Trigonometry ( help a girl out)

Resolving Vectors

Find the components of a car’s displacement if it travels 250 miles at an angle of 45 degrees north of west.

To Factorize:

\(~\)

Solution:

\( \: \: \: \: \sf \longrightarrow {x}^{2} - 10x + 24\)

\( \: \: \: \: \sf \longrightarrow {x}^{2} - 4x - 6x + 24\)

\( \: \: \: \: \sf \longrightarrow x(x - 4) - 6(x - 4)\)

\( \: \: \: \: \sf \longrightarrow (x - 6)(x - 4)\)

We are given with a quadratic equation and we have to factorise it , so let's proceed.

\({:\implies \quad \sf x^{2}-10x+24}\)

\({:\implies \quad \sf x^{2}-6x-4x+24}\)

\({:\implies \quad \sf x(x-6)-4(x-6)}\)

\({:\implies \quad \bf \underline{\underline{(x-6)(x-4)}}}\)

To factorise a quadratic polynomial ax² + bx + c we have to split it's middle term bx into say mx and nx and it will look like ax² + mx + nx + c ,also we should split it such that it follows the both conditions below :-

Answer:

30 movies in 5 months

102 movies in 17months

192 movies in 32 months

Answer: X=1 units

Y= 5 units

Z=3 units

Step-by-step explanation:

Answer:

X=1 units

Y= 5 units

Z=3 units

Step-by-step explanation:

Answer: 3 feet

Step-by-step explanation:

Here's the complete question:

The volume of the cylinder is 235.6 cubic feet the radius is 5ft. Find the height.

Note that Volume of a cylinder = πr²h

where Volume = 235.6 feet³

Radius = 5 feet

Height = Unknown

Then, we put the values back into the question and this will be:

V = πr²h

235.6 = 3.14 × 5² × h

235.6 = 3.14 × 25 × h

235.6 = 78.5 × h

h = 235.6 / 78.5

h = 3 feet

The height is 3 feet

The percentage of 5 7 inches should be very less because on average the height is 65 and that is what it means by mean of the data and the standard deviation is 2.5 that means on average the height goes up or down by 2.5 inches from the mean so what it means is that there can be (65+2.5) Inches or (65-2.5) Inches. now let us sort of do a mathematical guess of this percentage.

We have done a guess that is very close to the actual guess.

Answer:

a. you have removed 3/16 inches of material

b.The remaining thickness of the part is 3/16 inches.

Answer:

Step-by-step explanation:

Answer:

1/6 - 3/6 - 4/6

Step-by-step explanation:

because im right

Answer:

1/6, 3/6, 4/6

Step-by-step explanation:

its a basic question since there all have a denominater of 6. you go bye the numererator high to lower.

Answer:

806.5

Step-by-step explanation:

Answer:

1  9/10

Step-by-step explanation:

I was first make me brainliest. :)

Answer:

Joule

Step-by-step explanation:

it is the unit for the measurement of energy.

The completed square form is: -3(x-2)^2 + 46. The vertex is (2,46).

y = x^2 -8x + 9

In order to complete the square, we will first look at the x-term coefficient which is -8.

Half of -8 is -4, so we square this value to get 16 which will be added to both sides of the equation to make it a perfect square trinomial:

y = x^2 -8x + 9  

=  (x-4)^2 + 9 - 16

= (x-4)^2 - 7

So the completed square form is: (x-4)^2 - 7

The vertex is (4,-7).b) y= -3x^2 + 12x - 10

We need to factor out the coefficient of x^2 first: -3(x^2 - 4x) + 10

To make this a perfect square, we will use the formula: (b/2)^2, where b = -4Half of -4 is -2, so we square -2 to get 4.

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Answer:

i really wish i could help but i dont  know ether i'm

sry maybe some one else could help

A(n) "spanned" volume is similar to a primary partition, but in fact, is not a primary partition.

A spanned volume is similar to a primary partition, but in fact, is not a primary partition. In a spanned volume, you can combine free space from multiple disks to create a larger logical storage unit, while a primary partition is a segment of a hard disk drive that the operating system recognizes as a separate logical storage unit. A volume can span multiple partitions depending on how it is configured, or it can encompass a single partition. Different operating systems have different ways of configuring and managing volumes.

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When a prism is cut by a plane parallel to its bases and perpendicular to its height h, the shape of the intersection will be a rectangle. It is important to note that the rectangle may have different side lengths depending on the specific dimensions of the prism.

If a prism is cut by a plane that is parallel to the bases of the prism and perpendicular to its height h, the shape of the intersection between the prism and the plane would be a rectangle.

When a plane intersects a prism parallel to its bases, it creates cross-sections that are congruent to the bases. This means that the resulting shape of the intersection will have the same outline as the original bases of the prism.

Since the bases of a prism are typically quadrilaterals with right angles, such as rectangles or squares, the intersection shape will also have those characteristics. In this case, since the prism is cut by a plane parallel to its bases, the intersections will be congruent to the bases and have the same shape.

A rectangle is a quadrilateral with four right angles, and its opposite sides are equal in length. When a prism is cut by a plane parallel to its bases, the resulting intersection shape will maintain these properties and be a rectangle.

Therefore, when a prism is cut by a plane parallel to its bases and perpendicular to its height h, the shape of the intersection will be a rectangle. It is important to note that the rectangle may have different side lengths depending on the specific dimensions of the prism.

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Answer:

1. Angles 2, 3 and angles 1,3 are complementary angles(Given)

2. To prove :

Since Angles 2, 3 and angles 1,3 are complementary.

When angles are complementary, then the sum of the measures of angles is 90 degrees.

So,  and  (Definition of Complementary angles)

3.  (Substitution)

4.  (Subtraction property of equality)

Step-by-step explanation:

Answer:

a = 2

Step-by-step explanation:

ax² + 5x + 2 = 0

a ( - 2 )² +5 ( - 2 ) + 2 = 0

4a = 8

a = 2

ATTACHED IS THE SOLUTION!!

Answer:

\(x=\frac{-12}{5} y+\frac{79}{5}\)

Step-by-step explanation:

\(5(y-4)-3(y-2)+5(x-3)=10\)

Add -12y to both sides:

\(5x+12y-69-12y=10-12y\)

\(5x-69=-12y+10\)

Add 69 to both sides:

\(5x-69+69=-12y+10+69\)

\(5x=-12y+79\)

Divide both sides by 5:

\(\frac{5x}{5} =\frac{-12+79}{5}\)

\(x=\frac{-12}{5} y + \frac{79}{5}\)

Answer: 16m²

Step-by-step explanation:

A large rectangle has side lengths of 8 meters and 6 meters. This means that the area of the large rectangle will be:

= 8m × 6m

= 48m²

A smaller rectangle with side lengths of 4 meters and 2 meters is cut out of the large rectangle. Then, the area of the smaller rectangle will be:

= 4m × 2m

= 8m²

Since the smaller rectangle with side lengths of 4 meters and 2 meters is cut out of the large rectangle whose length is 8, meters and 6 meters, the remaining part of the rectangle will have length of (8m - 4m) = 4m and (6m - 2m) = 4m.

Area of the remaining part of the large rectangle will be:

= 4m × 4m

= 16m²

To estimate the mean amount of detergent in 64-ounce jugs at a 98% confidence level, and the sample should be taken so that the estimate is within 0.05 ounce of the population mean. Let us find the sample size required. Sample size, n = (Z² * σ²) / E².

Where; Z is the Z-value at the given level of confidenceσ is the standard deviation of the population E is the maximum error allowed Z-value at the 98% confidence level is 2.33σ = 0.23E = 0.05Therefore, the sample size required is: n = (2.33² * 0.23²) / 0.05²= 25.6 or 26 (rounded to the nearest integer)Hence, the company should take a sample of 26 64-ounce jugs to estimate the mean amount of detergent at a 98% confidence level.

Let the areas of the three rugs be a, b, and c. Then according to the given information, a + b + c = 2200Also, area of overlap of the rugs (covered by exactly two layers of rug) = 24m²Hence, (a + b + c) – 2(area covered by two layers of rug) = area covered by three layers of rug (2200 – 2 × 24)m² = 2152m².

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The graph of N(t) = 75t + 120 is a straight line with a positive slope of 75. It intersects the y-axis at (0, 120) and has a y-intercept of -8/5. As t approaches infinity, N(t) increases without bound, indicating a positive relationship between the number of days of training and the average number of components assembled per day.

To sketch the graph of N(t) = 75t + 120, we can plot points on the coordinate plane by substituting different values of t into the equation.

For example, when t = 0, N(0) = 75(0) + 120 = 120. So, we have the point (0, 120).

When t = 1, N(1) = 75(1) + 120 = 195. So, we have the point (1, 195).

We can continue to calculate more points using different values of t.

The intercept is when N(t) = 0:

0 = 75t + 120

-120 = 75t

t = -120/75

t = -8/5

So, we have the intercept (0, -8/5).

To find the asymptote, we need to check what happens to N(t) as t approaches infinity. As t becomes larger and larger, the constant term 120 becomes less significant compared to the term 75t. Therefore, as t approaches infinity, N(t) approaches infinity as well.

In practical terms, this means that as the number of days of training (t) increases, the average number of components assembled (N) per day also increases. However, it is important to note that this is based on past records and the actual performance of new employees may vary. The equation provides an average trend and does not account for individual variations or other factors that may affect productivity.

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Answer:

C x = -1

Step-by-step explanation:

-15 = 22x +7

-22 = 22x

x = -1

Step-by-step explanation:

as the formula says for the acid of symmetry :

x = -b/2a

in the function m(x) = 2x² + 8x +3

we have

a = 2

b = 8

c = 3

the axis of symmetry is

x = -8/(2×2) = -8/4 = -2

the vertex is (h, k) out of the form

m(x) = a(x - h)² + k

we know already, a = 2

for the rest we do all the multiplications and then we compare it with the original function :

m(x) = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k

a = 2

-2ah = 8

-2×2×h = 8

-4h = 8

h = -2

ah² + k = 3

2×(-2)² + k = 3

8 + k = 3

k = -5

so, the vertex is (-2, -5)

Answer:

1350 sq in

Step-by-step explanation: leangth times width is 15 x 15 so the face of one side is 225 multiply this by the number of faces in this case six and you get your awnser 1350 sq in

Probability of an event is the measure of its chance of occurrence. The correct probabilities are:

Suppose that the sample space is S. Out of which there are two events, A and B, subsets of S.

Then, we can interpret P(A|B) as the probability of that part of A which is in B, with the new sample space as B. (assuming probabililty of B isn't 0).

Symbolically, we write it as:

\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\)

For three sets, A, B and C:

\(n(A \cup B \cup C) = n(A) + P(B) + P(C) - n(A\cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)\)

The problem is incomplete. The corresponding venn diagram is attached below.

We can symbolize the venn diagram as:

\(n(A) = 12+8+6+5 =31\\n(B) = 11+8+5+3 = 27\\n(C) = 4+8+6+3 = 21\\n(A \cap B) = 5+8=13\\n(B\cap C) = 3+8=11\\n(A \cap C) = 6+8=14\\n(A \cap B \cap C) = 8\)

S = sample space = collection of all unique elements.

S is union of A, B and C.

\(n(S) = n(A \cup B\cup C) = 31 + 27 + 21 -13-11-14+8 = 49\)

Checking all the options for their correctness:

We have:

\(P(A|C) = P(A\cap C)/P(C) = \dfrac{n(A\cap C)/n(S)}{n(C)/n(S)} = \dfrac{n(A \cap C)}{n(C)} = \dfrac{14}{21} =\dfrac{2}{3}\)

Thus, its correct.

\(P(C|B) = P(C\cap B)/P(B) = \dfrac{n(C\cap B)/n(S)}{n(B)/n(S)} = \dfrac{n(C \cap B)}{n(B)} = \dfrac{11}{27} \neq \dfrac{8}{27}\)

Thus, this option is incorrect.

Thus, this option is incorrect.

\(P(C) = \dfrac{n(C)}{n(S)}= \dfrac{21}{49} =\dfrac{3}{7}\)

Thus, its correct.

\(P(B|A) = P(B\cap A)/P(A) = \dfrac{n(B\cap A)/n(S)}{n(A)/n(S)} = \dfrac{n(B\cap A)}{n(A)} = \dfrac{13}{31} \neq \dfrac{13}{27}\)

Thus, this option is incorrect.

Thus, the correct probabilities are:

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Answer:Irrational,2/9,22/100 11/50, Irrational, No Fraction Given, Perfect Square, Non-Perfect Square

Step-by-step explanation:Best fit options for each question.

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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The chi-square test for homogeneity is used if he wants to determine if the distributions are the same.

What is the chi-square test?

Chi-square is a statistical test that looks at how categorical variables from a random sample differ from one another to see if the expected and actual findings match together well.  It is a contrast of two sets of statistical data. Karl Pearson developed this test in 1900 for the analysis and distribution of categorical data.

Here,

We have to determine for which situations should the chi-square test for homogeneity be used.

We concluded from the given option that:

A researcher is trying to determine if salaries for men and women in the tech industry have the same distribution.

He surveys a random sample of men and women in the industry and records the distribution of salaries for each gender.

He wants to determine if the distributions are the same.

Hence, the chi-square test for homogeneity is used if he wants to determine if the distributions are the same.

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