Consider this bag of marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things? Make sure you show work, answer all questions, and write in complete sentences.

Answer:

t = 100 ln 100

Step-by-step explanation:

D(t) : The amount of dye (in g) at time t (in min)

D(0) = 800 L * 1 g/L = 800 g

the change in D is:

[tex]\frac{dD(t)}{dt} =D_{in}- D_{out} \\D_{in}: 0*8\ g/min \\D_{out}: \frac{D(t)}{800} *8\ g/min \\\frac{dD(t)}{dt} = -\frac{1}{100}D(t)[/tex]

[tex]\frac{dD(t)}{D(t)} =-\frac{1}{100}dt \\\int\limits^{D(t)}_{800} {\frac{1}{D(t)} } \, dD(t) =\int\limits^t_0 {t} \, dt \\ln(\frac{D(t)}{800})=-\frac{1}{100}t \\D(t) = 800e^{-\frac{1}{100}t} \\Solving\ D(t) = 0.01* D(0)=0.01*800 =8 \\8 = 800e^{-\frac{1}{100}t} \\ln (\frac{1}{100})=-\frac{1}{100}t \\100 ln 100 = t[/tex]

Answer:

b = 6 or b = -6 (non-zero vectors)

b = 0 (zero vector)

Step-by-step explanation:

Two vectors [tex]\vec{a}=\langle a_1,a_2,a_3\rangle[/tex] and [tex]\vec{b}=\langle b_1,b_2,b_3\rangle[/tex] are orthogonal if their dot product is equal to 0, or in other words

[tex]a_1\cdot b_1+a_2\cdot b_2+a_3\cdot b_3=0[/tex]

In your case,

[tex]\vec{a}=\langle -46, b, 10\rangle\\ \\\vec{b}=\langle b,b^2,b\rangle[/tex]

Hence, if vectors a and b are orthogonal, then

[tex]-46\cdot b+b\cdot b^2+10\cdot b=0\\ \\-46b+b^3+10b=0\\ \\b^3-36b=0\\ \\b(b^2-36)=0\\ \\b(b-6)(b+6)=0\\ \\b=0\text{ or }b=6\text{ or }b=-6[/tex]

Note, then if b = 0, then [tex]\vec{b}=\langle 0,0,0\rangle[/tex] and zero-vector is orthogonal to any other vectors.

Thus, b = 6 or b = -6.

Answer:

Step-by-step explanation:

independent quantity=60 m/h

dependent =time taken=t

60 t=325

t=325/60=65/12=5 5/12 hours

Answer:

[tex]-8 \sqrt{6}[/tex]

Step-by-step explanation:

[tex]4i\sqrt{-24} \\4i\sqrt{-1} *\sqrt{24} \\4i*i*\sqrt{4}*\sqrt{6}\\-4 * 2*\sqrt{6} \\-8 \sqrt{6}[/tex]

.

[tex]\sqrt{-1} =i \\i*i = -1[/tex]

Line segment AB - b) AB with a line above it.

Ray AB - c) AB with a line above it going only left.

The length of line segment AB - a) AB

Line AB - d) AB with a line with both arrows on either side.

To match the given terms with the correct letter options, let's define each term and find its corresponding notation:

These notations are crucial in geometry to clearly communicate different types of lines and measurements.

Answer:   C. 0.3

Step-by-step explanation:

Given : Number of English speaking households =350

Number of Spanish speaking households =50     (1)

Number of households in which the language is other than English or Spanish=100      (2)

Total households participates in this survey =350+50+100=500

No. of households not speak English =100+50=150    (Add (1) and (2))

If a psychologist approaches a house at random to conduct an interview, the chance that the language in that household will NOT be English will be :_

[tex]\dfrac{\text{No. of households not speak English}}{\text{Total households}}\\\\=\dfrac{150}{500}\\\\=\dfrac{3}{10}=0.3[/tex]

Hence, the correct option is option (c).

Answer:

The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

[tex]L+2W=58[/tex] ----> equation A

[tex]L=2W+6[/tex] ----> equation B

substitute equation B in equation A and solve for W

[tex]2W+6+2W=58[/tex]

[tex]4W+6=58[/tex]

[tex]4W=58-6[/tex]

[tex]4W=52[/tex]

[tex]W=13\ ft[/tex]

Find the value of L

[tex]L=2W+6[/tex]  ----> [tex]L=2(13)+6=32\ ft[/tex]

therefore

The length of the patio is 32 ft and the width is 13 ft

The required patio length(L) = 32 and width(w) = 13.

Given that,

Wayne is hanging a string of lights 58 feet long,

And the side along the house, is 6 feet long.

We have to find,

The length and width of the patio.

According to the question,

Let, the length of his patio be L and width w,

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.

L + 2W = 58

And The length of his patio, the side along the house, is 6 feet longer than twice its width.

L = 2W + 6

Solving the equation putting the of L from equation 2 in equation 1,

= 2W + 6 + 2W = 58

= 4W = 58 - 6

= 4W = 52

= W = [tex]\frac{52}{4}[/tex]

= W = 13

And L = 2(13) + 6 = 32

Patio length(L) = 32 And width(w) = 13.

Hence , The required patio length(L) = 32 And width(w) = 13.

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Answer: There are 8 $5 bills, 2 $10 bills, and 6 $1 bills.

Step-by-step explanation: If you have 6 more $5 bills than the number of $10 bills, that means you have at least 6 to start off with. This also means you have at least 1 $10 bill. If you have 1 $10 bill, then you have 3 $1 bills as well. Adding those bills up, you get $43. From here, you know you need $3 more. Meaning you have to add another $10 bill. Since you added another $10 bill, you have to equal out the $5 bills.

So if you know you have 2 $10 bills and 6 $1 bills, you can determine that you need 8 $5 bills to complete the set.

2 $10 = $20

8 $5 = $40

6 $1 = $6

$20 + $40 + $6 = $66

Answer:

540 feet

Step-by-step explanation:

225x(8/5)

360 feet in 1 hour

6 feet in 1 minute

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The expression of 225 divided by 5/8 as 225 x 8/5.

225 x (8/5)

So, the quotient says a sloth may move 360 feet in 1 hour.

360 feet in 1 hour

Then, 6 feet in 1 minute

90 minutes as 1 1/2 hour.

Multiply by 1 1/2 to get feet in 90 minutes.

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

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Answer:

y = 50 - 7.5x

Step-by-step explanation:

Given,

The original area for painting = 50 m²,

Let c meter per hour be the constant rate of painting,

So, after 2 hours, the area painted = 2c m²,

Thus, the area left to paint = 50 - 2c

According to the question,

50 - 2c = 35

2c = 15

⇒ c = 7.5

i.e. the constant rate of painting is 7.5 meters per hour,

Hence, the area left after x hours = 50 - 7.5x

If y represents the area left to paint after x hours,

Then,

y = 50 - 7.5x

Which is the required equation.

Answer:

Option c)  $78,250 unfavorable

Step-by-step explanation:

The given information in the question :

Standard cost = $810,000

Actual cost = $888,250

Cost variance can be calculated as using the following formula :

Cost variance = standard cost - actual cost

                       = 810,000 - 888,250

                       = ($78,250) unfavorable

Favorable indicates how much under budget the project.

unfavorable indicates how much over budget the project.

Therefore, Option c) 78,250 unfavorable is the answer.

Answer:

Step-by-step explanation:

Answer:

x = 2.4

Step-by-step explanation:

To find the value when f(x) = x, you just have to replace f(x) for x

[tex]f(x) =-\frac{1}{4}x +3 \\x = - \frac{1}{4}x +3 \\x +\frac{1}{4}x=3 \\\frac{5}{4} x= 3 \\ x = 3*\frac{4}{5} \\x = 2.4[/tex]

Answer:

The two clock will chime together in 75 minutes

Step-by-step explanation:

- Two clocks are turned on at the same time

- One clock chimes every 15 minutes

- The other clock chimes every 25 minutes

- We need to know in how many minutes they will chime together

- The two clock will chime together in the multiples of 15 and 25

- Lets find the first common multiple of 15 and 25

∵ 15 = 5 × 3

∴ The prime factors of 15 are 3 and 5

∵ 25 = 5 × 5

∴ The prime factor of 25 is 5

∴ The lowest common multiple of 15 and 25 = 5 × 3 × 5 = 75

∴ The two clocks will chime together every 75 minutes

The two clock will chime together in 75 minutes

Westbound boats speed = X

Southbound boats speed = X + 5

In 3 hours they are 27 miles apart:

3X + 3(x+5) = 27

Simplify:

3x + 3x +15 = 27

Combine like terms:

6x + 15 = 27

Subtract 15 from both sides:

6x = 12

Divide both sides by 6:

x = 12/6

x = 2

Westbound was 2 miles per hour

Southbound was 2 +5 = 7 miles per hour

Check:

2 miles per hour x 3 hours = 6 miles

7 miles per hour x 3 hours = 21 miles

21 + 6 = 27 miles

Answer:

Step-by-step explanation:

Since we know that the height is 0, we can figure out how long it took the ball to reach the ground by setting [tex]f(x) = 0[/tex] and solving for [tex]x[/tex]:

[tex]f(x) = 16(x^{2} - 6x - 7)[/tex]

[tex]0 = 16(x^{2} - 6x - 7)[/tex]

[tex]0 = x^{2} - 6x - 7[/tex]

[tex]0 = (x - 7)(x + 1)[/tex]

[tex]x = -1, 7[/tex]

Because time can only be positive, the answer is 7 seconds.

Answer:

7 seconds.

Step-by-step explanation:

height h = 16(x^2-6x-7) = 0

x^2 - 6x - 7 = 0

(x - 7)(x + 1) = 0

x = 7 seconds (we ignore the negative).

Answer:

[tex]{n \choose 4}[/tex] where n s the total number of employees

Step-by-step explanation:

Since [tex]{n \choose x}[/tex] gives the number of ways you can pick a subset of x elements from n.

remember in order to calculate the combination number ( for example if you know the number of office employees) is

[tex]{n \choose 4}=\frac{n!}{4! (n-4)!}[/tex]

using that 4! =1*2*3*4  and same idea for n!

Answer:

  A = 7

  B = 2

Step-by-step explanation:

The question is asking for the simplified form of √(-98). You are expected to know that √-1 = i, and you are expected to be able to factor the number 98.

[tex]\sqrt{-98}=\sqrt{(-1)(7^2)(2)}=7i\sqrt{2}[/tex]

Matching parts of the simplified expression to the form you are given, you see that ...

  A = 7

  B = 2

Answer:

  see below

Step-by-step explanation:

Ordinarily a graph like this will have arrowheads on the ends of the curve, indicating the curve continues on in the same direction. Here, we have to assume the existence of such arrowheads in order to choose a sensible answer.

As x goes to -∞, the curve continues to increase toward +∞. This is not an answer choice.

As x goes to +∞, the curve continues to decrease toward -∞. This matches the third answer choice.

Answer:

Step-by-step explanation:

In the graph you can observe the beahaviour of each variable.

Observe, as [tex]x[/tex] tend to ∞, then [tex]y[/tex] tend to -∞. This beahaviour is located in the IV quadrant.

So, in the options, the best answer is "as [tex]x[/tex] tend to ∞, tehn [tex]y[/tex] tend to -∞", because is true.

Other options are just false, for example, as [tex]x[/tex] tend to -∞, [tex]y[/tex] doesn't tendo to -∞.

As  [tex]x[/tex] tend to -∞ [tex]y[/tex] doesn't tendo to 0.

Therefore, the right answer is the third choice.

Answer: [tex]\frac{3}{8}\ kg[/tex]

Step-by-step explanation:

The table attached is part of the exercise (Without the table the question was incomplete).

We know that the cost of 1 kilogram of Chihuahua cheese is 78 and the Chihuhua cheese bought the day before cost 195.

The first step is to calculate the amount of cheese bought with 195:

[tex]\frac{195}{78}=\frac{5}{2}\ kg[/tex]

Now, we need to add the fractions provided in the table (This table shows the amount of cheese that was used in that day). Then:

[tex]\frac{1}{2}\ kg+\frac{7}{8}\ kg+\frac{3}{4}\ kg=\frac{17}{8}\ kg[/tex]

Finally, in order to find what fraction of Chihuahua cheese is left, we must subtract [tex]\frac{5}{2}\ kg[/tex] and [tex]\frac{17}{8}\ kg[/tex]:

[tex]\frac{5}{2}\ kg-\frac{17}{8}\ kg=\frac{3}{8}\ kg[/tex]

Final answer:

To find the actual number of productive FTEs, divide the total number of hours worked (55,267) by the number of hours worked per FTE. The answer is option a. 2.27.

Explanation:

To find the actual number of productive FTEs, we need to divide the total number of hours worked (55,267) by the number of hours worked per FTE. The number of hours worked per FTE can be calculated by dividing the total number of hours paid by the total number of productive FTEs. So, the equation becomes:

55,267 / (59,995 / x) = x

Multiplying both sides of the equation by (59,995 / x), we get:

55,267 = (59,995 / x) * x

Simplifying further:

55,267 = 59,995

Dividing both sides of the equation by 59,995, we get:

x = 55,267 / 59,995

x = 0.9213

Therefore, the actual number of productive FTEs is approximately 0.9213, which can be rounded to 0.92. Therefore, the answer is option a. 2.27.

Final answer:

The actual number of productive Full-Time Equivalents (FTEs) is calculated by dividing the total annual productive hours (55,267 hours/year) by the standard annual working hours for one full-time employee (2,080 hours/year), resulting in 26.57, which rounds to option c. 26.60.

Explanation:

To calculate the actual number of productive Full-Time Equivalents (FTEs) based on the hours worked in a hospital food service department, we use the given number of hours worked per year and divide it by the standard number of working hours in a year for one full-time employee.

First, let's establish the standard number of working hours in a year for one FTE, based on an 8-hour day:

To find the actual number of productive FTEs, we divide the number of hours worked by the standard number of working hours in a year:

Productive Hours Worked: 55,267 hours/year

Standard Hours for 1 FTE: 2,080 hours/year

Actual number of productive FTEs = Productive Hours Worked / Standard Hours for 1 FTE

Actual number of productive FTEs = 55,267 hours/year / 2,080 hours/year

Actual number of productive FTEs = 26.57

Therefore, the nearest option to our result is c. 26.60.

That number is 8,565,550.

Answer:

8,565,550.

Step-by-step explanation:

The number is 8,x6x,xx0   where  all the x's = 5 so the answer is:

8,565,550.

Answer:

The opportunity cost for Canada will be comparatively high in the production of shoes.

Step-by-step explanation:

An American worker can make 20 pairs of shoes or grow 100 apples per day.

A Canadian worker can produce 10 pairs of shoes or grow 20 apples per day.

In easy words, opportunity cost is defined as the value of ones next best alternative.

The opportunity cost for Canada will be comparatively high in the production of shoes.

Answer:

B

Step-by-step explanation:

the open circle at -9 indicates that x is "greater than" -9, whereas the filled circle at -5 indicates that x is " less than or equal" to -5

Answer:

A.[tex]m\angle ABD=m\angle ABC[/tex]

Step-by-step explanation:

We are given that a  ray BA bisects angle DBC.

We have to find true statement .

Angle bisector property:When a ray bisect any angle then the angles  made by bisection of angle are equal.

When ray BA bisects angle DBC

Then, [tex]m\angle ABD=m\angle ABC[/tex]

By angle bisector property.

Therefore, option A is true.

Answer:A.[tex]m\angle ABD=m\angle ABC[/tex]

Answer:

A

Step-by-step explanation:

Because I said this was the answer. I know all.

Two complementary angles equal 90 degrees.

If one is 20, the larger one would be 90 - 20 = 70 degrees.

Answer:

The answer is false

Step-by-step explanation:

In a sample above 30 obs  like this the confidence interval is defined as

X+- t* (s/sqrt(n)) where X is the mean t the tvalue for a given confidence level, n the size of sample and s standar deviation.

To find de appropiate value of t we must see the T table where rows are degrees of freedom and columns significance level

The significance is obtained:

significance = 1 - confidence level = 1 - 0.9 = 0.10

Degrees of freedom (df) for the inteval are

df = n - 1 = 18 - 1 = 17

So we must look for the value of a t with 17 values and significance of 0.10 which in t table is 1.740 not 1.746 ( thats the t for 16 df)

The statement is false because the critical t value for a 90% confidence interval depends on the degrees of freedom, which, for an independent measures study with 18 participants split into two groups, would be 16 (18 participants - 2 groups),

The statement regarding an independent-measures research study comparing two treatment conditions with 18 participants constructing a 90% confidence interval and having t values of ±1.746 is assessed as False. The critical t value is determined by the degrees of freedom, which in an independent-measures t-test, is generally calculated as the total number of participants minus the number of groups. With 18 participants divided into two groups, the degrees of freedom would be 16 (18 - 2), assuming equal group sizes. The exact t value for a 90% confidence interval would need to be looked up in a t distribution table or calculated using statistical software, and it would likely differ from ±1.746 for 16 degrees of freedom.

To accurately determine the critical t value, one would consult a t distribution table or statistical software tailored to the specific degrees of freedom for the study. It's important to note that confidence intervals, t-tests, and their interpretations are crucial in research for estimating the range within which the true population parameter lies and for assessing the significance of the findings, respectively.

Answer: x-10

Since you're finding the difference of a number, x, and 10, you would do x-10.

Final answer:

The variable expression for "the difference between a number and 10" is represented by x − 10, which implies the subtraction of 10 from a variable x.

Explanation:

The phrase "the difference between a number and 10" as a variable expression is represented by x − 10. When we discuss 'the difference' in mathematical terms, we are referring to the result of subtracting one number from another. Here, whatever the unknown number (represented by the variable x) is, we are subtracting 10 from it.

Answer: all real numbers greater than it equal to negative one.

Step-by-step explanation: if you graph this equation you see that the vertex is at (3,-1). We know that Range is all possible Y values.so, By looking at their graph we can see that the lowest point it touches is at -1. The rest of the graph goes off into positive and negative infinity.

Range= Y is greater than it equal to -1.

Answer:

All real numbers greater than or equal to −1

Step-by-step explanation:

Here, the given parabola,

[tex]f(x) = (x-4)(x-2)[/tex]

[tex]f(x) = x^2-4x-2x + 8[/tex]

[tex]f(x) = x^2 - 6x+8[/tex]

∵ Leading term = positive

So, the parabola is upward.

We know that an upward parabola is minimum at its vertex

Or it gives minimum output value at its vertex.

for instance, If (h, k) is the vertex of an upward parabola,

then its range = { x  : x ≥ k, x ∈ R }

Note : Range = set of all possible output values

We have given,

Vertex = (3, -1)

Hence, Range = all real numbers greater than or equal to −1

LAST option is correct.

Answer:

30%

Step-by-step explanation:

27 over 90 is equal to 0.3 in decimal form, turn that into percentage by multiplying by 100, and you get 30%