1 4/1 ​ ÷1 5/2 ​ = ???

Answers:

Common angles: ΔBGC and ΔGDC

Common sides: ΔGE and ΔAG

A common angle is a triangle that exists in two or both of the triangles.

Here, the common angles should be ΔBGC and ΔGDC.

These two angles are triangles, and they consist in both triangles.

A common side is when two angles have one vertex in the same area.

Here, we see that the common sides are ΔGE, because they intersect.

Another common side we see here is ΔAG, because they also intersect.

Hope this answer helps you!

The center of the circle will be equal to (-3,4) equation of the circle   x²+y²+6x-8y+16=4

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the out trace.

The general form of the equation of the circle is:-

(x-x₁)²+(y-y₁)²=r²

here x1 and y1 are the center of the circle

Now we will convert our equation in the general form:-

x²+y²+6x-8y+16=4

x²+6xy²-8y+16-4=0

x²+3x+3x+9-9+y²-4y-4y+16-16-4=0

(x+3)²+(y-4)²-9-16+16-4=0  (x+3)²+(y-4)²=13

By comparing with the general form we can see that the coordinate of the center of the circle will be {-3,4)

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Answer: 1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x + 18 = 48

Bringing like terms on one side

3x = 48 - 18

3x = 30

x = 30/10

x = 3

Answer:

x = 10

Step-by-step explanation:

Subtract 18 from both sides.

3x=48-18

Simplify  48-18 to 30.

3x=30

Divide both sides by 3.

x= 30/3

Simplify  30/3\ to 10

x=10

x=10

​

V + F = E + 2

If V=12 and F=8 Find E:

We have to replace the values given of V and F IN THE EXPRESSION:

12 + 8 = E+2

Now, we simply have to solve for E:

12+8 -2 =E

18=E

E=18

A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. No element of B is the image of more than one element in A.

a. To prove that if f ◦ g is onto, then f must also be onto, we assume f ◦ g is onto. This means that for every c ∈ C, there exists an a ∈ A such that (f ◦ g)(a) = f(g(a)) = c. Since g(a) ∈ B, we can say that for every c ∈ C, there exists a b = g(a) ∈ B such that f(b) = c. Hence, f is onto.

b. To prove that if f ◦ g is one-to-one, then g must also be one-to-one, we assume f ◦ g is one-to-one. This means that for any a1, a2 ∈ A, if g(a1) ≠ g(a2), then (f ◦ g)(a1) = f(g(a1)) ≠ f(g(a2)) = (f ◦ g)(a2). If g(a1) = g(a2), then we can conclude that a1 = a2 to maintain the one-to-one property of f ◦ g. Therefore, g must also be one-to-one.

c. If f ◦ g is a bijection, it means that it is both onto and one-to-one. From part a, we know that f must be onto. Now, to prove that g is onto if and only if f is one-to-one, we can use the contrapositive. If g is not onto, then there exists a b ∈ B that is not in the range of g. In that case, f(g(a)) cannot be one-to-one because there are multiple values of a that map to the same b. Similarly, if f is not one-to-one, then there exist b1, b2 ∈ B such that f(b1) = f(b2) but b1 ≠ b2. In this case, g(a) can't be one-to-one because there are multiple values of a that map to the same b. Therefore, g is onto if and only if f is one-to-one.

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Answer: what type of math is that?

Step-by-step explanation:

The probability that a congressman selected at random supports Bill A or Bill B is 0.83.

The probability that a congressman selected at random supports Bill A but not Bill B is 0.21.

The probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

P(Bill A or Bill B) = P(Bill A) + P(Bill B) - P(Bill A and Bill B) = 0.35 + 0.62 - 0.14 = 0.83

ii. The probability that a congressman selected at random supports Bill A but not Bill B is the probability in the Bill A circle that is not in the overlap:

P(Bill A but not Bill B) = P(Bill A) - P(Bill A and Bill B) = 0.35 - 0.14 = 0.21

iii. P(neither Bill A nor Bill B) = P(not Bill A and not Bill B) = 0.17

Therefore, the probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

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The correct answer is: The benefits of the data should be weighed against the costs.

This is because the first step in evaluating change outcomes is to determine what data should be collected and how it will be collected.

While it is important to collect as much data as possible, it is also important to consider the costs of collecting and analyzing the data.

The data collected should be relevant to the outcomes being evaluated, and should be collected at regular intervals to track progress over time.

It is not productive to analyze change effects based on insignificant data, as this can lead to inaccurate conclusions.

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Answer:

The first system goes with the last graph.

The second system goes with the first graph.

The last system goes with the second graph.

Step-by-step explanation:

In the first system, both equations are equal if you put both of the equations in simplified slope-intercept form. When the equations are exactly equal to each other, the lines are the same. And only in the last graph, the line are the exact same line.

In the second system, you can tell even without putting the equations in slope-intercept form that the only difference between the lines are the y-intercepts. When lines have the same slope but different y-intercepts, the lines are parallel, which is shown in graph 1.

For the last system, by elimination, the system matches with the second graph. In this system, you can tell that both the slopes and y-intercepts are different, which means that this equation would actually have one solution, as shown in graph 2.

Sorry it took a while, hope I was able to help. Good Luck!

Answer:

the  ratio of 15 sec to 55 sec is 3 : 15

The spinner illustrates probability, and it is expected that a vowel will be spun approximately 10 times

In the spinner, we have:

Sections = 6

Vowels = 2 i.e. A and E

The expected number of vowels in 30 spins is:

Expected = Vowels/Sections * 30

This gives

Expected = 2/6* 30

Evaluate the product

Expected = 10

Hence, it is expected that a vowel will be spun approximately 10 times

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Answer:

the answer is 10

Step-by-step explanation:

50% of those who liked orange flavored soda also like lime flavored soda.

To find what percent of those who liked orange flavored soda also like lime flavored soda:

Let A and B represent the following events.

It is given that 70% of the people surveyed said they like the orange-flavored soda.

35% of the people surveyed said they liked the orange-flavored soda AND the lime-flavored soda.

(1) Conditional probability:

(2) If we have two events X and Y, and we need to find the probability of event X as event Y is given then the formula for conditional probability is:

(3) We need to find the percentage of those who liked orange flavored soda also like lime flavored soda.

Substitute P(A)=0.70 and P(A∩B)=0.35 in the above formula.

Therefore, 50% of those who liked orange flavored soda also like lime flavored soda.

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The complete question is given below:

The marketing research department at the Fresno Mall plans to survey teenagers about a newly developed soft drink. 70% of the people surveyed said they like the orange-flavored soda. 35% of the people surveyed said they liked the orange-flavored soda AND the lime-flavored soda. Using this information and the Text Editor, answer the following questions:

1. What is conditional probability?

2. Explain the formula for conditional probability.

3. Explain how to solve this example.

What percent of those who liked orange flavored soda also like lime flavored soda, and how did you come to that conclusion?

Answer:

c

Step-by-step explanation:

because it makes sense

The highest credit score will be for a person who maintains a low debt-to-credit ratio. The correct option is C.

A credit score means that a person is assigned a score in numerical form that depends upon income, expense, credit, and timely payments. A higher number means a good credit score and vice versa.

Always make loan payments on time. Avoid approaching your credit limit. Lengthy credit history will boost your rating. Apply for credit only if you actually need it. Check the details on your credit reports.

Therefore, the highest credit score will be for a person who maintains a low debt-to-credit ratio. The correct option is C.

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The dress was on sale for a 20% discount.

To find the percent discount, we need to calculate the difference between the original price and the sale price, and then divide that amount by the original price and multiply by 100 to represent the answer as a percentage.

Percent discount refers to the amount by which the original price of a product is reduced when it is put on sale. It is represented as a percentage of the original price.

The difference between the original price and the sale price is

=> $75.00 - $60.00

=> $15.00.

The percent discount is

=> $15.00 / $75.00 * 100

=> 20%.

So, the dress was on sale for a 20% discount

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Given two points, the equation of the line may be determined by,

y - y1 = ((y2 - y1) / (x2 - x1))(x - x1)

Substituting the given values,

y - 7 = ((9 - 7) / (6 - 3))(x - 3)

Simplification will yield to an answer of,

y = 2x/3 +5

Therefore, the answer is the second choice.

Answer:

3.92 x \(10^{12}\)

Step-by-step explanation:

The first factor needs to be a number greater than 0, but less than 10.  That would be 3.92.  Next count how many places you moved the decimal.  In standard notation the decimal should be 12 spaces to the right.  This is the exponent.

Helping in the name of Jesus.

Answer:

Less Than,Less Than or Equal to,Greater Than,Greater Than or Equal to

Step-by-step explanation:

The line under plays the role of an equal sign and the others are pretty self explanatory

Answer: The first one is a greater sign, the second one is greater than or equal to, the third one is less than, and the last one is less than or equal to.

Step-by-step explanation: hope this helps

Given:

For cylinder P: radius = 4.25 in. and height = 14 in.

For cylinder Q: radius = 7 in. and height = 8.5 in.

To find:

The volume of each cylinder.

Solution:

Volume of a cylinder is

\(V=\pi r^2h\)

where, r is radius and h is height. Use 3.14 for \(\pi\).

Using the above formula, the volume of cylinder P is

\(V_P=(3.14)(4.25)^2(14)\)

\(V_P=794.0275\)

\(V_P\approx 794.03\)

Using the above formula, the volume of cylinder Q is

\(V_Q=(3.14)(7)^2(8.5)\)

\(V_Q=1307.81\)

Therefore, the volume of cylinder P is 794.03 sq. in. and volume of cylinder Q is 1307 sq. in.

The volume of cylinder P is 794.03 sq. in. and the volume of cylinder Q is 1307 sq. in.

Suppose that the radius of the considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \pi r^2 h \: \rm unit^3\)

The given information is

For cylinder P:

radius = 4.25 in. and height = 14 in.

For cylinder Q:

radius = 7 in. and height = 8.5 in.

To find the volume of each cylinder.

The volume of a cylinder

\(V = \pi r^2 h \: \rm unit^3\)

where r is radius and h is height.

Using the above formula,

the volume of cylinder P

\(V = \pi r^2 h \: \rm unit^3\)

\(V = 3.14 \times (4.25)^2 \times 14 \: \rm unit^3\\\\V = 794.03\)

The volume of cylinder Q

\(V = \pi r^2 h \: \rm unit^3\\\\V = 3.14 \times 7^2 \times 8.5 \: \rm unit^3\\\\V =1307.81\)

Therefore, the volume of cylinder P is 794.03 sq. in. and the volume of cylinder Q is 1307 sq. in.

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Answer:

\(x = 27\)

Step-by-step explanation:

A shape exterior angles add up to 360.

All of these angles are exterior angles so we can add up all of them to and set it equal to 360 to find x.

\(3x + 4x + 2x + 40 + x + 50\)

\(10x + 90 = 360\)

\(10x = 270\)

\(x = 27\)

in the formula, =1+(2-3)+5/6-6^2,  The final result of the formula is -35.1667.

In the formula =1+(2-3)+5/6-6^2, the order of operations dictates that the exponentiation operator (^) is evaluated first, followed by multiplication and division from left to right, and then addition and subtraction from left to right.

So, access will evaluate 6^2 first, which equals 36. Then, it will evaluate the division 5/6, which equals 0.8333 (rounded to four decimal places).

Next, it will evaluate the subtraction (2-3), which equals -1. Then, it will evaluate the addition (1+(-1)), which equals 0. Finally, it will evaluate the multiplication (-6 * 6), which equals -36.

Putting it all together, we get:

=1 + (2-3) + 5/6 - 6^2

= 1 + (-1) + 0.8333 - 36

= -35.1667

Therefore, the final result of the formula is -35.1667.

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The equation the line is, y = -3/2 *x -1

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have ,

from the given graph we get,

the line is passing through the points (0,-1)& ( -2,2)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

now, by solving we get,

-3x-2y=2

Hence, the required equation is, y = -3/2 *x -1

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Answer:

Sara is 9 years old while Yusuf's is 11 years old

Step-by-step explanation:

The given parameters are;

The ratio Sara and Yusuf share the money they receive = The ratio of their ages

The amount Sara and Yusuf received from their grandmother this year = R1,500

The amount of money Sara receives = R675

Therefore, the amount of money Yusuf receives = R1,500 - R675 = R825

Let 'x', and 'y' represent the ages of Sara and Yusuf

Therefore, the ratio of their ages, x/y = R675/R825) = 9/11

x·11 = y·9

x, and y < 18

When x = 9, y = 11, we  get;

9·11 = 11·9

Therefore a possible solution is Sara's age = x = 9 and a possible solution for Yusuf's age, y = 9

From the data set attached the median of time 7th graders spend online is 90 minutes and 8th graders spend online is 120 minutes. That is 8th graders spend more time online.

Therefore the answer is (b) eighth graders.

From the given data set, the amount of time twenty 7th graders spend online in the ascending order is

30, 30, 60, 60, 60, 60, 90, 90, 90, 90, 90, 90, 90, 120, 120, 120, 120, 150, 150, 180

The middle two values are 90 and 90, therefore median is the average which is 90 minutes.

Similarly in the case of 8th graders the data values are

30, 60, 60, 90, 90, 90, 120, 120, 120, 120, 120, 120, 120, 120, 150, 150, 150, 150, 180, 180

There are two values in the middle and they are 120 and 120, therefore the median is the average of the two values which is 120 minutes.

Thus comparing the median, eighth graders spend more time online.

--The question is incomplete, answering to the data set attached--

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The missing digits are 0, 4, and 5 in descending order

The complete division operation is

    8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

From the question, we are to determine the missing digits in the division operation

From the diagram,

The first two digits of the divided were divided by the divisor, this resulted into a quotient of 8 and a remainder of 1.

The divisor is 6

Let the value of the first two digits be x

Thus,

x / 6 = 8 1/6

x/6 = 49 / 6

By comparison,

The first two digits is 49

Therefore,

The dividend of the division operation is 4,925

Now, we can complete the division operation

      8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

Hence, the missing numbers are 0, 4, and 5

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The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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For given Step function also known as piecewise function, The range of g(x)  is {-3,2,5} i.e. C.

What exactly is a piecewise function?

A piecewise function has several definitions in various x intervals. The graph of a piecewise function is split into sections that correspond to each of its definitions. The absolute value function is an outstanding example of a piecewise function. Let us look at why it was given that name. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x x≥0)

-x if x<0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As range of a given function is given by its y values, here it will be given by values of g(x) and as we can see from question for values of x, g(x) is always equal to -3,2,5.

Hence,

           The range of g(x) is {-3,2,5}.

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Answer:

true

Step-by-step explanation:

3.5*2.5-6=2.75

2+0.75= 2.75

It is proven true.

Answer:

C

Step-by-step explanation:

A difference of squares can be factored in general as

a² - b² = (a - b)(a + b)

We are looking for 2 terms separated by a - and perfect squares on either side. The only one meeting this criteria is

25x² - 64y²

= (5x)² - (8y)²

= (5x - 8y)(5x + 8y) ← in factored form