What is the domain of this function?
f(x) = ²x - 3| + 1 ?

Approximately 795 newborn babies (88.3% of the 900 newborn babies) would be expected to weigh less than 7 pounds.

1. Approximately 728 newborn babies (81.3% of the 900 newborn babies) would be expected to weigh between 3 and 8 pounds.

2. Approximately 795 newborn babies (88.3% of the 900 newborn babies) would be expected to weigh less than 7 pounds.

3. Approximately 450 newborn babies (50% of the 900 newborn babies) would be expected to weigh more than 6 pounds.

4. Approximately 645 newborn babies (71.7% of the 900 newborn babies) would be expected to weigh between 6.6 and 9 pounds.

• Between 3 and 8 pounds: 0.6826*900 = 613.4 + 0.95*900 = 814.5 = 728

• Less than 7 pounds: 0.9545*900 = 859.05 = 795

• More than 6 pounds: 0.5*900 = 450

• Between 6.6 and 9 pounds: 0.6826*900 = 613.4 + 0.3413*900 = 306.17 = 64

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im gussing you mean 5x+10=7x-6

if so

5x+10=7x-6

  -5x = -5x

     10=2x-6

     +6=+6

     16=2x

     /2=/2

      8=x

The value of x = 8

here, 5x+10 is the 1st Equation

and 7x-6 is the 2nd Equation

We have to form an equation

        5x+10=7x-6

To solve for x, we need to isolate it on one side of the equation. To do this, we need to use inverse operations.

put the variable term on one side and the numerical term on the other side of the equal to sign, and while doing this change the sign from

             plus with minus and vice versa

             multiply with divide and vice versa

5x+10=7x-6

5x-7x=10+6

2x=16

x=[tex]\frac{16}{2}[/tex]

x=8

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a. The solution to the equation 1/3(5x - 9) = 2(1/3x + 6) is x = 15.

b. The solution to the 4(3x + 5) - 3 = 9x - 7 is x = -8.

c. The solution to the equation 5(x + 7) - 3(x - 4) = 7x + 2 is 9

a. Give the equation 1/3(5x - 9) = 2(1/3x + 6)

We want to find the value of x

5/3x - 3 = 2/3x + 13

x - 3 = 12

Collect the like terms

x = 12 + 3

x = 15

b. 4(3x + 5) - 3 = 9x - 7

12x + 20 - 3 = 9x - 7

Collect the like terms

3x + 17 = -7

3x = -24

Divide

x = -24 / 3

x = -8

c. 5(x + 7) - 3(x - 4) = 7x + 2

5x + 35 - 3x + 12 = 7x + 2

2x + 47 = 7x + 2

Collect the like terms

5x = 45.

Divide.

x = 45 / 5

x = 9

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The correct statement about the plotted value on the number line is given as follows:

The stock is 5.5 less than the original value, and the absolute value is 5.5.

The value plotted on the number line is given as follows:

-5.5.

The fact that the value is negative means that the stock is now less than the original amount, and the amount that it is less is the absolute value of the number plotted.

The absolute value of a number is represented by the number without the signal, hence the absolute value of -5.5 is given as follows:

|-5.5| = 5.5.

(just removed the negative symbol).

Hence the second statement is correct about the interpretation of the number line in this problem.

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Answer:

See below

Step-by-step explanation:

5z/(z-2) = - 1/z

1)  z [tex]\neq[/tex] 2  the expression (z-2) in 5z/(z-2) would be 0, leaving 5/0.  Division by 0 is undefined.

2)  Similiarly, the expression - (1/z) requires that z [tex]\neq[/tex] 0, since division by 0 is not allowed (undefined).

The graph with the dilated line segment is given by the image shown at the end of the answer.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.

The endpoints of the line segment in this problem are given as follows:

(0,0) and (5,5).

The scale factor of the dilation is given as follows:

k = 2.

Then the endpoints of the dilated line segment will be obtained multiplying each of the coordinates of each of the endpoints by the scale factor of 2, as follows:

(0,0) and (10,10).

Then the dilated line segment, connecting the endpoints (0,0) and (10,10), is given by the image shown at the end of the answer.

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Answer:

c

Step-by-step explanation:

Answer:

a) i) 6 numbers = 10^6=1000000

ii) 4 numbers followed by 2 letters= 10^4*26^2=6760000

iii)1 number followed by 5 letters : 10^1*26^5= 118,813,760

b)...

a) If Eddie repeat a digit or a letter:

i) The number of codes he can create with 6 numbers is 1,000,000.

ii) The number of codes he can create with 4 numbers followed by 2 letters is 67,600.

iii) The number of codes he can create with 1 number followed by 5 letters is 11,881,376.

b) If Eddie does not want to repeat a digit or a letter:

i) The number of codes he can create with 6 numbers is 15,120.

ii) The number of codes he can create with 4 numbers followed by 2 letters is 1,092,000.

iii) The number of codes he can create with 1 number followed by 5 letters is 7,893,600.

a) To calculate the number of codes Eddie can create for each scenario:

i) For a 6-digit code using only numbers, each digit can take on any value from 0 to 9 (10 options for each digit). So, the total number of codes is 10⁶ = 1,000,000.

ii) For a code with 4 numbers followed by 2 letters, there are 10 options for each digit and 26 options for each letter (assuming only uppercase letters). The total number of codes is 10⁴ * 26² = 67,600.

iii) For a code with 1 number followed by 5 letters, there are 10 options for the number and 26 options for each letter. The total number of codes is 10 * 26⁵ = 11,881,376.

b) If Eddie decides not to repeat a digit or a letter, the number of possibilities changes for each scenario:

i) Since he cannot repeat a digit, the first digit can be any of the 10 options. The second digit has only 9 options left, the third digit has 8 options, and so on. So, the total number of codes becomes 10 * 9 * 8 * 7 * 6 * 5 = 15,120.

ii) In this case, he cannot repeat any digit or letter. So, for the 4 numbers, there are 10 options for the first, 9 options for the second, 8 options for the third, and 7 options for the fourth. For the 2 letters, there are 26 options for the first and 25 options for the second (since no repetition is allowed). The total number of codes becomes 10 * 9 * 8 * 7 * 26 * 25 = 1,092,000.

iii) For the code with 1 number and 5 letters, the number has 10 options, and the first letter has 26 options. However, he cannot repeat any letter after the first, so the second letter has 25 options, the third has 24 options, and so on. The total number of codes becomes 10 * 26 * 25 * 24 * 23 * 22 = 7,893,600.

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The probability of 20% or more of the sample owning Harleys is 0.95. It is likely that your sample will contain 20% or more who own Harleys.

1. First, calculate the mean number of Harley owners in your sample using the 14% rate of Harley ownership among all motorcycle owners in the US:

2. Next, calculate the standard deviation of the number of Harley owners in your sample using the 14% rate of Harley ownership:

3. Calculate the number of standard deviations that 20% (100 Harley owners) is from the mean of 70 Harley owners:

4. Using a standard normal distribution table, we find that the probability of obtaining 1.79 standard deviations or more from the mean is about 0.9643. Therefore, it is likely that your sample will contain 20% or more who own Harleys.

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The predicted value of the car in 2009, to the nearest dollar, is $14,800.

The value of an exponentially depreciating asset can be calculated using the equation:

V = V_0 × [tex]e^{(-r*t)}[/tex]

where V is the current value of the asset, V_0 is the initial value of the asset, r is the rate of depreciation, and t is the time elapsed since the asset was purchased.

In this case, the initial value of the car was $27,600, the value in 2004 was $8,300, and the time elapsed since the car was purchased is 4 years.

To determine the predicted value of the car in 2009, we can set t equal to 9 years and solve for V:

V = 27,600 × [tex]e^{(-r*9)}[/tex] = 8,300

Solving for r gives us:

r = ln(8,300/27,600) / -9

= -0.069

To determine the predicted value of the car in 2009, we can plug the value for r into the equation and solve for V:

V = 27,600 × [tex]e^{(-0.069*9)}[/tex] = 14,800

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When we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept. The correct answers is concept

A concept is an abstract idea that takes form in your mind. This is known as the structures of thoughts and beliefs. They are important because it gives a clear explanation of a particular subject.

An automobile, byname auto, also called motorcar or car, a usually four-wheeled vehicle designed primarily for passenger transportation and commonly propelled by an internal-combustion engine using a volatile fuel, this term is generally used for an vehicle when refering to its category.

When we think of the word automobile, the first thing that comes to your mind is a category of transport. The mind connects the thoughts around the structures build. That’s a concept

Thus, when we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept.

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

Answer:

[tex] \sf \: -2x² + 6x + 4 [/tex]

Step-by-step explanation:

Given problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

Let's solve the problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

→ 3x² + 8x - 7 - 5x² - 2x + 11

→ (3x² - 5x²) + (8x - 2x) + (-7 + 11)

→ (3 - 5)x² + (8 - 2)x + 4

→ -2x² + 6x + 4

Hence, answer is -2x² + 6x + 4.

Answer:

84 Degrees

Step-by-step explanation:

This is because they are alternate interior angles

Which means they are both the same angle and are both inside the parallel line

The function is called an if/else statement function lets you test if something is true or false and then do different things depending on which result you get.

An if/else statement is a type of control flow statement that allows a program to execute different instructions depending on the result of a logical expression. The statement begins with an if condition, followed by a set of instructions to be performed if the condition is true. If the condition is false, the program executes the instructions after the optional else statement. The syntax for an if/else statement looks like this: if (condition) { // Instructions to execute if condition is true } else { // Instructions to execute if condition is false } By using an if/else statement, a program can make decisions and perform different actions based on the results of a logical expression.

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The value of function (f+g)(x) is x²-3x+7, (f-g)(x) is 3x²-3x+7, (fg)(x) is -2x⁴+3x³-7x² and (f/g)(x) is -2x²+3x-7/x²

A relation is a function if it has only One y-value for each x-value.

The given two functions are

f(x)=3x-2 and g(x)=4+x

at x=-1

f(-1)=-5, g(-1)=3

at x=2,

f(2)=4, g(2)=6

at x=5,

f(5)=13, g(5)=9

Now the functions are f(x)=2x²-3x+7  and g(x)=-x².

We need to find (f+g)(x)

f(x)+g(x)

2x²-3x+7-x².

x²-3x+7

(f-g)(x)

f(x)-g(x)

2x²-3x+7+x²

3x²-3x+7

(fg)(x)

(2x²-3x+7)(-x²)

-2x⁴+3x³-7x²

f/g(x)=-2x²+3x-7/x²

Hence, the functions (f+g)(x)=x²-3x+7, (f-g)(x)=3x²-3x+7, (fg)(x)=-2x⁴+3x³-7x² and (f/g)(x)=-2x²+3x-7/x²

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If the sales tax is 6. 35% then Claire's total is $15.63

In this questiion we have been given Claire buys a pair of earrings for $4, a necklace for $10, and a ring for $7.

So, her total purchase is:

4 + 10 + 7 = 21 dollars

She has a 30% off coupon for her whole transaction.

We find the 30 percent of 21

(30/100) * 21 = 6.3 dollars

So, she will get discount of 6.3 dollars.

So, the amount would be,

21 - 6.3 = $14.7

The sales tax is 6. 35%

Now we find 6.35 percent of 14.7

6.35% of 14.7

= 0.0635 × 14.7

= 0.933

So, the total purchase amount would be,

$14.7 + $0.933 = $15.63

Therefore, the total is $15.63

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Answer:

Step-by-step explanation:

do your work ok you go it  and who still do ixl

The number of miles Joseph traveled in one hour is calculated to be 20.25 miles

Since Joseph drove 27 miles in 1 1/3 hours, we first convert 1 1/3 into simpler form as follows;

1 1/3 hours = 4/3 hours

Now we can determine how far he traveled in one hour if he drove at a constant rate by cross multiplication as follows;

4/3 hours = 27 miles

1 hour = x

Here x represents the number of miles traveled in one hour;

1 × 27 = 4/3x

27 = 4/3x

x = 27/(4/3)

x = 27 × 3/4

x = 20.25 miles

Hence Joseph travels 20.25 miles in one hour.

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The exponent 1/5 meaning in the expression 64 1/5 is that a number that can be multiplied 5 times that will give 64.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4

It should be noted that the exponent 1/5 meaning in the expression 64 1/5 is that a number that can be multiplied 5 times that will give 64.

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Answer:

Step-by-step explanation:

answer is A. n is parallel to both l and m

The length of p is 411 cm.

Every three-sided polygon having three edges and three vertices is referred to as a triangle in geometry. The most important attribute of a triangle is that its internal angles sum to 180 degrees. The triangle's angle sum attribute is what is known as.

As per the given data:

We are given a triangle, and we know 2 angles of the triangle and one side.

In ΔPQR:

r = 38 cm

∠P = 49°

∠Q = 127°

From the angle sum property for a triangle:

∠P + ∠Q + ∠R = 180°

49° + 127° + ∠R = 180°

∠R = 180° - 176°

∠R = 4°

By using the sine rule in a triangle:

sin(∠P)/p = sin(∠R)/r

p = [sin(∠P)/sin(∠R)] × r

p = [sin(49°)/sin(4°)] × 38

p = 411 cm

The length of p is 411 cm.

Hence, the length of p is 411 cm.

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Answer:

in order of going down:
1) 77
2) 103
3) 77
4) 37
5) 53

Step-by-step explanation:

Answer:

77°

103°

77°

37°

Step-by-step explanation:

The outer quadrilateral in black is a rectangle because of the angles it has at the vertices.

Look at the upper green line. It intersects the vertical sides of the outer rectangle.

The upper green line intersects the left vertical segment of the outer rectangle at a 103° angle. That makes the top yellow box 77°.

The top yellow box is an angle of a quadrilateral.

360 - 77 - 66 - 114 = 103

The second yellow box is 103°.

The third yellow box is 77°.

The bottom yellow box is 180 - 66 - 77 = 37°

The area of the shaded region in the rectangle is given as follows:

42 units squared.

The area of a rectangle of base b and height h is given by the multiplication of these dimensions, as follows:

Area = base x height.

For the shaded region in this problem, given by the image shown at the end of the answer, the area can be obtained as the subtraction of the area of the entire rectangle by the area of the non-shaded region.

The entire rectangle has base 11 and height 12, hence it's area is given as follows:

Ar = 11 x 12 = 132 units².

The non-shaded region has base of 9 units and height of 10 units, hence it's area is given as follows:

An = 9 x 10 = 90 units².

Then the area of the shaded region on the rectangle is calculated as follows:

As = Ar - An = 132 - 90 = 42 units².

The rectangle is given by the image shown at the end of the answer.

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Answer:

n=2/5

Step-by-step explanation:

look it up

Answer:

n = 6

Step-by-step explanation:

8 x 6 = 48

48 + 9 = 57

=

7 x 6 = 42

42 + 15 = 57

So n = 6

Answer: the area of the triangle is (1/2) * √20 cm

Step-by-step explanation:

The area of a triangle is equal to one half of the product of the base and the height. In this case, the base of the triangle is √20 cm and the height is √8 cm, so we can find the area by doing this:

Area = (1/2) * (√20 cm) * (√8 cm)

To simplify this expression, we can first multiply the numerator and denominator by the square root of the denominator:

Area = (1/2) * (√20 cm * √8 cm) / (√8 cm)

This gives us:

Area = (1/2) * (√160 cm^2) / (√8 cm)

Now we can cancel out the square root of 8 in the numerator and denominator:

Area = (1/2) * √160 cm^2 / √8 cm

Area = (1/2) * √20 cm

Thus, the area of the triangle is (1/2) * √20 cm, which is the simplified radical form of the answer.

Answer:   [tex]2\sqrt{10} \ \ \text{square cm}[/tex]

==================================================

Work Shown:

[tex]\text{area} = 0.5*\text{base}*\text{height}\\\\\text{area} = 0.5*\sqrt{20}*\sqrt{8}\\\\\text{area} = 0.5*\sqrt{20*8}\\\\\text{area} = 0.5*\sqrt{160}\\\\\text{area} = 0.5*\sqrt{16*10}\\\\\text{area} = 0.5*\sqrt{16}*\sqrt{10}\\\\\text{area} = 0.5*4*\sqrt{10}\\\\\text{area} = 2\sqrt{10}\\\\[/tex]

The area units are in square centimeters.

----------------------------

Explanation:

As the steps above indicate, I used this rule

[tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex]

This is to combine the roots in the 3rd step, but also to pull them apart in the 6th step. The idea is to pull out the largest perfect square factor to simplify the square root.

With α = 0.05, 1.761 is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

Given that,

We have to find with α = 0.05, what is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

We know that,

α = 0.05

n = 15

One tailed t test for single sample.

We know from t-table

α = 0.05 (corresponding one -tail) and corresponding d.f = n - 1.

For sample t-test

d.f = 15 - 1 = 14

tα (0.05,14) for tail = 1.761       (from t-table)

Therefore, with α = 0.05, 1.761 is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

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Answer:

To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 on the right side of the equation to get 32(5x-1 + 8) = 32(5x-1) + 32(8). Then, we can subtract the area of the courtyard, 24(5x-1), from this expression to get 32(5x-1) + 32(8) - 24(5x-1) = 8(5x-1) + 32(8). This is an equivalent expression that represents the area of the cement walkway in square yards.

Samantha was receiving an interest rate of 12% on her account.

Present value is the present value of future cash flows discounted at a certain rate. Present value is based on the concept of the time value of money, where a dollar today is worth more than a dollar in the future.

PV = FV /(1 + r )ⁿ

Information provided to us ,

time period , n = 6 years

let " $x " be the present value of Samantha's account money.

After 6 years it becomes double that is

future value, F = $2x

let "r" be rate of interest was Samantha receiving on her account.

plugging all known values in above formula,

$x = $2x /(1+r)⁶

=> (1+r)^6 = 2

=> 1 + r = (2)^1/6 = 1.122

=> r = 1.122 - 1 = 0.122

=> r = 12%

So, rate of interest is 12% .

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