Question 41 of 53
Which of the following exponential equations is equivalent to the logarithmic
equation below?
x = In 9.45

Answer:

-5

Step-by-step explanation:

Δy =9-7=2

Δx = -12-(-2) =-10

-10/2= -5

the value of X must be more than 8.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

Call the number x, please. Since we know that adding 6 to it will result in a number smaller than 14, x + 6 14.

We obtain x = 14 - 6 = 8 by deducting 6 from both sides.

Therefore, x must be greater than 8.

We can use the following method to find the another in one is given.

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Answer:

Each pound of sugar costs $0.64

Step-by-step explanation:

4x = 2.56     Set up the equation. Divide both sides by 4 to isolate the x.

 x = 0.64

The two expressions that could represent the dimension of the rectangle are x + 2 and x - 7

The area of a rectangle can be represented by the product of its length and width. The formula for the area is given by:

A = l x w

where A is the area, l is the length and w is the width.

If the area is given by the expression x^2 - 5x - 14, then the two expressions for the dimensions can be determined by getting the factors of the expression.

x^2 - 5x - 14 = (x + 2)(x - 7)

Therefore, the dimensions of the rectangle can be expressed as x + 2 and x - 7.

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Whether the two ratios are 2: 3 and 2: 3 or a proportion

4: 6 and 12: 18

[tex]$\frac{4}{6}$[/tex]   and

[tex]$\frac{12}{18}=\frac{2}{3}$[/tex]   and

2/3

=2: 3 and 2: 3

Yes the given two ratios form a proportion.

The complete question is:

Check whether the given two ratios form a proportion or not: 4: 6  12: 18

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The required solution of the quadratic equation is given as x = -2 and -5. Option D is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² + 7x + 10 = 0

Factorize the above expression,

(x + 5)(x + 2) = 0

Now,
x + 5 = 0  ; x + 2 = 0
x = -5        : x = -2

Thus, the required solution of the quadratic equation is given as x = -2 and -5. Option D is correct.

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The integral using integration by parts with the indicated choices of u and dv is equal to,   [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

Basic Power Rule:

f(x) = cxⁿ

f’(x) = c· n xⁿ⁻¹

Integration

Integrals

[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]:              

[tex]\int\limits cf(x)dx[/tex] = c [tex]\int\limitsf(x) dx[/tex]

Integration Rule [Reverse Power Rule]:

[tex]\int\limits x^{n} dx[/tex] = [tex]\frac{x^{n+1} }{n+1}[/tex] + c

Integration by Parts:  

[tex]\int\limits u dv[/tex] = uv - [tex]\int\limits v du[/tex]

Given that,

= [tex]\int\limits 5x^{2} lnx dx[/tex]

Rewrite [Integration Property - Multiplied Constant]:

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]\int\limits x^{2} lnx dx[/tex]

Set u:  

u = [tex]lnx[/tex]

[u] Logarithmic Differentiation:          

du = [tex]\frac{1}{x}[/tex] dx

Set dv:  

dv = [tex]x^{2}[/tex]                                                                                                        

[dv] Integration Rule [Reverse Power Rule]:  

v = [tex]\frac{x^{3} }{3}[/tex]

Integration by Parts:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]( \frac{x^{3}ln(x) }{3} - \int\limits \frac{x^{2} }{3} dx )[/tex]

Rewrite [Integration Property - Multiplied Constant]:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex](\frac{x^{3}ln(x) }{3} -\frac{1}{3} \int\limits x^{2} dx )[/tex]

Factor:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \int\limits x^{2} dx )[/tex]

Integration Rule [Reverse Power Rule]:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \frac{x^{3} }{3} )[/tex] + c

Factor:

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

Therefore,

The integral using integration by parts with the indicated choices of u and dv is equal to,   [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

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The number of different groups of 4 people that a company could send to a job site, which is 27,720.

In the context of this question, a company has 30 people and wants to send 4 people to a job site.

To find out how many different groups of 4 people they could make, we need to use the concept of permutation.

To find the number of permutations, we use the formula nPk, where n is the total number of objects (30 in this case) and k is the number of objects we want to arrange (4 in this case).

So, the number of permutations will be

=> 30P4 = 30!/(30-4)!.

This simplifies to

=> 30!/(26!) = 27,720.

Therefore, the company has 27,720 different groups of 4 people that they could send to a job site. This means that they can send 27,720 different combinations of 4 people from their 30 employees to a job site.

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Answer:

1. B) x = 6

2. No solutions

3. D) x = 4​

4. A) x = -4

Step-by-step explanation:

1. -4x + 8 = -3x + 2

8 = x + 2  ==> add 4x on both sides to move x to one side of the equation

x = 6  ==> subtract 2 on both sides

B. x = 6

2. 9x - 7 = 5x - 19

4x - 7 = -19 ==> subtract 5x on both sides to move x to one side of the

                        equation

4x = -12  ==> add 7 on both sides to isolate x

x = -3  ==> divide 4 on both sides

x = -3 isn't one of the options, so problem 2 has no solutions.

3. 2x - 7 = 5x - 19

-7 = 3x - 19  ==> subtract 3x on both sides to move x to one side of the

                        equation

12 = 3x  ==> isolate x by adding 19 on both sides

x = 4  ==> divide both sides by 3

D. x = 4​

4. -7x + 3 = -3x +19

3 = 4x + 19  ==> add 7x on both sides to move x to one side of the equation

-16 = 4x  ==> subtract 19 on both sides to isolate x

x = -4  ==> divide both sides by 4

A. x = -4

(a) at least 4 people born in the same month,

(b) In order to ensure that at least two persons were born on the same day,

(a)

we have 37 people.

we want to know at least how many were born in the same month.

I would think that at least 4 people had to be born in the same month.

here's why.12 months in a year.

if every 12 people were born in a different month, then out of 37 people, at least 3 people were born in the same month.

first 12 people        1   2  3  4   5  6  7  8  9  10  11   12

second 12 people  1   2  3  4  5   6  7  8   9    10  11  12

third 12 people       1   2  3  4  5  6  7  8  9  10  11  12

remaining 1 person 1

we could have minimum 4 people that were born in the same month,

Hence,  at least 4 people born in the same month,

(b)

 Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

there are 365 days in the year.

You could have 365 people where no two persons were born on the same day, assuming that everyone was born on a different day.

However, the 366th individual would have to share the same birthday as another member of the group.

In order to ensure that at least two persons were born on the same day, the group's minimum size would consequently need to be 366.

The complete question is -

(a) Among 37 people at least how many were born in the same month?

(b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

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A statement could be used to describe the functions include the following: D. the domain of f(x) is (−∞, 0] while the domain of g(x) is [0, ∞).

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

Additionally, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using interval notation, the domain of this function shown in the graph above can be written as follows;

Domain of f(x) = {-∞, 0}

Domain of g(x) = {0, ∞}

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The histogram, time series, box plot, stem and leaf, and frequency polygon.

Dot plots, stem and leaf graphs, histograms, box plots, ogive graphs, and scatter plots are all used to graph numerical data. The dot plot: Stem and leaf: The stem represents the first digit of the number in these graphs, while the leaf/leaves indicate the second digit (s). A histogram or a polygon graph should be used for scores that fall on an interval or ratio scale. A bar is centered above each score (or interval) in a histogram, with the height corresponding to the frequency of that score or interval and the width according to the true boundaries of that score or period.

Scatterplot. Scatter plots are effective for displaying accurate, dense data visualizations, relationships, and groupings between variables.

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The number of orders placed in one quarter of the year and shipped in the next quarter will vary depending on the segment. To determine the exact number, you would need to analyze the data from each segment separately.

To determine the number of orders placed in one quarter of the year but shipped in the next quarter, you will need to analyze the data from each segment separately. Begin by extracting the data from the segment you are interested in and sorting it by order date and ship date. For example, if you are interested in orders placed in Q1 2009 and shipped in Q2 2009, you will need to identify all orders with an order date in Q1 2009 and a ship date in Q2 2009. Once you have identified these orders, you can count them up to determine the total number of orders in the segment that fit this criteria. You can then repeat this process for the other segments to determine the total number of orders placed in one quarter of the year but shipped in the next quarter across all segments.

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Answer:

the number of revolutions that are required to level the playground is 194 revolutions

Step-by-step explanation:

We know that LSA, that is lateral surface area of a cylinder is the area of a rectangular sheet, which when spread onto the ground, covers the area equal to the LSA of the cylinder.

Hence, area covered by the roller in one revolution = area of LSA of cylinder  = 32 cm².

Now, to cover the are of 6200 cm²,

the number of revolutions required  = Total area of the playground/ LSA of the cylinder = 6200/32 = 193.75 = 194

Hence the number of revolutions that are required to level the playground is 194.

Salut/Hello!

Answer: w = 20 cm and l = 28 cm

Step-by-step explanation:
l - length
w - width
P - perimeter
/ - fraction line
=> - results

we know that P = 2 x (l + w)
we also know that our ratio is l/w = 7/5

l/w = 7/5 => l = 7/5 x w
so now we can go back to the perimeter and replace l

96 = 2 x (7/5 x w + w)
96 = 2 x (7/5 x w/1 + w)   Why w/1? - We can't multiply unless w is also in a fraction, so we put it as w/1
96 = 2 x (7w/5 + w)
96 = 2 x (7w/5 + w/1)  and we amplify w/1 with 5
96 = 2 x (7w/5 + 5w/5)
96 = 2 x 12w/5
48 = 12w/5
48/1 = 12w/5
48 x 5 = 12w
240 = 12w
w = 20 cm

with that we can find l
96 = 2 x (l + 20)
48 = l + 20
l = 48 - 20
l = 28 cm

I hope it was helpful! :]

If Brenda plans to reduce her spending by $70 a month, the future value of this reduced spending over the next 12 years is $14710.5.

We are given that Brenda will be saving $70 every month for a period of 12 years.

So, the future value of the annuity formula will be used for the calculation of future value.

Future value = R [( (1 + i)^n - 1 ) / i], where R is the regular payment, i is the interest rate and n is the number of payments

Here R = monthly amount to be saved = $70

i = interest rate = 6/12 = 0.5%

n = Number of payments = 12 x 12 = 144 months

Future value=70 [( (1+0.5%)^144 - 1) / 0.5%] = $14710.5

Hence, the future value of this reduced spending over the next 12 years is $14710.5.

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The numeric value of the function for each case is given as follows:

5. f(-11) = 1841.

6. g(1/3) = 14.78.

7. h(-1/2) = -5/8.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Hence item 5 is solved as follows:

f(-11) = -(-11)³ + 5(-11)² + 9(-11) + 4

f(-11) = 1841.

Item 6 is solved as follows:

g(1/3) = 3(1/3)³ + 6(1/3)² + 12(1/3) + 10

g(1/3) = 14.78.

Item 7 is solved as follows:

h(-1/2) = 9(-1/2)³ - 8(-1/2)² + 11(-1/2) + 8

h(-1/2) = -5/8.

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The proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.

By scaling, we may create a drawing of an item that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are those that have been scaled.

Given that the scale on a map shows that 10 kilometers is represented by 4 centimeters.

We are to find the proportion can be used to find the actual distance, x, represented by 20 centimeters on the map.

We have

4 centimeters on the map = 10 kilometers.

So, 1 centimeter on the map

[tex]1 cm = \frac{10}{4}[/tex]

Also, 20 centimeters on the map = x kilometers.

So, 1 centimeter on the map

[tex]1cm = \frac{x}{20}[/tex]

Equating the two expressions:

[tex]\frac{10}{4} = \frac{x}{20}[/tex]

Therefore, the proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.

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Answer:

y = 8x+3

Step-by-step explanation:

hoping its correct for you

The numeric values for the function f(x) are given as follows:

1. At x = 3: -5.

2. At x = -2: -25/3.

3. At x = 6: -3.

4. At x = 1: -19/3.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, we have a piecewise function, which has different definitions based on the input of the function.

However, all the values at which we want to obtain the numeric value are greater than -4, hence the definition is given as follows:

f(x) = 2x/3 - 7.

The numeric values are found replacing the lone instance of x, hence:

1. At x = 3: 2(3)/3 - 7 = 2 - 7 = -5.

2. At x = -2: 2(-2)/3 - 7 = -4/3 - 7 = -4/3 - 21/3 = -25/3.

3. At x = 6: 2(6)/3 - 7 = 4 - 7 = -3.

4. At x = 1: 2(1)/3 - 7 = 2/3 - 7 = 2/3 - 21/3 = -19/3.

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Answer: 9

Step-by-step explanation:

g + 9 = 18

g = 18-9

  =9

The rate at which the area of the circle is increasing when the radius is 7 m is 527.52 m^2.

We already know that the area of a circle can easily be calculated using the formula -

= A = π(r^2)

So, in order to find out the rate at which it increases, we have to -

= dA/dt = dπ(r^2)/dt

= dA/dt = dπ(r^2)/dr × dr/dt

= dA/dt = 2πr × dr/dt

It has been mentioned that the value of dr/dt is 12 m/s.

So, after using this value, we find that the rate of increase is -

= dA/dt = 2π × 7 × 12

= dA/dt = 527. 52 m^2

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Answer:

a) 144π cm²

b) 248π cm²

Step-by-step explanation:

Using the formula, curved surface area of a cone = πrl where r = radius and l = slant height,

Curved surface area of large cone = π (10) (12 + 3) = π (10)(15) = 150π

Curved surface area of small cone = π(2)(3) = 6π

a) Curved surface area of frustum = 150π - 6π = 144π cm²

b)
The frustum has a top surface which is a circle of radius 2 and a bottom surface which is also a circle of radius 10

The area of a circle is πr²

So Total area of both circles = π(2)² + π(10)² = 4π + 100π = 104π

Total surface area of frustrum = 144π + 104π = 248π cm²

Answer:

Step-by-step explanation:

A triangle adds up to 180 degrees. Thus the answer to this question is

90°, 45°, and 45°.

90°+45°+45° = 180°

Answer:

90°, 45°, and 45°

Step-by-step explanation:

pls tell me if wrong have a good day/night<3

The shape of Banana is taking the shape of a parabola.

a plane curve created when a point moves so that the distance between it and a fixed point or line is equal.

y2=4ax, where is the distance from the parabola's vertex to focus, is the standard equation for a normal parabola.

Several examples of parabolas in real life

The wheel stance in yoga resembles a parabola.

Banana's shape is beginning to resemble a parabola.

A parabola is emerging from the Rainbow.

Antennas with a parabolic dish are resembling a parabola.

Mirror's concave surface.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

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Answer:

1

Step-by-step explanation:

[tex]\cos \left(\arccos \left(\frac{3}{5} \right)+\arcsin(-\frac{4}{5} \right)=\cos(\arccos(3/5))\cos(\arcsin(-4/5))-\sin(\arccos(3/5))\sin(\arcsin(-4/5)) \\ \\ =(3/5)\cos(\arcsin(-4/5))-(-4/5)(\sin(\arccos(3/5)) \\ \\ =(3/5)(3/5)-(-4/5)(4/5) \\ \\ =1[/tex]

Find the multiples of 8 and 12 (multiples of 8 = 8, 16, 24, 32; multiples of 12 = 12, 24, 36, 48) and select the lowest multiple that is precisely divisible by 8 and 12, which is 24.

The LCM of 8 and 12 is 24 regardless of the technique chosen. To obtain this number, the listing technique will display the first three multiples of 8 and the first two multiples of 24. The prime factor technique compares the two numbers’ prime factors and multiplies them together, omitting repeated factors.

The first approach to compute the least common multiple: This is the method we used previously; in other words, we write the initial multiples of each integer, record the common multiples, and pick the least common multiple.

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The number of pencils that each person has is given as follows:

The number of pencils that each person has is obtained by a system of equations, for which the variables are given as follows:

They have a total of 65 pencils, hence:

x + y = 65.

Ana has double Maria's amount plus 10 pencils, hence:

x = 2y + 10.

Replacing x = 2y + 10 on the first equation, Maria's amount is obtained as follows:

2y + 10 + y = 65

3y = 55

y = 55/3

y = 18.

Hence Ana's amount is given as follows:

x = 65 - 18 - 47.

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