Find the image of the given point
under the given translation.
P(8,-3) T(x, y) = (x-4, y + 7)
P' = ([?], [ ])
Enter the number that belongs in
the green box.
Enter

OA=5 and the length of arc AB is 3π. The x value is [tex]108[/tex]°.

The circle's radius and arc length are both provided. Finding the angle that the arc occupies on the center O is necessary.

The correct formula is

s=rФ

Where

arc length is measured in radians,

r is the radius, and

Ф is the angle (in radians)

If Ф is in degrees, we apply the formula.

s= Ф[tex]*\frac{\pi }{180} *r[/tex]

In order to determine the value of theta, we must enter the specified values of s and r into the formula above.

[tex]3\pi =[/tex]Ф[tex]*\frac{\pi }{180} *5[/tex]

[tex]3\pi *\frac{180}{\pi } *\frac{1}{5}=[/tex]Ф

Ф=[tex]108[/tex]°

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Answer: D

Step-by-step explanation:

-2 is not a repeating decimal.

It is not a fraction

And it is a rational number

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer:

  (b)  $9.45

Step-by-step explanation:

You want to know how much Marissa's mom spent at the coffee shop for ...

after her rewards program discount of $0.50 was applied.

Adding up the bill, we find it to be ...

  $3.95 + 2×1.50 +3.00 -0.50 = $9.45

Marissa's mom spent (b) $9.45 at the coffee shop.

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Answer:

V = 5πX^2 + 50πX + 75π

Step-by-step explanation:

The volume of a cylinder with radius r and height h is given by the formula:

V = πr^2h

Substituting the values for the radius and height of the cylinder in this formula, we get:

V = π(5X + 5)^2(5X + 3)

This can be written in standard form as:

V = 5πX^2 + 50πX + 75π

So, the polynomial in standard form that best describes the total volume of the cylinder is:

V = 5πX^2 + 50πX + 75π

A random variable is a quantitative outcome of a chance experiment.

A probability distribution includes the likelihood of each possible outcome.

A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.

A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.

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The value of sin (x - y) of the triangles is -33/65

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Given: sin x = 3/5 and cos y = 5/13.  Both triangles are in quadrant 1

(Consider the image attached)

For triangle with angle x

adjacent = √(5²-3²)  = 4

cos x = 4/5 (adjacent/hypotenuse)

For triangle with angle y

opposite = √(13²-5²)  = 12

sin y = 12/13 (opposite/hypotenuse)

Using the trigonometric identity:

sin(x-y) = sinxcosy - sinycosx

sin(x-y) = (3/5)×(5/13) - (12/13)×(4/5)

sin(x-y) = 3/13 - 48/65

sin(x-y) = -33/65

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We can rewrite the linear equation as:

y = -x + 3

There we can see that the slope is -1.

A linear equation written in the slope-intercept form is:

y = a*x + b

Where a is the slope.

Here the linear equation is written kinda weird, I guess that the line is:

y - 3 = -(x - 2) - 2

Let's isolate y and simpify the equation, we will get:

y - 3 = -(x - 2) - 2

y = -(x - 2) - 2 + 3

y = -(x - 2) + 1

Now we can apply the rule of signs in the right side:

y = -x + 2 + 1

y = -x + 3

y = -1*x + 3

So the slope of the linear equation is -1.

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The statements that are true in the right triangle are

A right angled triangle is a triangle in which one of its angles is 90°.

Since the area model at the right shows a right triangle with side lengths a, b, and c such that a² + b² = c².

If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, we  need to show which of the following statements will be true.

Now, if the side a increases by a small amount Δa, we have that

a + Δa > a

Squarring both sides, we have that

(a + Δa)² > a²

Adding b² to both sides, we have that

(a + Δa)² + b² > a² + b²

(a + Δa)² + b² > c²  since  a² + b² = c²

So, a² + b² > c² where a is the new value of a = a + Δa

Also, since a is perpendicular to b, we have that angle m∠ACB = 90°. Increasing a by a small amount  Δa does not change a from being perpendicular to b, so we still have that m∠ACB = 90°.

So, the statements that are true in the right triangle are

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Step-by-step explanation:

0.91666666...

is the sum of

0.91 and 0.006666666...

0.66666666... = 2/3

0.0066666666... = 2/300

0.91 = 91/100

so,

0.91666666... = 91/100 + 2/300 =

= 91×3/300 + 2/300 =

= 273/300 + 2/300 = 275/300 =

= 11/12

if you fail to find a fraction at the beginning (like the 2/3 we did), remember the following basics

0.1111111111... = 1/9

0.2222222... = 2/9

0.33333333... = 3/9 = 1/3

0.44444444... = 4/9

0.55555555... = 5/9

0.66666666... = 6/9 = 2/3

0.777777777... = 7/9

0.88888888... = 8/9

0.99999999... = 9/9 = 1

if you want to repeat a pattern like

0.125 to

0.125125125125125...

remember this simple trick

0.125 = 125/1000

0.125125125125125... = 125/999

you must use as many 9s as you have digits in the basic pattern.

227/999 = 0.227227227227227...

6382/9999 = 0.63826382638263826382...

and so on.

Answer:

11/12

Step-by-step explanation:

1. Let x = 0.916 (6 repeating)

2. Identify the FIRST repeating digit's place value:

   6 is in the 1000ths place

3. Multiply BOTH sides of x = ... by the value you got in step 2

   x = 0.916 (6 repeating)

   1000x = 916.6 (6 repeating)

4. Subtract the x = ... from the 1000x = ...:

   1000x = 916.666...

           x =     0.916...

    999x = 915.75

5. Divide both sides by 999:   [tex]x=\frac{915.75}{999}[/tex]

6. Rewrite as a corrected fraction: [tex]x=\frac{91575}{99900}[/tex]

7. Simplify as far as possible: [tex]x=\frac{91575}{99900}/\frac{8325}{8325}=\frac{11}{12}[/tex]

The equation for a line that passes through points (2,1) and (0,7) is y-7 = -3x or y= -3x+7

To find the equation of a line passing through two points you must first find the slope of the line.

The slope can be found by using the formula: [tex]m=\frac{y2-y1}{x2-x1}[/tex]

Where m is the slope and (x1,y1) and (x2,y2) are the two points. Substituting the two points given in the problem allows us to calculate the slope as:

[tex]m=\frac{7-1}{0-2} \\m= \frac{6}{-2} \\m= -3[/tex]

Next, we have to use the point-slope formula to find the equation for the line passing through these two points.

The point-slope formula states: (y-y1)=m(x-x1)

Where m is the slope and x1, and y1 are points from which the line passes.

Substituting the value of m and x1 and y1 in the given equation,

y-7=-3(x-0)

y-7= -3x-3*0

y-7+-3x

Solving for the slope-intercept form gives:

y-7+7= -3x+7

y-0 + -3x+7

y= -3x+7

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Answer:

e is 9x D is 4x c is 1× and a is 5× and b is 2×

We can rewrite the circle equation as:

(x - 1)^2 + y^2 = 9

Then the two true statements are:

"The center of the circle lies on the x-axis"

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

Remember that a general circle equation with a center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here the equation is:

x^2 + y^2- 2 x - 8 = 0

We can rewrite this as:

(x^2 - 2x) + y^2 = 8

Adding and subtracting 1 in the left side we can complete squares:

(x^2 - 2x + 1) - 1 + y^2 = 8

(x - 1)^2 + y^2 = 9

Tha is our equation, so the center is (1, 0) and the radius is 3 units.

Then the true statements are:

"The center of the circle lies on the x-axis"

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

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Answer:

x ≤ -12

Step-by-step explanation:

We solve for x by dividing both sides by 1/4:

[tex]1/4x\leq -3\\x\leq -12[/tex]

Thus, the two sentences you need to have two words from your work bank are (1) "divide" both sides by 1/4 and (2) x is "less than or equal to" -12

The computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10.

This statement is a false statement.

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample. First, a hazy assumption about the parameter or distribution is made.

The null hypothesis is that 50% is true, while the alternative hypothesis is that 50% is not accurate, for instance, if someone wants to test whether a penny has an exact 50% chance of landing on heads.

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The sample mean is 75.

Margin of error is 6.

Sample standard deviation is 17.53 .

What is the relationship between margin of error and confidence level?

Confidence level and marginal of error As the confidence level increases, the critical value increases and hence the margin of error increases. This is intuitive; the price paid for higher confidence level is that the margin of errors increases.

Part A:

The sample mean is at the midpoint of the lower and the upper values of the confidence interval.

Thus, the sample mean is given by:

=(69 + 81) / 2

= 150/2 = 75

Therefore, the sample mean is 75.

Part 2:

The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.

Thus, margin of error is given by 81 - 75 = 75 - 69 = 6 .

Therefore, margin of error is 6.

Part 3:

The margin of error is given by

ME = t₍ᵃ/₂₎ ([tex]\frac{s}{\sqrt{n} }[/tex] )

where t₍ᵃ/₂₎  is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.

Since the sample size is 25, the degree of freedom is 25 - 1 = 24.

[tex]\frac{a}{2}[/tex] = [tex]\frac{1-0.9}{2}[/tex] = [tex]\frac{0.1}{2}[/tex] = 0.05

From the t-distrbution table, we have:

t₍ᵃ/₂₎ = 1.710882

Thus, margin of error is given by:

6=1.710882 [tex](\frac{s}{\sqrt{25} })[/tex]

⇒[tex]\frac{s}{\sqrt{25} }[/tex]   = [tex]\frac{6}{1.710882}[/tex]

⇒s= 17.53

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(X+1) is the factor of the polynomial P(X) = (X³+4X+5)

Factorization is a method of expanding an equation or polynomial that help us to understand an equation properly. In order to factoring, we need to rewrite a polynomial in expanding form. In this method, we divide the polynomial into a product of its factor.

We are given a polynomial P(X) = X³+4X+5

 It is a 3-degree polynomial and in order to factoring we need to expand first.

- by expanding X³+X²-X²-X+5X+5

now factoring, X²(X+1) - X(X+1) + 5(X+1)

              (X+1) (X²-X+5)

hence, (X+1) is the factor of the polynomial.

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Answer:

x = 40°

y = 35°

Step-by-step explanation:

Let us take two triangles ∆ABC and ∆ADE

We know that, in a triangle the sum of all angles is equal to 180°

So,

For the traingle ABC

Now,

m∠A + m∠B + m∠C = 180°

80° + 60° + x° = 180°

140° + x° = 180°

x° + 140° - 140° = 180° - 140°

x = 40°

For the triangle ADE

Now,

m∠A + m∠D + m∠E = 180°

80° + 65° + y° = 180°

145° + y° = 180°

y° + 145° - 145° = 180° - 145°

y = 35°

Thus, The value of x and y is 40° and 35° respectively

Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:

a) Organizing the data into afrequency  distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.

b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.

c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.

Here are some of the benefits of using graphs of frequency distributions:

a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.

b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.

c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.

d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.

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The probability of rolling a number greater than 5 or doubles will be 0.78.

       P(A)  =  n(A)/n(S)

        where -

       n(A) = Number of outcomes favorable to event A.

        n(S) = Total number of outcomes.

We have two dices are rolled.

The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -

P(A) = 28/36 = 0.78

Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

Answer: 8x

Step-by-step explanation: We will start by writing out our equation which is 10x2y-2x2y. Next we will subtract using only like terms

10x - 2x = 8x

2y-2y=0

8x plus 0 = 8x.

If the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue with rational numbers.

In mathematics, a rational number is a number that can be written as the quotient or fraction p/q of two numbers, an integrand p and a non-zero denominator q.

For instance, −3/7 is a rational number, and so is every integer.

So, in that case, any even number would be 12 * 0.5 = 6.

The solution is reasonable because 12 began as rational (6).

Any odd number also is rational:

23 * 0.5 = 11.5

23 and 11.5: Both rational

1.818181818 is reasonable hence when multiplied by 0.5 the result will be rational 3.636363636.

Therefore, if we begin with an irrational number like π:

π*0.5: Not rational

Therefore, if the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue rational.

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Correct question:
Which number produces a rational number when multiplied by 0.5?

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:    c=a2+b2=372+152≈39.92493

Step-by-step explanation:

The total number of adults who attended the play are 210.

Here, we are given that tickets for a play cost $ 7 for students and $ 10 for adults.

Total number of seats = 380

Box office revenue on opening night =  $ 3290

Let the number of adults be x

Then, the number of students will be = (380 - x)

thus, we can form the following equation-

10x + 7(380 - x) = 3290

10x + 2,660 - 7x = 3290

3x + 2,660 = 3290

3x = 3290 - 2660

3x = 630

x = 630/3

x = 210

Thus, the total number of adults who attended the play are 210.

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The salt that is left after t minutes is y = 16e^[-t/100]

We have to mix problems we use:

dy / dt = (rate in) - (rate out)

The water entering the tank at a speed of 10 L / min but it has no salt, therefore

rate in = 0

The tank has 1000 liters of brine with 16 kg of salt initially, therefore the concentration of salt at time "t" is:

y (t) / 1000

then rate out would be:

rate out = y (t) / 1000 * 10 = y (t) / 100

The difference equation would then be:

dy / dt = 0 - y (t) / 100

1 / y (t) * dy = 1/100 * dt

We integrate from both sides and we have:

ln y = - (1/100) * t + C1

y = e ^ [- (1/100) * t + C1]

y = e ^ [- (1/100) * t] * e ^ [C1]

We assume that C = e ^ [C1]

Thus:

y = C * e ^ [- (1/100) * t]

now y = 16 to t = 0, replacing:

16 = C * e ^ [- (1/100) * 0]

16 = C, therefore we would have:

y = 16*e ^ [- t / 100]

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The only triangle dimensions that give a right angle triangle are;

3) 15, 36, 39

4) 15, 20, 25

6) 16, 30, 34

We are told that If a triangle has side lengths a, b, and c such that;

a² + b² = c² , then that triangle is a right triangle.

1) Using Pythagoras theorem, we can say that;

15² + 18² ≠ 21²

Thus, this is not a right angle triangle.

2) Using Pythagoras theorem, we can say that;

16² + 20² ≠ 24²

Thus, this is not a right angle triangle.

3) Using Pythagoras theorem, we can say that;

15² + 36² = 39²

Thus, this is a right angle triangle.

4) Using Pythagoras theorem, we can say that;

15² + 20² = 25²

Thus, this is a right angle triangle.

5) Using Pythagoras theorem, we can say that;

16² + 32² ≠ 48²

Thus, this is not a right angle triangle.

6) Using Pythagoras theorem, we can say that;

16² + 30² = 34²

Thus, this a right angle triangle.

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

There are numerous pairs of angles that are created when a transversal cuts any two parallel lines. These angles include consecutive interior angles, alternate interior and exterior angles, and comparable angles.

Each set of comparable angles are equal when a transversal cuts two parallel lines.

The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles. The matching angles are equivalent when the lines are parallel.

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Answer:

(2,4)

Step-by-step explanation: