What is the equation, in standard form, of a parabola that models the values in the table?

x: -1, 0, 2
y: 10, 5, 13

a: y=3x^2-2x+5
b: y=x^2-2x+5
c: y=2x^2-3x+5
d: y=-3x^2+2x+5

Answer:

They spend = $58

They earned = $35

Step-by-step explanation:

Answer:

8. 24

9. 10

2. 72

1. 113

5. 7.96 = 8

11. 30.19 = 30.2

6. 28.27 = 28

That's all I can answer right now, maybe study a bit more and your grades will get better! Good luck!

Answer:

The probability that two or fewer will withdraw will be 0.1985744.

What is the binomial theorem?

The expanded value of the algebraic expression of the form (x + y)n is largely determined with the aid of the binomial theorem. It is simple to get the value of (x + y)², (x + y²)³, and (a + b + c)² by algebraically multiplying the numbers according to the exponent value.

However, it requires too much computation to determine the expanded version of \((x+y)^{17}\) or other similar expressions with larger exponential values. The binomial theorem can assist to make things simpler.

Binomial theorem formula-

\((a+b)^n =\) ∑\(^{n} _{r=0} ^{n} C_{r=0} a^{n-r}b^r\)

where,

n= positive integer

a, b = real numbers,

and

0 < r ≤ n.

now according to the question we are given,

X~Binomial (n=36, p=0.18)

P(X=x) = xC36*(0.18^x)*((1-0.18)^(36-x))

So the probability is

P(X<=4)= P(X=0)+P(X=1)+...+P(X=4)

= 0.1985744

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Answer:

D. x + y = 125

   y = 1/2x + 11

Step-by-step explanation:

Rosa = y

Yareli = x

The number of days the book was late is 14 days.

The given parameters include;

The following algebraic equation will be set to calculate the number of days the book was late before it was returned;

\(0.25(4) + (x - 4)0.3 = 40\\\\\)

simplify the equation as follows;

\(1 + 0.3x - 1.2 = 4\\\\\)

collect similar terms together;

\(0.3x = 4.2\\\\\)

divide through by 0.3

\(x = \frac{4.2}{0.3} \\\\x = 14 \ days\)

Thus, the number of days the book was late is 14 days.

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Find how many days late was her book

The total days late is 14 days

charges per day for first 4 days = $0.25

charges per day for the remaining days = $0.30

Total amount Annika paid = $4.00

let x = number of days of the remaining days

Amount paid for first 4 days = $0.25 × 4

= $1

Amount paid for remaining days = 0.30 × x

= 0.30x

Total amount paid = Amount paid for first 4 days + amount paid for remaining days

4 = 1 + 0.30x

4 - 1 = 0.30x

3 = 0.30x

x = 3/0.30

x = 10 days

Total days late = 4 days + 10 days

= 14 days

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Answer: 5

Step-by-step explanation:

Hope this helps 100% Verified from math>way

Answer:

11 1/4

Hope I helped

To calculate the flux of the curl of the field f=5zi+2xj+yk across the surface s using the surface integral in Stokes' Theorem, follow these steps:

1. Determine the curl of the field f=5zi+2xj+yk. The curl of a vector field is given by the cross product of the gradient and the field itself. In this case, the curl of f is ∇ × f = ( ∂(yk)/∂y - ∂(2xj)/∂z )i + ( ∂(5zi)/∂z - ∂(5zi)/∂x )j + ( ∂(2xj)/∂x - ∂(yk)/∂y )k = 2i + 5j - 2k.

2. Calculate the surface integral of the curl of f across the surface s using Stokes' Theorem. Stokes' Theorem relates the surface integral of the curl of a vector field over a surface to the line integral of the vector field around the closed curve that bounds the surface. The surface integral is given by ∬s(∇ × f) · dS, where dS represents the vector area element of the surface.

3. Determine the vector area element dS for the given surface s. The vector area element dS is perpendicular to the surface and its magnitude is equal to the differential area element dA. In this case, the surface s is not specified, so the vector area element dS cannot be determined without further information.

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6.∠ADB = ∠BDC reason :(CPCTC)

7.BD bisects ∠ADC reason :(From statement 6)

Hope it helps you......

a: f(x) = 0, x >= 4

b)  P(2/3< X <3)= 5/6

c)  P(X>3. 5)=3/4

d) The 60th percentile 2.2

e) P(X = 3) = 0.

a). To find the pdf of X, we take the derivative of the cdf:

f(x) = F'(x) = 0, x < 2

f(x) = 1/2, 2 <= x < 4

f(x) = 0, x >= 4

b. Using the cdf, we have

P(2/3 < X < 3) = F(3) - F(2/3) = [(3-2)/2] - [(2/3-2)/2] = 5/6

c. Similarly,

P(X > 3.5) = 1 - F(3.5) = 1 - [(3.5-2)/2] = 3/4

d. The 60th percentile is the value x such that P(X <= x) = 0.6. Using the cdf,

0.6 = F(x)

x = (0.6*2) + 2 = 2.2

e. Since X is a continuous random variable, P(X = 3) = 0.

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Answer:

C

Step-by-step explanation:

13/18 is .72222222

.5+.222=.722

Therefore , the solution of the given problem of function comes out to be f(x) = -4.5199 * (1.5546)ˣ

The mathematics class covers  a broad variety of subjects, such as mathematics, numbers and their subsets, as well as expressions  building, construction, and both real and imagined geographic locations. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is comprised of several unique parts that work together to produce unique outcomes for each input.

Here,

We can see from the table that:

When x = -3, f(x) = -2.999.

f(x) equals -2.99 when x is two.

At x = 1, f(x) equals -2.9.

If x = 1, then f(x) = 7.

F(x) = 97 when x = 3.

x = 5 when f(x) = 997.

We can write: since f(x) is an exponential function.

f(x) = a + bˣ

Using the specified numbers for x and f(x), we obtain:

=> -2.999 = a * b⁻³

=> -2.99 = a * b⁻²

=> -2.9 = a * b⁻¹

=> 7 = a * b¹

=> 97 = a * b³

=> 997 = a * b⁵

Any two sets of the aforementioned equations can be used to find the values of a and b. By splitting the fourth equation by the third equation, for instance, we obtain:

7 / (-2.9) = (a * b^(1)) / (a * b⁻¹)

-2.4138 = b²

=> b ≈ -1.5546 or b ≈ 1.5546

Using b = 1.5546 as a replacement in the third equation, we obtain:

=> -2.9 = a * (1.5546)⁻¹

=> a ≈ -4.5199

Consequently, the exponential function's general form is as follows:

=> f(x) = -4.5199 * (1.5546)ˣ

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Answer:

=6.22??

Step-by-step explanation:

2.22+16-4-(4+4)

2.22+16-4-8

18.22-4-8

14.22-8

=6.22....

Answer:

I got 6.22

Step-by-step explanation:

I did 2.22+16-4(4+)

First : 2.22+16-4-4-4

Then: -4-4-4= -12

After: 2.22+16-12

Lastly: 2.22+4

And I got 6.22 and I checked my answer wit a calculator and its 6.22

Hope this helps

-Mercury

Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

Answer:

b = 6

Step-by-step explanation:

Let's solve for b.

(3x−1)2=9x2−bx+1

Step 1: Flip the equation.

−bx+9x2+1=9x2−6x+1

Step 2: Add -9x^2 to both sides.

−bx+9x2+1+−9x2=9x2−6x+1+−9x2

−bx+1=−6x+1

Step 3: Add -1 to both sides.

−bx+1+−1=−6x+1+−1

−bx=−6x

Step 4: Divide both sides by -x.

b = 6

Hope this helpss!!!

Slope is change in y over change in x.

Slope = (1-3)/(8 - -2)

Slope = -2/10

Slope = -1/5

Answer: -1/5

Answer:

1/5

Step-by-step explanation:

Slope:- [(1-3) / (8- -2)]

= -2/10

= -1/5

Answer:

19 units

Step-by-step explanation:

Perimeter of the rectangle = 124 units

width = x units

length = 5 + 2x units

The perimeter of a rectangle is given by;

P = 2(l + b)

Substituting values;

124 = 2[(5 + 2x) + x]

124 = 2[5 + 3x]

124 = 10 + 6x

124 - 10 = 6x

114 =6x

x= 114/6

x = 19

width = 19 units

Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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Answer:

\(m\angle STU=30^\circ\)

Step-by-step explanation:

Angles in a Circle

There are many theorems that relate angles inside and outside a circle.

To solve this question we need to recall the relation of any central angle and a subtended angle by the same arc.

The image below explains this relationship:

Central angle (2x) is twice any inscribed angle (x) subtended by the same arc (marked in red).

The image provided in the question shows an arc US subtended by the inscribed angle SVU and the central angle STU.

If we know the measure of the angle SVU as 15°, then the angle STU must be twice 15°, i.e., 30°.

\(\mathbf{m\angle STU=30^\circ}\)

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer: x=9

Step-by-step explanation:

Every internal angle within a triangle produces a sum of 180. Therefore we can make this equation:

180-(12x+13)+8x-3+52=180

From there we just solve step by step.

-12x-13+8x-3+52=0

-4x+36=0

-4x=-36

x=9

a)The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b)Standard deviation \(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

the probability that the mean daily commissions received is between \(\$561,116\)and \(\$697,016\) is approximately \(99.77\% - 0.01\% = 99.76\%.\)

To solve the given questions, we'll use the properties of the normal distribution.

1. Sampling Distribution:

a) Mean of the sampling distribution of the sample mean daily commissions received:

The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b) Standard deviation of the sampling distribution of the sample mean daily commissions received:

The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size:

Standard deviation\(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

2. Probability Calculations:

a) Probability that the mean daily commissions received is more than $581,652:

We'll calculate the z-score using the formula\(\[ z = \frac{{(\$581,652 - \$604)}}{{\left(\frac{{6.830}}{{\sqrt{15}}}\right)}} \approx -3.161 \]\)

Using a standard normal distribution table, we find that the probability is approximately 0.0008, or 0.08%.

b) Probability that the mean daily commissions received is between $561,116 and $697,016:

We'll calculate the z-scores for both values and find the probabilities associated with those z-scores:

\(z_1 = ($561,116 - $604) / (6.830 / \sqrt(15)) = -3.907\)

\(z2 = ($697,016 - $604) / (6.830 / \sqrt(15)) = 2.870\)

Using the standard normal distribution table, we find the probability associated with z1 as approximately 0.0001, or 0.01%, and the probability associated with z2 as approximately 0.9977, or 99.77%.

Therefore, the probability that the mean daily commissions received is between $561,116 and $697,016 is approximately 99.77% - 0.01% = 99.76%.

3. Maximum average daily commissions receivable from the lowest 7.5% volume trading days:

We'll find the z-score corresponding to the lowest 7.5%:

Using a standard normal distribution table, we find the z-score corresponding to the lowest 7.5% as approximately -1.15.

Now we'll find the corresponding value in the original scale:

\(\[ z = \frac{{(x - \mu)}}{\sigma} \]\)

\(-1.15 = (x - 99.7) / 2.9\)

\(x - 99.7 = -1.15 * 2.9\)

\(x - 99.7 = -3.335\)

\(x = 96.365\)

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable is approximately \(\$96,000.\)

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1. a) Mean = $6.04 thousand dollars
  b) Standard deviation = $6.823 thousand dollars
2. a) Probability = 100%
  b) Probability = 100%
3. Maximum average daily commissions receivable = $98,000

1. To determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars), we can use the following formulas:

a) Mean of the sampling distribution = Mean of the population = $6.04
b) Standard deviation of the sampling distribution = Standard deviation of the population / Square root of the sample size

= \(\frac{\$26.5}{\sqrt{15}} = \$6.823\)

2. To find the probabilities, we need to use the z-score formula:

a) To find the probability that the mean daily commissions received is more than $581,652, we first need to find the z-score.

The z-score formula is given by:

\(z = \frac{x - \mu}{\frac{\sigma}{\sqrt{n}}}\),

where x is the value we want to find the probability for, μ is the mean of the population, σ is the standard deviation of the population, and n is the sample size.

z = \(\frac{\$581,652 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z = 21518.78

Using a standard normal distribution table or a calculator, we find that the probability is approximately 1.

b) To find the probability that the mean daily commissions received is between $561,116 and $697,016, we need to find the z-scores for both values.

z₁ = \(\frac{(\$561,116 - \$6.04)}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₁ = 20618.03

z₂ = \(\frac{\$697,016 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₂ = 25618.23

Using the standard normal distribution table or a calculator, we find that the probability is approximately 1.

3. To find the maximum average daily commissions receivable from the lowest 7.5% volume trading days, we need to find the z-score that corresponds to a cumulative probability of 0.075.

Using the z-score formula and rearranging it to solve for x, we have: \(x = z \cdot \left(\frac{\sigma}{\sqrt{n}}\right) + \mu\)

First, we find the z-score using the standard normal distribution table or a calculator. For a cumulative probability of 0.075, the z-score is approximately -1.405.

Then, we plug in the values to find x:

x = \(-1.405 \cdot \left(\frac{$2.9}{\sqrt{29}}\right) + $99.7\)

x = $98.324

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable from the lowest 7.5% volume trading days is $98,000.

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Answer:

3x:4x for some real number x

Step-by-step explanation:

Since answer choices weren't provided, I generalized my answer.

First, notice we can simplify 6:4 into 3:2 because we can write the ratio as a fraction and simplify (6 and 4 are both multiples of 2).

Since 3 and 2 are relatively prime and the ratio cannot simplify anymore, we can say that the ratio of 6:4 = 3:2 = 3x:2x for some real number x because we can see that 3x:2x = 3:2  by simplifying  (3x and 3 are both multiples of x).

As long as the answer choice you choose matches the format above, you should be correct! I hope this helps! :)