-4 + 9(-3f + 6k), if f = -6 and k = 5

Answer:

See below

Step-by-step explanation:

6.)   angle 5   +   angle 2  =180°      ( since angle 1 = angle 5)

The probability that the end-of-month volume will remain greater than 18 million m³ is approximately 0.1922.

a)The mean water volume in the lake at the end of the month can be calculated using the formula given below:

Mean water volume = Starting water volume + Total rainfall + Total flow - Total evaporation - Water drawn from the lake

Given:

Starting water volume = 20 million m³

Total rainfall = random variable with mean = 1 million m³ and standard deviation = 0.5 million m³

Total flow = random variable with mean = 8 million m³ and standard deviation = 2 million m³

Total evaporation = 3 million m³

Water drawn from the lake = 10 million m³

Now, let's calculate the mean water volume at the end of the month.

Mean water volume = Starting water volume + Total rainfall + Total flow - Total evaporation - Water drawn from the lake= 20 + 1 + 8 - 3 - 10= 16 million m³

Therefore, the mean water volume at the end of the month is 16 million m³.

The standard deviation of the water volume in the lake at the end of the month can be calculated using the formula given below:

σ = √{σr² + σf² + σe²}

σr = standard deviation of rainfall = 0.5 million m³

σf = standard deviation of flow = 2 million m³

σe = standard deviation of evaporation = 1 million m³σ = √{σr² + σf² + σe²}σ = √{0.5² + 2² + 1²}= √{5.25}≈ 2.29 million m³

Therefore, the standard deviation of the water volume in the lake at the end of the month is approximately 2.29 million m³.b)Given that all the random variables in the problem are normally distributed, we can find the probability that the end-of-month volume will remain greater than 18 million m³ using the z-score formula.

z = (x - μ) / σ

Where,

z = z-scorex = 18 μ = 16σ = 2.29

Now, let's calculate the z-score.

z = (x - μ) / σ= (18 - 16) / 2.29= 0.87

Using the z-table, we can find that the probability of z being less than 0.87 is 0.8078.

Therefore, the probability of the end-of-month volume being greater than 18 million m³ is:

1 - 0.8078 = 0.1922 (rounded to 4 decimal places)

Hence, the probability that the end-of-month volume will remain greater than 18 million m³ is approximately 0.1922.

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The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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In the given angles, the values of R=31⁰, x=34⁰, m<S= 38⁰, m<Y = 111⁰

We know that a triangle is a polygon whose sum of angles is equal to 180 degress , with three sides and three vertices.

The given angles are

31⁰,  (x+4)⁰,  (3x+9)⁰

The sum of angles of the triangle

31+x+4+3x+9=180⁰

44+4x=180⁰

Collecting like terms

4x=136

Dividing by 4

x=34⁰

Substituting the value of x=34 in the given angles we have

R= 31⁰,             given

 (x+4)⁰   = 34+4=38⁰,  (3*34+9)⁰=111⁰

In conclusion the values of R= 31⁰, x=34⁰ , m<S=38⁰, m<T=111⁰

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Answer:

(10 workers × $150 +  88 workers × $85.50) × 6 working days

$54,144

Step-by-step explanation:

The amount and equation would be

There are 98 workers out of which 10 would received at $150 per day and rest 88 would received $85.50 per day and there is 6 working days in a week

So

= (10 workers × $150 +  88 workers × $85.50) × 6 working days

= ($1,500 + $7,524) × 6 working days

= $9,024 × 6 working days

= $54,144

Answer:

y = 0 and y = -3

Step-by-step explanation:

The horizontal asymptote of each graph is:

1. y=0

2. y= -3

An asymptote of a curve y = f (x) that has an infinite branch is called a line such that the distance between the point (x, f (x)) lying on the curve and the line approaches zero as the point moves along the branch to infinity.

1.Given function:

 t(x)= \(6^{x}\)

If we apply limit x→∞, then we get y=c as horizontal asymptote

So, \(\lim_{x \to \infty} 6^{x}\)= 0

Hence, the asymptote will by y=0.

2. Given function:

t(x)= \(5^{x}\)-3

If we apply limit x→∞, then we get y=c as horizontal asymptote

So, \(\lim_{x \to \infty} 5^{x} -3\)= -3

Hence, the asymptote will by y=-3.

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Answer:

Below

Step-by-step explanation:

.014 g / .0022 cm^3   = 6.364  gm / cc   = 6364 kg/m^3

    density is too low to be pure gold  

Answer:

!

Step-by-step explanation:

By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

The length of the tunnel is approximately 205.6 meters to the nearest tenth.

What is Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

       a²+b²=c²

Here's one way to find the length of the tunnel:

1) Draw a diagram to represent the situation

2) Draw the perpendiculars from the surveyor to each entrance, and label the height of the triangle formed by each entrance and the surveyor as h1 and h2, respectively

3) Use trigonometry to find h1 and h2:

h1 = 243 * sin(47) = 160.1

h2 = 186 * sin(27) = 105.8

4) Find the horizontal distance between the two entrances, which is the length of the tunnel, by using the Pythagorean theorem:

\(d = \sqrt{(h1^2 + h2^2) }\\\\ d = \sqrt{(160.1^2 + 105.8^2)}\\\\ d = 205.6\)

So, The length of the tunnel is approximately 205.6 meters to the nearest tenth.

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Answer:

the answer is 1/2

Step-by-step explanation:

3/4 - 1/4 = 2/4 = 1/1

Answer:

Step-by-step explanation:

To find the equation of the circle, we need to first find the center and radius.

We can start by finding the midpoint of the segment connecting the two given points, (-4, 2) and (2, 6):

Midpoint = ((-4+2)/2, (2+6)/2) = (-1, 4)

So, the center of the circle is (-1, 4).

Next, we can find the distance between the center and one of the given points, say (-4, 2), using the distance formula:

distance = sqrt[(-4 - (-1))^2 + (2 - 4)^2] = sqrt[9 + 4] = sqrt(13)

So, the radius of the circle is sqrt(13).

Therefore, the equation of the circle is:

(x + 1)^2 + (y - 4)^2 = 13.

Answer:

Step-by-step explanation:

1) Separate the equations that are in the "()" and solve.

2)solve the equations out of the "()".

~Don't forget to use the unit for the answer!

*unit is x*

Answer:

Approximately 13.660

Step-by-step explanation:

Answer:

13.660

Step-by-step explanation:

Answer:

15 cups of grapefruit juice

Step-by-step explanation:

60 / 4 = 15

Therefore, 15 cups of grapefruit juice were needed.

Hope this helps :)

Tell me if this is wrong

Answer:

48 flowers

Step-by-step explanation:

Since, the ratio of tulips to daisies are the same.

Hence, if we have x number of daisies, then the number of tulips will also be x.

Therefore, with number of tulips being 21 and equal ratio of daisies will also mean that Anna has 21 daisies .

The total number of flowers will be :

Number of tulips + Number of daisies

21 + 21 = 42 flowers

Answer:

If you are finding the amount for the variable x, then the answer is -3.

Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

What is Confidence interval?

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

As given,

n = 150 = drivers

x = 100 = wear seat belts.

We have to find 95% confidence interval for proportion P that do not wear seat belt.

From 150 we have 100 wear seat belts

Not wear seat belt = 150 - 100

Not wear seat belt = 50

P = 50/150

P = 0.33

95% confidence interval for P is

CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))

For 95% CI, zα/2 = 1.96

Substitute values,

CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))

CI = (0.33 - 0.075, 0.33 + 0.075)

CI = (0.255, 0.405)

Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

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Answer:

c

Step-by-step explanation:

Pythagoras theroem

\( \sqrt{(( {32}^{2}) + {12}^{2} ) } \)

= 4√73

The graph of the equation y = x^2 - 3 is a U-shaped curve that opens upwards.

To graph this equation, we can select various x-values, calculate the corresponding y-values using the equation, and plot the points on a graph. Let's choose a range of x-values and calculate the corresponding y-values:

For x = -3:

y = (-3)^2 - 3 = 9 - 3 = 6

So, we have the point (-3, 6).

For x = -2:

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

So, we have the point (-2, 1).

For x = -1:

y = (-1)^2 - 3 = 1 - 3 = -2

So, we have the point (-1, -2).

For x = 0:

y = (0)^2 - 3 = 0 - 3 = -3

So, we have the point (0, -3).

For x = 1:

y = (1)^2 - 3 = 1 - 3 = -2

So, we have the point (1, -2).

For x = 2:

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

So, we have the point (2, 1).

For x = 3:

y = (3)^2 - 3 = 9 - 3 = 6

So, we have the point (3, 6).

Now, let's plot these points on a graph:

markdown

 |

 |       .

 |    .

 | .  

 |__________________________

   -3 -2 -1  0  1  2  3

The graph of the equation y = x^2 - 3 is a U-shaped curve that opens upwards, crossing the y-axis at -3.

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Answer: M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)

Step-by-step explanation:

The slope is already given in the equation, which is 2

M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)

Answer:

12

Step-by-step explanation: 18/3=6 6(2)= 12

After answering the provided question, we can conclude that As a result, equation the cost of 2 pounds of candy is $7.00.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "\(2x + 3 = 9"\) asserts that the statement "\(2x + 3\)" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "\(x2 + 2x - 3 = 0\)," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Claim: To calculate the cost of 2 pounds of candy, multiply the cost per pound of candy by 2.

According to the data provided, the cost per pound of candy is $3.50.

Reasoning: In order to determine the cost of 2 pounds of candy, we must first determine the total cost of 2 pounds of candy. Because the price per pound of candy is $3.50, we can calculate the total cost by multiplying the price per pound by the number of pounds. In this case, we want to know how much it costs for two pounds, so we multiply $3.50 by two to get:

2 pounds of candy = $3.50 per pound x 2 pounds = $7.00

As a result, the cost of 2 pounds of candy is $7.00.

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Answer: I believe 20.

Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.

EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

combinations

C(n,r)= n! / (r! * (n−r)!)

n = 6 : total number of lines

r = 3 : because its 3 lines to make a triangle

6 lines

6C3 = 20 triangles

quora glenn clemens

mathplanet

Answer:

\(\frac{-3y^{21}}{x^{12}}\)

Step-by-step explanation:

\(Given: (-3x^{4}y^{-7})^{-3}\\\\= 3x^{4*-3}y^{-7*-3}\\\\= 3x^{-12}y^{21}\\\\\\\)

Hence we have   \(\frac{-3y^{21}}{x^{12}}\)