what fraction of the numbers from 1 to 20 contain the digit 7

Answer:

D. The denominator means three out of five are shaded

A ballast resistor is utilized inside the ignition system of automobile engines or balloons. it acts as a resistor for the ignition ballast.

Between the main source of both the ignition coil & the coil stud, there's an ignition ballast resistor. It lowers the ignition coil's risk of failure.

An ignition ballast resistance assists in lowering the coil voltage & coil current when the generator revs the engine.

Minimal current consequently results in a low-temperature increase. Additionally, the ignition coil lives a long time as a result.

However, an ignition system requires a greater voltage that is also the same as the power source's voltage. Therefore, a resistor for the ignition ballast is connected to the jumper wire. The jumper wire additionally supplies the ignition with the necessary voltage when starting the engine.

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}[/tex]

The marble that is heavier based on the ratio is purple marble.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

Red balloons float purple marbles at a ratio of 12: 4. This will be:

= 12/4

= 3

Red balloons float green marbles at a ratio of 15: 6. This will be:

= 15/6

= 2.5

In this case, the purple marble is heavier as 3 is more than 2.5.

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Answer:

$26.33

Step-by-step explanation:

Answer:

116.

Step-by-step explanation:

Your welcome <3.

Answer:

116

Step-by-step explanation:

Answer:

supplementary angles

Step-by-step explanation:

1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given

2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.

3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive

4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality

5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Answer: 21

Step-by-step explanation:

To simplify this, we would use Order of Operations (BEDMAS)

So, to simplify 3 + (3-8)^2 -7 we will follow the order of Operations

[tex]3 + (3-8)^{2} - 7\\3 + (-5)^{2} - 7\\3 + 25 - 7 \\28 - 7\\21[/tex]

So the answer is 21

Answer:

64 times

Step-by-step explanation:

Multiply 0.4, the chance of getting tails, which 160, the amount of times you flip the coin, and you get 64. This is reasonable, because the probability of getting heads is 0.6, and if you flip the coin 160 times, you will get heads 96 times. Hope this helped :)

Step-by-step explanation:

4x² + 12x + 8 = 0

this has the same solutions as

x² + 3x + 2 = 0

as we simply divided everything by 4. 0/4 = 0.

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case that is

x = (-3 ± sqrt(3² - 4×1×2))/(2×1) =

= (-3 ± sqrt(9 - 8))/2 = (-3 ± sqrt(1))/2

x1 = (-3 + 1)/2 = -2/2 = -1

x2 = (-3 - 1)/2 = -4/2 = -2

so, the 2 solutions are

x = -1

or

x = -2

The crate's density in pounds per cubic foot?

Since the crate of medicine with a density of 2050 kilograms per cubic meter will be shipped from England to the U.S, we require its density in pounds per cubic foot.

To do this, we convert the density in kilograms per cubic foot to pounds per cubic foot by using the ratios of conversion given

Since the density of the crate in kilograms per cubic meter is

2050 kg/m³, using the conversion ratios, we have

2050 kg/m³ = 2050 kg/m³ × 1 m³/35.3 ft³ × 2.2 lb/kg

= 4510 lb/m³ × 1 m³/35.3 ft³

= 127.76 lb/ft³

So, crate's density is 127.76 lb/ft³

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After solving the value of x is -1/6.

Given:

[tex]25^3^x^+^2[/tex] = 125

[tex]5^{2(3x+2)}[/tex] = [tex]5^3[/tex]

2(3x+2) = 3

6x + 4 = 3

6x = 3-4

6x = -1

divide by 6 on both sides

6x/6 = -1/6

x = -1/6.

Therefore after solving the value of x is -1/6.

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Step-by-step explanation:

Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present. How many yards does he have left?

5/6 - 2/6 = 3/6

3/6 reduces to 1/2 yards left

Answer: 2 Adult 3 Kid

Step-by-step explanation:

5.10 x 2 = 10.2

3.60 x 3 = 10.8

10.8 + 10.2 = 21

Joe has eaten 3.6 times more pizza than Jane has eaten.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Joe has eaten 3/5 of the pizza. Jane has eaten 1/6 of a pizza.

Divide the fraction number 3/5 by the fraction number 1/6. Then we have

⇒ (3/5) / (1/6)

Simplify the expression, then we have

⇒ (3/5) x 6

⇒ 3.6

Joe has eaten 3.6 times more pizza than Jane.

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The function which have Domain:{-5, -3, 0, 3, 11} and Range:{4, 0, 2} is  {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}.

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

What is domain?

The domain of a function is the set of values that we are allowed to plug into our function.

What is range?

The collection of potential output values for a function is known as its range. For instance, the range is the non-negative real numbers for the function fn(x)=x2 on the domain of all real numbers (x ∈ R), which may be represented as fn(x)≥0 (or [0,∞] using interval notation).

Given:

Domain: {-5, -3, 0, 3, 11)

Range: {4, 0, 2}

If the input of function is a and output is b then it is defined by (a, b).

a always belong to domain and b from range of function.

∴ By using given domain and range set of our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}

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Answer:our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}

Step-by-step explanation:

Answer:

d = 15

Step-by-step explanation:

(-5, 4), (4, -8)

(x₁, y₁)   (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4 - (-5))² + (-8 - 4)²

d = √(4 + 5)² + (-12)²

d = √(9)² + (-12)²

d = √81 + 144

d = √225

d = 15

I hope this helps!

The required feet added to both the length and width of the patio is 6 feet.

Given that,
A square patio had the same number of feet added to its length and width. The equation A(x) = x² + 12x + 36 represents the area of the new patio in square feet, where 'x' was the length and width of the original patio, in feet.

Here,

According to the question,
A(x) = x² + 12x + 36
A(x) = x² + 6x + 6x + 36
A(x) = (x + 6)(x + 6)

Length = width = x + 6

Thus, the required feet added to both the length and width of the patio is 6 feet.

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The graph of inequalities equation on coordinate plane is given below ↓↓↓

Difference between equality and inequality equations

Both mathematical phrases, equality and inequality , are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The inequalities equation is ,

y> 2x+4

x+y≤6

so, the graph is ↓↓↓

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Answer:272

Step-by-step explanation:

The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

Leticia contributes $200 at 5% interest. Assuming that y addresses how much cash after x time spans.

Then the exponential equation is written as,

y = 200(1 + 0.05)ˣ

y = 200 (1.05)ˣ

The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

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The partial fraction of the compound fraction [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] is  [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions.

When fractions become too cumbersome to solve we split them into simpler units called partial fractions so that mathematical operations can easily be carried out on them.

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] can be split into the form, [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

where A and B are constants.

so,

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  =   [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

taking the LCM of the denominators of the split fractions, we have

(x-3)(x-5)

multiply A by x -5 and B by x - 3

fraction becomes

   [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  = [tex]\frac{A(x - 5) + B(x - 3)}{(x - 3)(x - 5)}[/tex]

since the denominators of the Left hand side and right hand side are same, we equate the numerators

A(x - 5) + B( x - 3) = x + 7

Using the cover up rule method,

to find A, we substitute x = 3 into the equation so that B becomes zero

A(3 - 5) = 3 + 7

-2A = 10

A = 10/-2

A = -5

To find A put x = 5 so that A = 0

B(5 - 3) = 5 = 7

2B = 12

B = 12/2 = 6

Substituting B and A into the partial fractions above

we have,

 [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

In conclusion the partial fractions are   [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

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Answer:

y=4x+1

Step-by-step explanation:

Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.

-Hope this helped.

Answer:

the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, is equal to k, where k is the unit rate.

Answer:

15h >= 200

>= means greater than or equal to. Just but a horizontal line underneath the >

The amount in the account is $3499. 2

The formula for determining compound interest is given as;

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

Given that;

Substitute the values into the formula, we have;

A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)

Find the exponential value

A = $3000 ( 1 + 0. 04 / 0. 5) ^2

A =  $3000( 1+ 0. 08)^2

Expand the bracket, we get;

A = $3000 (1. 08)^2

A = $3000(1. 17)

multiply through

A = $3499. 2

Hence, the value is $3499. 2

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Using the given information, we can write the compound inequality for the variable n:

45 ≤ n ≤ 120

Here we know that Liz spends at least 45 minutes and no more than 120 minutes on her phone.

So if we define the variable n as:

n = number of minutes that Liz spends on her phone.

We know that n must be larger than or equal to 45, so we can write the first inequality:

45 ≤ n

And we also know that it must be smaller than or equal to 120, then the other inequality is:

n ≤ 120

Combining the two we can write the compound inequality:

45 ≤ n ≤ 120

That is what we wanted to get.

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Answer:

Luis had to make a $420 down payment

Step-by-step explanation:

10%: $2,100 / 10 = $210

20%: $210 x 2 = $420

The original price of the ring is  £250.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, the purchase price of a diamond ring increases by £20 when the rate of VAT is increased from 12% to 20%.

Let the original price of the ring be x, then according to question,

120% of x - 112% of x = 20

1.2x - 1.12x = 20

0.08x = 20

x = 20/0.08

x = 250

Hence, The original price of the ring is  £250.

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Step-by-step explanation:

we know the square numbers of the basic integer numbers :

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

so, we see when we square the inequality, the closest numbers are

81 < 91 < 100

and therefore

9 < sqrt(91) < 10