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A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?

Answer:

Step-by-step explanation:

Given that :

Mean = 7.8

Standard deviation = 0.5

sample size = 30

Sample mean = 7.3 5.4772

The null and the alternative hypothesis is as follows;

[tex]\mathbf{ H_o: \mu \geq 7.8}[/tex]

[tex]\mathbf{ H_1: \mu < 7.8}[/tex]

The test statistics can be computed as :

[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}[/tex]

[tex]z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}[/tex]

[tex]z = - 5.4772[/tex]

The p-value at  0.05 significance level is:

p-value = 1- P( Z < -5.4772)

p value = 0.00001

Decision Rule:

The decision rule is to reject the null hypothesis if  p value is less than 0.05

Conclusion:

At  the 0.05 significance level,  there is sufficient information to reject the null hypothesis. Therefore ,we  conclude that college students watch fewer movies a month than high school students.

Answer:

The answer is below

Step-by-step explanation:

Given that:

The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

a) For x < 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

From normal distribution table,  P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%

b) For x = 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

For x = 11:

[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]

From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337  

c) For x = 11:

[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]

From normal distribution table,  P(x < 11) = P(z < 1.67) = 0.9525

d) For x = 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

For x = 5:

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]

From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) =  0.2033- 0.0188 = 0.1845  

e) For x = 5:

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]

From normal distribution table,  P(x < 5) = P(z < -0.83) = 0.2033

Answer:

5.50 years

Step-by-step explanation:

A = P[tex](1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

3178 = 2000(1+.086/2)^2t

t = 5.499904413

Answer:

The answer is below

Step-by-step explanation:

Points A(-l, y) and B(5,7) lie on a circle with centre O(2, -3y). This means that AB is the diameter of the circle and OA = OB = radius.

For two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]), the coordinates of the midpoint (x, y) between the two points is given as:

[tex]x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex].

For A(-l, y) and B(5,7) with center O(2, -3y), the value of y can be gotten by:

[tex]For\ x\ coordinate:\\2=\frac{-1+5}{2}\\ 2=2.\\For\ y\ coordinate:\\-3y=\frac{y+7}{2}\\ -6y=y+7.\\-6y-y=7\\-7y=y\\y=-1[/tex]

The value of y is -1. Therefore A is at (-1, -1) and O is at (2, -3(-1))= (2, 3)

The radius of the circle = OA. The distance between two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]) is given as:

[tex]|OX|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Therefore\ the\ radius \ |OA|\ is :\\|OA|=\sqrt{(2-(-1))^2+(3-(-1))^2}=\sqrt{25}=5[/tex]

The radius of the circle is 5 units

Answer:38

Step-by-step explanation:multiple

Answer:

Step-by-step explanation:

Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,

Tan BEC = 6/3 = 2

Angle BEC = Tan^-1(2)

Angle BEC = 63.4°

The sum of the angles on a straight line is 180°. This means that

Angle AED + angle DEC + angle BEC = 180

Angle AED = 180 - (45 + 63.4) = 71.6°

Angle ADE = angle AED = 71.6°

Angle CDE + angle ADE = 180(sum of angles on a straight line)

Angle CDE = 180 - 71.6 = 108.4°

To get line EC, we would apply Pythagoras theorem. Therefore

EC² = 3² + 6² = 45

EC = √45 = 6.71 cm

The sum of the angles in a triangle is 180°

Therefore,

Angle ECD = 180 - (45 + 108.4) = 26.6°

By applying sine rule,

6.71/sin108.4 = ED/sin26.6 = DC/Sin45

6.71/sin108.4 = ED/sin26.6

Cross multiplying, it becomes

6.71sin26.6 = EDsin108.4

ED = 6.71sin26.6/sin108.4

ED = 3.00608/0.949 = 3.18cm

The area of a triangle is

Area = 1/2abSinC

Therefore, area of triangle EDC = 1/2 ×

ED × EC × SinDEC

Area = 1/2 × 6.71 × 3.18 × sin45

Area = 1/2 × 6.71 × 3.18 × 0.707

Area = 7.54 cm²

Answer:

-21

Step-by-step explanation:

We are told to find f(x) + g(x) for x= -3. Therefore, we must evaluate f(-3) and g(-3), then add them together.

First, evaluate f(-3).

f(x)=4x-7

To find f(-3), we need to substitute -3 in for x.

f(-3)= 4(-3)-7

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction First, multiply 4 and -3.

f(-3)= -12-7

Next, subtract 7 from -12

f(-3)= -19

Next, find g(-3).

g(x)=2x+4

To find g(-3), substitute -3 in for x.

g(-3)= 2(-3)+4

Solve according to PEMDAS. First, multiply 2 and -3.

g(-3)= -6+4

Next, add -6 and 4

g(-3)= -2

Now, we can add f(-3) and g(-3) together.

f(-3) + g(-3)

f(-3)= -19

g(-3)= -2

-19 + -2

Add

-21

Answer:

-21

Step-by-step explanation:

Adding f and g together, we get  (f + g)(x) = 4x + 2x -7 + 4, or

                                                                      = 6x - 3

Now replace x with -3.  We get:

(f + g)(-3) = 6(-3) - 3 = -21

Answer:

$3.25

Step-by-step explanation:

To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = 3.25

The cost of each cup of coffee is $3.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = $3.25

Hence, the cost will be $3.25.

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Answer:

[tex]3x^2 - 21[/tex] (did you mean for the equation to be [tex](5 - x^2 + 2) \cdot -3[/tex]?)

Step-by-step explanation:

Multiplying -3 by each term:

[tex]-3 \cdot 5 = -15[/tex]

[tex]-x^2 \cdot -3 = 3x^2[/tex]

[tex]-3 \cdot 2 = -6[/tex]

[tex]-15-6 = -21[/tex]

So the equation comes out to [tex]3x^2 - 21[/tex] .

Hope this helped!

Answer:

Step-by-step explanation:

AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:

[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]

Answer:

False roots are x = -1 or x = 5/2 or x = 3/2

Step-by-step explanation:

Solve for x:

4 x^3 - 12 x^2 - x + 15 = 0

The left hand side factors into a product with three terms:

(x + 1) (2 x - 5) (2 x - 3) = 0

Split into three equations:

x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0

Subtract 1 from both sides:

x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0

Add 5 to both sides:

x = -1 or 2 x = 5 or 2 x - 3 = 0

Divide both sides by 2:

x = -1 or x = 5/2 or 2 x - 3 = 0

Add 3 to both sides:

x = -1 or x = 5/2 or 2 x = 3

Divide both sides by 2:

Answer:  x = -1 or x = 5/2 or x = 3/2

Answer:

False

Step-by-step explanation:

f(x) = 4x³ - 12x² - x + 15

Set output to 0.

Factor the function.

0 = (x + 1)(2x - 3)(2x - 5)

Set factors equal to 0.

x + 1 = 0

x = -1

2x - 3 = 0

2x = 3

x = 3/2

2x - 5 = 0

2x = 5

x = 5/2

4 is not a lower bound for the zeros of the function.

Answer:

7 is the least.

Step-by-step explanation:

Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.

Answer:

Step-by-step explanation:

[tex] {x}^{2} - 13x + 30[/tex]

Write -13x as a difference

[tex] {x}^{2} - 3x - 10x + 30[/tex]

Factor out x from the expression

[tex]x(x - 3) - 10x + 30[/tex]

Factor out -10 from the expression

[tex]x(x - 3) - 10(x - 3)[/tex]

Factor out x-3 from the expression

[tex](x - 3)(x - 10)[/tex]

Hope I helped!

Best regards!!

Answer:

0.9

I guess.

If yes

.. Follow me..

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 4 and (a, b) = (- 3, - 4) , thus

y - (- 4) = 4(x - (- 3)) , that is

y + 4 = 4(x + 3) → C

Explanation:

The median is the center of the distribution. We see that the center of the shark's distribution is to the left compared to the koi's center. Therefore, the shark's median age is smaller. Choice A is one of the answers.

The spread is exactly what it sounds like: how spread out the data is. Mathematically we use the standard deviation, or sometimes the range, to find out how spread out things are. The koi distribution is more spread out. The shark's data is more clumped together. This is why choice B is the other answer.

Center: Sharks have lower median age than Koi.

Spreads: The ages of koi are more spread out.

A dot plot is a standardized way of displaying the distribution of data based on a five number summary.

The center line in the dot plot shows the median for the data .

Spread of data is measured in terms how far the data differs from the mean.

According to the given question

We have a dot plots for the two fishes sharks and Koi.

According to the given dot plot

Most ages of the sharks is lower than the koi.

⇒ Sharks are  lower than koi.

So, the center: Sharks have lower median age than Koi.

Also, the ages of Koi are wide spreading.

⇒ The ages of koi are more spread out

Therefore, Spreads: The ages of koi are more spread out.

Hence, option A and B are correct.

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Answer:

Null hypothesis; H0: μ = 3000

Alternative Hypothesis; Ha: μ ≠ 3000

Step-by-step explanation:

We are told that the FDA recommends that Americans get on average 3,000mg of salt in their daily diet.

Now we want to test this claim of whether Americans truly get an average of 3,000mg of salt in their daily diet.

Thus, the hypotheses is as follows;

Null hypothesis; H0: μ = 3000

Alternative Hypothesis; Ha: μ ≠ 3000

Null hypothesis; H0: μ = 3000

Alternative Hypothesis; Ha: μ ≠ 3000

Since

The FDA recommends that Americans get on average 3,000mg of salt in their daily diet.

So, here the hypothesis be like

Null hypothesis; H0: μ = 3000

Alternative Hypothesis; Ha: μ ≠ 3000

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Answer:

2nd option: the lowest point on the graph is (-2, -2). this is where both sides of the parabola converge. from this point, both lines go up. this means the vertex is a minimum.

Answer:

? = 35

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp /adj

tan ? = 33/48

Take the inverse tan of each side

tan ^ -1 ( tan ? ) = tan ^ -1 ( 33/48)

? =34.50852299

? = 35

Answer:

[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]

Step-by-step explanation:

We are asked to multiply the given polynomials.

[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]

Multiply each term of the first polynomial to each term of the second polynomial.

[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]

[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]

[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]

Add the results

[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]

Combine the like terms

[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]

The answer is written in descending powers of x.

Answer:

There is no price difference between the two stores.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine if there is a price difference between the two stores.

The hypothesis for the test can be defined as follows:

H₀: There is no price difference between the two stores, i.e. d = 0.

Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.

From the information provided the sample mean and standard deviation are:

 [tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]

The test statistic value is -1.44.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

The degrees of freedom is:

n - 1 = 10 - 1 = 9

Compute the p-value of the test as follows:

[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]

               [tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]  

*Use a t-table.

The p-value of the test is 0.184.

p-value= 0.184 > α = 0.10

The null hypothesis was failed to be rejected.

Thus, it can be concluded that there is no price difference between the two stores.

Answer:

(-1,0), (0,3) and (2,2.25)

Step-by-step explanation:

The qualitative graph is as follows:

A(-1,0) ------> B(0,3) ------> C(2,2.25)

Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3

∴ slope = 0.75

Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.

The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.

Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.

Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.

Thus, except for graph A all the graphs are qualitative graphs.

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Answer:

Step-by-step explanation:

In triangle DEF, we have:

Given:

<EDF=56°

<EFD=84°

So, <DEF =180° - 56° - 84° =40° (sum of triangle angles is 180°)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

. (DE) // (CB) "//"means parallel

. DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

Proof: (DE) // (FB) [(DE) // (CB)]

AND DE = FB

Then, <EBF = <EDF = 56°

___________

DEFC is parm.

Proof: (DE) // (CF) [(DE) // (CB)]

And DE = CF

Therefore, <DCF = <DEF =40°

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180° - 40° - 56° =84° (sum of triangle angles is 180°)

[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK![/tex]

Answer:Keith

x=5,x=12

Step-by-step explanation:

Answer:

the answers are keith and -5,-12

Step-by-step explanation:

I just took the test and got a 5/5 the other person is incorrect.

Answer:

The answer is B.

Step-by-step explanation:

You solve it using the number line. Starting with the point at 3/5 then, you have to go backwards by 7 steps which is -4/5.

You can ignore the denorminator as all the denorminators are the same.

Answer:

-4/5

Step-by-step explanation:

The parentheses can be removed immediately since they do not affect the outcome in this problem.  

then we have:

3/5 - 7/5 = -4/5

Answer:

Step-by-step explanation:

[tex] {x}^{2} + 3x - 54[/tex]

Write 3x as a difference

[tex] {x}^{2} + 9x - 6x - 54[/tex]

Factor out x from the expression

[tex]x(x + 9) - 6x - 54[/tex]

Factor out -6 from the expression

[tex]x(x + 9) - 6(x + 9)[/tex]

Factor out x+9 from the expression

[tex](x + 9)(x - 6)[/tex]

Hope I helped!

Best regards!

Answer:  (x + 9)(x - 6)

Step-by-step explanation:

x² + 3x - 54      Find 2 numbers whose product is -54 and sum is +3

               ∧

            -1 + 54

            -2 + 27

            -3 + 18

            -6 + 9 = +3   This works!

Place those digits in the parentheses and it is now factored.

(x - 6)(x + 9)

Answer:

x

Step-by-step explanation:

Answer:

113.625 miles

Step-by-step explanation:

3 hours at a rate of 30 mile/hr : 3*30=90 miles

2 1/4 hours at a rate of 10 1/2 miles/hr= 2 1/4 *10 1/2= 2.25*10.5=23.625

total miles the object traveled : 90+23.625=113.625 miles

Answer:

your welcome and hope this helps

Answer:

m= -29

Step-by-step explanation:

This is a bit of a complex equation, but let's work through it.

2/3 (m-1/2) +3= m/3-7

First, we need to distribute the 2/3.

(2/3)(m)+(2/3)(−1/2)+3=m/3+−7

Now we simplify that.

2/3m+−1/3+3=1/3m+−7

We can now combine like terms.

2/3m+8/3=1/3m+−7

The goal is to isolate the variable, so we should subtract 1/3m from both sides.

1/3m+8/3=−7

Lets keep going! We can subtract 8/3 from both sides.

1/3m=-29/3

Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!

m=-29

We did it! m=-29