If llm and m<6 = 4x - 15 and m<7 = x + 30, then m<6=

Answer:

pop music of 90

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

given

x + 2y + 6 = 0 ( subtract x + 6 from both sides )

2y = - x - 6 ( divide terms by 2 )

y = - \(\frac{1}{2}\) x - 3 ← in slope- intercept form

with gradient m = - \(\frac{1}{2}\) and y- intercept c = - 3

Answer:

a = 2x

b = 3

Step-by-step explanation:

Consider the sum of cubes identity

a³ + b³ =(a + b)(a² -ab +b²)

for the polynomial 8x³ +27, we factorise

8x³ + 27

∛8 = 2

∛8 = x

∛27 = 3

Therefore, we can say that :

8x³ + 27 = (2x)³ + 3³

Using this: a³ + b³ =(a + b)(a² -ab +b²)

We can say that

a = 2x

b = 3

To confirm that: a = 2x and b = 3 we factorise 8x³ + 27

= (2x)³ + 3³

= (2x + 3)((2x)²− 2x × 3 + 3²)

= (2x + 3)(4x² - 6x + 9)

= 8x³ - 12x² +18x + 12x² - 18x + 27

= 8x³ + 27

Therefore, a = 2x and b = 3 is correct.

=

The expression in terms of cosine is (1 - cos^2(x))^2

From the question, we have the following parameters that can be used in our computation:

sin^4(x)

This can be expressed as

sin^4(x) = (sin^2(x))^2

As a general rule:

sin^2(x) = 1 - cos^2(x)

Using the above as a guide, we have the following equation

sin^4(x) = (1 - cos^2(x))^2

Hence, the solution is (1 - cos^2(x))^2

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Answer:

Step-by-step explanation:

-3√(4)(10)  - √(16)(10)

-3(2)√(10) - 4√(10)

-6√(10) - 4√(10)

-10√(10)

The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\)  is an integer is 686.

We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer

To find the smallest positive integer n such that  \($\sqrt[4]{56 \cdot n}$\)   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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Answer:

m∠A = 78°

Step-by-step explanation:

The question tells us these angles are supplementary meaning they will add up to 180°. We can use the information to make an equation.

m∠A + m∠B = 180

3x + 18 + 5x + 2 = 180

8x + 20 = 180

8x = 160

x = 20

Now we can substitute the solution for x to find the measure of ∠A.

m∠A = 3(20) + 18

m∠A = 60 + 18

m∠A = 78

Answer:

3

Step-by-step explanation:

x^2=7/3x+2

3^2=7/3(3)+2

9=7+2

9=9

Explanation

Formula to be used,

Solution,

Putting all the values, we get

v=u + at

⇒0 = u + (-0.5) × 20

⇒-u=-0.5 × 20

⇒u = 10 m/s

Hence, the initial velòcity of the car is 10

city of the car is 10m/s.

Now, the distance covered,

v²-u² = = 2as

⇒ (0)²-(10)² = 2 × (-0.5) × s

⇒-100 = - 1s

⇒ s = 100 m

Hence, the distance covered is 100 m.

The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.

From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:

= 0.5π / 180

= 0.008727 radians

Distance from the sun = 150 × 10^6

The physical diameter of the sun will be:

= 150 × 10^6 × 0.008727

= 1309000km

The difference between the diameters will be:

= 1390000 - 1309000

= 8.1 × 10^4.

The percentage of difference will be:

= (8.1 * 10^4) / 1390000 × 100

= 5.8%

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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a) the slope is 40, in this case, it represents that for each day that passes, the balance increases by $40.

b) slope-intercept form is:

y = 40*x + 600

In standard form it is:

y - 40x = 600

In point-slope form is:

y - 720 = 40*(x - 3)

c) f(x) = 40*x + 600

d) After 7 days the balance is $880

By using the given table, we can see that the first two pairs are:

(0, 600) and (3, 720).

With the quotient between the difference of the y-values and the difference of the x-values we can find the slope:

Slope = (720 - 600)/(3 - 0) = 120/3 = 40

So the slope is 40, in this case, it represents that for each day that passes, the balance increases by $40.

b) The equation of the line in the slope-intercept form is:

y = 40*x + 600

In standard form it is:

y - 40x = 600

In point-slope form is:

y - 720 = 40*(x - 3)

c) Using the slope-intercept form we can write:

y = f(x) = 40*x + 600

d) We just need to evaluate the function above in x = 7

f(7) = 40*7 + 600 = 880

The balance after 7 days is $880.

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Answer:

Step-by-step explanation:

40-20 =20 then times 3 which is 60.

ANSWER

320 mL

EXPLANATION

Let x be the amount of the 65% dextrose solution. The original solution contained 480 mL of a 20% solution and the amount x we take from that solution, is the same amount we have to add of the 65% solution to obtain the 50% concentration required.

The amount of the 20% solution left in the bag will be (480 - x). The 20% of this amount plus the 65% of x should be equal to the 50% dextrose in the final 480 mL solution. We have to solve the equation,

Apply the distributive property to eliminate the parenthesis and solve the product on the right side of the equation,

Add like terms,

Subtract 96 from both sides,

And divide both sides by 0.45,

Hence, to get a 50% dextrose solution we have to replace 320 mL of the original solution with a 65% dextrose solution.

Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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The value of the x in the circle is 17.

'

The angle measure of the central angle is congruent to the measure of the intercepted arc.

Therefore, let's find the value of x.

Hence,

180 - 3x(angle on a straight line) = 7x + 10

180 - 3x = 7x + 10

add 3x to both side of the equation

180 - 3x = 7x + 10

180 - 3x + 3x = 7x + 3x + 10

180 = 10x + 10

180 - 10 = 10x

170 = 10x

x = 170 / 10

x = 17

Therefore,

x = 17

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Answer:

The y-intercept is -700

The y-intercept represents the initial amount of expenses.

Explanation:

The y-intercept of the graph is the point where the graph crosses the vertical axis. In this case, it is also the value of the profit when the number of tickets sold is 0.

Therefore, the answers are:

The y-intercept is -700

The y-intercept represents the initial amount of expenses.

Option a: Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price

Given,

Braxton’s average monthly usage of lotion = 8 ounces

The amount of two different brands of lotion are given:

Brand A: 24 ounces for $3.30

Brand B: 40 ounces for $4.60

We have to find the monthly savings of Braxton if he purchases the brand that has the lowest price per ounce versus the highest price:

We have to calculate amount for one ounce for the two brands given:

Brand A:

24 ounces for $3.30

Amount for one ounce = 3.30/24

Amount for one ounce = $0.1375

Brand B:

40 ounces for $4.60

Amount for one ounce = 4.60/40

Amount for one ounce = $0.115

Now, we have to calculate the amount for 8 ounces.

Brand A:

8 x 0.1375 = 1.1

$1.1 for 8 ounces of Brand A lotion.

Brand B:

8 x 0.115 = 0.92

$0.92 for 8 ounces of Brand B lotion.

Now, we have to calculate the savings:

Brand A – Brand B

1.1 – 0.92 = 0.18

That is, Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price.

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The exterior angle of the triangle is 62°.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Let us take the triangle as ABC.

Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].

We know that sum of all angles in triangle is add upto 180° Then,

=> \(m\angle A+m\angle B+m\angle C\)=180

=> 43°+3x°+180-5x+3=180°

=> -2x=180-180-43-3

=> -2x=-46

=> x=13°

Now exterior angle ,

=> 5x-3

=> 5*13-3

=> 65-3

=> 62°

Hence the exterior angle of the triangle is  62°.

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Answer:

4x - 10< 14

4x < 14 + 10

4x < 24

x < 6

from the answer c is the correct option.

Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

- BRAINLIEST answerer ❤️

Answer:

$20

Step-by-step explanation:

This is assuming all of the other games cost an equal amount, but if he bought Cyberpunk 2077 for $60, he would have had $80 left which left him to buy four $20 games.

140 - 60 = 80

80 / 4 = 20

Hope this helps.

Brainliest?

Answer:

$20

Step-by-step explanation:

$20 times 4 is $80 and $80+$60 is $140

Without using any calculus:

If x + y² = 5, then y² = 5 - x, so that

b = x y² = x (5 - x) = 5 x - x²

Complete the square to get

b = 25/4 - (x - 5/2)²

Then b gets a maximum value of 25/4 when x = 5/2.

Simple calculus method:

With b = 5 x - x², differentiate b with respect to x and set the derivative equal to 0 to solve for critical points:

db/dx = 5 - 2 x = 0   ==>   x = 5/2

Take the second derivative to determine whether b is concave or convex:

d²b/dx² = -2

The second derivative is negative, which means b is concave with respect to x, and this indicates x = 5/2 is the site of a local maximum, which is b (5/2) = 25/4.

More complicated calculus method:

Lagrange multipliers. The Lagrangian is

L (x, y, λ) = x y² - λ (x + y² - 5)

where we assume λ ≠ 0.

Take its derivatives:

dL/dx = y² - λ

dL/dy = 2 x y - 2 λ y

dL/dλ = x + y² - 5

Set each derivative equal to 0 to find the critical points. The first equation tells us y² = λ, and the second equation tells us x = λ, so

x + y² - 5 = 2 λ - 5 = 0

Solving this gives λ = x = y² = 5/2, so that b has an extreme value of

b = (5/2) (5/2) = 25/4

Deciding whether this is a maximum or minimum comes down to computing the Hessian determinant at the critical value. The Hessian is

\(H(x,y)=\begin{bmatrix}\dfrac{\partial^2b}{\partial x^2}&\dfrac{\partial^2b}{\partial x\partial y}\\\\\dfrac{\partial^2b}{\partial y\partial x}&\dfrac{\partial^2b}{\partial y^2}\end{bmatrix}=\begin{bmatrix}0&2y\\2y&2x\end{bmatrix}\)

with determinant |H (x, y)| = -4 y². At the critical point, the determinant is -10 < 0, which indicates a maximum value of 25/4.

Answer:

3/4y +5/3 = x

Step-by-step explanation:

y = 4(3x-5)/9

Multiply each side by 9

9y = 4(3x-5)/9*9

9y = 4(3x-5)

Divide each side by 4

9/4 y = 4/4 (3x-5)

9/4y = 3x-5

Add 5 to each side

9/4y +5 = 3x-5+5

9/4y +5 = 3x

Divide by 3

9/4 y *1/3 +5/3 = 3x/3

3/4y +5/3 = x

Answer:

yavonee can read 25 pages in 50 minutes with the same rate.

Step-by-step explanation:

calcuate how may pages does yavonee read in 1 minute

14/28

= 1/2 or 0.5

0.5 * 50

= 25

In 50 minutes Yavonee can read 100 pages with a unit rate of 2 pages per minute.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Yavonee reads 14 pages in 28 mins.

∴ In 1 minute she reads (28/14) = 2 pages.

So, In 50 minutes she can read (2×50) = 100 pages.

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the mοnthly periοdic interest rate, rοunded tο the nearest hundredth οf a percent is (C) 1.31%

Any lοans and bοrrοwings cοme with interest. the percentage οf a lοan balance that lenders use tο determine interest rates. Cοnsumers can accrue interest thrοugh lending mοney (via a bοnd οr depοsit certificate, fοr example), οr by making a depοsit intο a bank accοunt that pays interest.

We must divide its yearly percentage rate (APR) by 12 tο determine a mοnthly periοdic interest rate (the number οf mοnths in a year).

Hence, the periοdic interest rate fοr each mοnth is:

15.75% / 12 = 1.3125%

The result οf rοunding tο the clοsest hundredth οf such a percent is:

1.31%

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