Simplify: (7a − 9c) − (−12a − 33c) − (−21a + 10c)

Answer:

The given statement is true.

Step-by-step explanation:

Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions : TRUE statement.

Statistics helps the people to use limited sample to make accurate conclusions about a greater population. In stats we use tables, charts and graphs to present the data to draw some conclusions.

Answer:

  80 ft

Step-by-step explanation:

The area can be used to find the side length. The perimeter is the sum of side lengths.

  A = s² . . . . . the area of a square is the square of its side length

  s = √A . . . . the side length is the square root of the area

  s = √(400 ft²) = 20 ft

The perimeter is the sum of the four equal-length sides of the square, so is ...

  P = 4s

  P = 4(20 ft) = 80 ft

Mrs. Drew needs 80 ft of wood to make the sides of the sandbox.

Final answer:

To build a square sandbox with an area of 400 square feet, each side of the sandbox is 20 feet long, and Mrs. Drew will need a total of 80 feet of wood to construct the sides.

Explanation:

Finding the Total Length of Wood for a Sandbox

The question asks us to determine the total length of wood necessary to build a square sandbox with an area of 400 square feet. To find the length of one side of the sandbox, we take the square root of the area. The square root of 400 square feet is 20 feet, which means each side of the sandbox is 20 feet long. Since the sandbox is square, it has four equal sides.

The total length of wood Mrs. Drew needs for the sandbox is the sum of the lengths of all four sides:
20 feet + 20 feet + 20 feet + 20 feet = 80 feet.

Therefore, Mrs. Drew will require 80 feet of wood to construct the sides of the sandbox.

It's helpful to remember when working with square areas that the perimeter (or total length around the square) is always four times a single side. This is a key concept in geometry and is useful in practical applications such as planning the construction of a sandbox.

Answer:

True

Step-by-step explanation:

f is odd if the graph of f is symmetric with respect to the origin.

f is even if and only if f(-x) = f(x) for all x in the domain of f.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

The answer to your question is below

Step-by-step explanation:

Data

AB = 3y - 1

BC = 7y

AC = 29

Prove AB = 8

          AB + BC = AC

       3y - 1 + 7y = 29

     10y -1 = 29

     10y = 29 + 1

     10y = 30

     y = 30/10

     y = 3

AB = 3y - 1

     = 3(3) - 1

     = 9 - 1

     = 8

Answer:

The probability that the person gets a speeding ticket is 0.27

Step-by-step explanation:

The probability that the person receives a speeding ticket is the probability that the person passes through any of the speed limits and the radar is operating at that time.

Let [tex]P(L_1)[/tex] is the probability that the person passes through radar [tex]L_{1}[/tex] and it is operating at that time is

[tex]P(L_{1})=P(1)\times P(2)[/tex]

Where

P(1) is the probability of person passes through [tex]L_{1}[/tex]

P(2) is probability that the radar is operating

[tex]P(L_1)=0.2\times 0.4=0.08[/tex]

Similarly the probabilities are calculated for other radars in the similar manner as

[tex]P(L_2)=0.1\times 0.3=0.03[/tex]

[tex]P(L_3)=0.5\times 0.2=0.1[/tex]

[tex]P(L_4)=0.2\times 0.3=0.06[/tex]

Thus the reuired probability of the reuired event is

[tex]P(E)=P(L_1)+P(L_2)+P(L_3)+P(L_4)\\\\P(E)=0.08+0.03+0.1+0.06=0.27[/tex]

Answer:

2.5 gal

Step-by-step explanation:

let be x = galons of solution to be drained and replace with bleach

so, we have to substract to the current solution of bleach 0.04*120, x gallons that have a concentration of 0.04 x

and also, we have to add the same gallons of bleach to the solution, that is x

and have to obtain a final concentration of 0.06*120

we can express the problem with the follow equation:

0.04*120 - 0.04*x + x = 0.06*120

solving the equation for x:

4.8+0.96*x=7.2

0.96*x=7.2-4.8

0.96*x=2.4

x =2.5 gallons

Answer:

Step-by-step explanation:

When the perimeter of the rectangle is 360 yd, the sum of the lengths of two adjacent sides is 180 yd. If x is the length of one side of the rectangle, then the adjacent side is (180-x). The area is the product of these lengths,

  area = x(180 -x)

This describes a downward-opening parabola with zeros at x=0 and x=180. The vertex (maximum) of the parabola is halfway between, at x=90. The adjacent sides of the maximum-area rectangle are the same length: the rectangle is a square with sides 90 yards each.

The area is (90 yd)² = 8100 yd².

The maximum area is achieved when Alex uses the fencing to create a square. Dividing 360 yards by 4 gives each side a length of 90 yards. Thus, the maximum area that can be enclosed is 8100 square yards.

Alex is attempting to maximize the area of a rectangular enclosure by manipulating the length and width dimensions. In this circumstance, the maximum area will be achieved when the rectangle is square. This is because for a fixed perimeter, in this case 360 yards, a square provides the largest possible area.

The rectangle will be square if all its sides are equal. Hence, to find the dimensions of the rectangle, divide the total length of the fencing by 4 (as a square has 4 equal sides), i.e., 360 yards/4 = 90 yards. Thus, the rectangle's dimensions will be 90 yards by 90 yards.

To find the maximum area, multiply the length by the width, i.e., 90 yards * 90 yards = 8100 square yards. Therefore, the maximum area that can be enclosed by the fencing is 8100 square yards.

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The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.

Distances:

Gecko to ceiling edge: 1 foot

Ceiling edge to opposite wall edge: 10 feet (room width)

Opposite wall edge to fly: 1 foot

Path calculation:

Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet

Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet

Shortest path:

Add ceiling and wall paths: 9 feet + 12 feet = 20 feet

Therefore, the shortest path for the gecko is 20 feet long.

Answer:

Marta's house is 3.10 miles from Latanya's house

Step-by-step explanation:

Marta's house is at 3.1 miles fron Latanya's house.

From 12:30pM to 3:30pM there are a total of 3 hours, remember that.

Let's say that the distance between the two houses is D, then we can write the equations:

12mi/h*t₁ = D

2.5mi/h*t₂ = D

These are equations of the form:

speed*time = distance

Where t₁ is the time that Latanya takes to arrive to Marta's house, and t₂ is the time that they take to arrive to Latanya's house.

We know that the total time of this is 3 hours, and they spent 90 minutes = 1.5 hours in Marta's house, then:

t₁ + t₂ + 1.5 = 3

t₁ + t₂ = 3 - 1.5 = 1.5

Now we have a system of equations:

12*t₁ = D

2.5*t₂ = D

t₁ + t₂ =  = 1.5

We can write:

D/12 = t₁

D/2.5 = t₂

And replace that in the last equation:

D/12 + D/2.5 = 1.5

2.5*D + 12D = 1.5*2.5*12

14.5D = 45

D = 45/14.5

D = 3.10 miles

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You should expect to arrive at Terminal B approximately 17 minutes past the scheduled arrival time, factoring in remaining stops and travel times.

Let's calculate the expected delay in arrival at Terminal B.

Given:

- Scheduled departure from Terminal A: 9:18 a.m.

- Scheduled arrival at Terminal B: 10:03 a.m.

- Arrival at a stop on the route at 9:58 a.m.

- 5 more stops remaining, including the arrival at Terminal B.

- Average travel time between stops: 2 minutes

- Loading and unloading time: 1 minute

1. Total travel time from the current stop to Terminal B:

[tex]\[ 10:03 \text{ a.m.} - 9:58 \text{ a.m.} = 5 \text{ minutes} \][/tex]

2. Remaining stops:

[tex]\[ 5 \text{ stops} \times (2 \text{ minutes travel time} + 1 \text{ minute loading/unloading}) = 5 \text{ stops} \times 3 \text{ minutes per stop} = 15 \text{ minutes} \][/tex]

3. Total time from the current stop to Terminal B, including remaining stops:

[tex]\[ 5 \text{ minutes (travel time to Terminal B)} + 15 \text{ minutes (remaining stops)} = 20 \text{ minutes} \][/tex]

4. Determine how many minutes past the scheduled arrival time at Terminal B this would be:

[tex]\[ 20 \text{ minutes} - (10:03 \text{ a.m.} - 10:00 \text{ a.m.}) = 20 \text{ minutes} - 3 \text{ minutes} = 17 \text{ minutes} \][/tex]

Therefore, you should expect to arrive at Terminal B 17 minutes past the scheduled arrival time.

If the correct answer is indeed 10 minutes, then there might be a misunderstanding or a mistake in the problem statement.

You can expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time. This is calculated based on the average travel time and loading/unloading time for the remaining stops.

To determine how many minutes past your scheduled arrival time you should expect to arrive at Terminal B, let's break down the time required for the remaining stops.

Therefore, you should expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time.

Answer:

a = 14

Step-by-step explanation:

Since QR = QP then the triangle is isosceles and

QS is a perpendicular bisector, thus

RS = SP ← substitute values

3a = a + 28 ( subtract a from both sides )

2a = 28 ( divide both sides by 2 )

a = 14

Bao's initial investment is $1,000, the annual interest rate is 10% or 0.10, and the interest is compounded annually. Plugging in these values into the formula, Bao will earn a total interest of $331 after 3 years.

To calculate the total interest Bao will have earned after 3 years, we can use the formula for compound interest: [tex]A = P(1+r/n)^(nt)[/tex] where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, Bao's initial investment (P) is $1,000, the annual interest rate (r) is 10% or 0.10, and the interest is compounded annually (n = 1). We need to find the final amount (A) after 3 years (t = 3).

Plugging in these values into the formula:

[tex]A = 1000(1+0.10/1)^3[/tex]

= $1,331.

Therefore, Bao will earn a total interest of $331 after 3 years.

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Final answer:

Bao will have earned $331 in total interest after 3 years by investing his $1,000 at an annual compound interest rate of 10%.

Explanation:

The student's question involves calculating the amount of interest earned from a compound interest formula over a period of 3 years. To determine the total interest earned by Bao after 3 years, we need to apply the compound interest formula:

[tex]A = P (1 + r/n)^{nt}[/tex]

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the original sum of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

For Bao's investment:

P = $1,000

r = 10% or 0.10

n = 1 (since interest is compounded annually)

t = 3 years

Using the formula:

[tex]A = 1000 (1 + 0.10/1)^{(1*3)} = 1000 (1.10)^3 = 1000 * 1.331 = $1,331[/tex]
The total interest earned after 3 years is:

Interest = A - P = $1,331 - $1,000 = $331

So, Bao will have earned $331 in total interest 3 years later.

Answer:

can you elaborate

Step-by-step explanation:

I think you're talking about the slope formula so I'll tell you that y=x+b

y2-y1/x2-x1 (x1,y1) is the first coordinate and (x2,y2) is the second coordinate

Answer:

Step-by-step explanation:

1 ) the slope formula for the line passes by :   A(XA,YA)    B(XB,YB)

the slope is :   (YB - YA)/(XB -XA)

2) y intercept for the line when : x = 0

Final answer:

The correct general form of the equation of a circle with a center at (-2, 1) is x² + y² - 4x + 2y - 4 = 0, as it aligns with the pattern of the standard circle equation upon completion of the square.

Explanation:

The general form of the equation of a circle on a coordinate plane with a center at (-2, 1) can be found using the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Since we do not have the radius given, our primary goal is to expand and arrange the given options to match this standard form and check which one relocates the center to (-2, 1).

The equation that matches this pattern would be x² + y² - 4x + 2y - 4 = 0. Here's why: when you complete the square to revert it back to the standard equation, you'll add 4 to both sides to get (x - (-2))² + (y - 1)² = 4, which indicates a center at (-2, 1) when you compare with the standard equation.

When the girl is 45 ft away from the pole, the tip of her shadow is moving away from the light at a rate of approximately 4.8 ft/sec.

Given:

Height of the pole (h): 25 ft

Height of the girl (4 ft)

Rate of the girl walking away from the pole (dx/dt = 6 ft/sec)

Distance from the pole to the girl (x = 45 ft, when the girl is 45 ft away from the pole)

Objective:

Find the rate at which the tip of her shadow is moving away from the light (ds/dt) when the girl is 45 ft away from the pole.

Step 1: Set up the Similar Triangles Equation

s/x = h/(x + s)

Step 2: Differentiate both sides with respect to time t:

(1/x) * ds/dt - (s/x^2) * dx/dt = (h/(x + s)^2) * (dx/dt + ds/dt)

Step 3: Substitute Known Values:

Substitute x = 45, dx/dt = 6, and h = 25 into the equation.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 4: Solve for ds/dt:

Combine like terms and isolate ds/dt.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 5: Substitute x = 45 into the equation:

(1/45) * ds/dt - (4/2025) = (25/(90 + s)^2) * (6 + ds/dt)

Step 6: Solve for ds/dt:

ds/dt ≈ 4.8 ft/sec

To calculate the number of foot-long hot dogs served, divide the total number of hot dogs by the total parts of the ratio (80/5 = 16) and then multiply by the number of parts for foot-long hot dogs (2 * 16 = 32 foot-long hot dogs served).

If the ratio of regular hot dogs to foot-long hot dogs at a hot dog stand is 3 to 2, and there are a total of 80 hot dogs served, we can calculate the number of foot-long hot dogs served using proportional reasoning.

To find out how many foot-long hot dogs are served, first add up the parts of the ratio: 3 parts regular hot dogs + 2 parts foot-long hot dogs = 5 parts total. Since there are 80 hot dogs served in total, we divide this number by the total number of parts to find the value of one part.

80 hot dogs \/ 5 parts = 16 hot dogs per part.

Now, multiply the value of one part by the number of parts for foot-long hot dogs to get the total number of foot-long hot dogs served:

2 parts foot-long hot dogs x 16 hot dogs per part = 32 foot-long hot dogs.

Answer:

C

Step-by-step explanation:1 kilogram = 1000 grams so if you multiply 0.004 times 1000 you get 4 grams

Answer:

Step-by-step explanation:

let x and y be the distances of each car from the intersection after sometime.

let x<y

then y-x=7

and y+x=13

add 2y=20

y=10

x=13-10=3

slower car travels 3 miles and faster car travels 10 miles

Answer:

  about 93.6 km/h

Step-by-step explanation:

The speed westbound is ...

  14000 km/(22 h) ≈ 636.364 km/h

The speed eastbound is ...

  14000 km/(17 h) ≈ 823.529 km/h

The difference in speeds is twice the wind speed, so the wind speed is ...

  (823.529 -636.364)/2 km/h ≈ 93.6 km/h

To find the wind velocity, first calculate the plane's average speed in still air by averaging its speeds in opposite directions. Then subtract the plane's speed against the wind from its speed in still air. The result is the wind velocity, which in this case is 93.59 km/h.

To calculate the wind velocity, we will first need to find out the airplane's speed in still air. This can be calculated by getting the average of the two speeds in opposite directions. You see, when a plane flies from Los Angeles to Mumbai, it takes 22 hours, while the return flight from Mumbai to Los Angeles takes only 17 hours because of wind assistance. Here's how to work it out:

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The formula for secant lines is the outside x the overall length is equal to the outside times the overall length of the second line.

A) 5*(x+5) = 6*10

SImplify:

5x +25 = 60

Subtract 25 from both sides:

5x = 35

Divide both sides by 5:

x = 35/5

x = 7

B) 3*8 = 4*(x+4)

Simplify:

24 = 4x +16

Subtract 16 from both sides:

4x = 8

Divide both sides by 4:

x = 8/4

X = 2

Answer:

a) 0.0613 b)0.0803

Step-by-step explanation:

Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.

p = 0.025

Let's consider that an applicant is not be able to repay  his or her installment loan as a ''success''

p (success) = 0.025

Last month she made 40 loans ⇒ n = 40

For the poisson approximation to the binomial we need to calculate n.p that  will be the λ parameter in our poisson approximation

[tex]n.p=40.(0.025)=1[/tex]

λ=n.p=1

Let's rename λ = j

In our poisson approximation :

[tex]f(k,j)=\frac{e^{-j} .j^{k} }{k!}[/tex]

f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :

[tex]f(k,1)=\frac{e^{-1} .1^{k} }{k!}[/tex]

For a) We are looking the probability of 3 success :

[tex]f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613[/tex]

For b) We are looking for the probability of at least 3 success

If ''L'' is the number of success

[tex]P(L\geq 3)=1-P(L\leq 2)[/tex]

[tex]P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)[/tex]

[tex]P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)[/tex]

[tex]P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )[/tex]

[tex]P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803[/tex]

The probability that three loans will default is 0.0613

The probability that at least 3 loans will default is 0.0803

Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.

p = 0.025

Hence, we consider that an applicant is not able to repay his or her installment loan as a ''success''

p (success) = 0.025

Last month she made 40 loans ⇒

n = 40

For the Poisson approximation to the binomial, we need to calculate n.p which will be the λ parameter in our Poisson approximation

n.p= 40.(0.025) =1

λ=n.p=1

Let's rename λ = j

In our Poisson approximation :

f(k,1) = e^-j.j^k/k!

Hence, the probability of 3 success is:

f(3,1)= e^-1.1^3/3!

=0.0613.

The probability of at least 3 successes is:

If  ''L'' is the number of successes.

P(L≥ 3) = 1- P(L≤ 2)

P(L≥ 3)= 0.0803.

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Answer:

The answer to your question is: the last option   5a² + 3b + 6a

Step-by-step explanation:

                            7a² + 3b + 6a - 2a²

 look for like terms

                           7a² - 2a²        3b         6a

Simplify like terms

                          5a² + 3b + 6a

Given : Sample size : n= 16

Degree of freedom = n-1=15

The obtained t-statistic value = 1.94

Since, The treatment is expected to increase scores and the sample mean shows an increase.

Let [tex]\mu_0[/tex] be the population mean before and [tex]\mu[/tex] denotes the population mean after the treatment.

then the related hypothesis will be :-

[tex]\text{Null hypothesis }H_0:\mu_0=\mu\\\\\text{Alternative hypothesis } H_1:\mu_0<\mu[/tex]

Since the alternative hypothesis is left-tailed, so the test is a left tailed test.

The critical value for [tex]\alpha=0.05[/tex]=1.753

Since, the obtained value (1.94) is greater than the critical value (1.753) so we reject the null hypothesis  .

Therefore, we have enough evidence to support the alternative hypothesis.

Hence, we conclude that treatment may successful to increase scores and the sample mean shows an increase.

Answer:

%33.75

Step-by-step explanation:

I put the answer that the other person answered and I got it wrong so here is the right answer!

Answer:

33.75

Step-by-step explanation:

Answer:

The true balance is $562.43

Step-by-step explanation:

1. Check register balance of $459.70

2. Bank statement balance of $562.43

3. Two outstanding checks of $76.40 and $29.83

4. Service charge of $3.50.

The working is shown like -

Subtract the service charge from check register balance

[tex]459.70-3.50=456.20[/tex] dollars

Then add the outstanding checks to this

[tex]456.20+76.40+29.83=562.43[/tex] dollars

Hence, the true balance is $562.43.

Answer:

THIS ANSWER IS CORRECT!!

Step-by-step explanation:

What is the true balance?

$456.20

You have the Check registar balance which includes your outstanding checks. You minus the $3.50 fee to get the true balance.

Answer:

Stratified Sampling

Step-by-step explanation:

Since Keri divides the day into different strata and each unit is selected from each strata randomly. So, it is Stratified Sampling.

Further, In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.

Answer:

  90

Step-by-step explanation:

There are several ways you can go at this, but the basic idea is that "likes dogs" includes "likes both", as does "likes cats."

That means ...

  (likes dogs) + (likes cats) + (likes neither)

  = (likes dogs only + likes both) + (likes cats only + likes both) + (likes neither)

  = [likes dogs only +likes cats only +likes both +likes neither] + (likes both)

  = [total] + (likes both)

In numbers, ...

  186 + 105 + 58 = 259 + (likes both)

  90 = likes both . . . . . . subtract 259

Hey!

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

Solution:

5 1/5% = 0.052

325 x 0.052 = 16.9

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

Answer:

D. 16.899...

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

Hope This Helped! Good Luck!

Answer:

16,9

Step-by-step explanation:

To convert from a percentage to a decimal, move the decimal point twice to the left:

5,2% = 5⅕%

5,2% → 0,052

[tex](0,052)(325) = 16,9[/tex]

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

[tex]i=\sqrt{-1}\to i^2=-1\\\\(3+\sqrt{-16})(6-\sqrt{-64})\\\\\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\sqrt{-64}=\sqrt{(64)(-1)}=\sqrt{64}\cdot\sqrt{-1}=8i\\\\(3+4i)(6-8i)\\\\\text{use FOIL}\ (a+b)(c+d)=ab+ac+bc+bd\\\\=(3)(6)+(3)(-8i)+(4i)(6)+(4i)(-8i)\\\\=18-24i+24i-32i^2\qquad\text{cancel}\ 24i\\\\=18-32(-1)=18+32=50[/tex]