Mathematics College

Given log_7⁡3≈0.5646 and log_7⁡16≈1.4248, evaluate the expressions. Please show work using given values.

Answers

Answer 1

Answer:

(a) [tex]\log_72 \approx 0.3562[/tex]

(b) [tex]\log_7(\frac{147}{16} ) = 2[/tex]

Step-by-step explanation:

For the point a:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex]

16 can be re-write as [tex]2^4[/tex]. Then you have:

[tex]\log_72^4[/tex]

Using the power property of the logarithm we have:

[tex]\log_ba^c = c\log_ba[/tex]

[tex]\log_72^4 = 4\log_72[/tex]

And this expression is equal to:

[tex]4\log_72 \approx 1.4248\\\log_72\approx \frac{1.4248}{4} \approx 0.3562\\[/tex]

For the point b:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex] and [tex]\log_73 \approx 0.5646[/tex]

The first is use the quotient property in the given log.

[tex]\log_c\frac{a}{b} = \log_ca-\log_cb[/tex]

[tex]\log_7\frac{147}{16} = \log_7147 -\log_716[/tex]

We already know the value of [tex]\log_716[/tex] then we have to calculate the value of [tex]\log_7147[/tex].

So we factorize the number 147 in [tex]3 \cdot 7 \cdot 7[/tex] (for factorize the number start with the smaller prime and check if the remainder is 0, it is then is a primer factor of the number).

Now re-write [tex]\log_7147[/tex] as [tex]\log_73 \cdot 7^2[/tex] and by the product property get:

One must rearrange the function to decreasing value of exponents

f(x) = -7x⁴ + 8x³ - 3x² - 9x + 11

to see that it is a 4th degree polynomial with leading coefficient of -7

evaluate -x^3 - 3x^2 + 4 when x = -2

Answers

The answer = 0

-(-2)^3 = 8

-3(-2^2)= -12

Then add 4

-12 + 4 + 8 = 0

Answer:

Step-by-step explanation:

x = -2

-x^3 - 3x^2 + 4

-(-2)^3+6^2+4

8+36+4=48

Hope this helps :)

Please help please help please help please help

Answers

Answer:

2 , 3

Step-by-step explanation:

68% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number of US adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, (c) less than four.

Answers

Answer:

A) 12.29%

B) 81.33%

C) 1.55%

Step-by-step explanation:

This is a binomial model, and I assume you're meant to use a calculator to solve.

This is what I have in my notes for the binompdf function:

binompdf(n, p, x) - find the probability of exactly x successes in n trials given p probability

That is exactly what we want in this case, we're looking for exactly 5 people who meet the conditions (successes) given n trials and p probability.

Using a calculator:

binompdf(10, 0.68, 5) ≈ 0.1229

That means you have about a 12.29% chance to randomly select exactly 5 adults who have little confidence in newspapers.

For this one, use the binomcdf function:

binomcdf(n, p, x) - find the probability of x or fewer successes in n trials given p probability

In this case, we're looking for more, not less. However, you can think of the probability of getting more than 6 as just the probability of not getting less than 6.

With a calculator:

binomcdf(10, 0.68, 5) ≈ 0.1867

That means you have about an 18.67% chance to randomly select 5 or less people. We're looking for more though. As said above, the probability of getting 6 or more is just the probability of not getting 5 or less. To find the probability of something not happening, just subtract the probability from 1.

1 - 0.1867 = 0.8133

An 81.33% chance to randomly select at least 6 adults who have little confidence in newspapers.

Same as the above, I don't see a need to explain it all again. Use binomcdf:

binomcdf(10, 0.68, 3) = 0.0155

Notice I used 3 rather than 4. binomcdf calculates x or fewer, or 'rather less than or equal to'. We want just 'less than 4', and that means 'less than or equal to 3'.

That's a 1.55% chance to select less than 4 adults with little confidence in newspapers.

The table above shows the number of each type of plant in Robert's garden. What is the ratio of the total number of plants in Robert's garden to the number of tomato plants?

Answers

Answer: C.

Step-by-step explanation:

Total number of plants in Robert's garden = 8 + 4 + 16 + 22

= 50

Number of tomato plants in Robert's garden = 8

Ratio of total number of plants to the number of tomato plants = 50 : 8

Simplify

50 : 8 = 25:4

Simplify -3(xy + 2y) + 5y - x.

Answers

Answer:

Step-by-step explanation:

-3 (xy+2y)+5y-x

-3xy-6y+5y-x

-3xy-y-x

Write an equation of a line with an x-coefficient of - 3 and a y-intercept of 7

Answers

Answer:

y = -3x + 7

Step-by-step explanation:

For an equation in the format y = ax + b, a is the coefficient of x, and b is the y intercept.

Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?

Answers

He is going to have 21 nickels

p l s… h e l p… m e…

Match the unknown entries in the two matrices with their correct values

Answers

Answers:

v = 54y = 0u = 6w = -48x = -1

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

Explanation:

The left hand side is

[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}[/tex]

That -6 outside the matrix is multiplied with each item inside the matrix. This is known as scalar matrix multiplication. Effectively, it's very similar to the idea of the distributive property.

So for the first row, we have the three columns of: -6*3 = -18 and -6*(-1) = 6 and -6*3 = -18

The other two rows are handled the same way. This is what should result:

[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]

From here, you'll then match up the terms in the given right hand side matrix. The top row has the variable 'u' in the middle, which matches with the '6' in the middle of the top row shown. Therefore, u = 6.

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

Now to the second row.

The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.

Also, we have -6x in the middle which matches with the 6 in the same corresponding spot. Solving -6x = 6 leads to x = -1.

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

Finally, the third row.

There's only one variable here and that's the variable y in the bottom right corner. It pairs up with 0 in the same corresponding spot for the right hand side matrix. Therefore, y = 0.

Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?

Answers

9514 1404 393

Answer:

16 nickels

Step-by-step explanation:

Robert can group his coins into groups consisting of 1 nickel and 4 pennies. The value of each group is 9¢, so the number of groups Robert can make is ...

$1.44/$0.09 = 16 . . . groups

Since there is 1 nickel in each group, Robert has 16 nickels.

Answer:

Step-by-step explanation:

What percent of 80 is 84?

Answers

Answer: 105

Step-by-step explanation: if you are using a calculator, simply enter 84÷80×100 which will give you 105 as the answer.

b) Complete the table to show the total amount of calories Mary will burn for
cycling and running for 0, 10, 15, and 30 minutes. Show and explain your work.
Minutes (m)
Total Calories Burned (C)
0
10

Answers

For 0 minutes she can burn 0 calories

For 10 minutes she can burn 20-40 calories

For 15 mins she can burn 40-60 calories

For 30 minutes she can burn 140-295 calories

I hoped this helped!

Have a great day/night! :)

Forty six minus twenty

Answers

Answer:

26 po hahahahahahahahahahaha

find the length of fencing required to go all the way around the rectangular field that is 136000mm wide and 425m long

Answers

the answer is 57800m^2

do anyone know what’s the answer to this problem ?

Answers

your answer is -4
i tried to explain it best i could in the picture

What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?

Answers

Answer:

I will cryy because I only want to write 78 why it recorded as 98

I need help with number 9 please

Answers

Answer:

29.85

Step-by-step explanation:

1 month = 9.95

2 months = 19.9

3 months= 29.85

It shows the progression through three months and how much it was starting off from one month.

Answer: $29.85

per day it charges $9.95

she has the subscription for three months

we will then multiply the amount charged per month

$9.95 x 3 = $29.85

I hope this helps! :)

Jill had some candy to give to her five
children. She first took seven pieces for
herself and then evenly divided the rest
among her children. Each child received
five pieces. With how many pieces did
she start?

Answers

She started with 32 pieces.

Explanation: If she had 5 children and each child received 5 pieces, you can determine that she gave her children a total of 25 pieces because 5 x 5 = 25. If she took 7 pieces for herself before giving the rest away, you can determine that she had 32 pieces of candy to start with because 25 + 7 = 32.

Look at attached photo. Will give brainiest to correct answer. Trigonometry.

Answers

Answer:

Step-by-step explanation:

If 20% of a number is 28 and 25% of the same number is 35, find 45% of that number.

Answers

answer: 63
explanation: 20% + 25% = 45% and 20%= 28
25%= 35
thus, 28 + 35 = 45% = 63

Which statement is true?

Answers

The answer is a
Hope this helped!!

How do you evaluate (-12)3

Answers

Step-by-step explanation:

-1728 y'all i do by using calculator and it is correct

Answer:

its -1728

Step-by-step explanation:

i worked it out right.

Help me answer 5d, thank you!

Answers

Answer:

5. is III. Since there is a vertical asymptote at x= -3 and hole at x=0

Which fractions are equivalent to 1012?

Select each correct answer.

23

56

1224

3036

5060

6084

Answers

Answer:

5/6, 30/36, 50/60

Step-by-step explanation:

10/12 divided by 2= 5/6

10/12•3= 30/36

10/12•5= 50/60

PLEASE HELP ME WILL MARK BRAINLIEST AND PLZ EXPLAIN

Answers

Okay we have to begin by using the formula.
Y= a (x-h)^2 + k
Now we have to identify the vertex which is (-4,-3). Now substitute the vertex for (h,k). So now we have.
Y= a( x-(-4)^2 + (-3)
This gives us
Y = a(x+4)^2 -3
Now we have to pick a point from the graph to substitute for the x and y values. This can be any point expect for the vertex. I have chosen (-3,-1). Now let’s substitute:
-1= a(-3+4)^2-3
Now we have to solve for a:
-1=a(1)^2 -3
-1= a-3
-1+3=a
a= 2
Now that we know the value of a we can write the equation down:
Y= 2(x+4)^2 + 3

Can someone tell me what’s going on here

Answers

Answer:

c = 105 degres

Step-by-step explanation:

When two lines cross like that and form an x, the opposite sides are equal (so the angle below the 75 degree one is also 75 degees). Using this, you can figure out the rest.

If both the top an bottom are equal, you know that 150 degres are taken (75+75) and you know that there can only be 360 degres in total here, so you subtract 150 from 360 and get 210. Now you know that the last two sides together are 210, and since they are equal, you divide it by two to get 105 degrees.

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