Evaluate the expression.
3–6–(2+6)2

The probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

The probability that exactly 5 black cars and exactly 10 non-black cars drive by on a particular afternoon is

, where \($X_b$\) are the number of black cars and \($X_{nb}$\) the number of non-black cars passing by the playground in the afternoon. Since the color of the cars is independent of the number of cars that drive by, we can model the number of black and non-black cars using two separate Poisson distributions with means

\($\lambda_b = \frac{1}{5}\cdot25=5$ and $\lambda_{nb}=25-5=20$\), respectively.

Plugging in the values and simplifying, we get:

\($$P(X_b=5,X_{nb}=10)=\frac{e^{-5}5^{5}}{5!}\cdot\frac{e^{-20}20^{10}}{10!}\cdot\frac{1}{5^{5}}\cdot\frac{4^{10}}{5^{10}}\approx 0.00167$$\)

Therefore, the probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

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Answer:

answer is D :

√24 = 4.89

which is the nearest to 5 and possible answer

Answer:

EF is 61 units.

Step-by-step explanation:

EF is 61 units as we can assume that line EG intersects line FH in half, if we know that, then we can find out that EF is 61.

Answer:

b) 61

Step-by-step explanation:

Triangles FEG and HEG are congruent by HL.

That makes sides EF and EH congruent by CPCTC.

Answer: b) 61

50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

Step-by-step explanation:

The volume of a cylinder can be solved by finding the Surface area of its base, and multiplying it by the height.

Surface area is pi r^2

1. pi 7^2 * 15 = 2309.07

2. pi 8^2 * 20 = 4021.24

3. pi 5^2 * 14 = 1099.56

4. pi 15^2 * 50 = 35342.92

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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Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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Answer:

B&D

Step-by-step explanation:

i think this is correct, if not let me know, correct me.

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

Step-by-step explanation:

To convert, you will need to know how many times five will go into 42. Once found, that will be your whole number. The remainder will be the numerator, and the divisor of the current fraction will become the denominator.

Given fraction:

Knowing how many times five will go into 42.

The denominator of the given fraction will be the denominator of the created mixed fraction.

Hence, Option C is correct.

Answer:

c) $637.50

Step-by-step explanation:

Formula: I= PRT

2500×8.5%×3 = 637.5

Answer:

90°

Step-by-step explanation:

\((\pi /2) * 180 = 90\)

Whenever you are required to transfer from Radians to Degrees, simply multiply the Numerator by 180° (180). Treat the \(\pi\) as a variable such as x and y, and divide by the numerator.

Answer:

The current weight of the octopus is:

\(w = \frac{14}{15}\,kg\)

Step-by-step explanation:

The current weight is determine by addition and subtraction of rational numbers:

\(w = \frac{5}{6}\,kg + \frac{3}{10}\,kg -\frac{1}{5}\,kg\)

\(w = \frac{50 + 18}{60}\,kg - \frac{1}{5}\,kg\)

\(w = \frac{68}{60}\,kg - \frac{1}{5} \,kg\)

\(w = \frac{17}{15}\,kg - \frac{1}{5}\,kg\)

\(w = \frac{85-15}{75} \,kg\)

\(w = \frac{70}{75}\,kg\)

The current weight of the octopus is:

\(w = \frac{14}{15}\,kg\)

Answer:

  see attached

Step-by-step explanation:

Any of the vertical lines is perpendicular to any of the horizontal lines.

The open/close/adjust handle is perpendicular to the blind slats and the blind frame.

The threads that hold the slats, and the string that raises/lowers them are also perpendicular to the slats.

Answer:

%70

Step-by-step explanation:

percentage can be found by dividing the values than multiplying the values by 100

Formula: (value/totalvalue)100

plug in the formula with what we have;

28/40(100)

→ First step; dividing our value by total value (28/40)

28/40 = 0.7

  → Second step; multiplying our value by 100 (0.7)

0.7 * 100 = 70

Therefore cora got %70 correct on her grammar sheet

Answer:

70% correct

Step-by-step explanation:

We know that there are 40 questions on her grammar worksheet.

Out of those 40 questions, she got 28 right so 28/40 equals 0.7

Answer:

168cm

Step-by-step explanation:

Length: 8cm

Width: 3cm

Height: 7cm

I divided 8 and 7 first and got 56.

Next I multiplied 56 and 3 and got 168.

So the length is 168cm

(Hope this helped! <3)

(sorrry if its wrong I feel stupid today)

Answer:

Answer 1. C

Answer 2. There's not enough information. You didn't give us the radius or diameter.

Answer 3. B

Answer 4. A

Answer 5. D

Answer 6. A

Answer 7. We can't see the gameboard. Sorry!

Answer 8. We can't see the map. Sorry!

Answer 9. A

Hope that helps! Sorry for the missings! I'm not sure for Answer 4.

Hope that helps!

Step-by-step explanation:

The value of x for equation x /45 = 3 is 135, value of expression −5.8 + (−2.5) is -8.3, the sale price is $319.20, volume of cube is 125 cubic centimeter, y = x /8 represents a proportional relationship.

An expression is combination of variables, numbers and operators.

1. The given equation is x /45 = 3

Now value of x is 45×3

x=135

3. The expression is −5.8 + (−2.5)

−5.8 −2.5

The value of expression is -8.3

4.To find the sale price  after a 20% discount, we need to subtract 20% of the original price from the original price:

20% of $399 = (20/100) x $399 = $79.80

Sale price = $399 - $79.80 = $319.20

Therefore, the sale price is $319.20.

5.  The side length of cube is 5 cm

Volume = 5³

=125 cubic centimeter

6. y = 8/ x equation represents a proportional relationship

7. 5 ft² is area of the wall will the game board cover

9. The given expression is 5 /8 x 4 /5

20/40

1/2

Hence, the value of x for equation x /45 = 3 is 135, value of expression −5.8 + (−2.5) is -8.3, the sale price is $319.20, volume of cube is 125 cubic centimeter, y = x /8 represents a proportional relationship.

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Answer:

B

Step-by-step explanation:

(f+g)(x) = f(x) + g(x) = \(3x^{2} +4x-6+6x^3-5x^{2} -2\) = \(6x^{3}-2x^{2} +4x-8\)

Answer:

Step-by-step explanation:

69

The average rate of change is D. 2.

The average rate of change simply means the measure of how the function will change let unit of time.

In this case, it is important to look at the input and the output that wee given. It can seen that the difference between the output is given as:

13 - 11 = 2

15 - 13 = 2

In this case, the average change is 2.

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Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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Answer: 12 degrees

Step-by-step explanation:

6  hours multiplied by 2 degrees

6 X 2 = 12

In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.

h: hypotenuse

c1: shorter leg

c2: longer leg

Longer leg c2 is 3 inches longer than c1:

c2 = c1 + 3

hypotenuse h is 6 inches longer than c1:

h = c1 + 6

The formula for the calculation of the hypotenuse is:

h² = c1² + c2²

you replace for h and c2 in terms of c1:

(c1 + 6)² = c1² + (c1 + 3)²

You solve the previous equation for c1:

c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9

c1² - 6c1 - 27 = 0

the roots of the previous equation are:

(c1 - 9 )(c1 + 3) = 0

c1 = 9

c1 = -3

You take the positive number because there is no length of sides with negative values.

Then, c2 and h are:

c2 = c1 + 3 = 9 + 3 = 12

h = c1 + 6 = 9 + 6 = 15

Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches

The 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B is (0.027, 0.173). Treatment A appears to be more effective than Treatment B.

To find the 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B, we can use the formula:

CI = (p₁ - p₂) ± z * SE

where:

p₁ is the proportion of patients who survived in Treatment A

p₂ is the proportion of patients who survived in Treatment B

z is the z-score associated with the desired level of confidence (in this case, 95%)

SE is the standard error of the difference between two proportions, calculated as:

\(SE = \sqrt{p_1 \times \dfrac{(1-p_1)}{n_1} + p_2 \times \dfrac{(1-p_2)}{n_2}}\)

where n₁ and n₂ are the sample sizes for Treatment A and Treatment B, respectively.

Using the given proportions, we have:

p₁ = (0.8 + 0.6 + 0.4)/3 = 0.6

p₂ = (0.7 + 0.5 + 0.3)/3 = 0.5

n₁ = n₂ = 3

Plugging these values into the formula, we get:

SE = √((0.6 * 0.4)/3 + (0.5 * 0.5)/3) = 0.1768

z = 1.96 (for a 95% confidence level)

CI = (0.6 - 0.5) ± 1.96 * 0.1768 = (0.027, 0.173)

A possible conclusion based on this interval is that the true difference in proportions of patients who survived between Treatment A and Treatment B lies somewhere between 0.027 and 0.173, with 95% confidence. Since the interval does not include 0, we can conclude that there is a statistically significant difference in the proportions of patients who survived between the two treatments. Specifically, Treatment A appears to be more effective than Treatment B.

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--The complete question is, A medical study looked at the effectiveness of two different treatments for a certain disease. The study summarized the data by banding patients by age group and reporting the proportion of patients in each band who survived over a ten-year period. The proportions for the two treatments are as follows:

Treatment A:

Proportion survived in band 1: 0.8

Proportion survived in band 2: 0.6

Proportion survived in band 3: 0.4

Treatment B:

Proportion survived in band 1: 0.7

Proportion survived in band 2: 0.5

Proportion survived in band 3: 0.3

Assuming normal-based inference is appropriate, what is the 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B, based on the given data? Based on this interval, what is a possible conclusion about the true difference in proportions?--

Answer:

A. 12 + (-9)

Step-by-step explanation:

adding 8 to 4 is 12 and 9 remains as it is.

The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

What is a function?

A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.

To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.

The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2

Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

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