Answer: x = 10
Step-by-step explanation:ln20+ln5=2lnx
ln(20x5)=lnx^2
ln100=1nx^2
100=x^2
square root
x=10
The true solution is x = 10 of the expression ln 20 + ln 5 = 2 ln x which is correct answer would be option (B).
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
Given expression,
⇒ ln 20 + ln 5 = 2 ln x
⇒ ln(20×5) = lnx²
⇒ ln100 = lnx²
Take anti logarithms on both sides,
⇒ 100 = x²
Taking the square root,
⇒ x = 10
Hence, the true solution is x = 10.
Learn more about the logarithmic properties here:
brainly.com/question/24211708
#SPJ6
HELP PLEASE thank you!!
Answer:
x = 180 -117
x = 63°
y = 90 - 63
y = 27°
Step-by-step explanation:
last question of the day with 25 points.
help plzzz
I will give brainly for the fastest and with steps
Answer:
244 degrees
Step-by-step explanation:
Since one angle APE is 90 degrees, that means line segments AD and BE are perpendicular bisectors.
Since both segments go through the center, that means all the angles are central angles.
Since angle APE is 90 degrees, that also means that angle EPD is 90 degrees.
33k -9 = 90
33k = 99
k = 3
Since we know k we can substitute it to find angle CPD.
20 k + 4 = 20*3 + 4= 60+4= 64 degrees.
Central angles equal angles of arcs, so we can and angles APE, EPD, and DPC to find the measure of major arc CAD.
64+ 90 +90 = 244 degrees
Select the correct answer.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan has a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. If the test predicts that Nathan is not allergic to penicillin, what is the probability after the test that Nathan is not allergic to the drug?
A.
0.1135
B.
0.2450
C.
0.9423
D.
0.9932
( ik its not B tho )
Answer:
A
Step-by-step explanation:
Answer:
C = .9423
Step-by-step explanation:
i took the test and got it right.
Please help with this
Answer: She sold 5 shirts
Step-by-step explanation: 100 + 12x6 + 5t + 7x4 + 5x5 - 8x5
you get 100 + 72 + 28 + 25 - 45 + 5t
You add all that and subtract but not the 5t and you get 180 then you can do 205-180 and get 25 then you you find what times 5 equals 25 and then you get 5 t shirts sold
A.366
B.318
C.342
D.294
Answer:
318 mm2
Step-by-step explanation:
Please see the step-by-step solution in the picture attached below.
Hope this answer can help you. Have a nice day!
Answer:
[tex]318mm^{2}[/tex]
You can break the shape into pieces you can work with, and then add up the areas individually.
The value of 1 tenth is less the value of 3 tenth
Answer:
True, 3 tenths is closer to one whole
Step-by-step explanation:
↓ ↓
Aiden is grocery shopping and wants to know which packages are cheapest. He is
looking at four different bottles of liquid laundry detergent: Bottle A is 175 fluid
ounces for $19.25; Bottle B is 138 fluid ounces for $8.97; Bottle C is 100 fluid ounces
for $8.00; and Bottle D is 72 ounces for $7.56. Assuming the detergent is of equal
quality, which bottle is the best deal?
Answer:Bottle B
Step-by-step explanation:
Given
Bottle A has 175 fluid ounce and cost [tex]\$19.25[/tex]
So it cost [tex]\frac{175}{19.25}=9.09\ \text{ounce per}\ \$[/tex]
Bottle B has 138 fluid ounce and cost [tex]\$8.97[/tex]
So it cost [tex]\frac{138}{8.97}=15.38\ \text{ounce per}\ \$[/tex]
Bottle C has 100 fluid ounce and cost [tex]\$8.0[/tex]
So it cost [tex]\frac{100}{8}=12.5\ \text{ounce per}\ \$[/tex]
Bottle D has 72 fluid ounce and cost [tex]\$7.56[/tex]
So it cost [tex]\frac{72}{7.56}=9.52\ \text{ounce per}\ \$[/tex]
So, Bottle B delivers more ounces at same price
Which of the following represents the factorization of the trinomial below?
-2x3-14x2 - 12x
A. -2(x2 + 1)(x+6)
B. -202 + 1)(x-6)
C. -2x(x + 1)(x+6)
a
D. -2x(x + 1)(x-6)
Answer:
-2(x + 1)(x + 6)
Step-by-step explanation:
Please use " ^ " to denote exponentiation: -2x^3-14x^2 - 12x
Note that all three terms are evenly divisible by -2x, leaving the quotient x^2 + 7x + 6.
This quotient is also easily factored:
-2x^3-14x^2 - 12x = -2(x^2 + 7x + 6) = -2(x + 1)(x + 6)
Elise is a project manager
In 2016 she earned a monthly salary of £2,100
in 2017 she had a 3% raise
Given that in 2017 Elise worked 42 hours per week for 45 weeks, work out her average pay per hour for the year
please help :(
Answer:
£11.85
Step-by-step explanation:
In the question, we are told that:
In 2016 she earned a monthly salary of £2,100
In 2017 she had a 3% raise
This means 3% of £2,100
3/100×£2,100 = £63
This means her salary for 2017 =
£63 + £2,100 =£2,163
Step 2
We are told in the question that she worked 42 hours per week for 45 weeks in 2017
Since her monthly pay for 2017 = £2,163
She worked 42 hours per week
There are 7 days in one week
The number of hours she worked per day = 42 hours ÷ 7 = 6 hours per day
4.345 weeks= 1 month
The number of hours she worked per month = 42 hours × 4.345 weeks
= 182.49 hours.
We can say that for 182.49 hours she was paid = £2,163
Her average pay per hour is calculated as:
If 182.49 hours = £2,163
1 hour = represented by Y
Cross multiply
182.49Y = £2,163
Y = £2,163 ÷ 182.49
Y = £11.852704258
Approximately = £11.85
Therefore, Elise Average pay per hour for the year = £11.85
Answer:
poopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopopoop
Step-by-step explanation:
a right triangle has the coordinates a(6,0), b(0,0) and c(0,8). what is the perimeter of the triangle
Answer:
28
Step-by-step explanation:
sry if I'm wrong although I used calculator
Flora made 4 withdrawals of $80 each from her bank account. What was the overall change
in her account?
The total change in her account is $
Answer:
320$
Step-by-step explanation:
Answer:
Step-by-step explanation:
80 divided by 4 should be 20? sorry if i am wrong
i need to find the value of x
Answer:
x = 24
Step-by-step explanation:
Since all the angles share a common vertex 'U' lying on a straight line QT.
Therefore, sum of all angles formed at U will be equal to 180°.
m∠RUQ + m∠RUS + m∠SUT = 180°
(2x - 4) + (3x + 5) + (2x + 11) = 180°
(2x + 3x + 2x) + (5 - 4 + 11) = 180
7x + 12 = 180
7x = 180 - 12
x = [tex]\frac{168}{7}[/tex]
x = 24
Therefore, value of x = 24
Sarah picks two hats at random from 5 bill caps and 3 beanies. What is the probability she picks a BILL cap, DOES NOT REPLACE IT, then chooses ANOTHER BILL cap?
Answer:
The probability is 5/14
Step-by-step explanation:
Here, we are to calculate/estimate a probability
Firstly , we need to know the total number of caps
we have 5 bill caps and 3 beanies.
Total number of caps = 5 + 3 = 8 caps
The probability of picking the first bill cap is 5/8
Now after removing this and not replacing, we have 4 bill caps left and 3 beanies
Total cap remaining is 7 caps while the probability of picking a bill cap now is 4/7
The combined probability is thus 5/8 * 4/7 = 5/14
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function
Answer:
See Explanation
Step-by-step explanation:
Let our quadratic polynomial function [tex]f(x)=x^2-7x+6[/tex]
Let our linear binomial in the form (x − a)=x-1
Part 1: We use long division to divide the polynomial by the binomial.
[tex]\left|\begin{array}{c|c}&x-6\\-----&-----\\x-1&x^2-7x+6\\Subtract&-(x^2-x)\\&------\\&-6x+6\\Subtract&-6x+6\\&------\\&0\end{array}\right|[/tex]
Therefore:[tex]\dfrac{x^2-7x+6}{x-1}=x-6[/tex]
Part 2: In our chosen linear monomial x-1, a=1
[tex]f(a)=f(1)\\f(1)=1^2-7(1)+6=1-7+6=0\\f(a)=0[/tex]
Part 3:
To determine whether a linear binomial is a factor of a polynomial function using the remainder theorem
Given a linear binomial x-aSubstitute a into the polynomial function f(x)If the value of f(a)=0, the linear binomial is a factor. However, if f(a) is not equal to zero, then by the remainder theorem, x-a is not a factor of f(x)A net of a triangular prism is shown below. 42 8 ft 3 ft 5 f 5 ft What is the surface area, in square feet, of the triangular prism? A 44 B 96 C 108 D 120
Answer:
(C)108 square feet
Step-by-step explanation:
A net of triangular prism consists of two triangular and three rectangular faces.
The net attached is that of a right triangular prism.
Area of One Triangular Face =0.5 X 3 X 4=6 square feet
The rectangular faces are of dimension 4 ft by 8 ft, 5ft by 8ft and 3ft by 8 ft respectively.
Therefore:
Surface Area of the net =2(6)+(4X8)+(5X8)+(3X8)
=12+32+40+24
=108 square feet
The correct answer is C.
Answer:
108
this is correct, trust me
I need help with Tangents of circle problems
Answer:
With the information provided in picture, you can use the property of tangent line of circle to prove that two right triangle ACO and ABO are congruent (AO shared, ACO = ABO = 90 deg, OC = OB = radius of circle O).
Then AB = AC = 4
=> Hope this helps!
:)
Solve the following system by graphing:
Answer:
Option B (-3,-8)
Step-by-step explanation:
Use a graphing tool to graph the lines [tex]-4x+3y=-12[/tex] and [tex]-2x+3y=-18[/tex].
When graphed, the lines pass at the point (-3, -8).
Graph B matches this, so Option B is the answer.
5c+4 = 2 (c – 5)
What is the solution?
Answer:
0
Step-by-step explanation:
if I'm correct it's 0 because when you do all of the math that's what it came out to
If you multiply any number by zero, your answer will be
that same number.
impossible.
zero.
negative.
Answer:
zero
Step-by-step explanation:
for example,
2 x 0 = 0
124 x 0 = 0
its some number zero times so when you multiply by zero, its zero
2. Evaluate f(3) for f(x) = 2x - 9
Answer:
-3
Step-by-step explanation:
[tex]f(x) = 2x - 9[/tex]
[tex]f(3) = 2(3) - 9\\f(3) = 6 - 9\\f(3) = -3[/tex]
You have an ice cream scoop with a 2-inch diameter. You have an ice cream cone with a 2-inch diameter and a height of 5 inches. If you place one scoop of ice cream on the cone and let the ice cream melt, will it spill over the cone?
Answer:
No, because the volume of the cone is greater than the volume of the ice cream scoop.
Step-by-step explanation:
To solve this problem we just need to compare the volume of the ice scream scoop with the volume of the ice cream cone.
The ice scream scoop is a sphere with a diameter of 2 inches (so a radius of 1 inch), then the volume is:
V = (4/3) * pi * r^3
V = (4/3) * pi * 1^3
V = 4.1888 in3
Now, to find the volume of the ice cream cone, we just need to use the formula of the cone volume (with radius = 1 inch):
V = (1/3) * pi * r^2 * h
V = (1/3) * pi * 1^2 * 5
V = 5.236 in3
As the volume of the cone is greater than the volume of the ice cream scoop, the ice cream will not spill over the cone after melting.
I need help with this answer can you plz help
what is the square root of 144?
Answer:
12
Step-by-step explanation:
12 times 12 is 144
Hope this helps
The first term of a geometric sequence is 1 and its common ratio is 6. What is the sixth term?
a. 31
b. 3176
c. 7776
d. 46,656
Answer:
c. 7776
Step-by-step explanation:
1, 6, 36, 216, 1296, 7776
Therefore, c. 7776
I hope this helped and have a good rest of your day!
What’s the answer to this
Answer:
C is the correct answer. F(x) = -[tex]x^{3}[/tex]
Please help me in this question.I need it right now!!!
Answer:
X=102 y=288 =390
Step-by-step explanation:
X=50+32=82=180-82=102
Y= 50+32=82=360-82=288
Total answer is =390
Andrea uses 9.8 pints of blue paint to paint her bedroom walls. 2/5 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
5.88 pints
Step-by-step explanation:
Well the amount of white paint is 3 / 5 of 9.8
0.6 * 9.8 = 5.88
Answer: 14.7 pints of white paint
IF two different colors were used.
IF she mixed paint to get a light blue, 3/5 of the total would be about 5.9 pints.
Step-by-step explanation:
If 9.8 is 2/5 of the total amount used, set up the equation as 9.8= 2x/5
You get the total amount of paint used is 24.5 pints. Subtract the 9.8 of blue to find the amount of white. That's 14.7 pints.
In practical, real life, a quart of paint covers about 100 square feet. That's an average 8 ft high by 12 ft wide wall.
So that is why I edited this answer. 24 pints is 3 gallons-- that is enough for 3 bedrooms.
And I wish that Math teachers used more common measurements of paint!
A metal shop is cutting a rectangular piece of sheet metal with a width of 60 inches and a length of 144 inches. The shaded parts of the diagram represent two rectangular sections, A and B, that will be cut and removed.
Part A :What are the dimensions of section B?
Part B:What will be the area, in square inches, of the piece of sheet metal after both sections are cut and removed?
Answer:
Dimensions of section B = 36 inches, 48 inches
Area of the piece of sheet metal after both sections are cut and removed = 6336 square inches
Step-by-step explanation:
Given: Width and length of a rectangular piece of sheet metal are 60 inches and 44 inches.
To find: dimensions of section B, the area of the piece of sheet metal after both sections are cut and removed
Solution:
Length of rectangle B = TR = SR - ST = PQ - ST (As SR = PQ being opposite sides of rectangle)
Length of rectangle B = PQ - ST = 60 - 24 = 36 inches
Breadth of rectangle B = UR = QR - QV - VT - TU
Here, QR = PS = 144 inches (opposite sides of rectangle PQRS are equal )
QV = 36 inches
VT = WX = 24 inches ( opposite sides of rectangle WVTX are equal)
TU = 36 inches
So,
Breadth of rectangle B = 144 - 36 - 24 - 36 = 48 inches
Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches
Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches
Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches
Area of the piece of sheet metal after both sections are cut and removed =8640 - ( 1728 + 576 ) = 8640 - 2304 = 6336 square inches
Maureen earned some money doing odd jobs last summer and put it in a savings account that earns 9% interest compounded quarterly. After 10 years, there is $300.00 in the account. How much did Maureen earn doing odd jobs?
Answer:
Maureen earned $123.19 doing odd jobs
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
Compounded quarterly means that [tex]n = 4[/tex]
10 years, so [tex]t = 10[/tex]
9% interest, so [tex]r = 0.09[/tex]
There is $300.00 in the account, which means that [tex]A = 300[/tex]
How much did Maureen earn doing odd jobs?
This is P.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]300 = P(1 + \frac{0.09}{4})^{4*10}[/tex]
[tex](1.0225)^{40}P = 300[/tex]
[tex]P = \frac{300}{(1.0225)^{40}}[/tex]
[tex]P = 123.19[/tex]
Maureen earned $123.19 doing odd jobs
Please help! I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
1/6 and you got the comment why
Answer:
1/6
Step-by-step explanation:
Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!