . n/4

Nine less than that quotient means we have to subtract 9 to the quotient.

n/4-9

Increase by three: we simply have to add 3

n/4-9 +3

Feel free to ask for more if needed or if you did not understand something.

Answer:

n/4-9 +3

Step-by-step explanation:

2020-2021 edge

Answer:

D) y=x, x-axis, y=x, y-axis.

Step-by-step explanation:

hope it helps :3

We have been given that in triangle RST, angle S is marked as a right angle. Side RT is labeled as 40 centimeters. Side ST is labeled as 30 centimeters. We are asked to find the measure of angle R.

First of all, we will draw a right triangle using our given information as shown in the attachment.    

We can see that RT is hypotenuse and St is opposite side to angle R. We know that sine relates opposite side to hypotenuse of right triangle.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(\angle R)=\frac{ST}{RT}[/tex]

[tex]\text{sin}(\angle R)=\frac{30}{40}[/tex]

[tex]\text{sin}(\angle R)=\frac{3}{4}[/tex]

Now, we will use arcsin to solve for angle R as:

[tex]\angle R=\text{sin}^{-1}(\frac{3}{4})[/tex]

[tex]\angle R=48.59037789[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]\angle R\approx 48.59[/tex]

Therefore, the measure of angle R is approximately 48.59 degrees.

Answer:

48.59

Step-by-step explanation:

Just took the test!!