What is the value of x?
(7x-3)°
(11y-+5)°
Answer:
The answer is 9
Step-by-step explanation:
The given triangle is equivalent triangle
We know that in equivalent triangle all angles are equal to 60°
So,
(7x - 3)° = 60°
7x - 3° = 60°
7x - 3° + 3° = 60° + 3°
7x = 63°
x = 63°/7°
x = 9°
Thus, The value of x is 9°
For Verification Only;
(7x - 3)° = 60°
[7(9) - 3]° = 60°
(63 - 3) = 60°
60° = 60°
Hence,
L.H.S = R.H.S
I need help on a question.
the picture below should help
Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10. One piggy bank has $7.31 in it. Select the choices that make the inequality and statement about the possible amount of money in the other piggy bank correct.
The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.
∴ PB₁ + PB₂ ≤ 10.
One piggy bank has $7.31 in it.
∴ 7.31 + PB₂ ≤ 10.
PB₂ ≤ 2.69.
So, The amount in PB₂ can be 0 ≤ PB₂ ≤ 2.69.
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I need help with my home work
The value of x is 9 and the value of y is 4.
What is the congruent triangle?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
The system of equations is
x + 3 = 3y ....(i)
x = y + 5 .....(ii)
Putting x = y + 5 in equation (i):
y + 5 + 3 = 3y
y + 8 = 3y
3y = y + 8
3y - y = 8
2y = 8
y = 4
Putting y = 4 in equation (ii)
x = 4 + 5 = 9
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"Question 60
Find the probabilities below using a standard 52 card deck.
1. d. 8/52 (Ace ∪ 5)
2. h. 0 (Ace ∩ 5)
3. b. 20/52 (Even')
4. c. 36/52 (Even ∪ black)
5. a. 3/52 (Face ∩ Diamond)
What is probability?
Probability means the quality or state of being the outcome; the extent to which something is likely to happen or take place. Probability means the possibility of any outcome which can take place in any event.
Solution:
1. Probability of Ace ∪ 5 = (No. of Aces + no. of cards with face value 5)/52 = 8/52
2. Probability of Ace ∩ 5 = (Intersection of Ace and face value of card 5)/52 = 0
∵ Intersection of ace and 5 is 0 as there is no intersection in between the 2 subevents.
3. Probability of Even complement = No. of cards with odd values/52
{A,3,5,7,9,A,3,5,7,9,A,3,5,7,9,A,3,5,7,9}/52 =20/52
4. Probability of Even ∪ black = {(2,4,6,8, 10)×4 types of cards odd black spades + odd black clubs = 20+16/52
= 36/52
5. Probability of Face ∩ Diamond = No. of face cards in diamonds/52
= {Jack, Queen, King}/52
= 3/52
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What shapes use the area formula A = lw ?
O Parallelogram
O Triangle
O Trapezoid
O Rectangle
Answer:
Rectangle
Step-by-step explanation:
Welcome to Brainly! :]
A rectangle uses A=lw to calculate area
Where l is length and w is width
Hope this helps,
:]
PLEASE HELP ASAP!!!! FULL ANSWERS ONLY!!!!
Blake wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Blake has 950 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write a function for the area A of the enclosure in terms of w . (HINT: First write one equation with w and l and one equation with w and l and A. Solve for l in the first equation and substitute for l in the other). A ( w ) = ____________
b) What width w would maximize the area? w = __________________ ft
c) What is the maximum area? A = ______________ square feet
Answer:
(a) A(w) = w(950-2w) = 950w-2w^2
(b) w = 237.5
(c) A = 112812.5
Step-by-step explanation:
First of all the maximum area is always a square. You can get the answer first to check your work later.
950/4 = 237.5
One side is not needed so add that length to the non-parallel side.
237.5+237.5=475 feet is the length and 237.5 feet is the width(s)
A=475*237.5
A=112812.5 square feet
Doing the algebra...
P=l+2w
950=l+2w
950-2w=l
A=lw
A=(950-2w)w
A=950w-2w^2
Drag each label or value to the correct location on the image. Each label or value can be used more than once, but not all labels or values will be used.
A physics student drops a ball from a height of 64 feet into a vacant parking lot. After one bounce, the height of the ball is 48 feet, and after two bounces, the height of the ball is 36 feet.
This situation can be modeled by the following exponential function.
f(x)=64(0.75)ˣ
Complete the sentences below.
initial height height bounces 36 f(x) x
The variable, represents the number of times the ball bounces.
The variable, after The parameter, 64 , represents the
of the ball.
The parameter, 0.75, represents the percentage of left from each previous bounce.
The completed sentences that describe the height reached by the ball specified by the function, f(x), that indicates the balls height, based on the number of bounces, x, f(x) = 64·(0.75)ˣ, which is similar to a geometric progression, is presented as follows;
The variable, x, represents the number of times the ball bounces.
The variable f(x) represents the height of the ball after x bounces.
The parameter, 64, represents the initial height of the ball.
The parameter, 0.75, represent the percentage of height left from each previous bounce.
What is a geometric progression?A geometric progression is a number sequence, arranged such that the ratio between a term and the previous term is a constant, known as the common ratio of the geometric progression.
The exponential function that models the specified situation of finding the height of the ball is presented as follows;
f(x) = 64·(0.75)ˣ
The initial height from which the student drops the ball = 64 feet
The height the ball reaches after one bounce = 48 feet
Height of the ball after 2 bounces = 36 feet
The exponential function, f(x) = 64·(0.75)ˣ, is similar to the equation for a geometric progression, aₙ = a₁·r⁽ⁿ⁻¹⁾
Where;
a₁ = The first term = The initial height
r = The common ratio = 48/64 = 36/48 = 0.75
n = The number of times the ball bounces, in addition to the time the ball is dropped from the initial height, therefore;
x = n - 1, therefore;
x = The number of times the ball bounces
n = x + 1
The terms that complete the sentences are therefore:
The variable that represents the number of time the ball bounces = x
The variable that indicates the height of the ball after x bounces = f(x)
The initial height of the ball = The parameter 64
The percentage of the height the ball bounces to after the previous bounce = 0.75
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
I just answered this with all explanations.
Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $250 are affordable. The bank offers a 4-year loan at 6% APR, a 5-year loan at 6.5%, or a 6-year loan at 7% APR. Which loan best meets the person's needs? Explain.
Which loan best meets the person's needs? (Round to the nearest cent)
A. The first loan best meets the person's needs because the monthly payment of $___ is less than the maximum budgeted amount of $250 per month.
B. The second loan best meets the person's needs because the monthly payment of $___ is less than the maximum budgeted amount of $250 per month.
C. The thirdloan best meets the person's needs because the monthly payment of $___ is less than the maximum budgeted amount of $250 per month.
D. None of the loans meet the person's needs.
Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!
andom variable (RV) X-bar is computed from a set of n independent, normal RVs X 1...X.n. The sampling distribution refers to? the distribution on X-bar. the distribution on the X_ RVS. the distribution on the means of the Xi_RVS. the frequency distribution obtained from a set of n experimental data values. none of these
The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).
The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.
The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.
In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.
The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.
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In the isosceles triangle, solve for side AB
Please help me
Answer:
5
Step-by-step explanation:
In an isosceles triangle two of the angles are equal and the corresponding sides are also equal
Here ∠A = ∠B
AC = BC
3x + 4 = 10
3x = 6
x = 2
Side AB = x + 3 = 2 + 3 = 5
****
Write and graph the inverse of y=-x²+9
Write the inverse of y=-x²+9
y=
(Simplify your answer. Use a comma to separate answers as needed.)
The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]
What is Inverse of a Function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
The output of a function is returned by the inverse function, which also returns the initial value.
If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.
For instance, f(x) = 2x + 5 = y
Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).
The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.
A function is said to be an inverse function if its own inverse is represented by the symbol f-1.
[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex] is the inverse of y=-x²+9
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Gaspar writes the algebraic expression 5b +3.79.
It represents the total cost, in dollars, of buying 5 bagels
and a container of cream cheese. Identify any variables,
coefficients, and terms in the expression. Tell what
each represents.
5b+3.79 has two terms, 5b and 3.79.
The variable b seems to represent the cost of one bagel. Since we know Gaspar bought 5 bagels, 5b would represent the cost of 5 bagels.
In 5b, 5 is the coefficient and b is the variable.
Since 5b represents the cost of the bagels, then 3.79 would appear to be the cost of the cream cheese.
Answer:
The variable "b" represents the cost of one bagel (in dollars).
The coefficient "5" represents the number of bagels purchased.
The constant "3.79" represents the cost of one container of cream cheese (in dollars).
Step-by-step explanation:
Given algebraic expression:
5b + 3.79If the given algebraic expression represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese, then:
The variable "b" represents the cost of one bagel (in dollars).The coefficient "5" represents the number of bagels purchased.The constant "3.79" represents the cost of one container of cream cheese (in dollars).Need help making a frequency table
Here is the frequency table based on the data:
1 - 200 7
201 - 400 1
401 - 600 2
601 - 800 3
801 - 1000 1
1001 - 1200 1
1201 - 1400
1401 - 1600 1
1601 - 1800 1
What is a frequency table ?A frequency table is a table that is used to compress a large dataset into a smaller format that can be easily interpreted. A frequency table is usually made up of a class interval and frequency.
A class is the group of a numbers. The frequency of the class is the total number of times that numbers within the class appear in the dataset. For example in the class 100 - 200, there are 7 numbers in the dataset that have a value between 100 and 200. This means that the frequency of 100-200 is 7.
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Shauna borrows $500 from her parents to buy a phone. She agrees to pay them back plus 6% simple interest over one year. Write an equation to represent the total amount Shauna will owe her parents and solve to find the total amount.
The equation of the total amount is A = 500 + 500 * 6% * 1 and the value is $530
How to determine the equation of the total amount?From the question, we have the following parameters that can be used in our computation:
Principal, P = $500
Rate, r =6%
Time = 1 year
The amount is calculated as
A = P + PRT
Substitute the known values in the above equation, so, we have the following representation
A = 500 + 500 * 6% * 1
The above represents the equation
So, we have
A = 530
Hence, the amount is $530
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please help!! will give brainliest and extra credits
Answer: 5
Step-by-step explanation: To find the distance between 2 points, we should use this formula:
d=√((x_2-x_1)²+(y_2-y_1)²)
So, using that it would be written as:
[tex]\sqrt{9 + 16}[/tex] (after simplified)
Now, we need to find the square root of 25
The square root of 25= 5
So, that is how I got my answer.
The volume of a particular die is 7200 mm³. Use the fact that 10 mm equals 1 cm to convert this volume to cm³. Round your answer to the nearest tenth.
Answer: 720.0 cm³
Step-by-step explanation:
To convert the volume of the die from millimeters to centimeters, we need to divide the volume by the conversion factor that relates millimeters to centimeters. Since 10 millimeters is equal to 1 centimeter, the conversion factor is 10.
To convert the volume to centimeters, we can divide it by the conversion factor:
7200 mm³ / 10 = 720 cm³
This means that the volume of the die is 720 cm³. Rounded to the nearest tenth, the volume of the die is 720.0 cm³.
Which of the relations given by the following sets of ordered pairs is a function?
O ((-2,5), (7, 5), (-4, 0), (3, 0), (1, — 6)}
O ((3, 3), (3, — 1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(2,8), (1,-4), (0, 0), (1, 4), (2,8)}
Step-by-step explanation:
be a function, there needs to be one unique
value of +y+ for every +x+
-----------------------------
The 1st set has 5 different values of +y+
for +x+=+1+ and violates definition
--------------
The 2nd set is a function
-----------------------
The 3rd set has
( 1,2 ) & ( 1,1 )
( 2,3 ) & ( 2,2 )
( 3,4 ) & ( 3,3 )
Each of these pairs violates the definition
----------------
The 4th set has ( 2,-7 ) & ( 2,0 ) which
violate definition
a roulette wheel has 18 red slots, 18 black slots and 1 green slot. a ball is released onto the spinning wheel and lands in one o f the slots. if you bet on te slot the ball lands in you win. a ed on red will pay
The number of possible wins if the ball lands on red is 4.86 games.
Let there be 100 successive spins,
Random Variable (winnings): $1, -$1
Associated probabilities:
P($1) = 18/38 =9/19
P(-1) = 20/38 = 10/19
Expected winnings is (9/19)*1 + (10/19)*-1
= -1/19 on one spin.
= -2/19 on two spins
= -2/19 on a single spin for $2
= -100/19 on 100 successive spins
since there are 100 spins, n =100
18 out of 38 spots are red, thus p=18/37 =0.486
expected number of wins = np
= 100* 0.486
=4.86
Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability is defined as the degree to which something is likely to occur.
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
Answer:
1.2+2.56.7×3218°÷456.7820
7,701 divided by 36
7,701 divided by 36 is 213.91
What is division?The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in mathematics. For example, we can divide a group of 20 members into 4 groups of 5 members
The number 7701 is called the numerator or dividend, and the number 36 is called the denominator or divisor.
The quotient of 7701 and 36, the ratio of 7701 and 36, as well as the fraction of 7701 and 36 all mean (almost) the same:
7701 divided by 36, often written as 7701/36
Therefore, 7701 divided 36 is 213.91
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The U-Drive Rent-A-Truck company plans to spend $16 million on 320 new vehicles. Each commercial van will cost $25,000 each small truck $80,000, and each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
If each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. The number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.
How to find the number of vehicle?Since the company intends to purchase 320 vehicle, Let write this equation:
C + S + L = 320 (Eq. 1)
Total cost of the vehicles:
25C + 80S +70L = 16,000 (Eq. 2) (Divided by 1000 to keep the numbers small)
Number of commercial vans is twice the number of small trucks,
C = 2S
Substituting 2S in place of C in Eq. 1 and Eq. 2
2S + S + L = 320
25(2S) +80S +70L = 16,000
130S + 70L = 16,000
Multiplying the first of those equations by 70
210S + 70L = 22,400
130S + 70L = 16,000
Subtracting the second equation from the first:
80S = 6400
Divide both side by 80S
S = 6400/80
S = 80 (Small truck)
Then:
C = 2S
C= 2(80)
C= 160 (Commercial van)
So,
C + S + L = 320
160 + 80 + L = 320
L = 320 - 160 - 80
L =80 (Large van)
Therefore the number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 19 more than the secondLet and represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles
Provide your answer below:
X=
Y=
Z=
The value of x= 35.5, y= 43.75 and z= 62.75
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the three angles are x, y and z.
x+ y + z = 180............(E3)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, y+ z = 3x
3x- y- z= 0.............(E1)
and, third angle is 19 more than the second
z= y+ 19
y- z= -19..........(E2)
So, E1+E2, and E3-E2,
3x- 2z= -19
x+ 2z= 161
Now, adding above
4x = 142
x= 35.5
and, y + z = 106.5, y- z = -19
Again, adding
2y= 87.5
y= 43.75
and, z= 62.75
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(Score for Question 1: ___ of 5 points)
Simplify . Show your work.
Answer:
(Score for Question 2: ___ of 5 points)
Solve for x. Show your work.
Answer:
(Score for Question 3: ___ of 5 points)
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours? Show your work.
The bacteria after 24 hours will be equal to 450000.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.
The number of bacteria will be calculated as,
N = 125×(60×60)
N = 125×3600
N = 450000
Therefore, the bacteria after 24 hours will be equal to 450000.
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Stephen's current hourly pay is $10.30. If he receives a 4.5% hourly pay increase each year, what will his hourly pay be in two years?
$14.94
$11.25
$10.76
$15.00
Answer:
$11.25
Step-by-step explanation:
If Stephen receives a 4.5% hourly pay increase each year, his hourly pay will be $10.30 + (4.5% * $10.30) = $10.30 + $0.465 = $10.765 after the first year.
In the second year, his hourly pay will be $10.765 + (4.5% * $10.765) = $10.765 + $0.486 = $11.251.
Therefore, in two years, Stephen's hourly pay will be $11.251. This is closest to the answer choice of $11.25, so it is the correct answer.
Use the distributive property to write an equivalent expression.
2(m + 2n)
Marsha deposited $6,000 into a savings account 4 years ago. The simple interest rate is 4 %. How much money did earn in interest?
Answer:
960.00
Step-by-step explanation:
Interest = principle x rate x time
interest = 6000 x .04 x 4
960.00
Answer:
I = $ 960.00
Step-by-step explanation:
I = Prt
Since we are figuring out how much money was earned in interest, we will need to convert our R (which is the interest rate) into decimals, which will be, r = R/100 = 4%/100 = 0.04 per year.
Step 1. Divide R by 100, in this case, R is 4, so it will be 0.04.
Step 2. Times 6000 (the money that was deposited) by 0.04, then times it with 4 (the years) and you will get 960.
I = 6000 × 0.04 × 4 = 960
I = $ 960.00
I hope this helps you!
Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $2500
Total amount = $5000
Compounded semi -anually,
so formula becomes,
Total amount = amount (1+r/200)^2t
T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])
5000 = 2500 (1+3/100)^2t
2 = [tex](1+0.03)^{2t}[/tex]
2 = [tex]1.03^{2t}[/tex]
taking log on both sides
log 2 = 2t *log 1.03
0.3/0.012 = 2t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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given the following list of numbers: $\frac{3}{5}, \frac{5}{6}, \frac{2}{3}, \frac{9}{8}, \frac{7}{9}, \frac{3}{4}$ what is the smallest number subtracted from the biggest number? express your answer as a decimal.
The difference between the largest and the smallest fraction is 0.24.
What are fractions?A fraction is a component of a whole.
Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.
In a simple fraction, both are integers.
In a complex fraction, a fraction can be found in either the numerator or the denominator.
A suitable fraction has a numerator that is less than its denominator.
So, first, we will figure out the smallest and the greatest fraction:
We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4
LCM of denominators: 2*2*2*3*3*5 = 360
216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360
Smallest: 216/360
Largest: 300/360
Subtract smallest from largest:
300/360 - 216/360
84/360
7/30
0.2333
Round off: 0.24
Therefore, the difference between the largest and the smallest fraction is 0.24.
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