A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches.

There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)

There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by

The number of ways =  [tex]_{n+r-1}C_r[/tex]

Where the combination [tex]_{n}C_r[/tex] is calculated as

[tex]_{n}C_r=\frac{n!}{r!(n-r)!}[/tex]

It is given that there are 4 varieties of donuts in a shop. I.e., n = 4

Number of donuts to be selected r = 12 (one dozen)

And also given that at least one donut of every variety has to be selected.

Since there are 4 varieties, at least one from each of these means the count is 4.

So, the remaining number of donuts to be selected is 12 - 4 = 8.

So, r becomes 8 i.e., r = 8

On substituting,

the number of ways of selecting the remaining 8 donuts = [tex]_{4+8-1}C_4[/tex]

⇒ [tex]_{11}C_4[/tex]

⇒ [tex]\frac{11!}{4!(11-4)!}[/tex]

⇒ [tex]\frac{11!}{(4!)(7!)}[/tex]

⇒ 330

Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.

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The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.

Lateral surface area of cone = πrl

Lateral surface area of cylinder = 2πrh

Lateral surface area of cone A = πrl = πrh

Lateral surface area of cylinder B = 2πrh

This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.

The answer is: A. True.

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The matched answers are:

1. semicircle

2. central angle

3. Radius

4. Secant

5. center

6. tangent

7. diameter

8. minor arc

9. chord

10. major arc

A circle is the locus of points equidistant from a given point called the center of the circle.

A circle can be described if its radius and the center of the circle is known.

Analysis:

1. RCH  is called a semicircle when a diameter divides a circle into two equal parts, a part is called the semicircle.

2. ∠RAH is the central angle, because it is the angle subtended at the Center of the circle.

3. CA is the radius of the circle, a line drawn from the center to any point on the circumference of the circle.

4. MR is a secant, a line that cuts the circle into two parts.

5. A is the center of the circle.

6. MT is the tangent, because line MT touches the circle at a point T.

7. CH is the diameter of the circle, a line that divides the circle into two semi circles.

8. CT is the minor arc, the curved line that is found in the smaller part of the divided circle.

9. HT is chord, it is a line that divides the circle into two unequal parts.

10. CRH is  major arc, the curved line of the bigger portion of the divided circle.

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4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce. This can be obtained by multiplying the values.

Given that,

Density of pure beeswax = 0.555 ounce per cubic inch

Cost of beeswax per ounce = $8.00 per ounce

Selling price in dollars per cubic inch will be,

⇒0.555×$8.00 = $4.44

Hence 4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce.

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Answer:

  (c)  0.18

Step-by-step explanation:

If the x-values are exhaustive, then the p(X=x) values must total 1.00.

  0.11 +? +0.62 +0.09 = 1.00

  0.82 +? = 1.00 . . . . . . . simplify

  ? = 0.18 . . . . . . . . . subtract 0.82

P(X=3) = 0.18

Answer:

1 - 3090

2 - 12

3 - 2.16

Step-by-step explanation:

hope you find this helpful...

In quadrant II, [tex]\cos(A)[/tex] will be negative. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = -\sqrt{1 - \sin^2(A)} = -\dfrac{\sqrt{15}}4 \approx \boxed{-0.9682}[/tex]

The requried, rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.

To find cos(A) in quadrant II, we can use the given information and the trigonometric identity  [tex]sin^2(A) + cos^2(A) = 1[/tex].

Given [tex]sin(A) = 1/4[/tex], we can find  [tex]cos(A)[/tex]  as follows:

[tex]sin^2(A) + cos^2(A) = 1[/tex]

[tex](1/4)^2 + cos^2(A) = 1[/tex]

[tex]1/16 + cos^2(A) = 1[/tex]

Now, let's solve for [tex]cos^2(A)[/tex]:

[tex]cos^2(A) = 1 - 1/16[/tex]

[tex]cos^2(A) = 16/16 - 1/16[/tex]

[tex]cos^2(A) = 15/16[/tex]

Next, find the value of [tex]cos(A)[/tex] by taking the square root:

[tex]cos(A) = \pm \sqrt{(15/16)[/tex]

Since we are in quadrant II, where cosine is negative, we take the negative value:

[tex]cos(A) \approx -\sqrt{(15/16)[/tex]

Now, calculate the approximate value of cos(A):

[tex]cos(A) \approx -0.9682[/tex]

Rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

[tex]254 \frac{12}{17}[/tex] or approximately 254.71

Step-by-step explanation:

First, you need to find out how many gallons it will take to travel 866 miles. Because the car's avg miles/gallon is 13.6, you divide 866 by 13.6. However, this gets you an irrational number. To avoid this, make 13.6 into a fraction. Now divide 866 by [tex]13 \frac{3}{5}[/tex]. This becomes 866 ÷ [tex]\frac{68}{5}[/tex]. Convert this into a multiplication problem by converting [tex]\frac{68}{5}[/tex] into its reciprocal. This gets you 866 × [tex]\frac{5}{68}[/tex]. This gets you [tex]\frac{2165}{34}[/tex]. Now that you have the amount of gallons it will take to get to your destination, multiply it by 4. [tex]\frac{2165}{34}[/tex] × [tex]4[/tex][tex]= \frac{4330}{17}[/tex]. This becomes [tex]254 \frac{12}{17}[/tex] or approximately 254.71.

Answer:

B. (3x - 9) (x + 3i)

Step-by-step explanation:

[tex]\bf 3 {x}^{2} = + 27[/tex]

Therefore, B is your answer!!!!

The sequence of the ball is   3, 1, 1/3, 1/9,...

The ball starts bouncing with a height of 3 feet.

Each bounce reaches a third of the height of the previous bounce.

Therefore,

a = first term = 3

r = common ratio = 1 / 3

Therefore,

nth term = arⁿ⁻¹

where

First term = 3

2nd term = 3 × (1 / 3) = 1

Third term = 3 × (1 / 3)² = 1 / 3

Fourth term = 3 × (1 / 3)³ = 1 / 9

Therefore, the sequence of the ball is   3, 1, 1/3, 1/9,...

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Answer:

Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Step-by-step explanation:

Another example of  multiplying a Pythagorean triple is

Take the known Pythagorean triple 5, 12 and 13:

5 12 13   * 2  = 10 24 26

and 26^2 = 10^2 + 24^2

     676 = 100 + 576 = 676

The fill up are:

5. ∠B ≅ ∠B

6. AA Similarity Postulate          

7.   a/c = c/a

8. a² = cx

9. ∠CDA ≅ ∠BCA

10. ∠A ≅ ∠A

11. ΔCBA ~ ΔDBA  

The above answers shows that:

5. Reflexive Property

6. AA Similarity Postulate

7. Polygon Similarity Postulate

8. Cross Multiply and Simplify

9. All right angles are Congruent

10. Reflexive Property

11. AA similarity Postulate

To prove the above:

Note that the full proof of the Pythagorean theorem is that:

We are given: Δ ABC as a right triangle, with a right angle at ∠C.

Then the  Prove: A²+B² =C²

Therefore, If you follow the theories above, you will see that the answers given are correct.

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The probability that at least 9 customers ordered an item from the value menu is 0.927​.

In an experiment with two possible outcomes, the likelihood of precisely x successes on n repeated trials is known as the binomial probability (generally refereed as binomial experiment).

As per the given problem-

This likelihood is a binomial one, so take note. In this instance, a success is defined as a consumer placing an order from the value menu, hence we are looking for such probability between 9 to 14 success, inclusive.

The probability is indeed the complements of the likelihood of any success, ranging from 0 to 8. The procedures below can be used to figure out the probability from such a binomial distribution utilizing Excel.-

Subtract the preceding probability from 1 to get the likelihood of 9 to 14 people ordering out from value menu.

The likelihood is 1 x 0.073 = 0.927.

Therefore, the probability that at least 9 customers ordered an item from the value menu is 0.927.

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The solution to the system of equations is (-1, 3) and (3, -1)

The system of equation is given as:

y = -x^2 + x + 5

y = -x + 2

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-1, 3) and (3, -1)

Hence, the solution to the system of equations is (-1, 3) and (3, -1)

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Answer:

graph 1,

3,-1 and -1,3

Step-by-step explanation:

See screenshot

Answer:

2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle

Step-by-step explanation:

Large floods in 2007 and 2010 changed the flood recurrence curve.

What caused the Red River flood 1997?

A extremely unusual thawing of winter snow and river ice after a winter season that saw far above-normal precipitation across the Northern Plains was the main contributor to the flooding in 1997.

Why is the Red River called the Red River?

After it was explored in 1732–33 by the French voyageur Pierre Gaultier de Varennes et de La Vérendrye, the river, called Red because of the reddish brown silt it carries, served as a transportation link between Lake Winnipeg and the Mississippi River system.

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Answer:

2.8kg

Step-by-step explanation:

There are 7 parts of meat for every 3 parts so there are 7+3=10 parts in total.

4/10=1 "part"

there are 7 parts of meat so (4/10)*7=28/10=2.8kg of meat.

Answer:

-9/2

In alternate forms -4•5,-4 1/2

The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

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The length and width of the rectangle are 18 in and 1 in, respectively.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : b*h, where b = base and h =height.

For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=b*h

18=(W+17)*W

18=W²+17W

W²+17W-18=0

Solving this quadratic equation, you have:

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]

[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

w1=1 and w2= -18

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², see.

18=l*w

18=l*1

l=18 in

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These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

According to the statement

A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.

And we have to find the probability of tossing a head and drawing a red marble. and probability of drawing two blue marbles if the first marble is not replaced.

here we solve this problem by Probability

So, Probability of drawing red marble = Number of red marble / total number of marbles.

Probability = 2/6

Probability = 1/3.

Then

Probability of drawing blue marbles = number of blue marbles /total marbles

Probability = 3/6

Probability = 1/2.

1st blue marble Probability =1/2

2nd blue marble Probability = 1-(1/2) = 1/2.

These are non dependent events because they do no affect the probability of each others.

So, These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

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Answer: base = 12, altitude = 16

Step-by-step explanation:

The total bill paid for a person who uses 600 kWh in a month is $60.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the utility company charges $0.10 per kWh, hence:

Total charge in a month = 0.10 * 600 = $60

The total bill paid for a person who uses 600 kWh in a month is $60.

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The answers are:

Given that:

The perimeter of vegetable plot:

= 4m + 3.5m + 4m + 2m + (3.5 + 2m)

= 19m

Area of vegetable plot:

(1.3 x 5.5) + ( (4 - 1.3) x 3.5)

rounding up to one decimal place = 67.6m²

To know the numbers of meter fence that one can buy, the equation will be:

(perimeter of vegetable plot + the left plot)  - gates.

(19m + (6.5 + 4 + (6.5 - 2) ) )m  - (2.5ft x 2)

= 19m + 15m - 1.5424m

=32.476

=32.5m

Therefore, the answers are:

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Type of sequence: arithmetic progression

Explicit formula: 5n

Recursive formula: [tex]5_{n-1}[/tex] + 5

A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.

Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....

The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.

Therefore, the type of sequence is arithmetic progression

The difference d = 5 and the first term is also 5

An explicit formula will be

a + (n - 1)d

substitute a and d into the formula

5 + (n - 1)5

5 + 5n - 5

5n

Therefore, 5n gives the value of a specific term based on the position

A recursive formula will be

[tex]a_{n-1}[/tex] + d

substitute a and d into the formula

[tex]5_{n-1}[/tex] + 5

Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term

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Answer:

A. (-1, 3) (3, 2) (-2, 1)

B. [tex]\sqrt{17}[/tex]   [tex]\sqrt{5}[/tex]  [tex]\sqrt{26}[/tex]  

Step-by-step explanation:

The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].

MIDPOINTS

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)

Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].

DISTANCE

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]  

a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.

(4-6)/2=-1  (4+2)/2=3

Repeat for other sides.

(2-6)/2=-2 (2+0)/2=1

(2+4)/2=3  (4+0)/2=2

Coordinates of midpoints are (-1,3), (-2,1), (3,2)

b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.

sqrt((-1+2)^2 + (3-1)^2)

Sqrt(5)

Repeat.

Sqrt(17)

Sqrt(26)

The lengths of the inner triangle are as follows:

(-1,3), (-2,1) = Sqrt(5)

(-1,3), (3,2) = Sqrt(17)

(-2,1), (3,2) = Sqrt(26)

Answer:

18a-8b

Step-by-step explanation:

i think this right but i think u messed up putting an equal sign instead of a subtraction.

Answer: [tex]y=-\frac{5}{3}x-1[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.

Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]

The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.

A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.

Slope: A line's slope provides information on the steepness and direction of the line.

By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.

Relation between slope of two perpendicular lines are-

Calculation for the equation of the line.

Consider the given equation;

y=3/5x-3 (compare this with the standard equation)

The slope 'm' is 3/5

Use the relation of slopes of two perpendicular line.

The slope of orthogonal line will be -1/m

Slope = -5/3

Put the slope in the slope point equation of line.

(y - y1) = m(x - x1)

where (x1,y1) = (0,-1)

Substitute the coordinates in the equation

y - (-1) = (-5/3)×(x - 0)

y + 1 = -5x/3

Further simplifying the equation,

5x + 3y +3 = 0

Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.

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Answer:   [tex]\log_2(20)[/tex]

Work Shown:

[tex]\log_2(4) + \log_2(5)\\\\\log_2(4*5)\\\\\log_2(20)\\\\[/tex]

The rule used is [tex]\log_{b}(\text{x}) + \log_{b}(\text{y}) = \log_{b}(\text{xy})[/tex]

[tex]\large{\textbf{Heya !}}[/tex]

✏[tex]\large\sf{\bigstar Given:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar To\quad Find:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar Solution\quad steps:-}[/tex]

`To find what we want we need to apply ㏒ rules

[tex]\large{\sf{\longmapsto{log_ba+log_bc=log_b(ac)}[/tex]

using formula,

[tex]\large{\sf{\longmapsto{log_24+log_25=log_2(4\cdot5)}[/tex]

simplifying,

[tex]\large{\sf{\longmapsto{log_220}[/tex]

`hope it was helpful ! ~