inequality is shown 1/8

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

A table between two variables represents a linear relation if and only if every pair of values (x, y) have the same constant:

k = y/x     (1)

Now we proceed to check the existence of the constant of variation:

k₁ = 8/(- 2) = - 4

k₂ = (- 16)/4 = - 4

k₃ = (- 36)/9 = - 4

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

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Answer:

7-9.8g

-1.4(-5) = 7

7(-1.4g) = -9.8g

Answer:

7-9.8g

Step-by-step explanation:

Distributive property.

1. -1.4 x -5= 7

2. -1.4 x 7g= -9.8g

3. 7-9.8g

hope this helps!

Answer:

No, there is not sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.

This means that the null hypothesis is:

\(H_{0}: \mu = 434\)

It is believed that the machine is underfilling the bags.

This means that the alternate hypothesis is:

\(H_{a}: \mu < 434\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

434 is tested at the null hypothesis:

This means that \(\mu = 434\)

A 9 bag sample had a mean of 431 grams with a variance of 144.

This means that \(X = 431, n = 9, \sigma = \sqrt{144} = 12\)

Value of the test-statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{431 - 434}{\frac{12}{\sqrt{9}}}\)

\(z = -0.75\)

P-value of the test:

The pvalue of the test is the pvalue of z = -0.75, which is 0.2266

0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.

Answer: \(y=x-9\)

Step-by-step explanation:

To find the inverse of a function you must first swap the places of x and y

\(x=y+9\)

Now solve for y

Step 1: Flip the equation.

\(y+9=x\)

Step 2: Subtract 9 from both sides.

\(y+9-9=x-9\\y=x-9\)

Answer:

(see below)

Step-by-step explanation:

First, you know that the first statement given is Given.

Now that you have that, you want to concentrate on your goal, and that goal is to prove that ΔGHI is an isosceles. To do this, you need to prove that the two base angles or two adjacent sides are congruent.

To do this, you can prove ΔGHJ ≅ ΔIHJ first, then use CPCTC.

Because HJ is the perpendicular bisector of GI, GJ ≅ IJ. this will be under Definition of Perpendicular Bisectors because it's a line which cuts a line segment into two equal parts at 90°.

This also means that ∠GJI and ∠IJH are right angles under Definition of Perpendicular Bisectors. Do not combine the two statements.

To clarify everything, ∠GJI ≅ ∠IJH because "all right angles are congruent."

It's also clear that these two triangles share a side, so HJ ≅ HJ. This is the Reflexive Property of Congruence, stating that for any real number a, a ≅ a.

Now you can prove these two triangles congruent by the SAS Postulate.

Using CPCTC, corresponding parts of congruent triangles are congruent, GH ≅ HI.

Your last statement should be ΔGHI is an isosceles because of Definition of Isosceles Triangle. You also want to state the statement exactly as given as the question.

Your proof should look something like IMAGE.A.

The required three angle is 55 , 55 and 70

What is an angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Let each of the base angle of isosceles triangle = x

Vertex angle = (x+15)

Sum of the angle = 180

x + x + (x + 15) = 180

3x + 15 = 180

3x = 180 - 15

x = 165 / 3

x = 55

Each base angel = 55

Vertex angle = x + 15

                      = 55 + 15

                      = 70

Required three angles = 55 , 55 and 70

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The equations can be used to solve for y, the length of the room follows:

B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, we have

length L = y

width W = y - 5

Since the area of a rectangular room is 750 square feet.

So  L × W = 750

y(y - 5) = 750

y² – 5y = 750 ....(i)

This can be also written as:

750 – y(y – 5) = 0 ....(ii)

Factorizing the equation (i), we get

(y + 25)(y – 30) = 0

Thus, the correct answer would be options (B), (C), and (E).

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The logarithmic function can be written exponentially as follows.\(t = 8^y.\)

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is \(log_{8}(t) = y.\)

We know that if we have an equation in the form \(a^x = b\), we can rewrite it in logarithmic form as \(log_a(b) = x\) and vice versa.

Thus, \(log_{8}(t) = y\)

\(t = 8^y\)

Hence, the logarithmic function can be written exponentially as follows.\(t = 8^y.\)

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Answer:

Step-by-step explanation:

It has already been answered on the picture.

Answer:

infinite

Step-by-step explanation:

Answer:

  c.  71°

Step-by-step explanation:

You have isosceles triangle XYZ with a.pex angle Y = 38°. You want to know the measure of angle Z.

The base angles of the triangle are X and Z, which are congruent. The sum of all angles is 180°:

  X +Y +Z = 180°

  2Z +38° = 180° . . . . . . substitute for X and Y

  2Z = 142° . . . . . . . . . subtract 38°

  Z = 71° . . . . . . . . . . divide by 2

The measure of angle Z is 71°.

To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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Answer:

B

Step-by-step explanation:

In a boxplot, when the median is in the middle of the box, or when there are equal proportions around the median, the distribution is symmetric. As is shown here, the median is closer to the left side of the box, making it positively skewed (the mean is greater than the median) and not symmetric.

The error interval for the combined mass (m) of the car and the person is 2047.7 ≤ m < 2049.7

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

The error interval for the mass of car is given by:

Mass of car = 1990 ± 0.5;

Mass of car = 1990 + 0.5 = 1990.5

Mass of car = 1990 - 0.5 = 1989.5

The error interval for the mass of a person is given by:

b = 1990 ± 0.5;

b = 58.7 + 0.5 = 59.2

b = 58.7 - 0.5 = 58.2

For the value of a and b, we have:

a = 1989.5 + 58.2 = 2047.7

b = 1990.5 + 59.2 = 2049.7

Next, we would calculate the combined mass (m):

m = 1990 + 58.7

m = 2048.7

Now, we can write the error interval for the combined mass (m) of the car and the person as follows:

a ≤ m < b

2047.7 ≤ m < 2049.7

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Answer:

120 degrees

Step-by-step explanation:

50+70=120

Answer:

x

100

Step-by-step explanation:

Answer:

a = 5

Step-by-step explanation:

I'm 100% sure good luck!!

The answer for the right triangle is 5

Answer:

(a) The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) A 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) We should not reject the hypothesis since 80 km/h is in the interval found in (b).

(d) Decrease the Type I error probability.

Step-by-step explanation:

We are given that the average speed for a sample of 41 vehicles was 81.35 km/h, with the sample standard deviation being 4.52km/h.

(a) Since here we don't know about population standard deviation, so the distribution that will be used here is t-distribution as the data also follows the normal distribution.

The degrees of freedom; the relevant t distribution would have = n - 1 = 41 - 1 = 40.

(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~   \(t_n_-_1\)

where, \(\bar X\) = sample average speed of vehichles = 81.35 km/h

             s = sample standard deviation = 4.52 km/h

             n = sample of vehicles = 541

            \(\mu\) = population mean  

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-2.021 < \(t_4_0\) < 2.021) = 0.95  {As the critical value of t at 40 degrees of

                                               freedom are -2.021 & 2.021 with P = 2.5%}  

P(-2.021 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 2.021) = 0.95

P( \(-2.021 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(2.021 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-2.021 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.021 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-2.021 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+2.021 \times {\frac{s}{\sqrt{n} } }\) ]

                                      = [ \(81.35-2.021 \times {\frac{4.52}{\sqrt{41} } }\) , \(81.35+2.021 \times {\frac{4.52}{\sqrt{41} } }\) ]  

                                     = [79.92 km/hr, 82.78 km/hr]

Therefore, a 95% confidence interval for the mean speed of vehicles crossing the bridge is [79.92 km/hr, 82.78 km/hr] .

(c) The hypothesis given to us is;

Null Hypothesis, \(H_0\) : \(\mu\) = 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h}

Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) 80 km/hr    {means that the mean speed of vehicles over the bridge would be the speed limit of different from 80 km/h}

Here, we should not reject the null hypothesis since 80 km/h is in the interval found in (b) which means that we are 95% confident that the mean speed of vehicles over the bridge would be the speed limit of 80 km/h.

(d) Decreasing the significance level of the hypothesis test above would decrease the Type I error probability because Type I error probability is represented by the significance level.

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when \(h=(-\infty,3)U(3,\infty)\) and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

\(x_{1}+hx_{2}=3\)

so

\(x_{1}=3-hx_{2}\)

Next we can substitute this into the second equation so we get:

\(5(3-hx_{2})+15x_{2}=k\)

We distribute the 5 into the first parenthesis so we get:

\(15-5hx_{2}+15x_{2}=k\)

and group like terms:

\(-5hx_{2}+15x_{2}=k-15\)

we factor x2 so we get:

\(x_{2}(-5h+15)=k-15\)

and solve for x2:

\(x_{2}=\frac{k-15}{-5h+15}\)

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

\(-5h+15= 0\)

and solve for h:

\(-5h= -15\)

\(h=\frac{-15}{-5}\)

\(h= 3\)

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

\(5x_{1}+15x_{2}=k\)

we start by factoring a 5 from the left side of the equation so we get:

\(5(x_{1}+3x_{2})=k\)

Next, we divide both sides of the equation into 5 so we get:

\(x_{1}+3x_{2}=\frac{k}{5}\)

we now compare it to the first equation:

\(x_{1}+hx_{2}=3\)

\(x_{1}+3x_{2}=\frac{k}{5}\)

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and \(\frac{k}{5}=3\)

when taking the second condition and solving for k we get that:

\(k=3(5)\)

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

factorials

Step-by-step explanation:

0!=1,1!=1,2!=2,3!=6,4!=24,5!=120,6!=720,...

sequence is n! starting at 0

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

Step-by-step explanation:

False. They have one point in common meaning there is only 1 solution.