Jason and Beth are married and don’t have any kids yet. They are out of debt except for their house, and they have a full emergency fund. But Beth’s car has sputtered its last breath. Fortunately, she’s found a new one for hundreds less than invoice. The payments will be less than a fourth of their combined take- home pay. This fits Dave’s formula, and the payments can be squeezed into their budget. She’ll take $2,000 out of their emergency fund for the down payment. Jason thinks it’s a really bad idea. Why?​

Answer:

P(A ∩ B ∩ C) is 1/25 ⇒ answer D

Step-by-step explanation:

* Lets talk about the Venn diagram

- There are three circles intersect each other

- The number of elements ∈ (A ∩ B) and ∉ C = 5

∴ n(A ∩ B) and ∉ C = 5

- The number of elements ∈ (A ∩ C) and ∉ B = 6

∴ n(A ∩ C) and ∉ B = 6

- The number of elements ∈ (C ∩ B) and ∉ A = 4

∴ n(C ∩ B) and ∉ A = 4

- The number of elements ∈ (A ∩ B ∩ C) = 2

∴ n(A ∩ B ∩ C) = 2

- The number of elements ∈ A and ∉ B , C = 9

- The number of elements ∈ B and ∉ A , C = 8

- The number of elements ∈ C and ∉ A , B = 7

- The number of elements ∉ A , B , C = 9 ⇒ outside the circles

- The total elements in the Venn diagram is the sum of all

  previous numbers

∴ The total number in the Venn diagram = 5 + 6 + 4 + 2 + 9 + 8 + 7 + 9 =

  50

* To find the probability of (A ∩ B ∩ C), find the total number in

  the Venn diagram and the number of elements in the intersection

  part of the three circles

∵ The total elements in the Venn diagram = 50 elements

∵ n(A ∩ B ∩ C) = 2

∴ P(A ∩ B ∩ C) = 2/50 = 1/25

* P(A ∩ B ∩ C) is 1/25

Answer:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.

Step-by-step explanation:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.

Answer:

cos Ф = adj / hyp = √5 / 3

Step-by-step explanation:

If sin Ф is +, then Ф must be in either Quadrant 1 or Quadrant 2.

If tan Ф < 0, then Ф must be in either Quadrant 2 or Quadrant 3.  

So we conclude that Ф is in Quadrant 2.

If sin Ф = opp / hyp = 2/3, then opp = 2 and hyp = 3, and adj is found using the Pythagorean Theorem:

adj = √( 3² - 2² ) = √( 5 )

With adj = √5 and hyp = 3, cos Ф = adj / hyp = √5 / 3

Answer: Try D

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

Jennifer earned a total of $360 by making 30 plaques in one week.

The subject of this question is Mathematics. Your question is how much Jennifer earned for making 30 plaques in one week if she's paid $12 each. To find out, you simply multiply the number of plaques (30) by how much she earns for each one ($12). So, 30 plaques * $12/plaque = $360. Therefore, Jennifer's gross income for the week is $360.

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d= 157.5 when t is 2.25. all you need to do is plug in 2.25 for t which gives us: d=70(2.25) = 157.7

Multiply the rate, 70 miles per hour, by the given time, 2.25 hours, to find that the distance d is 157.5 miles when t is 2.25 hours.

The question asks for the value of d when t is 2.25 in the equation d = 70t, where d represents the distance in miles and t represents the time in hours. To find the value of d, simply multiply the rate (70 miles per hour) by the given time (2.25 hours).

Solution: d = 70×2.25 = 157.5 miles

Therefore, the distance d when t is 2.25 hours is 157.5 miles.

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Answer:

The correct option is option A

Step-by-step explanation:

We have the following expression:

sqrt(18x^3) - sqrt(9x^3) + 3sqrt(x^3) - sqrt(2x^3)

We know that sqrt(a*b) = sqrt(a)sqrt(b)

Applying this, we have:

sqrt(18)sqrt(x^3) - 3sqrt(x^3) + 3sqrt(x^3) - sqrt(2)sqrt(x^3)

sqrt(x^3)[ sqrt(18) - sqrt(2)]

sqrt(x^3)[ 3sqrt(2)- sqrt(2)]

sqrt(x^3)[2sqrt(2)]

Then we now that:

sqrt(x^3)[2sqrt(2)] = 2x*sqrt(2x)

The correct option is option A

Answer:

3/36 (1/12) or 0.08333... or approximately an 8% chance of rolling a sum greater than 10 (i.e., sum of 11 or 12)

Step-by-step explanation:

There are 36 unique combinations of the 6 sides of the 2 dice

Roll a 1 and a 1 = one combination

Roll a 6 and a 6 = another combination

But roll a 2 and a 3 is treated as unique and different from rolling a 3 and a 2

If you create a 6 x 6 grid where you map out all the possible unique sum combinations of rolling two 6-sided dice you'll find at the very end/bottom of the grid that there are two ways to roll an 11 (5 then a 6; 6 then a 5) and only one way to roll a 12 (6 then a 6). That means there are 3 ways to get a sum greater than 10 out of 36 unique possible combinations

Can you guess why the sum of 7 is "Lucky Seven"?

Answer:

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Step-by-step explanation:

Answer:

f(x)=7sin(4x)+3

Step-by-step explanation:

The word problem is Royal works part-time at a local store and earns $12 per hour.

The equation is y = 12x, the graph is attached and the table is

Hours Worked | Earnings ($)

     1       |      12      

     2       |      24      

     3       |      36      

     4       |      48      

     5       |      60      

Create/Write a direct variation word problem

A direct variation word problem is as follows

Royal works part-time at a local store and earns $12 per hour.

The above is a direct variation word problem and the equation can be represented as

y = 12x

Where

So, we have the table of values to be

Hours Worked | Earnings ($)

     1       |      12      i.e. 12 * 1

     2       |      24      i.e. 12 * 2

     3       |      36      i.e. 12 * 3

     4       |      48      i.e. 12 * 4

     5       |      60      i.e. 12 * 5      

The graph of the function is added as an attachment

Answer:

The answer is 21.4.

Step-by-step explanation: Thank me later :)

Answer:

21.4

Step-by-step explanation:

Answer:

Part 1) Helen's age is 32 years old and Jane's age is 24 years old

Part 2) 13 twenty-dollar bills

Step-by-step explanation:

Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?

Let

x----> Helen's age

y---> Jane's age

we know that

x=y+8 ----> equation A

(x-20)=3(y-20) -----> equation B

substitute equation A in equation B and solve for y

(y+8-20)=3(y-20)

y-12=3y-60

3y-y=60-12

2y=48

y=24 years

Find the value of x

x=y+8

x=24+8=32 years

Part 2)

Let

x-----> the number of five-dollar bills

y----> the number of twenty-dollar bills

we know that

5x+20y=305 -----> equation A

y=x+4 ------> x=y-4 ------> equation B

substitute equation B in equation A and solve for y

5(y-4)+20y=305

5y-20+20y=305

25y=325

y=13 twenty-dollar bills

Find the value of x

x=y-4

x=13-4=9  five-dollar bills

Answer:

The correct option is:  82°

Step-by-step explanation:

In the given diagram, two chords [tex]RT[/tex] and [tex]SU[/tex] are intersecting.

According to the Angle of intersecting chord theorem, "If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle."

That means here......

[tex]94\°=\frac{1}{2}(m\widehat{RS}+m\widehat{TU})\\ \\ 94\°=\frac{1}{2}(106\°+m\widehat{TU})\\ \\ 2(94\°)=106\°+m\widehat{TU}\\ \\ 188\°=106\°+m\widehat{TU}\\ \\ m\widehat{TU}=188\°-106\°=82\°[/tex]

So, the measure of arc [tex]TU[/tex] is 82°

Please mark me as brainliest if this answer is correct and nobody tops it.

So, 18.50/2 = 9.25, so you can just multiply 9.25 by 7

9.25 · 7 = 64.75.

So Sammy earned $64.75, hope she buys something nice for herself with it. :)

Answer:

  Stock A and Stock B

Step-by-step explanation:

After 1 year, the value of Stock A is 58/50 = 1.16 times what it was, an increase of 16%.

After 1 year, the value of Stock B is 29/25 = 1.16 times what it was, an increase of 16%.

The bond has coupon value of $298.90 each year, about 5.02% of the amount invested. (However, the value of the bond at the end of 4 years is only $3500, so represents a net loss of about $1254.40 over that time period. We're not quite sure why Norvin purchased this bond at that price.)

Stock A and Stock B have the highest rate of return.

A. Permutation; number of ways =24

Answer:

Option A. Permutation; number of ways = 24

Step-by-step explanation:

At a competition with 4 runners, 4 medals are rewarded for place place to fourth place.

We have to tell in this situation we will use permutation or combination to find the number of ways, medals can be rewarded.

We know when order matters then permutation is applied.

So number of ways to award the medals will be = 4! = 4×3×2×1 = 24

Therefore, option A. permutation : number of ways = 24 is the answer.

Answer:

x= 437.3 ft

Step-by-step explanation:

1: You need to find the angle opposite of x. :

         90-29 = 61 degrees.

2. Use the trig function sine and substitute values:

         sin61= (x/500)

         500sin61 = x

         x=437.309 ft

Answer:

158.9 mph E 12.7° S

Step-by-step explanation:

Since the components of the motion are perpendicular to each other then magnitude of the resultant can be found using the Pythagorean theorem:

|v| = √(155^2 +35^2) ≈ 158.9 . . . . mph

The angle can be found using the tangent relationship:

tan = opposite/adjacent

The angle south of east will be

angle = arctan(35/155) ≈ 12.7°

The velocity vector can be described by ...

158.9 mph E 12.7° S

_____

As a bearing, the vector might be described as either of ...

• 158.9 mph at 102.7°

• 158.9 mph S 77.3° E

Final answer:

The third side of a triangle with sides of 6 inches and 12 inches must be greater than 6 inches and less than 18 inches in length, without being exactly 6 or 18 inches.

Explanation:

The length of the third side of a triangle with two sides measuring 6 inches and 12 inches must adhere to the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Consequently, for the given triangle, the possible range for the length of the third side, denoted as x, is between 6 inches and 18 inches (exclusive), that is: 12 - 6 < x < 12 + 6. The value of x cannot be exactly 6 or 18 inches because the triangle would collapse into a straight line. Therefore, the permissible length can be any real number greater than 6 inches but less than 18 inches.

Answer:

Step-by-step explanation:

Be the sides x[tex]x, x+6[/tex] you know [tex]x(x+6) = 112[/tex] or [tex]x^2 +6x -112 = 0[/tex][tex]x= -3 \pm \sqrt{9+112} = -3\pm 11[/tex] the solution is [tex]x=8, x=-14[/tex] The negative answer is to be discarded, your rectangle has sides 8 and [tex]8+6=14[/tex] miles

The length of the rectangle is 14 miles and the width of the rectangle is 8 miles.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = (L × W) unit^2

Perimeter of the rectangle = 2(L + W) units

Let the width of the rectangle be represented by W, while the length is represented by L.

Given the width is 6 miles less than its length, therefore, the width can be written as,

W = (L - 6) miles

Now given the area of the rectangle is 112 sq. miles, therefore, the area of the rectangle can be written as,

Area of the rectangle = Length × Width

112 = L × W

112 = L × (L-6)

112 = L²-6L

L = 14, -8

Since the length, L can not be negative, the value of L is 14 miles, therefore, the width will be 8 miles.

Hence, the length of the rectangle is 14 miles and the width of the rectangle is 8 miles.

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Answer:

11.9 mm

Step-by-step explanation:

We can find d by applying the cosine rules.

d²  = 21² + 27² - 2(21)(27) cos (25)

d²  = 441 + 729 - 1027.75

d²  = 142.25

d = √142.25

d = 11.9 mm (nearest tenth)

Answer:

True

Step-by-step explanation:

Because it is going back and forth it is

the answer is B. hope this helps.

Answer:

the answer is B)

Step-by-step explanation:

Answer:

From the information we have, we can prove that ΔBDA is similar to ΔCDB:

∠BDA≅∠CDB, ∠BAD≅∠CBD

=> ΔBDA ~ ΔCDB

=> BD/CD = AD/BD

=> 8/x = 15/8

=> x = (8 · 8)/15 ≈ 4.267

And we also have:

AD/BD = AB/BC

=> 15/8 = 17/y

=> y = (17 · 8)/15 ≈ 9.067

*I could be wrong though

Answer:

x = 4.267 and y = 9.067

Step-by-step explanation:

The triangle on the left and the triangle on the bottom are similar triangles.

Therefore, the following equation of ratios is true:

   y         8

------- = ------

  17        15

resulting in 15y = 8(17).   Then 8(17)/15 = 9.067.

Also:

 x       9.067

----- = -----------

 8          17

resulting in 17x = 8(9.067) = 72.533

Then x = 72.533/17 / 17 = 4.267

In summary, x = 4.267 and y = 9.067.

Answer:

a=3.915 and b=1.106

Step-by-step explanation:

This is the answer on edju

Answer:

Your answer is A,B,AND D

Step-by-step explanation:

The standard deviation for a sample of test scores is 0 tells you that, B) all the test scores must be the same value.

Standard deviation is a measure in statistics which describes how much is each quantity given deviates from the mean of the whole population.

When a sample of test scores are having a standard deviation of 0, this tells you that, the deviation of each of the values from the mean is 0.

This means that all the values must have the same value.

Suppose the data set is, 1, 1, 1, 1, 1.

All the data points are same.

Mean = 1

Deviation of each of the point from mean = 0

So standard deviation = 0

All the test scores are 0 is a special case of the above case where all the test scores are same.

Hence option B is correct.

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Answer:

The measure of the other acute angle is 38°

Step-by-step explanation:

we know that

In a right triangle, the sum of the two acutes angles must be equal to 90 degrees (are complementary angles)

Let

x -----> the measure of the other acute angle

x+52°=90°

Solve for x

Subtract 52° both sides

x=90°52°

x=38°

13.05 is the answer because the area of a triangle is A=1/2bh (base times height divided by 2) and 2.9x9=26.1 and 26.1 divided by 2 is 13.05

Yes by definition of parallelogram

Answer:

False

Step-by-step explanation:

Answer:

y - 0.32y = 0.68y

y + 0.32y = 1.32 y

Step-by-step explanation:

To simplify expressions, add/subtract using the coefficients of the terms.

y – 0.32y should be 1 - 0.32 = 0.68. This simplifies to 0.68y.

y + 0.32y should be 1 + 0.32 = 1.32. This simplifies to 1.32y.

7/5y = y+2/5y

0.68y = y-0.32y

3/5y = y-2/5y

1.32y = y+0.32y

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Answer:

Part 1) Area of rectangle [tex]3,600\ ft^{2}[/tex]

Part 2) Area of semicircle [tex]1,413\ ft^{2}[/tex]

Par 3) Total area of grass [tex]2,187\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The total area of grass is equal to the area of rectangle minus the area of semicircle

step 1

Find the area of rectangle

The area of rectangle is equal to

[tex]A=45*80=3,600\ ft^{2}[/tex]

step 2

Find the area of semicircle

The area of semicircle is equal to

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

we have

[tex]r=60/2=30\ ft[/tex] -----> the radius is half the diameter

substitute

[tex]A=\frac{1}{2}(3.14)(30)^{2}[/tex]

[tex]A=1,413\ ft^{2}[/tex]

step 3

Find the total area of grass

[tex]3,600\ ft^{2}-1,413\ ft^{2}=2,187\ ft^{2}[/tex]