Dorothy runs for 3.35 kilometres every day .
After 7 days how many meters has Dorothy ran

Answer:

x = 17

Step-by-step explanation:

First, let's turn this into an equation:

twenty more ( +20 ) than four times a number ( 4x ) is equal ( = ) to the difference ( - ) between 139 and 3 times the number ( 3x ).

4x + 20 = 139 - 3x

Now let's solve:

Subtract 20 from each side:

4x = 119 - 3x

Add 3x to each side:

7x = 119

Divide each side by 7:

x = 17

Answer:

Angle T = 43°

Step-by-step explanation:

118+118+81 = 317

360-317 = 43

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that \(\sigma = 9.5\)

Sample of 60:

This means that \(n = 60\)

What is the standard deviation of the distribution of sample means for samples of size 60?

\(s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264\)

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

SOLUTION

Present the information in diagram

Then the venn diagram becomes

Then take the sum of the and equate to the total in the top of the table.

Hence

Subtract 1010 from both sides, we have

Therefore

The number of that owned neither a cat nor a dog is 50

Answer:

The expected flight time is 2 hours 10 minutes

Step-by-step explanation:

Given

\(a = 2\ hours\)

\(b = 2\ hours\ 20\ mins\)

Required

The expected flight time

To do this, we simply calculate the mean using:

\(Mean = \frac{a + b}{2}\)

So, we have:

\(Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}\)

\(Mean = \frac{4\ hours\ 20\ mins}{2}\)

\(Mean = 2\ hours\ 10\ mins\)

a. The function (f o g)(x) = 3/(3 + x)

b. In interval notation, the domain of the function (f o g)(x) is (-3, ∞).

A function is a mathematical equation that shows the relationship between two variables.

a. Given the functions f(x) = x/x + 2 and g(x) = 6/x, we desire to find (f o g)(x). We proceed as follows

We know that (f o g)(x) is a composite function and  (f o g)(x) = f(g(x))

Since  f(x) = x/x + 2 and g(x) = 6/x,

So f(g(x)) = x/(x + 2)

= g(x)/[g(x) + 2]

= 6/x ÷ (6/x + 2)

= 6/x ÷ (6 + 2x)/x

= 6/x × x/(6 + 2x)

= 6/(6 + 2x)

= 6/2(3 + x)

= 3/(3 + x)

So,  f(g(x)) = 3/(3 + x)

b. To find the domain of (f o g)(x) in interval notation, we proceed as follows

Since (f o g)(x) = f(g(x)) = 3/(3 + x)

Now, f(g(x)) is valid when (3 + x) > 0

So, 3 + x > 0

x > - 3

So, in interval notation, the domain of  (f o g)(x) is (-3, ∞). We use the open bracket on the left side of the - 3 since -3 is not included.

So, in interval notation, the domain of  (f o g)(x) is (-3, ∞).

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Answer:

Option 4:  A ║B

Step-by-step explanation:

Given the following statements:

\(\displaystyle\mathsf{\overline{X}}\) is ⊥ \(\displaystyle\mathsf{\overline{A}}\)

\(\displaystyle\mathsf{\overline{X}}\) is ⊥ \(\displaystyle\mathsf{\overline{B}}\)

We can apply the Lines Perpendicular to a Transversal Theorem, which states that if two lines intersect and are perpendicular to that same transversal, then those two lines are parallel.  

In the given conditional statement, \(\displaystyle\mathsf{\overline{X}}\) ⊥ \(\displaystyle\mathsf{\overline{A}}\)  and  \(\displaystyle\mathsf{\overline{X}}\) ⊥ \(\displaystyle\mathsf{\overline{B}}\), line \(\displaystyle\mathsf{\overline{X}}\) is the transversal that cuts through both lines  \(\displaystyle\mathsf{\overline{A}}\) and \(\displaystyle\mathsf{\overline{B}}\).  

Therefore, lines  \(\displaystyle\mathsf{\overline{A}}\) and \(\displaystyle\mathsf{\overline{B}}\) are perpendicular to line \(\displaystyle\mathsf{\overline{X}}\).  Hence, by the Lines Perpendicular to a Transversal Theorem,  \(\displaystyle\mathsf{\overline{A}}\) ║ \(\displaystyle\mathsf{\overline{B}}\).  

Answer:

The score separating the bottom 47% from the top 53% is 112.8

Step-by-step explanation:

Let X denote the random variable whose values are normal with a mean of 114.5 and a standard deviation of 23.

Compute the 47th percentile as follows:

\(P(X<x)=0.47\\\\P(\frac{X-\mu}{\sigma}<\frac{x-114.5}{23})=0.47\\\\P(Z<z)=0.47\)

The corresponding z-value is,

z = -0.075

*Use the z-table.

Compute the value of x as follows:

\(\frac{x-114.5}{23}=-0.075\\\\x=114.5-(0.075\times 23)\\\\x=112.775\\\\x\approx 112.8\)

Thus, the score separating the bottom 47% from the top 53% is 112.8

Given: Two equation:

Required: Solve the system of equation graphically.

Explanation:

The graph of two lines can be drawn as follows:

The blue line is

And green line is

From the graph, the solution is point of intersection of both lines. So, the solution is (5,0.5). that is (5,1/2).

Final Answer: Option 3 is correct answer.

Answer:

I. x = -1

II. y = 1

Step-by-step explanation:

Given the following algebraic expressions;

9x + 10y = 1 .......equation 1

9x - 6y = -15 ......equation 2

To solve using the elimination method, we would subtract eqn 1 from eqn 2.

(9x - 9x) + (-6y - 10y) = (-15 - 1)

0x - 16y = -16

-16y = -16

16y = 16

y = 16/16

y = 1

Next, we would find the value of x;

From eqn 1;

9x + 10y = 1

Substituting the value of y, we have;

9x + 10(1) = 1

9x + 10 = 1

9x = 1 - 10

9x = -9

x = -9/9

x = -1

Answer:

−

k

2

2

+

3

k

3

4

Step-by-step explanation:

Try solving this like you would solve an equation, but just with an inequality sign.

What we want to do is isolate the variable \(x\) through algebraic manipulation.

So if we have:

\(2x+8 < 3x-4\)

\(x > 12\)

After we subtract the \(2x\) from the left side and add \(4\) from the right side.

Hope this helps!

Answer:

135 small cubes fill the prism

Step-by-step explanation:

Find the volume of the prism.

V = l * w * h

l = 2 1/4 = 2.25

w = 3/4 = 0.75

h = 1 1/4 = 1.25

V = 2.25 * 0.75 * 1.25

V = 2.109375

I wouldn't round this quite yet.

V of 1 small cube = 1/4 * 1/4 * 1/4 = .015625

So divide the volume of the prism by the volume of the small cube

2.109375/0.015625 = 135

Let x = small drinks

Let y = large drinks

3 small drinks and 2 large drinks contain 108 ounces of cola, this is:

3x + 2y = 108

A small drink contains a third as much cola as a large drink, this is:

x = 1/3y

Then, we solve the system of equations:

First, substitute x in equation 1:

And solve for y:

Next, substitute y = 36 in x:

Answer:

Small drinks: 12 ounces of cola

Large drinks: 36 ounces of cola

Answer:

4 hr and 30 minutes?

Step-by-step explanation:

You didnt really specify soo.    11    12    1   2   2:30

                                                 1hr   2hr  3hr 4hr  30 min

Answer:7:30

Step-by-step explanation:

Step 1. Speed of the wolf.

The wolf can run 110m in 6.3s, to calculate the unit steep, we need to make the division between the meters and the seconds:

The result of this division is:

Rounding to the nearest whole unit:

Step 2. Steep of the tiger.

The tiger can run 85m in 4.2s, again we divide the meters and the seconds to find the unit speed:

Rounding to the nearest whole unit:

Step 3. Which one is faster?

Since the unit speed of the tiger is larger, 21m/s vs. 17m/s, the tiger is faster.

Answer:

Wolf speed? 17m/s

Tiger speed? 21m/s

Which one is faster? Tiger

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

Answer:

87-13 = 74

Step-by-step explanation:

Answer: -7, -0.75, -5, 0.5, 0.75, 9, 13

Step-by-step explanation:

Because negative numbers are always less

Answer:

in 2 there are 10 fifths 10 fifths + 1 fifth = 11 fifths.

Answer:

A- 11

Step-by-step explanation:

Number = 2 1/5 = 11 / 5

Fifths = 1/5

Answer = 11/5 ÷ 1/5 = 11/5 x 5/1 =11

I hope im right!!

Answer:

C

Step-by-step explanation:

30/2 = 15cm = r

(Pi)r^2 = area of circle

(Pi)(15)^2 =706.5cm

Area of circle x height = volume

706.5 x 325 = 229613cm^3

The probability of A would be lesser than or equal to that of B because A is a subset of B

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

The Venn diagram

On the Venn diagram, we have

A is inside B

This means that A is a subset of B

And as such the probability of A would be lesser than or equal to that of B

Here, we have

A = 1

B = 4

Outside = 9

So, we have

P(A) = 1/(1 + 4 + 9) = 1/14

P(B) = (1 + 4)/(1 + 4 + 9) = 5/14

Hence, the values of P(A) and P(B) are 1/4 and 5/14

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Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Answer: C.0

x + 45 is the angle outside the circle of shield 2 arcs with measurements 55 and 145

=> x + 45 = 1/2.(145 - 55)

⇔ x + 45 = 1/2. 90

⇔ x + 45 = 45

⇔ x = 0

Step-by-step explanation:

The exact binomial probability that 45 or more people in the survey get enough exercise is 0.0853.

The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

a. To calculate the probability that 45 or more people in the survey get enough exercise using a normal approximation for p hat, we need to first find the mean and standard deviation of the sample proportion.

The mean of the sample proportion is:

μ = p = 0.20

The sample proportion's standard deviation is:

σ = √[(p(1-p))/n] = √[(0.20)(0.80)/200] = 0.034

Using the normal distribution with a continuity correction, we can find the probability of 45 or more people getting enough exercise:

z = (45 - 0.20200 + 0.5) / √(0.200.80*200) = 1.24

P(Z > 1.24) = 0.1082

Therefore, the probability that 45 or more people in the survey get enough exercise is approximately 0.1082.

b. To find the exact binomial probability that 45 or more people in the survey get enough exercise, we can use the binomial cumulative distribution function (CDF) with n = 200 and p = 0.20:

P(X ≥ 45) = 1 - P(X < 45) = 1 - binomcdf(200, 0.20, 44) = 0.0853

Therefore, the exact binomial probability that 45 or more people in the survey get enough exercise is 0.0853.

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Using percentages we know that 62% or 62 students out of 100 students prefer biology.

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage.

When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100.

Thus, the proportion refers to a component per 100.

The word percent denotes a percentage of 100. It is represented by the symbol "%."

So, according to the given situation:

34 females enjoy biology

Do boys enjoy biology?

It is 34%≤

Then,

27% favor chemistry

10% favor physics.

The calculation would be:

27 + 11 = 38

100 - 38 = 62

Therefore, using percentages we know that 62% or 62 students out of 100 students prefer biology.

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Correct question:

100 students are interviewed to see which of biology, chemistry or physics they prefer.72 of the students are girls. 34 of the girls like biology best. 11 of the boys prefer physics. 24 out of the 27 who prefer chemistry are girls. What percentage of the students prefer biology?