Answer:
1000Step-by-step explanation:
[tex]log_{10}x = 3 + log_{10}y[/tex][tex]log_{10}x - log_{10}y = 3[/tex][tex]log_{10}(x/y) = 3[/tex][tex]x/y = 10^3[/tex][tex]x/y = 1000[/tex]Answer:
x/y = 10^3 = 1000
Step-by-step explanation:
The rules of logarithms tell you ...
log(x/y) = log(x) -log(y)
__
Here, we have ...
log(x/y) = log(x) -log(y)
= (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)
Taking the antilog, we get ...
log(x/y) = 3
x/y = 10^3 = 1000
_____
Additional comment
The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).
In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).
6) Over the course of 17 weeks Tiffany collected 18 pounds of cans to recycle and Tom
collected 8 times as much as Tiffany. Tom then put his collection into 6 bags to take to
the recycling center. How many pounds of cans did Tom put into each bag?
Answer:
24 per bag
Step-by-step explanation:
18x8=144 then divide by 6= 144÷6=24
Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer. ( Please Do Not Use Someone Else's Answer That's On Brainly Or Any Other Websites Please If So You'll Be Reported). Very Important.
Answer:
The ladder is not safe at this height. The height from ground to top of the ladder is < 11.6 ft for safety reasons and this can be determined by using trigonometry functions.
Step-by-step explanation:
The ladder is not safe at this height. The height from ground to top of the ladder is < 11.6 ft for safety reasons and this can be determined by using trigonometry functions.
Given :
Joshua has a ladder that is 12 ft long.
He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground.
For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°.
Check the angle that the ladder makes with the ground:
The ladder is safe when the angle the ladder makes with the ground to be no greater than 75° but is so, the ladder won't be safe.
To make the ladder safe, the height should not be 11.8ft.
The height from ground to top of the ladder is < 11.6 ft for safety reasons.
Diego rides his bicycle at a constant rate of 0.3 kilometers per minute. Which graph best represents y, the total number of kilometers Diego rides his bicycle in x minutes?
y(x)=0.3x
since he travels 0.3 kilometers for each minute (x)
then y as a function of x is 0.3×the number of minutes(x)
Diego is flying from Philadelphia to Barcelona. On the trip to Barcelona, the plane flies at a constant cruising
speed of 550 mph.
reaches its cruising speed, which is
On the trip home, Diego makes a chart of the plane's progress once
constant
Which is faster the cruising speed on the flight from Philadelphia to Barcelona, or the cruising speed on the flight home?
Hour
1
2
3
A
Miles
530
1060
1590
US
Choose 1 answer:
Со
The cruising speed on the flight from Philadelphia to Barcelona
The cruising speed on the flight home
Pro
Pro
© The two cruising speeds are the same.
The faster speed is the cruising speed on the flight from Philadelphia to Barcelona.
Which speed is faster?
Average speed is the total distance travelled per time. It is used to determine how fast an object is moving with respect to time.
Average speed = total distance / total time
Average speed on the flight back home = 530 / 1 = 530 mph
To learn more about average speed, please check: https://brainly.com/question/21734785
Evaluate the expression 21 ÷ 3 + 8 − 4. 19 17 15 11
Answer:
Your answer is D, 11
Step-by-step explanation:
PEMDAS, first you divide, 21/3 is 7
7+8 is 15
15 - 4 is 11
Hope this helps! :)
Answer:
[tex]\boxed{\sf{11}}[/tex]
Step-by-step explanation:
Solving this problem requires an order of operations.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract21÷3+8-4First, divide.
[tex]\sf{21\div3+8-4}[/tex]
[tex]\sf{21\div3=7}[/tex]
Then rewrite the problem.
[tex]\sf{7+8-4}[/tex]
Add.
[tex]\sf{7+8=15}[/tex]
Subtract.
[tex]\sf{15-4=\boxed{\sf{11}}[/tex]
11
Therefore, the correct answer is 11.
I hope this helps you! Let me know if my answer is wrong or not.
Help please!!! I don't understand
[tex]\left|x-\dfrac 12\right| = 3\dfrac 23\\\\\\\implies \left|x- \dfrac 12 \right| = \dfrac{11}3\\\\\\\implies x-\dfrac 12 = \dfrac{11}3 ~~~~~~~~~ \text{or}~~~~~~~ x - \dfrac 12 = - \dfrac {11}3\\\\\\\implies 2x -1 = \dfrac{22}3 ~~~~~~~~ \text{or}~~~~~~~~2x-1 =-\dfrac{22}3\\[/tex]
[tex]\implies x =\dfrac 12\left(\dfrac{22}3 +1 \right) ~~ \text{or}~~~~~~~~ x = \dfrac 12 \left(1-\dfrac{22}3\right)}\\\\\\\implies x = \dfrac{25}6~~~~~~~~~~~~~~~ \text{or}~~~~~~~~ x=-\dfrac{19}6\\\\\\\implies x = 4\dfrac 16 ~~~~~~~~~~~~~~~ \text{or}~~~~~~~~x = -3\dfrac16[/tex]
A Goodyear Blimp is positioned at a height of 1,500 feet over the M&T
Bank Stadium to broadcast the Baltimore Ravens game. The blimp is
observed by a car of fans as they look upward at an angle of 22º.
Another car closer to the stadium can see the blimp if they look
upward at an angle of 65º.
DEOOV
כשע
Figure not
drawn to scale
1500 ft
65
22
x ft.
Determine x, the distance between the two cars.
The distance between two cars comes to be 4412.06 feet.
Find the attached diagram to visualize it better.
From the attached diagram
The Distance between two cars is x+y
The angle of elevation for the first car = 22 degrees
The angle of elevation for the second car = 65 degrees.
Height of the Goodyear blimp = 1500 feet
What is the tangent of an angle?The tangent of an angle is the ratio of the opposite side to the adjacent side of that angle.
So, tan 22° = 1500/x
So, x= 1500/tan 22°
x = 3712.63 feet
tan 65° = 1500/y
So, y = 1500/tan 65°
y = 699.46 feet
x+y = 4412.06 feet
So, the distance between two cars = 4412.06 feet
Therefore, the distance between two cars comes to be 4412.06 feet.
To get more about the angle of elevation visit:
https://brainly.com/question/10217662
PLEASE help me. Please, I beg you.
How does the Vietnam War influence policies and decisions made in the United States today? Justify your response.
This is the war between the communist governmrnt of Vietnam North and the South Vietnam. The United States of America were the main ally of the Vietnam south during the war.
The communist Vietnam North later united with the south with a common name Socialist Reepublic of Vietnam, After a fierce onslaught that took the life of about 58000 americans and over 2 million Vietnamese.
The influence of the Vietnam war in United States today
1. End of the drafts
The drafts is the method of conscription to the military that requires vitually every male between the age of 18 - 25 in United States to register with the selective service. since the end of the Vietnam war in 1975 the draft stopped hence no penalty for not registering to the draft.
2. Granting 18 years old the right to vote
26th Amendment of the United States Constitution gave right to vote to the 18 years old citizens. Today 18 tear old American has right to vote. This was evolvement of the war and still holds till date.
3. It is easier getting into a war than getting out of a war
Americans was pulling out of the Vietnam war when they suffered the huge massacre. This lesson was helpful for president George H W Bush during the 1991 Persian Gulf War were he systematically exited after liberating Kuwait
Read more on Vietnam war here: https://brainly.com/question/24845081
John's employer increased his annual salary of $55,000 by $5,700. What percent was his raise, rounded to the nearest tenths place?
Answer:
3.64% (when rounded to the nearest hundredth)
Step-by-step explanation:
I'm assuming by 5700 you actually mean 57,000.
Calculate the percent change:
(57,000-55,000)/55,000 *100
(2000/55000)x100
0.036363x100
3.6363 rounded to the nearest hundredth is 3.64
The demand equation for a manufacturer's product is:
p = 50 x [tex](151 - q)^{0.02\sqrt{q+19} }[/tex]
(a) Find the value of dp/dq when 150 units are demanded.
(b) Using the result in part (a), determine the point elasticity of demand when 150 units are demanded. At this level, is demand elastic, inlastic, or of unit elasticity?
(c) Use the result in part (b) to approximate the price per unit it demand decreases from 150 to 140 units.
(d) If the current demand is 150 units, should the manufacturer increase or decrease price in order to increase revenue?
From the given price function, we have;
(a) [tex] \frac{dp}{dq} = - 13[/tex]
(b) The point elasticity of demand is 0.0256; inelastic demand
(c) $46.6
(d) Increase
How can the elasticity of demand be found?a. The given function is presented as follows;
[tex]p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} } [/tex]
Differentiating the above function with a graphing calculator and setting q = 150 gives;
[tex] \frac{dp}{dq} = - 13[/tex]
b. The point elasticity of demand is given by the formula;
[tex] e \: = \frac{dq}{dp} \times \frac{p}{q} [/tex]
When q = 150, we have;
P = 50
Which gives;
[tex]e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256[/tex]
The point elasticity of demand, E = 0.0256
The demand is inelastic (less than 1) when the quantity demanded is 150 unitsc. If the quantity demanded decreases from 150 to 140 units, we have;
[tex]0.0256 \: = \frac{1}{13} \times \frac{p}{140} = [/tex]
Which gives;
p = 46.6
The price when the quantity demanded decreases to 140 is $46.6d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;
The manufacturer should increase the price, p to increase the revenue, R.R = p × q
Learn more about elasticity of demand here;
https://brainly.com/question/19141990
Noah walked a family’s dog 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $6 at the end of the month. Noah earned $106 from dog walking.
1- This situation IS represented by the tape diagram.
2- This situation IS NOT represented by the tape diagram.
The situation IS NOT represented by the tape diagram.
How to represent the situationNumber of times Noah walked the dog = 5Amount earned each time = sExtra amount earned = $6Total amount earned = $106The situation can be represented by the equation:
s + s + s + s + s + 6 = 106
5s + 6 = 106
5s = 106 - 6
5s = 100
s = 100/5
s = 20
Therefore, the amount Noah earned each time he walked the dog is $20
Learn more about equation:
https://brainly.com/question/13763238
Find the volume of the cylinder
Volume:-
πr^2hπ(16)^2(17.5)π(256)(17.5)4480πmm^2To carpet a rectangular room, Erika must find the area of the floor. If the dimensions of the room are 9 yd by 15 yd, how much carpeting does she need?
Erika will need ______of carpeting?
Answer:
135 square yards
Step-by-step explanation:
9 yd * 15 yd = (9 * 15) yd^2 = 135 yd^2
Which number is a common multiple of 2 and 3?
A) 8
B) 16
C) 28
D) 36
Answer:
D
Step-by-step explanation:
36 can be divided by both 2 & 3
Answer:
The answer is D.
Step-by-step explanation:
2x18=36
3x12=36
Cody wanted to give each of his forty-five friends an equal amount of candy. At the store he bought six hundred eighty pieces total to give to them. How many more pieces should he have bought so he didn't have any extra pieces?
Divide total bought by number of people first:
680 / 45 = 15.111
round up to 16. Multiply 16 by 45:
45 x 16 = 720
He should have bought 720 pieces. Now by Tracy to find how many more pieces:
720 - 680 = 40
He should have bought 40 more pieces.
Need help with his geometry question. Find the value of x
Answer:
Step-by-step explanation:
Can someone help me with this question?
Step-by-step explanation:
hope it helps, I have chegg and they seem to have more answers and a lot of topics. you can scan your books bar code and get end of chapter questions
What is the exact value of tan(67.5°)?
StartRoot 3 EndRoot
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
StartStartRoot StartFraction 2 minus StartRoot 2 EndRoot Over 2 + StartRoot 2 EndRoot EndFraction EndEndRoot
StartStartRoot StartFraction 2 + StartRoot 2 EndRoot Over 2 minus StartRoot 2 EndRoot EndFraction EndEndRoot
Answer:
the answer is shown below
I truly hope this helps you -TJ
Step-by-step explanation:
here you go
Answer:
D
Step-by-step explanation:
Edge
which statement is true regarding the graphed functions?
f(0) = 2 and g(-2) = 0
f(0) = 4 and g(-2) = 4
f(2) = 0 and g(-2) = 0
f(-2) = 0 and g(-2) = 0
point (2 ; 0) on Cf so f(2) = 0
point (0 ; 4) on Cf so f(0) = 4
point (-2 ; 0) on Cg so g(-2) = 0
Will mark YOU brainliest!!
Express the following phrase as a unit rate:
135 miles on 9 gallons of gas
Answer: 15 miles per gallon
Step-by-step explanation:
135 divided by 9
15 miles per gallon
rate:
[tex]\sf \dfrac{distance}{amount \ of \ oil}[/tex]
[tex]\rightarrow \dfrac{135}{9}[/tex]
[tex]\sf \rightarrow15 \ miles \ per \ gallon[/tex]
Solve: |x-2|=3
Can someone explain how to do this please!!!
Step-by-step explanation:
after x^2-4x-5 do sum and product
How many times does 8 go into the 7 1/2
Answer:
0.9375
Step-by-step explanation:
1/2=0.5
7.5÷8
=0.9375
barely even once
There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
Answer:
85 dogs have signed up to compete
Step-by-step explanation:
its 85 small dogs because 49+36=85
QUESTION 20
Find the rate of interest required to achieve the conditions set forth.
A = $32,000
P = $8,000
t = 20 years
compounded annually
3.5265%
8%
5.6467%
7.1773%
The rate of interest required to achieve the conditions set forth is 7.1773%.
What is the interest rate?The interest rate is the rate at which the investment increases. The formula that can be used to determine interest rate is:
g = (FV / PV)^(1/N) - 1
Where:
FV = future value = $32,000PV = present value = $8000 n = number of years4^(1/20) - 1 = 7.1773%
To learn more about interest rate, please check: https://brainly.com/question/26164549
If the difference of 3 / 4 and 1 / 6 of a number is 7, find the number and also verify your answer.
The computation of the equation illustrates that the number will be 46.4.
How to solve the equation?Let the number be represented as x.
Therefore, the the difference of 3 / 4 and 1 / 6 of a number is 7 will be computed as follows:
(1/6 × x) - 3/4 = 7
0.167x = 7 + 3/4
0.167x = 7.75
x = 7.75/0.167
x = 46.4
Therefore, the number is 46.4.
Learn more about equations on:
https://brainly.com/question/2972832
In a small private school, 16 students are randomly selected from eighteen available students. What is the probability that they are the four youngest students?
Answer:
1/72
Step-by-step explanation:
16 * 18 = 288
4/288 = 1/72
what is the area of the parallelogram?
The area of a parallelogram is the product of:
--> length of the base and the height
length: 7ftheight: 5ftThus the area = 7 * 5 = 35 square feet
Hope that helps!
Graham carves a block of wood shaped like a cube with a square pyramid on top. How much paint will Graham need to paint the toy? Enter your answer in the box.
Divide the box into two parts for easy way answer
For cube:-
Side=a=12cmTSA
6a²6(12)²6(144)864cm^2Cancel one side area
TSA=864-144=720cm^2For triangular pyramid:-
Area of one base
0.5(Base)(Height)0.5(12)(15)6(15)90cm^2Area of four sides=90(4)=360cm^2
Total surface area:-720+3601080cm^2Answer:
1080 cm^2
Step-by-step explanation:
∴ Given:
Graham carves a block of wood shaped like a cube with a square pyramid on top.
∴To Find:
How much paint will Graham need to paint the toy?
∴Solve:
Base on the given:
[tex]S=5a^2+4ah\cdot\frac{1}{2}[/tex]
= [tex]5\cdot12^2+4\cdot12\cdot15\cdot\frac{1}{2}[/tex]
[tex]=1080cm^2[/tex]
Hence [tex]1080cm^2[/tex] of paint is needed.
~lenvy~
area of the base= 75square inches and heigh = 15 inches
75 ÷ 15 = 5
the width is 5 inches
GEOMETRY Find the diameter d of the circle in the figure at the right. Round to the nearest tenth if necessary.
18 ft
d ft
22 ft
12.6 ft
O 160 ft
O 4'ft
28,4 ft
Answer:
d = 12.6 ft
Step-by-step explanation:
From inspection of the given diagram, the diameter of the circle is equal to the shortest leg of the right triangle.
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, use Pythagoras Theorem to find the measure of d.
Given values:
a = db = 18 ftc = 22 ftSubstitute the given values into the formula and solve for d:
[tex]\implies d^2+18^2=22^2[/tex]
[tex]\implies d^2+324=484[/tex]
[tex]\implies d^2=484-324[/tex]
[tex]\implies d^2=160[/tex]
[tex]\implies d=\sqrt{160}[/tex]
[tex]\implies d=12.6491106...[/tex]
Therefore, d = 12.6 ft (nearest tenth).
Learn more about Pythagoras Theorem here:
https://brainly.com/question/27648540
https://brainly.com/question/27988757