Find the value of the trig function indicated .
A)7/24
B)24/25
C)/2/2
D)25/24
(Must show work ) please help

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

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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Step-by-step explanation:

(Pie)r^2 that is the area of a circle

Answer:

x power2+6x+4 is the answer

Answer:

190.67 ft/sec

Step-by-step explanation:

130 mi/hr x 5280 ft/mi x 1/60 hr/min x 1/60 min/sec = 190.67 ft/sec

It makes more sense if you write these as fractions and cancel units.

Answer:

the answer is x=3

Step-by-step explanation:

-3x=1-7

-3x=-6

-x=-6+3

-x=-3

x=3

Answer: B. When finding the midpoint between two points on a vertical line, keep the x-coordinate and find the average of the y-coordinates

That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Length of a text can be measured with ruler. Therefore, option C is the correct answer.

Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.

A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines.

Length of a text can be measured with ruler.

Therefore, option C is the correct answer.

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Answer:

C

Step-by-step explanation:

Answer:

|a| = 0.447

|b| = 0.547

|c| = 0.707

Step-by-step explanation:

From available data

Ψ1 = Ee = 10eV probability = 0.2

Ψ2 = Ee = 16eV, probability = 0.3

Ψ3 = Ee = 34eV, probability = 0.5

The magnitude of a

= a² = 0.2

= a = √0.2

|a| = 0.447

The magnitude of b

b² = 0.3

b = √0.3

|b| = 0.547

The magnitude of c

c² = 0.5

c = √0.5

|c| = 0.707

So in conclusion we have magnitude of a = 0.447

b = 0.547

c = 0.707

The magnitude of a , b and c are \(0.447, 0.547\) and \(0.707\) respectively.

The electron's wave function is given as,

          \(\psi=a\psi _{1}+b \psi _{2}+c\psi _ {3}\)

three values of the electron kinetic energy is given as,

\(\psi _{1}\) has E = 10 eV, with probability 0.2

\(\psi _{2}\) has E = 16 eV, with probability 0.3.

\(\psi _{3}\) has E= 34 eV, with probability 0.5.

The value of a, b and c shown below,

    \(a^{2}=0.2\\ \\a=\sqrt{0.2}=0.447\\ \\b=\sqrt{0.3}=0.547\\ \\c=\sqrt{0.5}=0.707\)

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

16s + 48

Step-by-step explanation:

8(2s) = 16

8(6) = 48

The measure of Angle C is approximately 26°.

A, B, C are vertices of a triangle, where AB = 8 cm, BC = 6 cm. To determine the measure of angle C, we need to use the cosine rule.

The cosine rule states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

Mathematically, we can represent it as follows:a² = b² + c² - 2bc cos(A)where a is the side opposite to angle A, b is the side opposite to angle B, c is the side opposite to angle C.

In this case, we have AB = c = 8 cm, BC = a = 6 cm, and AC = b. We need to find the measure of angle C, which is represented as cos(C).

Using the cosine rule, we can write the equation as follows:$$\begin{aligned} b^2 &= c^2 + a^2 - 2ca\cos(C) \\ \Right arrow b^2 &= 8^2 + 6^2 - 2 \times 8 \times 6 \cos(C) \\ \Right arrow b^2 &= 64 + 36 - 96 \cos(C) \\ \Right arrow b^2 &= 100 - 96 \cos(C) \end{aligned}$$We know that b is a positive length. Hence, b² > 0 or 100 - 96 cos(C) > 0. Solving for cos(C),  

we get: cos(C) < 100/96cos(C) < 1.0417Using a calculator, we can determine the inverse cosine of 1.0417 as:cos⁻¹(1.0417) = 0.4569 radians = 26.201° (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 26°.

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Answer:

1. The greatest common monomial factor is xy

2. xy(6 + 2y² + 3x²)

Step-by-step explanation:

6xy + 2xy³+ 3x³y

1. Determination of the greatest common monomial (GCM) factor.

6xy + 2xy³+ 3x³y

6xy => 2 × 3 × x × y

2xy³ = 2 × x × y × y × y

3x³y = 3 × x × x × x × y

GCM => xy

2. Rewrite the expression

6xy + 2xy³+ 3x³y

GCM => xy

6xy + 2xy³+ 3x³y = xy(6 + 2y² + 3x²)

Answer:

68°

Step-by-step explanation:

Every figure must sum 180°(Sides-2) degrees

Example: For a triangle (3 sides) 180°(3-2) => 180°(1) =>180°

In this case: 5 sides 180°(5-2) => 540°

So all the angles (5) must sum 540°

Mathematically expressed as:

\((119)+(z)+(2z)+(70)+(2z)+(11)=540\\119+z+2z+70+2z+11=540\\200+5z=540\\5z=540-200\\5z=340\\z=\frac{340}{5}\\z=68'\)

Lets see changing every Z by 68...

119+68+2(68)+70+2(68)+11

119+68+136+70+136+11=540°

In the given word problem amount does Teresa spends is $16.50.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

The amount does Jayson Spends = $3.75

According to the question,

Myra spends 3times as much as Jayson . then

Amount does Myra spends = 3× 3.75 = $11.25.

Now Teresa spends $5.25 more than Myra then,

Amount does Teresa spends = 11.25+5.25 = $ 16.50.

Hence In the given word problem amount does Teresa spends is $16.50.

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Answer:

I think it's the second one.

Step-by-step explanation:

y - 7 = 3(x - 2)

y - 7 = 3x - 6

y = 3x + 1

3x - y = -1

Answer:

D. all real numbers

Step-by-step explanation:

The domain is all the x's on a graph or that are permitted in an equation (if you have an equation instead of a graph)

If there is nothing on the graph to indicate the graph is a segment (endpoints that are either closed or open) or has other holes in it (literally a point on the line that is open) then the domain for a linear function (a line) is always all real numbers. The same is true for all of the above for the range as well, except the range is all the y's

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

Answer: 10

Step-by-step explanation:

The answer to the question is 9.33333 which would be 10 rounded

Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.

How to solve the question?

In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.

Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.

Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.

Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures

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Option (a) is the correct answer.  The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.

When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.

Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.

Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.

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Answer:

x = 15

Step-by-step explanation:

angles 2 and 4 are supplementary so they add up to 180

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15

Answer:

x=15

Step-by-step explanation:

Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.

Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:

\((2x+10)+(4x+80)=180\)

Solve for x. Remove the parentheses and combine like terms:

\(2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180\)

Work to isolate the variable, x. Subtract 90 from both sides:

\(6x+90-90=180-90\\\\6x=90\)

Isolate x. Divide both sides by 6:

\(\frac{6x}{6}=\frac{90}{6} \\\\x=15\)

The value of x is 15.

:Done

If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:

\(2x+10\\\\2(15)+10\\\\30+10\\\\40\)

∠2=40

\(4x+80\\\\4(15)+80\\\\60+80\\\\140\)

∠4=140

∠2+∠4=180

40+140=180

The value of x is true.

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

-------------

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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Answer: 50°

Step-by-step explanation:

Since angle 3 is in a right triangle we can assume one angle is 90° and then the other missing angle will be 40°

Because you take 180°-140°(the angle next to it) which will equal 40°

Now every triangle must add up to 180°

so lets take the angles we have now

90° +40°=130°

now take that 130°

180°-130°=50°

Now check your work

90°+40°+50°=180°

Angle 3 is 50°

The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.

Total distance the Andersons are planning to take is 960-mile

They will travel 840 miles by car

Distance they will not travel by car = total distance - distance travelled by car

= 960 - 840 miles

=120 miles

Percentage formula = (value/ total value) x 100

percent of the distance will they not travel by car =

         (total distance - distance travelled by car) x 100/total distance

=((960 - 840)/ 960) x100

=(120/ 960) x 100

12.5

If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then ​the percentage of distance they will not travel by car is 12.5%

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