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When f(x) = 9x² - 5x + 3, evaluate f(-3)
f(− 3) =
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The exact area of the circle with a radius of 9 cm is 81π cm².

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr².

Given, The radius of the circle is 9 cm.

Therefore, The area of the circle with a radius of 9 cm is,

= π(9)² cm².

= 81π cm².

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

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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The area that will be painted grey is approximately 38 ft².

The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.

Circumference of a circle = 2πr

30.77 = 2 x 3.14 x r

r = 30.77 / (2 x  3.14) = 4.9 feet

Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.

Area of a circle = π x r²

Area of half the circle = 0.5 x  π x r²

Area of half the circle = 0.5 x 3.14 x 4.9²

Area of half the circle = 37.73 ft²

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Answer:

The total number of registered doctors in this year are 307345.

Step-by-step explanation:

Let the total number of doctors who registered in this year are x

Given that the total number of female doctors in total registered doctors are 54400

According to the question 17.7 percent of the total registered doctors are the female doctors

Hence the total number of  registered doctors who are females are 17.7% of x

which is written as 17.7*x÷100

According to the question 17.7x÷100= 54400

as we are given that the total number of female doctors are 54400

now

17.7x = 54400×100

x= 54400×100÷17.7

x= 307344.633 ≈ 307345

Therefore there are 307345 doctors who registered that year.

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The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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Answer:

Step-by-step explanation:

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

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Answer:

It is -4/7

Step-by-step explanation:

\( \frac{168}{ - 294} \\ \\ = - \frac{4}{7} \)

Answer:

168/-294 × 5/5 = 840/1470

= - 840/ 1470

= 1470

Explanation

Answer:

y = x - 2

Step-by-step explanation:

To write the equation in the form y = mx + b, find the value of slope (m) and y-intercept (b) of the graph.

Slope (m) = change in y/change in x

Using two points on the line, say (0, -2) and (2, 0),

Slope (m) = (0 -(-2))/(2 - 0)

m = 2/2

m = 1

y-intercept (b) = -2 (this is the point where the y-axis is intercepted by the line, at this point, x = 0)

✔️To write the equation, substitute m = 1 and b = -2 into y = mx + b

y = 1(x) + (-2)

y = x - 2

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

Step-by-step explanation:

x4 – 6x2 – 27 = 0

                        x=2.49,-2.49

3x4 = 2x

x=6

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

The expressions that are equal to 7⁸ x 7 are:

B. For (7¹⁸)/7⁹

C. For (7³)³

E. For 7⁴ x 7⁵

Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.

A. For 7³ x 7³

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7³ ⁺ ³

Calculate the sum or difference: 7⁶

Calculate power : 117649

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

B. For (7¹⁸)/7⁹

Reduce the fraction: 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

C. For (7³)³

simplify using exponent power rule : 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

D. For 7⁴ + 7⁵:

Calculate the power: 2401 + 16807

Calculate the sum or difference: 19208

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

E. For 7⁴ x 7⁵:

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁴ ⁺ ⁵

Calculate the sum or difference: 7⁶

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

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I understand that the question you are looking for is:

Select all the expressions that are equivalent to 7⁸ x 7.

A. For 7³ x 7³

B. For (7¹⁸)/7⁹

C. For (7³)³

D. For 7⁴ + 7⁵:

E. For 7⁴ x 7⁵

Answer:

none

Step-by-step explanation:

point steeler

The measure of angle MTU m∠MTU is 114 degree.

From the figure in the diagram:

Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.

Since, angle STU composes or is the sum of angle STM and angle MTU.

To find angle MTU, simply subract angle STM from angle STU.

m∠STU = m∠STM + m∠MTU

Hence:

m∠MTU = m∠STU - m∠STM

Plug in the given values and simplify

m∠MTU = 145° - 31°

Subtract 31 from 145

m∠MTU = 114°

Therefore, angle MTU measure 114°.

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Answer:

4(x-8)(x-3)

Step-by-step explanation:

First take out a factor of 4:

4(x^2 -11x + 24)

Then factor the quadratic

4(x-8)(x-3)

Answer:

1 quart must be added

Step-by-step explanation:

To do this, set up an equation.

Let x be the number of quarts of antifreeze to be added. Then, you know that the new solution will have a total of 4 quarts with 2/5 of it being antifreeze, so \(\frac{2}{5} (x+3)\) would be the amount of antifreeze. Another way to represent the amount of antifreeze is \(x + \frac{3}{5}\) because the original mixture has 3/5 of quart of antifreeze, while the added stuff is fully antifreeze.

Now, you just solve the equation:

\(\frac{2}{5} (x + 3) = x + \frac{3}{5}\)

multiply both sides by 5

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

Use the distributive property on the left

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

subtract 2x from both sides

\(6 = 3x + 3\)

subtract 3 from both sides

\(3 = 3x\)

divide both sides by 3

\(1 = x \\x = 1\)

Therefore the answer is 1 quart

Answer:

TWO CRACKERS

Step-by-step explanation:

I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.

Hope this helped

Answer:

Yes it is correct

Step-by-step explanation:

right

Answer:

-9.25

Step-by-step explanation:

I don't really know how to explain this over a computer.

Hope that this helps!

Answer:

7

Step-by-step explanation:

Because there are 7 zeros :)

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Here's the solution ~

\(\qquad \sf  \dashrightarrow \:b(b + 12) = 0\)

Here, we have two cases :

\(\qquad \sf  \dashrightarrow \:b = 0\)

\(\qquad \sf  \dashrightarrow \:b + 12 = 0\)

\(\qquad \sf  \dashrightarrow \:b = - 12\)

Hence, 0 and -12 are the only possible solutions for given equation.

The linear function for the given graph is y = x + 20.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:

y = mx + b

From the graph,

The coordinates of the given graph are (0,20) and (20,40)

Then, slope (m) = (40-20)/(20-0) = 20/20 = 1

and y-intercept (b) = 20

So, the equation will be y = 1x + 20

Hence, the linear function for the given graph is y = x + 20.

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9514 1404 393

Answer:

  1/9^5

Step-by-step explanation:

  \(\dfrac{9^2}{9^7}=\dfrac{9\cdot 9}{9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9}=\dfrac{1}{9\cdot 9\cdot 9\cdot 9\cdot 9}=\boxed{\dfrac{1}{9^5}}\)

_____

An exponent is an indicator of repeated multiplication. As you can see, factors in the numerator cancel those in the denominator, so the result is the difference of the exponents.

Answer:

E. C= 80+ 12n

Step-by-step explanation:

____________

By assuming  the graph of a function of the form y=acros(k(x-b)) ,

The possible values for a, k, and b are: a = 4, k = 2, and b = π/4. So, option B is the right choice.

To determine the possible values for a, k, and b based on the given graph, we can analyze the characteristics of the graph.

The function y = a*cos(k(x-b)) represents a cosine function with parameters a, k, and b.

Looking at the given options:

A. a = 2, k = 4, and b = π/4

B. a = 4, k = 2, and b = π/4

C. a = 4, k = 2, and b = -π/4

D. a = 4, k = 1/2, and b = -π/4

We can eliminate options A and D based on the values of a and k not being consistent with the characteristics of the graph.

To determine the correct option between B and C, we need to consider the amplitude, period, and phase shift of the graph.

The amplitude of the cosine function is represented by |a|, which is the absolute value of a. Looking at options B and C, both have |a| = 4, so the amplitude is consistent.

The period of the cosine function is given by T = 2π/|k|. Option B has k = 2, resulting in T = 2π/|2| = π, which matches the period of the graph.

Lastly, the phase shift of the cosine function is represented by b. Option B has b = π/4, which matches the phase shift of the graph.

Therefore, based on consistency with the amplitude, period, and phase shift of the graph, the possible values for a, k, and b are:

B. a = 4, k = 2, and b = π/4.

The right answer is B. a = 4, k = 2, and b = π/4

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