Simplify the following expression by combining like terms: 4(6m + 4) - 2m

The value of function after differentiation will be;

⇒ dy/dx = 2 / (x log3)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ y = log ₃ 2x²

Now,

Since, The function is,

⇒ y = log ₃ 2x²

Differentiate with respect to x, we get;

⇒ dy/dx = 1 / (2x² log3) × d/dx (2x²)

             = 1 / (2x² log3) × 4x

             = 2 / (x log3)

Thus, The value of function after differentiation will be;

⇒ dy/dx = 2 / (x log3)

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Answer: 450

Step-by-step explanation:

300--12

 x   --18

[tex]x=300*18/12[/tex]

x=4350

The simplest form of the given expression, √196b^12, is 14b⁶

From the question, we are to simplify the given expression to its simplest form

The given expression is

√196b^12

The given expression can be written as ]

√196 × √b^12

14 × √b^12

From one of the laws of indices, we have that

√x^y = x^(y/2)

Thus, the expression becomes

14 × b^(12/2)

14 × b^6

14 × b⁶

14b⁶

Hence, the simplest form is 14b⁶

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The 98% confidence interval estimating the difference in mean shoulder condition score one year after such interventions in the population of patients with persistent shoulder pain is given by:

(-2.5, 5.1).

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error of the distribution of differences is given as follows:

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm ts[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 72 + 65 - 2 = 135 df, is t = 2.35.

Then the bounds of the interval are:

The missing information is given by the image shown at the end of the answer.

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The probability that a student is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

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The equation which represents the relationship between X values and Y values can be found by deriving the equation of line using slope intercept form. The equation of line is 3x - 5y = 25.

How to find equation of line using slope intercept form?

Equation of line using slope intercept form is y = mx + b

where m is slope of the line and b is y-intercept

The slope intercept can be used to form equation of line using two points on the line.

According to the given question:

The two points which lie on the line are (x, y) = (5, -2) and (x', y') = (0, -5)

Slope of the line m = y' - y/x' - x

                               = (-5 +2)/(0 - 5)

                               = 3/5

Now y intercept b = y - mx

                              = -2 - (3/5. 5)

                              = -5

Therefore the required equation of line is y = 3/5x - 5

On simplifying further 3x - 5y = 25

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Your answer would be C

a)Perimeter of given right angle triangle is 48.

Perimeter of dilated right angle triangle is 192.

b) Area of given figure is 96cm²

Area of figure after dilation is 1536cm².

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given,

Triangle given,

Base = 12

hypotenuse = 20

Leg =  16

Dimensions of new triangle after dilatated by scale factor of 4:

Base = 48

hypotenuse = 80

Leg = 64

Area of right angled triangle:

Base × Leg/2

Area of given figure:

12 × 16/2

12 × 8

96

Area of given figure is 96cm²

Area of figure after dilation:

48 × 64/2

24 × 64

1536

Area of figure after dilation is 1536cm².

Perimeter of right angle triangle:

Perimeter of given figure:

12 + 20 + 16

48

Perimeter of given right angle triangle is 48.

Perimeter of dilated figure:

48 + 80 + 64

192

Perimeter of dilated right angle triangle is 192.

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[tex] \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}[/tex]

Step-by-step explanation:

[tex] \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54[/tex]

An ungrouped frequency distribution would be ineffective because there is a large number of stories, hence they should be grouped into ranges.

A frequency distribution gives the percentages/proportions of each outcome in a distribution.

These frequencies distributions are classified as follows:

The measures in this problem are given by the image at the end of the answer, and we can see that there is a small amount of repeating values, they are in interval ranges, hence an ungrouped frequency distribution would be ineffective.

The list with the number of stories in the buildings is given by the image at the end of the answer.

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Answer:

(x+4)( 8x^{2}+1)

Step-by-step explanation:

:)

Answer:

28

Step-by-step explanation:

W = 3; L = 11

2W + 2L = 2(3) + 2(11) = 6 + 22 = 28

Answer:

28

Step-by-step explanation:

2(3)+2(11)

6+22

28

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The maximum number of knives Yaritza needed 7

According to the question,

Number of knives Yaritza needed to order  for restaurant at least 326 knives

Currently they have knives = 222 knives

One set of knife contain = 15 knives

The remaining amount of knives restaurant needed = 326 - 222

= 104 knives

The remaining amount of knives needed = 104 knives

If each set on sale contains 15 knives, the number of sets Isabella will need will be: 104 / 15

= 6.9333

This shows that maximum 7 set of knives Yaritza is needed to fulfill their demand for restaurant.

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The differentiation of the given function will be y' = 2xy (log 2).

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

[tex]\rm y = 2^{x^2}[/tex]

Take log on both sides, then we have

log y = x² log 2

Differentiate the function with respect to 'x', then we have

(1/y) y' = (log 2) 2x

y' = 2xy (log 2)

The differentiation of the given function will be y' = 2xy (log 2).

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Answer:

It is a little hard to read.  I cannot read the last choice,. but the two above it are correct

Step-by-step explanation:

When you raise an exponent to an exponent, you multiply the exponents

[tex]18^{\frac{15}{8} }[/tex]

[tex]18^{5x\frac{3}{8} }[/tex]

It takes 8 months for the investment to grow to $6000 if interest was compounded quarterly.

What is compound interest?
The interest charged on a loan as well as deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound as well as simple interest is this.

Given:

Principal amount = $5000

Annual amount interest = 2.6%

Compounded quarterly = 4

Final amount = $7000

Formula:

A = P(1 + r)^4n - 1

A is the quarterly compounded interest.

P would be the principal amount.

r is the quarterly compounded rate of interest.

n is the number of periods.

Solving it:

7000 = 5000 (( 1 + 0.026))^ 4t -1

7/5 = (( 1 + 0.026))^ 4t

7/5 = (1.026)^ 4t -1

ln (7/5) = 4t ln (1.006) - ln 1

t = 7.61 months

t ~ 8months

Hence, it takes 8 months for the investment to grow to $6000 if interest was compounded quarterly.

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Answer: x = - 10

Step-by-step explanation:

    We will use the equation given, substitute -1,000 in for y, and solve.

y = x³

(1,000) = x³

[tex]\sqrt[3]{ (1,000)} = \sqrt[3]{x^3}[/tex]

- 10 = x

x = - 10

The sales of raincoats next month is 140.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). By examining how the variables vary in relation to one another, correlation evaluates the association or relationship between two variables. Simultaneous changes in two variables are also described by statistical correlation, which is typically illustrated by linear relationships.

Given:

As, from the figure The type of correlation is Positive correlation.

and, when x= 70 the value of y is 140.

So, the sales of raincoats next month is 140.

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Answer:

if F = Gm^1(m^2)d^-2 is the formula for this question, the answer to question A. would be:  G = 6.67 x 10^17 N KG^2/KM^2

Step-by-step explanation:

Brainliest Please?

The sum of n terms of expression a is 4940 and b is 9405.

a.

5+6+7....+95

d = 6 - 5

d = 1

This expression is in arithmetic progression.

a = 5

n = 95

sum of n terms = n/2(2a+(n-1)d)

= 95/2(2*5+(95-1)1)

= 95/2(10+94)

= 95/2*104

= 95*52

= 4940.

b.

5+7+9....+95

d = 7 - 5

d = 2

This expression is in arithmetic progression.

a = 5

n = 95

sum of n terms = n/2(2a+(n-1)d)

= 95/2(2*5+(95-1)2)

= 95/2(10+94*2)

= 95/2*188+10

= 95/2*198

= 95*99

= 9405.

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Answer:

2794 m^2

Step-by-step explanation:

Area of Triangle - Area of Circle

1/2bh - piR^2

4050 - 1256

= 2794

Answer:

- sinu

Step-by-step explanation:

using the difference identity for sine

sin(a - b) = sinacosb - cosasinb

then

sin(u - π )

= sinucosπ - cosusinπ

= sinu(- 1) - cosu(0)

= - sinu - 0

= - sinu

∠(3x+7)° and ∠(10x- 22)° are the same side interior angles or supplementary angles thus x will be 15.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given angles,

∠(3x+7)° and ∠(10x- 22)° are supplementary angles.

∠(3x+7)° + ∠(10x- 22)° = 180°

3x + 10x + 7 - 22 = 180

13x = 180 +15

x = 15

Hence "∠(3x+7)° and ∠(10x- 22)° are the same side interior angles or supplementary angles thus x will be 15".

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As per the angle sum property, the interior angles that form the triangle is option

B. 60, 60, 60°

C. 40.50,90°

D. 30.60.90*

Angle sum property

Angle sum property states that the sum of all the interior angles of the triangle is equal to 180 degrees.

Given,

Here we have the list of interior angles

A. 45, 45, 45*

B. 60, 60, 60°

C. 40.50,90°

D. 30.60.90*

E. 90,90°, 45°

F. 90, 90, 90°

Now, we have to find in which for these angle will form the tringle.

As per the definition of the angle sum property, the sum of all the interior angle of the triangle is 180°.

Based on these we have to verify each of the given interior angles,

A) 45 + 45 + 45 = 135

B. 60 + 60 + 60 = 180

C. 40 + 50 + 90 = 180

D. 30 + 60 + 90 = 180

E. 90 + 90 + 45 = 225

F. 90 + 90 + 90 = 270

Therefore, based on these values we have identified that the options (B), (C), and (D) forms the triangle.

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The condition that is it preferable to use stratified random sampling rather than simple random sampling is C. The population can be divided into a large number of strata so that each stratum contains only a few individuals

Stratified sampling is a method of sampling from a population that can be divided into subpopulations in statistics. When sampling subpopulations within an overall population in statistical surveys, it may be advantageous to sample each subpopulation independently.

Stratified random sampling is a sampling method that divides a population into smaller subgroups known as strata. Strata are formed in stratified random sampling, or stratification, based on members' shared attributes or characteristics, such as income or educational attainment.

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Answer:

5.35

Step-by-step explanation:

Answer:

5.35 meters

Step-by-step explanation:

To find the answer, you divide the length value by 100

Answer:

The ordered pairs that are solutions for 3x - y = 1 would be:

A. (-2, -7)

B. (-1, -4)

D. (3, 8)

Explanation:

For A. (−2, −7); we have;

3(-2) − (-7) = 1

-6 + 7 = 1

1 = 1 ..... Solution

For B. (−1, -4); we have;

3(-1) − (-4) = 1

-3 + 4 = 1

1 = 1 ..... Solution

For C. (0, 1); we have;

3(0) − (1) = 1

0 - 1 = 1

-1 = 1 ..... No Solution

For D. (3, 8)

3(3) - (8) = 1

9 - 8 = 1

1 = 1..... Solution

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May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Each radical expression;

i)⁴√ (-5)⁴ ∛-5³  = 25

ii) ⁵√128 = 2 √2

iii) ⁶√729 = 3

If the following circumstances apply, a radical expression is said to be in standard form:

1. A positive radicand exists.

2. There is the least amount of radical index conceivable.

3. Each radicand factor's exponent is a natural integer lower than the radical index.

4. The radicand has no fractions.

5. A fraction's denominator has no radicals.

i)⁴√ (-5)⁴ ∛-5³

= -5 * -5

= 25

ii) ⁵√128

= ⁵√2 * 2 * 2 * 2 * 2 * 2

= 2 √2

iii) ⁶√729

=  ⁶√3 * 3 * 3 * 3 * 3 * 3

= 3

Hence, the radical expressions are 25, 2 √2, 3.

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The amount that Leo has earned as interest, given the amount that Leo deposited, and the compounding period, is $2, 945.12

First, find the weekly rate on the account:
= Annual rate / Number of weeks in a year

= 2.5 % / 52

= 0.048 %

The number of periods is:

= Number of years x Weeks per year

= 13 x 52

= 676 weeks

The amount  that Leo would have earned after 13 years is:

= Deposit x ( 1 + rate) ^ number of periods

= 7, 671.12 x ( 1 + 0.048%) ⁶⁷⁶

= $10, 616.24

The interest earned is:

= Amount earned - Amount deposited

= 10, 616.24 - 7, 671.12

= $2, 945.12

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