Suppose that the functions f and g are defined as follows.

Find f.g and f+ g. Then, give their domains using interval notation.

A line passes through point −9, 7 and has a slope of −43, the equation of the line in the =+AxByC form is 43x + y = -380.

To write the equation of a line in the form of Ax + By = C, we need to find values for A, B, and C.

We know that the line passes through the point (-9, 7) and has a slope of -43. We can use the point-slope form of the equation to find the equation of the line:

y - y1 = m(x - x1)

Where m is the slope and (x1, y1) is a point on the line.

Substituting the values we know:

y - 7 = -43(x + 9)

Expanding and rearranging:

y - 7 = -43x - 387

43x + y = -380

Thus, the equation of the line in the =+AxByC form is 43x + y = -380.

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The domain is the set of input or x-values.

The domain of the given function includes all values between - 4 and 4, both inclusive:

The range is the set of output or y-values.

The range of the given function f(t) includes all values between - 1 and 2, both inclusive:

The area of the triangle in the image is 24 square centimeters.

Remember that the area of a triangle of base B and height H is given by:

A = B*H/2

On the diagram, we can see that the base of the triangle is 8cm, and the height is 6cm, then we can replace these two values in the formula above, then we will get:

A = 8cm*6cm/2

A = 8cm*3cm

A = 24cm²

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Results:

(i) The vector −→EX in terms of a and/or b, →X = 1/2 (10b →OB + 10a →OA)

(ii) The vector −−→XY in terms of a and/or b→XY = →Y - 1/2 (10b →OB + 10a →OA)

(i) We can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints to express the vector −→EX in terms of a and/or b.

Since X is the midpoint of BC, we can express X as the average of the coordinates of B and C:

→X = 1/2 (→B + →C)

Since B is located at 10b units in the direction of vector →OB from O, and C is located at 10a units in the direction of vector →OA from O, we can express →B and →C in terms of a and b:

→B = 10b →OB

→C = 10a →OA

Substituting these values into the expression for →X, we get:

→X = 1/2 (10b →OB + 10a →OA)

(ii) To express the vector −→XY in terms of a and/or b, we can use the given ratio AB: BY = 3: 2.

Since AB is a vector from A to B, we can express it as →AB = →B - →A.

Substituting the expressions for →B and →A, we get:

→AB = 10b →OB - →OA

Since AB: BY = 3: 2, we can express BY as 2/3 of AB:

→BY = 2/3 (→AB)

Substituting the expression for →AB, we get:

→BY = 2/3 (10b →OB - →OA)

Finally, we can express →XY as the vector from Y to X, which is the opposite of →X to →Y:

→XY = →Y - →X

Substituting the expressions for →X and →Y, we get:

→XY = →Y - 1/2 (10b →OB + 10a →OA)

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Answer:

A

Step-by-step explanation:

In A, if G is 3, then P is -3.

This means that P = (-G)

In this hypothetical query, the key phrase is:leading word = x3.leading Coefficient is 2,1 is a fixed term.

An equation is a mathematical statement that states that two expressions are equal. It is written in the form of an equation, with an equals sign (=) between the two expressions. Equations can be used to solve for a single unknown variable, or to show a relationship between multiple variables. Equations can be used to describe the behavior of physical systems, such as the motion of a projectile, or to describe the properties of chemical reactions. Equations are also used to describe the behavior of abstract concepts, such as the rate of growth of a population over time.

There is no connected polynomial; taking the hypothetical

Answer:

leading word = x3.

leading Coefficient is 2

1 is a fixed term.

Detailed explanation:

Considering a fictitious circumstance;

Any polynomial, like 2x3 + 3x + 1,

This is how the polynomial is written: ax3 + bx + c

In this case, a = leading Coefficient;

leading phrase = x3

Constant phrase =

as a result;

In this hypothetical query, the key phrase is:

leading word = x3.

leading Coefficient is 2

1 is a fixed term.

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In this hypothetical query, the key phrase is leading word x³.leading Coefficient is 2,1 is a fixed term.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It is written in the form of an equation, with an equals sign (=) between the two expressions. Equations can be used to solve for a single unknown variable, or to show a relationship between multiple variables. Equations can be used to describe the behavior of physical systems, such as the motion of a projectile, or to describe the properties of chemical reactions. Equations are also used to describe the behavior of abstract concepts, such as the rate of growth of a population over time.

There is no connected polynomial; taking the hypothetical

Answer:

leading word x³.

leading Coefficient is 2

1 is a fixed term.

Detailed explanation:

Considering a fictitious circumstance;

Any polynomial, like 2x³ + 3x + 1,

This is how the polynomial is written: ax³ + bx + c

In this case, a leading Coefficient;

leading phrase = x³

Constant phrase =

As a result;

In this hypothetical query, the key phrase is:

leading word = x³.

leading Coefficient is 2

1 is a fixed term.

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Answer:

1/1

Step-by-step explanation:

The remaining person will take 4 days to finish the work.

Work has a completely different connotation in science than it does in ordinary life. Every time labour is performed, energy is transmitted, as shown by the definition of work in physics.

Let's assume that each man can do the whole job in "x" days.

According to the problem, three men can do the job in 10 days, so their combined work rate is:

3/x = 1/10

Solving for x, we get x = 30.

This means that one man can do the job in 30 days.

After three days, one man leaves, so only two men are left to complete the remaining job. They have already worked for 3 days, so the remaining work is:

(2/3) * (7/10) = 14/30

This means that two men can do the remaining work in 14 days.

After another three days, one more man leaves, so only one man is left to complete the remaining job. They have already worked for a total of 6 days (3 days + 3 days), so the remaining work is:

(1/3) * (4/10) = 4/30

This means that one man can do the remaining work in 4 days.

Therefore, the remaining person will take 4 days to finish the work.

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The probability that all 3 stolen books are not English novels is 0.6667

Given data ,

If there are 12 books in total, and 4 are English novels, then 8 are not English novels.

When 3 books are stolen, there are 9 books left, out of which 8 are not English novels.

The probability that the first stolen book is not an English novel is 8/9.

The probability that the second stolen book is also not an English novel is 7/8 (since there are now only 8 books left).

The probability that the third stolen book is also not an English novel is 6/7 (since there are now only 7 books left).

So the probability that all 3 stolen books are not English novels is:

(8/9) * (7/8) * (6/7) = 0.6667

Hence , the probability is 0.667

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Step-by-step explanation:

The two angles form a straight line (180 degrees)

4x-5       +    x+40     = 180   degrees

5x + 35 = 180

5x = 145

x = 29

The frequency table using this data is

Number of hours of sleep Number of employees

6                                                     2

7                                                     4

8                                                     3

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

6 7 8 7

7 8 7 6

From the baove data, we have the frequencies to be

Frequency of 6 = 2

Frequency of 7 = 4

Frequency of 8 = 2

So, we have the frequency table to be

Number of hours of sleep Number of employees

6                                                     2

7                                                     4

8                                                     3

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Answer:

2

4

2

Step-by-step explanation:

f(-2) = 151, means if Miguel hikes 2 miles to the south, his elevation would be 151 feet. This interpretation is true in the context of the problem

f(4) = 151, means if Miguel hikes 4 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem

f(1.5) = 170.25, means if Miguel hikes 1.5 miles to the north, his elevation would be 170.25 feet. This interpretation is true in the context of the problem

Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2.

Based on the information provided, the elevation h (in feet), of Miguel with respect to time when he hikes x miles north can be modeled by this quadratic function:

f(x) = (x + 3)² + 150

When x = -2, the quadratic function for his elevation is given by:

f(-2) = (-2 + 3)² + 150

f(-2) = 1 + 150

f(-2) = 151 feet.

When x = 4, the quadratic function for his elevation is given by:

f(4) = (4 + 3)² + 150

f(4) = 49 + 150

f(4) = 199 feet.

When x = 1.5, the quadratic function for his elevation is given by:

f(1.5) = (1.5 + 3)² + 150

f(1.5) = 49 + 150

f(1.5) = 170.25.

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To achieve your retirement goal of withdrawing $50,000 each year for 15 years after retirement, while earning 7% interest, you will need to deposit approximately $3,671.95 each year for the next 30 years. This calculation is based on the concept of annuity, which takes into account the future value of money and the time value of money. By consistently depositing this amount over the next 30 years, your account will accumulate enough funds to support your retirement withdrawals.

Answer:

6[tex]cm^{2}[/tex]

Step-by-step explanation:

0.5bh=0.5*3*4=6

Answer:

We should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the future value of the investment

P = the initial principal (the lump sum we need to deposit)

r = the annual interest rate (9% in this case)

n = the number of times the interest is compounded per year (since interest is compounded every 2 months, or 6 times per year, n = 6)

t = the number of years (32 years in this case)

We are given that we want the investment to grow to $100,000 in 32 years, so we can set A = $100,000 and solve for P:

$100,000 = P(1 + 0.09/6)^(6*32)

Simplifying the expression inside the parentheses:

$100,000 = P(1.015)^192

Dividing both sides by (1.015)^192:

P = $100,000 / (1.015)^192

Using a calculator:

P ≈ $14,408.92

Therefore, we should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.

The critical t value for a confidence level of 80% with a sample size of 11 is 1.833.

What is value?
Value in math is the numerical representation of a concept or quantity. It can be used to measure, compare, or describe a range of concepts, including distance, speed, time, money, and more. Value is an essential part of mathematics, as it allows for the comparison of different numbers and is used in equations and formulas to solve problems. Value is also used to represent specific ideas, such as the value of pi or the value of "infinity".

The critical t value represents the boundary between the middle two categories of a t-distribution with a confidence level of 80%. To calculate this value, we must first calculate the degrees of freedom (DF) which is equal to the sample size minus 1. In this case, the DF is 10.

Next, we must use a t-table to find the t value. Using the chart, we can see that for a confidence level of 80%, the t value is 1.833. This means that any value of t that is higher than 1.833 will fall within the highest category of the t-distribution and is considered statistically significant. Therefore, the critical t value for a confidence level of 80% with a sample size of 11 is 1.833.

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The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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The height of the cone is determined as 6.45 inches.

The height of the cone is calculated by applying the formula for the volume of a cone.

V = ¹/₃ π r²h

where;

let the radius of the cone = 5.6 inches

The height of the cone is calculated as follows;

h = ( 3V ) / (π r²)

h = (3 x 1,186.92 ) / (π r²)

h = 6.45 inches

Thus, the height of the cone is determined by using the formula for the volume of a cone.

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The function N(t)=t2−8t−1, for evaluating N(6) will be -13.

A function is the rule which assigns a unique output value for each input value. The input values are typically called the domain of the function, and the output values are called the range of the function.

To evaluate means to find the value of an expression or a function at a particular point or set of points. This typically involves substituting given values for any variables in the expression or function and then simplifying or solving the resulting equation to obtain a numerical result.

To evaluate N(6), we substitute t = 6 into the expression for N(t);

N(6) = 6² - 8(6) - 1

Simplifying;

N(6) = 36 - 48 - 1

N(6) = -13

Therefore, N(6) = -13.

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Answer: The following formula determines the total number of infected people after t days:

500,000 / (1 + 499e^(-1.617t))

We can enter t = 4 into the algorithm to determine the total number of affected 4 days after the outbreak and then assess:

Step-by-step explanation:

500,000 / (1 + 499e^(-1.617(4))) = 500,000 / (1 + 499e^(-6.468))

= 500,000 / (1 + 499(0.00155))

= 500,000 / (1 + 0.77445)

= 500,000 / 1.77445

When this is rounded to the closest whole number, we obtain:

281,580

Therefore, four days after the outbreak, about 281,580 people will be infected.

The missing value of y is -4 and the ordered pair (-1,2) is part of the ratio table. thus, Options (A) and (C) are correct.

The fact that analogous ratios have the feature that the ratio of the corresponding words is constant must be used to determine whether claims are true. Let's utilize this property to add the values that are missing:

x        y

-1        2

x        4 -> since (-1/2) = (x/4), we can solve for x: x = -2

1        -2

2        y -> since (2/(-2)) = (-1/2), we can solve for y: y = -4

Therefore, the missing x-value is -2, and the missing y-value is -4. Also, the ordered pair (-1,2) is part of the ratio table.

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Answer:

ok so here  is the ans i worked long for it like 15 min

plsssssssss mark branliest i beg u

Step-by-step explanation:

The value of f(12) for the function f(x) = (x - 4)/16 is 0.5.

Here we have been given the function

f(x) = (x - 4)/16

This function models the expression (x - 4)/16. This implies that we will get a different value of f(x) for every different value of x.

Now here we have been given to find the value of f(12). This implies that we need to find the value of f(x) = (x - 4)/16 when the value of x is 12.

Hence, to find f(12) we need to replace x with 1 in the function. This will give us

(12 - 4)/16

= 8/16

= 0.5

Therefore, f(12) is 0.5

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Part(A),
The given digits can be used to create 300 even four-digit numerals.

Part(B),

These four-digit numbers come in a set of 60.

A. If the numbers must be even:

The units digit has six options: 2, 4, 6, 8, or 0. The units digit cannot be 1, 3, 5, 7, or 9, as they are all odd numbers.

Use any of the last five digits; for the hundreds digit, use any of the last four digits. The tens digit can be represented by any of the last three digits.

The sum of the digits 1, 3, 5, 7, 8, and 9 yields the following number of even four-digit numbers:

5 × 5 × 4 × 3 = 300

The given digits can be used to create 300 even four-digit numerals.

A. If the sum is less than three thousand:

Four-digit numbers are less than 3000, hence a thousand digits must be 1. There are five possibilities for the units digit (since we cannot use 1 or 3).

With each digit appearing just once or twice, the total number of four-digit numbers that may be made that are fewer than 3000 is:

5 × 4 × 3 = 60

There are 60 such four-digit numbers.

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Answer:what are you solving for ? If it’s. X it equals 16

Step-by-step explanation:

The number of ways members of the Subcommittee can be chosen from the Committee is 12,077,462,720.

Number is a mathematical object used to count, measure, and label. It is a concept used in math, science, and everyday life. Number has been around since the dawn of time and is an integral part of the universe. Numbers can be used to identify objects, measure quantities, and understand relationships between things. They are also used to represent abstract concepts, such as money, time, and space. Numbers can be used to solve problems and make decisions.

The number of ways members of the Subcommittee can be chosen from the Committee is equal to the number of combinations of 8 Republicans and 7 Democrats out of the total 23 members. This can be calculated using the combination formula, which is:

C(23, 8) x C(15, 7) = 12,077,462,720

The combination formula is defined as C(n,r) = n!/(r!(n-r)!), where n is the total number of members in the Committee (23) and r is the number of Republicans and Democrats from the Subcommittee (8 and 7, respectively). In this case, the n! term is equal to 23!, which is 8,314,814,080, and the r! term is equal to 8! x 7!, which is 40,320. Therefore, 12,077,462,720 is the total number of ways members of the Subcommittee can be chosen from the Committee.

This number can also be interpreted as the number of possible permutations of the 8 Republicans and 7 Democrats within the Subcommittee. This means that there are 12,077,462,720 ways to assign the 8 Republicans and 7 Democrats to the Subcommittee, without changing the number of Republicans and Democrats in the Subcommittee.

In conclusion, the number of ways members of the Subcommittee can be chosen from the Committee is 12,077,462,720. This number can be calculated using the combination formula, and it represents the number of possible permutations of the 8 Republicans and 7 Democrats within the Subcommittee.

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Answer: 25,000

Step-by-step explanation: 10x10x16x16=25,000

Sweet Treats Bakery is ordering 1,860 kilograms of sugar this time.

If the Sweet Treats Bakery is ordering 25% less sugar than the last time, then they are ordering only 75% of the previous amount, or 0.75 times 2,480 kilograms.

75% can be rearranged as decimal form.

For that, divided by 100.

We get,

75/100 = 0.75.

To calculate this, you can multiply 0.75 by 2,480:

0.75 × 2,480 = 1,860

Therefore, Sweet Treats Bakery is ordering 1,860 kilograms of sugar this time.

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Answer: B

Step-by-step explanation:

The y intercept must be 1 from the chart.  So when y=mx+b   b is your intercept.  A and C do not have b=1

D does not hit y-axis at 1

Must be B