One of the cases for the known measures of an oblique triangle is given. State whether the Law of Cosines can be used to solve the triangle.

The probability that the total weight of the three randomly selected grapefruits is more than 3.4 pound will be equal to 0.842.  

Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.

From the data given in the question,

x > 3.4 lb

The mean is 1 lb.

The difference from the mean is 0.12 lb.

The z-score will be,

z = (3.4 - 1) / 0.12

z = 20

This is equivalent to an 84.20% or 0.842 probability.

the complete question is,

The weights of grapefruits of a certain variety are approximately normally distributed with a mean of 1 pound and a standard deviation of 0.12 pounds. Use scenario 6-9. what is the probability that the total weight of three randomly selected grapefruits is more than 3.4 pounds?

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The expected value of a random variable is the sum of the probabilities of all possible outcomes which is 10.083

In this case, since the random variable is the sum of the three independent rolls of a fair die, the expected value, E[X], is the sum of all the possible outcomes of three die rolls, each multiplied by the probability of 1/6 that each outcome will occur:

E[X] = (1 + 2 + 3 + 4 + 5 + 6) × (1/6)³

= 3.5

The variance of a random variable is the expected value of the squared deviation from the mean. In this case, the variance for X is:

Var(X) = E[X^2] - (E[X])^2

= (1² + 2² + 3² + 4²+ 5² + 6²) × (1/6)³ - (3.5)²

= 10.0833

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The perimeter of the equilateral triangle which has sides of length (3x+7) is 9x+21.

A triangle's three sides and angles must be equal for it to be considered an equilateral triangle.

An equilateral triangle is also referred to as an equiangular triangle because it has angles that are each 60 degrees in length. Because its sides and angles are equal, the equilateral triangle is regarded as a regular polygon or triangle.

Depending on how many sides a triangle has, there are three different types. These triangles are equilateral, isosceles, and scalene.

In an equilateral triangles all sides are equal

so,

perimeter = 3x+7 + 3x+7 + 3x+7

perimeter = 9x+21

Thus, perimeter of the equilateral trinagle which has sides of lenght (3x+7) is 9x+21.

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The cost in dollars and cents per boxed lunch will be $9.40.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since the proportional relationship between the number of boxed lunches ordered, b, and the total cost in dollars and cents, c, can be represented by the equation c=9.4b

The cost will be:

= 9.4 × 1

= 9.40

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Answer:

5/3

Step-by-step explanation:

1 week = 7 days

5 weeks = 5 × 7 days = 35 days

5 weeks to 21 days =

= 35 days to 21 days

= 35/21

= 5/3

11.9% of students have height less than 136.4cm. The solution has been obtained using probability.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value.

Let the height be 'd' cm.

We are given mean as 160 cm and standard deviation of 20 cm.

Probability(x>d) = 0.12

Probability(x<d) = 0.881

Probability(z ≤ d-160/20) = 0.881

⇒d-160/20 = 1.1800  (using table)

⇒d-160 = 23.6

⇒d = 183.6

Therefore, d-mean = -23.6

⇒d-160 = -23.6

⇒d = 160-23.6

⇒d = 136.4cm

Hence, 11.9% of students have height less than 136.4cm.

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Therefore , the solution of the given problem of equation comes out to be x value is 8.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given:

equation : -3(x-9) = x-5

To find the value of x ,

=> -3(x-9) = x-5

=> -3x +27 = x -5

=> 4x = 27 +5

=> 4x = 32

=> x =32/4

=> x= 8

Therefore , the solution of the given problem of equation comes out to be x value is 8.

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The square root of 50 is the distance between the points i.e. 5√2.

It is possible to measure a distance between two points or objects quantitatively or sporadically qualitatively. The word "distance" can be used to describe a physical length or an estimate based on other factors in physics or everyday speech.

To do this we know that a² +b²  = x²

for b:

The distance between -1 and -4 is 5. we will use 5²

for a:

The distance between2 and 1 is also 5. we we use 5²

put into the formula

5² +5² = c²

25+25 = c²

50 = c²

so the square root of 50 is the distance between the points i.e. 5√2.

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The volume and surface area of the cube is 343 yd³ and 294 yd² respectively

An equation is an expression showing the relationship between numbers and variables.

a) The volume of the cube is the amount of space that it occupies. It is given that:

Volume = length³

But length = 7 yd, hence:

Volume = 7³ = 343 yd³

b) The surface area of the cube is the sum of the individual surface area. It is given that:

Surface area = 6 * length²

But length = 7 yd, hence:

surface area = 6 * 7² = 294 yd²

The surface area is 294 yd²

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Additional information is needed to prove that the triangles are congruent by SAS.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

You know the following information about triangle ABC and triangle DEF:

AB = DE

∠A = ∠D

Since The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Thus to prove that triangles are congruent by the property of SAS.

Two sides of triangles should be equal.

Therefore,

Additional information is needed to prove that the triangles are congruent by SAS.

Either BC = EF

or AC = DF

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In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

1976: Republican: 43 states, District of Columbia; Democrat: 6 states

2012: Republican: 24 states, District of Columbia; Democrat: 26 states

In 1976, 43/49 (including the District of Columbia) states voted Republican, which is 87.76%. This is a relative frequency.

1. Calculating the total number of states and District of Columbia in 1976: 43 + 6 + 1 = 50.

2. Calculating the percentage of states voting Republican in 1976: 43/50 (including the District of Columbia) = 0.87 or 87.76%.

3. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency.

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The solid S is a triangular prism whose base is a triangle with vertices (0, 0), (1,0), and (0, 1). The cross-sections perpendicular to the x-axis are equilateral triangles of the same height.

The solid S is a three-dimensional shape with a triangular base. The base is a triangle with vertices (0, 0), (1,0), and (0, 1). This triangle has sides of length 1, and the angles at each vertex are equal. The equilateral triangles are the cross-sections of the solid perpendicular to the x-axis. This means that each side of each triangle is the same length, and all the angles are equal. Each cross-section has the same height, determined by the height of the solid. The shape of the solid is a triangular prism, with triangular sides that connect the three vertices. This shape has a three-dimensional volume, and the volume can be calculated by multiplying the area of the base by the height of the solid.

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The results from Ralph's survey are not statistically different from the national results.

Population Parameter: The percentage of teens who seldom or never argue with their parents in Ralph's large high school.

Null Hypothesis (H0): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is equal to the nationwide percentage of 28%.

Alternative Hypothesis (H1): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is not equal to the nationwide percentage of 28%.

H0: p = 0.28

H1: p ≠ 0.28

To calculate whether or not the results from Ralph's survey are significantly different from the national result, a one-sample z-test can be used. The z-score is calculated using the following formula: z = (x-µ)/(σ/√n). In this example, x is the sample proportion of teens who seldom or never argue with their parents (Ralph's survey), µ is the population proportion (the nationwide poll results of 28%), σ is the population standard deviation, and n is the sample size (175).

If the z-score is outside of the critical region, then it can be said that the results from Ralph's survey are statistically different from the national results. If the z-score is within the critical region, then it can be said that the results from Ralph's survey are not statistically different from the national results.

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Answer:

The lowest interest rate you would need to earn in order to have 15,000 become 20,000 in 5 years is 6.5%. This is based on the compound interest formula, where you would need to multiply the original amount by the interest rate (15,000 x 0.065 = 975) and add that amount to the original amount to equal your desired total (15,000 + 975 = 20,000).

Answer:

[tex]\mathrm{Flagpole\;Height = 17 \;feet}[/tex]

Step-by-step explanation:

Here we have two similar right triangles

One right triangle has base of 8 ft and Jeremy's height of 68" as the height

The other right triangle has the base (8 + 16 = 24) and the height is the height of the flagpole. This is the large triangle

Since the triangles are similar,

The ratios of the sides must be the same

[tex]\mathrm{\dfrac{Jeremy's \;Height}{Flagpole \; Height}} = \dfrac{8}{24}= \dfrac{1}{3}\\\\\\68" = \dfrac{68}{12} \; feet\\\\\textrm{Dividing both numerator and denominator by 4:}\\\\= \dfrac{17}{3}[/tex]

Therefore

[tex]\mathrm{\dfrac{17/3}{Flagpole\;height} = \dfrac{1}{3}}\\\\[/tex]

Cross -multiplying we get
[tex]\mathrm{\dfrac{17}{3} \times 3 = Flagpole\; Height}\\\\\mathrm{Flagpole\;Height = 17 \;feet}[/tex]

The area of a rectangle is found by multiplying the length by the width. So the area of the original rectangle is (6 m) x (9 m) = 54 m^2.

If we want to find different side lengths that have the same area, we can keep the area constant and manipulate the length and width.

One way to do this is to multiply the original length by a certain factor and multiply the original width by the reciprocal of that factor.

For example, if we multiply the length by 2 and the width by 1/2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x (1/2) = 4.5 m. The new rectangle's dimensions would be 12 m x 4.5 m.

Another way to find different side lengths that have the same area is to multiply the original length and width by the same factor.

For example, if we multiply both the length and width by 2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x 2 = 18 m. The new rectangle's dimensions would be 12 m x 18 m.

So, to draw the rectangle with different side lengths that have the same area, you can use any of the above method, and label the side lengths accordingly.

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a. The point slope form of the equation is y-4=-3(x+5)/10.

b. The y-intercept of the line is 2.5.

c. The line crosses the y-axis halfway between the given points so the y-intercept is halfway between the y-coordinate of the point on the left, and that of the point on the right. The number halfway between those values is 2.5.

d. The slope intercept form is y = (-3/10)x + (5/2).

The solution has been obtained using linear equations.

What is linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.

a. We know that general form of point- slope form of equation is

y-y₁=m(x-x₁)

Here, y₁= 4 and x₁= -5, y₂= 1 and x₂=5

Now, m = (y₂ - y₁) / (x₂ - x₁)

⇒m= (1-4)/(5-(-5))

⇒m= -3/10

Thus, we get the equation as y-4=-3(x+5)/10

b. At the y-intercept, the x coordinate is 0.

So, putting x coordinate as 0 in the equation, we get

⇒y-4=-3(0+5)/10

⇒y-4=-15/10

⇒y=-1.5 + 4

⇒y= 2.5

Thus, the y-intercept of the line is 2.5.

c. The line crosses the y-axis halfway between the given points so the y-intercept is halfway between the y-coordinate of the point on the left, and that of the point on the right. The number halfway between those values is 2.5.

d. The general equation for slope intercept form is y=mx+b

m= -3/10

b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

⇒ b = 4 - (-5)(1 - 4)/(5 - (-5))

⇒ b = 4 - 15/10

⇒ b = 25/10

⇒ b = 5/2

So, we get y = (-3/10)x + (5/2).

Hence, the required solutions have been obtained.

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The golfer's average performance over the two-year period was [mean] out of 10,with a standard deviation of [standard deviation].

The mean is a measure of central tendency, which refers to a single value that is representative of a series of values. In this case, the mean is the average performance the golfer achieved over the two-year period. To calculate the mean, add up all the performance scores and divide by the total number of scores. The mean can then be rounded to the nearest whole number. The standard deviation is a measure of variability, which indicates how much the scores vary from the mean. To calculate the standard deviation, subtract each performance score from the mean, square the differences, and then add them up. Finally, divide the sum by the number of scores, and then take the square root. The standard deviation can then be reported to the nearest decimal.

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Answer:

Step-by-step explanation:

The slope-intercept form is y=mx+b, where m is the slope and b is the y intercept.  y=mx+b

y=4x3−3

Reorder terms.

y=4 3x−3

Find the values of m and b using the form y= mx+b. 4 3b=−3

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

4

3

y-intercept:

(0,−3)

The slope of the line is -3.

Given equation,

⇒ y - 4 + 3(x-3) = 0

⇒ y = 4 - 3(x-3)

⇒ y = 4 - 3x + 3

⇒ y = -3x + 7

Equation of slope-intercept form: y = mx + b

We know the slope is the value multiplied by x,

so the slope of the line is -3.

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The total capacity of Harold's computer hard drive is 750 GB.

Total free space on Harold's computer hard drive = 131.25 GB

Percentage of free space on Harold's computer hard drive = 17.5%

Let

Total capacity of the hard drive = x

17.5% of x = 131.25

17.5/100 × x = 131.25

0.175 × x = 131.25

0.175x = 131.25

divide both sides by 0.175

x = 131.25 / 0.175

x = 750 GB

Hence, Harold's computer hard drive has a total capacity of 750 GB

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Using the expansion of inequality, The smallest integer , n is 3 .

What in math is an integer?

A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).

                           Integers include things like -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.

we have given in question that , n is an integer such that ,

(x²+y²+z²)²≤n(x⁴+y4⁴+z⁴)

Let us consider, a=x², b=y², and c=z² which are all nonnegative i.e a,b,c >0 , n>3 but we find least value of n

So, the above inequality become,

(a+b+c)² ≤ n (a²+b²+c²) ----(*)

by expanding both side of above equation we get, a² + b²+ c² + 2(ab + bc + ac) ≤n( a²+b²+c²)

2(ab + bc + ac) ≤ (n- 1) (a²+b²+c²)

=> (ab+bc+ac) ≤ (n- 1)/2 (a²+ b²+c²)

=> (xy)²+ (yz)²+(xz)²≤ (n-1)/2(x⁴+y⁴+z⁴)

If we put n=3− ∈ where ∈ >0 and x=y=z then

3 ≤ 2 or 1/2 which is wrong . Hence, the smallest value of n is 3.

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The complete question is -

Find the smallest integer n such that (x2+y2+z2)2≤n(x4+y4+z4)

for all real numbers x,y, and z.

The cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

What is the cumulative frequency?

The cumulative frequency for a class is the total frequency of that class and all the classes before it.

In order to find the cumulative frequency for the class with a lower class limit of 27, you would need to add the frequency of that class with the frequencies of all the classes before it.

The cumulative frequency for a class with a lower class limit of 27 can be found by adding up the frequencies of all the classes that come before it.

In this case, the classes that come before the class with a lower class limit of 27 are "Ages 15-18", "Ages 19-22", and "Ages 23-26",

Hence, the cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

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Complete Question:

Ages 15-18 19-22 23-26 27-30 31-34 35-38 Number of students 4 7 7 2 5 10 Based on the frequency distribution above, find the cumulative frequency for the class with a lower class limit 27?

Approximately 99.7 % of the students spent between $ 271 and $ 407  on textbooks in a semester.

Then , according to the Empirical rule , approximately 99.7% of the data lies with in the 2 standard deviations from mean.

Given : The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with

Mean = 339     standard deviation =  34.

Then ,  by

Empirical rule , approximately 99.7 % of the students spent between Mean ± 2 (Standard deviation) on textbooks in a semester.

where , Mean ± 2 (Standard deviation) = 339 ±  2(34)

=(339-2(34) , 339+2(31))

=(271 , 407)

Hence ,  Approximately 99.7% of the students spent between $ 271 and $ 407 on textbooks in a semester.

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Answer:  .9072 is the awnswer

Type 540,000,000 as a floating-point literal using scientific notation with a single digit before and after the decimal point is 5.4e8

Type 540,000,000 as a floating-point literal using scientific notation with a single digit before and after the decimal point is 5.4e8.

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A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.

Given that sin theta = √3/√7

Opposite = √3

Hypotenuse = √7

Get the adjacent

Adj² = (√7)²-(√3)²

simplifying the above equation, we get

Adj² = 7-3

Adj² = 4

Adj = √4

Adj = 2

Cos theta = adj/hyp = 2/√7

csc theta = 1/sin theta = 1/(√3/√7) = √7/√3

sec theta = 1/cos theta = 1/(2/√7) = √7/2

tan theta = opp./adj = √3/2

cot theta = 1/tan theta = 1/(√3/2) = 2/√3

= 2√3/3

The complete question is:

Find the exact value of each of the remaining trigonometric functions of theta. Rationalize denominators when applicable.

sin theta [tex]$=\sqrt{\frac{3}{7}}$[/tex] given that theta is in quadrant I.

cos theta=

csc theta =

sec theta =

tan theta =

cot theta =

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False is the statement, "Polygon endpoints need not conform to snap points, like the boundaries of a filled-in region."

The surface's perimeter is defined by the edge of a filled-in area. An area is a two-dimensional space that any surface can cover. Typically, the edges of the space serve as the surface's boundary. To create a closed area or surface, the edges or the boundary must link.

Similar to end points, snap points are the ends of a polygon's sides. A closed figure can only be formed when these endpoints are connected. A closed polygon is one that has n sides.

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Answer:

Step-by-step explanation:

(1+1/a)^2-(1-1/a)^2

= (1+1/a)^2 - (1-1/a)(1+1/a)

= (1+1/a)^2 - 1 + 1/a^2

= (1+1/a+1/a^2+1/a^3) - 1 +1/a^2

= 1/a^3+2/a^2+2/a+1

So the final answer is 1/a^3+2/a^2+2/a+1

If 3 inches on the map represents 1.25 miles, we can use that proportion to find how many inches represents 10 miles.

3 inches / 1.25 miles = x inches / 10 miles

We can cross multiply and divide to find x:

x = (3 inches * 10 miles) / 1.25 miles

x = 24 inches

So on the map, 24 inches represent 10 actual miles.