What makes composing functions different from doing an arithmetic operation of two functions such as adding or dividing them?

(50 points) please i beg xoxoxo

Answer:

step 3

Step-by-step explanation:

\(\frac{1}{4}\) (12x + 8) + 4 = 3 ← distribute parenthesis by \(\frac{1}{4}\)

3x + 2 + 4 = 3 ← simplify left side by collecting like terms

3x + 6 = 3 ← subtract 6 from both sides (subtraction property of equality )

3x + 6 - 6 = 3 - 6 , that is

3x = - 3 ( divide both sides by 3 )

x = - 1

Let the amount invested in stocks be x.

The amount invested in bonds is four times that invested in stockes.

Therefore, the amount invested in bonds is 4x.

Accordingly,

So, the amount invested in stocks is $6000.

The amount invested in bonds is

So, the amount invested in bonds is $24,000.

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

learn more on arc angle here: https://brainly.com/question/22826189

#SPJ1

Answer:

infinity

Explanation:

The formula for calculating slope is expressed as;

m = y2-y1/x2-x1

Given the coordinates

(12,7) and (12,-2)

m = -2-7/12-12

m = -9/0

m = infinity

This means that the slope of the line passing through the points is infinity

Answer:

slope is undefined

Step-by-step explanation:

calculate slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (12, 7 ) and (x₂, y₂ ) = (12, - 2 )

m = \(\frac{-2-7}{12-12}\) = \(\frac{-9}{0}\)

division by zero is undefined thus the slope is undefined

9514 1404 393

Answer:

  -7/48

Step-by-step explanation:

Put the numbers in place of the corresponding variables and do the arithmetic.

  \(\dfrac{-\left|1\dfrac{7}{8}+(-1)\right|}{2-(-4)}=\dfrac{-\dfrac{7}{8}}{6}=-\dfrac{7}{8\cdot6}=\boxed{-\dfrac{7}{48}}\)

Answer:

The total number of flowers that Maya plant is;

Explanation:

Given the model in the attached image.

The total length of the model is;

The width of the model is;

So, the total number of flowers Maya plant is the area of the model;

Therefore, The total number of flowers that Maya plant is;

Given info:- In triangle (∆)ABC , in which ∠A = 2x, ∠B = x+15° and ∠C = 2x + 10°. Then find the value of x , also find the measure of each angles of a triangle.

Explanation:-

Let the angles be 2x, x+15 and 2x+10 respectively.

∵ Sum of the three angles of a triangle is 180°

∴ ∠A + ∠B + ∠C = 180° [Sum of ∠s of a ∆=180°]

→2x + x+15 + 2x+10 = 180°

→ 2x + x + 2x + 15 + 10 = 180°

→ 3x + 2x + 15 + 10 = 180°

→ 5x + 15 + 10 = 180°

→ 5x + 25 = 180°

→ 5x = 180°-25

→ 5x = 155°

→ x = 155°÷5 = 155/5 = 31.

Now, finding the measure of each angles of a ∆ABC by putting the original value of “x”.

∴ ∠A = 2x = 2(31) = 62°

∠B = x+15 = 31 + 15 = 46°

∠C = 2x + 10 = 2(31) + 10 = 62 + 10 = 72°.

Answer:

x = 6

Step-by-step explanation:

Step 1: Write equation

2x/2 = 6

Step 2: Simplify

x = 6

Answer:

x=4

have a great day. mine sucks.

Step-by-step explanation:

Since P(C ∩ I) ≠ P(C) x P(I), we can conclude that choosing a cupcake with chocolate chips is not independent of choosing one with icing.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a) To determine if choosing a cupcake with chocolate chips is independent of choosing one with icing, Jonathon should calculate the following two probabilities:

b) To check if choosing a cupcake with chocolate chips is independent of choosing one with icing, we need to compare the probability of choosing a cupcake with both chocolate chips and icing (P(C ∩ I)) with the product of the probabilities of choosing a cupcake with chocolate chips (P(C)) and the probability of choosing a cupcake with icing (P(I)).

If the probability of choosing a cupcake with both chocolate chips and icing is equal to the product of the probabilities of choosing a cupcake with chocolate chips and the probability of choosing a cupcake with icing, then we can say that choosing a cupcake with chocolate chips is independent of choosing one with icing.

Let's calculate these probabilities using the information given in the table:

Now, let's check if P(C ∩ I) = P(C) x P(I):

P(C) x P(I) = (9 / 25) x (7 / 10) = 63 / 250

Since P(C ∩ I) ≠ P(C) x P(I), we can conclude that choosing a cupcake with chocolate chips is not independent of choosing one with icing.

To learn more about probability visit:

https://brainly.com/question/24756209

#SPJ1

The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.

To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.

The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.

Using this information, we can proceed to plot the circle on a graph:

Plot the center point: (3, -3).

From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.

Up: (3, -3 + 6) = (3, 3)

Down: (3, -3 - 6) = (3, -9)

Left: (3 - 6, -3) = (-3, -3)

Right: (3 + 6, -3) = (9, -3)

Connect the plotted points to form a circle.

The resulting graph should look like this:

    |            • (3, 3)

    |  

    |    •

    |                     •

__|_____________________________

    |

    |

    |

    |  

    |    • (3, -3)

The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.

For similar questions on circle

https://brainly.com/question/28162977

#SPJ11

To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.

For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938

For New York: Ratio = 911,216 / 18.6 million = 0.049019

For Cairo: Ratio = 10,598 / 19.1 million = 0.000554

For Beijing: Ratio = 959,611 / 21.2 million = 0.045270

For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234

To calculate the owners per 100, we multiply the ratio by 100.

For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)

For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)

For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)

For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)

For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)

Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:

Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7

New York: Ratio = 0.049019, Owners per 100 = 4.9

Cairo: Ratio = 0.000554, Owners per 100 = 0.1

Beijing: Ratio = 0.045270, Owners per 100 = 4.5

Tokyo: Ratio = 0.064234, Owners per 100 = 6.4

For such more question on Ratio

https://brainly.com/question/12024093

#SPJ8

Answer:

Step-by-step explanation:

To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.

Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.

Answer:

y=10/3x+5

(0,5), (3,15)

Step-by-step explanation:

First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.

-3y=-10x-15

Next, we divide by -3.

y=10/3x+5

If you don't know how to graph an equation with slope-intercept form,

it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.

(0,5).

Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).

Now that we have two points (0,5) and (3,15), just construct your line.

Answer:

14

Step-by-step explanation:

The pair that support Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ is option B

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

examples of these rules are

The problem requires the prove by Angle - Side- Angle = ASA to ensure that the the triangles are congruent

The Angle - Side - Angle = ASA have it that the two triangles being compared should have their two angles and the included side being equal

Learn more about congruent triangles here:

https://brainly.com/question/29393764
#SPJ1

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

For more such answers on incomes

https://brainly.com/question/28414951

#SPJ8

The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

To know more about cylinders visit:

brainly.com/question/15891031

#SPJ1

The system of equations that describes Tammy and Luke's outcomes is written below

It can be deduced form the question that

x represents the number of points for a catch

y to represent the number of points for a miss

Tammy makes 5 catches and misses 1, ending the game with 23 points

5x - y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points

8x - 5y = 30

The system of equations required are

5x - y = 23

8x - 5y = 30

Learn more about linear functions at:

https://brainly.com/question/29225098

#SPJ1

The logarithmic function that models the data is given as follows:

y = 1.0994 + 5.6403 ln(x).

The logarithmic function is used as from the table, the data has a initial fast increase and then the rate of the increase decreases, as the graph reaches it's horizontal asymptote.

The function is defined using a logarithmic regression calculator, inserting the points of the data-set.

From the table, the points are given as follows:

(0, 0.5), (1, 1.4), (2, 4.1), (3, 7.6), (4, 9.1), (5, 10).

(as x represents the number of years after 2005).

Inserting these points into the logarithmic regression calculator, the equation is given as follows:

y = 1.0994 + 5.6403 ln(x).

More can be learned about functions at https://brainly.com/question/10709685

#SPJ1

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

0.00002 = 0.002% probability of actually having the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Having the disease

Probability of having a positive test:

0.05 of 1 - 0.000001(false positive)

0.99 of 0.000001 positive. So

\(P(A) = 0.05*(1 - 0.000001) + 0.99*0.000001 = 0.05000094\)

Probability of a positive test and having the disease:

0.99 of 0.000001. So

\(P(A \cap B) = 0.99*0.000001 = 9.9 \times 10^{-7}\)

What is the probability of actually having the disease

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{9.9 \times 10^{-7}}{0.05000094} = 0.00002\)

0.00002 = 0.002% probability of actually having the disease

Answer:

r would be replaced with a and the answer is b so a2 + a - 72 = b

Step-by-step explanation:

The total surface area of the figure will be 1968.85 square meters.

To determine  the surface area of the figure, we need to find the area of each face and then add them together.

Surface Area of the rectangular prism = 2(lb + bh + hl)

= 2(16 × 9.5) + 2(9.5 × 14) + 2(16 × 14)

= 2(152 + 133 + 224) = 2(509)

= 1018 m²

Next, we need to find the area of the triangular prism on the front with dimensions 11 m, 12.7 m, and 14 m:

Surface Area of the triangular prism;

= (11 × 14) + 2(0.5 × 11 × 12.7) + 2(0.5 × 12.7 × 14)

= (154 + 350.35 + 445.5)

= 950.85 m²

Therefore, the total surface area of the figure will be;

Total Surface Area = Surface Area of rectangular prism + Surface Area of triangular prism

= 1018 m² + 950.85 m²

= 1968.85 m²

So, the surface area of the figure is 1968.85 square meters.

Learn more about a rectangular prism;

https://brainly.com/question/21308574

#SPJ1

In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

Learn more about costs at:

https://brainly.com/question/25109150

#SPJ1

The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

\(\rm log_2(\frac{1}{128}) = x\)

The expression is solved using the identity as;

\(\rm log_e1 = x\\\ e^x=1\)

Apply the identity;

\(\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7\)

Hence the value of x will bed -7.

To learn more about the logarithm refer;

https://brainly.com/question/7302008

#SPJ1

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer:

  y = 1/2x +7/2

Step-by-step explanation:

The two marked points are 2 units apart vertically, and 4 units apart horizontally. The slope of it is ...

  m = rise/run = 2/4 = 1/2

The value of the y-intercept can be found from

  b = y -mx . . . . . . where (x, y) is a point on the line

Using the point (-1, 3), we find the y-intercept to be ...

  b = 3 -(1/2)(-1) = 3 1/2 = 7/2

Then the slope-intercept equation is ...

  y = mx +b

  y = 1/2x +7/2

Answer:

11

Step-by-step explanation: