Answer:
[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]
Step-by-step explanation:
Given the initial value problem [tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\[/tex] subject to y(π) = 1. To solve this we will use the variable separable method.
Step 1: Separate the variables;
[tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\frac{1}{\theta}(\frac{dy}{sin\theta d\theta} ) =\frac{ y}{y^{2}+1 } \\\frac{1}{\theta}(\frac{1}{sin\theta d\theta} ) = \frac{ y}{dy(y^{2}+1 )} \\\\\theta sin\theta d\theta = \frac{ (y^{2}+1)dy}{y} \\integrating\ both \ sides\\\int\limits \theta sin\theta d\theta =\int\limits \frac{ (y^{2}+1)dy}{y} \\-\theta cos\theta - \int\limits (-cos\theta)d\theta = \int\limits ydy + \int\limits \frac{dy}{y}[/tex]
[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y +C\\Given \ the\ condition\ y(\pi ) = 1\\-\pi cos\pi +sin\pi = \frac{1^{2} }{2} + ln 1 +C\\\\\pi + 0 = \frac{1}{2}+ C \\C = \pi - \frac{1}{2}[/tex]
The solution to the initial value problem will be;
[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]
Using separation of variables, it is found that the solution of the initial value problem is:
[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} + \theta\cos{\theta} - \sin{\theta} = 0[/tex]The differential equation is given by:
[tex]\frac{1}{\theta}\left(\frac{dy}{d\theta}\right) = \frac{y\sin{\theta}}{y^2 + 1}[/tex]
Separation of variables:Applying separation of variables, we have that:
[tex]\frac{y^2 + 1}{y}dy = \theta\sin{\theta}d\theta[/tex]
[tex]\int \frac{y^2 + 1}{y}dy = \int \theta\sin{\theta}d\theta[/tex]
The first integral is solved applying the properties, as follows:
[tex]\int \frac{y^2 + 1}{y}dy = \int y dy + \int \frac{1}{y} dy = \frac{y^2}{2} + \ln{y} + K[/tex]
In which K is the constant of integration.The second integral is solved using integration by parts, as follows:
[tex]u = \theta, du = d\theta[/tex]
[tex]v = \int \sin{\theta}d\theta = -\cos{\theta}[/tex]
Then:
[tex]\int \theta\sin{\theta}d\theta = uv - \int v du[/tex]
[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \int \cos{\theta}d\theta[/tex]
[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \sin{\theta}[/tex]
Then:
[tex]\frac{y^2}{2} + \ln{y} + K = -\theta\cos{\theta} + \sin{\theta}[/tex]
[tex]y(\pi) = 1[/tex] means that when [tex]\theta = \pi, y = 1[/tex], which is used to find K.
[tex]\frac{1}{2} + \ln{1} + K = -\pi\cos{\pi} + \sin{\pi}[/tex]
[tex]\frac{1}{2} + K = \pi[/tex]
[tex]K = \pi - \frac{1}{2}[/tex]
Then, the solution is:
[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} = -\theta\cos{\theta} + \sin{\theta}[/tex]
[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} + \theta\cos{\theta} - \sin{\theta} = 0[/tex]
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Rachel measures the lengths of a random sample of 100 screws. The mean length was 2.6 inches, with a standard deviation of 1.0 inches. Using the alternative hypothesis (µ < µ0), Rachel found that a z-test statistic was equal to -1.25. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place.
Answer:
Step-by-step explanation:
Using the alternative hypothesis (µ < µ0),
To find the p-value with test statistic -1.25 and assuming a standard level of significance of 0.05, using a p value calculator, the p-value is 0.1057 which is great that 0.05. Thus, the results is not significant.
Using the p value calculation.
1. Check the left tailed z table as the test statistic is negative,
2. Then find the probabilitythat z is greater than your test statistic (look up your test statistic on the z-table- the value under 1.2 and 0.05 which is 0.8944
3. Then, find its corresponding probability, and subtract it from 1 to get your p-value- 1-0.8944 = 0.1056.
Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = ex, x = 0, Δx = 0.4
Answer:
0.492
Step-by-step explanation:
According to the given situation, the calculation of Δy and dy is shown below:-
[tex]y = e^x, x = o, \Delta x = 0.6[/tex]
[tex]dy = f'(x) = e^x[/tex]
[tex]dy = e^x dx[/tex]
[tex]= e^x (0.4)[/tex]
[tex]dy = 0.4e^x[/tex]
[tex]\Delta y = f(0.4) - f(0)[/tex]
[tex]= e^{0.4} - e^0[/tex]
Now we use the scientific calculator or spreadsheet to determine the exponential value
= 1.491824698 - 1
= 0.491824698
or
= 0.492
Therefore for computing the Δy and dy we simply applied the above formula.
Hence, the answer is 0.4918
e^2x -2e^x -24=0 please answer fast
Answer:
x = ln6
Step-by-step explanation:
e^2x - 2e^x - 24 = 0
a = e^x
=> a^2 - 2a - 24 = 0
=> (a + 4)(a - 6) = 0
=> a = -4 => e^x = -4 (invalid because e^x > 0)
=> a = 6 => e^x = 6 => x = ln6
A square has a perimeter of 12x+52 units. Which expression represents the side leagth of the square in units
Answer:
12x/2 or 52/2
Step-by-step explanation:
Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.
PLEASE HELP ASAP One day it took nick 20 mins to drive to work. His average speed was 27mph. When he had drove home using the same route, it had took Nick 45 minutes. work out the average speed of his journey in mph please.
Answer: 12 mph
Step-by-step explanation:
20 minutes = 1/3 hour
Distance = speed x time
D = 27 x 1/3 = 09 miles
He had taken 45 minutes when he drove home
45 minutes = 3/4 hour
Speed = distance / time
Speed = 9 / 3/4
Speed = 12 mph
The average speed of Nick's journey back home is 12 mph.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
The first average speed at what Nick travels is 27 mph.
One day it took Nick 20 mins to drive to work.
Here, Distance = Speed × Time
= 27 × 20/60
= 27 × 1/3
= 9 miles
Nick had drove home using the same route, it had took Nick 45 minutes.
Here, speed = Distance/Time
= 9÷45/60
= 9×4/3
= 12 mph
Therefore, the average speed of Nick's journey back home is 12 mph.
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Write the equation of a line that goes through point (0, -8) and has a slope of 0
Answer:
Step-by-step explanation:
y + 8 = 0(x - 0)
y + 8 = 0
y = -8
How do you write 89,700,000,000 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]89.7 \times {10}^{9} [/tex]
Or
[tex]8.97 \times {10}^{10} [/tex]
Hope this helps you
Answer:
8.97 * 10 ^10
Step-by-step explanation:
We want one nonzero digit to the left of the decimal
8.97
We moved the decimal 10 places to the left
The exponent is positive 10 since we moved 10 places to the left
8.97 * 10 ^10
Compute the following binomial probabilities directly from the formula for b(x|n,p): b(3|8, .35) b(5|8, .6) P(3 ≤ X ≤ 5) when n=7 and p=.6 P(1 ≤ X) when n=9 and p=.1
Answer:
Step-by-step explanation:
From the information given,
p represents the probability of success.
x represents the number of success
n represents the number of samples
Therefore,
1) b(x|n,p): b(3|8, .35)
x = 3
n = 8
p = 0.35
From the binomial probability distribution calculator,
P(x = 3) = 0.28
1) b(x|n,p): b(5|8, .6)
x = 5
n = 8
p = 0.6
From the binomial probability distribution calculator,
P(x = 5) = 0.28
c) n = 7
p = 0.6
P(3 ≤ X ≤ 5)
P(x ≥ 3) = 0.904
P(x ≤ 5) = 0.841
P(3 ≤ X ≤ 5) = 0.904 - 0.841 = 0.063
d) n = 9
p = 0.1
P(1 ≤ X) = p(x ≥ 1)
p(x ≥ 1) = 0.61
F (X) = x² - 2x and 6(x) = 3x+1
A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)
Answer: See bolded below
Step-by-step explanation:
With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.
A. f(g(-4))=143
g(-4)=3(-4)+1
g(-4)=-12+1
g(-4)=-11
With g(-4), we plug that into f(x) to find f(g(-4)).
f(-11)=(-11)²-2(-11)
f(-11)=121+22
f(-11)=143
------------------------------------------------------------------------------------
B. 9x²-1
(3x+1)²-2(3x+1)
(9x²+6x+1)-6x-2
9x²-1
------------------------------------------------------------------------------------
C. g⁻¹(x)=(x-1)/3
x=3y+1
x-1=3y
(x-1)/3=y
please help, will give brainliest
Answer:
B. Pentagonal prism with two pentagons and five rectangles
Step-by-step explanation:
if we use the other shapes the 3-D figure will be incomplete.
Hope I am correct and it helps! ;) <3
Answer:
Second Choice:
"Pentagonal prism with two pentagons and five rectangles"
Step-by-step explanation:
A prism has two congruent parallel bases shaped like a polygon.
A triangular prism has two congruent parallel triangular bases.
A square prism has two congruent parallel square bases.
A pentagonal prism has two congruent parallel [pentagonal bases.
etc.
What connects the bases are rectangular sides. There must be one rectangular side for each side of the polygon of a base. A triangular prism has 3 rectangular sides. A square prism has 4 rectangular sides. A pentagonal prism has 5 rectangular sides.
The answer must be the statement that has the correct number of sides for the chosen base.
The only choice in which the number of rectangular sides is correctly matched tot he number of sides of a base is the second choice:
"Pentagonal prism with two pentagons and five rectangles"
What is 200 percent of (0.020(5/4) + 3 ((1/5) - (1/4)))
Answer:
0.1/4-3/20=1/40-6/40=-1/8 200% of this is -1/4
Step-by-step explanation:
This shows that 200 percent of (0.020(5/4) + 3 ((1/5) - (1/4))) is -2.75
Given the expression as shown in the question:
[tex]200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{1}{5}- \frac{1}{4} )][/tex]
Expand the expression in the square bracket using the distribution law as shown:
[tex]=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{4-5}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{-1}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )-(\frac{3}{20} )]\\=200\% \ of \ [0.020(1.25 )-\frac{3}{20}]\\=\frac{200}{100} \times [0.025-0.15]\\=2 \times [-0.125]\\=-2.75[/tex]
Hence the correct answer to the expression is -2.75.
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Kelly's first four test grades of the period were 80, 72, 96, and 88. Which inequality represents the grades she can
earn on the fifth test to have a test average of no less than 80?
V
O gs16
O 92 16
O g564
O 9264
Answer: option D on edge 2020
Step-by-step explanation:
if you reverse the formula for mean, then you just insert the numbers and you have your answer
There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.
Answer:
620 comic books
2480 / 4 is 620.
620 x 3 is 1860.
1860 + 620 is 2480.
Done!
Thompson's hardware spent $66,170 this year on general insurance alone. if total sales were $713,200, what percent total sales was spent on general insurance? round to the nearest tenth of a percent, if necessary.
Answer:
We have our answer as approximately 10 %
Step-by-step explanation:
We are simply expected to express the sum of money spent on insurance as a percentage of the total sales in this question.
The first step is to set up a fraction, having the sum spent on insurance as the numerator, and the total sales as the denominator. This is shown below
[tex]\frac{66,170}{713,200}[/tex]
To convert this fraction to a percentage, we will have to multiply it by 100 and reduce it to its lowest term.
Here we have
[tex]\frac{66,170}{713,200} \times 100= 9.28 percent[/tex]
Rounding of to the nearest tenth, we have our answer as approximately 10 %
EXAMPLE 3 If f(x, y) = 4xy2 7x2 + y4 , does lim (x, y)→(0, 0) f(x, y) exist? SOLUTION Let's try to save some time by letting (x, y) → (0, 0) along any nonvertical line through the origin. Then y = mx, where m is the slope, and f(x, y) = f(x, mx) = 4x 2 7x2 + (mx)4 = 7x2 + m4x4 = 7 + m4x2 .
Answer:
Limit of the function exists.Step-by-step explanation:
Given the function f(x,y) = [tex]\frac{4xy^{2} }{7x^{2} + y^{4} }[/tex], we are to show that lim (x, y)→(0, 0) f(x, y) exist. To show that, the following steps must be followed.
[tex]\lim_{(x,y) \to (0,0)} \frac{4xy^{2} }{7x^{2} + y^{4} }\\[/tex]
substituting the limit x = 0 and y = 0 into the function we have;
[tex]\frac{4(0)^{2} }{7(0)^{2} + (0)^{4} }\\= \frac{0}{0} (indeterminate)[/tex]
Since we got an indeterminate function, we will then substitute y = mx into the function as shown;
[tex]\lim_{(x,mx) \to (0,0)} \frac{4x(mx)^{2} }{7x^{2} + (mx)^{4} }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{7x^{2} + m^{4}x^{4} }\\\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{x^{2}(7 + m^{4} x^{2}) }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2}x }{7 + m^{4} x^{2} }[/tex]
Substituting x = 0 , the limit of the function becomes;
[tex]\frac{4m^{2}(0) }{7 + m^{4} (0)^{2} }\\= \frac{0}{7}\\ = 0[/tex]
Since the limit of the function gives a finite value of 0 (the limit tends to 0). This shows that the limit exists.
Una persona se dirige a un edificio y observa lo alto del mismo con un ángulo de elevación “x”, después de caminar 10m observa al mismo punto anterior con ángulo de elevación “y”, si la altura del edificio es de 30m. Calcule: "3Tgx.Ctgy + Tgx"
Answer:
3
Step-by-step explanation:
To begin with notice that
[tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]
From that equation you get that
10 tan(x) + 30tan(x) cot(x) = 30
therefore
tan(x) + 3 tan(x) cot(x) = 3
Find tan , sin , and seco, where 0 is the angle shown in the figure.
Give exact values, not decimal approximations.
Answer:
tan(θ) = 5/3sin(θ) = 5√34/34sec(θ) = √34/3Step-by-step explanation:
The hypotenuse is given by the Pythagorean theorem:
h = √(3² +5²) = √34
The trig functions are the ratios of sides:
Tan = Opposite/Adjacent
tan(θ) = 5/3
__
Sin = Opposite/Hypotenuse
sin(θ) = 5/√34 = (5/34)√34
__
Sec = Hypotenuse/Adjacent
sec(θ) = √34/3
Help with one integral problem?
Answer: [tex]2\sqrt{1+tant}+C[/tex]
Step-by-step explanation:
To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.
[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]
Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.
[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]
[tex]u=\sqrt{1+tant}[/tex]
[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]
Now that we have u and du, we can plug them back in.
[tex]\int\limits {2} \, du[/tex]
[tex]\int\limits{2} \, du=2u[/tex]
Since we know u, we can plug that in.
[tex]2\sqrt{1+tant}[/tex]
This may seem like the correct answer, but we forgot to add the constant.
[tex]2\sqrt{1+tant}+C[/tex]
The rat population in major metropolitan city is given by the formula n(t)=89e^0.02t where t is measured in years since 1991 and n(t) is measured in millions. What does the model predict the rat population was in the year 2007?
Answer:
122.6 million
Step-by-step explanation:
Figure the value of t, then put that into the formula and do the arithmetic.
t = 2007 =1991 = 16
n(16) = 89e^(0.02·16) = 89·e^0.32 ≈ 122.6
The model predicts a rat population of 122.6 million in 2007.
Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. The article "Domestic Fuels, Indoor Air Pollution, and Children's Health" (Annals of the N.Y. Academy of Sciences, 2008: 209-217) pm-tented information on various pulmonary characteristics in samples of children whose households in India used either biomass fuel or liquefied petroleum gas (LPG). For the 755 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.30 Us, and the sample standard deviation was 1.20. For the 750 children whose households used liquefied petroleum gas, the sample mean PEF was 4.25 and the sample standard deviation was 1.75.
a. Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. What is the simultaneous confidence level for the two intervals?
b. Carry out a test of hypotheses at significance level .01 to decide whether true average PEF is lower for children in biomass households than it is for children in LPG households (the cited article included a P-value for this test).
c. FEV1, the forced expiratory volume in 1 second, is another measure of pulmonary function. The cited article reported that for the biomass households the sample mean FEY, was 2.3 L/s and the sample standard deviation was .5 L/s. If this information is used to compute a 95% CI for population mean FEV1, would the simultaneous confidence level for this interval and the first interval calculated in (a) be the same as the simultaneous confidence level deter-mined there? Explain.
Answer:
A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)
95% confidence interval for the population mean PEF for children in LPG households
= (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.
C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Step-by-step explanation:
A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.
Finding the critical value from the z-tables,
Significance level for 95% confidence interval
= (100% - 95%)/2 = 2.5% = 0.025
z (0.025) = 1.960 (from the z-tables)
For the children in the biomass households
Sample mean = 3.30
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.20
N = sample size = 755
σₓ = (1.20/√755) = 0.0436724715 = 0.04367
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 3.30 ± (1.960 × 0.04367)
CI = 3.30 ± 0.085598
95% CI = (3.214402, 3.385598)
95% Confidence interval = (3.214, 3.386)
For the children in the LPG households
Sample mean = 4.25
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.75
N = sample size = 750
σₓ = (1.75/√750) = 0.063900965 = 0.063901
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 4.25 ± (1.960 × 0.063901)
CI = 4.25 ± 0.125246
95% CI = (4.12475404, 4.37524596)
95% Confidence interval = (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.
The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.
Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂
The null hypothesis is
H₀: μ ≥ 0 or μ₁ ≥ μ₂
The alternative hypothesis is
Hₐ: μ < 0 or μ₁ < μ₂
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = 3.30
n₁ = 755
s₁ = 1.20
μ₂ = 4.25
n₂ = 750
s₂ = 1.75
σ = √[(1.20²/755) + (1.75²/750)] = 0.07740
z = (3.30 - 4.25) ÷ 0.07740 = -12.27
checking the tables for the p-value of this z-statistic
Significance level = 0.01
The hypothesis test uses a one-tailed condition because we're testing in only one direction.
p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001
The interpretation of p-values is that
When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.
Significance level = 0.01
p-value = 0.000000001
0.000000001 < 0.01
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.
C) For FEY for biomass households,
Sample mean = 2.3 L/s
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation = 0.5
N = sample size = 755
σₓ = (0.5/√755) = 0.0182
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 2.30 ± (1.960 × 0.0182)
CI = 2.30 ± 0.03567
95% CI = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Hope this Helps!!!
If Q(x) = x2 – X – 2, find Q(-3).
Answer:
10
Step-by-step explanation:
for this you need to sub the value of -3 for x
Q(-3)=(-3)^2-(-3)-2
=9+3-2
=10
Answer:
Q= x - X/x - 2/x
Step-by-step explanation:
hope this helps !
enson is picking out what to wear to school. He has three clean T-shirts: one white, one red, and one orange. He also has two clean pairs of jeans: one blue and one gray. The tree diagram shows the different outcomes of picking a pair of jeans and a T-shirt. What is the missing color in the diagram? A. blue B. orange C. red D. white
Answer:
white
Step-by-step explanation:
plato
The solution is Option D.
The missing color from the tree diagram is given by the equation A = white
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the missing color from the tree diagram be represented as A
Now , the value of A is
Jenson has 3 clean T-shirts of white , red and orange
Jenson has 2 clean pairs of jeans of blue and gray
Now , substituting the values in the equation , we get
For every blue jeans = { white , red , orange }
For every gray jeans = { A , red , orange }
From the equation , we get
The value of A = white
Therefore, the value of A is white
Hence , the missing color is white
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#SPJ2
Ava's bacteria population is modeled by an equation. Chase models his bacteria
population with a graph. Ava says that on day 14, she will have more bacteria than Chase
Is she right? Why or why not?
Answer:
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Step-by-step explanation:
Please refer to the attached image.
Ava's bacteria population is modeled by the following equation.
[tex]$ b(t) = 200(1+0.08)^t $[/tex]
Where t is time in days and b(t) is the population of the bacteria after t days.
The graph represents the population of Chase's bacteria.
Ava claims that on day 14, she will have more bacteria than Chase.
Let us compare the population of both bacteria.
Chase bacteria population when t = 14 days:
From the graph, the population is approximately 700 at t = 14 days
P(Chase) ≈ 700
Ava bacteria population when t = 14 days:
at t = 14 days
[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]
So, the population is approximately 587 at t = 14 days
P(Ava) ≈ 587
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Answer:
D
Step-by-step explanation:
Trust
A total of 259 tickets were sold to a benefit concert for a total of $5,312. Two types of tickets were sold: adult tickets were sold for $24 each and student tickets were sold for $16 each. How many student tickets were sold?
Answer:
113
Step-by-step explanation:
Let the number of adult tickets sold =a
Let the number of student tickets sold =s
A total of 259 tickets were sold, therefore:
a+s=259
Adult tickets were sold for $24 each and student tickets were sold for $16 each.
Total Revenue = $5,312
Therefore:
24a+16s=5,312
We solve the two derived equations simultaneously.
From the first equation
a=259-s
Substitute a=259-s into 24a+16s=5,312
24(259-s)+16s=5,312
6216-24s+16s=5,312
-8s=5,312-6216
-8s=-904
Divide both sides by -8
s=113
Therefore, 113 student tickets were sold.
What is the value of 500$ invested at 4% interest compounded annually for 7 years
Answer:
657.96
Step-by-step explanation:
use formula A=P(1+r/n)^nt
A=500(1+.04/1)^1*7
A=500(1.04)^7
A=500(1.3159~)
A= 657.96~
Find the lowest common denominator. 1/(x+2)^2, 1/(x-2)^2, 2/(x^2-4) A. (x+2)^2 (x-2)^2 B. (x^2+2) (x^2-2)
Answer:
(x + 2) ^2 (x - 2) ^ 2 so A is the answer.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
There are (7^13)^3 x 7^0 strawberries in a field . What is the total number of strawberries in the field
Answer:
Step-by-step explanation:
[tex]7^{0}=1[/tex]
[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]
Round off 3. 55 to one significant figure
Answer:
3.6
Step-by-step explanation:
We must first clarify how a number is rounded.
To round a number to unity we have to look at the first number after the comma.
If this number is less than 5 (1, 2, 3, 4) we should not do anything, but if that number is 5 or greater (5, 6, 7, 8, 9) we must add a unit to the number.
That is to say:
<5 do nothing
=> 5 round to the next number (+1)
So in the case of 3.55 it would be.
3.55 = 3.6
The hypotenuse of a right triangle is 10 cm long. One of the triangle’s legs is 3
times the length of the other leg. Find the lengths of the two legs of the
triangle. Round to the nearest tenth if necessary
Answer:
one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]
in decimal one side = 3.16
other side = 9.48
Step-by-step explanation:
In right angle
if two sides containing right angle is a and b and h is hypotenuse then
by Pythagoras theorem
a^2 + b^2 = h^2
__________________________________
let one side be x
given
One of the triangle’s legs is 3 times the length of the other leg
then other leg = 3x
given h = 10 cm
applying Pythagoras theorem
[tex]a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = \sqrt{10}[/tex]
Thus, one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]
[tex]\sqrt{10} = 3.16\\[/tex]
thus, in decimal one side = 3.16
other side = 3.16*3 = 9.48
Enter a range of value for x.
Answer:
-2 < x < 35
Step-by-step explanation:
We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.
The opposite angle of the 14 unit side is 37 °.
The opposite angle of the 13-unit side is (x + 2) °.
Since 13 <14, it would be:
x + 2 <37
we subtract 2 on both sides
x <35
The value of x must be less than 35.
Now, to form a triangle, the angle must be greater than 0.
x + 2> 0
we subtract 2 on both sides
x> -2
The value of x must be greater than - 2.
Therefore the answer would be:
-2 <x <35