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3 years ago

5

Suppose the distribution of the daily calcium intake of Americans is left skewed with a mean of 800 mg and a standard deviation

of 16 mg. What can we say about the sampling distribution of distribution X?

1 answer:

serious [3.7K]3 years ago

7 0

Answer:

Central limit theorem

Step-by-step explanation:

By central limit theorem. The sampling distribution will have the same mean as the original distribution.

The sampling distribution will have a standard deviation of $s/sqrt(n)$ , so it cannot be a fixed 16. Also,the normal approximation improves with increasing sample size.

Therefore, the correct answer about the sampling distribution of distribution X

is central limit theorem.

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A piggy bank is full of dimes and quarters. The total

Talja [164]

She has 27 quarters and 73 dimes.

Write a system of equations.

Let x be the number of quarters, and y be the number of dimes.

x+y=100

0.25x+0.10y=14.05

Solve by substitution:y=100−x

∴0.25x + 0.10(100 - x) = 14.05

0.25x+10−0.10x=14.05

0.15x+10=14.05

0.15x=4.05

x=27

Solve for y now:

y+27=100

y=100−27

y=73

Hence, She has 27 quarters and 73 dimes.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that cause the equality to hold true is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.

To learn more about account form the given link:

brainly.com/question/10413253

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3 0

1 year ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

What’s the probability of drawing one blue marble from a bag which contains 4 red marbles , 6 green marbles , 1 white marble and

Gemiola [76]

Answer:3/14

Step-by-step explanation:

The probability that it is a blue marble is 3 out of total marbles of 14

8 0

3 years ago

What is the least common denominator of 4/5 and 1/10

antiseptic1488 [7]

The least common denominator for the question you have supplied me with is 10. The least common multiple of the denominators, 5 and 10, is 10, making the LCD 10.

4 0

3 years ago

Read 2 more answers

I need to know the improper fractions answers for:

zmey [24]

Answer:

Part 1) $x=\frac{15}{2}\ units$

Part 2) $z=\frac{15\sqrt{3}}{2}\ units$

Part 3) $y= \frac{15\sqrt{3}}{4}\ units$

Part 4) $b= \frac{45}{4}\ units$

Step-by-step explanation:

step 1

Find the value of x

In the large right triangle

$cos(60^o)=\frac{x}{15}$ ----> by CAH (adjacent side divided by the hypotenuse)

Remember that

$cos(60^o)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{x}{15}$

solve for x

$x=\frac{15}{2}\ units$ ---> improper fraction

step 2

Find the value of z

In the large right triangle

Applying the Pythagorean Theorem

$15^2=x^2+z^2$

substitute the value of x

$15^2=(\frac{15}{2})^2+z^2$

solve for z

$z^2=15^2-(\frac{15}{2})^2$

$z^2=225-\frac{225}{4}$

$z^2=\frac{675}{4}$

$z=\frac{\sqrt{675}}{2}\ units$

simplify

$z=\frac{15\sqrt{3}}{2}\ units$

step 3

Find the value of y

In the right triangle of the right

$sin(30^o)=\frac{y}{z}$ ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$sin(30^o)=\frac{1}{2}$

so

$\frac{1}{2}=y:\frac{15\sqrt{3}}{2}$

solve for y

$\frac{1}{2}= \frac{2y}{15\sqrt{3}}$

$y= \frac{15\sqrt{3}}{4}\ units$

step 4

Find the value of b

In the right triangle of the right

$cos(30^o)=\frac{b}{z}$ ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$cos(30^o)=\frac{\sqrt{3}}{2}$

so

$\frac{\sqrt{3}}{2}=b:\frac{15\sqrt{3}}{2}$

solve for y

$\frac{\sqrt{3}}{2}= \frac{2b}{15\sqrt{3}}$

$b= \frac{45}{4}\ units$

7 0

3 years ago