Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be:

The length of one leg of the right triangle is 5√10

The leg of a right triangle can be found as follows;

Therefore, using trigonometric ratios,

sin 45 = opposite / hypotenuse

sin 45 = x / 10√5

1 / √2 = x / 10√5

cross multiply

10√5 = x√2

divide both sides by √2

x = 10√5 / √2

x = 10√5 / √2 × √2 / √2

x = 10√10 / 2 = 5√10

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Answer:

[tex]\sf Total \ amount \ of \ walnuts \ and \ pecans \ needed = \dfrac{7}{12}[/tex]

Step-by-step explanation:

    [tex]\sf Amount \ of \ walnut \ needed = \dfrac{1}{4}[/tex]

    [tex]\sf Amount \ of \ pecans \ needed =\dfrac{2}{6} =\dfrac{1}{3}[/tex]

To find the total amount of walnut and pecans, we have to add the fractions.

LCM of 4 & 3 = 12

Equivalent fractions:

      [tex]\sf \dfrac{1}{4}=\dfrac{1*3}{4*3}=\dfrac{3}{12}\\\\\dfrac{1}{3}=\dfrac{1*4}{3*4}=\dfrac{4}{12}[/tex]

Now, add

   [tex]\sf \dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}[/tex]

                  [tex]\sf = \dfrac{7}{12}[/tex]

Answer:

X=3

Step-by-step explanation:

First you can distribute the 4 to 2x-1 making is 8x-4

8x-4+2x+2=28

Now add like terms

8x+2x-4+2=28, 10x-2=28

Add 2 to both sides

10x=30

Divide both sides by 10

x=3

Answer:

t ≥ 192

Step-by-step explanation:

To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)

Answer:

10.63 inches

(b)2+(h)2=(H)2

(8)2+(7)2=(H)2

64+49=(H)2

113=(H)2

H=10.63

The diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

The diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

In the question, we are asked to determine the diagonal length of the photo frame bought by Mike, having measurements of 8 inches in length and 7 inches in width.

We know the photo frame is in the shape of a rectangle, as it has a length and a width.

We also know that the diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

So, by substituting l = 8 and w = 7, in the above relation, we can calculate the diagonal of the photo frame as:

d = √(8² + 7²),

or, d = √(64 + 49),

or, d = √113,

or, d = 10.63.

Therefore, the diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

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The next term in the sequence is -1.

Given a sequence is defined recursively by the formula f(n+1)=f(n)+3.

An ordered list of integers that frequently follows a pattern or function is known as a sequence. Sequences can have a finite or indefinite length. Terms refer to the distinct components of a sequence. The individual numbers or parts that make up a sequence are known as its terms.

The first term of the sequence is -4.

That means f(1)=-4            .......(1)

When compare f(1) with f(n+1), we get

n=0

So, when n=0 then it is the first term of the sequence.

When n=1 then substituting this in the given formula, we get

f(1+1)=f(1)+3

f(2)=f(1)+3

Now, Substitute the value of f(1) from equation (1), we get

f(2)=-4+3

f(2)=-1

Hence, the next term in the sequence when the sequence is defined recursively by the formula f(n+1) = f(n)+3 and the first term of the sequence is –4 is -1.

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Answer:

a. What is the measure of ∠CAT?   Answer:  70°

b. What is the measure of ∠BAR?  Answer:  50°

c. What is the measure of ∠RAT?  Answer:   110°

d. What is the measure of ∠CAB? Answer:   130°

e. What is the measure of ∠BAT? Answer:    60°

Step-by-step explanation:

I just looked at the degrees of the protractor.

Hope this helps!

If not, I am sorry.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain from the first point,

[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]

The height of the mountain from the second point,

[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]

Equating the height,

H = H

(1000+x) × tan(29°) = x tan( 34°)

x = 4611.5767 feet

Now, the height of the mountain is,

H = x tan(34°)

H = 3110.54776 feet

Hence, the height of the mountain is 3110.5767 feet.

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Using the rule of dilation, 5/4, the length of C'A' is: A. 10 units.

Dilation is a form of transformation that creates a new image that is similar to the original one.

The images formed are similar images shown in the diagram given, therefore, using the rule of dilation, Dy = 5/4, we would have:

CA × 5/4 = C'A'

Plug in the given value

8 × 5/4 = C'A'

10 = C'A'

C'A' = 10 units

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Answer:

159.3

Step-by-step explanation:

456 - 121.3 = 334.7

333.7 - 175.4 = 159.3

Hope this helped

Answer:

152

Step-by-step explanation:

You actually don't need to find the thirds number. Just by taking 456 and dividing it by three, you will get your answer and the average of the three numbers.

Answer:

ok sure will do the answer is

Step-by-step explanation:

The expressions that gives the number of online math classes is as follows:

y = x - 15

The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer.

Let

the number  of math classes offered face-to face = x

the  number of math classes offered online  = y

Therefore, the expression that gives the number of online math classes is as follows:

y = x - 15

x = y + 15

Hence,

y = x - 15

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Answer: 42.308%

Step-by-step explanation:

The missing term in the expression ___( 2a-1)  is 6b.

An expression is an algebraic statement that consists of variables, constants, and mathematical operators.

The expression 12ab-6b is equivalent to

6b( 2a-1)

(By taking the common factors out of the given expression.)

Therefore, the missing term in the expression is 6b.

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Answer:

was there a list to choose from

Step-by-step explanation:

19, 26, 33, 40, 47

Answer:

Elimination would be a better method for solving the system.

[tex]\Rrightarrow \sf12x+10y=2[/tex]

[tex]\Rrightarrow \sf6x+5y=1.......(i)[/tex]

[tex] \sf\Rrightarrow-x+4y= -5 ............(ii)[/tex]

[tex]\large \sf \red{ \blue{[ (ii)×6]}}[/tex]

[tex]\sf\Rrightarrow-6x+24y= -30 ............(iii)[/tex]

[tex] \large \sf \red{(i) + \blue{ (iii)}}[/tex]

[tex]\Rrightarrow \small\sf6x+5y=1+(-6x+24y= -30)[/tex]

[tex]\Rrightarrow \sf29y = - 29 \\ [/tex]

[tex]\Rrightarrow \blue{\sf \: y = - 1}[/tex]

putting the value in equation (i)

[tex]\Rrightarrow \sf6x+5 \times - 1=1[/tex]

[tex]\Rrightarrow \sf6x - 5=1[/tex]

[tex]\Rrightarrow \sf6x = 6[/tex]

[tex]\Rrightarrow \red{\sf \: x = 1}[/tex]

[tex]\overline{\underline{\rule{209pt}{2pt}}}[/tex]

Yes, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

For 35 long haired and 40 short haired member.
Put this values in the given equation.

For water 70L+60S < 5600
  70 x 35 + 60 x 40
2450+2400
4850 <5600
inequality holds

For shampoo 0.02L+0.01S ≤ 1.50
0.02 x 35 + 0.01 x 40
0.7 + 0.4
1.1 < 1.50
inequality holds

Thus, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.

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Answer:

Y intercept: (0,2) Slope: 1/3

Step-by-step explanation:

X is horizontal. Y is vertical the slope touches at (0,2).

The slope goes up by one and right by three cause it connects to the line

for the second one all you would have to do is increase the slope first number like 4/3

The total amount will be $889123 after 16 years if the starting salary is $350000

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]

where a is a constant and a>1

We have:

Starting salary is $350000 and you receive a 6% increase at the end of every year.

We can find the total amount, from the exponential formula:

T = a(1 + r)ⁿ

T is the total amount

a is the starting amount

r is the rate

n is the total number of years

T = 350000(1 + 6%)¹⁶

T = 350000(1 + 0.06)¹⁶

T = 889123.08 ≈ $889123

Thus, the total amount will be $889123 after 16 years if the starting salary is $350000

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Answer:

Step-by-step explanation:

[tex]1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta[/tex]

Step-by-step explanation:

Answer:

He will need to pay 5.4 Ghana cedis into his educational fund.

Step-by-step explanation:

We need to multiply 4 1/2 by 120 since it is a percentage. We convert 4 1/2 into a decimal which is 4.5. Now, we just need to multiply 120 by 4 1/2 to get an answer of 5.4.

Pn(Z>zp)=1−p%

Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a

is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:

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

The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.

The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.

Pn(Z>zp)=1−p%

Here Pn is the probability for the standard normal variable.

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Isolate x:

2x + 7y = -1

2x = -1 -7y

x = -1/2 - 7/2y

Substitute the equation of x:

4x - 3y = -19

4(-1/2 - 7/2y) - 3y = -19

-2 - 14 - 3y = -19

-3y = -19 + 14 + 2

-3y = -3

 y = 1

Substitute to find x:

2x + 7y = -1

2x + 7(1) = -1

2x = -1 - 7

2x = -8

x = -4

(-4, 1)

Multiply one or both equations through an integer in order that one time period has the same and contrary coefficients within the equations. Add the equations to provide a single equation with one variable. clear up for the variable. alternative the variable back into one of the equations and resolve for the other variable.

Conclusion: A system of equations is fixed of 1 or greater equations related to some of the variables. The solutions to systems of equations are the variable mappings such that every one component equations are satisfied—in other phrases, the locations at which all of these equations intersect.

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The average rate of change is illustrated below.

The average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a).

In this case the interval is [0,2], then a=0, b=2

r=[f(2)-f(0)]/(2-0)

r=[f(2)-f(0)]/2

1) First function: h(x)

r=[h(2)-h(0)]/2

x=2→h(2)=(2)^2+2(2)-6

h(2)=4+4-6

h(2)=2

x=0→h(0)=(0)^2+2(0)-6

h(0)=0+0-6

h(0)=-6

r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(2+6)/2

r=(8)/2

r=4

2) Second function: f(x)

A function, f, has an

x-intercept at (2,0)→x=2, f(2)=0

and a y-intercept at (0,-10)→x=0, f(0)=-10

r=[f(2)-f(0)]/2

r=[0-(-10)]/2

r=(0+10)/2

r=(10)/2

r=5

3) Third function: g(x)

r=[g(2)-g(0)]/2

From the graph:

g(2)=6

g(0)=2

r=(6-2)/2

r=(4)/2

r=2

4) Fourth function: j(x)

r=[j(2)-j(0)]/2

From the table:

x=2→j(2)=-8

x=0→j(0)=4

r=(-8-4)/2

r=(-12)/2

r=-6

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Answer:

8

Step-by-step explanation:

because there is 8 in the question

Answer:

{(-3, -2), (-4, 3), (-1, 0), (3, -7)}

Step-by-step explanation:

When you find the inverse of a function you swap the x and the y. So let's look at a couple examples and see what happens to the x and y values

Radical:

[tex]y=\sqrt{x}[/tex]

So let's just look at perfect squares so it's a bit easier to understand

(0, 0)

(4, 2)

(9, 3)

Now let's find the inverse:

[tex]x=\sqrt{y}[/tex]

Now to make this concept a bit easier to understand let's leave it in this form. Well the first notable thing, is that any operations applied to y will now apple to x, and any operations applied to x will apply to y (in this case the square root).

So if I input 9 as the y, the x will be 3

If I input 4 as y, the x will become 2

Some points are

(0, 0)

(2, 4)

(9, 3)

You'll notice the x and y values are swapped, well it's simply because you swap the x and y's place. this is also why the domain and range are swapped

So given the points {(-2, -3),  (3, -4), (0, -1), (-7, 3)} you simply swap the x and y to get:            {(-3, -2), (-4, 3), (-1, 0), (3, -7)}

Answer:

D

Step-by-step explanation:

The missing segment in the image below is 78 units.

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

The ratio or two corresponding sides of similar shapes are in the same proportion.

Let x represent the missing side, hence:

(x + 26)/26 = 48/12

x =78

The missing segment in the image below is 78 units.

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