Find the x-intercept of the equation x + y + z = 2.

Answer:

c 50

Step-by-step explanation:

Answer:

1) 10

Step-by-step explanation:

The equation for average rate of change is [f(x2) - f(x1)]/x2 - x1

f(4) = 32

f(1) = 2

x2 = 4

x1 = 1

Substitute to get 32-2/4-1, or 30/3, which is equal to 10

Answer:

-5/6

Step-by-step explanation:

A great way to divide fractions is to use the "leave it, change it, flip it" method.  You leave the first fraction as it is, change the division sign to a multiplication sign, and flip the second fraction so you get the reciprocal.  Like this:

-5/7 ÷ 6/7

-5/7 x 6/7

-5/7 x 7/6

Then you multiply through.  First -5 x 7, -35, and then 7 x 6, 42, to get -35/42.  Because both of these are divisible by 7, we can simplify to get -5/6.

Answer:

-5

6

Step-by-step explanation:

⇒ \(\frac{-5}{7}\) ÷ \(\frac{6}{7}\)

⇒ \(\frac{-5}{7}\) × \(\frac{7}{6}\)

(We do this because when dividing a fraction by another fraction we take the inverse of the second fraction and multiply it to the first fraction.)                                                                                                          

⇒ -5 × 7 = -35 (to simplify just divide both by 7) = -5

     7 × 6     42                                                             6

So the answer is -5

                            6

The pool is draining at a rate of 1.36% per hour according to Inayah's claim.

According to Inayah's claim, the pool is experiencing a draining at a rate of 1.36% per hour. This means that for every hour that passes, the pool's water level decreases by 1.36% of its total volume.

Understanding the rate at which a pool is draining is essential for monitoring and managing water levels. If the rate of drainage is accurate, it can help estimate how long it would take for the pool to reach a certain level or completely drain. Additionally, it aids in determining the necessary actions to maintain the pool's water balance and prevent potential issues such as overflow or inadequate water supply.

It is crucial to verify the accuracy of the claim by monitoring the pool's water level over a specific period. This can be done by measuring the change in water volume or using other reliable methods to ensure the drainage rate aligns with the claimed percentage.

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Answer:

first multiply numbrrs3*2=6ab

the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3

To determine if there is convincing evidence of a difference in the proportions of all teens and young adults who own an iPod or MP3 player, we can perform a hypothesis test.

Let's define the following parameters:

- p₁: Proportion of all teens who own an iPod or MP3 player.

- p₂: Proportion of all young adults who own an iPod or MP3 player.

The null hypothesis (H₀) assumes that there is no difference between the proportions:

H₀: p₁ = p₂

The alternative hypothesis (H₁) assumes that there is a difference between the proportions:

H₁: p₁ ≠ p₂

To test this hypothesis, we can use a two-proportion z-test. We calculate the test statistic using the formula:

z = ((p₁ - p₂) - 0) / √((\(\hat{p}_1\) * (1 - \(\hat{p}_1\)) / n₁) + (\(\hat{p}_2\) * (1 - \(\hat{p}_2\)) / n₂))

Where:

- \(\hat{p}_1\): Sample proportion of teens who own an iPod or MP3 player (79% or 0.79)

- \(\hat{p}_2\): Sample proportion of young adults who own an iPod or MP3 player (67% or 0.67)

- n₁: Sample size of teens (800)

- n₂: Sample size of young adults (400)

Using the given values, we can calculate the test statistic:

z = ((0.79 - 0.67) - 0) / √((0.79 * (1 - 0.79) / 800) + (0.67 * (1 - 0.67) / 400))

Calculating this yields the test statistic z = 5.525.

Next, we can determine the critical value or p-value associated with this test statistic using a significance level (α). Assuming a significance level of 0.05, for a two-tailed test, the critical values are approximately -1.96 and 1.96.

Since the calculated test statistic (5.525) is beyond the critical values of -1.96 and 1.96, we can reject the null hypothesis. There is convincing evidence to suggest that there is a difference in the proportions of all teens and young adults who own an iPod or MP3 player.

In conclusion, the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3 player.

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The appropriate hypotheses for testing the difference in proportions of all teens and young adults who own an iPod or MP3 player are:

Null Hypothesis (H0): The proportion of teens who own an iPod or MP3 player is equal to the proportion of young adults who own an iPod or MP3 player.

Alternative Hypothesis (Ha): The proportion of teens who own an iPod or MP3 player is not equal to the proportion of young adults who own an iPod or MP3 player.

To test if there is a significant difference in the proportions of all teens and young adults who own an iPod or MP3 player, we need to set up appropriate hypotheses. Let's denote the proportion of teens who own an iPod or MP3 player as p1 and the proportion of young adults who own an iPod or MP3 player as p2.

The null hypothesis (H0) assumes that there is no difference between the proportions, so we can state it as:

H0: p1 = p2

The alternative hypothesis (Ha) assumes that there is a difference between the proportions, so we can state it as:

Ha: p1 ≠ p2

Here, p1 represents the true proportion of teens who own an iPod or MP3 player, and p2 represents the true proportion of young adults who own an iPod or MP3 player.

To test these hypotheses, we can use a significance level (α) of 0.05, which is a common choice in hypothesis testing. If the p-value (the probability of observing a test statistic as extreme as the one calculated) is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportions.

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To use the Division Algorithm and synthetic division to express the polynomial P(x) = 5x^3 - 2x^2 - 5x-4 in the form (divisor)quotient, we first need to choose a divisor. Let's use x-2 as the divisor.

Next, we perform synthetic division using the chosen divisor:

2 | 5 -2 -5 -4
---|---------
 |  5  8 11
 
The numbers on the bottom row represent the coefficients of the quotient polynomial, which is 5x^2 + 8x + 11.

Therefore, we can express P(x) as (x-2)(5x^2 + 8x + 11).

In this expression, the divisor is x-2 and the quotient is 5x^2 + 8x + 11.

Overall, the steps we used were:

1. Choose a divisor (in this case, x-2)
2. Perform synthetic division
3. Write the polynomial in the form (divisor)quotient.

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Answer:

you are correct do not say any other answer

Answer:

The answer is either

y=50000 x 0.8^x

or

y=50000(20%)^x but this just seems wrong

Step-by-step explanation:

Answer:

Here we want to solve:

(cos(A) + sin(A))^2 + ( sin(A) - cos(A))^2 = 2

First, remember the two expansions:

(a + b)^2 = a^2 + 2*a*b + b^2

(a - b)^2 = a^2 - 2*a*b - b^2

Using these relations, we can expand:

(cos(A) + sin(A))^2 = cos(A)^2 + 2*cos(A)*sin(A) + sin(A)^2

( sin(A) - cos(A))^2 = sin(A)^2 - 2*sin(A)*cos(A) + cos(A)^2

Replacing that in our equation, we geT:

(cos(A)^2 + 2*cos(A)*sin(A) + sin(A)^2) + (sin(A)^2 - 2*sin(A)*cos(A) + cos(A)^2) = 2

We can simplify this to get:

2*cos(A)^2 + 2*sin(A)^2 + 2*cos(A)*sin(A) - 2*cos(A)*sin(A) = 2

2*cos(A)^2 + 2*sin(A)^2 = 2

We can take the 2 as a common factor to get:

2*cos(A)^2 + 2*sin(A)^2 = 2*( cos(A)^2 + sin(A)^2) = 2

Now we can divide both sides by 2:

2*( cos(A)^2 + sin(A)^2)/2 = 2/2

cos(A)^2 + sin(A)^2 = 1

And this is a trigonometric property that is true for any value of A.

So the equality:

(cos(A) + sin(A))^2 + ( sin(A) - cos(A))^2 = 2

is true for any real value of A.

The student is seeking assistance with their homework and requires clarification or help understanding a concept. They express the need for assistance and emphasize importance of the homework for their grade.

It is understandable to encounter challenges or confusion while working on homework assignments. It is essential to seek clarification and assistance to ensure a clear understanding of the topic and complete the assignment accurately. Seeking help from a teacher, tutor, or classmates can provide valuable guidance and support.

Explaining the specific concept or problem in detail to the person assisting you can help them provide targeted explanations and guidance. Remember that asking for help is an important part of the learning process and can contribute to better comprehension and improved grades. #

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The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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I am very unsure what your question is, but the simple tip is to divide it by two each year as it is decreasing by a half..

To find the number of copies sold in subsequent years, you can use the formula:

N = N0 * (1/2)^t

where N is the number of copies sold in a given year, N0 is the initial number of copies sold (in this case, 600,000), t is the number of years since the book was released.

For example, to find the number of copies sold in the second year after the book was released:

N = 600,000 * (1/2)^1

N = 300,000

So, 300,000 copies were sold in the second year. To find the number of copies sold in subsequent years, you can continue to plug in values of t and solve for N.

Answer:

If I understood what you mean properly... 0

Step-by-step explanation:

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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\( \frac{28}{ - 64} \\ = \frac{ - 28}{64} \\ dividing \: \: \: \: \: both \: \: \: \: \: numerator \: \: \: \: \: \\ and \: \: \: \: \: denominator \: \: \: \: \: by \: \: \: \: 4 \\ \: we \: \: \: \: \: get \\ \frac{ - 7}{16} \)

\(The \: \: \: \: \: answer \: \: \: \: \: is \: \: \: \: option \\ d. \frac{ - 7}{16} \)

Answer:

It represents 1 + the percent of the markup written in decimal form

Answer:

percent of original price being paid

Answer:

18 days

Explanation:

To determine the fewest number of days that will pass before both rooms are cleaned again on the same day, we list the multiple of each of the days.

The next multiple 6 and 9 have in common is 18.

Therefore, after 18 days has passed, the two rooms will be cleaned on the same day.

First, remember these two affirmations:

Two parallel lines have the same slope

Two perpendicular lines have the inverse slope, the slope of each one is multiplied by -1

So

We can see in the second option that equation one has the same slope that equation two except that the equation is multiplied by -1. So there are 2 perpendicular lines

In the third option, we can see the same slope in the two functions so is parallel

Finally, the first option doesn't have any relationship.

Since we have the following probabilities:

then, this is not a fair game, since Andrew has a 1/4 probability of winning and Liz has a 1/8 probability of winning

Answer:

The answer would be C. An obtuse equilateral triangle :)

The probability that a woman was wearing a belt given that she was also carrying a purse is 0.333 or 33.3%.

To find the probability that a woman was wearing a belt given that she was also carrying a purse, we need to use conditional probability.

We know that out of the 30 women observed, 18 were carrying purses and 6 were both carrying purses and wearing belts.

This means that the number of women carrying purses who were also wearing belts is 6.
Therefore, the probability that a woman was wearing a belt given that she was also carrying a purse is:
P(wearing a belt | carrying a purse) = number of women wearing a belt and carrying a purse / number of women carrying a purse
P(wearing a belt | carrying a purse) = 6 / 18
P(wearing a belt | carrying a purse) = 0.333
Given the information provided, we can determine the probability of a woman wearing a belt, given that she is also carrying a purse.

First, we need to find the number of women carrying a purse and wearing a belt, which is 6. There are 18 women carrying purses in total.
So, to find the probability, we will use the formula:
P(Belt | Purse) = (Number of women wearing belts and carrying purses) / (Number of women carrying purses)
P(Belt | Purse) = 6 / 18
P(Belt | Purse) = 1/3 or approximately 0.33
Therefore, the probability that a woman was wearing a belt, given that she was also carrying a purse, is 1/3 or approximately 0.33.

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Hello!

Answer:

x=0

Step-by-step explanation:

Hope this helps!

Answer:  The correct answer is:  " x = 0 " .

________

Step-by-step explanation:

Given:  " 8 + 8x = 8 " ;  Solve for "x" ;

________

Method 1)

________

Subtract "8" from each side of the equation:

________

  → " 8 + 8x − 8 = 8 − 8 " ;

  → On the "left-hand side" of the equation:

          Note the following "like terms" :

            " +8 − 8 = 0 " ;

  →  and we are left with "8x" on the "left-hand side" of the equation.

  → On the "right hand side" of the equation:

         The "(8 − 8)" = 0 ;

________

And we are left with:

  →  " 8x = 0 " ;

________

Now, divide each side of the equation by "8" ;

   to isolate "x" on one side of the equation;

   & to solve for "x" :

________

  →  8x / 8 =  0/8 ;

to get:

  →  " x = 0 " ;

  →  which is the correct answer.

________

Method 2)

________

Given:  " 8 + 8x = 8 " ;  Solve for "x" ;

________

Subtract "8" from each side of the equation; in the following manner:

________

   8  +  8x    =    8 ;

 - 8             =   - 8 ;

_____________

   0  +  8x    =    0 ;

→ We have:  " 0 + 8x = 0 " ;

→ Note: On the "left-hand side" ; we have:

                 " 0 + 8x " ;

  We can simplify this to "8x" ; since the "addition property of zero" states that when "0" is added to any value; the resulting value does not change.

Now, we can bring down the "0" from the "right-hand side" of the equation;

And we can rewrite our equation as:

________

   → " 8x = 0 " ;

Now, divide each side of the equation by "8" ;

   to isolate "x" on one side of the equation;

   & to solve for "x" :

________

  →  8x / 8 =  0/8 ;

to get:

  →  " x = 0 " ;

  →  which is the correct answer.

________

Method 3)

________

Given:  " 8 + 8x = 8 " ;  Solve for "x" ;

________

Divide each side of the equation by "8" ;

________

  → " \(\frac{(8 + 8x)}{8} =\frac{8}{8}\) " ;

________

To solve:

________

Note: On the "right-hand side" of the equation:

________

Take note that: " \(\frac{8}{8} =\) (8 ÷ 8) = 1 " ;

________

Rewrite the equation as:

________

 →  " \(\frac{(8 + 8x)}{8} =1\)  "  ;

________

To solve:

________

Note:  " \(\frac{x}{y} = z\) " ;  ↔ \(x = z*y\) ; \((y\neq 0)\) ;

________

 →  " \(\frac{(8 + 8x)}{8} =1\)  "  ;  

 →  From the "left-hand side" of the equation;

      Let us simplify:

________

 →  " \(\frac{(8 + 8x)}{8} = \frac{8}{8} + \frac{8x}{8} = 1 + x\) " ;  

Now, bring down the "1" from the "right-hand side" of the equation;

and rewrite the equation:

________

 →  " 1 + x = 1 " ;

Now, subtract "1" from each side of the equation;

   to isolate "x" on one side of the equation;

   & to solve for "x" :

________

     " 1 + x − 1 = 1 − 1 " ;

  → On the "left-hand side" of the equation:

          Note the following "like terms" :

            +1 − 1 = 0 " ;

  →  and we are left with "x" on the "left-hand side" of the equation.

  → On the "right hand side" of the equation:

         The "(1 − 1)" = 0 ;

  → And we are left with:

      →  " x = 0 " ;

      → which is the correct answer!

________

The correct answer is:  " x = 0 " .

________

Hope that this answer—and the corresponding explanations—

are helpful !

  WIshing you the best!

________

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z

2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.

Given,

The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.

1) Total cost = d

Total ounces = z

Equation

d = $5 + $0.40z

2) If cup weighs 14 ounces

d = $5 + 0.40(14)

d = $5 + $5.6

Total cost:

d = $10.6

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The lengths of the major and minor axis are 4√6 and 4√3.

A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.

(x−h)²/ b² +(y- k)² /a² = 1

Given:

(x−3)²/ 27+(y+4)² /45=1

The above equation can be compared to the standard equation of an ellipse

(x−h)²/ b² +(y- k)² /a² = 1

where, (h, k) = coordinates of the center of the ellipse

a =  length of the semi major axis

b = length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2 x√6

b = √(12) = 2 x√3

and, length of the major axis = 2a

length of the minor axis = 2b

Thus, The length of the major axis is

2x a = 2 × 2 x √6 = 4√6

and, length of the minor axis is

2•b = 2 × 2√3 = 4√3

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Answer: 6sqrt(5) and 6sqrt(3)

Step-by-step explanation:

I took the test and these were the correct answers.

Therefore, we would anticipate finding 150,000x golden fish throughout the entire lake based on the class average.

Volume is the measure of room within a particular 3D entity in mathematics. For illustration, a fish aquarium measures three feet long by one foot wide by two feet high. The capacity is calculated by multiplying the length, the breadth, and the height, or 3x1x2, that also equals six. The fish aquarium therefore has a 6 cubic foot capacity.

Let's say the class average is "x" yellow fish per liter of water.

If the sample contained 500 liters of water, we can estimate the number of yellow fish in the sample as:

500 * x = 500x

Now that we have an approximation, we can use it to determine the anticipated number of yellow fish in the 150,000,000-liter pool as a whole.

The expected number of yellow fish in the whole lake would be:

(500x / 500) * 150,000,000 = 150,000x

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To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.

To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).

In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.

While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.

For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.

Number of trees per acre: 1 tree per acre

Total yield: 1185 peaches per acre

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Answer:

C. x + 12 > 2

Step-by-step explanation:

Given:

Twelve more than x is greater than two

Required:

Translate to symbols

Solution:

Twelve more than x can be represented as "x + 12"

Greater than is represented by the symbol ">"

Two represented as "2"

Therefore, the translation to symbols would be:

x + 12 > 2

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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multinv(x*y) = (multinv x) * (multinv y) {proved}

To prove that for all nonzero real numbers x and y, multinv(x*y) = (multinv x) * (multinv y), we will follow these steps:

Step 1: Understand the terms
Multinv(x) refers to the multiplicative inverse of x, which is the reciprocal of x (1/x).

Step 2: Write down the given equation
We are given that multinv(x*y) = (multinv x) * (multinv y).

Step 3: Replace the terms with their definitions
The multiplicative inverse of x*y is 1/(x*y). Similarly, the multiplicative inverse of x is 1/x, and the multiplicative inverse of y is 1/y.

Step 4: Plug in the definitions
1/(x*y) = (1/x) * (1/y)

Step 5: Verify if both sides of the equation are equal
Using the properties of fractions, we know that (1/x) * (1/y) is equal to 1/(x*y).

Thus, the given equation holds true:
multinv(x*y) = (multinv x) * (multinv y)

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