The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
A.-4
B.-2
C. -1
D. 1

Answer: Use main properties of powers

to simplify given equation.

1.

2.

3. Then the equation is

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.

Step-by-step explanation:

Answer:

40/31

Step-by-step explanation:

4x = (1/8)x + 5

=> 4x - 5 = (1/8)x

=> 8(4x-5) = x

=> 32x - 40 = x

=> 32x - x = 40

=> 31x = 40

=> x = 40/31

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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Answer:

ok, here is your answer

Step-by-step explanation:

The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-

Answer:

78.54 ft²

Step-by-step explanation:

Hello!

The formula for the area of a circle is A = πr², where r is the radius.

Given r is 5, find the area:

The area is 78.54 ft²

Answer is the coordinates of endpoint F(6, 4).

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

let coordinate of F is (x,y).

4= (x + 2)/2

8= x +2

x = 6

6= (y +8)/2

12 = y + 8

y = 4

Answer is the coordinates of endpoint F(6, 4).

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Answer:

no it's not a solution because when you substitute the values of x= -3 and y=7 you won't get the equation

By the assumption of collinearity between points A, B and C and line segment properties, the length of the line segment BC is 7.

According to Euclidean geometry, a line is generated by two distinct points set on a plane and three points are collinear if they lie on one and same line. Algebraically speaking, we know that that line segments are contained in the following model:

AC = AB + BC

AC = AB + BC     (1)

If we know that AC = 19 and AB = 12, then the length of the line segment BC is:

19 = 12 + BC

BC = 19 - 12

BC = 7

By the assumption of collinearity between points A, B and C and line segment properties, the length of the line segment BC is 7.

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In the given experiment, the part that will yield discrete data is when the nurses answer "yes" or "no" to having an R.N. degree. Discrete data consists of distinct and separate values, and in this case, it is the count of nurses with an R.N. degree and those without.

There is no part of the experiment that will yield continuous data, as the experiment only involves collecting binary responses from the nurses. Continuous data usually involves measurements that can take any value within a range, but this experiment doesn't include such measurements.

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The median jump length would be 3.5 meters.

To calculate the median jump length, we will sum the figures for all the jump lengths recorded and then find the middle number of them all.

So, we will begin by summing all the figures while factoring in the key and then dividing by the total number of jumps as follows:

1. 7 + 1.9 + 2.3 + 2.9 + 3.4 + 3.6 + 3.7 + 3.8 + 4.0 + 4.3

= 3.4 + 3.6

= 3.5

So, the median jump length given the figures above is 3.5 meters.

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These functions are facilitated by the hardness of the skin in specific areas and a distinct pattern of lines.

These surfaces' hard exteriors resist abrasion, have high mechanical strength, and are highly impermeable to bacteria and fungi, which helps to avoid infection. To assist with performing simple and complex jobs, the hands and feet can be folded and unfolded appropriately thanks to the distinct patterns of lines on their surfaces.

The thick skin on the palms of the hands and soles of the feet, also known as the "glabrous skin," is adapted to withstand the constant friction and pressure that these areas are subjected to.

Here are some structural features of the skin that make it suited for its function:

Epidermal ridges: The skin on the palms and soles has a unique pattern of ridges and valleys that form fingerprints and footprints. These ridges increase the surface area of the skin in contact with the environment, which provides better grip and traction.

Thick stratum corneum: The outermost layer of the skin, called the stratum corneum, is thicker in the palms and soles than in other parts of the body. This layer is composed of many layers of dead, flattened skin cells (keratinocytes) that are filled with a tough protein called keratin. The thick stratum corneum provides mechanical strength and protection against abrasion.

Dermal papillae: The dermal layer of the skin contains small, finger-like projections called dermal papillae. These papillae interlock with the epidermal ridges to anchor the skin in place and prevent it from sliding around too much.

Sweat glands: The palms and soles contain a high density of sweat glands that produce sweat, which helps to cool the skin and maintain a good grip. The sweat glands also secrete a specialized type of sweat called "eccrine sweat,".

Meissner's corpuscles: These are specialized sensory receptors located in the dermis of the glabrous skin. They are sensitive to touch and pressure and help us to detect fine textures and shapes with our fingertips and toes.

Overall, the structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

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The structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

The thick skin on the palms of the hands and soles of the feet, also known as the "glabrous skin," is adapted to withstand the constant friction and pressure that these areas are subjected to.

Here are some structural features of the skin that make it suited for its function:

Epidermal ridges: The skin on the palms and soles has a unique pattern of ridges and valleys that form fingerprints and footprints. These ridges increase the surface area of the skin in contact with the environment, which provides better grip and traction.

Thick stratum corneum: The outermost layer of the skin, called the stratum corneum, is thicker in the palms and soles than in other parts of the body. This layer is composed of many layers of dead, flattened skin cells (keratinocytes) that are filled with a tough protein called keratin. The thick stratum corneum provides mechanical strength and protection against abrasion.

Dermal papillae: The dermal layer of the skin contains small, finger-like projections called dermal papillae. These papillae interlock with the epidermal ridges to anchor the skin in place and prevent it from sliding around too much.

Sweat glands: The palms and soles contain a high density of sweat glands that produce sweat, which helps to cool the skin and maintain a good grip. The sweat glands also secrete a specialized type of sweat called "eccrine sweat,".

Meissner's corpuscles: These are specialized sensory receptors located in the dermis of the glabrous skin. They are sensitive to touch and pressure and help us to detect fine textures and shapes with our fingertips and toes.

Overall, the structure of the thick skin on the palms and soles is well-suited to its function of providing a strong, durable, and sensitive surface for gripping and manipulating objects, as well as for supporting the weight of the body during standing and walking.

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The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Answer:

Domain: All real numbers greater than or equal to 0 and less than or equal to 50

Range: All real numbers greater than or equal to 0 and less than or equal to 100

Step-by-step explanation

The workout is at 100% at 50 mins. Anything less would be under these two numbers.  Since the percentage of workout is on the y-axis, anything between zero and 100 can be possible. The time is on the x-axis, so anything 0 to 50 can be possible.  

Answer:

-9df^3 - 3f^3 - 7d^2 - 8d - 15625

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

4, 8, 6, 10, 8, ... has the pattern of +4 then -2

so, 4+4=8

8-2=6

6+4=10

10-2=8

the pattern goes on

so, 8+4=12

so, you  can get the pattern 8, 6, 10, 8, 12, ...

and the answer is 12

Answer:

Step-by-step explanation:

 it's 125 for the radius and also 125-62 = 63

so 125+63 = 188

188 * 62 = X^2

11656 = X^2

107.96 = x

108.0  = x  ( to the nearest tenth )

The perpendicular distance x from the end of the passage to either side of the mound is : 107.93 feets

Diameter = 250

To obtain the perpendicular distance, x :

We use the relation : x × x = Length to either side of mound :

Mathematically ;

x × x = 62 ft × (250 - 62)

x² = 62 × 188

x² = 11656 ft²

Take the square root of both sides ;

x = √11656

x = 107.9629 ft

Hence, the perpendicular distance x from the end of the passage to either side of the mound is : 107.93 feets

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The point of intersections between y = x + 1 and y = x² +1 are (0, 1) and (1, 2)

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

y = x + 1

y = x² +1

(0,1): Yes, (0,1) is a point of intersection between the line y = x + 1 and the parabola y = x² +1, since 1 = 0 + 1 = 0² + 1.

(1,2): No, (1,2) is a point of intersection between the line y = x + 1 and the parabola y = x² + 1, since 2 = 1 + 1 = 1² + 1.

(2,0): Yes, (2,0) is not a point of intersection between the line y = x + 1 and the parabola y = x² +1, since 0 = 2 + 1 ≠ 2² + 1.

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Answer:

$54

Step-by-step explanation:

45 increase 20% =

45 × (1 + 20%) = 45 × (1 + 0.2) = 54

Answer:

The point can either lie on the second quadrant or the third quadrant

Step-by-step explanation:

Mathematically, we have the ordinate and the abscissa

The ordinate represents the y axis while the abscissa represents the x axis value

For the abscissa to be negative, it means we are talking about the negative x axis

Now, the y axis can either be positive or negative too

When it is positive , we are referring to the point lying on the second quadrant

when it is negative, we are referring to the point lying on the third quadrant

There are 176,851 ways to store the bikes in four distinct warehouses if the bikes are indistinguishable and the warehouses are distinct.

Let's consider the two scenarios separately:

Scenario 1: Bikes and warehouses are considered distinct.

In this case, each bike and each warehouse is considered distinct. We need to find the number of ways to distribute 100 distinct bikes among 4 distinct warehouses.

To solve this, we can use the concept of stars and bars. Imagine we have 100 stars representing the bikes, and we want to separate them into 4 distinct groups (warehouses) using 3 bars.

The number of ways to distribute the bikes can be calculated as (100 + 3) choose 3:

Number of ways = (100 + 3)C3 = 103C3 = (103 * 102 * 101) / (3 * 2 * 1) = 176,851.

Therefore, there are 176,851 ways to store the bikes in four distinct warehouses if the bikes and warehouses are considered distinct.

Scenario 2: Bikes are indistinguishable, warehouses are distinct.

In this case, the bikes are indistinguishable, but the warehouses are distinct. We need to find the number of ways to distribute 100 identical bikes among 4 distinct warehouses.

This problem can be solved using the concept of stars and bars again. Since the bikes are indistinguishable, the placement of bars doesn't matter.

We can think of it as distributing the 100 bikes into 4 distinct groups (warehouses) using 3 bars. The number of ways to do this can be calculated as (100 + 3) choose 3:

Number of ways = (100 + 3)C3 = 103C3 = (103 * 102 * 101) / (3 * 2 * 1) = 176,851.

Therefore, there are 176,851 ways to store the bikes in four distinct warehouses if the bikes are indistinguishable and the warehouses are distinct.

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Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.

A sample size of 76 would be required to estimate the population mean with a margin of error of 4 and a 98% level of confidence.

To determine the sample size required to estimate the population mean with a specific margin of error and level of confidence, we can use the formula:

n = (Z * σ / E)²

where

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = standard deviation of the population

E = desired margin of error

here, we have that

the standard deviation (σ) is given as 15,

the margin of error (E) is 4 and

the level of confidence is 98% and For a 98% confidence level, the Z-score is approximately 2.33.

Plugging the values into the formula:

n = (2.33 * 15 / 4)²

n = (8.7375)²

n ≈ 76.34

n = 76

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Answer:

watching game= 3 hours

practicing free throw= 2 hours

lifting weight=1 hour

Answer:

11

Step-by-step explanation:

\(c=\sqrt{a^{2} + b^{2} } \\14 = \sqrt{9^{2}+ b^{2} } \\14 = \sqrt{81 + b^{2} } \\14^{2} = 81+b^{2} \\196 = 81 + b^{2} \\81 + b^{2} = 196\\b^{2} = 196-81\\b^{2} = 115\\b = \sqrt{115} \\b = 10.72\\b = 11\)

Answer:

260 hours

Step-by-step explanation:

first take out the 20 fixed cost that doesn't change no matter how long he gardens from 800

divide the remainder which is 780 by 3 which is the amount he gets paid for every hour he gardens. He would have to work 260 hours for the bike if he only takes one yard job

Answer:

the time taken by Mrs Brown to catch up is 18.75 hours

Step-by-step explanation:

Given;

average speed of Mr Brown = 75 mph

average speed of Mrs Brown, = 85 mph

time first traveled by Mr Brown = 2.5 hours

The distance traveled by Mr Brown before Mrs Brown start her own Journey;

D = speed  x time

D = 75 mph x 2.5 h

D = 187.5 miles

Let the time taken by Mrs Brown to catch up = t

(85 - 75)t = 187.5

10t = 187.5

t = 18.75 hours

Check:

after 18.75 hours:  Mrs Brown will travel ⇒ 18.75 x 85 = 1593.75 miles

after (2.5 h + 18.75h) : Mr Brown will travel ⇒ 21.25 x 75 = 1593.75 miles

Answer:

84

Step-by-step explanation:

(7² - 5) × 2

(49 - 5) × 2

(42) × 2

84

Answer:

4+2d

Step-by-step explanation:

2(3+d-1)

6+2d-2=6+(-2)+2d

=4+2d

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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The mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

The average of a set of values is referred to as the mean. To calculate the mean of a dataset, add up all of the values and divide by the number of values.

We can calculate the mean of the given data set as follows:

Mean = (9 + 6 + 2 + 0 + 2 + 3 + 5 + 2 + 1 + 5)/10

Mean = 3.5

Variance:Variance is a measure of how much a set of data varies. In other words, variance tells us how far each value in the dataset is from the mean. The variance formula is as follows:

σ² = (Σ(x - μ)²) / N

Where σ² is the variance, Σ is the sum, x is each value in the data set, μ is the mean of the data set, and N is the number of values in the data set.

Using the above formula, we can calculate the variance for the given data as follows:

First, we need to calculate the mean of the data set.x f(x)

xf(x)4 1 45 3 15 6 4 24 7 4 28 8 2 16

Total 14 128

Mean (μ) = 128 / 14 = 9.14

σ² = (Σ(x - μ)²) / N

σ² = [1(4 - 9.14)² + 3(5 - 9.14)² + 4(6 - 9.14)² + 4(7 - 9.14)² + 2(8 - 9.14)²] / 14

σ² = 5.056

Approximating the Mean:

We can use the midpoint of each interval as an approximate value for the entire interval. We can calculate the approximate mean as follows:

Mean = Σ(midpoint × proportion of stocks)

Mean = (-0.80 × 0.03) + (-0.40 × 0.03) + (0.00 × 0.2) + (0.40 × 0.44) + (0.80 × 0.16) + (1.20 × 0.06) + (1.60 × 0.05) + (2.00 × 0.03)

Mean = 0.428

Therefore, the mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

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