Final answer:
The given system of equations has one unique solution because the lines represented by the equations have different slopes, hence they intersect at exactly one point.
Explanation:
To answer how many solutions there are for the given system of equations:
6y=12x+36
15y=45x+60 (Assuming the '+60' was meant instead of '60', as '+60' makes it a linear equation)
We first simplify both equations to determine if they are identical, parallel, or intersecting.
For the first equation, we divide by 6:
y = 2x + 6
For the second equation, assuming a typo and it should be '+60', we divide by 15:
y = 3x + 4
Since the slopes (2 and 3) are different, the lines are not parallel and will intersect at exactly one point. Therefore, there is one unique solution to this system.
Three runners — Andy, Blaise, and Susie — were competing in a 100-meter race. When Andy reached the finish line, Blaise was 10 meters behind him. When Blaise reached the finish line, Susie was 10 meters behind her. At the moment that Andy reached the finish line, Susie was how many meters behind him? Keep working and you will earn half credit for correctly solved problem.
Final answer:
Susie was 20 meters behind Andy when he reached the finish line in the 100-meter race.
Explanation:
To determine how many meters Susie was behind Andy at the moment Andy reached the finish line during the 100-meter race, let's consider the information given:
Andy finished the race.
Blaise was 10 meters behind Andy at that moment.
Susie was 10 meters behind Blaise when Blaise finished the race.
When Blaise reached the finish line, Andy would have already finished since Blaise was behind by 10 meters. However, at the moment Andy finished, Susie was also behind Blaise, who was 10 meters from finishing. Hence, Susie was 10 meters (the distance Blaise was behind Andy) + 10 meters (the distance Susie was behind Blaise at her finish) = 20 meters behind Andy when he finished the race.
In conclusion, Susie was 20 meters behind Andy when Andy reached the finish line.
Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a 0 bit and a 1 bit are equally likelyb) the probability that a bit is a 1 is 0.6c) the probability that the i-th bit is a 1 is 1/(2^i) for i=1,2,3,...,10
Answer:
A) 0.0009765625
B) 0.0060466176
C) 2.7756 x 10^(-17)
Step-by-step explanation:
A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10
If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5
Now the definition of binomial probability is given by;
P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)
Now, we want the definition of this probability at k = 10.
Thus;
P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)
P(x = 10) = 0.0009765625
B) here we are given that p = 0.6 while n remains 10 and k = 10
Thus;
P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)
P(x=10) = 0.0060466176
C) we are given that;
P((x_i) = 1) = 1/(2^(i))
Where i = 1,2,3.....,n
Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;
P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)
This gives;
P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]
This gives;
P(x = 10) = [1/(2^(55))]
P(x = 10) = 2.7756 x 10^(-17)
Final answer:
To find the probability that a randomly generated bit string of length 10 does not contain a 0, we consider each scenario separately. For equally likely 0s and 1s, the probability is (0.5)^10. For a 0.6 probability of 1, the probability is (0.4)^10. For varying probabilities of 1, the probability is calculated by multiplying the probabilities for each position.
Explanation:
To find the probability that a randomly generated bit string of length 10 does not contain a 0, we need to consider each scenario separately.
a) If a 0 bit and a 1 bit are equally likely, then the probability of getting a 0 in any position is 0.5. Since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.5)^10 = 0.00097656.
b) If the probability of a bit being a 1 is 0.6, then the probability of getting a 0 in any position is 1 - 0.6 = 0.4. Again, since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.4)^10 = 0.00604661.
c) If the i-th bit has a probability of 1/(2^i) of being a 1, then the probability of getting a 0 in the i-th position is 1 - 1/(2^i). Multiplying the probabilities for each position gives us the probability of not getting a 0 in any of the 10 positions.
P(Not getting a 0) = (1 - 1/(2^1))(1 - 1/(2^2))(1 - 1/(2^3))(1 - 1/(2^4))(1 - 1/(2^5))(1 - 1/(2^6))(1 - 1/(2^7))(1 - 1/(2^8))(1 - 1/(2^9))(1 - 1/(2^10)) = 0.00563108.
y=4x-9 what’s the missing value in the solution to the equation?
Answer:
x=2.25
Step-by-step explanation:
Let's break this down:
Saying "y=", is just like saying "0=", so we can say that;
0=4x-9
We need to isolate the variable, and to do that we should add 9 to both sides and cancel it out.
9=4x
Now we need to eliminate the coefficient by dividing both sides by four
[tex]9/4=4x/4[/tex]
Which cancels out four, giving us
2.25=x
Hope this helps and please correct me if I am wrong:)
<3
Solving Square Root Worksheet (x - k)^2 Part 2
4. 3(x - 2)^2 = 40
5. -2(x - 1)^2 = 36
6. 4(x - 1)^2 = 8
Answer:
4. x = 2 + 2sqrt(10/3), 2- 2sqrt(10/3)
5. No real solutions
x = 1 + 3sqrt(2) i, 1 - 3sqrt(2) i,
6. x = 1 + sqrt(2), 1 - sqrt(2)
Step-by-step explanation:
4. 3(x - 2)² = 40
(x - 2)² = 40/3
(x - 2) = +/- sqrt(40/3)
x - 2 = +/- 2sqrt(10/3)
x = 2 +/- 2sqrt(10/3)
5. -2(x - 1)² = 36
(x - 1)² = -18
A perfect square can never be negative for real values of x
(x - 1) = +/- i × sqrt(18)
x - 1 = +/- i × 3sqrt(2)
x = 1 +/- i × 3sqrt(2)
6. 4(x - 1)² = 8
(x - 1)² = 2
x - 1 = +/- sqrt(2)
x = 1 +/- sqrt(2)
Hey, please answer the attachment questions. 3 questions.
Answer:
A. Cat
B. 8
C. 6 people
Step-by-step explanation:
A. Just by looking at it Cat has the least amount of squares
B. There are 10 full squares in total (including the pieces). 80 people divided by 10 boxes is 8.
C. There is 1/2 and 1/4 more people who picked giraffe more than dogs. 1
1/2 of 8 is 4. 1/4 of 8 is 2. 4+2 = 6.
Explain why a cross section of a polyhedron does not always match the base of that polyhedron.
Explanation:
A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
For example, the cross sections of a cube include ...
triangle, square, rectangle, trapezoid, general quadrilateral, pentagon, hexagon
Answer: A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
Step-by-step explanation.
What’s the slope of (8,10) (-7,14)
Using the formula for slope, we calculated that the slope of the line passing through the points (8,10) and (-7,14) is -4/15.
Explanation:The slope of a line between two points ((x1,y1) and (x2,y2)) can be calculated using the formula for slope: m = (y2 - y1) / (x2 - x1).
In this case, your two points are (8,10) and (-7,14).
Therefore, we can calculate the slope using these points:
m = (14 - 10) / (-7 - 8) = 4/-15 = -4/15.
So, the slope of the line passing through the given points is -4/15.
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Write the number 0.00008623 in standard form
Answer:
8.623
Step-by-step explanation:
ik it
Answer: 8.623
Step-by-step explanation: you move the decimal down 6 points left and then you get your answer
A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 38,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 37,300 miles with a standard deviation of 1000 miles. At α= 0.05, does the test suggest that mean life is less than 39000 miles?
Answer:
[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]
[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.
Step-by-step explanation:
We assume this question: A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 38,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 37,300 miles with a standard deviation of 1000 miles. At α= 0.05, does the test suggest that mean life is less than 38000 miles? because if is not this one is not appropiate
Data given and notation
[tex]\bar X=37300[/tex] represent the sample mean
[tex]s=100[/tex] represent the sample standard deviation for the sample
[tex]n=18[/tex] sample size
[tex]\mu_o =7500[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 38000, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 38000[/tex]
Alternative hypothesis:[tex]\mu < 38000[/tex]
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]
P-value
The degrees of freedom are given by:
[tex] df = n-1= 18-1=17[/tex]
Since is a left tailed test the p value would be:
[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.
The shipping firm's hypothesis test determines that the mean lifespan of a particular brand of tires is indeed less than 38,000 miles based on their sample data and the significance level.
Explanation:The shipping firm is performing a hypothesis test about a population mean, where the suspected value is 38,000 miles. The null hypothesis (H0) would be that the mean life of the tires is equal to 38,000 miles, while the alternative hypothesis (H1) is that the mean life is less than 38,000 miles.
Using the provided sample data, we can calculate the test statistic (z-score), which helps us determine the p-value. The test statistic is given by (Sample Mean - Pop Mean) / (Standard Deviation / sqrt(n)) = (37300 - 38000) / (1000 / sqrt(18)). This gives us a test statistic of -3.1623.
We also know that our α is 0.05 for this problem. Now we find the p-value that is associated with this test statistic. If the p-value is less than our alpha, we reject the null hypothesis. Given our test statistic, we will indeed find a very low p-value, less than 0.05, which means we reject the null hypothesis and conclude the mean lifespan of the tires is less than 38,000 miles.
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Solve the inequality below; Which direction will the graph go in and will the dot be open or closed? m+5>-1
Answer:
The dot will be closed, and to the right from -6
Step-by-step explanation:
We can rearrange [tex]m+5>-1 = -6 < m[/tex]
As it is only a < we close the dots. It must go to the left as m is greater than -6 - all numbers greater than a value will be to the right on the number line.
Write a quadratic function whose graph has a vertex of (3, 2) and passes through the point (4, 7), using f(x) = a(x - h)^2 + k (vertex form).
THANK YOU FOR HELPING!!!
The quadratic function is f(x) = 5(x - 3)² + 2.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola.
We are given that the vertex is (3, 2), so we have:
h = 3
k = 2
We also know that the parabola passes through the point (4, 7).
We can use this point to find the value of a:
7 = a(4 - 3)² + 2
5 = a
Therefore, the quadratic function is:
f(x) = 5(x - 3)² + 2
This quadratic function has a vertex of (3, 2) and passes through the point (4, 7).
Thus,
The quadratic function is f(x) = 5(x - 3)² + 2.
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Olivia is cutting a 1 \dfrac12 \text{ m}1 2 1 m1, start fraction, 1, divided by, 2, end fraction, start text, space, m, end text by \dfrac34\text{ m} 4 3 mstart fraction, 3, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal. Find the area of each of the pieces.
Answer: 9/6 metre
Step-by-step explanation:
From the question, Olivia is cutting a 1 1/2m by 3/4m piece of rectangular paper into two pieces along its diagonal
This will result into two congruent triangular pieces.
Let us first find the area of each piece by finding the area of the original rectangle and dividing it by two.
The area of a rectangle is given by multiplying the length and the width:
1 1/2 × 3/4
We can change the first fraction to an improper fraction:
(1×2)+1 = 2+1 = 3; this gives us 3/2:
3/2 × 3/4 = 9/8 = 1 1/8
The area of the entire rectangle is 1 1/8 sq. m., or 1.125 sq. m.
Divide this by 2:
9/8 ÷ 2
9/8 × 1/2 = 9/16
The area of each rectangle is 9/16 sq. m., or 0.5625 sq.
Answer:
9/16
Step-by-step explanation:
Using the table tool, create a truth table for the compound statement ~(p^q)
Answer:
The image attach is the truth table for the compound statement
Step-by-step explanation:
g(x) = x^3 - 5; Find g(5)
Answer:
g(5) = 120
Step-by-step explanation:
g(x) = x^3 - 5;
Let x=5
g(5) = 5^3 -5
= 125 -5
= 120
Answer:
g(5) = 120
Step-by-step explanation:
We want to find g(x) when x is equal to 5, so we can substitute 5 in for x.
g(x) = x^3 - 5
g(5) = 5^3 - 5
Solve the exponent
g(5) = 125-5
Subtract
g(5) = 120
If m + n = m, what is the value of n?
a. 1
b. 0
C.-1
d.not enough information to tell
Answer:
B. 0
Step-by-step explanation:
if n is anything but 0 then the answer wouldn't be m it would be for example m - 1 or m + 1
for it to remain m then n must be 0
Someone please answer this will mark brainliest
Answer:
The answer to your question is the letter B.
Step-by-step explanation:
Data
√3/2 -2π 4/5 -6.5 7 2/3
Process
1.- Get the decimal values of each data
√3/ 2= 0.87 -2π = -6.28 4/5 = 0.2 -6.5 = -6.5 7 2/3 = 7.67
2.- Order the numbers from greatest to least
7.67 > 0.87 > 0.2 > -6.28 > -6.5
or 7 2/3 > √3/2 > 4/5 > -2π > -6.5
3.- Conclusion
The right answer is B.
a box used for shipping a volleyball set measures 10 inches by 20 inches by 40 inches. what is the longest length of support pole that will fit into the box, rounded to a tenth of an inch?
Answer:
45.8 inches
Step-by-step explanation:
Considering the given dimensions and taking 40 inches for length, 20 inches for height and 10 inches for width. The diagonal that runs from bottom to top of box will give the longest possible length of a pole.
Diagonal at the bottom of box
Diagonal=√(l²+w²)
Where l and w represent length and width respectively
Diagonal=√(40²+10²)=√1700
Diagonal between the height and bottom diagonal
Longest diagonal=√(20²+√1700)=√2100=45.8257569495584
Rounded off, the diagonal is approximately 45.8 inches
The longest length of a support pole that will fit into the box measures approximately 45.8 inches.
Explanation:To find the longest length of a support pole that will fit into the box, we need to determine the length of the diagonal of the box. The diagonal length can be found using the formula:
diagonal = √(length^2 + width^2 + height^2)
Substituting the given values:
diagonal = √(10^2 + 20^2 + 40^2) = √(100 + 400 + 1600) = √2100 ≈ 45.82 inches.
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An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary
Answer:
$40,500 I took a test and this was the answer to the question.
Answer:
$40500
Step-by-step explanation:
f(x) goes through the point (9,2) then the function f(3x) must go through what point
Answer:
(27,2)
Step-by-step explanation:
Multiply the x value by 3 to get the transformation
If a function f(x) goes through the point (9,2), the function f(3x) will go through the point (3,2) after substituting x with 3x in the original function.
If the function f(x) passes through the point (9,2), then to determine the corresponding point that f(3x) goes through, we must substitute x with 3x in the original function.
Since we know that f(9) = 2, to find f(3x) we look for a value of x that when multiplied by 3 gives us 9.
That value is x = 3.
Therefore, f(3×3) = f(9) = 2, meaning f(3x) will go through the point (3,2).
Ann wants to wallpaper the back wall of her bedroom. The wall is in the shape of a rectangle. Its length is 17 feet and its width is 13 feet. Suppose wallpaper costs $5 for each square foot. How much will wallpaper cost for the wall?
Answer:
The wallpaper would cost 1105 $
What's the volume of the cone? Round to tenths place please.
Given:
Given that the radius of the cone is 2 inches.
The height of the cone is 4 inches.
We need to determine the volume of the cone.
Volume of the cone:
The volume of the cone can be determined using the formula,
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
where r is the radius of the cone and h is the height of the cone.
Substituting r = 2 and h = 4 in the above formula, we get;
[tex]V=\frac{1}{3} (3.14) (2)^2 (4)[/tex]
[tex]V=\frac{1}{3} (3.14) (4) (4)[/tex]
[tex]V=\frac{1}{3}(50.24)[/tex]
[tex]V=16.75[/tex]
Thus, the volume of the cone is 16.75 cubic inches.
Santiago receives $143 per year in simple interest from three investments. Part is invested at 2%, part at 3%, and part at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount of each rate
Please answer I need a lot of help on this!!!
Answer:
02a+.03b+.04c=126,
b=a+500,
c=3b
a=300., b=800., c=2400.
Step-by-step explanation:
The amount of each rate of interest given the total simple interest received is
$400, $900 and $2,700 respectively
let
a = 2% investment
= 0.02
b = 3% investment
= 0.03
c = 4% investment
= 0.04
Total interest = (0.02×a) + (0.03×b) + (0.04×c)
143 = 0.02a + 0.03b + 0.04c (1)
b = a + 500 (2)
c = 3b (3)
substitute (3) into (1)
143 = 0.02a + 0.03b + 0.04(3b)
143 = 0.02a + 0.03b + 0.12b
0.02a + 0.15b = 143 (4)
from (2)
b - a = 500 (5)
multiply (5) by 0.02
0.02b - 0.02a = 10
0.02a + 0.15b = 143 (4)
Add
0.02b + 0.15b = 10 + 143
0.17b = 153
b = 900
substitute b into (3)
c = 3b (3)
c = 3(900)
c = 2700
Recall,
b = a + 500 (2)
900 = a + 500
900 - 500 = a
a = 400
Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively
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Is this statement true or false 16% of 250 is equal to 250% of 16
16% of 250 is .16 * 250, which is 40
250% of 16 is 2.5 * 15, which is also 40
So, it's true.
A percentage is a way to describe a part of a whole. The statement that 16% of 250 is equal to 250% of 16 is true.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The value of 16% of 250 can be written as,
[tex]16\%\ of\ 250\\\\=\dfrac{16}{100} \times 250\\\\=40[/tex]
The value of 250% of 16 can be written as,
[tex]250\%\ of\ 16\\\\=\dfrac{250}{100} \times 16\\\\=40[/tex]
Thus, the statement that 16% of 250 is equal to 250% of 16 is true.
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Suppose you put $1000 in an account earning 5.5% interest compounded continuously. How much will be in the account after four years?
a. $941
b. $1,246
c. $1,057
d. $1,839
Answer: The correct answer will be $1,220 in the account after four years.
Step-by-step explanation: For this problem we will use the "Simple Interest" equation to find the amount of interest you will earn after 4 years.
First, convert 5.5% to a decimal, 0.055.
I, interest = 1000 x 0.055 x 4
I = $220
Now add the interest to the total amount of money originally in the account.
1000 + 220 = $1,220
Final answer:
The amount in the account after four years, with continuous compound interest at a rate of 5.5%, is approximately $1246. Therefore, after four years, the amount in the account will be closest to option (b) $1,246.
Explanation:
To calculate the amount in the account after four years, we can use the formula for continuous compound interest: A = P [tex]e^{(rt)}[/tex], where A is the final amount, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, P = $1000, r = 5.5% = 0.055, and t = 4. Plugging these values into the formula, we have:
A = $1000 × [tex]e^{(0.055 \times 4)}[/tex]
A = $1000 × [tex]e^{0.22[/tex]
A ≈ $1000 × 1.246
Therefore, the amount in the account after four years is approximately $1246.
Which is a y-intercept of the continuous function in the table? (5, 0) (0, 1) (0, 5) (1, 0)
The possible y-intercepts for the given continuous function from the table are (0,1) and (0,5).
Explanation:In this mathematical problem, the student is asking about the y-intercept of a function represented in a table. The y-intercept of a continuous function is a point where the line of the function intersects or touches the y-axis on a graph. This point is always (0, y). If we look at the given points, only (0,1) and (0,5) can potentially be y-intercepts because they have 0 as their x-coordinate, which is the requirement for a point to be a y-intercept.
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Tristan has some dimes and some quarters. He has at least 20 coins worth at most $4.25 combined. If Tristan has 10 dimes, determine the maximum number of quarters that he could have. If there are no possible solutions, submit an empty answer.
Answer:
The maximum number of quarters that he could have is 13
Step-by-step explanation:
Let x represent the number of quarters he could have. If he has 10 dimes and has at least 20 coins, then
→ x + 10 >= 20
→ x >= 10 (1)
His coins worth at most $4.25. Also, it is known that 1 dollar is equal to 100 cents, 1 dime is equal to 10 cents and 1 quarter is equal to 25 cents.
→ (x * 25) + (10 * 10) <= (4.25 * 100)
→ 25x + 100 <= 425
→ 25x <= 325
→ x <= 13 (2)
If we combine the equation 1 and 2:
10 <= x <= 13
The maximum value of x is 13
Circle O has an area of 200m^2. Point A and B lie on the circle. Sector AOB has an area of 50m^2. What is the measure of angle AOB?
90
25
45
180
Edith needs 65 yards of yarn to knit a baby hat and 580 yards of yarn to knit a baby blanket. A ball of yarn contains 420 feet of yarn. How many balls of yarn does Edith need to buy to make the baby hat and baby blanket?
Answer:
5
Step-by-step explanation:
There are 3 feet in a yard, so 420 feet is 420/3 = 140 yards.
The total number of yards Edith needs is ...
65 yd + 580 yd = 645 yd
So, the total number of balls of yarn Edith needs is ...
(645 yd)/(140 yd/ball) ≈ 4.61 balls
Edith needs to buy 5 balls of yarn to make her projects.
What is the approximate value of irrational number e (round to 5 decimal places)?
Answer:
2.71828
Step-by-step explanation:
In this question, we are asked to give the approximate value of the irrational number e.
We should understand that just like Pi, which is the ratio of the circumference of a circle to the diameter, we have the number called e. It is also a consistent like Pi and has an approximate value of 2.71828.
What does it mean when it is called irrational? it is an irrational number because it doesn’t have an exact fraction which is the ratio of two numbers and thus it has a non-ending list of numbers after the decimal point.
Final answer:
The irrational number e, also known as Euler's number, is approximately 2.71828 when rounded to five decimal places. It is crucial in mathematics, particularly calculus.
Explanation:
The question asks for the approximate value of the irrational number e rounded to five decimal places. The number e is a fundamental constant in mathematics, often referred to as Euler's number, which is approximately equal to 2.71828 when rounded to five decimal places.
This number plays a crucial role in various branches of mathematics, especially in calculus, relating to the rate of growth or decay in natural phenomena.
Verify the identity. StartFraction sine (alpha plus beta )Over cosine alpha cosine beta EndFraction equals tangent alpha plus tangent beta Rewrite the numerator on the left side of the identity using one of the sum and difference formulas. StartFraction nothing Over cosine alpha cosine beta EndFraction Rewrite the fraction from the previous step such that it is a sum or difference of two expressions. Do not simplify the result. nothing Divide out any common factors in the expression from the previous step. nothing The expression from the previous step then simplifies to tangent alpha plus tangent beta using what? A. Quotient Identity B. Reciprocal Identity C. Even-Odd Identity D. Pythagorean Identity
Answer:
(A)Quotient Identity
Step-by-step explanation:
To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]
Rewrite the numerator on the left side of the identity using the sum and difference formulas.
[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]
Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]
[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below
[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Divide out any common factors in the expression from the previous step.
[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using the Quotient Identity
[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]