Answer:
9
Step-by-step explanation:
Given equation:
[tex]5 = \dfrac{x}{3} + 2[/tex]
To determine the solution (x) of the equation, we need to isolate it. To do this, we can subtract 2 both sides of the equation.
[tex]\implies 5 - 2 = \dfrac{x}{3} + 2 - 2[/tex]
[tex]\implies 3 = \dfrac{x}{3}[/tex]
To further isolate "x", we can use cross multiplication.
[tex]\implies 3 \times 3 = x[/tex]
Finally, simplify the expression on the left-hand-side to obtain the value of x.
[tex]\implies \boxed{9 = x}[/tex]
There is a leak in a container that holds a certain nontoxic gas. Each hour, it loses 10% of its volume.
Write an equation that models the amount of gas left in the container after x hours, assuming there were 300 cubic centimeters in the container before the leak. Then use your equation to determine the amount of gas left in the container after 11 hours. Round your answer to the nearest tenth.
Answer:
94.1 cm^3 to nearest tenth.
Step-by-step explanation:
Each hour 100 - 10 = 90% of the gas remains.
90% = 0.90.
At 0 hours the volume = 300 cm^3
The equation is
Amount (V) after x hours = 300(0.90)^x.
The amount after 11 hours:
V = 300(0.90)^11
= 94.14
Answer:
y = 300(0.9)^x
94.1 cm³
Step-by-step explanation:
This is an exponential decay.
y = 300(0.9)^x
where x is the number of hours, and y is the amount after x hours.
y = 300(0.9)^11
y = 94.1
Liz is taking guitar lessons and practices every night. Yesterday, she played a total of 40 chords in 8 minutes. Today, she will play chords for 5 minutes.
If she plays at the same rate, how many chords will Liz play today?
Answer:
25
Step-by-step explanation:
If you divide by eight, it is equivalent to five cords per minutes.
Now you know that she plays five cords per minute, right?
So you want to multiply five by five, because she plays a total of five minutes.
In a class test, (2) marks are given for every correct answers and (-1) marks for every
incorrect answers and no marks for not attending any questions.
Sreya scored 30 marks. If she got 16 correct answers, how many questions has she attempted
incorrectly?
Using a system of equations, it is found that she attempted two questions incorrectly.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this question, the variables are:
Variable x: Number of questions attempted correctly.Variable y: Number of questions attempted incorrectly.Sreya scored 30 marks, with 16 correct questions, hence, considering the amount of points for each question, we have that:
2x - y = 30.
Since x = 16:
32 - y = 30
y = 2.
She attempted two questions incorrectly.
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George wants to watch all 23 games that a football team will play at home next season.
He can buy
a season ticket costing £425
or 23 separate tickets costing £24 each ticket.
What percentage of the total cost of 23 separate tickets does George save by buying a
season ticket?
The percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
What are percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As the cost of the separate ticket is £24, and there are a total of 23 games, therefore, the total cost of the 23 games separate ticket can be written as,
= £24 × 23
= £552
Now, the cost of the season ticket is £425, therefore, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket can be written as,
[tex]\rm Percentage = \dfrac{\text{Total cost of 23 seperate ticket}-\text{Cost of season ticket}}{\text{Total cost of 23 seperate ticket}} \times 100\%[/tex]
[tex]\rm Percentage = \dfrac{552-425}{552} \times 100\% = \dfrac{127}{552} \times 100\% = 23\%[/tex]
Hence, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
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Is the following number rational or irrational?
-2π
Choose 1 answer:
А
Rational
00
B
Irrational
Answer:
B, Irrational number
Step-by-step explanation:
Irrational number because
[tex]\pi[/tex]
is Irrational number
Bobby is making bread using a total of 400 grams of gluten free flour. The recipe calls for 70% of the flour to be almond flour. She needs to know how much almond flour to use
280 grams of almond flour.
She needs 70% of the flour to be almond flour
70/100*400 = 280
find value of variable
Answer:
x = 23.5
Step-by-step explanation:
By inscribed angle theorem:
[tex](2x + 1) \degree = \frac{1}{2} \times 96 \degree \\ \\ \implies \: (2x + 1) \degree = 48 \degree \\ \\ \implies \: 2x + 1 = 48 \\ \\ \implies \: 2x = 48 - 1\\ \\ \implies \: 2x = 47\\ \\ \implies \: x = \frac{47}{2} \\ \\ \implies \: x = 23.5[/tex]
I need food to live, but if I eat dirt, I die. I am all-powerful, but I shrink back at the sight of water. What am I?
Answer:
Fire?
Step-by-step explanation:
fire would need and not need all of these things
Answer:
Fire.
Step-by-step explanation:
It has to be fire?
The radius of a circle is 4 m. Find its area to the nearest whole number.
Answer:
16π or around 50.26
Step-by-step explanation:
A=πr²
A=π(4)²
A=16π
A=16(3.1415926)
A=50.26
write an explicit formula for each geometric sequence
1000,200,40,...
Answer:
[tex]\text Explicit \ Formula :\ a_{n}= 1000\times (\frac{1}{5}) ^{n-1}[/tex]
Step-by-step explanation:
Let [tex]\left( a_{n}\right)[/tex] be our geometric sequence
The explicit formula for [tex]\left( a_{n}\right)[/tex] is :
[tex]a_{n}= a_1\times r^{n-1}[/tex]
where r is the common ratio
a1 is the first term
We notice that :
200/1000 = 1/5
40/200 = 1/5
⇒ r = 1/5
[tex]a_1 = 1000\ \ (given)[/tex]
Conclusion:
[tex]a_{n}= 1000\times (\frac{1}{5}) ^{n-1}[/tex]
© There are 5 times as many females as males on the maths course at university. What fraction
of the course are female?
Give your answer in its simplest form.
Answer: 5/6
Step-by-step explanation: Females are 5 times more
Ratio of female to male will be 5:1
Female will be 5/6 and males will be 1/6
The Red Mills Children's Hospital has raised 70% of the money they need for medical supplies. If they need a total of $900, how much money has the hospital raised so far?
Answer:
$630
Step-by-step explanation:
They raised 70% of $900.
70% of $900 = 70% × $900 = 0.7 × $900 = $630
Help me pls
[tex]{ x }^{ 2 } -7x+12[/tex]
Answer:
x is 3 or 4
Step-by-step explanation:
I assume that you want to find the solutions for this quadratic equationFirst of all, set it all to equal 0[tex]x^{2}-7x+12=0[/tex]Now you need to factorise your expressionYou need to find two numbers that multiply together to make 12, and ad together to make -7These two numbers are -3 and -4Your new equation is:[tex](x-3)(x-4)=0[/tex]For this equation to equal 0, just one of x - 6 and x - 1 has to equal 0For x - 3 to equal 0, x has to be 3For x - 4 to equal 0, x has to be 4x = 3 or 48x-1<2x+5
If x is a number greater than zero that satisfies the inequality above, what is one possible value of x?
Step-by-step explanation:
There is no number greater than zero that satisfy the above inequality
but if the sign is less than or equal to 1 will work
Answer:
0 < x < 1
any fraction bigger than zero and less than 1.
Step-by-step explanation:
8x - 1 < 2x + 5
Subtract 2x
6x - 1 < 5
Add 1.
6x < 6
Divide by 6.
x < 1
They are asking for a number bigger than zero. But 1 does not work because the answer has to be less than one. Pick any fraction between zero and one.
1) For what values is the statement true? sin(x+20)°=cos(y−10
x=20, y=60
x=20, y=50
x=30, y=40
x=30, y=60
2)In right triangle ABC with right angle C, sinA=4/5 and cosA=3/5. What is sinB+cosB?
1/5
7/5
35/12
5/7
3)In a right triangle ABC where sinA=cosB, what are the measures of acute angles A and B if the measure of angle A is three times the measure of angle B?
The measure of angle A is 67. 5° and the measure of angle B is 22. 5°.
The measure of angle B is 135° and the measure of angle A is 45°.
The measure of angle A is 135° and the measure of angle B is 45°.
The measure of angle B is 67. 5° and the measure of angle A is 22. 5°.
4)What is the value of b that makes the equation cos(17b+26)°=sin(15b)° true?
13
2
9. 5
3
Answer:
1) X =20° ,Y=60°
2) 7/5
3) first is correct
4) 2
You normally pay your line cooks $22 per hour, but one has worked overtime and should be paid time and a half. What is
the correct overtime pay per hour?
Answer:
$33 per hour
Step-by-step explanation:
"Time and a half" means the overtime rate is 1 1/2 times the base rate.
overtime rate = (1 1/2) × $22/hour = $(22 +1/2(22))/hour = $33/hour
The correct overtime rate is $33 per hour.
what is the system solution to 8x + 7y = 39
Answer:
-8/7
Step-by-step explanation:
I thinks this is the answer
Who invented mathematics??
can somebody help me and explain how to do this
Answer:
=> 24m²
Step-by-step explanation:
Area of small rectangle = l×b
=> 2m× 3m
=> 6m²
Area of large rectangle = L×B
=> 9m × 2m
=> 18 m²
Area of figure = area of small rectangle + area of large rectangle
=> 18 m² + 6m ²
=> 24m²
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 40 or older is chosen at random, what is the probability that they have completed a bachelor's degree and no more? Round your answer to the nearest thousandth.
Using it's concept, it is found that there is a 0.183 = 18.3% probability that the person has completed a bachelor's degree and no more.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, it is found that 529 + 1054 = 1583 out of 1911 + 6730 = 8641 people aged 40 or older have completed a bachelor's degree and no more, hence the probability is given by:
p = 1583/8641 = 0.183.
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5. Find the length of the highlighted arc from A to B
Answer: 9.4 cm
Step-by-step explanation:
formula is
2 pie r (m/360)
Jogging burns 375 calories in 45 minutes. Determine how many calories are burned per hour.
Answer:
500 calories an hour are burnt.
Step-by-step explanation:
45 is 3/4 of 60, so 375 is 3/4 of an hour of jogging. If we divide 375 by 3 we will get how many calories are burnt every 1/4 of an hour.
375 / 3 = 125
Now that we know what 1/4 of an hour equals we can add 125, 4 times to find the number of burnt calories in an hour of running.
125 + 125 + 125 + 125 = 500
that means jogging burns 500 calories an hour.
Consider the two solids shown.
What is the difference between the number of vertices of the two solids?
one
three
four
six
pls help me with this
Look at this set of ordered pairs:
(8,8)
(8, 12)
(17, -12)
Is this relation a function?
homework problem lol
Answer:
G is the answer hope that helpd
PLEASEEE HELP !!
Matching equations with diagrams & finding unknown ancies
is on line WY. Find the value of b.
Which equation(s) and angemeurerents go with the
diagram. Choose ALL that apply
(Select all that apply.)
Answer: b+95+34=180, b+129=180, 51
Step-by-step explanation:
b+95+34=180 works because the angles add to form a straight angle.
From this, we can obtain b+129=180 by adding the two constants.
Subtracting 129 from both sides, we get b=51.
What is the probability that a hand of 5 cards chosen randomly and without replacement from a standard deck of 52 cards (which has 4 kings and 4 queens) contains the king of spades, exactly 1 other king, and exactly 2 queens
Answer: Approximately 0.0003047
As a fraction, it is equal to exactly 792/(2,598,960)
===========================================================
Explanation:
The king of spades must be in the hand, and we can pick any other king. There are 3 ways to pick the other king. Then there are 4 C 2 = 6 ways to pick the two queens. The 4C2 refers to the nCr notation. Or you could use Pascal's Triangle.
Overall, there are 3*6 = 18 ways to pick the king of spades, another king, and exactly 2 queens.
Then we have one more card to pick that isn't a king nor a queen. There are 4+4 = 8 cards that are either a king or queen, leaving 52-8 = 44 cards that are neither.
So there are 18*44 = 792 ways to pick a king of spades, another king, exactly 2 queens, and some other card that isn't a king nor queen.
This is out of 52C5 = 2,598,960 possible five card hands.
The probability we're after is roughly 792/(2,598,960) = 0.0003047
Side note: order does not matter with card hands.
Select all of the equations that are equivalent to 4x+20=90
1. 4(x+5)=90
2. x+5=22.5
3. 4(x+20)=90
4. x+20=22.5
5. 4x=70
pls pls tell me
Answer:
The answer is num 1 I think, 4(x+5)=90
Claudio noticed that the sides of his $1 bill formed angles. Tell whether the angles are right angles, less than right angles, or greater than right angles. Explain.
(no picture to insert)