2x squared minus 1 equals 21​

Answer:

37,139

Step-by-step explanation:

Given the following :

Population in 2002 = Initial population (P0) = 22,800

Growth rate (r) = 5% = 0.05

Growth in 2012 using the exponential growth function?

Time or period (t) = 2012 - 2002 = 10years

Exponential growth function:

P(t) = P0 * (1 + r) ^t

Where P(t) = population in t years

P(10) = 22800 * (1 + 0.05)^10

P(10) = 22800 * (1.05)^10

P(10) = 22800 * 1.62889

P(10) = 37138.797

P(10) = 37,139 ( to the nearest whole number)

Answer:

[tex]\large \boxed{{p=2}}[/tex]

Step-by-step explanation:

9(p-4) = -18

Expand brackets.

9p -36 = -18

Add 36 on both sides.

9p -36 + 36 = -18 + 36

9p = 18

Divide both sides by 9.

(9p)/9 = 18/9

p = 2

Answer:

p = 2

Step-by-step explanation:

9(p - 4) = -18

You are solving for the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, divide 9 from both sides:

(9(p - 4))/9 = (-18)/9

(p - 4) = -18/9

p - 4 = -2

Isolate the variable, p. Add 4 to both sides:

p - 4 (+4) = -2 (+4)

p = -2 + 4

p = 4 - 2

p = 2

Check. Plug in 2 for p in the equation:

9(p - 4) = -18

9(2 - 4) = -18

9(-2) = - 18

-18 = -18.

~

To build the fleet of ships, Astrid must consider each of the given rates (i.e.  the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.

Given that:

Required quantities

[tex]Wood = 40\ tons[/tex]

[tex]Sailors = 300[/tex] per ship

Available quantities

[tex]Wood = 4\ tons[/tex] daily

[tex]Days = 100[/tex] at most

First, we calculate the total tons of woods Astrid can receive.

[tex]Total = Days \times Wood\ Available[/tex]

[tex]Total = 100 \times 4[/tex]

[tex]Total = 400\ tons[/tex] ---- in 100 days

Next, we calculate the number of ships that can be made from the 400 tons.

[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]

So, we have:

[tex]Ships = \frac{400}{40}[/tex]

[tex]Ships = 10[/tex]

This means that Astrid can build up to 10 ships

The number of sailors the ship can accommodate is:

[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]

So, we have:

[tex]Sailors = 10 \times 300[/tex]

[tex]Sailors = 3000[/tex]

It means the 10 ships can accommodate 3000 sailors.

3000 sailors is greater than 2100 sailors.

So, we can conclude that she can build enough ship for the 2100 sailors.

Read more about

https://brainly.com/question/17174491

Answer:

280 tons

Step-by-step explanation:

:)

Answer:

Sector

Step-by-step explanation:

A sector of a circle is the portion of circle enclosed by two radii and arc

Answer:

All real numbers are solutions. 0=0

Step-by-step explanation:

(x+3)(x−5)=(x+3)(x−5)

Step 1: Simplify both sides of the equation.

x2−2x−15=x2−2x−15

Step 2: Subtract x^2 from both sides.

x2−2x−15−x2=x2−2x−15−x2

−2x−15=−2x−15

Step 3: Add 2x to both sides.

−2x−15+2x=−2x−15+2x

−15=−15

Step 4: Add 15 to both sides.

−15+15=−15+15

0=0

All real numbers are solutions.

hope it helps.I was reading the same chapter

Answer:

The expression in factored form is (3x - 7)(3x + 7)

Step-by-step explanation:

Here in this question, we are interested in using the difference of two squares to factor the given expression.

Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.

By using the difference of two squares;

a^2-b^2 can thus be written as;

(a-b)(a + b)

Now, we can apply same approach to the problem at hand.

9x^2 - 49

kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2

So applying what we have said earlier about difference of two squares;

9x^2 - 49 will be ;

(3x-7)(3x + 7)

Answer:

The answer is (3x - 7) (3x +7)

Step-by-step explanation:

Answer:

y  = 0.45X + 39  

Answer:

y is 60⁰

because all sides are equal

Answer:

60 degrees

Step-by-step explanation:

In an equilateral triangle, the angles are equiangluar and the sides are equal.

180 degrees in a triangle/3 sides =

= 60 degrees per side

Answer:

The volume of the pyramid is 867 inch^3

Step-by-step explanation:

Here in this question, we are interested in calculating the volume of a square based pyramid.

Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.

V = a^2h/3

where a represents the length of the side of the square and h is the height of the pyramid

From the question, the length of the side of the square is 17 in while the height is 9 in

Plugging these values, we have ;

V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch

Answer:

900 outfits

Step-by-step explanation:

You just have to multiply them all together :)

Answer:

  the sides are different lengths as shown in the diagram

Step-by-step explanation:

Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.

A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.

Answer:2,3 hope it help you

Step-by-step explanation:

Answer:

21.627

Step-by-step explanation:

get the distance between all points then add

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

First, let's find how many total items there are in the box.

If there are 20 oranges and 10 grapes, then there are [tex]20+10=30[/tex] items in the box.

Now, if there are 10 grapes in this box, we know that the probability of picking a grape is [tex]\frac{10}{30}[/tex] because the total is the denominator and the number of items for that selection is the numerator.

We can simplify this fraction down to [tex]\frac{1}{3}[/tex].

Hope this helped!

Answer:

1/3

Step-by-step explanation:

Answer:

[tex]\huge\boxed{9,40,46}[/tex]

Step-by-step explanation:

Let's check it using Pythagorean Theorem:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the longest sides, a and b are rest of the 2 sides

1) 9 , 40 , 46

=> [tex]c^2 = a^2 + b^2[/tex]

=> [tex]46^2 = 9^2 + 40^2[/tex]

=> 2116 = 81 + 1600

=> 2116 ≠ 1681

So, this is not a Pythagorean Triplet

2) 16, 30 and 34

=> [tex]c^2 = a^2 + b^2[/tex]

=> [tex]34^2 = 16^2 + 30^2[/tex]

=> 1156 = 256 + 900

=> 1156 = 1156

No need to check more as we've found the one which is not a Pythagorean Triplet.

Answer:

Option A is the correct option.

Step-by-step explanation:

1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.

From Pythagoras theorem,

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Here, we know that the hypotenuse is always greater than perpendicular and base,

h = 46 , p = 40 , b = 9

⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]

⇒[tex]2116 = 1600 + 81[/tex]

⇒[tex] \sf{2116  ≠ 1681}[/tex]

Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9

So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.

------------------------------------------------------

2. 16 , 30 , 34

h = 34 , p = 30 , b = 16

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]

⇒[tex] \sf{1156 = 900 + 256}[/tex]

⇒[tex] \sf{1156 = 1156}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16

So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.

------------------------------------------------------

3. 10, 24 , 26

h = 26 , p = 24 , b = 10

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]

⇒[tex] \sf{676 = 576 + 100}[/tex]

⇒[tex] \sf{676 = 676}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10

So, the set of numbers 10, 24 , 26 is the Pythagorean triple.

-----------------------------------------------------

4. 50 , 120 , 130

h = 130 , p = 120 , b = 50

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]

⇒[tex] \sf{16900 = 14400 + 2500}[/tex]

⇒[tex] \sf{16900 = 16900}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50

So, the set of numbers 50, 120 , 130 is the Pythagorean triple.

-----------------------------------------------------

In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.

Hope I helped!

Best regards!!

Answer:

The y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)  

Answer:

3x +10y  is greater than or equal to 250.

Step-by-step explanation:

The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.

Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.

Answer:

3n + 10c > 250

Step-by-step explanation:

I confirmed it in grandpoint

Answer:

12 inches

Step-by-step explanation:

Raj tested his new flashlight by shinning it on his bedroom wall the beam of the light can be described by the equation (x^2-2x) + (y^2-4y) - 31=0. how many inches wide is the beam of light on the wall

Solution

Given:

(x^2-2x) + (y^2-4y) - 31=0

By completing the square

(x^2-2x) + (y^2-4y) - 31=0

(x^2-2x+1-1) + (y^2-4y+4-4)-31=0

(x-1)^2 -1 + (y-2)^2 - 4 - 31=0

(x-1)^2 + (y-2)^2 - 1 - 4 - 31=0

(x-1)^2 + (y-2)^2 - 36=0

(x-1)^2 + (y-2)^2=36

Writing the equation in the form: (x-h)^2+(y-k)^2=r^2

(x-1)^2+(y-2)^2=6^2

From the above, r=6

Where,

r=radius

how wide is the diameter ?

radius=6

Diameter= 2 × radius

=2×6

=12 inches

Answer:

12

Step-by-step explanation:

to graph it just scan the equation on photo math!!

Answer:

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= 2000π unit³

Volume= 6284 unit³

Step-by-step explanation:

The decimal value of the volume already given= 600π

The decimal value of the volume already given= 600*3.142

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= πr²h/3

Volume= 11²*12/3 *π

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume = πr²h/3

Volume= 4²*6/3(π)

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= πr²h/3

Volume= 20²*15/3(π)

Volume= 2000π unit³

Volume= 6284 unit³

Here's the right answer.

Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

Given:

Number of red balls, n(R) = 3

Number of green balls, n(G) = 9

Number of yellow balls, n(Y) = 2

Number of orange balls, n(O) = 2

Number of purple balls, n(P) = 4

Two balls are drawn one at a time with replacement.

To find:

Probability of drawing a green ball and an orange ball ?

Solution:

Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20

Formula for probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability that a green ball is drawn at first:

[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Green) = \dfrac{9}{20}[/tex]

Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]

[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]

Answer:

Step-by-step explanation:

When the quadratic is written in vertex form:

  x = a(y -k)^2 +h

the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.

For your given equation, ...

  x = (1/2)(y -5)^2 +7

you have a=1/2, k = 5, h = 7, so ...

  the vertex is (7, 5)

  the length of the latus rectum is 1/(1/2) = 2

The order of a matrix is m×n where m is the number of rows and n is the number of columns.

can you count and find what are m and n here?

Answer:

Step-by-step explanation:

Number of rows X Number of columns

Rows = 3

Columns = 2

answer = 3x2

Answer:

[tex]\huge \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]

Distribute negative sign.

[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]

Combine like terms.

[tex]0xe^2 +0x-1[/tex]

[tex]0-1=-1[/tex]

Answer:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

Test statistic, t = -0.00693

p- value = 0.498

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 level of significance

Step-by-step explanation:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

The test statistic for t test is;

[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]

The mean

Height of Father, h₁,  Height of Son h₂

72.4,      77.5

70.6,      74.1

73.1,       75.6

69.9,      71.7

69.4,      70.5

69.4,      69.9

68.1,       68.2

68.9,      68.2

70.5,       69.3

69.4,       67.7

69.5,       67

67.2,       63.7

70.4,       65.5

[tex]\bar x_1[/tex]  = 69.6      

s₁ = 1.58

[tex]\bar x_2[/tex] = 69.9

s₂ = 3.97

n₁ = 13

n₂ = 13

[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]

(We reversed the values in the square root of the denominator therefore, the sign reversal)

t = -0.00693

p- value = 0.498 by graphing calculator function

P-value > α Therefore, we do not reject the null hypothesis

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 lvel of significance

Answer:

4ny²+4n²-4n-8+y⁴-2y²

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Step-by-step explanation:

For a relation to be proportional

a:b = c:d

in other form

a/b = c/d

______________________________________________

Ratio for first type of fabric

cost of fabric/ area of fabric = 31.25/5 = 6.25

Ratio for other type of fabric

cost of fabric/ area of fabric = 71.50/11 = 6.5

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Answer:

The word problem is "How many $25 are there in $125?"

Step-by-step explanation:

Given

[tex]n(\$25) = \$125[/tex]

Required

Write a word problem for the expression

We start by solving the given equation

[tex]n(\$25) = \$125[/tex]

Divide both sides by $25

[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]

[tex]n = \frac{\$125}{\$25}[/tex]

[tex]n = 5[/tex]

This implies that there are 5, $25 in $125

Hence; The word problem is "How many $25 are there in $125?"

Answer:

6/25

Step-by-step explanation:

rise / run

24/100 = 6/25

Answer:

[tex]\frac{6}{25}[/tex]

Step-by-step explanation:

The slope of any relationship is always rise over run. This means the vertical distance traveled over the horizontal distance traveled will get us our slope.

We travels 24 feet vertically for every 100 feet horizontally, so:

[tex]\frac{24}{100}[/tex].

We can simplify this fraction to find the slope in fraction form.

[tex]\frac{24\div4}{100\div4} = \frac{6}{25}[/tex]

So the slope of this equation is [tex]\frac{6}{25}[/tex].

Hope this helped!

Sandy got 350 out of 2400.

Her portion is 350/2400 which can be reduced to:

35/240 = 7/48

The portion is 7/48