are the answers highlighted in yellow

correct?

The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

From the question, we have the following parameters that can be used in our computation:

First = tan(θ)

Second = cos(θ)

The basis trigonometry identity is

sin²(θ) + cos²(θ) = 1

Divide through the equation by cos²(θ)

So, we have

tan²(θ) + 1 = 1/cos²(θ)

Subtract 1 from both sides

tan²(θ) = - 1 + 1/cos²(θ)

Take the square root of both sides

tan(θ) = √[-1 + 1/cos²(θ)]

Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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Answer:

8) b. 15 m²

9) c. 63.5 ft²

Step-by-step explanation:

Area of composite figure:

8) To find the area of the composite figure, we have to add the area of rectangle, area of the top triangle and the area of the below triangle.

Rectangle:

            length = 3m

            width = 2.5 m

          [tex]\boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                           = 3 * 2.5

                                           = 7.5 m²

Area of triangle:

              [tex]\boxed{\text{\bf Area of triangle =$ \dfrac{1}{2}*base*height$}}[/tex]

       Triangle1:

                    base = 3 m  ; height = 1.5 m

                   [tex]\sf Area \ of \ triangle1 = \dfrac{1}{2}*3*1.5[/tex]

                                             [tex]= 2.25 \ m^2[/tex]

       Triangle2:

               base = 3 m ; height = 2.5 + 1 = 3.5 m

               [tex]\sf Area \ of \ triangle2 = \dfrac{1}{2}*3*3.5[/tex]

                                          = 5.25 m²

Area of the figure = 7.5 + 2.25 + 5.25

                               = 15 m²

_______________________________________________________

9) To find area of the given area, add the area of rectangle1 and area of rectangle2.

      length = 5 ft ;  width =  5.5 ft

Rectangle1:

         Area of rectangle1 = 5 * 5.5

                                         = 27.5 ft²

Rectangle2:

           length = 8ft

           width = 10 - 5.5

                      = 4.5 ft²

           Area of rectangle2 = 8 * 4.5

                                           = 36 ft²

Area of the given figure = area of rectangle1 + area of rectangle2

                                       = 27.5 + 36

                                        = 63.5 ft²

All the values of a 12-sided die will be represented by two 6-sided die. The probability of rolling a 7 on the 12-sided die is 1/12 and rolling a sum of 7 on the two 6-sided dice will be 1/6.

The 12-sided die which is dodecahedral consists of numbers up to 12. The 6-sided die consists of numbers up to 6. The suggestion of using two 6-sided dice instead of a 12-sided die will make a difference in the probabilities of a specific outcome.

Although, using a pair of 6-sided dice and adding their scores will represent all the values or outcomes you can get in a 12-sided die but still there will be a difference in the probabilities.

If we find the probability of rolling 7 on the 12-sided die, then it will be 1/12.

But, in the case of two 6-sided dice, we will obtain the sum of 7 in 6 outcomes which are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of outcomes, in this case, is 36.

Therefore, the probability of rolling a sum of 7 on the two 6-sided dice will be 6/36   =  1/6.

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A. The greatest number of packages that can fit the truck is 24000

B. The volume of the part that is filled is 375 cubic feet

Given that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

Also, we have

Package = 1/4 foot cube

So, we have

Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)

Evaluate

Number of packages = 24000

This means that the greatest number of packages is 24000

Recall that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

So, we have

Volume = (8 * 6 1/4 * 7 1/2)

Evaluate

Volume = 375

Hence, the volume is 375 cubic feet

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The author references a couple of situations that occured in the country and are occuring presently, justified by laws, which reduces the ability of social minorities to vote.

The author of this article cites several laws passed in states that make it harder for minorities, especially blacks, to vote regularly. He said that even after an amendment was passed allowing blacks to vote, he passed other laws preventing blacks from voting, such as requiring voter education.

These laws were enacted with increasing force until the passage of the Civil Rights Act in the 1960s.

Every year since civil rights, different laws have been passed making it harder for blacks, women, the working class, and homosexuals to vote among other members of social minorities. Many of these laws are still in effect.

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The expression [tex]3log_b(8) - log_b(7)[/tex] written as a single logarithm is [tex]log_b(\frac{512}{7})[/tex].

Given the logarithmetic expression in the question:

[tex]3log_b(8) - log_b(7)[/tex]

To rewrite the expression [tex]3log_b(8) - log_b(7)[/tex] as a single logarithm, we can use the properties of logarithms.

Using the quotient rule property, which states that:

logₙ(a) - logₙ(b) = logₙ(a/b)

Applying the quotient rule:

First, rewrite [tex]3log_b(8) - log_b(7)[/tex] as:

[tex]log_b(8^3) - log_b(7)[/tex]

Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).

[tex]log_b(\frac{8^3}{7})[/tex]

Simplify

[tex]log_b(\frac{512}{7})[/tex]

Therefore, the single logarithm is [tex]log_b(\frac{512}{7})[/tex].

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The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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The expression has no solution when k < - 5.

Hence, option B is correct.

The given inequality is

|2x + 7|-k ≤ 5

We know that,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.

A function with absolute values is another name for it.

No matter what input was provided to this function, the outcome is always favorable.

Now adding k both sides of inequality,

⇒ |2x + 7| ≤ 5 + k

When we take value of k less than -5

Then the expression |2x + 7| becomes negative.

Since it always gives absolute value,

Therefore,

There is no any solution when k < -5.

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We can see here that the dollar doesn't belong to the box.

We can see here that in order to known if the dollar belongs to the box or not, here is an explanation:

Let the single tickets = x

and the couples tickets = y

Note: $8 = 2 tickets (for couples),

Thus, 1 ticket = $4

5x + 4y = 200  -------(1)

x + y = 47 ----------- (2)

-4 × (2)

5x + 4y = 200  -------(1)

-4x - 4y = 188

x = 12

Substituting 12 in (2)

12 + y = 47

y = 47 - 12 = 35

y = 35

So, 5x + 4y = 200

5 (12) + 4 (35) = 200

60 + 140 = 200.

Thus, we see here that the dollar doesn't belong to the box.

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The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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Answer: x = 0

Step-by-step explanation:

Anything divided by 0 equals 0

Multiply -9 to the other side

x = 0 × -9

Anything Multiplied by 0 equals 0

x = 0

The margin of error for the two-proportion 95% confidence interval is 0.0662.

The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:

ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)

where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.

Using the given information, we have:

Sample 1: n₁ = 250, p₁ = 0.90

Sample 2: n₂ = 275, p₂ = 0.85

Level of confidence: 95%

Substituting these values into the formula, we get:

ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]

ME = 0.0662

Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.

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The vertex form of the equation of a parabola is equal to y + 1 = - (1 / 12) · (x - 2)².

In this problem we need to determine the equation of a parabola, this can be done by knowing the distance between vertex and focus and the coordinates of the focus. The vertex form of the equation of the parabola is:

y - k = [1 / (4 · p)] · (x - h)²

Where:

If we know that (h, k) = (2, - 1) and p = - 3, then the equation of the parabola in vertex form is:

y + 1 = - (1 / 12) · (x - 2)²

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Answer:

[tex](x-2)^2=-12(y+1)[/tex]

Step-by-step explanation:

From observation of the given diagram, we can see that the graphed conic section is a vertical parabola that opens downwards, with a vertex at (2, -1) and a focus at (2, -4).

The equation of a vertical parabola in standard form is:

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a vertical parabola}\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k + p)$\\\end{minipage}}[/tex]

Given the vertex is (2, -1):

Given the formula for the focus is (h, k+p), then:

[tex]\begin{aligned}(h, k+p)&=(2, -4)\\(2,-1+p)&=(2,-4)\\\\\implies -1+p&=-4\\p&=-4+1\\p&=-3\end{aligned}[/tex]

To write the equation of the graphed conic section, substitute the found values of h, k and p into the standard formula:

[tex](x-2)^2=4(-3)(y-(-1))[/tex]

[tex](x-2)^2=-12(y+1)[/tex]

Therefore, the equation of the graphed conic section is:

[tex]\boxed{(x-2)^2=-12(y+1)}[/tex]

The likelihood of  profit and loss in the following week is 18.75%. The Option D is correct.

A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.

To get  probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.

The probability of making a profit in one week is 0.75

The probability of making a loss in the following week will be:

= 1 - 0.75

= 0.25.

So, probability of the company making a profit in one week and then making a loss in the following week is:

= 0.75 * 0.25

= 0.1875

= 18.75%.

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The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2y+ 3/2x + 7/4

On simplifying , we get

A = ( -4y + 3 )/2x + 7/4

Taking LCM on both sides , we get

A = ( -16y + 12 + 7 ) / 8x

Hence , the expression is A = ( -16y + 12 + 7 ) / 8x

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The coordinates of V' include the following: V' (-5, -10).

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of V at (-2, -4) by applying a scale factor of 2.5 that is centered at the origin as follows:

V (-2, -4) → V' (-2 × 2.5, -4 × 2.5) = V' (-5, -10).

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The simplified form of 5x³y (2x + 3y - 4) will be 10x⁴y + 15x³y² - 20x³y.

Given that:

Expression, 5x³y (2x + 3y - 4)

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Simplify the expression, then we have

5x³y * 2x + 5x³y * 3y - 5x³y * 4

10x⁴y + 15x³y² - 20x³y

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Answer: 2.667

Step-by-step explanation:

Answer:

Can you mark me brainiest.

Step-by-step explanation:

Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.

Or 2.667

The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

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Sharon is correct in classifying the shape as a square, rectangle, and quadrilateral.

The shape satisfies the criteria for each classification: it has equal sides and right angles, making it a square; it has right angles, making it a rectangle; and it has four sides, making it a quadrilateral. Therefore, the shape can be accurately described and categorized using all four classifications.

Moreover, as a quadrilateral, this shape satisfies the general criteria of having four sides. Its defined boundaries encompassing an enclosed area are emblematic of a quadrilateral.

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Answer:

$3,080 for each person

Step-by-step explanation:

9,240 / 3 = 3,080

Since angles M and P are complementary, if m∠M = 3x - 45 and m∠P = 2x + 15, the value of x is 24
and the value of M and P are   27° and 63°   respectively.

Since M and P are complimentary, that means the sum of them is = 90°

So
3x - 45 + 2x + 15 = 90

Taking like terms

3x + 2x = 90 + 45 -15
5x = 120
x = 120/5

x = 24

to find M and P

since m∠M = 3x - 45

m = 3(24) -45

m = 27°

m∠P = 2x + 15

since x = 60

P = 2(24) + 15

P = 63°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Angles M and P are complementary. If m∠M = 3x - 45 and m∠P = 2x + 15, what is the value of x? What is the measure of each angle?

Note that from the coordinates of the above triangle, we can state that the triangle is an Isoceles triangle.

We can also state emphatically that it is NOT a right triangle.

a) we now that the triangle is a scalene triangle because all three sides have unequal lengths.

This can be determined with the use of distance formula.

d = √((x2 - x1)² + (y2 - y1)²)

PQ = √((2-4)² + (7-1)²)

= 6.32455532034

PQ ≈ 6. 33

Using the same steps above,

QR = 6.33

Using the same steps

RP = 5.66

From the above as well as is show on the attached graph, we can see that the triangle has two equal sides hence an Isosceles triangle.


b) We know for a fact using the graphical method that the above triangle is NOT a right triangle.

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Answer:

Step-by-step explanation:

For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:

t = 27n + 18

In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.

The outcome of 4 occurred 3 more times than expected. This is the resulting probability. Therefore, the correct option is option A.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which anything is probable to happen is basically what probability means. The outcome of 4 occurred 3 more times than expected.

Therefore, the correct option is option A.

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Human actions and behaviors towards our surroundings can have significant implications for human health, leading to the emergence of various health problems.

Our choices and activities encompassing lifestyle, pollution, and resource utilization exert direct impacts on our overall well-being. For instance, our exposure to environmental pollutants, encompassing air and water contaminants, toxic substances, and hazardous waste, can engender respiratory ailments, cancer, and an array of severe health conditions.

Similarly, the degradation of natural habitats, deforestation, and unsustainable practices contribute to the proliferation of infectious diseases, disrupt ecological balance, and undermine the stability of our food systems.

Moreover, unhealthy dietary patterns, sedentary behaviors, and limited access to healthcare services compound the complexities of prevailing health issues.

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The least common denominator will be (x-1)(x²-1).

When two or more fractions have the same denominators, they are termed as the common denominators.

The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.

For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.

The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.

Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,

So,

-2x/x-1 + x+3/x²-1

Taking the LCM,

-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).

Hence the least common denominator will be (x-1)(x²-1).

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Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

3a. 60

3b. 4

3c. It means that the individual speeds of the trucks are pretty close to the mean.

4. The temperature is not very consistent.

5. The values in the data set are close together, and the mean is pretty consistent.

6. Evelyn and Nova are correct

Pls give brainliest

Answer:

3a. 60

3b. 4

3c. represents the difference in speed from the mean, or data is close to mean

4. The temps are not consistent, data varies a lot

5. It means that the data does not vary much, data is basically exactly the same as the mean.

6. evelyn, nova

The division of x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 will have a quotient of x⁴ + 9x² + 9 and a remainder of -1 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall divide x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 as follows;

x⁵ divided by x equals x⁴

x - 1 multiplied by x⁴ equals x⁵ - x⁴

subtract x⁵ - x⁴ from x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 will give 9x³ - 9x² + 9x - 10

9x³ divided by x equals 9x²

x - 1 multiplied by 9x² equals 9x³ - 9x²

subtract 9x³ - 9x² from 9x³ - 9x² + 9x - 10 will give 9x - 10

9x divided by x equals 9

x - 1 multiplied by 9 equals 9x - 9

subtract 9x - 9 from 9x - 10 will give us a remainder of -1

Therefore by synthetic division, x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 divided by x - 1 will result to a quotient of x⁴ + 9x² + 9 and a remainder of -1.

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