Nancy performs a full backup of her server every Sunday at 1 A.M. and differential backups on Mondays through Fridays at 1 A.M. Her server fails at 9 A.M. Wednesday. How many backups does Nancy need to restore?

Answer:

Step-by-step explanation:

miles left to travel=51-15=36

more days required=36/9=4 days.

Answer: it will take 4 more days before DeAndre finishes

Step-by-step explanation:

DeAndre is 15 miles into a 51-mile backpacking trip in the wilderness. This means that he has already covered 15 miles and the total number of miles is 51. Number of miles left is 51 - 15 = 36 miles.

DeAndre can hike 9 miles per day. The number of days that it will take him to cover 36 miles would be 36/9 = 4 days

Answer:

not possible.

Step-by-step explanation:

number of invitations luanne  has to address after x days = 120-15x

number of invitations  Darius has to address after x days =  120 + 15(7-x)

so, if the number of invitations should be the same for both of them,

we have to equate their number of invitations

120-15x =  120 + 15(7-x)

subtracting 120 from both the sides,

-15x = 15(7-x) = 105 -15x

adding we 15x on both sides, we wont find any solution for x.

so, this isnt possible or the question must be wrong.

Answer:

Cost of 1 gallon of Regular gasoline is $2.45 and  Cost of 1 gallon of Premium gasoline is $2.90.

Step-by-step explanation:

Let the Cost of Regular gasoline be 'x'.

Let the Cost of Premium gasoline be 'y'.

Given:

Amount of regular gasoline bought yesterday = 2 gallons

Amount of premium gasoline bought yesterday = 3 gallons

Total Cost of yesterday = $13.60

Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.

Framing in equation form we get;

[tex]2x+3y=13.60 \ \ \ \ equation\ 1[/tex]

Also Given:

Amount of regular gasoline bought today = 3 gallons

Amount of premium gasoline bought Today = 4 gallons

Total Cost of Today = $18.95

Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.

Framing in equation form we get;

[tex]3x+4y=18.95 \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 3 we get;

[tex]2x+3y=13.60\\\\3(2x+3y)=13.60\times3\\\\6x+9y= 40.80 \ \ \ \ \ equation\ 3[/tex]

Now Multiplying equation 2 by 2 we get;

[tex]3x+4y=18.95\\\\2(3x+4y)=18.95\times2\\\\6x+8y= 37.90 \ \ \ \ \ \ equation\ 4[/tex]

Subtracting equation 4 from equation 3 we get;

[tex](6x+9y)- (6x+8y)= 40.80-37.90\\\\6x+9y-6x-8y= 2.9\\\\y=\$2.90[/tex]

Substituting the value of y in equation 1 we get;

[tex]2x+3y=13.60\\\\2x+3\times2.90 =13.60\\\\2x+8.7=13.6\\\\2x=13.6-8.7\\\\2x=4.9\\\\x=\frac{4.9}{2} =\$2.45[/tex]

Hence Cost of 1 gallon of Regular gasoline is $2.45 and  Cost of 1 gallon of Premium gasoline is $2.90.

Answer:

The correct option is

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

Step-by-step explanation:

Given:

RS ≅ SQ

∠PSR ≅ ∠PSQ = 90°

To Prove:

point P is equidistant from points R and Q

i.e PR ≅ PQ

Proof:

In  ΔPSR  and Δ PSQ

PS ≅ PS                         ……….{Reflexive Property}

∠PSR ≅ ∠PSQ = 90°     …………..{Measure of each angle is 90° given}

RS ≅ QS                         ……….{Given}

ΔPSR  ≅ ΔPSQ  ….{By Side-Angle-Side Congruence test}

∴ PR ≅ PQ .....{Corresponding Parts of Congruent Triangles}

i.e point P is equidistant from points R and Q    .......Proved

===============================

Explanation:

Let's say we had a triangle with side lengths a,b,c.

If we know that a = 12.25 and b = 12.25, then the third side c has its length restricted in such a way that

b-a < c < b+a

This is a variation of the triangle inequality theorem.

-------------

So,

b - a < c < b + a

12.25 - 12.25 < c < 12.25 + 12.25

0 < c < 24.5

which means the third side c is between 0 inches and 24.5 inches.

The value of c cannot be 0, and it cannot be 24.5 either.

Among the answer choices given, we see that only 24.0 is the only valid option here. The other two choices are too large.

-------------

Side Note: If your teacher gave you two angles (instead of two sides) to be 12.25 degrees, and wanted the third missing angle of the triangle, then you would be correct in having 12.25+12.25+x = 180 as your first step.

Answer:

[tex]Required\ number\ of\ minutes= \frac{x}{2}+10[/tex]

Step-by-step explanation:

Usual time(side streets) taken [tex]=x\ minutes[/tex]

Jade can travel two times faster by taking the toll road so the time taken will be half from the toll road.

So travel time[tex]=\frac{x}{2}[/tex]

Jade is [tex]10\ minutes[/tex] late

So total minutes after 5:00 PM to reach home[tex]=\frac{x}{2}+10[/tex]

Answer:

It will be answer choice D.

Step-by-step explanation:

It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late

Answer:38 t-shirts

Step-by-step explanation:

P=30t-640 main street

p=25t-450 broad street

30t-640=25t-450

30t-25t-640=-450

5t-640+640=-450+640

5t/5=190/5

t=38

enjoy

Answer:

Step-by-step explanation:

The area of a triangle is one-half times the base times the height.  The height of both triangles is 4 (the height of the triangle on the left is "outside" of the triangle).  So the area of the triangle on the left is

[tex]A=\frac{1}{2}(6)(4)[/tex] so the area is 12

The area of the triangle on the right is

[tex]A=\frac{1}{2}(8)(4)[/tex] so the area is 16.

Adding those 2 areas together gives you a total area of 28 in squared.

Answer:

Domain: {-4, -3, 1 }

Step-by-step explanation:

As we know that domain of a relation basically consists of all the first elements or x-coordinates of order pairs.

As the relation is : {(-4, 3), (-4, 4), (-3, 1), (1, 1)}

So,  

         Domain: {-4, -3, 1 }

Note: We can not duplicate an element when we determine the domain of any relation. As -4 was present in first and second order pairs i.e. (-4, 3), (-4, 4). But, we have to write it only once when we write the domain of any relation.

So, the domain will be listed as:

                                       Domain: {-4, -3, 1 }

Keywords:  domain, relation

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Answer:the total number of milkshake that the ice cream shop sold that day is 120

Step-by-step explanation:

Let x represent the total number of

vanilla milkshakes that the ice cream shop sold that day.

The ice cream shop sold 48 vanilla milkshakes in a day which is 40% of the total number of milkshake sold that day. It means that

40/100 × x = 48

0.4 × x = 48

0.4x = 48

x = 48/0.4 = 120

Answer: false is correct

The statement is false; a value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean due to the Empirical Rule for normal distributions.

The statement is false. A value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean. According to the Empirical Rule, which applies to bell-shaped and symmetric distributions, about 68 percent of the data lies within one standard deviation of the mean, while more than 99 percent of the data is within three standard deviations. This means that as you move further away from the mean, the likelihood of occurrence decreases.

Answer:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Step-by-step explanation:

Consider the provided information.

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.

Statement 1: 31 < p < 37

The value of p is greater than 31 and less than 37.

Thus the possible values of p are: 32, 33, 34, 35, 36

All these numbers can be expressed as the product of two integers. Each of which is greater than 1,

Hence, statement 1 Alone is Sufficient.

Statement 2: p is odd

The statement is not sufficient because All prime numbers are odd numbers and if p is a prime number then p can't be expressed as the product of two integers, each of which is greater than 1.

Although if p is odd it is not necessarily to be prime for example 9 is an odd number but not a prime number. 9 can be expressed as the product of two integers, each of which is greater than 1.

Therefore, statement 2 Alone is not sufficient.

Final answer:

1. Statement 1 alone is sufficient to determine if the integer p can be expressed as the product of two integers greater than 1 or not.

2. Statement 2 alone is not sufficient.

Explanation:

Consider the provided information. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.

Statement 1: 31 < p < 37

The value of p is greater than 31 and less than 37. The possible values of p are 32, 33, 34, 35, 36. All these numbers can be expressed as the product of two integers each greater than 1. Therefore, statement 1 alone is sufficient.

Statement 2: p is odd

The statement is not sufficient as odd numbers like 9 can be expressed as the product of two integers each greater than 1. Not all odd numbers are prime. Thus, statement 2 alone is not sufficient.

Answer:

True

Step-by-step explanation:

Check the values of [tex]f(x)[/tex] at [tex]x=0,\pm0.5\pi,\pm\pi,\pm1.5\pi,\pm2\pi[/tex]

[tex]x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f(x)\\0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0-180)-1=-1\\0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0.5\pi-180)-1=-2\\\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(\pi-180)-1=-1\\1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(1.5\pi-180)-1=0\\2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(2\pi-180)-1=-1\\-0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-0.5\pi-180)-1=0\\-\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-\pi-180)-1=-1\\\\[/tex]

[tex]-1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-1.5\pi-180)-1=-2\\-2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-2\pi-180)-1=-1[/tex]

Each [tex](x,y)[/tex] point is on the graph.

Hence graph represents the given function.

Answer:

  60

Step-by-step explanation:

The ratio of Barbies is ...

  Jenny : Sharon = 5 : 2 = 60 : 24  . . . . . .  multiplying ratio values by 12

Jenny owns 60 Barbies to Sharon's 24.

Answer:

25:2

Step-by-step explanation:

Answer:

The answer to your question is x³ + 11² + 30x

Step-by-step explanation:

Data

       x = 0; x = - 5; x = 6

Process

1.- Equal the zeros to zero

      x₁ = 0; x₂ + 5 = 0; x₃ + 6 = 0

2.- Multiply the results

      x(x + 5)(x + 6) = x [ x² + 6x + 5x + 30]

3.- Simplify

                             = x [ x² + 11x + 30]        

4.- Result

                             = x³ + 11² + 30x

The polynomial equation with zeros at x = 0, x = -5, and x = 6 is x^3 - x^2 - 30x.

To find a polynomial equation with zeros at x = 0, x = -5, and x = 6, you would use the relationship between zeros and factors of a polynomial. Each zero corresponds to a factor of the polynomial; for x = 0, the factor is x, for x = -5, the factor is (x + 5), and for x = 6, the factor is (x - 6). Therefore, the polynomial equation that has these zeros can be constructed by multiplying these factors together.

The result is the polynomial equation:

f(x) = x(x + 5)(x - 6)

Expanding this product gives:

f(x) = x³ - x² - 30x

Question:

A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/4 tons of dirt each hour. How long will it take to remove dirt

Answer:

It takes 32 hours to remove the dirt

Step-by-step explanation:

Given:

Total amount dirt to be removed =   24 tons

Dirt that can removed in one hour =  3/4 tons

To Find:

Time taken to remove all the dirt =?

Solution:

Let the time taken to remove the dirt from the company be x.

Then

x =  [tex]\frac{ \text { total amount of dirt in the company}}{\text{ amount of dirt removed in one hour}}[/tex]

Substituting the given values , we get

x = [tex]\frac{24}{\frac{3}{4}}[/tex]

x = [tex]24\times \frac{4}{3}[/tex]

x = [tex] \frac{96}{3}[/tex]

x= 32

Answer:

[tex]P(S|\bar{C} ) = 0.1739[/tex]

Step-by-step explanation:

We define the probabilistic events how:

S: Today is snowing

C: The class is canceled

If it is snowing, there is an 80% chance that class will be canceled, it means

P( C | S ) = 0.8  conditional probability

If it is not snowing, there is a 95% chance that class will go on

[tex]P( \bar{C} | \bar{S}) = 0.95[/tex]

and P(S) = 0.05

We need calculate

[tex]P( S |\bar{C} ) = \frac{P(\bar{C} | S) P(S)}{P(\bar{C})}[/tex]

[tex]P(\bar{C}) = P( \bar{C}|S)P(S) + P( \bar{C}|\bar{S})P(\bar{S})[/tex]

How

[tex]P(C | S) = 0.8[/tex]  then  [tex]P( \bar{C} | S) = 0.2[/tex]

[tex]P (\bar{C})[/tex] = (0.2)(0.5) + (0.95)(0.5)

                                =0.575

[tex]P(S |\bar{C} ) = \frac{(0.2)(0.5)}{(0.575)}[/tex]

[tex]P(S|\bar{C} ) = 0.1739[/tex]

Answer:

[tex]r=10\%[/tex]

Step-by-step explanation:

The correct question is

A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does the bank pay?

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=10\ years\\ P=\$1,000\\ A=\$2,000\\r=?[/tex]

substitute in the formula above

[tex]2,000=1,000(1+10r)[/tex]

Solve for r

Divide by 1,000 both sides

[tex]2=1+10r[/tex]

Subtract 1 both sides

[tex]10r=2-1[/tex]

[tex]10r=1[/tex]

Divide by 10 both sides

[tex]r=1/10[/tex]

[tex]r=0.10[/tex]

Convert to percentage (multiply by 100)

[tex]r=0.10*100=10\%[/tex]

Answer:

Option D) 10

Therefore the value of x is 10.

Step-by-step explanation:

Given:

BP is an angle bisector of ∠CBD.

m∠1 = 4x - 8 and

m∠2 = 3x + 2.

To Find:

x = ?

Solution:

Angle Bisector:

A line that splits an angle into two equal angles.

Bisect means to divide into two equal parts.

Here, BP is an angle bisector of ∠CBD.

∴ m∠ 1 = m∠ 2

Substituting the given values we get

[tex](4x-8)=(3x+2)\\\\4x-3x=8+2\\\\x=10\\\\\therefore x = 10[/tex]

Therefore the value of x is 10.

Answer:

7.6

Step-by-step explanation:

Final answer:

The relative change in the unemployment rate expressed as a percentage is approximately 31.34%.

Explanation:

The relative change in the unemployment rate expressed as a percentage can be computed by taking the difference between the two unemployment rates and dividing it by the initial unemployment rate. In this case, the initial unemployment rate was 6.7% and the new unemployment rate is 8.8%, so the change is 8.8% - 6.7% = 2.1%. To express this change as a percentage, we divide the change by the initial unemployment rate and multiply by 100: (2.1% / 6.7%) * 100 = 31.34%. Therefore, the unemployment rate has risen by approximately 31.34%.

Answer:

Right sum < trapezoidal rule value < Left sum

Non of the completed options are valid. Option c is incomplete but it starts correctly. If there are no more options, the answer is (c).

Step-by-step explanation:

Lets call a = x0, x1, x2, x3 and x4 = b the endpoints of the intervals in increasing order. Lets also call L the length of each subinterval. Note that b-a = 4L. Lets denote yi = f(xi) for i in {0,1,2,3,4}.

Lets compute each sum:

Left sum = x0*L + x1*L + x2*L + x3*L = (y0+y1+y2+y3)L

Similarly

Right sum = (y1+y2+y3+y4)L

and trapezoidal rule value = L((y0)/2 + y1+ y2 + y3+ (y4)/2)

Since f is decreasing, we have that y0 > y1 > y2 > y3 > y4. Therefore, y0 > y4 and, as a result, Left sum > Right sum, because the Right sum has y4 instead of y0 multiplying by L.

On the other hand, multiplying L we have (y0)/2 + y1+ y2 + y3+ (y4)/2 on the trapezoidal rule value, thus it has half of y0 and half of y4, and as a consecuence, the trapezoidal sum is between the left sum and the right sum.

The correct answer is

Right sum < trapezoidal rule value < Left sum

Answer:

answer is c, i took the test

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

48 - 6 = 42

42 divided by 3 = 14.

Mr. Kim's daughter is 14 years old.

Mr. Kim's daughter is 14 years old. This was determined by setting up the equation 48 = 3x + 6 and solving for x step-by-step, which resulted in x = 14.

To find Mr. Kim's daughter's age, we can set up an equation based on the problem statement.

Let's denote the daughter's age by x.

According to the problem, Mr. Kim's age is 6 more than 3 times his daughter's age. This can be written as:

48 = 3x + 6

We need to solve for x step-by-step:

Subtract 6 from both sides of the equation:

48 - 6 = 3x

Simplify the left side:

42 = 3x

Divide both sides by 3:

[tex]\frac{42}{3}[/tex] = x

Simplify the right side:

x = 14

Therefore, Mr. Kim's daughter is 14 years old.

Answer:

look at the photo below for the answer.

:)

The probability of a player winning depends on whether balls are replaced after each draw. With replacement, the probabilities remain constant and A has a higher chance of winning (9/20) compared to B and C (11/40 each). Without replacement, the probabilities change after each turn and require complex computation.

This is a probability problem involving sequence of events. The outcome is dependent on whether the balls are replaced or not after each draw.

For case a), if each ball is replaced after being drawn, the probabilities for A, B, and C stay constant each round. There are 4 white balls out of 12 total, so the probability of drawing a white ball is 4/12 = 1/3. Because the players draw successively and stop once a white ball is drawn, we need to consider the rounds of draws. For A to win, a white ball needs to be drawn on the 1st, 4th, 7th turns, and so on. For B to win, a white ball needs to be drawn on the 2nd, 5th, 8th rounds, and so forth. Similar logic applies to player C. Using geometric distribution to compute these, we have [tex]P(A) = 1/3 * (2/3)^0 + 1/3 * (2/3)^3 + 1/3 * (2/3)^6 +... = 9/20.[/tex] Applying similar logic to players B and C, we get P(B) = P(C) = 11/40. (Note that the sum of P(A), P(B), and P(C) = 1, which verifies our calculation is correct.)

For case b), if the balls are not replaced after each draw, the probability changes after each turn. Initially the probability of drawing a white ball is 4/12 = 1/3, then it becomes 4/11, 4/10, and so forth if a white ball is not drawn, and 3/11, 3/10, and so forth if a white ball is drawn. Therefore a recursive method computing the probability is needed in this case and the calculation could be quite complicated depending on when we stop the game.

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Answer:

The  gluten ratio in micrograms per milliliter is 13 µg/mL.

Step-by-step explanation:

Consider the provided information.

It is given that the food has a gluten ratio of [tex]13 \frac{mg}{L}[/tex].

Now we need to convert gluten ratio in micrograms per milliliter

To convert mg to micro grams use the information shown below:

1 mg = 1000 micro-grams.

1 L = 1000 milliliter

Now, substitute 1 mg = 1000 micro-grams and 1 L = 1000 milliliter in the above ratio.

[tex]13( \frac{1000 \ micro-grams}{1000 \ milliliter} )= 13( \frac{micro-grams}{milliliter})[/tex]

Hence, the  gluten ratio in micrograms per milliliter is 13 µg/mL.

Answer:

the answer is 4μm to the power of⁻1

Step-by-step explanation:

khan academy said

To calculate the number of different sandwich combinations at a sandwich shop, one multiplies the basic sandwich configurations (3 types of sandwiches on 2 types of bread, totaling 6) by the possible topping combinations (2^6 = 64, including the option of no toppings), resulting in 384 different sandwich combinations.

The question revolves around combinatorial mathematics, focusing on calculating the number of different sandwich combinations available at a sandwich shop with a given set of ingredients. The shop offers three types of sandwiches (ham, turkey, and chicken), each of which can be ordered on either white bread or multi-grain bread. Additionally, customers can add any combination of the six available toppings to their sandwiches. To calculate the total number of possible sandwich combinations, one would need to consider the choices for the type of sandwich, the bread, and the combinations of toppings.

For the sandwich and bread choices, since there are three types of sandwiches and two types of bread, there are a total of 3 * 2 = 6 basic sandwich configurations. For the toppings, since customers can choose any combination of the six available toppings, including the option of having no toppings at all, the total number of topping combinations can be calculated using the formula for combinations of a set: 2n, where n is the number of items (toppings) to choose from. Therefore, there are 26 = 64 possible topping combinations.

The total number of different sandwich combinations available can be calculated by multiplying the basic sandwich configurations by the topping combinations, which gives 6 * 64 = 384 different sandwich combinations. This calculation showcases the versatility of the menu and the vast array of options available to customers at the sandwich shop.

Let's say:

Ham sandwich: H

Turkey sandwich: T

Chicken sandwich: C

White bread: W

Multigrain bread: M

The representation using set notations would be:

[ (H,W), (H,M), (T,W), (T,M), (C,W), (C,M) ]

Complete question is here:

Represent the sample space using set notation.A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each sandwich can be ordered with white bread or multi- grain bread.

Answer:

The slope = 0.

Step-by-step explanation:

The midpoint of the first line =

(0+2)/2, (0+3)/ 2

= (1, 1.5).

For the second line :

(5+6)/2 , (0+3)/2

= (5.5, 1.5).

The required slope = rise / run

= (1.5-1.5)/(5.5-1))

= 0/4.5

= 0.

Answer:

0

Step-by-step explanation:

Ur welcome

Answer:

a) Max height it will reach is 327.55 ft above the ground

b) It will reach max height after 5.1 seconds

c) It will be 300 feet off the ground at 12 seconds

d) It will be 305 ft above the ground

e) The rocket will be 247.55 ft above the ground after seven seconds

Step-by-step explanation:

a) Using the equations of kinematics:

v² = v_i² + 2 g Δy

where

Therefore,

0² = 50² + 2(- 9.8) Δy        

(the negative sign shows that the positive direction is upwards. Gravity acts downwards)

Δy = -(50)² / 2(-9.8)

Δy = 127.55 ft

Thus, the maximum height that the rocket reaches will be

200 ft  + 127.55 ft

= 327.55 ft above the ground

b) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

t = Δy / [(v + v_i) / 2 ]

t = 127.55 / [(0 + 50) / 2]

t = 5.1 seconds

Therefore, the rocket will reach its maximum height after 5.1 seconds.

c) Using the equations of kinematics:

t₃₀₀ = Δy / [(v + v_i) / 2 ]

t₃₀₀ = 300 / [(0 + 50) / 2]

t₃₀₀ = 12 seconds

Therefore, the rocket will reach 300 feet after 12 seconds

d) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

Δy = [(0 + 50) / 2] × 4.2

Δy = 105 ft

Therefore, the rocket will be

105 ft + 200 ft

= 305 ft above the ground after 4.2 seconds

e) Using the equations of kinematics:

Δy = [(v + v_i) / 2 ] × t

Δy = [(0 + 50) / 2] × 7

Δy = 175 ft

Therefore,

175 - 127.55 = 47.55 ft

Thus, the rocket will be

47.55 ft + 200 ft

= 247.55 ft above the ground after seven seconds

Answer: 23

Step-by-step explanation:

let x=no. of students in both classes

no. of students in anatomy = 34

no. of students in anatomy only= 34 -x

no. of students in physics= 37

no. of students in physics only=37-x

48 = 34-x + 37-x + x

48 = 34 - x + 37

48 = 71 - x

x = 71 - 48

x = 23

Therefore the number of students in both classes are 23

Final answer:

To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. The number of students in both classes is 23.

Explanation:

To find the number of students in both the anatomy and physics classes, we can use the concept of sets and intersection. Let's assume A represents the set of students in the anatomy class, B represents the set of students in the physics class, and U represents the universal set of all students.

According to the given information, |A| = 34, |B| = 37, and |U| = 48.

The number of students in both classes can be found by using the formula:

|A ∩ B| = |A| + |B| - |U|

Substituting the values, we get:

|A ∩ B| = 34 + 37 - 48

|A ∩ B| = 71 - 48

|A ∩ B| = 23

Therefore, there are 23 students in both the anatomy and physics classes.

Answer:

It takes 3.5 hours for the second plane to catch the first plane.

Step-by-step explanation:

From the information given:

To find when the second plane catches the first plane, the distances of both planes must be equal.

We can use Distance = Rate x Time.

Let t be the time.

Distance of the first plane = Rate x Time = [tex]300\cdot t + 350[/tex]

Distance of the second plane = Rate x Time = [tex]400\cdot t [/tex]

Distance of the second plane = Distance of the first plane

[tex]400\cdot t=300\cdot t + 350[/tex]

Solving for t.

[tex]100\cdot t = 350[/tex]

t = 3.5 hours

It takes 3.5 hours for the second plane to catch the first plane.

The distance travelled by the two planes is an illustration of a linear function.

It will take the second plane 3.5 hours to catch up with the first plane

Let t represent time and d represent distance

The distance traveled by the first plane is represented as:

[tex]\mathbf{d_1 = 350 + 300t}[/tex]

The distance traveled by the second plane is represented as:

[tex]\mathbf{d_2 = 400t}[/tex]

Both planes will be at the same distance, when d1 = d2.

So, we have:

[tex]\mathbf{400t = 350 + 300t}[/tex]

Subtract 300t from both sides

[tex]\mathbf{400t - 300t = 350}[/tex]

Subtract

[tex]\mathbf{100t = 350}[/tex]

Divide both sides by 100

[tex]\mathbf{t = 3.50}[/tex]

Hence, it will take the second plane 3.5 hours to catch up with the first plane

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