The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.
What is Triangle Inequality Theorem ?According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:
a+b>c
a+c>b
b+c>a
In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:
9+13>15 (true)
9+15>13 (true)
13+15>9 (true)
Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.
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Fill in the y-intercept to complete the function equation.
Answer:
y=3x+5
Step-by-step explanation:
you do 4 times 3 then subtract that from 17
50 Points! Multiple choice geometry question. Photo attached. Thank you!
ABC forms a right-angled triangle
Let the distance between AB = x
Using Pythagoras theorem
Sin 30 = Opposite / Hypoteneuse
Sin 30 = 12 in/ x
However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.
Using Pythagoras' theorem, Sin 30 = 1/ 2
Substituting back into the equation, we get:
1/ 2 = 12 in / x
Cross multiplying, we get:
x = 24 in
Recall x = AB
AB = 24 inches
To remember the angles and their respective formula, use SOHCAHTOA
Where sin x = Opposite / Hypoteneuse
Cos x = Adjacent / Hypoteneuse
Tan x = Opposite / Adjacent
80% of the sixth graders have lunch during fourth period if 120 sixth graders had lunch fourth periods how many total six graders are there?
Answer: there is a total of 150 sixth graders
explanation :
0.8x = 120
120 / 0.8 = 150
6th graders at lunch = 150
asdaadadadasdadasdasdadsadasdasdasdasda
This is not a question. Next time, please add a question so that others might be able to help you with it
Erica is 33 years old. She has $580 in a checking account, $3400 in a savings
account, $22,000 in a retirement account, and owns a car worth $7700. What
is the total value of her liquid assets?
A. $3400
B. $3980
C. $33,680
D. $29,700
The total value of her liquid assets would be = $3,980. That is option B.
What is a liquid asset?An asset is said to be a liquid asset because it can easily be converted into cash in a short period of time.
Examples of liquid assets include the following:
Cash in checking accountCash in savings accountTherefore, the total value of liquid assets = $580+$3400 = $3980
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Which of the following graphs represent a function? Check all that apply.
A curve that rises from left to right, graphed in a coordinate plane
A graph in a coordinate plane. The graph starts as a line that ascends from left to right. Then it becomes a vertical line going up.
A graph in a coordinate plane. The graph begins at 0, 0 and curves up and down, creating peaks and valleys. As the graph moves to the right, the peaks and valleys get smaller and closer together.
Three-quarters of a circle, graphed in a coordinate plane
A graph in a coordinate plane. The graph curves up and down, creating peaks and valleys, but there is no pattern to these peaks and valleys.
A graph in a coordinate plane. The graph curves back and forth, from left to right.
6. A study of seatbelt users and nonusers yielded the randomly selected sample data summarized
in the table. Test the claim that the amount of smoking is independent of seat belt use. Use a
0.05 significance level and a test statistic of 1.358. Find the critical value and state the initial
conclusion.
Wear seat belts
Number of Cigarettes Smoked Per Day
0
1-14
15-34
35 and over
175
Don't wear seat belts 149
20
17
07.815; reject the null hypothesis
09.488; fail to reject the null hypothesis
09.488; reject the null hypothesis
42
41
6
9
(1 point)
Answer:
Step-by-step explanation:
ll hypothesis The critical value for this test is 9.488. Based on the test statistic of 1.358, we fail to reject the null hypothesis that the amount of smoking is independent of seat belt use. In other words, there is not enough evidence to support the claim that seat belt use and smoking habits are related.
Personal Note:
You really need to study, or you will end taking summer courses. trust me school isn't that easy and one time I failed I took summer courses but then I passed these summer courses with god's help. so please focus on your studys.
What is the meaning of "free variables"?
Free variables are variables used to represent parameters
What are free variables?Free variables are placeholders or symbols in mathematics and logic that are not constrained by any quantifiers or other specified conditions within an expression, formula, or equation.
When the expression is evaluated, they stand for values that can change or be given different values. In equations or functions, free variables are frequently employed to represent unknowns or parameters.
Free variables enable flexibility and generality in mathematical reasoning since they can be given various values to investigate various situations or solutions. In contrast, bound variables have a specific scope within a certain context or statement and are constrained by quantifiers.
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
626.71 cm^2
Step-by-step explanation:
Area of figure = area of half circle + Area of half circle + area of a rectangle
here, diameter=15 cm
radius = 15/2=7.5 cm
length=30cm
breadth=15cm
Now
Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth
=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15
=626.71 cm^2
An artist makes a hanging sculpture out of rhombus-shaped pieces. Each rhombus shape has diagonals of 3.5 centimeters and 5 centimeters. What is the area of each rhombus? 4.25 cm2 8.5 cm2 8.75 cm2 17.5 cm2
The area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
To find the area of each rhombus, we can use the formula for the area of a rhombus:
Area = (diagonal1 × diagonal2) / 2
Given that the diagonals of the rhombus-shaped pieces are 3.5 centimeters and 5 centimeters, we can substitute these values into the formula:
Area = (3.5 cm × 5 cm) / 2
Area = 17.5 [tex]cm^2[/tex] / 2
Area = 8.75 [tex]cm^2[/tex]
Therefore, the area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
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For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answer:
x= -3
Step-by-step explanation:
x-3
-----------
x+3
This expression is undefined when the denominator is zero.
x+3 =0
x= -3
Find the degrees of freedom, alpha or significance level, and the t-critical value using the t-table n = 27 ;CL=98\%
The degrees of freedom for a sample size of 27 is 26, the alpha or significance level for a 98% confidence level is 0.02, and the t-critical value can be found using the t-table corresponding to a 98% confidence level and 26 degrees of freedom.
To find the degrees of freedom, alpha (significance level), and the t-critical value using the t-table, we need to consider the given information:
n = 27: This represents the sample size, which is 27 in this case.
CL = 98%: CL stands for the confidence level.
It indicates the level of confidence we want to have in our interval estimate.
In this case, the confidence level is 98%.
Degrees of Freedom (df): For a t-distribution, the degrees of freedom depend on the sample size.
Since we have a sample size of 27, the degrees of freedom would be n - 1.
Therefore, the degrees of freedom would be 27 - 1 = 26.
Alpha (α): Alpha, or the significance level, represents the probability of making a Type I error, which is rejecting a true null hypothesis.
The alpha level is determined by subtracting the confidence level from 1. In this case, the alpha level would be 1 - 0.98 = 0.02.
T-Critical Value: To find the t-critical value corresponding to a specific confidence level and degrees of freedom, we can consult the t-table. Since we have a confidence level of 98% and degrees of freedom of 26, we need to find the value that corresponds to the area of 0.01 (half of 1 - 0.98) in the t-distribution table.
The t-critical value would be the value from the table that matches these criteria.
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Find the equation of the axis of symmetry of the following parabola algebraically. y=−3x^2−42x−159
The equation of the axis of symmetry is x = -7.
Given is an equation of a parabola, y = -3x² - 42x - 159, we need to find the equation of the axis of the symmetry.
To find the equation of the axis of symmetry of a parabola in the form of y = ax² + bx + c, you can use the formula x = -b / (2a).
In this case, the given equation is y = -3x² - 42x - 159.
Comparing it to the general form, we have a = -3 and b = -42.
Applying the formula, we can calculate the x-coordinate of the vertex (the axis of symmetry):
x = -b / (2a)
x = -(-42) / (2(-3))
x = 42 / (-6)
x = -7
Therefore, the x-coordinate of the vertex is -7.
To find the equation of the axis of symmetry, we use the value of x in the form x = h, where (h, k) is the vertex.
Hence, the equation of the axis of symmetry is x = -7.
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If you are traveling 14 miles per hour, how many inches would you travel in 3 seconds? (1 mile = 5280 feet; 1 foot = 12 inches) (Convert 3 seconds to inches)
Arlene has to unpack 4 1/2 boxes of canned pineapple juice. He unpacked 1/4 of them.
How many boxes are still unpacked?
There is a substance called sodium-24 that decays at a rate of 4.5% per hour, compounded continuously.
You start with a sample of 500 grams of this substance.
a) Write a function to model the amount remaining after t hours.
The function to model the amount remaining after t hours is:
[tex]A(t) = 500 \times e^{-0.045t}[/tex]
We have,
To model the amount remaining after t hours for the substance sodium-24, which decays at a rate of 4.5% per hour compounded continuously, we can use the formula for continuous exponential decay:
[tex]A(t) = A(0) \times e^{-rt}[/tex]
Where:
A(t) is the amount remaining after t hours,
A(0) is the initial amount,
e is the base of the natural logarithm (approximately 2.71828),
r is the decay rate (expressed as a decimal).
In this case,
The initial amount A(0) is 500 grams, and the decay rate r is 4.5% per hour, which can be expressed as 0.045 (decimal form).
Thus,
The function to model the amount remaining after t hours is:
[tex]A(t) = 500 \times e^{-0.045t}[/tex]
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The line r represents f ( x ) = x − 4 3 . Therefore, the line that represents f - 1 is and f - 1 ( x ) = x + .
Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):
y = (x - 4)/3
Now, let's interchange x and y:
x = (y - 4)/3
To solve for y, we can isolate it by multiplying both sides of the equation by 3:
3x = y - 4
Next, let's add 4 to both sides:
3x + 4 = y
Finally, we can write the inverse function as:
[tex]f^(-1)(x)[/tex] = 3x + 4
So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
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Express log 161 in the form of loga + logb.
log 161 can be expressed as log 7 + log 23 in the form of loga + logb.
To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their logarithmic product is equal to log 161.
Let's find the factors of 161 :
161 = 7 * 23
Now, we can express log 161 as product of two logarithms :
log 161 = log (7 + 23)
Using the logarithmic property log(a*b) = log a + log b :
log 161 = log 7 + log 23
Therefore, log 161 can be expressed as log 7 + log 23.
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solve each equation 1/3a= -15
The solution to the equation 1/3a = -15 is a = -45
How to determine the solution to the equationfrom the question, we have the following parameters that can be used in our computation:
1/3a = -15
Multiply 3 to both sides of the equation
so, we have the following representation
3 * 1/3a = -15 * 3
When the products are evalated, we have
a = -45
Hence, the solution to the equation is a = -45
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calculation of average speed of a car travelling at 200 km in 2 hours 30 minutes
The average speed of the car is 80 km per hour
Calculation of average speed of the carFrom the question, we have the following parameters that can be used in our computation:
Distance = 200 km
Time = 2 hours 30 minutes
using the above as a guide, we have the following:
Speed = Distance/Time
substitute the known values in the above equation, so, we have the following representation
Speed = 200/2.5
Evaluate
Speed = 80 km per hour
Hence, the average speed of the car is 80 km per hour
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variable of 10(n+3)=1,000,00
Answer: Distribute the 10 on the left side of the equation:
10n + 30 = 1,000,000
Subtract 30 from both sides of the equation to isolate the term with n:
10n = 1,000,000 - 30
10n = 999,970
Divide both sides of the equation by 10 to solve for n:
n = 999,970 / 10
n = 99,997
Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.
Step-by-step explanation:
In this picture b, d, and f are midpoints. Ac=50 ce=60 and bd=35. What is fe
The length of FE is equal to 35 units.
What is the triangle midpoint theorem?In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the triangle, we have the following:
AE = 1/2(FE)
BD ≅ FE (midpoints of AC and CE)
BD = FE = 35 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.
Given information:
AC = 50
CE = 60
BD = 35
Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.
We are given that BD = 35, so we can set up the equations:
35 = AC/2 ...(Equation 1)
35 = CE/2 ...(Equation 2)
Let's solve Equation 1 for AC:
AC = 35 * 2
AC = 70
Similarly, solving Equation 2 for CE:
CE = 35 * 2
CE = 70
Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.
In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:
FE/AC = FD/AD
Substituting the known values, we get:
FE/70 = 35/AC
Cross-multiplying, we have:
FE * AC = 70 * 35
Since we know AC is 70, we can solve for FE:
FE = (70 * 35) / 70
FE = 35
Therefore, the length of FE is 35 units.
the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
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The distribution of scores on a history test is close to normal. The scores are adjusted so that the mean score is about =75
and the standard deviation is =5
. What percent of the scores fall between 65 and 75?
13.5%
27.0%
47.5%
The percentage of scores that fall between 65 and 75 is approximately [tex]2 \times 34 = 68%.[/tex]%
To determine the percentage of scores that fall between 65 and 75, we can use the properties of the normal distribution.
Mean score = 75
Standard deviation = 5
We know that the normal distribution is symmetric around the mean, and approximately 68% of the data falls within one standard deviation from the mean.
This means that about 34% of the scores fall between the mean and one standard deviation above the mean.
To calculate the percentage of scores between 65 and 75, we need to determine how many standard deviations away from the mean 65 and 75 are.
For 65:
(65 - 75) / 5 = -2
For 75:
(75 - 75) / 5 = 0
From the calculations, we can see that 65 is 2 standard deviations below the mean, and 75 is at the mean.
Since the distribution is symmetric, we can consider the percentage of scores between the mean and one standard deviation above the mean (34%) and double it to account for the scores between the mean and one standard deviation below the mean.
Therefore, the percentage of scores that fall between 65 and 75 is approximately 2 [tex]\times[/tex] 34% = 68%.
However, none of the given answer options match the calculated result. Therefore, none of the provided answer options accurately represent the percentage of scores between 65 and 75 based on the given information.
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Help me a123 sq ft
B61 sq ft
C49sq ft
D110 sq ft
The area of the required shaded portion is 123 ft²
Given is figure having some shaded portion we need to find the area of the same,
So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,
So, to find the same, we will calculate the area of the triangles and add them,
Area of a triangle = 1/2 x base x height
Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14
= 122.5 ft²
≈ 123 ft²
Hence the area of the required shaded portion is 123 ft²
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What is the distance between $500 and $-61.63
Answer: $561.63
Step-by-step explanation: To find the distance you subtract 500 by -61.63
You get the equation 500--61.63
The two negative signs cancel out to become a positive sign
So the new equation is 500+61.63
So the distance is $561.63
Answer:
$561.63
Step-by-step explanation:
To find out the distance between 500 and -61.63 it will be $500-$-61.63. So 500 - (-61.63) becomes 500 + 61.63 because 2 negatives in a row make a positive. So when you do 500+61.63, you'll get 561.63.
What is the the measure of
A
B
40°
?
C
Answer:
Step-by-step explanation:
To find the measure of angle A
A custom cake baker charges a flat fee for each job, plus an hourly rate for the
number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h
where h is the hours it takes for the job.what does the coefficient of h, in the expression represent
The coefficient h in the expression means the time taken for the job to be completed in hours.
How to find the value of the coefficient in the expression?The custom cake baker charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h where h is the hours it takes for the job.
Therefore, the coefficient h in the expression can be interpreted as follows:
total amount of bills = 40 + 25h
where
40 dollars is the flat fee for each job
Then the coefficient h means the hourly rate for the time taken for the job to be completed.
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A population data set produced the following information N-250 Σx=9880, Σy=1456. Σxy-85080 Σx²=485870, Σy² = 135675 Find the value of oe and p²
The value of p² is approximately 0.999999528.
To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.
The formula for the standard error of estimate (oe) is:
oe = √((Σy² - (Σy)² / N) / (N - 2))
Substituting the given values, we have:
oe = √((135675 - (1456)² / 250) / (250 - 2))
oe = √((135675 - 2124736 / 250) / 248)
oe = √(541.96)
oe ≈ 23.27
Therefore, the value of oe is approximately 23.27.
The coefficient of determination (p²) can be calculated using the formula:
p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))
Substituting the given values:
p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))
p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))
p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)
p² = 1 - (27647.68) / (59022875580.02)
p² ≈ 0.999999528
Therefore, the value of p² is approximately 0.999999528.
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Does anyone know how to solve this?
What does the x-intercept of the graph represent in terms of the football?
a. The x-intercept represents the maximum vertical height that the football reaches.
b . The x-intercept represents the time it took for the football to reach its maximum height.
c. The x-intercept represents the height where the football was when the ball was kicked.
d. The x-intercept represents how far away the football landed from where it started horizontally.
The x-intercept in the graph represent the height where the football was when the ball was kicked.
How to find the x-intercept?The x-intercept is the point where the graph of the line crosses the x-axis.
Therefore, the x-intercept the value of x when y equals to zero.
Therefore, let's find what the x-intercept of the graph represent in terms of the football.
The graph shows the height of the ball in metres after t second.
The y axis represent the height while the x-axis represent the time.
Hence, he x-intercept represents the height where the football was when the ball was kicked.
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