In selecting one card from a deck of cards is obtaining a queen and obtaining a 2 mutually exclusive events?

A: Yes/True
B: No/False

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.

f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).

The area of a trapezoid is the height times the average of the bases.

a. f(x)=-2x+8  f(0)=8, f(4)=0;

   area = 4(8/2) = 16

b. f(x)=x+2; f(0)=2, f(4)=6;

   area = 4(8/2) = 16

c. f(x)=3x-2; f(0)=-2, f(4)=10;

    area = 4(8/2) = 16

d. f(x)=5x-6; f(0)=-6, f(4)=14;

    area = 4(8/2) = 16

e. f(x)=7x-9; f(0)=-9, f(4)=19;

     area = 4(10/2) = 20

Thus, The area is NOT 16 for choice e.

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Answer:

its 420

Step-by-step explanation:

420+69+69=420

Answer:

If in rectangular coordinates we have a point (x, y), then the angle defined between the x-axis and a ray that connects the point with the origin is defined by:

Tan(θ) = y/x

Cos(θ) = x/(√(x^2 + y^2))

Sin(θ) = y/(√(x^2 + y^2))

Ctg(θ) = x/y

Sec(θ) = √(x^2 + y^2)/x

Csc(θ) = √(x^2 + y^2)/y

Ok, now we have all the equations.

We know that:

Sec(C) = 30/24

Then:

√(x^2 + y^2) = 30

x = 24

Replacing x in the first equation we get:

√(24^2 + y^2) = 30

y = √(30^2 - 24^2) = 18

Then we have:

x = 24

y = 18

√(x^2 + y^2) = 30

So we can just replace these in the equations:

Tan(C) = y/x = 18/24

Cos(C) = x/(√(x^2 + y^2)) = 24/30

Sin(C) = y/(√(x^2 + y^2)) = 18/30

Ctg(θ) = x/y = 24/18

Sec(θ) = √(x^2 + y^2)/x = 30/24

Csc(θ) = √(x^2 + y^2)/y = 30/18

Answer:

The third option if you ment to type 54 and not 5.4 if you meant 5.4 then that would be 5 and four tenths.

Step-by-step explanation:

Hope this helps ❤️

Step-by-step explanation:

Perimeter of EFGH=2.5+1.5+4+2

=10

=

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

[tex]6(2)x + (2)y = 12(2) \\ + \\ - 4x - 2y = 0 \\ = \\ 8x = 24 \\ x = 24 \div 8 \\ x = 3[/tex]

Answer:

X=90

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

Answer:

Step-by-step explanation:

Answer:

A cross section parallel to the base is a square with side lengths of less than 2 ft.

A cross section perpendicular to the base through the top vertex is a triangle with different dimensions than the triangular sides of the pyramid.

A cross section that is perpendicular to the base that does not pass through the top vertex of the pyramid is a trapezoid.

B D E

Step-by-step explanation:

Answer:

BDE

Step-by-step explanation:

I GOT IT RIGHT

Answer:

R=9.5

Step-by-step explanation:

If anyone could pls do this for me  

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Answer:

Radius(r) = 9.5 cm

Happy learning!

Applepi101

Answer:

Perimeter = 9 . 4=36 ft

lateral area=(perimeter . slant height) / 2 = (36 . 12) /2 = 216 sq ft

area of the base=9*9=81 sq ft

Surface area = LA+BA = 216 + 81 = 297 sq ft

Answer:

14

Step-by-step explanation:

Given

See attachment for proper stem plots for both district

Required

The sample size for Southeastern

The stem plot for southeastern is:

[tex]Stem | Leaf[/tex]

[tex]0 | 5\ 5\ 7\ 8[/tex]

[tex]1 | 1\ 2\ 3\ 5\ 9\ 9[/tex]

[tex]2 |2\ 7[/tex]

[tex]3 | 3[/tex]

[tex]4 | 1[/tex]

[tex]5 |[/tex]

To get the sample size, we simply count the leaves

The leaves are:

[tex]Leaves = \{5, 5, 7, 8, 1, 2, 3, 5, 9 ,9,2,7,3,1\}[/tex]

The number of leaves is:

[tex]n(Leaves) = 14[/tex]

Hence, the sample size is 14

Answer:

1

Step-by-step explanation:

Answer:

1.) 3833.8

2.) (3428.81 ; 4238.79)

Step-by-step explanation:

1.)

Point estimate of the salary for student with GPA of 3.

Using the regression model given :

Y = 2090.5 + 581.1x

x = 3

Y = 2090.5 + 581.1(3)

= 3833.8

2.)

95% confidence interval :

Y ± Tcritical * √MSE

Y = point estimate at x =3 ; = 3833.8

MSE = 21,284

Tcritical at 95% ; df = n-2 = 6-2 = 4

Tcritical(0.025 ; 4) = 2.776

√MSE = √21284 = 145.89036

Lower boundary : 3833.8 - 2.776(145.89036) = 3428.81

Upper boundary : 3833.8 + 2.776(145.89036) = 4238.79

(3428.81 ; 4238.79)

Answer:

172,600

Step-by-step explanation:

hii so basically the mean is the same as average so add all together and divide by how many prices in this case there originally were

so 181,000+187,000+144,000+176,000+175,000=863,000

then divide by 5

863,000/5=172,600

hope this helped !

Answer:

[tex] log(2x) = 2 \\ 2x = {10}^{2} \\ 2x = 100 \\ x = 50[/tex]

The value of x that satisfies this equation log(2x) = 2 is 50

The equation is given as:

log(2x) = 2

Change the equation to an exponential equation

2x = 10^2

Evaluate the exponent

2x = 100

Divide both sides by 2

x = 50

Hence, the value of x that satisfies this equation log(2x) = 2 is 50

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Answer:

A

Step-by-step explanation:

Given p² varies inversely as q then the equation relating them is

p² = [tex]\frac{k}{q}[/tex] ← k is the constant of variation

To find use the condition when q = 6, p = 4 , then

4² = [tex]\frac{k}{6}[/tex]

16 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 )

96 = k

p² = [tex]\frac{96}{q}[/tex] ← equation of variation

When p = 12 , then

12² = [tex]\frac{96}{q}[/tex] ( multiply both sides by q )

144q = 96 ( divide both sides by 144 )

q = [tex]\frac{96}{144}[/tex] = [tex]\frac{2}{3}[/tex] → A

Answer:

the plane landed at 10:43 A.M

Answer:

8422

Step-by-step explanation:

Answer:

Hence, the answer is [tex]x>71.1515[/tex]

Step-by-step explanation:

We have,

[tex]n=100,\mu=70,\sigma=7[/tex]

The top percentage of the students is [tex]5\%[/tex]

The  lower percentage of the students is [tex]95\%[/tex]

The lowest [tex]95\%[/tex] is the left area from the normal distribution table, the area [tex]0.95[/tex] lies in the z-table

[tex]z=1.645[/tex]       from the z- table

[tex]P(z<1.645)=0.95\\P(z>1.645)=0.05\\z>1.645[/tex]

[tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{\mu}} } >1.645\\x>1.645\times \frac{\sigma}{\sqrt{n}} +\mu[/tex]

   [tex]>1.645\times \frac{7}{\sqrt{100}} +70[/tex]

   [tex]\Rightarrow x>71.1515[/tex]

Answer:

5. 2√6

6. 4

Step-by-step explanation:

5. x =√[3×(3+5] = √3×8 =√24=2√6

6. x(x+5)=6²

x²+5x=36

x²+5x-36=0

(x+9)(x-4) =0

x=-9 or x=4

Answer:

Mai

Step-by-step explanation:

1. 21.675 R $22

2. $21

Mai is the correct method because 15%-100%=85, which shows the percentage that is left to multiple. Then she multiples 0.85 times 2 as she was able to take off 15% twice. Elena's is incorrect because she added the two 15% off and subtracted that by 100 giving her 70. Which is the incorrect decimal to multiple by. Hope this helps.

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Answer:

a equal to five.b equal to three

b=3

intersection is the answer

Answer:

c=9.1 miles

Step-by-step explanation:

a^2+b^2=c^2

6.2^2+6.7^2=c^2

38.44+44.89=c^2

83.33=c^2

√83.33=c

c=9.12852671574

Round to nearest 10th

c=9.1

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Answer:

9.1 miles

Step-by-step explanation:

6.7²+6.2²=h² 44.89+38.44=h² 83.33=h² find the square root of 83.33

Answer:

C: 18

Step-by-step explanation:

Answer:

530!

Step-by-step explanation:

subtract the biggest value and the lowest value

Answer:

530

Step-by-step explanation:

Order the numbers from least to greatest, get the biggest and the lowest number and subtract both and then you find the range.

340,400,400,870

870-340= 530

Answer:

Scalene,right angled triangle

Hope it helps