The junior and senior students at Mathville High School are going to present an exciting musical entitled, "Math, What is it Good For?". A large group of students came out to an information meeting. After a brief introduction to the musical, 15 senior students decided that it was not for them and they left. At that point, twice as many junior students as senior students remained. Later in the meeting, after the 15 senior students had left, of the junior students and of the remaining senior students also left. This left 8 more senior students than junior students. All of the remaining students stuck it out and went on to produce an amazing product. How many students remained to perform in the school musical, "Math, What is it Good For?"

The probability of having wrinkled green peas is 25% or 0.25

Explanation:

Given:

Pea shape - smooth and wrinkled

Pea color - Yellow and green

Smooth is dominant to wrinkled

Yellow color is dominant to green

So, the genotype of smooth pea is SS or Ss

                                 wrinkled pea is ss

The genotype of yellow pea is YY or Yy

                                 green pea is yy

According to the question,

Ssyy X ssYy

Possible gametes of Ssyy - Sy , Sy, sy, sy

Possible gametes of ssYy - sY, sy, sY, sy

Cross between these gametes are shown in the punnett square drawn in the word file attached.

According to the cross,

The probability of having wrinkled green peas is 25% or 0.25

Step-by-step explanation:

∫₋₂² (f(x) + 6) dx

Split the integral:

∫₋₂² f(x) dx + ∫₋₂² 6 dx

Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0.  But we can also show this algebraically.

Split the first integral:

∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Using substitution, write the first integral in terms of -x.

∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Flip the limits and multiply by -1.

∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Rewrite f(-x) as -f(x).

∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

The integrals cancel out:

∫₋₂² 6 dx

Evaluating:

6x |₋₂²

6 (2 − (-2))

24

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:

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:

Step-by-step explanation:

372 + 1/4*372 = $465

$465 is her new savings and 33% of it is $153.45

$465 + $153.45 = $618.45

So yes she would have enough money to buy a plane ticket to alaska the cost $600

Answer: The number of revolutions the tire makes per minute= 840.76

Step-by-step explanation:

Given : Diameter of tire = 24 inches

Speed of car = 60 mi/ hr

We know that 1 mile =63360 inches and 1 hour = 60 minutes

Then, Speed of car =  ( 60 mi/ hr) x( 63360 inches) ÷ (60 minutes)

[tex]=\dfrac{60\times63360 }{60}[/tex]  inches/minute

=63360 inches / minute

Circumference of tire = [tex]\pi (diameter)[/tex]

[tex](3.14)(24)=75.36\ inches[/tex]

Now , the number of revolutions the tire makes per minute = [tex]\dfrac{\text{speed of car}}{\text{Circumference of tire}}[/tex]

[tex]=\dfrac{63360}{75.36}=840.76433121\approx840.76[/tex]

Hence, the number of revolutions the tire makes per minute= 840.76

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:

6,840cm³

Step-by-step explanation:

V = 360 * 19

V = 6,840cm³

Answer:

10208

Step-by-step explanation:

just 58x176

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:

subtract 27 from 85

Step-by-step explanation:

85

-27

———

58

7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracted from 15 and then the 8 tens becomes 7 tens so 7-2=5

58+27=85 to check your work

We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Given that regroup 1 ten as 10 one

85 -27 = 58

Since 7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracbecomem 15 and then the 8 tens becomes 7 tens thus, 7-2=5

Therefore,

58 + 27 = 85

We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85

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Answer:

5 km walking, 30 km on the bus.

Step-by-step explanation:

Let

w

be the distance walking and

b

be the distance on the bus.

The total distance is 35 km.

w

+

b

=

35

The total time is 1.5 hours. Each leg has time equal to distance/speed.

w

5

+

b

60

=

1.5

Multiply by 60 to clear the fractions.

12

w

+

b

=

90

Subtract the first equation,

11

w

=

90

−

35

=

55

w

=

5

b

=

30

Check:

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:

About 428 N

Step-by-step explanation:

Weight = 1,500 * 9.8 = 14,700 N

Density = Mass ÷ Volume

1,030 = 1,500 ÷ V

V = 1,500 ÷ 1,030  = 1.46 m^3.

Buoyant force = Density * g * V  

Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)

Buoyant force = 9,800 * (1,500 ÷ 1,030)  = 14,272 N.

Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]

The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.

The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).

In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:

Normal Force = 1500 kg × 9.81 m/s² = 14715 N.

This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.

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Answer:

  500

Step-by-step explanation:

The problem statement tells you ...

  300 = 0.60×voters

Dividing by the coefficient of the variable gives ...

  300/0.60 = voters = 500

500 students voted in the election.

Answer:

500

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:

Our answer is $2000

Step-by-step explanation:

Short term capital loss = $1000

Long term capital loss = $4000

Taxable Income = $30000

Long term capital loss carryover to 2019 = ($1000 + $4000) - $3000 = $2000

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:

The first one.

Step-by-step explanation:

We can say lines L and K are parallel, because they have the same slope and different y intercepts.

This would mean they will always be moving in the same direction, hence causing them to never touch.

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:

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.

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:

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:

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

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:

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.

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: 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.

Answer:

52.2

Step-by-step explanation:

Light reflects off a mirror at the same angle it hits it at (as shown in the image).  Since both triangles are right triangles, we can say they are similar by AA similarity.

Since they're similar, we can write a proportion.

HT / TV = JS / SV

Plugging in values:

5.8 / 4 = JS / 36

JS = 52.2

The wall is 52.2 feet tall.

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: