Landen used 1 1/2 gallons of paint to paint 3/4 of a room. At this same rate, how many gallons will it take to paint the whole room?

Answer:

The answer is D

Step-by-step explanation:

And u lied you said 18 points when this question is up for 9 points

Answer:

Below,...!

Step-by-step explanation:

1.6 * (2 1/6) - 4))

1.6 * (13/6 - 4)

1.6 * (-1 5/6)

2.904

Chow,...!

The product of the given expression (1.6)( 2 1/6 −4) will be equal to 2.904

A mixed fraction contains a sum of whole number and a proper fraction.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

First we will convert the mixed fraction into simple fraction then the product of the given expression;

1.6 x (\(2 \frac{1}{6}\) ) - 4))

1.6 x (13/6 - 4)

1.6 x (-11/6)

2.904

The product of the given expression (1.6)( 2 1/6 −4) will be equal to 2.904

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The negative solution is \(-\frac{3}{5}\)

First, add 3 on both sides.

\(-2|5x-1|=-8\)

Then, Divide both sides by -2

\(|5x-1|=4\)

We know 5x-1 = 4     or 5x-1=-4

\(x=1\)             (positive)

\(x=-\frac{3}{5}\)          (negative)

Answer:

8 and 9

Step-by-step explanation:

consider perfect squares either side of 78

64 < 78 < 81 , then

\(\sqrt{64}\) < \(\sqrt{78}\) < \(\sqrt{81}\) , that is

8 < \(\sqrt{78}\) < 9

Given the equation:

Let's solve the equation for y.

Take the following steps:

Step 1.

Cross multiply:

Step 2.

Divide both sides by 3:

ANSWER:

y = 14

The polynomial equation with rational coefficient has a root are 7+√3 and 2-√6 the additional two roots are 7-√3 and 2+√6.

Given that,

The polynomial equation with rational coefficient has a root are 7+√3 and 2-√6.

We have to find two additional roots.

We know that,

Take the roots,

7+√3 and 2-√6

If a polynomial with rational coefficients has irrational roots, they will always appear in pairs, according to the statement.

Given that a polynomial equation with rational coefficients and two roots, 7+√3 and 2-√6, the complex conjugate of this equation, which is 7-√3 and 2+√6, is likewise a root of the polynomial equation.

Therefore, The polynomial equation with rational coefficient has a root are 7+√3 and 2-√6 the additional two roots are 7-√3 and 2+√6.

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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

i got B and D

Step-by-step explanation:

-14 is less then -8 and is left of -8 on a number line.

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Translation is the movement of a point up, down, left or right.

Transformation is the movement of a point from its initial location to a new location.

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Therefore the coordinates remains same as previous figure.

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Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Answer:

C. 8x^2-5x+2=0

Step-by-step explanation:

The answer is Option C because it can only be solved by quadratic formula

If each bus holds ten students and there are three buses, then the total number of students going to the show is 10 x 3 = 30 students.

The mass of the bus, 1900, is most likely measured in kilograms (kg) because kilograms are a commonly used unit for measuring the mass of large objects like vehicles.

If there are five rows in the theatre and Mr. Murray wants an equal number of students to sit in each row, then the number of students in each row would be the total number of students (30) divided by the number of rows (5), which is 30 / 5 = 6 students per row.

If Mrs. Stewart has two times as many students as Mr. Murray, and Mr. Murray has 30 students, then Mrs. Stewart would have 2 x 30 = 60 high school students in the theatre for the show.

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Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Probability     No. of pies          Cost       Revenue      Profit

0.5                        100               500           300            -200

0.25                      150               500           450            -50

0.25                      200              500            600           100

Step-by-step explanation:

We are given that  The owner believes that on 50% of the days she sells 100 pies.

So, Probability of selling 100 pies = 0.5

On another 25% of the days she sells 150 pies

So, Probability of selling 150 pies = 0.25

She sells 200 pies on the remaining 25% of the days

So, Probability of selling 200 pies = 0.25

We are given that the owner bakes 200 pies each day at a cost of $2.50 each.

So, Cost per day =\(200 \times 2.50 =500\)

Probability     No. of pies          Cost

0.5                        100               500

0.25                      150               500

0.25                      200              500

Now we are given that  she sells the pies for $3 each

So, SP of 100 pies =\(3 \times 100 = 300\)

SP of 150 pies = \(150 \times 3 = 450\)

SP of 200 pies = \(200 \times 3 = 600\)

Probability     No. of pies          Cost       Revenue      Profit

0.5                        100               500           300            -200

0.25                      150               500           450            -50

0.25                      200              500            600           100

The Product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

To find the product and simplify completely, you need to perform multiplication and simplify the resulting fraction. Here, we are multiplying the following fractions and mixed numbers:1, 5/8, 2, and 3/5.The first step is to convert the mixed numbers into improper fractions.

We do that by multiplying the whole number by the denominator, and then adding the numerator.For 1 5/8, we get:$$1 \frac{5}{8} = \frac{8}{8} \times 1 + \frac{5}{8} = \frac{13}{8}$$For 2, we get:$$2 = \frac{2}{1} = 2 \times \frac{1}{1} = \frac{2}{1}$$For 3/5, we leave it as is since it's already a fraction.

Now that we have all the numbers as fractions, we can multiply them:$$\frac{13}{8} \times \frac{2}{1} \times \frac{3}{5} = \frac{13 \times 2 \times 3}{8 \times 1 \times 5} = \frac{78}{40}$$

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:$$\frac{78}{40} = \frac{2 \times 39}{2 \times 20} = \frac{39}{20}$$

Therefore, the product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

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Answer:

It means that the both sides of the expression in the given equation must be/are congruent.

Hope this helps!

The ratio of their volumes is equal to: D. 27:125.

Mathematically, the volume of a sphere can be calculated by using this formula:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the two spheres, an expression which models their surface areas (S) with respect to volumes (V) is given by;

S₁/S₂ = V₁/V₂

S₁/S₂ = 9/25

(4πr₁²)/(4πr₂²) = 9/25

r₁²/r₂² = 9/25

Taking the square root of both sides of the expression, we have:

r₁/r₂ = 3/4

From the volume of a sphere formula, we have:

V₁/V₂ = (4/3 × πr₁³)/(4/3 × πr₂³)

V₁/V₂ = r₁³/r₂³

V₁/V₂ = 3³/4³

V₁/V₂ = 27/125.

Therefore, the required ratio is 27:125.

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Answer:

2.86=28 tenths+6 hundredths.

Step-by-step explanation:

2.86=2 ones+8 tenths+6 hundredths.

2.86=28 tenths+6 hundredths.

Answer:

see

Step-by-step explanation:

ones .  tenths  hundredths

2      .     8          6

8 tenths

If we are not using the ones place

we have 28 tenths

The product of the vectors v and w is gotten as; v ⋅ w = 22

We are given the vectors;

r = <8, 8, -6>

v = <3, -8, -3>

w = <-4, -2, -6>

We want to evaluate v.w which is a product of both vectors.

The formula will be;

v.w = (v_x * w_x) + (v_y * w_y) + (v_z * w_z)

Plugging in the values and solving gives;

v.w = (3 * -4) + (-8 * -2) + (-3 * -6)

v.w = -12 + 16 + 18

v.w = 22

We can conclude that the vector expressions has a product of 22

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The answer to your problem is: X=17

Answer:

17

Step-by-step explanation:

x + 10 + 9x=14x-58

x + 9x + 10 =14x-58

10x + 10 =14x-58

By grouping like terms by moving 14x to the left and 10 to the right of the equation; we have:

10x - 14x =-58-10

-4x=-68

x=-68/-4=17{ dividing both sides by -4}

Answer:

a

Step-by-step explanation:

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The equation of the perpendicular line is y = -1/3x

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

y = 3x + 2

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 2

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/3

The equation of the line is then calculated as

y = mx

Where

m = -1/3

So, we have

y = -1/3x

Hence, the line has an equation of y = -1/3x

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Standard deviation does not mean independent events.

No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.

Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.

Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.

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