If f (x) = -12x + 34 What is the value of f (-2)?

It should be noted that the number of cupcakes that Cadence bake on Monday is 21 cupcakes.

It should be noted that Cadence baked 45 cupcakes on Tuesday and this was 3 more than twice the number of cupcakes she baked on Monday

2Let the number of cakes on Monday = x

Therefore, the expression will be:

(2 × x) + 3 = 45

2x + 3 = 45

Collect like terms

2x = 45 - 3.

2x = 42

Divide

x = 42 / 2

x = 21

Therefore, it should be noted that the number of cupcakes that Cadence bake on Monday is 21 cupcakes.

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When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

(2,-2)

Step-by-step explanation:

Point A is 2 units to the right of the origin so the x coordinate is 2

It is also 2 units down so the y coordinate is -2

The point is (x,y) so A = (2,-2)

Answer:

A.(2,-2)

Step-by-step explanation:

Thus, the one notebook' price n = $6 and the price of one pencil is p = $2.4.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. Once an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

Let cost of a notebook to be 'n' dollars

Let the cost of a pencil to be 'p' dollars,

Then, the system of equations are-

3n + 5p = 30   ..eq 1

n + 10p = 30  ....eq2

multiply eq 2 with 3

3n + 30p = 90 ...eq 3

Subtract eq 3 from eq 1

3n + 5p - 3n - 30p = 30 - 90

25p = 60

p = 2.4

n + 10(2.4) = 30

n = 30 - 24

n = 6

Thus, the price of one notebook n = $6 and the price of one pencil is p = $2.4.

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Answer:

In factored form: \(y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}\)

In standard form: \(y=\sqrt{-\frac{4}{25}x^2+4}\)

Step-by-step explanation:

Generally for these type of equations we want to get the term with "y" by it self (ignoring coefficients and any operations such as square root, etc...) so we want to get rid of the \(4x^2\) from the left side which we can do by subtracting this from both sides to maintain equality and get rid of it on the left side.

\(25y^2=-4x^2+100\)

One thing I want to note here is we can actually factor the right side which we generally want to do, we can rewrite it as: \(-(4x^2-100)\) and from here we have a difference of squares: \(a^2-b^2=(a-b)(a+b)\) so we can rewrite this as: \(-(2x-10)(2x+10)\)

\(25y^2=-(2x-10)(2x+10)\)

From here we divide both sides by 25:

\(y^2=-\frac{1}{25}(2x-10)(2x+10)\)

Now from here to get rid of that square we do the inverse which is taking the square root:

\(y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}\)

The reason factoring is useful in this case is we can now easily determine the domain of the function since inside the square root we have a quadratic which is opening down meaning it's only not negative between the zeroes (including the zeroes since they're... zero not negative) and this would be the domain of the graph. But if we wanted it to not be in factored form we would just put back what we had so we would have:

\(y=\sqrt{-\frac{1}{25}(4x^2-100)}\)

then distribute the -1/25 to get:

\(y=\sqrt{-\frac{4}{25}x^2+4}\)

Answer:

$4.42

Step-by-step explanation:

hope that helps :))

Answer:

1 hour and 15 min

Step-by-step explanation:

I think this is right but look it up just to be sure

Step-by-step explanation:48miles in 60 min. 1/4 of 60 is 1so 60 +15 = 1hr 15 min.

Answer:

The question is not complete, below is a complete question with the accompanying diagram:

Instructions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

AB is parallel to CD, and EF is perpendicular to AB

The number of 90° angles formed by the intersections of Ef and the two parallel lines AB and CD is ____

Answer:

The number of 90° angle formed = 8 angles

Step-by-step explanation:

From the question and attached diagram, the following information is given:

AB is parallel to CD

EF is perpendicular to AB

Required: number of 90° angles formed by the intersection of the perpendicular line and the parallel lines.

Note, the angle formed between a line and a perpendicular line = 90°

From the diagram:

Number of 90° angle formed by intersection of perpendicular line EF and line AB = ∠1, ∠2, ∠3 and ∠4 = 4 angles

Number of 90° angle formed by intersection of perpendicular line EF and line  CD = ∠5, ∠6, ∠7 and ∠8 = 4 angles

Total 90° angles formed by perpendicular line with lines = ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 = 8 angles

Answer:

u=6

Step-by-step explanation:

18=3u

6=u

Answer:

U=6

Step-by-step explanation:

Answer:

The answer would be C

Step-by-step explanation:

q equals cube root of 64

because if you want to get rid of cube. you take cube root on both side

(q^3)^1/3= (64)^(1/3)

q=64^(1/3)

Answer:

Step-by-step explanation:

Let's start by assigning variables to represent the unknowns in the problem. We can use "n" to represent the number of nickels and "d" to represent the number of dimes.

From the problem statement, we know that the total value of the coins in the purse is $0.70. We can write an equation to represent this information:

0.05n + 0.10d = 0.70

We also know that the number of nickels is two less than six times the number of dimes. We can write an equation to represent this information:

n = 6d - 2

Now we can substitute the expression for "n" into the first equation:

0.05(6d - 2) + 0.10d = 0.70

Simplifying the left side of the equation, we get:

0.30d - 0.10 + 0.10d = 0.70

Combining like terms, we get:

0.40d = 0.80

Dividing both sides by 0.40, we get:

d = 2

So there are 2 dimes in the coin purse. Now we can use the second equation to find the number of nickels:

n = 6d - 2 = 6(2) - 2 = 10

So there are 10 nickels in the coin purse.

Therefore, Sheri has 10 nickels and 2 dimes in the coin purse for her daughter.

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

The second option is correct

Step-by-step explanation:

a number times a negative is positive, but then if you multiply the positive by another negative, the answer is negative

Answer:

Both variables appear to have something in common.

Explanatory: crowd/sale

Response: win/loss

There are two possible effects of crowd size to this game one might be due to pressure and nervousness from crowd size or

Another factor( variable) which is related to crowd size and the outcome of the match.

Step-by-step explanation:

Given data:

Home games with sell out crowd

Win = 3

Loss = 15

Total = 18

Home games without sell out crowd

Win = 12

Loss = 11

Total = 23

Therefore:

Percentage of win with sellout crowd

= 3/18 * 100

= 0.166 * 100

= 16.7%

Percentage of win with smaller crowd

= 12/23 * 100

= 0.522 * 100

= 52.2%

Both variables appear to have something in common.

Explanatory: crowd/sale

Response: win/loss

There are two possible effects of crowd size to this game one might be due to pressure and nervousness from crowd size or

Another factor( variable) which is related to crowd size and the outcome of the match.

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

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Given the function:

The roots of the function are the value of x which make the function f(x) = 0

We can find the roots by drawing the function

The intersection between the function and the x-axis will give the roots of the function

The graph of the function is as shown in the following picture:

As shown, the points of intersection with the x-axis are:

( -3, 0 ) and ( -2, 0) and ( -1, 0 )

so, the roots of the function are:

x = { -3, -2, -1 }

Answer:the answer is 1/16

so none of the above

Step-by-step explanation:

Answer:

a) The claim is not plausible

b) claim is plausible and the type of bias here is response bias

Step-by-step explanation:

Given data:

Number of political parties = 4

coffee party got the support of 435 out of 1183 randomly selected voters in a poll conducted.

A) Construct and interpret a 98% confidence interval to estimate the proportion of voters who support the coffee party

H0 ( null hypothesis ) : p = 0.42

Ha ( alternate hypothesis ) : p ≠ 0.42

z value for 98% confidence interval = 2.326

using 98% confidence interval the value of p = ( 0.3668, 0.3686 )

hence the claim is not plausible

B) Determine the type of bias

Assume the actual number of people = 1200

and 17 people did not respond

hence number of people who responded = 1200 - 17 = 1183

Therefore the claim by the manager is plausible because 17 people did not respond and the type of bias here is response bias

attached below is a detailed solution of the problem of the A part

The equation for the polynomial in the standard form is:

P(x) = x^3 + x^2 - 2x

A polynomial of degree N with the n zeros {x₁, x₂, x₃, ..., xₙ} is written as:

P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)

That is called the factorized form of the polynomial, and we are assuming that the leading coefficient is equal to 1 just for simplicity.

In this case we have 3 zeros {-2, 0, 1}, so the polynomial is of degree 3, and we can write it as:

P(x) = (x + 2)*(x - 0)*(x - 1)

To write the polynomial in the standard form, we need to expand the product:

P(x) = (x + 2)*(x)*(x - 1)

P(x) = (x^2 + 2x)*(x - 1)

P(x) = (x^3 + 2x^2 - x^2 - 2x)

P(x) = x^3 + x^2 - 2x

That is the polynomial.

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Answer:

The ratio equivalent to the sin of ∠A will be:

sin ∠A = BC / AB

Hence, option 3) is correct.

Step-by-step explanation:

We know that some of the trigonometric ratios such as

In our case

Ф  = ∠A

As we have to determine the ratio equivalent to the sin of ∠A

so

sin Ф = Opposite / Hypotenuse

Here:

Ф  = ∠A

Opposite of ∠A = BC

Hypotenuse = AB

Thus,

substituting Ф  = ∠A, Opposite = BC, Hypotenuse = AB

sin Ф = Opposite / Hypotenuse

sin ∠A = BC / AB

Therefore, the ratio equivalent to the sin of ∠A will be:

sin ∠A = BC / AB

Hence, option 3) is correct.

Answer:

0.4444 = 44.44% probability that the sum of the two numbers is greater than 3 but less than 7.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A number is selected at random from each of the sets {2,3,4} and {1, 3, 5}.

The possible values for the sum are:

2 + 1 = 3

2 + 3 = 5

2 + 5 = 7

3 + 1 = 4

3 + 3 = 6

3 + 5 = 8

4 + 1 = 5

4 + 3 = 7

4 + 5 = 9

Find the probability that the sum of the two numbers is greater than 3 but less than 7?

​4 of the 9 sums are greater than 3 but less than 7. So

\(p = \frac{4}{9} = 0.4444\)

0.4444 = 44.44% probability that the sum of the two numbers is greater than 3 but less than 7.

Solution

For this case we can do the following:

We can do this:

Answer:

The answer is 0.34

Step-by-step explanation:

I'm sorry i don't have an explanation for this. please like this comment is my answer is right

Explanation:

You must find the probability of Gina playing at least three games before playing game A. The phrase “at least three” means “three, four, five, or more.” That means Gina would not play game A in the first two occurrences (n – 1 = 3 – 1 = 2). Search the table for all outcomes that do not have A in the first two occurrences. These occurrences represent the event you’re interested in. Estimate the probability using the formula

.

The answer is 0.34.

Answer:

a)

\begin{gathered} {5}^{2} = 25 \\ {6}^{2} = 36 \\ {7}^{2} = 49\end{gathered}

5

2

=25

6

2

=36

7

2

=49

Therefore:

25, 36 and 49

Answer:

No solution.

Step-by-step explanation:

To solve this problem, all you have to do is graph the lines and see where they intersect.

This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Answer:

see attached

Step-by-step explanation: