Find the Sum.
1/6+2/3=?

Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as  4 = 3x ⁽ˣ⁺²⁾

Which property of log function is used?

The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.

These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.

A log function can be written in exponential form using

logₐ m = x ⇒ m = ax

According to the given question:

The given logarithmic function is

log₍ₓ₊₂₎(4) = 3x

On applying the property we get

4 = 3x ⁽ˣ⁺²⁾

Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾

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Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

we multiply the fractions

1/8 x 12/1

12/8

1 4/8

1 1/2

Hopes this helps please mark brainliest

Answer: the one in blue

Step-by-step explanation:

The correct option for the lines of symmetry of a regular pentagon-

An image of a pentagon's five lines of symmetry is included below.

We can observe from the following photo that the lines for symmetry cut through a vertex angle, a side, and are perpendicular to either a side.

Options C, D, and E are the appropriate choices.

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Complete question is;

Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.

A) Every line connects two vertices.

B) Every line connects the midpoints of 2 sides.

C) Every line bisects a vertex angle.

D) Every line bisects a side.

E) Every line is perpendicular to a side.

Answer:

x=3,x=4

Step-by-step explanation:

(x-3)(x-4)=0

x=3, 4

Answer:

x = 3

x = 4

Step-by-step explanation:

"find the roots" means to find the solutions to the equation.

Roots are solutions are zeros are x-intercepts.

You are being asked to solve the equation.

First, factor the quadratic.

x^2 -7x + 12 = 0

(x - 3)(x - 4) = 0

This works because -3 × -4 is 12 and

-3 + -4 is -7

You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.

So we have

(x - 3)(x - 4) = 0

Separate the two factors into two separate tiny, one-step equations.

x - 3 = 0 , x - 4 = 0

Solve.

x = 3 , x = 4

These are the roots (solutions, zeros and x-intercepts)

When the population of a protozoa develops with a constant relative growth rate of 0.6685 per member per day, and there are two members on the day zero, the population after will consist of 7 at the end of seven days period.

The total population of the protozoa at the end of the seven days can be computed using the calculations given below,

Total Population = Growth Rate x Number of Days + Day zero Population

Total Population = (0.6685 x 7) + 2

Total Population = 6.667, or ~ 7.

Therefore, there will be 7 protozoa at the end of seven days.

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An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.

These steps are used to determine the Z score:

z = (x - μ)/σ

As mentioned in question-

x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Obtain the p-value from normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.

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Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

Answer:

48

Step-by-step explanation:

the ratio of blue cards to yellow cards can be expressed with

4:3.

the total amount of blue and yellow cards can be interpreted as 4x+3x=7x

then you can find the value of x by dividing 84/7, which is 12

since the value of blue cards is 4x, 4(12) = 48

The rate in the height of water changing for the given cylinder is equal to 0.318m/s.

As given in the question,

Change in volume represent the decrease in rate of change of water height in the cylinder in time t

dV/dt = 4m³/sec.

Decrease in volume represent the change in the height of the water

Let 'h' be the height

h = 10m

radius 'r' = 2m

V = πr²h

Rate of change of leaking water only change the height radius remain constant.

⇒V = (3.14)(2²) h

Differentiate both the side with respect to 't' to get the rate of change

dV/dt = (3.14)(4)dh/dt

⇒4 =(3.14)(4)dh/dt

⇒dh/dt = 4/ (3.14)(4)

⇒dh/dt = 0.318 m/s

Therefore, the rate of change of height is equal to 0.318m/s.

The complete question is:

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?

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No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.

This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.

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The factor by which the volume of cube increased is 0.0030

What is a cube ?

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

The fundamental distinction between a cube and a square is that the former has three dimensions—length, breadth, and height—while the latter only has two. A cube is composed of squares, which are a type of 2-dimensional (2D) shape (such as a circle, square, triangle, etc.).

let l be the side of a cube

the new length of cube is l' = 1.001l

Initial volume (v1) = l³

final volume (v2) = (1.001)³l³

The factor by which the volume increased is  = v1 / v2

                                                                           = ((1.001)³l³ - l³)/l³

                                                                           = 0.003003

                                                                           = 3 x 0.001

                                                                           ≅ 0.0030

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Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.

The dimension of the cylindrical container  that will minimize the cost of the container is a radius of 4.371 and a height of 25.85

since we know that the volume of a cylinder is :

355=πr²h, where r is the radius of the base and  h is the height

So, we can say h=355/πr², here we have two circular components with the areas 2A=2πr² , for the cost of   0. 02 cents per cm² and a rectangular  component  of area  A=2πrh , with cost of 0. 03 cents per cm².So the cost function will be :

C=0.02(2πr²)+0.03(2πrh)

C=0.04(πr²)+0.06(πrh), substuting the vale of h  

C=0.04(πr²)+0.06(πr(350/πr²))

C=0.04(πr²)+(21/r), differentiating both sides  we get .

C'=0

=>0.08(πr)-(21/r²)= 0, simplifying the equation we get

=>r= 3√525/2π =4.371

so for h, it will be: 355/π(3√(525/2π))  = 355/π(3√(83.55))  =350/π( 4.371) =25.85

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At 0.01 significance level the hypothesis is rejected.

Null Hypothesis (H₀): The sample data occurs purely from chance.

Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

Given that,

x = 28

s = 2.9

μ = 31

n = 8

α = 0.01

Then, the Null Hypothesis : H₀ = 31

          The Alternate Hypothesis : H₁ < 31

The average number of cigeratte smoker  per day is less than 31.

Test Statistics:

t = x -μ / s√n

   = 28 - 31/ 2.9√8

   = -3/ 8.41

   = -0.356

Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.

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Gregory has 10 ways to choose 3 boxes of cereal.

What do you mean by purchase?

A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.

According to data in the given question,

We have :

The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.

The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.

Use the combination formula:

[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:

[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]

Therefore, the required answer is 10 ways.

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The number of cards in the deck are either a jack or a heart are 17.

What is card deck?

A playing card is a specially made piece of card stock, heavy paper, thin cardboard, paper coated with plastic, cotton-paper blend, or thin plastic that is imprinted with distinctive motifs. To make handling easier, each card frequently has a finish on the front and back.

Given:

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.

We have to find the number of cards in the deck are either a jack or a heart.

Since, there are four Jack in a 52 card deck.

So, one jack can be chosen by 4C1 ways.

Also there are 13 cards of hearts in a 52 card deck.

So, one heart can be chosen by 13C1 ways.

The number of ways = 4C1 + 13C1 = 4 + 13 = 17.

Hence, the number of cards in the deck are either a jack or a heart are 17.

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This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.

The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.

This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.

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We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.

We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).

According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles  △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.

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The confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

On Subtracting 1 from your sample size, we get

330 – 1 = 229.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 229 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(330) = 1.37

Now, 2.262 × 1.37 = 31.06

So, the confidence interval be,

(150 - 31.06 , 150 + 31.06) = (138.94 , 181.06)

Hence, the confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

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Answer:

0.2

Step-by-step explanation:

First part yields 0.008 if you take sqrt((1/25)^3).

Then the cuberoot of 0.008 is 0.2.

Answer:

Look at the attachment! :D

Hope this helps!

Step-by-step explanation:

The amount of the salmon left after Mr Jones used some part is

Total amount of salmon  bought is 6 and 2/7 lb = 6 2/7 lb

The amount used is 1/5 of the amount Mr Jones bought

= 1/5 * 6 2/7

= 44 / 35

= 1 9/35

= 1.257

The amount left is calculated by subtraction

= 6 2/7 - 1 9/35

= 176 / 35

= 5 1/35

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For the square on the diagram, we can see that:

Remember that all the sides of a square have the same length.

Here we know that AC, the diagonal of the square, has a measure of 20 cm.

Then the length of DE, which is half of the diagonal of the square, is half of that, then:

20cm/2 = 10cm

DE = 10cm

DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:

D = √2*S

Then the sidelength is:

S = D/√2

Here we know that the diagonal measures 20 cm, then:

DC = S = 20cm/√2 = 14.14 cm

DC = 14.14cm

Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.

Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°

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[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]

The required number of ways to arrange the letters in the word mississippi so that either all the is are consecutive are 11!/4!2!4!..

factorial, in science, the result of all certain whole numbers not exactly or equivalent to a given positive whole number and meant by that whole number and an interjection point. Subsequently, factorial seven is composed 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is characterized as equivalent to 1.

We have,

All out no. of words = 11

Had all letters been unmistakable, the response would have been =11!. However, as it isn't the case we want a method for diminishing it to consider the way that a portion of its letter sets are same.

In each game plan of the expressions of "mississippi" :

Presently taking into truth the over three focuses decrease 11! by separating it by 4!2!4! also, you have your response.

Thus, required arrangement is 11!/4!2!4!.

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A ball must be fast rolled is 185.2cm/sec, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

Table height = h = 70cm

Distance = s = 70cm

g = 9.8[tex]ms^{-1}[/tex]

Now, we have to find the time of falling,

[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]

Horizontal velocity,

[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]

Therefore, the required answer is 185.2cm/sec.

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The measure of the value of [x] is x = √5/2

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle as shown in the image.

We can write -

sin(30) = x/(√5)

x = √5 sin (30)

x = √5/2

Therefore, the measure of the value of [x] is x = √5/2.

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Answer:

You can draw a picture like this:

Step-by-step explanation:

If we are working with fractions, then think of it as a circle.

3 circles divided by 8 people

(Draw 3 circles divided into eighths)

Now, on the first circle, write the number one into one of the slices.

Do the same to the second circle.

Now the third.

How many slices have the number 1 in it?

3 slices have the number 1 in it.

And each whole circle has 8 pieces.

3 (slices) divided by 8 (People) = 3/8

Fewer families with kids under 18 now have dinner together seven nights a week

Given,

Let p represent the percentage of households with kids under 18 that have supper together every night.

So, Null Hypothesis, : p 38%    (meaning that more or the same number of families with children under the age of 18 now have dinner together seven nights a week.)

Alternate Hypothesis, : p < 38%     {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

T.S.  =    ~  N(0,1)

Where,

p  = sample proportion of families = 403/1122 = 0.36

n = sample of adults with children under the age of 18 = 1122

So,

The test statistics =     -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

 P-value = P(Z < -1.32) = 1 - P(Z  1.32)

= 1 - 0.9066 = 0.0934

We have enough data to reject our null hypothesis since the test statistics will fall in the rejection region because the P-value for our test statistics is less than the level of significance, which in this case is 0.0934 <  0.10.

As a result, we draw the conclusion that fewer families with children under the age of 18 now have supper together seven nights a week.

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