which is the solution to dis system of equations
x+y=3
x-y=-3

Answer:

  x = 62°

Step-by-step explanation:

You want the base angle in an isosceles triangle with a vertex angle of 56°.

Isosceles triangle

The sides of any triangle are proportional to the sine of the opposite angle. When two sides have the same measure, their opposite angles will have the same measure. Since the sum of angles in a triangle is always 180*, this means ...

  56° +x° +x° = 180°

  2x = 124° . . . . . . . . . . subtract 56°

  x = 62° . . . . . . . . . . divide by 2

The measure of the angle marked x is 62°.

__

Additional comment

The sides are all specified. This means you can find the angles of the triangle by solving it based on the side lengths. If you do that, you find that x ≈ 61.641°, as shown in the first attachment. This rounds to 62°.

As you can see in the second attachment, a better length for the side opposite the 56° angle would be 5.6 units instead of 5.7.

In short, the answer you get depends on how you use the given information.

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Answer:    T= -4

Step-by-step explanation: Well i guess it would be that ? If it's not sorry but it should be that

As per the combination method, there are 42504 different campout crews are possible.

Combination method:

In math, combination method means a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given,

Scout troop 456 has 24 members. the scoutmaster appoints a 5-member campout crew composed of a leader, a cook, and a cleanup crew (3 scouts).

Here we need to find the number of different campout crews are possible.

According to the nCr formula, here the value of

n = 24

And the value of r = 5

Then the number of possible combinations are calculated as,

=> ²⁴C₅ = 24!/5!(24 - 5)!

=> ²⁴C₅ = 24!/5!19!

=> ²⁴C₅ = 42504

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The required probability is p(xS 2) =F(2).

Given that,

90% of the time, a novel surgical technique is deemed to be successful. Imagine that the technique is carried out five times. Count on the outcomes of each procedure being distinct from one another. in this application of the binomial distribution

BINOMDIST (2,5,90%, TRUE) is used to find the probability of 2 or fewer

to get 0.00856 because x =2 and n= 5 and TRUE indicates the cumulative

and the required probability is p(xS 2) =F(2)

Therefore, the required probability is p(xS 2) =F(2).

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Answer: 2/1 should be your answer

Step-by-step explanation:

4 x 3= 12/6

1 x 3= 3/3

12 divided by 2 = 2  3 divided 3= 1

2/1

The area of the actual office space is 36 yards if the scale is 1:6 yards.

An item is enlarged in a scale drawing. An expansion increases or decreases the size of an item by multiplying each of its lengths by a scale factor. A scale of 1:5, for instance, indicates that the size of 1 unit in the picture corresponds to the size of 5 units in the actual world.

The scale of office space is 1:6 yards. The scale drawing has an area of 6 square inches. This means that 1 scale represents 6 square inches of office. For the actual area multiply 6 by the area of the scale drawing which will give 36 yards.

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Answer:

Step-by-step explanation:

Measure of one angle= 96

one angle= 2x

other angle= x + 12

By using angle sum property, we know that sum of all angles in a triangle is 180 degree.

so,

96 + 2x + x+12 = 180

108 + 3x = 180

3x = 180 - 108

3x = 72

x = 72/3

x = 24

So,

one angle (2x) = 2 * 24

                        = 48

other angle ( x + 12 ) = 24 + 12

                                  = 36

Hence, the other two degree measures for the missing angles is [tex]36[/tex].

What is the angles?

Angles are an integral facet in the study of mathematics, particularly geometry. Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint.

The point at which the two rays meet (intersect) is called the vertex.

Here given that,

One measure of an angle in a triangle is [tex]96[/tex] degree. The other two angle measures are represented by [tex]2x[/tex] and [tex]x + 12[/tex].

So,

Measurement of one angle= [tex]96[/tex] degree

One angle= [tex]2x[/tex]

Other angle= [tex]x + 12[/tex]

As we know that sum of all angles in a triangle is [tex]180[/tex] degree.

So,

[tex]96 + 2x + x+12 = 180\\\\108 + 3x = 180\\\\3x = 180 - 108\\\\3x = 72\\\\x = \frac{72}{3}\\\\x = 24\\\\[/tex]

So,

One angle  is

[tex](2x) = 2 (24)\\=48[/tex]

Other angle is ( x + 12 ) = 24 + 12

[tex]( x + 12 ) = 24 + 12\\=36[/tex]

Hence, the other two degree measures for the missing angles is [tex]36[/tex].

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The formula for f , the specific antiderivative of f  is F(u) = 4㏑(u) + u²/2 + 11/2  .

In the question ,

it is given that ,

the function f(u) is f(u) = 4/u + u and f(1) = 6 ,

to find the antiderivative of f , we integrate it with respect to u ,

∫f(u) = 4∫(1/u)du + ∫u.du

On integrating ,

we get ,

F(u) = 4㏑(u) + u²/2 + c      ......equation(1)

Substituting the value of u = 1 in equation(1) ,

we get ,

F(1) = 4㏑(1) + 1/2 + c

6 = 0 + 1/2 + c

c = 6 - 1/2

c = 11/2 .

Now , substituting the value of c = 11/2 in equation(1) , we get

F(u) = 4㏑(u) + u²/2 + 11/2

Therefore , the formula for f is F(u) = 4㏑(u) + u²/2 + 11/2 .

The given question is incomplete , the complete question is

Write a formula for f, the specific antiderivative of f.  

f(u) = 4/u + u ; F(1) = 6  .

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Answer:

See below

Step-by-step explanation:

This is a hard to explain without showing you, if it does not make sense it is not you, it is just hard to explain without showing you.

This sentence is False, when the sample size is small, the sample percentage may not be equal to the population percentage.

In demographics, the sector population is the overall quantity of human beings presently residing. It turned into predicted by the United countries to have exceeded eight billion in November 2022. It took over 2 hundred,000 years of human prehistory and history for the human populace to attain one billion and only 219 years extra to attain 8 billion.

The human population experienced a non-stop boom following the Great Famine of 1315–1317 and the end of the Black dying in 1350 when it became nearly 370,000,000. the very best worldwide populace growth quotes, with increases of over 1.8% in line with 12 months, took place between 1955 and 1975, peaking at 2.1% between 1965 and 1970. The increased charge declined to one.1% between 2015 and 2020 and is projected to say no further within the twenty-first century. the worldwide population continues to increase, however, there's sizable uncertainty approximately its long-term trajectory due to converting fertility and mortality fees. The UN Department of Economics and Social Affairs tasks between 9 and 10 billion people by 2050 and offers an 80% self-assurance c language of 10–12 billion by using the cease of the twenty-first century, with a growth charge by using then of zero. other demographers are expecting that the human populace will start to decline in the 2d half of the 21st century.

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As per the volume of the rectangular tank, the dimensions are 13.78 x 379.82 x 13.78

Volume of rectangle:

The general formula to calculate the volume of the rectangle is

V = length x width x height.

Given,

A rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness.

Here we need to find the dimensions of the rectangular tank,

As per the given volume of rectangular tank, when we equate this with the formula, then we get,

=> 5234 = length x width x height.

Let us consider the length and the width are equal then we get the value of height as.

=> height = 5234/length

So, the value is calculated by using the surface area formula,

=> A = length² + 5234/length

When we differentiate the surface area with respect to

=> dA/dl = 2l - 5234/l²

To minimize the surface area, so dA/dl = 0,

=> 2l = 5324/l²

=> 2l³ = 5234

=> l³ = 2617

=> l = ∛2617

Therefore, the value of length is 13.78

Then the height is calculated as.

=> h = 5234/13.78 = 379.82

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a. There is a difference in the cholesterol levels between the two groups.

b. The confidence interval for the differences is of (1.7, 10.3), not containing 0 and thus verifying what was found in item a.

At the null hypothesis, it is tested that there is no difference, that is, the mean of the subtraction is of zero, hence:

[tex]H_0: \mu_d = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is, the mean of the subtraction is different of zero, hence:

[tex]H_1: \mu_d \neq 0[/tex]

We have a two-tailed test, as we are testing if the mean is different of value, with 30 + 25 - 2 = 53 df, with a significance level of 0.01, hence the critical value is of:

t = 2.6718

Hence the decision rule, considering the test statistic t, is given as follows:

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences is given as follows:

The test statistic is obtained as the division of the sample mean by the standard error, hence:

t = 6/1.61

t = 3.73.

t > 2.6718, hence the null hypothesis is rejected, and there is a difference in the cholesterol levels between the two groups.

The confidence interval is obtained as the sample mean plus/minus the multiplication of the standard error and of the critical value.

Hence the lower bound of the confidence interval is of:

6 - 2.6718 x 1.61 = 1.7.

The upper bound is of:

6 + 2.6718 x 1.61 = 10.3.

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Answer:

  h = 90°

Step-by-step explanation:

You want the measure of the inscribed angle in a semicircle.

An inscribed angle has a measure equal to half the arc it subtends. Angle h intercepts the circle at the endpoints of a diameter, so subtends an arc of 180° (half a circle).

The measure of angle h is half of 180°, or 90°.

  h = 90°

__

Additional comment

The fact that a triangle inscribed in a semicircle is a right triangle is useful for a variety of purposes. It is also useful to note that the circle center is the circumcenter, and is the midpoint of the hypotenuse.

The circle's area is 200.96 square inches.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

Any round form without edges or line segments is called a circle. In geometry, it has the shape of a closed curve.

radius, r =  8 inches

Area of a circle:

A = π r²

  = 3.14 * 8²

  = 200.96 square inches

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Answer:

afternoon and

a) =1

Step-by-step explanation:

because there is only one prime number in multiples of 5 that is 5

The number of Left Hand pitchers that the team have is 3 .

In the question ,

it is given that ,

the total number of pitchers in the baseball team is = 18

and the ratio of right hand to total pitchers is = 5 : 6

we have to find the number of left hand pitchers that the base ball team have .

From the ratio, the total number of pitchers is = 6x ,

and number of right hand pitchers = 5x ,

So , the number of left hand pitchers = x ,

that means , 6x = 18

Simplifying further ,

we get ,

x = 3,

Therefore , there are 3 left hand pitchers .

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Answer:

Volume = 2×2×2 = 8 feet3

Answer:

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

We can see three marked angles in the diagram.

One of them marked with the small square, it means this is a right angle.

The other two are marked with 3 small parallel curves, it means they are congruent:

You can name them differently but it doesn't change angles:

The probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.

According to the question,

We have the following information:

Words are:

Palasa Kasibugga

Now, total number of letters = 15

Number of a in these words = 4

Number of letters other than a = 11

We know that the following formula is used to find the probability of an event:

Probability = Number of favorable outcomes/total number of outcomes

Probability = 11/15

Hence, the probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.

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Answer:

b = 4

Step-by-step explanation:

Step 1: Divide 45 by 36 on the right side

    1. 5/b = 1.25

Step 2: Multiply both sides by b and flip the equation

    2. 1.25b = 5

Step 3: Divide both sides by 1.25

    3. b = 4

[tex]\fbox{b=4}[/tex]

Cross multiply:

[tex]\dfrac{5}{b} =\dfrac{45}{36}[/tex]

[tex](5)\times(36)=45\times(b)[/tex]

[tex]180=45b[/tex]

Flip the equation:

[tex]45b=180[/tex]

Divide both sides by 45:

[tex]\dfrac{45b}{45} =\dfrac{180}{45}[/tex]

[tex]b=4[/tex]

The degrees of freedom used to test the significance of the slope in a simple linear regression equation is n-2.

The maximum number of logically independent, or potentially different, values in the sample of data is referred to as the degree of freedom.

The degree of freedom is a fundamental concept that can be found throughout statistics in a variety of contexts, such as with hypothesis tests, probability distributions, and linear regression.

The degrees of freedom are n−k, however, in simple linear regression you estimate both a y-intercept and a slope, so k=2. Even though we generally don't worry about testing the intercept, it still uses up a degree of freedom, the slope would be very different and have a very different interpretation if we did not estimate an intercept along with the slope.

When we put the value of k=2 we get degrees of freedom are n-2.

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The equation of the parabola is  y -5 = (5/6) (x - 2)^2

a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.

A quadratic function's U-shaped curve is shown on a parabola graph. A right circular cone and a plane surface intersect to form one of the conic sections known as a parabola in mathematics. The plane is symmetrical. U-shaped bend

y - k = a (x - h)2

where the vertex is (h,k). Since the vertex is known to be at (7,-3), we know that h = 7 and k = -3. Consequently, the equation is

y -5 = a (x - 2)2

We utilize the fact that the parabola passes through point to determine a for (4,0). With x =- 4 and y = 0, we obtain

0 - 5 = a (-4 - 2)

-5 = a (-6)2

-5 = -6a

a = 5/6

Consequently, the parabola's equation is

y -5 = (5/6) (x - 2)^2

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The function that models the volume of  a rectangular box in terms of width is (lw²)/2.

The basic formula for volume is length×width, whereas the basic formula for area of a rectangular shape is length×width×height.

Given: The base of a rectangular box is square. Half of the base's width is its height.

Let,

length = w (since it has a square base)

width = w

height = w/2

Volume of a rectangular box = length×width×height

                                               V = w×w×(w/2)

                                            V  = (lw²)/2

Therefore, the function that models the volume of  a rectangular box in terms of width is (lw²)/2.

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Answer: x = 42

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a circle with radius 4 is 50.24.

Writing the equation form for area and radius of two circles -

(Area/radius²) for circle 1 = (Area/radius²) for circle 2

Keep the values in the relation to find the area of small circle.

314/10² = Area/4²

Area = (314 × 16)/100

Performing multiplication on Right Hand Side of the equation to find the area of circle

Area = 5024/100

Performing division on Right Hand Side of the equation to find the area of circle

Area = 50.24

Hence, we see the decrease in area based on decrease in radius. Thus, the area of circle is 50.24.

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The multiplication of the two arrays will be 360.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

The given arrays of the numbers are 5x6 and 2x6. The multiplication of the two numbers will be done as,

M = ( 5 x 6 ) x ( 2 x 6 )

Multiply both the numbers and solve,

M = 30 x 12

M = 360

Therefore, the multiplication of the two arrays will be 360.

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Answer: There are no values that make the equation true  .  No solution