**Answer:**

Probability (Physics Major or Female) = 28/40 = 0.7

**Step-by-step explanation:**

The probability of being a female is 17/40

The probability of being a physics major is 18/40

The number of students counted twice is 7/40

Probability (Physics Major or Female) = 17/40 + 18/40 - 7/40

Probability (Physics Major or Female) = 28/40 = 0.7

If f (x) = x

2 − 2 x , g (x) = x − 2

1) prove that : f(2) = g(2)

2) If g (K) = 7 , find : the value of k

The value of** k **is **9 **for the **function g.**

To solve this problem we should have a brief concept of** algebraic functions.**

To solve this problem we have to follow a few steps.

Here **f is a function of x** and the relation with the function denotes as **x²-2x**. Also,** g is a function of x** and the relation with the function denotes as** x− 2.**

If we put, **x = 2 **on f(x) = x²-2x. We can write, **f(2)** = 2²-2.2 = 4 - 4 =** 0**.

If we put,** x = 2** on g (x) = x − 2. We can write, ** g(2) **= x− 2= 2- 2 = **0**.

Hence, we can conclude that ** f(2) = g(2) = 0. ** ( proved)

Here, g(k) = 7. So,** x = k** in this relation.

We have to put x= k on g(x) = x− 2 ; now we can write, **g (k) = k− 2.**

g (k) = k− 2 = 7 as per the question. Therefore** **k = 7 + 2 = 9

The value of k is 9.

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The** correct question** is,

If f (x) = x²-2x

g (x) = x − 2

1) prove that : f(2) = g(2)

2) If g (K) = 7, find the value of k

Are these lines parallel or not: L1: (1,2), (3,1), and L2: (0,-1), (2,0)

First find the slope of the first line

L1

m = ( y2-y1)/(x2-x1)

m = ( 1-2)/(3-1)

= -1/2

Now find the slope of the second line

L2

m= ( y2-y1)/(x2-x1)

= ( 0 - -1)/(2 -0)

= (0+1)/(2-0)

= 1/2

Parallel lines have the same slope

These lines do not have the same slope, they are different by a negative sign.

These lines are not parallel.

Point m represents the opposite of negative 1/2 and point n represents the opposite of positive 5/2 which number line correctly shows points m and n great

If Point m represents the** opposite** of negative 1/2 and point n represents the opposite of **positive** 5/2. Then M is 1/2 and N is -5/2.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.

A **number line** is a picture of a graduated **straight line** that serves as visual representation of the real numbers.

Given that point M represents the opposite of** negative** 1/2. Which means **opposite **of -1/2. The opposite of -1/2 means positive of 1/2. The sign changes.

Point N represents the opposite of **positive** 5/2. Which means opposite of 5/2. The** opposite **of 5/2 means negative of 5/2. The sign changes.

opposite of positive 5/2 is -5/2.

Now let us plot this values on a** number line**. 1/2 is 0.5 and -5/2 means -2.5.

The **graph **is attached below.

Hence M is 1/2 and N is -5/2

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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the

rectangle: A(-8,-6), B(-3,-6), C(-3,-4), and D(-8,-4).

Given these coordinates, what is the length of side AB of this rectangle?

** **The length of side AB of this **rectangle** is = 5 units

**what is rectangle ?**

A shape with four straight sides and four **angles **of 90 degrees ( right angle ) . two of the sides are longer than the other two . a **rectangle** with four sides of equal length is **square** .

we could use distance formula to find the length

A (-8,-6) ; B (3 , -6 )

distance =(( X2 - X1 )^2 +( Y2 - Y1 ) ^2 ) ^1/2

AB = (( -3+8)^2+(-6-[-6]^2)^1/2

AB= 5^2

AB = 5 units .

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For each expression, combine like terms and write an equivalent expression with fewer terms.a. 4x+3xb. 3x+5x-1c. 5+2x+7+4xd. 4-2x+5xe. 10x-5+3x-2

To simplify the expressions you have to combine the like terms.

This means that you'll solve the operations between the terms that have the same variables, for example x + 2x=3x

Or the terms that have no variables and are only numbers, for example 4+5=9

a. The expression is

[tex]4x+3x[/tex]Both terms have the same variable "x", so you can add them together. To do so, add the coefficients, i.e. the numbers that are being multiplied by x

[tex]4x+3x=(4+3)x=7x[/tex]And you get that the simplified expression is **7x**

b. The expression is

[tex]3x+5x-1[/tex]In this expression you have two types of terms, the x-related terms and one constant. In this case you have to solve the operation for the x-related terms together and leave the constant as it is

[tex](3x+5x)-1=(3+5)x-1=8x-1[/tex]The simplified expression is **8x-1**

Find the area of ABC with vertices A(3,-6), B(5,-6), and C(7,–9).

**Area** of a **triangle** ABC with the given vertices is 3 square units.

Given that, the vertices of a triangle ABC, A(3,-6), B(5,-6), and C(7,–9).

What is the area of triangle formula in coordinate geometry?In Geometry, a **triangle** is a three-sided polygon that has three edges and three vertices. The **area** of the **triangle** is the **space** covered by the triangle in a two-dimensional **plane**.

Area of a triangle = [tex]\frac{1}{2} ( |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|)[/tex]

Here, (x1, y1) = A(3,-6), (x2, y2) = B(5,-6), and (x3, y3) = C(7,–9)

Now, the **area** of a **triangle** = 1/2 (|3(-6+9)+5(-9+6)+7(-6+6)|)

= 1/2 (|3(3)+5(-3)+7(0)|)

= 1/2 (|(9-15)|)

= 1/2 × 6

= 3 square units

Therefore, **area** of a **triangle** ABC with the given vertices is 3 square units.

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A grocer wants to mix two kinds of nuts. One kind sells for $2.00 per pound, and the other sells for $2.90 per pound. He wants to mix atotal of 16 pounds and sell it for $2.50 per pound. How many pounds of each kind should he use in the new mix? (Round off the answersto the nearest hundredth.)

Let

x -----> pounds of one kind of nuts ($2.00 per pound)

y ----> pounds of other kind of nuts ($2.90 per pound)

we have that

2x+2.90y=2.50(16) ------> equation 1

x+y=16-----> x=16-y -----> equation 2

solve the system of equations

substitute equation 2 in equation 1

2(16-y)+2.90y=40

solve for y

32-2y+2.90y=40

2.90y-2y=40-32

0.90y=8

y=8.89

Find out the value of x

x=16-8.89

x=7.11

therefore

the answer is

7.11 pounds of one kind of nuts ($2.00 per pound)8.89 pounds of other kind of nuts ($2.90 per pound)Write rules for the composition of translations.

**Answer: gurl you think i know**

**Step-by-step explanation: **

Bonus: Write the equation of a line in slope intercept form that is parallelto y=4/3x-7 and contains the point (5,-8)

The given equation is

[tex]y=\frac{4}{3}x-7[/tex]The slope of the given line is 4/3 because it's the coefficient of *x*.

Now, the new line has a slope of 4/3 too because parallel lines have equal slopes.

We know that the new line passes through the point (5, -8). Let's use the point-slope formula to find the equation.

[tex]y-y_1=m(x-x_1)[/tex]Replacing the points and the slope, we have.

[tex]\begin{gathered} y-(-8)=\frac{4}{3}(x-5) \\ y+8=\frac{4}{3}x-\frac{20}{3} \\ y=\frac{4}{3}x-\frac{20}{3}-8 \\ y=\frac{4}{3}x+\frac{-20-24}{3} \\ y=\frac{4}{3}x-\frac{44}{3} \end{gathered}[/tex]Therefore, the equation of the new line is y = (4/3)x - (44/3).Is z(x) = 1 + 6x^2 + 4x a quadratic function? I don't believe it's linear or constant, just wanted to make sure.

Given function is

[tex]z(x)=1+6x^2+4x[/tex]In the given function, the maximum power of x is 2 and it is of the form

[tex]ax^2+bx+c[/tex]**Therefore, it is a quadratic function.**

Give a negation of each inequality.

p < 9

**Answer: P can be anything from 8 to below**

**Example: 8, 7, 6, 5, 4, 3, 2, 1, 0, -1 .....**

The width of a Rectangle is 3.6 inches and the perimeter is 72 inches. What is the length of the rectangle?

We know that

• The width of the rectangle is 3.6 inches.

,• The perimeter is 72 inches.

The perimeter formula for a rectangle is

[tex]P=2(w+l)[/tex]Where P = 72, w = 3.6, and we have to solve for l.

[tex]\begin{gathered} 72=2(3.6+l) \\ \frac{72}{2}=3.6+l \\ 36=3.6+l \\ l=36-3.6 \\ l=32.4 \end{gathered}[/tex]Therefore, the length of the rectangle is 32.4 inches.Evaluate the expression for the given variable.9 - k ÷ 3/4 k=2/3

We are given the following expression:

[tex]9-k\div\frac{3}{4}[/tex]We are also given that k is equal to 2/3. So, we can substitute that into the expression:

[tex]9-\frac{2}{3}\div\frac{3}{4}[/tex]Due to order of operations, we have to do the division first, and then do the subtraction. To do division with fractions, we keep the first fraction the same and take the reciprocal of the second fraction. Then, we can multiply the two fractions. Let's do that:

[tex]9-(\frac{2}{3}\div\frac{3}{4})=9-(\frac{2}{3}*\frac{4}{3})=9-\frac{8}{9}[/tex]Now, we can do the subtraction:

[tex]9-\frac{8}{9}=\frac{81}{9}-\frac{8}{9}=\frac{73}{9}[/tex]Therefore, our answer is **73/9**

1260/27 as a mixed number

46 whole number 18/27 but can be further divided to 46 whole number 2/3

the quotient of two numbers is -1 their difference is 8 what are the numbers

Let the two numbers be represented with x and y.

Quotient of two numbers = -1:

[tex]\frac{x}{y}=-1\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}.(1)[/tex]Difference of two numbers = 8:

[tex]x\text{ - y = 8}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(2)[/tex]From the first equation, make x the the subject.

Thus, we have:

x = -y

Substitute -y for x in equation 2:

-y - y = 8

-2y = 8

Divide both sides by -2:

[tex]\begin{gathered} \frac{-2y}{-2}=\frac{8}{-2} \\ \\ y\text{ = -4} \end{gathered}[/tex]Now, substitute -4 for y in equation 2:

x - y = 8

x - (-4) = 8

x + 4 = 8

Subtract 4 from both sides:

x + 4 - 4 = 8 - 4

x = 4

Therefore,

x = 4 and y = -4

Thus, the numbers are 4 and -4

**ANSWER:**

**4 and -4**

A toy costs 35 000 lndonesian rupiah (Rp).

The conversion rate is Rp 1000 = 5$0.145 598.

Without using a calculator, estimate the price of

the toy in S$.

here is your answer I hope this helps

In the following figure PR is perpendicular to QS. PR= 14cm, QR=15 cm and QS =12 cm. What is the perimeter of PQR?

I don’t see an image of the figure, so I am assuming the figure is a triangle. If not, the answer may be different. The perimeter of triangle PQR = 41 cm.

If the figure looks like what I drew in this image, it should work as an answer. If not, remember that perimeter means adding all of the side lengths together. Ex. For a rectangle, P = 2l + 2w. And for a triangle, P = a + b + c, where the variables represent each of the sides.

If the figure looks like what I drew in this image, it should work as an answer. If not, remember that perimeter means adding all of the side lengths together. Ex. For a rectangle, P = 2l + 2w. And for a triangle, P = a + b + c, where the variables represent each of the sides.

Solve form. 2m - p = 11f

**ANSWER**

**EXPLANATION**

We want to solve for m in the equation:

[tex]2m-p=11f[/tex]This means that we want to** make m the subject of formula**.

That is:

[tex]\begin{gathered} \text{Add p to both sides of the equation:} \\ 2m-p+p=11f+p \\ 2m=11f+p \\ \text{Divide both sides by 2:} \\ \frac{2m}{2}=\frac{11f+p}{2} \\ m=\frac{11f+p}{2} \end{gathered}[/tex]That is the answer.

On a piece of paper, graph yz 2x - 3. Then determine which answer choicematches the graph you drew.ABсD(2, 1)(2, 1)(2, 1)((2, 1)(0-3)0,-3)(0-3)(0-3)A. Graph DOB. Graph BO C. Graph AD. Graph

The graph says

[tex]y\ge x-1[/tex]The upper section of the graph will be shaded since y is greater than or equals to x - 1.

**The answer is A . Graph A**

A firefighter has an annual income of $46,870. The income tax the firefighter has to pay is 16%. What is the amount of income tax in dollars and cents that the firefighter has to pay? (TEKS 7.13A-S)

amount of income tax:

[tex]Tax=46,870\times0.16=7499.2[/tex]Answer:

$7499.2

Consider that AABC is similar to AXYZ and the measure of ZB is 68º. What is the measure of ZY? A) 70° B) 68° C) 41° D) 22°

**Answer**

**Option B is correct.**

**Angle Y = 68º**

**Explanation**

Similar triangles have the same set of angles in them.

All the corresponding angles are equal to each other.

So, if **triangle ABC **is similar to **triangle XYZ**

**Angle A = Angle X**

**Angle B = Angle Y**

**Angle C = Angle Z**

The order in which they are named determines the angles that are corresponding to each other.

So, if **Angle B = 68º**

**Angle Y = Angle B = 68º**

**Hope this Helps!!!**

Line a is parallel to line b and line c is parallel to line d, using the diagram what can be said about angle 7 and 12

**Answer:**

C

**Step-by-step explanation:**

Angle 7 is congruent to angle 5 by the corresponding angles theorem, and angles 5 and 12 are supplementary because they are consecutive interior angles.

Thus, angles 7 and 12 are supplementary.

A quarterback completed 19 out of 30 attempts to pass the football.What was his percent of completion

[tex]\begin{gathered} the\text{ percentage of completion is as follows:} \\ percentageofcompletion=\frac{Attempted\text{ number}}{passed\text{ number}}\times100 \\ percentageofcompletion=\frac{19}{30}\times100 \\ percentageofcompletion=63.34\text{ } \end{gathered}[/tex]

The percentage of completion is 63.34%.

A single fair die is tossed. Find the probability of rolling a number greater than 5

Using the** probability** concept, the odds of rolling a number greater than 5 is 1 :5

**What is probability ?**

**probability** is the branch of mathematics concerning** numerical descriptions** of how likely an event is to occur or how likely it is that a proposition is true . the probability of an event is a number between 0 and 1 , where ,roughly speaking ,0 indicates impossibility of the event and 1 indicates certainty.

The odd of a particular experiment is defined thus :

Number of possible outcomes greater than 5 : number of possible below or equal to 5

Sample space = {1, 2, 3, 4, 5, 6}

Outcomes greater than 5 = {6} = 1

Outcomes below or equal to 5 = {1, 2, 3, 4, 5} = 5

The odds equals to 1 : 5

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URGENT!! ILL GIVE

BRAINLIEST!!!!! AND 100

POINTS!!!!!

**Angles** are given below.

When two straight lines or rays intersect at a single endpoint, an **angle** is created. The vertex of an angle is the location where two points come together. The Latin word "angulus ," which means "corner," is where the term "angle" originates. When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.

Given,

∠6 and ∠7 = **Vertical** angles

∠2 and ∠8 = Same side exterior angles

∠1 and ∠5 = **Corresponding** angles

∠3 and ∠6 = **Adjacent** angles

∠2 and ∠7 = **Alternate** **exterior** angles

∠4 and ∠6 = Same side **interior** **angles**

∠1 and ∠2 = Linear pair

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find the perimeter of ABC with vertices A(-4,4), B(5,-6) and C(7,-9)

**Answer:**

The answer is maybe about around 26

**Step-by-step explanation:**

Please correct me if I am wrong, but I hope this helped.

Which equation represents a line that is perpendicular to the line represented by

y=2/3x+1?

1) 3x+2y=12

2) 3x-2y=12

3) y=3/2x+2

4) y= -2/3x+4

**Answer: (1)**

**Step-by-step explanation:**

Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.

Rearranging equations 1 and 2 into slope intercept form,

[tex]3x+2y=12 \implies 2y=-3x+12 \implies y=-\frac{3}{2}x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=\frac{3}{2}x-6[/tex]

From this, we see that equation 1 is the answer.

A laptop computer is purchased for $2100. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth$300 or less?

**SOLUTION:**

After the first year, the price of the laptop computer is;

[tex]P_1=0.75\times2100=1575[/tex]After the second year, the price of the laptop computer is;

[tex]P_2=0.75\times1575=1181.25[/tex]After the third year, the price of the laptop computer is;

[tex]P_3=0.75\times1181.25=885.94[/tex]After the fourth year, the price of the laptop computer is;

[tex]P_4=0.75\times885.94=664.45[/tex]After the fifth year, the price of the laptop computer is;

[tex]P_5=0.75\times664.45=498.34[/tex]After the sixth year, the price of the laptop computer is;

[tex]P_6=0.75\times498.34=373.75[/tex]After the seventh year, the price of the laptop computer is;

[tex]P_7=0.75\times373.75=280.32[/tex]**CORRECT ANSWER: ****7 years**

3. Which of the following equations would be a parabola with vertex (2,-3) that opendownwards? Select ALL.a.h.y = -2(x - 2)2 – 3i.y = (-x + 2)2 + 3C.y = -(x - 2)2 – 3b. y = -(x + 2)2 – 3y = -(x - 2)2 + 3d. y=-(x + 2)2 +3y = -(x - 2)3 +3f. y = -(x - 2)3 – 3y=-{(x - 2)2 - 3j. y = (-x - 2)2 – 3k. y = (-x + 2)2 – 3: نه1. y = (-x - 2)2 – 3m. y =} (x - 2)2 – 3g.n.y = 2(x - 2)2 - 3

**Solution:**

**Given:**

**The equation of a parabola in vertex form is given by;**

**Hence, the equation of the parabola is;**

Hence, from the options, the equations that have **a **as negative and in the form gotten above will be selected.

**Therefore, the equations of a parabola with vertex (2,-3) that open downwards are;**

Rick Takei has a 4-wheel drive vehicle whose average retail value is $15,857. A used vehicle guide adds $60 for heated outside mirrors, $250 for rear and side air bags. $175 for cruise control, and $100 for remote keyless entry. It suggests deducting $750 for excessive mileage. What is the average retail price?

We are asked to find the final average retail price of the vehicle after the given additions and deductions.

The average retail value is $15,857

**Add $60 **for heated outside mirrors.

**Add $250** for rear and side airbags.

**Add $175** for cruise control.

**Add $100** for remote keyless entry.

**Deduct $750** for excessive mileage.

Therefore, the average retail price is **$15,692**

What is the full meaning of COPOOL
2 Lots of touristswhales.3 I(just arrive) to see the(never be) much of aconservationist. How about you?4 My friendsSierra Leone for the last six months.6(work) for a charity in5 Volunteers(comb) the coastline everyday this week, picking up plastic bottles and otherrubbish.(use) a sat navyoubefore? I don't know how this works.7 She(always love) travelling alone.
A segment that is both an altitude and a median of a triangle is a?
The cross country team ran 1.772 hours yesterday and 1.49 hours today. Each member of the team ran 3.5 miles every hour. How many miles did each member run yesterday?
Heads of Elysia cf. marginata sea slugs sometimes pull themselves free from their bodies. The heads just keep crawling around. Within a few hours, some heads start nibbling algae again. Within about 20 days, heads from young slugs can have regrown those missing body parts, including heart and all.Sayaka Mitoh and Yoichi Yusa are ecologists at Nara Women's University in Japan. They described the regrowth of cells and ultimately the sea slugs bodies March 8 in Current Biology.Mitoh first noticed the sea slugs' extreme regeneration by chance. It showed up in some Elysia slugs in his lab. "We were really surprised to see the head crawling," Yusa says.The head of a sea slug can take several hours to rip itself loose from its body. That's so slow that Mitoh and Yusa don't think the move helps slugs escape predators.Instead, a detachable body could give the sea slug a drastic, but effective, way of fighting parasites. Mitoh monitored 82 E. atroviridis slugs infested with copepods. Three of the slugs ditched their bodies along with a lot of those copepods. Two of the three managed to grow a new body. An additional 39 of the parasitized slugs let parts of their bodies slowly fall away. In contrast, 64 more sea slugs that had been collected at the same time had no pests. And none of them threw away its body. That supports the idea that parasites could drive slug heads to detach and crawl away from their bodies.What might help Elysia slug heads regrow a whole body is stealing, Yusa suggests. These animals can take the green sunlight-trapping energy factories called chloroplasts from algae. Very young slugs don't have any chloroplasts. "They need to pierce the cell walls of sea algae and sip the contents," he says. Once ingested, the chloroplasts remain alive inside the slugs for weeks to months.Biologists have debated what stealing chloroplasts does for the slugsUsing what you know about cellular differentiation and the description of sea slug regeneration explain what is happening at a cellular level:?A;Specialized cells undergo cellular differentiation to create stem cells that will grow and replace the old cellsB:Stem cells undergo cellular differentiation to create specialized cells to replace missing body parts like cardiac (heart) cells.C:Cellular differentiation is not necessary in order for the sea slugs to regrow its missing body parts.D:None of the above.
Calculate the number of atoms in 24.83g calcium phosphate.
Ammonia gas decomposes when heated.152NH(g) N(g) + 3H(g)In an experiment, a sample of 500 cm of ammonia was heated and 20% decomposed.The total volume of gas present at the end of the experiment, in cm, wasD A 20000= 100 cmB400C600D 1000
Rewrite in simplest terms: -2(k+1)-6k
Stephen can be pushy when trying to get his way.Stephen can be persuasive when trying to get his way.Which statement best explains the nuance between pushy and persuasive?Pushy implies irritating, while persuasive implies violent.Both words have negative connotations.Pushy implies irritating, while persuasive implies convincing.Both words have positive connotations.
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of errorof 13%. What is the maximum the company can expect for returned items?O $3268.20$3668.30O$4425.60O $4902.30
What are the four elements
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate. Compute a sample statistic from these data. Report your answer with three decimal places.
Who was appointed to head the committee to work on articles of confederation
suppose korie purchases the factory using $200,000 of her own money and $200,000 borrowed from a bank at an interest rate of 6 percent. what is korie's annual opportunity cost of purchasing the factory
What Hindu terms are correctly matched to ther definitions? Select all answers that are correct. Question 7 options: Vedas: holy texts that form the basis of Hinduism dharma: the idea that people should fulfill the duties that fit with their stations in life yoga: the practices designed to help link the mind, body, and breath Vishnu: Hindu god known as the Preserver Brahma: Hindu god known as the Destroyer
Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?
find the measure of each missing angle in the parallel lines and transversals below
One reason cell divide is that organisms can
what causes the appearance of the moon to change over time?
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)