Select all of the solutions for the linear inequality graphed below:

The total weight of the metal bar is 45.002 grams.

Given:

While mining, Peter found a large metal bar that contained 33 grams of gold.

Peter also determined that the bar was 73.33% gold.

73.33% = 33 grams

divide by 73.33 on both sides

73.33%/73.33 = 33/73.33 grams

1% = 0.45002 grams

Multiply on 100 on both sides

1%*100 = 0.45002*100

100% = 45.002 grams.

Therefore the total weight of the metal bar is 45.002 grams.

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68 calls she received in each evening .

A straight line equation and equations with a maximum order of one are referred to as "linear equations." The formula for the linear equation can be written as Y = mx + b, where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slopes tell us the direction and steepness of a line. The value of y when x is 0 is referred to as the y-intercept because (0,y) is the point where the line crosses the y-axis.

Let's say the number of calls on the second night was x.

The first evening was then x+7.

The third evening she received 4x calls.

Add them up to make 109 calls....

x + x+7 + 4x = 109

6x + 7 = 109

6x = 102

x = 17 calls

x+7 = 24 calls

4x = 68 calls

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If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]

Differentiating with respect to x, we get

d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])

= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex])  (2[tex]$$x^4[/tex] + 1)

d/dx (2[tex]$$x^4[/tex] + 1) = 8x³

d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

Simplify

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

= sin (2) (18[tex]$$x^8[/tex] +  5[tex]$$x^4[/tex]

Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

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The measure of the line AC is 15√3/2

The measure of the line BC is 15/2

Triangle ABC is the display style for a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.

Sin 60⁰=x/15

√3/2=x/15

x=15√3/2

The measure of the line AC is 15√3/2

Cos 60⁰= y/15

1/2=y/15

y=15/2

The measure of the line BC is 15/2

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Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.

In the question given, the trig ratio is

tan a + cot a

We can simplify this as

tan a = sin a / cos a

cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a

Adding both ratios together

tan a + cot a = (sin a / cos a) + (cos a / sin a)

tan a + cot a = (cos a + sin a) / sin a * cos a

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The first mechanic worked for 10 hours and second mechanic worked for 5 hours.

Given,

Price of first mechanic service =$85/hr

Price of second mechanic service=$45/hr

Total time they worked together=15 hours

Total combined price charged=$1075

Let

Time spend by first mechanic on work =x

Time spend by second mechanic on work =y

Price charged by first mechanic on total work =85x

Price charged by second mechanic on total work=45y

Equation for total time spend by them together on work can be written as,

[tex]x+y=15.....i\\\\y=15-x[/tex]

Equation for total price charged by them can be written as,

[tex]85x+45y=1075\\[/tex]

Substituting y,

[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]

Substituting x in eq.[tex]i[/tex],

[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]

Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.

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Step-by-step explanation:

the solution to a system of functions (lines or any other form of curve) is the point (or points), where they intersect.

in this case : the point (2, 0)

FYI : if there is no intersection, then there is no solution at all (like with parallel lines).

if the curves fully overlap for at least some distance, then we have infinitely many solutions (at least for real numbers). like for identical lines.

Answer:

There isn't one. There is no solution.

Step-by-step explanation:

There are multiple ways to solve this system, but here's what I did:

Solve the both equations for s:

   s/2 + 5t = 3 + 5t  ⇒  s = 6

   3t - 6s = 9 + 3t  ⇒  s = -3/2

Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.

If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.

Formulate an equation

1.30x + 1.60y = 3400

Hence,

x =4y Equation 1

1.30x + 1.60y = 3400 Equation 2

Substitute eq1 into eq2

1.30(4y) + 1.60y = 3400

5.2y +1.60y =3400

6.8y =3400

Divide both side by 6.8y

y =3400/6.8

y = 500

Number of euro

4y where y = 500

4(500)

=2000

Therefore  the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.

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The solution for the given inequality has been graphed in detail.

A linear inequality can be gives the values for a variable in an interval of numbers.

Given inequalities are as below,

2x - 7 > 3 and 4 - x < -4

They can be simplified as,

2x - 7 > 3    

=> 2x > 10    

=> x > 5

And,  

4 - x < -4

=> x - 4 > 4

=> x > 8

The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.

This is graphed as follows,

Hence, the given inequality has solution x > 8 which has been graphed.

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The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:

0.0723 = 7.23%.

The volume of a cube of side length s is given by the side length cubed, that is:

V = s³.

The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:

V = 1.2³ = 1.728 cubic meters.

Considering only the inner 0.5 meters of the cube, the volume is given as follows:

V = 0.5³ = 0.125 cubic meters.

A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:

p = 0.125/1.728 = 0.0723 = 7.23%.

(desired volume is of 0.125 m³, total is of 1.728 m³).

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Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123

H0: mean = 123

H1 : mean ≠ 123

We have the p value of the statistics stated already in the question as p value = 0.0037.

The level is significance that we have been given in the question is 5% = 0.05

We are to test here if the true mean is different from 123.

Hence we would be testing the p value against the significance level.

We can see that P value is  < level of significance.

0.0037 < 0.05

Hence we would reject the null hypothesis.

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The total number of movies that the students saw is 105.

I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.

The length of the segment CB in triangle ABC where [tex]\overline{AM}[/tex] is a median line and CM = 5·x - 2, MB = 3·x + 12, CM = MB, is 66 units

A median line is a line that is drawn from a vertex of a triangle to the middle of the opposite side such that the it bisects the opposite side.

The parameters are; [tex]\overline{AM}[/tex] = A median line

Length of segment CM = 5·x - 2

Length of segment MB = 3·x + 12

Required; The length of segment CB

The median line [tex]\overline{AM}[/tex] bisects the segment CB

Therefore; CM = MB

CB = CM + MB (Angle addition postulate)

Which gives; 5·x - 2 = 3·x + 12 (substitution property of equality)

2·x = 14

x = 14 ÷ 2 = 7

CB = CM + MB

CB = (5·x - 2) + (3·x + 12)

Which gives; CB = 8·x + 10

x = 7

CB = 8×7 + 10 = 66

The length of segment CB =  66

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Answer:

[tex]-9,-18,-27,-36[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-9[/tex] and the common difference is [tex]-9[/tex], then each successive term in the sequence is [tex]9[/tex] less than the previous term:

[tex]a_n=-9n[/tex]

Therefore, the first term is [tex]-9[/tex], followed by [tex]-18[/tex], [tex]-27[/tex], and [tex]-36[/tex].

Considering the given translation, the vertex that is not part of the image is:

H(3,0).

The translations to an image are represented as follows:

The vector notation of a translation is given as follows:

{x ± a, y ± a}

In this problem, this notation is:

{3, -3}.

Hence the rule applied to each vertex of the image is:

(x,y) -> (x + 3, y - 3).

The vertices of the original figure are as follows:

( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)

Applying the translation rule, the vertices of the image are given as follows:

(-4, 0), (-1, 3), (2, 0), (-1, -3).

The lone coordinate without a vertex of the image is H(3,0).

The problem is given by the image at the end of the answer.

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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Lois’ pay before the tax had been deducted is £660.

Given:

Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers.

22% = 514.80

divide by 22 on both sides

22%/22 = 514.80/22

1%= 23.4

= 514.8/0.78

= 5148/10/78/100

= 5148*100/10*78

= 66*100/10

= 66*10

= £660.

Therefore Lois’ pay before the tax had been deducted is £660.

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Answer:

[tex]y+10=\frac{13}{8}(x-20)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

The exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

Data;

f(x) = P(1 + r)ˣ

x = time

Substituting the values

1134 = 215(1 + 0.1663)^ˣ

x = 10.80

It will take approximately 10.8 years to reach a growth of 1134

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Answer: The correct answer is "10.0 years"

Step-by-step explanation:

I took the test

Complete steps to find domain of function is describe below.

Domain is defined as the all input values which satisfy the function or can say all inputs any function have.

suppose we have a function f(x) = 6x^2 + 5x - 4

For domain solve it for x

⇒ 6x^2 + 5x - 4

⇒ 6x^2+ 8x - 3x - 4

⇒ 2x(3x + 4)· -1(3x + 4)

⇒ (3x + 4) (2x - 1)

values of x are positive for quadratic  equation,

⇒ (3x + 4) (2x - 1)≥0

⇒ x ≥ 1/2  or  x ≥ -4/3

These  are the domain of function.

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The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.

The relation between two unequal expressions is defined as inequality.

The given inequalities are 3x + 6 < 15 and  2x - 5 >7.

Solve the first inequality:

3x + 6 <15

3x < 15 -6

3x < 9

x < 3

Solve the second inequality:

2x - 5 > 7

2x > 7 + 5

2x > 12

x > 6

Hence, the solution to the compound inequality is x < 3 and x >6.

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Answer:

use AAA congurency rule

Step-by-step explanation:

angle a=angle f

angle b=angle e

angle c= angle d(a+b+c=180 when the triangle 2 sides are equal that means 3 is also equal)

The area of the given figure is 25cm².

Area of rectangle

Area = length x width

Perimeter of rectangle

Perimeter = length + length + width + width

Hence, we have

length = 5cm

width = 5cm

then, by applying the Area of the rectangle, we get

Area = length x width

Area = 5 x 5

      = 25cm²

Hence, The area of the given figure is 25cm².

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Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

What is the Greatest Common Factor?

The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.

We have,

The number of coloured pencils Mr. Pinello has = 80.

The number of markers and pencils Mr. Pinello has = 60.

The most containers Mr. Pinello can create to ensure that each one contains an identical amount of coloured pencils and markers.

The GCD of the number of coloured pencils and markers will be the largest number of containers to have the same number of items when the same number of items must be preserved.

Calculating the gcd of  and 80 and 64 is:

The greatest common divisor (GCD) of both 80 and 64 is 16.

∴ GCD = 16

Therefore, If Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

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The value of 32/25 as mixed number is 1 7/25

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/7 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed fraction can be obtained wen there is improper fraction. Improper fraction is a fraction that it's numerator is larger than denominator for example 32/25.

To convert to mixed fraction we find the number of times 25 can go in 32, which is 1 and the remainder is 7

Therefore 32/25 = 1 7/25.

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