Use the laws of logarithms to combine the expression. 1 2 log2(7) − 2 log2(3)

Answer:

Axis Of Symmetry = -2

Vertex = (1,-2)

Min (0,-2)

Domain = All Real #'s

Range =  Y is greater than or equal to -2

The numbers : 4,-10 and -4 are integers.

A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero.

The Latin word "integer" signifies "whole" or "intact." Thus, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

"Negative 1 and one-third" includes a fractional part, so it is not an integer.

"2.5" and "0.ModifyingAbove 13 with Bar" contain a decimal, so it is also not an integer.

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The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.

If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.

Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.

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Based on the mean, standard deviation, and the graph, the indicated IQ score would be 115.

First, find the z value:

P(Z<z) = 1 - tail value

= 1 - 0.1587

= 0.8413

According to the z-value, this gives a value of:

z = 1

The indicated IQ score is:

= mean + z value z standard deviation

= 100 + 1 x 15

= 115

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Answer:

x = 103.8

Step-by-step explanation:

Calc: [2nd] [VARS] [invNorm]

area: 0.6

z = .2533471011

x = u + (z × o)

x = 103.8

The area of the parallelogram is 135 square meters.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).

Properties of parallelogram are-

The area of parallelogram = Base×Height

A = B×H

Calculation for the area of the given parallelogram.

The base is 15 meters.

The height is 9 meters

Area = 15×9

        = 135

Therefore, the area of the parallelogram is 135 square meter.

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Answer:

True.

Step-by-step explanation:

In this true or false question, the answer is true.

Hope this helps!

Answer:

False

Step-by-step explanation:

Not every function in a rectangular plane will be a function in every plane. Hope this helps

Answer:

Step-by-step explanation:

Discussion

She is correct.

An equilateral triangle is a specific acute triangle. An acute triangle can never be an equilateral triangle because it has 3 unequal angles. Your best choice is likely C, but none of the choices are first rate choices.

Answer: C

Each side of the hexagon is about 105.219 ft².

Note that:

A F: 30 ft long.

A O = 1/2 A F = 3ft

Δ C J X =  0 X = 1/2 (A F - A O)

= 1/2 (30-3)

= 13.5ft

Sin 60° =[tex]\frac{0x}{cx}[/tex]

cx = [tex]\frac{ox}{sn 60}[/tex]

= 15.558ft = CJ (Sides)

Hence: Each side of the hexagon is: 1/2 CJ  x OX  = 105.219 ft².

The area of the seating section is:

6 ( Each side of the hexagon )

=  6 x 105.219 ft².

631.315 ft².

The area of the entrance and seating section combines is:

CJ x AO = 46.764ft².

The area of the entrance is:

631.315 ft²+ 46.764ft².

= 678. 078ft².

Hence, Each side of the hexagon is about 105.219 ft².

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1+3+5+7+9+11+13+15

=4+12+20+28

=16+48

=64

Step-by-step explanation:

Look, you're taking these kinds of questions too serious and that's why you believe they're hard, now pay close attention:

the areas are defined in cm² but the radius is defined in cm, so you need find the positive root of cm².

[tex] \sqrt{ \frac{5500 {cm}^{2} }{220 {cm}^{2} } } = \frac{r}{5cm} = = > \\ 5 = \frac{r}{5} = = = > r = 25[/tex]

and the question wants the base area:

[tex]s = \pi {r}^{2} = = = > s = 3.14 \times {(25cm)}^{2} = = > 1963.5 {cm}^{2} [/tex]

Answer:

A

Step-by-step explanation:

[tex]\frac{x}{x-5}[/tex] × [tex]\frac{2x}{x+4}[/tex] ( no factors cancel on numerator/ denominator )

= [tex]\frac{x(2x)}{(x-5)(x+4)}[/tex]

= [tex]\frac{2x^2}{x^2-x-20}[/tex]

Answer:

Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?

Step-by-step explanation:

Answer:

y = 7x - 2

Step-by-step explanation:

first we need the slope of the line.

the slope is expressed a the ratio (y coordinate change / x coordinate change) when we go from one point on the line to another.

so, let's say we go from (0, -2) to (1, 5), we see

x changes by +1 (from 0 to 1).

y changes by +7 (from -2 to 5)

so the slope is +7/+1 = 7

the slope-intercept form is in general

y = ax + b

a being the slope, b being the y-intercept (the y-value for x = 0).

the point (0, -2) gives us therefore the y-intercept directly : -2.

by using the already established slope and the point (0, -2) for the y-intercept the equation of our line is

y = 7x - 2

Answer:

The width can either be 4 or 5 feet.

Step-by-step explanation:

Assuming the length is x and the width is y.2x+2y=18xy=202y=18−2xy=9−xx(9−x)=209x−x2=200=x2−9x+200=(x−5)(x−4)x=5and4 The width can either be 4 or 5 feet

By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

It is given that  the total weight of your backpack and its contents is 13 3/8 pounds.

Also given , we want to carry no more than 15 pounds.

Let the number of bottles we can carry be x.

Each bottles weigh 3/4 pounds.

Total weight of the bottles = 3x/4 pounds.

Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .

Thus the statement equation formed is -

⇒ 107/8 + 3x/4 = 15

⇒ 3x/4 = 13/8

⇒ x = 13/6 = 2.166

∴  x ≈ 2

Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

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The commission earned are R41123.17, R47931.67 and R15024.09

The VAT included prices are given as:

R271 800,00; R316 800,00 and R99 300,00.

The VAT rate is 12.36%.

So, the price before VAT is calculated as:

VAT included = Price without VAT * (1 + 12.36%)

This gives

VAT included = Price without VAT * 1.1236

So, we have:

Price without VAT = VAT included/1.1236

For the three cars, we have:

Price without VAT = R271 800.00/1.1236 = R241901

Price without VAT = R316800.00 /1.1236 = R281951

Price without VAT = R99300.00/1.1236 = R88377

Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377

This is calculated as:

Commission = Price * 17%

So, we have:

Commission = R241901 * 17% = R41123.17

Commission = R281951 * 17% = R47931.67

Commission = R88377 * 17% = R15024.09

Hence, the commission earned are R41123.17, R47931.67 and R15024.09

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Step-by-step explanation:

since there are z fishes

the number of angelfish = 1 × z

4

= 1 z

4

The solution of the equation are as follows:

x = 6 and y = -5

4x + 5y = -1

-5x - 8y = 10

Therefore,

20x + 25y = -5

-20x - 32y = 40

-7y = 35

y = -5

Hence,

4x + 5(-5) = -1

4x - 25 = -1

4x = -1 + 25

4x = 24

x = 24 / 4

x = 6

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write sec²x = 1/cos²x in two equivalent forms

sec²x = 1/cos²x

cos²x/cos²x = 1

sec²x = 1 + tan²x

Answer:

8.048 liters

Step-by-step explanation:

Convert 8542 ml to liters:  (8542 ml)(1 liter/1000 ml) = 8.542 liters

Now subtract 0.458 liters to find the amount that a fish tank can hold:

 8.542 liters

-0.458  liters

8.048 liters is the fish tank capacity

Considering right-angled triangle XYW, an approximate ratio WY/WX is equal to: A. 0.34.

Considering right-angled triangle XYW, we would apply the law of cosine to approximate the ratio WY/WX. Mathematically, the law of cosine is given by:

cos(θ) = Adj/Hyp

Where:

Substituting the given parameters into the formula, we have;

cos(θ) = WY/WX

cos(70) = 3.4/10

0.34 = 0.34.

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Complete Question:

Right triangles 1-2 and 3 are given with all their angle measures and approximate side lengths.

Use one of the triangles to approximate the ratio WY/WX

A. 0.34

B. 0.94

C. 1.06

D. 2.76​

The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

In the question,

The function is [tex]B(x) = 0. 06x^2 - 0. 2x^3[/tex]

To find the maximum or minimum, take the derivative and set it equal to zero.

⇒ [tex]B'(x) = 2(0. 06)x - 3(0. 2)x^{2}[/tex]

Setting it equal to zero, we get

⇒ [tex]0.12x - 0.6x^{2}=0[/tex]

⇒ 0.6x (0.2-x) = 0

⇒ x = 0 or x = 0.2

Now substitute x = 0.2 in B(x), we get

⇒ [tex]B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}[/tex]

⇒ B(0.2) = 0.0024 - 0.0016

⇒ B(0.2) = 0.0008

To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.

For x = 1,

⇒ [tex]B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}[/tex]

⇒ B(1) = 0.06-0.2

⇒ B(1) = -1.04

For x = 0.01,

⇒ [tex]B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}[/tex]

⇒ B(0.01) = 0.000006 - 0.0000002

⇒ B(0.01) = 0.0000058

Thus, x = 0.2 is the maximum.

Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

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Let [tex]n=abcba[/tex] be such a number. If 18 divides [tex]n[/tex], then both 2 and 9 divide [tex]n[/tex].

To be divisible by 2, we must have [tex]a\in\{2,4,6,8\}[/tex]. Meanwhile we can have [tex](b,c)\in\{0,1,2,\ldots,9\}^2[/tex].

To be divisible by 9, we the sum of the digits of [tex]n[/tex] must itself be divisible by 9, or

[tex]2a+2b+c=9k[/tex]

for some integer [tex]k[/tex].

The largest value of [tex]2a+2b+c[/tex] is 2•8 + 2•9 + 9 = 43, so we must have [tex]k\in\{1,2,3,4\}[/tex].

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If [tex]k=1[/tex], then [tex]2a+2b+c=9[/tex], and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 [tex](n = 20502)[/tex]

• If [tex]k=2[/tex], then [tex]2a+2b+c=18[/tex] and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 [tex](n = 23832)[/tex]

• If [tex]k=3[/tex], then [tex]2a+2b+c=27[/tex] and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 [tex](n = 27972)[/tex]

• If [tex]k=4[/tex], then [tex]2a+2b+c=36[/tex] and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 [tex](n = 68886)[/tex]

18% of the milk mixture and how much of the cream mixture should he use.

A dairyman wants to combine milk with 5 percent butterfat and cream with 75 percent butterfat to create a 56-liter combination. Butterfat should make up 53% of the final combination.

Let x represent the volume of MILK required for the combination, in liters.

Consequently, x/56 is the PROPORTION of milk in the mixture. [because the final mixture has 56 liters in total]

We require 56 - x liters of CREAM in the mixture because we have 56 liters overall in the mixture.

The PROPORTION of cream in the combination is therefore equal to (56 - x)/56.

Our goal is for the final mixture to have 75% butterfat.

Fill in the equation with each of these values to obtain:

50 = (x/60)(5) + ((60 - x)/60) (75)

Add 56 to both sides to get: 3000 = (5)(x) + (56 - x)(75)

The formula is:

Multiply both sides by 56 to get: 3000 = (5)(x) + (56 - x)(75)

Expand: 3000 = 5x + 4200 - 75x

Simplify: 3000 = 4200 - 70x

Subtract 4500 from both sides: -1300 = -70x

Solve: x = (-1300)/(-70) = (1300)/(70) = 130/7

If you don't want to divide 130 by 7, you can evaluate this quickly by first realizing that 30/7 = 18.

Consequently, 130/7 must be a little larger than 18.

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For a proportional relationship, the constant is found dividing all values of y by each respective value of x.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

The constant can be represented as follows:

[tex]k = \frac{y}{x}[/tex]

Hence the constant is found dividing all values of y by each respective value of x.

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Answer:

alan = 2 = 2x = 16

becky = 3 = 3x = 24

charlie = 4 = 4x = 32

Step-by-step explanation:

add 2 3 4 =

9

72 ÷ 9 = 8

alan = 2 = 2x = 16

becky = 3 = 3x = 24

charlie = 4 = 4x = 32

It is determined while using the binomial distribution that there is still a 1.145=114.5% chance that she produces no more than 11 of them.

There are just two possible results for each throw. Either she succeeds or she fails. The binomial probability distribution is employed to answer this issue since the probability of completing a shot is regardless of all other throws.

Binomial probability distribution-

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]C_{n,x} = n!/x! (n-x)![/tex]

where,

the no. of success= x

the no. of trials = n

the probability of a success on one trial = p

The probability of throwing not more than 11 will be:

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

Where,

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]P(X=0) = C_{18,0} .(0.689)^{0}(0.311)^{18}[/tex]≈0

[tex]P(X=1) = C_{18,1} .(0.689)^{1}(0.311)^{17}[/tex]≈0

[tex]P(X=2) = C_{18,2} .(0.689)^{2}(0.311)^{16}[/tex]≈0

[tex]P(X=3) = C_{18,3} .(0.689)^{3}(0.311)^{15}[/tex]≈0

[tex]P(X=4) = C_{18,4} .(0.689)^{4}(0.311)^{14}[/tex]≈0

[tex]P(X=5) = C_{18,5} .(0.689)^{5}(0.311)^{13}[/tex]= 0.0003

[tex]P(X=6) = C_{18,4} .(0.689)^{6}(0.311)^{12}[/tex]=0.0016

[tex]P(X=7) = C_{18,7} .(0.689)^{7}(0.311)^{11}[/tex]=0.0062

[tex]P(X=8) = C_{18,8} .(0.689)^{8}(0.311)^{10}[/tex]=0.0188

[tex]P(X=9) = C_{18,9} .(0.689)^{9}(0.311)^{9}[/tex]=0.0463

[tex]P(X=10) = C_{18,10} .(0.689)^{10}(0.311)^{8}[/tex]=0.9232

[tex]P(X=11) = C_{18,11} .(0.689)^{11}(0.311)^{7}[/tex]=0.1488

So,

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

=0+0+0+0+0+0.0003+0.0016+0.0062+0.0188+0.0463+0.9232+0.1488 =1.145

Therefore, she makes 1.145=114.5% probability, no more than 11 of them.

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