Need help with this one also

Answer:

A.

Step-by-step explanation:

2.8 x 10 -5mm

You can use the definition for the vertex form of a quadratic equation and then can can do conversion of that quadratic equation in that form.

The vertex form of the given equation is given by

\(g(x) = 4(x+11)^2 - 484\)

If a quadratic equation is written in the form

\(y = a(x-h)^2 + k\)

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point is called the vertex of the parabola that quadratic equation represents.

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

The given equation is \(g(x) = 4x^2 + 88x\)

Converting it in vertex form, we get:

\(g(x) = 88x + 4x^2\\\\\\g(x) = 4x^2 + 88x\\g(x) = 4(x^2 + 22x)\\g(x) = 4(x^2 + 22x +121 - 121) \\g(x)=4(x+11)^2 - 484\text{\: (Note how the form} \: a^2 + b^2 + 2ab = (a+b)^2 \:\rm got\: made)\)

Thus, we have h = -11 and k = -484

The plot of the given equation is attached below.

Thus,

The vertex form of the given equation is given by

\(g(x) = 4(x+11)^2 - 484\)

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Answer:

x = 117.8

Step-by-step explanation:

The tan value of an angle gives the ratio between the opposing side and the adjacent side of the angle.

Taking the tan value of the listed angle :

tan 50° = x/99

1.19 = x/99

x = 1.19 × 99

x = 117.8 (nearest tenth)

Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)

Answer: B

Step-by-step explanation:

Step-by-step explanation:

5x + 2 < 4x - 3

5x - 4x < -3 - 2

x < -5

The simple interest rate applied to the loan is approximately 11.76%.

To determine the simple interest rate applied to the loan, we can use the formula for calculating simple interest:

Simple Interest (I) = Principal (P) * Rate (R) * Time (T)

In this case, we have the following information:

Principal (P) = $850

Total amount to be paid back (P + I) = $1050

Time (T) = 2 years

We need to find the Rate (R), which is the interest rate. Rearranging the formula, we get:

Rate (R) = Simple Interest (I) / (Principal (P) * Time (T))

We can substitute the given values into the formula:

Rate (R) = (Total amount to be paid back - Principal) / (Principal * Time)

Rate (R) = ($1050 - $850) / ($850 * 2)

Rate (R) = $200 / $1700

Rate (R) ≈ 0.1176

To express the interest rate as a percentage, we multiply it by 100:

Rate (R) ≈ 11.76%

Therefore, the loan's basic interest rate is roughly 11.76%.

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Answer:

Step-by-step explanation:

\(tan \ 50 =\dfrac{opposite \ side}{adjacent side}\\\\\\1.19=\dfrac{21}{MD}\\\\\\1.19*MD=21\\\\MD = \dfrac{21}{1.19}\\\\\\MD = 17.65\)

The Taylor Rule predicts a target interest rate of 19.65 percent for the Fed in 1980. The Taylor Rule is a monetary policy guideline that suggests a target interest rate based on the inflation rate and unemployment rate.

In 1980, with an inflation rate of 13.5 percent and an unemployment rate of 7.8 percent, the Taylor Rule can be used to calculate the predicted target interest rate.

The Taylor Rule formula is given by:

Target Interest Rate = Real Interest Rate + Inflation Rate + (0.5 * Inflation Gap) + (0.5 * Output Gap)

In this case, the inflation rate is 13.5 percent, which exceeds the target rate of 3 percent. The inflation gap is the difference between the actual inflation rate and the target rate, so it is 13.5 - 3 = 10.5 percent.

The output gap is the difference between the actual unemployment rate and the full-employment rate. In this case, the unemployment rate is 7.8 percent and the full-employment rate is 6 percent, so the output gap is 7.8 - 6 = 1.8 percent.

Assuming a real interest rate of zero, we can calculate the target interest rate using the Taylor Rule formula:

Target Interest Rate = 0 + 13.5 + (0.5 * 10.5) + (0.5 * 1.8) = 13.5 + 5.25 + 0.9 = 19.65 percent

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Gary will be able to deduct $1,450 in medical expenses on his 2021 tax return.

Based on the information you provided, we can calculate Gary's deductible medical expenses using the following terms:

1. Qualified medical expenses: $5,200
2. AGI (Adjusted Gross Income): $50,000

According to the IRS, taxpayers can deduct qualified medical expenses that exceed 7.5% of their AGI for the tax year 2021. Here's the step-by-step calculation for Gary's deductible medical expenses:

Step 1: Calculate 7.5% of Gary's AGI
7.5% x $50,000 = $3,750

Step 2: Subtract the 7.5% AGI threshold from Gary's qualified medical expenses
$5,200 - $3,750 = $1,450

Gary will be able to deduct $1,450 in medical expenses on his 2021 tax return.

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Answer:

the correct answer is 6

Step-by-step explanation:

only reasonable answer

The power of 0.4467 indicates that there is a 44.67% chance that the hypothesis test will correctly support the claim that the mean amount of sleep for adults is less than 6 hours when the actual population mean is 3.5 hours of sleep.

The power of a hypothesis test represents the probability of correctly rejecting a null hypothesis when it is false. In this case, the null hypothesis is that the mean amount of sleep for adults is not less than 6 hours.

The alternative hypothesis is that the mean amount of sleep is less than 6 hours. The power is calculated based on the assumed population mean of 3.5 hours, which is different from the null hypothesis.

To find the power, we need to determine the critical value corresponding to the desired significance level (e.g., 0.05) and calculate the probability of obtaining a test statistic greater than this critical value, assuming the alternative hypothesis is true.

The power can be obtained using statistical software or by using a power analysis formula specific to the test being conducted (e.g., t-test or z-test).

In this case, the power is given as 0.4467, which means there is a 44.67% chance of correctly supporting the claim that the mean amount of sleep is less than 6 hours when the actual population mean is 3.5 hours of sleep.

The power value provides an indication of the test's sensitivity to detect a true effect, in this case, the difference between the assumed mean and the claimed mean amount of sleep.

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A simple random sampling of 5 observations from a population containing 400 elements was taken. Then, the point estimate of the population means is 18.

You have a simple random sample of 5 observations from a population containing 400 elements, and the observed values are 12, 18, 19, 20, and 21.

To calculate the point estimate of the population mean, we simply take the average of the sample values.

Point estimate of population mean = (12 + 18 + 19 + 20 + 21)/5 = 18

Therefore, the point estimate of the population means is 18.

To clarify the terms used in the question, a "random sample" is a sample that is selected randomly from the population, meaning that every element in the population has an equal chance of being included in the sample. In this case, a simple random sample of 5 observations was taken. "Elements" refers to the individual units or objects within the population that is being studied. In this case, there were 400 elements in the population.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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-------------

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

The probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

We are required to find the probability of having 90 or more wins in the next three hours of playing a mobile phone game similar to Pokémon, given that the number of successive win follows a Poisson distribution with a mean of 27 wins per hour.

The given mean of Poisson distribution is λ = 27.

The Poisson distribution formula is:P(X = x) = (e^-λ λ^x) / x!

We need to calculate the probability of having 90 or more wins in 3 hours.

We can combine these three hours and treat them as one large interval, for which λ will be λ1 + λ2 + λ3= (27 wins/hour) * 3 hours= 81 wins.

P(X ≥ 90) = 1 - P(X < 90)

To calculate P(X < 90), we can use the Poisson distribution formula with λ = 81.P(X < 90) = Σ (e^-81 * 81^k) / k!, k = 0, 1, 2, ....89= 0.9494

Using the above formula and values, we get P(X ≥ 90) = 1 - P(X < 90)= 1 - 0.9494= 0.0506

Therefore, the probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

Hence, the probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

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a). u(n) is the unit step function, b). the ROC includes the entire z-plane except for the pole at z = 0.9 , c). the pole at z = 0.9 lies outside the unit circle, so the system is unstable.

a. To calculate the right-sided (causal) inverse z-transform h(n) of the given transfer function H(z), we can use partial fraction decomposition. First, let's rewrite H(z) as follows:

H(z) = 1.7/(1 + 3.6z^-1) - 0.5/(1 - 0.9z^-1)

By using the method of partial fractions, we can rewrite the above expression as:

H(z) = (1.7/3.6)/(1 - (-1/3.6)z^-1) - (0.5/0.9)/(1 - (0.9)z^-1)

Now, we can identify the inverse z-transforms of the individual terms as:

h(n) = (1.7/3.6)(-1/3.6)^n u(n) - (0.5/0.9)(0.9)^n u(n)

Where u(n) is the unit step function.

b. To plot the poles and zeros of the transfer function, we examine the denominator and numerator of H(z):

Denominator: 1 + 3.6z^-1 Numerator: 1.7

Since the denominator is a first-order polynomial, it has one zero at z = -3.6. The numerator doesn't have any zeros.

The region of convergence (ROC) is determined by the location of the poles. In this case, the ROC includes the entire z-plane except for the pole at z = 0.9.

c. To determine the stability of the system, we need to examine the location of the poles. If all the poles lie within the unit circle in the z-plane, the system is stable. In this case, the pole at z = 0.9 lies outside the unit circle, so the system is unstable.

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Health Sciences or Teacher Prep?

Answers are B, C & E.

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²

b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:

Left side: 1³ = 1

Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

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a) The equation is not true for n = 1, so P(1) is false.

b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1

a) To find P(1), we substitute n = 1 into the equation given:

13 = (1(1 + 1) / 2)²

13 = (1 / 2)²

13 = 1/4

The equation is not true for n = 1, so P(1) is false.

b) To complete the basic step of the proof, we need to show that P(1) is true.

However, we have just shown that P(1) is false.

This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.

Therefore, the proof cannot proceed and is incomplete.

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Answer:

Discount=20%

Profit=14.20%

Step-by-step explanation:

Answer: the answer is gonna be a decimal which is Decimal: 145.333333 the 3 is repeated it keeps going forever

There is no solution to the system. This means that the equation 2 = -2 in the system is inconsistent.

What is a system of equations?

A system of equations is a collection of two or more equations that are solved simultaneously. Each equation in the system represents a constraint or condition that must be satisfied, and a solution to the system is a set of values that satisfies all of the equations in the system simultaneously.

If you attempt to solve a system of equations and you get a statement like 2 = -2, it means that the equations in the system are inconsistent. An inconsistent system of equations has no solution because there is no set of values that can simultaneously satisfy all of the equations.

Hence, as these equations are contradictory, there is no solution to the system. This means that the equations in the system are inconsistent.

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The number 13 is 3 times the number 54 with the remainder of 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number 54 is divided by 13 with some remainder. The division will be done as below,

13 )   54   ( 3

      -39

___________

       15

Hence, the division with the remainder can be written in mixed form as 3¹⁵/₁₃.

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a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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Answer:To divide 15a^6b^4 by 5a^2b, we can divide the coefficients and then divide the variables using the quotient rule of exponents, which states that when dividing two exponential terms with the same base, you can subtract the exponents.

So we have:

(15a^6b^4) / (5a^2b) = (15/5) * (a^6/a^2) * (b^4/b)

= 3a^(6-2)b^(4-1)

= 3a^4b^3

Therefore, the simplified result of dividing 15a^6b^4 by 5a^2b is 3a^4b^3

Step-by-step explanation:

The solution to the division is 3a⁴b³.

Given that we need to divide the expression (15a⁶b⁴) by (5a²b),

To divide the expression (15a⁶b⁴) by (5a²b), you need to apply the rules of division with variables and exponents.

Here's how you can simplify the expression:

When dividing with the same base, you subtract the exponents. In this case, the base is "a" and the exponents are 6 and 2.

Subtracting the exponents gives us a⁶ - a² = a⁶⁻² = a⁴.

Similarly, for the variable "b," the exponents are 4 and 1.

Subtracting the exponents gives us b⁴ - b¹ = b⁴⁻¹ = b³.

Now, let's simplify the coefficients. The coefficient 15 divided by 5 is 3.

Putting it all together, the expression (15a⁶b⁴) / (5a²b) simplifies to:

3a⁴b³

Hence the solution to the division is 3a⁴b³.

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Answer:

-24

Step-by-step explanation:

f(4) = 6

f(-4*4) = -4 * 6

-4*6

-24

9514 1404 393

Answer:

  (-1, 0)

Step-by-step explanation:

We want the point (4x, f(4x)) to match (-4, 0). We already know that f(-4) = 0, so we want 4x = -4.

  4x = -4

  x = -1 . . . . divide by 4

The desired point is (-1, 0).

_____

Comment on f(4x)

The attached graph shows that f(4x) represents a horizontal compression of the graph of f(x) by a factor of 4. The point on f(4x) with the same y-value, the corresponding point requested by this question, is shown to be (-1, 0).

The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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The system has no solution.

The solution to the system would be the intersection point of the two lines.  Since these lines don't appear to intersect, there's no solution.

Answer:

Step-by-step explanation:

standard form is:

Ax+By=C

for problem 2:

y= 1/2 x-8

y- 1/2 x - 8= 0

rearrange:

- 1/2x + y +8 = 0

2 (- 1/2x + y + 8) = 0

-x + 2y + 16= 0

-x + 2y = -16

leading coefficient can't be negative

so multiply everything by -1

x -2y = 16

Answer:

1 yes   no

Step-by-step explanation:

1 this is in standard form as it is  a linear form and the intercepts can be found  

2 This is not  in standard form as it is a linear equation and both the x and y intercepts cant  be found  so must be written in the form AX+BY=C

so

-x + 2y = -6

and leading coefficient cant be - so multiply by -1

so

x-2y=6

Answer: The Range

The range on the corn has more spread than the soybeans.