Which of these numbers is greater than 2.25 but less than 1? Is it 1 or 1.5 or 0 or 2.5....

I think the answer is 1.5 but can someone tell me how I came up with this answer. He has to write it down.

Answer:

The value of f(3) = -2.

Step-by-step explanation:

First of all, let's find f(2).

\(f(n+1)=f(n)^{2}-3\)

\(f(1+1)=f(1)^{2}-3\)

\(f(2)=f(1)^{2}-3=2^{2}-3=1\)

Now, we can find f(3):

\(f(2+1)=f(2)^{2}-3\)

\(f(3)=f(2)^{2}-3=1^{2}-3=-2\)

Therefore, the value of f(3) = -2.

I hope it helps you!

Answer:

c

Step-by-step explanation:

Answer:

28 degrees

Step-by-step explanation:

We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.

By combining like terms, we get 6x + 12 = 180.

Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.

Answer:

1

Step-by-step explanation:

a fourth is 1/4 meaning Fourth = 1/4

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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Answer:

1/2 of the soda:) sure yan

Answer:

sorry i dont know

Step-by-step explanation:

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

The expression that would represent the total number of students at the summer camp for all three years is (b) 5.5s - 54

Let the number of students in 2010 be s.

So, we have:

The total number of students is:

Total = s + 1/2s + s - 54

Evaluate

Total = 9s/2 - 54

Rewrite s:

Total = 5.5s - 54

Hence, the expression that would represent the total number of students at the summer camp for all three years is (b) 5.5s - 54

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Question below!

what do you need in order to construct in order to find a point/location that has the same distance away from 2 or more other points

Answer:

Hi, There! Mika-Chan I'm here to help! :)

To find the distance from a point to a line, first find the perpendicular line passing through the point. Then using the Pythagorean theorem, find the distance from the original point to the point of intersection between the two lines.

Hope this Helps!

Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

12.2

Step-by-step explanation:

Mean = average

8 + 12 + 24 + 13 + 4 =

61

61 / 5 =

12.2

Answer:

12.2

Step-by-step explanation:

Mean is the average number in a data set.

To find the mean:

Add every data value:

8 + 12 + 24 + 13 + 4 = 61

Divide 61 by 5:

61 / 5 = 12.2

12.2 represents the mean of this data set.

Answer:

12 minutes

Step-by-step explanation:

3 inches every 2 minutes, divide the 3 by 18 since the pool is that many inches deep and multiply 6 by 2 since it fills 3 more inches every 2 minutes and thats your answer.

Answer:

\(5x+11\)

Step-by-step explanation:

Step 1: Distribute

\(3x+6+2x+5\)

Step 2: Add like terms

\(5x+11\) < your answer

Answer:

It's C because its 2 to the power of 5

Step-by-step explanation:

2x2x2x2x2

Answer:

The test statistic is \(z = -2.1\)

The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A simple random sample of 400 parts from supplier 1 finds 20 defective.

This means that:

\(p_1 = \frac{20}{400} = 0.05, s_1 = \sqrt{\frac{0.05*0.95}{400}} = 0.0109\)

A simple random sample of 200 parts from supplier 2 finds 20 defective.

This means that:

\(p_2 = \frac{20}{200} = 0.1, s_2 = \sqrt{\frac{0.1*0.9}{200}} = 0.0212\)

Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Test whether the defective rates of the parts from two suppliers are significant different at the 1% significance level.

At the null hypothesis, we test if they are equal, that is, if the subtraction of the proportions is 0. So

\(H_0: p_1 - p_2 = 0\)

At the alternate of the null hypothesis, we test if they are different, that is, if the subtraction of the proportions is different of 0. So

\(H_a: p_1 - p_2 \neq 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the sample proportions:

\(X = p_1 - p_2 = 0.05 - 0.1 = -0.05\)

\(s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0109^2 + 0.0212^2} = 0.0238\)

Value of the test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.05 - 0}{0.0238}\)

\(z = -2.1\)

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.05, that is, P(|z| < 2.1), which is 2 multiplied by the p-value of Z = -2.1.

Z = -2.1 has a p-value of 0.0179

2*0.0179 = 0.0358.

The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.

Answer:

Cause 25/25 is a whole number and 25/38 is not

Step-by-step explanation:

9514 1404 393

Answer:

  $342.66

Step-by-step explanation:

For the 3 overtime hours Michael worked, he is paid at the rate of 1.5×$8.675 per hour. This is equivalent to $8.675 per hour for 1.5×3 = 4.5 hours. So, we can figure Michael's total pay as ...

  (35 h + 1.5×3 h)×($8.675 /h) = (39.5 h)×(8.675 /h) = $342.66

Michael's total pay for the week is $342.66.

The distance that would be covered after t seconds = 1.5t meters

The speed of the race=distance/time =1.5m/s

The time given = t seconds

The distance (d) = ?

From the formula of speed = distance/time, make distance the subject of formula,

distance (d) = speed×time

= 1.5×t

= 1.5t meters

Therefore, the distance covered is 1.5t meters after t seconds.

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Answer:

B is the better buy.

Step-by-step explanation:

A: conical container: volume = π(6/2)²*9/3 = 27π

B: cylindrical container: volume = π(6/2)²*9 = 81π

Cost per unit volume:

A: $1.75/(27π) = $0.0206

B: $3.75/(81π) = $0.0147

So B is cheaper.

B is the better buy.

Answer: A = 37°

c = 8.31

b = 6.63

Step-by-step explanation:

I suppose that the triangle is something like the one below.

Then we know the measure of an angle and the length of the adjacent cathetus.

a = 5

B = 53°

Now we can use the relationships:

Tan(B) = (opposite cathetus)/(Adjacent cathetus) = b/a

Cos(B) = (adjacent cathetus)/(hypotenuse) = a/c

Sin(B) = (opposite cathetus)/(hypotenuse) = b/c

Then we have:

Tan(53°) = b/5

Tan(53°)*5 = b = 6.63

So we found the length of b.

Now we can use the second relationship to find the length of c:

cos(53°) = 5/c

c = 5/cos(53°) = 8.31

Now, to find the angle A we can use the fact that the sum of all interior angles of a triangle must be equal to 180°

We know that is a triangle rectangle, so we have an angle equal to 90°, this one is C = 90°, and we also know that B = 53°

Then:

A + B + C = 180°

A + 53° + 90° = 180°

A + 53° = 180° - 90° = 90°

A = 90° - 53° = 37°

Then:

A = 37°

c = 8.31

b = 6.63

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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The expressions are solved and answered below.

Given are the expressions as shown in the image.

{ 1 } -

2\($\frac{5}{6}\) - 2\($\frac{1}{5}\)

17/6 - 11/5

17/6 - (11 x 1.2/5 x 1.2)

17/6 - 13.2/6

3.8/6

38/60

19/30

{ 2 } -

3\($\frac{5}{8}\) + 7/3

29/8 + 7/3

(29 x 3)/(8 x 3) + (7 x 8)/(3 x 8)

87/24 + 56/24

143/24

Similarly the remaining expressions can be evaluated.

Therefore, the expressions are solved and answered above.

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{Question in english -

Please help urgently with all the answers}

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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\( \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} \)

\( \\ \)

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

\( \\ \\ \)

\( \\ \\ \)

Let's recall that a complex number in algebraic form is written as \( \sf z = a + ib \) , where a is its real part and b is its imaginary part.

\( \\ \)

The modulus of said complex number is calculated as follows:

\( \sf | \sf z| = \sqrt{a^2 + b^2} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

Let's identify our values:

\( \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i \)

\( \\ \)

Now, substitute these values into our formula:

\( \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} \)

\( \\ \)

While this may be optional, the result can be simplified by using the following property:

\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}\)

\( \\ \)

\( \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

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Answer:

The angles remain the same for all values of n. After a dilation, the angle measurements for the image and the preimage are always equal.

Step-by-step explanation:

Answer:

The angles remain the same for all values of n. After a dilation, the angle measurements for the image and the preimage are always equal.

Step-by-step explanation:

A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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Answer:

a. 3

b. 5

c. 4

d. 4

e. 10

Step-by-step explanation:

Answer:

read below

Step-by-step explanation:

a.3

b.5

c.2

d.2

6. 8p