Michelle plans on raising $80 for her softball team. To raise the money, she is selling team shirts for $10 each.
So far she has raised $20. To calculate how many more shirts she needs to sell, Michelle subtracts 20 from 80
and then divides by 10.
Which of the equations below can be solved using the same steps?
A. 10x + 20 = 80
B. 20x + 10 = 80
C. 80x - 20x = 10
D. 10x + 20x = 80

Answer:

y = x - 2. Notice that option A and B are same.

Step-by-step explanation:

Two points on the given line are (3, 1) and (-2, -4).

Slope = (y2 - y1)/(x2 - x1) = (-4 - 1)/(-2 - 3) = 1

Using y - y1 = m(x - x1) :

=> y - 1 = 1(x - 3)

=> y - 1 = x - 3

=> y = x - 2

Answer: 854.5

Step-by-step explanation:

I got it wrong so it gave me the explanation

The distance between A and B is 853.75

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Height = 111 feet

Tan 5° = 111/base ⇒ base = 1268

Tan 15°=111/base-AB ⇒base-AB=414.25

                                             AB=853.75

Hence, The distance between A and B is 853.75

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To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.

Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:

sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x

Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:

x = cos θ
y = sin θ

Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1

From this, we can derive:

cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ

And then use the definitions of tangent and cotangent ratios:

tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ

Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:

1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side

Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:

Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)

Step 2: Solve for y using the sine ratio:
y = r * sin(θ)

So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).

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The least common multiple of the expression is \(10y^4w^7u^5.\)

An expression means the statement having minimum of two numbers, variables or both and an operator connecting them.

To get least common multiple (LCM) of two expressions, we need to determine the highest power of each variable that appears in either expression and multiply them together.

Expression 1: 10y^2w^6u^5

Expression 2: 6y^4w^7

The LCM will have the highest power of each variable present in either expression.

Therefore, the LCM of the given expressions is \(LCM = 10y^4* w^7*u^5\).

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By studying the change of the y-intercept, we can see that the shift is of one unit upwards.

We know that the original y-intercept of the line is y = -1, then the line is of the form:

y = a*x - 1

Where a is the slope.

Now we apply a vertical shift of N units, this is written as:

y = a*x - 1 + N

And we know that the new y-intercept is 0, so:

y = a*0 - 1 + N = 0

y = -1 + N = 0

-1 + N = 0

N = 1

The shift is of 1 unit up.

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The cumulative probability for the standard normal distribution,

of z > 2 ( NOT z = 2) is .0228 . The answer is true.

Let's have further explanation:

The cumulative probability for the standard normal distribution represents the probability that a random variable will be less than or equal to a certain value. In this case, the cumulative probability for z>2 is .0228, which means the probability that a random variable will be less than or equal to 2 is .0228.

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The answer of the given question on how to graph y=3/4x-1/2 the following steps are given below.

The y-intercept is point where  graph crosses y-axis. In other words, it is the point where x = 0 and the value of y is some number.

In the equation of a straight line in the form y = mx + b (where m is the slope of the line and b is the y-intercept), the y-intercept is the constant term (b) that appears without any x-variable.

For example, in the equation y = 2x + 3, the y-intercept is 3, since it is the value of y when x is zero. Similarly, in the equation y = -1/2x + 4, the y-intercept is 4, since it is the value of y when x is zero.

The y-intercept is an important property of a straight line, as it helps us to identify the starting point of the line and gives us an idea of the position of the line on the y-axis.

To graph the equation y = (3/4)x - (1/2), we can follow these steps:

Choose a range of x-values to plot. For example, we can choose x-values from -2 to 2.

Substitute each x-value into equation to find corresponding y-value. For example,

when x = -2, we have:

y = (3/4)(-2) - (1/2)

= -3/2

So the first point we can plot is (-2, -3/2).

Repeat step 2 for several more x-values to find additional points. For example, when x = -1, we have:

y = (3/4)(-1) - (1/2)

= -5/4

So we can plot the point (-1, -5/4).

Similarly, when x = 0, we have:

y = (3/4)(0) - (1/2)

= -1/2

So we can plot the point (0, -1/2).

Continuing this process for a few more values of x, we can get more points to plot.

Plot the points on the coordinate plane and connect them with a straight line.

Note that since the coefficient of x is positive (3/4), the line has a positive slope. Additionally, the y-intercept of the line is -1/2. Therefore, we can start by plotting the point (0, -1/2), which is where the line crosses the y-axis.

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If a random sample of 35 cars are loaded onto the ferry, the probability that the maximum safe weight will be exceeded is 0.014 or 1.4%.

Let X be the weight of a single passenger car. The mean weight of a car is μ = 1.7 tons and the standard deviation is σ = 0.8 tons.

The total weight of 35 cars is:

W = 35X

By the central limit theorem, the distribution of W is approximately normal with mean μ_W = 35μ = 59.5 tons and standard deviation σ_W = sqrt(35)σ = 3.44 tons.

The probability that the maximum safe weight of 67 tons will be exceeded is the same as the probability that W is greater than 67 tons:

P(W > 67) = P((W - μ_W) / σ_W > (67 - μ_W) / σ_W)

= P(Z > (67 - 59.5) / 3.44)

= P(Z > 2.18)

where Z is a standard normal random variable.

Using a standard normal distribution table or calculator, we can find that P(Z > 2.18) = 0.014.

Therefore, the probability that the maximum safe weight of 67 tons will be exceeded when 35 cars are loaded onto the ferry is approximately 0.014 or 1.4%.

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Answer: 6.4

Step-by-step explanation:

divide in half

Answer:

square feet per roll, this translates to about 188 square feet per person each week

Answer:

142

Step-by-step explanation:

It is equal to the one above it.

I hope this helps!!

Answer: 80 is the number of cupcakes for which the profit is equal to 0

Step-by-step explanation:

The best interpretation of the number 80 in the context of the given equation will be in option A, i.e. 80 is a number of cupcakes for which the profit is equal to $0.

Profit is the amount which we earned after selling something at a price more than its cost price.

We have,

P(q) = -0.01 (q - 250) (q- 80)

Where,

P(q) = profit earned by a cupcake bakery  in dollars

q = cupcakes produced

So,

Now,

We have to find out the context of 80 in given equation,

So,

Lets substitute q = 80, in the given equation,

i.e.

P(q) = -0.01 (q - 250) (q- 80)

⇒

P(80) = -0.01 (80 - 250) (80- 80)

We get,

P(80) =  -0.01 (- 170) (0)

i.e.

P(80) = 0

So, 80 is a number of cupcakes for which the profit is equal to $0.

Hence, we can say that the best interpretation of the number 80 in the context of the given equation will be in option A, i.e. 80 is a number of cupcakes for which the profit is equal to $0.

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The average time it will take for CJ to complete an appointment is 15 minutes, and the duration of the appointment follows an exponential distribution. The probability density function for an exponential distribution is f(x) = λe^(-λx) where λ is the rate parameter, which is the reciprocal of the mean, in this case 1/15. Let X be the time CJ spends with the first student, and Y be the time CJ spends with the second student.

Since the two students arrived at different times, X and Y are not independent.To find the probability that CJ will be able to see the second student when she arrives and not have to wait, we need to find P(Y ≤ 5 | X = x), the conditional probability that Y ≤ 5 given that X = x, where x is the duration of the appointment with the first student. This is equivalent to P(X + Y ≤ 5 + x | X = x) since the sum of two exponential distributions is a gamma distribution with parameters (2, λ).

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The angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.

The angle of depression from the top of the center support to the end of the support cable can be found using trigonometry. Let's call this angle "x". Using the given information, we can form a right triangle with the center support, the end of the support cable, and a point directly below the center support on the ground.

The height of the center support, 297 meters, is the opposite side of the right triangle, while the distance from the center of the bridge to the connection of the suspension cable, 995 meters, is the adjacent side. Using the tangent function, we can calculate the angle of depression as follows:

tan(x) = opposite/adjacent

tan(x) = 297/995

x = tan^-1(297/995)

Using a calculator, we can find that x is approximately 16.59 degrees. Therefore, the angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.

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In the 8 Axioms, 4 and 6 axioms fails to holds and S is not a vector space. Rest of the axioms try to hold the vector space.

To demonstrate that S is not a vector space, we must demonstrate that at least one of the eight vector space axioms fails to hold. Let us examine each axiom in turn:

Therefore, axioms 4 and 6 fail to hold, and S is not a vector space.

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The correct question:

Let S be the set of all ordered pairs of real numbers. Define scalar multiplication and addition on S by α(x₁, x₂) = (αx₁, αx₂); (x₁, x₂) ⊕ (y₁, y₂) = (x₁ + y₁, 0). We use the symbol ⊕ to denote the addition operation for this system in order to avoid confusion with the usual addition x + y of row vectors. Show that S, together with the ordinary scalar multiplication and the addition operation ⊕, is not a vector space. Which of the eight axioms fail to hold?

Given the system of equations:

The solution of the system will be as follows:

Substitute with y into the first equation to find x:

So, the solution of the system is:

Answer:

See below

Step-by-step explanation:

-4x -8y = 8

3x-5y = 16    <===== multiply this equation by   4/3 to get

4x - 20/3 y = 64/3      <=====add to first equation...this will eliminate 'x'

      -8y - 20/3 y = 8 + 64/3       solve for y = -2

   use this value of y in any of the equations to compute x

        -4x - 8(-2) = 8

         -4x = 8-16      shows x = 2

The soccer team can have 1,716 different starting lineups. The number of ways to choose 1 player out of 13 for the goalkeeper position is given by the combination formula: C(13, 1) = 13.

To calculate the number of different starting lineups, we need to determine the combinations of players that can be chosen for the starting lineup. Since there are 13 players on the team and 11 positions in the starting lineup, we need to choose 1 player for the goalkeeper position and 10 players for the regular positions. Similarly, the number of ways to choose 10 players out of the remaining 12 players for the regular positions is given by the combination formula:

C(12, 10) = 66.

To find the total number of different starting lineups, we multiply the number of choices for the goalkeeper position by the number of choices for the regular positions: 13 * 66 = 858.

However, the order of the players in the lineup doesn't matter, so we need to divide the result by the number of permutations of the 10 regular players: 858 / 10! = 1716. The soccer team can have 1,716 different starting lineups.

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Answer:

I think B

Step-by-step explanation:

I think

Answer:

The equation has no solution.

Step-by-step explanation:

\(2(3x - 8) = 8x - 2x - 8 \\ \\ 2 \times 3x - 2 \times 8 = 6x - 8 \\ \\ 6x - 16 = 6x - 8 \\ \\ 6x - 6x = 16 - 8 \\ \\ 0 = 8 \: (which \: is \: absurd) \\ \\ the \: equation \: has \: no \: solution \\ \)

Answer:

L'ensemble de définition d'une fonction est l'ensemble de tous les éléments d'un ensemble de départ (appelé ensemble de départ ou domaine) pour lesquels la fonction est définie. En d'autres termes, c'est l'ensemble des valeurs qui peuvent être utilisées en tant qu'entrée pour la fonction. Par exemple, si une fonction prend en entrée des nombres réels, l'ensemble de définition serait l'ensemble de tous les nombres réels.

The unit rate of the juice is 0.5 carrot juice per green apple juice

From the question, we have the following parameters that can be used in our computation:

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

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Answer:

i don't know

Step-by-step explanation:

mag-aral ka mabuti para maging matalino

Answer:

The fourth opition!

Step-by-step explanation:

180-2(72)=x. The reason being it says TWO angels of 72 and if you times that by two and subtract by 180 youll get the missing angle!!

Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

The volume of the solid created by revolving a curve f(x) around the y-axis is  2π \(\int\limits^a_b {xf(x)} \, dx\)

What is the cylindrical shell?

A region enclosed by two identically sized cylinders with the same central axis is known as a cylindrical shell. We often denote the height of the cylinders by H, the inner cylinder's radius by r, and the thickness of the shell by t, resulting in a larger cylinder's radius equal to r + t.

Here,

We consider a strip of height y = f(x), and width dx; it is x units away from the axis of rotation.

Now, we rotate this strip about the y-axis; we obtain a cylindrical shell with  

radius = x

height = f(x)

thickness = dx

The volume of cylindrical shell = (circumference)×(height)×thickness

= (2πx)×(f(x))×dx

The volume of revolution = 2π \(\int\limits^a_b {xf(x)} \, dx\)

Hence, the volume of the solid created by revolving a curve f(x) around the y-axis is  2π \(\int\limits^a_b {xf(x)} \, dx\)

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Answer: 12 miles

Step-by-step explanation:

Answer: Adam will run 12 miles in 1 hour.

Step-by-step explanation:

Ok, so we know 4 miles in 20 minutes, correct?

Multiply 20x2. You will get 40. Then, multiply 4x2. That is 8. So in 40 minutes he ran 8 miles. So if we multiply 20x3, we would get 60 minutes which is an hour. So we need to multiply 4 by 3–12.

Answer:

39

Step-by-step explanation:

Complementary angles add up to 90.

(6x - 15) + (3x + 6) = 90

9x - 9 = 90

9x = 99

x = 99/9 = 11

m∠2 = 3(11) + 6 = 39

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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Answer:

92in²

Step-by-step explanation:

A= 1/2(b1+b2)h = 1/2 (18+5)8=

1/2 (23)8= 1/2 184 = 92in²