You are working on a food budget for your family for the week. You know that you typically spend $90
at the grocery store, and you spend about $40
each time you go out to eat as a family.

Does the relationship between the number of times eating out and the total budget represent a linear function?

Answer:

1: 42

2: 42

Step-by-step explanation:

1: Subtract and plus the first equation using a calculator

2: Now subtract and plus the second equation using a calculator

Answers:

1: 42

2: 42

Hope this helps.

Answer:

hmmmmmm

Step-by-step explanation:

42 easyyyyyyyyyyyyyyyyyyyyyy tyyyyyb y u y y y y y y

When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

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A linear equation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

The answers are:

a) y = (-12 L/min)*t + 9,000 L

b) 6,840 L

a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am

We know that at 6:42 am  (at t = 42 mins) the tank has 8,496 liters.

And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.

Then we have two points of the line:

(42 mins, 8,496 liters)

(75 mins, 8,100 liters)

Then the slope is:

\(a = \frac{8,100 liters - 8,496 liters }{75 mins -42 mins } = -12 L/min\)

So the line will be something like:

y = (-12 L/min)*t + b

To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)

This means that if t = 75 mins, then we have y = 8,100 L

So we can replace these two on the above equation:

8,100 L = (-12 L/min)*75 mins + b

8,100L = -900L + b

8,100L + 900L = b = 9,000 L

Then the linear equation is:

y = (-12 L/min)*t + 9,000 L

b) Now we want to know how much water is in the tank at 9:00 am.

Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.

Then  9:00am is equivalent to t = 180 mins.

So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.

y = (-12 L/min)*180 mins + 9,000 L = 6,840 L

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The ball was in the air for 1.5 seconds. The answer is true.

The equation of the form ax² + bx +c is known as a quadratic equation.

The given equation is h(t) = -16t² + 20t + 6.

To find the time for which the ball was in the air, substitute h(t) =0.

0 = -16t² + 20t + 6

Use the quadratic formula to solve the equation:

\(t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}\)

t = (-20 + 28)/(-32) or t = (-20-28)/(-32)

t = -0.25 or t = 1.5

Since time cannot be negative, discard the negative value.

Hence, the ball was in the air for 1.5 seconds. The answer is true.

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Both sides of the equation simplify to a, and we can conclude that min(a, min(b, c)) = min(min(a, b), c) is true for all real numbers a, b, and c where a is the smallest.

One way to do this is through mathematical induction, which involves proving a statement for a specific set of values and then showing that it holds true for all other values. In this exercise, we will apply this method to prove two statements involving integers and real numbers.

Statement involving integers:

The given statement is n² + 1 ≥ 2n, where n is an integer in the range [1, 4]. In order to prove this statement, we need to verify it for all values of n in this range. We start with n = 1, which gives us 1² + 1 ≥ 2(1), or 2 ≥ 2. This is true, so we move on to n = 2, which gives us 2² + 1 ≥ 2(2), or 5 ≥ 4. This is also true. Continuing in this manner, we can verify that the statement is true for all values of n in the given range. Therefore, we can conclude that n² + 1 ≥ 2n is true for all integers in the range [1, 4].

Statement involving real numbers:

The given statement is min(a, min(b, c)) = min(min(a, b), c), where a, b, and c are real numbers and we assume that a is the smallest of the three. To prove this statement, we start with the left-hand side and simplify it using the assumption that a is the smallest real number:

min(a, min(b, c)) = min(a, b) if a ≤ b, otherwise min(a, b) = a

= min(min(a, b), c) if a ≤ min(a, b), otherwise min(min(a, b), c) = a

Next, we move on to the right-hand side of the equation and simplify it:

min(min(a, b), c) = min(a, c) if a ≤ c, otherwise min(a, c) = a

Since we assumed that a is the smallest real number, we know that a ≤ b and a ≤ c.

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The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is  21 square unit.

We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate

Equation of line passing through (0,5) and (2,-2) is

y-5 = [(-2-5)/(2-0)](x-0)

=>y-5 = (-7) /2x

=>y= (-7/2x)+5 -------(eq1)

Equation of line passing through (0,5) and (5,1) is

y-5 = [(1-5) / (5-0)](x-0)

=>y-5 = (-4/5)x

=>y = (-4/5)x+5-------(eq2)

Equation of line passing from (2,-2) and (5,1) is

y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)

=>y+2=(3/3)(x-2)

=>y=x-4--------(eq3)

Now, we use definite integration to find the area between the different equation of line.

So, area enclosed between the equations is given by the

area =\(\int\limits^5_2\)[(-4/5)x+5 - (-7/2)x + 5)dx  + \(\int\limits^5_1\)[(-4/5)x+5 -(x-4)]dx

=>area=\(\int\limits^5_2\)(7/2-4/5)x dx + \(\int\limits^5_1\)((-9/5)x+9)dx

Using properties of integration,\(\int\limits x\, dx=x^{2}/2\)

=>area=\(\int\limits^5_2\)(27/10)x dx + \(\int\limits^5_1\)(-9/5)x+9)dx

=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)

=>area=(27/20)×(25-4) + (-9/5)×24+9×4

=>area = (27×21)/20 + (-216)/5+ 36

=>area=(567/20) - (216/5) + 36

=>area= [(567-261×4)+(36×20)]/20

=>area=[(567-864)+720]/20

=>area=423/20

=>area=21 square unit.

Hence, area of triangle is 21 square unit.

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Answer:

2% loss

Step-by-step explanation:

Let the cost price be "x".

The current price is

x(1+40%)(1-30%)

= 1.4x*0.7

= 0.98x

Compared to x, 0.98x is 0.02 less

0.02 = 2%

The values of x is 6 and y is (-6).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

-4x-5y=6............(1)

9x+7y=12..................(2)

Solving Equation (1) and (2) we get

-36 x  - 45y = 54

36x + 28y = 48

____________

         -17y= 102

              y= -6.

and, -4x -5y= 6

-4x - 5(-6) = 6

-4x + 30 = 6

-4x = 6-30

-4x = -24

x= 6

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Answer:

0.8

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

consecutive even numbers are 2,4, 6...

Let the smallest of the 3 numbers be x.

2nd number= x+2

3rd number

=x+2+2

= x+4

sum of the 3 numbers= x +x+2 +x+4

114= 3x+6

3x= 114 -6 (-3 on both sides)

3x= 108 (simplify)

x= 108 ÷3

x= 36

Thus, the smallest number is 36.

Let's check!

36+38+40= 114 ✓

Answer:

A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.

B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.

C. The expected value of X is 6.75, and the standard deviation of X is 2.17.

Step-by-step explanation:

The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.

With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

\(P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.25^{k} 0.75^{25-k}\\\\\\\)

A. P(x=6)

\(P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.00024*0.00423=0.183\\\\\\\)

B. P(x≥10)

\(P(x\geq10)=1-P(x<10)=1-\sum_{i=0}^9P(x=i)\\\\\\\)

\(P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0.0008=0.0008\\\\\\P(x=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.25*0.001=0.0063\\\\\\P(x=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.0625*0.0013=0.0251\\\\\\P(x=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.0156*0.0018=0.0641\\\\\\P(x=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.0039*0.0024=0.1175\\\\\\P(x=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.001*0.0032=0.1645\\\\\\P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.0002*0.0042=0.1828\\\\\\\)

\(P(x=7) = \dbinom{25}{7} p^{7}(1-p)^{18}=480700*0.000061*0.005638=0.1654\\\\\\P(x=8) = \dbinom{25}{8} p^{8}(1-p)^{17}=1081575*0.000015*0.007517=0.1241\\\\\\P(x=9) = \dbinom{25}{9} p^{9}(1-p)^{16}=2042975*0.000004*0.010023=0.0781\\\\\\\)

\(P(x\geq10)=1-(0.0008+0.0063+0.0251+0.0641+0.1175+0.1645+0.1828+0.1654+0.1241+0.0781)\\\\P(x\geq10)=1-0.9287=0.0713\)

C. The expected value (mean) and standard deviation of this binomial distribution can be calculated as:

\(E(x)=\mu=n\cdot p=25\cdot 0.25=6.25\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot 0.25\cdot 0.75}=\sqrt{4.69}\approx2.17\)

Answer:

Domains are your x values and the range are your y values.

When listing your domain and range you do use brackets, and you list from least to greatest.

I personally would use an infinity sign but you can do both, and no you don't need brackets.

The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Answer:

\((g \cdot h)(x)=x^2-2x+23\)

Step-by-step explanation:

For composite functions, it's important to understand what the functions mean:

\((g\cdot h)(x)\)  which is read as "g of h, of x" means \(g ( \text{ }h(x) \text{ })\) which is read as "g of, h of x" (with slight pauses at the comma).  This means that x goes into the h function, and the output of the h function goes into the g function.

Putting "x" into the h function

\(h(x)=-x+4\)

Since it is just "x" going into the h function, the function as written is the output when x is the input.

Putting the h function output, into the g function

\(g(x)=x^2-6x+3\)

\(g(h(x))=(h(x))^2-6(h(x))+3\)

Substitute

\(g(h(x))=(-x+4)^2+-6(-x+4)+3\)

Squaring means the something multiplied by itself

\(g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3\)

Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):

\(g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3\)

Simplify the binomial terms:

\(g(h(x))=[x^2-8x+16]+[6x+4]+3\)

Group like terms:

\(g(h(x))=x^2-2x+23\)

Remember that \((g\cdot h)(x)\)  means \(g ( \text{ }h(x) \text{ })\)

\((g \cdot h)(x)=x^2-2x+23\)

So, \((g \cdot h)(x)=x^2-2x+23\)

Answer:

The answer should be like this;

a) A-B

b) BUC

c) C-A

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

By evaluating f(x) in x = 0 we will see that the value is 1, then we will get:

f²⁰²³(0) = 1²⁰²³ = 1

Remember that 1 is the identity of the multiplication, this means that any number times 1, is equal to the same number.

Then, for any real value n, we know that:

1ⁿ = 1

Now we have the function:

f(x) = 1/(1 + x²)

Evaluating in x = 0, we get:

f(0) = 1/(1 + 0²) = 1

Now we can apply the exponent n = 2023 we will get:

f²⁰²³(0) = 1²⁰²³ = 1

The answer is 1.

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Answer:

9.31st 91 35 5789 400th

Step-by-step explanation:

43.45+567=

9.3

Answer:

1.+25

2 -6

3 +6

4.

5. 0

Step-by-step explanation:

Sana Makatulong

Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

the given expression is,

g(x) = 2I f(2x + 1) I - 3

for g(2), we will put x = 2

g(2) = 2 I f(2(2) + 1) I - 3

= 2 I f(4 + 1 ) I - 3

= 2 I f(5) I - 3

as the value of f(5) is = -5 .......(Given)

put the value of f(5)

= 2 I-5I - 3

= 2(5) - 3

= 10 - 3

= 7

so,

g(2) = 7

thus, the value of g(2) is 7

Answer:

The distance traveled in one revolution is 282.6 cm.

Step-by-step explanation:

Diameter of wheel, d = 90 cm

The distance traveled by the wheel in one revolution is circumference.

The circumference of the wheel is

\(C = \pi\times d\\C =3.14\times 90\\C = 282.6cm\)

Answer:

(2x+5) (3x-7)

Step-by-step explanation:

(2x+5) (3x-7) is correct cause you multiply the two sides to get the answer

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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The answers are:

B. The graph of f(x) is shifted up 50 units

E. The graph of f(x) is shifted right 10 units

F. The graph of f(x) is reflected over the x-axis

The given function is f(x) = x²

This is an upward-facing vertical parabola.

The vertex is the smallest.

The vertex's origin is at (0, 0).

g(x) = –5x² + 100x – 450

This is an open downhill vertical parabola.

The vertex is the greatest

The first thing to notice is that fx) opens up whereas g(x) opens down, indicating that a reflection across the x-axis was used.

Find the g(x) vertex.

change the form to vertex

g(x) = –5x² + 100x – 450

Complete the square

g(x) = -5(x² - 20x) - 450

g(x) = -5(x² - 20x + 100) - 450 + 500

g(x) = -5(x² - 20x + 100) + 50

g(x) = -5( x - 10)² + 50

The vertex is located at (10, 50).

To the vertex from (0,0) to (10,50)

The translational principle is

(x,y) ------> (x+10,y+50)

This implies ----> The translation is 50 units up and 10 units to the right.

The adjustments are

The f(x) graph is moved forward by 50 units.

The f(x) graph is 10 units to the right.

Over the x-axis is a reflection of the f(x) graph.

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The complete question is,

Which transformations have been applied to the graph of f(x) = x² to produce the graph of g(x) = –5x² + 100x – 450? Check all that apply.

A.The graph of f(x) = x² is shifted up 25 units.

B.The graph of f(x) = x² is shifted up 50 units.

C.The graph of f(x) = x² is shifted down 950 units.

D.The graph of f(x) = x² is shifted left 10 units.

E.The graph of f(x) = x² is shifted right 10 units.

F.The graph of f(x) = x² is reflected over the x-axis.

Answer:

Step-by-step explanation:

Given function:

As any square root function, its range is all non-negative numbers:

The domain the x values when the expression under root is non-negative:

or

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats