In ΔRST, r = 18 inches, s = 46 inches and ∠T=158°. Find ∠R, to the nearest degree.

Answer: 0.175325

Step-by-step explanation:

Answer:

1231.5 units^2

Step-by-step explanation:

The formula for volume of a cone is

V = 1/3πr^2, where

We see from the diagram that the height is 24 cm and the radius is 7 cm.  Now, we can plug these values in for h and r respectively in the volume formula:

V = 1/3π(7)^2(24)

V = 1/3π(49)(24)

V = 1/3π*1176

V = 392π

V = 1231.50432

V = 1231.5 cm^3

Step-by-step explanation:

To find how many of the same cards the farmer can form at most, we need to find the greatest common factor (GCF) of 78 and 90. One way to do this is to list the factors of each number and find the largest one they have in common:

78: 1, 2, 3, 6, 13, 26, 39, 78

90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The largest factor they have in common is 6, so the farmer can form at most 6 baskets of the same size.

To find how much the farmer gets from the sale of 10 baskets, we need to first find the total number of artichokes and courgettes he has:

78 + 90 = 168

Next, we can find the total amount of money he gets from selling the artichokes and courgettes:

Money from artichokes = 78 × $0.70 = $54.60

Money from courgettes = 90 × $0.40 = $36.00

Total money = $54.60 + $36.00 = $90.60

If the farmer sells 10 baskets, then each basket would have 168/10 = 16.8 artichokes and courgettes. Since he can only form baskets of the same size, he would sell 6 baskets with 16 artichokes and 24 courgettes in each basket. The total amount of money he would get from selling these 6 baskets is:

Money from artichokes = 6 × 16 × $0.70 = $67.20

Money from courgettes = 6 × 24 × $0.40 = $57.60

Total money = $67.20 + $57.60 = $124.80

Therefore, the farmer would get $124.80 from the sale of 10 baskets.

Answer:

an=a1rn−1 a n = a 1 r n - 1

Step-by-step explanation:

multiplying the previous term in the sequence by 2 gives the next term

I hope this helps...

Have a nice day<3

The slope of the line is 3.

Given are the coordinates of points on a line, we need to find the slope of the line,

Considering the points (2, 7) and (4, 13).

We know that the slope = y₂-y₁ / x₂-x₁

slope = 13-7 / 4-2 = 6/2

Slope = 3

Hence the slope of the line is 3.

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The volume of the cone in terms of π is 168π in³

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is one- third of a volume of a cylinder. Therefore;

The volume of a cone is expressed as;

V = 1/3 πr²h

where r is the radius and h is the height

r = 6 in

h = 14 in

V = 1/3 × π × 6² × 14

V = 504π/3

V = 168π in³

Therefore the volume of the cone in terms of π is 168π in³

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The area of the bumper sticker is 28.3 square inches.

To find the area of the bumper sticker, we need to use the formula for the area of a circle, which is A=πr^2, where π is a constant value of 3.14 and r is the radius of the circle. In this case, we can see that the diameter of the circle is 6 inches, so the radius would be half of that, which is 3 inches.
Substituting these values into the formula, we get:
A=3.14 x 3^2
A=3.14 x 9
A=28.26
Therefore, the area of the bumper sticker to the nearest tenth is 28.3. This means that the bumper sticker covers an area of approximately 28.3 square inches.
In conclusion, to find the area of the bumper sticker, we used the formula A=πr^2 and substituted the given values. The answer we obtained was 28.3 square inches.

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Based on the above, the area of the bumper sticker is 98.91 square inches.

To find the area of the bumper sticker, we need to use the formula for the area of a circle,

Where:

π = 3.14

r = the radius of the circle.

r = 1.5 ft ->  that is half the diameter of 3 ft.

h = 6

Area of the cylinder bumper  = 2π r h + 2π r²

Substituting these values into the formula, we get:

A =  2 x 3.14 x 1.5² x 6 + 2 x 3.14  x  1.5²

A= 2 x 3.14 x 2.25 x 6 + 2 x 3.14  x  2.25

A=98.91

Therefore, the area of the bumper sticker to the nearest tenth is 98.91

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Answer:

---------------------

First, find the common ratio:

Next, use the formula for the nth term of a geometric sequence:

Plugging in the values we have:

1. The x-intercepts are: x = -1/2 and x = 2

2. The vertex is at (3/4, 19).

3. To graph the function f(x) = -16x² + 24x + 16,

1. Solve for x:

-16x² + 24x + 16 = 0

Dividing both sides by -8, we get:

2x² - 3x - 2 = 0

Using the quadratic formula, we have:

x = [3 ± ✓ (3² - 4(2)(-2))]/(2(2))

x = [3 ±  ✓ (25)]/4

x = [3 ± 5]/4

The x-intercepts are: x = -1/2 and x = 2

2. The vertex of the graph of f(x) can be found by using the formula x = -b/(2a) and plugging it into the function to find the corresponding y-value.

In this case, we have:

x = -24/(2(-16)) = 3/4

f(3/4) = -16(3/4)² + 24(3/4) + 16 = 19

Therefore, the vertex is at (3/4, 19).

3 To graph the function f(x) = -16x² + 24x + 16, you can follow these steps:

Find the vertex of the parabola: The vertex is given by the formula x = -b/2a, where a = -16 and b = 24.

Find the y-intercept: The y-intercept is the value of f(x) when x = 0. Therefore, f(0) = -16(0)² + 24(0) + 16 = 16. The y-intercept is (0, 16).

Find the x-intercepts: The x-intercepts are the values of x for which f(x) = 0. To find them, solve the quadratic equation -16x² + 24x + 16 = 0.

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The area to the left of the z-score corresponds to the cumulative probability up to that point. The correct answer is b. z=0.84.

To find the z-score that separates the top 70% from the bottom 30%, we need to look up the corresponding percentile in a standard normal distribution table.

The area to the left of the z-score corresponds to the cumulative probability up to that point. For example, if we look up a z-score of 0.84 in the table, we find that the area to the left of that value is 0.7995, or 79.95%.

Since we want to find the value that separates the top 70% from the bottom 30%, we subtract 0.30 (or 30%) from 1.00 to get 0.70 (or 70%). We then find the z-score that corresponds to that area, which is approximately 0.84.

Therefore, the answer is b. z=0.84.

To find the Z-score value that separates the top 70% of a normal distribution from the bottom 30%, you need to look for the Z-score corresponding to the 70th percentile. In this case, the correct answer is:

b. z=0.52

Here's a step-by-step explanation:

1. Determine the percentile you're looking for, which is the 70th percentile (separating the top 70% from the bottom 30%).
2. Consult a Z-score table or use a calculator to find the Z-score corresponding to the 70th percentile.
3. The Z-score for the 70th percentile is approximately 0.52.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{1}) \\\\\\ y-5=2x-2\implies {\Large \begin{array}{llll} y=2x+3 \end{array}}[/tex]

Birth weights of full-term babies in a certain area are normally distributed with a mean of 7.13 pounds and a standard deviation of 1.29 pounds. a newborn weighing 5.5 pounds or less is a low-weight baby. There is a 10.3 % probability that a randomly selected newborn is low-weight. The correct answer is option B.

Given that the birth weights of full-term babies in a certain area are normally distributed with a mean of 7.13 pounds and a standard deviation of 1.29 pounds. A newborn weighing 5.5 pounds or less is a low-weight baby. We need to find the probability that a randomly selected newborn is low-weight.

Probability of newborn weighing 5.5 pounds or less = P(x ≤ 5.5)

We need to convert x to standard normal variable z.z = (x - μ) / σz = (5.5 - 7.13) / 1.29z = -1.26

Now, we need to find the area under the normal curve to the left of z = -1.26, using normal tables or calculators we get 0.1038A

Approximately, the probability that a randomly selected newborn is low-weight is 10.3%. Hence, option (B) is the correct answer.

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Answer:

$21,366.54

Step-by-step explanation:

Assuming that the interest is compounded annually, we can use the formula:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the initial principal (or amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $18,000, r = 0.045, n = 1 (compounded annually), and t = 4. Plugging in these values, we get:

A = 18000(1 + 0.045/1)^(1*4) = $21,366.54

Therefore, Amelia's loan will be $21,366.54 after her 4 years in college.

Answer:

the mean is 8 for x

8 = x + 2x / 2

16 = 3x

x = 16/3

x = 5.3

therefore the coordinate of x are ( 5.3,10.6)

for the y coordinate

-10= y +2y /2

-20 = 3y

y = -6.6

The coordinate of y are ( -6.6, - 13.3 )

The calculated volume of the solid is 335.10 cubic feet

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

Radius = 4 feet

Height = 10 fet

The angle is given as

Angle = 120 degrees

Using the above as a guide, we have the following:

Volume = (360 - Angle)/360 * πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = (360 - 120)/360 * π * 4² * 10

Evaluate

Volume = 335.10

Hence. the volume of the solid is 335.10 cubic feet

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A clockwise rotation about the origin preserves distance, a dilation of 3/5 Preserves angle measures, a reflection in the y-axis and dilation of 3  angle measures and a translation down 2 units and right 4 units Preserves distance and angle measures.

A clockwise rotation about the origin:

Preserves distance, but not angle measures.

A dilation of 3/5:

Preserves angle measures, but not distance.

A reflection in the y-axis and dilation of 3:

Preserves angle measures, but not distance.

A translation down 2 units and right 4 units:

Preserves distance and angle measures.

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The Volume of a cone is,

⇒ V = 50π units³

We have to given that;

In a cone,

Diameter = 10 feet

Height = 6 feet

Hence, Radius of cone,

r = 10/2 = 5 feet

Since, Volume of cone is,

V = 1/3 (πr²h)

V = 1/3 (π × 5² × 6)

V = 50π units³

Thus, The Volume of a cone is,

⇒ V = 50π units³

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Therefore, the probability that Sam gets more heads than Max is 0.5.

Let X be the number of heads Max gets and Y be the number of heads Sam gets. Both X and Y follow a binomial distribution with parameters k and 0.5.

We want to find P(Y>X), which can be expressed as:

P(Y>X) = P(Y-X>0)

Let Z = Y - X. Then Z follows a binomial distribution with parameters k and p = 0.5 - 0.5 = 0.

The mean of Z is E(Z) = E(Y-X) = E(Y) - E(X) = k/2 - k/2 = 0.

The variance of Z is Var(Z) = Var(Y-X) = Var(Y) + Var(X) = k/4 + k/4 = k/2.

Using the normal approximation to the binomial distribution, we can approximate Z as a normal distribution with mean 0 and variance k/2, for large enough values of k.

Therefore, P(Y>X) = P(Z>0) can be approximated using the standard normal distribution:

P(Z>0) = P((Z-0)/sqrt(k/2) > (0-0)/sqrt(k/2)) = P(Z/sqrt(k/2) > 0)

Using a standard normal table or calculator, we find that P(Z/sqrt(k/2) > 0) = 0.5.

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The sum of the given expression from n = 3 to 7 is 241.

The given expression is to be evaluated from n = 3 to 7.  The given expression is,begin{align*}\sum_{n=3}^{7} (n^2 + 2n)\end{align*}Now, we can substitute the values of n and add them up to evaluate the expression. So, the sum of the expression is, \begin{align*}\sum_{n=3}^{7} (n^2 + 2n) &= (3^2 + 2 \cdot 3) + (4^2 + 2 \cdot 4) + (5^2 + 2 \cdot 5) \\&\qquad+ (6^2 + 2 \cdot 6) + (7^2 + 2 \cdot 7)\\&= 9 + 20 + 35 + 72 + 105\\&= \boxed{241}.\end{align*}.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

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The value of the original price is, $1,029

We have to given that;

At a sale this week a desk is being sold for $247 this is a 24% discount from the original price.

Let us assume that, the original price is x

Hence, we can formulate;

24% of x = 247

Solve for x;

24/100 × x = 247

24x = 24700

x = 24700/24

x = 1,029

Thus, The value of the original price is, $1,029

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The directions of the parabola are:

Other solutions are below

The equation of a parabola is represented as

y = ax² + bx + c

If a > 0, then the parabola will open up

If a < 0, then the parabola will open down

Using the above as a guide, we have the following:

This is calculated as (h, k)

Where

h = -b/2a

So, we have

1. f(x) = x² + 6x +2

2. f(x) = 2 - 5x + 2x²

3. f(x) = -0.25x² + 8x - 2

4. f(x) = 4x² + 3x -5

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You have $2.30 and would like to buy some rice flour buy 9.2 ounces of rice flour with $2.30.

To arrive at this answer, we need to first convert the price per pound to price per ounce. There are 16 ounces in a pound, so the price per ounce is $4/16 = $0.25 per ounce.

Next, we divide the amount of money you have ($2.30) by the price per ounce ($0.25).

$2.30/$0.25 = 9.2 ounces.

Therefore, the conclusion is that you can buy 9.2 ounces of rice flour with $2.30.
Hi! I'm happy to help you with your question.


You can buy 9.2 ounces of rice flour.


1. First, we need to find out how many dollars you have per ounce of rice flour: $4 per pound / 16 ounces per pound = $0.25 per ounce.
2. Next, we'll determine how many ounces of rice flour you can buy with $2.30: $2.30 / $0.25 per ounce = 9.2 ounces.


With $2.30, you can buy 9.2 ounces of rice flour at the given price of $4 per pound.

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Answer:

A

Step-by-step explanation:

Range = Highest value - Lowest value

At Park Zoo:

R = 44 - 38

= 6

At Countryside Zoo;

R = 45 - 38

= 7

So, it cannot be D, because the ranges are not the same and it cannot be B because the range is greater at countryside zoo

The mode is the value that appears the moat frequently.

At Park zoo, the mode is 41 since it has the most dots.

At Countryside zoo, the mode is 40, since it has the most dots

So, it cannot be C because Park zoo has a greater Mode.

so, the only answer is A

The event that covers the entire sample space of the experiment is given as follows:

D. The number is even or less than 12.

In probability theory, a sample space is the set of all possible outcomes of a random experiment.

The outcomes for this problem are given as follows:

2, 3, 4 and 10.

Hence the statement covering the entire sample space is given by option D, as:

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There are 34,650 distinct ways to order the letters of "mississippi" subject to the requirement that no two S's are adjacent and no two P's are adjacent.

To find the number of ways to order the letters of the word "mississippi" while satisfying the given conditions, we can use the principle of inclusion-exclusion.

First, we consider all the ways to order the letters without any restrictions. There are 11 letters in "mississippi", so there are 11! ways to order them.

Next, we consider the cases where two S's are adjacent and the cases where two P's are adjacent. To count these cases, we can treat each pair of adjacent S's or P's as a single letter. So we have 10 letters to order in the case of adjacent S's, and 9 letters to order in the case of adjacent P's.

For the case of adjacent S's, we have 10! ways to order the letters. However, we have overcounted the cases where both pairs of S's are adjacent, so we need to subtract those out. There are 9 letters in this case (M, I, S1, S2, I, P, P, I), so there are 9! ways to order them. Therefore, the number of cases where two S's are adjacent is 10! - 9!.

Similarly, for the case of adjacent P's, we have 9! ways to order the letters. But we have overcounted the cases where both pairs of P's are adjacent, so we need to subtract those out. There are 8 letters in this case (M, I, S1, S2, I, P1, P2, I), so there are 8! ways to order them. Therefore, the number of cases where two P's are adjacent is 9! - 8!.

Now we need to add back in the cases where both pairs of S's and both pairs of P's are adjacent, because we subtracted them out twice. There are 8 letters in this case (M, I, S1, S2, P1, P2, I, I), so there are 8! ways to order them. Therefore, the number of cases where both pairs of S's and both pairs of P's are adjacent is 8!.

Finally, we subtract all these cases from the total number of ways to order the letters:

11! - (10! - 9!) - (9! - 8!) + 8! = 34,650

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The angle formed at the gas station is 130.3°. The correct option is (D).

Recall that, the area of a triangle is:

area = 1/2 * base * height

In this case, the base of the triangle is the distance between the two cars after 2 hours, and the height of the triangle is the distance from the gas station to the midpoint of the base.

Let's first find the distance traveled by each car in 2 hours:

distance traveled by car 1 = 45 mph * 2 hours = 90 miles

distance traveled by car 2 = 60 mph * 2 hours = 120 miles

The total distance between the two cars is the sum of their distances, which is:

total distance = 90 miles + 120 miles = 210 miles

The midpoint of the base is located at a distance of half the total distance from the gas station:

distance to midpoint = 1/2 * 210 miles = 105 miles

Now we can use the formula for the height of a triangle, which is:

height = 2 * area / base

Plugging in the values we have, we get:

height = 2 * 5190.713 mi²/ 210 miles = 123.824 mi

Finally, we can use the inverse tangent function to find the angle formed at the gas station, which is:

angle = tan⁻¹(height / distance to midpoint)

angle = tan⁻¹(123.824 mi / 105 miles)

angle = tan⁻¹(1.1793)

angle = 49.7°

However, this angle is the internal angle of the triangle formed by the two cars and the gas station. To find the angle formed at the gas station, we need to subtract this angle from 180°, which gives:

angle at gas station = 180° - 49.7° = 130.3°

Therefore, the answer is not one of the choices provided.

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Answer:

Step-by-step explanation:

If the perimiter is 2X+2Y=36

then area should be X x Y=???

I dont know what the sides are so that is all I can come up with.

The volume of the solid enclosed by the two paraboloids is approximately 1365.34π cubic units.

Here, we have to find the volume of the solid enclosed by the two paraboloids [tex]y = x^2 + z^2[/tex] and [tex]y = 32 - x^2 - z^2[/tex],

we need to set up a triple integral in cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cos(θ)

z = r sin(θ)

y = y

The limits of integration for r, θ, and y will depend on the region of integration.

First, let's find the intersection points of the two paraboloids:

[tex]x^2 + z^2 = 32 - x^2 - z^2\\2x^2 + 2z^2 = 32\\x^2 + z^2 = 16[/tex]

This represents a circular region with radius r = 4 in the x-z plane.

Now, let's find the limits of integration for r, θ, and y:

For r:

Since the circular region has a radius of 4, the limits of r will be from 0 to 4.

0 ≤ r ≤ 4

For θ:

The intersection points form a complete circle in the x-z plane, so the limits of θ will be from 0 to 2π.

0 ≤ θ ≤ 2π

For y:

The lower paraboloid is given by [tex]y = x^2 + z^2[/tex], and the upper paraboloid is given by [tex]y = 32 - x^2 - z^2[/tex].

The limits of y will be from the lower paraboloid to the upper paraboloid.

[tex]x^2 + z^2 \leq y \leq 32 - x^2 - z^2[/tex]

Now, we can set up the triple integral to find the volume V:

V = ∫∫∫ (y) dy dθ dr

V = ∫∫∫ [tex](r^2 cos^2(\theta) + r^2 sin^2(\theta)) dy d\theta dr[/tex]

V = ∫∫∫ [tex](r^2) dy d\theta dr[/tex]

V = ∫∫ [tex](r^2) y|_{(x^2+z^2)}^{(32-x^2-z^2)} d\theta dr[/tex]

V = ∫∫ [tex](r^2) (32 - 2x^2 - 2z^2) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^2(x^2 + z^2)) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^2r^2) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^4) d\theta dr[/tex]

Now, integrate with respect to θ from 0 to 2π:

V = ∫(0 to 2π) ∫(0 to 4) [tex](32r^2 - 2r^4)[/tex] dr dθ

Now, integrate with respect to r from 0 to 4:

V = ∫(0 to 2π) [tex][(32/3)r^3 - (1/3)r^5] |_0 ^4[/tex] dθ

V = ∫(0 to 2π) [tex][(32/3)(4^3) - (1/3)(4^5)][/tex] dθ

V = ∫(0 to 2π) [(32/3)(64) - (1/3)(1024)] dθ

V = ∫(0 to 2π) [682.67] dθ

V = 682.67 * (2π) - 682.67 * (0)

V = 1365.34π cubic units

Therefore, the volume of the solid enclosed by the two paraboloids is approximately 1365.34π cubic units.

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The missing side (the adjacent side) is approximately 13.257 units long.

To find the missing side, we can use the cosine function which relates the cosine of an angle to the adjacent side and the hypotenuse of a right triangle.

cos(28°) = adjacent side / hypotenuse

We are given the measure of the angle and the length of one side, so we can plug in those values and solve for the missing side.

cos(28°) = adjacent side / 15

adjacent side = 15 cos(28°)

Using a calculator to evaluate cos(28°) to four decimal places:

cos(28°) ≈ 0.8838

Substituting into the equation:

adjacent side ≈ 15 × 0.8838

adjacent side ≈ 13.257

Therefore, the missing side (the adjacent side) is approximately 13.257 units long.

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