Given:
Consider the given expression is
[tex]\log_59+\log_521-\log_57[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\log_59+\log_521-\log_57[/tex]
It can be written as
[tex]=\log_5(9\times 21)-\log_57[/tex] [tex][\because \log_ax+\log_ay=log_a(xy)][/tex]
[tex]=\log_5\dfrac{9\times 21}{7}[/tex] [tex][\because \log_ax-\log_ay=log_a\dfrac{x}{y}][/tex]
[tex]=\log_5(9\times 3)[/tex]
[tex]=\log_527[/tex]
Therefore, the simplified form of the given expression is [tex]\log_527[/tex].
There are 28 students in a class. Sixteen of those students are boys. What percent of the class are girls? (Round to the nearest tenth)
Answer:
42.9% are girls
Step-by-step explanation:
A company sells an insurance policy against losses incurred during travel for $15. 40,000 customers buy the insurance policy. The policy pays the full amount claimed up till $5,000. Most policy holders claim nothing, the rest either $500 or $5,000. Each customer has the following probabilities of claiming a certain amount for damages, independent of the other customers.
Claim $0 $500 $5,000
Probability 99% 0.8% 0.2%
Estimate the probability that the company makes a positive net profit across the 40,000 contracts.
Which of these is an example of a literal equation?
A. ax - by = k
B. 8 - 2x = 14
C. 5x + 9y
D.4 + 12 = 42
Among the given equation, (ax - by = k) is the example of a literal equation.
What is a literal equation?"A literal equation is an equation which consists primarily of letters. Formulas are an example of literal equations.
Given equations are:
A. ax - by = k: is a literal equation as per definition.
B. 8 - 2x = 14: is not a literal equation. It is a linear equation with variable 'x'.
C. 5x + 9y: it is not an equation.
D.4 + 12 = 42: it is not an equation.
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The capacities of 3 buckets are in the ratio 3:2:4. If the total capacity of the 3 buckets is 36 liters, find the capacity of the smallest bucket?
Answer:
8 liters
Step-by-step explanation:
3x+2x+4x=9x
36/9=x
x=4
2x= smallest bucket= 8
The net below can be folded to form a square pyramid atop a cube. The net consists of 5 congruent squares and 4 congruent triangles.
A net of a square pyramid on top of a cube. The cube has side lengths of 4 centimeters. The pyramid has triangular sides with a height of 5 centimeters.
What is the surface area of the composite solid that can be formed by this net?
80 cm2
120 cm2
144 cm2
160 cm2 I know the answer its 144 but i want to know how to do it
Answer:
80cm2
Step-by-step explanation:
Answer: C 144 BABA
Step-by-step explanation:
Select the correct answer.
What is the simplified form of 3 squared 7 - 5 squared 7?
A. -2 squared 7
B. 2 squared 7
C. -14 squared
D. 15 squared 7
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Need the answer now!
Answer: -2√7
Step-by-step explanation:
Find the start time.
Start time:____ P.M.
Elapsed time: 2 1/4 hr
End time: 4:44 P.M.
Answer:
2:29 PM
Step-by-step explanation:
Answer:
2:30
Step-by-step explanation:
I think sorry if I'm wrong
5. Explain how you could use compatible numbers to estimate 245 ÷ 3. Then estimate the quotient.
Answer:
8
Step-by-step explanation:
Compatible numbers are defined as the numbers which are very close to the numbers that they are replacing that divides evenly into each other.
In the context, we have to estimate the quotient using the compatible numbers in order to estimate 245 divided by 3.
So, estimating 245 as 240 and 3 as 30.
Here, 240 is very close to 245 and 30 is close to 3. So the quotient is the result when we divide 240 by 30 and it divides evenly into 240.
We first divide the non zero parts of each number i.e. 24 by 3 to get the first part of the estimate.
Then we add on the zero if there were left in the problem to get your estimate.
Therefore,
240 / 30 = 8
So here, the quotient is estimated as 8.
In ΔRST, the measure of ∠T=90°, RS = 4.9 feet, and ST = 2.7 feet. Find the measure of ∠S to the nearest tenth of a degree.
Step-by-step explanation:
step 1. a diagram is important and can be uploaded. you will get a quicker answer with a diagram
step 2. triangle RST is a right triangle so we can use trigonometry to find <S
step 3. the adjacent side of <S is ST and the hypotenuse is RS so we will use cos
step 4. cosS = adj/hyp = ST/RS = 2.7/4.9
step 5. <S = 56.6° using inverse cos.
Answer:
42.43
Step-by-step explanation:
This is because you had to divbide by 3
(10p+10)+(8p−1) factored?
anyone know, please, i need this for school..
Answer:
the answer is
9(2p+1)
Answer:
18p +9
Step-by-step explanation:
Because you add the numbers in front of the p's (10+8) and then you add 10 plus -1, which is 9.
Hope this helps! Have a good day and remember to be tiger fierce!! :)
please answer! will give brainliest
Answer:
28
Step-by-step explanation:
Mean is just another word for "the average."
To get the mean, you first need to add up al of your values together.
30+15+30+20+45=140
You then divide your product by the number of original values. In this case, there are 5 values.
140/5=28
Find the polynomial of degree 3 such that the coefficient of x2
is three less than the coefficient
of x3
; the coefficient of x is 3 times the coefficient of x2
; and the constant term is two more than
the coefficient of x3
. The sum of the coefficients is -4.
Answer:
1/5[8x³ –7x² –21x + 18]
Step-by-step explanation:
Let the polynomial be:
ax³ + bx² + cx + d
Where:
a => is the coefficient of x³
b => is the coefficient of x²
c => is the coefficient of x
d => is the constant term.
From the question given above,
Coefficient of x² (b) = a – 3 ..... (1)
Coefficient of x (c) = 3b ...... (2)
Constant term (d) = 2 + a ..... (3)
Sum of coefficient (a + b + c) = –4
a + b + c = –4
b = a – 3
c = 3b = 3(a – 3)
a + b + c = –4
a + (a – 3) + 3(a – 3) = –4
a + a – 3 + 3a – 9 = –4
Collect like terms
a + a + 3a = –4 + 3 + 9
5a = 8
Divide both side by 5
a = 8/5
Substitute the value of a into equation (1)
b = a – 3
a = 8/5
b = 8/5 – 3
b = (8 – 15)/5
b = –7/5
Substitute the value of b into equation (2)
c = 3b
b = –7/5
c = 3(–7/5)
c = –21/5
Substitute the value of a into equation (3)
d = 2 + a
a = 8/5
d = 2 + 8/5
d = (10 + 8)/5
d = 18/5
SUMMARY:
a = 8/5
b = –7/5
c = –21/5
d = 18/5
Thus, the polynomial:
ax³ + bx² + cx + d
8/5x³ + (–7/5)x² + (–21/5)x + 18/5
8/5x³ –7/5x² –21/5x + 18/5
1/5[8x³ –7x² –21x + 18]
Write a polynomial function of least degree that has real coefficients, the following zeros: 1,5,3+i and a leading coefficient of 1
Answer:
no te entiendo
yo también la busco
help me find the length of the given arc please
Answer:
Step-by-step explanation:
use the formula s = Фr
where 's' is the length of the line segment along the circle
Ф = angle in radians , so use pi / 180 for degrees
and r is the radius
s = (75*pi / 180) * 12
s = 5 pi ft.
:)
derivative of cosx/x
Answer:
Step-by-step explanation:
I assume that you mean cos(x)/x, not cos(x/x).
Use the quotient rule.
At a parade, 2/10 of the beads Melissa caught were purple and 43/100of the bead she caught were gold. the rest of the beads she caught were green. What fraction of the beads that Melissa caught were either purple or gold?
Penzance, Edinburg and Aberdeen all lie in a straight line.
The distance from Penzance to Aberdeen is 660 miles.
The distance from Penzance to Edenburg is 542 miles.
Work out the distance from Edinburgh to Aberdeen.
Answer: 505
Step-by-step explanation:
I searched it up
Scientist are studying a bacteria sample. The function f(x) - 325(1.17)* gives the number of
bacteria in the sample at the end of x days.
Which statement is the best interpretation of one of the values in this function?
A The initial number of bacteria is 17.
B. The initial number of bacteria decreases at a rate of 83% each day.
C The number of bacteria increases at a rate of 17% each day,
D The number of bacteria at the end of one day is 325,
1)Find the angle of elevation of the sun from the ground when a tree that is
14ft tall casts a shadow 16ft long. Round to the nearest degrees
Answer:
[tex]\theta=41.18^{\circ}[/tex]
Step-by-step explanation:
Given that,
The height of the tree, h = 14 ft
The height of the shadow, b = 16 ft
We need to find the angle of elevation of the sun from the ground. Let the angle be θ. We can use trigonometry to find it. So,
[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{14}{16}\\\\\theta=41.18^{\circ}[/tex]
So, the required angle of elevation of the sun is equal to [tex]41.18^{\circ}[/tex].
25) Which number is a common factor of 16 and 56?
Answer:
Factors of 16: 1, 2, 4, 8, 16
Factors of 56: 1, 2 , 4, 7, 8, 14, 28, 56
GCF: 8
Step-by-step explanation:
Which expression is equivalent to (6c+9)(6c-9)?
36c2-81
36c2 + 54c-81
o 12c
36c² +81
D Question 2
What’s the answer???
Answer:
36c2-81
Step-by-step explanation:
It's a difference of squares so you Florida it (FL) do first and last to get 36c2-81
Each year a certain type of tree grows vertically 14/15 as much as it did the year before. If the tree grows 1.5m during the first year, how much growth will it have in 20 years?
https://answers.yahoo.com/question/index?qid=20180411132938AApZYZz
The required growth of the tree after 20 years is 3, 813 meters.Here,
Given that,
Each year a certain type of tree grows vertically 14/15 as much as it did the year before. If the tree grows 1.5m during the first year.
To determine how much growth will it have in 20 years.
The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
The tree grows vertically 14/15 as much as it did the year before.
= 1.5 * 14 / 15
= 1.5 * 0.94
= 1.41
Total growth after 1 year = 1.5 + 1.41
= 2.91
Percentage growth = 1.41 / 2.91 = 0.48%
Now,
Growth after 20 years,
= 1.5 (1 + 0.48)^20
= 1.5(1.48)^20
= 3,813.51
Thus, the required growth of the tree after 20 years is 3, 813 meters.
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PLEASE HELP ME!!!!!:)))
20. Find the length of BC in the figure below.
Answer:
Step-by-step explanation:
I'll let you solve it, but I will tell you how to
Ever heard of Thales theorem? If you haven't, here's what it is:
If a line parallel to one of the bases of a triangle is drawn, then the new triangle formed and the original triangle are similar
Why? They are similar because of AA (two equal angles):
∠AEB = ∠ADC since EB and DC are parallel (on a transversal they are corresponding angles which are congruent)
∠ABE = ∠ACD since EB and DC are parallel (on a transversal they are corresponding angles which are congruent)
Now this is enough information to determine that they are similar, but just for good measure, ∠A is common to both triangles so:
∠A = ∠A because of reflexive property
Now that we know they are similar, corresponding parts of similar triangles are similar
Create a ratio and solve is by cross-multiplying
Let me know if you have any questions! Hope this helps! Have a nice day/night :)
The length of BC in the figure below of triangle is 24.
We can use the Pythagorean Theorem to solve for the length of BC. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is BC, and the other two sides are AB and AC.
[tex]AB^2[/tex] + [tex]AC^2[/tex] = [tex]BC^2[/tex]
We are given that AB = 16 and AC = 12. Plugging these values into the equation, we get:
[tex]16^2[/tex] + [tex]12^2[/tex] = [tex]BC^2[/tex]
256 + 144 = [tex]BC^2[/tex]
400 = [tex]BC^2[/tex]
BC = 20
Therefore, the length of BC is 20.
Here are the steps in detail:
Identify the right triangle in the figure.
Label the sides of the triangle with the letters A, B, and C, where C is the hypotenuse.
Substitute the known side lengths into the Pythagorean Theorem.
Solve for the length of BC.
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in an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are __________.
A. On the same line
B. Unequal
C. Imaginary
D. The same point
Answer:
D. The same point
Step-by-step explanation:
An equilateral triangle can be defined as a type of triangle that has all of its sides being equal in length.
This ultimately implies that, an equilateral triangle comprises of three (3) congruent sides and as such creates three (3) congruent angles that measures 60° each. Also, the sum of the congruent angles of an equilateral is always equal to 180°.
Hence, in an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are the same point i.e all of the three (3) centers fall on the same point or spot.
a² + b² = c²
a = x
b = x
c = 9√2
please help me find the value of x, asap!
Answer:
x = 9
Step-by-step explanation:
According to Pythagoras theorem a² + b² = c²
Given that
a = x
b = x
c = 9√2
Substitute'
x² + x² = (9√2)²
2x² = 81 * 2
x² = 81
x = √81
x = 9
Hence the value of x is 9
Can someone help me? I’ll reward points + brainalist
(-3, 3), (1, 1), (0 -2), (1, -4), (5, -1) domain and range
is it a function plz help i aint no good at math
Answer:
not it is not aa function
Step-by-step explanation:
A seller has a house that is 1800 square feet. The neighborhood comps show
the line of best fit to be y = 0.074x +50 48. What is a fair price for this house?
A. $150,000
B. $183.68
C. $150.00
D. $184,000
SUBMIT
A fair price for the seller's 1800 square foot house is $183.68 thousand, option B is correct
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given linear equation represents a relationship between the square footage (x) and the price (y) of houses in the neighborhood.
We can use this equation to estimate the fair price for the seller's house by plugging in the square footage (x) of the house and solving for y:
y = 0.074x + 50
y = 0.074(1800) + 50
y = 133.2 + 50
y = 183.68
Hence, a fair price for the seller's 1800 square foot house is $183.68 thousand, option B is correct
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A rope 55 feet long is cut into two pieces. If one piece
is 23 feet longer than the other, what is the length, in
feet, of the shorter piece?
A. 2
B. 16
C. 23
D. 32
E. 51
Answer:
the answer is D
Step-by-step explanation:
55-23=32
Answer:
16
Step-by-step explanation:
shorter piece measures x
longer piece measures x +23
Together they measure 55 ft
x + (x+23) = 55
2x + 23 = 55
-23 = -23
____________________
2x = 32
x = 16
A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.34 per square foot, the material for the sides costs $0.05 per square foot, and the material for the top costs $0.16 per square foot, determine the dimensions of the box that can be constructed at minimum cost.
Answer:
The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.
Step-by-step explanation:
Geometrically speaking, the volume of the rectangular box ([tex]V[/tex]), in cubic feet, is represented by this formula:
[tex]V = l^{2}\cdot h[/tex] (1)
Where:
[tex]l[/tex] - Side length of the box, in feet.
[tex]h[/tex] - Height of the box, in feet.
In addition, the total cost of the box ([tex]C[/tex]), in monetary units, is defined by this formula:
[tex]C = (c_{b}+c_{t})\cdot l^{2} + 4\cdot c_{s}\cdot l\cdot h[/tex] (2)
Where:
[tex]c_{b}[/tex] - Unit cost of the base of the box, in monetary units per square foot.
[tex]c_{t}[/tex] - Unit cost of the top of the box, in monetary units per square foot.
[tex]c_{s}[/tex] - Unit cost of the side of the box, in monetary units per square foot.
By (1), we clear [tex]h[/tex] into the expression:
[tex]h = \frac{V}{l^{2}}[/tex]
And we expand (2) and simplify the resulting expression:
[tex]C = (c_{b}+c_{t})\cdot l^{2}+4\cdot c_{s}\cdot \left(\frac{V}{l} \right)[/tex] (3)
If we know that [tex]c_{b} = 0.34\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{s} = 0.05\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{t} = 0.16\,\frac{m.u.}{ft^{2}}[/tex] and [tex]V = 40\,ft^{3}[/tex], then we have the resulting expression and find the critical values associated with the side length of the base:
[tex]C = 0.5\cdot l^{2} + \frac{8}{l}[/tex]
The first and second derivatives of this expression are, respectively:
[tex]C' = l -\frac{8}{l^{2}}[/tex] (4)
[tex]C'' = 1 + \frac{16}{l^{3}}[/tex] (5)
After equalizing (4) to zero, we solve for [tex]l[/tex]: (First Derivative Test)
[tex]l-\frac{8}{l^{2}} = 0[/tex]
[tex]l^{3}-8 = 0[/tex]
[tex]l = 2\,ft[/tex]
Then, we evaluate (5) at the value calculated above: (Second Derivative Test)
[tex]C'' = 3[/tex]
Which means that critical value is associated with minimum possible total costs. By (1) we have the height of the box:
[tex]h = 5\,ft[/tex]
The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.