−28 = 7b

Solve for b
Tell what you did to find b

Answer:

Step-by-step explanation:

x(x+8) = 450

x² + 8x - 450 = 0

Quadratic formula:

x = [-8±√(8²-4(1)(-450))]/[2(1)]

= [-8±2√466]/2

= -4±√466

≅ 17.59, -25.59

-25.59 is an extraneous solution, so x ≅ 17.6 inches.

The dimensions of the blackboard are 17.59 inches by 25.59 inches  

Answer:

The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is

contained by the interval (0.54 , 5.18)

Step-by-step explanation:

Given that:

for women

sample size  = n₁ = 16

sample mean [tex](\bar X_1)[/tex] = 24.75

standard deviation s₁ = 2.84

for men

sample size for men = n₂ = 7

sample mean [tex](\bar X_2)[/tex] = 21.89

standard deviation s₂ = 3.29

degree of freedom = [tex](n_1 + n_2 )-2[/tex]

= 16 + 7 -2

= 21

The critical value for [tex]\alpha = 0.1 \ and \ df \ of \ 21 \ is :[/tex]

[tex]t_{0.005;21}= 1.721[/tex]

The pooled standard deviation can be calculated as follows since the population variances are assumed to be equivalent.

[tex]s_p = \sqrt{\dfrac{(n_1 -1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt{\dfrac{(16 -1)2.84^2+(7-1)3.29^2}{16+7-2}}[/tex]

[tex]s_p = \sqrt{\dfrac{(15)8.0656+(6)10.8241}{21}}[/tex]

[tex]s_p = 2.976[/tex]

The standard error is estimated as follow:

[tex]se = s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}[/tex]

[tex]se = 2.976\sqrt{\dfrac{1}{16} + \dfrac{1}{7}}[/tex]

se = 1.348

Finally, the confidence interval [tex]C.I = ( x_1 -x_2 -t_c \times se \ \ ; \ \ x_1-x_2 +t_c \times se)[/tex]

[tex]=(24.75 - 21.89 -1.721 \times 1.348 \ \ , \ \ 2475 - 21.89 + 1.721 \times 1.348) \\ \\ \mathbf{ = (0.54 \ \ , \ \ 5.18)}[/tex]

Answer:

she spend one hour and 43 minutes reading

Step-by-step explanation:

hope you have a great day kee learning

The question is incomplete. The complete question is :

The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile and c is measured in miles. What are the units of [tex]$\int_0^7 r(c) \ dc$[/tex]   ?

Solution :

The given continuous function is :

r(c), here c is measured in miles and the unit of r is measured in gallons per mile.

So the unit of  [tex]$\int_0^7 r(c) \ dc$[/tex] is given by :

= gallons per mile x mile

= gallons

So, the final unit is gallons.

Answer:

C.

Step-by-step explanation:

Length * width * height = volume

15*9*9 = 1215

The expression of 5.39 × 10⁷ metric tons in standard notation is; 53,900,000 metric tonnes

We are given the quantity of wheat produced each year as 5.39 × 10⁷ metric tons.

Now, that quantity is in exponent form and the way to express it in standard notation is to expand the exponent which gives;

5.39 × 10⁷ = 5.39 * 10 * 10 * 10 * 10 * 10 * 10 * 10

⇒ 5.39 * 10000000

⇒ 53,900,000 metric tonnes

The complete question is;

The U.S. produces 5.39 × 10⁷ metric tons of wheat each year. Express that number in standard notation

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Answer:

remainder = 6

Step-by-step explanation:

Hope it helps.....

Answer:

4.5%

Step-by-step explanation:

compound interest formula:

[tex]PV(1+\frac{i}{n})^{t*n}[/tex]

[tex]220=160(1+\frac{x}{365})^{365*7}\\\\1.375=(1+\frac{x}{365})^{2555}\\1.0001246=1+\frac{x}{365}\\x=.0454962254126[/tex]

this rounds to

x=4.5%

Aubrey would need an interest rate of 6.3%.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

A = P [tex](1 + r/n)^{nt}[/tex]

A = the final amount (in this case, $220)

P = the initial investment (in this case, $160)

r = the interest rate (what we are trying to find)

n = the number of times the interest is compounded per year (since it's compounded daily, n = 365)

t = the time period (in years, in this case, 7)

Substituting in the given values and solving for r:

220 = 160(1 + r/365)^(3657)

220/160 = (1 + r/365)^(3657)

1.375 = (1 + r/365)^2555

ln(1.375) = 2555 ln(1 + r/365)

ln(1 + r/365) = ln(1.375)/2555

1 + r/365 = e^(ln(1.375)/2555)

r/365 = e^(ln(1.375)/2555) - 1

r = 365(e^(ln(1.375)/2555) - 1)

r ≈ 6.3%

Therefore,

Aubrey would need an interest rate of 6.3%.

Learn more about compound interest here:

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Answer:

The 2 rays the form ACB ARE AC and CB

Answer:

15

Step-by-step explanation:

you would first have to put the numbers into this equation

180=(6x-8)+38+60

now you have to solve for x

180=(6x-8)+98

82=6x-8

100=6x

15=x

x=15

hope this helps! have a nice day :)

Answer:

its c

Step-by-step explanation:

because every angle in a acute triangle has to be less than 90 and the other two look bigger than angle x

Answer:

The length of the legs of the triangle is 8 units.

Step-by-step explanation:

45-45-90 triangle

A 45-45-90 triangle is a special case of a right triangle in which both legs l have the same value and the hypothenuse is h. By the Pythagorean Theorem:

[tex]2l^2 = h^2[/tex]

Hypothenuse of 8 V2

This means that [tex]h = 8\sqrt{2}[/tex]

So

[tex]2l^2 = h^2[/tex]

[tex]2l^2 = (8\sqrt{2})^2[/tex]

[tex]2l^2 = 64*2[/tex]

[tex]l^2 = 64[/tex]

[tex]l = \sqrt{64}[/tex]

[tex]l = 8[/tex]

The length of the legs of the triangle is 8 units.

Answer:

The colume of Ruslan's figure is 60 cubic centimeters.

Step-by-step explanation:

To find the volume of something, you have to multiply the length by the width, and then multiply that to the height. So you would multiply 5 and 3 to get 15, and then you would multiply 15 and 4 to which then you would get your answer of 60 cubic centimeters.

Answer:

60cm³ is your answer

Step-by-step explanation:

volume of cuboid =l×b×h=5×3×4=60cm³

Answer:

33%

Step-by-step explanation:

Answer:

y=5x

Step-by-step explanation:

first, we know that a rising line's slope is always positive, so the first one is incorrect

let's figure out the slope: y-y'/x-x' is the formula.

now, -5-5/-1-1= -10/-2= 5. so the slope of this line is 5.

Answer:

18 because of its addition

Step-by-step explanation:

πr²=3+2+7+2+2+2

=5+9+4

=18

Answer:

30 units²

Step-by-step explanation:

a=1/2 ×length × width

a=1/2 × 12 ×5

a=6×5

a=30units squared

Answer:

14 x 6.9 x 8 = 56

Step-by-step explanation:

Answer:

Mr. adhakari deposited a sum of RS 2400 in a bank at 5% per year simple interest. how much interest would he get at the end of 4 year ?​ - 480 rs

Answer:

B. 36π in²

Step-by-step explanation:

Given:

Volume = 54π in³

height (h) = 6 in.

Required:

Curved surface area of the can (area for the label needed to wrap around the can without overlapping)

Solution:

First, we need to find the radius (r) of the can.

Volume = πr²h

Plug in the given values and solve for r

54π = π*r²*6

54π = 6π*r²

54π/6π = r²

9 = r²

r = √9

r = 3 in

✔️Find the curved surface area:

Curved surface area = 2πrh

r = 3 in

h = 6 in

Plug in the values

C.S.A = 2*π*3*6

C.S.A = 36π in²

Answer:

The answer is A

Step-by-step explanation:

A closed circle means the number is included in the equation / solution. An open circle means it is not. The problem says greater than or equal to 36 inches tall which means that circle should be closed. And less than 48 inches. It does not say anything about being equal when it states the 48 inches so that one should be open.

Answer:

y = 1x + 6

Step-by-step explanation:

y = mx + b is the formula we need to use. b is the y intercept which is clearly 6 on the graph. Then we need to use rise over run to find our m. We can see for every x value that increases by 1, y also increases at 1. This means our x is 1.

Answer:

(0,6) ,(4,10)

y=(10-6)/×=(4-0)

4/4= 1

Answer:

1 bagel $3.5

1muffin $1.25

1ticket$9

1snack$2

Step-by-step explanation:

miffin(y)

bagel(x)

x+3y=7.25

x+2y=6

since x is similar in both equations you cancel it out

subtract this

3y=7.25

2y=6

question 8:ticket(x)

snack(y)

2x+3y=24×3

3x+4y=35×2

×3 and ×2 so we can eliminate the x

6x+9y=72

6x+8y=70

eliminate x

y=2

so snack is $2

2x+(3×2)=24

24-6=18

18÷2x=9

so a ticket is $9

Answer:

[tex]x + y \ge 10[/tex]

[tex]x + 2y \le 20[/tex]

Step-by-step explanation:

The question is incomplete as the graphs are not shown. So, I will derive the inequalities and plot the graph.

Given

[tex]Banana = \$1[/tex]

[tex]Orange = \$ 2[/tex]

[tex]Purchase = 10lb[/tex] --- At least

[tex]Spedings = \$20[/tex] --- Not more than

And we have:

[tex]x = Banana; y = Orange[/tex]

The number of purchase will be represented as:

[tex]x + y \ge Purchase[/tex] ---- (at least)

[tex]x + y \ge 10[/tex]

The amount spent will be represented as;

[tex]1 * x + 2 * y \le 20[/tex] --- (not more than)

[tex]x + 2y \le 20[/tex]

So, the inequalities are:

[tex]x + y \ge 10[/tex]

[tex]x + 2y \le 20[/tex]

See attachment for graph

Answer:

Step-by-step explanation:

F(x) = 2 - x²

Answer:

27 cubic units

Step-by-step explanation:

A cube has equal dimensions. So the volume is 3units × 3units × 3units or 27cubic units

Answer:

D. 100 cubic units

Step-by-step explanation:

There are 10 cubes in each layer (count at the top) and 10 layers (from top to bottom) in total. Multiply these to get volume.

10 x 10 =100

Answer:

B. 60 cubic units

Step-by-step explanation:

Formulas for a cube:

The volume of a cube:

V = a3

The surface area of a cube:

the area of each face (a x a) times 6 faces

S = 6a2

Face diagonal of a cube:

By the Pythagorean theorem, we know that

f2 = a2 + a2

Then f2 = 2a2

solving for f we get

f = a√2

Diagonal of the solid cube:

Again, by the Pythagorean theorem, we know that

d2 = a2 + f2

substituting f into this equation we get

d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2

solving for d we get

d = a√3

Answer:

A

Step-by-step explanation:

The point Y is the center of the circle

the correct answer for point y is c

Step-by-step explanation:

use pythagoras theorem

a squared +b squared =c squared

4.12 squared +8 squared =x squared

16.9744+64=x squared

take the square root of 80.9744

x=9