i need the answers to these

I Need The Answers To These

Answers

Answer 1

Required values are to be put in blank space,

a. 99

b. 10

c. 5

after using logarithmic properties.

What is logarithm?

The other technique to write exponents in mathematics is using logarithms. A numbers  base based logarithms is equal to other number. A logarithm performs exponentiation's exact opposite function

For example:

If 10² = 100 then log₁₀¹⁰⁰ = 2.

Some logarithmic properties used are:

logₐˣ + logₐⁿ = logₐˣⁿ  logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex]   logₐ⁽ˣ⁾ⁿ = n logₐˣ

All of the questions are based on simple logarithmic properties:

a. In this properties used are,

   logₐˣ + logₐⁿ = logₐˣⁿ

   log₅⁹ + log₅¹¹ = ?

   comparing with general form, we get

   log₅⁹ + log₅¹¹ = log₅⁹⁹

b. In this properties used are,

   logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex]

   ? - log₉⁷ = log₉[tex]^{10/7}[/tex]

   comparing with general form, we get

   log₉¹⁰ - log₉⁷ = log₉[tex]^{10/7}[/tex]

c. In this properties used are,

   logₐ⁽ˣ⁾ⁿ = n logₐˣ

   log₂[tex]^{1/25}[/tex] = log₂⁽[tex]^{1/5}[/tex]⁾² = -2 log₂⁽⁵⁾

   Comparing with general form, we get

   log₂[tex]^{1/25}[/tex] = -2log₂⁵

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Related Questions

Questions
Surds exam questions
Q1. Express √3+√12 in the form a√3 where a is an integer.

Answers

Answer 3(root)3

Explanation

What is the y-intercept of x = -4?

Answers

Answer:

  DNE

Step-by-step explanation:

You want to know the y-intercept of x = -4.

Y-intercept

The y-intercept is the point where a graph crosses the y-axis.

The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.

There is no y-intercept. It does not exist (DNE).

Johnny is 5 years younger than twice Bobby's age. If the sum of thier ages is over 66 years.
What is the Johnny's minimum age?

Answers

The minimum age of Johnny is 21 as calculated by linear inequality.

Let Johnny 's age be x.

hence bobby's age = (x+5)/2

Now the sum of their ages is over 66 years.

So we will set an inequality to find the minimum age of Johnny.

x + (x+5)/2 > 66

or, 2x + x + 5 > 66

or, 3x > 61

or, x > 20 1/3

Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is employed, it means that a is greater than b.

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Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.

$69
$90
$420
$1,080

Answers

Answer: The answer to this question is $90.

Step-by-step explanation:

The Simple interest is $90.

What is Simple Interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.

Given:

P= 1500

R = 12%

T= 6 month = 1/2 year

Using, formula of Simple Interest

I = P x R x T /100

I = 1500 x 12 x 1/ 2x100

I = 18000/200

I = 90

Hence, the interest is $90.

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F(n)= 3n -4 find term 3 of the explicit arithmetic sequence

Answers

The third term will be 5 in the explicit arithmetic sequence.

What is an arithmetic sequence?

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The formula to find the general term of an arithmetic sequence is,

aₙ = a₁ + (n-1)d

The explicit formula of an arithmetic sequence is given in the question as:

F(n) = 3n -4   ....(i)

To determine the term 3.

Substitute the value of n = 3 in equation (i),

T₃ = 3(3) - 4

T₃ = 9 - 4

Apply the subtraction operation,

T₃ = 5

Therefore, the third term will be 5 in the explicit arithmetic sequence.

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A survey asked 300 students to choose their favorite type of movie.
The results are shown in the following table.
(a) Find the percentage for each type of movie.
Type of movie
Action
Comedy
Drama
Thriller
Number of
students
27
42
120
111
Percentage
1%
%
%
%
X
5

Answers

Answer:

300/100%=3%

Step-by-step explanation:

sorry, can't explain.Ihave class tomorrow

2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?

A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds

Answers

If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.

How to determine the weight?

Let x represent the weight of Cooper

Let x +25 represent the weight of Daisy

Let 3x -20 represent the weight of Luna

Hence,

x + (x +25) + (3x -20) = 175

5x +5 =175

Combine like terms

5x = 175 -5

5x =170

Divide both side by 5x

x = 170/5

x =34

Weight of Luna

3x -20  where x= 34

3(32) -20

= 102 -20

= 82 pounds

Therefore the correct option is D.

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20. In Problem 14 in Chapter 11, we described a study
showing that students are likely to improve their test
scores if they go back and change answers after
reconsidering some of the questions on the exam
(Johnston, 1975). In the study, one group of students
was encouraged to reconsider each question and
to change answers whenever they felt it was appropri-
ate. The students were asked to record their original
answers as well as the changes. For each student, the
exam was graded based on the original answers and on
the changed answers. For a group of n = 40 students,
suppose that 26 had higher scores for the changed-
answer version and only 14 had higher scores for
the original-answer version. Is this result significantly
different from chance? Use a two-tailed test with
α = .01.

Answers

I got 0.1 I hope I helped you

A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then
returning. The total time for the trip was 7.0 hours. Use this information to find the speed of the current.
What is speed of the current is miles per hour?

Answers

The speed of the current is equal to 8 miles per hour.

How to calculate the speed of the current?

Mathematically, speed of any physical object can be calculated by using this formula;

Speed = distance/time

Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:

Speed downstream = 14 + c.

Speed upstream = 14 - c.

Additionally, the total time would be given by:

Total time = total distance/speed

Time upstream + time downstream = 6.5 hours

33/(14 - c) + 33/(14 + c) = 7.0

Multiplying both sides of the equation by (14 - c)(14 + c), we have:

33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)

462 + 33c + 462 - 33c = 7.0(196 - c²)

924 = 7.0(196 - c²)

Dividing both sides of the equation by 7.0, we have:

132 = 196 - c²

Speed of the current, c² = 196 - 132

Speed of the current, c² = 64

Speed of the current, c = √64

Speed of the current, c = 8 miles per hour.

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Pedro has $18 to spend at the grocery store. His mother wants him to use the money to buy fruit. Apples cost $2 a pound and pears cost $3 a pound

Answers

Answer:

Pedro can buy 4 pounds of pears and 3 pounds of apples.

Step-by-step explanation:

Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.

$2×3lb + $3×4lb=$18

A number line going from negative 20 to positive 20.
What is the absolute value of –20?

Use the number line to answer the question.
–20
0
20
40

Answers

Answer:

20

Step-by-step explanation:

Absolute value is the distance from zero. Absolute value is always positive.

| -20 | is positive. It is 20 units from 0. So it is 20.

| -20 | = 20

(Be careful, absolute value doesn't just flip the sign to the opposite.

| 20 | = 20 also because the distance from 0 to 20 is also 20.)

a sequence is defined by a term to term rule

iteration help please

Answers

By the sequence of term to term rule the value of : a)  [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4    b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19     c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .

What is the term to term rule like for you?

Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to

[tex]$$\mathrm{u}_0=1$$[/tex]

The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3

We have to simply put the value in their places to get the proper answer -

a). Put the [tex]$u_{n+1}=u_1$[/tex]

n+1 = 1  ⇒ n = 0

put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3

we wil get

[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4

b). Put the [tex]$u_{n+1}=u_2$[/tex]

n + 1 = 2 => n = 1

put  n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3

we wil get:

[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19

c). Put the  [tex]$u_{n+1}=u_3$[/tex]

n + 1 = 3 => n = 2

Put n=2 in the formula+3

we wil get :

[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364

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Is 4.5 greater, less than, or equal to 4 and 1/2

Answers

Answer:

equal to

Step-by-step explanation:

4 + 1/2= 4+ 0.5= 4.5

4.5=4.5

Question
Find the rate if a principal of $1,100 earned $1,089 interest in 12
years.

Answers

Answer:

Step-by-step explanation:

Intrest = PRT\100

$1089. =. ($1100x12xR)\100

$1089. = 132R

 Divide through by 132.

R. =. 8.25%

I had 35 assignments for the week. The ratio for English assignments to the rest of the assignments was 2:3. How many assignments were NOT English?

Answers

Answer:

21 Assignments were NOT English.

Calculate the number of different three-course meals a patron could choose from at the Butcher Shop Steakhouse during Restaurant Week. What conditions had to be met for you to calculate the number of different outcomes for this experiment?

Answers

The probability of getting watermelon is 3/58.

The given values are

A pineapple chew was selected 53 Times

A lemon chew was selected 2 times

A watermelon chew was selected 3 times

The probability that you Bella remove from the bag is pineapple chew.

probability is which we can't predict actual it is usually about the prediction

As we know

probability - expected outcome/total outcome

The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58

The probability of Bella pick chew of lemon -2/58

The probability of Bella pick watermelon is - 3/58

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Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units

Answers

Answer:

I think B. 3.85 units

Step-by-step explanation:

Show, by shading on the grid, the region defined by all three of the inequalities
x ≤ 5 y ≥ 3 y ≤ x

Answers

Answer:

See below

Step-by-step explanation:

The area (triangle) marked 'x' in the diagram below

The mean systolic blood pressure of people in the U.S. is
124
124​ with a standard deviation of
18
18​. Assume that systolic blood pressure follows a normal distribution. Round your answers to one decimal. Use the 68-95-99.7 Rule to answer the following questions.

a) What percentage of the people in the U.S. have systolic blood pressure between
106
106​ and
124
124?

%
%
Preview

b) What percentage of the people in the U.S. have systolic blood pressure between
88
88​ and
160
160​?

%
%
Preview

c) What percentage of the people in the U.S. have systolic blood pressure between
70
70​ and
124
124​?

%
%
Preview

d) What percentage of the people in the U.S. have systolic blood pressure above
160
160​?

%
%

Answers

The percentages, using the Empirical Rule, are given as follows:

a) Between 106 and 124: 32%.

b) Between 88 and 160: 95%.

c) Between 70 and 124: 49.85%.

d) Above 160: 2.5%.

What does the Empirical Rule state?

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.

The mean and the standard deviation in this problem are given as follows:

Mean of 124.Standard deviation of 18.

Considering the symmetry of the normal distribution, to facilitate the calculations, we have that:

49.85% of the measures are between 70 and 124.47.5% of the measures are between 88 and 124.32% of the measures are between 106 and 124.32% of the measures are between 106 and 142.47.5% of the measures are between 124 and 160.49.85% of the measures are between 124 and 178.

160 is two standard deviations above the mean, hence the percentage above it is of:

2.5%.

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Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32

Answers

The expression as power is written as 2¹⁰ and 2^9

The values are

2¹⁰= 1024 2^9 = 512

How to write expression as a power

power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.

8• 2^7

= 2 * 2 * 2 * 2^7

= 2^10

= 1024

16•32

2^5 = 2 * 2 * 2 * 2 * 2

2^4 = 2 * 2 * 2 * 2

16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2^9

= 512

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Pls help question 9 and 10

Answers

The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.

AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.

In the given figure FE║GE means FE is parallel to GE.

so ∠EFS = ∠HGS

and ∠FES = ∠GHS

also ∠S is common for both.

If two triangles are similar then ratio of corresponding sides are also same.

So, by applying this

[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]

54/24 = FE/20

( 54*20 ) / 24 = FE

FE = 45m.

Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.

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Question
In 8 years, Estelle's bank account earned $1,270
simple interest at 2.5%. How much had she
deposited in the account?

Answers

Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

According to the question,

We have the following information:

In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.

Now, let's take the principal amount to be $x.

We know that the following formula is used to find simple interest:

Simple interest = (principal*rate*time)/100

(x*2.5*8)/100 = 1270

Using the cross multiplication method:

20x = 127000

x = 127000/20

x = $6350

Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

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can you explain thia​

Answers

First find the equation of the line, the y intercept is -5,
So y= mx+5
Then the gradient is -2 (rise/run)
so y= -2x+5
Then just make it an inequality with the inequality sign, clearly it is a greater than or equal to inequality as the shaded part is going up and the line is a solid line, so
y>(line under) -2x-5

hope that made any sense

Question content area top Part 1 What is the constant of proportionality in the equation y=−7.48​x?

Answers

The constant of proportionality of the equation y =−7.48​x is - 7.48.

What is proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent

In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.

Therefore, a proportional relationship is one in which two quantities vary directly with each other.

Hence, in mathematical form,

y ∝ x

y = kx

where

k = constant of proportionality

y varies directly as the variable x.

In the equation,

k = - 7.48

Therefore, the constant of proportionality  is - 7.48.

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Write an exponential function in the form y = ab^x that goes through points (0, 14)
and (4,8750).

Answers

The exponential function will be written as y = 14⁰.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,

[tex]y = ab^x \\[/tex]

14 = ab⁰

a = 14

The equation will be written as,

y = 14b⁰

y = 14⁰

Therefore, the exponential function will be written as y = 14⁰.

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A school is arranging a field trip to the zoo. The school spends 895.28 dollars on passes for 36 students and 2 teachers. The school also spends 321.84 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?

Answers

Amount spend by school in passes = 868.48 dollars
Total number of students and teachers = 44+2 = 46
Amount spend on one pass =

Amount spend on lunch= 425.92 dollars
Amount spend on one lunch =

For calculating amount of lunch and pass for each student we will add the amounts;
Each student costed = Each lunch amount + Each pass amount
Total money for one student =
Total money for one student = 28.56 Dollars

I almost broke my brain doing this a brainliest answer would be nice

What is the correct answer

Answers

Answer: See coordinate graph below.

Step-by-step explanation: The black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

A': (1, -4)

Let me know if this is right! :)

Use the properties of congruent triangle to find the value of x and y. Be sure to show all your work

Answers

Answer:Angles in a triangle may or may not be congruent.

The values of x and y are 90 and 47, respectively.

From the figure, we have:

This means that, angle x is a right-angle.

So, we have:

Triangle ABC is an isosceles triangle.

So, we have:

The measure of y is then calculated as:

--- sum of angles in a triangle

This gives

Subtract 137 from both sides

Hence, the values of x and y are 90 and 47, respectively.

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Step-by-step explanation:

Find the Average Rate of Change (AROC) of y = 4(1/2)^x over the interval [-2, 0].
a) 6
b) -6
c) 4
d) -4

Answers

Answer:

b) -6

------------------------

Find the value of the function at the endpoints of the given interval

x = - 2 ⇒ y = 4(1/2)⁻² = 4(2)² = 4(4) = 16x = 0  ⇒ y = 4(1/2)⁰ = 4(1) = 4

Average rate of change is

Change in y / change in x =(4 - 16)/(0 - (-2)) = - 12 / 2 = - 6

Correct choice is B.

Answer:

b)  -6

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given the interval is [-2, 0]:

a = -2b = 0

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

tenths hundreths thousands
1. 67.925
2. 182.0051
3. 39.1432
4. 85. 0267
5. 97.7352

Answers

Answer:

Step-by-step explanation:

1) sixty-seventh and nine hundred and twenty-five thousands

2)one-eighty two and fifty-one thousands

3)thirty-nine and thousand four thirty two thousands

4) eighty five and two sixty seven thousands

5) ninety seven and seven thousand and three-fifty two thousands

Other Questions
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