Can you work out this math puzzle?

Answer:

The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072

Step-by-step explanation:

In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:

p(0) = (1 - 0.312)^(12) = 0.688^(12) = 0.01124

We now need to calculate the probability that one child learns to swim before 6 years of age.

p(1) = 12*0.312*(1 - 0.312)^(11) = 3.744*(0.688)^(11)

p(1) = 3.744*0.01634

p(1) = 0.0612

The probability of 1 or less children from that group to learn how to swim before 6 years of age is:

p = p(0) + p(1) = 0.01124 + 0.0612 = 0.07244

The probability that 1 or fewer of the 12 children will learn to swim before age 6 is approximately 0.072 when rounded to three decimal places.

1. Given:

  - Probability that a child will learn to swim before age 6, ( p = 0.312 )

  - Number of children, ( n = 12 )

2. Calculating ( P(X = 0) ):

[tex]\[P(X = 0) = \binom{12}{0} (0.312)^0 (1 - 0.312)^{12}\]\[P(X = 0) = 1 \times 1 \times (0.688)^{12}\]\[P(X = 0) \approx (0.688)^{12}\][/tex]

Using a calculator for [tex]\((0.688)^{12}\)[/tex]:

[tex]\[(0.688)^{12} \approx 0.0088\][/tex]

3. Calculating ( P(X = 1) ):

[tex]\[P(X = 1) = \binom{12}{1} (0.312)^1 (1 - 0.312)^{11}\]\[P(X = 1) = 12 \times 0.312 \times (0.688)^{11}\][/tex]

Using the binomial cumulative distribution function (CDF):

[tex]\[P(X \leq 1) = \sum_{k=0}^{1} \binom{12}{k} (0.312)^k (0.688)^{12-k}\][/tex]

Using the binomial probability tables or calculator, we get:

[tex]\[P(X = 0) \approx 0.0088\]\[P(X = 1) \approx 0.0623\][/tex]

Summing these:

[tex]\[P(X \leq 1) \approx 0.0088 + 0.0623 = 0.0711\][/tex]

Thus, the probability that 1 or fewer of the 12 children will learn to swim before age 6 is approximately 0.0711, which rounds to 0.072.

Answer:

The two expressions of an equation are separated by an equal sign. When the statement is given in words, the equal sign is indicated by the word “is” or the words “the same as.”

Step-by-step explanation:

Two expressions of the equation by properly interpreting the words into appropriate signs and digits.

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement. To achieve our goal, we use two principles of equality, the addition principle and the multiplication principle.

A binomial expression is an algebraic expression which is having two terms, which are unlike. Examples of binomial include 5xy + 8, xyz + x3, etc.

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

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Answer:

angle 5

Step-by-step explanation:

Answer:Which expression represents the distance between the points (a, 0) and (0, 5) on a coordinate grid? StartRoot a squared + 5 EndRoot StartRoot a squared + 25 EndRoot StartRoot (a minus 25) squared EndRoot StartRoot (a minus 5) squared EndRoot

Step-by-step explanation:

0, 5) on a coordinate grid? StartRoot a squared + 5 EndRoot StartRoot a squared + 25 EndRoot StartRoot (a minus 25) squared EndRoot StartRoot (a minus 5) squared EndRoot

The distance between the two points is given by:

[tex]d = \sqrt{a^2 + 25}[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Then for the given points, that are (a, 0) and (0, 5) the distance is given by:

[tex]d = \sqrt{(0 - a)^2 + (5 - 0)^2} \\\\d = \sqrt{a^2 + 25}[/tex]

Then the correct option is the second one, the square root of the sum between a squared and 25.

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Answer:2nd one

Step-by-step explanation:

Answer:

1/2 and 1/3

Step-by-step explanation:

1/2 can have a denominator of 6 by multiplying by 3

[tex]\frac{1}{2} *\frac{3}{3} =\frac{3}{6}[/tex]

1/3 can have a denominator of 6 by multiplying by 2

[tex]\frac{1}{3} *\frac{2}{2} =\frac{2}{6}[/tex]

Answer:

D. Yes, two sides are perpendicular, and the side lengths fit the

Pythagorean theorem.

Option B is correct as the shape lacks a right angle and its side lengths do not conform to the Pythagorean theorem, despite having two perpendicular sides.

A right-angled triangle is a geometric shape that has one internal angle measuring exactly 90 degrees. This angle, known as the right angle, is formed by the intersection of two sides of the triangle.

The other two angles in the triangle are acute angles, which means they measure less than 90 degrees. The side opposite the right angle is called the hypotenuse, and it is the longest side in the triangle.

The other two sides are called the legs, and they form the right angle. The lengths of the legs and the hypotenuse of a right-angled triangle are related by the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the legs.

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Answer:

12

Step-by-step explanation:

11.9781

After tenth digit it is 7>=5. So 1 should be added to 11.9

11.9 + 1 = 12.0 = 12

Answer:

The student is correct.

Step-by-step explanation:The circle's circumference is the distance around the circle.  To find out the circle's circumference, you will NEED the radius.  Without the radius OR diameter, there will be no way of telling what the circumference is with just the area.

Answer:

1250 Students applied.

Step-by-step explanation:

If you set it up as a proportion and then cross multiply, it comes out to 3x=3750 so then you would simplify and get x = 1250 as your answer!

Hope this helps!

I believe your answer is

C. i- 0.3i

Answer:

The dept of the lake will be 279 ft in 6 weeks

Step-by-step explanation:

We are given that the depth of a lake can be modeled by the function

[tex]y = 323(0.976)^{x}[/tex]

Where x is the number of weeks and y is the depth of lake in feet

The depth of the lake today is (x=0)

[tex]y = 323(0.976)^{0}[/tex]

[tex]y=323[/tex] [tex]ft[/tex]

The depth of the lake after 6 weeks will be (x=6)

[tex]y = 323(0.976)^{6}[/tex]

[tex]y = 323(0.864)[/tex]

[tex]y=279[/tex] [tex]ft[/tex]

Therefore, the dept of the lake will be 279 ft in 6 weeks.

Answer:

order: 37, 40, 42, 47, 52, 54, 57, 60

a) mean: 48.625

b) difference: 340.375

c) 47.5 difference (between mean and mad)

d) 7.125

Answer:

f(2) = - 16

Step-by-step explanation:

Given

f(x) = - [tex](4)^{x}[/tex]

To evaluate f(2) substitute x = 2 into f(x)

f(2) = - [tex](4)^{2}[/tex] = - 16

Answer:

182.12

Step-by-step explanation:

2πr , then substitute the numbers

Answer:

182.12ft

Step-by-step explanation:

Just remember to divide the diameter by two to get the radius.

58/2  = 29

C=2 π r    

C = 2 * 3.14 * 29= 182.12ft

Answer:

solve for y

Step-by-step explanation:

[tex]5x-2y=-10[/tex]

subtract 5x from both sides

[tex]5x-5x-2y=-10-5x[/tex]

[tex]-2y=-10-5x[/tex]

Divide each term in the equation by -2

[tex]\frac{-2y}{-2}=\frac{-10}{-2} -\frac{-5x}{-2}\\\\y=\frac{-10}{-2} +\frac{-5x}{-2} \\\\y=5+\frac{5x}{2}[/tex]

(negative+negative=positive)

re-write in slope-intercept form [tex]y=mx+b[/tex] , where m is the slope and b is the y-intercept

[tex]y=\frac{5}{2}x+5[/tex]

Now you know that the slope is [tex]\frac{5}{2}x[/tex] and the y-intercept is [tex]5[/tex].

Now, to graph, you just need to choose random values for x (like 0,1,2,3 or any other number) and insert into the equation [tex]y=\frac{5}{2}x+5[/tex] to find the points, or you can just use the slope. To find the x-intercept, do the following:

make y equal to 0

[tex]0=\frac{5}{2}x+5[/tex]

Solve for x:

simplify [tex]\frac{5}{2}x[/tex]

[tex]0=\frac{5x}{2} +5[/tex]

Subtract 5 from both sides

[tex]0-5=\frac{5x}{2}+5-5\\ \\-5=\frac{5x}{2}[/tex]

Multiply both sides by 2

[tex]2(-5)=2(\frac{5x}{2})\\\\-10=5x[/tex]

Divide both sides by 5

[tex]\frac{-10}{5}= \frac{5x}{5}\\\\-2=x[/tex]

Flip

[tex]x=-2[/tex]

The x-intercept is -2.

Answer:

D). 9

Step-by-step explanation:

Step 1: Graph the points

Step 2:  count the distance between point 1 (-3,4) and point 2 (-3,-5)

Step 3: Locate the answer on your multiply choices

Step 1: graph  ( the graphed points are located in the picture below)

Step 2: count the distance (Demonstration on how to do this is on the second image below)

Step 3: Locate your answer (9)

Answer:

1/2 or 3/6

Step-by-step explanation:

on a die theirs 6 numbers, and the numbers 1,2,3 are less than 4. So out the the six numbers 3/6 are les than 4 and 1/2 and 3/6 are equivalent.

Answer:

192 ft

Step-by-step explanation:

The volume of the prism with the given dimension of 2 feet, 8 feet, and 12 feet is 192 cubic feet.

The volume of a prism is the product of the base area and the height of the prism.

The given dimension of the prism is 2 feet, 8 feet, and 12 feet.

Therefore, the volume of the prism is

= (2 × 8 × 12) cubic feet

= 192 cubic feet.

Therefore, the volume is 192 cubic feet.

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Answer:

1 1/2

Step-by-step explanation:

60/40 = (60 ÷ 20)/(40 ÷ 20) = 3/2; 3 > 2 => improper fraction Rewrite: 3 ÷ 2 = 1 and remainder = 1 => 3/2 = (1 × 2 + 1)/2 = 1 + 1/2 = = 1 1/2, mixed number (mixed fraction)

Hope this helped!

Answer:

1 1/2

Step-by-step explanation:

40 can go into 60 1 time

simplify the rest

Answer:

False

Step-by-step explanation:

As integer is a whole number that is not a fractional number that can be positive, negative, or zero.

Answer:

false

Step-by-step explanation:

An integer is a whole number. integers can't have a decimal places.

Answer:

Time in weeks you mean not seconds.

His beard should be graphed at point xy 1, 8 and continue at a gradient rate 8 rise / 1 rise showing m = 8/1 . to show one week to be able to meet up with .

Step-by-step explanation:

There are 604800 seconds in a week so first multiply by 5.5 weeks to find the first green dot. 604800 x 5.5 = 3326400 so we know the .5 option shows a rounded next week number.

We can either work downwards to zero or start at 1,8 ever way they will be even balance as 8/32 = 4 8/36 = 4.4 growth and this for example would show a rounded amount, so that 8/8 would be 8 and show the first week, or can be skipped out and start with y = 2x + 10 and then when referring to show .5 growth it would still be a whole number within the equation representing 12 and still be a whole number representing 2 weeks.

The graph does not speak of seconds but weeks, but if you want to use the above and try for 604800 seconds as shown for 1 week, you will have a tough time graphing. Stick to 2,4,6 8, 10, 12, 14, 16, 18 weeks multiplied by 12 = y = 1 + 8 = 0  

y = 2x +8 +2 = 1

y = 3x + 8 +2 = 2  

etc etc....

Answer:

-->

Step-by-step explanation:

Graph (-5,-3) and use the slope, -2, to find another point. -2 can also be written as [tex]-\frac{2}{1}[/tex]

[tex]\frac{rise}{run} =\frac{-2}{1}[/tex] and  [tex]\frac{rise}{run} =\frac{2}{-1}[/tex] **

Use both. This works because either way, they will lie on the same line with the same slope. So, starting at (-5,-3), go down two points (-)* and to the left 1 (+)*, then, starting at (-5,-3) again, go up two points (+)* then to the right 1 point (-)*.

* If the number is negative, you either go down or to the right. If the number is positive, you go up and to the left.

**Rise over run refers to the change in the y-axis and the change in the x-axis: [tex]\frac{rise}{run} =\frac{y-axis}{x-axis}[/tex]. Only one number is negative because, if both were negative, that would make a positive number, but the slope is -2, not 2.

Another way you could do this is by finding points first. All you need to do is turn the slope into a "point". Remember, 2 is the y and 1 is the x:

[tex]-2=-\frac{2}{1} = (1,-2)[/tex] and [tex](-1,2)[/tex]

Then, using (-5,-3) and your new points, add them separately:

[tex](-5,-3)+(1,-2)\\(-5+1,-3+(-2))\\(-5+1,-3-2)\\(-4,-5)[/tex]

(-4,-5) is one point

[tex](-5,-3)+(-1,2)\\(-5+(-1),-3+2)\\(-5-1,-3+2)\\(-6,-1)[/tex]

(-6,-1) is another point. Connect the three points. You can check your work on the graph:

The equation of the first parabola with vertex (2, -1), opens upward with a focal width of 16 is (x-2)² = 16*(y+1). The equation of the second parabola with a focus (2, -3) and directrix x = 5 is (x-2)² = -24*(y-5).

1. For a parabola that opens upward with vertex (h, k) and focal width 4p, the equation is given by: (x-h)² = 4p*(y-k). Given the vertex (2, -1) and focal width of 16, we can deduce that 4p = 16, so p = 4. Plug these values into the formula to get the equation of the parabola: (x-2)² = 16*(y+1).

2. For a parabola with a focus (h, p) and directrix x=d, the equation is (x-h)² = 4p*(y-d). Given the focus (2, -3) and directrix x = 5, meaning h = 2, p = -3, and d = 5. This gives us the equation of the parabola: (x-2)² = -24*(y-5).

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The equation of the first parabola described is (y+1) = (x-2)^2. The equation of the second parabola, given the focus at (2,-3) and the directrix at x = 5, is (x-2) = -(1/12)(y+3)^2.

1. The standard form of a parabola that opens upward or downward is (y-k)=(1/4p)(x-h)^2, where (h,k) is the vertex and p is the distance from the vertex to the focus. In this case, h is 2, k is -1 and the focal width is 4p which is given as 16. So p = 16/4 = 4. So, the equation of the parabola is (y+1) = (x-2)^2.

2. The standard form of a parabola that opens to the right or to the left is (x-h)= (1/4p)(y-k)^2. In this case, the focus is (2,-3) and the directrix is x=5. From these, we know h=2, and since the directrix is to the right of the focus, p=h-5 is negative, so p=2-5=-3. The vertex of the parabola is thus (2,-3). So, the equation of the parabola is "(x-2) = -(1/12)(y+3)^2".

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Answer: B and C

Step-by-step explanation:they are odd

349,313,81 are odd numbers.

Explanation:

those numbers which are not divisible by 2 are called odd numbers.

Hope it will help u...

Answer:

B. Prices increase.

Step-by-step explanation:

When demand for a product is greater than the product's supply, that increases the value of said product, and thus they bring the price up.

When demand exceeds supply, it's referred to as a shortage or excess demand, and generally leads to an increase in prices. Sellers are able to charge more because more consumers are vying for a limited number of goods.

When demand exceeds supply in economic terms, it leads to a situation called excess demand or shortage. In this scenario, more people want a product than the amount of the product available. As a result of this excess demand, prices generally increase. This increase happens due to the basic law of demand and supply. Since more consumers are chasing a limited number of goods, sellers can charge higher prices. This increase in prices can help reduce the demand and bring the market back into equilibrium.

For instance, consider a situation where new smartphones are released, and the demand outstrips the supply. The prices will likely increase because people are willing to pay a higher price to secure one of the limited handsets.

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Answer:

all work is pictured and shown

Final answer:

To calculate the volume of the orange juice can, the formula V = πr²h is used. By finding the radius from the given area of the base and then using the height of the can, the volume is calculated as 3120 cm³, which corresponds to answer choice A.

Explanation:

The student has asked a question about calculating the volume of a cylindrical can of orange juice. Given the area of the circular base is 156 square centimeters and the height of the can is 20 centimeters, the volume can be found by using the formula V = πr²h, where V stands for volume, r is the radius of the base, and h is the height of the cylinder. First, we need to find the radius (r) of the base from the given area, and then substitute it into the volume formula along with the height (h).

To find the radius, we use the formula for the area of a circle, A = πr², where A = 156 cm². Solving for r, we have r = √(A/π). Plugging the area into this formula, the radius (r) is:

r = √(156/π) cm

Then we substitute the radius and height into the volume formula:

V = πr²h

V = π(√(156/π))^2 × 20 cm

V = 156 × 20 cm³

V = 3120 cm³

Therefore, the correct answer is A. 3120 cubic centimeters.

Final answer:

The expression log(c) log(20) - log(5) is simplified using the quotient rule for logarithms to log(c) log(4), by subtracting the logs and simplifying the inside expression from 20/5 to 4.

Explanation:

The student's question involves simplifying a logarithmic expression. The initial expression is log(c) log(20) - log(5). To simplify this expression, we can use logarithmic properties, specifically the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b).

Applying this property to the given expression, we combine the two logs that are subtracted:

log(20) - log(5) = log(20/5). Simplifying the division inside the log gives us:

log(4). Therefore, the simplified expression is log(c) log(4).