What are the solution(s) to the quadratic equation 50 - x2 = 0?
x = +2/5
x = +63
x = 15/2
no real solution

Answer:

17 feet

Step-by-step explanation:

Length of the diagonal=50 feet

Let the shorter part of the sidewalk =x

Since the longer part of the sidewalk is twice the shorter length,

Length of the longer part of the sidewalk =2x

First, we determine the value of x.

Using Pythagoras Theorem and noting that the diagonal is the hypotenuse.

[tex]50^2=(2x)^2+x^2\\5x^2=2500\\$Divide both sides by 5\\x^2=500\\x=\sqrt{500}=10\sqrt{5} \:ft[/tex]

The length of the shorter side =[tex]10\sqrt{5} \:ft[/tex]

The length of the longer side =[tex]20\sqrt{5} \:ft[/tex]

Total Distance =[tex]10\sqrt{5}+ 20\sqrt{5}=67 \:feet[/tex]

Difference in Distance

67-50=17 feet

The children are saving 17 feet by cutting the lawn diagonally.

Answer:

Degree 3

Step-by-step explanation:

Highest valued exponent of x variable is 3

Answer:

81+90

Step-by-step explanation:

9^2 + 2[(5+2)^2 -4]

PEMDAS says parentheses first , working inside out

9^2 + 2[(7)^2 -4]

PEMDAS says parentheses first, doe the exponents inside the parentheses

9^2 + 2[49 -4]

Then the subtraction inside the parentheses

9^2 + 2[45]

Then Exponents

81 +2[45]

Then Multiplication

81+90

Finally add

Answer:

A

Step-by-step explanation:

9² + 2[(5+2)² - 4]

81 + 2[(7)² - 4]

81 + 2[49 - 4]

81 + 2(45)

81 + 90

171

124

Answer:

infinite solutions

Step-by-step explanation:

2 ( n-1 ) + 4n= 2( 3n-1 )

Distribute

2n -2 +4n = 6n -2

Combine like terms

6n -2 = 6n -2

Subtract 6n from each side

6n-2-6n = 6n-2-6n

-2 = -2

This is always true so there are infinite solutions

Final answer:

With a p-value of 0.1071 exceeding the significance level of 0.05, we do not reject the null hypothesis and conclude there is insufficient evidence to support the union's claim about child-care benefits in manufacturing firms.

Explanation:

The reported p-value of 0.1071 is greater than the significance level alpha (0.05). Based on this result, the appropriate statistical decision would be to do not reject the null hypothesis.

Therefore, at the 5 percent significance level, there is insufficient evidence to support the claim made by the union that more than 85% of firms in the manufacturing sector do not offer child-care benefits to their workers.

The higher p-value suggests that the data collected from the random sample of 330 manufacturing firms does not provide strong enough evidence to refute the possibility that the percentage of firms not offering child-care benefits is at or below 85%.

Answer:

divide the numbers that are on the paper

Step-by-step explanation:

Answer:

divide

Step-by-step explanation:

hope ur having a good day :)

Answer:

Factor the denominators of each expression to find the LCD.

Rename each expression, if needed, by multiplying by a form of one to get the LCD.

Add the numerators, keeping the denominators the same.

If possible, simplify by factoring the numerator and dividing out common factors from both the numerator and denominator.

Step-by-step explanation:

If the assignment your working on is Explaining How to Add Rational Expressions, this is correct according to edg...  Good Luck!!!

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by stem explanation to the question

Answer:  117 centimeters

Step-by-step explanation:

Answer:

117 cm³

Step-by-step explanation:

To calculate the volume of a Rectangular Prism, we must use the formula:

l×w×h=V.

In this case, l= 13, w= 3, and h= 3.

When these values are substituted in, we get:

13×3×3= 117 cm³

Answer:

  [tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]

Step-by-step explanation:

A radical represents a fractional power. For example, ...

  [tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]

This makes sense in view of the rules of exponents for multiplication.

  [tex]a^ba^c=a^{b+c}\\\\a^{\frac{1}{2}}a^{\frac{1}{2}}=a^{\frac{1}{2}+\frac{1}{2}}=a\\\\(\sqrt{a})(\sqrt{a})=a[/tex]

So, a root other than a square root can be similarly represented by a fractional exponent.

____

The power of a radical and the radical of a power are the same thing. That is, it doesn't matter whether the power is outside or inside the radical.

  [tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}=(\sqrt[n]{x})^m[/tex]

Answer:

35

Step-by-step explanation:

On subtracting 28 from 63 by adding up we get 35.

To subtract by adding up is special method to find the difference between two numbers. For 63-28, we can do it in the following steps:

We start by using the smaller number, here 28. And add a number to 28 such that it we receive a number that is easy to use further. So, here we can add 2 to it which gives us:

[tex]28 + 2= 30[/tex]

Now we take 30 and we can add another 30 to it. This gives us:

[tex]30+30 = 60[/tex]

Now the goal is to add a number such that the sum of the number and 60 make 63. So, we add 3 to 60 which gives us:

[tex]60+3 = 63[/tex]

Now we need to take the second number we have added in each of the steps (2, 30 and 3) and add them. The sum of these numbers will give us the difference between 63 and 28. Thus we can write it as:

[tex]63-28 = 2+30+3\\\\63-28 = 35[/tex]

Thus on subtracting 28 from 63 by adding up method we get the answer as 35.

Answer:

7.8《 X《 8.2

Step-by-step explanation:

Let X be the weight of the product

8 - 0.2《 X《 8 + 0.2

7.8《 X《 8.2

Answer:

7.8《 X《 8.2

Step-by-step explanation:

Let X be the weight of the product

8 - 0.2《 X《 8 + 0.2

7.8《 X《 8.2p

EndFraction

StartFraction 24 Over 121 EndFraction

StartFraction 6 Over 11 EndFraction

StartFraction 10 Over 11 EndFraction

Answer:

StartFraction 24 Over 121 EndFraction

Step-by-step explanation:

Answer:

that answer is D

Step-by-step explanation:

I used pythagreum theurum a^2+b^2=c^2

then i divided square root 260 by 4 the largest perfect square factor which gives us 2 square root 65 because 4 is a perfect square that equal 2

Answer:

Step-by-step explanation:

Answer:

79.85% probability that at least 5 of them use their smartphones in meetings or classes.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they use their smartphone during meetings or classes, or they do not. The probability of an adult using their smartphone in these situations are independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Assume that when adults with smartphones are randomly​ selected, 58​% use them in meetings or classes.

This means that [tex]p = 0.58[/tex]

10 adults selected.

This means that [tex]n = 10[/tex]

Find the probability that at least 5 of them use their smartphones in meetings or classes.

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{10,5}.(0.58)^{5}.(0.42)^{5} = 0.2162[/tex]

[tex]P(X = 6) = C_{10,6}.(0.58)^{6}.(0.42)^{4} = 0.2488[/tex]

[tex]P(X = 7) = C_{10,7}.(0.58)^{7}.(0.42)^{3} = 0.1963[/tex]

[tex]P(X = 8) = C_{10,8}.(0.58)^{8}.(0.42)^{2} = 0.1017[/tex]

[tex]P(X = 9) = C_{10,9}.(0.58)^{9}.(0.42)^{1} = 0.0312[/tex]

[tex]P(X = 10) = C_{10,10}.(0.58)^{10}.(0.42)^{0} = 0.0043[/tex]

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2162 + 0.2488 + 0.1963 + 0.1017 + 0.0312 + 0.0043 = 0.7985[/tex]

79.85% probability that at least 5 of them use their smartphones in meetings or classes.

Answer:

π³/1296

Step-by-step explanation:

∫ [ (asin x)² dx / √(4 − 4x²) ]

Factoring the denominator:

∫ [ (asin x)² dx / √(4 (1 − x²)) ]

∫ [ (asin x)² dx / (2√(1 − x²)) ]

½ ∫ [ (asin x)² dx / √(1 − x²) ]

If u = asin x, then du = dx / √(1 − x²).

½ ∫ u² du

⅙ u³ + C

Substitute back:

⅙ (asin x)³ + C

Evaluate between x=0 and x=½.

⅙ (asin ½)³ − ⅙ (asin 0)³

⅙ (π/6)³ − ⅙ (0)³

π³/1296

Answer:

[tex]\dfrac{\pi^3}{1296}[/tex]

Step-by-step explanation:

Given integral:

[tex]\displaystyle \int^{1/2}_0 \dfrac{\arcsin^2 (x)}{\sqrt{4-4x^2}}\;dx[/tex]

To evaluate the integral, begin by simplifying the denominator of integrand:

[tex]\begin{aligned}\sqrt{4-4x^2}&=\sqrt{4(1-x^2)} \\ &=\sqrt{4}\sqrt{1-x^2}\\&=2\sqrt{1-x^2}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle \int^{1/2}_0 \dfrac{\arcsin^2 (x)}{2\sqrt{1-x^2}}\;dx[/tex]

Now, evaluate the integral using the method of substitution.

[tex]\textsf{Let $u = \arcsin(x)$}[/tex]

Find du/dx using the common derivative of arcsin(x):

[tex]\boxed{\begin{array}{c}\underline{\textsf{Derivative of $\arcsin(x)$}}\\\\\dfrac{\text{d}}{\text{d}x}\left(\arcsin(x)\right)=\dfrac{1}{\sqrt{1-x^2}}\end{array}}[/tex]

Therefore:

[tex]\dfrac{d}{dx}(u)=\dfrac{d}{dx}\left(\arcsin(x)\right) \\\\\\\dfrac{du}{dx}=\dfrac{1}{\sqrt{1-x^2}}[/tex]

Rearrange to isolate dx:

[tex]dx=\sqrt{1-x^2}\;du[/tex]

Calculate the new limits:

[tex]x=0 \implies u = \arcsin(0)=0[/tex]

[tex]x=\dfrac{1}{2} \implies u = \arcsin\left(\dfrac{1}{2}\right)=\dfrac{\pi}{6}[/tex]

Rewrite the original integral in terms of u and du:

[tex]\displaystyle \int^{\pi / 6}_0 \dfrac{u^2}{2\sqrt{1-x^2}}\;\sqrt{1-x^2}\;du \\\\\\\int^{\pi / 6}_0 \dfrac{u^2}{2}}\;du[/tex]

Evaluate:

[tex]\begin{aligned}\displaystyle \int^{\pi / 6}_0 \dfrac{u^2}{2}}\;du &=\left[\dfrac{u^3}{6}\right]^{\pi / 6}_0\\\\&=\dfrac{\left(\frac{\pi}{6}\right)^3}{6}-\dfrac{(0)^3}{6} \\\\&=\dfrac{\frac{\pi^3}{216}}{6}-0 \\\\ &=\dfrac{\pi^3}{1296}\end{aligned}[/tex]

Therefore, the value of the integral is:

[tex]\Large\boxed{\dfrac{\pi^3}{1296}}[/tex]

Answer:

4 is 133

Step-by-step explanation:

Simple 180-47 is 133

Answer:

They are both acute angles

Step-by-step explanation:

plz mark brainliest

Answer:

a = 65.37

b = 46.11

B = 35.2

Step-by-step explanation:

sin 54.8 = a / 80

a = 80 sin 54.8 = 65.3715 = 65.4

[tex]b^{2} = c^{2} - a^{2}[/tex]

b=[tex]\sqrt{80^2 - 65.3715^2}[/tex]

b=46.1147 = 46.11

B = 180 - 90 - 54.8 = 35.2

The sides and the angles as follows:

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

a ≈ 65.37

b ≈ 46.64

c = 80

The triangle is a right angle triangle. Using trigonometric ratios, let's find a.

sin 54.8 = opposite / hypotenuse

sin 54.8 = a / 80

a = 80 sin 54.8

a = 65.3715918668

a ≈ 65.37

let's use Pythagoras theorem to find b.

c² = a² + b²

b² = c² - a²

b² =  80² - 65²

b² = 6400 - 4225

b² = 2175

b = √2175

b = 46.6368952654

b ≈ 46.64

let's find ∠B

∠A +  ∠B +  ∠C = 180°

∠B = 180 - 54.8 - 90

∠B = 35.2°

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

The sides are as follows:

a ≈ 65.37

b ≈ 46.64

c = 80

read more: https://brainly.com/question/3770177?referrer=searchResults

Answer:

The distribution is uniform and is continuous probability distribution.

The mean of the distribution is μ= 35.5 minutes.

The standard deviation of the distribution is σ= 6.06

P(30<x<40)= 0.476

Step-by-step explanation:

a.The amount of time in minutes until the next bus departs is uniformly distributed between 25 and 46 inclusive.

The distribution is uniform and is continuous probability distribution.

b.Let X be the number of minutes the next bus arrives and a= 25 , b= 46. Hence mean = a+b/2= 25+ 46/ 2= 35.5 minutes.

The mean of the distribution is μ= 35.5 minutes.

c. Standard deviation =   √(b-a)²/12

Standard deviation= √(46-25)²/12= √(21)²/12= √441/12=√36.75= 6.06

The standard deviation of the distribution is σ= 6.06

d. P(30<x<40)

For this we draw a graph . It is also called the rectangular distribution because its total probability is confined to a rectangular region with base equal to (b-a) and height 1/(b-a) .

This can be calculated as

P(30<x<40)= base * height  (in this probability the base is 10)

= (40-30) *(1/ 21)= 10/21= 0.476  

The probability that the time until the next bus departs is between 30 and 40 minutes is 10/21.

The question is asking for the probability that the time until the next bus departs is between 30 and 40 minutes. Since the distribution is uniform, we can find the probability by calculating the fraction of the total range that falls within the desired interval. In this case, the total range is 46-25=21 minutes, and the desired interval is 40-30=10 minutes.

So the probability is 10/21, which can be simplified to 10/21.

https://brainly.com/question/22962752

#SPJ3

Answer:

-x

Step-by-step explanation:

8x - 9x

Factor out an x

x(8-9)

x (-1)

-x

Answer: The answer is D 12 i am pretty sure.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

20 cm.

Step-by-step explanation:

First, find the perimeter in inches. Since it's a square and all 4 sides are the same, you can multiply 2 x 4 to find the perimeter of 8. Now, convert it to cm by multiplying 8 by 2.5. 8 x 2.5 is 20 cm.

Answer:

a) 1/3

Step-by-step explanation:

a) Probability of drawing a king of any suit

Number of kings = 4

P(king) = 4/52

= 1/13

b) Probability of drawing a face card that is also a spade

Number of face =3

P(king) = 3/ 52

Answer:

See Explanation Below

Step-by-step explanation:

The image of the trianglular prism is missing.

However, I'll answer your question using the attachment below.

The volume of a triangular prism is calculated as follows.

V = ½lbh

Where l = length of the prism

b = base of the prism

h = height of the prism

V = volume of the prism.

From the attachment,

Length, l = 6 cm

Base, b = 3 cm

And Height, h = 4 cm

By substituting each of these values in the formula given above

V = ½lbh becomes

V = ½ * 6 * 3 * 4

V = 3 * 3 * 4

V = 36 cm³

If you follow these steps you'll get the volume of the trianglular prism as it is in your question.

Answer:

its 15

Step-by-step explanation:

ik its 15 because when i put in 24 it was wrong and gave me the awnser which was 15

Answer:

The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small.

Step-by-step explanation:

The complete question is:

The owner of a pita franchise with two locations is interested in the average time that customers spend waiting for service at each store. She believes that the average waiting time at the original location is higher than the average waiting time at the new location.

The pita‑franchise owner has observed in the past that waiting times tend to have a long tail to the right, with most customers served relatively quickly and a few rare customers required to wait a very long time.Is a two‑sample t ‑test appropriate in this setting?The two‑sample t ‑test is appropriate because this is a comparison of the means of two continuous, random variables.The two‑sample t ‑test is not appropriate because the two samples do not have the same size.The two‑sample t ‑test is not appropriate because the sample standard deviations are not equal.The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small.The two‑sample t ‑test is appropriate because the samples are random and contain no outliers, and the populations are normal.

For two sample t-test the distributions must be normal. Here the data, as mentioned in the questions is skewed to the right with long waiting times in the past.

Final answer:

The two-sample t-test is not appropriate for the pita-franchise owner's observations because the waiting times are not normally distributed and the sample sizes are small. A test that does not assume normality, like the Mann-Whitney U test, would be more suitable in this situation.

Explanation:

The two-sample t-test is a statistical method used to determine if the means of two groups are significantly different. One key assumption for a two-sample t-test, however, is that the data should come from populations that are approximately normally distributed, especially if the sample sizes are not large. If the assumption of normality is violated and the sample size is small, as indicated by a distribution with a long tail to the right, the two-sample t-test may not be appropriate. To make an informed decision, it would also be necessary to consider the equality of variances, sample sizes, and independence of the samples.

In the context of a pita-franchise with long-tailed waiting times, the distribution is not normal, indicating that the normality assumption is not met. Consequently, using the two-sample t-test might lead to inaccurate results, especially if the sample sizes are too small to compensate for the lack of normality. In such cases, a different test like the Mann-Whitney U test, which does not assume normality, might be a better choice.

Answer:

The critical value that should be used in constructing the interval is T = 5.8408.

The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the students t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 4 - 1 = 3

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 5.8408. This is the critical value.

The margin of error is:

M = T*s = 5.8408*7.99 = 46.668 bushels per acre

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 49.6 - 46.668 = 2.943 bushels per acre.

The upper end of the interval is the sample mean added to M. So it is 49.6 + 46.668 = 96.268 bushels per acre.

The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.

Answer:

  5

Step-by-step explanation:

Put -6 where x is and do the arithmetic.

  [tex]h(x)=1-\dfrac{2}{3}x\\\\h(-6)=1-\dfrac{2}{3}(-6)=1-\dfrac{-12}{3}=1-(-4)=1+4\\\\\boxed{h(-6)=5}[/tex]