Find: (6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)

Answer:

Gretta's Contribution = $52,500

Interest = $125,588.79

Step-by-step explanation:

Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).

125 x 12 x 35 = $52,500

Therefore, over the 35 years, Gretta contributed $52,500.

If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.

$178,088.79 − $52,500 = $125,588.79

There was $125,588.79 in interest earned on Gretta's account.

The height of the airplane after 7 hours would be 28770 feet above sea level.

Given the quadratic equation for the height of the airplane as a function of time after takeoff,

\(y = -8.2x^2 + 85.6x + 90.3,\)

Where x represents the time in hours and y represents the height in hundreds of feet above sea level.

To find the height of the airplane after 7 hours, we need to substitute x = 7 into the quadratic equation and solve for y:

\(y = -8.2*(7)^2 + 85.6*(7) + 90.3\)

\(y = -8.2(49) + 599.2 + 90.3\)

\(y = -401.8 + 599.2 + 90.3\)

\(y = 287.7\)

So, the height of the airplane after 7 hours would be 287.7 hundreds of feet above sea level. To convert it to regular feet, we multiply by 100 (since the equation is in hundreds of feet):

\(287.7 * 100 = 28770\) feet.

As a result, after 7 hours, the height of the aircraft would be 28770 feet above sea level.

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Answer:

can i see a ss of the question?

Step-by-step explanation:

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

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

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

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

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

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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The Software E costs in the long term is $10,500

Cost sharing is a term used to describe a situation in which two or more parties agree to share the cost of a particular expense or project. In other words, it refers to a joint financial contribution made by multiple parties towards a common goal.

Software E purchased in $6,000. If person will be satisfied then he will purchase it for long term, so the satisfaction rate is 75% of original cost.

Then, the Software E costs in the long term = $6,000 + ($6,000× 75%)

\(=6,000 + (6,000 * \frac{75}{100} )\)

\(=6,000 + (60 * 75 )\)

\(=6,000 + 4500\\= 10,500\)

Therefore, the Software E costs in the long term is $10,500

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Answer:

≈3.11

Step-by-step explanation:

The value of the quantity after 21 days, to the nearest hundredth, given the expoenential decay is 3.11.

When a quantity decays , it means that the value of the quantity declines with the passage of time.

The formula that can be used to determine the value of the quantity after a number of weeks is :

FV = P (1 - r)^n

Where:

920 x (1 - 0.85)^3

920 x 0.15^3 = 3.11

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Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

Answer:

It is a function!

Step-by-step explanation:

It wouldnt be a funtion if the arrows pointed to the same number hope this helps!:)

Answer:

\( - \frac{1}{3} \)

Step-by-step explanation:

The slope of a line passing through two points is given by

\(\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }\)

where \((x_1,y_1)\) is the 1st coordinate and \((x_2,y_2)\) is the 2nd coordinate

Given: (3, 0) and (0, 1)

Slope

\( = \frac{0 - 1}{3 - 0} \)

\( = - \frac{1}{3} \)

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Answer:

yes because 96/6 equals 16, and 6x16=96

Step-by-step explanation:

KA-BOOM!!! meh

Answer:

Yes it is

because 96/6 = 16

And if you flip it you'll get the same thing

Step-by-step explanation:

Answer:

c) Population parameter or Population statistic

Step-by-step explanation:

Population:-

The totality of observation with which we are concerned , whether this number be finite or infinite is called population

Sample :

A sample is subset of a Population

Given data  the USA today internet poll is called Population

Given data 73 percent of readers are satisfied with their lives.

This is called Population parameter.

Answer:

15

Step-by-step explanation:

Answer:

x=16

I hope this helped

Answer:

X = 16

Step-by-step explanation:

Answer:

A)20ac because if it takes him a minutes to run

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

The value is   \(Z_{\frac{\alpha }{2} } =  1.96\)

Step-by-step explanation:

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Answer:

Options A, C, E

hope it helps

please mark brainliest

Answer:

the graph crosses the y-axis at -5 and x-axis at -6

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer:

The calculated value of t= 0.1908 does not lie in the critical region t= 1.77 Therefore we accept our null hypothesis that  fatigue does not significantly increase errors on an attention task at 0.05 significance level

Step-by-step explanation:

We formulate null and alternate hypotheses are

H0 : u1 < u2 against Ha: u1 ≥ u 2

Where u1 is the group tested after they were awake for 24 hours.

The Significance level alpha is chosen to be ∝ = 0.05

The critical region t ≥ t (0.05, 13) = 1.77

Degrees of freedom is calculated df = υ= n1+n2- 2= 5+10-2= 13

Here the difference between the sample means is x`1- x`2= 35-24= 11

The pooled estimate for the common variance σ² is

Sp² = 1/n1+n2 -2 [ ∑ (x1i - x1`)² + ∑ (x2j - x`2)²]

= 1/13 [ 120²+360²]

Sp = 105.25

The test statistic is

t = (x`1- x` ) /. Sp √1/n1 + 1/n2

t=   11/ 105.25 √1/5+ 1/10

t=  11/57.65

t= 0.1908

The calculated value of t= 0.1908 does not lie in the critical region t= 1.77 Therefore we accept our null hypothesis that  fatigue does not significantly increase errors on an attention task at 0.05 significance level

Answer:

The nth term rule of the quadratic sequence is \(2n^{2} +5n-3\).

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  \(an^{2}+bn+c\)

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  \(\dfrac{4}{2}\) = 2

SO, the first term of the nth term rule equation is \(an^{2}\) = \(2n^{2}\).

Now, in the term \(2n^{2}\), put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then \(2n^{2}\) = \(2 \times (1)^{2}\) = 2

If n = 2, then \(2n^{2}\) = \(2 \times (2)^{2}\) = 8

If n = 3, then \(2n^{2}\) = \(2 \times (3)^{2}\) = 18

If n = 4, then \(2n^{2}\) = \(2 \times (4)^{2}\) = 32

If n = 5, then \(2n^{2}\) = \(2 \times (5)^{2}\) = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is \(2n^{2} +5n-3\).

The specialty fees will of the project will be $175,000.

What is specialty fee in a project?

Specialty fee of a project is associated with the cost or money that is given for some special task for e.g. hiring a architect or other specialist.

To calculate the amount of money that will be spent on specialty fees, we need to multiply the total amount of money raised (35,000,000) by the specialty fee percentage (0.5%).

specialty fees = 35,000,000 * 0.005 = 175,000

So, $175,000 will be spent on specialty fees.

Also, To calculate the amount of money that will be spent on service commission, we need to multiply the total amount of money raised (35,000,000) by the service commission percentage (2%).

service commission = 35,000,000 * 0.02 = 700,000

So, $700,000 will be spent on service commission.

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To raise $35,000,000 for a project's financing, a corporation will issue shares and bonds. The project's specialist fees will be $175,000 in total.

The cost or amount paid for a project's specialty work, such as employing an architect or another specialist, is known as the specialty fee. We must multiply the entire cash raised ($35,000,000) by the proportion of speciality fees ($0.5%) to determine the amount that will be used for fees.

35,000,000 * 0.005 = 175,000 in specialist fees.As a result, specialist fees will cost $175,000. Additionally, we must multiply the total sum of funds raised (35,000,000) by the service commission rate (2%), in order to get the amount that will be used for service commission. service commission: 35,000,000 * 0.02 = 700,000 , The service commission will therefore receive $700,000.

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How to calculate force?

.Inorder to calculate force we will use Newton's second law of motion.

\(\\ \sf\longmapsto Force=Mass\times Acceleration \)

\(\\ \sf\longmapsto F=ma\)

Here we can observe

\(\\ \sf\longmapsto F\propto a\)

\(\\ \sf\longmapsto F\propto m\)

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

Answer:

1) acute

2) obtuse

3) straight

4) right

Step-by-step explanation:

acute angle=less than 90

right angle=90 exactly

obtuse=greater than 90

straight=exactly 180

hope this helps

Answer:

a. ∆BAC & ∆DEC

b. they have a vertical angle because they both share c, and <a = <e. If two angles are congruent, the third must be congruent as well.

c. √90 = 3√10

a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.

b. The value of 2x + 5y is 25.

a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:

6a + 9b = 3(2a + 3b)

This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24

(ii) What is the value of 2x + 5y?

4x + 10y = 50

It should be noted that this can be divided through by 2. This will be;

(4x + 10y = 50) / 2

2x + 5y = 25

The value is 25.

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Answer: 13 miles per hour

Step-by-step explanation:

1/5mi=1/65hr

65/5mi=hr

13mi hr

Answer:

Sarah has 11 packages of sour patch kids and 6 packages of M&Ms

Step-by-step explanation:

11 + 6 = 17, and 11 is five more than 6, fulfilling the needs of the problem

Answer:

Sarah has 11 packages of sour patch kids and 6 packages of M&Ms

Step-by-step explanation:

11 + 6 = 17, and 11 is five more than 6, fulfilling the needs of the problem

hope this helps

The statement that best describes how to determine whether f(x) = 9 – 4x² is an odd function is:

Determine whether 9 - 4(-x)² is equivalent to -(9 – 4x²).

An odd function is a function in which the following statement holds true for all values of x.

f(-x) = -f(x).

For this problem, these values are given by:

Hence the statement that best describes how to determine whether f(x) = 9 – 4x² is an odd function is:

Determine whether 9 - 4(-x)² is equivalent to -(9 – 4x²).

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