The amount of snowfall in December was 5 7/8 feet. The amount of snowball in October was 1/4 feet. How much more snowfall was there in December? Write your answer as a mixed number in simplest form.

The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.

SSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.

By sine rule,

Y = sin156.78 × 44 / 34

= 29

sin Y = 0.499

Y = 29.93°

By the angle sum property. The last angle will be:

180 - 156.78 - 29.93

= 6.67°

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Step-by-step explanation:

This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.

When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:

y = -(x - 5) - (x + 5) = -2x

When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:

y = (x - 5) + (x + 5) = 2x

So the function y = |x - 5| + |x + 5| can be written as:

y =

-2x if -5 < x < 0

2x if 0 ≤ x < 5

Notice that the function is not defined for x ≤ -5 or x ≥ 5.

A​ T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.

The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.

To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.

The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.

t = -b/2a = -78/(2*(-16)) = 2.4375

Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.

To find the maximum height, we substitute this value of t into the equation for h:

h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet

Therefore, the maximum height of the T-shirt is approximately 97.19 feet.

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a)Traveled 0.3 miles in 1 hour.

b) The fraction representation is 3/10 miles per hour.

a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.

Distance traveled = 1/5 miles

Time taken = 3/2 hours

To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:

3/2 = 15/10

Now we can divide the distance by the time:

1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15

This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).

To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):

2/15 x 10/3 = 2/9

Therefore, the person traveled 2/9 miles per hour.

b) To write this as a model fraction representation, we can express it as a single fraction:

2/9 = 3/10 (rounded to the nearest tenth)

So the person traveled at a rate of 3/10 miles per hour.

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The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.

The body weight of the first individual = 200 pounds

The volume of blood = 6 quarts.

Therefore a person of 90 pounds = X quarts.

That is;

200 pounds = 6 quarts

90 pounds = X quarts

make X quarts the subject of formula;

X = 90×6/200

= 540/200

= 2.7 quarts

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The surface area of this cylinder is 942 millimeter square

The formula for the surface area of a cylinder is expressed as;

SA = 2πr h + 2πr²

Given that the parameters are identified as;

From the information given, we have that;

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 10²

Find the square values

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 100

Multiply the values

Surface area = 314 + 628

Now, add the values

Surface area = 942 mm²

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Okay, here are the steps to solve this:

* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.

* We are making 12 cups of granola.

* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.

* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.

Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.

Measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and arc length ADB  is 10.67π m

Given that the circle has a center O.

The radius of the circle is 8 m.

The measure of ∠AOB is 120°

We need to determine the area of the shaded region and the length of the arc ADB.

The measure of ∠ADB is given by

∠ADB = 360 - ∠AOB

= 360 - 120

=240 degrees

The area of the shaded region can be determined using the formula,

A = (θ/360) πr²

A = (θ/360) ×3.14× 8²

A = 42.67 m²

Thus, the area of the shaded region is 42.67π m²

The length of arc ADB can be determined using the formula,

Arc length =  (θ/360) 2πr

=10.67π m

Hence,  measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and  length of arc ADB  is 10.67π m

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Okay, let's evaluate each modeling equation candidate based on the r^2 value:

a. y=16.5839•1.0185^x

No r^2 value given, so cannot determine if this is the best fit.

b. y=0.985515x-2.81333

No r^2 value given for this linear model, so cannot determine if it is the best fit.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value, it would be the best fit.

Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.

Does this help explain the approach? Let me know if you have any other questions!

Given

ABCΔ  is a triangle.

D is a point on [BC]

|BD|=4

|AD|=|CD|

m(CBAˆ)=α=30∘

m(ACBˆ)=β=20∘

To Find

What is |AC|=x?

Solution

Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b

and applying law of cosines to all three triangles yields;

respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4

The complete question is -

In the given diagram find the value of x

a) 1

b) 2

c) 3

d) 4

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23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]

24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex]  and finally the side length opposite the [tex]60^\circ[/tex]  is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.

So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]

25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20

For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.

Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.

26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.

Answer: ∠EGF and/or ∠CGB

Step-by-step explanation:

Starting Angle: ∠CGE

Possible Supplements: ∠EGF and ∠CGB

The values of x are the two expressions equal to All real numbers except 2.

We are given that rational expression has been simplified below.

(x+4)(x-2)x+4

9(x-2)

WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.

The expression should be;

(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.

After simplification by (x - 2) , the remainder will be;

(x + 4)/9.

When x = -4,  both sides equal to zero.

When x = 0 , both sides equal to 4/9

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Answer: Area=3.125 square feet

Step-by-step explanation:

2.5x2.5=6.25

6.25/2= 3.125

Answer:

A = 50 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

given that 1 inch equals 4 feet , then

b = 2.5 in = 2.5 × 4 feet = 10 feet

h = 2.5 in = 2.5 × 4 feet = 10 feet

then

A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²

The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.

In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.

(a) The hypotheses that the businesswoman should test are:

H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.

Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.

(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.

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As a result, the item's final price is $53.50 and the sales tax is $3.50.

The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax

We can multiply the item's price by the applicable sales tax rate to determine the sales tax:

Price of Item  x   Sales Tax Rate equals Sales Tax

Sales Tax: $50.00 x 7% = $3.50

We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:

Price of Item + Sales Tax = Total Cost

$50.00 plus $3.50 equals $53.50 as a total

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Answer:

The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.

Step-by-step explanation:

We number of bags is 10 bags of fertilizer to complete the job.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.

In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.

The total area of the football field is:

360 feet × 160 feet = 57,600 square feet

To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:

57,600 square feet ÷ 1000 square feet/area = 57.6 areas

So there are 57.6 areas on the football field.

We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:

8 pounds/1000 square feet × 57.6 areas = 460.8 pounds

Therefore, we need 460.8 pounds of fertilizer to cover the football field.

Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:

460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags

We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.

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The complete question is:

You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?

Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]

[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]

[tex]f_o=460(1.247)[/tex]

[tex]f_o= 573.6 \ \text{Hz}[/tex]

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz

Answer:

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is

370.9 Hertz

The function is given as:

[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x  [tex]f_{s}[/tex]

From the question

[tex]c=332[/tex] --- speed of the sound

[tex]V_{o} =32[/tex] ---current speed of the train

[tex]V_{s} = 40[/tex] --- speed of the opposite train

[tex]f_{s} =460[/tex] --- frequency of the sound wave

This gives:

[tex]f_{o}= \frac{332-32}{332+40}[/tex]  ×[tex]460[/tex]

[tex]f_{o}= \frac{300}{372} x460[/tex]

Rewrite as:

[tex]f_{o}= \frac{300x460}{372}[/tex]

[tex]f_{o}= 370.9[/tex]

Answer:

The correct equation is C. d = 163t.

This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).

Step-by-step explanation:

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Step-by-step explanation:

We have the triple integral:

∫∫∫E x^2 + y^2 + z^2 dV

where E is the ball x^2 + y^2 + z^2 ≤ 81.

In spherical coordinates, the volume element is given by:

dV = ρ^2 sin φ dρ dθ dφ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).

Substituting into the integral, we get:

∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ

= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π

= (2π/5)(9^5)(-(-1 - 1))

= (4π/5)(9^5)

≈ 114413.73

Therefore, the value of the triple integral is approximately 114413.73.

Answer:

D. Quadratic

Step-by-step explanation:

The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative

The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces

A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.

Part of the question obtained from a similar question posted online can be presented as follows;

The amount of fudge the student has = 3 pounds

The amount of fudge the student eats = 1 pound of the fudge

Required; The amount of fudge the student has left

The amount of fudge the student has left = 3 - 1 = 2 pounds

The fraction of the remaining fudge the student gives to her sister = (1/2)

Therefore;

The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound

1 pound = 16 ounces

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the greatest common factor of 72 and 96 is 24

Answer:

Step-by-step explanation:

Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).

The slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).

The line goes through the origin (0, 0), so the slope is the ratio of y to x.

  m = y/x = 4/1 = 4

This is the constant of proportionality.

The constant of proportionality is 4, choice A.

The equation of a proportional relationship is ...

  y = kx . . . . . . where k is the constant of proportionality

Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...

  m = 4c . . . . . choice D

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Answer:

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When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.

Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.

How to determine this

When 60 seconds makes 1 minute

60 minutes makes 1 hour

14,277 seconds to minutes

When 60 seconds = 1 minute

14,277 seconds = x

x = 14,277/60 minutes

x = 237 minutes 7 seconds

By converting 237 minutes to hour

When 60 minutes = 1 hour

237 minutes = x

x = 237/60 hours

x = 3 hours 57 minutes.

Therefore, the conversion is 3 hours 57 minutes 7 seconds

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