1. region above both lines
2. Region below both lines
3. Region Between both lines
4. No Solution

100 POINYS

The intersection of this sphere with the -plane is (y+6)²+(z-4)²=21

The equation of a sphere centered at (h,k,l) and radius r is given by:

(x−h)²+(y−k)²+(z−l)²=r²

where x,y, and z represent the coordinates of the points on the surface of the surface.

so if the center is (-3,2,5) and radius r=4 then we can plug the values in the above formula:

consider the points  h=-3 k=2 l=5 and r=4.

(x−(-3))²+(y−2)²+(z−5)²=4²

(x+3)²+(y−2)²+(z−5)²=16.

If the sphere intersects the yz-plane then x=0

The resulting equation is an equation of a circle with a radius r=√21

and at the center with (6,-4) on the yz-plane

with yx-plane:

⇒(x−2)²+(y+6)²+(z−4)²=25

⇒ (0−2)²+(y+6)²+(z−4)²=25

⇒4+(y+6)²+(z−4)²=25

⇒(y+6)²+(z−4)²=25-4

⇒(y+6)²+(z−4)²=21

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The two numbers which could be used for two in function are 5/2 and - 3.

The definition of a function is a "well-behaved" relation is one in which, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. Because functions pair information, they are all relations, but not all relations are functions. A subset of all of your relations are well-behaved family members, just as all mathematical relations are well-behaved functions.)

Given f(x)=x²+x

and f(2t)=30

When x = 2t, x²+x = 30

Substitute the value of x in function

(2t)²+2t = 30

4t² + 2t = 30

2(2t² + t) = 30

2t² + t = 15

2t² + 3t - 5t - 15 = 0

2t(t +3) - 5(t + 3)

(2t - 5)(t + 3)

t = 5/2

t = -3

Thus, The two numbers which could be used for two in function are 5/2 and - 3.

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Answer:

brooooooooooo I got x=0

Option A is the correct Answer. The total cost of his loan if he paid it off 4 years early is 312,423.90

We have given:

The principal amount which is 30,000

Time which is 30 year

The rate which is 5.5%

And since, we have to find 4 years early so, the time would be: 20-4=16 years.

And since, we have to find for 12 months

Hence, n=12

We have the formula to calculate compound interest:

[tex]A=P(1+\frac{r}{n})^n^t[/tex]

Where

A=compound interest

P= Orginal amount deposited.

r= rate

n=times its compounds per year monthly

t= years.

P=155000, r=5.5, t=16

On substituting the values we get:

[tex]A=155000(1+\frac{0.055}{12})^1^2^*^1^6\\\\A=155000(1+\frac{0.055}{12})^1^9^6\\\\A=155000(14884.0754)\\\\A=312,423. 90[/tex]

Therefore, the compound interest is 312,423.90

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Kayla -24

Leanne-18

Step-by-step explanation:

4+3=7

42÷7=6

6x4=24

3x6=18

Answer: Let's call the number of marbles that Kayla gets x. Then, Leanne gets 3x marbles. The total number of marbles that the girls receive is x + 3x = 4x, so 4x must equal 42 marbles:

4x = 42

Dividing both sides by 4:

x = 10.5

Since the number of marbles that each girl receives must be an integer, we round down to the nearest whole number. So, Kayla gets 10 marbles and Leanne gets 3 * 10 = 30 marbles.

Step-by-step explanation:

Answer:

  {-√6, -1, 1, √6}

Step-by-step explanation:

You want the roots of the quartic 3x^4-21x^2+18.

We can find the roots by factoring to linear factors:

  = 3(x^4 -7x^2 +6)

  = 3(x^2 -6)(x^2 -1) . . . . . . . 6 = (-1)(-6) are factors with a sum of -7

  = 3(x -√6)(x +√6)(x -1)(x +1) . . . . . a^2 -b^2 = (a -b)(a +b)

The roots of the quartic are ±√6 and ±1.

Answer:6

Step-by-step explanation:

Let the number be x.

Now, 3x+6=24

3x=24-6

3x=18

x=18/3

x=6

Answer:

6

Step-by-step explanation:

We can work the problem backwards

Since something gives 24 that means it equals 24

= 24

Something increased by 6, so something added by 6

Something + 6 = 24

Making something = x

x + 6 = 24

If we subtract 6 from both sides

x = 18

Trice a number, so divide this number by 3

x = 6

Trice of 6 is 18... 18 increased by 6 gives 24

Answer:

Below

Step-by-step explanation:

Out of 50 + 10 = 60 tries, 3 + 20 = 23 times were tails

  23/60 chance of tails

The estimate of the probability that Audi gets tails is given as follows:

p = 23/60.

A probability is calculated via the division of the number of desired outcomes by the number of total outcomes.

Hence the probability of each person getting tails when they throw a biased coin is given as follows:

The total number of throws is given as follows:

50 + 10 = 60.

The number of tails is given as follows:

3 + 20 = 23.

Hence the probability for Audi is given as follows:

p = 23/60.

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The number of children and adult that were there are 117 aand 178 respectively.

Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The recipients admission total of 560.75 dollars.

The number of children and adult can be calculated as follows;

Using equations,

let

x = number of children

y = number of adult

Therefore,

x + y = 295

1.75x + 2y = 560.75

multiply equation(i) by 2

2x + 2y = 590

1.75x + 2y = 560.75

subtract the equation

0.25 x = 29.25

x = 29.25 / 0.25

x = 117

Hence,

y = 295 - 117

y = 178

Therefore,

number of children = 117

number of adult = 178

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The number of divisors of 1730 of the form 4n + 1 is 20.

An integer is a whole number, meaning it can be positive, negative, or zero, but it cannot be a fraction or a decimal. Integers are a subset of real numbers, which also include fractional and decimal numbers.

Integers are commonly used in mathematics and computer science for counting and for performing arithmetic operations such as addition, subtraction, multiplication, and division. They are also used to represent the magnitude of a quantity, such as the number of items in a set or the time elapsed in seconds.

In computer programming, integers are often stored as binary numbers, which are sequences of bits that represent positive or negative whole numbers. Different computer architectures have different numbers of bits for representing integers, with common sizes being 8, 16, 32, and 64 bits.

The number (10)10. (11)11. (13)13 is equal to 11 × 13 × 10 = 1730 in decimal.

A divisor of a number can be represented as (4n + 1) where n is a non-negative integer.

To find the number of divisors of 1730 of the form 4n + 1, we need to find the number of factors of 1730 that can be expressed as 4n + 1.

First, we find the prime factorization of 1730:

1730 = 2 × 3 × 5 × 29

Since 1730 is an odd number, one of its divisors must also be an odd number.

The only possible values for n are 0, 1, 2, ..., (number of odd divisors - 1).

In this case, the number of odd divisors of 1730 can be calculated as:

(number of ways to choose 0 odd factors) × (number of ways to choose 1 odd factor) × (number of ways to choose 2 odd factors) × ... × (number of ways to choose 4 odd factors)

= 1 × 4 × 5 × 1 = 20

Thus, the number of divisors of 1730 of the form 4n + 1 is 20.

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The numeric value of the exponential function at x = 7 is given as follows:

f(7) = -192.

The definition of an exponential function is given as follows:

y = ab^x

In which the parameters are defined as follows:

When x = 0, y = -1.5, hence the parameter a is given as follows:

y = -1.5.

When x = 2, y = -6, hence the parameter b is obtained as follows:

-1.5b² = -6

b² = 4.

b = 2.

Hence the function is defined as follows:

y = -1.5(2)^x.

Hence the numeric value at x = 7 is given as follows:

y = -1.5(2)^7

y = -192.

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The missing term in the polynomial is 8x³y² - __ + 3xy² - 4y³ is  x²y².

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A polynomial 8x³y² - __ + 3xy² - 4y³.

Now, If we observe the terms we can conclude 'x' has decreasing powers and y has increasing powers, therefore, the term could be put in the blank to create a fully simplified polynomial written in standard form is x²y².

So, The polynomial is 8x³y² - x²y² + 3xy² - 4y³.

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After three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

Given data :

Today,  he studies 15 minutes math and 75 minutes science and from now on, 50 minutes math and 30 minutes science. So if he studies for 1 day total time for math and  science will be:

Math = 15 + 50 = 65

Science = 75 + 30 = 105

2nd day:  

Math = 65 + 50 = 115

Science = 105 + 30 = 135

3rd day:  

Math = 115 + 50 = 165

Science = 135 + 30 = 165

So, after three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

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The length of side MN from triangle MNP is 30.78

Please see the attached picture below as reference of triangle MNP.

From the case, we know that:

∠M = 90°

∠P = 72°

∠N = 18°

PM = 10

To solve this problem we need to find the length of side NP first using cos formula to angle P.

Cos ∠P = PM

                 NP

Cos 72° = 10 / NP

0.309 = 10 / NP

NP = 32.36

Next, we will use the same approac to angle N:

Cos ∠N = MN

                 NP

Cos 18° = MN / 32.36

MN = 0.951 x 32.36

MN = 30.78

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for the functions f and g, fog is given by

fog (x) = 2 ( 2x ^2 +4x ) +3  = 4x^2 +8x+3

The equation of f(x) is  f ( x ) = 2 x+ 3 and g ( x ) = 2x^ 2+ 4x

then fog is given by

fog (x) = 2 ( 2x ^2 +4x ) +3

         = 4x^2 +8x+3

The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.

For horizontal translation, we follow the following rule >>>

Let parent function be f(x), then

• f(x+a) is the parent translated "a" units left

• f(x-a) is the parent translated "a" units right for function

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Answer:

Each child gets $36666.67, each grandchild gets $18333.33

Step-by-step explanation:

220000/6= 36666.67,

36666.67/2= 18333.33

If the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" then , the data are considered at the nominal level of measurement .

The Level Of Measurement of a data set refers to the type of values that a variable can take and the properties that these values have.

In the survey , the respondents are identified as 1 for "yes," 2 for "no," 3 for "maybe," and 4 for "anything else."

These values are categorical, meaning they are names or labels for different categories. The data collected at this level is referred to as nominal level of measurement. This level of measurement is used when the variables are categorical and the order of the categories does not matter.

Therefore , the data collected in this survey is nominal and is used to describe categories or names, rather than numerical values.

The given question is incomplete , the complete question is

In a survey, the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" . the average (mean) is calculated for 665 respondents and the result is 1.5 ,

the data are at what level of measurement ?

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The statement about Raj's data sets which true is The average boy plays 8.5 hours more per week than the average girl.

Technically, a dataset is a collection of related items that can be accessed individually or in certain management combinations as a single unit. Datasets can be organized into several types of data structures. Examples of dataset in the business world can be seen from names, salaries, employee contact information, to sales figures, and so on.

In conclusion, a dataset is a collection of data that is ordered and obtained from a collection of information. The collection of information itself is obtained from observation, measurement, study, or analysis to become data. Data can be facts, numbers, names, or even descriptions. Therefore, datasets are closely related to data mining activities which help data scientists analyze data into coherent information.

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The following statements is least accurate: When adding and subtracting, consider the number of buildings instead of Sf.

What does less accurate mean?

When adding or subtracting numbers, the number of digits in the result must be equal to the smallest number of digits after the decimal point of a term in the sum. How closely a measured value agrees with a reference or known value is referred to as accuracy. For example, if you get a weight measurement of 3.2 kg for a substance in a laboratory, but the actual or known weight is 10 kg, your measurement is not accurate.In this case, your measurement is nowhere near the known value.

Typically, bottom-up estimates fall into this category: the most accurate estimate is the final estimate because it is created by estimating individual costs for different parts of the project and then combining them into one estimate.

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The correct statements from the group of answer choices are:

The point satisfies both equation 1 and 2

The point is a solution to the system

What is linear equation ?

A linear equation is an algebraic equation with simply a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

To check whether the point (2, 11) is a solution to the system, we need to substitute these values into both equations and see if they hold true.

For equation 1:

-2 * 2 + 5 * 11 = -4 + 55 = 51

For equation 2:

-7 * 11 = -77

-61 - 8 * 2 = -61 - 16 = -77

Since both equations are true for the given point, the statement "The point satisfies both equation 1 and 2" is correct and "The point is a solution to the system" is also correct.

Therefore, the correct statements from the group of answer choices are:

The point satisfies both equation 1 and 2

The point is a solution to the system

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Answer: The sample space of rolling an eight-sided die would be (1, 2, 3, 4, 5, 6, 7, 8)

Step-by-step explanation: thank you

Answer: Plugging in the values x=2, y=3, and z=4 into the expression x(2y+z)², we get:

2(2(3)+4)² = 2(10)² = 2 * 100 = 200

So the expression evaluates to 200.

Step-by-step explanation:

The family would more likely choose the stock option, if the period of investment is 20 years,after calculating the simple & compound interest.

$999.60 is 1.02 times $980, and $1,019.59 is 1.02 times $999.60.

They may choose bonds or savings account depending on the assumptions they make about the time frame of the investment.

The value of the bonds b=1,000+20x and value of the stocks is s=980⋅(1.02)x , where x is the number of years since the investment were made.

For 10 years, the value of the bond will be

b=1,000+200=1,200 dollars.

The value of the stock will be s=980⋅(1.02)10≈1,195 dollars.

They should choose the bond option if the period of investment is 10 years.

For 20 years, the value of the bond will be

b=1000+400=1,400 dollars.

The value of the stock will be 980⋅(1.02)20=1,456980⋅(1.02)20=1,456 dollars.

So they choose the stock option, if the period of investment is 20 years.

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The complete question is attached below.

From least to greatest; Elliot, Jeanette, Lucy.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Elliot = 45/54 x 100%

Lucy = 88%

Jeanette = 38/44 x 100%

Elliot = 83%

Lucy = 88%

Jeanette = 86%

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Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1 gallon already in there, and leaves you with exactly 4 gallons.

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Fill the 3-gallon jug all the way.

Pour those 3 gallons of water into the 5-gallon jug.

Fill the 3-gallon jug all the way again, and pour as much as it takes to fill the 5-gallon jug (which is 2 gallons).

Now you have 5 gallons in the 5-gallon jug and 1 gallon in the 3-gallon jug.

Empty the 5-gallon jug.

Pour the 1 gallon in the 3-gallon jug into the 5-gallon jug.

Now fill the 3-gallon jug all the way, and pour all 3 gallons into the 5-gallon jug, which, added to the 1-gallon already in there, leaves you with exactly 4 gallons.

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The system of equations are 7x + 5y = 200 and 5x + y = 112. The cost of each t shirt is $20 while the cost of each pants is $12.

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the cost of each t shirt and y represent the cost of each pants.

The shopper purchased 7 t shirts and 5 pairs of pants for $200, hence:

7x + 5y = 200    (1)

Also, he purchased 5 t-shirts and one pair of pants for $112, hence:

5x + y = 112     (2)

Solving the two equations simultaneously gives:

x = 20, y = 12

The system of equations are 7x + 5y = 200 and 5x + y = 112

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Based on the scatterplot, 50 beats per minute is the best prediction of the resting heart rate, in beats per minute, of a person who exercises an average of ​​​​​​​8 hours each week.

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Green Probability: 2/5

Yellow Probability: 2/5

Black Number of Beads: 4

If the chance to get a black bead is 1/5 the chance to get green or yellow has to be 4/5. Since both have the same amount of beads, the chance is 2/5 for each of them.

Now we know that 8 beads = 2/5 chance.

To find the number for 1/5 we just divide by 2.

8/2 = 4

Answer:

green Probability:2/5

yellow Probability:2/5

black Number of Beads:4

Step-by-step explanation                                                                                  best of luck

Answer:

Step-by-step explanation:

Ln means log to the base e and 3x+1 is an exponent

So the answer is:

4 = e^(3x+1).

By applying normal approximation to the binomial concept, it can be concluded that the indicated probability is 0.62134

Normal approximation to the binomial is a method of approximating the probabilities associated with the binomial distribution using the normal distribution.

μ = n.p

σ = √np(1-p)

where μ is the mean, n is the number of trials, p is the success probability and σ is the standard deviation.

Now we have:

x = 6

n = 18

p = 0.3

Thus we can calculate the mean:

μ = np

  = 18 * 0.3

  = 5.4

Now we calculate the standard deviation

σ = √μ (1-p)

  = √ 5.4 (1 - 0.3)

  = √ 5.4 * 0.7

  = √ 3.78

  = 1.944

Then we can find the z-score using the mean and standard deviation found in the previous step:

z-score = (x – μ) / σ

            = (6 - 5.4) / 1.944

            = 0.6 / 1.944

            = 0.309

And finally, we can obtain from the z table that P(6) = P(x<0.309) = 0.62134

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