Two friends, Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 31 shifts that she had a mean of 5.3 calls per shift. She knows that the population standard deviation for her shift is 1.1 calls. Jodi calculates from a random sample of 41 shifts that her mean was 4.7 calls per shift. She knows that the population standard deviation for her shift is 1.5 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.01 level of significance. Let Karen's shifts be Population 1 and let Jodi's shifts be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places. Answer Tables Keypad Keyboard Shortcuts

This equation represents the solution to the given initial value problem.

[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]

To solve the initial value problem, we'll separate variables and integrate both sides.

Starting with the given differential equation:

[tex]dy/dx = e^{4(y - 2)}[/tex]

Separating variables:

[tex]e^{(4(y - 2))} dy = dx[/tex]

Integrating both sides:

[tex]\int e^{(4(y - 2))} dy = \int dx[/tex]

To integrate [tex]e^{4(y - 2)}[/tex], we can use the substitution u = 4(y - 2), du = 4dy:

[tex]1/4 \int e^u du = x + C[/tex]

Integrating [tex]e^u[/tex] gives us:

[tex]1/4 * e^u = x + C[/tex]

Substituting back u = 4(y - 2):

[tex]1/4 * e^{(4(y - 2))} = x + C[/tex]

Now, applying the initial condition y(0) = 6, we can solve for C:

[tex]1/4 * e^{(4(6 - 2))} = 0 + C[/tex]

[tex]1/4 * e^{(4(4))} = C[/tex]

[tex]1/4 * e^{(16)} = C[/tex]

Therefore, the solution to the initial value problem is:

[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]

This equation represents the solution to the given initial value problem.

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Answer:

About 700 billion bacteria

Step-by-step explanation:

Given

[tex]1oz \approx 28g[/tex]

[tex]1g = 25\ billion\ bacteria[/tex]

Required

Number of bacteria in 1 oz

[tex]1g = 25\ billion\ bacteria[/tex]

Multiply both sides by 28

[tex]28 * 1g = 25\ billion\ bacteria * 28[/tex]

[tex]28g = 700\ billion\ bacteria[/tex]

Recall that

[tex]1oz \approx 28g[/tex]

This means:

[tex]1oz \approx 700\ billion\ bacteria[/tex]

Answer:

x = 120 degrees or (c)

Step-by-step explanation:

It's 120 degrees...

...

Answer:

(7, 3 )

Step-by-step explanation:

Given the 2 equations

x = 4y - 5 → (1)

2x + 3y = 23 → (2)

Substitute x = 4y - 5 into (2)

2(4y - 5) + 3y = 23 , that is

8y - 10 + 3y = 23

11y - 10 = 23 ( add 10 to both sides )

11y = 33 ( divide both sides by 11 )

y = 3

Substitute y = 3 into (1) for corresponding value of x

x = 4(3) - 5 = 12 - 5 = 7

solution is (7, 3 )

Answer:

-3

Step-by-step explanation:

The answer is -3 because it is the number on the x-axis

Answer:

the probability that the sample mean would differ is 0.1164

Step-by-step explanation:

The computation of the probability is shown below

= 1 - P(Within 4.1 WPM)

= 1 - P( -4.1 ÷ 15÷ √3 <z < 4.1 ÷ 15÷ √3)

= 1 - P(-1.57 < z < 1.57)

= 1 - 0.8836

= 0.1164

Hence, the probability that the sample mean would differ is 0.1164

Therefore the same would be applied and relevant

Answer:

100

Step-by-step explanation:

an isosceles triangle is equal so if one side is 100 degrees, the other side is too

Answer:100 is the answer

Step-by-step explanation

Because the isoscles triangles are those whose two sides are equal

Answer:

80

Step-by-step explanation:

200/2.50=80

Using trigonometric identity, sin(α + β) = -28/85.

To compute sin(α + β), we can use the trigonometric identity:

sin(α + β) = sin α cos β + cos α sin β

Given the values:

sin α = 15/17 (π/2 < α < 3π/2)

sin β = -4/5 (π < β < 3π/2)

To find sin α, we can use the Pythagorean identity:

cos α = ±√(1 - sin² α)

Since α is in the range π/2 < α < 3π/2, sin α is positive, so cos α will be negative.

sin α = 15/17

cos α = -√(1 - (15/17)²)

      = -√(1 - 225/289)

      = -√(64/289)

      = -8/17

Now, we can substitute the values into the formula for sin(α + β):

sin(α + β) = (sin α cos β) + (cos α sin β)

          = (15/17) * (-4/5) + (-8/17) * (-4/5)

          = -60/85 + 32/85

          = -28/85

Therefore, sin(α + β) = -28/85.

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Answer:

Hope this helps :)

Answer:

a

Step-by-step explanation:

The five-number summary for the given data is as follows: Minimum = 40, First Quartile = 51.5, Median = 69, Third Quartile = 86, Maximum = 95.

To obtain the five-number summary, we consider the minimum, first quartile, median, third quartile, and maximum values of the dataset.

Minimum: The smallest value in the dataset is 40.

First Quartile: The first quartile (Q1) is the median of the lower half of the dataset. To find Q1, we arrange the data in ascending order: 40, 46, 50, 55, 58, 61, 64, 69, 74, 79, 85, 86, 90, 94, 95. Since there are 15 data points, the median is the 8th value (69), which becomes the first quartile.

Median: The median is the middle value of the dataset. In this case, since we have an odd number of data points, the median is the 8th value (69).

Third Quartile: The third quartile (Q3) is the median of the upper half of the dataset. Again, using the ordered data, we find Q3 as the median of the values above the median (69). This gives us the third quartile of 86.

Maximum: The largest value in the dataset is 95.

Thus, the five-number summary for the given data is Minimum = 40, Q1 = 51.5, Median = 69, Q3 = 86, and Maximum = 95.

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Answer:

Total Volume of composite figure = 635.2 cm³

Steps:

CV = h×3.14×(d/2)²

CV = 5×3.14(8/2)²

CV = 5×3.14(4)²

CV = 5×3.14×16

CV = 5×50.24

CV = 251.2 cm³

RV = h×w×l

RV = 4×8×12

RV = 4×96

RV = 384 cm³

TV = CV + RV

TV = 251.2 + 384

TV = 635.2 cm³

Answer:

91 or 525

Step-by-step explanation:

Multiply the objects width (How long it is), times height. For the smaller object inside the bigger object, it is 91. For the bigger object, it is 525.

The given number 87392 is rounded off to 87390.

Rounding off means a number is made simpler by maintaining its overall value but being closer to the next number.

The number to be rounded off is 87392.

The digit present in the once place is 2.

If the smallest place digit is greater than or equal to 5, then round up the digit.

As the digit in the smallest digit is less than 5, the digit gets rounded down.

Here, the smallest place digit is 2 which is smaller than 5.

So, the given number rounded off to 87390.

Hence, the answer is 87390.

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Answer:

3375 in³

Step-by-step explanation:

Volume of a cube = a³ ; where a = edge of the cube

Length of each face = edge of cube = 15 inches

Volume of cube = 15³

Volume of cube = 15 inch * 15 inch * 15 inch

Volume of cube = 3375 in³

a. For this study, we should use the z-test.

b. The null and alternative hypotheses would be: Null hypothesis: H0: p = 0.55

Alternative hypothesis: H1: p ≠ 0.55

Explanation:

We use the z-test when we are testing the difference between the sample mean and the population mean. Here we are testing the difference between the sample proportion (p) and the population proportion (P).

We should use the z-test for this study to check whether the proportion of voters who prefer the Democratic candidate is significantly different from 55% at a level of significance of a = 0.05. This is because we are testing the proportion of people who prefer a Democratic candidate from a population. Here, we will use the sample size, sample proportion, and level of significance to calculate the test statistic (z) value.

The null hypothesis is H0: p = 0.55, which states that there is no difference between the proportion of voters who prefer the Democratic candidate and the population proportion.

While the alternative hypothesis is H1: p ≠ 0.55, which states that there is a significant difference between the proportion of voters who prefer the Democratic candidate and the population proportion.

a. For this study, we should use the z-test.

b. The null and alternative hypotheses would be: Null hypothesis: H0: p = 0.55

Alternative hypothesis: H1: p ≠ 0.55

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Answer:

x = 10

Step-by-step explanation:

10 + 10 = 20

Good luck with your work!

Answer:

x = 10

Step-by-step explanation:

x + x = 20 can also be interpreted as 2x = 20. This makes it easier to solve for the variable.

To isolate x, do the inverse operation of multiplication. So, we have to divide both sides of the equation by 2.

[tex]\frac{2x}{2}[/tex] = [tex]\frac{20}{2}[/tex]

Simplify this equation for x = 10.

I hope this is helpful. Good luck ^^

Answer:

Step-by-step explanation:

common difference d=3-1=2

first term a=1

an=a+(n-1)d

2n-1=1+(l-1)2

2n-1=1+2l-2

2n-1=2l-1

l=n

(i used l for number of terms)

number of terms=n

[tex]S_{n}=\frac{n}{2} (first ~term+last~term)\\=\frac{n}{2} (1+2n-1)\\=n^2[/tex]

Answer:

median, 60

Step-by-step explanation:

Answer:

it is 60 my friend.

Step-by-step explanation:

Answer:

4x−2y=6 is 21

Step-by-step explanation:

Answer:

Y intercept=3

4(0)+2y=6

y=3

slop=m=-2

y=-2x+3

y=mx+b

M=-2

Step-by-step explanation:

The partial sums will cease to change when the terms of the series become smaller than the smallest representable number in the floating-point system.

In floating-point arithmetic, there is a finite range of representable numbers and a limited precision for calculations. When dealing with infinite series, the terms are added or subtracted sequentially, but due to the limitations of numerical precision, there is a point at which the terms become too small to affect the sum significantly.

For the series 1/n, as n increases, the terms approach zero but never actually reach zero. Eventually, the terms become smaller than the smallest representable number in the floating-point system, and at this point, they essentially contribute zero to the sum. As a result, the partial sums of the series will cease to change beyond this point.

It's important to note that although the sum of the series may appear to be finite in floating-point arithmetic, mathematically, the series diverges and does not have a finite sum. The convergence to a finite value in floating-point arithmetic is a result of the limitations of numerical representation and precision. A divergent infinite series, such as the sum of 1/n from n=1 to infinity, can have a finite sum in floating-point arithmetic due to the limitations of numerical precision.

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the answer is 30°

EXPLAINATION:

since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°

so, 90° + 60° + x = 180

150° + x = 180°

so x = 180° - 150° = 30°

hence, the other acute angle is 30°.

The solution to the equation is x = 69.

To solve the equation 345 = 5x for x, we can isolate the variable by dividing both sides of the equation by 5:

345/5 = 5x/5

69 = x

Therefore, the value of x = 69.

This means that if we substitute x with 69 in the equation 5x, we will obtain the left-hand side of the equation 345. The solution is accurate to the hundredth place, as there are no decimal places involved in this particular equation. It's important to note that the solution is a whole number, and in this case, it represents the value of x that satisfies the equation.

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Answer:

3a-2a+7-4

a+3

Step-by-step explanation:

like and unlike terms arranging

and add and subtraction

Answer:

39.837168574084177751131265854635

Step-by-step explanation:

If you plug it into a calculator, you get that.

Next time, please pay attention in class and save us all a little trouble.

Answer:

2 4/5

Step-by-step explanation:

4/5 divided by 2/7 is 2.8. 2.8 in the form of a fraction is 2 4/5.

The fraction 4/5 divided by 2/7 in the simplest form, is 14/5.

Given that, (4/5) divided by (2/7).

To divide fractions, multiply the first fraction by the reciprocal of the second fraction

Let a, b, c and d be real numbers. Divide a fraction (a/b) by another fraction (c/d), we can multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, the reciprocal of (c/d) is (d/c).

To divide (a/b) by (c/d), multiply the first fraction by the reciprocal of the second fraction:

(a/b) ÷ (c/d) = (a/b) x (d/c)

Multiplying the numerators and denominators:

(ad) / (bc)

Therefore, the result of (a/b) divided by (c/d) is (ad) / (bc).

To simplify this expression, and multiply the first fraction by the reciprocal of the second fraction:

(4/5) x (7/2)

Multiplying the numerators and denominators:

(4 x 7) / (5 x 2)

Simplifying the numerator and denominator:

28 / 10

To further simplify the fraction, and divide both the numerator and denominator by their greatest common divisor, which is 2:

28 ÷ 2 / 10 ÷ 2

This gives us:

14 / 5

Therefore, the fraction 4/5 divided by 2/7, in the simplest form, is 14/5.

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The question is incomplete:

Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here. Explain why Maria is incorrect and how she can find the correct answer.

Answer:

Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.

Step-by-step explanation:

You can find the number of necklaces Avan can make by dividing the number of beads she has by the amount in each necklace:

6048/24=252

According to this, you can say that Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.

Answer:

B, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Diagonals of a square are congruent so AC= 4

using pythagorean theorem we can then do [tex]x^{2} +x^{2}[/tex]=[tex]4^{2}[/tex]

[tex]2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}[/tex]

Then for perimeter we times the [tex]2\sqrt{2}[/tex] by 4 and get

[tex]8\sqrt{2}[/tex]

Hope this helps and please mark brainliest!!