[tex]\ln(5-x) = \ln 5 - \ln x\\\\\implies \ln(5-x) + \ln x = \ln 5\\\\\implies \ln[(5-x)x] =\ln 5\\\\\implies \ln(5x -x^2) = \ln 5\\\\\implies 5x -x^2 = 5\\\\\implies x^2 -5x +5 =0\\\\\implies x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 5}}{2(1)}\\\\\implies x = \dfrac{5 \pm \sqrt{5}}{2}\\\\\text{Hence} ~x = \dfrac 12\left(5 + \sqrt 5\right)=3.62~~ \text{and}~~ x =\dfrac 12 \left(5-\sqrt 5\right) =1.38[/tex]
Answer:
x1 = 3.618, x2 = 1.382
Step-by-step explanation:
ln(5-x) = ln5 - lnx
ln(5-x) + ln(x) = ln5
ln(5x-x^2) = ln5
5x-x^2=5
0=x^2-5x+5
x = -(-5)±√((-5)²-4(1)(5)) / 2(1)
x = 5±√(25-20) / 2
x = 5±√5 / 2
x1 = 3.618, x2 = 1.382
Find the polynomial for the shaded area of the figure
Answer:
59y² -65y
Step-by-step explanation:
The area of a rectangle is the product of length and width. The shaded area will be the difference between the areas of the larger and smaller rectangles.
A = (6y)(14y -5) -(5y +7)(5y)
A = 84y² -30y -(25y² +35y)
A = (84 -25)y² +(-30 -35)y
A = 59y² -65y
Help help help help math
Answer:
<6 = 158°
Step-by-step explanation:
we know a = 6
22 + a = 180
a = 180 - 22
a = 158
1[tex]\sqrt{5}[/tex]*3[tex]\sqrt{5}[/tex]
Answer:
[tex]1\sqrt5 \times 3\sqrt 5 =(1\times3)(\sqrt5\times\sqrt5) = 3\times (\sqrt5)^2=3\times 5=15[/tex]
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Answer: The last answer is correct.
Step-by-step explanation:
The Diamondbacks softball team orders a new baseball bat and pays $310.30 after tax. The tax rate is 7%. What is the original price of the baseball bat?
Answer: $255.58
Step-by-step explanation:
$310.30*0.07= $21.721
$310.30-$21.72= $255.579
Round
$255.579 --> $255.58
A certain shampoo is available in two sizes. A 14.2 -ounce bottle costs 3.98$ . A 33.9 -ounce bottle costs 9.98$ .
Find the unit price for each size. Then state which size is the better buy based on the unit price.
Round your answers to the nearest cent.
Answer:
14.2 ounce for $3.98 is more cheaper
Step-by-step explanation:
unit price formula; cost ÷ quantity
3.98 / 14.2 = 0.2802816901408
9.98 / 33.9 = 0.2943952802359
round answers to the nearest hundredth;
$0.28
$0.29
compare the answers
Can someone please help me
Answer:
that is so hard sorry
How many factor pairs does 15 have
Answer:
It has a total of 4 the factors are 1,3,5, and 15
On a game show, a contestant wins $200 by answering questions correctly but loses $300 for
each question answered incorrectly. How much money would a contestant win if she
answered 14 questions correct and I question incorrect?
Answer:
$2500
Step-by-step explanation:
$200×14=$2800
$2800-$300=$2500
true or false
A political party is a group of people who seek to control government by winning elections and holding office
Answer:
True
Step-by-step explanation:
Eg. Republican party nominates a candidate to be considered by the people [hopefully voted] into office. If they win the election, they control a part of government in office.
What is the vertical shift for the absolute value function below. Explain how you know using complete sentences. Include the direction and number of units of the shift. f(x)=9|x+1|+2
The vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up
The absolute function is given as:
[tex]f(x) = 9|x + 1| + 2[/tex]
An absolute function is represented as:
[tex]f(x) = a|x - h| + k[/tex]
Where k represents the vertical shift.
By comparison, the value of k is:
[tex]k = 2[/tex]
This means that the vertical shift is 2 units
Hence, the vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up
Read more about absolute value function at:
https://brainly.com/question/25971887
what is (1+1²×2²).....
Answer:
[tex](1 + {1}^{2} \times {2}^{2} ) = 1 + 1 \times 4 \\ = 1 + 4 \\ = 5[/tex]
[tex] \bold \pink{ \underline{hope \: it \: helps}}[/tex]
A house on the market was valued at $233,000. After several years, the value decreased by 15%. By how much did the house's value decrease in dollars? What
is the current value of the house?
Decrease in value:
Current house value:
Answer:
decrease: $34,950current value: $198,050Step-by-step explanation:
The decrease in value is ...
15% of $233,000 = $34,950
The current house value is ...
$233,000 -34,950 = $198,050
help me on my 7th grade math homework
Answer:
Step-by-step explanation:
divide the money or degrees by the hours or form of time they give. for the first one you divide 585/52 to get $11.25 an hour.
A bakery has 18 large trays of bagels and 20 small trays of bagels. Each large tray holds 30 bagels and each small tray holds 15 bagels.
Which equation could be used to find n, the total number of bagels the bakery has?
18 + 30 × 20 + 15 = n
18 × 30 + 20 × 15 = n
18 + 30 + 20 + 15 = n
18×30−20×15=n
Choose wisley
Solve for x given that AC = 4, CE = 8, AB = X - 8, and BD = 2.
What is the measurement of AB?
A box plot is shown
O
2
4
6
8
10
12
Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.
14
16
18
20
22 24 26
28
30
Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
1
2
3
4
11
5
12
6
ما تا ته
13
14
8
21
15
22
16
10
23
17
24
18
25
19
26
20
27
28
29
30
Please answer fast
Answer:
O
2
4
6
8
10
12
Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.
14
16
18
20
22 24 26
28
30
Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
1
2
3
4
11
5
12
6
ما تا ته
13
14
8
21
15
22
16
10
23
17
24
18
25
19
26
20
27
28
29
30
Please answer fast
I was absentee and i dont know how to solve it help plz
Answer:
-1/3
i think.
Step-by-step explanation:
if it's to find slope
Answer:
m = -1/3
Step-by-step explanation:
There are two easy ways you can find the slope. The first one is using the rise over run method which is to first count how much you need to go up or down to get to the other point, and then how much you need to go forward. In this case you go down one, and forward three. This means its -1/3. You can also use the slope formula which uses the coordinates of each point. I attached it to this answer. (m representing slope)
What is the slope of this graph?
a.4
b.−4
c.14
d.−14
Answer:
B
Step-by-step explanation:
just look at where the line crosses the coordinate plane
Help please!!!!!!!!!!!!!!!!!
Answer:
You are correct it is indeed mortgage!
Step-by-step explanation:
This is because a fixed expense is something that cannot be changed easily. Like a mortgage, car payments, rent payments, or insurance.
Hope this helps, I tried to just briefly explain! :)
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether under-filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted to obtain the proper filling.
a. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.
b. Comment on the conclusion and the decision when the null hypothesis cannot be rejected.
c. Comment on the conclusion and the decision when the null hypothesis can be rejected.
Answer:
b
Step-by-step explanation:
mark brainliest pls....
Two researchers, Justin and Henry, work together to study what proportion of subjects have a certain genotype in the population. They each collect a simple random sample and they find that the sample proportion is 0.70. When they construct a confidence interval based on this sample proportion, Henry comes up with (0.632, 0.768) while Justin gets (0.652, 0.788). Indicate which interval has to be wrong and why.
Using confidence interval concepts, it is found that Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
A confidence interval has two bounds, a lower bound and an upper bound. A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds. The margin of error is the difference between the two bounds, divided by 2.In this problem, the point estimate is of 0.7.
Henry's interval is symmetric, as [tex]0.768 - 0.7 = 0.7 - 0.632[/tex].Justin's is not, as [tex]0.788 - 0.7 \neq 0.7 - 0.652[/tex].Hence, Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
For more on confidence intervals, you can check https://brainly.com/question/25822483
The width of a rectangle is 6x−6.5 feet and the length is 6.5x+7 feet. Find the perimeter of the rectangle.
Answer: 25x+1
Step-by-step explanation:
We cam make an equation to find the perimeter, [tex]2(6x-6.5)+2(6.5x+7)[/tex].
then we can simplify it to [tex]12x-13+13x+14[/tex], which we can then further simplify to 25x+1
Andre draws a tape diagram for 3÷2/3
Andre says that 3÷2/3= 4 1/3 because there are 4 groups of 2/3 and 1/3 left. Do you agree with Andre? Explain your reasoning
Answer:
No I do not agree with Andre says that 3 divided by 2/3 Solving for 3 ÷ 2/3
3 ÷ 2/3
= 3 × 3/2
= 9/2
= 4 1/2
Therefore, 3 divided by 2/3 is 4 1/2
Andre's reasoning is wrong.
Step-by-step explanation:
It is incorrect
Let's divide and compare the sum
3 : 2/3 = 3*3/2 = 9/2 = 4 1/2
and
There are four 2/3 fractions and one 1/3 fraction
The 1/3 fraction is 1/2 of 2/3 fraction so instead of counting 1/3 as 1/3 it should be counted as 1/2
The two legs of right triangle measures 6 and 8 inches respectively. What is the area of the circle that contains all 3 verticals of the triangle
Answer:
See image.
Step-by-step explanation:
Remember if you have a right angle inside of a circle, the hypotenuse is going to land exactly on the diameter. Also, Area of a circle = (pi)r^2 Lastly, remember pythagorean triples such as 3,4,5 or at least, the Pythagorean theorem a^2 + b^2 = c^2
Mai skated x miles, and Clare skated 2 times farther than that. Write an equation to represent the relationship between the distance Mai skated (x) and the distance Clare skated (y).
at a community college a survey was taken to determine where students study on campus. Of the 270 students surveyed, it was determined that 177 studied in the library , 142 studied in the cafeteria, 82 studied in both the library and the cafeteria. Of those students surveyed, how many studied only in the library?
Answer:
177
Step-by-step explanation:
Although it says that 82 studied in both, the question is aksing for ONLY at the library. It says that of the 270 surveyed, 177 study at the library.
This means that 65.56% of the students studied at the library primarely.
Answer:
95
Step-by-step explanation:
Use a Venn diagram;
2 places are identified where students may study, the library and the cafeteria so there are 2 circles;
One represents library (L) and the other is cafeteria (C);
82 goes in the overlap since 82 study in both places;
177 study in the library, but this includes the 82 that also study in the cafeteria, so 177 - 82 will give us the number who study only in the library, i.e. 95;
If we wanted to find the number who study only in the cafeteria, it would be similar;
142 study in cafeteria, including the 82 who also study in the library, therefore 142 - 82 will give the number who only study in the cafeteria, i.e. 60;
The number who study in neither the library nor the cafeteria would be the total number of students surveyed (270) take the 82 who study in both places and take the 95 who study only in the library and take the 60 who study only in the cafeteria, which gives 33 (i.e. 270 - 82 - 95 - 60)
1/4, 3/4, 5/4, 7/4, ... 15th term
Answer:
29/4
Step-by-step explanation:
2/4 is added per step
14 steps from 1/4
1/4 + 14.(2/4) = 29/4
Answer:
29 / 4 is the 15th term
simplified : 7 1/4
Step-by-step explanation:
3/4 - 1/4 = 2/4
5/4 - 3/4 = 2/4
7/4 - 5/4 = 2/4
. Use Arithmetic equation
a1 = 1/4
d= common difference = 2/4
a15 = a1 + (n-1) d
a15 = 1/4 + (15 - 1) 2/4
a15 = 1/4 + 14 (2/4)
a15 = 1/4 + 7
a15 = 29/4 or 7 1/4
Three cards are dealt from a shuffled standard deck of playing cards. Find the probability that the first card dealt is red, the second is black, and the third is red. (Enter your probability as a fraction.)
There are 52 cards in a deck, half the cards aware red and half the cards are red.
First card being red is 26/52 = 1/2
After the first card is dealt there are 51 cards left and 26 are black so dealing a black card = 26/51
After 2 cards are dealt there are 50 cards left and 25 red ones left. The probability would be 25/50 = 1/2
The probability of all 3 happening = 1/2 x 26/51 x 1/2 = 13/102
Answer: 13/102
15/4= simplify it please
Answer:
[tex]The \: fraction \: \frac{15}{4} \: is \: equivalent \: to \: 3 \frac{3}{4 } .[/tex]
This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denomintor (4). So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction [tex]3 \frac{3}{4} [/tex]
The fraction [tex] \frac{15}{4} [/tex]
is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.
The fraction 15/4 is equivalent to 3 3/4.
Here, we have,
To simplify the fraction 15/4, you need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (4) and divide both the numerator and denominator by the GCD.
The GCD of 15 and 4 is 1 since there are no common factors other than 1.
Dividing both the numerator and denominator by 1, we get:
(15 ÷ 1) / (4 ÷ 1) = 15/4
This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denominator (4).
So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction 3 3/4.
The fraction 15/4 is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.
To learn more on fraction click:
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