Answer:
c = 6.25
Step-by-step explanation:
We are given the following piecewise function:
[tex]\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right[/tex]
Continuous function:
A function f(x) is continuous, at a point a, if:
[tex]\lim_{x \to a} f(x)[/tex] exists and [tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
Piece-wise function, so we have to verify if the limit exists.
The function changes at x = 3. So we verify at a = 3.
It will exist if:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
To the left:
Less than 3.
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6[/tex]
To the right:
Greater than 3.
[tex]\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c[/tex]
f continuous:
They have to be equal:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
[tex]9c + 6 = 81 - 3c[/tex]
[tex]12c = 75[/tex]
[tex]c = \frac{75}{12}[/tex]
[tex]c = 6.25[/tex]
Please answer this correctly
Answer:
7/8 chance
Step-by-step explanation:
There are 7 numbers that are either even or greater than 2: 2, 3, 4, 5, 6, 7, and 8. There is a 7/8 chance choosing either of those.
Answer:
7/8
Step-by-step explanation:
there are 6 numbers that are greater than 2: 3,4,5,6,7,8
there are 4 even numbers: 2,4,6,8
Actividad 1.1
Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que
la función
definida a continuación sea diferenciable en t = 2, luego construya su gráfica.
at +b, sit < 2
f(t) = {2t2 – 1, si 2 st
1
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单击上面的链接，回答以下问题，然后，我将回答您的问题。 （如果需要帮助，请回复此评论。）
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उपरोक्त लिंक पर क्लिक करें, निम्नलिखित प्रश्न का उत्तर दें, फिर, मैं आपके प्रश्न का उत्तर दूंगा। (यदि आप मदद की जरूरत है, यह टिप्पणी करने के लिए उत्तर दें।)
uparokt link par klik karen, nimnalikhit prashn ka uttar den, phir, main aapake prashn ka uttar doonga. (yadi aap madad kee jaroorat hai, yah tippanee karane ke lie uttar den.)
Need Assistance With This Problem
Answer:
not sure how to really answer this question.
Answer:
4.56, 4.65, 5.46, 5.64, 6.45, 6.54
Step-by-step explanation:
First we have to compare the first digits in each number as less is this digit as less is the number. So the least off all are
4.56 and 4.65
which of these two numbers is least ? Now we have to look to the 2-nd digits of these numbers:
they are 5 and 6 . 5<6 so 4.56<4.65
Lets select next numbers whicj first digit is 5. They are:
5.46 and 5.64. However the second digit of the number 5.64 -6 is bigger than the second digit of number 5.46 -4. That is why 5.46<5.64
Similarly 6.45< 6.54
Determine whether the sequence converges or diverges. If it converges, find the limit (if an answer does not exist, enter DNE.)
{lnn/ln3}
limn→[infinity]{lnn/ln3n}=________
Answer:
The sequence converges. The limit DNE.
Step-by-step explanation:
Find the limit of n as n tends to infinity (in other words, positive infinity) in {Ln(n)/ Ln(3n)}
Positive infinity values for n start from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,...,infinity
So I solved for values of n, up to n=20. All values are rounded up to 3 decimal places; for better accuracy.
When n is 1, the function is equal to 0.000
When n is 2, the function is = 0.387
When n is 3, the function = 0.500
When n is 4, the function = 0.558
When n is 5, the function = 0.594
When n is 6, the function = 0.619
When n is 7, the function = 0.639
When n is 8, the function = 0.654
When n is 9, the function = 0.667
When n is 10, the function = 0.677
When n is 11, the function = 0.686
When n is 12, the function = 0.693
When n is 13, the function = 0.700
When n is 14, the function = 0.706
When n is 15, the function = 0.711
When n is 16, the function = 0.716
When n is 17, the function = 0.721
When n is 18, the function = 0.725
When n is 19, the function = 0.728
When n is 20, the function = 0.732
We say there is a convergence because the space between the values of n gets smaller and smaller as n tends to infinity and there is no definite limit. Limit DNE.
please assist me with the power of i(imaginary)
Let's raise i to various powers starting with 0,1,2,3...
i^0 = 1
i^1 = i
i^2 = ( sqrt(-1) )^2 = -1
i^3 = i^2*i = -1*i = -i
i^4 = (i^2)^2 = (-1)^2 = 1
i^5 = i^4*i = 1*i = i
i^6 = i^5*i = i*i = i^2 = -1
We see that the pattern repeats itself after 4 iterations. The four items to memorize are
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.
To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.
This means i^25 = i^1 = i
Likewise,
i^5689 = i^1 = i
because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely
Simplify.
In e =
In e 2x=
In 1 =
Answer:
ln e = 1
ln e 2x = 2x
ln 1 = 0
Step-by-step explanation:
ln e
ln(2.718282) = 1
In e 2x
ln(2.718282)(2)x = 2x
ln 1 = 0
Which of the following is the graph of f(x)= |x| reflected on the x-axis, translated 3units left, 4 units up, and dilated by a factor of 4?
Answer:
Step-by-step explanation:
Reflecting on the x-axis is multiplying the formula by a -1. That is, the resulting form is pointing up. When translated to the left 3 units, the tip of the graph is at the point (-3,0). Then when shifted 4 units up the tip is at (-3,4). Dilated by a factor of 4 will affect the values in x, but not the values in y. So the tip remains at the point (-3,4) which corresponds to the second graph
The second graph is the right one.
A boat, which moves at 13 miles per hour in water without a current, goes 80 miles upstream and 80 miles back again in 13 hours. Find the speed of the current to the nearest tenth.
Answer:
Speed of current is 3 miles per hour.
Step-by-step explanation:
Speed of boat without current, u = 13 miles/hr
Let speed of current = v miles/hr
Speed upstream = (13 - v) miles/hr
Speed downstream = (13 + v) miles/hr
Distance traveled upstream, [tex]D_1[/tex] = 80 miles
Distance traveled downstream, [tex]D_2[/tex] = 80 miles
Total time taken, T ([tex]T_1+T_2[/tex]) = 13 hours
Formula for Total Time taken:
[tex]Time= \dfrac{Distance}{Speed}[/tex]
Time taken in Upstream:
[tex]T_1 = \dfrac{80}{13-v}\ hours[/tex]
Time taken in Downstream:
[tex]T_2 = \dfrac{80}{13+v}\ hours[/tex]
[tex]T = T_1+T_2 = 13\ hours\\\Rightarrow 13 = \dfrac{80}{13-v}+\dfrac{80}{13+v}\\\Rightarrow 13 = 80(\dfrac{13+v+13-v}{13^2-v^2})\\\Rightarrow 13^2-v^2 = \dfrac{80(26)}{13}\\\Rightarrow 169-v^2 = 80\times 2\\\Rightarrow v^2 = 169-160 = 9\\\Rightarrow v = 3\ miles/hr[/tex]
So, speed of current is 3 miles/hr
I hat is the length of leg s in the right triangle shown
Answer:
s=5
Step-by-step explanation:
This triangle is right and with two equal sides since it has two congruent angle so we will use the pythagorian theorem:
s²+s² = (5[tex]\sqrt{2}[/tex])²2s² = 25*2 divide both sides by 2s² = 25s = 5The straight line L has equation y = 1/2x+7 The straight line M is parallel to L and passes through the point (0, 3). Write down an equation for the line M.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes
line M crosses the y- axis at (0, 3) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M
Use PQR below to answer the question that follows:
Answer:
Angle P is congruent to itself due to the reflexive property.
Explanation:
Angle P must be congruent to angle S through corresponding angle theory.
Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.
Answer:
Angle P is congruent to itself due to the reflexive property.
Step-by-step explanation:
I need help on question 8.
Answer:
50.18°
Step-by-step explanation:
∠BAD = ∠BAC +∠CAD
102° = (8x+17)° +(9x+11)° . . . . . substitute given values
102 = 17x +28 . . . . . . . . . . simplify, divide by degrees
x = (102 -28)/17 = 74/17 . . . . . solve for x
Then the angle of interest is ...
∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°
∠CAD ≈ 50.18°
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.
Answer:
Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.
Test statistic t=2.238>tc=1.708.
The null hypothesis is rejected.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=370.69.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
The critical value for a right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.
As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).
What are the intercepts?
Answer:
A, C, E, and F.
Step-by-step explanation:
To find the y-intercept, simply plug in 0 for x since y-intercepts are (0,y):
[tex]f(0)=\frac{(0-3)(0+4)(0-1)}{(0+2)(0-12)} =\frac{(-3)(4)(-1)}{(2)(-12)} =\frac{12}{2(-12)}=-1/2[/tex]
[tex](0,-1/2)[/tex]
To find the x-intercepts, plug in 0 for y since x-intercepts have the format (x,0):
[tex]0=\frac{(x-3)(x+4)(x-1)}{(x+2)(x-12)}[/tex]
[tex]0=(x-3)(x+4)(x-1)[/tex]
[tex]x=3, -4, 1[/tex]
[tex](-4,0), (1,0), (3,0)[/tex]
The correct choices are:
A, C, E, and F.
Which expression is the simplest form of -(x + 5) - 3(x + 2)?
Answer:
-4x -11
Step-by-step explanation:
-(x + 5) - 3(x + 2)
Distribute
-x -5 -3x -6
Combine like terms
-x-3x -5-6
-4x -11
Answer:
[tex] = - (4x + 11)[/tex]
Step-by-step explanation:
[tex]-(x + 5) - 3(x + 2) \\ -x - 5 - 3x - 6 \\ -x - 3x -5 - 6 \\ - 4x - 11 \\ = -(4x + 11)[/tex]
The life in hours of a battery is known to be normally distributed, with a standard deviation of 1.25 hours. A random sample of 10 batteries has a mean life x = 40.5 hours.
a) Is there evidence to support the claim that battery life exceeds 40 hours? Use
α = 0.05.
b) What is the P-value for this test?
Answer:
a) Test statistic
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
b)
p- value = 0.8962
Step-by-step explanation:
Step(i):-
Given sample size 'n' =10
Mean of the sample x⁻ = 40.5 hours
Mean of of the Population μ = 40 hours
Standard deviation of the Population = 1.25 hours
Step(ii):-
Null Hypothesis:H₀: μ = 40 hours
Alternative Hypothesis :H₁ : μ < 40 hours
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]
Z = 1.265
Level of significance = 0.05
Z₀.₀₅ = 1.96
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
Step(iii):-
P - value
P( Z < 1.265) = 0.5 + A( 1.265)
= 0.5 + 0.3962
= 0.8962
P( Z < 1.265) = 0.8962
i ) p- value = 0.8962 > 0.05
Accept H₀
There is no significant
The battery life is not exceeds 40 hours
Please answer this correctly
Answer:
50%
Step-by-step explanation:
The numbers that are not odd are 2, 4, and 6 on a dice.
3 numbers out of 6.
3/6 = 1/2 = 0.5
P(not odd)= 50%
Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm. What hypotheses should be tested, and why?The appropriate hypotheses areH0: σ0.05 mmversusHa: σ0.05 mm.With this formulation, the burden of proof is on the data to show that the requirementbeen met.In this context, what are the type I and type II errors?In this context, the type I error occurs if wea shipment that should have been . A type II error occurs if we a shipment that should have been.Need Help? Read It Talk to a Tutor
Answer:
Null and alternative hypothesis:
[tex]H_0: \mu=0.05\\\\H_a:\mu< 0.05[/tex]
The alternative hypothesis is the one that needs evidence to be supported, while the null hypothesis is the one that can be nullified (reject).
Only if there is enough evidence that thickness is less than 0.05 the null hypothesis will be rejected and the alternative hypothesis claim supported.
A Type I error happens when a true null hypothesis is rejected. In this case we will be purchase a order that is not fulfilling the thickness required.
A Type II error happens when a false null hypothesis is failed to be rejected. In this case, the order has a thickness significantly smaller than 0.05, but the sample gives no enough evidence and the order will not be purchased.
Step-by-step explanation:
A hypothesis test to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm will have the following hypothesis:
[tex]H_0: \mu=0.05\\\\H_a:\mu< 0.05[/tex]
The alternative hypothesis Ha will state that the true mean is significantly smaller than 0.05, while the null hypothesis H0 will state the opposite: that the true mean is not significantly smaller than 0.05.
The alternative hypothesis is the one that needs evidence to be supported, while the null hypothesis is the one that can be nullified (reject).
Only if there is enough evidence that thickness is less than 0.05 the null hypothesis will be rejected and the alternative hypothesis claim supported.
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 186 pounds and a standard deviation of 29 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,417 pounds or 17 persons." What is the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds?
Answer:
the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
Step-by-step explanation:
The summary of the given statistical data set are:
Sample Mean = 186
Standard deviation = 29
Maximum capacity 3,417 pounds or 17 persons.
sample size = 17
population mean =3417
The objective is to determine the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds
In order to do that;
Let assume X to be the random variable that follows the normal distribution;
where;
Mean [tex]\mu[/tex] = 186 × 17 = 3162
Standard deviation = [tex]29* \sqrt{17}[/tex]
Standard deviation = 119.57
[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]
[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]
[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]
[tex]P(X>3417) = P(Z>2.133)[/tex]
[tex]P(X>3417) =1- 0.9834[/tex]
[tex]P(X>3417) =0.0166[/tex]
Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
convert 3days to minutes
Answer:
4320 minutes
Step-by-step explanation:
Recall,
1 day ---> 24 hours
but each hour has 60 minutes, hence 1 day can also be expressed:
1 day -----> 24 x 60 = 1440 minutes
3 days -----> 1440 min/day x 3 days = 4320 minutes
Answer: 4,320 minutes
Step-by-step explanation: 1 day = 1440 days. 1440 * 3 = 4,320 minutes
Solve the problem. The scores on a certain test are normally distributed with a mean score of 60 and a standard deviation of 5. What is the probability that a sample of 90 students will have a mean score of at least 60.527? Write your answer as a decimal rounded to 4 places.
Answer:
15.87%
Step-by-step explanation:
We have to calculate the value of z:
z = (x - m) / (sd / n ^ (1/2))
where x is the value to evaluate, m is the mean, n is the sample size and sd is the standard deviation, we replace:
p (x <60,527) = z = (x - m) / (sd / n ^ (1/2))
p (x <60,527) = z = (60,527 - 60) / (5/90 ^ (1/2))
z = 1
if we look in the attached table, for z = 1 it is 0.8413
p (x> 60,527) = 1 - 0.8413
p (x> 60,527) = 0.1587
Therefore the probability is 15.87%
The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 3.9 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?H0 : µ = 40
H1 : µ > 401. Compute the value of the test statistic. 2. What is your decision regarding H0?
Answer:
1. Test statistic t=1.581.
2. The null hypothesis H0 failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
NOTE: if the null hypothesis is µ = 40, there is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40 (test statistic t=3.161).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 41.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=41\\\\H_a:\mu> 41[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-41}{0.633}=\dfrac{1}{0.633}=1.581[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=1.581, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.581)=0.061[/tex]
As the P-value (0.061) is bigger than the significance level (0.025), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
For µ = 40:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 40.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu> 40[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-40}{0.633}=\dfrac{2}{0.633}=3.161[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=3.161, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.161)=0.002[/tex]
As the P-value (0.002) is smaller than the significance level (0.025), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40.
the figure below shows a square ABCD and an equilateral triangle DPC:
Answer: c) SAS Postulate
Step-by-step explanation:
DP = PC Sides are congruent
∠ADP ≡ ∠BCP Angles are congruent (angles are between the sides)
AD = BC Sides are congruent
To finish the proof, we can state that ΔADP ≡ ΔBCP by the Side-Angle-Side (SAS) Postulate
The perimeter of a rectangular city park is 1,428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.
Answer:
Length = 502 ft
Width = 212 ft
Step-by-step explanation:
Recall the formula for the perimeter of a rectangle of length "L" and width "W":
Perimeter = 2 L + 2 W = 1428 ft
Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:
L = 2 W +78
so, 2 W = L -7 8
and now replace "2 W" with it equivalent "L - 78" in the first perimeter equation and solve for "L":
2 L + L - 78 = 1428
3 L = 1428 + 78
3 L = 1506
L = 1506/3
L = 502 ft
Then the width W can be obtained via:
2 W = L - 78
2 w = 502 -78
2 W = 424
w = 212 ft
If A and Bare dependent events, which of these conditions must be true?
Answer:
Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.
Also, Two events are said to be independent if the outcome or occurrence of the first does not affects the outcome or occurrence of the second so that the probability is not changed.
Read more on Brainly.com
Answer:E. P(B\A)≠P(B)
Step-by-step explanation:
Find all the missing side lengths for the following triangles.
Answer:
Step-by-step explanation:
A) u = 4 v = 4/(sqrt)3
B) b = 5 c = 10
C) b = 2(sqrt)2 a = 4
D) m and n are both 7(sqrt)2/2
The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.
Here are the missing side lengths for the following triangles:
Triangle 1:
The missing side length is 15.
The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.
Triangle 2:
The missing side length is 12.
The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.
Triangle 3:
The missing side length is 8.
We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
100 = 36 +[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 64
x = 8
Therefore, the missing side length is 8.
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Identify an equation in point slope form for the line parallel to y=1/2x-7 that passes through (-3,-2)
Answer:
Step-by-step explanation:
The point slope form of a straight line is expressed as
y - y1 = m(x - x1)
Where
m represents slope of the line
y1 represents the initial value of y
x1 represents the initial value of x
If two lines are parallel, it means that they have the same slope. From the equation of the given line, slope = 1/2
Therefore,
m = 1/2
x1 = - 3
y1 = - 2
Substituting into the point slope equation, it becomes
y - - 2 = 1/2(x - - 3)
y + 2 = 1/2(x + 3)
The equation is
y + 2 = 1/2(x + 3)
Answer: The point slope form of a straight line is expressed as y - y1 = m(x - x1)Wherem represents slope of the liney1 represents the initial value of yx1 represents the initial value of xIf two lines are parallel, it means that they have the same slope. From the equation of the given line, slope = 1/2Therefore,m = 1/2x1 = - 3y1 = - 2Substituting into the point slope equation, it becomesy - - 2 = 1/2(x - - 3)y + 2 = 1/2(x + 3)The equation is y + 2 = 1/2(x + 3)
Step-by-step explanation:
You have different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the different video games in nothing different ways.
Answer:
See Explanation below
Step-by-step explanation:
This question has missing details because the number of video games is not stated;
However, you'll arrive at your answer if you follow the steps I'll highlight;
The question requests for the number of arrangement; That means we're dealing with permutation
Let's assume the number of video games is n;
To arrange n games, we make use of the following permutation formula;
[tex]^nP_n = \frac{n!}{(n-n)!}[/tex]
Simplify the denominator
[tex]^nP_n = \frac{n!}{0!}[/tex]
0! = 1; So, we have
[tex]^nP_n = \frac{n!}{1}[/tex]
[tex]^nP_n = n![/tex]
Now, let's assume there are 3 video games;
This means that n = 3
[tex]^3P_3 = 3![/tex]
[tex]^3P_3 = 3 * 2 * 1[/tex]
[tex]^3P_3 = 6\ ways[/tex]
So, whatever the number of video games is; all you have to do is; substitute this value for n;
A U.S. dime has a diameter of about 18 millimeters. What is the area of one side of a dime to the nearest square millimeter? Use 3.14 as an approximation for pi. The area of one side of a U.S. dime is approximately _____ square millimeters.
Area of one side of a U.S. dime is approximately 254 square millimeters.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that U.S. dime has a diameter of about 18 millimeters.
We need to find the area of one side of a dime to the nearest square millimeter.
Diameter=18 millimeters
Diameter is two times of radius
D=2R
18=2R
Divide both sides by 2
Radius is 9 millimeters.
Area of dime=πr²
=3.14×(9)²
=3.14×81
=254 square millimeters.
Hence, area of one side of a U.S. dime is approximately 254 square millimeters.
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You have a choice of receiving a wage of $39,000 per year,$2630 per month,$665 per week and 52 weeks of work per year
Answer:
$39,000
Step-by-step explanation:
This is the best answer because you recieve the most money. 2630*12 is 31560 dollars, and 665*52= $34580.