time was normally distributed with a mean of 1.5 and a standard deviation of 0.35. if 5 rats are selected, what is the probability that their total completion time in the maze for all rats is between

The solution for given linear equation are x=-99 and x=45 i.e. C.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Given linear equation is |1/3×+9|-3=21

so, -1/3x-12=21  --->1

and 1/3x+6=21 --> 2

From 1

1/3x=-33

x=-99

From 2

1/3x=15

x=45

Hence,

          The solution for given linear equation are x=-99 and x=45.

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21.9 is the answer to 131.4/6

Answer:

21.9

Step-by-step explanation:

learn how to use a calculator.

Answer:

I hope my answer is helpful!

"안녕하세요" is a formal and polite way of saying "hello" in Korean. It is commonly used as a greeting, both when meeting someone for the first time and when meeting someone again after a period of time. The literal translation of 안녕하세요 is "Are you at peace?"

The solution to the given logarithmic equation is log32

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which b must be raised in order to obtain a number x is its logarithm to the base b.

One of the law of logarithm is expressed as:

bloga = log a^b

Applying this law to the given question;

5 log(2) =log2⁵

Since 2⁵ = 32, hence the given expression is equivalent to log32.

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Answer:

We need 166.5 ml of soy sauce when we have 111 ml of vinegar.

We need 74 ml of vinegar when we have 111 ml of soy sauce.

Step-by-step explanation:

I think that you meant 150 and not 150150150 and 100 and not 100100100

[tex]\frac{soy sauce}{vinegar}[/tex] = [tex]\frac{soy sauce}{vinegar}[/tex]

[tex]\frac{150}{100}[/tex] is the same as [tex]\frac{3}{2}[/tex]  (simplified by dividing the top and the bottom by 50)

[tex]\frac{3}{2}[/tex] = [tex]\frac{x}{111}[/tex]  Cross multiply and solve for x

2x = 3(111)

2x = 333  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{333}{2}[/tex]

x = 166.5

We need 166.5 ml of soy sauce when we have 111 ml of vinegar.

[tex]\frac{3}{2}[/tex] = [tex]\frac{111}{x}[/tex]  Cross multiply and solve for x

3x = 2(111)

3x = 222  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{222}{3}[/tex]

x = 74

We need 74 ml of vinegar when we have 111 ml of soy sauce.

As a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.

We may utilize the knowledge that the rectangle's perimeter is 112 and that its sides are 5x and 3x+5 to determine the value of x and the lengths of each side. We can put up the following equation because the perimeter of a rectangle is equal to the sum of its four sides:

2(5x) + 2(3x + 5) = 112

We must simplify and account for x in order to solve for x. We'll start by allocating the two on the left side of the equation:

10x + 6x + 10 = 112

We'll then mix similar terms:

16x + 10 = 112

To get x alone, we will now deduct 10 from both sides, giving us 16x = 102.

Next, multiply both sides by 16 times to get 6.375.

Therefore as a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.

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The probability that at least 4 accounting majors are on the committee is P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)

We can use the complement rule to solve this problem. The complement rule states that the probability of an event happening plus the probability of the event not happening is equal to 1.

In this case, we can find the probability that less than 4 accounting majors are on the committee and then subtract that from 1 to find the probability that at least 4 accounting majors are on the committee.

There are 6 accounting majors and 9 finance majors, for a total of 15 students.

To find the probability that fewer than 4 accounting majors are on the committee, we can use the binomial probability formula:

P(k) = (combination(8,k)) [tex]\times (6/15)^k \times (9/15)^{(8-k)[/tex]

where k is the number of accounting majors on the committee.

To find the probability that fewer than 4 accounting majors are on the committee, we need to sum the probabilities for k = 0, 1, 2, and 3.

P(less than 4 accounting majors) = P(0) + P(1) + P(2) + P(3)

Finally, we can use the complement rule to find the probability that at least 4 accounting majors are on the committee:

P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)

You can calculate the exact probability using the binomial coefficient and the binomial probability formula and then subtract that from 1 to get the final probability.

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Answer:

We can use the trigonometric function sine to calculate the length of AB in a right-angled triangle.

The sine function relates the ratio of the side opposite an angle (in this case, AB) to the hypotenuse (AC) with the angle in question (in this case, angle C):

sin(C) = AB/AC

In this case, we know that angle C is 29 degrees and the hypotenuse AC is 5cm, so we can substitute these values into the equation to find AB:

sin(29) = AB/5

To solve for AB, we can multiply both sides of the equation by 5:

AB = 5sin(29)

AB=2.42cm

The probability that the students will have a pop quiz on a randomly selected day 0.77

Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42.

They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9.

Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz will be

P= 0.42*0.60 + 0.58*0.90

P = 0.252 + 0.522

P = 0.774

P ≈ 0.77

The probability that the students will have a pop quiz on a randomly selected day 0.77

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A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. It is a point at which there is no net change, or a point of equilibrium.

A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. The parameters of a problem can refer to the data, assumptions, constraints, or other factors that are used to define the problem. When the parameters are changed, a stable solution will remain intact, indicating that it is the best solution to the problem.

For example, if a mathematics problem has a solution of 3, this solution is considered to be stable, as changing any of the parameters of the problem will not alter the solution of 3.

Stable solutions are important as they provide a point of equilibrium, or a point at which there is no net change. This can help to ensure that the solution is the most effective one to the problem.

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As per the unitary method, the number of meatballs made using the the remaining turkey is 29 meatballs

The term unitary method is known as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have know that Amy has 4 pounds of ground turkey to make meatballs

And here we also know that she uses 3/8 pound per meatball to make 9 meatballs

Then in order to find the remaining we have to subtract 3/8 from 4

Then we get,

=> 4 - 3/8

=> 29/8

Therefore, here we have identified that there are 21/8 pounds of ground turkey left

As here we have given that the number of 1/8 pound meatball that can be produced from 21/8 pounds of ground turkey can be calculated as follows,

=> 29/8 ÷ 1/8

When we simplify this one then we get,

=> 29

So, Amy can make 29 meatballs

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Answer: If you mean simplify then here: 20d+5f+5h

Step-by-step explanation:

Use distributive property to remove the parentheses.

20d+5f+5h

Please give brainliest

Four fair six-sided dice are rolled. The probability that at least two dice show a 3 is 1/36.

In the given question, four fair six-sided dice are rolled.

We have to find the probability that at least two dice show 3.

There are four dice and each have 6 numbers to come.

So total number of cases = 6×6×6×6

Total number of cases = 1296

At least two dice show 3. So

The favorable outcome = 6 × 5

The favorable outcome = 30

The possible outcome = aabc, abac, abca, baac, baca, bcaa = 6

Total of outcomes = 30 + 6

Total of outcomes = 36

The probability that at least two dice show a 3 = 36/1296

The probability that at least two dice show a 3 = 1/36

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Answer:

A

Step-by-step explanation:

A run-on sentence occurs when independent clauses are not joined properly.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]x-2y=17\implies -2y=-x+17\implies y=\cfrac{-x+17}{-2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} x-\cfrac{17}{2}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/2 and that it passes through (-10 , 4)

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-10)}) \implies y -4= \cfrac{1}{2} (x +10) \\\\\\ y-4=\cfrac{1}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+9 \end{array}}[/tex]

Mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers,  The volume of the right rectangular prism is 14 x 14 x 8 = 1,536 cm3.

To get this answer, I first determined the number of cubes in the bottom layer. Since the bottom layer contains 14 cubes, the total length of the base of the prism is 14 cm. The height of the prism is 8 layers, so the total height of the prism is 8 cm. To calculate the volume of a right rectangular prism, you need the base length, the width, and the height. Since all three of these measurements are given, the volume can be calculated by multiplying the base length (14 cm) by the width (14 cm) by the height (8 cm). The result is 1,536 cm3.

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mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, what is the volume of the right rectangular prism?

Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x  -1/2 * √x .

A mathematical equation looks to be a formula that joins two statements and indicates equality when it uses the equals symbol (=). In algebra, an equation is a statement of fact that demonstrates the equality of different mathematical variables . For instance, the result obd + 6 = 12 has an equal sign between quantities ptdc + 6 and 12. There is a mathematical formula that describes the connection between the syllables on either side of each letter. The emblem and the statement are frequently the same.

Here,

y = √x ln(x)

To find the y'

=> dy/dx = d(√x ln(x)) /dx

=> dy/dx = 1/2√x * ln(x) + 1/x *√x

=> dy/dx =  1/2√x * ln(x) + 1/√x

To find the value of y ''

=> dy'/dx =  d(1/2√x * ln(x) + 1/√x ) / dx

=>  dy'/dx  =  1/2 * (-1/2* √x * ln(x) + 1/√x )  -1/2 * √x

=>dy'/dx = -1/4 *√x * ln(x) + 1/2√x  -1/2 * √x

Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x  -1/2 * √x .

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The missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

here,
As given in the quesiton,
Consider the triangle formed by the given construction,
ΔFDC and Δ FAB
AB║CD
∠FAB = ∠FCD
∠FBA = ∠FDC

So,  ΔFDC ≅ Δ FAB, by SAS congruency.

Thus, the missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.

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Answer: 25°F is approximately $375.

Step-by-step explanation:

The scatter plot shows a positive correlation between the average monthly temperature (x) and the family's monthly heating cost (y). The line of best fit appears to be a linear equation, and it can be approximated by the equation y = mx + b, where m is the slope and b is the y-intercept.

(a) One possible equation of the line of best fit for the data is y = 15x + 300. This equation is only an approximation as it is hard to determine the exact line of best fit without more data points.

(b) Using the equation y = 15x + 300, the predicted monthly heating cost for a month with an average temperature of 25°F can be found by plugging in x = 25 into the equation.

y = 15(25) + 300 = 375

Therefore, the predicted monthly heating cost for a month with an average temperature of 25°F is approximately $375.

The length of the rope in the question is; 277.5 ft

The angle of depression is defined as the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, and looking down at an object, you could measure the angle of depression.

The rope length can be calculated using the trigonometric ratio which is;

167/x = sin 37

x = 167/sin 37

x = 167/0.6018

x = 277.5 ft

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Answer

22.3 is correct i believe :)

Step-by-step explanation:

Answer:

1/5 of a minute they are equal.

The cost would be $18

Step-by-step explanation:

Something does not look right.  You would not have 3 variables.

Set the two equations equal to each other and solve for m.  I think that the variables t may be an error.

30m + 12 = 15m + 15  Subtract 15 m from both sides

30m -15 m + 12 = 15m -15m + 15

15m + 12 = 15  Subtract 12 from both sides

15m + 12 - 12 = 15 - 12

15m = 3  Divide both sides by 15

[tex]\frac{15m}{15}[/tex] = [tex]\frac{3}{15}[/tex]

m = [tex]\frac{1}{5}[/tex]

Cost:

y = 30m + 12

y = 30(1/5) + 12

y = 18

y = 15m + 15

y = 15(1/5) + 15

y = 3 + 15

y = 18

The value of variable d is 1120

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

D= wt²

Where W = 70 and T = 4

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

D = 70 * 4²

Evaluate the exponent

D = 70 * 16

Evaluate the products

D = 1120

Hence, the solution is 1120

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Answer:

-2

a open bracket

and then a and - a negate each other to give -2

The function shown on the graph is f(x) = - 1/2 cos x.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here,

We have given a graph and we have to determine which function is shown on the given graph.

We concluded that

The amplitude of the first graph is (1/2) which is the height from the midline to the peak.

The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function

The period of the graph is 2·π, which is the period of the parent cosine function.

Hence, the function shown on the graph is f(x) = - 1/2 cos x.

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Answer:

[tex]\textsf{1)} \quad y=x+\dfrac{17}{4}[/tex]

[tex]\textsf{2)} \quad y=2x+4[/tex]

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.

At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

[tex]y=4+2x-x^2[/tex]

Differentiate the given function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]

If the tangent to the parabola forms an angle of 45° with the negative direction of the x-axis, then the gradient of the tangent is 1.

Set the differentiated function to 1 to find the x-value of the point where the gradient of the tangent is 1:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=1[/tex]

[tex]\implies 2-2x=1[/tex]

[tex]\implies -2x=-1[/tex]

[tex]\implies x=\dfrac{1}{2}[/tex]

Substitute x = 1/2 into the given function to find the y-value of the point:

[tex]\implies y=4+2\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}\right)^2=\dfrac{19}{4}[/tex]

Therefore, the point at which the tangent of the parabola forms an angle of 45° with the negative direction of the x-axis is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-\dfrac{19}{4}=1\left(x-\dfrac{1}{2}\right)[/tex]

[tex]\implies y=x+\dfrac{17}{4}[/tex]

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

Given function:

[tex]y=4+2x-x^2[/tex]

Differentiate the given function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]

If the tangent to the parabola is parallel to the line y = 2x - 4 then the gradient of the tangent is 2 (since parallel lines have the same gradient).

Set the differentiated function to 2 to find the x-value of the point where the gradient of the tangent is 2:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2[/tex]

[tex]\implies 2-2x=2[/tex]

[tex]\implies -2x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the given function to find the y-value of the point:

[tex]\implies y=4+2\left(0\right)-\left(0\right)^2=4[/tex]

Therefore, the point at which the tangent of the parabola is parallel to the line y = 2x - 4 is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-4=2\left(x-0\right)[/tex]

[tex]\implies y=2x+4[/tex]

Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.

Distance between two sites can be determined by a measurement called length. Aside from height and width, it also determines how long an object is. In math classes, kids will study about length to assist them in solving real-world problems both as a part of their education and outside of it. the largest or longest dimension of a thing; a measurable length or width. Dimensions: 10 ft. Table of the Metric System, Weights and Measures Table: the characteristic of length. The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item.

given

Puppy drawn to scale measures 6 cm in length.

due to the scale's 1:9 cm

Utilize the ratio approach to determine the puppy's true length.

1 = 6 cm

9 = 6×9 = 54 cm

Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.

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(i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.

To check if the given measurements are possible sides of a right triangle, it must follow the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the legs.

c² = a² + b²

where c is the hypotenuse(longest side)

and a and b are the two other sides

(i) 2.5 cm, 6.5 cm, 6 cm

6.5² = 2.5² + 6²

42.25 = 6.25 + 36

42.25 = 42.25

(ii) 2 cm, 2 cm, 5 cm

5² = 2² + 2²

25 = 4 + 4

25 ≠ 8

(iii) 1.5 cm, 2cm, 2.5 cm

2.5² = 1.5² + 2²

6.25 = 2.25 + 4

6.25 = 6.25

Hence, (i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.

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The positive intervals are the y values over (0,∞ )

The negative intervals are the y values over (0,9]

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

The periods where a function is above the x-axis are considered its positive regions. Where the y-values are positive is where it is (not zero). Periods where a function is below the x-axis are referred to as its negative regions. This is the case when the y-values are negative (not zero).

The graph extends to infinity from the origin above x-axis

So, the positive intervals are the y values over (0,∞ )

The graph extends to y=9 from the origin below x-axis

So, the negative intervals are the y values over (0,9]

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The minimum and the maximum of the linear equation - 2 · a + b are - 4 and - 1, respectively.

In this question we find an algebraic expression that comprises two variables (a, b) and each variable is defined by following inequalities:

3 < a < 4

4 < b < 5

Herein we must determine the minimum and the maximum associated with linear equation - 2 · a + b:

Minimum (a = 4, b = 4)

m = - 2 · 4 + 4

m = - 4

Maximum (a = 3, b = 5)

M = - 2 · 3 + 5

M = - 1

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