A recent order for 15,000 items of building supplies was composed of bolts and nails. Nails cost 5 cents each. The entire order arrived at an expense of 1500 dollars. If there were 2500 bolts, what is the cost of each bolt?

We need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

The amount of each volume m = CV where

The amount of 50 % mixture, m = amount of 100 % powder + amount of 20 % powder.

M = m + m'

CV = C'V' + C"V" where

So, CV = C'V' + C"V"

0.5V = 1 × V' + 0.2 × 4

0.5V = V' + 0.8  (1)

Also, we have that the total volume V = V' + V"

V = V' + 4 (2)

Substituting equation (2)into (1), we have

0.5V = V' + 0.8

0.5(V' + 4) = V' + 0.8

0.5V' + 0.5 × 4 = V' + 0.8

0.5V' + 2 = V' + 0.8

0.5V' - V' = 0.8 - 2

-0.5V' = -1.2

V' = -1.2/-0.5

V' = 2.4 mL

So, we need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

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Answer:

4

Step-by-step explanation:

Proportionality between skein values

8:2=4:1

Proportionality between cost values

28:7=4:1

The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value

The function y = |x| - 1 is a translation of 1 unit downwards of the parent absolute value function, and its graph is the first one shown in the images.

Here we want to graph:

y = |x| - 1

Notice that if we take the parent absolute value function:

y = |x|

And we translate it one unit downwards, we will get:

y = |x| - 1

Which is the function that we want to graph.

So to select the correct graph, we need to find the one that is the parent absolute value function translated one unit downwards. It is the one with the vertex at (-1, 0), which is the graph that appears on the first image.

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Answer:

the answer will be 17.

Step-by-step explanation:

if, f (x) = 3x + 2

f (5) = 3 × 5 + 2 = 17.

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The polynomial within the numerator is 9x²+45x+54.

Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.

A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let's take the polynomial within the numerator is k.

So, rewrite the given expression as

[tex]\frac{k}{3x^2+15x+18}=3[/tex]

or it also can be written as

[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]

Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire

k=3(3x²+15x+18)

Simplify the above expression,

k=9x²+45x+54

Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.

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Answer:a

Step-by-step explanation:

Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

[tex]y = \frac{1}{2} x[/tex]

The solution has a positive answer (True).

Arithmetic operators are those signs such as addition, subtraction, multiplication, and division that are used to solve mathematical expressions such as fractions and linear equations.

1.

The solution to the expression:

= (-1)(1)(-1)(-1)(1)(-1)(-1)(-1)(-1)(1)(-1)(1)

= 1

Thus, the solution has a positive answer(True)

2.

The solution to the improper fraction:

[tex]\mathbf{\dfrac{5}{7}+(-\dfrac{2}{7})= \dfrac{3}{7} }[/tex]

3.

= -52.31 -(-7.44)

= -52.31 + 7.44

= -44.87

= - 4487/100

4.

The solution to the improper fraction is:

[tex]\mathbf{\dfrac{3}{5}\div -\dfrac{6}{15}=-\dfrac{3}{2} }[/tex]

5.

The given equation is:

-(-6.6) (-20) = 132  which is incorrect.

The correct solution is:

-(-6.6) (-20) = -132

Eric's mistake is that he forgot to multiply by -1 first.

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Answer:

Mixed Number: 11 1/5

Improper Fraction: 56/5

Step-by-step explanation:

Given:

It takes 3/7 tonnes of sand to make a tonne of concrete.

Mason has 4 4/5 tonnes of sand.

To Find:

How much concrete, in tonnes, can he make?

Give your answer as a fraction in its simplest form.

Solve:

By the given , takes 3/7 tonnes of sand = tonne of concrete.

Thus, we divide the total of tonnes of sand Mason have by how many it takes to make a tonne of concrete.

Hence, we have;

[tex]4\frac{4}{5}\div \frac{3}{7}[/tex]

Convert to improper fraction;

[tex]=\frac{24}{5}\div \frac{3}{7}[/tex]

Using the fraction rule;

[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{24}{5}\times \frac{7}{3}[/tex]

Cross-cancel common factor - 3

[tex]=\frac{8}{5}\times \frac{7}{1}[/tex]

Multiply fraction:

[tex]=\frac{56}{5}[/tex]

Convert improper to mixed number:

[tex]=11\frac{1}{5}[/tex]

Hence, the answer is [tex]\mathrm{11\frac{1}{5}\;or\;\frac{56}{5} }[/tex]

RevyBreeze

Answer:

[tex]\rm Improper \ fraction : \sf \sf \dfrac{56}{5} \ of \ concrete[/tex]

[tex]\rm Mixed \ fraction: \sf 11\dfrac{1}{5} \ of \ concrete[/tex]

Explanation:

[tex]\sf concrete = total \ tones \ of \ sand \ \div \ unit \ rate \ of \ sands \ required \ to \ make \ concrete[/tex]

Here given:

Concrete:

[tex]\sf \rightarrow 4\dfrac{4}{5} \div \dfrac{3}{7}[/tex]

[tex]\rightarrow \sf \dfrac{24}{5}\div \dfrac{3}{7}[/tex]

[tex]\rightarrow \sf \dfrac{24}{5}\times \dfrac{7}{3}[/tex]

[tex]\rightarrow \sf \dfrac{56}{5}[/tex]

[tex]\rightarrow \sf 11\dfrac{1}{5}[/tex]

The Arc Length BD from the given diagram is; 4.09π = 12.85 in

From the attached image, we are given;

m∠APC = 92°

Now, from the principle of vertical angles being congruent, we have;

m∠APC = m∠BPD = 92°

Thus;

Arc length BD = 2π * 8 * (92/360)

Arc Length BD = 4.09π = 12.85 in

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Answer:

156 cm²

Explanation:

This figure is a trapezium.

Formula of Area of Trapezium = 1/2 × (a + b)  × height

Here given:

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

Area of trapezium: 1/2  × (9 + 30)  × 8 = 156 cm²

Answer:

area of the trapezium is 156

Step-by-step explanation:

Step-by-step explanation:

Hi There! Let me help you :)

[tex] = 6.6.6.3.3[/tex]

[tex] = 6(1 + 1 + 1).3(1 + 1)[/tex]

[tex] = 6(3).3(2)[/tex]

The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672

Here,

The formula for the percentile probability is

[tex]P=\mu+z\sigma[/tex]

P=262 + 1.2816(45)

P = 319.672

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T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]

The inverse of the matrix is

[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]

So, the Inverse Transformation is given by

[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

So, no option is correct. And the answer is

[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

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The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;

x³(2x + 5) - 4(2x + 5)

2x⁴ + 5x³ - 8x - 20

Therefore,

2x⁴ + 5x³ - 8x - 20

x³(2x + 5) - 4(2x + 5)

Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:

2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)

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Answer:

25.99

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent)

For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse

the measurement of sin (opposite / hypotenuse) relates these two measurements

we can plug in our known values into sin:

sin = opposite / hypotenuse

sin (38) = 16 / x

(note: sin 38 = 0.61566147532, which we can round to 0.61566)

0.61566 = 16 / x

· x                   ·x           {multiply both sides by x to get rid of fraction}

0.61566(x) = 16

÷ 0.61566       ÷0.61566     {divide both sides by 0.61566 to isolate 1x}

x = 25.9883702043

{round to nearest hundredth}

x = 25.99

so, the measure of x is 25.99  {rounded to the nearest hundredth}

hope this helps!! have a lovely day :)

Answer:

cosx=adjacent/hypotenuse

triangle angle =180-(90+38)

=52°

cos(52°)=16/x

x=16/cos52

x≈23.373

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = x - 1/2, (-5, -2)

we can plug in the point (-5, -2)

-2 = (-5) - 1/2

-2 = -5.5

-2 does not equal -5.5 so this point is not on the line

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Work Shown:

[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]

Therefore,

[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]

Answer: 188

Step-by-step explanation: If you plug in all the values, you get 188.

So, 3(-6){squared} - 5(-6)(2) + 5(2){squared)

3(36)+60+20

3(36)+80

108 + 80 = 188

I hope this helps!

Answer:

188

Step-by-step explanation:

3x² - 5xy + 5y² for x = -6 and y = 2

3(-6)² - 5(-6)(2) + 5(2)² =

= 3(36) + 60 + 5(4)

= 108 + 60 + 20

= 188

Step-by-step explanation:

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Answer:

300 feet

Step-by-step explanation:

The absolute value of a number is defined as that number's distance from 0 (the origin) on a number line, regardless of direction.

In this case, the origin can be represented by sea level. Since the lowest point of 300 feet is taken by reference to sea level, it can be said that the absolute value of the point is 300 feet, since this represents its vertical distance from sea level.

Hope this helps!

Answer:

the answer is just 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

An absolute value of a number is written like this | x |, where x could be any number that you want.

The absolute value is a math function that counts from your given number to 0.

Example: If you put the number 3, the function will count from 3 to 0, and the number will be 3.

| 3 | = 3

If you input the number 8, from 8 to 0 are 8 numbers. So, the output's function will be 8.

| 8 | = 8

If you input a negative number, for example, -6, the function will do the same thing. It will count from -6 to 0. From -6 to 0, are 6 numbers.

| -6 | = 6

Any number that you input in this function, will always output the same number, but positive

| -10 | = 10

| -46348 | = 46348

Hope I helped !

Answer:

x=0

Step-by-step explanation:

[tex]4 \cos(x) = - \sin {}^{2} (x) + 1[/tex]

[tex]4 \cos(x) = 1 - \sin {}^{2} (x) [/tex]

[tex]4 \cos(x) = \cos {}^{2} (x) [/tex]

[tex]4 \cos(x) - \cos {}^{2} (x) = 0[/tex]

[tex] \cos(x) (4 - \cos(x) ) = 0[/tex]

[tex] \cos(x) = 0[/tex]

[tex]x = 0[/tex]

[tex]4 - \cos(x) = 0[/tex]

[tex] \cos(x) = 4[/tex]

There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.

The value of the number n as 1.5 * [tex]10^{-18}[/tex].

A power is the product of multiplying a number by itself.

(8.4*[tex]10^{9} \\[/tex])/n = (5.6* [tex]10^{27}[/tex])

n= (5.6* [tex]10^{27}[/tex]) / (8.4*[tex]10^{9} \\[/tex])

n= 1.5 * [tex]10^{-18}[/tex]

Hence, the value of n is n= 1.5 * [tex]10^{-18}[/tex]

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Answer: she would have 6 bottles left, (18/2)/6

Step-by-step explanation:

she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.

Answer:

A

Step-by-step explanation:

f(x) = x²

f(x) becomes f(13x) + 6

the "+ 6" at the end tells us already everything, because there is only one aber option listed that contains a shift up. and that is exactly what that "+ 6" did. it adds 6 to every possible y value of the function. so, the whole function moves up by 6 units.

and yes, the 13x of f(13x) stretches the function horizontally (along the x axis).

simply said, whenever the x value for the original function increased by 1, it increases for the new function by 13.

Answer:

3125

Step-by-step explanation:

And

Answer:

100

Step-by-step explanation:

explanation is shown in the picture

Let's set all the information into equations:

 ⇒ 3/4 of Ojo's money is €600.00 ⇒ [tex]\frac{3}{4} x = 600[/tex]

     (Where x is the total amount of money)

Let's solve the equation:

 ⇒ to find the total amount of money that Ojo has:

   [tex]\frac{3}{4}x=600\\ 3x=2400\\x=800[/tex]

 ⇒ total money is €800

Original question: what is 1/8 of this pocket money

     [tex]\frac{1}{8} *800=100[/tex]  

Answer: €100 is 1/8 of his pocket money

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Answer:

C

Step-by-step explanation:

7 × ln(x) = 2.4

ln(x) = 2.4/7 = 0.342857143...

x = e^0.342857143... = 1.408967466... ≈ 1.41