⎯⎯⎯⎯⎯⎯⎯⎯⎯
is a common tangent of ⊙
and ⊙
. =10
, =6
, and =36
. Find
.
A larger circle with center at point A and a smaller circle with center at point B intersect each other at two points. D is a point on the larger circle and E is a point on the smaller circle. Points A and D are connected by a line segment and points B and E are connected by a line segment. Points D, E, and C are connected by a line segment and points A, B, and C are connected by a line segment.

Answer:

1023/4

Step-by-step explanation:

shown in the picture

Answer:

all of that?

Step-by-step explanation:

Answer: One way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/2 teaspoon measuring spoon 3 times to measure 3/2 = 1 1/2 teaspoons

and use the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

3 1/2 + 2/3 = 3 1/6

Another way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

and use the 1/2 teaspoon measuring spoon 6 times to measure 6 * 1/2 = 3 teaspoons

3 + 2/3 = 3 1/6

So, there are two ways to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2-teaspoon measuring spoon, one is by using 3 times 1/2 teaspoon measuring spoon and 6 times 1/3 teaspoon measuring spoon and the second one is by using 6 times 1/3 teaspoon measuring spoon and 3 times 1/2 teaspoon measuring spoon.

Step-by-step explanation:

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

A. 1/5

Step-by-step explanation:

First off, ignore the "each one is five tickets" part, that's just there to confuse you. There are ten tickets total sold, of which two are sold to girls. You can express this as 2/10, which simplifies to 1/5.

The equation for the perpendicular Bisector y = -2x + 2.

A perpendicular bisector of either a line segment is a line segment that is perpendicular to and passes through the midway of a line segment (left figure). A perpendicular bisector of a line segment can be drawn using a compass by drawing circles centered around and often with radius as well as connecting their two intersections.

A perpendicular bisector cuts through the midway of a line segment. It is simple to build with a ruler as well as a compass. It forms a 90° angle on both sides of the bisected line segment.

The perpendicular bisector is located at the middle of a line.

Let us determine the midpoint of (-7. -4) and (-1, 8).

(x1 + x2)/2 , (y1 + y2)/2

(-7 -1)/2 , (-4 + 8)/2

-4 , 2

The midpoint of the points (-4, 2).

the slope of the given line (-7. -4) and (-1, 8).

slope = ( (y1 + y2)/(x1 + x2))

          = -8/4

           = -2

the slope of the line is -2.

So slope of perpendicular line is -2.

Putting in the slope line equation:

y - y1 = m(x-x1)

y - 2 = -2(x+4)

y = -2x + 2

The equation for the perpendicular Bisector y = -2x + 2.

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Answer:

41

Step-by-step explanation:

\(24*2-7=\\48-7=\\41\)

Answer: 2(x+3)(x+2)

Step-by-step explanation:

Answer:

(5 · x) + (8 · y) + (2 · 1)

Answer:

5x + 2 ( 4y + 1 )

Step-by-step explanation:

i just factorised 8y + 2

The area of the smaller rectangle is 27 cm^2

Students will accurately translate fractions into decimals and decimals into fractions.

What is fraction?
A fraction is a mathematical expression that represents a part or parts of a whole. Fractions are written in the form a/b, where a and b are two integers and b cannot be equal to zero. Fractions indicate how many parts of the whole are being considered. For example, the fraction 3/4 indicates that three out of the four parts of the whole are being considered. Fractions can also be used to represent ratios and divisions. Fractions are used in many areas of mathematics such as algebra, geometry, and calculus and are also used in everyday life.

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Complete Question:

Which one of the following instructional objectives is consistent with the recommendations?

A) "Students will correctly convert decimals to fractions and fractions to decimals".

B) Teachers will demonstrate how to convert decimals to fractions and how to convert fractions to decimals."

C) "Students will work on problems that involve decimals and fractions."

D) "Students will study the relationship between decimals and fractions."

Answer:

6 stations

Step-by-step explanation:

24=1,2,3,4,6,8,12,24

18=1,2,3,6,9,18

Now we have to find which numbers are the same but that are the largest.

so It would be 6.

So Mrs.Davis can have every student participate in 6 stations.

Answer:

X\Y={3,12}

Explanation:

Given the sets X and Y below:

The set X\Y is the set of elements in X but not in Y.

Therefore:

The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 \(\times\) (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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Answer:

65 cm^2 or centimeter squared

Step-by-step explanation:

area of a triangle is

1/2 * b * h

1/2 * 13 * 10

65

Answer:

The area of isosceles triangle is 65 cm².

Step-by-step explanation:

SOLUTION :

Here's the required formula to find the area of Isosceles triangle :

\(\longrightarrow{\pmb{\sf{A = \dfrac{1}{2} bh}}}\)

Substituting all the given values in the formula to find the area of Isosceles triangle :

\(\implies{\sf{A_{(\triangle)} = \dfrac{1}{2} bh}}\)

\(\implies{\sf{A_{(\triangle)} = \dfrac{1}{2} \times b \times h}}\)

\(\implies{\sf{A_{(\triangle)} = \dfrac{1}{2} \times 13 \times 10}}\)

\(\implies{\sf{A_{(\triangle)} = \dfrac{1}{\cancel{2}} \times 13 \times \cancel{10}}}\)

\(\implies{\sf{A_{(\triangle)} = 1 \times 13 \times 5}}\)

\(\implies{\sf{A_{(\triangle)} = 13 \times 5}}\)

\(\implies{\sf{A_{(\triangle)} = 65}}\)

\( \star{\boxed{\sf{\red{A_{(\triangle)} = 65 \: {cm}^{2}}}}}\)

Hence, the area of isosceles triangle is 65 cm².

\(\rule{200}2\)

LEARN MORE :

\(\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Triangle:-}\\ \\ \star\sf Triangle \:area = \dfrac{1}{2}\times b \times h\\ \\ \star\sf Triangle \: perimeter=a+b+c\\\\ \star\sf Scalene\:\triangle=\sqrt{s (s-a)(s-b)(s-c)}\\\\\star\sf Equilateral\: \triangle\:area = \dfrac{\sqrt{3}}{4}\times{side}^{2}\\\\\star\sf Equilateral \:\triangle\:perimeter = 3 \times side\\\\\star\sf Isosceles\: \triangle\:area= \dfrac{3}{4}\sqrt{{4b}^{2}-{a}^{2}}\\\\\star\sf Isosceles\:\triangle\:perimeter=a+2b\end{minipage}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)

\(\rule{220pt}{3.5pt}\)

Answer:

one is 3-x

two is 1

three is x

four is 5-x

hope it helps :)

Answer:

1: 3-x

2: 1

3: x

4: 5-x

Step-by-step explanation:

Hope this helped

The requried population increased by approximately 60.53%.

To find the absolute increase, we subtract the initial population from the final population:

Absolute increase = Final population - Initial population

Absolute increase = 6100 - 3800

Absolute increase = 2300

Therefore, the population increased by 2300 people.

To find the relative increase, we first calculate the percent change:

Percent change = (New value - Old value) / Old value x 100%

Percent change = (6100 - 3800) / 3800 x 100%

Percent change = 2300 / 3800 x 100%

Percent change = 60.53%

Therefore, the population increased by approximately 60.53%.

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The average wait time to see an E.R. doctor is significantly less than 150 minutes, and we can recommend to the winery that the wait time is actually less than what is reported.

To test the hypothesis that the average wait time to see an E.R. doctor is less than 150 minutes, we can follow these steps:

State the null hypothesis: The null hypothesis is the assumption that there is no difference between the observed result and what we expect to see. In this case, the null hypothesis is that the average wait time to see an E.R. doctor is 150 minutes.

State the alternative hypothesis: The alternative hypothesis is the opposite of the null hypothesis. In this case, the alternative hypothesis is that the average wait time to see an E.R. doctor is less than 150 minutes.

Calculate the test statistic: The test statistic is a measure of the difference between the observed result and the expected result. In this case, the test statistic is the difference between the observed average wait time of 148 minutes and the expected average wait time of 150 minutes, divided by the standard deviation of 5 minutes.

Determine the critical value: The critical value is the value that determines whether the test statistic is significant or not. To determine the critical value, we need to determine the p-value of the test statistic using a significance level of 0.05.

Compare the test statistic to the critical value: If the test statistic is greater than the critical value, then the null hypothesis can be rejected. If the test statistic is less than the critical value, then the null hypothesis cannot be rejected.

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Answer:

a has two solutions for this case.

a₁: \(a=-9-b\)

a₂: \(a=-1+b\)

Step-by-step explanation:

         \(a+b-b=-9-b\\a=-9-b\)

         \(a-b+b=-1+b\\a=-1+b\)

➲ I hope this helps you.

Answer:

  4x^4y(9y^3z^4 -5x^4)

Step-by-step explanation:

The two terms have a common factor of 4x^4y, so we can rewrite the expression as ...

  = 4x^4y(9y^3z^4 -5x^4)

a) The rule that represents the height as a function of the number of bounces is described by H(n) = 1.5 · (71 / 100)ˣ⁻¹. (Correct choice: B)

b) The height at the top of the sixth path is equal to 0.27 meters. (Correct choice: B)

In this problem we need to derive the equation that represents maximum height as a function of the number of bounces:

H(n) = a · (r / 100)ˣ⁻¹

Where:

If we know that a = 1.5 m and r = 71, then the rule for the sequence is:

H(n) = 1.5 · (71 / 100)ˣ⁻¹

And the height at the top of the sixth path:

H(6) = 1.5 · (71 / 100)⁶⁻¹

H(6) = 0.27 m

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Answer:

C) 16

Step-by-step explanation:

(3x + 5) + 37 = 90

3x = 90 - 5 - 37

3x = 48

x = 48/3 = 16

Answer:

x = 16°

Step-by-step explanation:

It is 90° angle so their sum must be 90°( complement) .

3x + 5° + 37° = 90°

3x + 42° = 90° ... simplify the like term

3x = 90° - 42°

3x = 48°

3x/3 = 48°/3

x = 16°

So the answer is C, 16

The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

The required equation of the line representing line CD is y = x + 2. Option C is correct.

The equation of the line passing through two points is given by the equation,

y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)  - - - -- -(1)

Here,
Line CD passes through points (0, 2) and (4, 6)
Let (0, 2) and (4, 6) equal to (x₁, y₁) and (x₂, y₂) respectively.
Substitute this point in equation 1 to get the equation of the line representing CD,

So,
y - 2 = (6 - 2)/(4-0) (x - 0)
y = x + 2

Thus, the required equation of the line representing line CD is y = x + 2. Option C is correct.

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10 - c/2...

2 will be below 10-c

The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.

Herein we find that the temperature, in grades Fahrenheit, decreases linearly inasmuch as the altitude, in miles, increases. In accordance with the statement, we solve for T in the following inequality:

63 - 29 · x < 4.4

63 - 4.4 < 29 · x

58.6 < 29 · x

29 · x > 58.6

x > 2.021 mi

The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.

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Answer:

120

Step-by-step explanation:

The prism shown is a rectangular prism with a height of 3 in a length of 5 in and a width of 8 in

The volume of a rectangular prism can easily be calculated by multiplying the height by the length by the width

So V = 3 * 5 * 8

3 * 5 = 15

15 * 8 = 120

V = 120

Therefore your answer is 120