Solve the following inequality. Graph the solution set and write it in interval notation . 11x < 10x + 6

Answer:

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

hope this helped:)

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The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Here, we have,

The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.

Factors of 54: 1,2,3,6,9,18,27 and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.

To find the factors of a number, 54, we will use the factorization method.

To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.

54 ÷ 1 = 54

54 ÷ 2 = 27

54 ÷ 3 = 18

54 ÷ 6 = 9

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The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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Answer:

thanks for the points

Step-by-step explanation:

Answer:

W=13.2

Step-by-step explanation:

W-9.96=3.24

Add both sides by 9.96

W=13.2

1. Solution of the rational equation \(\frac{x}{3} -6=\frac{9}{3}\)   is x = 27

How is the equation solved?

\(\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27\)

2.The two numbers = 2, 6

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x+ y =8 --- (1)

1/x+1/y = 2/3 ---(2)

Considering (2),

\(\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6\)

Substituting  x in (1)

We have,

When x = 2 ; y= 6

When x = 6 ; y = 2

So, the two numbers = 2, 6

3. The two numbers = 3, 9

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x- y =6 --- (1)

1/y -1/x = 2/9 ---(2)

Considering (2),

\(\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9\)

Since x and y are whole numbers we will have y = 3

When y = 3 ; x=9 (substituting in (1))

So, the two numbers = 9,3

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Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

i had this in rsm a long time ago, i think the answer(if it's an equation) should be:

6x + x = 7x

yeah sorry i forgot scream scream

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

im 100% sure i hope this helps :)

Answer:

\(4x + 12 = 60 \\ 4x = 60 - 12 \\ 4x = 48 \\ x = \frac{48}{4} \\ x = 12\)

=> 12 IՏ Tᕼᗴ ᑕOᖇᖇᗴᑕT ᗩᑎՏᗯᗴᖇ.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

Answer:

its the first two

It is possible that the population mean is 3.53, but the sample result is greater than that due to sampling variability.

It is possible that the school administrator made a mistake, and the population mean is greater than 3.53.

Step-by-step explanation:

edg 2021

Answer:

A

B

Step-by-step explanation:

EDG 2020-2021

Answer:

a = 35°

Step-by-step explanation:

The sum of the measure of the given three angles add up to 180°.

To find the m < a:

m < a + 90° + 55° = 180°

m < a + 145° = 180°

Subtract 145° from both sides to isolate m < a:

m < a + 145° -  145° = 180° -  145°

m < a = 35°

The equation of the axis of symmetry of the quadratic function is given by y = -2x² + 8x - 5.

x = 4 is the x-coordinate of the vertex.

x = 0 and x = 4 are the x-coordinates of the x-intercepts.

y = -5 is the y-coordinate of the y-intercept.

A quadratic function has two variables that can be used to model real-world problems. It has a distinct shape of a parabola, which is a symmetrical U-shaped curve.

The coordinates of the vertex of the function can be calculated by taking the derivative of the given equation and setting it equal to 0.

This yields x = 4 as the x-coordinate of the vertex.

Substituting this value in the given equation gives us the y-coordinate of the vertex, which is y = 11.

The coordinates of the x-intercepts of the function can be found by setting y = 0 in the given equation.

This yields x = 0 and x = 4 as the x-coordinates of the x-intercepts. Substituting these values in the given equation gives us the corresponding y-intercepts, which are

y = -5 and y = 0 respectively.

The coordinates of the y-intercept of the function can be found by setting x = 0 in the given equation.

This yields y = -5 as the y-coordinate of the y-intercept.

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Answer:

point p. ok. vrvxfff77t.

Answer: 1/6

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

Answer:

29. x=5

30. a=7

31. r=8

32. c=4

33. w=3

34. m=9

Step-by-step explanation:

Hope this helps.

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

straight line

Step-by-step explanation:

because of y=mx+c

Answer:

I believe it's either C. or D.

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

False

Step-by-step explanation:

63 x 42= 2646

216 x 16= 3456

have a great day

Answer:

m∠2 = 53°

Step-by-step explanation:

We will use two properties of a rhombus to solve this problem.

1). Opposite angles of a rhombus are equal.

2). Diagonals bisect the angles.

Since ∠JFG and ∠JHG are the opposite angles of the rhombus,

m∠JFG = m∠JHG

Since, diagonal FH bisect ∠JHG,

m∠FHJ = m∠GHF = m∠JFH = m∠GFH = 37°

In triangle JFH,

m∠FHJ + m∠JFH + m∠HJF = 180°

37° + 37° + m∠HJF = 180°

m∠HJF = 180 - 74

            = 106°

Since, diagonal GJ bisects angle HJF,

m∠FJG = \(\frac{106}{2}\) = 53°

Therefore, m∠2 = 53°.

Answer:

m∠2 = 53*

Step-by-step explanation:

The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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Answer:

distributive

Step-by-step explanation:

distributive

$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

where:

PV is the present value of the annuity

PMT is the payment amount per period

r is the interest rate per period

n is the total number of periods

In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.

The interest rate per period is 7% / 12 = 0.5833%.

Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833

Solving for PMT, we get:

PMT = PV × r / [1 - (1 + r)⁻ⁿ]

PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]

PMT = $3,244.21

Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

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Answer:

Suppose that you have a square of side length x, the area of this square will be:

A = x^2.

Now, by dynamics, we know that the position of an object that is falling down from a height H, can be written as:

H(t) = (-g/2)*t^2 + H.

We can see a pattern, x^2 is used in both.

Now, profit can be also modeled with quadratic equations, where our objective is to find the maximum of the quadratic (so we can have the maximum profit)

Then the parent function that is useful for gravity, calculating area and profit is the quadratic function:

f(x) = x^2

Answer:

Step-by-step explanation:

Mean = (11.4 + 13.9 + 11.2 + 14.5 + 15.2 + 8.1 + 12.4 + 8.6 + 10.5 + 17.1 + 9.8 + 15.9)/12 = 12.4

Standard deviation = √(summation(x - mean)²/n

n = 12

Summation(x - mean)² = (11.4 - 12.4)^2 + (13.9 - 12.4)^2 + (11.2 - 12.4)^2+ (14.5 - 12.4)^2 + (15.2 - 12.4)^2 + (8.1 - 12.4)^2 + (12.4 - 12.4)^2 + (8.6 - 12.4)^2 + (10.5 - 12.4)^2 + (17.1 - 12.4)^2 + (9.8 - 12.4)^2 + (15.1 - 12.4)^2 = 89.62

Standard deviation = √(89.62/13) = 2.7

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

µ ≤ 15

For the alternative hypothesis,

µ > 15

This is a right tailed test

b) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 12,

Degrees of freedom, df = n - 1 = 12 - 1 = 11

t = (x - µ)/(s/√n)

Where

x = sample mean = 12.4

µ = population mean = 15

s = samples standard deviation = 2.7

t = (12.4 - 15)/(2.7/√12) = - 3.34

We would determine the p value using the t test calculator. It becomes

p = 0.0034

c) Assuming level of significance = 0.05.

Since alpha, 0.05 > than the p value, 0.0034, then we would reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the water from this source does meets the EPA standard. They are higher than 15ppb

Using the t-distribution, we have that:

a)

The null hypothesis is: \(H_0: \mu \geq 15\)

The alternative hypothesis is: \(H_1: \mu < 15\)

b) The p-value is of 0.0051.

c) Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

Item a:

At the null hypothesis, it is tested if the mean is of at least 15 ppb, that is:

\(H_0: \mu \geq 15\)

At the alternative hypothesis, it is tested if the mean is of less than 15 ppb, that is:

\(H_1: \mu < 15\)

Item b:

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

In this problem, we have that \(\mu = 15, n = 12\). Additionally, using a calculator, the other parameters are: \(\overline{x} = 12.38, s = 2.93\)

Hence, the value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{12.38 - 15}{\frac{2.93}{\sqrt{12}}}\)

\(t = -3.1\)

The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.1 and 12 - 1 = 11 df.

Item c:

Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.

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Number of persons to be interviewed = 599.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

To calculate the required sample size for the survey, the formula for a confidence interval for a proportion can be used:

n = (Z-score)²×p×(1-p)/margin of error²

Where:

Z-score = 1.96 (this is the z-score for the 99% confidence level from the z-distribution table)

p = 0.167 (this is the proportion of the sample that hold two or more jobs, 8/48)

margin of error = 0.03 (this is the margin of error you have specified)

Therefore, the required sample size is:

n = (1.96)²×0.167×(1-0.167)/(0.03)²

n = 598.8

To meet your requirements, you should interview 599 persons (rounding up the answer to the next whole number).

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Answer: each base angle in an isosceles right triangle measures 45 degrees.

Step-by-step explanation:

In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).

Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.

To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:

x + x + 90 = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

Answer:

75%

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Answer:

1/2x+10=22

Step-by-step explanation:

"ten more" means +10
"half a number" means 1/2x
"is twenty-two" =22

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)