suppose that the heights, in inches, of orangutans are normally distributed with an unknown mean and standard deviation. the orangutan heights of 27 randomly sampled orangutans are used to estimate the mean of the population. what t-score should be used to find the 99% confidence interval for the population mean?

The actual value is 8.42 x 7.24 = 59.6576.

as an estimate she has rounded the values up to the nearest whole number ;

i.e. 8.42 ≅ 9 and 7.24 ≅ 8

to obtain 9 x 8 to get 72.

What is rounded value?

Making a number simpler while maintaining a value that is close to what it was is known as rounding.

Although less accurate, the outcome is simpler to utilize.

For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is. However, 76 rises to 80.

What is whole number?

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

What is natural number?

Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.

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Answer:

  (a) in 2001: 150.4 thousand

  (b) in 2018: 467.5 thousand

Step-by-step explanation:

You want the value of the expression modeling the number of students abroad for different values of x. That expression is 123.1(1.069^x).

The value of x is the difference between the year (2001) and the reference year (1998). In the attachment, we let the calculator find that difference. It tells us, for x = 2001 -1998 = 3, the number of students is about ...

  y = 123.1(1.069^3) ≈ 150.4 . . . . thousand

In 2018, the value of x is 2008 -1998 = 10, and the number of students studying abroad is ...

  y = 123.1(1.069^10) ≈ 467.4 . . . . thousand

The consumption of minutes should be less than or equal to 500 for each month.

A linear equation is a first-order (linear) term and a constant in an algebraic equation of the form y=mx+b.

The telephone bill of Chris can be written in the form of linear equation.

C(x)=$26.00+$0.12x

Here x is the number of minutes, for every one minute there is a charge of $0.12.

Chris can afford monthly bill of $86 or less not more. The linear inequality can be written as,

$26.00+$0.12x<=$86

$0.12x<=$86-$26.00

$0.12x<=$60

x<=$60/$0.12

x<=500.

The number of minutes that Chris should use should be less than or equal tp 500.

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The probability that five cars will arrive during the next thirty minute interval is 0.0361

What is probability?

Probability is a way of calculating how likely something is to happen. Numerous things are difficult to forecast with absolute confidence.

Main Body:

Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.

The average number of cars arriving in 15 minutes is 6.

The average number of cars arriving in 1 minute is = 6/15 = 2/5

The average number of cars arriving in 5 minutes is, (2/5)*5 = 2

The random variable X follows a Poisson distribution with parameter λ = 2.

The probability mass function of X is:

P(X=[tex]x[/tex]) = [tex](e^{-2} 2^{x} )/x![/tex]  , x = 0,1 ,2 ,3...

Compute the probability that 5 cars will arrive in 5 minutes as follows:

P(X=5) =[tex](e^{-2} 2^{5} )/5![/tex]

P (X= 5) = 0.0361

Hence probability is 0.0361

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Answer:

B.  6 units

Step-by-step explanation:

Given equations:

[tex]y = -2x^2 + 8x[/tex]

[tex]x-2.23y + 10.34 = 0[/tex]

The points at which the rod is attached to the archway are the points of intersection of the two equations.

Rearrange the second equation to make x the subject:

[tex]\implies x=2.23y-10.34[/tex]

Substitute this into the first equation to create a quadratic:

[tex]y = -2(2.23y-10.34)^2 + 8(2.23y-10.34)[/tex]

[tex]y = -2(4.9729y^2-46.1164y+106.9156) + 17.84y-82.72[/tex]

[tex]y=-9.9458y^2+92.2328y-213.8312+17.84y-82.72[/tex]

[tex]y=-9.9458y^2+110.0728y-296.5512[/tex]

[tex]-9.9458y^2+109.0728y-296.5512=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Solve the quadratic using the quadratic formula:

[tex]\implies y=\dfrac{-(109.0728) \pm \sqrt{(109.0728)^2-4(-9.9458)(-296.5512)}}{2(-9.9458)}[/tex]

[tex]\implies y=\dfrac{-109.0728 \pm \sqrt{99.12}}{-19.8916}[/tex]

[tex]\implies y=\dfrac{109.0728 \pm \sqrt{99.12}}{19.8916}[/tex]

[tex]\implies y=5.983867702, \quad y=4.982851918[/tex]

As point B is at a higher level than point A, the y-value of point B is approximately 6 units.  

Therefore, point B is 6 units from ground level.

Answer:

i think its C. The median points per game is not affected

Step-by-step explanation:

The required group of software packages that can be selected is 28.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Examples of permutation and combination, Organizing people, numbers, numerals, alphabets, notes, and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.

Here,

Choice of six free software packages. there are 8 different software packages from which to select.

n = 8,  r = 6

Groups of software packages can be selected= 8C6

8C6 = n!/r!(n - r)!

8C6 = 8! / 4! 2!

8C6 = 8 * 7 / 2 / 1

8C6 = 28

Thus, the required group of software packages that can be selected is 28.

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If the measurement of ∠3 & ∠6 is given,i.e.∠3 = 4x + 7 and ∠6 = 2x + 53 then ∠1 = 120 - 6x.

Given, ∠3 = (4x + 7) and ∠6 = (2x + 53)

Let ∠1 = a,

Now, as we know the angle sum property in triangles,

the sum of all the angles in a triangle is 180°.

So, ∠1 + ∠3 + ∠6  = 180°

a + (4x + 7) + (2x + 53) = 180°

a + 6x + 60 = 180

a = 180 - 60 - 6x

a = 120 - 6x

Hence, ∠1 = 120 - 6x, if the ∠3 = 4x + 7 and ∠6 = 2x + 53

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The intervals where the graph is decreasing are given as follows:

The behavior of the function regarding increase or decrease depends on the orientation of the graph, as follows:

Hence the intervals describing the behavior of the function are given as follows:

The decreasing interval can be divided into two intervals, as follows:

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The system of inequalities and a possible solution is by working 2 hours removing wires and 6 hours tutoring.

What is Inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

Here are the variables defined:

x is the quantity of tutoring hours worked.

Y = quantity of h

clearing cables is our job.

Since we know she can only work a maximum of 9 hours per week:

x + y ≤ 9

She also wants to earn at least $130 each week, so:

x*$22 + y*$10 ≥ $130

As a result, we have the inequality system listed below:

x + y ≤ 9

x*$22 + y*$10 ≥ $130

The graph of this system can be shown in the graphic below, where the intersection of the two shaded regions shows where the system's solutions are.

There are some solutions there, including:

y = 0, x = 8

y = 2, x = 6.

As a result, her situation might be resolved by working 2 hours removing wires and 6 hours tutoring.

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Answer:

C

Step-by-step explanation:

Answer:

8,333.312

Step-by-step explanation:

I did the test...

Option2 and 4 are the exponential decay from the equation.

Given that,

We have to find which one is exponential decay function.

Exponential decay function is in the form of y=abˣ where a is the initial value and b≠0,  0<b<1. power is x.

Now, Take the 1st option

y=0.25(2)ˣ

Here a is 0.25 and 2 is b

b>1

So, Option 1 is not an exponential decay.

Now, Take the 2nd option

y=2(0.20)ˣ

Here a is 2 and 0.20 is b

b<1

So, Option 2 is an exponential decay.

Now, Take the 3rd option

y=4.2(1.25)ˣ

Here a is 4.2 and 1.25 is b

b>1

So, Option 3 is not an exponential decay.

Now, Take the 4th option

y=0.55(0.91)ˣ

Here a is 0.55 and 0.91 is b

b<1

So, Option 4 is an exponential decay.

Therefore, Option2 and 4 are the exponential decay from the equation.

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Answer:

(3x + 36) is equal to (6x + 9) because they are vertically opposite angles.

3x + 36 = 6x + 9

3x = 27

x = 9

Substitute x = 9 into one of the angles to find the measure.

3(9) + 36 = 63

Angle measure is 63°.

The measure of the angles is 63 degrees.

Both (3x + 36) and (6x + 9) are equal to 63 degrees.

Given that are two vertically opposite angles (3x+36) and (6x+9) we need to find the measure of the angles,

Vertically opposite angles are formed when two lines intersect, and they are equal in measure.

In this case, we have two vertically opposite angles: (3x + 36) and (6x + 9).

Since the angles are equal, we can set them equal to each other and solve for x:

3x + 36 = 6x + 9

To isolate the x term, let's subtract 3x from both sides:

36 = 6x - 3x + 9

Combining like terms:

36 = 3x + 9

Next, let's subtract 9 from both sides:

36 - 9 = 3x

27 = 3x

To solve for x, we divide both sides by 3:

27/3 = 3x/3

9 = x

Now that we know the value of x, we can substitute it back into either of the original equations to find the measure of the angles.

Let's use the first angle (3x + 36):

Angle = 3x + 36

= 3(9) + 36

= 27 + 36

= 63

Hence, the measure of the angles is 63 degrees.

Both (3x + 36) and (6x + 9) are equal to 63 degrees.

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Haley’s Percentage Decrease from Test 1 to Test 2 to the nearest tenth is 7.5%

Nearest tenth can be defined as , Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5

Given that,

Haley’s Percent score in Test 1 = 93 %

Haley’s Percent score in Test 2 = 86%

Formula For calculating the Percentage Decrease is :

(Beginning Percentage – Final Percentage) / Beginning Percentage * 100

So, by using this formula we can calculate the percentage decrease of Haley’s Test

Percentage Decrease = (93% - 86%)/93% * 100

                 = 7.5%

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The probability that a standard normal random variable will be between. 3 and 3. 2 is 0.99932.

What is standard normal random?

We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Z∼N(0,1)

P(Z<3)=.99865

P(Z>3.2)=.99931

P(3<Z<3.2)=2(0.99931-0.99865)−1=0.99932

Hence the standard normal random variable will be 0.99932.

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Answer:

yes

Step-by-step explanation:

Given that [tex]\cos x\sin x\tan x+\cos^2x=1[/tex]

Substitute [tex]\tan x=\frac{\sin x}{\cos x}[/tex], we obtain:

[tex]\cos x\sin x\frac{\sin x}{\cos x}+\cos^2 x=1[/tex]

Simplifying this, we get:

[tex]\sin x\sin x+\cos^2x=1[/tex]

This is equivalent to:

[tex]\sin^2x+\cos^2x=1[/tex]

The cake slice with 15m due west and 15m due north is closer

Here , the slice of cake is 20m due east and then 10 m due south.

consider it as triangle ABC.

Required Displacement can be calculated by Pythagoras theorem -

AC = √ ( AB )² + ( BC )²

By substitution,

⇒ AC = √ ( 20 )² + ( 10 )²

⇒ AC = √ ( 400 + 100 )

Simplifying this equation, we get

⇒ AC = √500

⇒ AC = 10 √5

⇒ AC = 22.56

Thus , The cake slice is 22.56 m far away.

Here another slice of cake is 15m due west and 15m due north.

consider it as a triangle DEF.

Therefore,

⇒ DF = √ ( DE )² + ( EF )²

By substitution,

⇒ DF =  √ ( 15 )² + ( 15 )²

Simplifying this equation, we get

⇒ DF = √ ( 225 + 225 )

⇒ DF = √ 450

⇒ DF = 15 √2

⇒ DF = 21.21

Thus the cake slice is 21.21 m far away.

Therefore this slice is closer.

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Answer:

y + 9 = -2 (x - 9)

Step-by-step explanation:

M (slope) = -2

X=9 and Y=-9

Point-slope form

y - y1 = m(x - x1)

y - - 9 = -2( x - 9)

y + 9 = -2(x -9)

If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

Number of cups of blue paint for each art station = 2 cups

Given that,

One cup = 8 ounce

1 gallon = 128 ounce

2 cups of blue paint = 2 × 8

= 16 ounce of blue paint

1 gallon of blue paint = 128 ounce of blue paint

Number of jars that he can fill with 1 gallon of blue paint =  1 gallon of blue paint / 2 cups of blue paint

Here we have to use division

= 128/16

= 8 jars

Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

The complete question is:

Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce

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By using the concept of confidence interval, it is obtained that the sample needed  in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% = 601

What is confidence interval?

Let the quantity which is to be estimated is [tex]\theta[/tex] .  A confidence interval for the parameter θ, with confidence level  is the interval (a, b), where

P(a < [tex]\theta[/tex] < b) = , P is the probability

Here,

the formula for sample size n = [tex]\frac{p(1-p)z^2}{e^2}[/tex]

p is the sample proportion,

z is the z score associated with the level of confidence

e is the margin of error

Now,

e = 0.04

p = [tex]\frac{1}{2}[/tex]

z = 1.96

n = [tex]\frac{0.5(1-0.5) \times 1.96^2}{0.04^2}[/tex]

n = 600.25

Sample size needed = 601

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By solving a linear inequation, it is obtained that

Victoria should get a minimum marks of 94 to get 'a' in science

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]

A one degree inequation is known as linear inequation.

Here, an inequation needs to be solved

Suppose the full marks of Victoria in each subject is 100

Marks obtained by Victoria in Science = 88, 86, 92

Let the fourth marks be x,

Average marks = [tex]\frac{88 + 86 + 92 + x}{4}[/tex]

                          = [tex]\frac{266 +x}{4}[/tex]

By the Problem,

                         [tex]\frac{266 + x}{4} \geq 90\\266 +x \geq 90\times 4\\266 +x \geq 360\\x \geq 360-266\\x\geq 94[/tex]

Victoria should get a minimum marks of 94 to get 'a' in science

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The coordinates of triangle PQR under the translation (x,y) → (x+2,y-4) are P'(-1,-6), Q'(1,0), R'(4,-6).

Translation of coordinates is done by adding the horizontal translation at each vertex of the triangle. It is the process of shifting the location of the figure without changing the size and dimensions of the figure.

The coordinates of the triangle PQR are given as P(-3,-2), Q(-1,4), R(2,-2). The property under translation is given as (x,y) → (x+2,y-4). Now, let us apply this for all vertices.

P(-3,-2) → P'(-3+2,-2-4) → P'(-1,-6)

Q(-1,4) → Q'(-1+2,4-4) → Q'(1,0)

R(2,-2) → R'(2+2,-2-4) → R'(4,-6)

Thus, the vertices after translation are P'(-1,-6), Q'(1,0), R'(4,-6).

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Answer:

y = -7x + 10

Step-by-step explanation:

As the y's are decreasing by 7, the x are increasing by 1.  This gives us a slope of -7.  When x is 0, y is 10 that is our y intercept.

Based on expression for each side of the equation, the number is -2.

Let us assume the number to be x. So, there will be two sides of equation, that is Left Hand Side and Right Hand Side. Writing the equation for each side.

Left Hand Side = 11x - 21

Right Hand Side = 7x - 29

Equating both sides of the equation.

11x - 21 = 7x - 29

Rewriting the equation with identical values on each side

11x - 7x = 21 - 29

Performing subtraction on both sides of the equation

4x = -8

Shifting 4 to Right Hand Side of the equation

x = -8 ÷ 4

Performing division on Right Hand Side of the equation

x = -2

Thus, the number is -2.

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