ANSWER INCLUDED: What is the solution of log3x + 4 4096 = 4?

x=-1

x=0

x=4/3

x=3

We solve for x by simplifying both sides of the equation, then isolate the variable.

ANSWER:

C (x=4/3)

Answer:

50050050

Step-by-step explanation:

There is a 50% chance for the coin to either land on heads or tales so you divide 100100100 by 2 to get 50050050 this would work with anything else say you need to figure out the chance of a coin landing on heads and the coin flips 550 times to figure out the chance you do 550 divided by 2 and you get 225. But anyways the answer is 50050050. the reason you divide by two is because the coin has 2 sides, if it were a dice, for instance, you would divide by 6 because it has 6 sides

Answer:

90 cents

Step-by-step explanation:

If a crate holds 48 bottles and you want to make exactly $34 on selling them, before you find out exactly how much to charge for each bottle, you have to subtract the amount you paid for the crate from the profit.  The unknown here is the cost per bottle that you have to make in order to reach your goal of $34.  If you have 48 bottles of water and you want to know how much to charge PER bottle, the algebraic expression for that would be 48x.  Now from that profit of 48x you need to subtract the $9.20 and set it equal to what you'd like to earn:

48x - 9.20 = 34.00

Solve this by adding 9.2 to both sides, and then dividing by 48.  That gives you a cost per bottle of 90 cents.  Plug .90 in for x in the equation above and see that the left side does indeed equal the right side.

To make a profit of $34 per crate along with the original cost of $9.20, the concession stand should charge $0.90 per bottled water.

The question is asking for the price the concession stand should charge per bottle of water in order to make a profit of $34.00 per crate. We start by determining the total desired income from each crate, which is cost plus profit ($9.20 cost + $34.00 profit = $43.20 total income per crate). Next, we divide the total income per crate by the number of bottles in each crate, which is 48. So, $43.20 / 48 = $0.90. Therefore, the concession stand should charge customers $0.90 per bottle of water to achieve the desired profit of $34.00 per crate.

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[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{small}{large}\qquad \stackrel{ratio}{\cfrac{3}{4}}\qquad \qquad \cfrac{3}{4}=\stackrel{areas}{\cfrac{\sqrt{a}}{\sqrt{100}}}\implies \cfrac{3}{4}=\cfrac{\sqrt{a}}{10}\implies 30=4\sqrt{a} \\\\\\ \cfrac{30}{4}=\sqrt{a}\implies \left( \cfrac{30}{4} \right)^2=a\implies \cfrac{900}{16}=a\implies \cfrac{225}{4}=a[/tex]

The area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Let's suppose the area of the smaller figure is x

Area of larger figure = 100 square units

The ratio of the areas:

= x/100

We also have:

Two similar figures have a side ratio of 3:4

= 3/4

Square it we will get ratio of the area

= 9/16

x/100  =  9/16

x = 900/16  = 225/4 or 56.25 square units

Thus, the area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.

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Answer:  The correct option is (A) [tex]5x^2-2x+4.[/tex]

Step-by-step explanation:  We are given to select the polynomial that represents the following difference :

[tex]D=(8x^2+9)-(3x^2+2x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the required difference, we need to subtract the coefficients of the same powers of the unknown variable x.

From (i), we get

[tex]D\\\\=(8x^2+9)-(3x^2+2x+5)\\\\=8x^2+9-3x^2-2x-5\\\\=(8-3)x^2-2x+(9-5)\\\\=5x^2-2x+4.[/tex]

Thus, the required difference is [tex]5x^2-2x+4.[/tex]

Option (A) is CORRECT.

Answer:

  136

Step-by-step explanation:

The two scales are supplementary, so the value on the second scale is ...

  180° -44° - 136°

Answer:

251.047804213 miles

Step-by-step explanation:

c1 t=3.5+1     speed 40 mph

c2 t=3.5       speed  50 mph

c1 40 *4.5= 180

c2 50 *3.5= 175

a^2+ b^2= c^2

180^2+175^2=c^2

32400+30625=c^2

63025=c^2

251.047804213=c

Answer:

It is 188 miles

Step-by-step explanation:

This is correct on Odyssey :)

Variance = 864

Standard Deviation= 29.4

Answer:

Standard Deviation = 29.40

Variance = 864

Step-by-step explanation:

A contractor records all of the bedroom areas, in square feet of a 5 bedroom house as : 100, 100, 120, 120, 180

To calculate the standard deviation first we have to calculate the mean of the data

( 100 + 100 + 120 + 120 + 180 ) / 5

= 620 / 5 = 124

Then for each number subtract the mean and square the result :

-24, -24, -4, -4, 56

square the result = 576, 576, 16, 16, 3136

Now work out the mean of these squared differences.

( 576 + 576 + 16 + 16 + 3136 ) / 5 = 4320 / 5 = 864

This value is Variance, so the variance = 864

Now we take the square root of 864 to get standard deviation

[tex]\sqrt{864}[/tex] = 29.39 rounded to 29.40

Standard Deviation = 29.40

Variance = 864

Answer: 240 minutes should be it

Answer:

Step-by-step explanation:240 minutes should be it

Answer:

3/40

Step-by-step explanation:

3/8 numbers less than four

1/5 chance for brown

And=Multiplication

Or=Addition

3/8×1/5=3/40

[tex]\bf \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[cos(\alpha)+isin(\alpha)]}{r_2[cos(\beta)+isin(\beta)]}\implies \cfrac{r_1}{r_2}[cos(\alpha - \beta)+isin(\alpha - \beta)] \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \begin{cases} z1=9[cos(225^o)+i~sin(225^o)]\\\\ z2=3[cos(45^o)+i~sin(45^o)] \end{cases}\implies \cfrac{z1}{z2}\implies \cfrac{9[cos(225^o)+i~sin(225^o)]}{3[cos(45^o)+i~sin(45^o)]} \\\\\\ \cfrac{9}{3}[cos(225^o-45^o)+isin(225^o-45^o)]\implies 3[cos(180^o)+i~sin(180^o)] \\\\\\ 3[(-1)+i~(0)]\implies -3+0i[/tex]

Answer:

-1

Step-by-step explanation:

Use DeMoivre's Theorem for division of complex polar numbers.  Set it up like this:

[tex]\frac{9(cos225+sin225i)}{3(cos45+sin45i)}[/tex]

The rule is

[tex]\frac{z_{1} }{z_{2} }cis(\theta_{1}-\theta _{2} )[/tex]

Our z1 is 9 and our z2 is 3, so the division of those gives you 3.  The subtraction of the angles 225 - 45 = 180, therefore:

3 cis 180° = 3(cos 180 + sin 180 i)

The cos of 180 is -1 and the sin of 180 is 0, so 3(-1 + 0) = -3

Answer:

[tex]\frac{6}{\pi }[/tex] or 1.9099

Step-by-step explanation:

Look for y values at each of those given values of "x" and apply the slope formula.  When x = pi. y = -1 so the coordinate is [tex](\pi,-1)[/tex].  When x = 3pi/2, y = 2 so the coordinate is [tex](\frac{3\pi }{2},2)[/tex]

Plug those values into the slope formula:

[tex]\frac{2-(-1)}{\frac{3\pi }{2}-\pi}[/tex]

You need a common denominator of pi:

[tex]\frac{3}{\frac{3\pi-2\pi}{2} }=\frac{3}{\frac{\pi }{2} }[/tex]

Do the math on that to get a slope of [tex]\frac{6}{\pi } =1.9099[/tex]

You can do substitution 2x-2=x^2 -x -6; isolate all terms on one side 0= x^2 -x-2x -6+2; combine like terms x^2 -3x -4=0; factor the quadratic (x-4)(x+1)=0; each term is zero x-4=0 so x=4 and x+1=0 so x=-1. Now, y=2•4-2=6 and y=2•(-1) -2= -4 ; solutions for the system are ( 4,6) and ( -1, -4)

Answer:

(4,6) or (-1,-4)

Step-by-step explanation:

since both equations about x are equal to y, you can make x^2-x-6=2x-2

solve this quadratic equation, you get x=4 or -1

substitute x into y=2x-2

you get y=6 when x=4, or y= -4 when x=-1

In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.

So, in your case, we have

[tex]\sin(Z) = \dfrac{XY}{XZ}[/tex]

In order to find XY, we have

[tex]XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24[/tex]

So, the ratio for the sine is

[tex]\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}[/tex]

Answer:

Experiment, observational study, survey

Step-by-step explanation:

The first one is an experiment.  The vet selects random samples and compares the effects of the injection to the nose drips.

The second one is an observational study.  The reaction of the dogs to the treats is being observed.

The third one is a survey.  The owners are given specific questions to answer.

The terms 'survey', 'experiment', and 'observational study' are methods of data collection in mathematics, specifically in statistics. A 'survey' collects data systematically from a group of individuals, an 'experiment' tests hypotheses in controlled conditions, and an 'observational study' records data without influencing the subjects of the study.

The terms 'survey', 'experiment, and 'observational study' represent distinct methods of data collection in statistics. A survey is a data collection tool used to gather information about individuals systematically. An experiment involves carrying out a procedure under controlled conditions to test a hypothesis. An observational study refers to a study where researchers observe and record data without influencing the subjects of the study.

Now let’s identify each of the provided situations:

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The new graph will go down 4 point so y coordinate will go down 4. (-6,5) becomes ( -6, 1)

The corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a point (-6, 5) is on graph of f(x) find the corresponding point for the function f(x)-4

As we know, if f(x) is subtracted by 4 the function f(x) will go down by 4 units.

The corresponding point on the function f(x)-4 will be:

= (-6, 5-4)

= (-6, 1)

Thus, the corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).

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I got 64 square feet.

My work is shown in the image.

For possible questions:

1: you can find x+7 and x-2 because the sides of the square can be measured as x, and x+7 means 7 more than the original; x-2 means 2 less than the original.

2: solved via factoring. Not sure if you've learned it or not.

3: reject the negative numbers because you can't have negative sides in a square.

Area of rectangle is multiplication of length and width.

Original area of square will be 64 square feet.

Let us consider the each side of square is x feet.

Since, one dimension is increased by 7 feet and the other is decreased by 2 feet . then, it become a rectangle have length (x + 7) and width (x - 2) feet.

Area of resulting rectangle = (x + 7)(x - 2)

                  [tex](x + 7)(x - 2)=90\\\\x^{2} +5x-104=0\\\\x^{2} +13x-8x-104=0\\\\x(x+13)-8(x+13)=0\\\\(x-8)(x+13)=0\\\\x=8,x=-13[/tex]

Since, length can not be negative. So  x = 8 feet

Original are of square =  [tex]x^{2} =8^{2}[/tex]

                                     = 64 square feet

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Answer:

[tex]\frac{63}{55}[/tex]

Step-by-step explanation:

Evaluate by substituting x = - 7 into f(x) and value obtained into g(x)

f(- 7) = (- 7)² + 6 = 49 + 6 = 55

g(55) = [tex]\frac{55+8}{55}[/tex] = [tex]\frac{63}{55}[/tex]

Answer:

The simplified form is -26x^2 + 56x -15

Step-by-step explanation:

We need to solve the expression:

3x(-2x+7)-5(x-1)(4x-3)

Multiplying the terms outside the bracket with the terms inside the bracket.

=-6x^2+21x-5(x(4x-3) -1(4x-3))

= -6x^2+21x-5(4x^2-3x-4x+3)

= -6x^2+21x-5(4x^2-7x+3)

Now multiply -5 with the terms inside the bracket

= -6x^2+21x -20x^2 +35x -15

Now, Combining the like terms:

= -6x^2 -20x^2 +21x+35x -15

Adding the like terms

= -26x^2 + 56x -15

So, the simplified form is -26x^2 + 56x -15

Answer: [tex]-26x^2+56x-15[/tex]

Step-by-step explanation:

The first  step is to apply Distributive property.

You also need to remember the Product of powers property, which states the following:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Applying these properties:

[tex]3x(-2x+7)-5(x-1)(4x-3)=\\=-6x^2+21x-5(4x^2-3x-4x+3)\\=-6x^2+21x-20x^2+15x+20x-15[/tex]

And finally, you need to add the like terms.

Therefore, you get:

[tex]=-26x^2+56x-15[/tex]

Answer:

338 in

Step-by-step explanation:

Tangents to a circle from an external point are congruent, thus counting from the bottom left in a clockwise direction gives

perimeter = 98 + 22 + 22 + 27 + 27 + 22 + 22 + 98 = 338 in

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

4 = Red

3 = Blue

2 = White

1 = Yellow

What is probability that it is not yellow ?

[tex]\frac{9}{10}[/tex]

Because only 1 marble is yellow and they are 9 other colours apart from yellow it must be [tex]\frac{9}{10}[/tex]

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

Probability of an event occurring is

P = [tex]\frac{outcomerequired}{total outcomes}[/tex]

P( yellow) = [tex]\frac{1}{10}[/tex]

P( not yellow ) = 1 - [tex]\frac{1}{10}[/tex] = [tex]\frac{9}{10}[/tex]

Answer:

3

Step-by-step explanation:

1 person eats 2/5 of a pizza

6 people eat 2/5 * 6 pizzas

But what value is 2/5 * 6?

You could do it this way

12/5 = 2 2/5

This number is telling you that you need 2/5 of a pizza over 2.

The group should order 3 pizzas. There will be left overs, but that won't matter. Everyone will get at least 2/5 of a pizza.

Answer:

D) None are true

Step-by-step explanation:

- Data sets with influential points can be linear or nonlinear.

- Influential points can increase the coefficient of determination.

- Outliers are influential only if they have a big effect on the regression equation.

Hope his helps

-Amelia

In regression analysis, statement III is not true. All outliers are not necessarily influential data points. And statement II is not always true

Hence, option I is correct.

Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the appropriate technique of data collection and the use of those samples in the appropriate analysis process in order to effectively create the results. In short, statistics is an important procedure that assists in making data-driven decisions.

Since we know that,

A point with a significant residual is considered an outlier.

An influential point is one that has a significant impact on the regression. Surprisingly, these are not synonymous. A point can be an outlier without having any influence. Without being an anomaly, a point can be influential.

Therefore,

statement I can be true - data sets with influential points can indeed be non-linear.

And statement II is not always true - influential points can either increase or decrease the coefficient of determination, depending on whether they are positively or negatively correlated with the response variable.

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Answer:

Step-by-step explanation:

6 of 30 chose Glow in the Dark

That is 1/5 of the students

Out of 200, 40 would choose glow in the dark

40 is 1/5 of 200

The answer is 40

Out of 200, 40 students should Janis expect to choose Glow-in-the-Dark as their favorite theme.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

6 of 30 chose Glow in the Dark.

So, if there are 200 middle school students then the number of students choose Glow-in-the-Dark as their favorite theme

= 6/30 x 200

= 1/5 x 200

= 40

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[tex]-(x^2+24x+144)=12y+12...[/tex]Answer:

(-12, 8)

Step-by-step explanation:

The standard form of this parabola, the one we can use to determine the vertex coordinates and the value of p is:

[tex](x-h)^2=4p(y-k)[/tex]

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus.  We need that p value to determine how far above the vertex the focus is.  In this case, the focus will lie on the same x-coordinate as the focus, we just need to find how far that distance away is.  That requires us to do some algebraic gymnastics on that original equation.  Putting it into vertex form.

Begin by multiplying everything by 12 to get rid of the pesky fraction:

[tex]12y=-x^2-24x-12[/tex]

Now we need to complete the square.  The easiest way to do this is to have just the x terms on one side of the equals sign and everything else on the other side, so we will add 12 to both sides:

[tex]-x^2-24x=12y+12[/tex]

The leading coefficient when you complete the square has to be a positive 1; ours is a negative 1, so factor out the negative:

[tex]-(x^2+24x)=12y+12[/tex]

The rules for completing the square are as follows:  Take half the linear term (ours is a 24), square that half, then add it into the parenthesis.

Half of 24 is 12 so

[tex]-(x^2+24x+144)=12y+12[/tex]

BUT...since this is an equation, if we add something to one side we have to add it to the other side too.  BUT we didn't just add in a 144, we have to take into account the -1 sitting outside the parenthesis that will not be ignored. So we didn't add in 144, we added in -1(144) which is -144.

[tex]-(x^2+24x+144)=12y+12-144[/tex]

What we have done on the left by completing the square is to create a perfect square binomial.  Rewriting it as such and combining like terms on the right:

[tex]-(x+12)^2=12y-132[/tex]

Don't forget the purpose of this is to find the value of p.  We're almost there.  On the right, factor out a 12:

[tex]-(x+12)^2=12(y-11)[/tex]

From this we can determine the coordinates of the vertex and the value of p.  The vertex sits at (-12, 11).  

The equation for p is 4p = 12 so p = 3

That means that the focus is 3 units below the vertex on the same x coordinate.  The focus then is at (-12, 8)

Answer:

Step 1: x^2 + 8x + 15 + 1 = 0 + 1

Step 2: x^2 + 8x + 16 = 1

Step 3: (x + 4)^2 = 1

Step-by-step explanation:

You want the constant on the left to be the square of half the x-coefficient.

  (8/2)^2 = 4^2 = 16

You already have a constant that is 15, so you need to add 1 to both sides of the equation. That is the Step 1 shown here. Step 2 is simplifying the result of Step 1. Step 3 is rewriting the trinomial as the square of a binomial.

Answer:

Step 1 x2 + 8x + 15 + 1 = 0 + 1

Step 2 x2 + 8x + 16 = 1

Step 3 (x + 4)2 = 1

Step-by-step explanation:

took the test

Yes, all cubes are similar.

Similarity in geometry refers to the property where two shapes have the same shape but not necessarily the same size. In the case of cubes, all cubes share the same shape characteristics: they have six square faces, with each face having four equal sides and all angles being right angles. The only difference between one cube and another is their size, or the length of their sides. Similarity does not depend on size; it is solely based on shape. Therefore, regardless of how large or small a cube is, it maintains its geometric properties and thus, all cubes are similar to each other. This means any two cubes you pick, regardless of their size, will be similar as they share these fundamental properties.

Answer:

∠C=90°

∠A=67°

∠B=23°

Step-by-step explanation:

For angle C:

  Thales' Theorem states that an angle inscribed across a circle's diameter is always a right angle.

  Therefore, since AB is the diameter(hypotenuse) then angle C is the right angle. (90°)

For Angle A:

  The measure of arc BC= 134 degrees. We can just use a formula for an inscribed triangle. ∠A = 1/2 (mBC)

  ∠A= (1/2)134

  ∠A= 77°

For angle B:

  All triangle angles all add up to 180. We can just subtract angles A and C from 180°:

  ∠B = 180-(90+67)

  ∠B = 23°

Answer:

1,595.34

Step-by-step explanation:

A=33

2a2=3·3

2·24.782≈1595.34454

Answer:

80 ft²

Step-by-step explanation:

The area of the path is equal to the area of the overall square minus the area of the garden.

Area of a square is the side length squared:

A = s²

The overall square has a side length of 12 feet.  The side length of the garden is 12 - 2 - 2 = 8 feet.  So the area of the path is:

A = 12² - 8²

A = 144 - 64

A = 80

The area of the path is 80 ft².

Final answer:

To find the cost for each call minute, set up a system of equations and solve for x and y. The cost per call minute for Scott is approximately $0.087, and the cost per call minute for Maria is approximately $0.072.

Explanation:

To find the cost for each call minute, we can set up a system of equations using the given information. Let's assume the cost per call minute for Scott is x and for Maria is y. The total cost for Scott is 95x + 207y = $23.55, and the total cost for Maria is 162x + 124y = $17.26.

Using these equations, we can solve for x and y. After solving, we find that the cost per call minute for Scott is approximately $0.087, and the cost per call minute for Maria is approximately $0.072.