Using the constant if proportionality, write an equation that represents this proportional relationship. Let x be the number of kilograms, and let y be the number of inches.

Given:

Consider the expression is

[tex]\log_63+\log_68-\log_64[/tex]

To find:

The value of given expression.

Solution:

We have,

[tex]\log_63+\log_68-\log_64[/tex]

Using properties of logarithm, we get

[tex]=\log_6(3\times 8)-\log_64[/tex]       [tex][\because \log_am+\log_an=\log_amn][/tex]

[tex]=\log_6(24)-\log_64[/tex]

[tex]=\log_6\left( \dfrac{24}{4}\right)[/tex]       [tex][\because \log_am-\log_an=\log_a\dfrac{m}{n}][/tex]

[tex]=\log_66[/tex]

[tex]=1[/tex]                    [tex][\because \log_aa=1][/tex]

Therefore, the value of given expression is 1.

(C) 1 is the correct answer.

Answer:

210

Step-by-step explanation:

You can multiply 52 by 4 which is 208.

Next, you can add that to the number 2 which is 210.

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Answer:

Question incomplete

Step-by-step explanation:

Answer:

0$

Hope this helped ;)

Answer:It would be -54

Step-by-step explanation:

Because you deposited money into the account so you will add -27 and 27 to get -54.

Answer:

23

Step-by-step explanation:

Hope this helps

Answer:

23

Step-by-step explanation:

9 + 8 × 3 - (5 × 2)

9 + 8 × 3 - (10)

9 + 24 - 10

33 - 10

23

Answer: 50

Step-by-step explanation:

Formula for sample size(n) if population standard deviation [tex](\sigma)[/tex] is known:

[tex]n=(\dfrac{\sigma\times z_c}{E})^2[/tex] , E = Margin of error , [tex]z^c[/tex] =  Critical z-value

As per given,

[tex]\sigma= 128[/tex] kilowatt-hours.

Critical z-value for 90% confidence = 1.645

E =  30

Required sample size : [tex]n=(\dfrac{128\times1.645}{30})^2=(7.01867)^2[/tex]

[tex]=49.2617285689\approx50[/tex]

Hence,  the smallest sample size to provide a 90% confidence interval for the population mean with a margin of error of 30 or less = 50

Answer:

See below

Step-by-step explanation:

All of the sides are the same length so all of the angles are the same in this equilateral triangle....each is 60°

60 = 2.5 x + 6

54 = 2.5 x

x = 21.6 °

Answer:

124200

Step-by-step explanation:

i think this is the answer

Answer:

124200

Step-by-step explanation:

Answer:

no table

Step-by-step explanation:

Answer:

angle = 48 supplement = 132

Step-by-step explanation:

Answer:

angle 48 and supplement 132

Answer:

40 degrees

Step-by-step explanation:

It would be 40 degrees because every triangle will add up to 180 degrees. Angle Q and R are equal (pulled from the sign that the two lines from P are equal) So 180 - 70 = 110 - 70 = 40

The measure of angle P is 55 degrees.

The given image is an isosceles triangle. An  isosceles triangle is a three sided polygon that has two equal angles. Angles in a triangle add up to 180 degrees.

The triangle is an  isosceles triangle because of the two lines on the triangle.

<p + <r + <q = 180 degrees

70 + <r + <q = 180

<r + <q = 180 - 70

<r + <q = 110

<r + <q = 110/2 = 55

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Answer:

X=29°

Step-by-step explanation:

Since triangles ABC and DEC are congruent, Angle A = Angle D = 74°

Sum of all angles in a triangle is 180°

So, Angle A + Angle B + Angle C =180°

74°+2X+48°=180°

2X=180°-122°

2X=58°

X=29°

======================================================

Explanation:

When it comes to congruence statements like this, the order of the letters is important. This is so we pair up the letters properly.

ABC has A first, B second, C third

DEC has D first, E second, C third

So we have these pairings

Which leads to

Due to the fact that congruent triangles have congruent corresponding parts.

Since B = E and B = 2x, we can say that E = 2x by either substitution or the transitive property. Both effectively say the same thing.

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

Now focus on triangle CDE

The three angles we have are

Those three angles add to 180. This is true for any triangle.

C+D+E = 180

48+74+2x = 180

122+2x = 180

2x = 180-122

2x = 58

2x = 58/2

x = 29

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

Side note: since x = 29, this means angle B = 2x = 2*29 = 58, and this is the measure of angle E as well.

We can check the answer by doing C+D+E = 48+74+58 = 180. So we have confirmed the answer.

Answer:

the answer is -3 1/4

Step-by-step explanation:

The additive Inverse of 3 1/4​ will be - 3 1/4.

Suppose that the given function is [tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

We are given the number as;

3 1/4​ = 13/4

Therefore, the additive Inverse of 3 1/4​ will be;

Negative 13/4 = - 3 1/4

Hence, the additive Inverse of 3 1/4​ will be - 3 1/4.

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Answer:

Step-by-step explanation:

A

Answer:

First table

Step-by-step explanation:

It will be the first table as on the other ones there is two of the same X

Answer:

251,000$

Step-by-step explanation:

This question is incomplete, the complete question is;

Find the volume of the described solid of revolution or state that it does not exist.

The region bounded by ​f(x) = x⁻⁷ and the​ x-axis on the interval ​[ 1​,​ ∞) is revolved about the​ x-axis.  

Answer: volume of the cubic units is π/13

Step-by-step explanation:

Given that;

​f(x) = x⁻⁷  

in the image, Area of ring = πR²

we substitute

Area = π (x⁻⁷)²

= π(x⁻¹⁴)

Now

Volume = ₁∫^∞ π(x⁻¹⁴) dx

= [ -π/13  x⁻¹³ ]₁^∞

= 0 + π/13

= π/13

therefore volume of the cubic units is π/13

Answer:

5 capsules

Step-by-step explanation:

A doctor may prescribe Keflex for an ear infection. One capsule = 0.250 g of Keflex. The recommended daily dose for a child is (40.0mg of Keflex)/(kg that the child weighs).

Step 1

We convert the capsules form grams to milligrams

1 gram = 1000 milligrams

0.250grams = x

Cross Multiply

x = 0.250 × 1000 milligrams

x = 250 mg

Hence, 1 capsule = 250 mg

How many Keflex capsules would a 69-pound child take for one daily dose? (Round to the nearest whole number of capsules) Given: 1 pound = 0.453592 kg

The recommended daily dose for a child is (40.0mg of Keflex)/(kg that the child weighs).

The child weighs 69 pounds

1 pound = 0.453592 kg

69 pounds = x kg

Cross Multiply

x kg = 69 × 0.453592kg

x kg = 31.297848kg

Hence,

1 kg= 40.0 mg

31.297848 kg = x

x = 31.297848 × 40.0mg

x = 1251.91392mg

Therefore, the child would take 1251.91392 mg

From the first calculation we know that:

1 capsule = 250 mg

250mg = 1 capsule

1251.91392 mg = x capsules

250mg × x = 1251.91392 mg × 1 capsule

x = 1251.91392 mg/250mg

x = 5.00765568 capsules

Approximately = 5 capsules

Hence, a child that weighs 69 pounds takes 5 capsules of keflex

Answer: (-5,1)

Step-by-step explanation:

−2.5x+y=13.5

−2.5x+y+2.5x=13.5+2.5x(Add 2.5x to both sides)

y=2.5x+13.5

Step: Substitute

5x+13.5  and 2.25x−y=−12.25:

2.25x−y=−12.25

2.25x−(2.5x+13.5)=−12.25

−0.25x−13.5=−12.25(Simplify both sides of the equation)

−0.25x−13.5+13.5=−12.25+13.5(Add 13.5 to both sides)

−0.25x=1.25

−0.25=1.25−0.25(Divide both sides by -0.25)

x=−5

Step: Substitute−5forxiny=2.5x+13.5:

y=2.5x+13.5

y=(2.5)(−5)+13.5

y=1(Simplify both sides of the equation)

Answer:

x = -4, y = 3.5

Step-by-step explanation:

-2.5x + y = 13.5 ------ (1)

2.25x - y = -12.25 ---(2)

you can substitute (1) into (2) or vice versa

We are going to substitute (2) into (1)

but first we have to rewrite it in terms of x or y

Lets do y

from (2), (after subtracting -2.25x from both sides), y = 12.25 + 2.25x ----(3)

plug in (3) into (1)

-2.5x + (12.25 + 2.25x) = 13.5

-2.5x + 12.25 + 2.25x = 13.5

-2.5x + 2.25x = 13.5 - 12.5

-0.25x = 1

x = -(1/.25)

x = -4

Now we have x

We already used (2), lets plug in x = -4 into (1)

-2.5(-4) + y = 13.5

10 + y = 13.5

y = 13.5 - 10

y = 3.5

−2(7−y)+4=−4

Simplify −2(7−y)+4.

2y−10=−4

Move all terms not containing y to the right side of the equation.

2y=6

Divide each term by 2 and simplify.

y=3

When they distributed the 2 they did -2×y but it was supposed to be -2×-y, which equals a positive 2y

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Answer:

Which two ratios represent quantities that are proportional?

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Step-by-step explanation:

Can u please answer my recent question!!!!!

Answer:

A or C

Step-by-step explanation:

Answer: The population is 523 and the sample is 112.

Step-by-step explanation:

In statistical parlance, a population is referred to as all the entire individuals or subject which makes up a certain group of interest. In the scenario above, the group of interest refers to the consumers who buys the vitamin brand each month. Hence, the population encompasses all the buyers for for a particular month which sums up to 523 customers.

The sample is a subset culled from the population. It refers to a smaller group of individuals or subject which are chosen by a sampling method from the entire population. In the scenario above, the number of randomly selected consumers who were sent surveys are the sample. The fact that not all those who were sent surveys responded does not change the fact that they were randomly selected from the larger population pool and will hence be considered to be a part of the sample.Hence the sample is 112.

Answer:

x=9

Step-by-step explanation:

f(x) = −(x − 7)2 + 4

(substitute f(x) = 0)

0= −(x − 7)2 + 4

(distribute 2 into brackets)

0= −(2x - 14) + 4

(remove brackets and change the sign of each expression inside the brackets)

0= - 2x + 14 + 4

(add the numbers)

0= - 2x + 18

(move variable to the other side and change its sign)

2x = 18

(divide both sides by 2)

x = 9

The given expression is quadratic, parabolic graph, relative maxima and real zeros. The correct options are (a), (c) and (f).

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given expression is f(x) = -(x - 7)² + 4

Since the degree of the expression is 2, it is quadratic.

The graph of the given equation will be parabolic.

By comparing from the general vertex form (x - h)² + k, its vertex can be found as (7, 4).

Axis of symmetry is x = 7.

y-intercept can be obtained by plugging x = 0 as,

-(0 - 7)² + 4 = 53.

Maxima or minima can be found as below,

f'(x) = 0

⇒ -2(x - 7) = 0

⇒ x = 7

In order to find the solution write the expression as follows,

-(x - 7)² + 4 = 0

⇒ -x² + 14x - 49 + 4 = 0

⇒ x² - 14x + 45 = 0

⇒ x = 5,9

Thus, the equation has real solutions.

Hence, the properties of the given equation are derived as quadratic, parabolic graph, relative maxima and real zeros.

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Answer:

[tex]n = 7\frac{1}{4}[/tex]

Step-by-step explanation:

See attachment for complete question.

From the attachment, we have:

[tex]Length = 4\frac{1}{4}ft[/tex]

[tex]Width = n[/tex]

[tex]Perimeter = 23fr[/tex]

Required

Determine n

Perimeter is calculated as:

[tex]Perimeter = 2(Length + Width)[/tex]

Substitute in values

[tex]23 = 2(4\frac{1}{4} + n)[/tex]

Convert to decimal

[tex]23 = 2(4.25 + n)[/tex]

Open Bracket

[tex]23 = 8.5 + 2n[/tex]

Collect Like Terms

[tex]2n = 23 - 8.5[/tex]

[tex]2n = 14.5[/tex]

[tex]n = 14.5/2[/tex]

[tex]n = 7.25[/tex]

[tex]n = 7\frac{1}{4}[/tex]

Answer: 73

Step-by-step explanation: