Find the domain and range of this function.

Answer:

[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]

Step-by-step explanation:

Given

[tex]n=10[/tex]

[tex]Mean = 72[/tex]

[tex]Median = 74[/tex]

[tex]Mode = 68[/tex]

[tex]Range = 21[/tex]

Required

The complete dataset

The question has missing options (available online)

From the mean, we have:

[tex]Mean = \frac{\sum x}{n}[/tex]

This gives:

[tex]72 = \frac{\sum x}{10}[/tex]

Cross  multiply

[tex]\sum x = 72 * 10[/tex]

[tex]\sum x = 720[/tex]

This means that the sum of all elements of the dataset is 720

Next, we test the median

Since n = 10, then:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{10 + 1}{2}[/tex]

[tex]Median = \frac{11}{2}[/tex]

[tex]Median = 5.5th[/tex]

This implies that the median is the average of the 5th and 6th item.

So, we have:

[tex]Median = \frac{5th + 6th}{2}[/tex]

Cross multiply

[tex]5th + 6th = 2 * Median[/tex]

[tex]5th + 6th = 2 * 74[/tex]

[tex]5th + 6th = 148[/tex]

This means that the 5th and 6th element add up to 148

Also, we have:

[tex]Mode = 68[/tex]

This means that 68 has to appear at least twice in the dataset

[tex]Range = 21[/tex]

This implies that the difference between the highest and the least is 21.

The dataset that satisfies the above condition is:

[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]

Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

[tex]n=(x+5)\times 10+x\times 1[/tex]

[tex]n=10x+50+x[/tex]

[tex]n=11x+50[/tex]

Reversed number is:

[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]

[tex]x\times 10+(x+5)\times 1=11x+5[/tex]

If you subtract double the reversed number from it, the result is a fourth of the original number.

[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]

[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]

[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]

Multiply both sides by 4.

[tex]160-44x=11x+50[/tex]

[tex]160-50=11x+44x[/tex]

[tex]110=55x[/tex]

Divide both sides by 55.

[tex]\dfrac{110}{55}=x[/tex]

[tex]2=x[/tex]

The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].

Therefore, the original number is 72.

Answer:

4/3

Step-by-step explanation:

Since this is a right triangle,

tan C = opp side / adjacent side

tan C = 36/ 27

tan C = 4/3

Given set:- x - 7 > - 2

Solving It:-

x - 7 > - 2

x > -2 + 7 [Here '7' is greater than '-2' So Sign Changes To Positive]

x > 5

So Correct Solution Set Will Be

Option C= {x | x R, x > 5}

Answer:

x = 3 y y = 2

Step-by-step explanation:

a) Metodo de reduccion:

Para aplicar este metodo debemos multiplcar por 3 la ecuacion 2 y sumarlas.

[tex]4x-3y=6[/tex]

[tex]5x+y=17[/tex] *3

[tex]4x-3y=6[/tex]

[tex]15x+3y=51[/tex]

-------sumamos las ecuacioens--------

[tex]19x=57[/tex]

[tex]x=3[/tex]

Ahora, remplazamos x en la ecuacion 2.

[tex]5(3)+y=17[/tex]

[tex]y=2[/tex]

b) Igualacion

Debemos despejar x en ambas y luego igualarlas

[tex]x=\frac{6+3y}{4}[/tex]

[tex]x=\frac{17-y}{5}[/tex]

Igualando:

[tex]\frac{6+3y}{4}=\frac{17-y}{5}[/tex]

[tex]5(6+3y)=4(17-y)[/tex]

[tex]19y=8[/tex]

[tex]y=2[/tex]

Ahora, remplazamos y en la ecuacion 2.

[tex]5x+2=17[/tex]

[tex]5x=15[/tex]

[tex]x=3[/tex]

c) Sustitucion

Despejamos x de la primero ecuacion y lo remplazamos en dos.

[tex]x=\frac{6+3y}{4}[/tex]

[tex]5\frac{(6+3y)}{4}+y=17[/tex]

Multiplicamos por 4

[tex]5(6+3y)+4y=68[/tex]

[tex]30+15y+4y=68[/tex]

[tex]30+19y=68[/tex]      

[tex]19y=38[/tex]  

[tex]y=2[/tex]  

Remplazando en 1.

[tex]4x-3(2)=6[/tex]

[tex]4x-6=6[/tex]

[tex]4x=12[/tex]

[tex]x=3[/tex]          

Step-by-step explanation:

What traumatic stressors have you faced in your life? What chronic stressors have you faced or do you currently face? What coping strategies and lifestyle choices do you employ to respond to such stressors?

Answer:

730.88

Step-by-step explanation:

Area of the entire circle = pi * r^2

r = 16

Area = 3.14 * 16^2

Area = 803.84

1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84

Area of 1/4 circle =

200.96

the area of the triangle

Area = 1/2 AG * G?

AG and G? are equal

Area = 1/2 * 16^2

Area = 128

Area of 1/4 circle - area of the triangle = area of the shaded portion

shaded portion = 200.95 - 128

Shaded Portion = 72.96

So the area of the unshaded part

unshaded = 803.84 - 72.96

Unshaded = 730.88

Answer:

1. (3^3 + 3^2)^2 actually equals (27 + 9)^2

which is the first mistake

2. (27 + 9)^2 does not equal (3^5)2, so (36)^2 does not equal 3^7

3. 3^7 DOES NOT EQUAL 21

Step-by-step explanation:

when you add powered numbers together, it does not multiply it, as your example:

1. (3^3 + 3^2)^2 actually equals (27 + 9)^2

which is the first mistake

2. (27 + 9)^2 does not equal (3^5)2, so (36)^2 does not equal 3^7

3. 3^7 DOES NOT EQUAL 21

Hi there!

Error 1

[tex](3^3+3^2)^2\\= (3^5)^2[/tex]

The student added the exponents of 3³ and 3² and wrote 3⁵. This rule can only be applied to exponents with the same base that are being multiplied. 3³ and 3² were being added, not multiplied, so this rule can't be applied.

Error 2

[tex](3^5)^2\\= 3^7[/tex]

When a power has a power, we multiply them, not add. Here is the correct way of doing it:

[tex](3^5)^2\\= 3^5^*^2\\= 3^1^0[/tex]

Error 3

[tex]3^7\\= 21[/tex]

The student multiplied 3 and 7 to get 21, but 3⁷ actually means 3 multiplied by itself 7 times. The correct answer for this part would be 2187.

I hope this helps!

Answer:

We have 197 g of Co-60 after 18 months.

Step-by-step explanation:

We can use the decay equation.

[tex]M_{f}=M_{i}e^{-\lambda t}[/tex]

Where:

[tex]M_{f}=228e^{-\frac{ln(2)}{7} 1.5}[/tex]    

[tex]M_{f}=197\: g[/tex]    

Therefore, we have 197 g of Co-60 after 18 months.

I hope it helps you!

Answer:

-1

Step-by-step explanation:

are you sure this is the right equation ? it would mean that the more toppings the cheaper the ice cream.

but as it is written, the slope is -1.

the slope of a line is always the factor of the variable in the equation.

it is the ratio of y/x indicating how many units y is changing for a given change of x.

in our example here, if x changes 1 unit to the right (+1), then y changes 1 unit down (-1).

so, -1/+1 = -1

The slope of the function f(t) = 3 - t is -1

"It defines a relation between input and output values."

"It is the rate of change of the dependent variable of the function with respect to that of the independent variable."

For given question,

We have been given a function f(t) = 3 - t

We need to find the slope of the function.

[tex]m=\frac{d}{dt}f(t)\\\\ m=\frac{d}{dt}( 3 - t)\\\\m=-1[/tex]

Therefore, the slope of the function f(t) = 3 - t is -1

Learn more about the slope of the function here:

https://brainly.com/question/9554035

#SPJ2

Answer:

6

Step-by-step explanation:

I think I just answered that question.

"image" 7 means the functional result is 7, and we need to find the value of x to make this happen.

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

Answer:

x = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(1) + 12(x + 3) - 6(x - 5) = 4(12) + 4(x)

Step 2: Solve for x

Answer:

below

Step-by-step explanation:

that is the procedure above

The factorized form of x² + 6x + 5 - 4y - y² is:(x + 1)(x + 5) - (4y + y²)

To factorize the expression x² + 6x + 5 - 4y - y², group the terms and factor them separately.

Rearranging the terms

(x² + 6x + 5) - (4y + y²)

Now let's factor each group separately:

1. Factoring x² + 6x + 5:

The quadratic expression x² + 6x + 5 can be factored into two binomial factors. We look for two numbers that multiply to give 5 and add up to 6 .

These numbers are 1 and 5:

(x + 1)(x + 5)

2. Factoring -4y - y²:

The terms -4y - y² have a common factor of -1.

Factoring out -1 gives

-1(4y + y²)

Combining the factorization of both groups

(x + 1)(x + 5) - 1(4y + y²)

Therefore, the factorized form is (x + 1)(x + 5) - (4y + y²).

Learn more about Factorization here:

https://brainly.com/question/31379856

#SPJ4

Answer:

x=10  x=-2

Step-by-step explanation:

(x − 3)(x − 5) = 35

FOIL

x^2 -5x-3x+15 = 35

Combine like terms

x^2 -8x+15 = 35

Subtract 35 from each side

x^2 -8x+15-35 = 35-35

x^2 -8x-20 =0

Factor

What 2 numbers multiply to -20 and add to -8

-10*2 = -20

-10 +2 = -8

(x-10)(x+2) =0

Using the zero product property

x-10 =0  x+2 = 0

x=10  x=-2

Answer:

200

Step-by-step explanation:

Answer:

Step-by-step explanation:

25/5 ÷ 1/4 =

25/5 * 4 = 100/5 = 20

~~~~~~~~~~~~~~~~

2/5 ÷ 1/4 =

5/2 * 4 = 20/4 = 5  

Answer: 5?

Step-by-step explanation: 25/5 ÷ 1/4 =

25/5 * 4 = 100/5 = 20

2/5 ÷ 1/4 =

5/2 * 4 = 20/4 = 5  

Answer:

y=4x-7

Step-by-step explanation:

here,

the equation of straight line in slope intercept form is;

y=mx+c

( m= slope

c= y-intercept )

soo..

the question has asked for slope 4 i.e. m=4

and y- intercept -7 i.e. c= -7

now.

the required equation is

y= 4x-7

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Answer:

[tex]\frac{16}{45}x-\frac{11}{12}[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]

We have to find the equivalent expression.

[tex]\frac{2}{5}(\frac{1}{3}x-\frac{15}{8})-\frac{1}{3}(\frac{1}{2}-\frac{2}{3}x)[/tex]

[tex]\frac{2}{5}\times \frac{1}{3}x-\frac{2}{5}\times \frac{15}{8}-\frac{1}{3}\times \frac{1}{2}-\frac{1}{3}\times (-\frac{2}{3}x)[/tex]

Using the the property

[tex]a\cdot (c-b)=a\cdot c-a\cdot b[/tex]

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]

[tex]=\frac{2}{15}x-\frac{3}{4}-\frac{1}{6}+\frac{2}{9}x[/tex]

[tex]=\frac{6x+10x}{45}+\frac{-9-2}{12}[/tex]

[tex]=\frac{16}{45}x-\frac{11}{12}[/tex]

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)=\frac{16}{45}x-\frac{11}{12}[/tex]

Answer:

7x - 3

Step-by-step explanation:

3x+(4x-3)

Remove parenthesis

3x + 4x - 3

Combine like terms

3x + 4x = 7x

7x - 3

Answer:

7x-3

Step-by-step explanation:

Removing the parantheses, we get 3x+4x-3. Adding like terms we get 7x-3.

7x-3.

Answer:

angle c = 32.204°

the value of a is 32°.

Answer:

Solution given:

2a+10=74

Subtract both side by 10

2a+10-10=74-10

2a=64

divide both side by 2

2a/2=64/2

a=32°

Answer:

a = 32

Step-by-step explanation:

2a + 10 = 74.

We have to find the value of a.

Let's begin.

Step 1 :- Move constant to the right-hand side and change their sign.

Step 2 :- Subtract 10 from 74.

Step 3 :- Divide both side by 2.

Step 4 :- Reduce the fractions.

Answer:

d

Step-by-step explanation:

alr, 15 fruits total, 6 are apples.

6/15 = 2/5

2/5 is also the same as 40% or 0.4, therefore the option is d.

go to gauthmath's sub reddit if needing more help ^^

Answer:

- 34u^2

Step-by-step explanation:

8u^2 - 42u^2

= ( 8 - 42 )u^2

= - 34u^2

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{The only thing we can do to solve for this equation is to COMBINE}\\\large\textsf{the LIKE TERMS. }[/tex]

[tex]\mathsf{8u^2 - 42u^2}\\\mathsf{= (8u^2- 42u^2)}\\\mathsf{= 8 - 42 \rightarrow \bf -34}\\\textsf{Thus this means }\mathsf{8u^2 - 42u^2}\textsf{ has to equal to }\mathsf{ \bf -34u^2}\\\\\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \bf-34u} \mathsf{\bf ^2}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

to add on to what the other dude said its 4

Step-by-step explanation:

Answer:

D H and E i think .........

Answer:

It's A.)

Step-by-step explanation:

Answer:

multiply them

Step-by-step explanation:

trust me on this one i love using that hack

Answer:

Step-by-step explanation:

I think it is C