An office manager just got back from vacation, so she has a pile of 424 letters to read. Then, the mail carrier comes and delivers 41 more letters for her. How many letters does the office manager have now?
465
383
455
373

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:

The top question = 189.25 rounded = 189.3 sq in

explanation: area= radius square x pi so radious is 5..sq will 25 then 25xpi(3.14)=78.50 78.50/2= 39.25 + 150 (area of rect) =189.25 rounded to 189.3

for the bottom question = 488 square cm

Step-by-step explanation:

17x22= 374

22-10=12

12x19=228 / 2 = 114

114 + 374 = 488 sq 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:

Step-by-step explanation:

The equation can be rearranged to vertex form:

  x^2 -4x = -5 . . . . . . . . . subtract 4x

  x^2 -4x +4 = -5 +4 . . . . add 4

  (x -2)^2 = -1 . . . . . . . . . show the left side as a square

  x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary

  x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.

_____

Comment on the question

Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.

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:

Degree 3

Step-by-step explanation:

Highest valued exponent of x variable is 3

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

Answer:

for AAS triangles or SSA

Step-by-step explanation:

Answer:

ny triangle whose two sides and 1 angle is known or 2 angles are known and 1 side is known

Step-by-step explanation:

Answer:

Step-by-step explanation:

The nth term of a geometric sequence is expressed as Tn = [tex]ar^{n-1}[/tex] where;

a is the first term

r is the common ratio

n is the number of terms

Since we are to insert three geometric means between 2 and 81/8, the total number of terms in the sequence will be 5 terms as shown;

2, a, b, c, 81/8

a, b, and c are the 3 geometric mean to be inserted

T1 = [tex]ar^{1-1}[/tex] = 2

T1 = a = 2....(1)

T5= [tex]ar^{5-1}[/tex]

T5 = [tex]ar^{4}[/tex] = 81/8... (2)

Dividing equation 1 by 2 we have;

[tex]\frac{ar^{4} }{a}= \frac{\frac{81}{8} }{2}[/tex]

[tex]r^{4} = \frac{81}{16}\\\\r = \sqrt[4]{\frac{81}{16} } \\r = 3/2[/tex]

Given a =2 and r = 3/2;

[tex]T2=ar\\T2 = 2*3/2\\T2 = 3\\\\T3 = ar^{2} \\T3 = 2*\frac{3}{2} ^{2} \\T3 = 2*9/4\\T3 = 9/2\\\\T4 = ar^{3}\\T4 = 2*\frac{3}{2} ^{3} \\T4 = 2*27/8\\T4 = 27/4\\[/tex]

Therefore the three geometric means are 3, 9/2 and 27/4

In a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

[tex]\mathbf{T_2 =3 }[/tex]

[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]

Recall:

Given a geometric sequence, 2 . . . 81/8, with three other terms in the middle, first, find the value of r.

Thus:

First Term:

Fifth Term:

[tex]T_5 = ar^{n - 1}[/tex]

a = 2

n = 5

r = ?

T5 = 81/8

[tex]\frac{81}{8} = 2r^{5 - 1}\\\\\frac{81}{8} = 2r^4\\\\[/tex]

[tex]\frac{81}{8} \times 8 = 2r^4 \times 8\\\\81 = 16r^4\\\\[/tex]

[tex]\frac{81}{16} = \frac{16r^4}{16} \\\\\frac{81}{16} = r^4\\\\[/tex]

[tex]\sqrt[4]{\frac{81}{16}} = r\\\\\frac{3}{2} = r\\\\\mathbf{r = \frac{3}{2}}[/tex]

Find the three geometric means [tex]T_2, T_3, $ and $ T_4[/tex] between 2 and 81/8.

[tex]\mathbf{T_n = ar^{n - 1}}[/tex]

a = 2

r = 3/2

[tex]T_2 = 2 \times (\frac{3}{2}) ^{2 - 1}\\\\T_2 = 2 \times (\frac{3}{2}) ^{1}\\\\\mathbf{T_2 = 3}[/tex]

[tex]T_3 = 2 \times \frac{3}{2} ^{3 - 1}\\\\T_3 = 2 \times (\frac{3}{2}) ^{2}\\\\T_3 = 2 \times \frac{9}{4}\\\\\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]T_4 = 2 \times \frac{3}{2} ^{4 - 1}\\\\T_4 = 2 \times (\frac{3}{2}) ^{3}\\\\T_4 = 2 \times \frac{27}{8}\\\\\mathbf{T_4 =\frac{27}{4} }[/tex]

Therefore, in a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

[tex]\mathbf{T_2 =3 }[/tex]

[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]

Learn more here:

https://brainly.com/question/12115906

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

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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

Answer:

Step-by-step explanation:

Answer:

There is a 11/14 chance that the result is a multiple of 3 or a multiple of 2.

Step-by-step explanation:

Since the spinner is from 1 to 14, find all of the multiples of 3 and multiples of 2.

There are 4/14 multiples of 3 and 7/14 multiples of 2.

Add both of these numbers together 4/14 + 7/14 = 11/14

If this answer is correct, please make me Brainliest!

The probability of landing on a multiple of 2 or 3 when spinning a spinner numbered 1 through 14 is 4/7.

The student asked about the probability of getting a multiple of 3 or a multiple of 2 when spinning a spinner numbered 1 through 14. To determine this, we first list the multiples of 3 and 2 within the range of numbers on the spinner.

Multiples of 3: 3, 6, 9, 12
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Note that 6 and 12 are multiples of both 2 and 3, so we should not count them twice.

The total number of distinct multiples of 2 or 3 is 3 (multiples of 3) + 7 (multiples of 2) - 2 (common multiples) = 8 unique numbers. Since there are 14 possible outcomes on the spinner, the probability of landing on a multiple of 3 or 2 is 8 (favorable outcomes) divided by 14 (total possible outcomes).

The probability calculation is: 8/14, which simplifies to 4/7.

Answer:

D. c+14≤24

Step-by-step explanation:

A. c+14<24 is c<10 (subtract 14)

B. c+18≥24 is c≥6 (subtract 18)

C. c+18>24 is c>6 (subtract 18)

D. c+14≤24 is c≤10 (subtract 14)

The set is {5, 6, 8, 9, 10}, so it should include each one of those numbers. C and A don't include 6 and 10 respectively, so they can't be the answer. B contains all numbers 6 and above, which doesn't include 5. The remaining letter is D, so that's the final answer.

Answer:

no

Step-by-step explanation:

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:

V≈14,137.17m³ or 4500π

Step-by-step explanation:

Formula: V=(1 /6)πd³

V=(1/6)π(30³)= 14137.16694115406957308189522475776297888726229718797619438.....

Answer:

14137.17 meters cubed

Step-by-step explanation:

volume = 14137.17 meters cubed

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

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:

The correct answer to the following question will be "0.0367".

Step-by-step explanation:

The given values are:

[tex]p1=p2=0.06[/tex]

[tex]q1=q2=1-p1=0.94[/tex]

[tex]n1=n2=400[/tex]

As we know,

[tex]E(p1-p2)=p1-p2=0\\[/tex]

[tex]SE(p1-p2)=\sqrt{\frac{p1q1}{n1}+\frac{p2q2}{n2}}[/tex]

On putting the given values in the above expression, we get

                   [tex]= \sqrt{p1q1(\frac{1}{400}+\frac{1}{400})}[/tex]

                   [tex]=0.0168[/tex]

Now, consider

[tex]P(p1-p2>0.03)=P[\frac{(p1-p2)-E(p1-p2)}{SE(p1-p2)}>\frac{0.03-0}{0.0168}][/tex]

                            [tex]=P(Z>1.7857)[/tex]

                            [tex]=P(Z>1-79)[/tex]

                            [tex]=0.036727[/tex]

Therefore, "0.0367" is the right answer.

Calculating the probability of the difference between two sample proportions being more than 0.03 involves executing a hypothesis test via a z-test due to our large sample size. We formulate and employ a formula to get the z-score and then determine the associated p-value using a statistical tool.

This question falls within the area of statistics, particularly dealing with hypothesis testing and comparison of two independent population proportions. Given that 0.06 of each population possess a certain characteristic and samples of size 400 are drawn from each, we are required to calculate the probability that the difference between the sample proportions exceeds 0.03.

First, we establish the null hypothesis (H0) and alternative hypothesis (Ha) for the test. H0: P1 = P2 and Ha: P1 ≠ P2. Here, P1 and P2 represent the populations respectively. Given a sufficiently large sample size (n > 30), we use a z-test for comparing the proportions.

In computing the z-score, we use the following formula: z = (P1 - P2) / √ ((P*(1 - P*) / n1) + (P*(1 - P*) / n2)). Here, P* = (x1 + x2) / (n1 + n2), where x is the number of successes in each sample (0.06*400 = 24 per population logistically).

The p-value associated with the calculated z-score, which represents the probability that the difference between the first sample proportion and the second sample proportion being more than 0.03, can be found using a statistical calculator or statistical software. The precise numerical value for p will depend on the computed z-score.

https://brainly.com/question/34171008

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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:

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: The answer is D 12 i am pretty sure.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

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]

Answer:

20 meters square

Step-by-step explanation:

Surface Area of this square based pyramid =  A  = base area + 4* (face area)

A = (2 *2)  +  4* ( (1/2)*2 * 4) )

A = 4 + 4*(4)

A = 4 + 16 = 20

A = 20 square meters

Answer:

C. The divergence of F is StartFraction 1 Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction

∇•F = 1/|r|²

Step-by-step explanation:

The position vector r = (x, y, z)

r = xi+yj+zk

|r| = √x²+y²+z²

|r|² = x²+y²+z²

Given the radial field F = r/|r|²

Divergence of the radial field is expressed as:

∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {(r/|r|²)

∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {xi/|r|² + yj/|r|² + zk/|r|²}

∇•F = δ/δx(x/|r|²) + δ/δy(y/|r|²)+δ/δz(z/|r|²)

Check the attachment for the complete solution.

Answer:

b. 4:35 p.m

Step-by-step explanation:

Her speed in t minutes after 4:30 p.m. is modeled by the following equation:

[tex]v(t) = v(0) + at[/tex]

In which v(0) is her speed at 4:30 pm and a is the acceleration.

At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.

This means that [tex]v(0) = 45[/tex]

Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.

This means that [tex]v(10) = 55[/tex]

So

[tex]v(t) = v(0) + at[/tex]

[tex]55 = 45 + 10a[/tex]

[tex]10a = 10[/tex]

[tex]a = 1[/tex]

So

[tex]v(t) = 45 + t[/tex]

When was she moving exactly 50 mph?

This is t minutes after 4:30 p.m.

t is found when v(t) = 50. So

[tex]v(t) = 45 + t[/tex]

[tex]50 = 45 + t[/tex]

[tex]t = 5[/tex]

5 minutes after 4:30 p.m. is 4:35 p.m.

So the correct answer is:

b. 4:35 p.m

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.

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: