5^x=62 Giving 20 points!

Algebra 2, Chapter 6-7. Common Logarithms.
The answer key says its 2.5, but I need some help to understand how to get that answer by showing work.

Answer:

I think the answer is (x-4)2 + y2 = 12 :) sorry if i am wrong***

Step-by-step explanation:

Answer:

it is 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

replace the values.

5(6) - 6(3)

Using PEMDAS, you would do multiplication first.

30 - 18

Next, subtraction.

12

Answer:

1 piece of fry

Step-by-step explanation:

Given:

You want to buy a milkshake and some fries. You look up prices for two different places.

Restaurant 1 sells milkshakes for $4 and fries for $1. Restaurant 2 sells milkshakes for $3 and fries for $2.

Question asked:

At what amount of fries bought will the restaurants be the same price?

Solution;

Let at [tex]x[/tex] amount of fries bought the restaurants will be the same price.

As you want to buy a milkshake and [tex]x[/tex] fries, the equation will be:-

For Restaurant 1

[tex]4+1\times x[/tex]

For Restaurant 2

[tex]3+2\times x[/tex]

Now, at [tex]x[/tex] amount of fries bought the restaurants will be the same price.

[tex]4+x=3+2x\\ \\ By\ subtracting\ both\ sides\ by\ 3\\ \\ 4-3+x=3-3+2x\\ \\ 4-3+x=2x\\ \\ 1+x=2x\\ \\ By\ subtracting\ both\ sides\ by\ x\\ \\ 1+x-x=2x-x\\ \\ 1=x[/tex]

Therefore, at 1 piece of fry bought the restaurants will be the same price.

Answer:

312 square feet

Step-by-step explanation:

Each square is 11 x 12 feet which is 132 times 2 for the front and back, which is 264 feet. Then, the triangles at the top have a height of 4 feet (15-11) and a base of 12 feet, so because there are 2 triangles, the result is 12x4=48. Then, you add 264 to 48 and all done.

Hiromi will need to buy 19 cans of paint to cover the entire front and back of the barn.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, The front and back of the barn each have an area of;

11ft x 12ft = 132 square feet.

Since Hiromi is painting the front and back, the total area to be painted is:

2 x 132 = 264 square feet

Similarly, the two sides of the barn each have an area of

11ft x 15ft = 165 square feet.

Since there are two sides, the total area of the sides to be painted is:

2 x 165 = 330 square feet

The total area to be painted is the sum of the front/back area and the side area:

264 + 330 = 594 square feet

Since each can of paint covers 32 square feet, the number of cans of paint Hiromi needs is:

594 / 32 ≈ 18.56 cans

Since, Hiromi cannot buy a fraction of a can of paint,

Hence, she will need to buy 19 cans of paint to cover the entire front and back of the barn.

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Answer:

= 1/5

Step-by-step explanation:

We can find the slope using

m = (y2-y1)/(x2-x1)

    = (-3- -7)/(5--15)

    = (-3+7)/(5+15)

    = 4/20

    = 1/5

Answer:

The slope of the line is 1/5x.

Step-by-step explanation:

I graphed the points on the graph below. Then, I found the slope by counting the number of spots right and up from the first point to the second point.

Answer:

area is 6.9cm2

Step-by-step explanation:

you just multiply it out and divide by 2

Answer:

618 birds.

Step-by-step explanation:

Let the estimated number of birds=x

Out of x birds, he tied a belt around the legs of 40 birds.

When he observed 520 birds, 34 of which had belts.

Expressing each as a ratio

[tex]\frac{x}{40}=\frac{520}{34}[/tex]

Cross Multiply

34x=520X40

x=520X40÷34=611.7≈618

There are an estimated 618 birds.

Answer:

The best estimate for the bird population is 613 birds

Step-by-step explanation:

Let x be the total of number of estimated bird

From x, 40 birds are with belt

he observed 520 birds, 34 of which had belts.

Then taking reciprocal of both statements

x/40 = 520/34

34x = 520*40 = 20800

x = 20800/34

x = 613The total of number of estimated birds is 613 birds

The total of number of estimated birds is 613 birds

Answer:

y=43

x=137

z=137

Step-by-step explanation:

Answer:

(B)[tex]\sqrt{2} ft[/tex]

Step-by-step explanation:

Given a Square of side 1 foot, the length of the diagonal is determined using the Pythagoras theorem.

The diagonal is the hypotenuse of the right triangle obtained.

From Pythagoras Theorem,

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=1^2+1^2\\=1+1\\Hypotenuse^2=2\\Therefore, Hypotenuse=\sqrt{2} ft[/tex]

The length of the diagonal is [tex]\sqrt{2} ft[/tex]

Answer:

B

Step-by-step explanation:

Answer:

2 book cases

Step-by-step explanation:

If she has 1 1/4 gallons of paint then she has two (1/2) gallons and one (1/4) gallon. Each book case takes 1/2 gallon of paint and if you multiply it by 2 it equals 1 gallon. You only have 1/4 gallon left.

1 bookcase (1/2 gallon) + 1 bookcase (1/2 gallon) = 1 gallon. There is only 1/4 gallon left which is less than 1/2.

Answer:

20

Step-by-step explanation:

We need to determine what we are adding each time.

Take the 2nd term and subtract the first term

-1 - (-8)

-1 +8 = 7

We add 7 each time

To find the 5th term, add 7 to the 4th term

the 4th term is 13

13+7 = 20

Answer:

20

Step-by-step explanation:

a = -8

d = -1 - (-8) = 7

An = a + (n - 1)d

A5 = -8 + (5 - 1)(7)

A5 = -8 + 28

20

Answer:

90 degrees I think

Step-by-step explanation:

Answer:90°

Step-by-step explanation:

All right angles are 90° and all triangles = 180°

To check it add 45° and 90° then you have the other angle

Answer: 5 hours

Step-by-step explanation:

1)

[tex] \frac{475}{75} = \frac{19}{3} = 6 \frac{1}{3} \\ [/tex]

2)

[tex] \frac{100}{75} = \frac{4}{3} = 1\frac{1}{3} \\ [/tex]

3)

[tex]6 \frac{1}{3} - 1 \frac{1}{3} = 5[/tex]

Answer: 5 hours

Answer:

14.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is Arithmetic sequence

a = first term= 4;

d= difference =second term - first term = 7 - 4 = 3

n= position

nth term = a + (n-1)*d

1st term = 4 + (1-1)*3 = 4 + 0 = 4

2nd term = 4 + (2-1)*3 = 4 + 1*3 = 4+3 = 7

5th term = 4 + (5-1)*3 = 4 + 4*3 = 4 + 12 = 16

6th term = 4 + (6-1)*3 = 4 + 5*3 = 4 + 15 = 19

or

To get the next term add the difference [3] to the previous term.

5th term = 13 +3 = 16

6th term = 16 + 3= 19

Answer:

The correct answers are Option 4 55(108/100)  and Option 1 55(1.08)

Step-by-step explanation:

To begin, we must analyze the information we have and establish the result, in order to compare it with the results of the operations that the answers offer.

We know that the total Charlie pays for his cell phone plan is $ 55 + 8% tax.

One of the possible ways in which you can calculate a percentage would be in this case:

(55.8) : 100

440 : 100 = 4.40

This indicates that the tax was 4.4 added to 55, giving us a total of 59.4.

Now we just have to check that options 4 and 1 are correct. Let's see:

55 (108/100) =

55 (1.08) = 59.94

This last section is exactly the same as option 1, which also makes it a correct answer.

Jane is correct because Jane correctly simplified the expression to [tex]\(3x\)[/tex].

Let's carefully simplify the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\)[/tex] step-by-step to determine who is correct, Jane or Jill.

Starting with the given expression:

[tex]\[(2x^2 + x) + 2(-x^2 + x)\][/tex]

We first distribute the [tex]\(2\)[/tex] in [tex]\(2(-x^2 + x)\):[/tex]

[tex]\[(2x^2 + x) + (-2x^2 + 2x)\][/tex]

Next, we combine like terms. We combine the \(x^2\) terms and the \(x\) terms separately:

[tex]\[(2x^2 - 2x^2) + (x + 2x)\][/tex]

Simplify each group of like terms:

[tex]\[0x^2 + 3x\][/tex]

This simplifies to:

[tex]\[3x\][/tex]

Therefore, the correct simplification of the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\) is \(3x\)[/tex].

Jane’s solution is:

[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) + (-x^2 + x) + (-x^2 + x) \\& = (2x^2 - x^2 - x^2) + (x + x + x) \\& = 3x\end{aligned}\][/tex]

Jill’s solution is:

[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) - 2x^2 + 2x \\& = 2x\end{aligned}\][/tex]

Jane correctly simplified the expression to [tex]\(3x\)[/tex], while Jill made an error by not correctly distributing the [tex]\(2\)[/tex] in the term [tex]\(2(-x^2 + x)\)[/tex].

The complete question is

Jane and jill were simplifying the expression (2x²+x) +2(-x²+x) and obtained different answers. Who is right and why?​

Jane                                                

[tex]$$\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)+\left(-x^2+x\right)+\left(-x^2+x\right) \\& =\left(2 x^2-x^2-x^2\right)+(x+x+x) \\& =3 x\end{aligned}$$[/tex]

Jill

[tex]\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)-2 x^2+x \\& =2 x\end{aligned}[/tex]

P(red & blue) = 16/21

Answer:

There is a 76% chance of either getting a blue or red marble

Step-by-step explanation:

8 + 5 + 8 = 21

There are 21 marbles in the bag

21 - 16 = 5

16/21 = 76%

To find the cos(40°), you can use the trigonometric identity sin²θ + cos²θ = 1. Since 50° and 40° are close angles, you can approximate the cos(40°) as 0.6393.

To find the cos(40°), we can use the trigonometric identity

sin²θ + cos²θ = 1.

Since we know that sin(50°) = 0.77, we can square this value to find the cos²(50°):

cos²(50°) = 1 - sin²(50°) = 1 - 0.77²

Simplifying, we get cos²(50°) ≈ 0.4089. Since cosine is positive in the first and fourth quadrants, the positive square root of this value gives us the cos(50°) ≈ 0.6393.

Therefore, we can approximate the cos(40°) as 0.6393 as well, since these are close angles.

Answer:

[tex]7.0248\sqrt{x}[/tex]

Step-by-step explanation:

We want to find the answer to the expression: [tex]\sqrt{\pi ^2*5x}[/tex]

We can easily calculate the product of the constants on the inside:

[tex]\sqrt{\pi ^2*5x}=\sqrt{49.348x}[/tex]

Now, we can split this radical into two:

[tex]\sqrt{49.348x}=\sqrt{49.348} *\sqrt{x} =7.0248\sqrt{x}[/tex]

Thus, the answer is [tex]7.0248\sqrt{x}[/tex].

Hope this helps!

Answer:

sqrt(5x) pi

Step-by-step explanation:

(pi² × 5x)^½

(pi²)^½ × (5x)^½

pi × sqrt(5x)

Answer:

Step-by-step explanation:

45 times 7= 315

326-315=11

125 times 2=250

250+11=261

so the answer is C. $261

The integer which represent the balance in Monique's account at the end of the week is 261.

The addition is taking two or more numbers and adding them together, that is, it is the total sum of 2 or more numbers.

Subtraction means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.

According to the given question.

Amount of money Monique have initially = $326

The amount of money Monique withdrawal from her savings each day is $45.

⇒ For the seven days the withdrawal amount = 7 × $45 = $315

Also, she made two deposits of $125

So, the total amount se deposited = 2 × $125 = $250

Therefore,

The total balance in Monique's account at the end

= $326 - the amount she withdrawn + the amount she deposited

= $326 - $315 + $250

= $261

Hence, the integer which represent the balance in Monique's account at the end of the week is 261.

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Question- How can you determine the best measure of center and measure of variability to use based on the shape of the distribution?

Answer- Mean and median both try to measure the "central tendency" in a data set. Summarizing center of distributions (central tendency) .

The following is the way:

To determine the best measure of center and variability based on the shape of the distribution, you must first examine the shape of the data. If the distribution is symmetric and has no outliers, the mean is generally considered the best measure of center, and the standard deviation is a suitable measure of variability. However, for skewed distributions or those with outliers, the median is a more appropriate measure of center, as it is not as affected by extreme values. In such cases, the interquartile range (IQR) is often used to describe variability, since it focuses on the middle 50% of the data, reducing the influence of outliers.

Robust vs. Non-Robust Measures: Measures of center and variability can be robust or non-robust. Robust measures, like the median and IQR, are less affected by outliers and skewed data. Non-robust measures, like the mean and standard deviation, are greatly influenced by extreme values. Therefore, in the presence of outliers or a skewed distribution, robust measures are preferred.

Chebyshev's Rule is helpful in understanding the spread of data in relation to the mean. This rule states that a certain percentage of data must lie within a set number of standard deviations from the mean, regardless of the distribution's shape. In a bell-shaped distribution, which is symmetric and normal, the mean, median, and mode coincide at the peak of the curve, and measures like the mean and standard deviation reflect the data's center and spread effectively

Answer:

D. 100.

Step-by-step explanation:

-m + 0.02 + 2.1m = -1.45 -4.81m

Multiply by 100:

-100m + 2 + 210m = -145 - 481m

​

Answer:

36 students

Step-by-step explanation:

right on edge

The total number of students bought their lunch from cafeteria is 36.

Given data:

The total number of girls is 35 and the total number of boys is 50.

Probability of boys bought their lunch from cafeteria = 0.44

Since total no. of boys =50

So, number of boys bought their lunch from cafeteria P ( B ) = 50*0.44

And, the value of P ( B ) = 22

Probability of girls bought their lunch from cafeteria = 0.4

Since total no. of girls =35

So, number of girls bought their lunch from cafeteria P ( G ) = 35*0.4

So, the value of P ( G ) = 14

The total number of students , n = P ( B ) + P ( G )

So, n = 22 + 14

n = 36

Hence , the number of students is 36

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The complete question is attached below:

35 total girls and 50 total boys were surveyed. How many students bought their lunch from the cafeteria? Round to the nearest whole number.

Answer:

P 81 = 73.5

Step-by-step explanation:

This is a normal distribution problem with a mean of 63.2 and standard deviation of 11.7.

Let the number that separates the bottom 81% from the top 19% be x' and let it's z-score be z'.

P(x ≤ x') = P(z ≤ z') = 0.81

Using the normal distribution table,

z' = 0.878

But note that the z-score for any value is that value minus the mean divided by standard deviation.

z' = (x' - μ)/σ

0.878 = (x' - 63.2)/11.7

x' = 73.4726 = 73.5 to 1 d.p

Hope this Helps!!!

Final answer:

To find the value that separates the bottom 81% from the top 19%, you can use the z-score formula and the given mean and standard deviation to calculate the desired value.

Explanation:

To find the value that separates the bottom 81% from the top 19%, we need to find the z-score corresponding to the 81st percentile.

Using the formula Z = (X - μ) / σ where X is the given value, μ is the mean, and σ is the standard deviation, we can rearrange it to solve for X as:

X = Z * σ + μ

Since we know the mean is 63.2 and the standard deviation is 11.7, we can calculate the z-score corresponding to the 81st percentile (0.81) using the standard normal distribution table or a calculator.

Once we have the z-score, we can substitute it into the formula to find the corresponding value.

Answer:

Step-by-step explanation:is the divide by 7×10=70is

Answer:

5 grams provided for 4 calories

Step-by-step explanation:

20 grams at 4 calories per gram.

20*4=80 Calories.

Answer:

88,88,888

Step-by-step explanation:

Answer:

4^2 + 4x= 1

Step-by-step explanation:

4x^2 - 4x - 5= 8x +6

4x^2- 4x+8x =6-5

4x^2 + 4x =1