. A random sample of 100 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.6 days. Provide a 98% confidence interval for the average number of days absent per term for all the children. a. Write down the equation you should use to construct the confidence interval for the average number of days absent per term for all the children. (10 points) b. Determine a 98% confidence interval estimate for the average number of days absent per term for all the children. (10 points)

The legs are defined by \(L(x) = 2x\). The Hypotenuse if defined by \(h(x) = L(x)\cdot \sqrt{2}\). The perimeter is defined by:

\(p(x) = h(x)+2\cdot L(x) \\~\\p(x) = L(x)\cdot\sqrt{2} +2\cdot L(x) \\~\\p(x) = L(x)\cdot\left(\sqrt{2}+2\right) \\~\\p(x) = 2x\cdot\left(\sqrt{2}+2\right) \\~\\p(x)= 2\sqrt{2}x+4x\)

D. P(x) = 2x √2 + 4x

The perimeter of the isosceles right triangle will be P(x) = x√2 + 2x. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The sum of all the sides of the triangle will be known as the perimeter of the triangle.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

An isosceles right triangle has a hypotenuse length that can be modeled with the function h(x) = x√2.

The combined length of the legs can be modeled with the function L(x) = 2x.

Then the perimeter of the isosceles right triangle will be

P(x) = h(x) + L(x)

P(x) = x√2 + 2x

Thus, the perimeter of the isosceles right triangle will be P(x) = x√2 + 2x.

Then the correct option is B.

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Answer:

6(x + 4)

opening brackets

=6x+24 is the answer

Step-by-step explanation:

Answer:

The ratios are not equal, so this is not a dilation.

Step-by-step explanation:

4/3 is the first ratio

3/4 is the second ratio

Since these ratios are not equal there is not a dilation.

Answer:

3

Step-by-step explanation:

subtract 4 from 1/6 of 42. In middle school my traxhers always told me that of menas multiply, and in this situation it still holds. 1/6 x 42 is 42/6 or 42 divided by 6 which is 7. So now that makes this simpler, its saying subtract 4 from 7, so 7-4 =3

The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:

C. 118,764

Step-by-step explanation:

118764/12=9897

3*4=12 which is why I divided it by 12.

Answer:

C.

Step-by-step explanation:

Answer:

x-0.75x=9.00

-0.74x=9.00

x=0.74+9.00

x=9.74

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-3}\) = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - \(\frac{1}{3}\) + c ( add \(\frac{1}{3}\) to both sides )

5 \(\frac{1}{3}\) = c ⇒ c = \(\frac{16}{3}\)

y = \(\frac{1}{3}\) x + \(\frac{16}{3}\) ( multiply through by 3 to clear the fractions )

3y = x + 16

The matrix operation add -4(row 1) to row 3 is\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right]\)

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

Using the above as a guide, we have the following:

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

Hence, the result of the matrix expression is \(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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El dato que falta para determinar si Nicole dibujará un cuadrado es que todos los lados tienen la misma medida.

Answer:

im an expert

Step-by-step explanation:

If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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The monthly payments for the loan to be paid off at the rate given would be = $1,504.4

The total cost of the house = $243, 950.

The time for the payment of the loan = 25 years.

The rate of the payment = 7.4%

The simple interest = principal×time×rate/100

Si = 243, 950.×25×7.4/100

si = 45130750/100

si = 451,307.50

The total number of months is 25 years = 300

The amount paid per month = 451,307.50/300 = $1,504.4

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In the above problem, the annual interest rate on this loan is 1.15%, rounded to the nearest percent.

To calculate the annual interest rate on this loan, we can use the following formula:

r = (I / P) / n

where r is the annual interest rate, I is the total amount of interest paid over the life of the loan, P is the initial loan amount, and n is the number of years for the loan.

Using the information provided in the amortization schedule, we can calculate I as the sum of all the interest payments:

I = 750 + 748.92 + 216.45 = 1715.37

We can calculate P as the initial balance on the loan:

P = 149,783.55

Since the loan is being paid off over 123 months, we can calculate n as:

n = 123 / 12 = 10.25

Substituting these values into the formula for r, we get:

r = (1715.37 / 149,783.55) / 10.25

r = 0.0115

To convert this to a percentage, we multiply by 100:

r = 1.15%

Therefore, the annual interest rate on this loan is 1.15%, rounded to the nearest percent.

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Answer:

30:27 i think

Step-by-step explanation:

Answer:

14.62 I believe

Step-by-step explanation:

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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When the solid figure shown is sliced parallel to the base, the resulting figure is two cuboids

Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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Answer:

I cant see the whole image

Step-by-step explanation:

please show it.

Answer:

  A(-4, 1)

Step-by-step explanation:

The parts being equal means ...

  A - P = P - B

  A = 2P - B . . . . . . . . useful to remember for P being the midpoint of AB

  A = 2(-1, 4) -(2, 7) = (-2-2, 8-7)

  A = (-4, 1)

Answer:

the probability of exactly 5 out of the next 10 children born to couples where one parent has Huntington's disease having the disease is 0.246, or about 24.6%.

Step-by-step explanation:

The probability of a child being born with Huntington's disease when one parent is a carrier is 50%, since it is an autosomal dominant disease. To calculate the probability of exactly 5 out of the next 10 children born to such couples having the disease, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting k successes (in this case, 5 children with the disease)

n is the total number of trials (in this case, 10 children born)

k is the number of successes we want (in this case, 5 children with the disease)

p is the probability of success (in this case, 0.5, since the disease has a 50% chance of being inherited)

(1-p) is the probability of failure (in this case, also 0.5)

Using this formula, we get:

P(X = 5) = (10 choose 5) * 0.5^5 * 0.5^(10-5)

P(X = 5) = (252) * 0.5^10

P(X = 5) = 0.246

Therefore, the probability of exactly 5 out of the next 10 children born to couples where one parent has Huntington's disease having the disease is 0.246, or about 24.6%.

Three or more line segments that only intersect at their ends form closed, two-dimensional shapes known as polygons.

A polygon is a closed, two-dimensional shape with straight sides that is flat or plane. It has straight sides. Polygons are a different category that belongs to the category of two-dimensional figures because two-dimensional (2D) figures are flat because they lack volume.

Polygons are flat 2D shapes that have straight lines and all lines are closed, meaning that they don't have any disconnected lines. Polygons are a subcategory of 2D figures because they carry all traits of 2D figures but also have special ones of their own. Examples of polygons are squares, rectangles, and triangles. Examples of nonpolygons but still are 2D figures are circles, ovals, and any other flat shape.

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Complete question

How can polygons be considered a subcategory of two-dimensional figures?

Step-by-step explanation:

-2x=34 prove x=-17

34=34

because

-2 time -17 is 34

The density of the metal is  determined as  6.1 g / cm³.

We have,

The density of the metal is defined as the ratio of the mass per unit volume of the metal.

Mathematically, the formula for density is given as;

ρ = m / V

where;

m is the mass of the metal

V is the volume of the metal

The density of the metal is  calculated as follows;

ρ = ( 0.47 kg x 1000 g/kg ) / ( 77 cm³ )

ρ = 6.1 g / cm³

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complete question:

Or this assignment, you submit answers by question parts. The number of submissions remaining for each

ssignment Scoring

our last submission is used for your score.

DETAILS

………….

Compute the density in g/cm³ of a piece of metal that has a mass of 0.470 kg and a volume of 77 cm³.

X g/cm³

Enter a number.

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SHIPPS15 1.6.E.019.

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Answer:

angle v and angle w,  

angle x and angle y

(the first one)

Answer:

Let M represent the amout at any time.

She saves $40 per week so total amount becomes 40x in any specified week.

where x is the number of weeks.

In the start she has $500 in her bank account so we 'll add this amount into the savings per week. So expression becomes

M = 40x+500

Simply put number of week in place of x and find the total amount.

Step-by-step explanation:

Answer:

for c it is no

Step-by-step explanation:

it is no because she deposits 40 a week, in 4 weeks she deposits 40x4=160, which is nowhere close to the 700 she needs. Even if you count the 500 in her account it is still no since it would total up to 660, not 700