these are two angles that are formed by two coplanar lines and a transversal. they occupy the same relative positions.

Answer:

Step-by-step explanation:

3(15.50 + x) = 60

46.5 + 3x = 60

3x = 60-46.5

x = 13.5/3

x = 4.5 or $4.50

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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The slope of the line is  4/3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

In the slope marked,

vertical length = change in y values = number of unit squares = 4

Horizontal length = change in x values = number of unit squares = 3

Slope= ( change in y values  )/ ( change in x values ) = 4/3

Thus, the slope = 4/3

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P is the subject of the formula if we rewrite it as:

p = m*(nx - y²)/3n

The subject of a formula is the variable that is isolated, so here we only need to isolate the variable p.

The formula is:

m*(nx - y²)/p = 3n

First, we can multiply both sides by p to get:

m*(nx - y²) = 3n*p

Now we can divide both sides by 3n, then we will get:

m*(nx - y²)/3n = p

Now p is the subject of that formula.

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Answer:  m∠5 = 116°

Step-by-step explanation:

Because m∠4 and m∠6 are consecutive interior angles, then we know

         m∠4 + m∠6 = 180

(106 - y) + (3y - 10) = 180

   104 - y + 3x - 10 = 180

                96 + 2y = 180

                         2y = 84

                           y = 42

And also the m∠4 and m∠5 are alternate interior angles, we get:

m∠5 = m∠4 = 3y - 10

Since we also calculate what y is, we just plugin.

mm∠5 = m∠4 = 3(42) - 10 = 126 - 10 = 116

Solving the given equations using substitution method we get (x,y) as (2, -1) i.e option (2) is correct answer.

Substitution method

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Given: 4x + 2y = 6      --------- (1)

            x = 2y + 4        ----------(2)      

Put the value of x from the 2nd equation in the 1st equation

4(2y+4) +2y = 6

8y + 16 + 2y = 6

10y + 16 = 6

10y = 6-16

10y = -10

y = -1 --------------- (3)

put the value of y in the (2) from (3)

x = 2(-1) + 4

x = -2+4

x = 2

Therefore, its solution is (2, -1)

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Answer: B

Step-by-step explanation: Did the test

Answer: It takes 3 cups of sugar for 4 cups of cranberry

Step-by-step explanation:

12 cups of sugar, 16 cups of cranberry

Divide both numbers by 4

12/4=3

16/4=4

It takes 3 cups of sugar for 4 cups of cranberry

If f:RR, then Munkres' definition (f′(a) is a 11 matrix) is the definition of the derivative as it is presented in elementary calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).

Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.

The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is

According to our question-

The linear mapping Dfa:RmRn that obeys limh0f(a+h)f(a)Dfa(h)h2=0 is typically used to compute the derivative (or "total derivative") of a function f:RmRn at some point aRm.

both are true. If f:RR, then Munkres' formulation (f′(a) is an 11 matrix) is the definition of the derivative as taught in introductory calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

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The matrices A and B are not inverse matrices

From the question, we have the following parameters that can be used in our computation:

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

[tex]B = \left[\begin{array}{cc}1&-1&-1&2\end{array}\right][/tex]

To determine if the matrices are inverse matrices, we simply calculate the inverse of matrix A and then make the comparison.

The matrix A is given as

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

Calculate the determinant of the matrix A

So, we have the following representation

|A| = -2 * -2 + 3 * 2

Evaluate the sum of products

|A| = 10

The inverse is then calculated as

[tex]A^{-1} = \frac 1{10} * \left[\begin{array}{cc}-2&3&-2&-2\end{array}\right][/tex]

Evaluate

[tex]A^{-1} = \left[\begin{array}{cc}-\frac 1{5}&\frac 3{10}&-\frac 1{5}&-\frac 1{5}\end{array}\right][/tex]

When compared to matrix B, both matrices are different

Hence, the matrices are not inverse matrices

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Answer:

The answer should be 8.

Step-by-step explanation:

The value of x (B) 5 makes the inequality 5x + 6 ≤ 2x + 15 FALSE.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.

The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.

So,  we have the inequality:

5x + 6 ≤ 2x + 15

Now put the given values and check as follows:

(A) -2

5x + 6 ≤ 2x + 15

-10 + 6 ≤ -4 + 15

-4 ≤ 11

TRUE

(B) 5

5x + 6 ≤ 2x + 15

25 + 6 ≤ 10 + 15

31 ≤ 25

Correct: 31 > 25

FALSE

Therefore, the value of x (B) 5 makes the inequality FALSE.

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Complete question:
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.

a:{−2}

b:{5}

c:{2}

d:{−5}

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

[tex]\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}[/tex]

Now, differentiate P with respect to x, and we get,

[tex]\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}[/tex]

Solving the above equation to zero, we get,

[tex]\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}[/tex]

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

[tex]\begin{aligned}y&=108-36\\y&=72\end{aligned}[/tex]

Thus, the two positive numbers are 36 and 72.

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Answer: The correct answer is C

Step-by-step explanation: Let's find each equation without any inequalities first. We have a dotted line at y = 1, so we can already remove A and B. Now, a dotted line represents exclusivity and hence; it should not include the = sign.

P(tail) = Probability of getting a tail on the coin

P(tail)=1/2

P(4)=Probability of getting the number '4' on the dice.

P(4)=1/6

P(tail and 4)=Probability of getting tail on the coin and number '4' on the dice.

P(tail and 4)=p(tail multiply with 4)

P(tail and 4)= 1/2×1/6

P(trail and 4)=1/12

Hope this helps!

If 250 bricks are used to build a wall of 15 ft high then, there is total 1250 bricks will be used to build a wall that is 75 ft high.

Proportion:

A proportion is an equation between two ratios or rates that is useful in solving for a single unknown.

We have given that,

It takes 250 bricks to build a 15 ft high wall. Let us consider x bricks , is needed for a 75 ft high wall, use the ratio given for a 15 ft high wall and equate it to the ratio for the unknown number of bricks for a 75-ft high wall.

In making proportions, make sure that the rate on one side has the same units as the rate on the other as shown :

x/75 = 250/15

=> 15 × x = 250 ×75

=> x = 250×75/15

=> x = 1250

Thus, it will take 1250 bricks to build a wall 75 feet high.

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Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

Answer:

[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]

Step-by-step explanation:

See picture below :)

The tree statements of the circle are

1) The radius of the circle is 3 units.

2) The center of the circle lies on x-axis.

3) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is center of a circle?

A circle's center is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.

Given equation of circle is

x² + y² - 2x - 8 =0

x² - 2x + 1 - 1 + y² - 8 =0

(x - 1)² - 1 + y² - 8 =0

(x - 1)² + y² - 9 =0

(x - 1)² + y² = 3²

Compare the equation above equation with (x - h)² + (y - k)² = r²:

h = 1, k=0, r=0

The radius of the circle is 3 units. The center of the circle is (1,0) which lies on the x-axis.

Rewrite the equation of circle x² + y² = 9:

x² + y² = 3²

The radius of the circle is 3 units:

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Answer:

To solve this problem, we can set up a system of two equations to represent the given information:Let A be the cost of an apple and B be the cost of a banana.Then the first equation is: 4A + 3B = 4.48

The second equation is: 3A + 4B = 4.76To find the values of A and B, we can solve this system of equations using substitution or elimination.Using substitution, we can solve for A in the first equation and substitute that expression into the second equation:4A + 3B = 4.48

A = (4.48 - 3B)/4Substituting this expression for A into the second equation gives:3((4.48 - 3B)/4) + 4B = 4.76

3(4.48 - 3B) + 4B = 4.76

13.44 - 9B + 4B = 4.76

4.44 - 5B = 4.76

-5B = -0.32

B = 0.064Now that we have found the value of B, we can substitute it back into the first equation to find the value of A:4A + 3(0.064) = 4.48

4A + 0.192 = 4.48

4A = 4.288

A = 1.072Therefore, the cost of an apple is £1.072 and the cost of a banana is £0.064.

Step-by-step explanation:

Answer:

The answer is below

Answer:

x(x-2)

Step-by-step explanation:

First up is 5x+2y-2z=-57

5x+2y-2z=-57 /You gotta subtract 27 and 2z from both sides

5x+2y-2z- (2y-2z)=-57- (2y-2z) Then simplify-5x =-57-2y+2z

Then divide by both sides:

Answer is: x=-57-2y+2z / over 5

Answer:

Step-by-step explanation:

find x

7x+10=2x+40+3x

2x=30

x=15

ABD = 7(15)+10 = 115

ABD + ABC =180

115+ABC=180

ABC=65

The probability the researcher will make a type i error 0.10

The hypothesis testing, type I error involves rejecting true null hypothesis also referred to as 'false-positive' conclusion and type II error occurs when false null hypothesis is not rejected. It is also known as 'false negative' conclusion. And they are opposite to each other.

Here we have given that suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean

And we need to find the probability the researcher will make a type i error

While looking into the given question,

We know that,

Significance level = 5%

alternative value of the mean = 0.90

Then the probability the researcher will make a type i error is calculated as,

mean = 1 - error

0.90 = 1 - error

=> error = 0.10

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The value of R is 7 , we can find answer using concept of greatest integer and square root .

What is square root of a number ?

Square root , in mathematics , a factor of a number that , when multiplied by itself , returns the original number.

e.g. Square root of 9 are both 3 and -3.

Symbol = " √ "

In given que, we need to find greatest integer smaller than √51.

Root of 51 will not give exact integer value.

As we know root of 49 is 7 and root of 64 is 8.

And 51 lie between 49 and 64,

So, Square root of 51 will also lie between 7 and 8.

So, the greatest integer smaller than √51 will be 7.

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Answer:

y < -1x + 2

y [tex]\geq \\[/tex] 2x + 4

Step-by-step explanation:

The steps taken to find the two inequalities are on the GraphInequalities worksheet.  The derived equations are graphed on DESMOS and attached, for comparison.

The basic steps are to find the slopes of the two lines and to identify the y-intercepts from the graph.  The inequalities can be assigned based on the darkened areas and presence of either a solid or dashed line.  All are outlined in the worksheet.

Answer: 3 sports drinks

Step-by-step explanation:

6 divde by 2= 3

36 divided by 12 =3

in other words

3x2=6

12x3=36

hope this helps

The probability that the entire batch will be accepted.

What is Acceptance Sampling?

Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.

abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).

Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.

If 3 of these cds are randomly selected for testing without replacement,

The probability that the entire batch will be accepted

= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)

= 0.8750 × 0.8742 × 0.8733 × 0.8725

=0.5828

The probability that the entire batch will be accepted is 0.5828 .

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Answer:

Option B is the correct answer

Step-by-step explanation:

h(x) = 5x + 2, h(8)

h(8) = 5(8) + 2

h(8) = 40 + 2

h(8) = 42

Thus, The answer is 42

Answer:

[tex]y > 3+\frac{x}{2}[/tex]

Hope this helps!

Answer: x<2y-6

Step-by-step explanation:

x-2y<-6

=(x-2y)+6<-6+6

=x-2y+6<0

=(x-2y+6)+(2y-6)<2y-6

=x-2y+6+2y-6<2y-6

=x-2y+2y+6-6<2y-6

=x<2y-6

Answer:

No solution

Step-by-step explanation:

-6x - 9y = 0

-24x -36y = 0

Multiply the top equation by -4 and add that to the second equation

24x + 36y = -4

-24x - 36y = 0

0 + 0 = -4

0 ≠ -4  Since this is a false statement, the answer is no solution.