You have 5 math books and 6 history books to put on a shelf with five slots. In how many ways can you put the books on the shelf if the first two slots are to be filled with math books and the next three with history books?

Answer:

your answer will be -1.2

Step-by-step explanation:

hope it helps you

have a great day

The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).

The correct answer option is option B and C

y ≥ 2/3x + 2

y < - 1/3x + 1

Check all that applies:

(x, y) = (−6, −3)

(x, y) = (−6, −2)

(x, y) = (−6, 3)

(x, y) = (−6, 4)

y ≥ 2/3x + 2

substitute x = -6 into the inequality

y ≥ 2/3(-6) + 2

y ≥ -12/3 + 2

y ≥ - 4 + 2

y ≥ - 2

(x, y) = (-6, -2)

y < - 1/3x + 1

substitute x = -6 into the inequality

y < -1/3(-6) + 1

y < 6/3 + 1

y < 2 + 1

y < 3

(x, y) = (-6, 3)

So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).

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Answer:

the value of the expression is 22

Step-by-step explanation:

a2 + 12 + b

- input numbers..

(-2)2 + 12 + 14

-4 + 12 + 14

8 + 14

22

final answer 22

Answer:

18 (see picture for detailed explanation)

Step-by-step explanation:

Plato/Edmentum

Answer:

V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3

Step-by-step explanation:

hope it will help you dear

you told only formula if you need derevation then say :)

Answer:

6

Step-by-step explanation:

2/ 1/3= 6

Answer:

= 6

Step-by-step explanation:

you can do the keep, switch, flip strategy

keep 2/1, switch division to multiplication, and flip 1/3 to 3

2 x 3 = 6

The required number of litres of pure and 85% maple syrup required to produce 150 litres of 96% maple syrup is 40 litres and 110 litres respectively.

Let :

Amount of pure (100%) maple syrup = a

Amount of 85% map’e syrup = b

Creating a system of equation :

From (1)

Substitute a = 150 - b into (2)

From (1)

Therefore, 40 litres of pure maple syrup and 110 litres of 85% maple syrup will be used.

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Answer:

m= -1

y intercept= 1

y= - x + 1

Step-by-step explanation:

The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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The equation of the perpendicular line is y = -5

We have to recall that the general form of the equation of a line can be given by the expression that is written as y = mx + c. m is the slope of the graph while c is the intercept of the graph.

We would then have;

y - \(y_{1}\) = m(x - \(x_{1}\))

We can see that m = 0 from the first line that has been given the we have;

y - (-5) = 0(x - 4)

y + 5 = 0

y = -5

This is the equation that has been required in the problem above.

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Answer:

C: infinitely many solutions

Step-by-step explanation:

Answer:

answer is (2,-4)

Step-by-step explanation:

I did it's process in next question

Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

Answer:

The surface area is 23

Step-by-step explanation:

Good Luck!

Answer:

A=2(wl+hl+hw)=2·(8·10+5·10+5·8)=340

Step-by-step explanation:

When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The form of the polynomial is given as:

ax2 + bx + c

Where a, b, and c are positive real numbers.

Since a, b, and c are positive real numbers. then the form of the expansion would be:

ax2 + bx + c = (dx + e)(fx + g)

Take for instance, we have the following quadratic equation

x^2 + 6x +  8

Expand the equation

x^2 + 6x +  8 = x^2 + 4x + 2x +  8

Factorize the equation

x^2 + 6x +  8 = (x + 2)(x + 4)

Hence, the signs in the binomials should be both positive

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Answer: your question is poorly written attached below is the complete and well written question

answer : The minimal polynomial has degree m + 1 hence Z^m+1

Step-by-step explanation:

Given that

N ∈ L(V) is nilpotent

attached below is the required prove

Answer:

To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:

x y

0 1

1 3

2 5

3 7

4 9

To get the value of y, we substitute each value of x into the equation and simplify:

When x = 0:

y = 2(0) + 1 = 1

When x = 1:

y = 2(1) + 1 = 3

When x = 2:

y = 2(2) + 1 = 5

When x = 3:

y = 2(3) + 1 = 7

When x = 4:

y = 2(4) + 1 = 9

Therefore, the table of values for the equation y = 2x + 1 is:

x y

0 1

1 3

2 5

3 7

4 9

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

Work Shown:

\(\frac{\text{KM}}{\text{NM}} = \frac{\text{KL}}{\text{NO}}\\\\\frac{\text{KN}+\text{NM}}{\text{NM}} = \frac{\text{KL}}{\text{NO}}\\\\\frac{7+x}{x} = \frac{15}{10}\\\\10(7+x) = 15x\\\\\)

\(70+10x = 15x\\\\70 = 15x-10x\\\\5x = 70\\\\x = \frac{70}{5}\\\\x = 14\\\\\text{NM} = 14\)

Side note: The triangles are similar, which allows us to set up the proportion in step 1.

Answer:

Answer is A I believe

Step-by-step explanation:

The value of w from the given triangle VWX is 5 units. Therefore, option D is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle VWX, ∠X=51°, ∠W=16° and VW=x=14.

Here, sinX/x=sinW/w

sin51°/14=sin16°/w

0.7771/14=sin16°/w

0.7771/14=0.2756/w

0.0555=0.2756/w

w=0.2756/0.0555

w=4.965

w≈5

Therefore, option D is the correct answer.

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Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.

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Answer:

x = 3

Step-by-step explanation:

using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\)

\((2^2)^{x}\) = 64

\(2^{2x}\) = \(2^{6}\)

since the bases on both sides are equal , then equate the exponents

2x = 6 ( divide both sides by 2 )

x = 3

The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.

The length of a section of a circle's circumference is known as an arc length.

The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.

To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:

m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)

m(EGD) = 360° - 80° - 47° - 90°

m(EGD) = 143°

The formula for arc length is:

Arc length = (central angle / 360) x (2πr)

We can use this information to find the radius of the circle:

FG = 2r

27 yd = 2r

r = 13.5 yd

Now we can use the formula for arc length to find the length of arc FED:

Arc length FED = ((∠FED) / 360) x (2πr)

We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):

∠(FED) = 360° - ∠(EGD)

∠(FED) = 360° - 143°

∠(FED) = 217°

Plugging in the values, we get:

Arc length FED = (217° / 360) x (2π x 13.5 yd)

Arc length FED = (0.6028) x (84.78 yd)

Arc length FED = 51.11 yd

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Answer:

the berry-scented pillar candle

Step-by-step explanation:

khan academy

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

Answer:

this is just division

6/4=1/2

each book weighs 1/2

Hope This Helps!!!

Answer:

the answer is 1.5 pounds

Step-by-step explanation:

just took the the test

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ? [Hint: Let Y = the number among the 1000 intervals that contain μ. What kind of random variable is Y?]

(Round your answer to four decimal places.)

Answer:

The expected value is

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

\(P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

There is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients.

From the above information, we know that,

n = 1000

p = 0.98

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

The expected value is given by

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and p is also greater than 0.50.

n×p ≥ 10

1000×0.98 ≥ 10

980 ≥ 10  (satisfied)

n×(1 - p) ≥ 10

1000×(1 - 0.98) ≥ 10

20 ≥ 10 (satisfied)

Let Y be the random number among the 1000 intervals that contain μ

\(P(970 < Y < 990) = P(Y < 990) - P(Y < 970) \\\\P(970 < Y < 990) = P( Z < \frac{Y - \mu}{\sigma}) - P( Z < \frac{Y - \mu}{\sigma} )\\\\\)

Where the mean is

\(\mu = 980\)

and the standard deviation is

\(\sigma = \sqrt{n \times p(1-p)} \\\\\sigma = \sqrt{1000 \times 0.98(1-0.98)} \\\\\sigma = 4.4272\)

Finally, the required probability is

\(P(970 < Y < 990) = P( Z < \frac{990 - 980}{4.4272}) - P( Z < \frac{970 - 980}{4.4272} )\\\\\)

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution)  to approximate discrete probability distribution (Binomial distribution).

\(P(970 < Y < 990) = P( Z < \frac{989.5 - 980}{4.4272}) - P( Z < \frac{969.5 - 980}{4.4272} )\\\\P(970 < Y < 990) = P( Z < \frac{9.5}{4.4272}) - P( Z < \frac{-10.5}{4.4272} )\\\\P(970 < Y < 990) = P( Z < 2.15) - P( Z < -2.37 )\\\\\)

From the z-table, the z-score corresponding to 2.15 is 0.9842

From the z-table, the z-score corresponding to -2.37 is 0.0089

\(P(970 < Y < 990) = 0.9842 - 0.0089\\\\P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

Therefore, there is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

The compound interest rate of the investment is 1.10%

The given parameters about the compound interest are

Principal, P = $11,000

Amount, A = $20,000

Time, t = 9

Number of times, n = 12 i.e. monthly interest

To calculate the amount, we have:

A = P(1 + R/n)^nt

Substitute the known values in the above equation, so, we have the following representation

20000 = 11000 * (1 + r/12)^(12 * 9)

This gives

1.82 = (1 + r/12)^108

Take the 108th root of both sides

1 + r/2 = 1.0055

Subtract 1 from both sides

r/2 = 0.0055

Multiply by 2

r = 0.011

Express as percentage

r = 1.10%

Hence, the value of the interest rate is 1.10%

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Answer:

6.66%

Step-by-step explanation:

Compounded Monthly:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

20000

�

=

11000

�

=

9

�

=

12

A=20000P=11000t=9n=12

Given values

20000

=

20000=

11000

(

1

+

�

12

)

12

(

9

)

11000(1+

12

r

​

)

12(9)

Plug in values

20000

=

20000=

11000

(

1

+

�

12

)

108

11000(1+

12

r

​

)

108

Multiply

20000

11000

=

11000

20000

​

=

11000

(

1

+

�

12

)

108

11000

11000

11000(1+

12

r

​

)

108

​

Divide by 11000

1.8181818

=

1.8181818=

(

1

+

�

12

)

108

(1+

12

r

​

)

108

(

1.8181818

)

1

/

108

=

(1.8181818)

1/108

=

[

(

1

+

�

12

)

108

]

1

/

108

[(1+

12

r

​

)

108

]

1/108

Raise both sides to 1/108 power

1.0055509

=

1.0055509=

1

+

�

12

1+

12

r

​

−

1

−1=

−

1

−1

Subtract 1

0.0055509

=

0.0055509=

�

12

12

r

​

12

(

0.0055509

)

=

12(0.0055509)=

(

�

12

)

12

(

12

r

​

)12

Multiply by 12

0.0666108

=

0.0666108=

�

r

6.66108

%

=

6.66108%=

�

r

Convert to percent (multiply by 100)

�

≈

r≈

6.66

%

6.66%

Round to the nearest hundredth of a percent

Answer:

the having of the record is that