misty is building a triangular plainting bed. two of the sides have lengths of eight feet and five feet. what are the possible lengths for the third side?
The length of the third side of the triangle Misty is building should be more than 3 feet and less than 13 feet, according to the Triangle Inequality Theorem.
Explanation:This question pertains to the numerical properties of a triangle, in which two side lengths of the triangle are provided, specifically eight feet and five feet. The length of the third side of the triangle is not set, but it has certain parameters due to the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the possible lengths of the third side would be greater than the absolute difference of the two given sides (eight feet and five feet), and less than the sum of the lengths of the two given sides. Thus, the third side's length should be more than 3 feet (8 - 5) and less than 13 feet (8 + 5).
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Write 24.652 as a mixed number.
Juan's baseball card collection was worth 800$. Over the last 5 years,thw collection decreased $300 in value. What integer representa the average decrease in value each year.
Final answer:
The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.
Explanation:
Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.
Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.
Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.
Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3
gerard is buying pencils in boxes of 10 he has 20 pencils but needs a total of 60 pencils
For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply.
If a polygon is regular, then it has congruent angles and congruent sides.
conditional
converse
inverse
contrapositive
Answer:
Conditional and Converse.
Step-by-step explanation:
If a polygon is regular, then it has congruent angles and congruent sides.
We can say that;
Hypothesis is : If a polygon is regular
Conclusion is : then it has congruent angles and congruent sides.
A conditional statement will not be true when the hypothesis is true but the conclusion is false. In the given statement, the above conditional statement has a truth value of true.
We can write the converse statement as : If it has congruent angles and congruent sides, then the polygon is regular.
This also has a truth value of true.
So, correct options are :
Conditional and converse
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether
The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation 20,000e^0.15t=28,000 represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
A. 2 years
B.9 years
C. 17 years
D. 22 years
The correct option is: A. 2 years
Explanation
The given growth equation is: [tex]20000e^0^.^1^5^t = 28000[/tex], where [tex]t[/tex] is the number of years the population has been growing.
For finding the number of years, we will solve the above equation for [tex]t[/tex].
First, dividing both sides by 20000, we will get........
[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]
Now taking 'natural log' on both sides, we will get........
[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]
So, the population of the town has been growing about 2 years.
The town has been growing for 17 years
Exponential functionsGiven the exponential function
Given the expressions 20,000e^0.15t=28,000
We are to find the value of "t" which is the time.
e^0.15t = 28000/20000
e^0.15t = 7/5
e^0.15t = 1.4
Take the ln of both sides
lne^0.15t = ln 1.4
0.15t = 2.639
t = 2.639/0.15
t = 17years
Hence the town has been growing for 17 years
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The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month? 0.2158 0.8750 0.0362 0.1151
Answer:
0.1151
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 75[/tex].
What is the probability that a family spends less than $410 per month?
This probability is the pvalue of Z when X = 410. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{410 - 500}{75}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.
While free diving in the ocean Samantha once set a record by diving 525 feet in 3 1/2 minutes how many feet per minute did she dive?
If sinθ =4/5 , then cosθ = _____.
Answer:
cosθ = [tex]\frac{3}{5}[/tex] .
Step-by-step explanation:
Given : If sinθ =4/5 .
To find : cosθ = _____.
Solution : We have given that sinθ =4/5 .
By the trigonometric identity
cos²θ + sin²θ = 1.
Plugging the value of sinθ =4/5 .
cos²θ + [tex](\frac{4}{5}) ^{2}[/tex] = 1.
cos²θ + [tex]\frac{16}{25}[/tex] = 1.
On subtracting [tex]\frac{16}{25}[/tex] from both sides
cos²θ = 1 - [tex]\frac{16}{25}[/tex] .
cos²θ = [tex]\frac{25 -16}{25}[/tex] .
Taking square root both sides.
[tex]\sqrt{cos^{2}theta} = \sqrt{\frac{9}{25}}[/tex] .
cosθ = [tex]\frac{3}{5}[/tex] .
Therefore, cosθ = [tex]\frac{3}{5}[/tex] .
Let f = {(–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5)}. Let g = {(–3, 3), (–1, 1), (0, –3), (1, –4), (3, –6)}. What is g(f(2))? -5 -1 2 The composition is undefined.
Explain why you add to find the sum of two integers, but subtract to find the sum of a positive and negative integer
a 26 inch piece of Steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 2 in more than three times the length of the first piece find the links of the pieces
The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. men the same age have mean height 69.3 inches with standard deviation 2.8 inches. what are the z-scores for a woman 6 feet tall and a man 6 feet tall? what information do the z-scores give that the actual heights do not?
In the parabola y = (x + 1)2 + 2, what is the vertex?
The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)
Vertex form of an equationThe vertex form of a quadratic equation is expressed as:
y = a(x - h)^2 + k
where (h, k) is the vertex of the equation
Given the equation of the parabola as y = (x - 1)^2 + 2, On comparing;
h = -1
k =2
Hence the vertex of the parabola is (-1, 2)
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You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of your pump has a radius of 4.5 millimeters. What is the volume flow rate of the air being pumped into the football?
Answer:
The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.
Explanation:
To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.
Given:
- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.
The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Converting the radius from millimeters to feet:
[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]
Now, let's calculate the cross-sectional area:
[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]
Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:
[tex]\[ Q = A \times \text{Speed} \][/tex]
Given:
- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s
Now, let's calculate the volume flow rate:
[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]
[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]
What is the expression for the calculation double 5 and then multiply by 3?
What is the fourth term in the arithmetic sequence 13,10,7
The fourth term in the arithmetic sequence 13, 10, 7 is 4.
Explanation:The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.
if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?
The cost of a new house can be represented by the regression equation c = 120f + 90,000, where $120 is the cost per square foot and $90,000 is the cost of the lot. A new house on a lot costs $438,000. How many square feet does it have?
Answer: 2900 Square Feet
Step-by-step explanation: i took the test
The sum of three consecutive integers is −261−261. Find the three integers.
a can of coffee weighs 13 ounces. what is the smallest number of cans that must be used to package 1,000 kilograms of coffee
The Sears tower in Chicago is 1,454 feet tall. Write the height as an integer
evaluate the expression 4(2x + 3) + 2(x + 1)-7
Jonathan can jog 3 2/5 miles in 7/8 hour.Find his average speed in miles per hour
Three consecutive integers whose sum is 36
Each U.S. penny weighs 2.5 grams. How many pennies,x is how many pennies it an equation, are on scale if their total weight is 37.5 grams:A. 2.5+x=37.5 x=12,B. 2.5x=37.5 x=15, C. x-2.5=37.5 x=40,D. 2.5x=37.5 x=18???? please answer quick.
Find the exact circumference of a circle with the given radius. 36 inches C = 72 in. 36 in. 18 in. IN PIE TERMS PLEASE!!!!!:)
Answer:
The circumference of a circle is [tex]72\pi [/tex] .
Step-by-step explanation:
Forrmula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of the circle .
As given in the question
The radius of the circle is 36 inches .
Put all the values in the formula
[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]
[tex]Circumference\ of\ a\ circle = 72\pi [/tex]
Therefore the circumference of a circle is [tex]72\pi [/tex] .
Express the side length of a square as a function of the length d of the square’s diagonal. then express the area as a function of the diagonal length.