Extra Credit
Where does this function cross the x-axis?
y = 25x² - 49

The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability

Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:

P(A ∨ B)=P(A)+P(B)+P(A ∧ B)

Annotation:

P(A ∨ B) = probability own a dog or a cat

P(A) = probability own a dog

P(B) = probability own a cat

P(A ∧ B) = probability own a dog and a cat.

Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability

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The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.

It is vital to note that an inequality simply shows that the expressions aren't equal.

In this case, the sum of two consecutive integers is less than -9.

Let the integers be x and x + 1.

Therefore, x + x + 1 < -9

2x + 1 < -9

Collect like terms

2x < -9 - 1

2x < -10

Divide

x < - 10 / 2

x < - 5

The value is x < - 5.

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Answer:

[tex] = 3 + \sqrt{25 } - \sqrt{12} \\ = 3 + 5 - \sqrt{12 \\ } \\ = 8 - \sqrt{12} [/tex]

[tex] = 8 - 2 \sqrt{3} [/tex]

option d is correct

Answer:

Note: A percentage is always a number over 100.      (34% = [tex]\frac{34}{100}[/tex])

Cost of meal = 100%

Cost of tip = 34%

Total = 134%

134% = [tex]\frac{134}{100}[/tex]

To find the total and the tip, you must multiply it by [tex]\frac{134}{100}[/tex]

Answer:

Bill times the 0.34 percent equals the price of the tip. After you find what the tip is, you add the base price (the bill price) to the tip and you get the total number paid. However, another way you can solve (in one step) this is by adding 1.00 to the percent you are multiplying by which in this case we add 0.34 by 1.00 and this gives us 1.34. Suppose we set the bill to 4 dollars and use the normal way (2-step equation) by doing 3(0.34) which is 1.02 and 1.02 + 3 = 4.02 as our final answer / final bill. However, when we do our one-step equation, we can write this as 3x(1.34) and this is equal to 4.02.

1st Step

Bill(0.34) = tip

tip + bill = total

2nd Step (one-step equation)

Note: we are going to set the bill in this equation as $4

4(1.34) = total; Total = 4.02 ← We added 1.00 to the tip percentage in decimal form.

The value of the equation g(x+1) is -2x²-x

Given equation,

g(x) = -2x²+3x-1

Replacing x in the equation by x+1

g(x+1) = -2(x+1)² +3(x+1) -1

g(x+1) = -2(x²+1+2x) +3x +3 -1

g(x+1) = -2x² -2 -4x +3x +3 -1

g(x+1) = -2x²- x

Hence the final answer is g(x+1) = -2x²-x

Since this, the question says to find the value g(x+1) we need to replace the value of x in the given equation g(x) by x+1 to find value. After replacing we get -2(x+1)² +3(x+1) -1. Next, we need to solve the bracket (x+1)² which will give us x²+1+2x. We will multiply this by -2, which will give us -2x² -2 - 4x. Next, we will solve 3(x+1) which will give us 3x+3. Finally, we need to solve the whole equation to get the answer -2x²- x

I hope this answer helps.

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Answer: x=43

Step-by-step explanation:

3x-19=110

3x-19+19=110+19

3x=129

3x/3=129/3

x=43

Answer:

y = x - 3

Step-by-step explanation:

Consider the equation "y = mx + b" :

y = mx + b

Since the slope is 1, you could input that into the equation:

y = (1)x + b

The variable "b" represents the y-intercept, therefore, to find the y - intercept, you would have to subtract 7 from each side of the coordinate points to get 0 as the x - coordinate to find the y - intercept:

(7    4)

-7 || -7

(0, -3)

Therefore, the y - intercept would be -3 and the equation would be:

y = x - 3

Answer: See the image below for the table and graph

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

Explanation:

We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.

For instance, if x = -2, then...

[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]

If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.

We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.

Repeat for x values x = -1 through x = 2.

Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.

Based on an exponential model of the data, the predicted temperature of the water at 7 minutes is 39.7 °C using desmos graphing calculator.

Similar to how you discovered linear and quadratic models in prior chapters, exponential models can be found by fitting data to them. As you may already be aware, exponential functions take the form y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time. Based on an equation like this one, the exponential model represents the degradation failure process: Y = deterioration; T = time; A and B = parameters to be calculated using the regression approach based on historical data. An expansion within a population that happens at the same pace across time is represented by the function of exponential growth. It is reasonable to suppose that data grows exponentially as populations double or triple in size.

Graph all the points on a graph. Then from the graph, we can find that at 7 minutes the temperature is 39.7°C.

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Answer: 38.2 degrees

Step-by-step explanation:

enter into desmos

use y1 ~ abx2

then input numbers provided

(22.9178)1.07564^7

equals 38.18049

round 38.2

Answer: 76

Step-by-step explanation: simplify equation

60+16=x-16+16 (cancel out 16 and add 60+16)

76=x

60+16=x-16+16
76=x
x=76

The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.

We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).

y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.

Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).

Hence, the line perpendicular  to y = 5 and that passes through the point (-7, -5)  is x = -7.

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In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.

Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.

An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.

Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.

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The equation in standard form is x - y = 9

From the question, we have the following parameters that can be used in our computation:

Points = (8, –1) and (2, –5)

Point-slope form is y + 1 = (x – 8).

Recall that the point-slope form is y + 1 = (x – 8).

So, we have

y + 1 = (x – 8)

Open the brackets

y + 1 = x – 8

Subtract 1 from both sides

y = x - 9

Rewrite as

-x + y = -9

Multiply through by -1

x - y = 9

Hence, the equation is x - y = 9

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Answer:

5.8 cm

Step-by-step explanation:

the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:

4^2 + 4.2^2 = a^2

Simplify: 16 + 17.64=a^2

Simplify again: 33.64 = a^2

Square root both sides: 5.8 = a

Answer:73.33

Step-by-step explanation:

The answer is 73.33 because 73.33 multiplied by 3 = 219.99

The equation of line parallel to the given line is found as y = -6x + 13.

The equation of the line is-

y = -6x + 1

The second line is parallel to the above line, thus the slopes of both the line are equal.

m1 = m2 = -6

The new line also passes from the point (1, 7)

(x1, y1) = (1,7)

Thus, the equation of the line will be calculated as-

y - y 1 = m2(x - x1)

y - 7 = -6(x - 1)

y - 7 = -6x + 6

y = -6x + 13

Thus, the equation of line parallel to the given line is found as y = -6x + 13.

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The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.

What is a perpendicular line?

Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.

Here,

The slope of ax + by = c is given by m = -a/b

m = -(-4)/3 = 4/3

m = 4/3 for this line.  

A perpendicular line will have a slope -1/m = -3/4

The line through (6, 8) with slope -3/4

y = (-3/4)x + b

8 = (-3/4)(6) + b

b = 8 + 9/2 = 25/2

y = (-3/4)x + 25/2

4y = -3x + 50

3x + 4y = 50

Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.

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Using the properties of arithmetic mean and average we get the value of 'w' is 22.

We know that mean is calculated by dividing the sum by the frequency.

Here n= 3

Sum = 5+6+7+w = 18+w

Now , (18+w )/4 = 10 which is the mean

or, 18 + w = 40

or, w = 40 - 18

or, w = 22

The value of w is 22.

By adding together all the observations and then dividing the sum by the same total sample sizes, the arithmetic mean of the supplied data can be calculated.

In order to determine the data's central tendency, an arithmetic mean formula computes the mean, or average, of the numbers. It can alternatively be described as the total number of observations multiplied by the sum of all the observations that were provided.

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Answer: The answer is -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

-4 + (-1) - (-3)      Distribute the + and - since they are outside the parenthesis

-4 - 1 + 3            Subtract 1 to -4

-5 +3                 Add 3 to -5

-2

The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.

A combination is a grouping of items where order does not matter. The formula of combination is

[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]

Where

Given the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.

What is the probability that no two adjacent people will stand?

First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.

The number of arrangements according to the number of people standing.

Case 1: 0 people standing = 1 arrangement.

Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.

Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.

Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.

Case 5: 4 people standing but no two adjacent people = 2 arrangements.

The number of arrangements that no two adjacent people will stand.

n(A) = 1 + 8 + 20 + 16 + 2 = 47

The probability that no two adjacent people will stand is

P(A) = n(A)/n(S)

P(A) = 47/256

Hence, the probability that no two adjacent people will stand is 47/256.

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Answer:

y = - 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line

m = [tex]\frac{-4-2}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = - 2x + 4 ← equation of line

Answer:

[tex]\frac{17}{76}[/tex]

Step-by-step explanation:

expressing the ratio in fractional form

[tex]\frac{11\frac{1}{3} }{50\frac{2}{3} }[/tex] ← change mixed number to improper fractions

= [tex]\frac{\frac{34}{3} }{\frac{152}{3} }[/tex] ( multiply numerator and denominator by 3 )

= [tex]\frac{34}{152}[/tex] ( divide numerator and denominator by 2 )

= [tex]\frac{17}{76}[/tex] ← in simplest form

Answer:

-2x+18, and -2(x-9)

Step-by-step explanation:

4x+18-6x

4x-6x+18

-2x+18

-2(x-9)

-2x+18

m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.

What is the angle of the triangle?

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.

Here, we have

In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.

AB=4p-1 , AC=p+4 , BC=3p

where p+4 < 3p        [as p≥3]

3p < 4p-1          [as p≥3]

⇒  4p-1> 3p > p+4

⇒AB > BC > AC

Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.

m∠C > m∠B > m∠A    [∵Angle opposite to greater side is greater]

Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.

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Answer:  [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

90 degree counter-clockwise rotation around the origin.

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

Explanation:

Focus on A(-1,2) and A'(-2,-1)

The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"

In other words, we've gone from (x,y) to (y,x) to (-y,x)

Representing this with arrows looks like:

[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]

or in short

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

which represents a 90 degree counter-clockwise rotation around the origin.

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

Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]

Sure enough, it works for point B.

Lastly, let's check if it works for point C.

We should go from C(3,-4) to C'(4,3).

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]

All points have been confirmed.

The statement that cannot be assumed from the figure is

B) BD bisects ∠ADE

What are Supplementary and Complementary Angles?

Supplementary angles are two angles that have a sum of 180°.

Complementary angles are two angles that have a sum of 90°.

Given data ,

From the figure we can arrive at each conclusions

A)

∠ABD and ∠DBE are supplementary

Now , from the figure we can see that point B lies on the line AE

And , ∠ABD + ∠DBE = 180°

Hence , ∠ABD and ∠DBE are supplementary and the statement is TRUE

B)

Bisecting a line means dividing the line into two equal parts

And from the figure BD does not bisect ∠ADE

Hence , BD does not bisect ∠ADE so the statement is FALSE

C)

∠CDA and ∠ADE are complementary

From the figure we can see that ∠EDC is 90°

And , ∠CDA + ∠ADE = ∠EDC

So , ∠CDA + ∠ADE = 90°

Hence , ∠CDA and ∠ADE are complementary and the statement is TRUE

D)

∠EDB and ∠BDA are adjacent and are not complementary

From the figure we can see that ∠EDB and ∠BDA are adjacent

∠EDB + ∠BDA ≠ 90°

Hence , they are not complementary and the statement is TRUE

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Answers:

decimal form = 0.124

simplified fraction = 31/250

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

Explanation:

To convert from percent to decimal, we move the decimal point 2 spots to the left.

12.4% converts to the decimal form 0.124

Optionally you could use your calculator to say 12.4/100 = 0.124

--------

To convert from a terminating decimal to a fraction, we write the decimal digits over some power of 10. In this case, we write the "124" over 10^3 aka 1000. We write it over 1000 since the '4' is in the thousandths place value. Then reduce as much as possible.

124/1000 = (31*4)/(250*4) = 31/250 is the simplified fraction form

Use your calculator to see that 31/250 = 0.124 to confirm the answer.

The cost of each bottle of water is equal to the cost of each bag of chips.

The expression:

The expression is defined as a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)

Here it is given that 4 bottles, 2 bags of chips, and a fruit salad.

The price of a fruit salad is $5.

The expression given is:

4x + 2x + 5

To find the relation between the price of a bottle and a bag of chips, we have:

Price of bottles = 4x/4 = x

Price of bag of chips = 2x/ 2 = x

Therefore we get that the cost of each bottle and each bag of chips is the same.

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The complete question is:

Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad. the cost of the fruit salad was $5. this expression was used to represent the amount Jalen should pay. 4x +2x +5 based on the expression, the cost of each bottle of water is ______the cost of each bag of chips.