x= twin 1 and 2
x=5x-60
x-5x=-60
-4x=-60
x=15
check 15=5(15)-60
15=75-60
15=15
The hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters. Find the length of the other leg.
The first person who answers I'll give brainlyest
Answer:
6√3 cm
Step-by-step explanation:
The hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters then the other leg is 6√3
A family on a vacation drives 123 miles in 2 hours then gets stuck in traffic and goes 4 miles in the next 15 minutes. The remaining 191 miles of the trip take 3 3/4 hours. What was their average rate of speed to the nearest tenth of a mile per hour
Answer:
13
Step-by-step explanation:
Answer:
Their average rate of speed is 53 miles per hour.
Step-by-step explanation:
Given : A family on a vacation drives 123 miles in 2 hours then gets stuck in traffic and goes 4 miles in the next 15 minutes. The remaining 191 miles of the trip take [tex]3\frac{3}{4}[/tex] hours.
To find : What was their average rate of speed to the nearest tenth of a mile per hour ?
Solution :
We know, [tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Total distance traveled by family on vacation is
D= 123 miles + 4 miles + 191 miles = 318 miles
Total time taken by family on vacation is
T= 2 hours + 15 minutes + [tex]3\frac{3}{4}[/tex] hours
T= 2 hours + [tex]\frac{15}{60}[/tex] hours + [tex]3\frac{3}{4}[/tex] hours
T= [tex]2+ \frac{1}{4}+ \frac{15}{4}[/tex] hours
T= [tex]\frac{8+1+15}{4}[/tex] hours
T= [tex]\frac{24}{4}[/tex] hours
T= 6 hours
Substitute the value in the formula,
[tex]\text{Speed}=\frac{318}{6}[/tex]
[tex]\text{Speed}=53[/tex] miles per hour.
Therefore, Their average rate of speed is 53 miles per hour.
Dennis drew the rectangle on grid paper. What is the perimeter of the rectangle dennis drew.
(2l+2w) is that right
Evaluate e y2z2 dv, where e lies above the cone ϕ = π/3 and below the sphere ρ = 1.
In spherical coordinates, we set
[tex]x=\rho\cos\theta\sin\varphi[/tex]
[tex]y=\rho\sin\theta\sin\varphi[/tex]
[tex]z=\rho\cos\varphi[/tex]
so that the volume element under this transformation becomes
[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
The region [tex]E[/tex] is given by the set
[tex]\left\{(\rho,\theta,\varphi)\mid0\le\rho\le1,0\le\theta\le2\pi,0\le\varphi\le\dfrac\pi3\right\}[/tex]
so that the integral is
[tex]\displaystyle\iiint_Ey^2z^2\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^6\sin^2\theta\sin^3\varphi\cos^2\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]\displaystyle=\left(\int_0^{\pi/3}\sin^3\varphi\cos^2\varphi\,\mathrm d\varphi\right)\left(\int_0^{2\pi}\sin^2\theta\,\mathrm d\theta\right)\left(\int_0^1\rho^6\,\mathrm d\rho\right)[/tex]
[tex]=\dfrac{47}{480}\cdot\pi\cdot\dfrac17=\dfrac{47\pi}{3360}[/tex]
The volume of the solid using the triple integral [tex]\mathbf{\iiint_E y^2z^2 dV \ \ is \ \ = \dfrac{47 \pi}{3360}}[/tex]
Given that;
The solid E lies above the cone [tex]\mathbf{\pi = \dfrac{\pi}{3}}[/tex] as well as;Below the sphere [tex]\mathbf{\rho = 1}[/tex]Then the spherical coordinates can be expressed as:
[tex]\mathbf{\rho^2 =x^2 +y^2 +z ^2}[/tex]where;
[tex]\mathbf{x = \rho \ sin \phi \ cos \theta}[/tex] [tex]\mathbf{y= \rho \ sin \phi \ sin \theta}[/tex] [tex]\mathbf{z = \rho\ cos \theta}[/tex] [tex]\mathbf{dxdydz = \rho^2 \ sin \phi \ d \rho\ d \phi \ d \theta}[/tex]Now, the expression for the solid E in the spherical coordinates can be computed as:
[tex]\mathbf{E = \Big \{ ( \rho , \theta, \phi )\Big| 0 \leq \rho \leq 1, 0 \leq \phi \leq \dfrac{\pi}{3}, 0 \leq \theta \leq 2 \pi \Big \} }[/tex]
and the volume of the solid using the triple integral is calculated as:
[tex]\mathbf{\iiint_E y^2z^2 dV = \iiint _E \ y^2 z^2 \ dx dy dz }[/tex]
[tex]\mathbf{\implies \iiint _E \ y^2 z^2 \ dx dy dz = \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \int ^1_0 \ (\rho sin \phi sin \theta )^2 ( \rho cos \phi )^2 \rho^2 sin \phi d \rhod \phi d \theta }[/tex]
[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \ \int^1_0 \ \rho^6 d \rho d \phi d \theta }[/tex]
[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \Big [ \dfrac{\rho^7}{7} \Big]^1_0 \ d \phi d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi \ d \phi d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin \phi( 1- cos^2 \phi)cos^2 \phi \ d \phi d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \phi}{5}- \dfrac{cos ^3 \phi}{3} \Bigg ] ^{\dfrac{\pi}{3}}_{0} d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \dfrac{\pi}{3}}{5}- \dfrac{cos ^3 \dfrac{\pi}{3}}{3}- \dfrac{cos^5 0}{5}+ \dfrac{cos^3 0}{3} \Bigg ] d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{2}{15}- \dfrac{17}{480} \Bigg ] d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{(480\times 2) -(15\times 17)}{15\times 480}\Bigg ] d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{705}{15\times 480}\Bigg ] d \theta }[/tex]
[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} 2sin ^2 d \theta}[/tex]
[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} (1-cos 2\theta) \ d \theta}[/tex]
[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [\theta - \dfrac{sin 2 \theta }{2}\Bigg] ^{2 \pi}_{0}}[/tex]
[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [2 \pi\Bigg] }[/tex]
[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \times 2 \pi}{6720}} }[/tex]
[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \pi}{3360} }[/tex]
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the question is down below
Answer:
C) 132 sq. cmStep-by-step explanation:
We must calculate the lateral area of a cylinder.
The formula is:
[tex]A=2\pi rH[/tex]
r - radius
H - height
We have H = 6 cm and r = 3.5.
Substitute:
[tex]A=2\pi(3.5)(6)=42\pi\ cm^2[/tex]
Use [tex]\pi\approx\dfrac{22}{7}[/tex]
[tex]A\approx42\left(\dfrac{22}{7}\right)=(6)(22)=132\ cm^2[/tex]
This is a number greater than one, which can only be divided by itself and one.
Answer:
Step-by-step explanation:
Well 7 is the only number that can be divided by itself and 1
Answer:
Hello!
Great question.
The correct answer would be "Prime Number."
Step-by-step explanation:
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
Find the exact value of sine, cosine, and tangent of A and T for each triangle.
Answer:
See below
Step-by-step explanation:
7)
AT² = 11² + 4² = 121 + 16 = 137
AT = √137
sinA = DT/AT = 11/√137 = (11√137)/137
cosA = AD/AT = 4/√137 = (4√137)/137
tanA = DT/AD = 11/4
sinT = AD/AT = 4/√137 = (4√137)/137
cosT = DT/AT = 11/√137 = (11√137)/137
tanT = AD/DT = 4/11
9)
AT² = 8² + 3² = 64 + 9 = 73
AT = √73
sinA = LT/AT = 8/√73 = (8√73)/73
cosA = AL/AT = 3/√73 = (3√73)/73
tanA = LT/AL = 8/3
sinT = AL/AT = 3/√73 = (3√73)/73
cosT = LT/AT = 8/√73 = (8√73)/73
tanT = AL/LT = 3/8
11)
6² = 4² + RT²
36 = 16 + RT²
RT² = 20
RT =√20 = √(4× 5) = 2√5
sinA = RT/AT = (2√5)/6 = (√5)/3
cosA = AR/AT = 4/6 = 2/3
tanA = RT/AR = (2√5)/4 = (√5)/2
sinT = AR/AT = 4/6 = 2/3
cosT = RT/AT = (2√5)/6 = (√5)/3
tanT = AR/RT = 4/(2√5) = (2√5)/5
Find the limit if it exits.
Answer:
C. 20
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to 2} (3x^3 +x^2-8)[/tex]
This a limit of a polynomial function.
We plug in the limit directly to obtain;
[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(2)^3+(2)^2-8[/tex]
We simplify to get;
[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(8)+4-8[/tex]
[tex]\lim_{x \to 2} (3x^3 +x^2-8)=24+4-8[/tex]
[tex]\lim_{x \to 2} (3x^3 +x^2-8)=20[/tex]
The correct choice is C
Evan's family drove to a theme park for vacation. They drove the same speed throughout the trip. The first day, they drove 300 miles in 6 hours. The second day, they drove 250 miles in 5 hours. The third day, they arrived at the park after driving for 3 hours. How many miles did they drive on the third day?
Answer:
150 miles
Step-by-step explanation:
Find the unit rate (MPH) by dividing miles travlled by hours.
300/6 = 50 MPH
250/5 = 50 MPH
Multiply the hours on day 3 (3) by 50 MPH
3*50 = 150 miles
Answer:
150 miles
Step-by-step explanation:
The relationship between speed, time and distance is such that the product of speed and time is distance.
Given that they drove the same speed throughout the trip
Speed on day one given that distance covered is 300 miles in 6 hours,
Speed = 300 miles/ 6 hours
= 50 miles per hour
Speed on day two given that distance covered is 250 miles in 5 hours
= 250 miles/ 5 hours
= 50 miles per hour
If on the third day, the speed is maintained and they drove for 3 hours,
Distance covered = 50 miles per hour × 3 hours = 150 miles
If x varies inversely with y and x = 4 when y = 8, find x when y = 16.
Answer:
x=2
Step-by-step explanation:
The formula for inverse variation is
xy = k
We know x = 4 and y = 8
4*8= k
32 = k
xy = 32
We want to find x when y = 16
x*16 = 32
Divide each side by 16
16x/16 = 32/16
x =2
Answer:
xy=32
16x=32
x=2
Show all work and explain in words
Findthe value of x. Then find the measure of each labeled angle.
Answer:
Part 5) [tex]x=50\°[/tex]
Part 6) [tex]x=15\°[/tex]
Step-by-step explanation:
Part 5) we know that
[tex](2x-10)\°+90\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
solve for x
[tex]2x=180\°-80\°[/tex]
[tex]2x=100\°[/tex]
[tex]x=50\°[/tex]
Find the value of the labeled angle
[tex](2x-10)\°=2(50\°)-10\°=90\°[/tex] ----> is a right angle
Verify the answer
we know that
In a quadrilateral the sum of the internal angles must be equal to 360 degrees
so
[tex](2x-10)\°+90\°+(180-x)\°+x\°=360\°[/tex]
[tex](2x+260)\°=360\°[/tex]
substitute the value of x
[tex]2(50\°)+260\°=360\°[/tex]
[tex]360\°=360\°[/tex] ------> is true, therefore the value of x is correct
Part 6) we know that
[tex](8x+10)\°+(4x-10)\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
solve for x
[tex]12x=180\°[/tex]
[tex]x=15\°[/tex]
Find the value of each labeled angle
[tex](8x+10)\°=8(15\°)+10\°=130\°[/tex]
[tex](4x-10)\°=4(15\°)-10\°=50\°[/tex]
[tex]130\°[/tex] and [tex]50\°[/tex] are supplementary angles
Tommy has 5 jars of marbles. Each jar is 2/3 filled with marbles. How many jars of marbles does Tommy have
Tommy has 3 and 1/3 jars but 3 of them are full .
Okay so 5*2/3 =10/3 which is 3 1/3
Each hour, the number of bacteria in Dr. Nall's petri dish tripled. What percent is the population compared to the population the hour before?
Answer:THE ANSWER IS
300% PLEASE BRAINEST ME!
Answer:
The answer is D hope this helps
Step-by-step explanation:
Courtney is a retail store manager and will make $40000 this year. She expects to pay 28% of her income in tax, how much money will she make after taxes?
➷ Find the multiplier:
28/100 = 0.28
1 - 0.28 = 0.72
Multiply the total amount by this multiplier:
40,000 x 0.72 = 28,800
She will make $28,800
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
She will make 28,800 dollars after tax.
Step-by-step explanation:
just subtract 28 percent of 40,000.
Or even simpler just follow peachy's instructions cause she/he did her crud right. a percentage is the same as a decimal. 1 percent is 0.01. since 28 percent is 0.28 we subtract 0.28 from one, because 1 is 100 percent. Also,all of this is the same as subtracting 28 percent of 40,000 from 40,000 1 - 0.28= 0.72, and multiply 40,000 by 0.72.
All credit on this part is peachy's thank her/his answer and give her/him brainliest. :)
btw why i say him/her, he/she, and her/his is because I dot want to assume gender
You want to find the height of a tower used to transmit cellular phone calls. You stand 100 feet away from the tower and mesure the angle of elevation to be 40° . How high is the tower to the nearest foot
Answer:
84 feet to the nearest foot.
Step-by-step explanation:
We have a right angled triangle with adjacent side (A) = 100 and you want to find the height of the tower, the opposite side (O).
A = 100 , O = ? so we need the tangent , (from SOH-CAH-TOA).
tan 40 = O/ 100
O = 100 tan 40
= 83.9 feet.
Final answer:
To determine the height of the tower, we can use the tangent of the angle of elevation, 40 degrees, multiplied by the distance, 100 feet, which results in approximately 84 feet.
Explanation:
To find the height of a tower with an angle of elevation of 40°, observed from 100 feet away, you can use trigonometric functions. Specifically, the tangent function, which is defined as the ratio of the opposite side (the height of the tower we're looking for) to the adjacent side (the distance from the tower).
We have:
The angle of elevation (θ) = 40°
The distance from the tower (adjacent side) = 100 feet
The height of the tower can be calculated as:
height = tan(θ) × adjacent side
= tan(40°) × 100 feet
Using a calculator, we find:
height = tan(40°) × 100
= 0.8391 × 100
≈ 84 feet (to the nearest foot)
Therefore, the tower is approximately 84 feet high.
( please help this is the last question and i have 15 min left, thank you for the help!)
Find the difference.
Answer: Defualt
Step-by-step explanation: Dan
Each car has 5 wheels. There are 74 wheels. How many cars are there? How many wheels left over?
Answer: 14 cars 4 left over
Step-by-step explanation:
74/5=14.8
14 x 5 = 70
4 wheels left over
Consider a binomial experiment with n = 20 and p = .70. if you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. compute f(12) (to 4 decimals). 0.1143 compute f(16) (to 4 decimals). 0.1304 compute p(x 16) (to 4 decimals). 0.2375 compute p(x 15) (to 4 decimals). 0.7624 compute e(x). 14
Answer:
Step-by-step explanation:
The question is incomplete. p(x 16) is actually [tex]P(X\geq 16)[/tex] ; p(x 15) is actually [tex]P(X\leq 15)[/tex] and e(x) is [tex]E(X)[/tex]
Wherever a random variable X can be modeled as a binomial random variable we write :
X ~ Bi (n,p)
Where ''n'' is the number of Bernoulli experiments taking place (whose variable is called binomial random variable).
And where ''p'' is the success probability.
In a Bernoulli experiment we define which event will be a ''success''
In order to calculate the probabilities for the variable X we can use the following equation :
[tex]P(X=x)=f(x)=(nCx).(p^{x}).(1-p)^{n-x}[/tex]
Where ''[tex]P(X=x)[/tex]'' is the probability of the variable X to assume the value x.
Where ''[tex]nCx[/tex]'' is the combinatorial number define as :
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
In our question
X ~ Bi (20,0.70)
Now let's calculate the probabilities :
[tex]f(12)=P(X=12)=(20C12).(0.70)^{12}.(1-0.70)^{20-12}=0.1144[/tex]
[tex]f(16)=P(X=16)=(20C16).(0.70)^{16}.(1-0.70)^{20-16}=0.1304[/tex] (I)
[tex]P(X\geq 16)[/tex] ⇒
[tex]P(X\geq 16)=P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)[/tex] (II)
[tex]P(X=17)=(20C17).(0.70)^{17}.(1-0.70)^{20-17}=0.0716[/tex] (III)
[tex]P(X=18)=(20C18).(0.70)^{18}.(1-0.70)^{20-18}=0.0278[/tex] (IV)
[tex]P(X=19)=(20C19).(0.70)^{19}.(1-0.70)^{20-19}=0.0068[/tex] (V)
[tex]P(X=20)=(20C20).(0.70)^{20}.(1-0.70)^{20-20}=0.0008[/tex] (VI)
Using (I), (III), (IV), (V) and (VI) in (II) :
[tex]P(X\geq 16)=0.1304+0.0716+0.0278+0.0068+0.0008=0.2374[/tex]
Now :
[tex]P(X\leq 15)[/tex]
[tex]P(X\leq 15)=1-P(X\geq 16)[/tex]
[tex]P(X\leq 15)=1-0.2374=0.7626[/tex]
Finally,
[tex]E(X)=[/tex] μ (X)
[tex]E(X)[/tex] is the mean of the variable X
In this case, X is a binomial random variable and its mean can be calculated as
[tex]E(X)=(n).(p)[/tex]
In the question :
[tex]E(X)=(20).(0.70)=14[/tex]
The binomial experiment with n = 20 and p = 0.70 indicates that the probabilities are;
f(12) ≈ 0.1144
f(16) ≈ 0.1304
P(X ≥ 16) ≈ 0.2375
P(X ≤ 15) ≈ 0.7265
E(X) = 14
What is a binomial experiment?
A binomial experiment is a statistical experiment that consists of a specified number of independent trials, in which each the trials has only two possible outcomes. The probability of success is the same for all trials and the trials are independent, such that the outcome of one trial does not affect the outcome of the other trials.
In a binomial experiment with n = 20 and p = 0.7, the probability of exactly k successes in n independent trials can be found from the following probability mass function.
f(k) = [tex]_nC_k[/tex] × [tex]p^k[/tex] × [tex](1 - p)^{(n-k)}[/tex]
Where [tex]_nC_k[/tex] is the binomial coefficient, which can be calculated an [tex]_nC_k[/tex] = n!/(k!·(n - k)!)
Using the formula the probabilities can be calculated as follows;
f(12) = ₂₀C₁₂ × 0.70¹² × 0.3⁸ = 125970 × 0.70¹² × 0.3⁸ ≈ 0.1144
f(16) = ₂₀C₁₆ × 0.70¹⁶ × 0.3⁴ = 4845 × 0.70¹⁶ × 0.3⁴ ≈ 0.1304
P(X ≥ 16) = f(16) + f(17) + f(18) + f(19) + f(20) ≈ 0.2375
P(X ≤ 15) = 1 - P(X ≥ 16) ≈ 1 - 0.2375 = 0.7625
The expected value of the binomial random variable X is; E(X) = n·p, where n is the number of trials and p is the probability of success on a single trial.
E(X) = n·p = 20 × 0.7 = 14
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Find the specific solution of the differential equation dy/dx equals the quotient of 2 times y and x squared with condition y(-2) = e. (4 points)
A. y equals negative 1 minus 2 divided by x
B. y equals e raised to the negative 2 over x power
C. y equals negative 1 times e raised to the 1 over x power
D. None of these
Answer:
B. y = e^(-2/x).
Step-by-step explanation:
dy/dx = 2y / x^2
Separate the variables:
x^2 dy = 2y dx
1/2 * dy/y = dx/x^2
1/2 ln y = = -1/x + C
ln y = -2/x + C
y = Ae^(-2/x) is the general solution ( where A is a constant).
Plug in the given conditions:
e = A e^(-2/-2)
e = A * e
A = 1
So the specific solution is y = e^(-2/x).
Final answer:
The separable differential equation [tex]dy/dx = 2y/x^2[/tex] can be solved by separating variables, integrating both sides, and then applying the given initial condition y(-2) = e to find the specific solution, which is [tex]y = e^{-2/x},[/tex] corresponding to answer option B.
Explanation:
To solve the given separable differential equation [tex]dy/dx = 2y/x^2[/tex], we first separate the variables:
[tex]\( \frac{dy}{y} = \frac{2}{x^2}dx \)[/tex]
Next, we integrate both sides:
[tex]\( \int \frac{1}{y}dy = \int 2x^{-2}dx \)[/tex]
Which gives:
[tex]ln|y| = -2/x + C[/tex]
Now, we apply the initial condition y(-2) = e to find C:
ln(e) = [tex]-2/(-2) + C \Rightarrow 1 = 1 + C \Rightarrow C = 0[/tex]
Thus, the specific solution is:
[tex]y = e^{-2/x}[/tex]
So, the correct answer is option B, y equals e raised to the negative 2 over x power.
PLLLLZ I WILL GIVE BRAINIEST ANSWER AND 72 PTS
A 500 mg known substance in fossils decays at a rate of 10% per year. Scientists find a fossil with 295.25 mg of the known substance. How old is the fossil?
Answer:
x ≈ 5 years
Step-by-step explanation:
Given amount = A = 500 mg
Decay rate = r = 10% per year
Remaining amount = L = 295.25 mg
The formula to calculate remaining amount after x years decay =
L = A((100-r)/100)^x
By putting values in this formula, we get
295.25 = 500 ((100-10)/10)^x
295.25 = 500 (0.90)^x
295.25/500 = 0.90^x
0.5905 = 0.90^x
0.90^x =0.5905
taking log on both sides
ln(0.90^x) =ln(0.5905)
x*ln(0.90) =ln(0.5905) using property of log
x = ln(0.5905)/ln(0.90)
x = 4.9984
x ≈ 5 years
An example of dependent events is drawing a blue marble out of one jar and then drawing a
blue marble out of the another jar.
red marble out of the same jar, after replacing the first marble.
red marble out of the same jar, without replacing the first marble.
red marble out of another jar.
An example of dependent events is drawing a red marble from the same jar without replacing the first marble, which changes the probabilities for the second draw. This is known as sampling without replacement, which contrasts with independent events where the item is replaced and the probabilities remain unchanged.
An example of dependent events is drawing a red marble out of the same jar, without replacing the first marble. This creates a dependency because removing the first marble affects the outcome chances for the subsequent draw. If the jar starts with four blue and three white marbles and you draw one blue marble and do not replace it, the jar then contains three blue and three white marbles. Therefore, the probability of drawing another blue marble has changed from the original draw.
Dependent events are associated with sampling without replacement, which means once an item is drawn, it is not put back into the population from which it was taken, altering the probabilities of subsequent draws. In contrast, independent events, such as drawing and replacing a marble, do not affect the subsequent probabilities, since the composition of the jar remains unchanged with each draw.
Jakes family was on vacation for two weeks and five days. Seth's family was on vacation for three weeks and two days.How many fewer days was Jake on vacation than Seth.
Answer:
j:19 days
s:23 days
23-19=4
4 days
Step-by-step explanation:
A park is shaped like a rectangle with a length 5 times its width (w). What is a simplified expression for the distance between opposite corners of the park?
Answer:
w√26
Step-by-step explanation:
A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. The width here is w and the length is 5w or 5 times the width. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = w and b = 5w. Substitute these values and simplify using a square root operation.
w² + (5w)² = c²
w² + 25w² = c²
26w² = c²
√26w² = c
w√26 = c
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. How many banana splits were sold?
Answer:
The number of banana splits sold was [tex]28[/tex]
Step-by-step explanation:
Let
x-----> the number of sundaes sold
y-----> the number of banana splits sold
we know that
[tex]2x+3y=156[/tex] -----> equation A
[tex]x=y+8[/tex] ----> equation B
substitute equation B in equation A and solve for y
[tex]2(y+8)+3y=156[/tex]
[tex]2y+16+3y=156[/tex]
[tex]5y=156-16[/tex]
[tex]5y=140[/tex]
[tex]y=28[/tex]
A chef cooked 5 kilograms of mashed potatoes for a dinner party. If the guests only ate 4/12 of the amount he cooked, how much did they eat?
Answer:
[tex]1\frac{2}{3}\ kg[/tex]
Step-by-step explanation:
we know that
To find out how much the guests ate, multiply the total amount of kg of mashed potatoes by the 4/12 fraction
so
[tex]5(\frac{4}{12})=\frac{20}{12}\ kg[/tex]
convert to mixed number
[tex]\frac{20}{12}=\frac{12}{12}+\frac{8}{12}=1\frac{8}{12}\ kg[/tex]
simplify
[tex]1\frac{8}{12}=1\frac{2}{3}\ kg[/tex]
The guests consumed 1.67 kilograms of the 5 kilograms of mashed potatoes that the chef had made.
Explanation:To solve this problem, we need to multiply the total amount of mashed potatoes made by the fraction that the guests consumed.
Given that the chef cooked 5 kilograms of mashed potatoes and the guests ate 4/12 (which simplifies down to 1/3) of this amount, we multiply these two together.
So, the calculation would be 5 × 1/3 = 1.67 kilograms.
Therefore, the guests ate 1.67 kilograms of mashed potatoes.
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Stephen purchases a square-shaped canvas to use for a painting. The diagonal of the square is 10 inches longer than the length of its sides. Stephen uses the Pythagorean theorem to create the equation x2 + x2 = (x + 10)2 to determine the side length, x, of the canvas. The side length of the canvas is best found by because the equation is . Solving the equation produces two measurements, and must be discarded for being unreasonable.
The side length of the canvas is best found by using the quadratic formula
because the equation is prime. Solving the equation produces two
approximate measurements, and one must be discarded for being
unreasonable.
I took the test and this was correct.
Which of the following describes graphing y > Ixl +4?
Translate y = lxl down 4 units and shade inside the V.
Translate y = |xl up 4 units and shade inside the V.
Translate y = 1xl left 4 units and shade inside the V.
Translate y = Ixl right 4 units and shade inside the V.
Answer:
B
Step-by-step explanation:
Since the d value is changed, we're talking about a vertical transformation. Since d > 0, the graph is shifted up.
Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth term is 54?
now, let's recall that a geometric sequence is one that uses some "r" common ratio to get the next term, by simply multiplying the current term by it.
[tex]\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&\underline{\qquad }\\&\\ a_2&6\\&\\ a_3&\underline{6(r)}\\&\\ a_4&6(r)(r)\\&\\ &54\\ \cline{1-2} \end{array}\qquad \implies \begin{array}{llll} 54=6r^2\implies \cfrac{54}{6}=r^2\implies 9=r^2\\\\ \sqrt{9}=r\implies 3=r \end{array} \\\\[-0.35em] ~\dotfill\\\\ a_1=6\div 3\implies a_1=2~\hfill a_3=6(3)\implies a_3=18[/tex]
and of course, the next term or a₅ = 54(3) --> a₅ = 162.
The first five terms are 2, 6, 18, 54, 162
Given,
The second term is 6.
The fourth term is 54.
We need to find the first five terms of a geometric sequence.
What is a geometric sequence?A sequence where each term after the first is found by multiplying the previous one with a common ratio.
The sequence is given by:
a, ar, ar^2, ar^3, ar^4, ar^5,...
The nth term is given by:
a_n = ar^(n-1)
We have,
Second term = 6
a_2 = ar^(2-1)
6 = ar^1
6 = ar
a = 6/r _____(1)
Fourth term = 54
a_4 = ar^(4-1)
54 = ar^3
a = 54/r^3 ______(2)
From (1) and (2)
6/r = 54/r^3
r^3/r = 54/6
r^2 = 9
r = 3
Putting in (1)
a = 6/r
a = 6/3
a = 2
We have,
a = 2 and r = 3
Find the first five terms of a geometric sequence.
It is given by:
a, ar, ar^2, ar^3, ar^4
2, 2x3, 2x9, 2x27, 2x81
2, 6, 18, 54, 162
The first five terms are 2, 6, 18, 54, 162
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Beer bottles are filled so that they contain an average of 335 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. [You may find it useful to reference the z table.] a. What is the probability that a randomly selected bottle will have less than 332 ml of beer? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 332 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Answer:
A) 0.3336; B) 0.8531
Step-by-step explanation:
For part A,
We use the z-score formula for an individual score:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our X value is 332, our mean, μ, is 335, and our standard deviation, σ, is 7:
z = (332-335)/7 = -3/7 ≈ -0.43
Using a z table, we see that the area under the curve less than this (the probability that X is less than this value) is 0.3336.
For part B,
We use the z-score formula for the mean of a sample:
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our X-bar value is 332, our mean, μ, is 335, our standard deviation, σ, is 7, and our sample size, n, is 6:
z = (332-335)/(7÷√6) = 3/2.8577 ≈ 1.05
Using a z table, we see that the are under the curve to the left of this, or the probability less than this, is 0.8531.
Using the Z-score formula, the probability of a single beer bottle having less than 332 ml is 33.36%, and the probability of a 6-pack having a mean amount less than 332 ml is 14.69%.
Explanation:To solve this problem, we can use the Z-score. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution. The formula for the Z-score is (X-µ)/σ, where X represents the value of interest, µ represents the population mean, and σ represents the standard deviation.
So, let's calculate the Z-score:
a) We use the formula Z = (X-µ)/σ = (332-335)/7 = -0.43 (rounded to 2 decimal places). To find the probability that a bottle of beer contains less than 332 ml, we refer to the standard Z-table, which gives us approximately 0.3336. Therefore, there is a 33.36% chance a randomly selected beer bottle contains less than 332 ml of beer.
b) For a 6-pack, the standard deviation decreases because it is now σ/√n (with n being the size of the sample, in this case, 6). The new standard deviation is 7/√6 = 2.86 ml (rounded to 2 decimals). Using the same Z-score formula, Z= (332-335)/2.86= -1.05, and referring to the Z-table, the probability is approximately 0.1469. This means there's about a 14.69% chance that a randomly selected 6-pack will have a mean amount of less than 332 ml.
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(75 points to correct answer!) Use the diagram to solve for segments SW and WQ. Show your work and/or explain how you determined the answer.
Show your work, please!
Answer:
Check out lesson 3.09, It'll help ;)