What is the solution to the equation below? 4+square root of x =10

Answer:

5(n - 3)

Step-by-step explanation:

Answer:

262 square feet

Step-by-step explanation:

The required expression model for the cost of the ramp is y = 2.20x.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let the area of the ramp be x and the cost to build the ramp be y,

According to the question,
The material Santiago will use to build the ramp costs $2.20 per square foot.

Total cost = 2.20 × area of the ramp

Substitute the variable in the above expression,

y = 2.20x

The above equation represents the equation model for the cost of ramp y for the x square foot area of the ramp.

Thus, the required expression model for the cost of the ramp is y = 2.20x.

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The margin of error of the random selection is 0.29

The given parameters are:

\(n = 320\) --- the sample size

\(\sigma = 2.9\) --- the standard deviation

\(\bar x = 24\) --- the mean

\(\alpha = 90\%\) --- the confidence level.

The margin of error (E) is calculated as follows:

\(E = z \times \sqrt{\frac{\sigma^2}{n}}\)

So, we have:

\(E = z \times \sqrt{\frac{3.2^2}{320}}\)

\(E = z \times \sqrt{\frac{10.24}{320}}\)

The z-value for 90% confidence level is 1.645.

Substitute 1.645 for z

\(E = 1.645 \times \sqrt{\frac{10.24}{320}}\)

\(E = 1.645 \times \sqrt{0.032}\)

Take square roots

\(E = 1.645 \times 0.1789\)

Multiply

\(E = 0.2943\)

Approximate

\(E = 0.29\)

Hence, the margin of error is 0.29

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\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)

Answer: 5π         OR       15.70796327

Step-by-step explanation:

Formula for circumference is C=2πr (radius)   OR      C=πd    (diameter)

Our radius is 5 units, so our diameter is 10 units

C=10π

However, the question is only asking for length of semicircle

So you have to divide: 10π/2=5π

The probability is 9 favorable outcomes out of 1000 total outcomes, which simplifies to 9/1000.

The correct answer is option a. 9/1000.

To determine the probability, we need to count the favorable outcomes and divide by the total number of possible outcomes.

Let's consider the range of numbers from 11 to 1010, inclusive. There are 1000 possible numbers in this range (1010 - 11 + 1 = 1000).

For Al's number to be a whole number multiple of Bill's, we can see that the possible values for Bill's number are 11, 22, 33, ..., 1010. This is because Al's number must be a multiple of Bill's, so it will be some multiple times 11.

Similarly, for Bill's number to be a whole number multiple of Cal's, the possible values for Cal's number are 11, 22, 33, ..., 1010.

Now, we need to count the favorable outcomes where all three numbers satisfy the conditions.

The numbers that are multiples of 11 in the given range are 11, 22, 33, ..., 1010.

There are 91 such numbers in the range.

Out of these 91 numbers, we need to find the ones that are multiples of 11 for both Bill and Cal.

Since Bill's number must be a multiple of Al's, and Cal's number must be a multiple of Bill's, it means that they must be multiples of 11 as well.

So, we have 9 numbers (11, 22, 33, ..., 99, 110) that satisfy all the conditions.

Therefore, the probability is 9 favorable outcomes out of 1000 total outcomes, which simplifies to 9/1000.

The correct answer is option a. 9/1000.

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Answer:

-8

Step-by-step explanation:

;

you put in 2*-2+3*-3+5 and the answer is-8

Answer:

60

Step-by-step explanation:

Let x = the number

x - 10%x = 54

x - 0.1x = 54

0.9x = 54

x = 54 / 0.9 = 60

Answer:

2x4=8+3=11

Step-by-step explanation:

first multiply 2 times 4 equals 8 and add 3 which equals 11.

Answer:

Solution given:

<J=90°[tangent to the circle is perpendicular to radius]

In right angled triangle ∆KJL

base[b]=10

hypotenuse [h]=x+10

perpendicular [p]=24

by using Pythagoras law

p²+b²=h²

24²+10²=(x+10)²

(x+10)²=676

x+10=√676

x=26-10

x=16

Answer:

I am pretty sure it is 19 blocks because it is 14 blocks before going back home. She needs to walk 3 blocks west and 2 blocks south. 14+3+2=19

Step-by-step explanation:

Answer:

The answer is 13/100.

Step-by-step explanation:

In order to convert percentage to fraction, you have to divide it by 100 :

\(13\% = \frac{13}{100} \)

Answer:

13/100

Step-by-step explanation

percentage just means "out of 100"

To find the total volume, we integrate this expression over the interval (0, ln(19)]:

V = ∫[0, ln(19)] 2π(e^(-x))(x - ln(19)) dx

Evaluating this integral will give us the exact volume of the solid.

To find the volume of the solid generated by revolving the region bounded by f(x) = e^(-x) and the x-axis on the interval (0, ln(19)], about the line x = ln(19), we can use the method of cylindrical shells.

Consider an infinitesimally thin vertical strip of width Δx at a distance x from the line x = ln(19). The height of this strip is f(x) = e^(-x), and the length of the strip is the circumference of the shell, which is given by 2π(r), where r is the distance from the line x = ln(19) to the strip, i.e., r = x - ln(19).

The volume of each cylindrical shell is given by the product of the height, the circumference, and the width:

dV = 2π(e^(-x))(x - ln(19)) Δx

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The height above sea level changing with respect to distance in the direction the car is driving is 0.98 feet per mile.

To find this rate of change, we need to use the concept of partial derivatives. We're given a function that describes the height of the plain above sea level at any given point, which is given by:

h(x,y) = 1000 + 0.01x² + 0.02xy + 0.01y²

Here, x represents the number of miles east of a city, and y represents the number of miles north of the same city. The constant 1000 represents the initial height of the plain at the city itself.

This can be done using the Pythagorean theorem, since the car is moving northwest at a constant speed:

d² = x² + y²

Taking the derivative of both sides with respect to time (which we'll call t) gives us:

2dd/dt = 2x(dx/dt) + 2y(dy/dt)

Specifically, we know that:

dx/dt = -dy/dt

Substituting this relationship into our earlier equation gives us:

dd/dt = (-x/y)dx/dt

Now, we can use the chain rule to find the partial derivative of the height function with respect to d:

∂h/∂d = ∂h/∂x x ∂x/∂d + ∂h/∂y x ∂y/∂d

Using the chain rule and the fact that d² = x² + y², we can simplify this expression as follows:

∂h/∂d = (2xdx/dt + 2ydy/dt) x (∂h/∂x x x/d + ∂h/∂y x y/d)

Plugging in the expressions we derived earlier for dx/dt and dy/dt, we get:

∂h/∂d = (-2xy/y)dx/dt x (0.01x + 0.01y + 0.02xy/y) + (2xy/x)dy/dt x (0.01

Now, we need to plug in the expressions for ∂h/∂x and ∂h/∂y. These are given by:

∂h/∂x = 0.02x + 0.02y

∂h/∂y = 0.02x + 0.02y

Substituting these expressions into our earlier equation, we get:

∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.01x(0.02x + 0.02y) + 0.02y(0.02x + 0.02y) + 0.01y(0.02x + 0.02y) + 0.02x(0.02x + 0.02y)

Simplifying this expression, we get:

∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.04xy + 0.02x² + 0.03xy + 0.02y²

Collecting like terms, we get:

∂h/∂d = -0.02xdx/dt - 0.02ydy/dt + 0.07xy + 0.02(x² + y²)

Now, we can substitute in our expression for dx/dt in terms of dy/dt:

dx/dt = -dy/dt

This gives us:

∂h/∂d = 0.02ydy/dt - 0.02xdx/dt + 0.07xy + 0.02(x² + y²)

Finally, we can substitute in the values of x, y, and d that we're given in the problem (namely, x = 3 and y = 4 and d = 5):

∂h/∂d = 0.02(4)dy/dt - 0.02(3)(-dy/dt) + 0.07(3)(4) + 0.02(3² + 4²)

Simplifying this expression, we get:

∂h/∂d = 0.1dy/dt + 0.98

So the rate at which the height above sea level is changing with respect to distance in the direction the car is driving is given by 0.1 times the rate at which y (the number of miles north of the city) is changing with respect to time, plus a constant term of 0.98 feet per mile.

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The correct option is b which tells that an optimal solution to a linear programming problem must lie at the intersection of at least two constraints.

Linear programming is an optimization technique that is fine for the purpose of getting the best solution such as maximizing profit or certain 4th-era quantities.

When there are just two choice variables, the graphic method of solving a linear programming issue can be employed.

It is fine by modelling real-life problems into mathematical models that have linear relationships or constraints such as in the form of objective functions.

In linear programming, an objective function defines the formula for quantity optimization and the goal from this is to determine variable values that maximize or minimize the objective function depending on the problem robbery solved.

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The variance of a binomial distribution with parameters n and p cannot exceed n/2.

The binomial distribution is characterized by two parameters: n, which represents the number of trials, and p, which represents the probability of success in each trial. The variance of a binomial distribution is given by Var(X) = np(1-p).

To prove that the variance cannot exceed n/2, we can start by analyzing the expression np(1-p). Rearranging the terms, we have np - np^2. Since p^2 is always non-negative, np - np^2 is maximized when p is equal to 0.5 (the midpoint between 0 and 1).

When p is equal to 0.5, the expression np(1-p) simplifies to 0.25n, which is n/4. This implies that the maximum value of the variance is n/4.

Since n/4 is smaller than n/2 for any positive value of n, we can conclude that the variance of a binomial distribution with parameters n and p cannot exceed n/2.

Therefore, the variance of a binomial distribution is bounded above by n/2, indicating that as the number of trials increases, the variability or spread of the distribution is limited.

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The sample space for this event is given as follows:

{Red 1, Red 2, Red 3, Red 4, Red 5, Red 6, Green 1, Green 2, Green 3, Green 4, Green 5, Green 6, Blue 1, Blue 2, Blue 3, Blue 4, Blue 5, Blue 6}

The sample space is the set that contains all possible outcomes for a given trial.

The trials for this problem are given as follows:

Hence the outcomes are:

That is:

{Red 1, Red 2, Red 3, Red 4, Red 5, Red 6, Green 1, Green 2, Green 3, Green 4, Green 5, Green 6, Blue 1, Blue 2, Blue 3, Blue 4, Blue 5, Blue 6}

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A larger sample size results in a narrower confidence interval, indicating a more precise estimate of the population mean.

If you are constructing a confidence interval for a single mean, the confidence interval will narrow with an increase in the sample size. This is because a larger sample size provides more information and reduces the variability of the data, making the estimate of the population mean more precise.

When constructing a confidence interval, the size of the interval is influenced by two factors: the level of confidence and the sample size. A higher level of confidence will result in a wider interval, as there is a greater chance that the true population mean falls within that range.

However, increasing the sample size will reduce the standard error of the mean, which is the measure of the variability of the sample means from different samples. As a result, the confidence interval will be narrower, indicating a more precise estimate of the population mean.

For example, if we want to estimate the average height of adult males in a population, we could take a sample of 20 men and calculate the mean height and standard deviation. With this information, we can construct a confidence interval, such as 95% confidence interval.

As we increase the sample size to 100, the standard error of the mean will decrease, resulting in a narrower confidence interval. This means that we can be more confident that the true population mean falls within this interval.

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Answer:

B (22%) is the answer.

Skills needed: Financial Math, Percentage Computations

Step-by-step explanation:

1) First, let's calculate the cost of the extended warranty. That would be the new price minus the old price.

    - This is due to the fact that the new price is phone + warranty, while the old price is just the phone.

    - So \(\text{new price } - \text{old price} = 289-225=64\)...warranty=64$

2) The warranty is 64 dollars. To find out what percent of the cost it takes up, we do \(\frac{warranty}{totalprice}\) --> In this case, the \(totalprice\) is the new price, since the warranty is included in this price.

    - Our fraction would be: \(\frac{64}{289}\)

    - Divide this out, you get a decimal of: 0.2214...

    - To get a percent, multiply by the decimal by 100, and it is \(22.14\)%

22.14 rounds to 22, so 22% is the answer, and that is b.

--------------------------------------------------------------------------------------------------------------Hope you have a nice day!

A) 28% not B.

Step-by-step explanation:

Answer:

12 inches.

Step-by-step explanation:

You have to use the pythagorean formula. The measurements you stated form a right angle. Therefore, a^2 + b^2 = c^2. In this equation, we know c=13, and b=5. So therefore c^2 - b^2 = 144. We have to solve for a, so square root 144 to get 12.

Answer:12 in

Step-by-step explanation:

The arc angles in the circle are as follows:

x = 20 degrees

z = 160 degrees

A = 180 degrees

The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Therefore, the measure of the arc angle x in the circle is 20 degrees.

Let's find z

z = 180 - 20(sum of angles on a straight line)

z = 160 degrees

Let's find the angle A.

The angle A is as follows
A = 360 - 160 - 20(sum of angle in a point is 360 degrees)

Therefore,

A = 360 - 180

A = 180 degrees.

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The value of RS is 21.57

Trigonometric ratios are used to calculate the measures of one (or both) of the acute angles in a right triangle, if you know the lengths of two sides of the triangle.

sin(θ) = opp/hyp

cos(θ) = adj/hyp

tan(θ) = opp/adj

The side facing the acute angle is the opposite and the longest side is the hypotenuse.

therefore, adj is 22 and RS is the hypotenuse.

Therefore;

cos(θ) = 20/x

cos 22 = 20/x

0.927 = 20/x

x = 20/0.927

x = 21.57

Therefore the value of RS is 21.57

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

x

Step-by-step explanation:

The formula of a line in its slope-intercept form is

y= mx + b

the slope is indicated by “m” that multiply the x

Therefore, the line integral is:

∫c xy^4 ds = 125∫[0,pi] cos(t)sin^4(t) dt = 125(48/5) = 1200

The right half of the circle x^2 + y^2 = 25 can be parameterized as c(t) = (5cos(t), 5sin(t)) for t in [0, pi], where the orientation is counterclockwise.

The line integral of xy^4 along c is given by:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

where ||c'(t)|| is the magnitude of the derivative of c with respect to t.

We have:

c'(t) = (-5sin(t), 5cos(t))

||c'(t)|| = sqrt[(-5sin(t))^2 + (5cos(t))^2] = 5sqrt(sin^2(t) + cos^2(t)) = 5

So the line integral becomes:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

= 5∫[0,pi] 25cos(t)sin^4(t) dt

= 125∫[0,pi] cos(t)sin^4(t) dt

To evaluate this integral, we can use integration by substitution. Let u = sin(t), then du/dt = cos(t) and dt = du/cos(t). So we have:

∫cos(t)sin^4(t) dt = ∫u^4 du/cos(t) = ∫u^4 sec(t) du

We can evaluate this integral as follows:

∫u^4 sec(t) du = sec(t)u^5/5 - 2/5 ∫u^2 sec(t) du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 4/15 ∫u^2 du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3 + C

where C is the constant of integration.

Substituting back u = sin(t) and integrating over [0,pi], we obtain:

∫[0,pi] cos(t)sin^4(t) dt

= [sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3]_0^pi

= (0 - 0 + 2/5(5^3)) - (1/5 - 0 + 0)

= 48/5

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To solve the system of equations [x - y = 3, 2x - y = -1] using an inverse matrix, we can represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.The solution to the system of equations [x - y = 3, 2x - y = -1] is x = -4 and y = -5.

The coefficient matrix A is:

| 1 -1 |

| 2 -1 |

The variable matrix X is:

| x |

| y |

The constant matrix B is:

| 3 |

| -1 |

To find the solution X, we need to compute the inverse of matrix A and then multiply it by matrix B.

First, calculate the inverse of matrix A:

A^(-1) = | -1 1 |

| -2 -1 |

Next, multiply the inverse of A by B:

X = A^(-1) * B

| x | | -1 1 | | 3 |

| y | = | -2 -1 | * | -1 |

Performing the matrix multiplication, we get:

x = (-1)(3) + (1)(-1) = -3 - 1 = -4

y = (-2)(3) + (-1)(-1) = -6 + 1 = -5

Therefore, the solution to the system of equations [x - y = 3, 2x - y = -1] is x = -4 and y = -5.

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Answer:

60 feet. :)

Step-by-step explanation:

This is the formula you want to use:

\(l*w*h=V\)

It means that length·width·height = Volume. So, 5 · 4 · 3 = 60 ft.

Step-by-step explanation:

For crossing chords in a circle, the products of the segments are equal

6 * 4  =   x   *   14 -x

24 = -x^2 + 14x

-x^2 + 14x - 24 = 0      Use quadratic Formula ( or factoring ) to find:

x = 2   or  12      ( drawing is not to scale)

Answer:

It's 8

Step-by-step explanation:

\( 16 ^{ \frac{3}{4} } = \sqrt[4]{16 ^{3} } = \sqrt[4]{2 ^{4 \times 3} } = 2^{ \frac{12}{4} } = 2^{3} = 8\)

Answer:

8

Step-by-step explanation:

Step-by-step on how to solve it is in the image below.

Happy to help! :)