Answer:
The exact solution is
[tex]x = \frac{Ln(60)}{7*Ln(5)}[/tex]
And the approximation to three decimal places is:
x = 0.363
Step-by-step explanation:
Here we have the equation:
[tex]5^{7*x} = 60\\[/tex]
Now we can remember a property of the natural logarithm function:
Ln(a^n) = n*Ln(a)
Now we can apply the Ln( ) function to both sides of that equation to get:
[tex]Ln(5^{7*x}) = Ln(60)[/tex]
Then we get:
[tex]7*x*Ln(5) = Ln(60)[/tex]
Solving that for x we get:
[tex]x = \frac{Ln(60)}{7*Ln(5)} = 0.363[/tex]
So the exact solution is:
[tex]x = \frac{Ln(60)}{7*Ln(5)}[/tex]
And the approximation to three decimal places is:
x = 0.363
Help me and show work plz <3
Please help-
Sam has 3 shirts, 3 pairs of shorts, and 2 pairs of shoes. How many possible combinations does Sam have if she wears 1 shirt, 1 pair of shorts and 1 pair of shoes at a time?
Answer:
The answer should be 18: 3 x 3 x 2
There were 300 people at a dance. Tickets cost $5 for visitors and $3 for students. The total ticket sales were $1100. How many visitors and how many students attended the dance?
(NO LINKS) I BEG U HALP FELLOW SMART PPL
Answer: See the image below for the filled out table.
The other root is x = -2
===========================================================
Explanation:
The turning point is at (1, -45) which is the vertex. This is where the graph goes downhill, and then turns around to go uphill, or vice versa. Depending on the direction, the vertex is the lowest point or the highest point on the parabola.
We have (h,k) = (1,-45) as the vertex, so h = 1 and k = -45
y = a(x-h)^2 + k
y = a(x-1)^2 + (-45)
y = a(x-1)^2 - 45
Now plug in any other point from the table. You cannot pick (1,-45) or else you won't be able to solve for the variable 'a'. Let's go for (0,-40)
We'll plug x = 0 and y = -40 into the equation above to solve for 'a'
y = a(x-1)^2 - 45
-40 = a(0-1)^2 - 45
-40 = a(-1)^2 - 45
-40 = a - 45
a-45 = -40
a = -40+45
a = 5
Therefore, the equation for this parabola is
y = 5(x-1)^2 - 45
As a way to check, we can plug in something like x = -3 to find that...
y = 5(x-1)^2 - 45
y = 5(-3-1)^2 - 45
y = 5(-4)^2 - 45
y = 5(16) - 45
y = 80 - 45
y = 35
Which matches what the table shows in the first column. I'll let you verify the other columns. As you can probably guess at this point, we'll plug in the x values to get the corresponding y values.
So for x = -2, we get...
y = 5(x-1)^2 - 45
y = 5(-2-1)^2 - 45
y = 5(-3)^2 - 45
y = 5(9) - 45
y = 45 - 45
y = 0
The result of 0 here indicates we have a root at x = -2. This is the other x intercept. The x intercept already given to us was x = 4.
The rest of the table is filled out using the same idea. You should get what you see below.
state study on labor reported that one-third of full-time teachers in the state also worked part-time at another job. For those teachers, the average number of hours worked per week at the part-time job was 13. After an increase in state teacher salaries, a random sample of 400 teachers who worked part-time at another job was selected. The average number of hours worked per week at the part-time job for the teachers in the sample was 12.5 with a standard deviation of 6.5 hours. Is there convincing statistical evidence, at the level of α=0.05, that the average number of hours worked per week at part-time jobs decreased after the salary increase?
(A) No. The p-value of the appropriate test is greater than 0.05.
(B) No. The p-value of the appropriate test is less than 0.05.
(C) Yes. The p-value of the appropriate test is greater than 0.05.
(D) Yes. The p-value of the appropriate test is less than 0.05.
(E) Not enough information is given to determine whether there is convincing statistical evidence
answer a show work, please
Answer: a) no. The p value of the appropriate test is greater than 0.05
Step-by-step explanation:
The statement "No. The p-value of the appropriate test is greater than 0.05." is a correct option (A) is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
Sample size n = 400 teachers
Sample mean X = 12.5 hours
Standard deviation S = 6.5 hours
Population mean u = 13 hours
Null hypothesis H0: u = 13
Alternativ hypothesis u <13
T-test:
[tex]\rm t = \frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
[tex]\rm t = \frac{12.5-13}{\frac{6.5}{\sqrt{400} } }[/tex]
t = -1.5385
Now degree freedom df = n -1 = 400 - 1
df = 399, α = 0.05
P-value = p[1+t<-1.5385]
P-value = 0.0624
∴ P-value is greater than α because of this the null hypothesis failed.
Thus, the statement "No. The p-value of the appropriate test is greater than 0.05." is a correct option (A) is correct.
Learn more about the standard deviation here:
brainly.com/question/12402189
#SPJ2
The starting salary for delivery driver is 35,000 per year with a yearly increase of 3% which type of function best models this situation
Answer:
Option B
Step-by-step explanation:
The complete question is
The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. which type of function best models this situation? a) exponential b) linear c) quadratic d) radical
Solution
After 1 year the salary of delivery boy will be
[tex]35000 + 35000*0.03\\35000+1050\\36050[/tex]
Salary of delivery boy after 2nd year =
[tex]36050 + 36050*0.3 = 37131.5[/tex]
Salary after 3rd year
[tex]37131.5 + (37131.5*0.03) = 38245.45[/tex]
The growth in salary is linear as depicted from the values obtained.
Hence, option B is correct
5 Ava consistently makes 75% of the free throws she attempts in basketball games,
The equation f = 0.75a can be used to find 7, the number of free throws Ava makes
out of a attempts, if she made 36 free throws during the last game, how many did
she attempt?
A 111
B 39
C 27
D 48
1.x3 + 2x
Name the polynomial by number of terms. select the correct response
4 term polynomial
monomial
binomial
trinomial
A person places $757 in an investment account earning an annual rate of 8.2%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years.
Answer: 3902.4633
Step-by-step explanation: 3902.46 from deltamath
Mary built a square picture frame. She wants to put ribbon on the border of the picture frame. If the sides of her picture frame measure 6 inches, how much ribbon will she need?
a. 36 inches of ribbon
b. 24 inches of ribbon
c. 10 inches of ribbon
d. 12 inches or ribbon
Answer:
B. 24 inches of ribbon
Step-by-step explanation:
Since her picture frame is a square we can multiply 6 × 4 to get our answer.
6 × 4 = 24
You can also add.
6 + 6 + 6 + 6 = 24
So, your answer is, B. 24 inches of ribbon.
Have a beautiful day! :)
need help with mathematics
Need now please
Step-by-step explanation:
3. a & d
4. b
5. d
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Find the measure of A
Help ASAP
NO LINKS!
Answer:
42 degrees
Step-by-step explanation:
The measure of the inscribed angle is half of the angle of the measure bc
1/2 * 84 = 42
of 7−3x+x2−2x
7
-
3
x
+
x
2
-
2
x
Answer:
hahah 0x
Step-by-step explanation:
Hey do any of you guys know the answer to this? I’m struggling and I need help. Thanks!
Answer and Step-by-step explanation:
1.
We are told to give the transformations needed to map the triangle ABC onto the triangle XYZ.
First off, we should move the triangle to the right. We need to have point B of triangle ABC to overlap point Y of triangle XYZ.
Once that is done, we need to do a dilation by scale 1.5. This would perfectly align triangle ABC onto triangle XYZ.
2.
To find the length of XZ, we need to find the dilation factor. Since we know that the triangles are similar, we can divide the bigger side by the little side (though only the sides that correspond).
We will divide side CB by ZY to get the dilation scale factor.
6 divided by 4 equals 1.5.
Now, to find the length, we will divide side CA by 1.5.
21 divided by 1.5 equals 14.
The length of ZY is 14.
#teamtrees #PAW (Plant And Water)
2x + y - z = -8
2y + 3z = -6
-1/2x + y + z = -4
For the following matrix, which of the following matrix operations would result in a11 = 1?
Multiply row 2 by -1 and add it to row 1.
Multiply row 1 by - 1/2.
Multiply row 1 by 1/2.
Multiply row 3 by -4 and add it to row 1.
(please show your solution if possible & pls just type in the comments if unsure abt your answer.. thank you)
Answer:
Multiply row 1 by [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
The augmented matrix of the system of linear equation is described below:
[tex]\left[\begin{array}{cccc}2&1&-1&-8\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right][/tex]
Where [tex]a_{11} = 2[/tex], if we need to create [tex]a_{11} = 1[/tex], we need to multiply row 1 by [tex]\frac{1}{2}[/tex], that is to say:
[tex]\left[\begin{array}{cccc}1&\frac{1}{2} &-\frac{1}{2} &-4\\0&2&3&-6\\-\frac{1}{2} &1&1&-4\end{array}\right][/tex]
Hence, the correct answer is: Multiply row 1 by [tex]\frac{1}{2}[/tex].
Kelsey takes out a loan for $6000 to start a business after high school. The bank charges her 8% simple interest for the loan for 5 years, how much interest will she pay?
Answer:
$2400
Step-by-step explanation:
Given data
Principal= $6000
Rate= 8%
Simple interest= ???
Time= 5 years
The expression for the simple interest is
Simple interest= PRT/100
Simple interest= 6000*8*5/100
Simple interest= 240000/100
Simple interest= $2400
Hence the simple interest after 5 years is $2400
Find the median number: 10,7,4,12,11,5,8,13,11
Answer:
10 median number
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
So, the median is the middle number, so first we have to arrange our numbers in order:
4, 5, 7, 8, 10, 11, 11, 12, 13
Now, as you can see, the middle number is 10
So the median of the set is 10
hope this helps:)
PLEASE HELPPPP ILL GIVE BRAINLIEST!!!
Dan, Anna, and Todd are walking in a city park. Each time Dan takes 3 steps, Anna takes 5 steps. Each time Anna takes 3 steps, Todd takes 5 steps. If Anna and Todd take a combined total of 400 steps, how many steps does Dan take?
Answer:
1200
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
ax+b=cx+d; a is not equal to c
Answer:
[tex]x = \frac{d - b}{a - c} [/tex]
H(x)= ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ 8+6x x+4 10 4x−3 , , , x<−7 −7≤x<−5 x≥−5
Answer:
[tex]h(-6) = -\frac{1}{5}[/tex]
Step-by-step explanation:
Given
[tex]h(x) =\left[\begin{array}{cc}8 + 6x\ \ &x < -7\\\frac{x + 4}{10} &-7 \le x <-5 \\4x - 3\ &x \ge -5\end{array}\right[/tex]
Required
Determine h(-6)
To do this, we make use of:
[tex]h(x) = \frac{x + 4}{10}[/tex]
Because [tex]-7 \le -6 <-5[/tex]
So, we have:
[tex]h(x) = \frac{x + 4}{10}[/tex]
[tex]h(-6) = \frac{-6 + 4}{10}[/tex]
[tex]h(-6) = \frac{-2}{10}[/tex]
Simplify
[tex]h(-6) = -\frac{1}{5}[/tex]
2. Find the radius of the circle.
La
12 in.
Answer:
Hello! answer: radius is 6
Step-by-step explanation:
It shows that the diameter is 12 the radius is half of that therefore the radius is 6 hope that helps!
PLZ HELP ME!! THE PICTURE IS BELOW!! NO LINKS!!!
Find the value for x to the nearest tenth.
Select one:
A. 6.4
B. 5.2
C. 5.8
D. 4.5
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Explanation:
Refer to the diagram below. I've added the points A, B, C, D, and E. Point A is the center of the circle while points B, C and D are along the circle's edge. The radius AC and chord BD intersect at point E.
Recall that whenever we have a radius perpendicular to a chord like this, it means that the radius bisects the chord. So that means chord BD is cut into two equal pieces BE and ED. The diagram given to you tells us that ED = x, so BE is also x units long as well. Overall, BD = BE+ED = x+x = 2x units.
Since BE = ED, the arcs formed are congruent as well. Minor arc BC is the same measure as minor arc CD. Both are 45 degrees. They combine to 90 degrees. In turn, this leads to central angle DAB to be 90 degrees.
Note how triangle DAB is an isosceles right triangle. The two equal legs are the two radii AB and AD, both which are 9 units long. The hypotenuse BD is equal to sqrt(2) times the leg length, so BD = 9*sqrt(2) units long.
Earlier I mentioned that BD = 2x also. We'll equate the two right hand side expressions and solve for x like so:
2x = 9*sqrt(2)
x = (9*sqrt(2))/2
x = (9/2)*sqrt(2)
x = 4.5*sqrt(2)
x = 6.36396103067892
That value is approximate. Rounding to the nearest tenth leads to the final answer of 6.4; therefore, the answer is choice A.
Cate and Elena were playing a card game. The stack of cards in the middle had 27 cards in it to begin with.
Cate added 7 cards to the stack. Elena then took 10 cards from the stack. Finally, Cate took 6 cards from
the stack. How many cards were left in the stack?
There were
cards left in the stack.
Answer:
18
Step-by-step explanation:
You would have 27 then add 7 subtract 10 and subtract 6 to get 18.
کرا
1
A ball is rolling on a flat surface. It is slowing down until it comes to a stop which graph model this situation
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y=2x-5
Step-by-step explanation:
i took algebra
Katrina is going to paint the front door of her house. What is the area of the door? Use 3.14 for π.
Answer:
'
Step-by-step explanation:
'
help please :) show work?! NO LINKS BRO
Amanda and Ameilio are sharing 72 candies in the ratio of 5:7 respectively. How many candies will Ameilia receive
Answer:
Ameilia will receive 42 candles.
Step-by-step explanation:
5+7=12
72/12=6
6*7=42
Ameilia will recieve 42 candles.
6*5=30
Amanda will recieve 30 candles.
hope this helped have an amazing day! :)
What is the median of this data set? Help NO links are you will be reported and NO fake answers for points. Thank you
Answer:
hey
Step-by-step explanation:
Anita and Brad are each riding on the same bicycle path. Anita began riding at the start of the park and is riding at a rate of 18 miles per hour. Brad began from a spot 10 minutes ahead of her and us riding at a rate of 13 miles per hour. Part A write a system of equations to represent x, the number of hours it takes Anita and abroad to travel y miles along the path. Part B after how many hours do Anita and Brad meet on the path
Answer:
Part A
The system of equations are;
x = y/18
x + 1/6 = y/13
Part B
13/30 hours
Step-by-step explanation:
The path on which Anita is riding = The path on which Brad is riding
The point at which Anita starts riding = The start of the park
The rate at which Anita is riding = 18 miles per hour
The time at which Bras began = 10 minutes ahead of Anita
The rate at which Brad is riding = 13 miles per hour
Part A
Let 'x' represent the number of hours it takes Anita and Brad to travel 'y' miles along the path, we have;
The 'x' number of hours it takes Anita to travel 'y' miles is given as follows;
x = y/18
For Brad, we have;
10 minutes = 1/6 of an hour
The 'x'' number of hours it takes Brad to travel 'y' miles is given as follows;
x' = y/13
The duration Brad has traveled, when Anita has traveled for 'x'' hours = x + 1/6 hour
x' = x + 1/6
∴ x + 1/6 = y/13
Part B
Therefore, to travel the same 'y' mile as Anita , we have;
x + 1/6 = y/13
y = 13 × (x + 1/6) = 13·x + 13/6
y = 13·x + 13/6
For Anita, we had; x = y/18
∴ y = x × 18 = 18·x
Equating both y-values gives;
y = y
∴ 13·x + 13/6 = 18·x
18·x - 13·x = 5·x = 13/6
x = 13/(5 × 6) = 13/30 hours
The number of hours it will take Anita and Brad to meet on the path = 13/30 hours (equivalent to 13/30 hour × 60 minutes/hour = 26 minutes)