The sοlutiοn fοr the given expressiοn is 98h - 56k.
Define the sοlutiοn οf an equatiοn?A sοlutiοn οf an equatiοn is a value οr set οf values that, when substituted intο the equatiοn, makes it true. In οther wοrds, a sοlutiοn is a value that satisfies the equatiοn. Equatiοn is a statement οf equality between twο expressiοns that cοntain variables and/οr numbers.
In essence, equatiοns are questiοns, and the develοpment οf mathematics has been driven by effοrts tο find systematic answers tο thοse questiοns. The cοmplexity οf equatiοns ranges frοm simple algebraic equatiοns (which invοlve οnly additiοn οr multiplicatiοn) tο differential equatiοns, expοnential equatiοns (which invοlve expοnential expressiοns), and integral equatiοns.
Given value is,
9(7h-4k) + 10k - 5(6k - 7h)
Distribute,
63h-36k+10k - 5(6k-7h)
Expand,
63h-36k+10k - 30k + 35h
Add similar elements:
[−36k+ 10k - 30k = -56k] and [63h+35h = 98h]
Grοup like terms
98h - 56k
The result is
98h - 56k
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Find the number of different ways that an instructor can choose 4 students from a class of 31 students for a field trip.
There are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.
Describe Permutatiοns and cοmbinatiοn?Permutatiοns and cοmbinatiοns are twο cοncepts in mathematics that deal with cοunting the number οf pοssible οutcοmes in a given situatiοn.
Permutatiοns refer tο the number οf ways in which a set οf οbjects can be arranged οr οrdered. Fοr example, if we have three οbjects A, B, and C, there are six pοssible permutatiοns: ABC, ACB, BAC, BCA, CAB, and CBA. The fοrmula fοr calculating the number οf permutatiοns οf n οbjects taken r at a time is n! / (n-r)!, where n! represents the factοrial οf n.
The number οf ways that an instructοr can chοοse 4 students frοm a class οf 31 students is given by the cοmbinatiοn fοrmula:
C(31,4) = (31!)/(4!(31-4)!)
= (31 × 30 × 29 × 28)/(4 × 3 × 2 × 1)
= 31,465
Therefοre, there are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.
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Francesca knows her pedometer underestimates her step count by 4% of the actual amount. Yesterday, her pedometer said she walked 8,256 steps. How many steps did Francesca actually walk? steps
Answer: If Francesca's pedometer underestimates her step count by 4%, then the actual number of steps she walked can be found by dividing the pedometer reading by 0.96 (100% - 4% underestimation).
So, actual number of steps = 8,256 / 0.96 = 8,600.
Therefore, Francesca actually walked 8,600 steps.
Your welcome, comment on my answer, for anymore answers on questions.
Newton and his friends were watching a movie. They watch 50% of the movie and then take a break. Then they watch the remaining 65 minutes of the movie. How long was the whole movie
The length of the whole movie was 130 minutes.
Let's call the length of the whole movie "x". According to the problem, Newton and his friends watch 50% of the movie before taking a break. This means they watched 0.5x minutes of the movie.
After the break, they watch the remaining 65 minutes of the movie. So the total time they watched the movie is:
0.5x + 65
But we know that the total time they watched the movie is the same as the length of the whole movie "x". So we can set these two expressions equal to each other and solve for "x":
0.5x + 65 = x
Subtracting 0.5x from both sides, we get:
65 = 0.5x
Dividing both sides by 0.5, we get:
x = 130
Therefore, the length of the whole movie was 130 minutes.
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Unit 7: right triangles and trigonometry homework 2: special right triangles
Special right triangles are triangles whose angles and side lengths have specific ratios that make them easier to solve without using complex trigonometry functions.
The two types of special right triangles are the 45-45-90 and 30-60-90 triangles trigonometry.
The 45-45-90 triangle, also known as an isosceles right triangle, has two congruent legs and a hypotenuse that is [tex]\sqrt{2}[/tex] times the length of a leg. The angles in this triangle measure 45 degrees, and the side lengths are in the ratio 1:1:[tex]\sqrt{2}[/tex]. This triangle is commonly found in constructions, as it is easy to create using a compass and straightedge.
The 30-60-90 triangle has angles that measure 30, 60, and 90 degrees, with the hypotenuse twice the length of the shortest side and the longer leg equal to the shortest side multiplied by [tex]\sqrt{3}[/tex]. The side lengths have ratio 1:[tex]\sqrt{3}[/tex]:2. This triangle is also commonly used in real-world applications, such as construction and engineering.
Knowing the ratios of the side lengths in these special right triangles can help simplify trigonometric calculations and make solving problems involving right triangles easier.
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b The pencils cost 2c dollars and the pens
cost 6k dollars.
Fatima spends $30, so 2c +6k = 30
Exercise 10.1
1 The cost of hiring a ladder is a fixed charge of $10 plus $3 per day.
Work out the cost of hiring the ladder for one week.
Explain why y = 3x + 10 where x is the number of days' hire and
y is the total cost in dollars.
Step-by-step explanation:
y = 3x + 10 the fixed charge is 10$ so our constant should be 10, there is a 3$ fee every day so x represents the days so we can multiply the amount of days with 3 to find the total amount paid in fees.
For example, if we hired a ladder for 3 days then
y = 3x + 10
= 3 x 3 +10
= 9 + 10
= 19$
So, we spent 19$ dollars in total cost
A square playground has a perimeter of 100 feet. What is the area of the playground?
*
200 square feet
625 square feet
2,500 square feet
10,000 square feet
Answer:
Step-by-step explanation:
If a square has a perimeter of 100 feet, then each side of the square must be 25 feet long, since all four sides of a square are equal.
The area of a square is given by the formula A = s^2, where s is the length of one side of the square. Substituting s = 25 feet, we get:
A = (25 feet)^2
A = 625 square feet
Therefore, the area of the playground is 625 square feet.
Answer:
625 ft^2
Step-by-step explanation:
A square will have all 4 sides equal to each other. Let x be the length of 1 side. The perimeter, P, of such a square would be:
P = 4x
We are told that p = 100 feet
100 feet = 4x
x = 25 feet
Each side has a length of 25 feet.
The area of this square wuld be (25')*(25') = 625 ft^2
The line I passes through the points (-4, 0) and (1, –1).
Find the gradient of line L.
Answer:
gradient = - [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
calculate the gradient ( slope ) m of the line using the slope formula.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (1, - 1 )
m = [tex]\frac{-1-0}{1-(-4)}[/tex] = [tex]\frac{-1}{1+4}[/tex] = - [tex]\frac{1}{5}[/tex]
Mr. Alquist made strawberry milkshake at a party. He used:
4 bottles of milk that contained 1.5 pints each, and
8 fluid ounces of strawberry syrup.
How many cups of the milkshake did Mr. Alquist make?
Answer:
16cups
Step-by-step explanation:
1 pint of milk is 2cups
1.5pint of milk is 3cups
If 1 bottle contained 3 cups of milk,
8 ounces of strawberry is 1 cup
1 bottle contained 3cups of milk and 1 cup of strawberry syrup
1 bottle has 4 cups of milkshake
4 bottles have (4x4) cups of milkshake
Ans 16
Answer: it is 13
Step-by-step explanation:
it is 13 if you are on study island
Area of a triangle is 110 cm and its base is 20 CM. find its attitude
Answer:
11 cm.
Step-by-step explanation:
The formula for the area of a triangle is given by:
A = (1/2)bh
where A is the area, b is the base, and h is the height (or altitude) of the triangle.
We are given that the area of the triangle is 110 cm and the base is 20 cm. Substituting these values in the formula, we get:
110 = (1/2) × 20 × h
Simplifying the equation, we get:
110 = 10h
h = 11 cm
Therefore, the height (or altitude) of the triangle is 11 cm.
1.6 x 0.7 in unit form
In unit form, 1.6 x 0.7 equals 1.12 square meters.
What kind of unit would that be?The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).
We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.
By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:
1.12 square meters is equal to 1.6 x 0.7 meters.
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complete question is:
Write the expression 1.6 x 0.7 in unit form.
In unit form, 1.6 x 0.7 equals 1.12 square meters.
What kind of unit would that be?
The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).
We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.
By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:
1.12 square meters is equal to 1.6 x 0.7 meters.
Therefore, In unit form, 1.6 x 0.7 equals 1.12 square meters.
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A school has 200 seniors of whom 140 will be going to college next year. Forty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college are on their school's sports teams. Thirty of the seniors going directly to work are on their school's sports teams. Five of the seniors taking a gap year are on their school's sports teams. What is the probability that a senior is going to college and plays sports?
There is 0.25 or 25% of probability that a senior is going to college and plays sports
We can start by using the given information to construct a probability table:
College Work Gap year Total
Sports team 50 30 5 85
Not on sports team 90 10 55 155
Total 140 40 60 200
From the table, we see that there are 50 seniors going to college who are on their school's sports teams. Therefore, the probability that a senior is going to college and plays sports is:
P(college and sports) = number of seniors going to college and on sports team / total number of seniors
= 50 / 200
= 0.25
Therefore, the probability that a senior is going to college and plays sports is 0.25 or 25%.
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Brody calculated the area of a square to be
16
36
16
36
square foot. Which shows the side length of the square?
A. 2
9
2
9
ft
B. 1
3
1
3
ft
C. 4
9
4
9
ft
D. 2
3
2
3
ft
As the area of the square is given 16/36 square feet for that the length of sides of the square is 4/6 feet.
A square is a quadrilateral with four sides. The length of each side is equal. The sum of angles in a square is 360 degrees. Each angle in a square is a right angle.
Area of a square = side²
If the area of a square is given, in order to determine the length, find the square root of the area.
Thus, Area of square = 16 / 36 feet².
s² = 16/36 feet²
So, s = √16/36 feet²
s = 4/6 feet
Hence sides of the square would be 4/6 feet.
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—-------- Correct question format is given below —--------
(Q). Brody calculated the area of a square to be 14/36 square feet. Which shows the side length of the square?
simplify the expression 6c+ – 4–8c+ – 2c
Answer:
-4c-4
Step-by-step explanation:
The simplified expression for 6c + (-4) - 8c + (-2c) is -4 - 4c.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression is (Number/variable, Math Operator, Number/variable)
We have the expression, 6c + (-4) - 8c + (-2c)
Now, simplifying the expression as
6c - 4 - 8c - 2c
= -4 + c(6 - 8 - 2)
= -4 + c(-4)
= -4 - 4c
Thus, the simplified expression is -4 -4c.
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Rate Of 5 Grams Per Square Centimeter Per Year. At The Same Time, These Leaves Decompose At A Continuous Rate Of 65 Percent Per Year.A. Write A Differential Equation For The Total Quantity Q Of Dead Leaves (Per Square Centimeter) At Time T:Dt/DQ= ?B. Sketch A Solution To Your Differential Equation Showing
Dead leaves accumulate on the ground in a forest at a rate of 5 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 65 percent per year.
A. Write a differential equation for the total quantity Q of dead leaves (per square centimeter) at time t:
dt/dQ= ?
B. Sketch a solution to your differential equation showing that the quantity of dead leaves tends toward an equilibrium level. Assume that initially (t=0) there are no leaves on the ground.
What is the initial quantity of leaves? Q(0)= ?
What is the equilibrium level? Qeq= ?
Differential equation of the total quantity Q of dead leaves at time t= dt/dQ = -0.65Q + 5. and 7.69 grams per square centimeter is the equilibrium level.
The differential equation for the total quantity Q of dead leaves (per square centimeter) at time t is given by:dt/dQ = -0.65Q + 5.B.
Assuming that there are no leaves on the ground initially, t = 0.
Q(0) = 0.
Qeq = 7.69 grams per square centimeter.
The solution to the differential equation is given by: Q(t) = (20/13) + Ce^(-0.65t) where C is an arbitrary constant. At equilibrium, dQ/dt = 0, or -0.65Q + 5 = 0.Qeq = 7.69 grams per square centimeter is the equilibrium level.
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PLEASE HELPPP 50 POINTS !!! 4b) Use the Fact that exponents are repeated multiplication to expand the expression 2x^3 • 5x^2 and prove why the Product Rule works. Does 4a match 4b?
We have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
What is the prοduct rule οf expοnent?The prοduct rule οf expοnents states that when multiplying twο terms with the same base, yοu can add the expοnents. Specifically, [tex]a^m * a^n = a^{(m+n)[/tex].
Tο expand the expressiοn [tex]2x^3[/tex] •[tex]5x^2[/tex] using the fact that expοnents are repeated multiplicatiοn, we can write:
[tex]2x^3[/tex] • [tex]5x^2[/tex]= (2 • x • x • x) • (5 • x • x)
Using the cοmmutative prοperty οf multiplicatiοn, we can rearrange the factοrs tο grοup the x's and the numbers:
[tex]2x^3[/tex] • [tex]5x^2[/tex] = 2 • 5 • x • x • x • x
[tex]= 10x^5[/tex]
Nοw, let's prοve why the Prοduct Rule fοr expοnents wοrks. The Prοduct Rule states that when multiplying twο expοnential expressiοns with the same base, we can add their expοnents:
[tex]a^m[/tex] • [tex]a^n = a^{(m+n)[/tex]
Tο see why this is true, let's cοnsider the repeated multiplicatiοn οf a base a with expοnent m and a base a with expοnent n:
[tex]a^m[/tex]• [tex]a^n[/tex] = (a • a • ... • a) • (a • a • ... • a)
We can cοmbine the twο grοups οf factοrs by using the assοciative prοperty οf multiplicatiοn:
[tex]a^m[/tex] •[tex]a^n[/tex] = [tex]a^{(1+1+...+1)[/tex]• (a • a • ... • a) (m times)
[tex]= a^{(m+n)[/tex] • (a • a • ... • a) (m times)
Using the fact that a tο the pοwer οf 1 is just a, we can simplify the expressiοn tο:
[tex]a^m[/tex] • [tex]a^n[/tex] [tex]= a^{(m+n)[/tex]•[tex]a^m[/tex]• [tex]a^n[/tex]
Dividing bοth sides by [tex]a^m[/tex] • [tex]a^n[/tex], we get:
[tex]1 = a^{(m+n)[/tex] / ([tex]a^m[/tex] • [tex]a^n[/tex])
Using the rule fοr dividing expοnential expressiοns with the same base, we get:
[tex]1 = a^{(m+n)[/tex] • [tex]a^{(-m)[/tex] • [tex]a^{(-n)[/tex]
Using the rule fοr adding expοnents with the same base, we can simplify the expressiοn tο:
[tex]1 = a^{(m+n-m-n)[/tex]
Simplifying further, we get:
[tex]1 = a^0[/tex]
Therefοre, we have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.
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Two of the math courses Business majors need to take are Elementary Statistics and Business Calculus. In a random survey of 100 students who have declared as Business majors and are currently enrolled in at least one of the two courses, 77 are enrolled in Elementary Statistics and 52 are enrolled in Business Calculus. How many are currently enrolled in both courses? Hint: A Venn diagram can be helpful in organizing the given information.
There are now 29 business majors enrolled in both business calculus and elementary statistics based on Venn Diagram.
To find the number of students who are currently enrolled in both Elementary Statistics and Business Calculus, we need to use the information given in the problem and draw a Venn diagram. Let's assume that the set of students who are enrolled in Elementary Statistics is E, and the set of students who are enrolled in Business Calculus is C. We want to find the size of the intersection of these two sets, denoted by E ∩ C.
From the problem, we know that the total number of Business majors who are currently enrolled in at least one of the two courses is 100. This means that the size of the union of the sets E and C is 100. We also know that 77 students are enrolled in Elementary Statistics and 52 students are enrolled in Business Calculus.
Using this information, we can set up an equation that relates the sizes of the sets E, C, and E ∩ C:
E + C - E ∩ C = 100
77 + 52 - E ∩ C = 100
E ∩ C = 29
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The National Park Service observers also reported that 3% of whale-ship encounters occurred within 985 feet of the bow of the ship. Let ¡ be the sample proportion of encounters where a whale came within 985 feet of the bow in a sample of 85 encounters Whats the mean
Answer:
Step-by-step explanation:
The sample proportion of encounters where a whale came within 985 feet of the bow is given by p-hat = 0.03, and the sample size is n = 85.
The mean of a sample proportion can be calculated using the formula:
μ = p
where p is the population proportion.
In this case, we do not have the population proportion, but we can use the sample proportion as an estimate of the population proportion. Therefore, the mean of the sample proportion is:
μ = p = p-hat = 0.03
So the mean of the sample proportion is 0.03.
khomo and peter bought a house 575 000 as an investment.khomo payed 245000and Peter payed the rest. they sold the house 5 year later and made a profit of 234500 if they share the profit in the same ratio as their respective investment,how much profit will Peter receive
When Khomo and Peter sold the house 5 years later and made a profit of $234,500, Peter's share of the profit is $134,603 based on his sharing ratio.
What is the sharing ratio?The sharing ratio refers to the ratio or relative size of profit that a partner receives.
Sharing ratios are usually based on the initial capital contribution or some other agreed factors.
Total investment in a house by Khomo and Peter = $575,000
Capital Contributions:Khomo = $245,000
Peter = $330,000 ($575,000 - $245,000)
Percentage Contributions:Khomo = 42.6% ($245,000/$575,000 x 100)
Peter = 57.4% ($330,000/$575,000 x 100)
Profit generated from the investment = $234,500
Peter's share of the profit = $134,603 ($234,500 x 57.4%)
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(c) If Nigeria continues to grow at the same relative change over the following decade, what would be its predicted population in 2020 in millions, rounded to the nearest million?
million people
Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.
Describe Relative Change?Relative change, also known as percent change, is a measure of the percentage increase or decrease in a quantity over time. In the context of population, relative change refers to the percentage change in the size of a population over a given period.
To calculate relative change in population, you would take the difference between the final population size and the initial population size, divide by the initial population size, and multiply by 100 to get the percentage change.
To find the relative change in Nigeria's population over the decade from 2000 to 2010, we use the formula:
Relative change = (new value - old value) / old value
Relative change in Nigeria's population from 2000 to 2010:
= (160 - 123) / 123
= 0.300813
So Nigeria's population increased by approximately 30.08% over the decade from 2000 to 2010.
To predict Nigeria's population in 2020, we apply this same relative change to the 2010 population:
Population in 2020 = Population in 2010 + (Relative change × Population in 2010)
Population in 2020 = 160 + (0.300813 × 160)
Population in 2020 = 160 + 48.13008
Population in 2020 = 208.13008 million
Rounding this to the nearest million, we get:
Population in 2020 = 208 million
Therefore, Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.
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Find t - 2r using the following image:
Suppose vectors u= (5,0,0), v= (0,5,0), w= (0,0,5) and t= (-5,5,0)
The cube has edges of length 5
From the given vectors the value of t - 2r is - 15i - 5j - 10k.
What are Vectors:In mathematics, vectors are mathematical objects that have both magnitude (length) and direction. Vectors can be represented as arrows in space, where the length of the arrow corresponds to the magnitude of the vector and the direction of the arrow corresponds to the direction of the vector.
Here we have
A cube and the vectors are u = (5,0,0), v = (0,5,0), w = (0,0,5) and
t = (-5,5,0)
The cube has edges of length 5
Consider u = 5i, v = 5j, w = 5k, and t = -5i + 5j
From the figure,
r = u + v + w
= 5i + 5j + 5k
Now the value of t - 2r can be calculated as follows
=> t - 2r = - 5i + 5j - 2(5i + 5j + 5k )
= - 5i + 5j - 10i - 10j - 10k
= - 15i - 5j - 10k
Therefore,
From the given vectors the value of t - 2r is - 15i - 5j - 10k.
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I dont know how to do this
pls answer if u know with simple working
Answer:
21 sticks
Step-by-step explanation:
In order to solve an equation like this its best to count all the sticks each step and figure out the pattern
1st: 6 sticks
2nd: 11 sticks
3rd: 16 sticks
Now we notice that it adds 5 sticks each step so the 4th picture must have 21 sticks.
Hope this helps!
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Solve for x :
2x = 100
[tex] \\ \\ \\ \\ [/tex]
Thank You! :)
Answer:
x=50
Step-by-step explanation:
2x=100
divided both sides by 2
x=50
answer: x=50
Answer:
50
Step-by-step explanation:
2x = 100, divide 2 from 2x and also 100, you will be left with x = 50
Duane decided to purchase a $31,000 MSRP vehicle at a 5. 5% interest rate for
5 years. The dealership offered him a $4500 cash-back incentive, which he
accepted. Taking all these factors into consideration, what monthly payment
amount can he expect?
O
A. $506. 18
O B. $592. 14
O C. $517. 39
O D. $442. 28
SUBMT
Duane can expect to make a monthly payment amount of $506.18 over the 5-year term of his loan, including both the principal and the interest.
The monthly payment amount for Duane's MSRP vehicle purchase can be calculated using the following formula: ((MSRP - cash-back incentive) x interest rate) / (term in years x 12). In this case, the calculation is ((31,000 - 4,500) x 0.055) ÷ (5 x 12) = 506.18. Thus, Duane can expect to make a monthly payment of $506.18 over the 5-year term of his loan. This amount includes both the principal and the interest accrued on the loan. It is important to note that the monthly payment may change slightly due to the addition of taxes, registration fees, and other charges that may be included in the loan. Additionally, the amount of the monthly payment may vary slightly depending on the lender's terms and conditions.
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1.The solutions to h of x = 0 are x = negative 8 and 8. Which quadratic function could represent h?
f the solutions to h(x) = 0 are x = -8 and 8, then the quadratic function must have factors of (x+8) and (x-8), since those are the values of x that make h(x) equal to zero. So, one possible quadratic function that could represent h is: h(x) = (x+8)(x-8) Expanding this out, we get: h(x) = x^2 - 64x + 64 So, the quadratic function that could represent h is: h(x) = x^2 - 64x + 64
A coin is selected random from pot A and placed in pot B. Then a coin is selected at random from pot B and placed in pot A. Finally a coin is selected from Pot A. Find the probability that this coin is gold
The equation to calculate the probability that this coin is gold is (X / (X + Y)) x (R / (R + S)) x (T / (T + U))
Let's assume that after the first transfer, there are M gold coins and N silver coins in pot A, and R gold coins and S silver coins in pot B. The probability of selecting a gold coin from pot B after the first transfer is R / (R + S).
After the second transfer, the number of gold and silver coins in each pot changes again. Let's assume that there are T gold coins and U silver coins in pot A, and V gold coins and W silver coins in pot B. The probability of selecting a gold coin from pot A after the second transfer is T / (T + U).
To find the probability that a gold coin is selected from pot A after all transfers are complete, we need to multiply the individual probabilities together. That is:
Probability of selecting a gold coin from pot A after all transfers = (X / (X + Y)) x (R / (R + S)) x (T / (T + U))
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A number from 0-9 is randomly selected and then a letter from a-d is randomly selected. What is the probability that the number 3 and a constant are selected?
If a number from 0-9 is randomly selected and then a letter from a-d is randomly selected, the probability that the number 3 and a constant are selected is 0.1 or 10%.
There are 10 possible numbers that could be selected, ranging from 0 to 9, and 4 possible letters that could be selected, ranging from a to d.
To calculate the probability that the number 3 and a constant are selected, we need to determine how many outcomes satisfy this condition, and then divide that number by the total number of possible outcomes.
There is only one outcome where the number 3 and a constant are selected, which is if the number 3 is selected and any of the four letters (a, b, c, or d) are chosen. Therefore, the number of outcomes that satisfy this condition is 4.
The total number of possible outcomes is found by multiplying the number of possible numbers (10) by the number of possible letters (4).
Total number of possible outcomes = 10 x 4 = 40
Thus, the probability that the number 3 and a constant are selected is,
Probability = number of favorable outcomes / total number of possible outcomes
Probability = 4 / 40
Probability = 0.1
This means that out of all possible outcomes, 10% will result in the selection of the number 3 and any of the four letters.
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4x - 10 = 5 (find value of x)
Answer:
x = 15/4
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 4x - 10 = 5
Then the value of x will be,
→ 4x - 10 = 5
→ 4x = 5 + 10
→ 4x = 15
→ [ x = 15/4 ]
Hence, the value of x is 15/4.
A water tank is a cylinder with radius 30cm and depth 160cm. It is filled at the rate of 0.1 litres per second. 1 litre = 1000cm^3. Does it take longer than 1 hours to fill the tank? You must show your working
The time it will take to fill the tank is 1.256 hours and this it will take longer than an hour to fill the tank
What is rate?A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.
The volume of the cylinder needs to be calculated first. Volume of a cylinder is expressed as ;
V = πr²h, where r is the radius and h is the height of the cylinder.
V = 3.14 × 30² × 160
V = 452160 cm³
Since 1litres = 1000cm³
452160cm³ = 452160/1000 = 452.16litres
The rate at which it is filled is 0.1 litres per second
therefore for a volume of 452.16litres
= 452.16/0.1 = 4521.6 sec
3600sec = 1 hour
therefore 4521.6 sec = 4521.6/3600 = 1.256hours.
Therefore it takes longer than 1 hour to fill the tank.
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3. Ashima sold a watch for 1350 and suffered a loss of 10
a. Find the CP of the watch
b. Find her gain if she sells the watch for INO
Ashima will gain INR from selling the watch for INR, as the Cost Price of the watch is 1360 and the Selling Price is INR.
a. The Cost Price (CP) of the watch is the amount that Ashima paid to purchase the watch. In this case, Ashima sold the watch for 1350 and suffered a loss of 10. This means that the CP of the watch is 1350 + 10 = 1360.
b. To calculate her gain, we need to know the Selling Price (SP) of the watch. If she sells the watch for INR, then the SP of the watch is INR. The formula to calculate gain or loss is as follows:
Gain or Loss = SP – CP
In this case, the SP of the watch is INR and the CP of the watch is 1360. Applying the formula, Ashima’s gain is:
Gain = INR – 1360
= INR - 1360
Therefore, Ashima will gain INR from selling the watch for INR.
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Find all values of x between 0 and 180
• cos(x+50)= 1/2
• sin(2x)= -0.6
Answer:
Step-by-step explanation:
cos(x+50) = 1/2
We know that cos(60) = 1/2, so we can write:
cos(x+50) = cos(60)
Using the identity cos(a) = cos(b) if and only if a = ±b + 2πn, we get:
x+50 = ±60 + 2πn
Solving for x, we have:
x = -50 ±60 + 2πn
x = 10 + 2πn or x = -110 + 2πn
Since we want to find all values of x between 0 and 180, we only need to consider the values of x that satisfy 0 ≤ x ≤ 180.
For x = 10 + 2πn, we have:
0 ≤ 10 + 2πn ≤ 180
-10/2π ≤ n ≤ 85/2π
For x = -110 + 2πn, we have:
0 ≤ -110 + 2πn ≤ 180
-35/2π ≤ n ≤ 25/2π
Therefore, the solutions for cos(x+50) = 1/2 in the interval [0, 180] are:
x = 10° + 360°n or x = 150° + 360°n, where n is an integer.
sin(2x) = -0.6
We know that sin(θ) = -0.6 has two solutions in the interval [0, 360]: θ ≈ -36.87° and θ ≈ 216.87° (using a calculator).
Using the double angle identity sin(2x) = 2sin(x)cos(x), we can write:
2sin(x)cos(x) = -0.6
Dividing both sides by 2cos(x), we get:
sin(x) = -0.3/cos(x)
Using the identity cos²(x) + sin²(x) = 1, we can substitute sin²(x) = 0.09/cos²(x) and simplify to get:
cos³(x) - 3cos(x) + 0.9 = 0
We can solve this equation using numerical methods or approximations. One possible approximation is to use the intermediate value theorem and test for sign changes in the function f(x) = cos³(x) - 3cos(x) + 0.9:
f(0) = 0.9 > 0
f(π/2) ≈ -0.84 < 0
f(π) ≈ 0.49 > 0
Therefore, there is a root of f(x) = 0 in the interval (0, π/2) and another root in the interval (π/2, π).
Using a numerical solver or more advanced methods, we can find the approximate values of x that satisfy cos³(x) - 3cos(x) + 0.9 = 0 in the intervals (0, π/2) and (π/2, π):
x ≈ 68.58° or x ≈ 111.42°
Therefore, the solutions for sin(2x) = -0.6 in the interval [0, 180] are:
x ≈ 34.29° or x ≈ 55.71°