A long novel is opened to a random page; the probability that the page is numbered something between 21 and 31.

Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.

The standard deviation and sample size are given, respectively, by:

s = 1400, n = 69.

Hence, the margin of error in dollars is given by:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

[tex]M = 1.9955\frac{1400}{\sqrt{69}}[/tex]

M = 336.

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Answer:

x = 3 or x = 1

y = 3 or y = -1

(x, y) = (3, 3)

(x, y) = (1, -1)

Step-by-step explanation:

Answer: A triangle that only has two congruent sides is called an isosceles triangle. Two equal sides and two equal angles.

Answer:

Here,

[tex](a + b) [(a + b)(a + b)][/tex]

[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]

[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]

Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]

Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.

Answer:

I hope you can help

The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.

An equation is an expression that shows the relationship between two or more variables and numbers.

The lowest salary is $32000, hence to increase to $40000, we need an additional $8000.

Also, giving every employee a $1,000 raise accounts for $5000 since there are 5 staff.

The total cost of increment = 8000 + 5000 = 13000

The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.

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The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.

Hence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

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Answer:

The correct answer is:

Plane.

Step-by-step explanation: There are three terms generally considered to be undefined in geometry:  point, line and plane.

A circle is the set of all points in a plane the same distance from a given point called the center.  The only of our options that is used in this definition is

The correct answer is;

⇒ Plane.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, We know that;

There are three terms generally considered to be undefined in geometry:  point, line and plane.

Hence, A circle is the set of all points in a plane the same distance from a given point called the center.

And, The only of our options that is used in this definition is plane.

Thus, The correct answer is;

⇒ Plane.

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The purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

The question is incomplete.

The complete question is in the picture, please refer to the picture.

Total number of pieces = 3+5 = 8

So, the purple pieces = 5(5/8) = 35

Total pieces = 20/(5/8) = 4×8 = 32

Thus, the purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.

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Answer:

15

Step-by-step explanation:

Isolate the b by subtracting 6 from both sides

Question: b + 6 = 21
Subtract 6 from both sides

b + 6 - 6 = 21 - 6

b = 15

Answer:b=15

Step-by-step explanation:

Just subtract 6 from 21 to get b.

The acute angles of a right triangle are complementary, so:

[tex]m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}[/tex]

This are interest added on a sum of money invested. Jack will have $168.95 more than Maya in his account

This are interest added on a sum of money invested. The formula for calculating compound amount is given as;

A = P(1 +r/n)^nt

Given the following parameter

P =$2100

rate r = 7 5/8% = 0.07625

time t = 12 years

n =12 (monthly)

Substitute

A = 1200(1+0.07625/12)^12(12)
A = 1200 (2.4895)
A = $2987.46

For Maya

A = 1200(1+0.07375)^12

A = 2818.50

Take the difference

Difference =$2987.46 - $ 2818.5

Difference = $168.95

Hence Jack will have $168.95 more than Maya in his account

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[tex]~~~(x^2 -4)(x^2 +6x +9)\\\\=(x^2 -2^2)(x^2 +2 \cdot 3x +3^2)\\\\=(x+2)(x-2)(x+3)^2[/tex]

Answer:

Calculate it you will now the answer and im elementery school

[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]

Substitute the values according to the formula.

[tex]r=\frac{94}{2}[/tex]

[tex]\large\boxed{r=47 \: cm}[/tex]

Now, let's find the area.

[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]

So, we'll have to multiply π, 47 and 47.

Substitute the values according to the formula.

[tex]a= \pi{47}^{2}[/tex]

[tex]a= 6939.778172 \: {cm}^{2}[/tex]

[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]

Hence, the area of the given circle is 6939.8 square centimeters.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the radius & area of the circle.

To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:

[tex]\star~\bf{94\div2}[/tex]

[tex]\star~\bf{Radius=47}\star[/tex]

Now that we have the radius, let's compute the area! :)

///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\

                            Calculating the Area

We can work out the area of a circle by using this formula:

[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]

Where

[tex]\dag[/tex] A=Area of a circle

[tex]\dag[/tex] [tex]\pi =3.14...[/tex]

[tex]\dag[/tex] r=radius

Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.

Now it's time to substitute the values:

[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]

Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)

Here's what it stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

2 is an exponent.

So what do you think we should do first?

[tex]\square[/tex] Square 47.

[tex]\square[/tex] Multiply 3.14 times 47 and then square.

That's right, we should square 47 first. :)

[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]

Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:

[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]

Remember, the area of any shape is measured in units squared.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]

Hope this helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]

The number of years it would take $4000 to grow to $4616 is 2.92 years.

When an amount earns compound interest compounded semi annually, it means that both the amount invested and the interest accrued increases in value twice yearly.

Number of years = (In FV / PV) / r

(In 4616 / 4000) / 0.049 = 2.92 years

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Answer:

10 miles

Step-by-step explanation:

total amount=$44.80

pick up fee=$4.80+$4 per mile

to get the miles of the taxi ride it will be=total amount-pick up fee÷$4

$44.80-$4.80÷$4

$40÷$4

=10 miles

THANK YOU

The table in which y varies directly with x is table C.

When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.

The equation that is used to represent direct variation is:

y = kx

Where y is the constant of proportionality

In table c, k is equal to 26

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If Mr. Price adds two more CDs that are 38 minutes and 40 minutes, the third quartile would increase.

A box plot is used to study the distribution and level of a set of scores. The two whiskers represent the minimum and maximum value.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

When the two CDs are added, the median would decrease. The first quartile and the third quartile would increase. The interquartile range would increase.

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The description of the area of a square is (c) as the length of the side increases, the area increases.

The table of values is given as:

Side Length (cm)        Area (cm²)

1                                       1

2                                      4

3                                      9

4                                      16

5                                    25

In the above table, we can see that:

As length increases, the area also increases

Hence, the description of the area is (c) as the length of the side increases, the area increases.

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Answer:

a. $3150

b. $3307.50, $3472.875

c. B(n) = 3000(1.05)^t

Step-by-step explanation:

just a disclaimer i havent done interest in a while so this might not be right

also im assuming this is compound interest

a. P = original amount; r = interest percentage, x = amount of total money

x = P(1 + (r/100)) = 3000(1 + 0.05) = 3150

b. x = 3000(1.05)^2,3 = 3307.5, 3472.875

c. B(n) = P(1+(r/100)^t for t in years. plug in the values to get B(n) = 3000(1.05)^t

The minimum distance  between the point(-3,2) and the line y = -x + 1  is [tex]\sqrt{2}[/tex] units.

The line that joins  two points on a cartesian plane is a line segment.

Analysis:

The formula for calculating distance between a line and a point is

d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]

where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.

x1 and y1 are coordinates of the point.

for the line y = -x + 1 which is  = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units

In conclusion, the distance between the point and the line is  [tex]\sqrt{2}[/tex] units

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Answer:The result follows from manipulating the conditional probability. By definition,

By the law of total probability,

So we have

Step-by-step explanation:

P(A|B) = P(B|A)×P(A)/P(B)

so, in our case

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)

I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.

so,

P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =

= 0.25 + 0.05 + 0.1 = 0.4

therefore,

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1

Answer:

38 minutes

Step-by-step explanation:

Yards covered in a minute = 4850/20 = 242.5

Time needed to cover 9215 yards = 9215/242.5 = 38 min

The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:

D.                  Visit Dentist Yearly Don’t Visit Dentist Yearly

Below 40                    0.27                         0.73

Above 40                   0.57                          0.43

The relative frequency of those older than 40 and don't go annually to a dentist can be found as:

= Number of over 40 who don't go to dentist / Total of those over 40 surveyed

Solving gives:

= 13 / (17 + 13)

= 13 / 30

= 0.43

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Answer:

Its D, I got it right on a test :)

Step-by-step explanation:

Answer:

3rd

Step-by-step explanation:

If you know about linear eq. it's just a simple rule no worry

Step-by-step explanation:

the answer is 5 percentage because the formula is 100 * 400 over 4000 * 2

Answer:

1.052 × 10⁶

Step-by-step explanation:

82,000 + 970,000 = 1,052,000

Answer:

[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)=1,052,000[/tex]

Step-by-step explanation:

[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)\\=8.2\cdot \:10^4+9.7\cdot \:10^5\\\\\rightarrow 10^4 = 10000\\= 8.2 \cdot 10000\\= 82000\\\rightarrow 10^5 = 100000\\= 9.7 \cdot 100000\\= 970000[/tex]

[tex]970000 + 82000 = 1052000[/tex]

Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884