If a single die is rolled what is the probability of getting a prime number. (The die has 6 sides) Write the fraction in lowest terms. O a. 1 - 2 O b. 2 3 Oc. 1 6 O d. 5 6

We can expect that 4 of the next 9 children to enroll will be elementary school students.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

Based on the information given, the proportion of elementary school students who enrolled in the last 18 children is:

8/18 = 4/9

Therefore, it can be expected that 4 out of every 9 children who enroll in the day care center will be elementary school students.

To determine the number of elementary school students among the next 9 children who enroll, we can use this proportion:

(4/9) x 9 = 4

Thus, we can expect that 4 of the next 9 children to enroll will be elementary school students.

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As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.

Confidence interval

Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.

Given,

A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.

And we need to find the 95% confidence interval for the true average age of all students in the university.

While we looking through the given question we have identified the following,

Number of samples = 64

Average age = 23

Standard deviation = 3

Confidence interval = 95%

Based on this confidence interval, the z score is 1.96

According to the formula,

u = 23 ± 1.96 x 3/√64

u = 23  ± 1.96 x (3/8)

u = 23  ± 1.96 x 0.375

u = 23  ± 0.735

u = 23.735, 22.635

Therefore, the average age of the student is approximately 23 to 24.

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Answer:

Step-by-step explanation:

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

given that

volume = 4,000\(cm^{3}\)

let height = h

    width = w

    length = l

width and length are equal

height = length = h

volume of box = height × width × height

             4000  = h × w × h

             4000 = \(h^{2}\)w

                  w = 4000/\(h^{2}\)

surface area(SA) = area of base + sum of area of each side

                           =  \(h^{2}\) + hw + hw + hw + hw

                           =  \(h^{2}\) + 4hw

substitute y = 4000/\(h^{2}\)

SA =  \(h^{2}\)  + 4x(4000/ \(h^{2}\) )

SA =  \(h^{2}\)  + 16000/h

Taking the derivative:

SA' = 2h - 16000/ \(h^{2}\)

making SA' = 0:

0 = 2h - 16000/ \(h^{2}\)

2h = 16000/ \(h^{2}\)

2\(h^{3}\) = 16000

\(h^{3}\) = 8000

h = 20 cm

w = 4000 /  \(h^{2}\)  = 4000 / 20² = 10 cm

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

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Answer:

A

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{120}{360}\)

     = 2π × 8 × \(\frac{1}{3}\)

    = 16π × \(\frac{1}{3}\) = \(\frac{16\pi }{3}\) m

Answer:

The correct option is;

LeftAngleBracket negative 16, 14 RightAngleBracket which is \(\left \langle -16, 14 \right \rangle\)

Step-by-step explanation:

The given coordinates of the points are;

The starting point, Q(23, 48) and the final point, R(7, 62)

Therefore, we have;

The x component = The x-value of R - The x-value of R = 7 - 23 = -16

The y component = The y-value of R - The y-value of R = 62 - 48 = 14

Therefore, the component form of the vector QR = \(\left \langle -16, 14 \right \rangle\)

Answer:

B on Edg.

Step-by-step explanation:

Yay

The baby is 6 months old (or x = 6), the predicted weight would be11 pounds

Step-by-step explanation:

We can use the slope-intercept form of a linear equation to model the baby's weight as it grows over time:

y = mx + b

where y is the weight of the baby in pounds, x is the age of the baby in months, m is the rate of weight gain per month (in pounds per month), and b is the weight of the baby at birth (in pounds).

From the given information, we know that the baby's weight at 2 months old (or x = 2) is 9 pounds. We also know that the baby gains 0.5 pounds each month (or m = 0.5).

Substituting these values into the slope-intercept equation, we get:

y = 0.5x + b

To find b, we can use the fact that the baby's weight at 2 months old is 9 pounds:

9 = 0.5(2) + b

b = 8

Therefore, the equation that models the baby's weight as it grows over time is:

y = 0.5x + 8

So, for example, when the baby is 6 months old (or x = 6), the predicted weight would be:

y = 0.5(6) + 8 = 11 pounds

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Answer:

Step-by-step explanation:

__________________________________________________________

According to Calculator Soup,

Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal. The shortcut way to convert from a percentage to a decimal is by removing the percent sign and moving the decimal point 2 places to the left. Express 50% as a decimal. "Percent" means "per 100" or "over 100".

__________________________________________________________

The answers are Divide by 100 and Move the decimal point two places to the left.

__________________________________________________________

Hope this helps! <3

__________________________________________________________

Answer:

B: The function approaches 1 as x approaches -∞  and ∞

Step-by-step explanation:

Plato Answer

Answer:

-29/15 or -1 14/15

Step-by-step explanation:

Answer:

-29/15 or mixed form -1 14/15

==========================================================

Explanation:

Let's say that we had 9 blocks that were each one-tenth of a pound.

This means we have 9*(1/10) = 9/10 of a pound total.

Take 1/3 of this to get (1/3)*9 = 9/3 = 3. So we take away 3 blocks to represent the amount of oranges she has eaten so far.

We're left with 9-3 = 6 blocks.

Divide these 6 blocks among 3 bags getting 6/3 = 2 blocks per bag.

Each block is 1/10 of a pound, so 2*(1/10) = 2/10 = 1/5 of a pound goes per bag.

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

Another approach:

1/3 of 9/10 = (1/3)*(9/10) = 9/30 = 3/10

She has eaten 3/10 of a pound of oranges, leaving 9/10-3/10 = 6/10 = 3/5 of a pound left.

Dividing 3/5 over 3 leads to

(3/5) divided by (3/1) = (3/5)*(1/3) = 3/15 = 1/5

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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Answer:

22 units

Step-by-step explanation:

What we know is that the legs of the triangle is 4 units (a) and the other is three units (b).

Plug these values into the formula and solve for c

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

√25 = √c^2

c = 5

Then, add the values.

5 + 5 + 4 +5 + 3

= 22 units

Answer:

Hopefully this makes sense. All you're doing is inputting your X VALUES (or your inputs) and using those numbers to find our what your Y VALUES (or your outputs) are

x: -2     -1      0     1      2      3

y: 49     7       1     \(\frac{1}{7}\)       \(\frac{1}{49}\)      \(\frac{1}{343}\)

The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.

(x/3) + 5 - 5 ≥ 1/6 - 5

x/3 ≥ -29/6

Multiply both sides by 3.

3(x/3) ≥ 3(-29/6)

x ≥ -29/2

To check, let x = -29/2

x = -29/2 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

(-29/2)/3 + 5 ≥ 1/6

1/6 ≥ 1/6

let x = -14,

x = -14 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

-14/3 + 5 ≥ 1/6

1/3 ≥ 1/6

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Answer:

Step-by-step explanation:

They're both right angle triangles and have the same length and size , hence congruency

Answer:

tienes que hacer cuadritos

Answer:

doh as djdjndjejehehdhdhdhdhehenejenenejenejenenenejrenenenenenenenenennenejeuehenejeiebenrkrbrndornrjebeydhrjjrhrhrhrb4hrhrhr

Step-by-step explanation:

rhdhdhuridnfhdjjdjfkf

Answer:

x = 10, y = 5

Step-by-step explanation:

The sine of 60 is given by the division of the opposite side of 60º by the hypothenuse.

We have that:

sine of 60 is sqrt(3)/2

The oopposite side is 5sqrt(3)

The hypothenuse is x.

So

Then we apply cross multiplication.

The cosine of 60 is the adjacent side divided by the hypothenuse.

The cosine of 60 is 1/2.

The adjacent side is y.

The hypothenuse is x = 10. So

Applying cross multiplication

2y = 10

y = 5

Answer:

\(1.0 \times {10}^{4} \)

This represents 10,000 in scientific notation.

For the given expression 12x + 3y = -3 , the value of y-intercept is equal to -1.

As given in the question,

Given expression is equal to 12x + 3y = -3

To get the value of y-intercept simplify the given expression first for y

12x + 3y = -3

⇒ 3y = -3 -12x

Divide both the side of the given expression 12x + 3y = -3 by 3 we get,

3y / 3 = ( -3 -12x) / 3

⇒ y = -1 -4x  __(1)

To get the value of y-intercept substitute x = 0  in equation (1) we get,

y = - 1 - 4(0)

⇒ y = -1

Therefore,  for the given expression 12x + 3y = -3 , the value of

y-intercept is equal to -1.

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Answer:

The first one

Step-by-step explanation:

We simplify this inequality to x>4. This means it is moving past the four to the right with an open dot

\(\boxed{\boxed{\pink{\bf \leadsto Option \ A \ is \ correct . }}}\)

For the number line refer to the attachment :

A linear inequality is given to us . And we need to find the correct number line. So the given linear inequality is :-

\(\bf \implies 5x + 3 > 4x + 7 \\\\\bf\implies 5x - 4x > 7 - 3 \\\\\bf\implies \boxed{\red{\bf x > 4 }}\)

This implies that the value of x is Greater than 4 . That is the inequality can have all the values more than 4. So when we see the given number lines we see that the first number line represents all values greater than 4 .

Rate is the same thing as gradient so to work out the gradient you need to use the formula

change in y / change in x

Change in y = y2 - y1

Pick any two points on the graph

Change in y = 30 - 15

Change in y = 15

Change in x = x2 - x1

Change in x = 2 - 1

Change in x = 1

15/1

= 15 dollars per day.

We can double check this by seeing the increase of money per day, for example, here from day two to day three, the money needed increases by 15, so our answer is correct.

Answer:

5 years

Step-by-step explanation:

Firstly, Let's use a function to find how much Jenny owes every year.

Using f(t)=3,000(1.18)^t

We can find the amount of money jenny owes every year.

Now let's try to find how many years it would take her to double her credit card debt.

If we change t=5, we can see that the function gives us an output of 6,863.27 which is double the amount of which she currently owes.

Answer:

It would be 5000

Step-by-step explanation:

It would be 500 b/c the number is a greater number that is 4802 and it is closer to 5000 than 4000

Answer:

8

Step-by-step explanation:

4/5 ÷ 10​

4/5 ÷ 10/1 Multiply the denominators  and numerators

= 40/5 then Simplify

8

Answer:

2.85

Step-by-step explanation:

It would be 2.85 because half of 3.00 is 1.50 and half of 2.70 is 1.35 add 1.35 and 1.50 together that makes 2.85

Hope that helps :))

Answer:

3 x X - 14

Step-by-step explanation:

Is your algebra expression.

Answer:

3x-14

Step-by-step explanation:

Product of 3 and number is 3*x

For " 14 fewer than.." we simply subtract 14.

So we get 3x-14

The answer to the integral is -1/6.

To evaluate the integral below ∫3πsin4(2πx)cos3(2πx)dx,

we can use the trigonometric identity sin2Acos2A

= 1/4sin(4A).

we have the integral∫3πsin4(2πx)cos3(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)sin2(2πx)cos(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)(1-sin2(2πx))cos(2πx)dx

= 1/2∫3πsin2(2πx)cos2(2πx)(cos(2πx)-cos3(2πx))dx

= 1/2∫3π(sin2(2πx)cos(2πx)-sin2(2πx)cos3(2πx))cos2(2πx)dx

= 1/8∫3π(2sin(4πx)-sin(6πx))cos2(2πx)dx.

Let u= 2πx and du= 2πdx,

then we have the integral as 1/8∫6π(sin2u-sin3u)cos2udu

= 1/8[∫6πsin2ucos2udu-∫6πsin3ucos2udu]

We solve the first integral as follows; using the identity sin2ucos2u= 1/4sin(4u), we have the integral as

∫6πsin2ucos2udu

= 1/4∫6πsin(4u)du

= -1/16cos(4u)]6π03π

= -1/16cos(4(6π))-(-1/16cos(4(0)))

= 0.

We solve the second integral using the identity sin3u= 3sinu-4sin3u,

we have∫6πsin3ucos2udu

= 1/3∫6πsinudu-4/3∫6πsin3udu

= 1/3[-cos(6π)+cos(0)]-4/3[-1/12cos(4(6π))+1/12cos(4(0))]

= 4/3.

To complete our solution, we substitute our values into the integral as 1/8[0-4/3]

= -1/6.

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Answer:

aₙ= 6n+1

Step-by-step explanation:

7,13,19,25,31

Given, AP with the first term of 7, and common difference of 6

Nth term: