Find the measure of b

Answer:

The answer is "$ 4450"

Step-by-step explanation:

Purchased policy price = $50,000

10th anniversary cash value = ?

The after calculation its final value is = $ 4450

We have been given that in △CDE , CD=10 , DE=7 , and m∠E=62 degrees. We are asked to find the measure of angle D.

We will use law of sines to solve our given problem.

[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex], where, a, b and c are opposite sides to angles A, B and C respectively.

First of all we will find measure of angle C as:

[tex]\frac{7}{\sin(C)}=\frac{10}{\sin(62^{\circ})}[/tex]

[tex]\sin(C)=\frac{7\cdot \sin(62^{\circ})}{10}[/tex]

[tex]\sin(C)=\frac{7\cdot 0.882947592859}{10}[/tex]

[tex]\sin(C)=0.6180633150013[/tex]

Now we will use arcsin to solve for C as:

[tex]C=\sin^{-1}(0.6180633150013)[/tex]

[tex]C=38.174844995363^{\circ}[/tex]

[tex]C\approx 38.2^{\circ}[/tex]

Now we will use angle sum property to find measure of angle D.

[tex]\angle D+\angle C+\angle E=180^{\circ}[/tex]

[tex]\angle D+38.2^{\circ}+62^{\circ}=180^{\circ}[/tex]

[tex]\angle D+100.2^{\circ}=180^{\circ}[/tex]

[tex]\angle D+100.2^{\circ}-100.2^{\circ}=180^{\circ}-100.2^{\circ}[/tex]

[tex]\angle D=79.8^{\circ}[/tex]

Therefore, the measure of angle D is approximately [tex]79.8^{\circ}[/tex].

  Measure of angle D will be 79.8°.

          [tex]\frac{c}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{e}{\text{sinE}}[/tex]

        Here, c, d and e are the sides and C, D, E are the angles opposite

        to these sides of the given triangle.

Given in the question,

In ΔCDE,

CD = 10 units

DE = 7 units

m∠E = 62°

By applying sine rule,

[tex]\frac{7}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{10}{\text{sin(62)}}[/tex]

[tex]\frac{7}{\text{sinC}}= \frac{10}{\text{sin(62)}}[/tex]

[tex]\text{sin(C)}=\frac{\text{sin(62)}\times 7}{10}[/tex]

          [tex]=0.618063[/tex]

C = [tex]\text{sin}^{-1}(0.618063)[/tex]

C = 38.175°

   ≈ 38.2°

By triangle sum theorem of a triangle,

m∠C + m∠D + m∠E = 180°

38.2 + m∠D + 62° = 180°

m∠D = 79.8°

       Therefore, measure of angle D will be 79.8°.

Learn more about the sine rule here,

https://brainly.com/question/13152249?referrer=searchResults

Answer:

there are more magnets that  longer than 2 1/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

From the photo, we can see that:

Length of the magnet:

=> the total number of magnets that  longer than 2 1/2 are: 4+1+2 = 7

=> the total number of magnets that  shorter than 2 1/2 are: 1+2+3 = 6

Hence, there are more magnets that  longer than 2 1/2

Hope it will find you well.

Answer:

Step-by-step explanation:

Answer:

18pi, or 56.52

Step-by-step explanation:

To start off, if you were to find the area of any whole circle, you would use the formula: pi x radius^2 = area of circle

However, since this is a semi-circle (half of a whole circle) you would divide the whole expression by 2, and then solve:

(pi x radius^2)/2 = area of semi-circle

(pi x 6^2)/2 = area of semi-circle

(36 x pi)/2 = area of semi-circle

18 x pi = area of semi-circle

18 x 3.14 = area of semi-circle

56.52 = area of semi-circle

The area of a circle is

[tex]\pi \: {r}^{2} [/tex]

So the area of a semicircle would be half of that, or

[tex] \frac{\pi}{2} {r}^{2} [/tex]

So just plug in the radius, six, to get this

[tex]18\pi[/tex]

Answer:

$390

Step-by-step explanation:

3250 x 0.12 = 390

Answer:

The answer is $390

Step-by-step explanation:

12 to the 2nd power=144

15 to the 2nd power =225

225-144=81

square root of 81 is 9

We have been given that the 5th term in a geometric sequence is 160. The 7th term is 40. We are asked to find the possible values of 6th term of the sequence.

We know that an geometric sequence is in form [tex]a_n=a\cdot r^{n-1}[/tex], where,

[tex]a_n[/tex] = nth term of sequence,

a = First term,

r = Common ratio,

n = Number of terms.

We will get two equations using our given information as:

[tex]160=a\cdot r ^{5-1}...(1)[/tex]

[tex]160=a\cdot r ^{4}...(1)[/tex]

[tex]40=a\cdot r ^{7-1}...(2)[/tex]

[tex]40=a\cdot r ^{6}...(2)[/tex]

Upon dividing equation (2) by equation (1), we will get:

[tex]\frac{40}{160}=\frac{a\cdot r^6}{a\cdot r^4}[/tex]

[tex]\frac{1}{4}=r^{6-4}[/tex]

[tex]\frac{1}{4}=r^{2}[/tex]

[tex]r^{2}=\frac{1}{4}[/tex]

[tex]\sqrt{r^{2}}=\pm\sqrt{\frac{1}{4}}[/tex]

[tex]r=\pm\frac{1}{2}[/tex]

Let us solve for a.

[tex]160=a\cdot (\frac{-1}{2})^{4}[/tex]

[tex]160=a\cdot \frac{1}{16}[/tex]

[tex]160\cdot 16=a\cdot \frac{1}{16}\cdot 16[/tex]

[tex]2560=a[/tex]

So our formula would be [tex]a_n=2560\cdot (\pm\frac{1}{2})^{n-1}[/tex].

We cannot determine whether the common ratio would be positive or negative, so we will take both values.

[tex]a_6=2560\cdot (\pm\frac{1}{2})^{6-1}[/tex]

[tex]a_6=2560\cdot (\pm \frac{1}{2})^{5}[/tex]

[tex]a_6=2560\cdot \pm \frac{1}{32}[/tex]

[tex]a_6=\pm 80[/tex]

Therefore, the 6th term of the sequence would be [tex]\pm 80[/tex] and option C is the correct choice.

Answer:

C.+- 80

Step-by-step explanation:

Answer:

13n + 52 + 91m

Step-by-step explanation:

you multiply 13 by every number in the parenthesis

13×n=13n

13×4=52

13×7m=91m

Answer:

Check the explanation

Step-by-step explanation:

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

Answer:

It will produce 6450 bicycles in 30 days

Aaron has 8 apples and Ben has 12 apples

Step-by-step explanation:

A)

A bicycle factory produces 1505 bicycles in a week.

No. of days in 1 week = 7

So, Number of bicycles produced in 7 days = 1505

Number of bicycles produced in 1 day =[tex]\frac{1505}{7}[/tex]

Number of bicycles produced in 30 days = [tex]\frac{1505}{7} \times 30=6450[/tex]

So, It will produce 6450 bicycles in 30 days

B)20 apples are distributed between Aaron and Ben in the ratio 2 : 3.

Let the ratio be x

So, Aaron has apples = 2x

Ben has apples = 3x

So, 2x+3x=20

5x=20

x=4

Aaron has apples = 2x =2(4)=8

Ben has apples = 3x =3(4)=12

Hence Aaron has 8 apples and Ben has 12 apples

Answer:

The answer is 20

Step-by-step explanation:

Given that the smallest angle of rotation for a regular hexagon is 18°. We are to find the number of sides of the polygon. Since the polygon is regular, so all its sides and angles are equal.

Answer:

its 20

Step-by-step explanation:

got it right on my test

Answer:

8/225

Step-by-step explanation:

The probability of each event would be the number of the type of currency that you have specified divided by the total number of coins, in this case the total amount of coins does not change as the coin returns to the bag.

The total number of coins is: 10 + 12 + 8 = 30

The probability of finding a quarter is:

10/30

The probability of finding dime is:

8/30

The probability of finding nickel is:

12/30

The final probability then is:

(10/30) * (8/30) * (12/30) = 960/27000

If we simplify this, dividing both numbers by 120, we are left with:

8/225

Answer:

11/15 pi radians

Step-by-step explanation:

To convert from degrees to radians, multiply by pi/180

132 * pi/180

11/15 pi

Answer:

2.304 radians

hope this helps :)

Answer:

2 nights

Step-by-step explanation:

We need to find how many nights Francesca will have to spend to knit the rest of the scarf.

First, we have to find how much she has left to knit, and then find how many nights it will take her.

She has already knit 28 centimeters of scarf.

She wants to knit a total of 42 centimeters of scarf.

Therefore, the length of scarf left to knit is:

42 - 28 = 14 centimeters

She can knit 7 centimeters each night.

Therefore, the number of nights more she needs to knit 14 centimeters is:

14 / 7 = 2 nights

She will spend 2 nights to knit a total of 42 centimeters of scarf.

Answer:

Step-by-step explanation:

Given the limit function

Lim x → 2: f(x)

1. When f(x) = 9

Then,

From limit theorem

Lim x → xo: K = K

Where k is a constant. Then, the limit of a constant is that constant.

Lim x → 2: 9 = 9

So limit is 9.

2. Lim x → 2: f(x)

Lim x → 2: x

When x = 2

Lim x → 2: 2 = 2

Then, x = 2.

Answer: D- 1,728

Step-by-step explanation: I did the quiz

Answer:

d

Step-by-step explanation:

Answer:

The integers are:

44,46,48

Step-by-step explanation:

Answer:

Value of h greater than 5.4 will make inequality false.

Step-by-step explanation:

This question is incomplete; here is the complete question.

The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel 750 ≥ 75 + 125h. What value of h does NOT make the inequality true?

From the given question,

Per night expense (expected) = $125

If Jones family stays in the hotel for 'h' days then total expenditure on stay = $125h

Charges for scuba diving = $75

Total charges for stay and scuba diving = $(125h + 75)

Since Jones family has saved $750 for the vacation trip so inequality representing the expenses will be,

125h + 75 ≤ 750

125h ≤ 675

h ≤ [tex]\frac{675}{125}[/tex]

h ≤ 5.4

That means number of days for stay should be less than equal to 5.4

and any value of h greater than 5.4 will make the inequality false.

Answer :

9

Explanation :

The expression above signifies the Permutation expression

Permutation expression is given as nPr

The Permutation expression is calculated as:

nPr = P(n, r) = n! / (n - r)!

It the above question, we were asked to evaluate the expression 9P1

From the above question, we can see that:

n = 9 and r = 1

Therefore, the expression

9P1 = 9! / ( 9 - 1) !

9P1 = 9! / 8!

= 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 362880 /40320

= 9

Therefore, the evaluation of the expression 9P1 = 9

Final answer:

To evaluate the expression 9P1, we calculate the permutation for selecting 1 item from 9, which simplifies to 9/1, giving us the answer of 9.

Explanation:

The student has asked to evaluate the expression 9P1, which is a permutation problem. To find 9P1, we use the permutation formula, which is P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, and k is the number of items to choose. In this case, since we want to choose 1 item from 9, the permutation is calculated as:

Therefore, the value of 9P1 is 9.

Answer:

339604.65 cubic feet

Step-by-step explanation:

We are given that 1 m is equal to 3.3 ft.

1 m = 3.3 ft

This means that if we find the volume of a cube of 1 m, we have its volume as:

[tex]1^3 = 1 m^3[/tex]

In the same way, the volume of a cube of 3.3 ft (1 m) is:

[tex]3.3^3 = 35.937 ft^3[/tex]

This means that:

[tex]1m^3 = 35.937 ft^3[/tex]

The Kuroshio sea tank has volume of [tex]9450 m^3[/tex]. Its volume in cubic feet is therefore:

[tex]1m^3 = 35.937 ft^3\\\\9450 m^3 = 9450 * 35.937 = 339604.65 ft^3[/tex]

The volume of the tank is 339604.65 cubic feet.

Answer:

A. Circle

Step-by-step explanation:

Perpendicular to m is parallel to the base of the cones (circular).

Therefore the cross section would be a circle (except at the vertex)

Answer:

24.75m ≤ 30m < 35.75m

Step-by-step explanation:

Minimum area:

5.5 (lower bound of 6m) * 4.5 (lower bound of 5m) = 24.75m

Maximum area:

6.5 (upper bound of 6m) * 5.5 (upper bound of 5m) = 35.75m

Normal area:

6*5=30m

I hope that makes some sense or helps a little!

Answer:

2(2-n)

Step-by-step explanation:

4 - 2n

Factor out a 2

2*2 -2n

2(2-n)

Answer:

75 percent

Step-by-step explanation:

3/4 = 75%

75 - 56 = 19%

Answer:

the first and third

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

Full text:

Here are the low temperatures (in degrees Fahrenheit) for one week in Montreal, Canada:

                          -3.5ºF, 5ºF, 1.5ºF, -0.5ºF, -2ºF, 2.5ºF, -4ºF

Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.

You have to choose two days at random and compare the values of temperature registered those days and compare them, for example:

Day 1: 3rd day: 1.5ºF

Day 2: 7nth day: -4ºF

Comparison of Day 1 and Day 2:

Remember:

"<" indicates that the value from the left is less than the value from the right.

">" indicates that the value from the left is greater than the value from the right.

The temperature registered on Day 1 is 1.5ºF and the temperature registered on Day 2 is -4ºF, as you notice the second temperature is negative and therefore is less than the first temperature:

                                            1.5ºF > -4ºF

Comparison of days with absolute value:

To compare absolute values you have to disregard the sign and consider only the number of the temperature:

|Day 1|= |1.5ºF|

|Day 2|= |4ºF|

Then the registered temperature of Day 1 is less than the registered temperature on Day 2:

                                              |1.5ºF| < |4ºF|

I hope this helps!

Answer:

-4ºF and 1.5ºF

Step-by-step explanation:

Answer:

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]

[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]

Step-by-step explanation:

The area of a rectangle is given by [tex] A = L *W[/tex]

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]

[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]

And the area would be (2.2)^2 times the initial area since is defined as [tex]A = L_f W_f [/tex]

Answer:

The length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Length = 7.5 inches[/tex]

[tex]Width = 3 inches[/tex]

[tex]Scale factor = 2.2[/tex]

Required

Dimension of the new rectangle

The dimensions of the new rectangle can be solved by multiplying the scale factor by the old dimensions;

This means that

New Length = Scale factor * Old Length

and

New Width = Scale factor * Old Width

Calculating the new length

New Length = Scale factor * Old Length

Substitute 2.2 for scale factor and 7.5 for old length; This gives

[tex]New Length = 2.2 * 7.5 inches[/tex]

[tex]New Length = 16.5 inches[/tex]

Calculating the new width

New Width = Scale factor * Old Width

Substitute 2.2 for scale factor and 3 for old width; This gives

[tex]New Width = 2.2 * 3 inches[/tex]

[tex]New Width= 6.6 inches[/tex]

Hence, the length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively

Answer:

30

Step-by-step explanation:

unknown number = x

3/10 × x = 9

3x/10 = 9

3x = 90

x = 30

Answer:

2.7  or 2 7/10.

Step-by-step explanation:

9 * 3/10

= 27 / 10

= 2.7.

Answer:

  (a)  a maximum of 130 and a lower quartile of 10

Step-by-step explanation:

The whiskers of a box plot extend from the minimum to the maximum. The box ranges from the lower quartile to the upper quartile. The middle line divides the box at the median.

Your plot has ...

The maximum and lower quartile are correctly described as 130 and 10, respectively.

Answer:

A. a maximum of 130 and a lower quartile of 10

Step-by-step explanation: