Why is the answer C?

Answer:

3(x-6)(x+2) and (3x+6)(x-6)

Step-by-step explanation:

The other two answers are wrong because the value for their x will be positive.

Part (1) : The solution is [tex]729[/tex]

Part (2): The solution is [tex]$\frac{1}{16 x^{8}}$[/tex]

Part (3): The solution is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Explanation:

Part (1): The expression is [tex]3^{2} \cdot3^{4}[/tex]

Applying the exponent rule, [tex]$a^{b} \cdot a^{c}=a^{b+c}$[/tex], we get,

[tex]$3^{2} \cdot 3^{4}=3^{2+4}$[/tex]

Adding the exponent, we get,

[tex]3^{2} \cdot3^{4}=3^6=729[/tex]

Thus, the simplified value of the expression is [tex]729[/tex]

Part (2): The expression is [tex]$\left(2 x^{2}\right)^{-4}$[/tex]

Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,

[tex]$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$[/tex]

Simplifying the expression, we have,

[tex]\frac{1}{2^4x^8}[/tex]

Thus, we have,

[tex]$\frac{1}{16 x^{8}}$[/tex]

Thus, the value of the expression is [tex]$\frac{1}{16 x^{8}}$[/tex]

Part (3): The expression is [tex]$\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$[/tex]

Applying the exponent rule, [tex]$\frac{x^{a}}{x^{b}}=x^{a-b}$[/tex], we have,

[tex]\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}[/tex]

Adding the powers, we get,

[tex]\frac{2x^{2}y^{-1}z^{-7}}{3}[/tex]

Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,

[tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Thus, the value of the expression is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Answer:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the age of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(37.5,6.2)[/tex]  

Where [tex]\mu=37.5[/tex] and [tex]\sigma=6.2[/tex]

We are interested on this probability:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}[/tex]

We can begin finding [tex] P(X>40)[/tex] using the z score formula given by:

[tex] z = \frac{a-\mu}{\sigma}[/tex]

Using this formula we have:

[tex] P(X>40)= P(Z>\frac{40-37.5}{6.2}) = P(Z>0.403)[/tex]

And using the complement rule and the normal standard table or excel we have this:

[tex]P(Z>0.403)=1-P(Z<0.403)= 1-0.657= 0.343[/tex]

Now we can find [tex] P(X>45)[/tex] using the z score formula given by:

[tex] z = \frac{a-\mu}{\sigma}[/tex]

Using this formula we have:

[tex] P(X>45)= P(Z>\frac{45-37.5}{6.2}) = P(Z>1.210)[/tex]

And using the complement rule and the normal standard table or excel we have this:

[tex]P(Z>1.210)=1-P(Z<1.210)= 1-0.887= 0.113[/tex]

And replacing into our original probability we got:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]

Answer: 3/8

Step-by-step explanation:

Firstly, let's look at the possible outcome when 3 coins are tossed.

If two coins are first tossed, the possible outcome will be,

{HH, HT, TH, TT}

if one more coin is tossed together with the two to make it 3coins, the possible outcome will be gotten by matching the H and T of the third coin with the set of sample space above to give us,

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

This gives a total sample space of 8.

Outcomes that has at least two consecutive heads in the sequence are {HHH, HHT, THH} which is the possible outcome i.e 3

Probability that the outcome has at least two consecutive heads in the sequence will be;

Possible outcome/total outcome

= 3/8

For Janay's art project, the blue wire must be longer than 4 inches and shorter than 10 inches to create a triangle. This is based on the Triangle Inequality Theorem, which states that the length of any side of a triangle should be less than the sum of the lengths of the other two sides, but more than the difference of the two sides' lengths.

To determine how long the blue wire should be for Janay's art project, we need to understand a rule in geometry related to triangles, specifically the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.

Here, we have side lengths of 3 inches (purple wire) and 7 inches (pink wire), so the blue wire can be any length that is less than 3+7=10 inches, and more than |7-3|=4 inches. So the blue wire should be more than 4 inches and less than 10 inches to form a triangle.

This ensures that Janay will be able to form a valid triangle for her art project. If the length of the blue wire is less than 4 inches or greater than 10 inches, a triangle cannot be formed.

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Proof

Provide the missing reasons for the proof of part of the triangle midsegment theorem.

Given: K is the midpoint of MJ.

           L is the midpoint of NJ.

Prove: MN = 2KL

The complete answer is attached in the diagram below.

The complete answer for the missing reasons is attached below in the diagram.

Please check the figure.

Keywords: statement, proof, reason

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Answer:

Absolute magnitude

Step-by-step explanation: Astronomy deals with the study of stars and other heavenly bodies. Astronomers use apparent magnitude to define how bright a star appears and shines from the earth.

Answer:

0 N

Step-by-step explanation:

We are given that

[tex]m_1=7 kg[/tex]

[tex]m_2=0.7 kg[/tex]

Total mass =[tex]m_1+m_2=7+0.7=7.7 Kg[/tex]

We have to find the magnitude of the normal force with which the bottom cube is acting on the top cube.

When both cube are fall freely then

g=[tex]0m/s^2[/tex]

Then, the weight=[tex]mg=7.7\times 0=0 N[/tex]

The direction of weight is downward.

We know that

Normal force is equal to weight and act in opposite direction of weight.

When the weight is zero N then

The magnitude of the normal force with which the bottom cube is acting on the top cube=0 N

Answer:

Option (d)

Step-by-step explanation:

Given,

y" +y=sin x ...........(1)

The particular solution

[tex]y_p=A x sinx +Bx cosx[/tex]

[tex]y'_p=Axcosx+Asinx+B cosx-Bxsinx[/tex]

[tex]y"_p=Acosx-Axsinx+Acosx-Bsinx-Bsinx-Bxcosx[/tex]

[tex]y"_p=2Acosx-Axsinx-2Bsinx-Bxcosx[/tex]

Putting the value of y" and y in equation (1)

[tex]2Acosx-Axsinx-2Bsinx-Bxcosx+Axsinx+Bxcosx = sinx[/tex]

[tex]\Rightarrow 2Acosx-2Bsinx=sinx[/tex]

Therefore 2A =0              -2B=1

              ⇒A=0                 [tex]\rightarrow B=-\frac{1}{2}[/tex]

Therefore [tex]y_p=-\frac{1}{2} x cosx[/tex]

The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:

Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

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Answer:

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

Assuming that the cylindrical cup is open at the top, the formula becomes

Area = πr² + 2πrh

From the information given,

Radius = 1.8 inches

Height = 4 inches

Therefore, the surface area of the coffee cup is

(3.14 × 1.8²) + (2 × 3.14 × 1.8 × 4)

= 10.1736 + 45.216

= 55.4 inches² to the nearest tenth.

Answer:

55.4 :))

Step-by-step explanation:

Answer: Waters on 7th day

Step-by-step explanation:

If she waters everyday then days= 1,2,3,4,5,6,7,8,9

If she waters every other day= 1,3,5,7,9

If she waters every third day= 1,4,7,10,13

So the common day to all is either 1st day or 7th day.

This is a comparison problem involving rates. We multiply the rate of draining by the time and subtract the result from the initial amount, which gives us the amount of water after that time.

This problem is considerate a comparison problem that involves rates of draining water from two pools. In these cases, it's crucial to keep the rates and the initial amounts separate to correctly solve the problem.

The first pool is initialy with 3700 liters of water and the draining rate is 31 liters per minute. The second pool from the start has 4228 liters and is being drained at a rate of 42 liters per minute.

To know the amount of water in each pool after any given time in minutes, we would multiply the rate by that time, and subtract the result from the initial amount of water.

For example, if we wanted to find out how much water was left after 10 minutes, we would do the following calculations:

Therefore, after 10 minutes, the first pool had 3700 liters and the second one had 3828 liters of water.

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Answer:

The answer is 39 degrees by 6:00 in the evening.

Step-by-step explanation:

Since it is 2:00 in the afternoon and there is 4 hours, with 8 degrees dropping every hour, 8 times 4 equals 32, so 71 degrees minus 32 degrees is 39 degrees.

Answer: the temperature at 6:00 in the evening is 39°F

Step-by-step explanation:

If the temperature drops 8 °F every hour after that, then the rate is linear and the rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 71 °F

d = - 8 °F (since it is decreasing)

n = 5 (2pm to 6pm)

We want to determine the value of the 5th term, T5. Therefore,

T5 = 71 - 8(5 - 1)

T5 = 71 - 32 = 39

Answer: T⊂U⊂W are subspaces of V

Step-by-step explanation:

Proof: This is the easier direction.

If T⊂U⊂W or W⊂U⊂T then we have U⊂T⊂W = T or T⊂U⊂W = U

orT⊂U⊂W=W respectively.

SoT⊂U⊂W is a subspace as T, U and W are subspaces.

1st case :T⊂U⊂W is true Then the disjunction W⊂U⊂T or U⊂T⊂W is trivially true.

Let x∈W1 and y∈W2−W1.

By the definition of the union, we have x∈W∪T∪C and y∈T⊂U⊂W

As T∪U∪W is a subspace, x+y∈T∪C∪W which, again by the definition of the union, means that x+y∈W∪T∪C

V∈W∪T∪C

As V was arbitrary, as desired.

Final answer:

If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one.

Explanation:

If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one. We can prove this by contradiction. Assume that none of the subspaces is contained in the other. This means that there is an element in T that is not in U ∪ W, an element in U that is not in T ∪ W, and an element in W that is not in T ∪ U. If we take any two of these elements, one from each subspace, and add them together, the result will not be in T ∪ U ∪ W, which contradicts the assumption.

Therefore, two of the subspaces must be contained in the other one.

Answer:

1. (1,10) 2. (2,-3) 3. (3,3)

The reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).

Given that,
To determine the function as a set of ordered pairs.
​f(1)=10​, ​f(2)=-3​, ​f(3)=3

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,
Since order pair of function f(x) = y is given as (x, y)
Similarly ordered pair of the function given is,
f(1) = 10
ordered pair = (1, 10)

f(2) = 3
ordered pair = (2, -3)

f(3) = 3
ordered pair = (3, 3)  

Thus, the reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).

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Answer: 8 cups of white paint is used.

Step-by-step explanation:

In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red. This means that the percentage of red paint in the mixture is 100 - (40 + 20) = 40%

There are four cups of blue paint used in a batch of lilac paint. This means that 20% of the total number of cups of paint used in a batch of lilac paint is 4.

Assuming that the total number of cups of paint in the mixture is x, then,

20/100 × x = 4

0.2x = 4

x = 4/0.2 = 20

Therefore, the number of cups of white paint used is

40/100 × 20 = 0.4 × 20

= 8 cups

Final answer:

In the lilac paint mixture, for every 4 cups of blue paint, which accounts for 20% of the mixture, there are 8 cups of white paint, corresponding to 40% of the mixture.

Explanation:

The question involves determining the amount of white paint used in a batch of lilac paint given that 40% of the paint mixture is white, 20% is blue, and the remainder is red. We're told that 4 cups of blue paint are used. Since blue paint represents 20% of the mixture, we can use this information to find out the total amount of the paint mixture and then calculate the amount of white paint needed.

First, find the total amount of the paint mixture by calculating the full 100% that the 4 cups of blue paint (20%) contribute to. This calculation is as follows:

Now that we know the total paint mixture is 20 cups, we can determine the amount of white paint, which is 40% of the total mixture:

Therefore, 8 cups of white paint are used in the mixture.

Answer:

c = -18

d = 2

Step-by-step explanation:

[[6,8],[-11,15]]-[[c+2,3],[-5,d-4]]=[[22,5],[-6,17]]

First we arrange the subtraction to clear the unknowns

- [[c+2,3],[-5,d-4]] = [[22,5],[-6,17]] - [[6,8],[-11,15]]

  [[c+2,3],[-5,d-4]] = [[6,8],[-11,15]]  - [[22,5],[-6,17]]

Now we solve what can be done

  [[c+2,3],[-5,d-4]] = [[6-22 , 8-5],[-11+6 , 15-17]]

  [[c+2,3],[-5,d-4]] = [[-16 , 3] , [-5 , -2]

we match each term with its corresponding one and we will obtain

c + 2 = -16             d - 4 = -2

c = -16 - 2              d = -2 + 4

c = -18                    d = 2

Answer:

15/28

Step-by-step explanation:

Let the number of berries Lisa picked be y

Number of berries she used to make pie = 2y/8 = y/4

Number of berries left = y - y/4 = 3y/4

Number of berries she gave her friend = 5/7 × 3y/4 = 15y/28

Fraction of the berries she gave her friend = 15/28

Answer:

6,840cm³

Step-by-step explanation:

V = 360 * 19

V = 6,840cm³

Answer: speed at the equator =

1047.33 miles per hour

Step-by-step explanation:

The radius of earth is 4000miles

The earth rotates on its axis, hence we calculate the circumference at the equator

Circumference, C = 2 π R

C = 2 x 3.142 x 4000miles

C = 25,136 miles

Since the total time of one complete rotation about it's axis is 24hours

Hence, the speed at the equator is

speed = 25,136/24 = 1047.33 miles per hour

The speed of the person on the equator due to daily rotation of the earth is;

Speed = 1047.221 miles per hour

Formula for circumference is;

C = 2πR

Thus;

C = 2 × π × 4000miles

C = 25,132.74 miles

C ≈ 25133 miles

We know that formula for speed is;

speed = distance/time

Thus;

Speed on the equator is;

speed = 25133/24 = 1047.221 mph

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Answer:

Option C) 88                                          

Step-by-step explanation:

We are given the following in the question:

Unit cost of sweatpants = $7

Unit cost of jackets = $14

Let x be the number of sweatpants sold and y be the number of jackets sold.

Customers bought 8 times as many sweatpants as jackets

Then, we can write,

[tex]x = 8y[/tex]

Total sales = $6,160

[tex]7x + 14y = 6160[/tex]

Substituting the values, we get,

[tex]7(8y) + 14y = 6160\\70y = 6160\\y = 88\\x = 704[/tex]

Thus, 88 jackets were sold.

Option C) 88

Answer:

3

Step-by-step explanation:

the initial statement is  

y ∝ 1 /x

 to convert to an equation multiply by k the constant

of variation

y = k × 1 /x = k /x

to find k use the given condition

y = 5  when  x = 6

y = k/ x ⇒ k = y x = 5 × 6 = 30

y = 30 /x

when  

x = 10

then

y = 30 /10 = 3

Answer: y = 3

Step-by-step explanation:

In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.

We would introduce a constant of proportionality, k. Therefore,

y = k/x

When y = 5 , x = 6

Therefore,

5 = k/6

Cross multiplying by 6, it becomes

k = 6 × 5 = 30

The expression becomes

y = 30/x

Therefore, when x is 10,

y = 30/10

y = 3

Study the figure attached below:

Answer:

240951.33km      

Step-by-step explanation:

For this type of question first we need to draw the figure as shown in the attached file (Figure.1).

Looking at the figure, we can see that triangle ABC is formed by bisecting the angle 35 degree (i.e. if the angle is bisected, it will divide into two equal parts, so 35 degree will divide into two equal parts of 17.5 degree).

As the triangle ABC is a right triangle, so we can use the trigonometric ratios to find the diameter of the sun.

[tex]tan(\theta )= \frac{perpendicular}{Base}[/tex]

In the triangle ABC, perpendicular (opposite side to [tex]\theta[/tex] ) is BC and base (Adjacent side) is AC

[tex]tan(\theta)=\frac{BC}{AC}[/tex]

[tex]\theta[/tex]=17.5 degree

AC=382100km

Putting the values, we get

[tex]tan(17.5)=\frac{BC}{382100}\\ \\BC=tan(17.5)*382100km\\\\BC=0.315*382100km\\\\BC=120475.66km[/tex]

Diameter=d=2*Radius

As BC is the distance from center of the sun, it is the radius, so we can find the diameter if we multiply it by 2.

Diameter of the sun=d=2*120475.66km

[tex]The\ diameter\ of\ the\ sun\ = 240951.33km[/tex]

Final answer:

To find the diameter of the Sun based on its angular diameter and distance from Earth, use the trigonometric function tan to calculate the true diameter, resulting in an approximate value of 865,373 miles.

Explanation:

To find the diameter of the Sun:

Final answer:

By setting up an equation with x representing the number of correct answers, we find that Peter answered 11 questions correctly on his quiz.

Explanation:

To determine how many questions Peter answered correctly on his quiz, we first need to set up an equation to represent the situation. Let's let x be the number of questions Peter got right, and since he answered 15 questions in total, it means he got (15 - x) questions wrong. Since he gets 3 points for each correct answer and loses 1 point for each wrong answer, we can write the equation as:

3x - (15 - x) = 29

Now, we will solve for x:

3x - 15 + x = 29

4x - 15 = 29

4x = 29 + 15

4x = 44

x = 44 / 4

x = 11

So, Peter answered 11 questions correctly.

Answer:

The answer is D.

Step-by-step explanation: A monomial is an algebraic expression that consists of one term. D consists of 2 terms and is considered a binomial.

Answer:

The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.

Step-by-step explanation:

It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.

Let the acute angle be m∠A.

For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.

The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,  

                                 [tex]Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }[/tex]

So for acute angle 45° the ratio of Sin 45° and Cos 45° is:

                                         [tex]\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1[/tex]

Hence one of the angles of a triangle is, m∠A = 45°.

Comparing with the options provided the triangle is,

Triangle ABC that has angle measures 45°, 45° and 90°.

Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.

Answer:

IT'S the second option

Step-by-step explanation:

Answer:

3 gallons

Step-by-step explanation:

If two gallons of paint covers 800 square feet, 'x' gallons of paints will cover 1200square feet room where x is the number of gallons needed to paint the 1200 square feet room.

Mathematically,

2 gallons = 800sq.ft

x gallons = 1,200sq.ft

x × 800 = 2 × 1200

x = 2 × 1200/800

x = 3 gallons

Therefore Leah will need 3gallons of paint for 1200sq.ft room

Answer:

10208

Step-by-step explanation:

just 58x176

Graph A is the correct representation, as it aligns with the functions f(x) and g(x), resulting in the accurate intersection point (2, 4). Graph B does not accurately represent the functions based on the reported intersection point (4, 1).

The correct graph can be determined by analyzing the given functions and the specified intersection points. The functions are f(x) = -3/4 * x^2 + 3x + 1 and g(x) = 2x, and the reported intersection points are (2, 4) for graph A and (4, 1) for graph B.

To verify the accuracy, substitute the x-values into both functions:

Graph A (Intersection at (2, 4)):

f(2) = -3/4 * (2)^2 + 3 * 2 + 1 = 4

g(2) = 2 * 2 = 4

Both functions align, confirming the correctness of the reported intersection point.

Graph B (Intersection at (4, 1)):

f(4) = -3/4 * (4)^2 + 3 * 4 + 1 = 1

g(4) = 2 * 4 = 8

There is a discrepancy here, as the y-values do not match. Therefore, graph B does not accurately represent the functions f(x) and g(x).

In conclusion, graph A is correct since it accurately reflects the given functions and results in the reported intersection point (2, 4).

Answer:

449 millimeters.

Step-by-step explanation:

Each millimeter  corresponds to 20 feet.

Therefore the length of the model = 8980 / 20 = 449 millimeters.

Answer:

HI! I'VE DONE THIS B4, IT IS 449 MILLIMETERS. DOES ANYONE KNOW HOW TO TURN THE CAPS BUTTON OFF? ANYWAYS, PLZ MARK BRAINLIEST

Step-by-step explanation: