MIXED APPLICATIONS
21. In 1960, the average speed of passenger
aircraft within the U.S. was 235 miles per
hour. By 1978 the average speed was 1.74
times that amount. To the nearest whole
number, what was the average speed in 1978?
Help mepleaee

Answer:

the answer is exactly one solution

Answer:

Step-by-step explanation:

No

Answer:  No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

Answer:

81 students.

Step-by-step explanation:

If 10% of the 90 students were absent, then that means that 9 students were absent. To find the number of students present, simply subtract.

90 - 9 = 81.

- Hope this helped.

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Data provided in the question

There is a total group of 45 students

Art + biology = 5

8 study biology but not Art

Neither subject studied = 9

Based on the above information, the probability of student that studies

art and biology is

Since there is a group of 45 students out of which 5 study both art and biology

So, the ratio is

4: 5

Now divide both sides by 5

So, now the ratio is

9:1

Therefore it means the probability is [tex]\frac{1}{9}[/tex]

Answer:

0.03 feet

Step-by-step explanation:

d = 0.03r² + r

When d = 0: 0.03r² + r = 0

r(0.03r + 1) = 0

∴ r = 0

When r = 0: d = 0.03 feet

Answer:

They are congruent by AAS.

Step-by-step explanation:

Side BD is common to both  triangles and 2 pairs of corresponding angles are congruent.

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

hello,

the first term is 250 so this is the initial invested amount

[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

Answer:

[tex]\boxed{\sf \ \ \ 3x^2-7x+2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

There are a lot of polynomials which have 2 and 1/3 as zeroes,

I can show you one below

[tex]3(x-2)(x-\dfrac{1}{3})=(x-2)(3x-1)=3x^2-x-6x+2=3x^2-7x+2[/tex]

hope this helps

Answer:

a b. c=19 it is equal to 19

Answer:

20.3854

Step-by-step explanation:

Answer: The correct option is 5.7/20 = x/200

Step-by-step explanation: Please refer to the diagram attached for more details.

From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;

Mean = Summation of observed data / Number of observations

Mean  = (3 + 5 + 7 + 5 + 6 + 8)/6

Mean = 34/6

Mean = 5.6667

Mean ≈ 5.7

Also the mean number of all fish is derived as follows;

Mean = Summation of observed data / Number of observations

Mean = (20 + 20 + 20 + 20 + 20 + 20)/6

Mean = 120/6

Mean = 20

Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.

Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;

StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.

OR better expressed as;

5.7/20 = x/200

Answer:

5.7/20 = x/200

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

This system of equation has no solution because...

-3x+4y=12

1/4x-1/3y=1

[tex]-3x+4y-4y=12-4y[/tex]

[tex]-3x=12-4y[/tex]

[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]x=-\frac{12-4y}{3}[/tex]

substitute

[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]

[tex]-1=1[/tex]

-1=1 is false so therefore this system has no solution

Answer:

x = 6.73 (corrected to 3 significant figures.)

Step-by-step explanation:

(x-5)^2=3

Square root both sides of the equation.

[tex]\sqrt{(x-5)^2} =\sqrt{3}[/tex]

[tex](x-5) = \sqrt{3}[/tex]

Add 5 to both sides.

[tex]x = \sqrt{3} + 5[/tex]

x = 6.73 (corrected to 3 significant figures.)

Answer:

x=-22 or -13

Step-by-step explanation:

(x-5)^2=3

Or,x^2-10x+25=3

Or,x^2-10x=3-25

Or,x (x-10)=-22

Either

x=-22

Or,

x-10=-22

x=-22+10

x=-12

x=-22,-12

Answer:

Step-by-step explanation:

5x+y-7=0 isolate y

y=-5x+7 (m=-5,b=7)

9x+7y-14=0

7y=14-9x ( divide both sides by 7)

y=-9x/7 +14/7

y=-9/7 + 2  (m=-9/7, b=2)

x+y=1000

4x+3y=3600 ( multiply the first equation by 3 to eliminate y)

3x+3y=3000

4x+3y=3600 ( subtract the two equations)

3x+3y-(4x+3y)=3000-3600

3x+3y-4x-3y=-600

-x=-600

x=600 ( substitute x in the equation)

x+y=1000

600+y=1000

y=1000-600=400

check : x+y=1000 , (600+400)=1000

check : 4x+3y=3600 = (4(600)+3(400))=2400+1200=3600

how many tickets are sold :

adults x=600/4=150

kids (y)=400/3=133 tickets+1 dollars left

unless( x represent kids then x=200, y represent adult = 100)

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Question 1:

[tex]5x+y-7=0[/tex]

Write in slope intercept form.

[tex]y=-5x+7 \\m=-5,b=7\\9x+7y-14=0[/tex]

Write in slope intercept form.

[tex]7y=14-9x\\y=-9x/7 +14/7\\y=-9/7 + 2\\m=-9/7, b=2[/tex]

Question 2:

[tex]x+y=1000\\4x+3y=3600[/tex]

[tex]3x+3y=3000\\4x+3y=3600\\3x+3y-(4x+3y) = 3000-3600\\3x+3y-4x-3y=-600\\-x=-600\\x=600[/tex]

[tex]x+y=1000\\600+y=1000\\y=1000-600=400[/tex]

Tickets sold:

Adults:

[tex]x=600[/tex]

Kids:

[tex]y=400[/tex]

Answer:

The correct choices are;

g(0) = 0

g(1) = 1

and ;

g(-1) = 1

Step-by-step explanation:

In this question, we are to select the correct options.

So let’s take a look at the options

The term g(0) is correct

We can see that the base of the graph is sitting on the origin. At the point where x = 0, then g(x) is also = 0

g(1) is not equal to -1.

g(1) is equal to 1, mark the point 1 on the positive x-axis and trace towards the graph.

g(4) = -2 is another wrong option

The graph has no values on the negative y-axis i.e its smallest value is 0

g(1) = 1 is correct

We can trace this out from the graph

g(-1) = 1 is also correct. This is also traceable from the graph also

Answer:

x=(π+√π)/1-π

or x=(π-√π)/1-π

Step-by-step explanation:

since it is a square all sides are equal

Area of square=x*x=x^2

Area of a circle=πr^2

A=π(x-1)^2

two areas are equal

x^2=π(x^2-2x_1)

x^2=πx^2-2πx-π  

x^2-πx^2-2πx-π=0

x^2(1-π)-2πx-π=0  

using quadratic formula with a=1-π , b=-2π and c=-π

equation of the form ax^2+bx+c=0 by using the quadratic formula:

x=(−b±√b2−4ac)/2a

x=(π+√π)/1-π

or x=(π-√π)/1-π

Answer:

1800 (packages )muffins

Step-by-step explanation:

360  muffins         x muffins

--------                 =    --------

12 min                       60 min

Answer:

1800 maybe

Step-by-step explanation:

in 12 minutes can wrap 360

in 1 hr have 60 minutes

60/12=5

than 360*5 = 1800

Answer:

200

Step-by-step explanation:

Given the first term 39 and the last term 11 then the sum of the 8 layers can be calculated as

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( f + l) ← f is the bottom layer anf f the top layer, thus

[tex]S_{8}[/tex] = [tex]\frac{8}{2}[/tex] (39 + 11) = 4 × 50 = 200

Answer: 6 cajas de cada tipo de fruta.

Step-by-step explanation:

En cada caja de manzanas, tenemos 13 manzanas.

En cada caja de limones, tenemos 17 limones.

Si el numero total de cajas es C, entonces el numero total de manzanas es:

C*13

y el numero total de limones es: C*17.

Si en total tenemos 180 frutas, entonces tenemos que:

C*13 + C*17 = 180

C*(13 + 17) = 180

C*30 = 180

C = 180/30 = 6

Tenemos 6 cajas de cada tipo de fruta.

Answer:

[tex]\large \boxed{\text{6 boxes of apples and 6 boxes of lemons}}[/tex]

Step-by-step explanation:

     Let m = the number of boxes of apples. Then

        13m = the number of apples

       Let l = the number of boxes of lemons. Then  

          17l = the number of lemons and

13m + 17l = the total number of fruits

You have two conditions:

[tex]\begin{array}{rrclr}(1) & m & = &l\\(2) & 13m + 17l & = & 180\\\end{array}[/tex]

Solve the equations for m and l

[tex]\begin{array}{rrcll}(1) & m & = & l&\\(2) & 13m + 17l & = & 180\\(3)&13m +17m & = & 180 & \text{Substituted (1) into (2)}\\&30m& = &180 &\text{Simplified}\\(4)&m& = &\mathbf{6} &\text{Divided each side by 30}\\& 6& = &l& \text{Substituted (4) into (1)}\\& l& = &\mathbf{6}& \\\end{array}\\\text{You have $\large \boxed{\textbf{6 boxes of apples and 6 boxes of lemons}}$}[/tex]

Check:

[tex]\begin{array}{ccc}6 = 6 & \qquad & 13(6) + 17(6) = 180\\& \qquad & 78 + 102 =180\\& \qquad & 180 = 180\\\end{array}[/tex]

It checks.

Answer:

She practiced for 28 hours.

Step-by-step explanation:

x = 16 - Filipe's hours

y =? - Bianca's hours

Filipe practiced 12 hours less than Bianca so we get the following equation:

y - 12 = x which is y - 12 = 16.

Now we solve the equation by adding 12 to the both sides:

y - 12 + 12 = 16 + 12

y + 0 = 28

y = 28.

Answer:

equation: a statement that two expressions are equal operation: a mathematical process such as addition, subtraction, multiplication, or division solution: a value of the variable in an equation or inequality that makes the equation or inequality true variable: a letter or symbol used to represent an unknown quantity

Section 1 00:00:00 TEACHER: Welcome. In this lesson, we're going to be answering the question what situations can you model with one-step equations? Let's begin. Section 2 00:00:00 TEACHER: We'll start with the goals for this lesson. We're going to be writing and solving one-step equations. And to do this, we're going to use one-step equations to solve word problems. And we're also going to be using one-step equations to solve word problems involving rational numbers. Now there's some words you're going to need to know in this lesson. 00:00:21 We have equation, operation, solution, and variable. Make sure you familiarize yourself with the definitions for these words before we continue. Section 3 00:00:00 TEACHER: We're answering the question, what situations can you model with one-step equations? Now, you already know that inverse operations like multiplication and division, they undo each other. In this lesson, you're going to learn how to use what you already know in order to learn how to solve real world problems.

Section 1 00:00:00 TEACHER: In this lesson, we're answering the question, what situations can you model with one-step equations? Now, you already know how to use inverse operations and equality properties to solve equations. In the first part of this lesson, we're going to learn how to solve real world problems by writing and solving one-step equations. Section 2 00:00:00 TEACHER: Let's take a look at equations and word problems. Now, there are some steps that you can use in order to be able to write and solve a one-step equation involving a word problem. The first step is to identify the variable. We need to find out what is unknown in the problem and then let our variable represent that unknown. Next, we identify the operation, whether we're using 00:00:21 addition, subtraction, multiplication, or division. And we can do that by looking at key words in our scenario. Then we can write the equation. Once we have an equation, then we can solve it. And we can solve that expressing it as an equation, like an x equals 5, or even model that value on a number line. We can then check the solution. 00:00:43 We want to check back with the original problem to see if that answer make sense. Let's go ahead and take a look at this scenario right here. And we're going to identify what the equation would be for this scenario. Now, the total cost of 3 tickets to a play was $42. What was the cost of each ticket? Notice the question. 00:01:02 What was the cost of each ticket? That's unknown. I don't know what the cost is yet. So in identifying my variable, we're going to identify that unknown. We're going to let c equal the cost of 1 ticket because that is unknown at this time. Well, now that we've done that, we've 00:01:22 completed step one. So now let's go ahead and see what we can do to write the equation. But we need to identify the operation. Well, knowing the variable, let's go ahead and go back to the clues that we were given. The total cost of 3 tickets to a play was $42. Now, here in my table, I have different words in a situation 00:01:42 that would describe what operation I'm using. If I see words like increasing, I know that means addition. Difference means subtraction. Finding part of a total means multiplication. And that's what we're looking at in this scenario, the total cost of 3 tickets to a play. We're finding part of a total. 00:02:00 Let's look at the last thing in the table-- sharing or grouping. That would tell us we were using a division problem. So let's go back to this multiplication. Since we're going to be finding part of a total because I'm trying to find out the cost of 1 ticket, which is a part of the total cost of tickets, then I can go ahead and use the fact that 3 tickets times the cost of 1 00:02:24 ticket is equivalent to $42. So notice I have the equation 3 times c is equal to 42. And then once you have your equation, you would be able to move to the next step in solving that equation.

Step-by-step explanation:

There’s 6 numbers that can be used.

The first digit can be any of the 6

The 2nd digit can be any of the 5 left

The 3rd digit can be any of the 4 left

The 4th did fit can be any of the 3 left

The 5th digit can be any of the 3 left

The 6th digit would be the last number left.

Total combinations = 6 x 5 x 4 x 3 x 2 x 1 = 720

Answer:

15.56%

Step-by-step explanation:

The force applied, F,  to the surface is 90N.

The area, A, of the surface is [tex]20 cm^2[/tex] = [tex]0.002m^2[/tex]

The pressure on the surface is:

P = F / A = 90 / 0.002 = 45000 Nm^2

The force is increased by 5N, the new force is 95N.

The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.

The pressure is now:

P = 95 / 0.0025 = 38000 Nm^2

The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.

=> Difference = 45000 - 38000 = 7000

% decrease is therefore:

= 7000 / 45000 * 100 = 15.56%

There was a 15.56% decrease.

The ratio of the applied force to the area to which the force is applied,

gives the amount of pressure applied.

The outcome decreases by [tex]\underline{15.\overline 5 \%}[/tex]

Reasons:

[tex]\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}[/tex]

The initial force, F₁ = 5 N

The initial area, A₁ = 20 cm²

[tex]\mathrm{ } P_1=\dfrac{F_1}{A_1 }[/tex]

[tex]\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa[/tex]

The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N

The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²

The new pressure after the increase is given by the equation;

[tex]\mathrm{ } P_2=\dfrac{F_2}{A_2 }[/tex]

[tex]\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}[/tex]

[tex]Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100[/tex]

[tex]Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%[/tex]

The outcome decreases by 15.[tex]\overline 5 \%[/tex]

Learn more:

https://brainly.com/question/22294092

Answer:

its c.

rotate 90 ccw then mirror from y-axis

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The measure of the tangent- chord angle XYZ is half the measure of its intercepted arc, thus

arc YZ = 2 × 84° = 168° → B

Answer:

B. [tex]y = 3x^2 -6x -3[/tex]

Step-by-step explanation:

Well, we can use the following formula to find the x coordianate of the vertex  -b / 2a.

So let’s start with a)

-6 / 6

-1

A. is wrong because its vertex starts with -1.

b)

6 / 6

1

now that we have our x coordinate we can plug it into the equation to get our y.

3 - 6 - 3

So the y coordinate is -6.

Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]

look at the image below.

Answer:

h(x) = 12x – 6

Step-by-step explanation:

To know which is the function that represents the area of a triangle, you take into account the degree of the given polynomials.

If the degree is 2, the graph of the function is a parabola.

If the degree is 1, the graph of the function is a line.

By comparing all functions you can conclude that only the last option (h(x)=12-x-6) is convenient to construct a triangle. The y-intersect of the function is at y=-6, the slope is positive and the x-intersect is x=1/2. This forms a triangle in the fourth quadrant of the coordinate system.

Answer:

B. g(x) = 12x2 – 6x

Step-by-step explanation:

correct on edge 2020

Answer:

The answers are options A and E

x² + 4x-9 = 5x + 3

Group like terms

x² + 4x - 5x - 9 - 3 = 0

x² - x - 12 = 0

Using factorization method

(x + 3)( x - 4) = 0

x = - 3 x = 4

Hope this helps

Answer:

The mean egg production 2499 million

Step-by-step explanation:

P(Z > a) = 3% = 0.03

P(Z > a) = 1 - ∅(a)

1 - ∅(a) = 0.03

∅(a) = 1 - 0.03

∅(a) = 0.97

Checking the normal distribution curve, for ∅(a) = 0.97, z = 1.88

This means that area under the normal curve is 3% (0.03) to the right of z = 1.8808

X = μ + (zб)

X = 2,655 millions

б = 83 million

2655 =  μ + (1.88 * 83)

2655 =  μ + 156.04

μ  = 2655 - 156.04

μ = 2498.96

The mean egg production, is therefore, 2499 million

Answer:

x=8.

Step-by-step explanation:

x+(-13)=-5 makes x =8.

reason:

(-13)+??=-5.

-5+8=-13

therefore x=8