Sam and his friend are working at the body shop. Sam can do the work in 7hours. When his friend is helping him they do the same work in 4 hours. How long does it take Sam's friend to do this work alone?

Answer:

25.5

Step-by-step explanation:

first find the area od the rectangle than the triangle.

to find the area count the number of squares and use A=b*h

than do the same for the triangle using A=.5*b*h

15=3*5

10.5=.5*3*7

10.5+15=25.5

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

3. x= 20.1

4. x = 22.0

Step-by-step explanation:

SohCahToa. S= sin, C= cos, T=tan.

o = Opposite (the side on the other side of the given angle, also referred to as theta.)

h = Hypotenuse (the side on the other side of the right angle, represented as the square thing.)

a = Adjacent (side next to the given angle.)

3. We have opposite = x, adjacent = 24. We can use tan (Toa.)

  tan(40º) = x/24         Multiply both sides times 24.

  x = 24*tan(40º)         Put into calculator

  x = 20.1

4. We have adjacent = 12, hypotenuse = x. We can use cos (Cah.)

  cos(57º) = 12/x         Multiply both sides by x

  x*cos(57º) = 12         Divide by cos(57º)

  x = 12/cos(57º)         Put into calculator

  x = 22.0

Answer:

351.48cm²

Step-by-step explanation:

Heron’s Formula

Find half the perimeter (30+30+26)/2=43

It’s the square root of each side subtracted from 43, multiplied together, times 43.

√(43-30)*(43-30)*(43-26)*43=√13*13*17*43=√=123539=351.481cm²

Area of triangle is, 351. 39 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

All the sides of triangles are,

⇒ 30 cm, 30 cm, and 26 cm

We know that;

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

Where, 's' is the semi perimeter of the triangle, and a, b and c are three sides of triangle.

Here, Sides are,

⇒ a = 30

⇒ b = 30

⇒ c = 26

Hence, We get;

⇒ s = (a + b + c) / 2

⇒ s = (30 + 30 + 26) / 2

⇒ s = 86 / 2

⇒ s = 43 cm

So, The area of triangle is,

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

⇒ Area of triangle = √ 43 (43 - 30) (43 - 30) (43 - 26)

⇒ Area of triangle = √ 43 × 13 × 13 × 17

⇒ Area of triangle = 13 √ 731

⇒ Area of triangle = 13 × 27.03

⇒ Area of triangle = 351. 39 cm²

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The null hypothesis would be H0: p = 0.05. The alternative hypothesis would be Ha: p < 0.05.

When forming hypotheses in this context, we typically state a null hypothesis (H0) and an alternative hypothesis (H1). Here's how you can fill in the blanks:

Null hypothesis (H0): The percentage of U.S. adults who suffer from a mental illness has not changed. H0: p = 0.05

Alternative hypothesis (H1): The percentage of U.S. adults who suffer from a mental illness has decreased. H1: p < 0.05

In this case, "p" represents the percentage of U.S. adults with a mental illness. The social worker will use statistical tests to analyze data and determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Answer: 2/9 divided by 7/9 = 2/7

Step-by-step explanation:

1. Write out the problem on a piece of paper.

2. Change the second fraction, which is 7/9, into a reciprocal fraction (means flipping the 7 and 9 around). Now, our equation has the fraction 9/7 in it.

3. Change the division symbol to a multiplication symbol. Your equation should be 2/9 x 9/7.

4. Solve the equation. You should get the answer of 18/63 without simplification.

5. Simplify. 18/63 = 2/7

Conclusion: 2/7 is the correct answer.

The equation that can be used to tell whether the ball reaches 35 m is:

35 = -5t² + 10t + 22. The roots are imaginary, hence the ball does not reach the height of 35m.

The imaginary roots of quadratic equations that have been represented as complex numbers are known as complex roots. The square root of a negative number is not conceivable and so we change it into a complex number.

The given equation is h(t) = -5t² + 10t + 22.

Given that, the ball reaches the height of 35m.

The equation that can be used to tell whether the ball reaches 35 m is:

35 = -5t² + 10t + 22.

The equation can be written as:

5t² - 10t + 35 - 22 = 0

5t² - 10t + 13 = 0

The quadratic formula is given as:

t = -b ± √b² - 4ac/ 2a

Substituting the values:

5t² - 10t + 13 = 0

t = 10 ± √(10)² - 4(5)(13) / 2(5)

t = 10 ± √-160 / 10

The roots are imaginary, hence the ball does not reach the height of 35m.

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Answer:

Inverse operation

Step-by-step explanation:

Basically it is an operation that reverses the effect of another operation.

Answer:

\(y=\frac{3}{4} x-2\)

Step-by-step explanation:

The line has a positive slope, that much is clear. If we just count from the y-intercept up to the next clear point, we can see that it is 3 up and 4 to the right. That gives us a rise over run of 3 over 4, or \(\frac{3}{4}\).

The y-intercept is -2, so that is the latter half of the equation.

Answer:

multiply 15 by 0.75 and you get $11.25

Answer:

96

Step-by-step explanation:

Let's assume that the marks needed in the next exam is \(x\). Then if the average becomes 90,

\(\frac{80 + 93 + 91 + x}{4}= 90\)

Now we can simply solve for \(x\):

⇒ \(\frac{264 + x}{4}= 90\)

⇒ \(264 + x = 360\)            [Multiplying both sides by 4]

⇒ \(x = 360 - 264\)            [Subtracting 264 from both sides]

⇒ \(x = \bf96\)

Therefore, you need to score 96 in your next exam to have an average of 90 on the four exams.

A required confidential interval is 0.11 ≤ σ ≤ 0.27 when a two-sided 95% confidence interval for the standard deviation.

Given that,

We have to find a two-sided 95% confidence interval for the standard deviation.

We know that,

The data has of size n = 12

That is 2.32, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97, 2.02.

Let S be the sample standard deviation,

S = \(\sqrt{\frac{Z(X_i-\bar X)^2}{n-1} }\)

Here \(\bar X\) is the sample mean

By using the formula we estimate the value of S

Construct 95% confidence interval for population standard deviation σ.

Formula is \(\sqrt{\frac{(n-1)S^2}{X^2_{\frac{\alpha }{2},n-1} } }\leq \sigma\leq \sqrt{\frac{(n-1)S^2}{X^2_{1-\frac{\alpha }{2},n-1} } }\)

Here, n= 12 ⇒ n-1 = 11

c = 95% = 0.95

α =1 -c =1 -0.95 =0.05

\(\frac{\alpha }{2}\) = 0.025 and 1 - \(\frac{\alpha }{2}\) = 0.975

\(X^2_{\frac{\alpha }{2},n-1}\) = \(X^2_{0.025,11}\) = 21.92

\(X^2_{1-\frac{\alpha }{2},n-1}\) = \(X^2_{0.975,11}\) = 3.82

The required confidential interval is

\(\sqrt{\frac{(11)(0.156)^2}{21.92 } }\leq \sigma\leq \sqrt{\frac{(11)(0.156)^2}{3.82 } }\)

0.11 ≤ σ ≤ 0.27

Therefore, A required confidential interval is 0.11 ≤ σ ≤ 0.27 when a two-sided 95% confidence interval for the standard deviation.

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The complete question is not given so the one that appears here is the full question:

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinics follows 2.32, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97, 2.02. Find a two-sided 95% confidence interval for the standard deviation.

The height of the building is approximately 125 feet to the nearest foot.

What is angle of incidence?

The angle of incidence is the angle formed by a ray of light or other wave as it approaches a surface, and a line perpendicular to that surface (known as the normal). It is the angle between the incident ray and the normal

We can use trigonometry to solve this problem. Let's assume the height of the building "h".

First, we need to find the distance between the man's eye level and the ground. We can use tangent function:

tan(85°) = h / 20

Solving for h, we get:

h = 20 * tan(85°)

h ≈ 125.36 feet

Therefore, the height of the building is approximately 125 feet to the nearest foot.

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The function g in vertex form is g (x) = –5x^2 – 3.

In this case, the parent function is:

f (x) = x^2

First, after the reflection across the x-axis, we will get:

f (x) = –f (x)

And, the function will be:

g (x) = –x^2

Then, vertically stretched by a factor of 5, we will get:

g (x) = –5x^2

Last, translated 3 units down, we will get:

g (x) = –5x^2 – 3

Thus, the vertex form of the function g will be:

g (x) = –5x^2 – 3

In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.

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1. The x-axis represents the sample mean (\(\bar x\)), and the y-axis represents the probability density.

2. The probability represents the area under the standard normal curve to the right of z = 2.197.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

a. To depict the sampling distribution of all possible values of the sample mean, we can use a probability distribution graph, specifically a normal distribution graph.

Given that the population mean (µ) is 12 ounces and the population standard deviation (s) is 0.5 ounces, and assuming that the sample size is sufficiently large (n = 30), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as a normal distribution.

The mean of the sampling distribution (\(\mu_\bar x\)) will be the same as the population mean, which is 12 ounces.

The standard deviation of the sampling distribution (\(\sigma_\bar x\)) can be calculated using the formula \(\sigma_\bar x\) = s / √n, where s is the population standard deviation and n is the sample size. In this case, \(\sigma_\bar x\) = 0.5 / √30 ≈ 0.091 ounces.

Using these values, we can plot a normal distribution curve with the mean at 12 ounces and the standard deviation of 0.091 ounces. The x-axis represents the sample mean (\(\bar x\)), and the y-axis represents the probability density.

b. To find the probability of selecting a sample of 36 cans with a sample mean greater than 12.2 ounces, we need to calculate the area under the sampling distribution curve to the right of 12.2 ounces.

First, we need to standardize the value of 12.2 ounces using the formula z = (\(\bar x\) - \(\mu_\bar x\)) / \(\sigma_\bar x\), where \(\bar x\) is the given sample mean, \(\mu_\bar x\) is the mean of the sampling distribution, and \(\sigma_\bar x\) is the standard deviation of the sampling distribution.

In this case, \(\bar x\) = 12.2 ounces, \(\mu_\bar x\) = 12 ounces, and \(\sigma_\bar x\) = 0.091 ounces.

z = (12.2 - 12) / 0.091 ≈ 2.197

Now, we can find the probability using the standard normal distribution table or statistical software. The probability represents the area under the standard normal curve to the right of z = 2.197.

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Answer:

2y=3x=-4

Step-by-step explanation:

grouping like terms

y+ly =4x-x=-4

2y=3x=-4

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance  statistic is computed.

What is Analysis of variance ?

What are some instances where ANOVA has been applied?

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The real number line is an infinitely long line that consists of all the rational and irrational numbers. Since the irrational numbers cannot be expressed as a ratio of two integers, they cannot be represented as terminating or repeating decimals.

Therefore, finding the location of an irrational number on the real number line requires using a system of equations that can only be solved by approximation.

One such system of equations is the decimal expansion of the irrational number.

For example, the square root of 2 is an irrational number that can be approximated by the decimal expansion 1.41421356...

To find the location of the square root of 2 on the real number line, we can use the equation x^2=2 and solve for x using iterative methods such as the Newton-Raphson method.

Another method to find the location of an irrational number on the real number line is to use the concept of limits. We can define a sequence of rational numbers that approach the irrational number, and use the limit of the sequence to approximate the location of the irrational number on the real number line.

In summary, finding the location of an irrational number on the real number line requires using approximation methods such as decimal expansion, iterative methods, or limits.

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India has one of the youngest populations in the world, and this demographic dividend has the potential to drive the country's economic growth in the coming years.

The BRICS (Brazil, Russia, India, China, and South Africa) are a group of five major emerging economies that are expected to play a significant role in the world economy in the coming years. Among these countries, India is known to have one of the youngest populations in the world, with an average age of 28.1 years.

India has a population of approximately 1.3 billion people, and it is projected to become the world's most populous country by 2027. The country has a large youth population, with about 50% of its population below the age of 25 and around 65% below the age of 35. This young population has the potential to be a significant asset for the country's economic growth, provided that adequate employment opportunities are created.

The youth in India are increasingly educated and tech-savvy, and they are playing a vital role in the country's growth story. India has a growing middle class, and this group of young, educated, and skilled individuals is driving the country's consumption story. The government of India has also launched several initiatives to harness the potential of the youth, such as Skill India, Make in India, and Digital India, to name a few.

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Answer:

D. The trench has become shallower because -32 is farther from 0 on a number line than -27

Answer: D

Step-by-step explanation: -27 is closer to zero than -32. Since these numbers were negative and the depth of the trench went from -32 to -27, we can assume that the trench had gotten more shallow.

I hope this helps!

Answer:

Step-by-step explanation:

-10*9*x^3*x*y^2 = -90x^4y^2

Solution:

Simplify the distributive property and solve.

The solution to the equation is 15.

Your required solution :

Let us solve this equation..!!

Firstly multiplying 2 by (x - 2)

⇒ 2 × (x - 2) = 26

⇒ 2x - 4 = 26

On transposing -4 to R.H.S. it would be positive,

⇒ 2x = 26 + 4

⇒ 2x = 30

On dividing 30 by 2 we gets,

⇒ x = 30/2

⇒ x = 15

Therefore, value of x is 15.

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

Answer:

1 1/4 or 1.25

Step-by-step explanation:

Have a nice day

Answer:

28.26

Step-by-step explanation:

A=3.14r^2

A=3.14(3)^2

A=3.14(9)

A=28.26

Answer: 28 cm

Step-by-step explanation: Area=π·r² and diameter =2r

So if we need to  find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.

Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26

Now round to the nearest whole number ⇒ 28.

Answer:

Mark these points on the graph:

(0,3)

(1,4)

(2,5)

(3,6)

(4,7)

(5,8)

(6,9)

(7,10)

Then draw a line on the points.

Answer:

The required coordinates are;

A''(-3, -5), B''(0, -4), C''(0, -2), and D''(-3, 0)

Step-by-step explanation:

The given coordinates of the trapezoid ABCD are;

A(-5, -3) B(-4, 0), C(-2, 0) and D(0, -3)

Therefore, we have;

For a rotation 90° counterclockwise, we have for a given coordinates of the preimage (x, y) after a rotation 90° counterclockwise, the image will be located at (y, -x)

Therefore, for the points of the trapezoid, we have;

Preimage A(-5, -3) rotated 90° counterclockwise gives image A'(-3, 5)

Preimage B(-4, 0) rotated 90° counterclockwise gives image B'(0, 4)

Preimage C(-2, 0) rotated 90° counterclockwise gives image C'(0, 2)

Preimage D(0, -3) rotated 90° counterclockwise gives image D'(-3, 0)

For a reflection across the x-axis gives the transformation, preimage location (x. y), image location after reflection (x, -y)

Therefore, we have;

For the point A'(-3, 5), reflection across the x-axis gives A''(-3, -5)

For B'(0, 4), reflection across the x-axis gives B''(0, -4)

For C'(0, 2), reflection across the x-axis gives C''(0, -2)

For D(-3, 0), reflection across the x-axis gives D''(-3, 0)

Therefore, the required coordinates are;

A''(-3, -5), B''(0, -4), C''(0, -2), and D''(-3, 0).