Solve equation.
27-6 d=7+4 d

The value of the inequality 0.34 < ( 1/2 ) and 0.34 ≠ 3/4

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first number be p = 0.34

Let the second number be q = ( 1/2 )

Now , the value of q = 0.5

So , the inequality is q > p

The value of ( 1/2 ) > 0.34

And , 0.34 = 34/10

Hence , the inequality is ( 1/2 ) > 0.34

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Answer:

∠FCD ∠CFE

Step-by-step explanation:

I actually saw the answer on another site but I got it correct so I decided to share it :D

Have a good Day!

From the given figure ∠FCD and ∠CFE are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Given that, BD and EG, are parallel lines and transversal AH.

Here, ∠FCD=∠CFE are alternate interior angles.

Therefore, from the given figure ∠FCD and ∠CFE are alternate interior angles.

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When the process of observing or measuring yields results that consistently deviate in some way from the true value, this is known as observer/measurement bias. Because of the systematic mistake this adds into the data, the conclusions are incorrect or unreliable.

Observer/measurement bias is a sort of systematic error that happens when the technique used for observation or measurement yields results that consistently deviate in some way from the true value. The observer's own preconceived ideas or expectations, the measurement equipment, and the environment in which the observation or measurement is being conducted can all contribute to this form of bias.An observer's bias, for instance, could cause them to see or measure something in a way that favours one particular result or outcome over another. Similar to how external influences like noise, light, or temperature can skew results, the environment in which the observation or measurement is taking place may add a bias. If feasible, results that are inaccurate or unreliable because of observer/measurement bias should be avoided because they can lead to incorrect inferences about the data.

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Answer:

equals

COS

Step-by-step explanation:

because cos×3=COS

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Answer:

Step-by-step explanation:

The arithmetic sequence

Let the first term a₁ = x, and common difference = d then we have:

The difference of the 6th and  2nd terms:

Then we get the first term and other missing terms:

-25, 4, 4+29 = 33, 33+29 = 62, 62 + 29= 91, 91+29 = 120, ...

The solution to the system of equations is x = 3/2 and y = 6

The system of equations is given as:

1/2x = 3/4 and y = 6

The variables x and y in each of the above equations are independent

This is so because they only occur in one equation at a time

So, we have:

1/2x = 3/4

Multiply both sides by 2

x = 3/2

Hence, the solution to the system of equations is x = 3/2 and y = 6

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Answer:

8

Step-by-step explanation:

3(3)-1

=9-1

=8

PLS GIVE BRAINLIEST

Answer:

\(\frac{1170pi}{360m}\)km

Step-by-step explanation:

To find the length of the minor arc, you find the circumference of the circle multiplied by the arc angle, which is \(\frac{45}{m}\) over 360 degrees.

Circumference of the circle with center B = 13×2×pi

                                                                     = 26pi

Length of minor arc = 26pi × \(\frac{45}{m}\) ×\(\frac{1}{360}\)

                                 = \(\frac{1170pi}{360m}\)km

The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

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Answer:

y=10 ( number of acrobat)

Step-by-step explanation:

let x be the elephant and y the acrobat

elephant has 4 legs and acrobat 2

4x+2y=40

x+y=15  ⇒x=15-y

substitute for x in the equation:

4(15-y)+2y=40

60-4y+2y=40

-2y=40-60

y=-20/-2

y=10 ( number of acrobat)

number of elephant=15-10=5 elephants

The pooled estimate of the variance is 187.650 and the test statistic is -2.32

The dataset is given as:

Regular price 138 124 89 112 116 123 98

Reduced price 124 134 154 135 118 126 133 132

Let the regular price be dataset 1 and the reduced price be dataset 2.

So, we have:

#1: 138 124 89 112 116 123 98

#2: 124 134 154 135 118 126 133 132

Calculate the sample means and the sample standard deviations using a graphing calculator.

#1

\(\sigma_1 = 16.56\)

\(\bar x_1 = 114.29\)

\(\sigma_1^2 = 274.24\)

#2

\(\sigma_2 = 10.65\)

\(\bar x_2 = 132\)

\(\sigma_2^2 = 113.43\)

The pooled estimate of the variance is:

\(\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}\)

This gives

\(\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}\)

Evaluate the factors

\(\sigma_p^2 = \frac{2439.45}{13}\)

Divide

\(\sigma_p^2 = 187.65\)

Hence, the pooled estimate of the variance is 187.650

This is calculated using:

\(t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}\)

This gives

\(t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}\)

This gives

\(t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}\)

Evaluate the product

\(t = \frac{-17.71}{\sqrt{58.08214}}\)

Evaluate the exponent

\(t = \frac{-17.71}{7.62}\)

Divide

t = -2.32

Hence, the test statistic is -2.32

The critical value at 0.025 significance level is -1.96

-2.32 is less than -1.96

This means that we accept the null hypothesis

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Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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Answer:

4×102 +5×101 +6×100 +8 × 10-1 +1 × 10-2

I hope that made sense lol

Answer:

400 + 50 + 6 + 0.8 + 0.01

Step-by-step explanation:

This is the answer because:

1) Expanded form means to write a number with its full value. It is shown as a sum of each digit multiplied by its matching place value

2) Therefore, the answer is 400 + 50 + 6 + 0.8 + 0.01

Hope this helps!

There are 680 combinations of four teachers include Mrs. Vera(only)

The given parameters are

Teachers, n = 18

Selected teachers. r = 4

The selection must include Mrs. Vera.

So, the remaining parameters are:

Teachers, n = 17

Selected teachers. r = 3

The combination is then calculated as:

Ways = nCr

This gives

Ways = 17C3

Apply the combination formula

Ways = 17!/(14!3!)

Evaluate the expression

Ways = 680

Hence, there are 680 combinations of four teachers include Mrs. Vera(only)

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Answer:

1536 cm²

Step-by-step explanation:

  A square pyramid is a three-dimensional shape. It is a pyramid with square base.

     base length = a = 24 cm

               height = h = 16 cm

       \(\boxed{Area \ of \ square \ pyramid = a^2 + 2a\sqrt{\dfrac{a^2}{4}+h^2}}\)

                                                  \(=24^2+2*24+\sqrt{\dfrac{24^2}{4}+16^2}\\\\\\= 576 + 48*\sqrt{\dfrac{576}{4}+256}\\\\\\=576+48*\sqrt{144+256}\\\\=576+ 48*\sqrt{400}\\\\=576+48*20\\\\=576+960\\\\=1536 \ cm^2\)

a. Area of the exposed water of the prism pool: 33.5 ft²

b. The area of exposed water for the cone pool = 102.1 ft²

c. Hemisphere pool = πr² = π(4²) = 50.3 ft²

Volume = (2/3)πr

Volume = 1/3πr²h

Volume = Base area × height

a. Area of the exposed water = area of the square top = base area of the prism

Find base area using, Volume = Base area × height. Thus:

134 = Base area × 4

Base area = 134/4 = 33.5 ft²

Area of the exposed water for the prism pool = 33.5 ft²

b. Find the radius of the cone using, volume = 1/3πr²h.

134 = 1/3πr²(4)

(3)(134) = πr²(4)

402/4π = r²

32 = r²

r = 5.7 ft

The area of exposed water for the inverted cone pool = πr² = π(5.7)² = 102.1 ft²

c. The radius is the depth of the hemisphere pool

The area of the exposed water for the hemisphere pool = πr² = π(4²) = 50.3 ft²

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The translated phrase into an algebraic expression is 15 + 2g

The phrase is given as:

15 more than twice Gail's height

Use the variable g to represent Gail's height.

So, we have:

15 + 2g

Hence, the translated phrase into an algebraic expression is 15 + 2g

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Answer:

4(4a+5) = 16 a + 20 = True

Step-by-step explanation:

Therefore , the solution of the given problem of angles comes out to be  marked angle ≈ 106.2602 degrees.

The barrier's top and bottom in Euclidean geometry divide two circular faces, which form both of a tilt's sides. It is possible for two rays to join to form a point of intersection. Angle is another outcome of two entities interacting. They mirror dihedral shapes the most. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.

Here,

Triangle ABC is an isosceles triangle with basis BC because we are told that

=> BAP = CAP. As a result, we can say that AB = AC.

We can determine the cosine of an angle using the Rule of Cosines:

=> cos(BAC) = (AB² + AC² - BC²) / (2 * AB * AC)

=> cos(BAC) = (6² + 5² - 4²) / (2 * 6 * 5)

=> cos(BAC) = 49 / 60

We discover: by taking the inverse cosine of both sides.

=> BAC = cos⁻¹(49/60)

Calculating the answer, we obtain:

=> ∠BAC ≈ 36.8699 degrees

The indicated angle is as a result:

=> marked angle = 180 - 2 * BAC

=> marked angle = 180 - 2 * 36.8699

=> marked angle ≈ 106.2602 degrees

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Answer:

16 blocks

Step-by-step explanation:

the number of blocks increases exponentially

Answer:

(36^5-6^9)(38^9-38^8) is divisible by both 2, 3, and 37, and hence it is divisible by 30 and 37.

Step-by-step explanation:

To prove that (36^5-6^9)(38^9-38^8) is divisible by 30, we need to show that it is divisible by both 2 and 3.

To prove that it is divisible by 2, we note that (36^5-6^9) is even, since it contains at least one factor of 2. We also note that (38^9-38^8) is even, since it can be factored as 38^8(38-1), and 38-1 is even. Therefore, their product is even and divisible by 2.

To prove that it is divisible by 3, we note that (36^5-6^9) is divisible by 3, since the sum of its digits is 3+6+5+6+9 = 29, which is divisible by 3. We also note that (38^9-38^8) is divisible by 3, since the sum of its digits is 3+8+9 = 20, which is divisible by 3. Therefore, their product is divisible by 3.

To prove that (36^5-6^9)(38^9-38^8) is divisible by 37, we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) is congruent to 1 mod p. Since 37 is a prime number and 6 is not divisible by 37, we have:

6^36 ≡ 1 (mod 37)

Therefore, we can rewrite the expression as:

(36^5-6^9)(38^9-38^8) ≡ (36^5-6^9)(1-38) (mod 37)

Simplifying further, we get:

(36^5-6^9)(1-38) ≡ (1-6^9)(1-38) (mod 37)

= (1-531441)(1-38)

= (531440)(-37)

Since 531440 is divisible by 37, we have shown that (36^5-6^9)(38^9-38^8) is divisible by 37.

Therefore, we have proved that (36^5-6^9)(38^9-38^8) is divisible by both 2, 3, and 37, and hence it is divisible by 30 and 37.

Answer:

30%

Step-by-step explanation:

Profit(Gain)% = \(\frac{Selling price - Cost price}{Cost price} * 100%\)

Selling price = N6.50

Cost price = N5

∴ Profit% = \(\frac{N6.50 - N5 }{N5} * \frac{100}{1}\)

                 = \(\frac{1.5}{5} * \frac{100}{1}\)

                 = (1.5 * 20)%

                 = 30%

Hope this helps!!!

Step-by-step explanation:

Using a calculator, if you typed in 7 divided by 8, you'd get 0.875. You could also express 7/8 as a mixed fraction: 0 7/8. If you look at the mixed fraction 0 7/8, you'll see that the numerator is the same as the remainder (7), the denominator is our original divisor (8), and the whole number is our final answer (0).

hope that help mark me brinilylist pls

Answer:601.85

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+1=x-4

2x-x= -4-1

1x=-5

Answer:

I think they both are linear

Answer:

x = 2 or x = -2

Step-by-step explanation:

5x² - 15 = 5​

⇌

5x² = 15 + 5

⇌

5x² = 20

⇌

x² = 20/5 = 4

⇌

x² = 2²

⇌

x² - 2² = 0

⇌

(x - 2)(x + 2) = 0

⇌   we use the zero product property

x - 2 = 0 or x + 2 = 0

⇌

x = 2 or x = -2