Which expression is always equivalent to sin x when 0° < x < 90°?
(1) cos (90°- x)
(3) cos (2x)
(2) cos (45° - x)
(4) cos x

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

Answer:

Let's denote:

- A as the event "student is accepted at FSU"

- B as the event "student is accepted at UF"

We have the following probabilities given:

- P(A) = 0.4 (probability of being accepted at FSU)

- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)

- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).

We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.

To calculate this, we can use Bayes' Theorem, which states that:

P(A|B') = P(B'|A) * P(A) / P(B')

We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:

P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4

Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7

Finally, we can substitute these values into Bayes' theorem:

P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229

Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.

The mean of the scores to the nearest tenth is 83.7.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given the question above, we need to find the mean of the scores to the nearest tenth.

We can find the mean by using the formula below:

[tex]\text{Mean} = \dfrac{\text{Sum of all the observations}}{\text{Total number of observations}}[/tex]

Now,

[tex]\text{Mean} = \dfrac{70(6)+75(3)+80(9)+85(5)+90(7)+95(8)}{6+3+9+5+7+8}[/tex]

[tex]\text{Mean} = \dfrac{420+225+720+425+630+760}{38}[/tex]

[tex]\text{Mean} = \dfrac{3180}{38}[/tex]

[tex]\text{Mean} = 83.7[/tex]

Therefore, the mean of the scores to the nearest tenth is 83.7.

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Answer:

A acute angle is a angle that is less than 90*

Answer:

-5/4

Step-by-step explanation:

Let [tex](x_1,y_1)=(-4,4)[/tex] and [tex](x_2,y_2)=(0,-1)[/tex]. The slope of the line would be:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}[/tex]

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

Answer:

Here's an example:

convert 2.5 into a mixed number.

Make the denominator less than the original.

The easy way for this is to do 25/10

when you put it through a calculator it ends up being 2.5

(essentially the mixed number and the decimal are the SAME numbers.)

Hope this clarified. :)

To convert a decimal to a mixed number, follow these steps:

Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.

Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.

Step 3: Express the decimal part as a fraction by using the place value of the last digit.

Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 5: Combine the whole number part, the fraction, and simplify if necessary.

Here's an example:

Let's say we have the decimal 2.75.

Step 1: The whole number part is 2.

Step 2: The decimal part is 0.75.

Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.

Step 4: The fraction 3/4 is already in its simplest form.

Step 5: Combining the whole number part and the fraction, we have 2 3/4.

So, the decimal 2.75 can be written as the mixed number 2 3/4.

Remember to always simplify the fraction part if possible.

Answer: 88.94

Step-by-step explanation:

First, l found what was 8.125 out of 110 which is 8.94

then added 8.125 and 8.94 which got 118.94

But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94

Group A is performing most consistently in terms of quality and associate engagement compared to last month.

To determine which performance area the groups are performing most consistently compared to last month, we need to compare the scores of each performance area between the two months.

Let's analyze each performance area:

Quality:

For Group A, the quality score increased from 90 to 94, indicating an improvement in quality performance. However, for Group B, the quality score decreased from 74 to 70, indicating a decline in quality performance. Therefore, Group A is performing more consistently in terms of quality compared to last month.

Productivity:

For Group A, the productivity score decreased from 79 to 62, showing a significant decline in productivity performance. Similarly, for Group B, the productivity score decreased from 86 to 58, indicating a notable decline as well. Both groups experienced a decrease in productivity performance, but Group A had a larger decline. Therefore, neither group is performing consistently in terms of productivity compared to last month.

Associate Engagement:

For Group A, the engagement score increased from 68 to 70, suggesting a slight improvement in associate engagement. Conversely, for Group B, the engagement score increased from 76 to 72, indicating a slight decline. Both groups had minor changes in engagement scores, but Group A had a smaller change. Therefore, Group A is performing more consistently in terms of associate engagement compared to last month.

Based on the analysis, Group A is performing most consistently in terms of quality and associate engagement compared to last month. However, neither group is performing consistently in terms of productivity. It is important to address the productivity decline and identify areas for improvement to ensure consistent performance across all categories.

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Answer:

Step-by-step explanation:

The correct answer is A. A rectangle the same size as the base.

When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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The person is approximately 7.73 miles from home.

To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.

If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).

To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:

d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles

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Answer:

56

Step-by-step explanation:

f(x)=4x^2-7

f'(x)=8x

f'(7)=56

Answer:

True

EXPLANATIONDETAIL STEPS:

(A)Determine whether y = 5 is a function: Click for video explanations: True

(B)Determine whether x = -2 is a function: Click for video explanations: False

(7)Determine whether y = 2x-5 is a function: Click for video explanations: True

(D)Determine whether 2y = x-4 is a function: Click for video explanations: True

(A)Determine whether

=

is a function: Click for video explanations: True

(B)Determine whether

=

is a function: Click for video explanations: False

(7)Determine whether

=

is a function: Click for video explanations: True

(D)Determine whether

=

is a function: Click for video explanations: True

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

Let's denote the total number of boxes the hawker bought as "x".

The cost of each box is R18, so the total cost of buying "x" boxes is 18x.

He sold all but 5 boxes, so he sold (x - 5) boxes at R25 per box. The revenue from selling these boxes is 25 * (x - 5).

The profit is calculated by subtracting the cost from the revenue, so we have:

Profit = Revenue - Cost

155 = 25 * (x - 5) - 18x

Simplifying the equation:

155 = 25x - 125 - 18x

155 + 125 = 25x - 18x

280 = 7x

Dividing both sides by 7:

x = 280 / 7

x = 40

Therefore, the hawker bought 40 boxes of tomatoes.

We can conclude that there are no ordered triples of positive integers (x, y, z) that satisfy the given equation and the condition x < y.

We are given that the product of three positive integers (x, y, z) is equal to four times their sum:

xyz = 4(x + y + z)

Rearranging the equation, we get:

xyz - 4x - 4y - 4z = 0

We can factor out a common factor of 4 from the terms on the right-hand side:

4(xy - x - y - z) = 0

Now, we have two cases to consider:

Case 1: xy - x - y - z = 0

In this case, we can rewrite the equation as:

x(y - 1) - (y + z) = 0

From this equation, we observe that (y + z) must be divisible by (y - 1). Since x < y, the minimum value of (y - 1) is 1, which means (y + z) should also be 1. However, since we are looking for positive integers, this case does not yield any solutions.

Case 2: xy - x - y - z = 4

In this case, we can rewrite the equation as:

x(y - 1) - (y + z) = 4

Similarly, we observe that (y + z) must be divisible by (y - 1), and now (y - 1) can take on a minimum value of 2. We can analyze different possibilities based on this:

If (y - 1) = 2, then (y + z) = 2. Since we are dealing with positive integers, the only possibility is y = 3 and z = -1, which does not satisfy the condition.

If (y - 1) = 3, then (y + z) = 3. The only possibility is y = 4 and z = -1, which also does not satisfy the condition.

If (y - 1) = 4, then (y + z) = 4. The only possibility is y = 5 and z = -1, which does not satisfy the condition.

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Step-by-step explanation:

We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.

h0 = 43 meters (the top of the cliff)

v = 11 meters per second (upwards direction)

To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:

10 = -4.9t^2 + 11t + 43

0 = -4.9t^2 + 11t + 33

Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.

Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.

Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).

After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 3ft per year, where t is time in years. So, the tree will grow 5 feet in the first year.

We have to find the number of feet the tree will grow in the first year, given that 5(t + 1)³. The rate of growth of a tree is given as 3ft/year. Therefore, in the first year, the tree will grow 3 feet.

To find the number of feet the tree will grow in the first year, we substitute t = 0 in the given expression.

5(t + 1)³ = 5(0 + 1)³= 5(1)³= 5(1)= 5. Therefore, the tree will grow 5 feet in the first year.

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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.

The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.

Consider the square root of 2 (√2) and the square root of 3 (√3), both of which are irrational numbers. When you multiply √2 and √3, you get √6, which is also an irrational number. In this case, the product of two irrational numbers is irrational.

However, there are cases where the product of two irrational numbers can be rational. For example, consider √2 and its reciprocal (1/√2), both of which are irrational. When you multiply these two numbers, you get 1, which is a rational number. So, in this case, the product of two irrational numbers is rational.

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The values of L and M in the triangle displayed are 55 and 60 respectively.

The value of angle L can be obtained thus :

125 + L = 180 (sum of angles in a triangle)

L = 180 - 125 = 55°

B.

The value of L can be calculated thus:

55 + (2x - 10) + 65 = 180 (sum of internal angles of a triangle)

120 + 2x - 10 = 180

110+2x = 180

2x = 180-110

x = 35

M = 2(35) -10 = 60°

Therefore, L = 55 and M = 60.

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Answer:

11 : 1

Step-by-step explanation:

The probability of obtaining a head when a dime is flipped is 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.

The probability of rolling any particular number on a fair six-sided die is 1/6, since there are six equally likely outcomes (the numbers 1 through 6).

To find the odds against obtaining a head and rolling any number on the die, we need to multiply the probabilities of the two events. This gives us

(1/2) x (1/6) = 1/12

So the probability of obtaining a head and rolling any number on the die is 1/12.

To find the odds against this event, we need to compare the probability of the event happening to the probability of it not happening. The probability of the event not happening is 1 - 1/12 = 11/12.

Therefore, the odds against obtaining a head and rolling any number on the die are:

11 : 1

Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

The angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°

To calculate for the angle between the intersection of a secant and a tangent we need to know the measure of the intercepted arc, and then divide it by 2 to get the angle.

If the measure of the arc HM is given to be equal to 108°, then the measure of angle MHU is calculated as:

angle MHU = 108°/2

m∠MHU = 54°

Therefore, the angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°

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The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

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The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

Percentage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.

Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.

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Answer:

102

Step-by-step explanation:

we substitute x by 7

7^2+9(7)-10

49+63-10

=102

To find an object's maximum height, we need to find the vertex of this quadratic equation.

Answer: 5.50 seconds

Terms to know:

Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.

Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).

Step-by-step explanation:

The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]

Since we only are looking at the time it takes to reach maximum height we will only look at the x value.

[tex]x= \frac{-176}{2(-16)}[/tex]

[tex]x= 5.50[/tex]