Jonah's favourite number is a positive integer. One day, he decided to write down all of the positive integers starting at 1 and ending with his favourite number. He noticed, in doing so, that he wrote the digit 7 exactly 30 times. What is Jonah's favourite number?

Answer:

x = -3

Step-by-step explanation:

Okay, the first thing to do is get that 8 away from the fraction. How can we do it? When you have 2³ you have 8, is the same thing, so let's do it:

2³⁰/(2³)⁹ = 2^x

When you have a number with the shape (a^x)^y, you can write it as a^(x•y), so:

(2³)⁹ = 2^3•9 = 2²⁷

Now we have:

2³⁰/2²⁷ = 2^x

When you have a division like this: (a^x)/(a^y), you can write it as a^(x-y), so:

2^(30-27) = 2^x

2^-3 = 2^x

Now you know that x = -3

Answer:

2.8 square inches

Step-by-step explanation:

Area of the triangle PQR = 1/2 rp sin <Q

Given

r = 9in

p = 6.6in

<Q =6°

Substitute into the formula;

Area of the triangle PQR = 1/2 * 9 * 6 sin6°

Area of the triangle PQR = 9 * 3 sin6°

Area of the triangle PQR  = 27 sin6°

Area of the triangle PQR = 27(0.1045)

Area of the triangle PQR = 2.82

Hence the area to the nearest 10th of a square inch is 2.8 square inches

Answer:

3.104 which is equal to 3.1 it your answer.

Step-by-step explanation:

I did it on DeltaMath

Answer:

7x + 8y - 5

Step-by-step explanation:

Like terms are terms with the same variable as well as the same amount of said variable:

Set the expression:

4x + 3y - 4 + 5y + 3x - 1

4x + 3x + 3y + 5y - 4 - 1

Combine like terms:

(4x + 3x) + (3y + 5y) + (-4 - 1)

(7x) + (8y) + (-5)

7x + 8y - 5 is your answer.

~

Answer:

81

Step-by-step explanation:

Any number, wether it is negative or postive, will always be postive when there is a even exponent.

In this case, we have a -9, and a exponent thats 2.

Since 2 is a even number, -9^2 will be a postive value.

Now, what is the actual value of this?

Well, a exponent of 2 basiclly means 2 numbers being multiplied together.

Or in this case, 2 negative 9s being multiplied together.

THis will be:

-9*-9

=

As I said above, a even exponent makes a negative number postive.

You see here that a negative 9 is being multiplied by -9. When two negative numbers multiply together, they make a postive.

THis is why a even exponent makes a postive.

Hope this helps!

[tex]\longrightarrow{\blue{ 141x - 8y }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]97x + 58y - 66y + 44x[/tex]

Let us rewrite the expression so that the like terms are next to each other.

[tex] = 97x + 44x+ 58y - 66y[/tex]

Combine the coefficients.

[tex] = (97 + 44)x + (58 - 66)y[/tex]

[tex] = 141x - 8y[/tex]

[tex]\sf\pink{Happy\:learning! }[/tex]

Step-by-step explanation:

hakdogg happyly ever after

Answer:

I'm guessing 46 if its actually adding

Answer:

Its a

Step-by-step explanation:

3*3 =9

4*4 =16

5*5 =36

Answer:

A. y=x^2

Step-by-step explanation:

A. y=x^2

when x=0 and y=o

0=0^2

0=0(true)

when x=1 and y=1

1=1^2

1=1 (true)

when x=3 and y=9

9=3^2

9=9 (true)

Answer:

[tex]{ \tt{2 \cos60 \degree + \tan(45 \degree) }} \\ \\ = 2(0.5) + 1 \\ = 1 + 1 \\ = 2[/tex]

Answer:

pretty sure it’s 35.6

Step-by-step explanation:

Step-by-step explanation:

x+2x+8 =200

3x=200-8

3x=192

x = 64

Martha has 64 pence

Peter jas 136 pence

Answer:

x<5

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

Math

Answer:

75

Step-by-step explanation:

add up all the numbers, then divide by how many numbers there are

Answer:

IQ scores of at least 130.81 are identified with the upper 2%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 100 and a standard deviation of 15.

This means that [tex]\mu = 100, \sigma = 15[/tex]

What IQ score is identified with the upper 2%?

IQ scores of at least the 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.054 = \frac{X - 100}{15}[/tex]

[tex]X - 100 = 15*2.054[/tex]

[tex]X = 130.81[/tex]

IQ scores of at least 130.81 are identified with the upper 2%.

Answer:

4.375

Step-by-step explanation:

s=1/t

s=k/t

0.5=k/7

k=7x0.5=3.5

s=3.5/0.8

s=4.375

Answer:

$7,680

$34,240

Step-by-step explanation:

Amount Tessa earns in 2019 = $32000

a. She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018.

Percent of tax = 24%

Amount of tax paid = 24% of $32,000

= 24/100 * 32,000

= 0.24 * 32,000

= $7,680

Amount of tax paid = $7,680

b. Tessa's earnings increased by 7%. Work out her earnings in 2020.

Percentage increase in earnings = 7%

Amount of increase in earnings = 7% of $32,000

= 7/100 * 32,000

= 0.07 * 32,000

= $2,240

Amount of increase in earnings = $2,240

Total earnings in 2020 = Amount Tessa earns in 2019 + Amount of increase in earnings

= $32,000 + $2,240

= $34,240

Total earnings in 2020 = $34,240

Answer:

Mean: 52.8

Median:52

Mode:54

Step-by-step explanation:

Mean: 54+48+37+55+51+54+42+52+53=476

476/9=52.8

Median: 37,42,48,51,52,53,54,54,55. The middle one is 52.

Mode: Most common one = 54

Hope this helps! Have a nice day!

Answer:

C

Step-by-step explanation:

AE 40+60 = 100

CD 20+60 = 80

Answer:

C..............................

Answer:

1/6 gallon of water

Step-by-step explanation:

Number of hikers = 3

Quantity of water shared = 1/2 gallon of water

If the water was shared equally among the hikers, then,

Amount of water each hiker drank = Quantity of water shared ÷ Number of hikers

= 1/2 ÷ 3

Multiply 1/6 by the reciprocal of 3

The reciprocal of 3 = 1/3

1/2 ÷ 3

= 1/2 × 1/3

= (1 * 1) / (2 * 3)

= 1/6

Amount of water each hiker drank = 1/6 gallon of water

Answer:

Sample Response: Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1

6

of a gallon.

Step-by-step explanation:

UwU

Answer:

X+2Y=7 and 4X+8Y=19

Step-by-step explanation:

Step 1: Write the equations in the form y=mx+c, where m represents the gradient.

In this case, gradient is equal to -0.5

Step 2: Now fix arbitrary values on the equation, y=mx+c while maintaining the value of m as - 0.5

You can make endless equations

Answer:

we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm

Answer:

Second option - 6

Explanation:

Trust! (And the image)

I really ope this helped! :)

Answer:

2 and 3

Step-by-step explanation:

Let us start by representing the first consecutive number with x. In a similar sense, the next consecutive number would be x+1. According to the given question, we can write the following equation:

[tex]x+x+1=3x-1[/tex]

Solving for the equation by isolating the term containing x, we have:

[tex]2x+1=3x-1\\2x+2=3x\\\fbox{x=2}[/tex]

Since we have designated x as the first consecutive integer, the other integer we are looking for is x+1, or [tex]\fbox{3}[/tex] .

I hope this helps! Let me know if you have any questionss :)

The general formula for the total surface area of a right prism is T. S. A. =ph+2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.

Answer:

A. 3

Step-by-step explanation:

Section 1: decrease

Section 2: level, no increase, no decrease

In section 3, the slope is positive. The graph goes up to the right. The level of water increases in section 3.

Section 4: decrease

Section 5: decrease

Answer: A. 3

Answer:

A. 3

Step-by-step explanation:

Answer:

72-57-24=-9

Step-by-step explanation:

simple subtraction

Answer:

x = 16

Step-by-step explanation:

These are corresponding angles meaning they are equal to each other.

4x + 30 = 94

4x = 64

x = 16

Answer:

i think its 2

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

Easy divide 1/5 as a decimal and you should get a decimal form number 0.2

1÷5=0.2

Hope this helps