HELP 50 POINTS!!!!

a. Is 8.3 a solution of 73.8 < 9x? =

b. is 6.5 a solution of 12x < 78?

c.Is 7 a solution of 9x > 45?

d. is 17 a solution of 19 - x >2?
=
e. is 6 a solution of x + 12 > 18?

Answer:

Do it your self

Step-by-step explanation:

Gross

Answer:

30.5

Step-by-step explanation:

Cos (72°) = x/20

x=cos(72°)×20

x=6.2

x≈6

Answer:

x=6

Step-by-step explanation:

Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

Answer:

  see attached

Step-by-step explanation:

The boundary lines are drawn by considering the relation as an equation.

The first "equation" describes a line with slope -8/3 through the y-intercept point (0, 6). Another point on that line would be 8 units down and 3 units right of (0, 6), at (3, -2). Both inequalities include the "or equal to" case, so both boundary lines are solid lines.

Since we have y ≥ ( ), the shading is above the line.

__

The second "equation" describes a line with a slope of 5/3 through the y-intercept point (0, -7). Another point would be 5 units up and 3 units right of (0, -7), at (3, -2). Since we have y ≤ ( ), the shading is below the line.

That is, the solution region is in the right-hand quadrant of the X where the lines cross. It includes the lines themselves.

Answer:

Perimeter, P = 5.2 cm

Step-by-step explanation:

Perimeter is the sum of all the sides.

All sides of a square is equal. Here, the side of a square is 1.3 cm.

The perimeter of a square is given by :

P = 4 × side

It means,

P = 4 (1.3 cm)

P = 5.2 cm

Hence, the perimeter of the square is 5.2 cm.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

DC=12, AD=5, DB=13, 90 degrees

Step-by-step explanation:

Hope this helps!!!

Let me know if you want an explanation!

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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1. The difference in the distance of Jupiter from the sun than Mercury will be 4.816.

2. The difference in the distance of Neptune from the sun than Mars will be

3. The greatest distance between Earth and Uranus is Uranus.

4. The greatest distance between Venus and Saturn is Saturn

From the information, the average distance from the sun to each planets have been given. The difference in the distance of Jupiter from the sun than Mercury will be:

= 5.203 - 0.387

= 4.816

The difference in the distance of Jupiter from the sun than Mars will be:

= 30.07 - 1.524

= 28.546

The greatest distance between Earth and Uranus is Uranus and the greatest distance between Venus and Saturn is that of Saturn.

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Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

60(.15)= 9

answer is 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.

To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.

However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.

Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.

To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.

Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.

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9514 1404 393

Answer:

  S > 2

Step-by-step explanation:

In this context, "over" means "greater than." The problem statement tells you the weight (S) is greater than 2 kilograms:

  S > 2

Answer:

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If an egg is randomly chosen from each duck, what is the probability that Duck #2’s egg weighs more than Duck #1’s egg?

Duck #2 egg will weigh more if the subtraction of duck's 2 egg by duck's 1 egg is larger than 0.

When we subtract normal distributions, the mean is the subtraction of the means. So

\(\mu = 65 - 70 = -5\)

The standard deviation is the square root of the sum of the variances. So

\(\sigma = \sqrt{6^2+5^2} = \sqrt{61} = 7.81\)

Now, we have to find 1 subtracted by the pvalue of Z when X = 0. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0 - (-5)}{7.81}\)

\(Z = 0.64\)

\(Z = 0.64\) has a pvalue of 0.7389

1 - 0.7389 = 0.2611

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

Answer:

9.09, 309.09

Step-by-step explanation:

Year1 300x.01=3. Balance is 303/(300+3)

Year2 303x.01=3.03 balance is 306.03

Year3 306.03x.01=3.06 balance=309.09

Answer:

Interest earned = $9

Balance after 3 years = $309

Step-by-step explanation:

For simple interest, the formula is I = PRT, where I is the interest earned or paid, P is the principal amount borrowed/deposited, R is the rate as a decimal, and T is the time in years.

I = PRT

I = (300)(0.01)(3)

I = 9

Add that to the amount deposited to start, and you have the balance aftere 3 years. $300 + 9 = $309

The monthly Payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

The monthly payment of a 2-year loan of $1590 with 9% interest which needs to be repaid in 254 equal monthly installments, we need to use the loan repayment formula. The formula is given as:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Here,

Loan Amount = $1590

Interest Rate = 9% per annum

Time = 2 years = 24 months

number of Months = 254 (as there are 254 monthly installments)

First, we need to calculate the Monthly Interest Rate using the following formula:

Monthly Interest Rate = Annual Interest Rate / 12

The Annual Interest Rate is 9%,

so the Monthly Interest Rate is:  Monthly Interest Rate = 9 / 12 = 0.75%Putting the given values into the loan repayment formula,

we get: Monthly Payment = (1590 x 0.0075) / (1 - (1 + 0.0075)^(-254))= 11.92 (approx)

Therefore, the monthly payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

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Answer:

B) 47 units²

Step-by-step explanation:

It can be done by finding the area of the black, but it will be much easier to find the area of the white and subtract.

Total area of the grid equals 10x8=80

There are two rectangles at the bottom.  6+8=14

There are 4 triangles that each equal 4.5.  4.5*4=18

There is 1 small triangle at the top that equals 1.

80-14-18-1=47

Answer:

a) y = 2,035(1.03)^t

b) 2,359

Step-by-step explanation:

a)

Exponential growth:

y = a(1 + r)^t

where

y = future vale

a = initial value

r = periodic rate of growth

t = number of periods

y = 2,035(1 + 0.03)^t

y = 2,035(1.03)^t

b)

Here we have a = 2,035; r = 3% = 0.03; t = 5

y = 2,035(1 + 0.03)^5

y = 2,359

2,359

Answer:

No.

Step-by-step explanation:

It's simpler than you might expect.

If \((x - 4)\)  is a factor, then it means that it the function \(f(x) = x^3 - 2x^2 + 5x + 1\) can have \((x - 4)\) factorised out.

This means that we can say \((x - 4) = 0\)

Therefore \(x = 4\)

If we put \(x = 4\) into the equation:

\(f(4) = (4)^3 - 2(4)^2 + 5(4) + 1\\= 64 - 32 + 20 + 1\\= 53\)

We didn't get 0, therefore it isn't a factor!

Answer:  I belive it is 360 inches cubed. I could be wrong

Step-by-step explanation:

Answer:$2346

Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.

Answer:

The correct range is -2 < y < 5.

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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The answer is 9.

We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.            

First of all we will convert dimensions of poster from feet to inches.

Now, let us compare sides of our original photo with corresponding sides of poster.

Now, let us compare the second pair of corresponding sides.

We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.      

Step-by-step explanation:

= 700 + 500 + 100 - 1000

= 1200 + 100 - 1000

= 1300 - 1000

= 300

The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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