Fertiliser is applied at the rate of a grams per square metre. It
takes b kilograms to cover a field of area c square metres. Find a
formula for b in terms of a and c.

Answer:

12 and 14

Step-by-step explanation:

12 * 14 = 168

Answer:

12 & 14

Step-by-step explanation:

the work: x = first even number, (x+2) = second even number

The equation

[tex]x(x+2)=168[/tex]

[tex]x^{2} +2x=168[/tex]

[tex]x^{2} +2x-168=0[/tex]

Factoring

[tex](x-12)(x+14)=0[/tex]

first factor

[tex]x-12=0\\x=12[/tex]

Second factor

[tex]x+14=0\\x=-14[/tex]

The solution is the positive number

x = 12     is the first even number

x + 2 = 12 + 2 = 14    is the second even number

Hope this helps

sinE is 0.5

What are similar triangles?

Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

Clearly, given triangle AFB and triangle DFE are similar.

We know that Similar Triangles have the same corresponding angle

We can find sinE as show below:

From diagram clearly

∠A=∠E

and ∠B=∠D

Since, ∠A=∠E

Taking sin on both sides

sinA=sinE

Give, sinA=0.5

sinA=sinE=0.5

⇒ sinE=0.5

Hence, sinE is 0.5

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Answer:

[tex]\frac{5}{100}\times35[/tex]

[tex]0.05\times35[/tex]

Step-by-step explanation:

Given:

Which of the following options have the same value as 5% 35, percent of 35?

Following Options:

[tex]5 \times 35[/tex]

[tex]\frac{5}{100}\times35[/tex]

[tex]0.5\times0.35[/tex]

[tex]0.05\times35[/tex]

[tex]\frac{5}{10}\times35[/tex]

Solve:

[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]

Thus the following options:

[tex]5 \times 35[/tex]           [ False x ]

5 does not equal 5%

[tex]\frac{5}{100}\times35[/tex]         [True √ ]

[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]

[tex]0.5\times0.35[/tex]      [ False x ]

[tex]0.5 = 0.50[/tex]

[tex]0.05\times35[/tex]       [True √ ]

[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]

[tex]\frac{5}{10}\times35[/tex]          [ False x ]

[tex]\frac{5}{10}=0.50[/tex]

Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.

Kavinsky

Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.

The concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.

Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.

In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:

[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]

This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.

In this case, you know:

Replacing in the definition of mass volume percent:

[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]

Solving:

mass volume percent= 28 %

Finally, the percent composition of lactose in skim milk is 28%.

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The length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³. This can be obtained using the formula of finding the volume of the pyramid with base as square.

The formula of finding the volume of the pyramid with base as square is,

⇒ V = s²h/3

where V is the volume of the square pyramid, s is the side length of the base and h is the height of the square pyramid.

Here in the question it is given that,

that is, s = 11 ft, V = 400 ft³

By using the formula of finding the volume of the pyramid with base as square we get,

V = s²h/3

400 = (11)²h/3

By rearranging the equation we get,

h = 400 × 3/11²

h = 9.92 ft

Hence the length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³.

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Answer:

Step-by-step explanation:

cosA×cos 2A-sin4A×sinA

=cosAcos2A-2sin2Acos2A sin A

=cos 2A(cosA-2sin2AsinA)

=cos 2A(cosA-2×2sinAcosAsin A)

=cos2A×cosA(1-4sin²A)

=cos 2AcosA(1-4(1-cos²A))

=cos2A×cosA(1-4+4cos²A)

=cos 2A(-3cosA+4cos³A)

=cos 2A(4cos³A-3cosA)

=cos 2A×cos3A

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

where s = side length.

If a diagonal is drawn to create 2 halves, then area of each half is 8.

So, The area of a square = 1/2 ( 4 · 4 ) = 16.

If a square has a side length of 4, then the area of the square is 16.

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

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The solution to the question is mathematically given as

1)

H0: M [tex]\geqslant[/tex] 300

H0: M [tex]\geqslant[/tex] 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]

(1):

H0: M [tex]\geqslant[/tex] 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M [tex]\geqslant[/tex] 300 dollars:

(This is a left-tailed test)

(2):

when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.

(3):

[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]

(4):

[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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Answer: -1

Step-by-step explanation:

Evaluate 4x if x = -1/4

4(-1/4) = -1

Answer: -1

Step-by-step explanation:

4x and x = -1/4

plug x into the expression

[tex]4(-\frac{1}{4} )[/tex]

simplifies to:

[tex]-\frac{4}{4}[/tex]

4 divided by 4 is just 1, but it is negative so your final answer is

-1

Based on the total number of people who want the steakhouse option, the probability that a student will not want the seafoodbuffet if they want the steakhouse option is 24%

The probability that a student does not want the seafood buffet given that they want the steakhouse option is:

= Number of people who want steakhouse but not seafood / Total surveyed

Solving gives:

= 9 / (16 + 8 + 9 + 4)

= 9 / 37

= 24%

Full question is:

If a student wants the steakhouse option, what is the probability that they will not want the seafoodbuffet?

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Answer:

The area of the figure is C. 48.5 cm²

The vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

The quadratic function is given as:

f(x) = x^2 - 3x

Differentiate the function

f'(x) = 2x - 3

Set the function to 0

2x - 3 = 0

Add 3 to both sides

2x = 3

Divide by 2

x = 3/2

Set x = 3/2 in f(x) = x^2 - 3x

f(x) = 3/2^2 - 3 * 3/2

Evaluate

f(x) = -9/5

So, we have:

(x, f(x)) = (3/2, -9/5)

The above represents the vertex of the quadratic function.

This is properly written as:

(h, k) = (3/2, -9/5)

The vertex form of a quadratic function is

f(x) = a(x - h)^2 + k

So, we have:

f(x) = a(x - 3/2)^2 - 9/5

In f(x) = x^2 - 3x,

a = 1

So, we have:

f(x) = (x - 3/2)^2 - 9/5

Hence, the vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

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Answer:

  c > 5

Step-by-step explanation:

The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.

We can subtract 3 from both sides to solve this.

  c +3 > 8 . . . . . . given

  c +3 -3 > 8 -3 . . . . subtract 3 from both sides

  c > 5 . . . . . . . . . simplify

The solution is c > 5.

__

Additional comment

Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.

Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.

Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)

As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.

Answer:

(3+3) x (3+1)

Step-by-step explanation:

nice

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

Answer: 250:1

Step-by-step explanation:

Divide the measurement of appearance by the actual measurement.

[tex]100,000/400=250[/tex]

The magnification scale is 250:1. The scale is used by a 250X magnifying lense.

Step-by-step explanation:

I= 74810

II=66733

III=71392

iv=239904

If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]

Given an expression 8v(v+3)(v+3).

We are required to rewrite the given expression.

Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.

The expression is 8v(v+3)(v+3). There are three terms in which variable is v.

To rewrite the expression we have to multiply all the three terms with each other which can be done as under:

=8v(v+3)(v+3)

=[tex](8v^{2}+24v)(v+3)[/tex]

=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]

=[tex]8v^{3}+48v^{2} +72v[/tex]

Now divide it by 8.

=[tex]v^{3}+6v^{2} +9v[/tex]

Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:6 = 2(y + 2)[/tex]

[tex] \qquad❖ \: \sf \:(y + 2) = \cfrac{6}{2} [/tex]

[tex] \qquad❖ \: \sf \:y + 2 = 3[/tex]

[tex] \qquad❖ \: \sf \:y = 3 - 2[/tex]

[tex] \qquad❖ \: \sf \:y = 1[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

W = (P -2L)/2

Step-by-step explanation:

P = 2(L + W)  Distribute the 2

P = 2L + 2W   Subtract 2L from both sides

P - 2L = 2W  Divide both sides by 2

(P-2L)/2 = W  

Question 13

Part (a)

[tex]\frac{3840-3905}{110}=\boxed{0.5\overline{90}}[/tex]

By similar logic, the other answers are

(b) 2.6818181....

(c) 3.5909090...

(d) 1.1363636...

Question 14

Part (a)

[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]

Part (b)

[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]

Answer:

Options 1 and 2

Step-by-step explanation:

radius -15

Surface Area of a sphere =4πr^2

=4x22/7x15x15

=19800/7

=2828.57

Step-by-step explanation:

1/4×48

=12

So if 12people are out of state

48-12=36,is the number of people living in the state

Answer:

9

Step-by-step explanation:

6 ÷ 2/3   =    6 /  (2/3 )   =  (6/1) / (2/3)  = 6/1  x  3/2 = 18/2 = 9

The volume of the cylinder in discuss in which case, the radius of the cylinder is 3 inches and the height is inches is; V = 141.3in³.

The cylinder in discuss according to the task content has radius, 3 inches and height, 5 inches.

Since the volume of a cylinder by convention is given as; V = πr²h

Therefore, the volume of the cylinder in discuss is;

V = π (3²)×5

V = 3.14 × 45

V = 141.3in³

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If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].

The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].

So, the surface area is given by the definite integral

[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]

Answer:

8 ^-11

Step-by-step explanation:

It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:

8^-2 × 8^-9

= 8^(-2 + -9)

= 8^-11

Answer:

1,680

Step-by-step explanation:

8 positions with basically 8 choices.

that is 8! arrangements.

but 2 is there 2 times.

8 is there 2 times.

5 is there 3 times.

only 3 is a single digit.

so, we need to eliminate every arrangement, where the 2s trade places, where the 5s trade places, and where the 8s trade places, because they are the same numbers.

that means we have to divide the 8! by 2!, then again by 2!, and again by 3!.

8! / (2! × 2! × 3!) = 8! / 24 = 1,680