Answers
Answer:
x ∈ {-0.465, 1.014}
Step-by-step explanation:
The equation can be cast in the form f(x) = 0, and solved easily using a graphing calculator. That shows x ≈ -0.465 and x ≈ 1.014. The same calculator can iterate the roots to full calculator precision.
__
The equation can be made a quadratic by the substitution ...
z = e^(2x)
Then we have ...
\(2\cosh(2x)-\sinh(2x)=4\\\\2\cdot\dfrac{e^{2x}+e^{-2x}}{2}-\dfrac{e^{2x}-e^{-2x}}{2}-4=0\qquad\text{use exponential identities}\\\\2z+2z^{-1}-z+z^{-1}-8=0\qquad\text{multiply by 2, substitute z}\\\\z^2 -8z+3=0\qquad\text{multiply by z}\\\\z=\dfrac{8\pm\sqrt{(-8)^2-4(1)(3)}}{2(1)}=4\pm\sqrt{13}\\\\x=\dfrac{\ln(z)}{2}=\dfrac{\ln(4\pm\sqrt{13})}{2}\approx\{-0465133,1.014439\}\)
Related Questions
Question 1 of 20
What is the solution to the following inequality?
Answers
Please help !
The kinetic energy of an object is the energy it has due to its motion. The kinetic energy E, in joules, of an object with a mass of m kilograms moving at v meters per second is modeled by the function -
Answers
Answer:
v (E) = √(2E/m)
Step-by-step explanation:
From the question given:
E = ½mv²
E is the kinetic energy
m is the mass of object
v is the velocity.
To find a model v(E) for the velocity of the object, we simply make V the subject of the above equation.
This can be obtained as follow:
E = ½mv²
Cross multiply
mv² = 2E
Divide both side by m
v² = 2E/m
Take the square root of both side
v = √(2E/m)
Therefore, the model v(E) for the velocity of the object is given by:
v (E) = √(2E/m)
the problems. Su drew a rectangle that is 6 inches long and 5 inches wide. What is the perimeter of the rectangle?
Answers
Let us have a sketch of the rectangle
Since we have obtained the sketch, the perimeter can be obtained as follow.
The perimeter of any shape is simply the sum of all its sides
So we will have the perimeter to be
\(\begin{gathered} perimeter=5+5+6+6 \\ \text{perimeter}=10+12=22 \\ \text{perimeter}=22 \end{gathered}\)The perimeter is 22 inches
Rearrange g
=
fr to make f the subject.
Answers
Answer:
f=g/rStep-by-step explanation:
divide by R
X,(x-36) What is the value of x
Answers
The value of x is 63
How to determine the valueTo determine the value of the variable, we have that;
Angles at a point is equal to 360 degreesComplementary angles are defined as angles that sum up to 90 degreesSupplementary angles are defined as angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesFrom the information given, we have that;
x and x - 36 are complementary angles
Now, equate the angles to 90 degrees, we have;
x + x - 36= 90
collect the like terms, we get;
2x = 90 + 36
add the terms
2x =1 26
Divide by the coefficient
x = 63
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Complete question:
The angles X,(x-36) are complementary. What is the value of x
Al-unit by 3-unit rectangle is shown below.
What is the area of the shaded rectangle?
Answers
Answer: 1.5 square units
The area of the whole rectangle is 3 units. Area is found by multiplying length by width. Only half of the rectangle is shaded, so if you take the whole area of the rectangle, and divide it in half, you get the area of that half rectangle.
By doing this, you divide 3 in half, and get 1.5 square units.
Hope this helps :)
Laura invests $100 in an account that continuously compounds. In 50 years, her money will triple. What is the interest rate for this account
Answers
Answer:
its something close 5%
Step-by-step explanation:
i need help with the question
Answers
The intersection points are: (0, -3) and (10, 2)
The bounded area is -20.83 unit²
How to find the intersection points?(a) The intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:
(0, -3) and (10, 2)
(b) The integral terms of y which gives the area bound are:
a = -3, b = 2 (These are the y values of the intersection points)
Since we have x = y² + 3y and x = 2y + 6, we can say:
y² + 3y = 2y + 6
y² + 3y - 2y - 6 = 0
y² + y - 6 = 0
Thus, h(y) =
Using a = -3 and b = 2 with h(y) = y² + y - 6, we have the bounded area as:
\(Area = \int\limits^b_a {y} \, dy\)
\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)
Integrating the area:
Area = [y³/3 + y²/2 - 6y + C]²₋₃
Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]
Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]
Area = [-22/3] - [27/2]
Area = -125/6
Area = -20.83 unit²
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LOOK AT PICTURE, WHOEVER HAS CORRECT ANSWER, I WILL MARK BRAINIEST :)
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
17. 17. The scores for a math test are shown below, ordered from smallest to largest. 60 61 62 63 63 64 64 65 66 66 66 69 72 72 72 74 75 80 82 84 86 86 87 87 89 89 90 93 94 98 Fill out the stem and leaf plot below for this data. Enter the leaves separated by commas (ex: 1,1,2,3). Stems Leaves
Answers
Answer:
Filling the values we have;
Explanation:
Given the data on the given table, we want to fill them in a stem leaves plot.
The tens values would be in the stems while the unit values will be written in their corresponding leaves.
Filling the values we have;
Select a personal or professional example of a measurement you use routinely. Convert the measurement either from U.S customary units to metric units, or from metric units to U.S. customary units. You may choose more than one measurement and may choose among weight, length, temperature, etc. Show each step of your conversion and be sure to include all units from the original and converted measurements (for example, yards to meters, degrees Celsius to degrees Fahrenheit).
Answers
A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.
For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:
150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms
Therefore, 150 pounds is approximately equal to 68.0388 kilograms.
In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.
It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.
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Consider the function \(y=\sqrt{5x-5}+1\)
Which inequality is used to find the domain?
Answers
The inequality is used to find the domain of the given function is
5x-5 ≥ 0
What is a function?A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.
Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.
Since, the function is a square root function.
We know that,
The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.
The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :
5x-5 ≥ 0
Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0
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The triangle shown below has an area of 25 units?
Find the missing side.
Length is 10
Answers
Missing side in the triangle is equal to \(\boldsymbol{5}\) units.
Define triangle.A triangle is a polygon that consists of three sides.
A right angled triangle in which one angle is equal to \(\boldsymbol{90^{\circ}}\)
Area of a triangle \(=\boldsymbol{\frac{1}{2}bh}\) where \(b,h\) denote base and height of a triangle respectively.
So,
\(25=\frac{1}{2}(10)h\)
\(h=\frac{50}{10}\)
\(=\boldsymbol{5}\) units
So, missing side is equal to \(\boldsymbol{5}\) units.
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The paper scissors pencils stickers and paint belong on the top shelf of the craft closet.
Select the best sentence that demonstrates the needed corrections for the sentence.
Group of answer choices
The paper scissors pencils stickers, and paint belong on the top shelf of the craft closet.
The paper scissors, pencils, stickers and paint belong on the top shelf of the craft closet.
The paper, scissors, pencils, stickers, and paint belong on the top shelf of the craft closet.
The paper, scissors, pencils, stickers and, paint belong on the top shelf of the craft closet.
Answers
Explanation: When you are listing items, you need to place a comma in between them. The comma in between the “stickers” and “and” is the Oxford comma. When you lost multiple items, you need a comma after the word before “and”.
im pretty sure what the other guy said is right
Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, she will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result?
a. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05.
b. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05.
c. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
d. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05
Compute the estimated Cohen’s d to measure the size of the treatment effect.
Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment.
Estimated Cohen’s d =
Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.
Answers
The correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
What is standard deviation?A statistical measure known as the standard deviation depicts how variable or dispersed a set of data is. It is determined by taking the square root of the variance, which is the sum of the squared deviations from the data set mean. While a large standard deviation suggests that the data points are more dispersed, a small standard deviation suggests that the data points tend to be close to the mean. It can be used to assess the variability between different data sets and is frequently used as a gauge of a data set's consistency or reliability.
Given, level of significance = 0.05.
n = 49 and sample > 30
Thus, using z-score we have:
z = 4.04 - 3.68 / (0.70/7) = 3.60
Now, p-value = 0.000318
Now, for P < 0.05 we have:
cohens D = 4.04 - 3.67 / 0.70 = 0.51
This shows a medium increase.
Hence, the correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
The estimated Cohen’s d is given as:
Cohen’s d = (M - μ) / σ
The sample standard deviation is not given, so we cannot calculate the exact value of Cohen's d.
The sample standard deviation will determine the estimated Cohen's d in this situation, although if it is greater than 0.2, it might be regarded as having a small effect size.
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Consider an urn containing 4 white balls and 1 black ball, and suppose that balls will be sequentially drawn (without replacement) from the urn until the black ball is obtained. Letting X denote the number of white balls drawn before the black one is selected, give the pmf of X.
Answers
Answer:
\(P(X = 0) = 0.2\)
\(P(X = 1) = 0.2\)
\(P(X = 2) = 0.2\)
\(P(X = 3) = 0.2\)
\(P(X = 4) = 0.2\)
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
pmf of X.
Probability of each outcome, 0, 1, 2, 3 or 4 white balls drawn.
Before the trials, you are equally as likely to get the black ball in the 1st trial(0 white balls drawn) to the 5th trial(4 white balls drawn). So this is an uniform distribution with \(P(X = x) = \frac{1}{5} = 0.2\)
Thus, the pmf is:
\(P(X = 0) = 0.2\)
\(P(X = 1) = 0.2\)
\(P(X = 2) = 0.2\)
\(P(X = 3) = 0.2\)
\(P(X = 4) = 0.2\)
There is a sale on a gallon of milk at the grocery store. The original price was $2.99 and the new price is $2.49. What is the percentage of decrease on the gallon of milk? Round your answer to the nearest whole percent
A) 17%
B) 50%
C) 23%
D) 20%
Answers
URGENT DUE IN FEW MINS6th grade math Calculate to TOTAL Surface Area.
Do NOT count the surface under the pyramid.
Answers
The surface area of the solid is 281 ft².
Given that, a solid figure made of a rectangular prism and a square pyramid,
We need to find its surface area,
To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,
So,
Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,
= 2×5×5 + 2(4·12+12·5+4·5)-5²
= 50+256-25
= 281 ft²
Hence the surface area of the solid is 281 ft².
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Graph the linear equation by plotting points. x +y = 1
Answers
On solving the provided question, we got to know that - the points (0,1) and (1,0) to be used to plot the graph .
What is a linear equation?An algebraic equation of the form y=mx+b (where m is the slope and b is the y-intercept) with one constant and only one first-order (linear) term is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.
To draw a straight line, just two points are needed.
Finding the points where the graph intersects is one approach.
\(the intercepts of the x and y axes\)
\(Let x = 0 in the y-intercept equation.\\ Let y = 0 in the x-intercept equation.\)
x =0→y=0+y=1⇒y=1←y-intercept
y =0→x+0=1⇒x=1←x-intercept
plot the points (0,1) and (1,0)
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Identify the property that justifies the statement: 5(x-3)=5x-15
Answers
Answer:
Distributive
Step-by-step explanation:
5 was distributed to (x-3) so the distributive propierty justifies the given statement
Answer:
Distributive
Step-by-step explanation:
5 was distributed to ( x - 3 ) so the Distribute Property justifies the given statement.
Find all Values of b that will make the polynomial a perfect square trinomial.
25z^2+bz+36
Please write out how to do this so I can see the steps of what I am doing wrong. thank you!
Answers
Answer:
There are two solutions for \(b\): \(b = + 30\cdot z\), \(b = -30\cdot z\)
Step-by-step explanation:
By Algebra, we know that a polynomial is a perfect square trinomial if it is of the form:
\(a^{2} + 2\cdot a \cdot c + c^{2} = (a + c)^{2}\) (1)
By direct comparison, we have the following system:
\(a^{2} = 25\cdot z^{2}\), \(c^{2} = 36\), \(2\cdot a \cdot c = b\).
There are two possible solutions for \(b\):
1) \(a = \pm 5\cdot z\), \(c = \pm 6\), \(b = + 30\cdot z\)
2) \(a = \pm 5\cdot z\), \(c = \mp 6\), \(b = -30\cdot z\)
Which of the following represents the ratio of the given side to the
hypotenuse?
HELP if you’re good at GEOMETRY!!
Answers
When Jack began his persuit Jill was already 60 miles ahead. If jill travels at 60 miles per hour how many hours will it take jack to catch up with jill
Answers
It takes 3 hours for jack to catch up with jill
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
The distance Jack needs to cover is 60 miles.
The rate at which Jack closes the distance:
difference in speeds
= 80-60
=20 mph.
That's the rate at which Jack is closing that distance.
We have formula:
D=RT. , D=distance, R=rate, t= time
60 = 20t
divide both sides by 20, we get
60/20=t
t=3 hours.
It takes 3 hours for jack to catch up with jill
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When jack began his pursuit, Jill was already 60 miles ahead. If Jill travels at 60mph and jack travels at 80mph how many hours will it take jack to catch up with Jill?
Luis includes sit ups and push ups as part of his training for the race. This graph shows his plan for increasing the number of sit ups and push ups he does each week. Write an equation that can be used to find the number of sit ups, y, luis will do during week x.
Answers
Answer:
y = 10x
Step-by-step explanation:
y = number of sit-ups
x = number of weeks
Equation of that can be used to find the number of sit-ups can be generated using the graph in the slope-intercept form, y = mx + b. Where, slope = m, and y-intercept is b.
Let's find slope using two points on the blue line, (0, 0) and (3, 30):
Slope (m) = change in y/change in x
m = (30 - 0)/(3 - 0)
m = 30/3
m = 10
b = 0 (the point where the line intercepts the y-axis)
✔️To write the equation, substitute m = 10 and b = 0, into y = mx + b
y = 10x + 0
y = 10x
3 1/3 divided by 1 1/5
Answers
Answer:
25/9
Step-by-step explanation:
3 1/3 ÷ 1 1/5
3 1/3 = 10/3
1 1/5 = 6/5
10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9
So, the answer is 25/9
Which situation is modeled by the graph? PLEASE HELP!
Answers
Answer:
Height of jump rope used over time.
Step-by-step explanation:The Height is stable and even so not an elevator as it goes to multiple floors not just one and is not used frequently after the same amount of time.Not the rest for the same reason.Jump rope as it can be uniform in height and time unlike the rest.
how do you find answer to 9/35 - 1/5?
Answers
Answer:
2/35
Step-by-step explanation:
\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)
A publishing company conducted a survey asking readers whether they use e readers. Of the 3000 readers surveyed, 1954 said they read books on e reader. The approximate sample proportion is? Which means that? %of the readers surveyed don’t use e readers
Answers
Approximately 34.87% of the readers surveyed don't use e-readers.
To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):
Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed
Approximate sample proportion = 1954 / 3000 ≈ 0.6513
To express this as a percentage, we multiply the sample proportion by 100:
Approximate sample proportion as a percentage = 0.6513 × 100
= 65.13%
Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.
This means that approximately 65.13% of the readers surveyed use e-readers.
To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:
Percentage of readers who don't use e-readers = 100% - 65.13%
= 34.87%
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The perimeter of the rectangle below is 104 units. Find the length of side AD.
Write your answer without variables.
D
52-2
4z
C
B
AD =
0
HELP PLEASE!
Answers
Answer: 28
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
\(2(5z-2+4z)=104\\\\9z-2=52\\\\9z=54\\\\z=6\\\\\therefore AD=5(6)-2-28\)
can someone find what x please?
5x + 14 = 614
Answers
5x = 600
Divide by 5
x = 120