Solve for a and d

6x^2+14x+4=(ax+b)(cx+d)

b=1 and c=2

Answer:

The sample size required is 102.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error for this interval is:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

Given:

σ = 9.2

(1 - α)% = 90%

MOE = 1.5

The critical value of z for 90% confidence level is:

[tex]z_{0.10/2}=1.645[/tex]

*Use a z-table.

Compute the value of n as follows:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]

         [tex]=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102[/tex]

Thus, the sample size required is 102.

To calculate the sample size for a 90% confidence interval with a 1.5 margin of error using a known standard deviation of 9.2, you would need a sample size of approximately 101.

90% Confidence Interval Sample Size Calculation

To determine the required sample size for a 90% confidence interval with a maximum margin of error of 1.5, and a known population standard deviation of 9.2, you can use the following formula:

n = (Z*σ/E)^2

Here, 'n' is the sample size, 'Z' is the Z-score corresponding to the desired confidence level, 'σ' is the population standard deviation, and 'E' is the maximum margin of error. For a 90% confidence level, the Z-score is approximately 1.645 (since 5% is in each tail of the normal distribution). Plugging in the values we have:

n = (1.645 * 9.2 / 1.5)^2

The calculation yields:

n = (15.074 / 1.5)^2

n = (10.049)^2

n = 101.0

Therefore, you would need a sample size of approximately 101 to ensure the sample mean does not deviate from the population mean by more than 1.5 with a 90% confidence interval.

Answer:

x =(3-√37)/2=-1.541

x =(3+√37)/2= 4.541

Step-by-step explanation:

to long to explain sorry but trust me

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation     x² + 3x + 7 = 0

Let's solve this equation by two methods.

1) Completing the perfect square trinomial

                 x² + 3x      = -7

                 x² + 3x + (3/2)² = -7 + (3/2)²

                (x + 3/2)² = -7 + 9/4

                 (x + 3/2)² = -19/4

                 x + 3/2 = √-19/√4

                 x = -3/2 + √-19/2         It has imaginary solutions.

2.- Graph the equation

See the graph below.

In the graph we notice that the equation does not cross the x-axis so it does not have real solution.

Answer:

0.28142

Explanation

First change 0.792 into standard form

To evaluate the square root of 0.792 using tables, you would typically refer to a set of pre-calculated square root values in the form of a table. These tables were commonly used before calculators and computers became widely available.

To begin the evaluation process, you would follow these steps:
**Step 1: Locate the closest square values**
First locate the two perfect square values that surround 0.792. If you have a comprehensive table, you may find an exact value, but often you'll need to interpolate between two values.
**Step 2: Interpolation**
If 0.792 is not a value directly found in the table, you use interpolation. Let's assume that your table shows that the square root of 0.784 (which is \( 0.28²  \)) is 0.28, and the square root of 0.81 (which is \( 0.9²  \)) is 0.9. Your value, 0.792, lies between these two.
**Step 3: Estimation**
Since \( 0.28² \) is 0.784 and \( 0.9² \) is 0.81, 0.792 is closer to 0.784 than 0.81. You would then estimate it to be closer to 0.28 than 0.9.
**Step 4: Fine-tuning**
Now, find the difference between the square roots and the differences between the squares:
- The difference between 0.28 and 0.9 is 0.62.
- The difference between 0.784 and 0.81 is 0.026.
Next, find out where 0.792 falls between 0.784 and 0.81 in proportion to the difference between the square roots.
- The difference between 0.792 and 0.784 is 0.008.
- To find the proportion of 0.008 to the total difference 0.026, you divide 0.008 by 0.026 to get approximately 0.308.
- Now, multiply this proportion by the difference between the square roots to refine your estimate: 0.62 * 0.308 ≈ 0.191.
**Step 5: Calculate your estimate**
Add this value to the lower square root to get an approximation of the square root of 0.792:
0.28 + 0.191 ≈ 0.471.
**Final Answer**
The square root of 0.792 is approximately 0.471 using interpolation with table values.

Answer:

C is the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

120 m

Step-by-step explanation:

Let the length of the pole be a and the shadow be b at 58° and b+90 at 36°.

Then, as the pole and its shadow form a right triangle, we have:

As,

The equations change to:

Comparing the two equations:

Then

Answer:

y = [tex]\frac{1}{2}[/tex]x+1

Step-by-step explanation:

To find a right angle we need to find the perpendicular line. The trick here is to do the flip of your slope and since there is no "that passes through the point (#, #) you're done after that. So the answer is

y = [tex]\frac{1}{2}[/tex]x+1

Answer:

Step-by-step explanation:

We take all the blues and all the reds and  1 green and divide it at the total number of bages.

14/20

The probability of Carol pulling a green chip from the bag is 7 out of 20. This is calculated by dividing the number of green chips by the total number of chips.

The subject of this question is Probability which falls under Mathematics. In this particular question, Carol has a total of 20 chips: 3 red, 10 blue, and 7 green.

Probability is calculated as 'the number of ways an event can occur' divided by 'the total number of outcomes'. Here, the event is pulling out a green chip. There are 7 green chips, and 20 total chips. So, the probability would be calculated as:

Number of green chips (Favorable outcomes) / Total chips (Total outcomes)

Which translates to: 7/20

That means, the probability of pulling out a green chip from the bag is 7 out of 20 times, if we repeat this experiment infinite times under the same conditions.

https://brainly.com/question/22962752

#SPJ3

Answer: There’s a .35 % chance that the marble will be green. When drawing all 3, the chance is .04%

Step-by-step explanation:

The dimensions of the tank that minimize the surface area are a square base of 24 ft × 24 ft and a height of 12 ft.

To minimize the surface area, we need to minimize the sum of the areas of the five sides of the tank. Let's denote the side length of the square base as x and the height of the tank as h.

Given that the volume V = 6912 ft³, and for a rectangular tank, the volume is V = base area × height = x² × h.

So, we have x² × h = 6912.

To minimize the surface area, we differentiate the surface area formula with respect to x, set it equal to zero, and solve for x.

The surface area A = x² + 4xh.

Differentiating A with respect to x, we get [tex]\frac{dA}{dx}[/tex] = 2x + 4h.

Setting [tex]\frac{dA}{dx}[/tex] = 0 gives us 2x + 4h = 0, so x = -2h.

Since x cannot be negative, we ignore this solution.

Now, using x² × h = 6912, we can solve for h:

h = [tex]\frac{6912}{x^{2} }[/tex]

Substituting x = -2h:

[tex]\[ h = \frac{6912}{(-2h)^2} = \frac{6912}{4h^2} = \frac{1728}{h^2} \][/tex]

Solving for h:

[tex]h^3 = \frac{1728}{h^2}\\h^5 = 1728\\h = \sqrt[5]{1728} = 12[/tex]

Now, substituting h = 12 back into x² × h = 6912:

[tex]x^2 \times 12 = 6912\\x^2 = \frac{6912}{12} = 576\\x = \sqrt{576} = 24[/tex]

Answer:

The answer is A.

Step-by-step explanation:

(Only if your question "Amos’s solution is (2, –14). What did he do wrong? ")

Trust me, I got it right

Answer:

Step-by-step explanation:

%17 because you take %78 of %22

(the second part is more tricky...

17% were first time takers who past.

%60  of %78 = %46.8 = percentage of people who were first time takers who failed.

so total percentage of first time takers = 46.8 +17 = %63.8.

Then 17/63.8 X %100 = percent of first time takers who passed.

=26.6 percent therefore %27 is correct.

Answer:

30 fruits

Step-by-step explanation:

Let

x ----> number of plums on the plate

y ----> number of apples on the plate

we know that

The ratio of the number of plums to the number of apples was 3:2

so

[tex]\frac{x}{y} =\frac{3}{2}[/tex]

[tex]x=1.5y[/tex] ----> equation A

After Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples

so

[tex]x-6=y[/tex] ----> equation B

substitute equation A in equation B

[tex]1.5y-6=y[/tex]

solve for y

[tex]1.5y-y=6\\0.5y=6\\y=12[/tex]

Find the value of x

[tex]x=1.5(12)=18[/tex]

therefore

Mon put on the table

[tex]x+y=18+12=30\ fruits[/tex]

Answer:

30

Step-by-step explanation:

Answer:

x=15.08 cm

y=7.54 cm

Step-by-step explanation:

We are given that

Volume of box=1715 cubic cm

Side length of base=x

l=b=x

Height of box=h=y

Volume of box=lbh=x^2y

[tex]1715=x^2y[/tex]

[tex]y=\frac{1715}{x^2}[/tex]

Surface area of box=Area of bottom+area of four faces=[tex]x^2+4xy[/tex]

[tex]S=x^2+4x(\frac{1715}{x^2}=x^2+\frac{6860}{x}[/tex]

Differentiate w.r.t x

[tex]S'(x)=2x-\frac{6860}{x^2}[/tex]

[tex]S'(x)=0[/tex]

[tex]2x-\frac{6860}{x^2}=0[/tex]

[tex]2x=\frac{6860}{x^2}[/tex]

[tex]x^3=\frac{6860}{2}=3430[/tex]

[tex]x=(3430)^{\frac{1}{3})=15.08[/tex]

Again differentiate w.r.t x

[tex]S''(x)=2+\frac{13720}{x^3}[/tex]

Substitute x=15.08

[tex]S''(x)=2+\frac{13720}{(15.08)^3}>0[/tex]

Hence, the surface area is minimum at x=15.08 cm

[tex]y=\frac{1715}{(15.08)^2}=7.54 cm[/tex]

The dimensions of the bin that will minimize the surface area are:

Base side (x): 7.5cm

Height (y): 36.13cm

Let's express the surface area and volume of the box in terms of x and y:

Surface area (A):

A = 2x^2 + 4xy

Volume (V)V = x^2y

We are given that the volume of the box must be 1715cm3:

1715cm3 = x^2y

Solving for y, we get:

y = 1715/x^2

Now, we want to minimize the surface area (A) subject to the constraint that the volume (V) is 1715cm3. We can use Lagrange multipliers to solve this optimization problem.

L(x, y, λ) = A - λ(V - 1715)

L(x, y, λ) = 2x^2 + 4xy - λ(x^2y - 1715)

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 4x + 4y - 2λxy = 0

∂L/∂y = 4x - λx^2 = 0

∂L/∂λ = -x^2y + 1715 = 0

Substituting V = x^2y into the third partial derivative, we get:

∂L/∂λ = -V + 1715 = 0

Solving these equations simultaneously, we get:

x = 7.5

y = 36.13

Answer:

50

Step-by-step explanation:

An angle that measures 50° Turns through 50 1° angles because 50 *1 = 50

1 degree * 50 turns = 50 degrees

Final answer:

When Mai turns 65, the value of her individual Retirement Account will be $61,917.28.

Explanation:

To calculate the future value of an investment with compound interest, we can use the formula:

FV = P(1+r)^n

Where FV is the future value, P is the principal amount (initial investment), r is the interest rate (as a decimal), and n is the number of compounding periods.

In this case, Mai invested $2000 and the interest rate is 10% compounded annually.

So, when Mai turns 65, the number of compounding periods would be 65 - 21 = 44 years.

Plugging in the values into the formula:

FV = $2000(1+0.10)^44 = $61,917.28

Therefore, the value of Mai's individual Retirement Account when she turns 65 will be $61,917.28.

The function [tex]k(x) = 2x^2[/tex] is which the average rate of change over the interval 1 < x < 5 greater than the average rate of change of g(x).

Given data:

The function is represented as [tex]g(x)=1.8x^2[/tex].

Now, the average rate of change of the function is S.

The value of [tex]S=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex].

The interval of the function is from 1 < x < 5.

So, for g(x), [tex]S=\frac{f(5)-f(1)}{5-1}[/tex].

The value of S = 10.8

For the function [tex]k(x) = 2x^2[/tex], the rate of change is:

[tex]S=\frac{k(5)-k(1)}{4}[/tex]

[tex]S=\frac{50-2}{4}[/tex]

So, the value of S = 12 and is greater than 10.8

Hence, the function is [tex]k(x) = 2x^2[/tex].

To learn more about rate of change of function, refer:

https://brainly.com/question/29548786

#SPJ4

The complete question is attached below:

For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x^2?
A.=f(x) = x^2

B.=g(x) = 1.2x^2

C.=h(x) = 1.5x^2

D.=k(x) = 2x^2

Answer:

The total income after 29 days is $16,106,127.33

Step-by-step explanation:

This is a geometric progression with the first element being 0.03 and the ratio is 2. So if we want to know the total income after 29 days we can use the formula for the sum of elements in a series of that kind, this is given by:

sum(29 elements) = [(first element)*(1 - r^(29))]/(1 - r)

sum(29 elements) = [0.03*(1 - 2^(29))]/(-1)

sum(29 elements) =(0.03*(-536870911))/(-1)

sum(29 elements) = -16106127.33/(-1) = 16106127.33

The total income after 29 days is $16,106,127.33

Answer:

73.8 degrees because 96.5-22.7=73.8

Step-by-step explanation:

Answer:

It makes the solution of the equation easier

Step-by-step explanation:

Here we have the formula relating Celsius and Fahrenheit given as follows;

[tex]C = \frac{5\times (F - 32)}{9}[/tex]

From the above Celsius to Fahrenheit equation, we have that to solve for F we rearrange the formula as follows

[tex]C =\frac{5F}{9} - \frac{32\times 5}{9}[/tex]

Which is the same as

[tex]C =\frac{5F}{9} - 17\frac{7}{9}[/tex]

It is then seen that rearranging the equation between Celsius and Fahrenheit makes it easier to solve for either °C or °F.

Answer:

It’s easier to find the solution to a variable when that variable is by itself on one side of the equal sign. Rearranging formulas before substituting values for each variable makes calculations more straightforward. With this approach, we only need to perform operations such as multiplication, division, addition, and subtraction on one side of the equal sign, and we simplify instead of solving by using the properties of equality.

Step-by-step explanation:

Answer:

y=6x-2

Step-by-step explanation:

Answer:

y is 6

Step-by-step explanation:

they are very similar in alot of ways but im not sure how to discribe im good at putting them onto a graph

Answer:

23

Step-by-step explanation:

Answer:

31.42 yards

Step-by-step explanation:

The formula for the circumference is pi multiplied by the diameter.

To work this out you would first multiply 5 by 2, which would be 10 yards. This is because the radius is half of the diameter. Then you would multiply pi by 10, which would be 31.416.

radius=[tex]\frac{1}{2}[/tex] of diameter

Circumference=[tex]\pi d[/tex]

1) Multiply 5 by 2.

[tex]5*2=10[/tex]

2) Multiply pi by 10.

[tex]\pi *10=31.416[/tex]

3) Round to 2 decimal places.

[tex]31.42[/tex]

Answer:

The answer is $206,451

Step-by-step explanation

This scenario is asking to subtract 19 percent away from 229,390 .

Step one :  Divide 229,390 by 10 ( take away the zero behind the 9 )

Step 2 : Subtract 22,939 from 229,390 since we know ten percent of 229,390 is 22,939 = 206451

Answer:

Joe makes $206,451 annually

Step-by-step explanation:

 229,390 divided by 10 = 22,939

Then Subtract 22,939 from 229,390 = 206,451

Answer:

Refer below.

Step-by-step explanation:

True statements for Approximately 25 men in the sample weigh are:

More than 150 lbs.

More than 162 lbs.

Between 150 and 155 lbs.

Between 155 and 162 lbs.

Based on the experimental data, approximately 25 men in this sample weigh:

A boxplot simply refers to a type of chart that can be used for the graphical representation of the five-number summary of any data set, especially based on skewness, locality, and spread.

Additionally, the five-number summary of a data comprises the following:

In this scenario, the true statement is that approximately 25 men in this sample would weigh:

Read more on boxplots here: https://brainly.com/question/14277132

#SPJ5

The amount of cement is needed to create the walkway around the rectangular pool will be 176 square yards . Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The area is the combination of two rectangles of 12 by 4, and four triangles of 4 by 4, and two rectangles of 6 by 4.

Then the area will be

A = 2(12 x 4) + 4(1/2 x 4 x 4) + 2(6 x 4)

A = 96 + 32 + 48

A = 176 square yards

Then the correct option is A.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ5

Final answer:

The concentrations of Solution A, Solution B, and the final alcohol mixture are needed to determine how many milliliters of Solution B to mix with Solution A. Without these specifics, we provide a general approach using the method of allegations and unit conversion.

Explanation:

The student's question pertains to the mixing of two solutions with different concentrations of alcohol to achieve a specific concentration in the resulting mixture. We cannot provide a direct answer to the question as stated because the concentrations of Solution A, Solution B, and the resulting mixtures are not specified. To calculate the amount of Solution B needed, we must know the concentration (percentage by volume or molarity) of alcohol in Solution A and Solution B, as well as the desired concentration of the final mixture.

For instance, if we were given a situation where Solution A is 60% alcohol and we need to mix it with Solution B, which is 40% alcohol, to make a resulting mixture that is 50% alcohol, we could use the method of allegations to find the correct proportions. Using the formula:

Solution A concentration + Solution B concentration = Total concentration of mixture

We can then solve for the unknown by inputting the given values and applying algebraic methods to find the volume of Solution B.

Assuming we use mL for milliliters and L for liters, to accurately measure and mix the solutions, we may also need to convert units between mL and L, taking into account that there are 1,000 milliliters in 1 liter.

Answer:

(a)The percentage of hatchbacks that run on gasoline.=78%

(b) The percentage of diesel vehicles that are hatchbacks.=21%

(c)The percentage of SUVs that run on gasoline=30%

(d)The percentage of gasoline vehicles that are sedans=42%

(e)The percentage of sedans that run on diesel =44%

(f)The percentage of gasoline vehicles that SUVs.=8%

Step-by-step explanation:

This table gives information about vehicles sold at a dealership in a month.

------------------Gasoline-------Diesel

Hatchback------18---------------5

Sedan------------15---------------12

SUV----------------3----------------7

(a)The percentage of hatchbacks that run on gasoline.

Total Number of Hatchbacks=23

Number that run on Gasoline=18

Percentage that run on gasoline=(17/23)X100=78%

(b) The percentage of diesel vehicles that are hatchbacks.

Total Number of Diesel Vehicles=5+12+7=24

Number of Diesel Hatchbacks=5

Percentage of diesel vehicles that are hatchbacks=(5÷24)X100=21%

(c)The percentage of SUVs that run on gasoline

Total Number of SUVs=10

Number of Gasoline SUVs=3

Percentage of SUVs that run on gasoline=(3÷10)X100=30%

(d)The percentage of gasoline vehicles that are sedans.

Total Number of Gasoline Vehicles=18+15+3=36

Number of Gasoline sedans=15

Percentage of Sedans that run on gasoline=(15÷36)X100=42%

(e)The percentage of sedans that run on diesel

Total Number of Sedans=15+12=27

Number of Diesel Sedans=12

Percentage of sedan that run on diesel=(12÷27)X100=44%

(f)The percentage of gasoline vehicles that SUVs.

Total Number of Gasoline Vehicles=18+15+3=36

Number of Gasoline SUVs=3

Percentage of SUVs that run on gasoline=(3÷36)X100=8%

Answer:

(a)The percentage of hatchbacks that run on gasoline.=78%

(b) The percentage of diesel vehicles that are hatchbacks.=21%

(c)The percentage of SUVs that run on gasoline=30%

(d)The percentage of gasoline vehicles that are sedans=42%

(e)The percentage of sedans that run on diesel =44%

(f)The percentage of gasoline vehicles that SUVs.=8%

Step-by-step explanation:

hope that helps

When x=0 we get y=1

1 = 3(0) + ?

1 = ?

Answer: 1

Answer:

1

Step-by-step explanation:

This equation is written in slope intercept form, which is y=mx+b

This is where m is the slope, and b is the y intercept. What we need to find here, is the y intercept.

The y intercept is what y equals when x is 0.

Based on the table, we know that y is 1, when x is 0.

Therefore, the equation completed, would be y=3x+1

Answer:

37 students

Step-by-step explanation:

Final answer:

To determine the number of students on the trip, multiply the number of adults by their ticket cost, subtract this from the total cost, and then divide the remainder by the student ticket cost to find that 37 students went on the trip.

Explanation:

The question involves a group pricing problem where the wildlife club spent $350 on zoo admission, adults tickets cost $7.50 each, and student tickets cost $5 each. If there were 22 adults on the trip, we need to calculate the number of students who attended.

To solve this, we first calculate the total cost for adult admissions by multiplying the number of adults by the cost per adult ticket: 22 adults × $7.50/adult = $165. Then, we subtract this amount from the total cost to determine the amount spent on student tickets: $350 total - $165 for adults = $185 for students.

Finally, we divide the remaining amount by the cost per student ticket to find the number of student tickets: $185 ÷ $5/student = 37 students. Therefore, 37 students went on the trip.