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The inequality expression 9|x - 8| < 36 when solved for x is 4 < x < 12

To solve the inequality 9|x - 8| < 36, we can divide both sides by 9:

|x - 8| < 4

This means that the distance between x and 8 is less than 4. So, the solution can be expressed in two parts:

x is less than 4 units away from 8 to the left:

x < 8 - 4 = 4

x is less than 4 units away from 8 to the right:

x > 8 + 4 = 12

Therefore, the solution is 4 < x < 12, or in interval notation: (4, 12).

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Answer:

If y varies directly as x, then we can express this relationship using a proportionality constant k, such that:

y = kx

To solve for k, we can use the initial condition given:

y = 21 when x = 3

Substituting these values into the equation above, we get:

21 = k * 3

Solving for k, we get:

k = 7

Now that we have k, we can use the equation to find y when x = 2:

y = kx

y = 7 * 2

y = 14

Therefore, when x = 2, y = 14.

Step-by-step explanation:

Answer/Step-by-step explanation:

A. Tens means groups the units into groups of 10. On the other hand,  tenth means one part in ten equal parts written as 1/10. Therefore:

30 tens = 30 x 10 = 300

3 tens = 3 x 10 = 30

3 tenths = 3/10 = 0.3

Thus:

30 tens - 3 tens 3 tenths = 300 - 30.3 = 269.7

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B. 3.4

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C. To find 24 tenths - 1 and 3 tenths, you need to convert the mixed number 1 and 3 tenths into a fraction. 1 and 3 tenths = 1/1 + 3/10. To add these fractions, find a common denominator by multiplying both the numerator and denominator of 1/1 by 10. Thus, 1 and 3 tenths = 10/10 + 3/10 = 13/10. Now you can subtract 24/10 - 13/10 by subtracting the numerators to find the correct answer: 24/10 - 13/10 = 11/10, or 1 and 1 tenth

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D. 6 ones 7 hundredths -2.3

We make a place chart for 6 ones 7 hundredths. We write 0 in the remaining place value.

Hundred     tens    Ones   point     tenths     hundredths       thousandths

 0                0          6            .             0             7                             0

6 one 7 hundredths is 6.07

Now subtract 2.3 from 6.07

6.07 - 2.3 = 3.77

Answer : 3.77

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E. 8.246 - 5 hundredths is equal to 8.196

5 hundredths in number form is 0.050

     8.246

   - 0.050

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

     8.196

In subtracting decimals, line up the decimal points to avoid confusion.

Use 0 as padding so that the decimals will contain the same number of digits after the decimal.

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F. In order to determine the result, we have to know about the notation numbers. In a rational number, every position number has a notation.

So, according to the image, we have to change "5 ones 3 tenths":

5 ones 3 tenths= 5*1+3*0.1=5+0.3=5.3

Then:

=5.3-0.53

=4.77

The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way

This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is\(10 (300/30=10).\) This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.

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The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).

The divergence of a vector field in Cartesian coordinates is given by the following formula:

∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),

where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.

In this case, we have:

Fx = (5x^2 + 7 - sin(xz)),

Fy = 0, and

Fz = (5x^2 + 7 - sin(xz)).

Taking the partial derivatives, we get:

∂Fx/∂x = 10x - zcos(xz),

∂Fy/∂y = 0, and

∂Fz/∂z = 10x - zcos(xz).

Now, substituting these derivatives into the divergence formula, we have:

∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).

Simplifying further, we get:

∇ · F = 20x - 2zcos(xz).

Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

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Here’s what you need to know about intercepts. The x intercept of a graph has y coordinate zero. The y intercept of a graph has x coordinate zero.

AN EXAMPLE OF THIS IS:

So if you have a function y = 2x + 8 you would set x = 0 to find the y intercept. So we would get y = 8. To find the x intercept we would set y = 0 and get 0 = 2x + 8

or -8 = 2x or x = -4

Now if you have a more difficult like function y = 3x^2 + 10x - 4 we proceed the same way. To find the y intercept we would set x = 0 and get y = -4 so the y intercept is (0,-4)

To find the x intercept we would set y = 0 and get 3x^2 + 10x - 4 = 0. If you know the quadratic formula you could solve this by:

x = [-b +- SR(b^2 - 4*a*c] / 2a

so in our case x = [-10 +- SR(100 - 4*3*(-4))] / (2*3)

x = [-10 +- SR(100 + 48)] / 6

x = [-10 +- SR (148)] / 6

x = [-10 +- 12.2] / 6 approximately

x = [-10 - 12.2] / 6 or [-10 + 12.2 / 6]

x = -22.2/6 or 2.2/6

Answer:9.73

Step-by-step explanation:

Answer:

2:5= 2/5

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

48 + 30m

Step-by-step explanation:

The perimeter of a hexagon is 6 times its side length.

6(8 + 5m)

= 48 + 30m (Distributive property)

Answer:

below given.

Step-by-step explanation:

(A) √16/4 = √4 = 2

(B) 0/5 = 0

(C) √5³ / 5 = √125 / 5 = √5  = 2.236

(d)  -30/15 = -2

Answer:

x = 50

Step-by-step explanation:

\(\log _{10}\left(x\right)=\log _{10}\left(2x^2\right)-2\)

\(\log _{10}\left(x\right)=\log _{10}\left(2x^2\right)-\log _{10}\left(100\right)\)

\(\log _{10}\left(x\right)=\log _{10}\left(\frac{2x^2}{100} \right)\)

\(x = \frac{2x^2}{100}\)

\(100x=2x^2\)

\(x^2 = 50x\)

\(x = 50\)

Answer:

36

Step-by-step explanation:

2(10)+4^2

20+4^2

20+16

36

Answer: The result of the math formula =2*10+4^2 is 28.

To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.

Answer:

first find the area of triangle on right side using1/2×b×h and find area if remained parallelogram using b×h formula.

hope it helps <3

Answer:

C

Step-by-step explanation:

Answer:

Given : A=(1,2)≡(x  

1 ,y  

1

​

) and B=(3,−2)≡(x  

2

​

,y  

2

​

)

Let M=(x,y) be the midpoint of AB

x=(  

2

x  

1

​

+x  

2

​

​

) and  y=(  

2

y  

1

​

+y  

2

​

​

)

Then, x=  

2

1+3

​

and y=  

2

2−2

​

⟹x=2 and y=0

∴M=(2,0)

∴ Coordinates of the midpoint of AB is (2,0)

Step-by-step explanation:

The elements in (A ∩ B) ∪ C are 1, 2, 3, 5, 7, 9.Option B) 02 is the answer.

We are given that A = {1, 2, 3, 4, 5, 6, 7, 8), B = {2, 3, 5, 7, 11} and C = {1, 3, 5, 7, 9}.Now, A ∪ B is the set of elements in either A or B (or in both).So, A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 11}.Now, A ∪ B ∪ C is the set of elements in A or B or C (or in two or three of them).So, A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11}.

Now, (A ∩ B) is the set of elements common to both A and B.So, A ∩ B = {2, 3, 5, 7}.Now, (A ∩ B) ∪ C is the set of elements in both A and B or in C.So, (A ∩ B) ∪ C = {1, 2, 3, 5, 7, 9}.

So, the elements in (A ∩ B) ∪ C are 1, 2, 3, 5, 7, 9.Option B) 02 is the answer.

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The correct option from the list provided is 03.

Let A = {1, 2, 3, 4, 5, 6, 7, 8), let B = {2, 3, 5, 7, 11} and let C = {1, 3, 5, 7, 9).

The union of two sets A and B is denoted by A U B, is the set of elements that belong either to set A or to set B or to both A and B.

The intersection of sets A and B is denoted by A ∩ B, is the set of elements that belong to both A and B.So, A ∩ B = {2, 3, 5, 7}Then, (A ∩ B) U C = {1, 2, 3, 5, 7, 9}.

Therefore, the elements in (A ∩ B) U C are:1, 2, 3, 5, 7, and 9.

So, the correct option from the list provided is 03.

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The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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Answer:

38.28 .........................

Answer:

57.13..................................................

Answer:

The slope is -3/2

Given the provided information, if a woman over 35 tests positive for ovarian cancer, the probability that she actually has cancer is approximately 1.96%.

To determine the probability that a woman over 35 actually has ovarian cancer given a positive test result, we can create a contingency table and use conditional probability. Let's consider a hypothetical sample of 100,000 women:

Out of 100,000 women, 1 in every 2,500 (or 40 out of 100,000) actually has ovarian cancer. Since the test has a 0% rate of false negatives, all the women with ovarian cancer will test positive.

The test also has a 5% rate of false positives. This means that out of the remaining 99,960 women who do not have ovarian cancer, approximately 5% (or 4,998) will test positive incorrectly.

Therefore, out of a total of 5,038 positive test results (40 true positives + 4,998 false positives), only 40 are true positives for ovarian cancer. The probability that a woman who tests positive actually has ovarian cancer can be calculated as the ratio of true positives to the total positive tests:

Probability = (True Positives) / (Total Positive Tests) = 40 / 5,038 ≈ 0.00795 ≈ 0.795%

Thus, the probability that a woman over 35 actually has ovarian cancer given a positive test result is approximately 1.96%. This calculation highlights the importance of considering both the prevalence of the disease and the accuracy of the test in interpreting the results correctly.

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Answer:

  1728 in³

Step-by-step explanation:

You want the volume in cubic inches of a cubic foot.

The volume of a cube is equal to the cube of its edge dimension. The cube with edge 12 inches will have a volume of ...

  V = s³

  V = (12 in)³ = 1728 in³

A cubic foot is a volume of 1728 cubic inches.

__

Additional comment

Perhaps this illustrates for you why the volume varies as the cube of the dilation factor. 1 in³ × 12³ = (12 in)³ = 1728 in³

Cost for 5 tickets = $20

Cost for 1 ticket = ?

To find the cost of 1 ticket we must divide 20 by 5 (in general, to find the cost of 1 thing we must divide the money by the number of things).

So,

Cost of 1 ticket = 20/5

Cost of 1 ticket = $4

_________

RainbowSalt2222 ☔

Answer:

$4

Step-by-step explanation:

20 dollar total of five tickets. divide the cost between each ticket to get your answer

20÷5=4

Answer:

\(x = 4\)

Step-by-step explanation:

\(4.5x = 18 \\ \\ \frac{4.5}{4.5} x = \frac{18}{4.5} \\ \\ x = \frac{18}{4.5} \\ \\ x = \frac{180}{45} \\ \\ x = 4\)

I hope I helped you^_^

To balance the equation MnO4−​ + IO3−​ → MnO2​ + IO4−​ in acid solution, we need to make sure that the number of atoms of each element is the same on both sides of the equation.

First, let's balance the oxygen atoms:

On the left side, we have 4 oxygen atoms from MnO4−​ and 3 oxygen atoms from IO3−​, giving a total of 7 oxygen atoms.

On the right side, we have 2 oxygen atoms from MnO2​ and 4 oxygen atoms from IO4−​, giving a total of 6 oxygen atoms.

To balance the oxygen atoms, we can add H2O molecules to the equation. By adding 1 H2O molecule on the left side, the equation becomes:

MnO4−​ + IO3−​ + H2O → MnO2​ + IO4−​

Now, let's balance the hydrogen atoms:

On the left side, we have 2 hydrogen atoms from H2O.

On the right side, we have 0 hydrogen atoms.

To balance the hydrogen atoms, we can add H+ ions to the equation. By adding 4 H+ ions on the right side, the equation becomes:

MnO4−​ + IO3−​ + H2O → MnO2​ + IO4−​ + 4H+

Now, let's count the total coefficients of the reactants:

On the left side, we have a coefficient of 1 for MnO4−​, a coefficient of 1 for IO3−​, and a coefficient of 1 for H2O, giving a total of 3.

On the right side, we have a coefficient of 1 for MnO2​, a coefficient of 1 for IO4−​, and a coefficient of 4 for H+, giving a total of 6.

Therefore, the sum of coefficients of reactants is 3. Answer choice (a) 5, (b) 6, (c) 7, (d) 8, and (e) 10 are incorrect.

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A) The equation is 22 + (d * 1/2) = 30

B) The plant that still have to grow 8 cm more

C) d = 16 days, d represents the number of days

Step-by-step explanation:

Given:

Initial height (basil plant at buying) = 22cm

Plant grows on everyday = 1/2cm

A) Given:

Total  height (to be grown) = 30 cm.

The equation is,

Initial height+ ( number of days * plant grows on everyday) =  Total height

22 + (d * 1/2) = 30  →  equation 1

B) The plant that still have to grow = Total height - Initial height

= 30 - 22

= 8 cm

C) Solving the value d using equation 1:

22 = 30 - (d * 1/2)

    44 = 60 - d 

      d = 16 days

Hence, A) The equation is 22 + (d * 1/2) = 30.

B) The plant that still have to grow 8 cm more.

C) d = 16 days, d represents the number of days.

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