Problem 2a. A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. The scores are normally distributed. Test the claim that the mean score is above 70 at a 10% alpha level.

The expansion of Cos(A-B) is:

We are provided with the following:

We will have to obtain the values of Cos B and Sin A. Thus, we have:

To be obtain Sin A, we have to get the value of the third side, which is the opposite side, by applying the pythagoras theorem. Thus, we have:

To be obtain Cos B, we have to get the value of the third side, which is the adjacent side, by applying the pythagoras theorem. Thus, we have:

Now that we have obtained the values of Cos B and Sin A, we can then go on to solve the original problem.

Moon Software Inc. must issue approximately 3,927 OID bonds to raise $3,000,000.

The par bonds have a coupon rate of 10% and a par value of $1,000. To raise $3,000,000, Moon Software Inc. needs to issue 3,000 par bonds since $3,000,000 divided by $1,000 equals 3,000.

The OID bonds have a semiannual coupon rate of 7.75% and a par value of $1,000. Since these bonds need to provide investors with the same effective yield as the par bonds, they must be offered at a discount. To calculate the number of OID bonds required, we need to determine the discount needed to match the effective yield of the par bonds.

The effective yield of the par bonds is 10%. The OID bonds have a coupon rate of 7.75%, so the discount needed to match the effective yield is 10% - 7.75% = 2.25%.

To raise $3,000,000 with OID bonds, we divide the amount by the discount rate: $3,000,000 / 2.25% = $133,333,333.33.

Since each OID bond has a par value of $1,000, we divide the total amount by $1,000: $133,333,333.33 / $1,000 = approximately 133,333.33 bonds.

Since we need a whole number of bonds, we round up to the nearest whole number, which gives us 133,334 bonds.

Therefore, Moon Software Inc. must issue approximately 133,334 OID bonds to raise $3,000,000.

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Answer:

7.006*10⁻³ = 0.007006

Step-by-step explanation:

7.006*10⁻³ = 0.007006

Answer:

b

Step-by-step explanation:

The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

hD = m

To solve for D make the subject as D

As we know the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Divide by h on both the sides:

hD/h = m/h

Here h ≠ 0

D = m/h

Thus, the expression in  terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

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The chromatic number of the graph K33, which is a complete bipartite graph with 33 vertices, each connected to every vertex in the other set, is 2. This means that the graph can be colored using only two colors.

The chromatic number of a graph represents the minimum number of colors needed to color its vertices such that no adjacent vertices have the same color.

In the case of K33, the graph is a complete bipartite graph, which means it can be divided into two sets of vertices, where each vertex in one set is connected to every vertex in the other set. In this specific graph, we have 33 vertices in each set.

To determine the chromatic number, we observe that in a complete bipartite graph, no vertices within the same set are connected to each other. Therefore, we can assign one color to all the vertices in one set and a different color to all the vertices in the other set.

In K33, we can color one set of 33 vertices, let's say set A, with color 1, and the other set of 33 vertices, set B, with color 2. Since no vertices within the same set are connected, there will be no adjacent vertices with the same color.

Hence, we conclude that the chromatic number of the graph K33 is 2, as it can be colored using only two colors.

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Answer:

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

Answer:

B just took the test

Step-by-step explanation:

have a good rest of your day

Answer:

a=m-n

(Add n to both sides)

a+n=m-n+n

(The -n and +n cancel out, on the right side of the equation)

a+n=m

(Now subtract a from both sides)

a+n-a=m+a

(The +a and -a cancel out, on the right side of the equation)

n=m+a

Answer:

\(\huge \boxed{n=-a+m}\)

Step-by-step explanation:

\(a=m-n\)

Adding \(n\) to both sides.

\(a+n=m-n+n\)

\(a+n=m\)

Subtracting \(a\) from both sides.

\(a+n-a=m-a\)

\(n=m-a\)

Answer:

5/21

hope this helps

There will be 24 highway signs on the road trip.

What is a division in mathematics?

In mathematics, the division is the process of finding the number of times one number, called the divisor, is contained in another number, called the dividend. The division is often represented using the symbol "/" or "÷".

To find the number of highway signs on the road trip, we need to divide the total length of the road trip (14.4 hours) by the interval between signs (0.6 hours).

The number of highway signs on the road trip is:

14.4 hours / 0.6 hours/sign = 4.4/0.6=24 signs

Hence, there will be 24 highway signs on the road trip.

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Answer:

35 dogs

Step-by-step explanation:

let dogs ratio be 7x

let cats ratio be 3x

7x/3x = a/15

15÷3 = 5

so, 7×5 = 35

Let's use the variables x and y to represent the cost of a hot dog meal and a hamburger meal, respectively.

Then, we can write the following system of equations to describe the situation:

2x + 3y = 33 (Mrs. Dotson's purchases)

1x + 3y = 27 (Mr. Kent's purchases)

To solve this system of equations using elimination, we can multiply the second equation by 2 and subtract it from the first equation:

2x + 3y = 33

-2x - 6y = -54

0x - 3y = -21

Simplifying the equation, we get:

y = 7

Substituting this value of y into either equation, we can solve for x:

2x + 3(7) = 33

2x + 21 = 33

2x = 12

x = 6

Therefore, hot dog meals cost $6 each, and hamburger meals cost $7 each.

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B

...........................

Answer:

It is A and D

Step-by-step explanation:

65% of 20 is also

.65 * 20 or

65/100 * 20

I did Khan Academy too :)

Answer:

87.9\(m^2\)

Step-by-step explanation:

Surface area of a cylinder: 2*π*r*h + 2*π*\(r^2\)

π = 3.14

r = 2mm

h = 5mm

A = 2*π*r*h + 2*π*\(r^2\)

2*3.14*2*5 + 2*3.14*\(2^2\)(4)

62.8 + 25.12

87.92\(m^2\) rounded to the nearest tenth is 87.9\(m^2\)

Hope this helps!

Răspuns:

Trandafiri = 105

Lalele = 632

Crizanteme = 105

Explicație pas cu pas:

Lăsa :

Trandafiri = x

Lalea = y

Crizanteme = z

x + y + z = 840

x = z + 2

y / (z + z + 2) = 3 r 8

y / (2z + 2) = 3 restul 8

y = (2z + 2) (3) + 8

y = 6z + 6 + 8

y = 6z + 14

x = z + 2

y = 6z + 14

x + y + z = 840

Înlocuiți x și y în ecuația:

z + 2 + 6z + 14 + z = 840

8z + 16 = 840

8z = 840 - 16

8z = 824

z = 824/8

z = 103

x = z + 2

x = 103 + 2

x = 105

y = 6z + 14

y = 6 (103) + 14

y = 632

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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==============================================================

ANSWER:

x° = 24°

y° = 72°

Analysis on picture hope it helps

To find the minimum sum-of-products expression for the function f = x1x2x3 x1x2x4 x1x2x3x4 using algebraic manipulation, the following steps need to be followed:

Step 1: Write the SOP expression f = x1x2x3 x1x2x4 x1x2x3x4

Step 2: Create a K-map with the input variables x1, x2, x3, and x4 on the top and left side

Step 3: Identify the minterms using the K-map, which is 2, 5, 6, 7, 8, 9, 10, 11, 12, and 13

Step 4: Plot the minterms on the K-map using 1s

Step 5: Look for groups of 1s on the K-map and combine them to create an SOP expression with the fewest possible terms.

In this case, two groups can be combined:

Group 1 includes minterms 2, 6, 10, and 14.

Group 2 includes minterms 5, 7, 13, and 15.

The minimum sum-of-products expression is thus:

f = (x1'x2'x3'x4) + (x1'x2x3'x4')

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Answer:

They are parallel

Step-by-step explanation:

(3,8)(-6,5): do sloe formula (y1-y2 over x2-x1)

AB: 1/3 slope       (Full formula y=1/3x+7)

(-6,7)(-3,8) --->  8-7 over -3-(-6) = 1/3

CD: 1/3 slope      (Full formula y=1/3x +9)

They have the same slope so they are parallel

Option E should be chosen, which is to explore the assignable causes because the second, fourth, and fifth samples are above the mean.

In an x-bar chart, the control limits (UCL and LCL) are based on the process variability and are used to determine if the process is in control. The central line represents the mean of the process.

Looking at the given sample means of 18, 23, 17, 21, 24, and 16, we can see that the second, fourth, and fifth samples are above the mean of 20. This suggests a potential shift or deviation from the expected process mean.

In an x-bar chart, if any sample mean falls outside the control limits or exhibits a non-random pattern, it indicates the presence of assignable causes, which are factors that can be identified and addressed to improve the process. Since the second, fourth, and fifth samples are above the mean, it is advisable to explore the assignable causes, as stated in option E.

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Since these two operations cancel each other out, the order in which we apply them does not matter, which is why E and F commute.

The correct choice is B. According to the Invertible Matrix Theorem, if EF = I, then both E and F are invertible matrices with inverses F⁻¹ and E⁻¹ respectively. This is because if EF = I, then both E and F are one-to-one and onto, which implies that they have inverses.

Since E and F are invertible matrices, it follows that FE = E⁻¹(EF)F⁻¹ = E⁻¹IF⁻¹ = F⁻¹E⁻¹ = (EF)⁻¹ = I⁻¹ = I. Therefore, we have shown that E and F commute.

To explain this result, note that if two matrices A and B commute, then AB = BA. In other words, the order in which we multiply A and B does not matter. In this case, we have shown that EF = I implies that FE = I, which means that the order in which we multiply E and F does not matter.

Intuitively, we can think of E and F as performing opposite operations that cancel each other out. When we apply E and then F, we get back to where we started, which is the identity matrix I.

Similarly, when we apply F and then E, we also get back to I.

Since these two operations cancel each other out, the order in which we apply them does not matter, which is why E and F commute.

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∠1 and ∠4 are vertical interior angle.

∠1 ≅ ∠5 follows Transitive property of congruence

g ║h  by corresponding angle theorem

The diagram is to prove alternate interior angles converse.

Therefore,

∠4 ≅ ∠5 (Alternate interior angles)

By, the vertical interior angle congruence, ∠1 ≅ ∠4

Vertically opposite angles are congruent. Vertically opposite angles share the same vertex.

Then by the Transitive property of congruence, ∠1 ≅ ∠5.

So, by the corresponding angles theorem, g ║h

Corresponding angles are usually congruent.

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Answer:

A = 36√3 - 12π

Step-by-step explanation:

Make 2 identical 30-60-90 triangles out of the "wedge"

For each 30-60-90 triangle:

Since the short leg is 6 the long leg is 6√3

short leg is the base and long leg is the height

a = (1/2)bh

a = (1/2)(6)(6√3)

a = 3(6√3)

a = 18√3

Since there are 2 triangles

a = 36√3

--------------------------------

Then subtract off the area of the 120º sector

a = (120/360)πr^2

a = (1/3)π(6^2)

a  = (1/3)π(36)

a = 12π

Shaded area

a = 36√3 - 12π

Step-by-step explanation:

we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).

since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.

basically, the area of a triangle is

1/2 × b×c × sin(A)

A being the angle between the 2 sides b and c. for any 2 sides of the triangle.

one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.

we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.

remember, the sum of all angles in a triangle is 180 degrees.

so, via the law of sines we can then calculate all sides :

a/sin(A) = b/sin(B) = c/sin(C)

with the angles being opposite of the sides.

6/sin(30) = baseline/sin(90)

6/0.5 = baseline/1

12 = baseline

top side² + 6² = 12²

top side² = 12² - 6² = 144 - 36 = 108

top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.

the area of the 2 triangles is then

6×sqrt(3)×6×sin(90) = 36×sqrt(3)

and the circle segment to be deducted is

pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12

so, the complete answer is

A = 36×sqrt(3) - 12×pi

A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.

B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.

Leah runs M miles everyday during the week except for Wednesday or Sunday.

We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.

We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.

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Answer:

(5 , 0)

Step-by-step explanation:

7 * (−9y+4x−20)=0

9 * (−7y+16x−80)=0

-63y + 28x -140 = 0 ......a

-63y + 144x -720 = 0 .....b

b-a:  116x - 580 = 0

116x = 580

x = 5

y = (4x-20)/-9 = 0/-9 = 0

Answer:

Step-by-step explanation: 14 = x

Answer:

The answer to your question would be 14

Step-by-step explanation:

Simple equation

14 - 10 = 4

I hope this helps and have a wonderful day!

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

Answer:

A. deoxyribose sugar molecules

C. adenine

D. phosphate molecules

F. cytosine

G. thymine

Step-by-step explanation:

I got it correct

DNA is a biomolecule that is made up of, deoxyribose sugar, phosphate group, and nitrogenous base cytosine, thymine, and adenine.

DNA is a double helix structure, in which hydrogen bonds between purines and pyrimidines, making the material for storage of the genetic information.

DNA stands for deoxyribonucleic acid, it is a polynucleotide made by repeated units of nitrogenous base attach by a glycosidic bond with the sugar and this repeated nucleoside unit is attached to the phosphate group-making nucleotide.

This structure of DNA is best suited for the storing of genetic information, on the other hand, RNA is a single-stranded molecule, which is not stable as DNA.

Therefore, DNA consists of deoxyribose sugar, adenine, phosphate molecules, cytosine, and thymine.

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