A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps

the answer would be (0,5)

Answer: 93°

Step-by-step explanation:

[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

She travels 61.2 miles for work each week.

Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We have been given that the healthcare worker has 3 shifts each week. The route from her house to the hospital is 9.9 miles and the route back to her house is 10.5 miles.

The distance from her house to the hospital = 9.9 miles

The distance back to her house = 10.5 miles.

The total distance travel in one shift = 9.9 + 10.5 = 20.4 miles

The total distance travel in 3 shift = 3 x 20.4 = 61.2 miles

Hence, She travels 61.2 miles for work each week.

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The sample proportion is option(d) i.e, 0.32

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

Given,

Number of successful outcomes  = 16

Total number of outcomes = 50

The sample proportion =

Number of successful outcomes / Total number of outcomes

Sample proportion = 16 / 50

                               = 0.32

Hence, the sample proportion is option(d) i.e, 0.32

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we know that

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y

so

In this problem

The domain is the interval {-1,3}

so

The range is the interval {-4,5}

so

answer Option A

The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624, or 96.24%.

We must comprehend the central limit theorem and the normal probability distribution in order to answer this query.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean

u=p= 0.09

s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)= 0.0144

What is the likelihood that the sample percentage and population proportion will deviate by less than 3%?

The ratio of 0.09 - 0.03 = 0.06 to 0.09 + 0.03 = 0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p-value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z= x-u/s

Z=2.08  has a p-value of 0.9812

X = 0.06

Z= x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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Answer:

Step-by-step explanation:

The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p- value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean u=p=0.09 s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)=0.0144

The ratio of 0.09 -0.03=0.06 to 0.09 + 0.03 =0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p- value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z=x-u/s

Z-2.08 has a p-value of 0.9812

X = 0.06

Z=x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 -0.0188=0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

$128,000 represents 100%

To find how much is 4% we can use the next proportion:

Solving for x:

Her commission is $5,120

Answer:18

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. b. (2,14)

2. a. (-1,4)

3. c. (-2,2)

Answer:  1. b

               2. a

               3. c

Step-by-step explanation:

We will change the second equation to y form, then we get:

2x - y = - 6

    - y = -2x - 6

      y = 2x + 6

Then we plug in each point to see whether it fixes the equations.

a) 1. y = 3x + 8

      4 ?= 3(-1) + 8

      4 ?= -3 + 8

        4 x 5    

a) 2. y = 2x + 6

      4 ?= 2(-1) + 6

      4 ?= -2 + 6

        4 = 4

Point a is a solution of the second equation, but not a solution for the first equation.

b) 1. y = 3x + 8

   14 ?= 3(2) + 8

   14 ?= 6 + 8

     14 = 14  

b) 2. y = 2x + 6

   14 ?= 2(2) + 6

   14 ?= 4 + 6

     14 x 10  

Point b only fits the first equation, but does not fix (not a solution) of the second equation.

c) 1. y = 3x + 8

 2 ?= 3(-2) + 8

 2  ?= -6 + 8

    2 = 2

c) 2. y = 2x + 6

     2 ?= 2(-2) + 6

     2 ?= - 4 + 6

       2 =  2

Point c fits both the first equations and the second equations.

Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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Answer:

x intercept is -3

Step-by-step explanation:

We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1)     = (2- -4)/(6- -3)     = (2+4)/(6+3)     =6/9     = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x  Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3  

Answer:

There is no dot plot below

Step-by-step explanation:

The system of equations has no solution when solving with elimination or substitution

so No solution is the answer

checking

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

y =5x +2------(2)

5x +2 = 5x-6

5x -5x = -6 -2

0 =-8

hence there is no solution since all variables are eliminated

SOLUTION

From the image above

Considering the bigger right angle triangle,

We can obtain the expression of y from the smaller right angle triangle,

Using pythagora's rule, we have

Then, recall

Substite the expression for y², we have

Expand the paranthesis, we have

subtract 9 from both sides, we have

Divide both sides by 6, we obtain

Therefore

Answer: x= 12

The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.

For the given question;

The function is given as;

y=4ˣ

Interchange the variables of the function.

x = 4∧y

Taking log both side.

㏑ x =  ㏑(4∧y)

Using the power rule of log function.

㏑ x =  y㏑(4)

y = ㏑ x/㏑(4)

Now, replace y with f⁻¹(x).

f⁻¹(x) = ㏑ x/㏑(4)

Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.

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The correct question is-

Evaluate the inverse when y=4ˣ. Show all of your work.

Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2

Order of operations:

Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.

The order using PEMDAS:

Parentheses,

Exponents,

Multiplication and Division (from left to right),

Addition and Subtraction (from left to right).

Given,

Here we have the expression. 3.2+2(-1.5)-3.4

Now, we have to use the order of operations concept in order to solve it.

The highest priority for the order of operation is brackets and the next priority is for division and multiplication,

So, here we have to solve those things first, then we get,

=> 3.2 + (-3) - 3.4

We know that (+) x (-) = -, so, the expression is rewritten as,

=> 3.2 - 3 - 3.4

The next priority is for addition and subtraction,

So, the result is,

=> 3.2 - 6.4

=> -3.2

Therefore, the resulting number is -3.2

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The measure of ∠C in the given triangle is 58°.

According to the question,

We have the following information:

ACD is a triangle where we have BD as an altitude on the side AC.

Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.

Now, we have two right-angled triangle: ABD and CBD.

We have ∠ADB = 32°.

Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).

We know that the sum of the three angles in a triangle is 180°.

In ΔCBD, we have:

∠B + ∠C + ∠CDB = 180°

90° + ∠C + 32° = 180°

∠C + 122° = 180°

∠C = (180-122)°

(Moving 122 from the left hand side to right hand side will result in the change of sign.)

∠C = 58°

Hence, the measurement of ∠C in the given triangle is 58°.

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We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

The graph of the linear function 5x + 3y = 20 is given at the end of the answer.

To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.

In this problem, the function is:

5x + 3y = 20.

The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:

5x = 20

x = 20/5

x = 4.

Meaning that point (4,0) is on the graph of the function.

The y-intercept is the value of y when x = 0, hence:

3y = 20

y = 20/3

y = 6.67.

Meaning that point (0, 6.67) is on the graph of the function.

The graph is plotted with a line passing through the points (4,0) and (0, 6.67).

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Answer:

16%.

Explanation:

In a recent math test:

• The average score = 75

• Standard Deviation = 10

To find: The percentage of people who scored an 85 or higher, P(X>85).

First, find the z-score when X=85.

Substitute the given values:

The people who scored an 85 or higher are 1 standard deviation away from the mean.

The percentage of people who scored an 85 or higher is 16%.

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34

+7x

4x - 6 = 34

+6

4x = 40

/4

x = 10

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34  Add 7x to both sides

4x - 6 = 34  Add 6 to both sides

4x = 40  Divide both sides by 4

x = 10

Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.

The sum of 12 and P can be written as 12 + P

Then, f decreased by the sum of 12 and P can be written as:

f - (12 + P)

Answer: it isn't correct, the correct answer is f - (12 + P)

The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.

According to the question,

We have the following information:

Amira is younger than Marques.

Their ages are consecutive integers.

The sum of Amira's age and 2 times Marques's age is 38.

Now, let's take Amira's age to be x years.

Then, Marques's age will be (x+1) years.

So, we have:

x + 2(x+1) = 38

x + 2x + 2 = 38

3x+2 = 38

3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)

3x = 36

x = 36/3

x = 12 years

Hence, Amira's age is 12 years.

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